Subgroups — #72341571

Order 4096.

At least 42110 conjugacy classes of subgroups; only the 1037 normal subgroups are shown.

The subgroup lattice has 874 nodes (normal subgroups only) — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#72341541	C₂	1	1	yes	maximal, characteristic, complemented
2	#72341530	C₂	1	1	yes	maximal, characteristic, complemented
3	#72341502	C₂	1	1	yes	maximal, characteristic, complemented
4	#72341499	C₂	1	1	yes	maximal, characteristic, complemented
5	#72341495	C₂²	1	1	yes	characteristic
6	#72341478	C₂	1	1	yes	maximal, characteristic, complemented
7	#72341475	C₂²	1	1	yes	characteristic, complemented
8	#72341474	C₂	1	1	yes	maximal, characteristic, complemented
9	#72341473	C₂²	1	1	yes	characteristic, complemented
10	#72341472	C₂	1	1	yes	maximal, characteristic, complemented
11	#72341471	C₂²	1	1	yes	characteristic
12	#72341469	C₂	1	1	yes	maximal, characteristic, complemented
13	#72341467	C₂	1	1	yes	maximal, characteristic, complemented
14	#72341466	C₂²	1	1	yes	characteristic, complemented
15	#72341465	C₂²	1	1	yes	characteristic, complemented
16	#72341382	C₂	1	1	yes	maximal, characteristic, complemented
17	#72341374	C₂	1	1	yes	maximal, characteristic, complemented
18	#72341363	C₂²	1	1	yes	characteristic, complemented
19	#72341362	C₂²	1	1	yes	characteristic, complemented
20	#72341347	C₂	1	1	yes	maximal, characteristic, complemented
21	#72341322	C₂	1	1	yes	maximal, characteristic, complemented
22	#72341322	C₂	1	1	yes	maximal, characteristic, complemented
23	#72341320	C₂²	1	1	yes	characteristic, complemented
24	#72341315	C₂	1	1	yes	maximal, characteristic, complemented
25	#72341312	C₂²	1	1	yes	characteristic, complemented
26	#72341305	C₂	1	1	yes	maximal, characteristic, complemented
27	#72341286	C₂²	1	1	yes	characteristic, complemented
28	#72341286	C₂²	1	1	yes	characteristic, complemented
29	#72337584	C₂	1	1	yes	maximal, characteristic, complemented
30	#72311323	C₂	1	1	yes	maximal, characteristic, complemented
31	#72311315	C₂²	1	1	yes	characteristic, complemented
32	#72311295	C₂²	1	1	yes	characteristic, complemented
33	#72311270	C₂	1	1	yes	maximal, characteristic, complemented
34	#72311266	C₂²	1	1	yes	characteristic, complemented
35	#72311264	C₂²	1	1	yes	characteristic, complemented
36	#72311254	C₂²	1	1	yes	characteristic
37	#72311253	C₂	1	1	yes	maximal, characteristic, complemented
38	#72311246	C₂²	1	1	yes	characteristic, complemented
39	#72311237	C₂²	1	1	yes	characteristic, complemented
40	#72311231	C₂²	1	1	yes	characteristic, complemented
41	#72311231	C₂²	1	1	yes	characteristic, complemented
42	#72311163	C₂	1	1	yes	maximal, characteristic, complemented
43	#72311157	C₂²	1	1	yes	characteristic, complemented
44	#72311152	C₂²	1	1	yes	characteristic, complemented
45	#72311152	C₂²	1	1	yes	characteristic, complemented
46	#72311150	C₂²	1	1	yes	characteristic, complemented
47	#72311147	C₂²	1	1	yes	characteristic, complemented
48	#72311145	C₂²	1	1	yes	characteristic, complemented
49	#72311145	C₂²	1	1	yes	characteristic, complemented
50	#72311145	C₂²	1	1	yes	characteristic, complemented
51	#72311145	C₂²	1	1	yes	characteristic, complemented
52	#72311140	C₂²	1	1	yes	characteristic, complemented
53	#72311140	C₂²	1	1	yes	characteristic, complemented
54	#72311115	C₂²	1	1	yes	characteristic, complemented
55	#72306419	C₂²	1	1	yes	characteristic
56	#72306419	C₂²	1	1	yes	characteristic, complemented
57	#72306417	C₂²	1	1	yes	characteristic
58	#72306417	C₂²	1	1	yes	characteristic, complemented
