Subgroups — #72265580

Order 2048.

At least 10062 conjugacy classes of subgroups; only the 1392 normal subgroups are shown.

The subgroup lattice has 923 nodes (normal subgroups only) — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#72265574	C₂	1	1	yes	maximal, characteristic, complemented
2	#72265573	C₂	1	1	yes	maximal, characteristic, complemented
3	#72265570	C₂	1	1	yes	maximal, characteristic, complemented
4	#72265565	C₂	1	1	yes	maximal, characteristic, complemented
5	#72265560	C₂	1	1	yes	maximal, characteristic, complemented
6	#72265556	C₂	1	1	yes	maximal, characteristic, complemented
7	#72265550	C₂	1	1	yes	maximal, characteristic, complemented
8	#72265544	C₂	1	1	yes	maximal, characteristic, complemented
9	#72265539	C₂	1	1	yes	maximal, characteristic, complemented
10	#72265536	C₂	1	1	yes	maximal, characteristic, complemented
11	#72265531	C₂	1	1	yes	maximal, characteristic, complemented
12	#72265528	C₂	1	1	yes	maximal, characteristic, complemented
13	#72265526	C₂	1	1	yes	maximal, characteristic, complemented
14	#72265350	C₂	1	1	yes	maximal, characteristic, complemented
15	#72265248	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#382863	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂×#382865	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×#6462906	C₂	1	1	yes	maximal, characteristic, complemented
19	C₂×#6462912	C₂	1	1	yes	maximal, characteristic, complemented
20	#72250855	C₂	1	1	yes	maximal, characteristic, complemented
21	#72239650	C₂	1	1	yes	maximal, characteristic, complemented
22	#72239603	C₂	1	1	yes	maximal, characteristic, complemented
23	#72239575	C₂	1	1	yes	maximal, characteristic, complemented
24	#72239546	C₂	1	1	yes	maximal, characteristic, complemented
25	#72239429	C₂	1	1	yes	maximal, characteristic, complemented
26	#72239324	C₂	1	1	yes	maximal, characteristic, complemented
27	#72239267	C₂	1	1	yes	maximal, characteristic, complemented
28	#72238753	C₂	1	1	yes	maximal, characteristic, complemented
29	#72238738	C₂	1	1	yes	maximal, characteristic, complemented
30	#72237189	C₂	1	1	yes	maximal, characteristic, complemented
31	#72237171	C₂	1	1	yes	maximal, characteristic, complemented
32	C₂×#60454	C₂²	1	1	yes	characteristic
33	C₂×#60469	C₂²	1	1	yes	characteristic
34	C₂×#60444	C₂²	1	1	yes	characteristic
35	C₂²×#3068	C₂²	1	1	yes	characteristic
36	C₂×#60141	C₂²	1	1	yes	characteristic
37	C₂×#60182	C₂²	1	1	yes	characteristic
38	C₂×#60168	C₂²	1	1	yes	characteristic
39	#7629122	C₂²	1	1	yes	characteristic
40	C₂×#35514	C₂²	1	1	yes	characteristic
41	C₂×#23652	C₂²	1	1	yes	characteristic
42	C₂²×#2081	C₂²	1	1	yes	characteristic
43	C₂×#23649	C₂²	1	1	yes	characteristic
44	C₂×#23649	C₂²	1	1	yes	characteristic
45	#6432185	C₂²	1	1	yes	characteristic
46	#6432177	C₂²	1	1	yes	characteristic
47	C₂×#23443	C₂²	1	1	yes	characteristic
48	#6431764	C₂²	1	1	yes	characteristic
49	C₂×#23414	C₂²	1	1	yes	characteristic
50	C₂²×#2010	C₂²	1	1	yes	characteristic
51	C₂²×#2010	C₂²	1	1	yes	characteristic
52	C₂²×#2010	C₂²	1	1	yes	characteristic
53	C₂×#23412	C₂²	1	1	yes	characteristic
54	C₂×#23412	C₂²	1	1	yes	characteristic
55	C₂²×#2008	C₂²	1	1	yes	characteristic
56	C₂×#23402	C₂²	1	1	yes	characteristic
57	#6431707	C₂²	1	1	yes	characteristic
58	C₂×#23391	C₂²	1	1	yes	characteristic
59	C₂×#23391	C₂²	1	1	yes	characteristic
60	C₂×#21012	C₂²	1	1	yes	characteristic
61	C₂²×#1911	C₂²	1	1	yes	characteristic
62	C₂×#20998	C₂²	1	1	yes	characteristic
63	C₂²×#1904	C₂²	1	1	yes	characteristic
64	#6371484	C₂²	1	1	yes	characteristic
65	#6371482	C₂²	1	1	yes	characteristic
66	#6371477	C₂²	1	1	yes	characteristic
67	C₂×#20973	C₂²	1	1	yes	characteristic
68	C₂²×#1891	C₂²	1	1	yes	characteristic
69	C₂²×#1891	C₂²	1	1	yes	characteristic
70	C₂×#20939	C₂²	1	1	yes	characteristic
71	C₂×#20939	C₂²	1	1	yes	characteristic
72	C₂×#20776	C₂²	1	1	yes	characteristic
73	#6371047	C₂²	1	1	yes	characteristic
74	C₂×#20757	C₂²	1	1	yes	characteristic
75	C₂×#20757	C₂²	1	1	yes	characteristic
76	C₂×#20675	C₂²	1	1	yes	characteristic
77	C₂×#20675	C₂²	1	1	yes	characteristic
78	C₂×#20671	C₂²	1	1	yes	characteristic
79	C₂×#20667	C₂²	1	1	yes	characteristic
80	#6370799	C₂²	1	1	yes	characteristic
81	#6370796	C₂²	1	1	yes	characteristic
82	#5956073	C₂²	1	1	yes	characteristic
83	#358613	C₂²	1	1	yes	characteristic
84	C₂×#11362	C₂²	1	1	yes	characteristic
85	C₂×#11361	C₂²	1	1	yes	characteristic
86	C₂×#11360	C₂²	1	1	yes	characteristic
87	C₂×#11356	C₂²	1	1	yes	characteristic
88	C₂×#11356	C₂²	1	1	yes	characteristic
89	C₂×#11133	C₂²	1	1	yes	characteristic
90	C₂×#11132	C₂²	1	1	yes	characteristic
91	C₂×#11131	C₂²	1	1	yes	characteristic
92	C₂×#11129	C₂²	1	1	yes	characteristic
93	#357748	C₂²	1	1	yes	characteristic
94	#357748	C₂²	1	1	yes	characteristic
95	#357744	C₂²	1	1	yes	characteristic
96	#357743	C₂²	1	1	yes	characteristic
