Subgroups — #72311335

Order 2048.

At least 8276 conjugacy classes of subgroups; only the 6230 normal subgroups are shown.

The subgroup lattice has 894 nodes (normal subgroups only) — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#72311324	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#360531	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#417702	C₂	1	4	yes	maximal, complemented
4	#72311305	C₂	1	4	yes	maximal, complemented
5	#72311298	C₂	1	2	yes	maximal, complemented
6	#72311293	C₂	1	2	yes	maximal, complemented
7	#72311288	C₂	1	2	yes	maximal, complemented
8	#72311282	C₂	1	2	yes	maximal, complemented
9	#72311278	C₂	1	2	yes	maximal, complemented
10	#72311274	C₂	1	2	yes	maximal, complemented
11	#72311206	C₂	1	1	yes	maximal, characteristic, complemented
12	#72311147	C₂	1	16	yes	maximal, complemented
13	C₂×#359529	C₂	1	1	yes	maximal, characteristic, complemented
14	#72303796	C₂	1	2	yes	maximal, complemented
15	#72303711	C₂	1	2	yes	maximal, complemented
16	C₂×#392136	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂×#10574841	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×#10574841	C₂	1	1	yes	maximal, characteristic, complemented
19	#72241303	C₂	1	16	yes	maximal, complemented
20	C₂²×H(7,𝔽₂)	C₂²	1	1	yes	characteristic
21	C₂×#63090	C₂²	1	2	yes	complemented
22	C₂×#63090	C₂²	1	2	yes	complemented
23	C₂×#62852	C₂²	1	1	yes	characteristic
24	C₂×#62852	C₂²	1	1	yes	characteristic
25	C₂×#60469	C₂²	1	4	yes	complemented
26	#10574841	C₂²	1	16	yes	complemented
27	#10574839	C₂²	1	2	yes	complemented
28	C₂×#60389	C₂²	1	8	yes	complemented
29	C₂×#60388	C₂²	1	8	yes	complemented
30	C₂×#60387	C₂²	1	2	yes	—
31	C₂×#60387	C₂²	1	2	yes	—
32	C₂×#60387	C₂²	1	2	yes	—
33	C₂×#60387	C₂²	1	2	yes	—
34	C₂×#60387	C₂²	1	1	yes	characteristic, complemented
35	C₂×#60387	C₂²	1	1	yes	characteristic, complemented
36	C₂²×#3019	C₂²	1	4	yes	complemented
37	C₂²×#3019	C₂²	1	2	yes	complemented
38	C₂²×#3019	C₂²	1	2	yes	complemented
39	#10574202	C₂²	1	2	yes	complemented
40	C₂×#60076	C₂²	1	1	yes	characteristic, complemented
41	C₂×#60093	C₂²	1	2	yes	complemented
42	C₂×#60093	C₂²	1	2	yes	complemented
43	C₂²×#2888	C₂²	1	1	yes	characteristic
44	C₂²×#2888	C₂²	1	1	yes	characteristic
45	#6442596	C₂²	1	32	yes	complemented
46	#6437987	C₂²	1	16	yes	complemented
47	#6437986	C₂²	1	16	yes	complemented
48	#6437453	C₂²	1	8	yes	complemented
49	#6437452	C₂²	1	8	yes	complemented
50	C₂×#23527	C₂²	1	4	yes	complemented
51	C₂×#23525	C₂²	1	4	yes	complemented
52	#6431784	C₂²	1	4	yes	complemented
53	#6431784	C₂²	1	4	yes	complemented
54	C₂×#23434	C₂²	1	4	yes	complemented
55	C₂×#23402	C₂²	1	2	yes	complemented
56	C₂×#23402	C₂²	1	2	yes	complemented
57	#6379034	C₂²	1	8	yes	complemented
58	#6379033	C₂²	1	8	yes	complemented
59	#6372017	C₂²	1	4	yes	complemented
60	C₂×#21219	C₂²	1	2	yes	complemented
61	C₂×#21017	C₂²	1	2	yes	complemented
62	#6371514	C₂²	1	2	yes	complemented
63	C₂×#20990	C₂²	1	2	yes	complemented
64	#6371494	C₂²	1	2	yes	complemented
65	C₂×#20964	C₂²	1	2	yes	complemented
66	#6371454	C₂²	1	1	yes	characteristic, complemented
67	#6371454	C₂²	1	1	yes	characteristic, complemented
68	C₂×#20939	C₂²	1	4	yes	complemented
69	C₂×#20860	C₂²	1	2	yes	complemented
70	C₂×#20673	C₂²	1	2	yes	complemented
71	#6370781	C₂²	1	1	yes	characteristic, complemented
72	C₂×#20612	C₂²	1	2	yes	complemented
73	C₂×#20612	C₂²	1	2	yes	complemented
74	C₂×#20612	C₂²	1	2	yes	complemented
75	C₂×#20612	C₂²	1	2	yes	complemented
76	C₂×#20612	C₂²	1	2	yes	complemented
77	#6370703	C₂²	1	1	yes	characteristic, complemented
78	C₂×#20592	C₂²	1	1	yes	characteristic
79	C₂×#20592	C₂²	1	1	yes	characteristic
80	C₂×#20592	C₂²	1	4	yes	complemented
81	#6369826	C₂²	1	1	yes	characteristic, complemented
82	#419044	C₂²	1	32	yes	complemented
83	#419041	C₂²	1	32	yes	complemented
84	#417702	C₂²	1	64	yes	complemented
85	#395561	C₂²	1	16	yes	complemented
86	#395560	C₂²	1	16	yes	complemented
87	#395528	C₂²	1	32	yes	complemented
88	#394033	C₂²	1	16	yes	complemented
89	#394032	C₂²	1	16	yes	complemented
90	#393908	C₂²	1	16	yes	complemented
91	#393907	C₂²	1	16	yes	complemented
92	#392136	C₂²	1	16	yes	complemented
93	#366624	C₂²	1	32	yes	complemented
94	#364504	C₂²	1	32	yes	complemented
95	#360531	C₂²	1	16	yes	complemented
96	#359529	C₂²	1	16	yes	complemented
97	C₂×#11159	C₂²	1	4	yes	complemented
98	C₂×#11139	C₂²	1	4	yes	complemented
99	C₂×#11118	C₂²	1	4	yes	complemented
100	#357746	C₂²	1	4	yes	complemented
101	C₂×#11037	C₂²	1	4	yes	complemented
102	C₂×#11032	C₂²	1	4	yes	complemented
103	C₂×#11032	C₂²	1	4	yes	complemented
