Subgroups — #72282884

Order 2048.

At least 16143 conjugacy classes of subgroups; only the 1934 normal subgroups are shown.

The subgroup lattice has 1170 nodes (normal subgroups only) — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#72282797	C₂	1	8	yes	maximal, complemented
2	#72282782	C₂	1	8	yes	maximal, complemented
3	#72282405	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#146595	C₂	1	1	yes	maximal, characteristic, complemented
5	#72281693	C₂	1	1	yes	maximal, characteristic, complemented
6	#72280868	C₂	1	1	yes	maximal, characteristic, complemented
7	#72280808	C₂	1	1	yes	maximal, characteristic, complemented
8	#72280797	C₂	1	1	yes	maximal, characteristic, complemented
9	#72280748	C₂	1	1	yes	maximal, characteristic, complemented
10	#72280714	C₂	1	1	yes	maximal, characteristic, complemented
11	#72280674	C₂	1	1	yes	maximal, characteristic, complemented
12	#72280582	C₂	1	1	yes	maximal, characteristic, complemented
13	#72280582	C₂	1	1	yes	maximal, characteristic, complemented
14	#72280532	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×#494587	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#7622868	C₂	1	1	yes	maximal, characteristic
17	C₂×#493561	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×#62729	C₂²	1	1	yes	characteristic
19	#10585883	C₂²	1	1	yes	characteristic, complemented
20	C₂×#60398	C₂²	1	1	yes	characteristic
21	C₂²×#3025	C₂²	1	1	yes	characteristic
22	C₂×#60387	C₂²	1	1	yes	characteristic
23	C₂×#60231	C₂²	1	1	yes	characteristic
24	#7625530	C₂²	1	1	yes	characteristic
25	#7622868	C₄	1	4	yes	complemented
26	#7622868	C₄	1	4	yes	complemented
27	#7622868	C₂²	1	4	yes	—
28	#7622868	C₂²	1	4	yes	—
29	C₂×#33556	C₄	1	2	yes	complemented
30	C₂×#33555	C₄	1	2	yes	complemented
31	C₂×#33554	C₄	1	2	yes	complemented
32	C₂×#33553	C₄	1	2	yes	complemented
33	C₂×#33358	C₂²	1	1	yes	characteristic
34	C₂×#33358	C₂²	1	1	yes	characteristic
35	C₂×#33347	C₂²	1	1	yes	characteristic
36	C₂×#33347	C₂²	1	1	yes	characteristic
37	C₂²×#2120	C₂²	1	1	yes	characteristic
38	C₂²×#2120	C₂²	1	1	yes	characteristic
39	#6393518	C₂²	1	4	yes	complemented
40	#6393517	C₂²	1	4	yes	complemented
41	#6374181	C₂²	1	1	yes	characteristic
42	#6374181	C₂²	1	1	yes	characteristic
43	#6372729	C₂²	1	4	yes	complemented
44	C₄×#3025	C₂²	1	4	yes	complemented
45	C₂×#21014	C₂²	1	1	yes	characteristic
46	C₂×#21012	C₂²	1	1	yes	characteristic
47	#6371494	C₂²	1	1	yes	characteristic
48	#6371494	C₂²	1	1	yes	characteristic
49	C₂×#20959	C₂²	1	1	yes	characteristic
50	#6371336	C₂²	1	1	yes	characteristic, complemented
51	C₂×#20620	C₂²	1	1	yes	characteristic, complemented
52	C₂×#20612	C₂²	1	1	yes	characteristic, complemented
53	#6370734	C₂²	1	1	yes	characteristic, complemented
54	#6369817	C₂²	1	1	yes	characteristic, complemented
55	#494587	C₂²	1	4	yes	complemented
56	#494587	C₂²	1	4	yes	complemented
57	#493561	C₂²	1	4	yes	complemented
58	#493561	C₂²	1	4	yes	complemented
59	C₂×#12589	C₂²	1	1	yes	characteristic, complemented
60	C₂×#12589	C₂²	1	1	yes	characteristic, complemented
61	#492906	C₂²	1	1	yes	characteristic, complemented
62	#492899	C₂²	1	1	yes	characteristic, complemented
63	C₂×#12577	C₂²	1	1	yes	characteristic, complemented
64	C₂×#12577	C₂²	1	1	yes	characteristic, complemented
65	#392718	C₂²	1	8	yes	complemented
66	#392711	C₂²	1	8	yes	complemented
67	C₂×#10756	C₂²	1	1	yes	characteristic, complemented
68	C₂×#10743	C₂²	1	1	yes	characteristic, complemented
69	#353324	C₂²	1	1	yes	characteristic, complemented
70	#353324	C₂²	1	1	yes	characteristic, complemented
71	#148243	C₂²	1	8	yes	complemented
72	#148240	C₂²	1	8	yes	complemented
73	#147761	C₂²	1	8	yes	complemented
74	#147757	C₂²	1	8	yes	complemented
75	#147519	C₂²	1	8	yes	complemented
76	#147519	C₂²	1	8	yes	complemented
77	#146668	C₂²	1	4	yes	complemented
78	#146667	C₂²	1	4	yes	complemented
79	#146595	C₂²	1	4	yes	complemented
80	#146595	C₂²	1	4	yes	complemented
81	C₂²×#585	C₂³	1	1	yes	characteristic
82	#62729	C₂×C₄	1	2	yes	complemented
83	#62729	C₂×C₄	1	2	yes	complemented
84	#62729	C₂³	1	2	yes	—
85	#62729	C₂³	1	2	yes	—
86	C₂×#3540	C₂×C₄	1	1	yes	characteristic, complemented
87	C₂×#3540	C₂×C₄	1	1	yes	characteristic, complemented
88	C₂×#3538	C₂×C₄	1	1	yes	characteristic, complemented
89	C₂×#3537	C₂×C₄	1	1	yes	characteristic, complemented
90	C₂×#3449	C₂³	1	1	yes	characteristic
91	C₂×#3449	C₂³	1	1	yes	characteristic
92	C₂²×#525	C₂³	1	1	yes	characteristic
93	C₄×#585	C₂³	1	4	yes	complemented
94	C₂×#3428	C₂³	1	1	yes	characteristic
95	C₂×#3428	C₂³	1	1	yes	characteristic
96	C₂³×#117	D₄	1	1	yes	characteristic, complemented
97	#60398	C₂×C₄	1	4	yes	complemented
98	#60398	C₂³	1	4	yes	—
99	C₂×#3028	C₂×C₄	1	2	yes	complemented
100	C₂×#3027	C₂×C₄	1	2	yes	complemented
101	C₂×#3025	C₂×C₄	1	2	yes	—
102	C₂×#3025	C₂×C₄	1	2	yes	—
103	C₂×#3025	C₂×C₄	1	2	yes	—
104	C₂×#3025	C₂×C₄	1	2	yes	—
105	C₂×#3025	D₄	1	2	yes	—
106	C₂×#3025	D₄	1	2	yes	—
107	C₂×#3025	D₄	1	2	yes	—
108	C₂×#3025	D₄	1	2	yes	—
109	C₂×#3025	D₄	1	2	yes	—
110	C₂×#3025	D₄	1	2	yes	—
111	C₂×#3025	C₂³	1	2	yes	—
112	C₂×#3025	C₂³	1	2	yes	—
113	C₂²×#458	D₄	1	2	yes	—
114	C₂²×B(4,𝔽₂)	D₄	1	2	yes	—
115	#60387	C₂×C₄	1	4	yes	complemented
116	#60387	C₂³	1	4	yes	—
117	C₂×#3022	C₂×C₄	1	2	yes	complemented
118	C₂×#3021	C₂×C₄	1	2	yes	complemented
119	#60231	C₂³	1	2	yes	—
120	#60231	C₂³	1	2	yes	—
121	C₂²×#421	D₄	1	1	yes	characteristic, complemented
122	C₂²×#421	D₄	1	1	yes	characteristic, complemented
123	C₂²×#421	D₄	1	1	yes	characteristic, complemented
124	C₂²×#421	D₄	1	1	yes	characteristic, complemented
125	C₂²×#413	C₂³	1	1	yes	characteristic
126	C₂²×#413	C₂³	1	1	yes	characteristic
127	C₂²×#410	C₂³	1	1	yes	characteristic
128	C₂²×#410	C₂³	1	1	yes	characteristic
129	C₂²×#410	C₂³	1	1	yes	characteristic
130	C₂²×#410	C₂³	1	1	yes	characteristic
131	C₂×#2879	C₂³	1	1	yes	characteristic
132	C₂×#2879	C₂³	1	1	yes	characteristic
133	#34065	D₄	1	2	yes	complemented
134	#34065	C₂³	1	2	yes	—
135	#34052	D₄	1	1	yes	characteristic, complemented
136	#34044	C₂³	1	1	yes	characteristic
137	C₄×#525	D₄	1	2	yes	complemented
138	C₄×#525	C₂³	1	2	yes	—
139	C₂×#2280	D₄	1	1	yes	characteristic, complemented
140	#33996	D₄	1	1	yes	characteristic, complemented
141	#33556	C₂×C₄	1	8	yes	complemented
142	#33556	C₂×C₄	1	8	yes	complemented
143	#33555	C₂×C₄	1	8	yes	complemented
144	#33555	C₂×C₄	1	8	yes	complemented
145	#33554	C₂×C₄	1	8	yes	complemented
146	#33554	C₂×C₄	1	8	yes	complemented
147	#33553	C₂×C₄	1	8	yes	complemented
148	#33553	C₂×C₄	1	8	yes	complemented
149	#33358	C₂×C₄	1	4	yes	complemented