97	C₂×#11110	C₂²	1	1	yes	characteristic
98	C₂×#11109	C₂²	1	1	yes	characteristic
99	C₂×#11101	C₂²	1	1	yes	characteristic
100	C₂×#11100	C₂²	1	1	yes	characteristic
101	#357593	C₂²	1	1	yes	characteristic
102	C₂×#11036	C₂²	1	1	yes	characteristic
103	C₂×#11036	C₂²	1	1	yes	characteristic
104	C₂×#11034	C₂²	1	1	yes	characteristic
105	#357586	C₂²	1	1	yes	characteristic
106	C₂×#11030	C₂²	1	1	yes	characteristic
107	#357583	C₂²	1	1	yes	characteristic
108	#357577	C₂²	1	1	yes	characteristic
109	#357573	C₂²	1	1	yes	characteristic
110	C₂×#11014	C₂²	1	1	yes	characteristic
111	#357564	C₂²	1	1	yes	characteristic
112	C₂×#11012	C₂²	1	1	yes	characteristic
113	#357561	C₂²	1	1	yes	characteristic
114	C₂×#11004	C₂²	1	1	yes	characteristic
115	C₂×#11003	C₂²	1	1	yes	characteristic
116	C₂×#11000	C₂²	1	1	yes	characteristic
117	#357553	C₂²	1	1	yes	characteristic
118	#357552	C₂²	1	1	yes	characteristic
119	C₂×#10994	C₂²	1	1	yes	characteristic
120	C₂×#10994	C₂²	1	1	yes	characteristic
121	C₂×#10994	C₂²	1	1	yes	characteristic
122	C₂×#10994	C₂²	1	1	yes	characteristic
123	C₂×#10993	C₂²	1	1	yes	characteristic
124	#357529	C₂²	1	1	yes	characteristic
125	C₂×#11006	C₂²	1	1	yes	characteristic
126	C₂×#10984	C₂²	1	1	yes	characteristic
127	#357440	C₂²	1	1	yes	characteristic
128	#357433	C₂²	1	1	yes	characteristic
129	C₂×#10967	C₂²	1	1	yes	characteristic
130	#357420	C₂²	1	1	yes	characteristic
131	C₂×#10785	C₂²	1	1	yes	characteristic
132	#353465	C₂²	1	1	yes	characteristic
133	C₂×#10784	C₂²	1	1	yes	characteristic
134	C₂×#10783	C₂²	1	1	yes	characteristic
135	C₂×#10743	C₂²	1	1	yes	characteristic
136	#353422	C₂²	1	1	yes	characteristic
137	C₂×#10742	C₂²	1	1	yes	characteristic
138	C₂×#10740	C₂²	1	1	yes	characteristic
139	C₂×#10778	C₂²	1	1	yes	characteristic
140	C₂×#10778	C₂²	1	1	yes	characteristic
141	C₂×#10729	C₂²	1	1	yes	characteristic
142	C₂×#10729	C₂²	1	1	yes	characteristic
143	#123943	C₂²	1	1	yes	characteristic
144	#123943	C₂²	1	1	yes	characteristic
145	#123940	C₂²	1	1	yes	characteristic
146	#123940	C₂²	1	1	yes	characteristic
147	#123938	C₂²	1	1	yes	characteristic
148	#123938	C₂²	1	1	yes	characteristic
149	#123937	C₂²	1	1	yes	characteristic
150	#123937	C₂²	1	1	yes	characteristic
151	#123911	C₂²	1	1	yes	characteristic
152	#123911	C₂²	1	1	yes	characteristic
153	#123909	C₂²	1	1	yes	characteristic
154	#123908	C₂²	1	1	yes	characteristic
155	#123846	C₂²	1	1	yes	characteristic
156	#123842	C₂²	1	1	yes	characteristic
157	#123841	C₂²	1	1	yes	characteristic
158	#123832	C₂²	1	1	yes	characteristic
159	#123774	C₂²	1	1	yes	characteristic
160	#123773	C₂²	1	1	yes	characteristic
161	#123768	C₂²	1	1	yes	characteristic
162	#123756	C₂²	1	1	yes	characteristic
163	#123626	C₂²	1	1	yes	characteristic
164	#123624	C₂²	1	1	yes	characteristic
165	#123619	C₂²	1	1	yes	characteristic
166	#123619	C₂²	1	1	yes	characteristic
167	#123619	C₂²	1	1	yes	characteristic
168	#123616	C₂²	1	1	yes	characteristic
169	#123616	C₂²	1	1	yes	characteristic
170	#123614	C₂²	1	1	yes	characteristic
171	#123614	C₂²	1	1	yes	characteristic
172	#123613	C₂²	1	1	yes	characteristic
173	#123613	C₂²	1	1	yes	characteristic
174	#123611	C₂²	1	1	yes	characteristic
175	#123608	C₂²	1	1	yes	characteristic
176	#123608	C₂²	1	1	yes	characteristic
177	#123600	C₂²	1	1	yes	characteristic
178	#123598	C₂²	1	1	yes	characteristic
179	#123571	C₂²	1	1	yes	characteristic
180	#123568	C₂²	1	1	yes	characteristic
181	#123562	C₂²	1	1	yes	characteristic
182	#123536	C₂²	1	1	yes	characteristic
183	#123535	C₂²	1	1	yes	characteristic
184	#123531	C₂²	1	1	yes	characteristic
185	#123516	C₂²	1	1	yes	characteristic
186	#123508	C₂²	1	1	yes	characteristic
187	C₂²×#575	C₂³	1	1	yes	characteristic
188	C₂²×#575	C₂³	1	1	yes	characteristic
189	C₂²×#575	C₂³	1	1	yes	characteristic
190	C₂²×#575	C₂³	1	1	yes	characteristic
191	C₂³×AGL(1,ℤ/8)	C₂³	1	1	yes	characteristic
192	C₂³×AGL(1,ℤ/8)	C₂³	1	1	yes	characteristic
193	C₂²×#568	C₂³	1	1	yes	characteristic
194	C₂²×#568	C₂³	1	1	yes	characteristic
195	C₂²×#568	C₂³	1	1	yes	characteristic
196	C₂⁴×M₁₆	C₂³	1	1	yes	characteristic
197	C₂×#3449	C₂³	1	1	yes	characteristic
198	C₂×#3449	C₂³	1	1	yes	characteristic
199	C₂²×#535	C₂³	1	1	yes	characteristic
200	C₂²×#535	C₂³	1	1	yes	characteristic
201	C₂²×#525	C₂³	1	1	yes	characteristic
202	C₂²×#525	C₂³	1	1	yes	characteristic
203	C₂²×#525	C₂³	1	1	yes	characteristic
204	C₂²×#525	C₂³	1	1	yes	characteristic
205	C₂³×#121	C₂³	1	1	yes	characteristic
206	C₂×#3428	C₂³	1	1	yes	characteristic
207	C₂²×#518	C₂³	1	1	yes	characteristic
208	#60182	D₄	1	8	yes	complemented
209	C₂×#2949	D₄	1	4	yes	complemented
210	C₂×#2948	D₄	1	4	yes	complemented
211	C₂×#2930	D₄	1	4	yes	complemented
212	C₂×#2929	D₄	1	4	yes	complemented
213	C₂²×#430	C₂³	1	1	yes	characteristic
214	C₂²×#430	C₂³	1	1	yes	characteristic
215	C₂²×#430	C₂³	1	1	yes	characteristic
216	C₂×#2911	C₂³	1	1	yes	characteristic