104	#357567	C₂²	1	4	yes	complemented
105	C₂×#10973	C₂²	1	4	yes	complemented
106	#354118	C₂²	1	4	yes	complemented
107	C₂×#10756	C₂²	1	2	yes	complemented
108	C₂×#10744	C₂²	1	2	yes	complemented
109	C₂×#10767	C₂²	1	2	yes	complemented
110	C₂×H(7,𝔽₂)	C₂³	1	8	yes	—
111	C₂²×#585	C₂³	1	1	yes	characteristic
112	C₂²×#585	C₂³	1	2	yes	—
113	C₂²×#585	C₂³	1	2	yes	—
114	C₂²×#585	C₂³	1	1	yes	characteristic
115	C₂³×H(5,𝔽₂)	C₂³	1	2	yes	—
116	C₂³×H(5,𝔽₂)	C₂³	1	1	yes	characteristic
117	#63090	C₂³	1	16	yes	—
118	C₂×#3586	C₂³	1	8	yes	complemented
119	C₂×#3585	C₂³	1	8	yes	complemented
120	C₂²×#575	C₂³	1	4	yes	—
121	C₂²×#575	C₂³	1	4	yes	—
122	C₂²×#575	C₂³	1	4	yes	—
123	C₂²×#575	C₂³	1	4	yes	—
124	C₂²×#575	C₂³	1	2	yes	complemented
125	C₂²×#575	C₂³	1	2	yes	complemented
126	C₂²×#568	C₂³	1	2	yes	—
127	C₂²×#568	C₂³	1	2	yes	—
128	C₂²×#568	C₂³	1	2	yes	complemented
129	#62852	C₂³	1	8	yes	—
130	C₂×#3500	D₄	1	4	yes	—
131	C₂×#3500	C₂³	1	4	yes	—
132	C₂×#3498	D₄	1	4	yes	—
133	C₂×#3498	C₂³	1	4	yes	—
134	C₂×#3449	D₄	1	4	yes	—
135	C₂×#3449	C₂³	1	2	yes	—
136	C₂×#3449	C₂³	1	1	yes	characteristic
137	C₂×#3449	C₂³	1	1	yes	characteristic
138	C₂²×#535	D₄	1	4	yes	—
139	C₂²×#535	C₂³	1	1	yes	characteristic
140	C₂²×#535	C₂³	1	1	yes	characteristic
141	C₂²×#535	C₂³	1	2	yes	—
142	C₂×#3428	C₂³	1	1	yes	characteristic
143	C₂×#3428	C₂³	1	1	yes	characteristic
144	#60469	C₂³	1	32	yes	complemented
145	#60387	D₄	1	16	yes	complemented
146	#60387	D₄	1	16	yes	complemented
147	#60387	D₄	1	16	yes	complemented
148	#60387	C₂³	1	16	yes	—
149	#60387	C₂³	1	16	yes	—
150	C₂×#3022	D₄	1	8	yes	complemented
151	C₂×#3022	C₂³	1	8	yes	—
152	C₂×#3022	C₂³	1	4	yes	complemented
153	C₂×#3021	D₄	1	8	yes	complemented
154	C₂×#3021	C₂³	1	8	yes	—
155	C₂×#3021	C₂³	1	4	yes	complemented
156	C₂×#3019	C₂³	1	32	yes	—
157	C₂×#3019	C₂³	1	16	yes	complemented
158	C₂×#3018	C₂³	1	16	yes	—
159	C₂×#3018	C₂³	1	8	yes	complemented
160	C₂²×#455	C₂³	1	8	yes	complemented
161	C₂²×#453	C₂³	1	8	yes	complemented
162	#60368	C₂³	1	8	yes	complemented
163	#60367	C₂³	1	8	yes	complemented
164	#60144	C₂³	1	16	yes	complemented
165	C₂²×#430	C₂³	1	4	yes	complemented
166	C₂×#2905	C₂³	1	2	yes	complemented
167	#60093	C₂³	1	16	yes	—
168	C₂×#2901	C₂³	1	16	yes	complemented
169	C₂²×#421	C₂³	1	4	yes	—
170	C₂²×#421	C₂³	1	4	yes	—
171	C₂²×#421	C₂³	1	4	yes	—
172	C₂²×#421	C₂³	1	4	yes	—
173	C₂²×#421	C₂³	1	2	yes	complemented
174	C₂²×#421	C₂³	1	2	yes	complemented
175	C₂×#2896	C₂³	1	2	yes	complemented
176	C₂×#2896	C₂³	1	2	yes	complemented
177	C₂×#2889	C₂³	1	4	yes	complemented
178	C₂×#2888	D₄	1	8	yes	—
179	C₂×#2888	C₂³	1	8	yes	—
180	C₂×#2888	C₂³	1	8	yes	—
181	C₂×#2888	C₂³	1	4	yes	complemented
182	C₂²×#413	D₄	1	4	yes	—
183	C₂²×#413	C₂³	1	1	yes	characteristic
184	C₂²×#413	C₂³	1	4	yes	—
185	C₂²×#413	C₂³	1	1	yes	characteristic
186	C₂²×#413	C₂³	1	1	yes	characteristic
187	C₂²×#413	C₂³	1	1	yes	characteristic
188	C₂²×#413	C₂³	1	2	yes	—
189	C₂²×#413	C₂³	1	4	yes	—
190	C₂²×#413	C₂³	1	1	yes	characteristic
191	C₂²×#413	C₂³	1	1	yes	characteristic
192	C₂²×#413	C₂³	1	4	yes	complemented
193	C₂²×#413	C₂³	1	2	yes	complemented
194	C₂²×#413	C₂³	1	2	yes	complemented
195	C₂³×#100	D₄	1	4	yes	—
196	C₂³×#100	C₂³	1	2	yes	—
197	C₂³×#100	C₂³	1	2	yes	—
198	C₂³×#100	C₂³	1	2	yes	—
199	C₂³×#100	C₂³	1	2	yes	—
200	C₂×#2879	C₂³	1	2	yes	—
201	C₂×#2879	C₂³	1	2	yes	—
202	C₂×#2879	C₂³	1	4	yes	—
203	C₂×#2879	C₂³	1	4	yes	—
204	C₂×#2879	C₂³	1	2	yes	complemented
205	C₂×#2879	C₂³	1	4	yes	complemented
206	C₂×#2873	C₂³	1	2	yes	complemented
207	C₂×#2050	C₂³	1	32	yes	complemented
208	C₂×#2049	C₂³	1	16	yes	complemented
209	C₂×#2048	C₂³	1	16	yes	complemented
210	#23440	C₂³	1	16	yes	complemented
211	#23440	C₂³	1	16	yes	complemented
212	#23439	C₂³	1	16	yes	complemented
213	#23439	C₂³	1	16	yes	complemented
214	#23434	C₂³	1	32	yes	complemented
215	#23402	C₂³	1	16	yes	complemented
216	C₂×#2004	C₂³	1	8	yes	complemented
217	C₂×#2002	C₂³	1	8	yes	complemented
218	#21241	C₂³	1	32	yes	complemented
219	C₂×#1967	C₂³	1	8	yes	complemented
220	C₂×#1965	C₂³	1	8	yes	complemented
221	#21017	C₂³	1	16	yes	complemented
222	#20991	C₂³	1	8	yes	complemented
223	#20990	C₂³	1	8	yes	complemented
224	#20990	C₂³	1	16	yes	complemented
225	#20980	C₂³	1	16	yes	complemented
226	#20964	C₂³	1	16	yes	complemented
227	#20956	C₂³	1	4	yes	complemented
228	#20955	C₂³	1	4	yes	complemented
229	#20952	C₂³	1	8	yes	complemented
230	#20939	C₂³	1	32	yes	complemented
231	#20860	C₂³	1	16	yes	complemented
232	#20673	C₂³	1	16	yes	complemented
233	#20637	C₂³	1	8	yes	complemented
234	#20612	C₂³	1	16	yes	—
235	#20612	C₂³	1	16	yes	—