59	#72306415	C₂²	1	1	yes	characteristic
60	#72306415	C₂²	1	1	yes	characteristic, complemented
61	#72303101	C₂	1	1	yes	maximal, characteristic, complemented
62	#72303095	C₂²	1	1	yes	characteristic, complemented
63	#72303091	C₂²	1	1	yes	characteristic, complemented
64	#72303086	C₂²	1	1	yes	characteristic, complemented
65	#72303086	C₂²	1	1	yes	characteristic, complemented
66	#72303081	C₂²	1	1	yes	characteristic, complemented
67	#72303066	C₂²	1	1	yes	characteristic, complemented
68	#72303066	C₂²	1	1	yes	characteristic, complemented
69	#72303055	C₂²	1	1	yes	characteristic, complemented
70	#72303055	C₂²	1	1	yes	characteristic, complemented
71	#72302998	C₂²	1	1	yes	characteristic, complemented
72	#72302950	C₂²	1	1	yes	characteristic, complemented
73	#72302950	C₂²	1	1	yes	characteristic, complemented
74	#72285520	C₂	1	1	yes	maximal, characteristic, complemented
75	#72285500	C₂²	1	1	yes	characteristic, complemented
76	#72285500	C₂²	1	1	yes	characteristic, complemented
77	#72285407	C₂²	1	1	yes	characteristic, complemented
78	#72285407	C₂²	1	1	yes	characteristic, complemented
79	#72285407	C₂²	1	1	yes	characteristic, complemented
80	#72285407	C₂²	1	1	yes	characteristic, complemented
81	#72284823	C₂²	1	1	yes	characteristic, complemented
82	#72283936	C₂²	1	1	yes	characteristic, complemented
83	#72283640	C₂²	1	1	yes	characteristic, complemented
84	#72260657	C₂²	1	1	yes	characteristic, complemented
85	#72260657	C₂²	1	1	yes	characteristic, complemented
86	#72241340	C₂	1	1	yes	maximal, characteristic, complemented
87	#72241339	C₂	1	1	yes	maximal, characteristic, complemented
88	#72241339	C₂	1	1	yes	maximal, characteristic, complemented
89	#72241338	C₂	1	1	yes	maximal, characteristic, complemented
90	#72241337	C₂²	1	1	yes	characteristic, complemented
91	#72241337	C₂²	1	1	yes	characteristic, complemented
92	#72241337	C₂²	1	1	yes	characteristic, complemented
93	#72241337	C₂²	1	1	yes	characteristic, complemented
94	#72241337	C₂²	1	1	yes	characteristic, complemented
95	#72241337	C₂²	1	1	yes	characteristic, complemented
96	#72241334	C₂	1	1	yes	maximal, characteristic, complemented
97	#72241333	C₂²	1	1	yes	characteristic, complemented
98	#72241333	C₂²	1	1	yes	characteristic, complemented
99	#72241332	C₂²	1	1	yes	characteristic, complemented
100	#72241332	C₂²	1	1	yes	characteristic, complemented
101	#72241332	C₂²	1	1	yes	characteristic, complemented
102	#72241332	C₂²	1	1	yes	characteristic, complemented
103	#72241332	C₂²	1	1	yes	characteristic, complemented
104	#72241332	C₂²	1	1	yes	characteristic, complemented
105	#72241316	C₂²	1	1	yes	characteristic, complemented
106	#72241316	C₂²	1	1	yes	characteristic, complemented
107	#72241315	C₂²	1	1	yes	characteristic, complemented
108	#72241315	C₂²	1	1	yes	characteristic, complemented
109	#72241315	C₂²	1	1	yes	characteristic, complemented
110	#72241315	C₂²	1	1	yes	characteristic, complemented
111	#72241305	C₂²	1	1	yes	characteristic, complemented
112	#72241305	C₂²	1	1	yes	characteristic, complemented
113	#72241304	C₂²	1	1	yes	characteristic, complemented
114	#72241303	C₂²	1	1	yes	characteristic, complemented
115	#72241301	C₂²	1	1	yes	characteristic, complemented
116	#72241085	C₂	1	1	yes	maximal, characteristic, complemented
117	#72241079	C₂²	1	1	yes	characteristic, complemented
118	#72241079	C₂²	1	1	yes	characteristic, complemented
119	#72241079	C₂²	1	1	yes	characteristic, complemented
120	#72241079	C₂²	1	1	yes	characteristic, complemented
121	#72238017	C₂	1	1	yes	maximal, characteristic, complemented