217	C₂×#2911	C₂³	1	1	yes	characteristic
218	C₂×#2911	C₂³	1	1	yes	characteristic
219	C₂×#2905	C₂³	1	1	yes	characteristic
220	C₂²×#421	C₂³	1	1	yes	characteristic
221	C₂²×#421	C₂³	1	1	yes	characteristic
222	C₂²×#421	C₂³	1	1	yes	characteristic
223	C₂²×#421	C₂³	1	1	yes	characteristic
224	C₂²×#421	C₂³	1	1	yes	characteristic
225	C₂²×#421	C₂³	1	1	yes	characteristic
226	C₂²×#421	C₂³	1	1	yes	characteristic
227	C₂²×#421	C₂³	1	1	yes	characteristic
228	C₂²×#421	C₂³	1	1	yes	characteristic
229	C₂²×#421	C₂³	1	1	yes	characteristic
230	C₂²×#421	C₂³	1	1	yes	characteristic
231	C₂²×#421	C₂³	1	1	yes	characteristic
232	C₂×#2896	C₂³	1	1	yes	characteristic
233	C₂×#2896	C₂³	1	1	yes	characteristic
234	C₂×#2896	C₂³	1	1	yes	characteristic
235	C₂×#2896	C₂³	1	1	yes	characteristic
236	C₂×#2896	C₂³	1	1	yes	characteristic
237	C₂×#2896	C₂³	1	1	yes	characteristic
238	C₂×#2896	C₂³	1	1	yes	characteristic
239	C₂×#2896	C₂³	1	1	yes	characteristic
240	C₂²×#417	C₂³	1	1	yes	characteristic
241	C₂²×#417	C₂³	1	1	yes	characteristic
242	C₂²×#418	C₂³	1	1	yes	characteristic
243	C₂²×#418	C₂³	1	1	yes	characteristic
244	C₂²×#418	C₂³	1	1	yes	characteristic
245	C₂²×#418	C₂³	1	1	yes	characteristic
246	C₂²×#418	C₂³	1	1	yes	characteristic
247	C₂²×#418	C₂³	1	1	yes	characteristic
248	C₂²×#413	C₂³	1	1	yes	characteristic
249	C₂²×#413	C₂³	1	1	yes	characteristic
250	C₂²×#413	C₂³	1	1	yes	characteristic
251	C₂³×#100	C₂³	1	1	yes	characteristic
252	C₂³×#100	C₂³	1	1	yes	characteristic
253	C₂²×#410	C₂³	1	1	yes	characteristic
254	C₂²×#410	C₂³	1	1	yes	characteristic
255	C₂²×#410	C₂³	1	1	yes	characteristic
256	C₂²×#410	C₂³	1	1	yes	characteristic
257	C₂²×#410	C₂³	1	1	yes	characteristic
258	C₂×#2879	C₂³	1	1	yes	characteristic
259	C₂×#2879	C₂³	1	1	yes	characteristic
260	C₂²×#407	C₂³	1	1	yes	characteristic
261	C₂²×#407	C₂³	1	1	yes	characteristic
262	C₂²×#407	C₂³	1	1	yes	characteristic
263	C₂²×#407	C₂³	1	1	yes	characteristic
264	C₂²×#407	C₂³	1	1	yes	characteristic
265	C₂×#2873	C₂³	1	1	yes	characteristic
266	#34052	C₂³	1	1	yes	characteristic
267	C₂×#2317	C₂³	1	1	yes	characteristic
268	#34044	C₂³	1	1	yes	characteristic
269	#34044	C₂³	1	1	yes	characteristic
270	C₂×#2311	C₂³	1	1	yes	characteristic
271	C₂×#2311	C₂³	1	1	yes	characteristic
272	C₂×#2309	C₂³	1	1	yes	characteristic
273	C₂×#2280	C₂³	1	1	yes	characteristic
274	C₂×#2280	C₂³	1	1	yes	characteristic
275	C₂×#2280	C₂³	1	1	yes	characteristic
276	C₂×#2280	C₂³	1	1	yes	characteristic
277	#20765	D₄	1	4	yes	complemented
278	#20764	D₄	1	4	yes	complemented
279	#20757	D₄	1	8	yes	complemented
280	#20757	D₄	1	8	yes	complemented
281	C₂²×#344	C₂³	1	1	yes	characteristic
282	C₂²×#344	C₂³	1	1	yes	characteristic
283	C₂²×#344	C₂³	1	1	yes	characteristic
284	C₂²×#344	C₂³	1	1	yes	characteristic
285	C₂²×#344	C₂³	1	1	yes	characteristic
286	C₂²×#344	C₂³	1	1	yes	characteristic
287	C₂²×#344	C₂³	1	1	yes	characteristic
288	C₂²×#344	C₂³	1	1	yes	characteristic
289	C₂²×#344	C₂³	1	1	yes	characteristic
290	C₂²×#344	C₂³	1	1	yes	characteristic
291	C₂²×#344	C₂³	1	1	yes	characteristic
292	C₂²×#344	C₂³	1	1	yes	characteristic
293	C₂²×#344	C₂³	1	1	yes	characteristic
294	C₂²×#344	C₂³	1	1	yes	characteristic
295	C₂²×#344	C₂³	1	1	yes	characteristic
296	C₂²×#344	C₂³	1	1	yes	characteristic
297	C₂²×#344	C₂³	1	1	yes	characteristic
298	C₂²×#344	C₂³	1	1	yes	characteristic
299	C₂²×#344	C₂³	1	1	yes	characteristic
300	C₂²×#344	C₂³	1	1	yes	characteristic
301	C₂×#1742	C₂³	1	1	yes	characteristic
302	C₂²×#343	C₂³	1	1	yes	characteristic
303	C₂²×#343	C₂³	1	1	yes	characteristic
304	C₂×#1740	C₂³	1	1	yes	characteristic
305	C₂×#1740	C₂³	1	1	yes	characteristic
306	C₂×#1740	C₂³	1	1	yes	characteristic
307	C₂×#1740	C₂³	1	1	yes	characteristic
308	C₂×#1740	C₂³	1	1	yes	characteristic
309	C₂×#1738	C₂³	1	1	yes	characteristic
310	C₂×#1738	C₂³	1	1	yes	characteristic
311	C₂×#1738	C₂³	1	1	yes	characteristic
312	C₂×#1738	C₂³	1	1	yes	characteristic
313	#20347	C₂³	1	1	yes	characteristic
314	#20347	C₂³	1	1	yes	characteristic
315	#20347	C₂³	1	1	yes	characteristic
316	#20347	C₂³	1	1	yes	characteristic
317	#20347	C₂³	1	1	yes	characteristic
318	#20347	C₂³	1	1	yes	characteristic
319	C₂×#1736	C₂³	1	1	yes	characteristic
320	C₂×#1736	C₂³	1	1	yes	characteristic
321	C₂×#1736	C₂³	1	1	yes	characteristic
322	C₂×#1736	C₂³	1	1	yes	characteristic
323	C₂×#1736	C₂³	1	1	yes	characteristic
324	C₂×#1736	C₂³	1	1	yes	characteristic
325	C₂×#1733	C₂³	1	1	yes	characteristic
326	C₂×#1733	C₂³	1	1	yes	characteristic
327	C₂×#1733	C₂³	1	1	yes	characteristic
328	C₂×#1733	C₂³	1	1	yes	characteristic
329	C₂×#1733	C₂³	1	1	yes	characteristic
330	C₂×#1733	C₂³	1	1	yes	characteristic
331	C₂×#1733	C₂³	1	1	yes	characteristic
332	C₂×#1733	C₂³	1	1	yes	characteristic
333	C₂×#1733	C₂³	1	1	yes	characteristic
334	C₂×#1733	C₂³	1	1	yes	characteristic
335	C₂²×#338	C₂³	1	1	yes	characteristic
