Subgroups — #72260751

Order 2048.

At least 10315 conjugacy classes of subgroups; only the 1580 normal subgroups are shown.

The subgroup lattice has 831 nodes (normal subgroups only) — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#72260748	C₂	1	1	yes	maximal, characteristic, complemented
2	#72260589	C₂	1	1	yes	maximal, characteristic, complemented
3	#72260537	C₂	1	2	yes	maximal, complemented
4	#72260412	C₂	1	4	yes	maximal, complemented
5	#72258978	C₂	1	1	yes	maximal, characteristic, complemented
6	#72237599	C₂	1	2	yes	maximal, complemented
7	#72237037	C₂	1	2	yes	maximal, complemented
8	C₂×#139700	C₂	1	2	yes	maximal, complemented
9	#72233637	C₂	1	1	yes	maximal, characteristic, complemented
10	#72233078	C₂	1	4	yes	maximal, complemented
11	#72231753	C₂	1	4	yes	maximal, complemented
12	#72231467	C₂	1	4	yes	maximal, complemented
13	#72225786	C₂	1	1	yes	maximal, characteristic, complemented
14	#72219302	C₂	1	1	yes	maximal, characteristic, complemented
15	#72216064	C₂	1	1	yes	maximal, characteristic
16	#10586066	C₂²	1	1	yes	characteristic
17	C₂²×#3484	C₂²	1	1	yes	characteristic
18	C₂×#60399	C₄	1	2	yes	complemented
19	#6437633	C₄	1	4	yes	complemented
20	#6437632	C₄	1	4	yes	complemented
21	#6437632	C₄	1	4	yes	complemented
22	#6437623	C₂²	1	2	yes	—
23	#6437621	C₂²	1	2	yes	—
24	#6437621	C₂²	1	2	yes	—
25	#6437616	C₂²	1	2	yes	—
26	C₂×#23900	C₂²	1	2	yes	—
27	C₂×#23900	C₂²	1	2	yes	—
28	#6371558	C₄	1	2	yes	complemented
29	#6370704	C₂²	1	1	yes	characteristic
30	#6370693	C₂²	1	1	yes	characteristic
31	#6370693	C₂²	1	1	yes	characteristic
32	#581562	C₂²	1	2	yes	complemented
33	#581561	C₂²	1	2	yes	complemented
34	#556752	C₂²	1	1	yes	characteristic, complemented
35	#552677	C₂²	1	1	yes	characteristic, complemented
36	#552677	C₂²	1	1	yes	characteristic, complemented
37	#532097	C₂²	1	2	yes	complemented
38	#531607	C₂²	1	2	yes	complemented
39	#517592	C₂²	1	1	yes	characteristic
40	#517592	C₂²	1	1	yes	characteristic
41	C₂×#14134	C₂²	1	1	yes	characteristic, complemented
42	#493359	C₂²	1	2	yes	complemented
43	#493357	C₂²	1	2	yes	complemented
44	#493357	C₂²	1	2	yes	complemented
45	#493352	C₂²	1	2	yes	complemented
46	C₂×#12687	C₂²	1	2	yes	complemented
47	C₂×#12687	C₂²	1	2	yes	complemented
48	#187944	C₂²	1	2	yes	complemented
49	#187931	C₂²	1	4	yes	complemented
50	#187928	C₂²	1	4	yes	complemented
51	C₂×#8534	C₂²	1	2	yes	complemented
52	#186835	C₂²	1	2	yes	complemented
53	#186814	C₂²	1	4	yes	complemented
54	#186808	C₂²	1	4	yes	complemented
55	C₂×#8453	C₂²	1	2	yes	complemented
56	#139774	C₂²	1	8	yes	complemented
57	#139774	C₂²	1	8	yes	complemented
58	#139773	C₂²	1	8	yes	complemented
59	#139773	C₂²	1	8	yes	complemented
60	#139702	C₂²	1	8	yes	complemented
61	#139700	C₂²	1	8	yes	complemented
62	#139700	C₂²	1	8	yes	complemented
63	#139700	C₂²	1	8	yes	complemented
64	#128074	C₂²	1	4	yes	complemented
65	#128073	C₂²	1	4	yes	complemented
66	#128058	C₂²	1	4	yes	complemented
67	#128057	C₂²	1	4	yes	complemented
68	#128033	C₂²	1	2	yes	complemented
69	C₂×#7304	C₂²	1	2	yes	complemented
70	#128009	C₂²	1	2	yes	complemented
71	C₂×#7307	C₂²	1	2	yes	complemented
72	C₂×H(7,𝔽₂)	C₂×C₄	1	1	yes	characteristic, complemented
73	C₂³×H(5,𝔽₂)	C₂³	1	1	yes	characteristic
74	C₂⁵×D₄	D₄	1	1	yes	characteristic
75	#62852	C₂×C₄	1	2	yes	complemented
76	#62842	C₂×C₄	1	2	yes	complemented
77	#62842	C₂×C₄	1	2	yes	complemented
78	#62811	C₂³	1	2	yes	—
79	C₂×#3484	C₂×C₄	1	2	yes	—
80	C₂×#3484	C₂×C₄	1	2	yes	—
81	C₂×#3484	C₂×C₄	1	2	yes	—
82	C₂×#3484	C₂×C₄	1	2	yes	—
83	C₂×#3484	D₄	1	2	yes	—
84	C₂×#3484	D₄	1	2	yes	—
85	C₂×#3484	D₄	1	2	yes	—
86	C₂×#3484	D₄	1	2	yes	—
87	C₂×#3484	C₂³	1	2	yes	—
88	C₂×#3484	C₂³	1	2	yes	—
89	C₂²×#535	D₄	1	1	yes	characteristic
90	C₂²×#535	C₂³	1	1	yes	characteristic
91	C₂²×#534	D₄	1	1	yes	characteristic
92	C₂²×#534	D₄	1	1	yes	characteristic
93	C₂²×#534	C₂³	1	1	yes	characteristic
94	C₂²×#534	C₂³	1	1	yes	characteristic
95	C₂²×#525	D₄	1	1	yes	characteristic
96	C₂²×#525	C₂³	1	1	yes	characteristic
97	C₂³×#120	D₄	1	1	yes	characteristic
98	C₂³×#120	D₄	1	1	yes	characteristic
99	C₂³×#120	C₂³	1	1	yes	characteristic
100	C₂³×#120	C₂³	1	1	yes	characteristic
101	#62652	C₂×C₄	1	1	yes	characteristic, complemented
102	C₂²×#518	D₄	1	1	yes	characteristic
103	C₂×#3027	C₂×C₄	1	4	yes	complemented
104	C₂×#3026	C₂×C₄	1	4	yes	complemented
105	C₂×#3026	C₂×C₄	1	4	yes	complemented
106	C₂×#3025	C₂×C₄	1	4	yes	complemented
107	C₂²×B(4,𝔽₂)	C₂×C₄	1	4	yes	complemented
108	C₂²×B(4,𝔽₂)	C₂×C₄	1	4	yes	complemented
109	C₂×#2883	C₂×C₄	1	2	yes	complemented
110	C₂×#2339	D₄	1	2	yes	complemented
111	C₂×D₄×C₂²⋊C₄	D₄	1	2	yes	complemented
112	#23904	C₂×C₄	1	8	yes	complemented
113	#23903	C₂×C₄	1	8	yes	complemented
114	#23903	C₂×C₄	1	8	yes	complemented
115	#23902	C₂×C₄	1	8	yes	complemented