122	#72238016	C₂²	1	1	yes	characteristic, complemented
123	#72238016	C₂²	1	1	yes	characteristic, complemented
124	#72238015	C₂²	1	1	yes	characteristic, complemented
125	#72238015	C₂²	1	1	yes	characteristic, complemented
126	#72238015	C₂²	1	1	yes	characteristic, complemented
127	#72238015	C₂²	1	1	yes	characteristic, complemented
128	#72238015	C₂²	1	1	yes	characteristic, complemented
129	#72238015	C₂²	1	1	yes	characteristic, complemented
130	#72238014	C₂²	1	1	yes	characteristic, complemented
131	#72238014	C₂²	1	1	yes	characteristic, complemented
132	#72238013	C₂²	1	1	yes	characteristic, complemented
133	#72238013	C₂²	1	1	yes	characteristic, complemented
134	#72238013	C₂²	1	1	yes	characteristic, complemented
135	#72238013	C₂²	1	1	yes	characteristic, complemented
136	#72238013	C₂²	1	1	yes	characteristic, complemented
137	#72238013	C₂²	1	1	yes	characteristic, complemented
138	#72238012	C₂²	1	1	yes	characteristic, complemented
139	#72238010	C₂²	1	1	yes	characteristic, complemented
140	#72238010	C₂²	1	1	yes	characteristic, complemented
141	#72236975	C₂²	1	1	yes	characteristic, complemented
142	#72236925	C₂²	1	1	yes	characteristic, complemented
143	#72236925	C₂²	1	1	yes	characteristic, complemented
144	#72236925	C₂²	1	1	yes	characteristic, complemented
145	#72236711	C₂²	1	1	yes	characteristic, complemented
146	#72236702	C₂²	1	1	yes	characteristic, complemented
147	#72236680	C₂²	1	1	yes	characteristic, complemented
148	#72236680	C₂²	1	1	yes	characteristic, complemented
149	#72236657	C₂²	1	1	yes	characteristic, complemented
150	#72234146	C₂²	1	1	yes	characteristic
151	#72234146	C₂²	1	1	yes	characteristic, complemented
152	#72233917	C₂²	1	1	yes	characteristic, complemented
153	#72227588	C₂²	1	1	yes	characteristic, complemented
154	#72213565	C₂	1	1	yes	maximal, characteristic, complemented
155	#72213523	C₂²	1	1	yes	characteristic, complemented
156	#72213523	C₂²	1	1	yes	characteristic, complemented
157	#72213523	C₂²	1	1	yes	characteristic, complemented
158	#72213513	C₂²	1	1	yes	characteristic, complemented
159	#72213513	C₂²	1	1	yes	characteristic, complemented
160	#72213513	C₂²	1	1	yes	characteristic, complemented
161	#72213504	C₂²	1	1	yes	characteristic, complemented
162	#72213504	C₂²	1	1	yes	characteristic, complemented
163	#72213504	C₂²	1	1	yes	characteristic, complemented
164	#72213504	C₂²	1	1	yes	characteristic, complemented
165	#72213504	C₂²	1	1	yes	characteristic, complemented
166	#72213504	C₂²	1	1	yes	characteristic, complemented
167	#72213504	C₂²	1	1	yes	characteristic, complemented
168	#72213504	C₂²	1	1	yes	characteristic, complemented
169	#72213504	C₂²	1	1	yes	characteristic, complemented
170	#72213504	C₂²	1	1	yes	characteristic, complemented
171	#72213504	C₂²	1	1	yes	characteristic, complemented
172	#72213504	C₂²	1	1	yes	characteristic, complemented
173	#72213462	C₂²	1	1	yes	characteristic, complemented
174	#72213462	C₂²	1	1	yes	characteristic, complemented
175	#72213435	C₂²	1	1	yes	characteristic, complemented
176	#72213435	C₂²	1	1	yes	characteristic, complemented
177	#72213435	C₂²	1	1	yes	characteristic, complemented
178	#72213435	C₂²	1	1	yes	characteristic, complemented
179	#72213423	C₂²	1	1	yes	characteristic, complemented
180	#72213210	C₂²	1	1	yes	characteristic, complemented
181	#72213210	C₂²	1	1	yes	characteristic, complemented
182	#72210439	C₂²	1	1	yes	characteristic, complemented
183	#72210035	C₂²	1	1	yes	characteristic, complemented
184	#72210025	C₂²	1	1	yes	characteristic, complemented