336	C₂²×H(3,ℤ/4)	C₂³	1	1	yes	characteristic
337	C₂²×H(3,ℤ/4)	C₂³	1	1	yes	characteristic
338	C₂²×H(3,ℤ/4)	C₂³	1	1	yes	characteristic
339	C₂²×H(3,ℤ/4)	C₂³	1	1	yes	characteristic
340	C₂²×H(3,ℤ/4)	C₂³	1	1	yes	characteristic
341	C₂²×H(3,ℤ/4)	C₂³	1	1	yes	characteristic
342	C₂²×H(3,ℤ/4)	C₂³	1	1	yes	characteristic
343	C₂²×H(3,ℤ/4)	C₂³	1	1	yes	characteristic
344	C₂²×H(3,ℤ/4)	C₂³	1	1	yes	characteristic
345	C₂²×H(3,ℤ/4)	C₂³	1	1	yes	characteristic
346	C₂²×H(3,ℤ/4)	C₂³	1	1	yes	characteristic
347	C₂²×H(3,ℤ/4)	C₂³	1	1	yes	characteristic
348	C₂²×H(3,ℤ/4)	C₂³	1	1	yes	characteristic
349	#20335	C₂³	1	1	yes	characteristic
350	#13795	C₂³	1	1	yes	characteristic
351	C₂³×#41	C₂⁴	1	1	yes	characteristic
352	C₂³×#41	C₂⁴	1	1	yes	characteristic
353	C₂³×#41	C₂⁴	1	1	yes	characteristic
354	C₂³×#41	C₂⁴	1	1	yes	characteristic
355	C₂⁴×D₄	C₂⁴	1	1	yes	characteristic
356	C₂⁵×C₄	C₂⁴	1	1	yes	characteristic
357	C₂×#575	C₂×D₄	1	4	yes	—
358	C₂³×SD₁₆	C₂×D₄	1	2	yes	—
359	C₂³×D₈	C₂×D₄	1	2	yes	—
360	C₂×#568	C₂×D₄	1	4	yes	—
361	C₂×#568	C₂×D₄	1	4	yes	—
362	C₂²×#131	C₂×D₄	1	4	yes	—
363	C₂³×M₁₆	C₂×D₄	1	2	yes	—
364	C₂³×M₁₆	C₂⁴	1	1	yes	characteristic
365	C₂³×M₁₆	C₂⁴	1	1	yes	characteristic
366	C₂³×M₁₆	C₂⁴	1	1	yes	characteristic
367	C₂³×M₁₆	C₂⁴	1	1	yes	characteristic
368	C₂³×M₁₆	C₂⁴	1	1	yes	characteristic
369	C₂³×M₁₆	C₂⁴	1	1	yes	characteristic
370	C₂³×M₁₆	C₂⁴	1	1	yes	characteristic
371	C₂³×M₁₆	C₂⁴	1	1	yes	characteristic
372	C₂³×M₁₆	C₂⁴	1	1	yes	characteristic
373	C₂³×M₁₆	C₂⁴	1	1	yes	characteristic
374	C₂³×M₁₆	C₂⁴	1	1	yes	characteristic
375	C₂³×M₁₆	C₂⁴	1	1	yes	characteristic
376	C₂⁴×C₈	C₂×D₄	1	2	yes	—
377	C₂×#525	C₂×D₄	1	2	yes	—
378	C₂×#525	C₂×D₄	1	2	yes	—
379	C₂×#519	C₂×D₄	1	2	yes	—
380	C₂×#518	C₂×D₄	1	2	yes	—
381	C₂×#518	C₂×D₄	1	4	yes	—
382	C₂²×#117	C₂⁴	1	1	yes	characteristic
383	C₂²×#117	C₂⁴	1	1	yes	characteristic
384	C₂²×#117	C₂⁴	1	1	yes	characteristic
385	C₂²×#117	C₂⁴	1	1	yes	characteristic
386	C₂²×#117	C₂⁴	1	1	yes	characteristic
387	C₂²×#117	C₂⁴	1	1	yes	characteristic
388	C₂²×#117	C₂⁴	1	1	yes	characteristic
389	C₂²×#117	C₂⁴	1	1	yes	characteristic
390	C₂²×#117	C₂⁴	1	1	yes	characteristic
391	C₂²×#117	C₂⁴	1	1	yes	characteristic
392	C₂²×#117	C₂⁴	1	1	yes	characteristic
393	C₂²×#117	C₂⁴	1	1	yes	characteristic
394	C₂³×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
395	C₂×#430	C₂×D₄	1	4	yes	—
396	C₂×#430	C₂×D₄	1	4	yes	—
397	C₂×#430	C₂×D₄	1	4	yes	—
398	#2911	C₂×D₄	1	4	yes	—
399	#2911	C₂×D₄	1	4	yes	—
400	C₂×#427	C₂×D₄	1	4	yes	—
401	C₂×#424	C₂×D₄	1	4	yes	—
402	C₂×#421	C₂×D₄	1	4	yes	—
403	C₂×#421	C₂×D₄	1	4	yes	—
404	C₂×#419	C₂×D₄	1	2	yes	—
405	C₂×#418	C₂×D₄	1	2	yes	—
406	C₂×#418	C₂×D₄	1	4	yes	—
407	C₂×#408	C₂×D₄	1	4	yes	—
408	C₂×#407	C₂×D₄	1	2	yes	—
409	C₂×#407	C₂×D₄	1	2	yes	—
410	#2873	C₂×D₄	1	4	yes	—
411	#2873	C₂×D₄	1	4	yes	—
412	#2873	C₂×D₄	1	4	yes	—
413	#2873	#41	1	4	yes	—
414	C₂×#405	C₂×D₄	1	4	yes	—
415	C₂×#405	C₂×D₄	1	4	yes	—
416	C₂×C₄×M₁₆	C₂×D₄	1	4	yes	—
417	#2285	C₂×D₄	1	4	yes	—
418	C₂×#384	C₂×D₄	1	2	yes	—
419	C₂×#382	C₂×D₄	1	2	yes	—
420	C₂×#344	C₂×D₄	1	4	yes	—
421	C₂×#344	C₂×D₄	1	4	yes	—
422	C₂×#344	C₂×D₄	1	4	yes	—
423	C₂×#344	C₂×D₄	1	4	yes	—
424	#1736	C₂×D₄	1	2	yes	—
425	#1736	C₂×D₄	1	4	yes	—
426	#1736	C₂×D₄	1	2	yes	—
427	#1736	C₂×D₄	1	2	yes	—
428	#1736	C₂×D₄	1	4	yes	—
429	#1736	C₂×D₄	1	2	yes	—
430	C₂×H(3,ℤ/4)	C₂×D₄	1	4	yes	—
431	C₂×H(3,ℤ/4)	C₂×D₄	1	4	yes	—
432	C₂×H(3,ℤ/4)	C₂×D₄	1	4	yes	—
433	C₂×H(3,ℤ/4)	C₂×D₄	1	4	yes	—
434	C₂⁶	H(5,𝔽₂)	1	1	yes	characteristic
435	C₂²×#41	C₂²×D₄	1	2	yes	—
436	C₂²×#41	C₂²×D₄	1	2	yes	—
437	C₂²×#41	C₂²×D₄	1	2	yes	—
438	C₂²×#41	H(5,𝔽₂)	1	2	yes	—
439	C₂²×#41	H(5,𝔽₂)	1	2	yes	—
440	C₂²×#41	H(5,𝔽₂)	1	2	yes	—
441	C₂²×#41	H(5,𝔽₂)	1	2	yes	—
442	C₂²×#41	H(5,𝔽₂)	1	2	yes	—
443	C₂³×Q₈	C₂²×D₄	1	1	yes	characteristic
444	C₂³×Q₈	H(5,𝔽₂)	1	1	yes	characteristic
445	C₂³×Q₈	H(5,𝔽₂)	1	1	yes	characteristic
446	C₂³×Q₈	H(5,𝔽₂)	1	1	yes	characteristic
447	C₂³×D₄	C₂²×D₄	1	2	yes	—
448	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
449	C₂³×D₄	H(5,𝔽₂)	1	2	yes	—
450	C₂³×D₄	H(5,𝔽₂)	1	2	yes	—
451	C₂³×D₄	H(5,𝔽₂)	1	1	yes	characteristic
452	C₂³×D₄	H(5,𝔽₂)	1	1	yes	characteristic
453	C₂³×D₄	H(5,𝔽₂)	1	1	yes	characteristic
454	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
455	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
456	C₂⁴×C₄	H(5,𝔽₂)	1	1	yes	characteristic
457	C₂⁴×C₄	H(5,𝔽₂)	1	1	yes	characteristic
458	C₂⁴×C₄	H(5,𝔽₂)	1	1	yes	characteristic
459	C₂⁴×C₄	C₂⁵	1	1	yes	characteristic
460	C₂²×M₁₆	C₂²×D₄	1	2	yes	—
461	C₂²×M₁₆	C₂²×D₄	1	2	yes	—
462	C₂²×M₁₆	C₂²×D₄	1	2	yes	—
463	C₂²×M₁₆	C₂²×D₄	1	2	yes	—
464	C₂²×M₁₆	C₂²×D₄	1	2	yes	—
465	C₂²×M₁₆	C₂²×D₄	1	2	yes	—
466	C₂²×M₁₆	C₂²×D₄	1	2	yes	—
467	C₂²×M₁₆	C₂²×D₄	1	2	yes	—
468	C₂²×M₁₆	C₂²×D₄	1	2	yes	—
469	C₂²×M₁₆	C₂²×D₄	1	2	yes	—
470	C₂²×M₁₆	C₂²×D₄	1	2	yes	—
471	C₂²×M₁₆	C₂²×D₄	1	2	yes	—
472	C₂²×M₁₆	C₂²×D₄	1	2	yes	—
473	C₂²×M₁₆	C₂²×D₄	1	2	yes	—
474	C₂²×M₁₆	C₂²×D₄	1	2	yes	—