116	#23901	C₂³	1	4	yes	—
117	#23900	C₂×C₄	1	8	yes	complemented
118	#23900	C₂×C₄	1	8	yes	complemented
119	#23900	C₂³	1	4	yes	—
120	#23900	C₂³	1	4	yes	—
121	#23900	C₂³	1	4	yes	—
122	#20961	C₂×C₄	1	4	yes	complemented
123	#20960	C₂×C₄	1	4	yes	complemented
124	#20960	C₂×C₄	1	4	yes	complemented
125	#20959	C₂×C₄	1	4	yes	complemented
126	C₂×#1889	C₂×C₄	1	4	yes	complemented
127	C₂×#1889	C₂×C₄	1	4	yes	complemented
128	#20591	C₂³	1	2	yes	—
129	C₂×#1783	C₂³	1	2	yes	—
130	C₂×#1783	C₂³	1	2	yes	—
131	#20586	C₂×C₄	1	2	yes	complemented
132	#20585	C₂×C₄	1	2	yes	complemented
133	#20585	C₂×C₄	1	2	yes	complemented
134	#20584	C₂³	1	2	yes	—
135	#20584	C₂³	1	2	yes	—
136	C₂×#1781	C₂³	1	2	yes	—
137	C₂×#1781	C₂³	1	2	yes	—
138	C₂×#1781	C₂³	1	2	yes	—
139	C₂×#1781	C₂³	1	2	yes	—
140	#14657	C₂³	1	2	yes	complemented
141	#14506	C₂³	1	2	yes	complemented
142	#14506	C₂³	1	2	yes	complemented
143	#14358	C₂³	1	2	yes	complemented
144	#14358	C₂³	1	2	yes	complemented
145	#14337	D₄	1	1	yes	characteristic, complemented
146	#14337	D₄	1	1	yes	characteristic, complemented
147	#14335	D₄	1	1	yes	characteristic, complemented
148	#14335	D₄	1	1	yes	characteristic, complemented
149	#14335	C₂³	1	1	yes	characteristic
150	#14335	C₂³	1	1	yes	characteristic
151	#14134	C₂³	1	2	yes	complemented
152	#14134	C₂³	1	2	yes	complemented
153	#14134	C₂³	1	2	yes	complemented
154	#13956	D₄	1	2	yes	complemented
155	#13956	C₂³	1	2	yes	—
156	#13937	C₂³	1	2	yes	—
157	#13902	C₂³	1	2	yes	—
158	#13867	D₄	1	2	yes	complemented
159	#13867	C₂³	1	2	yes	—
160	#13851	D₄	1	1	yes	characteristic, complemented
161	#13851	D₄	1	1	yes	characteristic, complemented
162	C₂×#1438	D₄	1	1	yes	characteristic, complemented
163	C₂×#1438	D₄	1	1	yes	characteristic, complemented
164	C₂×#1438	C₂³	1	1	yes	characteristic
165	C₂×#1438	C₂³	1	1	yes	characteristic
166	#12688	C₂³	1	4	yes	complemented
167	#12687	C₂³	1	4	yes	complemented
168	#12687	C₂³	1	4	yes	complemented
169	#12687	C₂³	1	4	yes	complemented
170	#8534	C₂³	1	8	yes	—
171	#8534	C₂³	1	8	yes	—
172	#8453	C₂³	1	8	yes	—
173	#8453	C₂³	1	8	yes	—
174	#7307	C₂³	1	8	yes	complemented
175	#7307	C₂³	1	8	yes	complemented
176	#7304	C₂³	1	8	yes	complemented
177	#7304	C₂³	1	8	yes	complemented
178	C₂⁷	C₂×D₄	1	1	yes	characteristic
179	C₂⁷	C₂×D₄	1	1	yes	characteristic
180	C₂×#585	C₂²×C₄	1	2	yes	complemented
181	C₂²×H(5,𝔽₂)	C₂²×C₄	1	2	yes	—
182	C₂²×H(5,𝔽₂)	C₂²×C₄	1	1	yes	characteristic
183	C₂²×H(5,𝔽₂)	C₂²×C₄	1	1	yes	characteristic
184	C₂²×H(5,𝔽₂)	C₂²×C₄	1	1	yes	characteristic
185	C₂²×H(5,𝔽₂)	C₂²×C₄	1	1	yes	characteristic
186	C₂²×H(5,𝔽₂)	C₂²×C₄	1	2	yes	complemented
187	C₂²×H(5,𝔽₂)	C₂×D₄	1	1	yes	characteristic
188	C₂²×H(5,𝔽₂)	C₂×D₄	1	1	yes	characteristic
189	C₂²×H(5,𝔽₂)	C₂×D₄	1	1	yes	characteristic
190	C₂²×H(5,𝔽₂)	C₂×D₄	1	1	yes	characteristic
191	C₂²×H(5,𝔽₂)	#41	1	1	yes	characteristic
192	C₂²×H(5,𝔽₂)	#41	1	1	yes	characteristic
193	C₂²×H(5,𝔽₂)	#41	1	1	yes	characteristic
194	C₂²×H(5,𝔽₂)	#41	1	1	yes	characteristic
195	C₂²×H(5,𝔽₂)	#41	1	1	yes	characteristic
196	C₂²×H(5,𝔽₂)	#41	1	1	yes	characteristic
197	C₂²×H(5,𝔽₂)	#41	1	1	yes	characteristic
198	C₂²×H(5,𝔽₂)	#41	1	1	yes	characteristic
199	C₂³×#41	C₂×D₄	1	1	yes	characteristic
200	C₂³×#41	C₂×D₄	1	1	yes	characteristic
201	C₂³×#41	C₂×D₄	1	1	yes	characteristic
202	C₂³×#41	C₂×D₄	1	1	yes	characteristic
203	C₂³×#41	C₂×D₄	1	1	yes	characteristic
204	C₂³×#41	C₂⁴	1	1	yes	characteristic
205	C₂⁴×D₄	C₂²⋊C₄	1	2	yes	—
206	C₂⁴×D₄	C₂²⋊C₄	1	2	yes	—
207	C₂⁴×D₄	C₂²⋊C₄	1	2	yes	—
208	C₂⁴×D₄	C₂²⋊C₄	1	2	yes	—
209	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
210	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
211	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
212	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
213	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
214	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
215	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
216	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
217	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
218	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
219	C₂⁴×D₄	C₂⁴	1	1	yes	characteristic
220	C₂⁴×D₄	C₂⁴	1	1	yes	characteristic
221	C₂⁵×C₄	C₂×D₄	1	1	yes	characteristic
222	#3485	C₂²×C₄	1	4	yes	complemented
223	#3484	C₂²×C₄	1	4	yes	—
224	#3484	C₂²×C₄	1	4	yes	complemented
225	#3484	C₂⁴	1	4	yes	—
226	C₂×#535	C₂²⋊C₄	1	2	yes	—
227	C₂×#535	C₂²⋊C₄	1	2	yes	—
228	C₂×#535	C₂²⋊C₄	1	2	yes	—
229	C₂×#535	C₂²⋊C₄	1	2	yes	—
230	C₂×#535	C₂²×C₄	1	2	yes	—
231	C₂×#535	C₂²×C₄	1	2	yes	—
232	C₂×#535	C₂×D₄	1	2	yes	—
233	C₂×#535	C₂×D₄	1	2	yes	—
234	C₂×#534	C₂²⋊C₄	1	2	yes	—
235	C₂×#534	C₂²⋊C₄	1	2	yes	—
236	C₂×#534	C₂²⋊C₄	1	2	yes	—
237	C₂×#534	C₂²⋊C₄	1	2	yes	—
238	C₂×#534	C₂²⋊C₄	1	2	yes	—
239	C₂×#534	C₂²⋊C₄	1	2	yes	—
240	C₂×#534	C₂²⋊C₄	1	2	yes	—
241	C₂×#534	C₂²⋊C₄	1	2	yes	—