236	#20612	C₂³	1	16	yes	complemented
237	#20612	C₂³	1	16	yes	complemented
238	#20612	C₂³	1	16	yes	complemented
239	#20593	C₂³	1	4	yes	complemented
240	#20592	C₂³	1	8	yes	—
241	#20592	C₂³	1	8	yes	—
242	#20592	C₂³	1	32	yes	complemented
243	#20592	C₂³	1	4	yes	complemented
244	C₄×#413	C₂³	1	8	yes	complemented
245	C₂²×#344	C₂³	1	4	yes	complemented
246	C₂²×#344	C₂³	1	4	yes	complemented
247	C₂×#1742	C₂³	1	2	yes	complemented
248	C₂×#1742	C₂³	1	2	yes	complemented
249	C₂×#1738	C₂³	1	4	yes	complemented
250	C₂×#1738	C₂³	1	4	yes	complemented
251	C₂×#1733	C₂³	1	2	yes	complemented
252	C₂×#1733	C₂³	1	2	yes	complemented
253	C₂²×#338	C₂³	1	4	yes	complemented
254	#11159	C₂³	1	32	yes	complemented
255	#11139	C₂³	1	32	yes	complemented
256	#11118	C₂³	1	32	yes	complemented
257	#11080	C₂³	1	32	yes	complemented
258	#11037	C₂³	1	32	yes	complemented
259	#11032	C₂³	1	32	yes	complemented
260	#11032	C₂³	1	32	yes	complemented
261	#11015	C₂³	1	16	yes	complemented
262	#11014	C₂³	1	16	yes	complemented
263	#10973	C₂³	1	32	yes	complemented
264	#10946	C₂³	1	32	yes	complemented
265	#10767	C₂³	1	16	yes	complemented
266	#10756	C₂³	1	16	yes	complemented
267	#10744	C₂³	1	16	yes	complemented
268	C₂×#585	C₂×D₄	1	8	yes	—
269	C₂×#585	C₂×D₄	1	8	yes	—
270	C₂×#585	C₂×D₄	1	8	yes	—
271	C₂×#585	C₂×D₄	1	8	yes	—
272	C₂×#585	C₂⁴	1	8	yes	—
273	C₂×#585	C₂⁴	1	8	yes	—
274	C₂×#585	C₂⁴	1	4	yes	—
275	C₂²×2₋¹⁺⁴	C₂×D₄	1	2	yes	—
276	C₂²×2₋¹⁺⁴	C₂⁴	1	2	yes	—
277	C₂²×H(5,𝔽₂)	C₂×D₄	1	2	yes	—
278	C₂²×H(5,𝔽₂)	C₂×D₄	1	4	yes	—
279	C₂²×H(5,𝔽₂)	C₂×D₄	1	4	yes	—
280	C₂²×H(5,𝔽₂)	#41	1	4	yes	—
281	C₂²×H(5,𝔽₂)	C₂⁴	1	8	yes	—
282	C₂²×H(5,𝔽₂)	C₂⁴	1	2	yes	—
283	C₂²×H(5,𝔽₂)	C₂⁴	1	4	yes	—
284	C₂³×#41	C₂×D₄	1	4	yes	—
285	C₂³×#41	C₂×D₄	1	2	yes	—
286	C₂³×#41	C₂×D₄	1	2	yes	—
287	C₂³×#41	C₂⁴	1	2	yes	—
288	C₂³×#41	C₂⁴	1	1	yes	characteristic
289	C₂³×#41	C₂⁴	1	4	yes	—
290	C₂³×#41	C₂⁴	1	1	yes	characteristic
291	C₂³×#41	C₂⁴	1	1	yes	characteristic
292	C₂³×#41	C₂⁴	1	1	yes	characteristic
293	C₂⁴×D₄	C₂×D₄	1	2	yes	—
294	C₂⁴×D₄	C₂×D₄	1	2	yes	—
295	C₂⁴×D₄	#41	1	4	yes	—
296	C₂⁴×D₄	C₂⁴	1	1	yes	characteristic
297	C₂×#575	C₂×D₄	1	16	yes	complemented
298	C₂×#575	C₂×D₄	1	16	yes	complemented
299	C₂×#575	C₂×D₄	1	16	yes	complemented
300	C₂×#575	C₂⁴	1	16	yes	—
301	C₂×#575	C₂⁴	1	16	yes	—
302	C₂×#575	C₂⁴	1	16	yes	—
303	C₂×#575	C₂⁴	1	8	yes	complemented
304	C₂²×#137	C₂×D₄	1	8	yes	complemented
305	C₂²×#137	C₂⁴	1	8	yes	—
306	C₂²×#137	C₂⁴	1	4	yes	complemented
307	C₂²×AGL(1,ℤ/8)	C₂×D₄	1	8	yes	complemented
308	C₂²×AGL(1,ℤ/8)	C₂⁴	1	8	yes	—
309	C₂²×AGL(1,ℤ/8)	C₂⁴	1	4	yes	complemented
310	C₂×#568	C₂×D₄	1	8	yes	—
311	C₂×#568	C₂⁴	1	8	yes	—
312	C₂×#568	C₂⁴	1	8	yes	—
313	C₂×#568	C₂⁴	1	8	yes	complemented
314	C₂³×M₁₆	C₂×D₄	1	8	yes	—
315	C₂³×M₁₆	C₂⁴	1	2	yes	—
316	C₂³×M₁₆	C₂⁴	1	2	yes	—
317	C₂³×M₁₆	C₂⁴	1	2	yes	—
318	C₂³×M₁₆	C₂⁴	1	2	yes	—
319	C₂³×M₁₆	C₂⁴	1	2	yes	—
320	C₂³×M₁₆	C₂⁴	1	4	yes	—
321	C₂³×M₁₆	C₂⁴	1	2	yes	—
322	#3449	C₂×D₄	1	8	yes	—
323	#3449	C₂×D₄	1	8	yes	—
324	#3449	C₂×D₄	1	8	yes	—
325	#3449	C₂⁴	1	8	yes	—
326	C₂×#536	C₂×D₄	1	4	yes	—
327	C₂×#536	C₂×D₄	1	2	yes	—
328	C₂×#536	C₂×D₄	1	8	yes	—
329	C₂×#536	C₂×D₄	1	2	yes	—
330	C₂×#536	C₂×D₄	1	2	yes	—
331	C₂×#536	C₂⁴	1	2	yes	—
332	C₂×#535	C₂×D₄	1	4	yes	—
333	C₂×#535	C₂×D₄	1	2	yes	—
334	C₂×#535	C₂×D₄	1	8	yes	—
335	C₂×#535	C₂×D₄	1	4	yes	—
336	C₂×#535	C₂×D₄	1	8	yes	—
337	C₂×#535	C₂×D₄	1	8	yes	—
338	C₂×#535	C₂×D₄	1	4	yes	—
339	C₂×#535	C₂×D₄	1	4	yes	—
340	C₂×#535	C₂×D₄	1	2	yes	—
341	C₂×#535	C₂×D₄	1	2	yes	—
342	C₂×#535	C₂⁴	1	2	yes	—
343	C₂×#535	C₂⁴	1	4	yes	—
344	C₂×#535	C₂⁴	1	8	yes	—
345	C₂×#532	C₂×D₄	1	4	yes	—
346	C₂×#532	C₂×D₄	1	8	yes	—
347	C₂×#532	C₂×D₄	1	8	yes	—
348	C₂×#532	C₂⁴	1	4	yes	—
349	C₂²×#127	C₂×D₄	1	2	yes	—
350	C₂²×#127	C₂×D₄	1	8	yes	—
351	C₂²×#127	C₂⁴	1	2	yes	—
352	C₂²×#124	C₂×D₄	1	2	yes	—
353	C₂²×#124	C₂×D₄	1	8	yes	—
354	C₂²×#124	C₂⁴	1	2	yes	—
355	#3428	C₂⁴	1	4	yes	—
356	C₂×C₄×#41	C₂×D₄	1	4	yes	—
357	C₂×C₄×#41	C₂⁴	1	4	yes	—
358	C₂²×#117	C₂×D₄	1	4	yes	—
359	C₂²×#117	C₂⁴	1	1	yes	characteristic
360	C₂²×#117	C₂⁴	1	2	yes	—
361	C₂²×#117	C₂⁴	1	1	yes	characteristic
362	#3022	C₂×D₄	1	64	yes	complemented
363	#3021	C₂×D₄	1	64	yes	complemented
364	#3018	C₂×D₄	1	128	yes	complemented
365	C₂×#430	C₂⁴	1	16	yes	complemented
366	C₂×#423	C₂⁴	1	8	yes	complemented
367	C₂×#421	C₂×D₄	1	16	yes	complemented
368	C₂×#421	C₂×D₄	1	16	yes	complemented
369	C₂×#421	C₂×D₄	1	16	yes	complemented
370	C₂×#421	C₂×D₄	1	16	yes	complemented
371	C₂×#421	C₂⁴	1	16	yes	—
372	C₂×#421	C₂⁴	1	16	yes	—
373	C₂×#421	C₂⁴	1	16	yes	—
374	C₂×#421	C₂⁴	1	8	yes	complemented
375	C₂²×#104	C₂⁴	1	16	yes	—
376	C₂²×#104	C₂⁴	1	8	yes	complemented