185	#72210025	C₂²	1	1	yes	characteristic, complemented
186	#72210025	C₂²	1	1	yes	characteristic, complemented
187	H(9,𝔽₂)	C₂³	1	1	yes	characteristic
188	#10586106	C₂³	1	1	yes	characteristic
189	#10586097	C₂³	1	1	yes	characteristic
190	#10574841	C₂³	1	1	yes	characteristic
191	#10574841	C₂³	1	1	yes	characteristic
192	#10574841	C₂³	1	1	yes	characteristic
193	#10574841	C₂³	1	1	yes	characteristic
194	C₂×#60389	C₂³	1	1	yes	characteristic
195	C₂×#60389	C₂³	1	1	yes	characteristic
196	C₂×#60390	D₄	1	1	yes	characteristic, complemented
197	C₂×#60388	D₄	1	1	yes	characteristic, complemented
198	C₂×#60388	C₂³	1	1	yes	characteristic
199	C₂×#60388	C₂³	1	1	yes	characteristic
200	#10574064	C₂³	1	1	yes	characteristic
201	#10574064	C₂³	1	1	yes	characteristic
202	#8934366	C₂³	1	1	yes	characteristic
203	#8926849	C₂³	1	1	yes	characteristic
204	#7743195	C₂³	1	1	yes	characteristic
205	#7742598	C₂³	1	1	yes	characteristic
206	#7737411	C₂³	1	1	yes	characteristic
207	#7737041	C₂³	1	1	yes	characteristic
208	#7674604	C₂³	1	1	yes	characteristic
209	C₂²×#2200	D₄	1	2	yes	complemented
210	C₂²×#2199	D₄	1	2	yes	complemented
211	C₂²×#2197	D₄	1	2	yes	complemented
212	C₂²×#2196	D₄	1	2	yes	complemented
213	#6628972	D₄	1	1	yes	characteristic, complemented
214	#6628970	D₄	1	1	yes	characteristic, complemented
215	#6628901	C₂³	1	1	yes	characteristic
216	#6628897	C₂³	1	1	yes	characteristic
217	#6628897	C₂³	1	1	yes	characteristic
218	#6628897	C₂³	1	1	yes	characteristic
219	#6628896	C₂³	1	1	yes	characteristic
220	#6628896	C₂³	1	1	yes	characteristic
221	#6628896	C₂³	1	1	yes	characteristic
222	#6628896	C₂³	1	1	yes	characteristic
223	#6628896	C₂³	1	1	yes	characteristic
224	#6628896	C₂³	1	1	yes	characteristic
225	#6628896	C₂³	1	1	yes	characteristic
226	#6628896	C₂³	1	1	yes	characteristic
227	#6628896	C₂³	1	1	yes	characteristic
228	#6628874	D₄	1	1	yes	characteristic, complemented
229	#6628873	D₄	1	1	yes	characteristic, complemented
230	#6628872	C₂³	1	1	yes	characteristic
231	#6628872	C₂³	1	1	yes	characteristic
232	#6470235	C₂³	1	1	yes	characteristic
233	#6470235	C₂³	1	1	yes	characteristic
234	#6470234	C₂³	1	1	yes	characteristic
235	#6470234	C₂³	1	1	yes	characteristic
236	#6470234	C₂³	1	1	yes	characteristic
237	#6470234	C₂³	1	1	yes	characteristic
238	#6470234	C₂³	1	1	yes	characteristic
239	#6470234	C₂³	1	1	yes	characteristic
240	#6443332	D₄	1	1	yes	characteristic, complemented
241	#6443331	D₄	1	1	yes	characteristic, complemented
242	#6442560	D₄	1	1	yes	characteristic, complemented
243	#6442560	D₄	1	1	yes	characteristic, complemented
244	#6437971	D₄	1	1	yes	characteristic, complemented
245	#6437970	D₄	1	1	yes	characteristic, complemented
246	#6437969	C₂³	1	1	yes	characteristic
247	#6437969	C₂³	1	1	yes	characteristic
248	#6437630	C₂³	1	1	yes	characteristic
249	#6437454	D₄	1	1	yes	characteristic, complemented
250	#6437453	C₂³	1	1	yes	characteristic
251	#6437452	D₄	1	1	yes	characteristic, complemented
252	#6437452	C₂³	1	1	yes	characteristic
253	#6385981	C₂³	1	1	yes	characteristic
254	#6385981	C₂³	1	1	yes	characteristic
255	#6385980	C₂³	1	1	yes	characteristic
256	#6385980	C₂³	1	1	yes	characteristic
257	#6379034	C₂³	1	1	yes	characteristic
258	#6379033	C₂³	1	1	yes	characteristic
259	#6372704	D₄	1	1	yes	characteristic, complemented
260	#6372704	D₄	1	1	yes	characteristic, complemented
261	#498928	D₄	1	2	yes	complemented
262	#498928	D₄	1	2	yes	complemented
263	#498927	D₄	1	2	yes	complemented
264	#498927	D₄	1	2	yes	complemented
265	#498927	D₄	1	2	yes	complemented
