Subgroups — #72225136

Order 4096.

At least 6726 conjugacy classes of subgroups; only the 1185 normal subgroups are shown.

The subgroup lattice has 804 nodes (normal subgroups only) — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#72225121	C₂	1	1	yes	maximal, characteristic, complemented
2	#72225118	C₂	1	1	yes	maximal, characteristic, complemented
3	#72225110	C₂	1	1	yes	maximal, characteristic, complemented
4	#72225107	C₂	1	1	yes	maximal, characteristic, complemented
5	#72225104	C₂	1	2	yes	maximal, complemented
6	#72225102	C₂	1	1	yes	maximal, characteristic, complemented
7	#72225096	C₂	1	1	yes	maximal, characteristic, complemented
8	#72225094	C₂	1	2	yes	maximal, complemented
9	#72225092	C₂	1	1	yes	maximal, characteristic, complemented
10	#72225089	C₂	1	2	yes	maximal, complemented
11	#72225088	C₂	1	2	yes	maximal, complemented
12	#72225087	C₂	1	1	yes	maximal, characteristic, complemented
13	#72225084	C₂	1	2	yes	maximal, complemented
14	#72225083	C₂²	1	2	yes	complemented
15	#72225082	C₂²	1	2	yes	complemented
16	#72225081	C₂²	1	2	yes	complemented
17	#72225080	C₂²	1	2	yes	complemented
18	#72225079	C₂²	1	2	yes	complemented
19	#72225078	C₂²	1	2	yes	complemented
20	#72225077	C₂²	1	2	yes	complemented
21	#72225075	C₂²	1	2	yes	complemented
22	#72225073	C₂	1	2	yes	maximal, complemented
23	#72225070	C₂²	1	2	yes	—
24	#72225070	C₂²	1	2	yes	complemented
25	#72225068	C₂²	1	2	yes	complemented
26	#72225068	C₂²	1	2	yes	complemented
27	#72225065	C₂	1	2	yes	maximal, complemented
28	#72225062	C₂²	1	2	yes	complemented
29	#72225061	C₂²	1	2	yes	—
30	#72225060	C₂²	1	2	yes	complemented
31	#72225059	C₂²	1	2	yes	complemented
32	#72225058	C₂²	1	2	yes	complemented
33	#72225057	C₂²	1	2	yes	complemented
34	#72225056	C₂²	1	2	yes	complemented
35	#72225055	C₂²	1	2	yes	—
36	#72225054	C₂	1	2	yes	maximal, complemented
37	#72225050	C₂²	1	2	yes	complemented
38	#72225050	C₂²	1	2	yes	complemented
39	#72225048	C₂²	1	2	yes	complemented
40	#72225048	C₂²	1	2	yes	complemented
41	#72225046	C₂	1	1	yes	maximal, characteristic, complemented
42	#72225043	C₂²	1	1	yes	characteristic
43	#72225042	C₂²	1	1	yes	characteristic
44	#72225041	C₂²	1	1	yes	characteristic
45	#72225040	C₂²	1	2	yes	complemented
46	#72225039	C₂²	1	2	yes	complemented
47	#72225037	C₂²	1	1	yes	characteristic
48	#72225036	C₂²	1	2	yes	complemented
49	#72225034	C₂²	1	2	yes	complemented
50	#72225032	C₂	1	1	yes	maximal, characteristic, complemented
51	#72225029	C₂²	1	1	yes	characteristic, complemented
52	#72225028	C₂²	1	1	yes	characteristic, complemented
53	#72225027	C₂²	1	2	yes	complemented
54	#72225026	C₂²	1	2	yes	complemented
55	#72225025	C₂²	1	1	yes	characteristic, complemented
56	#72225024	C₂²	1	2	yes	complemented
57	#72225023	C₂²	1	2	yes	complemented
58	#72225022	C₂²	1	1	yes	characteristic, complemented
59	#72225019	C₂	1	1	yes	maximal, characteristic
60	#72225016	C₄	1	1	yes	characteristic
61	#72225014	C₄	1	1	yes	characteristic
62	#72225012	C₄	1	1	yes	characteristic
63	#72225010	C₄	1	1	yes	characteristic
64	#72225008	C₄	1	2	yes	—
65	#72225006	C₄	1	2	yes	—
66	#72225004	C₄	1	1	yes	characteristic
67	#72225002	C₄	1	1	yes	characteristic
68	#72225000	C₄	1	2	yes	—
69	#72224998	C₄	1	2	yes	—
70	#72224996	C₄	1	1	yes	characteristic
71	#72224994	C₄	1	1	yes	characteristic
72	#72224992	C₂²	1	1	yes	characteristic
73	#72224991	C₂²	1	1	yes	characteristic
74	#72224990	C₂²	1	1	yes	characteristic
75	#72224989	C₂²	1	2	yes	—
76	#72224988	C₂²	1	2	yes	—
77	#72224987	C₂²	1	1	yes	characteristic
78	#72224985	C₂²	1	2	yes	—
79	#72224983	C₂²	1	2	yes	—
80	#72224981	C₂	1	1	yes	maximal, characteristic, complemented
81	#72224979	C₂²	1	1	yes	characteristic, complemented
82	#72224978	C₂²	1	1	yes	characteristic, complemented
83	#72224977	C₂²	1	1	yes	characteristic, complemented
84	#72224976	C₂²	1	2	yes	complemented
85	#72224975	C₂²	1	2	yes	complemented
86	#72224974	C₂²	1	1	yes	characteristic, complemented
87	#72224973	C₂²	1	2	yes	complemented
88	#72224971	C₂²	1	2	yes	complemented
89	#72224968	C₂	1	1	yes	maximal, characteristic, complemented
90	#72224956	C₂²	1	1	yes	characteristic, complemented
91	#72224955	C₂²	1	1	yes	characteristic, complemented
92	#72224954	C₂²	1	2	yes	complemented
93	#72224951	C₂²	1	1	yes	characteristic, complemented