377	#2896	C₂⁴	1	8	yes	complemented
378	C₂×#419	C₂⁴	1	4	yes	complemented
379	C₂×#418	C₂⁴	1	4	yes	complemented
380	C₂×#413	C₂×D₄	1	8	yes	—
381	C₂×#413	C₂×D₄	1	8	yes	—
382	C₂×#413	C₂×D₄	1	8	yes	—
383	C₂×#413	C₂×D₄	1	8	yes	—
384	C₂×#413	C₂×D₄	1	4	yes	—
385	C₂×#413	C₂×D₄	1	32	yes	—
386	C₂×#413	C₂×D₄	1	4	yes	—
387	C₂×#413	C₂⁴	1	4	yes	—
388	C₂×#413	C₂⁴	1	4	yes	—
389	C₂×#413	C₂⁴	1	16	yes	—
390	C₂×#413	C₂⁴	1	4	yes	—
391	C₂×#413	C₂⁴	1	4	yes	—
392	C₂×#413	C₂⁴	1	8	yes	—
393	C₂×#413	C₂⁴	1	16	yes	—
394	C₂×#413	C₂⁴	1	4	yes	—
395	C₂×#413	C₂⁴	1	4	yes	—
396	C₂×#413	C₂⁴	1	16	yes	complemented
397	C₂²×#101	C₂×D₄	1	2	yes	—
398	C₂²×#101	C₂×D₄	1	2	yes	—
399	C₂²×#101	C₂⁴	1	4	yes	complemented
400	C₂²×#101	C₂⁴	1	4	yes	complemented
401	C₂²×#100	C₂×D₄	1	2	yes	—
402	C₂²×#100	C₂×D₄	1	32	yes	—
403	C₂²×#100	C₂×D₄	1	8	yes	—
404	C₂²×#100	C₂×D₄	1	8	yes	—
405	C₂²×#100	C₂×D₄	1	2	yes	—
406	C₂²×#100	C₂⁴	1	8	yes	—
407	C₂²×#100	C₂⁴	1	8	yes	—
408	C₂²×#100	C₂⁴	1	8	yes	—
409	C₂²×#100	C₂⁴	1	8	yes	—
410	C₂²×#100	C₂⁴	1	4	yes	complemented
411	C₂²×#100	C₂⁴	1	4	yes	complemented
412	#2879	C₂⁴	1	8	yes	—
413	#2879	C₂⁴	1	8	yes	—
414	#2879	C₂⁴	1	16	yes	—
415	#2879	C₂⁴	1	16	yes	—
416	#2879	C₂⁴	1	8	yes	complemented
417	#2879	C₂⁴	1	16	yes	complemented
418	C₂×C₄×M₁₆	C₂⁴	1	8	yes	complemented
419	C₂×#344	C₂⁴	1	16	yes	complemented
420	C₂×#344	C₂⁴	1	16	yes	complemented
421	#1742	C₂⁴	1	8	yes	complemented
422	#1742	C₂⁴	1	8	yes	complemented
423	#1738	C₂⁴	1	16	yes	complemented
424	#1738	C₂⁴	1	16	yes	complemented
425	#1733	C₂⁴	1	8	yes	complemented
426	C₂×#339	C₂⁴	1	8	yes	complemented
427	C₂×#338	C₂⁴	1	16	yes	complemented
428	C₂⁶	#121	1	4	yes	—
429	C₂⁶	C₂×#41	1	2	yes	—
430	#585	C₂²×D₄	1	32	yes	—
431	#585	C₂²×D₄	1	32	yes	—
432	C₂²×#41	#121	1	8	yes	—
433	C₂²×#41	#121	1	8	yes	—
434	C₂²×#41	C₂²×D₄	1	4	yes	—
435	C₂²×#41	C₂²×D₄	1	4	yes	—
436	C₂²×#41	C₂²×D₄	1	8	yes	—
437	C₂²×#41	C₂²×D₄	1	8	yes	—
438	C₂²×#41	C₂²×D₄	1	8	yes	—
439	C₂²×#41	C₂²×D₄	1	8	yes	—
440	C₂²×#41	C₂²×D₄	1	2	yes	—
441	C₂²×#41	C₂²×D₄	1	2	yes	—
442	C₂²×#41	C₂²×D₄	1	4	yes	—
443	C₂²×#41	C₂²×D₄	1	2	yes	—
444	C₂²×#41	C₂²×D₄	1	4	yes	—
445	C₂²×#41	C₂²×D₄	1	4	yes	—
446	C₂²×#41	C₂²×D₄	1	8	yes	—
447	C₂²×#41	C₂²×D₄	1	8	yes	—
448	C₂²×#41	C₂²×D₄	1	2	yes	—
449	C₂²×#41	C₂²×D₄	1	2	yes	—
450	C₂²×#41	C₂²×D₄	1	4	yes	—
451	C₂²×#41	C₂²×D₄	1	4	yes	—
452	C₂²×#41	C₂²×D₄	1	4	yes	—
453	C₂²×#41	C₂²×D₄	1	4	yes	—
454	C₂²×#41	C₂²×D₄	1	2	yes	—
455	C₂²×#41	C₂²×D₄	1	2	yes	—
456	C₂²×#41	C₂×#41	1	2	yes	—
457	C₂²×#41	C₂×#41	1	2	yes	—
458	C₂²×#41	H(5,𝔽₂)	1	8	yes	—
459	C₂²×#41	H(5,𝔽₂)	1	4	yes	—
460	C₂²×#41	H(5,𝔽₂)	1	4	yes	—
461	C₂²×#41	H(5,𝔽₂)	1	4	yes	—
462	C₂²×#41	H(5,𝔽₂)	1	4	yes	—
463	C₂²×#41	C₂⁵	1	4	yes	—
464	C₂²×#41	C₂⁵	1	2	yes	—
465	C₂²×#41	C₂⁵	1	8	yes	—
466	C₂²×#41	C₂⁵	1	2	yes	—
467	C₂²×#41	C₂⁵	1	2	yes	—
468	C₂³×Q₈	C₂²×D₄	1	2	yes	—
469	C₂³×Q₈	C₂²×D₄	1	1	yes	characteristic
470	C₂³×Q₈	C₂²×D₄	1	4	yes	—
471	C₂³×Q₈	C₂²×D₄	1	1	yes	characteristic
472	C₂³×Q₈	C₂²×D₄	1	1	yes	characteristic
473	C₂³×Q₈	H(5,𝔽₂)	1	4	yes	—
474	C₂³×Q₈	C₂⁵	1	1	yes	characteristic
475	C₂³×D₄	#121	1	4	yes	—
476	C₂³×D₄	#121	1	4	yes	—
477	C₂³×D₄	#121	1	8	yes	—
478	C₂³×D₄	#121	1	8	yes	—
479	C₂³×D₄	#121	1	16	yes	—
480	C₂³×D₄	C₂²×D₄	1	2	yes	—
481	C₂³×D₄	C₂²×D₄	1	2	yes	—
482	C₂³×D₄	C₂²×D₄	1	2	yes	—
483	C₂³×D₄	C₂²×D₄	1	2	yes	—
484	C₂³×D₄	C₂²×D₄	1	2	yes	—
485	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
486	C₂³×D₄	C₂²×D₄	1	8	yes	—
487	C₂³×D₄	C₂²×D₄	1	8	yes	—
488	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
489	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
490	C₂³×D₄	C₂²×D₄	1	4	yes	—
491	C₂³×D₄	C₂×#41	1	16	yes	—
492	C₂³×D₄	C₂×#41	1	2	yes	—
493	C₂³×D₄	C₂×#41	1	2	yes	—
494	C₂³×D₄	C₂×#41	1	2	yes	—
495	C₂³×D₄	H(5,𝔽₂)	1	4	yes	—
496	C₂³×D₄	C₂⁵	1	1	yes	characteristic
497	C₂³×D₄	C₂⁵	1	2	yes	—
498	C₂⁴×C₄	#121	1	4	yes	—
499	C₂⁴×C₄	C₂²×D₄	1	2	yes	—
500	C₂⁴×C₄	C₂²×D₄	1	2	yes	—
501	C₂⁴×C₄	C₂⁵	1	1	yes	characteristic
502	#575	C₂²×D₄	1	64	yes	complemented
503	C₂×#137	C₂²×D₄	1	32	yes	—
504	C₂×AGL(1,ℤ/8)	C₂²×D₄	1	32	yes	—
505	C₂²×M₁₆	C₂²×D₄	1	4	yes	—
506	C₂²×M₁₆	C₂²×D₄	1	8	yes	—
507	C₂²×M₁₆	C₂²×D₄	1	8	yes	—
508	C₂²×M₁₆	C₂²×D₄	1	4	yes	—
509	C₂²×M₁₆	C₂²×D₄	1	32	yes	—
510	C₂²×M₁₆	C₂²×D₄	1	4	yes	—
511	C₂²×M₁₆	C₂²×D₄	1	4	yes	—
512	C₂²×M₁₆	C₂²×D₄	1	8	yes	—
513	C₂²×M₁₆	C₂²×D₄	1	8	yes	—
514	C₂²×M₁₆	C₂⁵	1	4	yes	—
515	C₂²×M₁₆	C₂⁵	1	4	yes	—
516	C₂²×M₁₆	C₂⁵	1	4	yes	—
517	C₂²×M₁₆	C₂⁵	1	4	yes	—
518	C₂²×M₁₆	C₂⁵	1	4	yes	—
519	C₂²×M₁₆	C₂⁵	1	8	yes	—
520	C₂²×M₁₆	C₂⁵	1	4	yes	—
521	#536	#120	1	8	yes	—
522	#536	#120	1	8	yes	—
523	#536	#120	1	16	yes	—
524	#536	C₂²×D₄	1	16	yes	—
525	#535	#120	1	8	yes	—