150	#33358	C₂³	1	4	yes	—
151	#33358	C₂³	1	4	yes	—
152	C₂×#2129	C₂×C₄	1	2	yes	complemented
153	C₂×#2128	C₂×C₄	1	2	yes	complemented
154	#33347	C₂×C₄	1	4	yes	complemented
155	#33347	C₂³	1	4	yes	—
156	#33347	C₂³	1	4	yes	—
157	C₂×#2123	C₂×C₄	1	2	yes	complemented
158	C₂×#2122	C₂×C₄	1	2	yes	complemented
159	C₂×#2120	C₂×C₄	1	2	yes	complemented
160	C₂×#2120	C₂×C₄	1	2	yes	complemented
161	C₂×#2120	C₂×C₄	1	2	yes	complemented
162	C₂×#2120	C₂×C₄	1	2	yes	complemented
163	C₂×#2120	C₂³	1	2	yes	—
164	C₂×#2120	C₂³	1	2	yes	—
165	C₂×#2120	C₂³	1	2	yes	—
166	C₂×#2120	C₂³	1	2	yes	—
167	#21775	C₂³	1	4	yes	—
168	#21775	C₂³	1	4	yes	—
169	#21014	C₂³	1	4	yes	—
170	#21012	C₂³	1	4	yes	—
171	#20980	D₄	1	4	yes	complemented
172	#20980	D₄	1	4	yes	complemented
173	#20980	C₂³	1	4	yes	—
174	#20980	C₂³	1	4	yes	—
175	#20959	D₄	1	2	yes	complemented
176	#20959	D₄	1	2	yes	complemented
177	#20959	C₂³	1	2	yes	—
178	#20959	C₂³	1	2	yes	—
179	C₂×#1890	D₄	1	2	yes	complemented
180	C₂×#1889	D₄	1	2	yes	complemented
181	#20888	C₂³	1	4	yes	complemented
182	#20620	C₂³	1	4	yes	complemented
183	#20612	C₂³	1	4	yes	complemented
184	#20608	C₂³	1	4	yes	complemented
185	C₄×#410	C₂³	1	4	yes	complemented
186	C₂×#1733	D₄	1	1	yes	characteristic, complemented
187	C₂×#1733	D₄	1	1	yes	characteristic, complemented
188	C₂×#1733	D₄	1	1	yes	characteristic, complemented
189	C₂×#1733	D₄	1	1	yes	characteristic, complemented
190	#12589	C₂³	1	4	yes	complemented
191	#12589	C₂³	1	4	yes	complemented
192	#12585	C₂³	1	4	yes	complemented
193	#12581	C₂³	1	4	yes	complemented
194	#12577	C₂³	1	4	yes	complemented
195	#12577	C₂³	1	4	yes	complemented
196	#10758	C₂³	1	4	yes	complemented
197	#10758	C₂³	1	4	yes	complemented
198	#10756	C₂³	1	4	yes	complemented
199	#10743	C₂³	1	4	yes	complemented
200	C₂×#585	C₂²×C₄	1	2	yes	—
201	C₂×#585	C₂²×C₄	1	2	yes	—
202	C₂×#585	C₂×D₄	1	2	yes	—
203	C₂×#585	C₂×D₄	1	2	yes	—
204	C₂×#585	C₂×D₄	1	2	yes	—
205	C₂×#585	C₂⁴	1	2	yes	—
206	C₂²×H(5,𝔽₂)	C₂×D₄	1	2	yes	—
207	C₂³×#41	C₂×D₄	1	1	yes	characteristic
208	C₂³×#41	C₂×D₄	1	1	yes	characteristic
209	C₂³×#41	C₂⁴	1	1	yes	characteristic
210	C₂⁵×C₄	C₂×D₄	1	1	yes	characteristic
211	C₂³×M₁₆	C₂×D₄	1	1	yes	characteristic
212	C₂³×M₁₆	C₂×D₄	1	1	yes	characteristic
213	C₂³×M₁₆	C₂×D₄	1	1	yes	characteristic
214	C₂³×M₁₆	C₂×D₄	1	1	yes	characteristic
215	#3540	C₂²×C₄	1	2	yes	complemented
216	#3540	C₂²×C₄	1	2	yes	complemented
217	#3540	C₂²×C₄	1	2	yes	complemented
218	#3540	C₂²×C₄	1	2	yes	complemented
219	#3538	C₂²×C₄	1	2	yes	complemented
220	#3538	C₂²×C₄	1	2	yes	complemented
221	#3537	C₂²×C₄	1	2	yes	complemented
222	#3537	C₂²×C₄	1	2	yes	complemented
223	#3449	C₂²×C₄	1	2	yes	—
224	#3449	C₂²×C₄	1	2	yes	—
225	#3449	C₂×D₄	1	2	yes	—
226	#3449	C₂×D₄	1	2	yes	—
227	#3449	#41	1	2	yes	—
228	#3449	#41	1	2	yes	—
229	#3449	C₂⁴	1	2	yes	—
230	#3449	C₂⁴	1	2	yes	—
231	C₂×#536	C₂²×C₄	1	1	yes	characteristic
232	C₂×#536	C₂²×C₄	1	1	yes	characteristic
233	C₂×#536	#41	1	1	yes	characteristic
234	C₂×#536	#41	1	1	yes	characteristic
235	C₂×#535	C₂²×C₄	1	1	yes	characteristic
236	C₂×#535	C₂²×C₄	1	1	yes	characteristic
237	C₂×#535	#41	1	1	yes	characteristic
238	C₂×#535	#41	1	1	yes	characteristic
239	C₂×#525	C₂²×C₄	1	1	yes	characteristic
240	C₂×#525	C₂²×C₄	1	1	yes	characteristic
241	C₂×#525	C₂²×C₄	1	1	yes	characteristic
242	C₂×#525	C₂²×C₄	1	1	yes	characteristic
243	C₂×#525	C₂×D₄	1	1	yes	characteristic
244	C₂×#525	C₂×D₄	1	1	yes	characteristic
245	C₂×#525	C₂×D₄	1	1	yes	characteristic
246	C₂×#525	C₂×D₄	1	1	yes	characteristic
247	C₂×#525	C₂×D₄	1	1	yes	characteristic
248	C₂×#525	C₂×D₄	1	1	yes	characteristic
249	C₂×#525	C₂×D₄	1	1	yes	characteristic
250	C₂×#525	C₂×D₄	1	1	yes	characteristic
251	C₂×#525	C₂×D₄	1	1	yes	characteristic
252	C₂×#525	C₂×D₄	1	1	yes	characteristic
253	C₂×#525	#41	1	1	yes	characteristic
254	C₂×#525	#41	1	1	yes	characteristic
255	C₂×#525	#41	1	1	yes	characteristic
256	C₂×#525	#41	1	1	yes	characteristic
257	C₂×#525	#41	1	1	yes	characteristic
258	C₂×#525	#41	1	1	yes	characteristic
259	C₂×#525	#41	1	1	yes	characteristic
260	C₂×#525	#41	1	1	yes	characteristic
261	C₂×#525	C₂⁴	1	1	yes	characteristic
262	C₂×#525	C₂⁴	1	1	yes	characteristic
263	C₂²×#123	C₂×D₄	1	1	yes	characteristic
264	C₂²×#123	C₂×D₄	1	1	yes	characteristic
265	C₂²×#120	C₂×D₄	1	1	yes	characteristic
266	C₂²×#120	C₂×D₄	1	1	yes	characteristic
267	#3428	C₂×D₄	1	2	yes	—
268	#3428	C₂⁴	1	2	yes	—
269	C₂×#518	C₂×D₄	1	2	yes	—
270	C₂×C₄×#41	C₂×D₄	1	2	yes	—
271	C₂×C₄×#41	C₂×D₄	1	2	yes	—
272	C₂×C₄×#41	C₂×D₄	1	2	yes	—
273	C₂×C₄×#41	C₂⁴	1	2	yes	—
274	C₂²×#117	C₂×D₄	1	1	yes	characteristic
275	C₂²×#117	C₂×D₄	1	1	yes	characteristic
276	C₂²×#117	C₂×D₄	1	1	yes	characteristic
277	C₂²×#117	C₂×D₄	1	1	yes	characteristic
278	C₂²×#117	C₂×D₄	1	1	yes	characteristic
279	C₂²×#117	C₂×D₄	1	1	yes	characteristic
280	C₂²×#117	C₂×D₄	1	1	yes	characteristic
281	C₂²×#117	C₂×D₄	1	1	yes	characteristic
282	C₂²×#117	C₂×D₄	1	1	yes	characteristic
283	C₂²×#117	C₂×D₄	1	1	yes	characteristic
284	C₂²×#117	C₂×D₄	1	1	yes	characteristic
285	C₂²×#117	C₂×D₄	1	2	yes	complemented
286	C₂³×C₄²	C₂×D₄	1	2	yes	complemented
287	#3028	C₂²×C₄	1	8	yes	—
288	#3027	C₂²×C₄	1	8	yes	—
289	#3025	C₂²⋊C₄	1	4	yes	—
290	#3025	C₂²⋊C₄	1	4	yes	—
291	#3025	C₂²⋊C₄	1	4	yes	—
292	#3025	C₂²⋊C₄	1	4	yes	—
293	#3025	C₂²⋊C₄	1	4	yes	—
294	#3025	C₂²⋊C₄	1	4	yes	—
295	#3025	C₂²⋊C₄	1	4	yes	—
296	#3025	C₂²⋊C₄	1	4	yes	—
297	#3025	C₂²×C₄	1	4	yes	—
298	#3025	C₂²×C₄	1	4	yes	—
299	#3025	C₂²×C₄	1	4	yes	—
300	#3025	C₂²×C₄	1	4	yes	—
301	#3025	C₂×D₄	1	4	yes	—
302	#3025	C₂×D₄	1	4	yes	—
303	#3025	C₂×D₄	1	4	yes	—
304	#3025	C₂×D₄	1	4	yes	—
305	C₂×#458	C₂²⋊C₄	1	4	yes	—
306	C₂×#458	C₂²⋊C₄	1	4	yes	—
307	C₂×#458	C₂²⋊C₄	1	4	yes	—
308	C₂×#458	C₂²⋊C₄	1	4	yes	—
309	C₂×#458	C₂×D₄	1	4	yes	—
310	C₂×#458	C₂×D₄	1	4	yes	—
311	C₂×B(4,𝔽₂)	C₂²⋊C₄	1	4	yes	—
312	C₂×B(4,𝔽₂)	C₂²⋊C₄	1	4	yes	—
313	C₂×B(4,𝔽₂)	C₂²⋊C₄	1	4	yes	—
314	C₂×B(4,𝔽₂)	C₂²⋊C₄	1	4	yes	—
315	C₂×B(4,𝔽₂)	C₂×D₄	1	4	yes	—
316	C₂×B(4,𝔽₂)	C₂×D₄	1	4	yes	—
317	#3022	C₂²×C₄	1	8	yes	—
318	#3021	C₂²×C₄	1	8	yes	—
319	C₂×#421	C₂×D₄	1	4	yes	complemented
320	C₂×#421	C₂×D₄	1	4	yes	complemented
321	C₂²×#104	C₂×D₄	1	4	yes	complemented
322	C₂²×#104	C₂×D₄	1	4	yes	complemented
323	C₂×#413	C₂²×C₄	1	2	yes	—
324	C₂×#413	C₂²×C₄	1	2	yes	—
325	C₂×#413	C₂⁴	1	2	yes	—
326	C₂×#413	C₂⁴	1	2	yes	—
327	C₂×#410	C₂²×C₄	1	2	yes	—
328	C₂×#410	C₂²×C₄	1	2	yes	—
329	C₂×#410	C₂²×C₄	1	2	yes	—
330	C₂×#410	C₂²×C₄	1	2	yes	—
331	C₂×#410	C₂×D₄	1	2	yes	—
332	C₂×#410	C₂×D₄	1	2	yes	—
333	C₂×#410	C₂×D₄	1	2	yes	—
334	C₂×#410	C₂×D₄	1	2	yes	—
335	C₂×#410	C₂⁴	1	2	yes	—