266	#498927	D₄	1	2	yes	complemented
267	#498927	D₄	1	2	yes	complemented
268	#498927	D₄	1	2	yes	complemented
269	#496241	C₂³	1	1	yes	characteristic
270	#496241	C₂³	1	1	yes	characteristic
271	#496240	C₂³	1	1	yes	characteristic
272	#496240	C₂³	1	1	yes	characteristic
273	#496240	C₂³	1	1	yes	characteristic
274	#496240	C₂³	1	1	yes	characteristic
275	#496240	C₂³	1	1	yes	characteristic
276	#496240	C₂³	1	1	yes	characteristic
277	#496203	C₂³	1	1	yes	characteristic
278	#496203	C₂³	1	1	yes	characteristic
279	#496203	C₂³	1	1	yes	characteristic
280	#496203	C₂³	1	1	yes	characteristic
281	#494682	C₂³	1	1	yes	characteristic
282	#494682	C₂³	1	1	yes	characteristic
283	#494682	C₂³	1	1	yes	characteristic
284	#494682	C₂³	1	1	yes	characteristic
285	#494682	C₂³	1	1	yes	characteristic
286	#494682	C₂³	1	1	yes	characteristic
287	#494682	C₂³	1	1	yes	characteristic
288	#494682	C₂³	1	1	yes	characteristic
289	#494682	C₂³	1	1	yes	characteristic
290	#494682	C₂³	1	1	yes	characteristic
291	#494682	C₂³	1	1	yes	characteristic
292	#494682	C₂³	1	1	yes	characteristic
293	#494681	C₂³	1	1	yes	characteristic
294	#494681	C₂³	1	1	yes	characteristic
295	#494681	C₂³	1	1	yes	characteristic
296	#494681	C₂³	1	1	yes	characteristic
297	#494597	D₄	1	2	yes	complemented
298	#494597	D₄	1	2	yes	complemented
299	#494596	D₄	1	2	yes	complemented
300	#494596	D₄	1	2	yes	complemented
301	#493433	C₂³	1	1	yes	characteristic
302	#493433	C₂³	1	1	yes	characteristic
303	#493433	C₂³	1	1	yes	characteristic
304	#493433	C₂³	1	1	yes	characteristic
305	#493430	C₂³	1	1	yes	characteristic
306	#493430	C₂³	1	1	yes	characteristic
307	#493430	C₂³	1	1	yes	characteristic
308	#493430	C₂³	1	1	yes	characteristic
309	#493397	C₂³	1	1	yes	characteristic
310	#493397	C₂³	1	1	yes	characteristic
311	#493397	C₂³	1	1	yes	characteristic
312	#493397	C₂³	1	1	yes	characteristic
313	#493397	C₂³	1	1	yes	characteristic
314	#493397	C₂³	1	1	yes	characteristic
315	#493397	C₂³	1	1	yes	characteristic
316	#493397	C₂³	1	1	yes	characteristic
317	#449492	D₄	1	2	yes	complemented
318	#417813	D₄	1	2	yes	complemented
319	#417568	D₄	1	2	yes	complemented
320	#417566	D₄	1	2	yes	complemented
321	#392138	C₂³	1	1	yes	characteristic
322	#392138	C₂³	1	1	yes	characteristic
323	#392136	C₂³	1	1	yes	characteristic
324	#392135	C₂³	1	1	yes	characteristic
325	#392135	C₂³	1	1	yes	characteristic
326	#392135	C₂³	1	1	yes	characteristic
327	#392135	C₂³	1	1	yes	characteristic
328	#392135	C₂³	1	1	yes	characteristic
329	#392135	C₂³	1	1	yes	characteristic
330	#392135	C₂³	1	1	yes	characteristic
331	#392135	C₂³	1	1	yes	characteristic
332	#392135	C₂³	1	1	yes	characteristic
333	#392135	C₂³	1	1	yes	characteristic
334	#392135	C₂³	1	1	yes	characteristic
335	#392135	C₂³	1	1	yes	characteristic
336	#374009	C₂³	1	1	yes	characteristic
337	#360531	C₂³	1	1	yes	characteristic
338	#360531	C₂³	1	1	yes	characteristic
339	#359606	C₂³	1	1	yes	characteristic
340	#359605	C₂³	1	1	yes	characteristic
341	#359529	C₂³	1	1	yes	characteristic
342	#359529	C₂³	1	1	yes	characteristic
343	#356056	C₂³	1	1	yes	characteristic
344	#213860	C₂³	1	1	yes	characteristic
345	#213860	C₂³	1	1	yes	characteristic
346	#213855	C₂³	1	1	yes	characteristic
347	#213854	C₂³	1	1	yes	characteristic
348	#213854	C₂³	1	1	yes	characteristic
349	#213854	C₂³	1	1	yes	characteristic
350	#146577	C₂³	1	1	yes	characteristic
351	#146577	C₂³	1	1	yes	characteristic
352	#146577	C₂³	1	1	yes	characteristic
353	#146577	C₂³	1	1	yes	characteristic
354	#146577	C₂³	1	1	yes	characteristic
355	#146577	C₂³	1	1	yes	characteristic