475	C₂²×M₁₆	C₂²×D₄	1	2	yes	—
476	C₂²×M₁₆	C₂²×D₄	1	2	yes	—
477	C₂²×M₁₆	C₂×#41	1	2	yes	—
478	C₂²×M₁₆	C₂×#41	1	2	yes	—
479	C₂³×C₈	C₂²×D₄	1	2	yes	—
480	C₂³×C₈	C₂²×D₄	1	2	yes	—
481	C₂³×C₈	C₂²×D₄	1	2	yes	—
482	C₂×#117	C₂²×D₄	1	2	yes	—
483	C₂×#117	C₂²×D₄	1	2	yes	—
484	C₂×#117	C₂²×D₄	1	2	yes	—
485	C₂×#117	C₂²×D₄	1	2	yes	—
486	C₂×#117	C₂²×D₄	1	2	yes	—
487	C₂×#117	C₂²×D₄	1	2	yes	—
488	C₂×#117	C₂²×D₄	1	2	yes	—
489	C₂×#117	C₂²×D₄	1	2	yes	—
490	C₂×#117	C₂²×D₄	1	2	yes	—
491	C₂×#117	C₂²×D₄	1	2	yes	—
492	C₂×#117	C₂²×D₄	1	2	yes	—
493	C₂×#117	C₂²×D₄	1	2	yes	—
494	C₂×#117	C₂²×D₄	1	2	yes	—
495	C₂×#117	C₂×#41	1	2	yes	—
496	C₂²×C₄⋊C₄	C₂²×D₄	1	2	yes	—
497	C₂²×C₄⋊C₄	C₂²×D₄	1	1	yes	characteristic
498	C₂²×C₄⋊C₄	C₂²×D₄	1	1	yes	characteristic
499	C₂²×C₄²	C₂²×D₄	1	2	yes	—
500	#405	#120	1	16	yes	—
501	#405	#120	1	16	yes	—
502	#405	#121	1	16	yes	—
503	#405	#121	1	16	yes	—
504	C₄×M₁₆	#121	1	16	yes	—
505	C₄×M₁₆	#127	1	16	yes	—
506	C₂×#97	#120	1	8	yes	—
507	C₂×C₄×C₈	#120	1	8	yes	—
508	C₂⁵	#535	1	1	yes	characteristic
509	C₂⁵	#535	1	1	yes	characteristic
510	C₂⁵	C₂×H(5,𝔽₂)	1	1	yes	characteristic
511	C₂²×Q₈	#535	1	2	yes	—
512	C₂²×Q₈	#535	1	2	yes	—
513	C₂²×Q₈	#535	1	2	yes	—
514	C₂²×Q₈	#535	1	2	yes	—
515	C₂²×D₄	#535	1	2	yes	—
516	C₂²×D₄	#535	1	4	yes	—
517	C₂²×D₄	#535	1	2	yes	—
518	C₂²×D₄	#535	1	2	yes	—
519	C₂²×D₄	#535	1	2	yes	—
520	C₂³×C₄	#535	1	1	yes	characteristic
521	C₂³×C₄	#535	1	1	yes	characteristic
522	C₂³×C₄	C₂³×D₄	1	1	yes	characteristic
523	C₂³×C₄	C₂³×D₄	1	1	yes	characteristic
524	C₂³×C₄	C₂³×D₄	1	1	yes	characteristic
525	C₂³×C₄	C₂³×D₄	1	1	yes	characteristic
526	C₂³×C₄	C₂³×D₄	1	1	yes	characteristic
527	C₂³×C₄	C₂³×D₄	1	1	yes	characteristic
528	C₂³×C₄	C₂²×#41	1	1	yes	characteristic
529	C₂³×C₄	C₂×H(5,𝔽₂)	1	1	yes	characteristic
530	C₂³×C₄	C₂×H(5,𝔽₂)	1	1	yes	characteristic
531	C₂³×C₄	C₂×H(5,𝔽₂)	1	1	yes	characteristic
532	C₂³×C₄	C₂×H(5,𝔽₂)	1	1	yes	characteristic
533	C₂³×C₄	C₂×H(5,𝔽₂)	1	1	yes	characteristic
534	C₂³×C₄	C₂×H(5,𝔽₂)	1	1	yes	characteristic
535	C₂³×C₄	C₂×H(5,𝔽₂)	1	1	yes	characteristic
536	C₂³×C₄	C₂×H(5,𝔽₂)	1	1	yes	characteristic
537	C₂³×C₄	C₂×H(5,𝔽₂)	1	1	yes	characteristic
538	C₂³×C₄	C₂×H(5,𝔽₂)	1	1	yes	characteristic
539	C₂³×C₄	C₂×H(5,𝔽₂)	1	1	yes	characteristic
540	C₂³×C₄	#585	1	1	yes	characteristic
541	C₂³×C₄	#585	1	1	yes	characteristic
542	C₂³×C₄	#585	1	1	yes	characteristic
543	C₂³×C₄	#585	1	1	yes	characteristic
544	C₂³×C₄	#585	1	1	yes	characteristic
545	C₂³×C₄	#585	1	1	yes	characteristic
546	C₂³×C₄	#585	1	1	yes	characteristic
547	C₂³×C₄	#585	1	1	yes	characteristic
548	C₂³×C₄	#585	1	1	yes	characteristic
549	C₂³×C₄	#585	1	1	yes	characteristic
550	C₂³×C₄	#585	1	1	yes	characteristic
551	C₂³×C₄	#585	1	1	yes	characteristic
552	C₂×M₁₆	C₂×#120	1	4	yes	—
553	C₂×M₁₆	C₂×#120	1	4	yes	—
554	C₂×M₁₆	C₂×#121	1	4	yes	—
555	C₂×M₁₆	C₂×#121	1	4	yes	—
556	C₂×M₁₆	C₂×#121	1	4	yes	—
557	C₂×M₁₆	C₂×#121	1	4	yes	—
558	C₂×M₁₆	C₂×#127	1	4	yes	—
559	C₂×M₁₆	C₂×#127	1	4	yes	—
560	C₂²×C₈	C₂×#120	1	4	yes	—
561	C₂²×C₈	C₂×#120	1	4	yes	—
562	C₂²×C₈	C₂×#120	1	4	yes	—
563	C₂²×C₈	C₂×#120	1	4	yes	—
564	C₂²×C₈	C₂×#121	1	4	yes	—
565	C₂²×C₈	C₂×#121	1	4	yes	—
566	#117	C₂×#120	1	4	yes	—
567	#117	C₂×#120	1	4	yes	—
568	#117	C₂×#121	1	4	yes	—
569	#117	C₂×#121	1	4	yes	—
570	C₂×C₄²	C₂×#120	1	4	yes	—
571	C₂×C₄²	C₂×#121	1	4	yes	—
572	C₂×C₄²	C₂×#127	1	4	yes	—
573	#97	#392	1	32	yes	complemented
574	C₄×C₈	#392	1	32	yes	complemented
575	C₂⁴	C₂×#535	1	1	yes	characteristic
576	C₂⁴	#3484	1	1	yes	characteristic
577	C₂⁴	#3484	1	1	yes	characteristic
578	C₂⁴	#3488	1	1	yes	characteristic
579	C₂⁴	#3488	1	1	yes	characteristic
580	C₂⁴	#3488	1	1	yes	characteristic
581	C₂⁴	#3494	1	1	yes	characteristic
582	C₂⁴	#3532	1	1	yes	characteristic
583	C₂⁴	#3532	1	1	yes	characteristic
584	C₂⁴	#3534	1	1	yes	characteristic
585	C₂⁴	#3534	1	1	yes	characteristic
586	C₂⁴	#3534	1	1	yes	characteristic
587	C₂⁴	#3534	1	1	yes	characteristic
588	C₂⁴	#3560	1	1	yes	characteristic
589	C₂⁴	#3560	1	1	yes	characteristic
590	C₂²×C₄	C₂²×#120	1	1	yes	characteristic
591	C₂²×C₄	C₂²×#120	1	1	yes	characteristic
592	C₂²×C₄	C₂²×#120	1	1	yes	characteristic
593	C₂²×C₄	C₂²×#121	1	1	yes	characteristic
594	C₂²×C₄	C₂²×#121	1	1	yes	characteristic
595	C₂²×C₄	C₂²×#121	1	1	yes	characteristic
596	C₂²×C₄	C₂²×#127	1	1	yes	characteristic
597	C₂²×C₄	C₂×#535	1	1	yes	characteristic
598	C₂²×C₄	C₂×#535	1	1	yes	characteristic
599	C₂²×C₄	C₂×#535	1	1	yes	characteristic
600	C₂²×C₄	C₂×#535	1	1	yes	characteristic
601	C₂²×C₄	C₂×#535	1	1	yes	characteristic
602	C₂²×C₄	#3449	1	1	yes	characteristic
603	C₂²×C₄	#3449	1	1	yes	characteristic
604	C₂²×C₄	#3449	1	1	yes	characteristic
605	C₂²×C₄	#3449	1	1	yes	characteristic
606	C₂²×C₄	#3449	1	1	yes	characteristic
607	C₂²×C₄	#3449	1	1	yes	characteristic
608	C₂²×C₄	#3484	1	1	yes	characteristic
609	C₂²×C₄	#3484	1	1	yes	characteristic
610	C₂²×C₄	#3484	1	1	yes	characteristic