336	C₂×#410	C₂⁴	1	2	yes	—
337	C₂×#410	C₂⁴	1	2	yes	—
338	C₂×#410	C₂⁴	1	2	yes	—
339	C₂²×#99	C₂×D₄	1	2	yes	—
340	C₂²×#99	C₂×D₄	1	2	yes	—
341	#2879	C₂×D₄	1	2	yes	—
342	#2879	C₂×D₄	1	2	yes	—
343	#2879	C₂⁴	1	2	yes	—
344	#2879	C₂⁴	1	2	yes	—
345	#2297	C₂×D₄	1	2	yes	—
346	#2297	C₂⁴	1	2	yes	—
347	#2296	C₂×D₄	1	2	yes	complemented
348	#2296	C₂×D₄	1	2	yes	complemented
349	#2280	C₂×D₄	1	2	yes	complemented
350	#2280	C₂×D₄	1	2	yes	complemented
351	C₄×#117	C₂×D₄	1	2	yes	complemented
352	C₄×#117	C₂×D₄	1	2	yes	complemented
353	#2129	C₂²×C₄	1	8	yes	complemented
354	#2128	C₂²×C₄	1	8	yes	complemented
355	#2123	C₂²×C₄	1	8	yes	complemented
356	#2122	C₂²×C₄	1	8	yes	complemented
357	#2120	C₂²×C₄	1	4	yes	complemented
358	#2120	C₂²×C₄	1	4	yes	complemented
359	#2120	C₂²×C₄	1	4	yes	complemented
360	#2120	C₂²×C₄	1	4	yes	complemented
361	#1890	C₂×D₄	1	4	yes	complemented
362	#1890	C₂×D₄	1	4	yes	complemented
363	#1889	C₂×D₄	1	4	yes	complemented
364	#1889	C₂×D₄	1	4	yes	complemented
365	#1733	C₂×D₄	1	4	yes	complemented
366	#1733	C₂×D₄	1	4	yes	complemented
367	C₂×#339	C₂×D₄	1	4	yes	complemented
368	C₂×#339	C₂×D₄	1	4	yes	complemented
369	C₂⁶	#120	1	1	yes	characteristic
370	#585	C₂×C₂²⋊C₄	1	4	yes	—
371	#585	C₂×C₂²⋊C₄	1	4	yes	—
372	#585	C₂³×C₄	1	4	yes	—
373	#585	C₂²×D₄	1	4	yes	—
374	C₂×H(5,𝔽₂)	C₂×C₂²⋊C₄	1	4	yes	—
375	C₂×H(5,𝔽₂)	C₂×C₂²⋊C₄	1	4	yes	—
376	C₂×H(5,𝔽₂)	C₂²×D₄	1	4	yes	—
377	C₂²×#41	C₄×D₄	1	2	yes	complemented
378	C₂²×#41	C₄×D₄	1	2	yes	complemented
379	C₂²×#41	C₂³×C₄	1	1	yes	characteristic
380	C₂²×#41	C₂³×C₄	1	1	yes	characteristic
381	C₂²×#41	C₂²×D₄	1	2	yes	—
382	C₂²×#41	C₂²×D₄	1	2	yes	—
383	C₂²×#41	C₂²×D₄	1	1	yes	characteristic
384	C₂²×#41	C₂²×D₄	1	1	yes	characteristic
385	C₂²×#41	C₂²×D₄	1	1	yes	characteristic
386	C₂²×#41	C₂²×D₄	1	1	yes	characteristic
387	C₂²×#41	C₂²×D₄	1	1	yes	characteristic
388	C₂²×#41	C₂²×D₄	1	1	yes	characteristic
389	C₂²×#41	C₂²×D₄	1	1	yes	characteristic
390	C₂²×#41	C₂×#41	1	1	yes	characteristic
391	C₂²×#41	C₂×#41	1	1	yes	characteristic
392	C₂²×#41	C₂×#41	1	1	yes	characteristic
393	C₂²×#41	C₂×#41	1	1	yes	characteristic
394	C₂²×#41	C₂×#41	1	1	yes	characteristic
395	C₂²×#41	C₂×#41	1	1	yes	characteristic
396	C₂²×#41	C₂×#41	1	1	yes	characteristic
397	C₂²×#41	C₂×#41	1	1	yes	characteristic
398	C₂²×#41	H(5,𝔽₂)	1	1	yes	characteristic
399	C₂²×#41	H(5,𝔽₂)	1	1	yes	characteristic
400	C₂²×#41	H(5,𝔽₂)	1	1	yes	characteristic
401	C₂²×#41	H(5,𝔽₂)	1	1	yes	characteristic
402	C₂²×#41	H(5,𝔽₂)	1	1	yes	characteristic
403	C₂²×#41	H(5,𝔽₂)	1	1	yes	characteristic
404	C₂²×#41	C₂⁵	1	1	yes	characteristic
405	C₂³×Q₈	C₄×D₄	1	1	yes	characteristic, complemented
406	C₂³×Q₈	C₄×D₄	1	1	yes	characteristic, complemented
407	C₂³×Q₈	H(5,𝔽₂)	1	1	yes	characteristic
408	C₂³×D₄	C₄×D₄	1	1	yes	characteristic, complemented
409	C₂³×D₄	C₄×D₄	1	1	yes	characteristic, complemented
410	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
411	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
412	C₂³×D₄	H(5,𝔽₂)	1	1	yes	characteristic
413	C₂⁴×C₄	C₄×D₄	1	1	yes	characteristic
414	C₂⁴×C₄	C₄×D₄	1	1	yes	characteristic
415	C₂⁴×C₄	C₄×D₄	1	1	yes	characteristic
416	C₂⁴×C₄	C₄×D₄	1	1	yes	characteristic
417	C₂⁴×C₄	#120	1	1	yes	characteristic
418	C₂⁴×C₄	#120	1	1	yes	characteristic
419	C₂⁴×C₄	#120	1	1	yes	characteristic
420	C₂⁴×C₄	#121	1	1	yes	characteristic
421	C₂⁴×C₄	#121	1	1	yes	characteristic
422	C₂⁴×C₄	#121	1	1	yes	characteristic
423	C₂⁴×C₄	#121	1	1	yes	characteristic
424	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
425	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
426	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
427	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
428	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
429	C₂²×M₁₆	C₂²×D₄	1	2	yes	—
430	C₂²×M₁₆	C₂²×D₄	1	2	yes	—
431	C₂²×M₁₆	C₂²×D₄	1	2	yes	—
432	C₂²×M₁₆	C₂²×D₄	1	2	yes	—
433	#536	C₄×D₄	1	2	yes	complemented
434	#536	C₄×D₄	1	2	yes	complemented
435	#536	C₄×D₄	1	2	yes	complemented
436	#536	C₄×D₄	1	2	yes	complemented
437	#536	C₂³×C₄	1	2	yes	—
438	#536	C₂³×C₄	1	2	yes	—
439	#536	C₂×#41	1	2	yes	—
440	#536	C₂×#41	1	2	yes	—
441	#535	C₄×D₄	1	2	yes	complemented
442	#535	C₄×D₄	1	2	yes	complemented
443	#535	C₄×D₄	1	2	yes	complemented
444	#535	C₄×D₄	1	2	yes	complemented
445	#535	C₂³×C₄	1	2	yes	—
446	#535	C₂³×C₄	1	2	yes	—
447	#535	C₂×#41	1	2	yes	—
448	#535	C₂×#41	1	2	yes	—
449	#525	C₂×C₂²⋊C₄	1	1	yes	characteristic
450	#525	C₂×C₂²⋊C₄	1	1	yes	characteristic
451	#525	C₂×C₂²⋊C₄	1	1	yes	characteristic
452	#525	C₂×C₂²⋊C₄	1	1	yes	characteristic
453	#525	C₂×C₂²⋊C₄	1	1	yes	characteristic
454	#525	C₂×C₂²⋊C₄	1	1	yes	characteristic
455	#525	C₂×C₂²⋊C₄	1	1	yes	characteristic
456	#525	C₂×C₂²⋊C₄	1	1	yes	characteristic
457	#525	C₄×D₄	1	1	yes	characteristic
458	#525	C₄×D₄	1	1	yes	characteristic
459	#525	C₄×D₄	1	1	yes	characteristic
460	#525	C₄×D₄	1	1	yes	characteristic
461	#525	C₄×D₄	1	1	yes	characteristic
462	#525	C₄×D₄	1	1	yes	characteristic
463	#525	C₄×D₄	1	1	yes	characteristic
464	#525	C₄×D₄	1	1	yes	characteristic
465	#525	C₄×D₄	1	1	yes	characteristic
466	#525	C₄×D₄	1	1	yes	characteristic
467	#525	C₄×D₄	1	1	yes	characteristic
468	#525	C₄×D₄	1	1	yes	characteristic
469	#525	C₄×D₄	1	1	yes	characteristic
470	#525	C₄×D₄	1	1	yes	characteristic
471	#525	C₄×D₄	1	1	yes	characteristic
472	#525	C₄×D₄	1	1	yes	characteristic
473	#525	#121	1	1	yes	characteristic
474	#525	#121	1	1	yes	characteristic
475	#525	#121	1	1	yes	characteristic
476	#525	#121	1	1	yes	characteristic
477	#525	#121	1	1	yes	characteristic
478	#525	#121	1	1	yes	characteristic
479	#525	#121	1	1	yes	characteristic
480	#525	#121	1	1	yes	characteristic
481	#525	#121	1	1	yes	characteristic
482	#525	#121	1	1	yes	characteristic
483	#525	#121	1	1	yes	characteristic
484	#525	#121	1	1	yes	characteristic
485	#525	#121	1	1	yes	characteristic
486	#525	#121	1	1	yes	characteristic
487	#525	#121	1	1	yes	characteristic
488	#525	#121	1	1	yes	characteristic
489	#525	#123	1	1	yes	characteristic
490	#525	#123	1	1	yes	characteristic
491	#525	#123	1	1	yes	characteristic
492	#525	#123	1	1	yes	characteristic
493	#525	#123	1	1	yes	characteristic
494	#525	#123	1	1	yes	characteristic
495	#525	#123	1	1	yes	characteristic
496	#525	#123	1	1	yes	characteristic
497	#525	C₂³×C₄	1	1	yes	characteristic
498	#525	C₂³×C₄	1	1	yes	characteristic
499	#525	C₂³×C₄	1	1	yes	characteristic
500	#525	C₂³×C₄	1	1	yes	characteristic
501	#525	C₂²×D₄	1	1	yes	characteristic
502	#525	C₂²×D₄	1	1	yes	characteristic
503	#525	C₂²×D₄	1	1	yes	characteristic
504	#525	C₂²×D₄	1	1	yes	characteristic