356	#146577	C₂³	1	1	yes	characteristic
357	#146577	C₂³	1	1	yes	characteristic
358	#146577	C₂³	1	1	yes	characteristic
359	#146577	C₂³	1	1	yes	characteristic
360	#146577	C₂³	1	1	yes	characteristic
361	#146577	C₂³	1	1	yes	characteristic
362	#146577	C₂³	1	1	yes	characteristic
363	#146577	C₂³	1	1	yes	characteristic
364	#146577	C₂³	1	1	yes	characteristic
365	#146577	C₂³	1	1	yes	characteristic
366	#128079	C₂³	1	1	yes	characteristic
367	#128079	C₂³	1	1	yes	characteristic
368	#128079	C₂³	1	1	yes	characteristic
369	#128079	C₂³	1	1	yes	characteristic
370	#128079	C₂³	1	1	yes	characteristic
371	#128079	C₂³	1	1	yes	characteristic
372	#128079	C₂³	1	1	yes	characteristic
373	#128079	C₂³	1	1	yes	characteristic
374	#128062	C₂³	1	1	yes	characteristic
375	#128062	C₂³	1	1	yes	characteristic
376	#128062	C₂³	1	1	yes	characteristic
377	#128062	C₂³	1	1	yes	characteristic
378	C₂×2₋¹⁺⁶	C₂×D₄	1	1	yes	characteristic, complemented
379	C₂×H(7,𝔽₂)	C₂×D₄	1	1	yes	characteristic
380	C₂×H(7,𝔽₂)	C₂⁴	1	1	yes	characteristic
381	C₂×H(7,𝔽₂)	C₂⁴	1	1	yes	characteristic
382	C₂×H(7,𝔽₂)	C₂⁴	1	1	yes	characteristic
383	#62859	C₂×D₄	1	1	yes	characteristic, complemented
384	#62852	C₂×D₄	1	1	yes	characteristic
385	#62852	C₂⁴	1	1	yes	characteristic
386	#62852	C₂⁴	1	1	yes	characteristic
387	#62812	C₂×D₄	1	1	yes	characteristic
388	#62812	C₂×D₄	1	1	yes	characteristic, complemented
389	C₂×#3500	C₂×D₄	1	1	yes	characteristic
390	C₂×#3500	C₂⁴	1	1	yes	characteristic
391	C₂×#3498	C₂×D₄	1	1	yes	characteristic
392	C₂×#3498	C₂⁴	1	1	yes	characteristic
393	C₂²×#551	C₂×D₄	1	1	yes	characteristic
394	C₂²×D₄²	C₂×D₄	1	1	yes	characteristic
395	C₂²×H(3,𝔽₄)	C₂×D₄	1	1	yes	characteristic
396	C₂²×#560	C₂×D₄	1	1	yes	characteristic
397	C₄×#585	C₂×D₄	1	1	yes	characteristic
398	C₄×#585	C₂×D₄	1	1	yes	characteristic, complemented
399	C₂²×#458	C₂×D₄	1	2	yes	—
400	C₂²×#458	C₂×D₄	1	2	yes	complemented
401	C₂²×B(4,𝔽₂)	C₂×D₄	1	2	yes	—
402	C₂²×B(4,𝔽₂)	C₂×D₄	1	2	yes	—
403	C₂²×B(4,𝔽₂)	C₂×D₄	1	2	yes	—
404	C₂²×B(4,𝔽₂)	C₂×D₄	1	2	yes	—
405	C₂²×B(4,𝔽₂)	C₂×D₄	1	2	yes	—
406	C₂²×B(4,𝔽₂)	C₂×D₄	1	2	yes	complemented
407	C₂×#3022	C₂×D₄	1	1	yes	characteristic
408	C₂×#3022	C₂×D₄	1	1	yes	characteristic
409	C₂×#3022	C₂×D₄	1	1	yes	characteristic
410	C₂×#3021	C₂×D₄	1	1	yes	characteristic
411	C₂×#3021	C₂×D₄	1	1	yes	characteristic
412	C₂×#3021	C₂×D₄	1	1	yes	characteristic
413	C₂×#3021	C₂×D₄	1	1	yes	characteristic
414	C₂×#3021	C₂×D₄	1	1	yes	characteristic
415	C₂×#3021	C₂×D₄	1	1	yes	characteristic
416	C₂×#3021	C₂×D₄	1	1	yes	characteristic, complemented
417	C₂×#3021	C₂×D₄	1	1	yes	characteristic, complemented
418	C₂×#3021	C₂×D₄	1	1	yes	characteristic, complemented
419	C₂×#3019	C₂×D₄	1	2	yes	—
420	C₂×#3019	C₂×D₄	1	2	yes	—
421	C₂×#3019	C₂×D₄	1	2	yes	—
422	C₂×#3019	C₂×D₄	1	2	yes	—
423	C₂×#3019	C₂×D₄	1	2	yes	—
424	C₂×#3019	C₂×D₄	1	2	yes	complemented
425	C₂×#3018	C₂×D₄	1	1	yes	characteristic
426	C₂×#3018	C₂×D₄	1	1	yes	characteristic
427	C₂×#3018	C₂×D₄	1	1	yes	characteristic
428	C₂×#3018	C₂×D₄	1	1	yes	characteristic
429	C₂×#3018	C₂×D₄	1	1	yes	characteristic
430	C₂×#3018	C₂×D₄	1	1	yes	characteristic
431	C₂²×#455	C₂×D₄	1	2	yes	—
432	C₂²×#455	C₂×D₄	1	2	yes	—
433	C₂²×#455	C₂×D₄	1	2	yes	complemented
434	C₂²×#453	C₂×D₄	1	2	yes	—
435	C₂²×#453	C₂×D₄	1	2	yes	—
436	C₂²×#453	C₂×D₄	1	2	yes	—
437	C₂×#2889	C₂×D₄	1	1	yes	characteristic, complemented
438	C₂×#2888	C₂×D₄	1	1	yes	characteristic
439	C₂×#2888	C₂⁴	1	1	yes	characteristic
440	C₂×#2888	C₂⁴	1	1	yes	characteristic
441	C₂×#2888	C₂⁴	1	1	yes	characteristic