611	C₂²×C₄	#3484	1	1	yes	characteristic
612	C₂²×C₄	#3484	1	1	yes	characteristic
613	C₂²×C₄	#3484	1	1	yes	characteristic
614	C₂²×C₄	#3484	1	1	yes	characteristic
615	C₂²×C₄	#3484	1	1	yes	characteristic
616	C₂²×C₄	#3484	1	1	yes	characteristic
617	C₂²×C₄	#3484	1	1	yes	characteristic
618	C₂²×C₄	#3485	1	1	yes	characteristic
619	C₂²×C₄	#3485	1	1	yes	characteristic
620	C₂²×C₄	#3485	1	1	yes	characteristic
621	C₂²×C₄	#3485	1	1	yes	characteristic
622	C₂²×C₄	#3485	1	1	yes	characteristic
623	C₂²×C₄	#3485	1	1	yes	characteristic
624	C₂²×C₄	#3487	1	1	yes	characteristic
625	C₂²×C₄	#3487	1	1	yes	characteristic
626	C₂²×C₄	#3487	1	1	yes	characteristic
627	C₂²×C₄	#3487	1	1	yes	characteristic
628	C₂²×C₄	#3487	1	1	yes	characteristic
629	C₂²×C₄	#3487	1	1	yes	characteristic
630	C₂²×C₄	#3488	1	1	yes	characteristic
631	C₂²×C₄	#3488	1	1	yes	characteristic
632	C₂²×C₄	#3488	1	1	yes	characteristic
633	C₂²×C₄	#3488	1	1	yes	characteristic
634	C₂²×C₄	#3488	1	1	yes	characteristic
635	C₂²×C₄	#3488	1	1	yes	characteristic
636	C₂²×C₄	#3488	1	1	yes	characteristic
637	C₂²×C₄	#3488	1	1	yes	characteristic
638	C₂²×C₄	#3488	1	1	yes	characteristic
639	C₂²×C₄	#3488	1	1	yes	characteristic
640	C₂²×C₄	#3488	1	1	yes	characteristic
641	C₂²×C₄	#3488	1	1	yes	characteristic
642	C₂²×C₄	#3488	1	1	yes	characteristic
643	C₂²×C₄	#3488	1	1	yes	characteristic
644	C₂²×C₄	#3488	1	1	yes	characteristic
645	C₂²×C₄	#3488	1	1	yes	characteristic
646	C₂²×C₄	#3488	1	1	yes	characteristic
647	C₂²×C₄	#3488	1	1	yes	characteristic
648	C₂²×C₄	#3488	1	1	yes	characteristic
649	C₂²×C₄	#3488	1	1	yes	characteristic
650	C₂²×C₄	#3488	1	1	yes	characteristic
651	C₂²×C₄	#3488	1	1	yes	characteristic
652	C₂²×C₄	#3488	1	1	yes	characteristic
653	C₂²×C₄	#3488	1	1	yes	characteristic
654	C₂²×C₄	#3488	1	1	yes	characteristic
655	C₂²×C₄	#3488	1	1	yes	characteristic
656	C₂²×C₄	#3488	1	1	yes	characteristic
657	C₂²×C₄	#3488	1	1	yes	characteristic
658	C₂²×C₄	#3488	1	1	yes	characteristic
659	C₂²×C₄	#3488	1	1	yes	characteristic
660	C₂²×C₄	#3488	1	1	yes	characteristic
661	C₂²×C₄	#3488	1	1	yes	characteristic
662	C₂²×C₄	#3488	1	1	yes	characteristic
663	C₂²×C₄	#3494	1	1	yes	characteristic
664	C₂²×C₄	#3494	1	1	yes	characteristic
665	C₂²×C₄	#3494	1	1	yes	characteristic
666	C₂²×C₄	#3494	1	1	yes	characteristic
667	C₂²×C₄	#3494	1	1	yes	characteristic
668	C₂²×C₄	#3494	1	1	yes	characteristic
669	C₂²×C₄	#3494	1	1	yes	characteristic
670	C₂²×C₄	#3494	1	1	yes	characteristic
671	C₂²×C₄	#3494	1	1	yes	characteristic
672	C₂²×C₄	#3494	1	1	yes	characteristic
673	C₂²×C₄	#3494	1	1	yes	characteristic
674	C₂²×C₄	#3532	1	1	yes	characteristic
675	C₂²×C₄	#3532	1	1	yes	characteristic
676	C₂²×C₄	#3532	1	1	yes	characteristic
677	C₂²×C₄	#3532	1	1	yes	characteristic
678	C₂²×C₄	#3532	1	1	yes	characteristic
679	C₂²×C₄	#3532	1	1	yes	characteristic
680	C₂²×C₄	#3534	1	1	yes	characteristic
681	C₂²×C₄	#3534	1	1	yes	characteristic
682	C₂²×C₄	#3534	1	1	yes	characteristic
683	C₂²×C₄	#3534	1	1	yes	characteristic
684	C₂²×C₄	#3534	1	1	yes	characteristic
685	C₂²×C₄	#3534	1	1	yes	characteristic
686	C₂²×C₄	#3534	1	1	yes	characteristic
687	C₂²×C₄	#3534	1	1	yes	characteristic
688	C₂²×C₄	#3534	1	1	yes	characteristic
689	C₂²×C₄	#3534	1	1	yes	characteristic
690	C₂²×C₄	#3534	1	1	yes	characteristic
691	C₂²×C₄	#3534	1	1	yes	characteristic
692	C₂²×C₄	#3534	1	1	yes	characteristic
693	C₂²×C₄	#3534	1	1	yes	characteristic
694	C₂²×C₄	#3534	1	1	yes	characteristic
695	C₂²×C₄	#3534	1	1	yes	characteristic
696	C₂²×C₄	#3534	1	1	yes	characteristic
697	C₂²×C₄	#3534	1	1	yes	characteristic
698	C₂²×C₄	#3534	1	1	yes	characteristic
699	C₂²×C₄	#3534	1	1	yes	characteristic
700	C₂²×C₄	#3560	1	1	yes	characteristic
701	C₂²×C₄	#3560	1	1	yes	characteristic
702	C₂²×C₄	#3560	1	1	yes	characteristic
703	C₂²×C₄	#3560	1	1	yes	characteristic
704	C₂²×C₄	#3560	1	1	yes	characteristic
705	C₂²×C₄	#3560	1	1	yes	characteristic
706	C₂²×C₄	#3560	1	1	yes	characteristic
707	C₂²×C₄	#3560	1	1	yes	characteristic
708	C₂²×C₄	#3560	1	1	yes	characteristic
709	C₂²×C₄	#3560	1	1	yes	characteristic
710	C₂²×C₄	#3560	1	1	yes	characteristic
711	C₂²×C₄	#3560	1	1	yes	characteristic
712	C₂²×C₄	#3560	1	1	yes	characteristic
713	C₂²×C₄	#3560	1	1	yes	characteristic
714	C₂²×C₄	#3560	1	1	yes	characteristic
715	C₂²×C₄	#3560	1	1	yes	characteristic
716	C₂²×C₄	#3560	1	1	yes	characteristic
717	C₂²×C₄	#3560	1	1	yes	characteristic
718	C₂²×C₄	#3560	1	1	yes	characteristic
719	C₂²×C₄	#3560	1	1	yes	characteristic
720	C₂²×C₄	#3560	1	1	yes	characteristic
721	C₂²×C₄	#3560	1	1	yes	characteristic
722	C₂²×C₄	#3567	1	1	yes	characteristic
723	C₂²×C₄	#3567	1	1	yes	characteristic
724	C₂²×C₄	#3567	1	1	yes	characteristic
725	C₂²×C₄	#3567	1	1	yes	characteristic
726	C₂²×C₄	#3567	1	1	yes	characteristic
727	C₂²×C₄	#3567	1	1	yes	characteristic
728	C₂²×C₄	#3567	1	1	yes	characteristic