505	#525	C₂×#41	1	1	yes	characteristic
506	#525	C₂×#41	1	1	yes	characteristic
507	#525	C₂×#41	1	1	yes	characteristic
508	#525	C₂×#41	1	1	yes	characteristic
509	#525	C₂×#41	1	1	yes	characteristic
510	#525	C₂×#41	1	1	yes	characteristic
511	#525	C₂×#41	1	1	yes	characteristic
512	#525	C₂×#41	1	1	yes	characteristic
513	C₂×#123	C₂×C₂²⋊C₄	1	1	yes	characteristic
514	C₂×#123	C₂×C₂²⋊C₄	1	1	yes	characteristic
515	C₂×#123	C₂×C₂²⋊C₄	1	1	yes	characteristic
516	C₂×#123	C₂×C₂²⋊C₄	1	1	yes	characteristic
517	C₂×#123	C₄×D₄	1	1	yes	characteristic
518	C₂×#123	C₄×D₄	1	1	yes	characteristic
519	C₂×#123	C₄×D₄	1	1	yes	characteristic
520	C₂×#123	C₄×D₄	1	1	yes	characteristic
521	C₂×#123	#120	1	1	yes	characteristic
522	C₂×#123	#120	1	1	yes	characteristic
523	C₂×#123	#120	1	1	yes	characteristic
524	C₂×#123	#120	1	1	yes	characteristic
525	C₂×#123	#121	1	1	yes	characteristic
526	C₂×#123	#121	1	1	yes	characteristic
527	C₂×#123	#121	1	1	yes	characteristic
528	C₂×#123	#121	1	1	yes	characteristic
529	C₂×#123	#123	1	1	yes	characteristic
530	C₂×#123	#123	1	1	yes	characteristic
531	C₂×#123	#123	1	1	yes	characteristic
532	C₂×#123	#123	1	1	yes	characteristic
533	C₂×#123	C₂²×D₄	1	1	yes	characteristic
534	C₂×#123	C₂²×D₄	1	1	yes	characteristic
535	C₂×#123	C₂²×D₄	1	1	yes	characteristic
536	C₂×#123	C₂²×D₄	1	1	yes	characteristic
537	C₂×#120	C₂×C₂²⋊C₄	1	1	yes	characteristic
538	C₂×#120	C₂×C₂²⋊C₄	1	1	yes	characteristic
539	C₂×#120	C₂×C₂²⋊C₄	1	1	yes	characteristic
540	C₂×#120	C₂×C₂²⋊C₄	1	1	yes	characteristic
541	C₂×#120	C₄×D₄	1	1	yes	characteristic
542	C₂×#120	C₄×D₄	1	1	yes	characteristic
543	C₂×#120	C₄×D₄	1	1	yes	characteristic
544	C₂×#120	C₄×D₄	1	1	yes	characteristic
545	C₂×#120	#120	1	1	yes	characteristic
546	C₂×#120	#120	1	1	yes	characteristic
547	C₂×#120	#120	1	1	yes	characteristic
548	C₂×#120	#120	1	1	yes	characteristic
549	C₂×#120	#121	1	1	yes	characteristic
550	C₂×#120	#121	1	1	yes	characteristic
551	C₂×#120	#121	1	1	yes	characteristic
552	C₂×#120	#121	1	1	yes	characteristic
553	C₂×#120	#123	1	1	yes	characteristic
554	C₂×#120	#123	1	1	yes	characteristic
555	C₂×#120	#123	1	1	yes	characteristic
556	C₂×#120	#123	1	1	yes	characteristic
557	C₂×#120	C₂²×D₄	1	1	yes	characteristic
558	C₂×#120	C₂²×D₄	1	1	yes	characteristic
559	C₂×#120	C₂²×D₄	1	1	yes	characteristic
560	C₂×#120	C₂²×D₄	1	1	yes	characteristic
561	#518	C₂²×D₄	1	4	yes	—
562	C₂×#117	C₄×D₄	1	1	yes	characteristic
563	C₂×#117	C₄×D₄	1	1	yes	characteristic
564	C₂×#117	C₄×D₄	1	1	yes	characteristic
565	C₂×#117	C₄×D₄	1	1	yes	characteristic
566	C₂×#117	C₄×D₄	1	1	yes	characteristic, complemented
567	C₂×#117	C₄×D₄	1	1	yes	characteristic, complemented
568	C₂×#117	C₄×D₄	1	2	yes	complemented
569	C₂×#117	C₄×D₄	1	1	yes	characteristic, complemented
570	C₂×#117	C₄×D₄	1	1	yes	characteristic, complemented
571	C₂×#117	C₄×D₄	1	2	yes	complemented
572	C₂×#117	#120	1	1	yes	characteristic
573	C₂×#117	#120	1	1	yes	characteristic
574	C₂×#117	#120	1	2	yes	—
575	C₂×#117	#120	1	1	yes	characteristic
576	C₂×#117	#120	1	1	yes	characteristic
577	C₂×#117	#120	1	2	yes	—
578	C₂×#117	#120	1	2	yes	—
579	C₂×#117	#120	1	1	yes	characteristic
580	C₂×#117	#120	1	1	yes	characteristic
581	C₂×#117	#121	1	1	yes	characteristic
582	C₂×#117	#121	1	1	yes	characteristic
583	C₂×#117	#121	1	1	yes	characteristic
584	C₂×#117	#121	1	1	yes	characteristic
585	C₂×#117	C₂²×D₄	1	2	yes	—
586	C₂×#117	C₂²×D₄	1	2	yes	—
587	C₂×#117	C₂²×D₄	1	2	yes	—
588	C₂×#117	C₂²×D₄	1	1	yes	characteristic
589	C₂×#117	C₂²×D₄	1	1	yes	characteristic
590	C₂×#117	C₂²×D₄	1	2	yes	—
591	C₂×#117	C₂²×D₄	1	2	yes	—
592	C₂×#117	C₂²×D₄	1	2	yes	—
593	C₂²×C₂²⋊C₄	#120	1	1	yes	characteristic
594	C₂²×C₂²⋊C₄	#120	1	1	yes	characteristic
595	C₂²×C₄²	#120	1	2	yes	—
596	C₂²×C₄²	#120	1	2	yes	—
597	C₂²×C₄²	#120	1	2	yes	—
598	C₂²×C₄²	C₂²×D₄	1	2	yes	—
599	C₂²×C₄²	C₂²×D₄	1	2	yes	—
600	C₂²×C₄²	C₂²×D₄	1	2	yes	—
601	C₂²×C₄²	C₂²×D₄	1	2	yes	—
602	#458	C₂×C₂²⋊C₄	1	8	yes	—
603	#458	C₂×C₂²⋊C₄	1	8	yes	—
604	#458	C₂×C₂²⋊C₄	1	8	yes	—
605	#458	C₂×C₂²⋊C₄	1	8	yes	—
606	B(4,𝔽₂)	C₂×C₂²⋊C₄	1	8	yes	—
607	B(4,𝔽₂)	C₂×C₂²⋊C₄	1	8	yes	—
608	B(4,𝔽₂)	C₂×C₂²⋊C₄	1	8	yes	—
609	B(4,𝔽₂)	C₂×C₂²⋊C₄	1	8	yes	—
610	#413	C₂³×C₄	1	4	yes	—
611	#410	C₂×C₂²⋊C₄	1	4	yes	—
612	#410	C₂×C₂²⋊C₄	1	4	yes	—
613	#410	C₂³×C₄	1	4	yes	—
614	#410	C₂³×C₄	1	4	yes	—
615	#410	C₂²×D₄	1	4	yes	—
616	C₂×#99	C₂×C₂²⋊C₄	1	4	yes	—
617	C₂×#99	C₂×C₂²⋊C₄	1	4	yes	—
618	C₂×#99	C₂²×D₄	1	4	yes	—
619	C₂×#99	C₂²×D₄	1	4	yes	—
620	C₂⁵	#386	1	1	yes	characteristic
621	C₂⁵	#386	1	1	yes	characteristic
622	C₂⁵	#386	1	1	yes	characteristic
623	C₂⁵	#386	1	1	yes	characteristic
624	C₂⁵	C₂×#120	1	1	yes	characteristic
625	C₂⁵	C₂×#120	1	1	yes	characteristic
626	C₂⁵	C₂×#120	1	1	yes	characteristic
627	C₂⁵	D₄²	1	1	yes	characteristic
628	C₂⁵	D₄²	1	1	yes	characteristic
629	H(5,𝔽₂)	C₂²×C₂²⋊C₄	1	8	yes	—
630	C₂×#41	C₂²×C₂²⋊C₄	1	1	yes	characteristic
631	C₂×#41	C₂²×C₂²⋊C₄	1	1	yes	characteristic
632	C₂×#41	C₂×C₄×D₄	1	1	yes	characteristic
633	C₂×#41	C₂×C₄×D₄	1	1	yes	characteristic
634	C₂×#41	C₂×C₄×D₄	1	1	yes	characteristic
635	C₂×#41	C₂×C₄×D₄	1	1	yes	characteristic
636	C₂×#41	C₂×C₄×D₄	1	1	yes	characteristic
637	C₂×#41	C₂×C₄×D₄	1	1	yes	characteristic
638	C₂×#41	C₂×C₄×D₄	1	1	yes	characteristic
639	C₂×#41	C₂×C₄×D₄	1	1	yes	characteristic
640	C₂×#41	#518	1	1	yes	characteristic
641	C₂×#41	#518	1	1	yes	characteristic
642	C₂×#41	#518	1	1	yes	characteristic
643	C₂×#41	#518	1	1	yes	characteristic
644	C₂×#41	C₂×#121	1	1	yes	characteristic
645	C₂×#41	C₂×#121	1	1	yes	characteristic
646	C₂×#41	C₂×#121	1	1	yes	characteristic
647	C₂×#41	C₂×#121	1	1	yes	characteristic
648	C₂×#41	C₂×#123	1	1	yes	characteristic
649	C₂×#41	C₂×#123	1	1	yes	characteristic
650	C₂×#41	#525	1	1	yes	characteristic
651	C₂×#41	#525	1	1	yes	characteristic
652	C₂×#41	#525	1	1	yes	characteristic
653	C₂×#41	#525	1	1	yes	characteristic
654	C₂×#41	#525	1	1	yes	characteristic
655	C₂×#41	#525	1	1	yes	characteristic
656	C₂×#41	#535	1	1	yes	characteristic
657	C₂×#41	#535	1	1	yes	characteristic
658	C₂×#41	#538	1	1	yes	characteristic
659	C₂×#41	#538	1	1	yes	characteristic
660	C₂×#41	#538	1	1	yes	characteristic
661	C₂×#41	#538	1	1	yes	characteristic
662	C₂×#41	D₄²	1	1	yes	characteristic
663	C₂×#41	D₄²	1	1	yes	characteristic
664	C₂×#41	D₄²	1	1	yes	characteristic
665	C₂×#41	D₄²	1	1	yes	characteristic
666	C₂×#41	#546	1	1	yes	characteristic
667	C₂×#41	#546	1	1	yes	characteristic
668	C₂×#41	#546	1	1	yes	characteristic
669	C₂×#41	#546	1	1	yes	characteristic
670	C₂×#41	#546	1	1	yes	characteristic
671	C₂×#41	#546	1	1	yes	characteristic