242	C₂×#534	C₂²×C₄	1	2	yes	—
243	C₂×#534	C₂²×C₄	1	2	yes	—
244	C₂×#534	C₂²×C₄	1	2	yes	—
245	C₂×#534	C₂²×C₄	1	2	yes	—
246	C₂×#534	C₂×D₄	1	2	yes	—
247	C₂×#534	C₂×D₄	1	2	yes	—
248	C₂×#534	C₂×D₄	1	2	yes	—
249	C₂×#534	C₂×D₄	1	2	yes	—
250	C₂×#525	C₂²⋊C₄	1	2	yes	—
251	C₂×#525	C₂²⋊C₄	1	2	yes	—
252	C₂×#525	C₂²⋊C₄	1	2	yes	—
253	C₂×#525	C₂²⋊C₄	1	2	yes	—
254	C₂×#525	C₂²×C₄	1	2	yes	—
255	C₂×#525	C₂²×C₄	1	2	yes	—
256	C₂×#525	C₂×D₄	1	2	yes	—
257	C₂×#525	C₂×D₄	1	2	yes	—
258	C₂²×#123	C₂×D₄	1	1	yes	characteristic
259	C₂²×#123	C₂×D₄	1	1	yes	characteristic
260	C₂²×#123	C₂×D₄	1	1	yes	characteristic
261	C₂²×#123	C₂⁴	1	1	yes	characteristic
262	C₂²×#120	C₂²⋊C₄	1	2	yes	—
263	C₂²×#120	C₂²⋊C₄	1	2	yes	—
264	C₂²×#120	C₂²⋊C₄	1	2	yes	—
265	C₂²×#120	C₂²⋊C₄	1	2	yes	—
266	C₂²×#120	C₂²⋊C₄	1	2	yes	—
267	C₂²×#120	C₂²⋊C₄	1	2	yes	—
268	C₂²×#120	C₂²⋊C₄	1	2	yes	—
269	C₂²×#120	C₂²⋊C₄	1	2	yes	—
270	C₂²×#120	C₂²×C₄	1	2	yes	—
271	C₂²×#120	C₂²×C₄	1	2	yes	—
272	C₂²×#120	C₂²×C₄	1	2	yes	—
273	C₂²×#120	C₂²×C₄	1	2	yes	—
274	C₂²×#120	C₂×D₄	1	2	yes	—
275	C₂²×#120	C₂×D₄	1	2	yes	—
276	C₂²×#120	C₂×D₄	1	2	yes	—
277	C₂²×#120	C₂×D₄	1	2	yes	—
278	C₂²×#120	C₂×D₄	1	1	yes	characteristic
279	C₂²×#120	C₂×D₄	1	1	yes	characteristic
280	C₂²×#120	C₂×D₄	1	1	yes	characteristic
281	C₂²×#120	C₂×D₄	1	1	yes	characteristic
282	C₂²×#120	C₂×D₄	1	1	yes	characteristic
283	C₂²×#120	C₂×D₄	1	1	yes	characteristic
284	C₂²×#120	C₂×D₄	1	1	yes	characteristic
285	C₂²×#120	C₂×D₄	1	1	yes	characteristic
286	C₂²×#120	C₂×D₄	1	1	yes	characteristic
287	C₂²×#120	C₂⁴	1	1	yes	characteristic
288	C₂²×#120	C₂⁴	1	1	yes	characteristic
289	C₂²×#120	C₂⁴	1	1	yes	characteristic
290	#3428	C₂²×C₄	1	2	yes	complemented
291	C₂×#518	C₂²⋊C₄	1	2	yes	—
292	C₂×#518	C₂²⋊C₄	1	2	yes	—
293	C₂×#518	C₂²⋊C₄	1	2	yes	—
294	C₂×#518	C₂²⋊C₄	1	2	yes	—
295	C₂×#518	C₂²×C₄	1	2	yes	—
296	C₂×#518	C₂²×C₄	1	2	yes	complemented
297	C₂²×#117	C₂×D₄	1	1	yes	characteristic
298	C₂²×#117	C₂×D₄	1	1	yes	characteristic
299	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
300	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
301	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
302	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
303	C₂³×C₂²⋊C₄	C₂×D₄	1	2	yes	complemented
304	C₂³×C₂²⋊C₄	C₂×D₄	1	2	yes	complemented
305	C₂×#458	C₂²×C₄	1	8	yes	complemented
306	C₂×B(4,𝔽₂)	C₂²×C₄	1	8	yes	—
307	C₂×B(4,𝔽₂)	C₂²×C₄	1	8	yes	—
308	C₂×B(4,𝔽₂)	C₂²×C₄	1	8	yes	complemented
309	C₂×#410	C₂²×C₄	1	4	yes	complemented
310	C₂²×#99	C₂²×C₄	1	4	yes	—
311	C₂²×#99	C₂²×C₄	1	4	yes	complemented
312	C₂×#381	C₂×D₄	1	2	yes	complemented
313	C₂×#381	C₂×D₄	1	2	yes	complemented
314	C₂×#380	C₂×D₄	1	2	yes	complemented
315	C₂×#380	C₂×D₄	1	2	yes	complemented
316	C₂×#379	C₂×D₄	1	2	yes	complemented
317	C₂×#379	C₂×D₄	1	2	yes	complemented
318	C₂×C₄×C₂²⋊C₄	C₂×D₄	1	2	yes	complemented
319	C₂×C₄×C₂²⋊C₄	C₂×D₄	1	2	yes	complemented
320	C₂²×#95	C₂×D₄	1	2	yes	complemented
321	C₂²×#95	C₂×D₄	1	2	yes	complemented
322	#1890	C₂²×C₄	1	8	yes	complemented
323	#1889	C₂²×C₄	1	8	yes	—
324	#1889	C₂²×C₄	1	8	yes	—
325	#1889	C₂²×C₄	1	8	yes	complemented
326	#1783	C₂⁴	1	4	yes	—
327	#1782	C₂²×C₄	1	4	yes	complemented
328	#1781	C₂²×C₄	1	4	yes	—
329	#1781	C₂²×C₄	1	4	yes	complemented
330	#1781	C₂⁴	1	4	yes	—
331	#1781	C₂⁴	1	4	yes	—
332	#1446	C₂×D₄	1	2	yes	complemented
333	#1446	C₂×D₄	1	2	yes	complemented
334	#1438	C₂×D₄	1	1	yes	characteristic, complemented
335	#1438	C₂×D₄	1	1	yes	characteristic, complemented
336	#1438	C₂×D₄	1	1	yes	characteristic, complemented
337	#1438	C₂×D₄	1	2	yes	complemented
338	#1438	C₂×D₄	1	1	yes	characteristic, complemented
339	#1438	C₂×D₄	1	2	yes	complemented
340	#1438	C₂×D₄	1	1	yes	characteristic, complemented
341	#1438	C₂×D₄	1	1	yes	characteristic, complemented
342	#1438	C₂×D₄	1	2	yes	complemented
343	#1438	C₂×D₄	1	1	yes	characteristic, complemented
344	#1438	C₂×D₄	1	2	yes	complemented
345	#1438	C₂×D₄	1	2	yes	complemented
346	#1438	C₂×D₄	1	1	yes	characteristic, complemented
347	#1438	C₂×D₄	1	2	yes	complemented
348	#1438	C₂⁴	1	2	yes	—
349	#1438	C₂⁴	1	2	yes	—
350	#1438	C₂⁴	1	2	yes	—
351	#1438	C₂⁴	1	2	yes	—
352	C₂⁶	C₂×C₂²⋊C₄	1	2	yes	—
353	C₂⁶	C₂×C₂²⋊C₄	1	2	yes	—
354	C₂⁶	C₂×C₂²⋊C₄	1	2	yes	—
355	C₂⁶	C₂×C₂²⋊C₄	1	2	yes	—
356	C₂⁶	#120	1	1	yes	characteristic
357	C₂⁶	#120	1	1	yes	characteristic
358	C₂⁶	C₂²×D₄	1	1	yes	characteristic
359	C₂⁶	C₂²×D₄	1	1	yes	characteristic
360	C₂⁶	C₂²×D₄	1	1	yes	characteristic
361	C₂⁶	C₂²×D₄	1	1	yes	characteristic
362	C₂⁶	C₂²×D₄	1	1	yes	characteristic
363	C₂⁶	C₂²×D₄	1	1	yes	characteristic
364	C₂⁶	C₂²×D₄	1	1	yes	characteristic
365	C₂×H(5,𝔽₂)	C₂³×C₄	1	4	yes	—
366	C₂²×#41	C₂×C₂²⋊C₄	1	1	yes	characteristic
367	C₂²×#41	C₂×C₂²⋊C₄	1	1	yes	characteristic
368	C₂²×#41	C₂×C₂²⋊C₄	1	1	yes	characteristic
369	C₂²×#41	C₂×C₂²⋊C₄	1	1	yes	characteristic