442	C₂×#2888	C₂⁴	1	1	yes	characteristic
443	#36955	C₂×D₄	1	1	yes	characteristic
444	#36955	C₂×D₄	1	1	yes	characteristic
445	#36702	C₂×D₄	1	1	yes	characteristic
446	#36702	C₂×D₄	1	1	yes	characteristic
447	#36702	C₂×D₄	1	1	yes	characteristic
448	#36702	C₂×D₄	1	1	yes	characteristic
449	#36702	C₂×D₄	1	1	yes	characteristic
450	#36702	C₂×D₄	1	1	yes	characteristic
451	#35676	C₂×D₄	1	1	yes	characteristic
452	#35616	C₂×D₄	1	1	yes	characteristic
453	#35527	C₂×D₄	1	1	yes	characteristic
454	#35527	C₂×D₄	1	2	yes	complemented
455	#35527	C₂⁴	1	1	yes	characteristic
456	#35446	C₂⁴	1	1	yes	characteristic
457	#35346	C₂⁴	1	1	yes	characteristic
458	#35346	C₂⁴	1	1	yes	characteristic
459	#35346	C₂⁴	1	1	yes	characteristic
460	#35327	C₂×D₄	1	1	yes	characteristic
461	#35327	C₂×D₄	1	1	yes	characteristic
462	#35272	C₂×D₄	1	1	yes	characteristic
463	#35272	C₂×D₄	1	1	yes	characteristic
464	C₂×#2657	C₂×D₄	1	1	yes	characteristic
465	#34366	C₂×D₄	1	1	yes	characteristic
466	#34366	C₂×D₄	1	1	yes	characteristic
467	#34364	C₂×D₄	1	1	yes	characteristic
468	#34364	C₂×D₄	1	1	yes	characteristic
469	#34070	C₂×D₄	1	1	yes	characteristic
470	#34070	C₂×D₄	1	1	yes	characteristic
471	C₂×#2127	C₂×D₄	1	2	yes	—
472	C₂×#2127	C₂×D₄	1	2	yes	—
473	C₂×#2127	C₂×D₄	1	2	yes	—
474	C₂×#2127	C₂×D₄	1	2	yes	—
475	C₂²×#354	C₂×D₄	1	2	yes	—
476	C₂²×#354	C₂×D₄	1	2	yes	—
477	C₂²×#353	C₂×D₄	1	2	yes	—
478	C₂²×#353	C₂×D₄	1	2	yes	—
479	C₂²×#352	C₂×D₄	1	2	yes	—
480	C₂²×#352	C₂×D₄	1	2	yes	complemented
481	C₂²×AΣL(1,𝔽₁₆)	C₂×D₄	1	2	yes	—
482	C₂²×AΣL(1,𝔽₁₆)	C₂×D₄	1	2	yes	—
483	C₂²×AΣL(1,𝔽₁₆)	C₂×D₄	1	2	yes	—
484	C₂²×AΣL(1,𝔽₁₆)	C₂×D₄	1	2	yes	—
485	C₂²×AΣL(1,𝔽₁₆)	C₂×D₄	1	2	yes	—
486	C₂²×AΣL(1,𝔽₁₆)	C₂×D₄	1	2	yes	complemented
487	#20956	C₂×D₄	1	1	yes	characteristic
488	#20956	C₂×D₄	1	1	yes	characteristic
489	#20956	C₂×D₄	1	1	yes	characteristic, complemented
490	#20955	C₂×D₄	1	1	yes	characteristic
491	#20952	C₂×D₄	1	1	yes	characteristic
492	#20952	C₂×D₄	1	1	yes	characteristic
493	#20855	C₂×D₄	1	1	yes	characteristic
494	#20855	C₂×D₄	1	1	yes	characteristic, complemented
495	#20637	C₂×D₄	1	1	yes	characteristic
496	#20637	C₂×D₄	1	1	yes	characteristic, complemented
497	#20615	C₂×D₄	1	1	yes	characteristic
498	#20615	C₂×D₄	1	1	yes	characteristic
499	#20615	C₂×D₄	1	1	yes	characteristic
500	#20615	C₂×D₄	1	1	yes	characteristic, complemented
501	#20615	C₂×D₄	1	1	yes	characteristic, complemented
502	#20615	C₂×D₄	1	1	yes	characteristic, complemented
503	#20609	C₂×D₄	1	2	yes	—
504	#20609	C₂×D₄	1	2	yes	—
505	#20609	C₂×D₄	1	2	yes	—
506	#20609	C₂×D₄	1	2	yes	—
507	#20609	C₂×D₄	1	2	yes	—
508	#20609	C₂×D₄	1	2	yes	—
509	#20609	C₂×D₄	1	2	yes	complemented
510	#20609	C₂×D₄	1	2	yes	complemented
511	#20593	C₂×D₄	1	1	yes	characteristic, complemented
512	#20592	C₂×D₄	1	1	yes	characteristic
513	#20592	C₂⁴	1	1	yes	characteristic
514	#20592	C₂⁴	1	1	yes	characteristic
515	#20586	C₂×D₄	1	2	yes	complemented
516	#20586	C₂⁴	1	1	yes	characteristic
517	#20585	C₂⁴	1	1	yes	characteristic
518	#20585	C₂⁴	1	1	yes	characteristic
519	#20585	C₂⁴	1	1	yes	characteristic
520	#20585	C₂⁴	1	1	yes	characteristic
521	#20585	C₂⁴	1	1	yes	characteristic
522	#20585	C₂⁴	1	1	yes	characteristic
523	#20585	C₂⁴	1	1	yes	characteristic
524	#20585	C₂⁴	1	1	yes	characteristic
525	#20585	C₂⁴	1	1	yes	characteristic
526	#20585	C₂⁴	1	1	yes	characteristic
527	#20585	C₂⁴	1	1	yes	characteristic
528	#20585	C₂⁴	1	1	yes	characteristic
529	C₄×#413	C₂×D₄	1	1	yes	characteristic
530	C₄×#413	C₂×D₄	1	1	yes	characteristic, complemented
531	#12574	C₂×D₄	1	2	yes	—
532	#12574	C₂×D₄	1	2	yes	—