94	#72224949	C₂²	1	2	yes	complemented
95	#72224948	C₂²	1	1	yes	characteristic, complemented
96	#72224946	C₂²	1	2	yes	complemented
97	#72224944	C₂²	1	2	yes	complemented
98	#72223653	C₂²	1	2	yes	complemented
99	#72223653	C₂²	1	2	yes	complemented
100	#72223646	C₂²	1	2	yes	—
101	#72223646	C₂²	1	2	yes	complemented
102	#72217290	C₂²	1	1	yes	characteristic
103	#72217272	C₂²	1	1	yes	characteristic
104	#72217250	C₂	1	1	yes	maximal, characteristic, complemented
105	#72217231	C₂²	1	1	yes	characteristic, complemented
106	#72217224	C₂²	1	2	yes	complemented
107	#72217219	C₂²	1	1	yes	characteristic, complemented
108	#72217215	C₂²	1	1	yes	characteristic, complemented
109	#72217203	C₂²	1	2	yes	complemented
110	#72217199	C₂²	1	1	yes	characteristic, complemented
111	#72217188	C₂²	1	2	yes	complemented
112	#72217185	C₂²	1	2	yes	complemented
113	#72217183	C₂²	1	1	yes	characteristic
114	#72217183	C₂²	1	1	yes	characteristic
115	#72217162	C₂	1	1	yes	maximal, characteristic, complemented
116	#72216759	C₂²	1	1	yes	characteristic
117	#72216759	C₂²	1	1	yes	characteristic, complemented
118	#72216740	C₂²	1	1	yes	characteristic
119	#72216740	C₂²	1	1	yes	characteristic, complemented
120	#72216730	C₂²	1	1	yes	characteristic
121	#72216730	C₂²	1	1	yes	characteristic, complemented
122	#72216720	C₂²	1	1	yes	characteristic, complemented
123	#72216710	C₂²	1	1	yes	characteristic, complemented
124	#72216702	C₂²	1	1	yes	characteristic, complemented
125	C₂×#483961	C₂²	1	1	yes	characteristic, complemented
126	#72216688	C₂²	1	1	yes	characteristic
127	#72216671	C₂²	1	1	yes	characteristic
128	#72216670	C₂²	1	1	yes	characteristic
129	#72216441	C₂²	1	1	yes	characteristic
130	#72216441	C₂²	1	1	yes	characteristic, complemented
131	#72216330	C₂²	1	2	yes	complemented
132	#72216330	C₂²	1	2	yes	complemented
133	C₂×AGL(1,ℤ/32)	C₂²	1	2	yes	complemented
134	C₂×AGL(1,ℤ/32)	C₂²	1	2	yes	complemented
135	#7625195	C₂×C₄	1	1	yes	characteristic
136	#7623968	C₂×C₄	1	1	yes	characteristic
137	#7623933	C₂×C₄	1	1	yes	characteristic
138	#7623847	C₂×C₄	1	1	yes	characteristic
139	#7623826	C₂×C₄	1	1	yes	characteristic
140	#7623826	C₂×C₄	1	1	yes	characteristic
141	#7623644	C₂×C₄	1	1	yes	characteristic
142	#7623618	C₂×C₄	1	1	yes	characteristic
143	#7623618	C₂×C₄	1	1	yes	characteristic
144	#7623252	C₂³	1	1	yes	characteristic
145	#7623252	C₂³	1	1	yes	characteristic
146	C₂×#33748	C₂³	1	1	yes	characteristic
147	#7622661	D₄	1	1	yes	characteristic
148	#7622661	C₂³	1	1	yes	characteristic
149	#7622628	C₂³	1	1	yes	characteristic
150	#7622620	C₂³	1	1	yes	characteristic
151	#7622620	C₂³	1	1	yes	characteristic
152	C₄×#3414	C₂³	1	1	yes	characteristic
153	#6342482	D₄	1	1	yes	characteristic
154	#512993	C₂×C₄	1	1	yes	characteristic
155	#512991	C₂×C₄	1	1	yes	characteristic
156	#512972	C₂×C₄	1	2	yes	—
157	#512929	C₂×C₄	1	2	yes	—
158	#512849	C₂×C₄	1	2	yes	—
159	#512843	C₂×C₄	1	1	yes	characteristic
160	#512841	C₂×C₄	1	1	yes	characteristic
161	#512840	C₂×C₄	1	2	yes	—
162	#512781	C₂×C₄	1	2	yes	—
163	#512779	C₂×C₄	1	2	yes	—
164	#512778	C₂³	1	2	yes	—
165	#512778	C₂³	1	2	yes	—
166	C₂×#13658	C₂³	1	2	yes	—
167	C₂×#13658	C₂³	1	2	yes	—
168	#512736	C₂³	1	1	yes	characteristic
169	#512736	C₂³	1	1	yes	characteristic
170	#512724	C₂×C₄	1	1	yes	characteristic
171	#512702	C₂×C₄	1	1	yes	characteristic
172	#512698	C₂×C₄	1	1	yes	characteristic
173	#512548	C₂³	1	1	yes	characteristic
174	#512548	C₂³	1	1	yes	characteristic
175	#506439	C₂×C₄	1	2	yes	—
176	#506361	C₂×C₄	1	2	yes	—
177	#505706	C₂×C₄	1	1	yes	characteristic
178	#505705	C₂×C₄	1	1	yes	characteristic
179	#500852	C₂×C₄	1	1	yes	characteristic
180	#500851	C₂×C₄	1	1	yes	characteristic
181	#495894	C₂³	1	2	yes	—
182	#495885	C₂³	1	2	yes	—
183	#494212	C₂³	1	1	yes	characteristic
184	#483965	D₄	1	2	yes	complemented
185	#483962	D₄	1	2	yes	complemented
186	#483961	D₄	1	2	yes	complemented
187	#483958	D₄	1	2	yes	complemented
188	#483844	C₂³	1	1	yes	characteristic
189	#483844	C₂³	1	1	yes	characteristic
190	#483843	C₂³	1	1	yes	characteristic
191	#483843	C₂³	1	1	yes	characteristic
192	C₂×#12089	C₂³	1	1	yes	characteristic
193	C₂×#12089	C₂³	1	1	yes	characteristic
194	#483601	C₂³	1	2	yes	—
195	C₂×#12068	C₂³	1	2	yes	—
196	#483597	D₄	1	2	yes	complemented
197	#483597	C₂³	1	1	yes	characteristic