370	C₂²×#41	C₄×D₄	1	1	yes	characteristic
371	C₂²×#41	C₄×D₄	1	1	yes	characteristic
372	C₂²×#41	C₄×D₄	1	1	yes	characteristic
373	C₂²×#41	C₄×D₄	1	1	yes	characteristic
374	C₂²×#41	C₄×D₄	1	1	yes	characteristic
375	C₂²×#41	C₄×D₄	1	1	yes	characteristic
376	C₂²×#41	C₄×D₄	1	1	yes	characteristic
377	C₂²×#41	C₄×D₄	1	1	yes	characteristic
378	C₂²×#41	C₄×D₄	1	1	yes	characteristic
379	C₂²×#41	C₄×D₄	1	1	yes	characteristic
380	C₂²×#41	C₄×D₄	1	1	yes	characteristic
381	C₂²×#41	C₄×D₄	1	1	yes	characteristic
382	C₂²×#41	C₄×D₄	1	1	yes	characteristic
383	C₂²×#41	C₄×D₄	1	1	yes	characteristic
384	C₂²×#41	C₄×D₄	1	1	yes	characteristic
385	C₂²×#41	C₄×D₄	1	1	yes	characteristic
386	C₂²×#41	#121	1	1	yes	characteristic
387	C₂²×#41	#121	1	1	yes	characteristic
388	C₂²×#41	#121	1	1	yes	characteristic
389	C₂²×#41	#121	1	1	yes	characteristic
390	C₂²×#41	#121	1	1	yes	characteristic
391	C₂²×#41	#121	1	1	yes	characteristic
392	C₂²×#41	#121	1	1	yes	characteristic
393	C₂²×#41	#121	1	1	yes	characteristic
394	C₂²×#41	#121	1	1	yes	characteristic
395	C₂²×#41	#121	1	1	yes	characteristic
396	C₂²×#41	#121	1	1	yes	characteristic
397	C₂²×#41	#121	1	1	yes	characteristic
398	C₂²×#41	#121	1	1	yes	characteristic
399	C₂²×#41	#121	1	1	yes	characteristic
400	C₂²×#41	#121	1	1	yes	characteristic
401	C₂²×#41	#121	1	1	yes	characteristic
402	C₂²×#41	#123	1	1	yes	characteristic
403	C₂²×#41	#123	1	1	yes	characteristic
404	C₂²×#41	#123	1	1	yes	characteristic
405	C₂²×#41	#123	1	1	yes	characteristic
406	C₂²×#41	C₂³×C₄	1	1	yes	characteristic
407	C₂²×#41	C₂³×C₄	1	1	yes	characteristic
408	C₂²×#41	C₂²×D₄	1	1	yes	characteristic
409	C₂²×#41	C₂²×D₄	1	1	yes	characteristic
410	C₂²×#41	C₂×#41	1	1	yes	characteristic
411	C₂²×#41	C₂×#41	1	1	yes	characteristic
412	C₂²×#41	C₂×#41	1	1	yes	characteristic
413	C₂²×#41	C₂×#41	1	1	yes	characteristic
414	C₂³×Q₈	#120	1	1	yes	characteristic
415	C₂³×Q₈	C₂²×D₄	1	1	yes	characteristic
416	C₂³×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
417	C₂³×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
418	C₂³×D₄	C₂×C₂²⋊C₄	1	2	yes	—
419	C₂³×D₄	C₂×C₂²⋊C₄	1	2	yes	—
420	C₂³×D₄	C₂×C₂²⋊C₄	1	2	yes	—
421	C₂³×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
422	C₂³×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
423	C₂³×D₄	C₂×C₂²⋊C₄	1	2	yes	—
424	C₂³×D₄	C₂×C₂²⋊C₄	1	2	yes	—
425	C₂³×D₄	C₂×C₂²⋊C₄	1	2	yes	—
426	C₂³×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
427	C₂³×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
428	C₂³×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
429	C₂³×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
430	C₂³×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
431	C₂³×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
432	C₂³×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
433	C₂³×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
434	C₂³×D₄	C₄×D₄	1	1	yes	characteristic
435	C₂³×D₄	C₄×D₄	1	1	yes	characteristic
436	C₂³×D₄	C₄×D₄	1	1	yes	characteristic
437	C₂³×D₄	C₄×D₄	1	1	yes	characteristic
438	C₂³×D₄	C₄×D₄	1	1	yes	characteristic
439	C₂³×D₄	C₄×D₄	1	1	yes	characteristic
440	C₂³×D₄	C₄×D₄	1	1	yes	characteristic
441	C₂³×D₄	C₄×D₄	1	1	yes	characteristic
442	C₂³×D₄	C₄×D₄	1	1	yes	characteristic
443	C₂³×D₄	C₄×D₄	1	1	yes	characteristic
444	C₂³×D₄	C₄×D₄	1	1	yes	characteristic
445	C₂³×D₄	C₄×D₄	1	1	yes	characteristic
446	C₂³×D₄	C₄×D₄	1	1	yes	characteristic
447	C₂³×D₄	C₄×D₄	1	1	yes	characteristic
448	C₂³×D₄	C₄×D₄	1	1	yes	characteristic
449	C₂³×D₄	C₄×D₄	1	1	yes	characteristic
450	C₂³×D₄	#120	1	1	yes	characteristic
451	C₂³×D₄	#120	1	1	yes	characteristic
452	C₂³×D₄	#120	1	1	yes	characteristic
453	C₂³×D₄	#120	1	1	yes	characteristic
454	C₂³×D₄	#120	1	1	yes	characteristic
455	C₂³×D₄	#120	1	1	yes	characteristic
456	C₂³×D₄	#120	1	1	yes	characteristic
457	C₂³×D₄	#120	1	1	yes	characteristic
458	C₂³×D₄	#120	1	1	yes	characteristic
459	C₂³×D₄	#121	1	1	yes	characteristic
460	C₂³×D₄	#121	1	1	yes	characteristic
461	C₂³×D₄	#121	1	1	yes	characteristic
462	C₂³×D₄	#121	1	1	yes	characteristic
463	C₂³×D₄	#121	1	1	yes	characteristic
464	C₂³×D₄	#121	1	1	yes	characteristic
465	C₂³×D₄	#121	1	1	yes	characteristic
466	C₂³×D₄	#121	1	1	yes	characteristic
467	C₂³×D₄	#121	1	1	yes	characteristic
468	C₂³×D₄	#121	1	1	yes	characteristic
469	C₂³×D₄	#121	1	1	yes	characteristic
470	C₂³×D₄	#121	1	1	yes	characteristic
471	C₂³×D₄	#121	1	1	yes	characteristic
472	C₂³×D₄	#121	1	1	yes	characteristic
473	C₂³×D₄	#121	1	1	yes	characteristic
474	C₂³×D₄	#121	1	1	yes	characteristic
475	C₂³×D₄	#123	1	1	yes	characteristic
476	C₂³×D₄	#123	1	1	yes	characteristic
477	C₂³×D₄	#123	1	1	yes	characteristic
478	C₂³×D₄	#123	1	1	yes	characteristic
479	C₂³×D₄	#123	1	1	yes	characteristic
480	C₂³×D₄	#123	1	1	yes	characteristic
481	C₂³×D₄	#123	1	1	yes	characteristic