729	C₂²×C₄	#3567	1	1	yes	characteristic
730	C₂×C₈	C₂×#392	1	8	yes	—
731	C₂×C₈	C₂×#392	1	8	yes	—
732	C₄²	C₂×#392	1	8	yes	—
733	C₂³	#35222	1	1	yes	characteristic
734	C₂³	#35250	1	1	yes	characteristic
735	C₂³	#35252	1	1	yes	characteristic
736	C₂³	#35512	1	1	yes	characteristic
737	C₂³	#35514	1	1	yes	characteristic
738	C₂³	#35563	1	1	yes	characteristic
739	C₂³	#35565	1	1	yes	characteristic
740	C₂³	#40588	1	1	yes	characteristic
741	C₂³	#40588	1	1	yes	characteristic
742	C₂³	#40588	1	1	yes	characteristic
743	C₂³	#40588	1	1	yes	characteristic
744	C₂³	#40588	1	1	yes	characteristic
745	C₂³	#40606	1	1	yes	characteristic
746	C₂³	#40606	1	1	yes	characteristic
747	C₂³	#40606	1	1	yes	characteristic
748	C₂³	#41410	1	1	yes	characteristic
749	C₂³	#41410	1	1	yes	characteristic
750	C₂³	#41410	1	1	yes	characteristic
751	C₂³	#41420	1	1	yes	characteristic
752	C₂³	#47704	1	1	yes	characteristic
753	C₂³	#47704	1	1	yes	characteristic
754	C₂³	#47706	1	1	yes	characteristic
755	C₂³	#47706	1	1	yes	characteristic
756	C₂³	#50644	1	1	yes	characteristic
757	C₂³	#50644	1	1	yes	characteristic
758	C₂³	#50644	1	1	yes	characteristic
759	C₂³	#50644	1	1	yes	characteristic
760	C₂³	#50864	1	1	yes	characteristic
761	C₂³	#50864	1	1	yes	characteristic
762	C₂³	#50864	1	1	yes	characteristic
763	C₂³	#50864	1	1	yes	characteristic
764	C₂³	#50864	1	1	yes	characteristic
765	C₂³	#50864	1	1	yes	characteristic
766	C₂³	#50864	1	1	yes	characteristic
767	C₂³	#50864	1	1	yes	characteristic
768	C₂×C₄	C₂²×#392	1	1	yes	characteristic
769	C₂×C₄	#35149	1	1	yes	characteristic
770	C₂×C₄	#35149	1	1	yes	characteristic
771	C₂×C₄	#35149	1	1	yes	characteristic
772	C₂×C₄	#35222	1	1	yes	characteristic
773	C₂×C₄	#35222	1	1	yes	characteristic
774	C₂×C₄	#35250	1	1	yes	characteristic
775	C₂×C₄	#35250	1	1	yes	characteristic
776	C₂×C₄	#35250	1	1	yes	characteristic
777	C₂×C₄	#35250	1	1	yes	characteristic
778	C₂×C₄	#35250	1	1	yes	characteristic
779	C₂×C₄	#35252	1	1	yes	characteristic
780	C₂×C₄	#35252	1	1	yes	characteristic
781	C₂×C₄	#35252	1	1	yes	characteristic
782	C₂×C₄	#35252	1	1	yes	characteristic
783	C₂×C₄	#35252	1	1	yes	characteristic
784	C₂×C₄	#35512	1	1	yes	characteristic
785	C₂×C₄	#35512	1	1	yes	characteristic
786	C₂×C₄	#35512	1	1	yes	characteristic
787	C₂×C₄	#35512	1	1	yes	characteristic
788	C₂×C₄	#35512	1	1	yes	characteristic
789	C₂×C₄	#35514	1	1	yes	characteristic
790	C₂×C₄	#35514	1	1	yes	characteristic
791	C₂×C₄	#35514	1	1	yes	characteristic
792	C₂×C₄	#35514	1	1	yes	characteristic
793	C₂×C₄	#35514	1	1	yes	characteristic
794	C₂×C₄	#35563	1	1	yes	characteristic
795	C₂×C₄	#35563	1	1	yes	characteristic
796	C₂×C₄	#35563	1	1	yes	characteristic
797	C₂×C₄	#35563	1	1	yes	characteristic
798	C₂×C₄	#35563	1	1	yes	characteristic
799	C₂×C₄	#35565	1	1	yes	characteristic
800	C₂×C₄	#35565	1	1	yes	characteristic
801	C₂×C₄	#35565	1	1	yes	characteristic
802	C₂×C₄	#35565	1	1	yes	characteristic
803	C₂×C₄	#35565	1	1	yes	characteristic
804	C₂×C₄	#40588	1	1	yes	characteristic
805	C₂×C₄	#40588	1	1	yes	characteristic
806	C₂×C₄	#40588	1	1	yes	characteristic
807	C₂×C₄	#40588	1	1	yes	characteristic
808	C₂×C₄	#40588	1	1	yes	characteristic
809	C₂×C₄	#40588	1	1	yes	characteristic
810	C₂×C₄	#40588	1	1	yes	characteristic
811	C₂×C₄	#40606	1	1	yes	characteristic
812	C₂×C₄	#40606	1	1	yes	characteristic
813	C₂×C₄	#40606	1	1	yes	characteristic
814	C₂×C₄	#40606	1	1	yes	characteristic
815	C₂×C₄	#40606	1	1	yes	characteristic
816	C₂×C₄	#40606	1	1	yes	characteristic
817	C₂×C₄	#40606	1	1	yes	characteristic
818	C₂×C₄	#40606	1	1	yes	characteristic
819	C₂×C₄	#40606	1	1	yes	characteristic
820	C₂×C₄	#41410	1	1	yes	characteristic
821	C₂×C₄	#41410	1	1	yes	characteristic
822	C₂×C₄	#41410	1	1	yes	characteristic
823	C₂×C₄	#41410	1	1	yes	characteristic
824	C₂×C₄	#41410	1	1	yes	characteristic
825	C₂×C₄	#41410	1	1	yes	characteristic
826	C₂×C₄	#41410	1	1	yes	characteristic
827	C₂×C₄	#41410	1	1	yes	characteristic
828	C₂×C₄	#41410	1	1	yes	characteristic
829	C₂×C₄	#41420	1	1	yes	characteristic
830	C₂×C₄	#41420	1	1	yes	characteristic
831	C₂×C₄	#41420	1	1	yes	characteristic
832	C₂×C₄	#41420	1	1	yes	characteristic
833	C₂×C₄	#41420	1	1	yes	characteristic
834	C₂×C₄	#41420	1	1	yes	characteristic
835	C₂×C₄	#41420	1	1	yes	characteristic
836	C₂×C₄	#41420	1	1	yes	characteristic
837	C₂×C₄	#41420	1	1	yes	characteristic
838	C₂×C₄	#41420	1	1	yes	characteristic
839	C₂×C₄	#41420	1	1	yes	characteristic
840	C₂×C₄	#47704	1	1	yes	characteristic
841	C₂×C₄	#47704	1	1	yes	characteristic
842	C₂×C₄	#47704	1	1	yes	characteristic
843	C₂×C₄	#47704	1	1	yes	characteristic
844	C₂×C₄	#47704	1	1	yes	characteristic
845	C₂×C₄	#47704	1	1	yes	characteristic
846	C₂×C₄	#47706	1	1	yes	characteristic
847	C₂×C₄	#47706	1	1	yes	characteristic
848	C₂×C₄	#47706	1	1	yes	characteristic
849	C₂×C₄	#47706	1	1	yes	characteristic
850	C₂×C₄	#47706	1	1	yes	characteristic