198	#483597	C₂³	1	1	yes	characteristic
199	#483596	D₄	1	2	yes	complemented
200	#483596	C₂³	1	1	yes	characteristic
201	#483596	C₂³	1	1	yes	characteristic
202	#483589	D₄	1	2	yes	complemented
203	#483589	C₂³	1	1	yes	characteristic
204	#483589	C₂³	1	1	yes	characteristic
205	#483589	C₂³	1	1	yes	characteristic
206	#483589	C₂³	1	1	yes	characteristic
207	C₂×#12067	D₄	1	2	yes	complemented
208	C₂×#12067	C₂³	1	1	yes	characteristic
209	C₂×#12067	C₂³	1	1	yes	characteristic
210	#483414	C₂³	1	1	yes	characteristic
211	#483399	C₂³	1	1	yes	characteristic
212	#483399	C₂³	1	1	yes	characteristic
213	C₂×#12020	C₂³	1	1	yes	characteristic
214	#483327	C₂³	1	1	yes	characteristic
215	#483326	C₂³	1	1	yes	characteristic
216	#483326	C₂³	1	1	yes	characteristic
217	#483322	C₂³	1	1	yes	characteristic
218	#479968	D₄	1	1	yes	characteristic
219	#479968	D₄	1	1	yes	characteristic
220	#479966	D₄	1	1	yes	characteristic
221	#479961	D₄	1	1	yes	characteristic
222	#479961	D₄	1	1	yes	characteristic
223	#479960	C₂³	1	1	yes	characteristic
224	#479960	C₂³	1	1	yes	characteristic
225	#479959	D₄	1	1	yes	characteristic
226	#479959	C₂³	1	1	yes	characteristic
227	#479908	C₂³	1	1	yes	characteristic
228	#479908	C₂³	1	1	yes	characteristic
229	C₂×#11404	C₂³	1	1	yes	characteristic
230	#153330	C₂×C₄	1	2	yes	—
231	#153327	C₂×C₄	1	2	yes	—
232	#153274	C₂×C₄	1	2	yes	—
233	#153268	C₂×C₄	1	2	yes	—
234	#153257	C₂×C₄	1	2	yes	—
235	#153255	C₂×C₄	1	2	yes	—
236	#153255	C₂×C₄	1	2	yes	—
237	#153253	C₂×C₄	1	2	yes	—
238	#153218	C₂×C₄	1	2	yes	—
239	#153213	C₂×C₄	1	2	yes	—
240	#153111	C₂×C₄	1	2	yes	—
241	#153105	C₂×C₄	1	2	yes	—
242	#153092	C₂×C₄	1	2	yes	—
243	#153090	C₂×C₄	1	2	yes	—
244	#153090	C₂×C₄	1	2	yes	—
245	#153088	C₂×C₄	1	2	yes	—
246	#153025	C₂×C₄	1	2	yes	—
247	#153004	C₂×C₄	1	2	yes	—
248	#152901	C₂×C₄	1	2	yes	—
249	#152887	C₂×C₄	1	2	yes	—
250	#152649	C₂×C₄	1	1	yes	characteristic
251	#152647	C₂×C₄	1	1	yes	characteristic
252	#152646	C₂×C₄	1	1	yes	characteristic
253	#152644	C₂×C₄	1	1	yes	characteristic
254	#152545	C₂×C₄	1	2	yes	—
255	#152542	C₂×C₄	1	2	yes	—
256	#152539	C₂×C₄	1	2	yes	—
257	#152539	C₂×C₄	1	2	yes	—
258	#152520	C₂×C₄	1	2	yes	—
259	#152517	C₂×C₄	1	2	yes	—
260	#152499	C₂×C₄	1	1	yes	characteristic
261	#152499	C₂×C₄	1	1	yes	characteristic
262	#152492	C₂×C₄	1	1	yes	characteristic
263	#152492	C₂×C₄	1	1	yes	characteristic
264	#152451	C₂×C₄	1	2	yes	—
265	#152449	C₂×C₄	1	2	yes	—
266	#152449	C₂×C₄	1	2	yes	—
267	#152447	C₂×C₄	1	2	yes	—
268	#152432	C₂×C₄	1	2	yes	—
269	#152430	C₂×C₄	1	2	yes	—
270	#152372	C₂×C₄	1	1	yes	characteristic
271	#152371	C₂×C₄	1	1	yes	characteristic
272	#152286	C₂×C₄	1	2	yes	—
273	#152284	C₂×C₄	1	2	yes	—
274	#152176	C₂×C₄	1	2	yes	—
275	#152171	C₂×C₄	1	1	yes	characteristic
276	#152169	C₂×C₄	1	1	yes	characteristic
277	#152166	C₂×C₄	1	2	yes	—
278	#151971	C₂³	1	2	yes	—
279	#151971	C₂³	1	2	yes	—
280	#151969	C₂³	1	2	yes	—
281	#151969	C₂³	1	2	yes	—
282	#151895	C₂³	1	2	yes	—
283	#151895	C₂³	1	2	yes	—
284	#151893	C₂³	1	2	yes	—
285	#151893	C₂³	1	2	yes	—
286	#151024	C₂³	1	2	yes	—
287	#151024	C₂³	1	2	yes	—
288	C₂×#7457	C₂³	1	2	yes	—
289	C₂×#7457	C₂³	1	2	yes	—
290	#150074	C₂³	1	2	yes	—
291	#150074	C₂³	1	2	yes	—
292	#150074	C₂³	1	2	yes	—
293	#150074	C₂³	1	2	yes	—
294	C₂×#7390	C₂³	1	2	yes	—
295	C₂×#7390	C₂³	1	2	yes	—
296	C₂×#7390	C₂³	1	2	yes	—
297	C₂×#7390	C₂³	1	2	yes	—
298	#150071	C₂³	1	2	yes	—
299	#150071	C₂³	1	2	yes	—
300	C₂×#7389	C₂³	1	2	yes	—
301	C₂×#7389	C₂³	1	2	yes	—
302	#149504	C₂³	1	2	yes	—
303	#149504	C₂³	1	2	yes	—
304	C₂×#7333	C₂³	1	2	yes	—
305	C₂×#7333	C₂³	1	2	yes	—
306	#140753	C₂³	1	2	yes	—
307	#140752	C₂³	1	2	yes	—
308	#140357	C₂³	1	2	yes	—
309	#140356	C₂³	1	2	yes	—
310	#134666	C₂³	1	2	yes	—
311	#134663	C₂³	1	2	yes	—
312	#129176	C₂³	1	2	yes	—
313	#129164	C₂³	1	2	yes	—
314	#94057	C₂³	1	2	yes	—
315	#94057	C₂³	1	2	yes	—
316	#94056	C₂³	1	2	yes	—
317	#94056	C₂³	1	2	yes	—
318	#94031	C₂³	1	2	yes	—
319	#94031	C₂³	1	2	yes	—
320	#94030	C₂³	1	2	yes	—
321	#94030	C₂³	1	2	yes	—
322	#93997	C₂³	1	2	yes	—
323	#93997	C₂³	1	2	yes	—
324	#93996	C₂³	1	2	yes	—
325	#93995	C₂³	1	2	yes	—
326	#62635	C₂²×C₄	1	1	yes	characteristic
327	C₂×#3415	C₂²×C₄	1	1	yes	characteristic
328	C₂×#3415	C₂²×C₄	1	1	yes	characteristic
329	C₂×#3414	C₂²×C₄	1	1	yes	characteristic
330	#60204	C₂×D₄	1	1	yes	characteristic