526	#535	#120	1	8	yes	—
527	#535	#120	1	16	yes	—
528	#535	C₂²×D₄	1	16	yes	—
529	#532	C₂²×D₄	1	32	yes	—
530	C₂×C₄⋊Q₈	C₂²×D₄	1	4	yes	—
531	C₂×C₄⋊Q₈	C₂²×D₄	1	4	yes	—
532	C₂×#127	C₂²×D₄	1	4	yes	—
533	C₂×#127	C₂²×D₄	1	8	yes	—
534	C₂×#127	C₂²×D₄	1	8	yes	—
535	C₂×#127	C₂²×D₄	1	4	yes	—
536	C₂×#124	C₂²×D₄	1	4	yes	—
537	C₂×#124	C₂²×D₄	1	4	yes	—
538	C₂×#124	C₂²×D₄	1	8	yes	—
539	C₂×#124	C₂²×D₄	1	8	yes	—
540	C₂×#124	C₂²×D₄	1	4	yes	—
541	C₂×#124	C₂²×D₄	1	4	yes	—
542	C₂×#117	C₂²×D₄	1	4	yes	—
543	C₂×#117	C₂²×D₄	1	4	yes	—
544	C₂×#117	C₂²×D₄	1	2	yes	—
545	C₂×#117	C₂²×D₄	1	8	yes	—
546	C₂×#117	C₂²×D₄	1	4	yes	—
547	C₂×#117	C₂²×D₄	1	4	yes	—
548	C₂×#117	C₂²×D₄	1	2	yes	—
549	C₂×#117	C₂²×D₄	1	2	yes	—
550	C₂×#117	C₂⁵	1	4	yes	—
551	C₂×#117	C₂⁵	1	2	yes	—
552	C₂²×C₄²	C₂²×D₄	1	2	yes	—
553	C₂²×C₄²	C₂²×D₄	1	8	yes	—
554	C₂²×C₄²	C₂⁵	1	2	yes	—
555	#421	C₂²×D₄	1	64	yes	—
556	C₂×#104	C₂²×D₄	1	64	yes	complemented
557	#413	#120	1	32	yes	—
558	#413	C₂²×D₄	1	32	yes	—
559	#413	C₂²×D₄	1	32	yes	—
560	C₂×#101	#120	1	8	yes	—
561	C₂×#101	#120	1	8	yes	—
562	C₂×#101	C₂²×D₄	1	8	yes	—
563	C₂×#101	C₂²×D₄	1	8	yes	—
564	C₂×#100	#120	1	8	yes	—
565	C₂×#100	#120	1	8	yes	—
566	C₂×#100	C₂²×D₄	1	8	yes	—
567	C₂×#100	C₂²×D₄	1	32	yes	—
568	C₂×#100	C₂²×D₄	1	8	yes	—
569	C₂⁵	C₂×#121	1	4	yes	—
570	C₂⁵	C₂×#121	1	4	yes	—
571	C₂⁵	C₂×#121	1	16	yes	—
572	C₂⁵	C₂×#121	1	2	yes	—
573	C₂⁵	C₂×#121	1	2	yes	—
574	C₂⁵	C₂²×#41	1	4	yes	—
575	C₂⁵	C₂²×#41	1	1	yes	characteristic
576	C₂×#41	C₂×#120	1	4	yes	—
577	C₂×#41	C₂×#120	1	4	yes	—
578	C₂×#41	C₂×#120	1	8	yes	—
579	C₂×#41	C₂×#120	1	8	yes	—
580	C₂×#41	#534	1	8	yes	—
581	C₂×#41	#535	1	8	yes	—
582	C₂×#41	D₄²	1	16	yes	—
583	C₂×#41	D₄²	1	16	yes	—
584	C₂×#41	D₄²	1	8	yes	—
585	C₂×#41	D₄²	1	8	yes	—
586	C₂×#41	D₄²	1	8	yes	—
587	C₂×#41	D₄²	1	8	yes	—
588	C₂×#41	#546	1	8	yes	—
589	C₂×#41	#546	1	8	yes	—
590	C₂×#41	#546	1	8	yes	—
591	C₂×#41	#546	1	8	yes	—
592	C₂×#41	C₂³×D₄	1	8	yes	—
593	C₂×#41	C₂³×D₄	1	16	yes	—
594	C₂×#41	C₂³×D₄	1	16	yes	—
595	C₂×#41	C₂³×D₄	1	8	yes	—
596	C₂×#41	C₂³×D₄	1	8	yes	—
597	C₂×#41	C₂×H(5,𝔽₂)	1	8	yes	—
598	C₂×#41	C₂×H(5,𝔽₂)	1	8	yes	—
599	C₂²×Q₈	C₂×#120	1	4	yes	—
600	C₂²×Q₈	C₂×#120	1	2	yes	—
601	C₂²×Q₈	C₂×#120	1	2	yes	—
602	C₂²×Q₈	C₂×#120	1	2	yes	—
603	C₂²×Q₈	C₂×#120	1	2	yes	—
604	C₂²×Q₈	C₂×#121	1	2	yes	—
605	C₂²×Q₈	C₂×#121	1	2	yes	—
606	C₂²×Q₈	#534	1	2	yes	—
607	C₂²×Q₈	#534	1	2	yes	—
608	C₂²×Q₈	#535	1	2	yes	—
609	C₂²×Q₈	#535	1	2	yes	—
610	C₂²×Q₈	D₄²	1	8	yes	—
611	C₂²×Q₈	D₄²	1	8	yes	—
612	C₂²×Q₈	C₂³×D₄	1	4	yes	—
613	C₂²×Q₈	C₂³×D₄	1	2	yes	—
614	C₂²×Q₈	C₂³×D₄	1	2	yes	—
615	C₂²×Q₈	C₂³×D₄	1	2	yes	—
616	C₂²×Q₈	C₂³×D₄	1	2	yes	—
617	C₂²×Q₈	C₂×H(5,𝔽₂)	1	8	yes	—
618	C₂²×D₄	C₂×#120	1	4	yes	—
619	C₂²×D₄	C₂×#120	1	2	yes	—
620	C₂²×D₄	C₂×#120	1	2	yes	—
621	C₂²×D₄	C₂×#120	1	2	yes	—
622	C₂²×D₄	C₂×#120	1	2	yes	—
623	C₂²×D₄	C₂×#121	1	4	yes	—
624	C₂²×D₄	C₂×#121	1	4	yes	—
625	C₂²×D₄	C₂×#121	1	16	yes	—
626	C₂²×D₄	C₂×#121	1	16	yes	—
627	C₂²×D₄	C₂×#121	1	4	yes	—
628	C₂²×D₄	C₂×#121	1	2	yes	—
629	C₂²×D₄	C₂×#121	1	4	yes	—
630	C₂²×D₄	C₂×#121	1	2	yes	—
631	C₂²×D₄	#534	1	2	yes	—
632	C₂²×D₄	#534	1	2	yes	—
633	C₂²×D₄	#535	1	2	yes	—
634	C₂²×D₄	#535	1	2	yes	—
635	C₂²×D₄	D₄²	1	8	yes	—
636	C₂²×D₄	D₄²	1	8	yes	—
637	C₂²×D₄	#546	1	8	yes	—
638	C₂²×D₄	#546	1	8	yes	—
639	C₂²×D₄	#546	1	8	yes	—
640	C₂²×D₄	#546	1	8	yes	—
641	C₂²×D₄	C₂³×D₄	1	2	yes	—
642	C₂²×D₄	C₂³×D₄	1	4	yes	—
643	C₂²×D₄	C₂³×D₄	1	4	yes	—
644	C₂²×D₄	C₂³×D₄	1	4	yes	—
645	C₂²×D₄	C₂³×D₄	1	2	yes	—
646	C₂²×D₄	C₂³×D₄	1	2	yes	—
647	C₂²×D₄	C₂³×D₄	1	2	yes	—
648	C₂²×D₄	C₂²×#41	1	4	yes	—
649	C₂²×D₄	C₂²×#41	1	4	yes	—
650	C₂²×D₄	C₂×H(5,𝔽₂)	1	8	yes	—
651	C₂³×C₄	C₂×#121	1	16	yes	—
652	C₂³×C₄	C₂×#121	1	4	yes	—
653	C₂³×C₄	C₂×#121	1	2	yes	—
654	C₂³×C₄	C₂×#121	1	4	yes	—
655	C₂³×C₄	C₂×#121	1	2	yes	—
656	C₂³×C₄	D₄²	1	8	yes	—
657	C₂³×C₄	D₄²	1	8	yes	—
658	C₂³×C₄	D₄²	1	8	yes	—
659	C₂³×C₄	D₄²	1	8	yes	—
660	C₂³×C₄	C₂³×D₄	1	4	yes	—
661	C₂³×C₄	C₂³×D₄	1	4	yes	—
662	C₂³×C₄	C₂³×D₄	1	1	yes	characteristic
663	C₂³×C₄	C₂³×D₄	1	1	yes	characteristic
664	C₂³×C₄	C₂³×D₄	1	1	yes	characteristic
665	C₂³×C₄	C₂³×D₄	1	1	yes	characteristic
666	C₂³×C₄	C₂³×D₄	1	2	yes	—
667	C₂³×C₄	C₂³×D₄	1	2	yes	—
668	C₂³×C₄	C₂³×D₄	1	2	yes	—
669	C₂³×C₄	C₂³×D₄	1	2	yes	—
670	C₂³×C₄	C₂²×#41	1	1	yes	characteristic
671	C₂³×C₄	C₂×H(5,𝔽₂)	1	2	yes	—
672	C₂³×C₄	C₂×H(5,𝔽₂)	1	2	yes	—
673	C₂³×C₄	C₂×H(5,𝔽₂)	1	2	yes	—
674	C₂³×C₄	C₂×H(5,𝔽₂)	1	2	yes	—
675	C₂³×C₄	C₂×H(5,𝔽₂)	1	4	yes	—
676	C₂³×C₄	C₂×H(5,𝔽₂)	1	4	yes	—
677	C₂³×C₄	C₂⁶	1	1	yes	characteristic
678	C₂×M₁₆	C₂×#120	1	8	yes	—
679	C₂×M₁₆	C₂×#120	1	8	yes	—
680	C₂×M₁₆	C₂×#120	1	16	yes	—
681	C₂×M₁₆	C₂³×D₄	1	8	yes	—