672	C₂×#41	#546	1	1	yes	characteristic
673	C₂×#41	#546	1	1	yes	characteristic
674	C₂×#41	#546	1	1	yes	characteristic
675	C₂×#41	#546	1	1	yes	characteristic
676	C₂×#41	#546	1	1	yes	characteristic
677	C₂×#41	#546	1	1	yes	characteristic
678	C₂×#41	#546	1	1	yes	characteristic
679	C₂×#41	#546	1	1	yes	characteristic
680	C₂×#41	#546	1	1	yes	characteristic
681	C₂×#41	#546	1	1	yes	characteristic
682	C₂×#41	#551	1	1	yes	characteristic
683	C₂×#41	#551	1	1	yes	characteristic
684	C₂×#41	#551	1	1	yes	characteristic
685	C₂×#41	#551	1	1	yes	characteristic
686	C₂×#41	C₂⁴×C₄	1	1	yes	characteristic
687	C₂×#41	C₂³×D₄	1	1	yes	characteristic
688	C₂×#41	C₂²×#41	1	1	yes	characteristic
689	C₂×#41	C₂²×#41	1	1	yes	characteristic
690	C₂×#41	C₂²×#41	1	1	yes	characteristic
691	C₂×#41	C₂²×#41	1	1	yes	characteristic
692	C₂×#41	C₂×H(5,𝔽₂)	1	1	yes	characteristic
693	C₂×#41	C₂×H(5,𝔽₂)	1	1	yes	characteristic
694	C₂²×Q₈	C₂×C₄×D₄	1	2	yes	—
695	C₂²×Q₈	C₂×C₄×D₄	1	2	yes	—
696	C₂²×Q₈	#518	1	1	yes	characteristic
697	C₂²×Q₈	#518	1	1	yes	characteristic
698	C₂²×Q₈	#534	1	1	yes	characteristic
699	C₂²×Q₈	#538	1	1	yes	characteristic
700	C₂²×Q₈	#538	1	1	yes	characteristic
701	C₂²×Q₈	D₄²	1	1	yes	characteristic
702	C₂²×Q₈	D₄²	1	1	yes	characteristic
703	C₂²×Q₈	#546	1	1	yes	characteristic
704	C₂²×Q₈	#546	1	1	yes	characteristic
705	C₂²×Q₈	#551	1	1	yes	characteristic
706	C₂²×Q₈	#551	1	1	yes	characteristic
707	C₂²×Q₈	C₂×H(5,𝔽₂)	1	1	yes	characteristic
708	C₂²×D₄	C₂²×C₂²⋊C₄	1	1	yes	characteristic
709	C₂²×D₄	C₂²×C₂²⋊C₄	1	1	yes	characteristic
710	C₂²×D₄	C₂×C₄×D₄	1	1	yes	characteristic
711	C₂²×D₄	C₂×C₄×D₄	1	1	yes	characteristic
712	C₂²×D₄	C₂×C₄×D₄	1	2	yes	—
713	C₂²×D₄	C₂×C₄×D₄	1	2	yes	—
714	C₂²×D₄	#518	1	1	yes	characteristic
715	C₂²×D₄	#518	1	1	yes	characteristic
716	C₂²×D₄	C₂×#120	1	1	yes	characteristic
717	C₂²×D₄	C₂×#120	1	1	yes	characteristic
718	C₂²×D₄	C₂×#121	1	1	yes	characteristic
719	C₂²×D₄	C₂×#121	1	1	yes	characteristic
720	C₂²×D₄	C₂×#123	1	1	yes	characteristic
721	C₂²×D₄	C₂×#123	1	1	yes	characteristic
722	C₂²×D₄	#534	1	1	yes	characteristic
723	C₂²×D₄	#538	1	1	yes	characteristic
724	C₂²×D₄	#538	1	1	yes	characteristic
725	C₂²×D₄	D₄²	1	1	yes	characteristic
726	C₂²×D₄	D₄²	1	1	yes	characteristic
727	C₂²×D₄	D₄²	1	1	yes	characteristic
728	C₂²×D₄	D₄²	1	1	yes	characteristic
729	C₂²×D₄	D₄²	1	1	yes	characteristic
730	C₂²×D₄	D₄²	1	1	yes	characteristic
731	C₂²×D₄	#546	1	1	yes	characteristic
732	C₂²×D₄	#546	1	1	yes	characteristic
733	C₂²×D₄	#546	1	1	yes	characteristic
734	C₂²×D₄	#546	1	1	yes	characteristic
735	C₂²×D₄	#546	1	1	yes	characteristic
736	C₂²×D₄	#546	1	1	yes	characteristic
737	C₂²×D₄	#546	1	1	yes	characteristic
738	C₂²×D₄	#546	1	1	yes	characteristic
739	C₂²×D₄	#546	1	1	yes	characteristic
740	C₂²×D₄	#546	1	1	yes	characteristic
741	C₂²×D₄	#551	1	1	yes	characteristic
742	C₂²×D₄	#551	1	1	yes	characteristic
743	C₂²×D₄	C₂³×D₄	1	1	yes	characteristic
744	C₂²×D₄	C₂³×D₄	1	1	yes	characteristic
745	C₂²×D₄	C₂×H(5,𝔽₂)	1	1	yes	characteristic
746	C₂³×C₄	#386	1	1	yes	characteristic
747	C₂³×C₄	#386	1	1	yes	characteristic
748	C₂³×C₄	#386	1	1	yes	characteristic
749	C₂³×C₄	#386	1	1	yes	characteristic
750	C₂³×C₄	#386	1	1	yes	characteristic
751	C₂³×C₄	#386	1	1	yes	characteristic
752	C₂³×C₄	#386	1	1	yes	characteristic
753	C₂³×C₄	#386	1	1	yes	characteristic
754	C₂³×C₄	#386	1	1	yes	characteristic
755	C₂³×C₄	#386	1	1	yes	characteristic
756	C₂³×C₄	#386	1	1	yes	characteristic
757	C₂³×C₄	#386	1	1	yes	characteristic
758	C₂³×C₄	C₂×C₄×D₄	1	1	yes	characteristic
759	C₂³×C₄	C₂×C₄×D₄	1	1	yes	characteristic
760	C₂³×C₄	C₂×C₄×D₄	1	1	yes	characteristic
761	C₂³×C₄	C₂×C₄×D₄	1	1	yes	characteristic
762	C₂³×C₄	C₂×C₄×D₄	1	1	yes	characteristic
763	C₂³×C₄	C₂×C₄×D₄	1	1	yes	characteristic
764	C₂³×C₄	C₂×C₄×D₄	1	1	yes	characteristic
765	C₂³×C₄	C₂×C₄×D₄	1	1	yes	characteristic
766	C₂³×C₄	C₂×C₄×D₄	1	1	yes	characteristic
767	C₂³×C₄	C₂×C₄×D₄	1	1	yes	characteristic
768	C₂³×C₄	C₂×#120	1	1	yes	characteristic
769	C₂³×C₄	C₂×#120	1	1	yes	characteristic
770	C₂³×C₄	C₂×#120	1	1	yes	characteristic
771	C₂³×C₄	C₂×#120	1	1	yes	characteristic
772	C₂³×C₄	C₂×#120	1	1	yes	characteristic
773	C₂³×C₄	C₂×#120	1	1	yes	characteristic
774	C₂³×C₄	C₂×#120	1	1	yes	characteristic
775	C₂³×C₄	C₂×#121	1	1	yes	characteristic
776	C₂³×C₄	C₂×#121	1	1	yes	characteristic
777	C₂³×C₄	C₂×#121	1	1	yes	characteristic
778	C₂³×C₄	C₂×#121	1	1	yes	characteristic
779	C₂³×C₄	C₂×#121	1	1	yes	characteristic
780	C₂³×C₄	C₂×#121	1	1	yes	characteristic
781	C₂³×C₄	#525	1	1	yes	characteristic
782	C₂³×C₄	#525	1	1	yes	characteristic
783	C₂³×C₄	#525	1	1	yes	characteristic
784	C₂³×C₄	#525	1	1	yes	characteristic
785	C₂³×C₄	#525	1	1	yes	characteristic
786	C₂³×C₄	#525	1	1	yes	characteristic
787	C₂³×C₄	#534	1	1	yes	characteristic
788	C₂³×C₄	#534	1	1	yes	characteristic
789	C₂³×C₄	#535	1	1	yes	characteristic
790	C₂³×C₄	#535	1	1	yes	characteristic
791	C₂³×C₄	D₄²	1	1	yes	characteristic
792	C₂³×C₄	D₄²	1	1	yes	characteristic
793	C₂³×C₄	D₄²	1	1	yes	characteristic
794	C₂³×C₄	D₄²	1	1	yes	characteristic
795	C₂³×C₄	D₄²	1	1	yes	characteristic
796	C₂³×C₄	D₄²	1	1	yes	characteristic
797	C₂³×C₄	D₄²	1	1	yes	characteristic
798	C₂³×C₄	D₄²	1	1	yes	characteristic
799	C₂³×C₄	D₄²	1	1	yes	characteristic
800	C₂³×C₄	D₄²	1	1	yes	characteristic
801	C₂³×C₄	#546	1	1	yes	characteristic
802	C₂³×C₄	#546	1	1	yes	characteristic
803	C₂³×C₄	#546	1	1	yes	characteristic
804	C₂³×C₄	#546	1	1	yes	characteristic
805	C₂³×C₄	C₂³×D₄	1	1	yes	characteristic
806	C₂³×C₄	C₂³×D₄	1	1	yes	characteristic
807	C₂³×C₄	C₂³×D₄	1	1	yes	characteristic
808	#123	#386	1	1	yes	characteristic
809	#123	#386	1	1	yes	characteristic
810	#123	#386	1	1	yes	characteristic
811	#123	#386	1	1	yes	characteristic
812	#123	#386	1	1	yes	characteristic
813	#123	#386	1	1	yes	characteristic
814	#123	#386	1	1	yes	characteristic
815	#123	#386	1	1	yes	characteristic
816	#123	#386	1	1	yes	characteristic
817	#123	#386	1	1	yes	characteristic
818	#123	#386	1	1	yes	characteristic
819	#123	#386	1	1	yes	characteristic
820	#123	#386	1	1	yes	characteristic
821	#123	#386	1	1	yes	characteristic
822	#123	#386	1	1	yes	characteristic
823	#123	#386	1	1	yes	characteristic
824	#123	C₂²×C₂²⋊C₄	1	1	yes	characteristic
825	#123	C₂²×C₂²⋊C₄	1	1	yes	characteristic
826	#123	C₂²×C₂²⋊C₄	1	1	yes	characteristic
827	#123	C₂²×C₂²⋊C₄	1	1	yes	characteristic
828	#123	C₂×C₄×D₄	1	1	yes	characteristic
829	#123	C₂×C₄×D₄	1	1	yes	characteristic
830	#123	C₂×C₄×D₄	1	1	yes	characteristic
831	#123	C₂×C₄×D₄	1	1	yes	characteristic
832	#123	C₂×#121	1	1	yes	characteristic