331	#33981	C₂²×C₄	1	2	yes	—
332	#33981	C₂²×C₄	1	2	yes	—
333	C₂×#2263	C₂²×C₄	1	2	yes	—
334	C₂×#2263	C₂²×C₄	1	2	yes	—
335	#33974	C₂²×C₄	1	1	yes	characteristic
336	#33974	C₂²×C₄	1	1	yes	characteristic
337	#33750	C₂×D₄	1	2	yes	—
338	#33748	C₂×D₄	1	2	yes	—
339	#33742	#41	1	2	yes	—
340	#33740	#41	1	2	yes	—
341	#33730	C₂²×C₄	1	1	yes	characteristic
342	#33730	C₂²×C₄	1	1	yes	characteristic
343	C₂×#2254	C₂²×C₄	1	1	yes	characteristic
344	#33720	C₂²×C₄	1	1	yes	characteristic
345	#33720	C₂²×C₄	1	1	yes	characteristic
346	C₂×#2246	C₂²×C₄	1	1	yes	characteristic
347	#33617	C₂²×C₄	1	2	yes	—
348	#33611	C₂²×C₄	1	1	yes	characteristic
349	#33611	C₂²×C₄	1	1	yes	characteristic
350	#33607	C₂²×C₄	1	1	yes	characteristic
351	#33607	C₂²×C₄	1	1	yes	characteristic
352	#33604	C₂²×C₄	1	2	yes	—
353	C₂×#2218	C₂²×C₄	1	1	yes	characteristic
354	C₂×#2218	C₂²×C₄	1	1	yes	characteristic
355	#33474	C₂²×C₄	1	1	yes	characteristic
356	#33474	#41	1	1	yes	characteristic
357	#33465	C₂²×C₄	1	2	yes	—
358	C₂×#2179	C₂⁴	1	2	yes	—
359	#33460	C₂²×C₄	1	1	yes	characteristic
360	#33460	C₂²×C₄	1	1	yes	characteristic
361	#33460	#41	1	2	yes	—
362	#33456	C₂²×C₄	1	1	yes	characteristic
363	#33456	C₂²×C₄	1	1	yes	characteristic
364	#33456	#41	1	2	yes	—
365	#33451	C₂×D₄	1	2	yes	—
366	#33451	C₂⁴	1	1	yes	characteristic
367	#33451	C₂⁴	1	1	yes	characteristic
368	C₂×#2177	C₂×D₄	1	2	yes	—
369	C₂×#2177	C₂⁴	1	1	yes	characteristic
370	C₂×#2177	C₂⁴	1	1	yes	characteristic
371	C₄×#508	C₂²×C₄	1	1	yes	characteristic
372	C₄×#508	C₂²×C₄	1	1	yes	characteristic
373	#33434	C₂²×C₄	1	1	yes	characteristic
374	#33434	#41	1	1	yes	characteristic
375	#33433	C₂²×C₄	1	1	yes	characteristic
376	#33433	C₂²×C₄	1	1	yes	characteristic
377	#33433	#41	1	1	yes	characteristic
378	#33433	#41	1	1	yes	characteristic
379	#33421	C₂×D₄	1	1	yes	characteristic
380	#33421	C₂×D₄	1	1	yes	characteristic
381	#33421	C₂×D₄	1	1	yes	characteristic
382	#33421	C₂×D₄	1	1	yes	characteristic
383	#33418	C₂×D₄	1	1	yes	characteristic
384	#33418	C₂×D₄	1	1	yes	characteristic
385	#33414	C₂²×C₄	1	1	yes	characteristic
386	#33411	C₂²×C₄	1	1	yes	characteristic
387	#33411	C₂²×C₄	1	1	yes	characteristic
388	#33409	C₂²×C₄	1	1	yes	characteristic
389	#33326	C₂×D₄	1	1	yes	characteristic
390	#33326	C₂×D₄	1	1	yes	characteristic
391	#33326	C₂⁴	1	1	yes	characteristic
392	#33326	C₂⁴	1	1	yes	characteristic
393	C₂×C₄×M₃₂	C₂×D₄	1	1	yes	characteristic
394	C₂×C₄×M₃₂	C₂⁴	1	1	yes	characteristic
395	#17336	C₂×D₄	1	1	yes	characteristic
396	#17336	C₂×D₄	1	1	yes	characteristic
397	#17323	C₂×D₄	1	1	yes	characteristic
398	#17316	C₂×D₄	1	1	yes	characteristic
399	#17316	C₂×D₄	1	1	yes	characteristic
400	C₂²×#322	C₂×D₄	1	1	yes	characteristic
401	#13638	C₂²×C₄	1	2	yes	—
402	#13638	C₂²×C₄	1	2	yes	—
403	C₂×#1426	C₂²×C₄	1	2	yes	—
404	C₂×#1426	C₂²×C₄	1	2	yes	—
405	#13630	C₂²×C₄	1	2	yes	—
406	#13625	C₂²×C₄	1	2	yes	—
407	#13625	C₂²×C₄	1	2	yes	—
408	C₂×#1419	C₂²×C₄	1	2	yes	—
409	C₂×#1419	C₂²×C₄	1	2	yes	—
410	C₂×#1419	C₂²×C₄	1	2	yes	—
411	C₂×#1419	C₂²×C₄	1	2	yes	—
412	#13622	C₂²×C₄	1	2	yes	—
413	#13622	C₂²×C₄	1	2	yes	—
414	#13622	C₂²×C₄	1	2	yes	—
415	#13622	C₂²×C₄	1	2	yes	—
416	C₂×#1418	C₂²×C₄	1	2	yes	—
417	C₂×#1418	C₂²×C₄	1	2	yes	—
418	#13620	C₂²×C₄	1	2	yes	—
419	#13620	C₂²×C₄	1	2	yes	—
420	#13617	C₂²×C₄	1	2	yes	—
421	#13617	C₂²×C₄	1	2	yes	—
422	#13558	C₂²×C₄	1	2	yes	—
423	#13558	C₂²×C₄	1	2	yes	—
424	#13556	C₂²×C₄	1	1	yes	characteristic
425	#13556	C₂²×C₄	1	1	yes	characteristic
426	C₂×#1400	C₂²×C₄	1	2	yes	—
427	C₂×#1400	C₂²×C₄	1	2	yes	—
428	#13551	C₂²×C₄	1	2	yes	—
429	C₂×#1398	C₂⁴	1	2	yes	—
430	C₂×#1398	C₂⁴	1	2	yes	—
431	C₂×#1398	C₂⁴	1	2	yes	—
432	C₂×#1398	C₂⁴	1	2	yes	—
433	#13243	C₂²×C₄	1	2	yes	—
434	#13241	C₂²×C₄	1	2	yes	—
435	#13173	C₂²×C₄	1	2	yes	—
436	#13169	C₂²×C₄	1	2	yes	—
437	#12911	C₂²×C₄	1	2	yes	—
438	#12841	C₂²×C₄	1	2	yes	—
439	#12840	C₂²×C₄	1	1	yes	characteristic
440	#12839	C₂²×C₄	1	1	yes	characteristic
441	#12838	C₂²×C₄	1	2	yes	—
442	#12671	C₂⁴	1	2	yes	—
443	#12089	C₂×D₄	1	2	yes	—
444	#12089	C₂×D₄	1	2	yes	—
445	#12089	C₂×D₄	1	2	yes	—
446	#12088	C₂×D₄	1	2	yes	—
447	#12067	C₂×D₄	1	2	yes	—
448	#12067	C₂×D₄	1	1	yes	characteristic
449	#12067	C₂×D₄	1	2	yes	—
450	#12067	C₂×D₄	1	2	yes	—
451	#12067	C₂×D₄	1	2	yes	—
452	#12067	C₂×D₄	1	2	yes	—
453	#12067	C₂×D₄	1	2	yes	—
454	#12067	C₂×D₄	1	2	yes	—