682	C₂×M₁₆	C₂³×D₄	1	16	yes	—
683	C₂×M₁₆	C₂³×D₄	1	8	yes	—
684	C₂×M₁₆	C₂³×D₄	1	16	yes	—
685	C₄⋊Q₈	C₂×#120	1	16	yes	—
686	#127	C₂×#120	1	16	yes	—
687	#124	C₂×#120	1	16	yes	—
688	#124	C₂×#120	1	16	yes	—
689	#117	C₂×#120	1	4	yes	—
690	#117	C₂×#120	1	4	yes	—
691	#117	C₂×#120	1	8	yes	—
692	#117	C₂³×D₄	1	8	yes	—
693	C₂×C₄²	C₂³×D₄	1	4	yes	—
694	C₂×C₄²	C₂³×D₄	1	4	yes	—
695	C₂×C₄²	C₂³×D₄	1	8	yes	—
696	#101	C₂×#120	1	32	yes	—
697	#100	C₂×#120	1	32	yes	—
698	C₂⁴	#2408	1	4	yes	—
699	C₂⁴	#2408	1	4	yes	—
700	C₂⁴	#2410	1	4	yes	—
701	C₂⁴	#2410	1	4	yes	—
702	C₂⁴	C₂²×#121	1	8	yes	—
703	C₂⁴	C₂²×#121	1	4	yes	—
704	C₂⁴	C₂²×#121	1	4	yes	—
705	C₂⁴	C₂²×#121	1	1	yes	characteristic
706	C₂⁴	C₂²×#121	1	1	yes	characteristic
707	C₂⁴	C₂×#546	1	2	yes	—
708	C₂⁴	C₂×#546	1	2	yes	—
709	C₂⁴	C₂×#546	1	2	yes	—
710	C₂⁴	C₂×#546	1	2	yes	—
711	C₂⁴	#3490	1	2	yes	—
712	C₂⁴	#3490	1	2	yes	—
713	C₂⁴	C₂³×#41	1	1	yes	characteristic
714	C₂×Q₈	#2408	1	4	yes	—
715	C₂×Q₈	#2408	1	4	yes	—
716	C₂×Q₈	#2410	1	4	yes	—
717	C₂×Q₈	#2410	1	4	yes	—
718	C₂×Q₈	C₂²×#120	1	4	yes	—
719	C₂×Q₈	C₂²×#120	1	4	yes	—
720	C₂×Q₈	C₂²×#120	1	4	yes	—
721	C₂×Q₈	C₂×#534	1	4	yes	—
722	C₂×Q₈	C₂×#535	1	4	yes	—
723	C₂×Q₈	C₂×D₄²	1	16	yes	—
724	C₂×D₄	#2408	1	16	yes	—
725	C₂×D₄	#2408	1	4	yes	—
726	C₂×D₄	#2408	1	4	yes	—
727	C₂×D₄	#2410	1	16	yes	—
728	C₂×D₄	#2410	1	4	yes	—
729	C₂×D₄	#2410	1	4	yes	—
730	C₂×D₄	C₂²×#120	1	4	yes	—
731	C₂×D₄	C₂²×#120	1	4	yes	—
732	C₂×D₄	C₂²×#120	1	4	yes	—
733	C₂×D₄	C₂×#534	1	4	yes	—
734	C₂×D₄	C₂×#535	1	4	yes	—
735	C₂×D₄	C₂×D₄²	1	16	yes	—
736	C₂×D₄	C₂×#546	1	16	yes	—
737	C₂×D₄	C₂×#546	1	16	yes	—
738	C₂²×C₄	#2408	1	4	yes	—
739	C₂²×C₄	#2408	1	16	yes	—
740	C₂²×C₄	#2408	1	4	yes	—
741	C₂²×C₄	#2410	1	16	yes	—
742	C₂²×C₄	#2410	1	4	yes	—
743	C₂²×C₄	#2410	1	4	yes	—
744	C₂²×C₄	C₂²×#120	1	2	yes	—
745	C₂²×C₄	C₂²×#120	1	1	yes	characteristic
746	C₂²×C₄	C₂²×#120	1	1	yes	characteristic
747	C₂²×C₄	C₂²×#120	1	1	yes	characteristic
748	C₂²×C₄	C₂²×#120	1	2	yes	—
749	C₂²×C₄	C₂²×#120	1	1	yes	characteristic
750	C₂²×C₄	C₂²×#121	1	4	yes	—
751	C₂²×C₄	C₂²×#121	1	4	yes	—
752	C₂²×C₄	C₂²×#121	1	1	yes	characteristic
753	C₂²×C₄	C₂²×#121	1	1	yes	characteristic
754	C₂²×C₄	C₂×#534	1	2	yes	—
755	C₂²×C₄	C₂×#534	1	1	yes	characteristic
756	C₂²×C₄	C₂×#534	1	1	yes	characteristic
757	C₂²×C₄	C₂×#535	1	1	yes	characteristic
758	C₂²×C₄	C₂×#535	1	2	yes	—
759	C₂²×C₄	C₂×#535	1	1	yes	characteristic
760	C₂²×C₄	C₂×D₄²	1	16	yes	—
761	C₂²×C₄	C₂×D₄²	1	16	yes	—
762	C₂²×C₄	C₂×D₄²	1	2	yes	—
763	C₂²×C₄	C₂×D₄²	1	2	yes	—
764	C₂²×C₄	C₂×D₄²	1	2	yes	—
765	C₂²×C₄	C₂×D₄²	1	2	yes	—
766	C₂²×C₄	C₂×D₄²	1	2	yes	—
767	C₂²×C₄	C₂×D₄²	1	2	yes	—
768	C₂²×C₄	C₂×D₄²	1	2	yes	—
769	C₂²×C₄	C₂×D₄²	1	2	yes	—
770	C₂²×C₄	C₂×D₄²	1	4	yes	—
771	C₂²×C₄	C₂×D₄²	1	4	yes	—
772	C₂²×C₄	C₂×D₄²	1	4	yes	—
773	C₂²×C₄	C₂×D₄²	1	4	yes	—
774	C₂²×C₄	C₂×#546	1	2	yes	—
775	C₂²×C₄	C₂×#546	1	2	yes	—
776	C₂²×C₄	C₂×#546	1	2	yes	—
777	C₂²×C₄	C₂×#546	1	2	yes	—
778	C₂²×C₄	#3484	1	2	yes	—
779	C₂²×C₄	#3484	1	4	yes	—
780	C₂²×C₄	#3484	1	2	yes	—
781	C₂²×C₄	#3484	1	4	yes	—
782	C₂²×C₄	#3484	1	4	yes	—
783	C₂²×C₄	#3484	1	4	yes	—
784	C₂²×C₄	#3484	1	4	yes	—
785	C₂²×C₄	#3484	1	2	yes	—
786	C₂²×C₄	#3484	1	2	yes	—
787	C₂²×C₄	#3484	1	4	yes	—
788	C₂²×C₄	#3484	1	4	yes	—
789	C₂²×C₄	#3484	1	4	yes	—
790	C₂²×C₄	#3484	1	4	yes	—
791	C₂²×C₄	#3484	1	4	yes	—
792	C₂²×C₄	#3490	1	4	yes	—
793	C₂²×C₄	#3532	1	4	yes	—
794	C₂²×C₄	#3532	1	4	yes	—
795	C₂²×C₄	#3532	1	4	yes	—
796	C₂²×C₄	#3532	1	4	yes	—
797	C₂²×C₄	C₂⁴×D₄	1	1	yes	characteristic
798	C₂²×C₄	C₂⁴×D₄	1	1	yes	characteristic
799	C₂²×C₄	C₂⁴×D₄	1	2	yes	—
800	C₂²×C₄	C₂⁴×D₄	1	2	yes	—
801	C₂²×C₄	C₂²×H(5,𝔽₂)	1	4	yes	—
802	C₂²×C₄	C₂²×H(5,𝔽₂)	1	2	yes	—
803	C₂²×C₄	C₂²×H(5,𝔽₂)	1	2	yes	—
804	M₁₆	C₂²×#120	1	16	yes	—
805	C₄²	C₂²×#120	1	8	yes	—
806	C₂³	C₂×#2410	1	8	yes	—
807	C₂³	C₂×#2410	1	1	yes	characteristic
808	C₂³	C₂×#2410	1	1	yes	characteristic
809	C₂³	C₂×#2410	1	2	yes	—
810	C₂³	C₂×#2408	1	8	yes	—
811	C₂³	C₂×#2408	1	1	yes	characteristic
812	C₂³	C₂×#2408	1	2	yes	—
813	C₂³	C₂×#2408	1	1	yes	characteristic
814	C₂³	#35348	1	1	yes	characteristic
815	C₂³	#35348	1	1	yes	characteristic
816	C₂³	#35348	1	2	yes	—
817	C₂³	#58991	1	4	yes	—
818	C₂³	#58991	1	4	yes	—
819	C₂³	#58991	1	4	yes	—
820	C₂³	#58991	1	4	yes	—
821	C₂³	C₂³×#121	1	1	yes	characteristic
822	C₂³	C₂²×#546	1	2	yes	—
823	C₂³	C₂²×#546	1	2	yes	—
824	C₂³	C₂×#3490	1	2	yes	—
825	C₂×C₄	C₂×#2410	1	8	yes	—
826	C₂×C₄	C₂×#2410	1	2	yes	—
827	C₂×C₄	C₂×#2410	1	1	yes	characteristic
828	C₂×C₄	C₂×#2410	1	1	yes	characteristic
829	C₂×C₄	C₂×#2408	1	8	yes	—
830	C₂×C₄	C₂×#2408	1	1	yes	characteristic
831	C₂×C₄	C₂×#2408	1	2	yes	—