833	#123	C₂×#121	1	1	yes	characteristic
834	#123	C₂×#121	1	1	yes	characteristic
835	#123	C₂×#121	1	1	yes	characteristic
836	#123	C₂×#123	1	1	yes	characteristic
837	#123	C₂×#123	1	1	yes	characteristic
838	#123	C₂×#123	1	1	yes	characteristic
839	#123	C₂×#123	1	1	yes	characteristic
840	#120	#386	1	1	yes	characteristic
841	#120	#386	1	1	yes	characteristic
842	#120	#386	1	1	yes	characteristic
843	#120	#386	1	1	yes	characteristic
844	#120	#386	1	1	yes	characteristic
845	#120	#386	1	1	yes	characteristic
846	#120	#386	1	1	yes	characteristic
847	#120	#386	1	1	yes	characteristic
848	#120	#386	1	1	yes	characteristic
849	#120	#386	1	1	yes	characteristic
850	#120	#386	1	1	yes	characteristic
851	#120	#386	1	1	yes	characteristic
852	#120	#386	1	1	yes	characteristic
853	#120	#386	1	1	yes	characteristic
854	#120	#386	1	1	yes	characteristic
855	#120	#386	1	1	yes	characteristic
856	#120	C₂²×C₂²⋊C₄	1	1	yes	characteristic
857	#120	C₂²×C₂²⋊C₄	1	1	yes	characteristic
858	#120	C₂²×C₂²⋊C₄	1	1	yes	characteristic
859	#120	C₂²×C₂²⋊C₄	1	1	yes	characteristic
860	#120	C₂×C₄×D₄	1	1	yes	characteristic
861	#120	C₂×C₄×D₄	1	1	yes	characteristic
862	#120	C₂×C₄×D₄	1	1	yes	characteristic
863	#120	C₂×C₄×D₄	1	1	yes	characteristic
864	#120	C₂×#121	1	1	yes	characteristic
865	#120	C₂×#121	1	1	yes	characteristic
866	#120	C₂×#121	1	1	yes	characteristic
867	#120	C₂×#121	1	1	yes	characteristic
868	#120	C₂×#123	1	1	yes	characteristic
869	#120	C₂×#123	1	1	yes	characteristic
870	#120	C₂×#123	1	1	yes	characteristic
871	#120	C₂×#123	1	1	yes	characteristic
872	#117	#386	1	1	yes	characteristic
873	#117	#386	1	1	yes	characteristic
874	#117	#386	1	1	yes	characteristic
875	#117	#386	1	1	yes	characteristic
876	#117	#386	1	1	yes	characteristic
877	#117	#386	1	1	yes	characteristic
878	#117	#386	1	1	yes	characteristic
879	#117	#386	1	1	yes	characteristic
880	#117	B(4,𝔽₂)	1	2	yes	—
881	#117	B(4,𝔽₂)	1	2	yes	—
882	#117	B(4,𝔽₂)	1	2	yes	—
883	#117	B(4,𝔽₂)	1	2	yes	—
884	#117	C₂×C₄×D₄	1	2	yes	—
885	#117	C₂×C₄×D₄	1	2	yes	—
886	#117	C₂×C₄×D₄	1	2	yes	—
887	#117	C₂×C₄×D₄	1	2	yes	—
888	#117	C₂×C₄×D₄	1	1	yes	characteristic
889	#117	C₂×C₄×D₄	1	1	yes	characteristic
890	#117	C₂×C₄×D₄	1	1	yes	characteristic
891	#117	C₂×C₄×D₄	1	1	yes	characteristic
892	#117	C₂×#121	1	1	yes	characteristic
893	#117	C₂×#121	1	1	yes	characteristic
894	#117	C₂×#121	1	1	yes	characteristic
895	#117	C₂×#121	1	1	yes	characteristic
896	C₂×C₂²⋊C₄	#386	1	1	yes	characteristic
897	C₂×C₂²⋊C₄	#386	1	1	yes	characteristic
898	C₂×C₂²⋊C₄	#386	1	1	yes	characteristic
899	C₂×C₂²⋊C₄	#386	1	1	yes	characteristic
900	C₂×C₂²⋊C₄	#386	1	1	yes	characteristic
901	C₂×C₂²⋊C₄	#386	1	1	yes	characteristic
902	C₂×C₂²⋊C₄	#386	1	1	yes	characteristic
903	C₂×C₂²⋊C₄	#386	1	1	yes	characteristic
904	C₂×C₂²⋊C₄	C₂×#120	1	1	yes	characteristic
905	C₂×C₂²⋊C₄	C₂×#120	1	1	yes	characteristic
906	C₂×C₂²⋊C₄	C₂×#120	1	1	yes	characteristic
907	C₂×C₂²⋊C₄	C₂×#120	1	1	yes	characteristic
908	C₂×C₄²	C₂×#120	1	2	yes	—
909	C₂×C₄²	C₂×#120	1	2	yes	—
910	C₂×C₄²	C₂×#120	1	2	yes	—
911	C₂×C₄²	C₂×#120	1	2	yes	—
912	#99	C₂²×C₂²⋊C₄	1	8	yes	—
913	C₂⁴	C₂×#386	1	1	yes	characteristic
914	C₂⁴	C₂×#386	1	1	yes	characteristic
915	C₂⁴	C₂×#386	1	1	yes	characteristic
916	C₂⁴	C₂×#386	1	1	yes	characteristic
917	C₂⁴	C₂×#386	1	1	yes	characteristic
918	C₂⁴	C₂×#386	1	1	yes	characteristic
919	C₂⁴	D₄×C₂²⋊C₄	1	1	yes	characteristic
920	C₂⁴	D₄×C₂²⋊C₄	1	1	yes	characteristic
921	C₂⁴	#2358	1	1	yes	characteristic
922	C₂⁴	#2358	1	1	yes	characteristic
923	C₂⁴	#2403	1	1	yes	characteristic
924	C₂⁴	#2403	1	1	yes	characteristic
925	C₂⁴	#2403	1	1	yes	characteristic
926	C₂⁴	#2403	1	1	yes	characteristic
927	C₂⁴	#2404	1	1	yes	characteristic
928	C₂⁴	#2404	1	1	yes	characteristic
929	C₂⁴	#2418	1	1	yes	characteristic
930	C₂⁴	#2418	1	1	yes	characteristic
931	C₂⁴	#2424	1	1	yes	characteristic
932	C₂⁴	#2424	1	1	yes	characteristic
933	C₂⁴	C₂²×#120	1	1	yes	characteristic
934	C₂⁴	C₂×D₄²	1	1	yes	characteristic
935	C₂⁴	C₂×D₄²	1	1	yes	characteristic
936	C₂×Q₈	#2321	1	1	yes	characteristic
937	C₂×Q₈	#2321	1	1	yes	characteristic
938	C₂×Q₈	D₄×C₂²⋊C₄	1	1	yes	characteristic
939	C₂×Q₈	D₄×C₂²⋊C₄	1	1	yes	characteristic
940	C₂×Q₈	#2358	1	1	yes	characteristic
941	C₂×Q₈	#2358	1	1	yes	characteristic
942	C₂×Q₈	#2418	1	1	yes	characteristic
943	C₂×Q₈	#2418	1	1	yes	characteristic
944	C₂×Q₈	#2424	1	1	yes	characteristic
945	C₂×Q₈	#2424	1	1	yes	characteristic
946	C₂×Q₈	#2534	1	1	yes	characteristic
947	C₂×Q₈	#2534	1	1	yes	characteristic
948	C₂×Q₈	C₂×#518	1	1	yes	characteristic
949	C₂×Q₈	C₂×#538	1	1	yes	characteristic
950	C₂×Q₈	C₂×#546	1	1	yes	characteristic
951	C₂×Q₈	C₂×#551	1	1	yes	characteristic
952	C₂×D₄	C₂×#386	1	1	yes	characteristic
953	C₂×D₄	C₂×#386	1	1	yes	characteristic
954	C₂×D₄	C₂×#386	1	1	yes	characteristic
955	C₂×D₄	C₂×#386	1	1	yes	characteristic
956	C₂×D₄	#2321	1	1	yes	characteristic
957	C₂×D₄	#2321	1	1	yes	characteristic
958	C₂×D₄	D₄×C₂²⋊C₄	1	1	yes	characteristic
959	C₂×D₄	D₄×C₂²⋊C₄	1	1	yes	characteristic
960	C₂×D₄	D₄×C₂²⋊C₄	1	1	yes	characteristic
961	C₂×D₄	D₄×C₂²⋊C₄	1	1	yes	characteristic
962	C₂×D₄	D₄×C₂²⋊C₄	1	1	yes	characteristic
963	C₂×D₄	D₄×C₂²⋊C₄	1	1	yes	characteristic
964	C₂×D₄	#2358	1	1	yes	characteristic
965	C₂×D₄	#2358	1	1	yes	characteristic
966	C₂×D₄	#2358	1	1	yes	characteristic
967	C₂×D₄	#2358	1	1	yes	characteristic
968	C₂×D₄	#2358	1	1	yes	characteristic
969	C₂×D₄	#2358	1	1	yes	characteristic
970	C₂×D₄	#2404	1	1	yes	characteristic
971	C₂×D₄	#2404	1	1	yes	characteristic
972	C₂×D₄	#2404	1	1	yes	characteristic
973	C₂×D₄	#2404	1	1	yes	characteristic
974	C₂×D₄	#2418	1	1	yes	characteristic
975	C₂×D₄	#2418	1	1	yes	characteristic
976	C₂×D₄	#2418	1	1	yes	characteristic
977	C₂×D₄	#2418	1	1	yes	characteristic
978	C₂×D₄	#2418	1	1	yes	characteristic
979	C₂×D₄	#2418	1	1	yes	characteristic
980	C₂×D₄	#2424	1	1	yes	characteristic
981	C₂×D₄	#2424	1	1	yes	characteristic
982	C₂×D₄	#2424	1	1	yes	characteristic
983	C₂×D₄	#2424	1	1	yes	characteristic
984	C₂×D₄	#2424	1	1	yes	characteristic
985	C₂×D₄	#2424	1	1	yes	characteristic
986	C₂×D₄	#2534	1	1	yes	characteristic
987	C₂×D₄	#2534	1	1	yes	characteristic
988	C₂×D₄	C₂³×C₂²⋊C₄	1	1	yes	characteristic
989	C₂×D₄	C₂²×C₄×D₄	1	1	yes	characteristic
990	C₂×D₄	C₂×#518	1	1	yes	characteristic
991	C₂×D₄	C₂²×#121	1	1	yes	characteristic
992	C₂×D₄	C₂²×#123	1	1	yes	characteristic
993	C₂×D₄	C₂×#538	1	1	yes	characteristic
994	C₂×D₄	C₂×#546	1	1	yes	characteristic
995	C₂×D₄	C₂×#546	1	1	yes	characteristic
996	C₂×D₄	C₂×#546	1	1	yes	characteristic
997	C₂×D₄	C₂×#546	1	1	yes	characteristic