455	#12067	C₂×D₄	1	1	yes	characteristic
456	#12067	C₂×D₄	1	1	yes	characteristic
457	#12067	C₂×D₄	1	1	yes	characteristic
458	#12066	C₂×D₄	1	2	yes	—
459	#12066	C₂×D₄	1	1	yes	characteristic
460	#12066	C₂×D₄	1	1	yes	characteristic
461	#12066	C₂×D₄	1	1	yes	characteristic
462	#12066	C₂×D₄	1	1	yes	characteristic
463	#12021	C₂×D₄	1	2	yes	—
464	#12020	C₂×D₄	1	2	yes	—
465	C₂×#1369	C₂⁴	1	2	yes	—
466	C₂×#1369	C₂⁴	1	2	yes	—
467	#11999	C₂×D₄	1	2	yes	—
468	#11999	C₂⁴	1	1	yes	characteristic
469	#11999	C₂⁴	1	1	yes	characteristic
470	C₂×#1368	C₂×D₄	1	2	yes	—
471	C₂×#1368	C₂⁴	1	1	yes	characteristic
472	C₂×#1368	C₂⁴	1	1	yes	characteristic
473	#11406	C₂×D₄	1	1	yes	characteristic
474	#11406	C₂×D₄	1	1	yes	characteristic
475	#11406	C₂×D₄	1	1	yes	characteristic
476	#11406	C₂×D₄	1	1	yes	characteristic
477	#11406	C₂×D₄	1	2	yes	—
478	#11405	C₂×D₄	1	1	yes	characteristic
479	#11405	C₂×D₄	1	1	yes	characteristic
480	#11405	C₂×D₄	1	2	yes	—
481	#11405	C₂⁴	1	1	yes	characteristic
482	#11405	C₂⁴	1	1	yes	characteristic
483	#11404	C₂×D₄	1	1	yes	characteristic
484	#11404	C₂×D₄	1	1	yes	characteristic
485	#11404	C₂×D₄	1	1	yes	characteristic
486	#11404	C₂×D₄	1	1	yes	characteristic
487	#11404	C₂×D₄	1	2	yes	—
488	C₂×#1313	C₂×D₄	1	1	yes	characteristic
489	C₂×#1313	C₂×D₄	1	1	yes	characteristic
490	C₂×#1313	C₂×D₄	1	2	yes	—
491	C₂×#1313	C₂⁴	1	1	yes	characteristic
492	C₂×#1313	C₂⁴	1	1	yes	characteristic
493	#7480	C₂²×C₄	1	2	yes	—
494	#7480	C₂²×C₄	1	2	yes	—
495	#7477	C₂²×C₄	1	2	yes	—
496	#7477	C₂²×C₄	1	2	yes	—
497	#7475	C₂²×C₄	1	2	yes	—
498	#7475	C₂²×C₄	1	2	yes	—
499	#7474	C₂²×C₄	1	2	yes	—
500	#7474	C₂²×C₄	1	2	yes	—
501	#7469	C₂²×C₄	1	2	yes	—
502	#7469	C₂²×C₄	1	2	yes	—
503	#7467	C₂²×C₄	1	2	yes	—
504	#7467	C₂²×C₄	1	2	yes	—
505	#3444	AGL(1,ℤ/8)	1	1	yes	characteristic
506	C₂×#508	C₄×D₄	1	2	yes	—
507	C₂×#508	C₂³×C₄	1	1	yes	characteristic
508	C₂×#508	C₂³×C₄	1	1	yes	characteristic
509	C₂×#508	C₂³×C₄	1	2	yes	—
510	C₂²×D₁₆	C₄×D₄	1	2	yes	—
511	C₂²×D₁₆	C₂³×C₄	1	1	yes	characteristic
512	C₂²×D₁₆	C₂³×C₄	1	1	yes	characteristic
513	C₂×#504	C₂³×C₄	1	1	yes	characteristic
514	C₂×#504	C₂³×C₄	1	1	yes	characteristic
515	C₂×#504	C₂×#41	1	1	yes	characteristic
516	C₂×#504	C₂×#41	1	1	yes	characteristic
517	C₂²×M₃₂	C₂³×C₄	1	1	yes	characteristic
518	C₂²×M₃₂	C₂×#41	1	1	yes	characteristic
519	#2960	C₄×D₄	1	1	yes	characteristic
520	#2960	AGL(1,ℤ/8)	1	1	yes	characteristic
521	#2931	C₄×D₄	1	1	yes	characteristic
522	#2931	AGL(1,ℤ/8)	1	1	yes	characteristic
523	#2929	C₄×D₄	1	1	yes	characteristic
524	#2929	C₄×D₄	1	1	yes	characteristic
525	#2929	AGL(1,ℤ/8)	1	1	yes	characteristic
526	#2929	AGL(1,ℤ/8)	1	1	yes	characteristic
527	#2922	AGL(1,ℤ/8)	1	1	yes	characteristic
528	#2922	AGL(1,ℤ/8)	1	1	yes	characteristic
529	#2920	AGL(1,ℤ/8)	1	1	yes	characteristic
530	C₄×#131	C₂²×D₄	1	1	yes	characteristic
531	C₄×#131	C₂²×D₄	1	1	yes	characteristic
532	C₂²×C₄×C₈	C₂²×D₄	1	1	yes	characteristic
533	#2264	#131	1	4	yes	complemented
534	#2263	#131	1	4	yes	complemented
535	C₂×M₆₄	C₂³×C₄	1	2	yes	—
536	C₂×M₆₄	C₂³×C₄	1	2	yes	—
537	C₂×M₆₄	C₂³×C₄	1	2	yes	—
538	C₂×M₆₄	C₂³×C₄	1	2	yes	—
539	#2254	C₄×D₄	1	2	yes	—
540	#2253	C₄×D₄	1	2	yes	—
541	#2249	C₄×D₄	1	2	yes	—
542	#2246	C₄×D₄	1	2	yes	—
543	#2219	C₄×D₄	1	2	yes	—
544	#2218	C₄×D₄	1	2	yes	—
545	#2218	C₄×D₄	1	2	yes	—
546	#2218	C₄×D₄	1	2	yes	—
547	#2177	C₄×D₄	1	2	yes	—
548	#2177	C₄×D₄	1	2	yes	—
549	#2177	C₄×D₄	1	2	yes	—
550	#2177	C₂²×D₄	1	1	yes	characteristic
551	#2177	C₂²×D₄	1	2	yes	—
552	#2177	C₂²×D₄	1	1	yes	characteristic
553	#2177	C₂²×D₄	1	2	yes	—
554	#2177	C₂×#41	1	2	yes	—
555	#2177	C₂×#41	1	2	yes	—
556	#2177	C₂×#41	1	1	yes	characteristic
557	#2177	C₂×#41	1	1	yes	characteristic
558	#2176	C₄×D₄	1	2	yes	—
559	#2176	C₂²×D₄	1	1	yes	characteristic
560	#2176	C₂²×D₄	1	1	yes	characteristic
561	#2176	C₂×#41	1	1	yes	characteristic
562	#2176	C₂×#41	1	1	yes	characteristic
563	C₂×#368	C₂³×C₄	1	2	yes	—
564	C₂×#368	C₂³×C₄	1	2	yes	—
565	#2158	C₄×D₄	1	2	yes	—
566	#2158	C₂³×C₄	1	2	yes	—
567	#2158	C₂³×C₄	1	1	yes	characteristic
568	#2158	C₂³×C₄	1	1	yes	characteristic
569	C₂×#367	C₄×D₄	1	2	yes	—
570	C₂×#367	C₂³×C₄	1	1	yes	characteristic
571	C₂×#367	C₂³×C₄	1	1	yes	characteristic
572	#2151	C₄×D₄	1	1	yes	characteristic
573	#2151	C₄×D₄	1	1	yes	characteristic
574	#2151	C₄×D₄	1	1	yes	characteristic