482	C₂³×D₄	#123	1	1	yes	characteristic
483	C₂³×D₄	#123	1	1	yes	characteristic
484	C₂³×D₄	#123	1	1	yes	characteristic
485	C₂³×D₄	#123	1	1	yes	characteristic
486	C₂³×D₄	#123	1	1	yes	characteristic
487	C₂³×D₄	C₂³×C₄	1	1	yes	characteristic
488	C₂³×D₄	C₂³×C₄	1	1	yes	characteristic
489	C₂³×D₄	C₂³×C₄	1	1	yes	characteristic
490	C₂³×D₄	C₂³×C₄	1	1	yes	characteristic
491	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
492	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
493	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
494	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
495	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
496	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
497	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
498	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
499	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
500	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
501	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
502	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
503	C₂³×D₄	C₂×#41	1	1	yes	characteristic
504	C₂³×D₄	C₂×#41	1	1	yes	characteristic
505	C₂³×D₄	C₂×#41	1	1	yes	characteristic
506	C₂³×D₄	C₂×#41	1	1	yes	characteristic
507	C₂³×D₄	C₂×#41	1	1	yes	characteristic
508	C₂³×D₄	C₂×#41	1	1	yes	characteristic
509	C₂³×D₄	C₂×#41	1	1	yes	characteristic
510	C₂³×D₄	C₂×#41	1	1	yes	characteristic
511	C₂³×D₄	C₂⁵	1	1	yes	characteristic
512	C₂⁴×C₄	C₂×C₂²⋊C₄	1	2	yes	—
513	C₂⁴×C₄	C₂×C₂²⋊C₄	1	2	yes	—
514	C₂⁴×C₄	#120	1	1	yes	characteristic
515	C₂⁴×C₄	#120	1	1	yes	characteristic
516	C₂⁴×C₄	#120	1	1	yes	characteristic
517	C₂⁴×C₄	#120	1	1	yes	characteristic
518	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
519	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
520	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
521	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
522	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
523	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
524	C₂×#123	C₂×C₂²⋊C₄	1	2	yes	—
525	C₂×#123	C₂×C₂²⋊C₄	1	2	yes	—
526	C₂×#123	C₂×C₂²⋊C₄	1	2	yes	—
527	C₂×#123	C₂×C₂²⋊C₄	1	2	yes	—
528	C₂×#123	C₂×C₂²⋊C₄	1	2	yes	—
529	C₂×#123	C₂×C₂²⋊C₄	1	2	yes	—
530	C₂×#123	C₂³×C₄	1	2	yes	—
531	C₂×#123	C₂²×D₄	1	2	yes	—
532	C₂×#120	#99	1	16	yes	complemented
533	C₂×#120	C₂×C₂²⋊C₄	1	2	yes	—
534	C₂×#120	C₂×C₂²⋊C₄	1	2	yes	—
535	C₂×#120	C₂×C₂²⋊C₄	1	2	yes	—
536	C₂×#120	C₂×C₂²⋊C₄	1	2	yes	—
537	C₂×#120	C₂×C₂²⋊C₄	1	2	yes	—
538	C₂×#120	C₂×C₂²⋊C₄	1	2	yes	—
539	C₂×#120	C₂×C₂²⋊C₄	1	2	yes	—
540	C₂×#120	C₂×C₂²⋊C₄	1	2	yes	—
541	C₂×#120	C₂×C₂²⋊C₄	1	2	yes	—
542	C₂×#120	C₂×C₂²⋊C₄	1	2	yes	—
543	C₂×#120	C₂×C₂²⋊C₄	1	2	yes	—
544	C₂×#120	C₂×C₂²⋊C₄	1	2	yes	—
545	C₂×#120	C₂×C₂²⋊C₄	1	2	yes	—
546	C₂×#120	C₂×C₂²⋊C₄	1	2	yes	—
547	C₂×#120	C₂×C₂²⋊C₄	1	2	yes	—
548	C₂×#120	C₂×C₂²⋊C₄	1	2	yes	—
549	C₂×#120	C₂×C₂²⋊C₄	1	2	yes	—
550	C₂×#120	C₂×C₂²⋊C₄	1	2	yes	—
551	C₂×#120	C₂³×C₄	1	2	yes	—
552	C₂×#120	C₂³×C₄	1	2	yes	—
553	C₂×#120	C₂³×C₄	1	2	yes	—
554	C₂×#120	C₂²×D₄	1	2	yes	—
555	C₂×#120	C₂²×D₄	1	2	yes	—
556	C₂×#120	C₂²×D₄	1	2	yes	—
557	#518	C₂³×C₄	1	4	yes	—
558	C₂×#117	C₂×C₂²⋊C₄	1	2	yes	—
559	C₂×#117	C₂×C₂²⋊C₄	1	2	yes	—
560	C₂×#117	C₂×C₂²⋊C₄	1	2	yes	—
561	C₂×#117	C₂×C₂²⋊C₄	1	2	yes	—
562	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	2	yes	—
563	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	2	yes	—
564	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	2	yes	—
565	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	2	yes	—
566	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	2	yes	—
567	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	2	yes	—
568	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	2	yes	—
569	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	2	yes	—
570	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
571	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
572	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
573	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
574	C₂²×C₂²⋊C₄	C₂²×D₄	1	2	yes	—
575	C₂²×C₂²⋊C₄	C₂²×D₄	1	2	yes	—
576	C₂²×C₂²⋊C₄	C₂²×D₄	1	2	yes	—
577	C₂²×C₂²⋊C₄	C₂²×D₄	1	2	yes	—
578	C₂×#99	C₂³×C₄	1	8	yes	—
579	C₂×#95	C₂²×D₄	1	2	yes	—
580	C₂×#95	C₂²×D₄	1	2	yes	—
581	C₂×#95	C₂²×D₄	1	2	yes	—
582	C₂×#95	C₂²×D₄	1	2	yes	—
583	C₂⁵	#386	1	1	yes	characteristic
584	C₂⁵	#386	1	1	yes	characteristic
585	C₂⁵	#386	1	1	yes	characteristic
586	C₂⁵	#386	1	1	yes	characteristic
587	C₂⁵	#386	1	1	yes	characteristic
588	C₂⁵	#386	1	1	yes	characteristic
589	C₂⁵	#386	1	1	yes	characteristic
590	C₂⁵	#386	1	1	yes	characteristic
591	C₂⁵	C₂×#99	1	8	yes	complemented
592	C₂⁵	C₂²×C₂²⋊C₄	1	1	yes	characteristic
593	C₂⁵	C₂²×C₂²⋊C₄	1	1	yes	characteristic
594	C₂⁵	C₂²×C₂²⋊C₄	1	1	yes	characteristic
595	C₂⁵	C₂²×C₂²⋊C₄	1	1	yes	characteristic