851	C₂×C₄	#47706	1	1	yes	characteristic
852	C₂×C₄	#50644	1	1	yes	characteristic
853	C₂×C₄	#50644	1	1	yes	characteristic
854	C₂×C₄	#50644	1	1	yes	characteristic
855	C₂×C₄	#50644	1	1	yes	characteristic
856	C₂×C₄	#50644	1	1	yes	characteristic
857	C₂×C₄	#50644	1	1	yes	characteristic
858	C₂×C₄	#50644	1	1	yes	characteristic
859	C₂×C₄	#50644	1	1	yes	characteristic
860	C₂×C₄	#50644	1	1	yes	characteristic
861	C₂×C₄	#50644	1	1	yes	characteristic
862	C₂×C₄	#50644	1	1	yes	characteristic
863	C₂×C₄	#50644	1	1	yes	characteristic
864	C₂×C₄	#50644	1	1	yes	characteristic
865	C₂×C₄	#50644	1	1	yes	characteristic
866	C₂×C₄	#50644	1	1	yes	characteristic
867	C₂×C₄	#50644	1	1	yes	characteristic
868	C₂×C₄	#50644	1	1	yes	characteristic
869	C₂×C₄	#50644	1	1	yes	characteristic
870	C₂×C₄	#50644	1	1	yes	characteristic
871	C₂×C₄	#50644	1	1	yes	characteristic
872	C₂×C₄	#50864	1	1	yes	characteristic
873	C₂×C₄	#50864	1	1	yes	characteristic
874	C₂×C₄	#50864	1	1	yes	characteristic
875	C₂×C₄	#50864	1	1	yes	characteristic
876	C₂×C₄	#50864	1	1	yes	characteristic
877	C₂×C₄	#50864	1	1	yes	characteristic
878	C₂×C₄	#50864	1	1	yes	characteristic
879	C₂×C₄	#50864	1	1	yes	characteristic
880	C₂×C₄	#50864	1	1	yes	characteristic
881	C₂×C₄	#50864	1	1	yes	characteristic
882	C₂×C₄	#50864	1	1	yes	characteristic
883	C₂×C₄	#50864	1	1	yes	characteristic
884	C₂×C₄	#50864	1	1	yes	characteristic
885	C₂×C₄	#50864	1	1	yes	characteristic
886	C₂×C₄	#50864	1	1	yes	characteristic
887	C₂×C₄	#50864	1	1	yes	characteristic
888	C₂²	#4388540	1	1	yes	characteristic
889	C₂²	#4388540	1	1	yes	characteristic
890	C₂²	#4388540	1	1	yes	characteristic
891	C₂²	#4388540	1	1	yes	characteristic
892	C₂²	#4388540	1	1	yes	characteristic
893	C₂²	#4388540	1	1	yes	characteristic
894	C₂²	#4421184	1	1	yes	characteristic
895	C₂²	#4421184	1	1	yes	characteristic
896	C₂²	#4421184	1	1	yes	characteristic
897	C₂²	#4421184	1	1	yes	characteristic
898	C₂²	#4422091	1	1	yes	characteristic
899	C₂²	#4422091	1	1	yes	characteristic
900	C₂²	#5025123	1	1	yes	characteristic
901	C₂²	#5025123	1	1	yes	characteristic
902	C₂²	#5956073	1	1	yes	characteristic
903	C₄	#4388540	1	1	yes	characteristic
904	C₄	#4388540	1	1	yes	characteristic
905	C₄	#4388540	1	1	yes	characteristic
906	C₄	#4388540	1	1	yes	characteristic
907	C₄	#4388540	1	1	yes	characteristic
908	C₄	#4388540	1	1	yes	characteristic
909	C₄	#4421184	1	1	yes	characteristic
910	C₄	#4421184	1	1	yes	characteristic
911	C₄	#4422091	1	1	yes	characteristic
912	C₄	#4422091	1	1	yes	characteristic
913	C₄	#4422091	1	1	yes	characteristic
914	C₄	#4422091	1	1	yes	characteristic
915	C₄	#5025123	1	1	yes	characteristic
916	C₄	#5025123	1	1	yes	characteristic
917	C₄	#5956073	1	1	yes	characteristic
918	C₄	#5956073	1	1	yes	characteristic
919	C₂	#72216037	1	1	yes	characteristic
920	C₂	#72233928	1	1	yes	characteristic
921	C₂	#72264914	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²	#4421184
commutator, Frattini, cosocle	C₂⁴×C₄	C₂⁵
LCS	G ▷ C₂⁴×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂² ◁ C₂⁴×C₄ ◁ G
LECS	G ▷ C₂⁴×C₄ ▷ C₂ ▷ C₁

Complements

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

N	H ≅ G/N	type
1. #72265574	C₂	semidirect
2. #72265573	C₂	semidirect
3. #72265570	C₂	semidirect
4. #72265565	C₂	semidirect
5. #72265560	C₂	semidirect
6. #72265556	C₂	semidirect
7. #72265550	C₂	semidirect
8. #72265544	C₂	semidirect
9. #72265539	C₂	semidirect
10. #72265536	C₂	semidirect
11. #72265531	C₂	semidirect
12. #72265528	C₂	semidirect
13. #72265526	C₂	semidirect
14. #72265350	C₂	semidirect
15. #72265248	C₂	semidirect
16. C₂×#382863	C₂	semidirect
17. C₂×#382865	C₂	semidirect
18. C₂×#6462906	C₂	semidirect
19. C₂×#6462912	C₂	semidirect
20. #72250855	C₂	semidirect
21. #72239650	C₂	semidirect
22. #72239603	C₂	semidirect
23. #72239575	C₂	semidirect
24. #72239546	C₂	semidirect
25. #72239429	C₂	semidirect
26. #72239324	C₂	semidirect
27. #72239267	C₂	semidirect
28. #72238753	C₂	semidirect
29. #72238738	C₂	semidirect
30. #72237189	C₂	semidirect
31. #72237171	C₂	semidirect
208. #60182	D₄	semidirect
209. C₂×#2949	D₄	semidirect
210. C₂×#2948	D₄	semidirect
211. C₂×#2930	D₄	semidirect
212. C₂×#2929	D₄	semidirect
277. #20765	D₄	semidirect
278. #20764	D₄	semidirect
279. #20757	D₄	semidirect
280. #20757	D₄	semidirect
573. #97	#392	semidirect
574. C₄×C₈	#392	semidirect

Maximal subgroups

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

subgroup	index
#72265574	2
#72265573	2
#72265570	2
#72265565	2
#72265560	2
#72265556	2
#72265550	2
#72265544	2
#72265539	2
#72265536	2
#72265531	2
#72265528	2
#72265526	2
#72265350	2
#72265248	2
C₂×#382863	2
C₂×#382865	2
C₂×#6462906	2
C₂×#6462912	2
#72250855	2
#72239650	2
#72239603	2
#72239575	2
#72239546	2
#72239429	2
#72239324	2
#72239267	2
#72238753	2
#72238738	2
#72237189	2
#72237171	2