575	#2151	C₄×D₄	1	1	yes	characteristic
576	#2150	C₄×D₄	1	1	yes	characteristic
577	#2150	C₄×D₄	1	1	yes	characteristic
578	#2113	C₄×D₄	1	1	yes	characteristic
579	#2113	C₄×D₄	1	1	yes	characteristic
580	#2113	C₄×D₄	1	1	yes	characteristic
581	#2113	C₄×D₄	1	1	yes	characteristic
582	#2112	C₄×D₄	1	1	yes	characteristic
583	#2112	C₄×D₄	1	1	yes	characteristic
584	#2108	C₂³×C₄	1	1	yes	characteristic
585	#2108	C₂³×C₄	1	1	yes	characteristic
586	#2108	C₂×#41	1	1	yes	characteristic
587	#2108	C₂×#41	1	2	yes	—
588	#2108	C₂×#41	1	2	yes	—
589	#2108	C₂×#41	1	1	yes	characteristic
590	C₄×M₃₂	#120	1	2	yes	—
591	C₄×M₃₂	C₂²×D₄	1	1	yes	characteristic
592	C₄×M₃₂	C₂²×D₄	1	1	yes	characteristic
593	C₄×M₃₂	C₂²×D₄	1	1	yes	characteristic
594	C₄×M₃₂	C₂²×D₄	1	2	yes	—
595	C₄×M₃₂	C₂²×D₄	1	1	yes	characteristic
596	C₂×#346	#120	1	2	yes	—
597	C₂×#346	C₂²×D₄	1	1	yes	characteristic
598	C₂×#346	C₂²×D₄	1	1	yes	characteristic
599	C₂×#346	C₂²×D₄	1	1	yes	characteristic
600	C₂×#346	C₂²×D₄	1	2	yes	—
601	C₂×#346	C₂⁵	1	1	yes	characteristic
602	C₂×C₄×C₁₆	C₂³×C₄	1	1	yes	characteristic
603	C₂×C₄×C₁₆	C₂×#41	1	1	yes	characteristic
604	#1455	AGL(1,ℤ/8)	1	2	yes	—
605	#1453	AGL(1,ℤ/8)	1	2	yes	—
606	#1450	#120	1	2	yes	—
607	#1450	C₂²×D₄	1	1	yes	characteristic
608	#1450	C₂²×D₄	1	1	yes	characteristic
609	C₂×#322	#120	1	2	yes	—
610	C₂×#322	C₂²×D₄	1	1	yes	characteristic
611	C₂×#322	C₂²×D₄	1	1	yes	characteristic
612	#1368	C₂²×D₄	1	1	yes	characteristic
613	#1368	C₂²×D₄	1	1	yes	characteristic
614	#1368	C₂²×D₄	1	1	yes	characteristic
615	#1368	C₂²×D₄	1	1	yes	characteristic
616	#1368	C₂²×D₄	1	2	yes	—
617	#1368	C₂²×D₄	1	2	yes	—
618	#1313	#120	1	2	yes	—
619	#1313	#120	1	2	yes	—
620	#1313	#120	1	2	yes	—
621	#1313	#120	1	2	yes	—
622	#1313	C₂²×D₄	1	1	yes	characteristic
623	#1313	C₂²×D₄	1	1	yes	characteristic
624	#1313	C₂²×D₄	1	1	yes	characteristic
625	#1313	C₂²×D₄	1	1	yes	characteristic
626	#1313	C₂²×D₄	1	2	yes	—
627	#1313	C₂²×D₄	1	2	yes	—
628	C₂×#131	C₂×C₄×D₄	1	1	yes	characteristic
629	C₂×#131	C₂×C₄×D₄	1	1	yes	characteristic
630	C₂×#131	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
631	C₂×#131	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
632	C₂³×C₈	C₂×C₄×D₄	1	1	yes	characteristic
633	C₂³×C₈	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
634	#533	#442	1	1	yes	characteristic
635	#532	#442	1	1	yes	characteristic
636	#525	#442	1	1	yes	characteristic
637	#525	#442	1	1	yes	characteristic
638	C₄×#41	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
639	C₄×#41	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
640	C₂²×C₄²	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
641	#508	C₂×#131	1	4	yes	—
642	C₂×Q₃₂	C₂×C₄×D₄	1	1	yes	characteristic
643	C₂×Q₃₂	C₂×C₄×D₄	1	1	yes	characteristic
644	C₂×Q₃₂	C₂×#131	1	2	yes	complemented
645	C₂×D₁₆	C₂×C₄×D₄	1	2	yes	—
646	C₂×D₁₆	C₂×C₄×D₄	1	2	yes	—
647	C₂×D₁₆	C₂×C₄×D₄	1	1	yes	characteristic
648	C₂×D₁₆	C₂×C₄×D₄	1	1	yes	characteristic
649	C₂×D₁₆	C₂×#131	1	2	yes	complemented
650	C₂×M₃₂	C₂×C₄×D₄	1	1	yes	characteristic
651	C₂×M₃₂	C₂×C₄×D₄	1	1	yes	characteristic
652	C₂×M₃₂	C₂×C₄×D₄	1	2	yes	—
653	C₂×M₃₂	C₂×C₄×D₄	1	1	yes	characteristic
654	C₂×M₃₂	C₂×C₄×D₄	1	1	yes	characteristic
655	C₂×M₃₂	#525	1	2	yes	—
656	C₂²×C₁₆	C₂×C₄×D₄	1	1	yes	characteristic
657	C₂²×C₁₆	C₂×C₄×D₄	1	1	yes	characteristic
658	C₂²×C₁₆	C₂×C₄×D₄	1	2	yes	—
659	C₂²×C₁₆	#525	1	2	yes	—
660	C₂²×C₁₆	C₂⁴×C₄	1	1	yes	characteristic
661	C₂²×C₁₆	C₂²×#41	1	1	yes	characteristic
662	#424	#442	1	1	yes	characteristic
663	#424	#442	1	1	yes	characteristic
664	#424	#442	1	1	yes	characteristic
665	#424	#442	1	1	yes	characteristic
666	#423	#442	1	1	yes	characteristic
667	#423	#442	1	1	yes	characteristic
668	#408	#442	1	1	yes	characteristic
669	#408	#442	1	1	yes	characteristic
670	#408	#442	1	1	yes	characteristic
671	#408	#442	1	1	yes	characteristic
672	#407	#442	1	1	yes	characteristic
673	#407	#442	1	1	yes	characteristic
674	#405	C₂×C₄×D₄	1	1	yes	characteristic
675	#405	C₂×C₄×D₄	1	1	yes	characteristic
676	#405	#525	1	2	yes	—
677	#405	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
678	#405	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
679	#405	#575	1	2	yes	—
680	C₄×M₁₆	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
681	C₄×M₁₆	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