596	C₂⁵	C₂²×C₂²⋊C₄	1	2	yes	—
597	C₂⁵	C₂²×C₂²⋊C₄	1	2	yes	—
598	C₂⁵	C₂²×C₂²⋊C₄	1	2	yes	—
599	C₂⁵	C₂×C₄×D₄	1	1	yes	characteristic
600	C₂⁵	C₂×C₄×D₄	1	1	yes	characteristic
601	C₂⁵	C₂×C₄×D₄	1	1	yes	characteristic
602	C₂⁵	C₂×C₄×D₄	1	1	yes	characteristic
603	C₂⁵	C₂×#120	1	1	yes	characteristic
604	C₂⁵	C₂×#120	1	1	yes	characteristic
605	C₂⁵	C₂×#120	1	1	yes	characteristic
606	C₂⁵	C₂×#120	1	1	yes	characteristic
607	C₂⁵	C₂×#120	1	1	yes	characteristic
608	C₂⁵	C₂×#120	1	1	yes	characteristic
609	C₂⁵	C₂×#120	1	1	yes	characteristic
610	C₂⁵	C₂×#121	1	1	yes	characteristic
611	C₂⁵	C₂×#121	1	1	yes	characteristic
612	C₂⁵	C₂×#121	1	1	yes	characteristic
613	C₂⁵	C₂×#121	1	1	yes	characteristic
614	C₂⁵	C₂×#123	1	1	yes	characteristic
615	C₂⁵	C₂×#123	1	1	yes	characteristic
616	C₂⁵	C₂×#123	1	1	yes	characteristic
617	C₂⁵	C₂×#123	1	1	yes	characteristic
618	C₂⁵	C₂³×D₄	1	1	yes	characteristic
619	C₂⁵	C₂³×D₄	1	1	yes	characteristic
620	C₂²×Q₈	#386	1	1	yes	characteristic
621	C₂²×Q₈	#386	1	1	yes	characteristic
622	C₂²×Q₈	#386	1	1	yes	characteristic
623	C₂²×Q₈	#386	1	1	yes	characteristic
624	C₂²×Q₈	C₂×C₄×D₄	1	1	yes	characteristic
625	C₂²×Q₈	C₂×C₄×D₄	1	1	yes	characteristic
626	C₂²×Q₈	C₂×#121	1	1	yes	characteristic
627	C₂²×Q₈	C₂×#121	1	1	yes	characteristic
628	C₂²×D₄	#386	1	1	yes	characteristic
629	C₂²×D₄	#386	1	1	yes	characteristic
630	C₂²×D₄	#386	1	1	yes	characteristic
631	C₂²×D₄	#386	1	1	yes	characteristic
632	C₂²×D₄	#386	1	1	yes	characteristic
633	C₂²×D₄	#386	1	1	yes	characteristic
634	C₂²×D₄	#386	1	1	yes	characteristic
635	C₂²×D₄	#386	1	1	yes	characteristic
636	C₂²×D₄	#386	1	1	yes	characteristic
637	C₂²×D₄	#386	1	1	yes	characteristic
638	C₂²×D₄	#386	1	1	yes	characteristic
639	C₂²×D₄	#386	1	1	yes	characteristic
640	C₂²×D₄	#386	1	1	yes	characteristic
641	C₂²×D₄	#386	1	1	yes	characteristic
642	C₂²×D₄	#386	1	1	yes	characteristic
643	C₂²×D₄	#386	1	1	yes	characteristic
644	C₂²×D₄	#386	1	1	yes	characteristic
645	C₂²×D₄	#386	1	1	yes	characteristic
646	C₂²×D₄	#386	1	1	yes	characteristic
647	C₂²×D₄	#386	1	1	yes	characteristic
648	C₂²×D₄	#386	1	1	yes	characteristic
649	C₂²×D₄	#386	1	1	yes	characteristic
650	C₂²×D₄	#386	1	1	yes	characteristic
651	C₂²×D₄	#386	1	1	yes	characteristic
652	C₂²×D₄	#386	1	1	yes	characteristic
653	C₂²×D₄	#386	1	1	yes	characteristic
654	C₂²×D₄	#386	1	1	yes	characteristic
655	C₂²×D₄	#386	1	1	yes	characteristic
656	C₂²×D₄	#386	1	1	yes	characteristic
657	C₂²×D₄	#386	1	1	yes	characteristic
658	C₂²×D₄	#386	1	1	yes	characteristic
659	C₂²×D₄	#386	1	1	yes	characteristic
660	C₂²×D₄	#386	1	1	yes	characteristic
661	C₂²×D₄	#386	1	1	yes	characteristic
662	C₂²×D₄	#386	1	1	yes	characteristic
663	C₂²×D₄	#386	1	1	yes	characteristic
664	C₂²×D₄	C₂×#99	1	8	yes	—
665	C₂²×D₄	B(4,𝔽₂)	1	8	yes	—
666	C₂²×D₄	C₂²×C₂²⋊C₄	1	1	yes	characteristic
667	C₂²×D₄	C₂²×C₂²⋊C₄	1	1	yes	characteristic
668	C₂²×D₄	C₂²×C₂²⋊C₄	1	1	yes	characteristic
669	C₂²×D₄	C₂²×C₂²⋊C₄	1	1	yes	characteristic
670	C₂²×D₄	C₂²×C₂²⋊C₄	1	1	yes	characteristic
671	C₂²×D₄	C₂²×C₂²⋊C₄	1	1	yes	characteristic
672	C₂²×D₄	C₂×C₄×D₄	1	1	yes	characteristic
673	C₂²×D₄	C₂×C₄×D₄	1	1	yes	characteristic
674	C₂²×D₄	C₂×C₄×D₄	1	1	yes	characteristic
675	C₂²×D₄	C₂×C₄×D₄	1	1	yes	characteristic
676	C₂²×D₄	C₂×C₄×D₄	1	1	yes	characteristic
677	C₂²×D₄	C₂×C₄×D₄	1	1	yes	characteristic
678	C₂²×D₄	C₂×C₄×D₄	1	1	yes	characteristic
679	C₂²×D₄	C₂×C₄×D₄	1	1	yes	characteristic
680	C₂²×D₄	C₂×C₄×D₄	1	1	yes	characteristic
681	C₂²×D₄	C₂×C₄×D₄	1	1	yes	characteristic
682	C₂²×D₄	C₂×#121	1	1	yes	characteristic
683	C₂²×D₄	C₂×#121	1	1	yes	characteristic
684	C₂²×D₄	C₂×#121	1	1	yes	characteristic
685	C₂²×D₄	C₂×#121	1	1	yes	characteristic
686	C₂²×D₄	C₂×#121	1	1	yes	characteristic
687	C₂²×D₄	C₂×#121	1	1	yes	characteristic
688	C₂²×D₄	C₂×#121	1	1	yes	characteristic
689	C₂²×D₄	C₂×#121	1	1	yes	characteristic
690	C₂²×D₄	C₂×#121	1	1	yes	characteristic
691	C₂²×D₄	C₂×#121	1	1	yes	characteristic
692	C₂²×D₄	C₂×#123	1	1	yes	characteristic
693	C₂²×D₄	C₂×#123	1	1	yes	characteristic
694	C₂²×D₄	C₂×#123	1	1	yes	characteristic
695	C₂²×D₄	C₂×#123	1	1	yes	characteristic
696	C₂²×D₄	C₂×#123	1	1	yes	characteristic
697	C₂²×D₄	C₂×#123	1	1	yes	characteristic
698	C₂²×D₄	C₂⁴×C₄	1	1	yes	characteristic
699	C₂²×D₄	C₂³×D₄	1	1	yes	characteristic
700	C₂²×D₄	C₂²×#41	1	1	yes	characteristic
701	C₂²×D₄	C₂²×#41	1	1	yes	characteristic
702	C₂³×C₄	#386	1	1	yes	characteristic
703	C₂³×C₄	#386	1	1	yes	characteristic
704	C₂³×C₄	#386	1	1	yes	characteristic
705	C₂³×C₄	#386	1	1	yes	characteristic
706	C₂³×C₄	#386	1	1	yes	characteristic
707	C₂³×C₄	#386	1	1	yes	characteristic
708	C₂³×C₄	#386	1	1	yes	characteristic
709	C₂³×C₄	#386	1	1	yes	characteristic
710	C₂³×C₄	#386	1	1	yes	characteristic
711	C₂³×C₄	#386	1	1	yes	characteristic
712	C₂³×C₄	#386	1	1	yes	characteristic
713	C₂³×C₄	#386	1	1	yes	characteristic