998	C₂×D₄	C₂×#546	1	1	yes	characteristic
999	C₂×D₄	C₂×#551	1	1	yes	characteristic
1000	C₂²×C₄	C₂×#386	1	1	yes	characteristic
1001	C₂²×C₄	C₂×#386	1	1	yes	characteristic
1002	C₂²×C₄	C₂×#386	1	1	yes	characteristic
1003	C₂²×C₄	C₂×#386	1	1	yes	characteristic
1004	C₂²×C₄	C₂×#386	1	1	yes	characteristic
1005	C₂²×C₄	C₂×#386	1	1	yes	characteristic
1006	C₂²×C₄	C₄×#120	1	1	yes	characteristic
1007	C₂²×C₄	C₄×#120	1	1	yes	characteristic
1008	C₂²×C₄	C₄×#120	1	1	yes	characteristic
1009	C₂²×C₄	C₄×#120	1	1	yes	characteristic
1010	C₂²×C₄	C₄×#120	1	1	yes	characteristic
1011	C₂²×C₄	C₄×#120	1	1	yes	characteristic
1012	C₂²×C₄	C₄×#120	1	1	yes	characteristic
1013	C₂²×C₄	C₄×#120	1	1	yes	characteristic
1014	C₂²×C₄	#2321	1	1	yes	characteristic
1015	C₂²×C₄	#2321	1	1	yes	characteristic
1016	C₂²×C₄	#2321	1	1	yes	characteristic
1017	C₂²×C₄	#2321	1	1	yes	characteristic
1018	C₂²×C₄	D₄×C₂²⋊C₄	1	1	yes	characteristic
1019	C₂²×C₄	D₄×C₂²⋊C₄	1	1	yes	characteristic
1020	C₂²×C₄	D₄×C₂²⋊C₄	1	1	yes	characteristic
1021	C₂²×C₄	D₄×C₂²⋊C₄	1	1	yes	characteristic
1022	C₂²×C₄	D₄×C₂²⋊C₄	1	1	yes	characteristic
1023	C₂²×C₄	D₄×C₂²⋊C₄	1	1	yes	characteristic
1024	C₂²×C₄	#2358	1	1	yes	characteristic
1025	C₂²×C₄	#2358	1	1	yes	characteristic
1026	C₂²×C₄	#2358	1	1	yes	characteristic
1027	C₂²×C₄	#2358	1	1	yes	characteristic
1028	C₂²×C₄	#2358	1	1	yes	characteristic
1029	C₂²×C₄	#2358	1	1	yes	characteristic
1030	C₂²×C₄	#2403	1	1	yes	characteristic
1031	C₂²×C₄	#2403	1	1	yes	characteristic
1032	C₂²×C₄	#2403	1	1	yes	characteristic
1033	C₂²×C₄	#2403	1	1	yes	characteristic
1034	C₂²×C₄	#2404	1	1	yes	characteristic
1035	C₂²×C₄	#2404	1	1	yes	characteristic
1036	C₂²×C₄	#2408	1	1	yes	characteristic
1037	C₂²×C₄	#2408	1	1	yes	characteristic
1038	C₂²×C₄	#2408	1	1	yes	characteristic
1039	C₂²×C₄	#2408	1	1	yes	characteristic
1040	C₂²×C₄	#2408	1	1	yes	characteristic
1041	C₂²×C₄	#2408	1	1	yes	characteristic
1042	C₂²×C₄	#2408	1	1	yes	characteristic
1043	C₂²×C₄	#2408	1	1	yes	characteristic
1044	C₂²×C₄	#2418	1	1	yes	characteristic
1045	C₂²×C₄	#2418	1	1	yes	characteristic
1046	C₂²×C₄	#2418	1	1	yes	characteristic
1047	C₂²×C₄	#2418	1	1	yes	characteristic
1048	C₂²×C₄	#2418	1	1	yes	characteristic
1049	C₂²×C₄	#2418	1	1	yes	characteristic
1050	C₂²×C₄	#2424	1	1	yes	characteristic
1051	C₂²×C₄	#2424	1	1	yes	characteristic
1052	C₂²×C₄	#2424	1	1	yes	characteristic
1053	C₂²×C₄	#2424	1	1	yes	characteristic
1054	C₂²×C₄	#2424	1	1	yes	characteristic
1055	C₂²×C₄	#2424	1	1	yes	characteristic
1056	C₂²×C₄	#2534	1	1	yes	characteristic
1057	C₂²×C₄	#2534	1	1	yes	characteristic
1058	C₂²×C₄	#2534	1	1	yes	characteristic
1059	C₂²×C₄	#2534	1	1	yes	characteristic
1060	C₂²×C₄	C₂×B(4,𝔽₂)	1	1	yes	characteristic
1061	C₂²×C₄	C₂×B(4,𝔽₂)	1	1	yes	characteristic
1062	C₂²×C₄	C₂×B(4,𝔽₂)	1	1	yes	characteristic
1063	C₂²×C₄	C₂×B(4,𝔽₂)	1	1	yes	characteristic
1064	C₂²×C₄	#3025	1	1	yes	characteristic
1065	C₂²×C₄	#3025	1	1	yes	characteristic
1066	C₂²×C₄	#3025	1	1	yes	characteristic
1067	C₂²×C₄	#3025	1	1	yes	characteristic
1068	C₂²×C₄	C₂²×C₄×D₄	1	1	yes	characteristic
1069	C₂²×C₄	C₂²×C₄×D₄	1	1	yes	characteristic
1070	C₂²×C₄	C₂²×C₄×D₄	1	1	yes	characteristic
1071	C₂²×C₄	C₂²×#120	1	1	yes	characteristic
1072	C₂²×C₄	C₂²×#121	1	1	yes	characteristic
1073	C₂²×C₄	C₂×#525	1	1	yes	characteristic
1074	C₂²×C₄	C₂×#525	1	1	yes	characteristic
1075	C₂²×C₄	C₂×#525	1	1	yes	characteristic
1076	C₂²×C₄	C₂×#534	1	1	yes	characteristic
1077	C₂²×C₄	C₂×#535	1	1	yes	characteristic
1078	C₂²×C₄	C₂×D₄²	1	1	yes	characteristic
1079	C₂²×C₄	C₂×D₄²	1	1	yes	characteristic
1080	C₂²×C₄	C₂×D₄²	1	1	yes	characteristic
1081	C₂²×C₄	C₂×D₄²	1	1	yes	characteristic
1082	C₂²×C₄	C₂×#546	1	1	yes	characteristic
1083	C₂²×C₄	C₂×#546	1	1	yes	characteristic
1084	C₂²⋊C₄	C₂×#386	1	1	yes	characteristic
1085	C₂²⋊C₄	C₂×#386	1	1	yes	characteristic
1086	C₂²⋊C₄	C₂×#386	1	1	yes	characteristic
1087	C₂²⋊C₄	C₂×#386	1	1	yes	characteristic
1088	C₂²⋊C₄	C₂×#386	1	1	yes	characteristic
1089	C₂²⋊C₄	C₂×#386	1	1	yes	characteristic
1090	C₂²⋊C₄	C₂×#386	1	1	yes	characteristic
1091	C₂²⋊C₄	C₂×#386	1	1	yes	characteristic
1092	C₄²	C₂×B(4,𝔽₂)	1	4	yes	—
1093	C₄²	C₂×B(4,𝔽₂)	1	4	yes	—
1094	C₂³	#13967	1	1	yes	characteristic
1095	C₂³	#13967	1	1	yes	characteristic
1096	C₂³	#13967	1	1	yes	characteristic
1097	C₂³	#13967	1	1	yes	characteristic
1098	C₂³	#13967	1	1	yes	characteristic
1099	C₂³	#13967	1	1	yes	characteristic
1100	C₂³	#13967	1	1	yes	characteristic
1101	C₂³	#13967	1	1	yes	characteristic
1102	C₂³	#23900	1	1	yes	characteristic
1103	C₂³	#23900	1	1	yes	characteristic
1104	C₂³	#23902	1	1	yes	characteristic
1105	C₂³	#23902	1	1	yes	characteristic
1106	C₂³	C₂²×#386	1	1	yes	characteristic
1107	C₂³	C₂×D₄×C₂²⋊C₄	1	1	yes	characteristic
1108	C₂³	C₂×#2358	1	1	yes	characteristic
1109	C₂³	C₂×#2403	1	1	yes	characteristic
1110	C₂³	C₂×#2418	1	1	yes	characteristic
1111	C₂³	C₂×#2424	1	1	yes	characteristic
1112	C₂³	C₂×#2404	1	1	yes	characteristic
1113	C₂×C₄	#13967	1	1	yes	characteristic
1114	C₂×C₄	#13967	1	1	yes	characteristic
1115	C₂×C₄	#13967	1	1	yes	characteristic
1116	C₂×C₄	#13967	1	1	yes	characteristic
1117	C₂×C₄	#13967	1	1	yes	characteristic
1118	C₂×C₄	#13967	1	1	yes	characteristic
1119	C₂×C₄	#13967	1	1	yes	characteristic
1120	C₂×C₄	#13967	1	1	yes	characteristic
1121	C₂×C₄	C₄×B(4,𝔽₂)	1	1	yes	characteristic
1122	C₂×C₄	C₄×B(4,𝔽₂)	1	1	yes	characteristic
1123	C₂×C₄	C₄×B(4,𝔽₂)	1	1	yes	characteristic
1124	C₂×C₄	C₄×B(4,𝔽₂)	1	1	yes	characteristic
1125	C₂×C₄	C₄×B(4,𝔽₂)	1	1	yes	characteristic
1126	C₂×C₄	C₄×B(4,𝔽₂)	1	1	yes	characteristic
1127	C₂×C₄	C₄×B(4,𝔽₂)	1	1	yes	characteristic
1128	C₂×C₄	C₄×B(4,𝔽₂)	1	1	yes	characteristic
1129	C₂×C₄	#23900	1	1	yes	characteristic
1130	C₂×C₄	#23900	1	1	yes	characteristic
1131	C₂×C₄	#23902	1	1	yes	characteristic
1132	C₂×C₄	#23902	1	1	yes	characteristic
1133	C₂×C₄	#24260	1	1	yes	characteristic
1134	C₂×C₄	#24260	1	1	yes	characteristic
1135	C₂×C₄	#24260	1	1	yes	characteristic
1136	C₂×C₄	#24260	1	1	yes	characteristic
1137	C₂×C₄	#24260	1	1	yes	characteristic
1138	C₂×C₄	#24260	1	1	yes	characteristic
1139	C₂×C₄	#24260	1	1	yes	characteristic
1140	C₂×C₄	#24260	1	1	yes	characteristic
1141	C₂×C₄	C₂×C₄×#120	1	1	yes	characteristic
1142	C₂×C₄	C₂×#2321	1	1	yes	characteristic
1143	C₂×C₄	C₂×D₄×C₂²⋊C₄	1	1	yes	characteristic
1144	C₂×C₄	C₂×#2358	1	1	yes	characteristic
1145	C₂×C₄	C₂×#2418	1	1	yes	characteristic
1146	C₂×C₄	C₂×#2424	1	1	yes	characteristic
1147	C₂×C₄	C₂×#2408	1	1	yes	characteristic
1148	C₂×C₄	C₂×#2534	1	1	yes	characteristic
1149	C₂×C₄	C₂²×B(4,𝔽₂)	1	1	yes	characteristic
1150	C₂×C₄	C₂²×B(4,𝔽₂)	1	1	yes	characteristic