682	C₄×M₁₆	C₂×AGL(1,ℤ/8)	1	2	yes	—
683	C₂×C₄×C₈	C₂×C₄×D₄	1	1	yes	characteristic
684	C₂×C₄×C₈	C₂×#120	1	2	yes	—
685	C₂×C₄×C₈	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
686	C₂×C₄×C₈	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
687	C₂×C₄×C₈	C₂³×D₄	1	1	yes	characteristic
688	M₆₄	C₂×#131	1	4	yes	complemented
689	#367	C₂×C₄×D₄	1	1	yes	characteristic
690	#367	C₂×C₄×D₄	1	2	yes	—
691	#367	C₂×C₄×D₄	1	2	yes	—
692	#367	C₂×C₄×D₄	1	1	yes	characteristic
693	#367	C₂×C₄×D₄	1	1	yes	characteristic
694	#367	C₂×C₄×D₄	1	1	yes	characteristic
695	#346	C₂×C₄×D₄	1	2	yes	—
696	#346	C₂×#120	1	1	yes	characteristic
697	#346	C₂×#120	1	2	yes	—
698	#346	C₂×#120	1	1	yes	characteristic
699	#346	C₂×#120	1	2	yes	—
700	#346	#525	1	2	yes	—
701	#346	C₂³×D₄	1	1	yes	characteristic
702	#346	C₂³×D₄	1	1	yes	characteristic
703	#346	C₂²×#41	1	1	yes	characteristic
704	#346	C₂²×#41	1	1	yes	characteristic
705	C₄×C₁₆	C₂×C₄×D₄	1	2	yes	—
706	C₄×C₁₆	#525	1	2	yes	—
707	C₄×C₁₆	#525	1	2	yes	—
708	#322	C₂×#120	1	1	yes	characteristic
709	#322	C₂×#120	1	1	yes	characteristic
710	#322	C₂×#120	1	2	yes	—
711	#322	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
712	#322	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
713	C₈²	C₂×AGL(1,ℤ/8)	1	2	yes	—
714	C₂×#41	C₂×#442	1	1	yes	characteristic
715	C₂×#41	C₂×#442	1	1	yes	characteristic
716	C₂³×C₄	C₂×#442	1	1	yes	characteristic
717	C₂×M₁₆	C₂×#442	1	1	yes	characteristic
718	C₂×M₁₆	C₂×#442	1	1	yes	characteristic
719	C₂×M₁₆	C₂×#442	1	1	yes	characteristic
720	C₂×M₁₆	C₂×#442	1	1	yes	characteristic
721	C₂×M₁₆	C₄×AGL(1,ℤ/8)	1	2	yes	—
722	C₂×M₁₆	#3109	1	2	yes	—
723	C₂²×C₈	C₄×#120	1	2	yes	—
724	C₂²×C₈	C₂×#442	1	1	yes	characteristic
725	C₂²×C₈	C₂×#442	1	1	yes	characteristic
726	C₂²×C₈	#3006	1	2	yes	—
727	C₂²×C₈	C₂²×C₄×D₄	1	1	yes	characteristic
728	C₂²×C₈	C₂²×AGL(1,ℤ/8)	1	1	yes	characteristic
729	C₄⋊Q₈	AGL(1,ℤ/16)	1	1	yes	characteristic
730	#127	AGL(1,ℤ/16)	1	1	yes	characteristic
731	#124	AGL(1,ℤ/16)	1	1	yes	characteristic
732	#124	AGL(1,ℤ/16)	1	1	yes	characteristic
733	#123	AGL(1,ℤ/16)	1	2	yes	—
734	#120	AGL(1,ℤ/16)	1	2	yes	—
735	#117	C₂×#442	1	1	yes	characteristic
736	#117	C₂×#442	1	1	yes	characteristic
737	#117	#3114	1	2	yes	—
738	C₂×C₄²	C₂×#442	1	1	yes	characteristic
739	C₂×C₄²	#3003	1	2	yes	—
740	C₂×C₄²	C₂²×AGL(1,ℤ/8)	1	1	yes	characteristic
741	Q₃₂	#2929	1	2	yes	—
742	D₁₆	#2929	1	2	yes	—
743	C₂×C₁₆	C₄×#120	1	2	yes	—
744	C₂×C₁₆	C₄×#120	1	2	yes	—
745	C₂×C₁₆	C₂²×C₄×D₄	1	1	yes	characteristic
746	C₂×C₁₆	C₂²×C₄×D₄	1	1	yes	characteristic
747	C₂×C₁₆	C₂×#525	1	1	yes	characteristic
748	C₂×C₁₆	C₂×#525	1	1	yes	characteristic
749	C₂×C₁₆	C₂²×#131	1	2	yes	—
750	C₂×C₁₆	#3573	1	2	yes	—
751	#97	C₄×AGL(1,ℤ/8)	1	2	yes	—
752	#97	#3109	1	2	yes	—
753	#97	#3114	1	2	yes	—
754	C₄×C₈	C₄×#120	1	2	yes	—
755	C₄×C₈	#3003	1	2	yes	—
756	C₄×C₈	#3006	1	2	yes	—
757	C₄×C₈	C₂²×#120	1	1	yes	characteristic
758	C₄×C₈	C₂×#525	1	1	yes	characteristic
759	C₄×C₈	C₂²×AGL(1,ℤ/8)	1	1	yes	characteristic
760	C₄×C₈	C₂×#575	1	1	yes	characteristic
761	C₂⁴	C₂×AGL(1,ℤ/16)	1	1	yes	characteristic
762	C₂×Q₈	C₂×AGL(1,ℤ/16)	1	1	yes	characteristic
763	C₂×Q₈	C₂×AGL(1,ℤ/16)	1	1	yes	characteristic
764	C₂×D₄	C₂×AGL(1,ℤ/16)	1	2	yes	—
765	C₂×D₄	C₂×AGL(1,ℤ/16)	1	1	yes	characteristic
766	C₂×D₄	C₂×AGL(1,ℤ/16)	1	1	yes	characteristic
767	C₂²×C₄	#21452	1	2	yes	—
768	C₂²×C₄	C₂×AGL(1,ℤ/16)	1	1	yes	characteristic
769	C₂²×C₄	C₂²×#442	1	1	yes	characteristic
770	C₂×C₈	#21452	1	2	yes	—
771	C₂×C₈	#21452	1	2	yes	—
772	C₂×C₈	C₂×C₄×#120	1	1	yes	characteristic
773	C₂×C₈	D₄×#131	1	2	yes	—
774	C₂×C₈	C₂×C₄×AGL(1,ℤ/8)	1	1	yes	characteristic
775	C₂×C₈	#60184	1	2	yes	—
776	C₂×C₈	C₂×#3006	1	1	yes	characteristic
777	C₂×C₈	C₂×#3109	1	1	yes	characteristic
778	C₂²⋊C₄	C₂×AGL(1,ℤ/16)	1	2	yes	—
779	C₄²	#21452	1	2	yes	—
780	C₄²	C₂×AGL(1,ℤ/16)	1	1	yes	characteristic
781	C₄²	C₂×AGL(1,ℤ/16)	1	1	yes	characteristic
782	C₄²	C₂×#3003	1	1	yes	characteristic
783	C₄²	C₂×#3114	1	1	yes	characteristic
784	C₁₆	C₂×#2929	1	1	yes	characteristic
785	C₁₆	#60140	1	1	yes	characteristic
786	C₁₆	D₄×#131	1	2	yes	—
787	C₂³	#495725	1	2	yes	—
788	C₂³	C₂²×AGL(1,ℤ/16)	1	1	yes	characteristic
789	C₂×C₄	#495725	1	2	yes	—
790	C₂×C₄	#6345807	1	2	yes	—
791	C₂×C₄	C₂×#21452	1	1	yes	characteristic
792	C₂×C₄	C₂²×AGL(1,ℤ/16)	1	1	yes	characteristic