714	C₂³×C₄	#386	1	1	yes	characteristic
715	C₂³×C₄	#386	1	1	yes	characteristic
716	C₂³×C₄	#386	1	1	yes	characteristic
717	C₂³×C₄	#386	1	1	yes	characteristic
718	C₂³×C₄	C₂²×C₂²⋊C₄	1	1	yes	characteristic
719	C₂³×C₄	C₂²×C₂²⋊C₄	1	1	yes	characteristic
720	C₂³×C₄	C₂²×C₂²⋊C₄	1	2	yes	—
721	C₂³×C₄	C₂×C₄×D₄	1	1	yes	characteristic
722	C₂³×C₄	C₂×C₄×D₄	1	1	yes	characteristic
723	C₂³×C₄	C₂×C₄×D₄	1	1	yes	characteristic
724	C₂³×C₄	C₂×C₄×D₄	1	1	yes	characteristic
725	C₂³×C₄	C₂×C₄×D₄	1	1	yes	characteristic
726	C₂³×C₄	C₂×C₄×D₄	1	1	yes	characteristic
727	C₂³×C₄	C₂×C₄×D₄	1	1	yes	characteristic
728	C₂³×C₄	C₂×C₄×D₄	1	1	yes	characteristic
729	C₂³×C₄	C₂×#120	1	1	yes	characteristic
730	C₂³×C₄	C₂×#120	1	1	yes	characteristic
731	C₂³×C₄	C₂×#120	1	1	yes	characteristic
732	C₂³×C₄	C₂×#120	1	1	yes	characteristic
733	C₂³×C₄	C₂×#120	1	1	yes	characteristic
734	C₂³×C₄	C₂×#121	1	1	yes	characteristic
735	C₂³×C₄	C₂×#121	1	1	yes	characteristic
736	C₂³×C₄	C₂×#121	1	1	yes	characteristic
737	C₂³×C₄	C₂×#121	1	1	yes	characteristic
738	C₂³×C₄	C₂×#121	1	1	yes	characteristic
739	C₂³×C₄	C₂×#121	1	1	yes	characteristic
740	C₂³×C₄	C₂×#121	1	1	yes	characteristic
741	C₂³×C₄	C₂×#121	1	1	yes	characteristic
742	C₂³×C₄	C₂×#123	1	1	yes	characteristic
743	C₂³×C₄	C₂×#123	1	1	yes	characteristic
744	C₂³×C₄	C₂³×D₄	1	1	yes	characteristic
745	#120	C₂×#99	1	8	yes	complemented
746	#120	C₂×#99	1	8	yes	complemented
747	#120	C₂×#99	1	8	yes	complemented
748	#120	C₂×#99	1	8	yes	complemented
749	C₂×C₂²⋊C₄	C₂×#99	1	8	yes	complemented
750	C₂×C₂²⋊C₄	C₂²×C₂²⋊C₄	1	2	yes	—
751	C₂×C₂²⋊C₄	C₂²×C₂²⋊C₄	1	2	yes	—
752	C₂×C₂²⋊C₄	C₂²×C₂²⋊C₄	1	2	yes	—
753	C₂×C₂²⋊C₄	C₂²×C₂²⋊C₄	1	2	yes	—
754	C₂⁴	#1898	1	4	yes	—
755	C₂⁴	C₂×#386	1	1	yes	characteristic
756	C₂⁴	C₂×#386	1	1	yes	characteristic
757	C₂⁴	C₂×#386	1	1	yes	characteristic
758	C₂⁴	C₂×#386	1	1	yes	characteristic
759	C₂⁴	C₂×#386	1	1	yes	characteristic
760	C₂⁴	C₂×#386	1	1	yes	characteristic
761	C₂⁴	C₂×#386	1	1	yes	characteristic
762	C₂⁴	C₂×#386	1	1	yes	characteristic
763	C₂⁴	C₂×#386	1	1	yes	characteristic
764	C₂⁴	C₂×#386	1	1	yes	characteristic
765	C₂⁴	C₂×#386	1	1	yes	characteristic
766	C₂⁴	C₂×#386	1	1	yes	characteristic
767	C₂⁴	C₂×#386	1	1	yes	characteristic
768	C₂⁴	C₂×#386	1	1	yes	characteristic
769	C₂⁴	C₂²×#99	1	4	yes	—
770	C₂⁴	C₂²×#99	1	4	yes	—
771	C₂⁴	C₂²×#99	1	4	yes	—
772	C₂⁴	C₂×B(4,𝔽₂)	1	4	yes	—
773	C₂⁴	C₂×B(4,𝔽₂)	1	4	yes	—
774	C₂⁴	C₂³×C₂²⋊C₄	1	1	yes	characteristic
775	C₂⁴	C₂²×C₄×D₄	1	1	yes	characteristic
776	C₂⁴	C₂²×#120	1	1	yes	characteristic
777	C₂⁴	C₂²×#121	1	1	yes	characteristic
778	C₂⁴	C₂²×#123	1	1	yes	characteristic
779	C₂×D₄	#1889	1	4	yes	—
780	C₂×D₄	#1889	1	4	yes	—
781	C₂×D₄	#1889	1	4	yes	—
782	C₂×D₄	#1889	1	4	yes	—
783	C₂×D₄	#1898	1	4	yes	—
784	C₂×D₄	#1898	1	4	yes	—
785	C₂×D₄	#1913	1	4	yes	—
786	C₂×D₄	C₂²×#99	1	4	yes	—
787	C₂×D₄	C₂²×#99	1	4	yes	—
788	C₂²×C₄	#1898	1	4	yes	—
789	C₂²×C₄	C₂×#386	1	1	yes	characteristic
790	C₂²×C₄	C₂×#386	1	1	yes	characteristic
791	C₂²×C₄	C₂×#386	1	1	yes	characteristic
792	C₂²×C₄	C₂×#386	1	1	yes	characteristic
793	C₂²×C₄	C₂×#386	1	1	yes	characteristic
794	C₂²×C₄	C₂×#386	1	1	yes	characteristic
795	C₂²×C₄	C₂×#386	1	1	yes	characteristic
796	C₂²×C₄	C₂×#386	1	1	yes	characteristic
797	C₂²×C₄	C₂×#386	1	1	yes	characteristic
798	C₂²×C₄	C₂×#386	1	1	yes	characteristic
799	C₂²×C₄	C₂×B(4,𝔽₂)	1	4	yes	—
800	C₂²×C₄	C₂²×C₄×D₄	1	1	yes	characteristic
801	C₂²×C₄	C₂²×#121	1	1	yes	characteristic
802	C₂²⋊C₄	C₂²×#99	1	4	yes	—
803	C₂²⋊C₄	C₂²×#99	1	4	yes	—
804	C₂³	C₂×#1889	1	2	yes	—
805	C₂³	C₂×#1889	1	2	yes	—
806	C₂³	C₂×#1889	1	2	yes	—
807	C₂³	C₂×#1889	1	2	yes	—
808	C₂³	C₂×#1898	1	2	yes	—
809	C₂³	C₂×#1898	1	2	yes	—
810	C₂³	C₂×#1898	1	2	yes	—
811	C₂³	C₂×#1898	1	2	yes	—
812	C₂³	C₂×#1913	1	2	yes	—
813	C₂³	C₂×#1913	1	2	yes	—
814	C₂³	C₂²×#386	1	1	yes	characteristic
815	C₂³	C₂³×#99	1	2	yes	—
816	C₂³	C₂²×B(4,𝔽₂)	1	2	yes	—
817	C₂×C₄	C₂×#1889	1	2	yes	—
818	C₂×C₄	C₂×#1889	1	2	yes	—
819	C₂×C₄	C₂×#1898	1	2	yes	—
820	C₂×C₄	C₂×#1898	1	2	yes	—
821	C₂×C₄	C₂×#1913	1	2	yes	—
822	C₂²	#201664	1	4	yes	—
823	C₂²	C₂²×#1889	1	1	yes	characteristic
824	C₂²	C₂²×#1898	1	1	yes	characteristic
825	C₂²	C₂²×#1913	1	1	yes	characteristic
826	C₂²	#7622880	1	2	yes	—
827	C₂²	#7622881	1	2	yes	—
828	C₂	#72234799	1	2	yes	—
829	C₂	C₂×#201664	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²	C₂²×#1889
commutator	C₂²×D₄	C₂⁴×C₄
Frattini, cosocle	C₂³×D₄	C₂⁵
prime radical	#72216064	C₂
LCS	G ▷ C₂²×D₄ ▷ C₂³ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂² ◁ C₂³×D₄ ◁ C₂³×H(5,𝔽₂) ◁ G
LECS	G ▷ C₂³×D₄ ▷ C₂³ ▷ C₂ ▷ C₁

Complements

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

N	H ≅ G/N	type
1. #72260748	C₂	semidirect
2. #72260589	C₂	semidirect
3. #72260537	C₂	semidirect
4. #72260412	C₂	semidirect
5. #72258978	C₂	semidirect
6. #72237599	C₂	semidirect