832	C₂×C₄	C₂×#2408	1	1	yes	characteristic
833	C₂×C₄	#35348	1	2	yes	—
834	C₂×C₄	#35348	1	2	yes	—
835	C₂×C₄	D₄×#120	1	2	yes	—
836	C₂×C₄	D₄×#120	1	2	yes	—
837	C₂×C₄	D₄×#120	1	4	yes	—
838	C₂×C₄	D₄×#120	1	2	yes	—
839	C₂×C₄	D₄×#120	1	2	yes	—
840	C₂×C₄	D₄×#120	1	4	yes	—
841	C₂×C₄	D₄×#120	1	4	yes	—
842	C₂×C₄	D₄×#120	1	4	yes	—
843	C₂×C₄	D₄×#120	1	2	yes	—
844	C₂×C₄	D₄×#120	1	2	yes	—
845	C₂×C₄	D₄×#120	1	2	yes	—
846	C₂×C₄	D₄×#120	1	2	yes	—
847	C₂×C₄	#37644	1	2	yes	—
848	C₂×C₄	#37644	1	2	yes	—
849	C₂×C₄	#37644	1	4	yes	—
850	C₂×C₄	#37644	1	2	yes	—
851	C₂×C₄	#37644	1	2	yes	—
852	C₂×C₄	#37644	1	4	yes	—
853	C₂×C₄	#37645	1	2	yes	—
854	C₂×C₄	#37645	1	2	yes	—
855	C₂×C₄	#37645	1	4	yes	—
856	C₂×C₄	#37645	1	2	yes	—
857	C₂×C₄	#37645	1	2	yes	—
858	C₂×C₄	#37645	1	4	yes	—
859	C₂×C₄	#58991	1	4	yes	—
860	C₂×C₄	#58991	1	4	yes	—
861	C₂×C₄	#58991	1	4	yes	—
862	C₂×C₄	#58991	1	4	yes	—
863	C₂×C₄	C₂³×#120	1	1	yes	characteristic
864	C₂×C₄	C₂³×#120	1	1	yes	characteristic
865	C₂×C₄	C₂²×#534	1	1	yes	characteristic
866	C₂×C₄	C₂²×#535	1	1	yes	characteristic
867	C₂×C₄	C₂²×D₄²	1	2	yes	—
868	C₂×C₄	C₂²×D₄²	1	4	yes	—
869	C₂×C₄	C₂²×D₄²	1	2	yes	—
870	C₂×C₄	C₂×#3532	1	4	yes	—
871	C₂×C₄	C₂×#3484	1	4	yes	—
872	C₂×C₄	C₂×#3484	1	2	yes	—
873	C₂×C₄	C₂×#3484	1	4	yes	—
874	C₂×C₄	C₂×#3484	1	2	yes	—
875	C₂²	#647670	1	1	yes	characteristic
876	C₂²	#647670	1	1	yes	characteristic
877	C₂²	#647670	1	1	yes	characteristic
878	C₂²	#647670	1	1	yes	characteristic
879	C₂²	#647670	1	4	yes	—
880	C₂²	C₂²×#2410	1	1	yes	characteristic
881	C₂²	C₂²×#2408	1	1	yes	characteristic
882	C₂²	C₂×#35348	1	1	yes	characteristic
883	C₂²	C₂×#58991	1	4	yes	—
884	C₄	#647670	1	2	yes	—
885	C₄	#647670	1	2	yes	—
886	C₄	#647670	1	2	yes	—
887	C₄	#647670	1	2	yes	—
888	C₄	C₂×D₄×#120	1	2	yes	—
889	C₄	C₂×D₄×#120	1	2	yes	—
890	C₄	C₂×#37644	1	2	yes	—
891	C₄	C₂×#37645	1	2	yes	—
892	C₂	C₂×#647670	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂	C₂×#647670
commutator, Frattini, cosocle	C₂³×C₄	C₂⁶
LCS	G ▷ C₂³×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂ ◁ C₂⁴×C₄ ◁ G
LECS	G ▷ C₂³×C₄ ▷ C₂ ▷ C₁

Complements

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

N	H ≅ G/N	type
1. #72311324	C₂	semidirect
2. C₂×#360531	C₂	semidirect
3. C₂×#417702	C₂	semidirect
4. #72311305	C₂	semidirect
5. #72311298	C₂	semidirect
6. #72311293	C₂	semidirect
7. #72311288	C₂	semidirect
8. #72311282	C₂	semidirect
9. #72311278	C₂	semidirect
10. #72311274	C₂	semidirect
11. #72311206	C₂	semidirect
12. #72311147	C₂	semidirect
13. C₂×#359529	C₂	semidirect
14. #72303796	C₂	semidirect
15. #72303711	C₂	semidirect
16. C₂×#392136	C₂	semidirect
17. C₂×#10574841	C₂	semidirect
18. C₂×#10574841	C₂	semidirect
19. #72241303	C₂	semidirect
21. C₂×#63090	C₂²	semidirect
22. C₂×#63090	C₂²	semidirect
25. C₂×#60469	C₂²	semidirect
26. #10574841	C₂²	semidirect
27. #10574839	C₂²	semidirect
28. C₂×#60389	C₂²	semidirect
29. C₂×#60388	C₂²	semidirect
34. C₂×#60387	C₂²	semidirect
35. C₂×#60387	C₂²	semidirect
36. C₂²×#3019	C₂²	semidirect
37. C₂²×#3019	C₂²	semidirect
38. C₂²×#3019	C₂²	semidirect
39. #10574202	C₂²	semidirect
40. C₂×#60076	C₂²	semidirect
41. C₂×#60093	C₂²	semidirect
42. C₂×#60093	C₂²	semidirect
45. #6442596	C₂²	semidirect
46. #6437987	C₂²	semidirect
47. #6437986	C₂²	semidirect
48. #6437453	C₂²	semidirect
49. #6437452	C₂²	semidirect
50. C₂×#23527	C₂²	semidirect
51. C₂×#23525	C₂²	semidirect
52. #6431784	C₂²	semidirect
53. #6431784	C₂²	semidirect
54. C₂×#23434	C₂²	semidirect
55. C₂×#23402	C₂²	semidirect
56. C₂×#23402	C₂²	semidirect
57. #6379034	C₂²	semidirect
58. #6379033	C₂²	semidirect
59. #6372017	C₂²	semidirect
60. C₂×#21219	C₂²	semidirect
61. C₂×#21017	C₂²	semidirect
62. #6371514	C₂²	semidirect
63. C₂×#20990	C₂²	semidirect
64. #6371494	C₂²	semidirect
65. C₂×#20964	C₂²	semidirect
66. #6371454	C₂²	semidirect
67. #6371454	C₂²	semidirect
68. C₂×#20939	C₂²	semidirect
69. C₂×#20860	C₂²	semidirect
70. C₂×#20673	C₂²	semidirect
71. #6370781	C₂²	semidirect
72. C₂×#20612	C₂²	semidirect
73. C₂×#20612	C₂²	semidirect
74. C₂×#20612	C₂²	semidirect
75. C₂×#20612	C₂²	semidirect
76. C₂×#20612	C₂²	semidirect
77. #6370703	C₂²	semidirect
80. C₂×#20592	C₂²	semidirect
81. #6369826	C₂²	semidirect
82. #419044	C₂²	semidirect
83. #419041	C₂²	semidirect
84. #417702	C₂²	semidirect
85. #395561	C₂²	semidirect
86. #395560	C₂²	semidirect
87. #395528	C₂²	semidirect
88. #394033	C₂²	semidirect
89. #394032	C₂²	semidirect
90. #393908	C₂²	semidirect
91. #393907	C₂²	semidirect
92. #392136	C₂²	semidirect
93. #366624	C₂²	semidirect
94. #364504	C₂²	semidirect
95. #360531	C₂²	semidirect