793	C₂×C₄	#7622637	1	2	yes	—
794	C₈	#6345821	1	2	yes	—
795	C₈	#6372605	1	1	yes	characteristic
796	C₈	#6372691	1	1	yes	characteristic
797	C₂²	#72216771	1	2	yes	—
798	C₂²	C₂×#495725	1	1	yes	characteristic
799	C₄	#72216771	1	2	yes	—
800	C₄	#72225125	1	1	yes	characteristic
801	C₄	#72225127	1	1	yes	characteristic
802	C₂	#72225133	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂	#72225133
commutator	C₂²×C₁₆	C₂⁴×C₄
Frattini, cosocle	C₂×#346	C₂⁵
prime radical	#72225019	C₂
LCS	G ▷ C₂²×C₁₆ ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂ ◁ C₂²×C₄ ◁ #60204 ◁ #72216670 ◁ G
LECS	G ▷ C₂×#346 ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁

Complements

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

N	H ≅ G/N	type
1. #72225121	C₂	semidirect
2. #72225118	C₂	semidirect
3. #72225110	C₂	semidirect
4. #72225107	C₂	semidirect
5. #72225104	C₂	semidirect
6. #72225102	C₂	semidirect
7. #72225096	C₂	semidirect
8. #72225094	C₂	semidirect
9. #72225092	C₂	semidirect
10. #72225089	C₂	semidirect
11. #72225088	C₂	semidirect
12. #72225087	C₂	semidirect
13. #72225084	C₂	semidirect
14. #72225083	C₂²	semidirect
15. #72225082	C₂²	semidirect
16. #72225081	C₂²	semidirect
17. #72225080	C₂²	semidirect
18. #72225079	C₂²	semidirect
19. #72225078	C₂²	semidirect
20. #72225077	C₂²	semidirect
21. #72225075	C₂²	semidirect
22. #72225073	C₂	semidirect
24. #72225070	C₂²	semidirect
25. #72225068	C₂²	semidirect
26. #72225068	C₂²	semidirect
27. #72225065	C₂	semidirect
28. #72225062	C₂²	semidirect
30. #72225060	C₂²	semidirect
31. #72225059	C₂²	semidirect
32. #72225058	C₂²	semidirect
33. #72225057	C₂²	semidirect
34. #72225056	C₂²	semidirect
36. #72225054	C₂	semidirect
37. #72225050	C₂²	semidirect
38. #72225050	C₂²	semidirect
39. #72225048	C₂²	semidirect
40. #72225048	C₂²	semidirect
41. #72225046	C₂	semidirect
45. #72225040	C₂²	semidirect
46. #72225039	C₂²	semidirect
48. #72225036	C₂²	semidirect
49. #72225034	C₂²	semidirect
50. #72225032	C₂	semidirect
51. #72225029	C₂²	semidirect
52. #72225028	C₂²	semidirect
53. #72225027	C₂²	semidirect
54. #72225026	C₂²	semidirect
55. #72225025	C₂²	semidirect
56. #72225024	C₂²	semidirect
57. #72225023	C₂²	semidirect
58. #72225022	C₂²	semidirect
80. #72224981	C₂	semidirect
81. #72224979	C₂²	semidirect
82. #72224978	C₂²	semidirect
83. #72224977	C₂²	semidirect
84. #72224976	C₂²	semidirect
85. #72224975	C₂²	semidirect
86. #72224974	C₂²	semidirect
87. #72224973	C₂²	semidirect
88. #72224971	C₂²	semidirect
89. #72224968	C₂	semidirect
90. #72224956	C₂²	semidirect
91. #72224955	C₂²	semidirect
92. #72224954	C₂²	semidirect
93. #72224951	C₂²	semidirect
94. #72224949	C₂²	semidirect
95. #72224948	C₂²	semidirect
96. #72224946	C₂²	semidirect
97. #72224944	C₂²	semidirect
98. #72223653	C₂²	semidirect
99. #72223653	C₂²	semidirect
101. #72223646	C₂²	semidirect
104. #72217250	C₂	semidirect
105. #72217231	C₂²	semidirect
106. #72217224	C₂²	semidirect
107. #72217219	C₂²	semidirect
108. #72217215	C₂²	semidirect
109. #72217203	C₂²	semidirect
110. #72217199	C₂²	semidirect
111. #72217188	C₂²	semidirect
112. #72217185	C₂²	semidirect
115. #72217162	C₂	semidirect
117. #72216759	C₂²	semidirect
119. #72216740	C₂²	semidirect
121. #72216730	C₂²	semidirect
122. #72216720	C₂²	semidirect
123. #72216710	C₂²	semidirect
124. #72216702	C₂²	semidirect
125. C₂×#483961	C₂²	semidirect
130. #72216441	C₂²	semidirect
131. #72216330	C₂²	semidirect
132. #72216330	C₂²	semidirect
133. C₂×AGL(1,ℤ/32)	C₂²	semidirect
134. C₂×AGL(1,ℤ/32)	C₂²	semidirect
184. #483965	D₄	semidirect
185. #483962	D₄	semidirect
186. #483961	D₄	semidirect
187. #483958	D₄	semidirect
196. #483597	D₄	semidirect
199. #483596	D₄	semidirect
202. #483589	D₄	semidirect
207. C₂×#12067	D₄	semidirect
533. #2264	#131	semidirect
534. #2263	#131	semidirect
644. C₂×Q₃₂	C₂×#131	semidirect
649. C₂×D₁₆	C₂×#131	semidirect
688. M₆₄	C₂×#131	semidirect

Maximal subgroups

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

subgroup	index
#72225121	2
#72225118	2
#72225110	2
#72225107	2
#72225104	2
#72225102	2
#72225096	2
#72225094	2
#72225092	2
#72225089	2
#72225088	2
#72225087	2
#72225084	2
#72225073	2
#72225065	2
#72225054	2
#72225046	2
#72225032	2
#72225019	2
#72224981	2
#72224968	2
#72217250	2
#72217162	2