7. #72237037	C₂	semidirect
8. C₂×#139700	C₂	semidirect
9. #72233637	C₂	semidirect
10. #72233078	C₂	semidirect
11. #72231753	C₂	semidirect
12. #72231467	C₂	semidirect
13. #72225786	C₂	semidirect
14. #72219302	C₂	semidirect
18. C₂×#60399	C₄	semidirect
19. #6437633	C₄	semidirect
20. #6437632	C₄	semidirect
21. #6437632	C₄	semidirect
28. #6371558	C₄	semidirect
32. #581562	C₂²	semidirect
33. #581561	C₂²	semidirect
34. #556752	C₂²	semidirect
35. #552677	C₂²	semidirect
36. #552677	C₂²	semidirect
37. #532097	C₂²	semidirect
38. #531607	C₂²	semidirect
41. C₂×#14134	C₂²	semidirect
42. #493359	C₂²	semidirect
43. #493357	C₂²	semidirect
44. #493357	C₂²	semidirect
45. #493352	C₂²	semidirect
46. C₂×#12687	C₂²	semidirect
47. C₂×#12687	C₂²	semidirect
48. #187944	C₂²	semidirect
49. #187931	C₂²	semidirect
50. #187928	C₂²	semidirect
51. C₂×#8534	C₂²	semidirect
52. #186835	C₂²	semidirect
53. #186814	C₂²	semidirect
54. #186808	C₂²	semidirect
55. C₂×#8453	C₂²	semidirect
56. #139774	C₂²	semidirect
57. #139774	C₂²	semidirect
58. #139773	C₂²	semidirect
59. #139773	C₂²	semidirect
60. #139702	C₂²	semidirect
61. #139700	C₂²	semidirect
62. #139700	C₂²	semidirect
63. #139700	C₂²	semidirect
64. #128074	C₂²	semidirect
65. #128073	C₂²	semidirect
66. #128058	C₂²	semidirect
67. #128057	C₂²	semidirect
68. #128033	C₂²	semidirect
69. C₂×#7304	C₂²	semidirect
70. #128009	C₂²	semidirect
71. C₂×#7307	C₂²	semidirect
72. C₂×H(7,𝔽₂)	C₂×C₄	semidirect
75. #62852	C₂×C₄	semidirect
76. #62842	C₂×C₄	semidirect
77. #62842	C₂×C₄	semidirect
101. #62652	C₂×C₄	semidirect
103. C₂×#3027	C₂×C₄	semidirect
104. C₂×#3026	C₂×C₄	semidirect
105. C₂×#3026	C₂×C₄	semidirect
106. C₂×#3025	C₂×C₄	semidirect
107. C₂²×B(4,𝔽₂)	C₂×C₄	semidirect
108. C₂²×B(4,𝔽₂)	C₂×C₄	semidirect
109. C₂×#2883	C₂×C₄	semidirect
110. C₂×#2339	D₄	semidirect
111. C₂×D₄×C₂²⋊C₄	D₄	semidirect
112. #23904	C₂×C₄	semidirect
113. #23903	C₂×C₄	semidirect
114. #23903	C₂×C₄	semidirect
115. #23902	C₂×C₄	semidirect
117. #23900	C₂×C₄	semidirect
118. #23900	C₂×C₄	semidirect
122. #20961	C₂×C₄	semidirect
123. #20960	C₂×C₄	semidirect
124. #20960	C₂×C₄	semidirect
125. #20959	C₂×C₄	semidirect
126. C₂×#1889	C₂×C₄	semidirect
127. C₂×#1889	C₂×C₄	semidirect
131. #20586	C₂×C₄	semidirect
132. #20585	C₂×C₄	semidirect
133. #20585	C₂×C₄	semidirect
140. #14657	C₂³	semidirect
141. #14506	C₂³	semidirect
142. #14506	C₂³	semidirect
143. #14358	C₂³	semidirect
144. #14358	C₂³	semidirect
145. #14337	D₄	semidirect
146. #14337	D₄	semidirect
147. #14335	D₄	semidirect
148. #14335	D₄	semidirect
151. #14134	C₂³	semidirect
152. #14134	C₂³	semidirect
153. #14134	C₂³	semidirect
154. #13956	D₄	semidirect
158. #13867	D₄	semidirect
160. #13851	D₄	semidirect
161. #13851	D₄	semidirect
162. C₂×#1438	D₄	semidirect
163. C₂×#1438	D₄	semidirect
166. #12688	C₂³	semidirect
167. #12687	C₂³	semidirect
168. #12687	C₂³	semidirect
169. #12687	C₂³	semidirect
174. #7307	C₂³	semidirect
175. #7307	C₂³	semidirect
176. #7304	C₂³	semidirect
177. #7304	C₂³	semidirect
180. C₂×#585	C₂²×C₄	semidirect
186. C₂²×H(5,𝔽₂)	C₂²×C₄	semidirect
222. #3485	C₂²×C₄	semidirect
224. #3484	C₂²×C₄	semidirect
290. #3428	C₂²×C₄	semidirect
296. C₂×#518	C₂²×C₄	semidirect
303. C₂³×C₂²⋊C₄	C₂×D₄	semidirect
304. C₂³×C₂²⋊C₄	C₂×D₄	semidirect
305. C₂×#458	C₂²×C₄	semidirect
308. C₂×B(4,𝔽₂)	C₂²×C₄	semidirect
309. C₂×#410	C₂²×C₄	semidirect
311. C₂²×#99	C₂²×C₄	semidirect
312. C₂×#381	C₂×D₄	semidirect
313. C₂×#381	C₂×D₄	semidirect
314. C₂×#380	C₂×D₄	semidirect
315. C₂×#380	C₂×D₄	semidirect
316. C₂×#379	C₂×D₄	semidirect
317. C₂×#379	C₂×D₄	semidirect
318. C₂×C₄×C₂²⋊C₄	C₂×D₄	semidirect
319. C₂×C₄×C₂²⋊C₄	C₂×D₄	semidirect
320. C₂²×#95	C₂×D₄	semidirect
321. C₂²×#95	C₂×D₄	semidirect
322. #1890	C₂²×C₄	semidirect
325. #1889	C₂²×C₄	semidirect
327. #1782	C₂²×C₄	semidirect
329. #1781	C₂²×C₄	semidirect
332. #1446	C₂×D₄	semidirect
333. #1446	C₂×D₄	semidirect
334. #1438	C₂×D₄	semidirect
335. #1438	C₂×D₄	semidirect
336. #1438	C₂×D₄	semidirect
337. #1438	C₂×D₄	semidirect
338. #1438	C₂×D₄	semidirect
339. #1438	C₂×D₄	semidirect
340. #1438	C₂×D₄	semidirect
341. #1438	C₂×D₄	semidirect
342. #1438	C₂×D₄	semidirect
343. #1438	C₂×D₄	semidirect
344. #1438	C₂×D₄	semidirect
345. #1438	C₂×D₄	semidirect
346. #1438	C₂×D₄	semidirect
347. #1438	C₂×D₄	semidirect
532. C₂×#120	#99	semidirect
591. C₂⁵	C₂×#99	semidirect
745. #120	C₂×#99	semidirect
746. #120	C₂×#99	semidirect
747. #120	C₂×#99	semidirect
748. #120	C₂×#99	semidirect
749. C₂×C₂²⋊C₄	C₂×#99	semidirect

Maximal subgroups

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

subgroup	index
#72260748	2
#72260589	2
#72260537	2
#72260412	2
#72258978	2
#72237599	2
#72237037	2
C₂×#139700	2
#72233637	2
#72233078	2
#72231753	2
#72231467	2
#72225786	2
#72219302	2
#72216064	2