96. #359529	C₂²	semidirect
97. C₂×#11159	C₂²	semidirect
98. C₂×#11139	C₂²	semidirect
99. C₂×#11118	C₂²	semidirect
100. #357746	C₂²	semidirect
101. C₂×#11037	C₂²	semidirect
102. C₂×#11032	C₂²	semidirect
103. C₂×#11032	C₂²	semidirect
104. #357567	C₂²	semidirect
105. C₂×#10973	C₂²	semidirect
106. #354118	C₂²	semidirect
107. C₂×#10756	C₂²	semidirect
108. C₂×#10744	C₂²	semidirect
109. C₂×#10767	C₂²	semidirect
118. C₂×#3586	C₂³	semidirect
119. C₂×#3585	C₂³	semidirect
124. C₂²×#575	C₂³	semidirect
125. C₂²×#575	C₂³	semidirect
128. C₂²×#568	C₂³	semidirect
144. #60469	C₂³	semidirect
145. #60387	D₄	semidirect
146. #60387	D₄	semidirect
147. #60387	D₄	semidirect
150. C₂×#3022	D₄	semidirect
152. C₂×#3022	C₂³	semidirect
153. C₂×#3021	D₄	semidirect
155. C₂×#3021	C₂³	semidirect
157. C₂×#3019	C₂³	semidirect
159. C₂×#3018	C₂³	semidirect
160. C₂²×#455	C₂³	semidirect
161. C₂²×#453	C₂³	semidirect
162. #60368	C₂³	semidirect
163. #60367	C₂³	semidirect
164. #60144	C₂³	semidirect
165. C₂²×#430	C₂³	semidirect
166. C₂×#2905	C₂³	semidirect
168. C₂×#2901	C₂³	semidirect
173. C₂²×#421	C₂³	semidirect
174. C₂²×#421	C₂³	semidirect
175. C₂×#2896	C₂³	semidirect
176. C₂×#2896	C₂³	semidirect
177. C₂×#2889	C₂³	semidirect
181. C₂×#2888	C₂³	semidirect
192. C₂²×#413	C₂³	semidirect
193. C₂²×#413	C₂³	semidirect
194. C₂²×#413	C₂³	semidirect
204. C₂×#2879	C₂³	semidirect
205. C₂×#2879	C₂³	semidirect
206. C₂×#2873	C₂³	semidirect
207. C₂×#2050	C₂³	semidirect
208. C₂×#2049	C₂³	semidirect
209. C₂×#2048	C₂³	semidirect
210. #23440	C₂³	semidirect
211. #23440	C₂³	semidirect
212. #23439	C₂³	semidirect
213. #23439	C₂³	semidirect
214. #23434	C₂³	semidirect
215. #23402	C₂³	semidirect
216. C₂×#2004	C₂³	semidirect
217. C₂×#2002	C₂³	semidirect
218. #21241	C₂³	semidirect
219. C₂×#1967	C₂³	semidirect
220. C₂×#1965	C₂³	semidirect
221. #21017	C₂³	semidirect
222. #20991	C₂³	semidirect
223. #20990	C₂³	semidirect
224. #20990	C₂³	semidirect
225. #20980	C₂³	semidirect
226. #20964	C₂³	semidirect
227. #20956	C₂³	semidirect
228. #20955	C₂³	semidirect
229. #20952	C₂³	semidirect
230. #20939	C₂³	semidirect
231. #20860	C₂³	semidirect
232. #20673	C₂³	semidirect
233. #20637	C₂³	semidirect
236. #20612	C₂³	semidirect
237. #20612	C₂³	semidirect
238. #20612	C₂³	semidirect
239. #20593	C₂³	semidirect
242. #20592	C₂³	semidirect
243. #20592	C₂³	semidirect
244. C₄×#413	C₂³	semidirect
245. C₂²×#344	C₂³	semidirect
246. C₂²×#344	C₂³	semidirect
247. C₂×#1742	C₂³	semidirect
248. C₂×#1742	C₂³	semidirect
249. C₂×#1738	C₂³	semidirect
250. C₂×#1738	C₂³	semidirect
251. C₂×#1733	C₂³	semidirect
252. C₂×#1733	C₂³	semidirect
253. C₂²×#338	C₂³	semidirect
254. #11159	C₂³	semidirect
255. #11139	C₂³	semidirect
256. #11118	C₂³	semidirect
257. #11080	C₂³	semidirect
258. #11037	C₂³	semidirect
259. #11032	C₂³	semidirect
260. #11032	C₂³	semidirect
261. #11015	C₂³	semidirect
262. #11014	C₂³	semidirect
263. #10973	C₂³	semidirect
264. #10946	C₂³	semidirect
265. #10767	C₂³	semidirect
266. #10756	C₂³	semidirect
267. #10744	C₂³	semidirect
297. C₂×#575	C₂×D₄	semidirect
298. C₂×#575	C₂×D₄	semidirect
299. C₂×#575	C₂×D₄	semidirect
303. C₂×#575	C₂⁴	semidirect
304. C₂²×#137	C₂×D₄	semidirect
306. C₂²×#137	C₂⁴	semidirect
307. C₂²×AGL(1,ℤ/8)	C₂×D₄	semidirect
309. C₂²×AGL(1,ℤ/8)	C₂⁴	semidirect
313. C₂×#568	C₂⁴	semidirect
362. #3022	C₂×D₄	semidirect
363. #3021	C₂×D₄	semidirect
364. #3018	C₂×D₄	semidirect
365. C₂×#430	C₂⁴	semidirect
366. C₂×#423	C₂⁴	semidirect
367. C₂×#421	C₂×D₄	semidirect
368. C₂×#421	C₂×D₄	semidirect
369. C₂×#421	C₂×D₄	semidirect
370. C₂×#421	C₂×D₄	semidirect
374. C₂×#421	C₂⁴	semidirect
376. C₂²×#104	C₂⁴	semidirect
377. #2896	C₂⁴	semidirect
378. C₂×#419	C₂⁴	semidirect
379. C₂×#418	C₂⁴	semidirect
396. C₂×#413	C₂⁴	semidirect
399. C₂²×#101	C₂⁴	semidirect
400. C₂²×#101	C₂⁴	semidirect
410. C₂²×#100	C₂⁴	semidirect
411. C₂²×#100	C₂⁴	semidirect
416. #2879	C₂⁴	semidirect
417. #2879	C₂⁴	semidirect
418. C₂×C₄×M₁₆	C₂⁴	semidirect
419. C₂×#344	C₂⁴	semidirect
420. C₂×#344	C₂⁴	semidirect
421. #1742	C₂⁴	semidirect
422. #1742	C₂⁴	semidirect
423. #1738	C₂⁴	semidirect
424. #1738	C₂⁴	semidirect
425. #1733	C₂⁴	semidirect
426. C₂×#339	C₂⁴	semidirect
427. C₂×#338	C₂⁴	semidirect
502. #575	C₂²×D₄	semidirect
556. C₂×#104	C₂²×D₄	semidirect

Maximal subgroups

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

subgroup	index
#72311324	2
C₂×#360531	2
C₂×#417702	2
#72311305	2
#72311298	2
#72311293	2
#72311288	2
#72311282	2
#72311278	2
#72311274	2
#72311206	2
#72311147	2
C₂×#359529	2
#72303796	2
#72303711	2
C₂×#392136	2
C₂×#10574841	2
#72241303	2