1151	C₂×C₄	C₂×#3025	1	1	yes	characteristic
1152	C₂×C₄	C₂×#3025	1	1	yes	characteristic
1153	C₂²	#364513	1	1	yes	characteristic
1154	C₂²	#364513	1	1	yes	characteristic
1155	C₂²	#364513	1	1	yes	characteristic
1156	C₂²	#364513	1	1	yes	characteristic
1157	C₂²	C₂×#13967	1	1	yes	characteristic
1158	C₂²	C₂×#23900	1	1	yes	characteristic
1159	C₂²	C₂×#23902	1	1	yes	characteristic
1160	C₄	#364513	1	1	yes	characteristic
1161	C₄	#364513	1	1	yes	characteristic
1162	C₄	#364513	1	1	yes	characteristic
1163	C₄	#364513	1	1	yes	characteristic
1164	C₄	C₂×C₄×B(4,𝔽₂)	1	1	yes	characteristic
1165	C₄	C₂×C₄×B(4,𝔽₂)	1	1	yes	characteristic
1166	C₄	C₂×#24260	1	1	yes	characteristic
1167	C₄	C₂×#24260	1	1	yes	characteristic
1168	C₂	C₂×#364513	1	1	yes	characteristic

	subgroup	G/H
center	C₄	C₂×#24260
commutator	C₂×#41	C₂⁴×C₄
Frattini, cosocle	C₂²×#41	C₂⁵
socle	C₂	C₂×#364513
prime radical	C₂×#7622868	C₂
LCS	G ▷ C₂×#41 ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄ ◁ C₂³×C₄ ◁ C₂×#3428 ◁ G
LECS	G ▷ C₂²×#41 ▷ C₂² ▷ C₂ ▷ C₁

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. #72282797	C₂	semidirect
2. #72282782	C₂	semidirect
3. #72282405	C₂	semidirect
4. C₂×#146595	C₂	semidirect
5. #72281693	C₂	semidirect
6. #72280868	C₂	semidirect
7. #72280808	C₂	semidirect
8. #72280797	C₂	semidirect
9. #72280748	C₂	semidirect
10. #72280714	C₂	semidirect
11. #72280674	C₂	semidirect
12. #72280582	C₂	semidirect
13. #72280582	C₂	semidirect
14. #72280532	C₂	semidirect
15. C₂×#494587	C₂	semidirect
17. C₂×#493561	C₂	semidirect
19. #10585883	C₂²	semidirect
25. #7622868	C₄	semidirect
26. #7622868	C₄	semidirect
29. C₂×#33556	C₄	semidirect
30. C₂×#33555	C₄	semidirect
31. C₂×#33554	C₄	semidirect
32. C₂×#33553	C₄	semidirect
39. #6393518	C₂²	semidirect
40. #6393517	C₂²	semidirect
43. #6372729	C₂²	semidirect
44. C₄×#3025	C₂²	semidirect
50. #6371336	C₂²	semidirect
51. C₂×#20620	C₂²	semidirect
52. C₂×#20612	C₂²	semidirect
53. #6370734	C₂²	semidirect
54. #6369817	C₂²	semidirect
55. #494587	C₂²	semidirect
56. #494587	C₂²	semidirect
57. #493561	C₂²	semidirect
58. #493561	C₂²	semidirect
59. C₂×#12589	C₂²	semidirect
60. C₂×#12589	C₂²	semidirect
61. #492906	C₂²	semidirect
62. #492899	C₂²	semidirect
63. C₂×#12577	C₂²	semidirect
64. C₂×#12577	C₂²	semidirect
65. #392718	C₂²	semidirect
66. #392711	C₂²	semidirect
67. C₂×#10756	C₂²	semidirect
68. C₂×#10743	C₂²	semidirect
69. #353324	C₂²	semidirect
70. #353324	C₂²	semidirect
71. #148243	C₂²	semidirect
72. #148240	C₂²	semidirect
73. #147761	C₂²	semidirect
74. #147757	C₂²	semidirect
75. #147519	C₂²	semidirect
76. #147519	C₂²	semidirect
77. #146668	C₂²	semidirect
78. #146667	C₂²	semidirect
79. #146595	C₂²	semidirect
80. #146595	C₂²	semidirect
82. #62729	C₂×C₄	semidirect
83. #62729	C₂×C₄	semidirect
86. C₂×#3540	C₂×C₄	semidirect
87. C₂×#3540	C₂×C₄	semidirect
88. C₂×#3538	C₂×C₄	semidirect
89. C₂×#3537	C₂×C₄	semidirect
93. C₄×#585	C₂³	semidirect
96. C₂³×#117	D₄	semidirect
97. #60398	C₂×C₄	semidirect
99. C₂×#3028	C₂×C₄	semidirect
100. C₂×#3027	C₂×C₄	semidirect
115. #60387	C₂×C₄	semidirect
117. C₂×#3022	C₂×C₄	semidirect
118. C₂×#3021	C₂×C₄	semidirect
121. C₂²×#421	D₄	semidirect
122. C₂²×#421	D₄	semidirect
123. C₂²×#421	D₄	semidirect
124. C₂²×#421	D₄	semidirect
133. #34065	D₄	semidirect
135. #34052	D₄	semidirect
137. C₄×#525	D₄	semidirect
139. C₂×#2280	D₄	semidirect
140. #33996	D₄	semidirect
141. #33556	C₂×C₄	semidirect
142. #33556	C₂×C₄	semidirect
143. #33555	C₂×C₄	semidirect
144. #33555	C₂×C₄	semidirect
145. #33554	C₂×C₄	semidirect
146. #33554	C₂×C₄	semidirect
147. #33553	C₂×C₄	semidirect
148. #33553	C₂×C₄	semidirect
149. #33358	C₂×C₄	semidirect
152. C₂×#2129	C₂×C₄	semidirect
153. C₂×#2128	C₂×C₄	semidirect
154. #33347	C₂×C₄	semidirect
157. C₂×#2123	C₂×C₄	semidirect
158. C₂×#2122	C₂×C₄	semidirect
159. C₂×#2120	C₂×C₄	semidirect
160. C₂×#2120	C₂×C₄	semidirect
161. C₂×#2120	C₂×C₄	semidirect
162. C₂×#2120	C₂×C₄	semidirect
171. #20980	D₄	semidirect
172. #20980	D₄	semidirect
175. #20959	D₄	semidirect
176. #20959	D₄	semidirect
179. C₂×#1890	D₄	semidirect
180. C₂×#1889	D₄	semidirect
181. #20888	C₂³	semidirect
182. #20620	C₂³	semidirect
183. #20612	C₂³	semidirect
184. #20608	C₂³	semidirect
185. C₄×#410	C₂³	semidirect
186. C₂×#1733	D₄	semidirect
187. C₂×#1733	D₄	semidirect
188. C₂×#1733	D₄	semidirect
189. C₂×#1733	D₄	semidirect
190. #12589	C₂³	semidirect
191. #12589	C₂³	semidirect
192. #12585	C₂³	semidirect
193. #12581	C₂³	semidirect
194. #12577	C₂³	semidirect
195. #12577	C₂³	semidirect
196. #10758	C₂³	semidirect
197. #10758	C₂³	semidirect
198. #10756	C₂³	semidirect
199. #10743	C₂³	semidirect
215. #3540	C₂²×C₄	semidirect
216. #3540	C₂²×C₄	semidirect
217. #3540	C₂²×C₄	semidirect
218. #3540	C₂²×C₄	semidirect
219. #3538	C₂²×C₄	semidirect
220. #3538	C₂²×C₄	semidirect
221. #3537	C₂²×C₄	semidirect
222. #3537	C₂²×C₄	semidirect
285. C₂²×#117	C₂×D₄	semidirect
286. C₂³×C₄²	C₂×D₄	semidirect
319. C₂×#421	C₂×D₄	semidirect
320. C₂×#421	C₂×D₄	semidirect
321. C₂²×#104	C₂×D₄	semidirect
322. C₂²×#104	C₂×D₄	semidirect
347. #2296	C₂×D₄	semidirect
348. #2296	C₂×D₄	semidirect
349. #2280	C₂×D₄	semidirect
350. #2280	C₂×D₄	semidirect
351. C₄×#117	C₂×D₄	semidirect
352. C₄×#117	C₂×D₄	semidirect
353. #2129	C₂²×C₄	semidirect
354. #2128	C₂²×C₄	semidirect
355. #2123	C₂²×C₄	semidirect
356. #2122	C₂²×C₄	semidirect
357. #2120	C₂²×C₄	semidirect
358. #2120	C₂²×C₄	semidirect
359. #2120	C₂²×C₄	semidirect
360. #2120	C₂²×C₄	semidirect
361. #1890	C₂×D₄	semidirect
362. #1890	C₂×D₄	semidirect
363. #1889	C₂×D₄	semidirect
364. #1889	C₂×D₄	semidirect
365. #1733	C₂×D₄	semidirect
366. #1733	C₂×D₄	semidirect
367. C₂×#339	C₂×D₄	semidirect
368. C₂×#339	C₂×D₄	semidirect
377. C₂²×#41	C₄×D₄	semidirect
378. C₂²×#41	C₄×D₄	semidirect
405. C₂³×Q₈	C₄×D₄	semidirect
406. C₂³×Q₈	C₄×D₄	semidirect
408. C₂³×D₄	C₄×D₄	semidirect
409. C₂³×D₄	C₄×D₄	semidirect
433. #536	C₄×D₄	semidirect
434. #536	C₄×D₄	semidirect
435. #536	C₄×D₄	semidirect
436. #536	C₄×D₄	semidirect
441. #535	C₄×D₄	semidirect
442. #535	C₄×D₄	semidirect
443. #535	C₄×D₄	semidirect
444. #535	C₄×D₄	semidirect
566. C₂×#117	C₄×D₄	semidirect
567. C₂×#117	C₄×D₄	semidirect
568. C₂×#117	C₄×D₄	semidirect
569. C₂×#117	C₄×D₄	semidirect
570. C₂×#117	C₄×D₄	semidirect
571. C₂×#117	C₄×D₄	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
#72282797	2
#72282782	2
#72282405	2
C₂×#146595	2
#72281693	2
#72280868	2
#72280808	2
#72280797	2
#72280748	2
#72280714	2
#72280674	2
#72280582	2
#72280532	2
C₂×#494587	2
C₂×#7622868	2
C₂×#493561	2