533	#12574	C₂×D₄	1	2	yes	—
534	#12574	C₂×D₄	1	2	yes	—
535	#12574	C₂×D₄	1	2	yes	—
536	#12574	C₂×D₄	1	2	yes	—
537	#12574	C₂×D₄	1	2	yes	complemented
538	#12574	C₂×D₄	1	2	yes	complemented
539	#11167	C₂×D₄	1	2	yes	complemented
540	#10989	C₂×D₄	1	2	yes	—
541	#10989	C₂×D₄	1	2	yes	complemented
542	#10981	C₂×D₄	1	2	yes	complemented
543	#10977	C₂×D₄	1	2	yes	complemented
544	#10975	C₂×D₄	1	2	yes	—
545	C₂×#585	C₂²×D₄	1	1	yes	characteristic
546	C₂×#585	C₂²×D₄	1	1	yes	characteristic
547	C₂×#585	C₂²×D₄	1	1	yes	characteristic
548	C₂×#585	C₂²×D₄	1	1	yes	characteristic
549	C₂×#585	C₂²×D₄	1	1	yes	characteristic
550	C₂×#585	C₂²×D₄	1	1	yes	characteristic
551	C₂²×2₋¹⁺⁴	C₂²×D₄	1	1	yes	characteristic
552	C₂²×H(5,𝔽₂)	#120	1	1	yes	characteristic, complemented
553	C₂²×H(5,𝔽₂)	C₂²×D₄	1	1	yes	characteristic
554	C₂²×H(5,𝔽₂)	C₂²×D₄	1	2	yes	—
555	C₂²×H(5,𝔽₂)	C₂²×D₄	1	2	yes	—
556	C₂²×H(5,𝔽₂)	C₂²×D₄	1	2	yes	—
557	C₂²×H(5,𝔽₂)	C₂²×D₄	1	2	yes	—
558	C₂²×H(5,𝔽₂)	C₂²×D₄	1	2	yes	—
559	C₂²×H(5,𝔽₂)	C₂⁵	1	1	yes	characteristic
560	C₂×#536	#120	1	1	yes	characteristic, complemented
561	C₂×#536	C₂²×D₄	1	1	yes	characteristic
562	C₂×#536	H(5,𝔽₂)	1	1	yes	characteristic
563	C₂×#536	H(5,𝔽₂)	1	1	yes	characteristic
564	C₂×#535	#120	1	1	yes	characteristic, complemented
565	C₂×#535	C₂²×D₄	1	1	yes	characteristic
566	C₂×#535	C₂²×D₄	1	1	yes	characteristic
567	C₂×#535	C₂²×D₄	1	1	yes	characteristic
568	C₂×#535	C₂²×D₄	1	1	yes	characteristic
569	C₂×#535	C₂²×D₄	1	1	yes	characteristic
570	C₂×#535	C₂²×D₄	1	1	yes	characteristic
571	C₂×#535	C₂²×D₄	1	1	yes	characteristic
572	C₂×#535	C₂²×D₄	1	1	yes	characteristic
573	C₂×#535	C₂²×D₄	1	1	yes	characteristic
574	C₂×#535	H(5,𝔽₂)	1	1	yes	characteristic
575	C₂×#535	H(5,𝔽₂)	1	1	yes	characteristic
576	C₂×#532	C₂²×D₄	1	1	yes	characteristic
577	C₂×#532	C₂²×D₄	1	1	yes	characteristic
578	C₂×#532	H(5,𝔽₂)	1	1	yes	characteristic
579	C₂×#532	H(5,𝔽₂)	1	1	yes	characteristic
580	C₂×#532	H(5,𝔽₂)	1	1	yes	characteristic
581	C₂×#532	H(5,𝔽₂)	1	1	yes	characteristic
582	C₂²×#127	#120	1	1	yes	characteristic, complemented
583	C₂²×#127	C₂²×D₄	1	1	yes	characteristic
584	C₂²×#127	C₂²×D₄	1	1	yes	characteristic
585	C₂²×#127	C₂²×D₄	1	1	yes	characteristic
586	C₂²×#127	C₂²×D₄	1	1	yes	characteristic
587	C₂²×#124	#120	1	1	yes	characteristic, complemented
588	C₂²×#124	#120	1	1	yes	characteristic, complemented
589	C₂²×#124	C₂²×D₄	1	1	yes	characteristic
590	C₂²×#124	C₂²×D₄	1	1	yes	characteristic
591	C₂²×#124	C₂²×D₄	1	1	yes	characteristic
592	C₂²×#123	C₂²×D₄	1	1	yes	characteristic
593	C₂²×#123	C₂²×D₄	1	1	yes	characteristic
594	C₂²×#123	H(5,𝔽₂)	1	1	yes	characteristic
595	C₂²×#120	C₂²×D₄	1	1	yes	characteristic
596	C₂²×#120	C₂²×D₄	1	1	yes	characteristic
597	C₂²×#120	C₂²×D₄	1	1	yes	characteristic
598	C₂²×#120	C₂²×D₄	1	1	yes	characteristic
599	C₂²×#120	C₂²×D₄	1	1	yes	characteristic
600	C₂²×#120	C₂²×D₄	1	1	yes	characteristic
601	C₂²×#120	H(5,𝔽₂)	1	1	yes	characteristic
602	C₂²×#120	H(5,𝔽₂)	1	1	yes	characteristic
603	C₂²×#120	H(5,𝔽₂)	1	1	yes	characteristic
604	#3428	C₂²×D₄	1	1	yes	characteristic
605	#3428	C₂²×D₄	1	1	yes	characteristic
606	C₂×C₄×#41	#120	1	1	yes	characteristic, complemented
607	C₂×C₄×#41	#120	1	1	yes	characteristic, complemented
608	C₂×C₄×#41	C₂²×D₄	1	1	yes	characteristic
609	C₂×C₄×#41	C₂²×D₄	1	1	yes	characteristic
610	C₂×#455	#120	1	2	yes	—
611	C₂×#455	#120	1	2	yes	—
612	C₂×#455	#120	1	2	yes	—
613	C₂×#455	#120	1	2	yes	—
614	C₂×#455	#120	1	2	yes	—
615	C₂×#455	#120	1	2	yes	—
616	C₂×#455	#120	1	2	yes	—
617	C₂×#455	#120	1	2	yes	—
618	C₂×#453	#120	1	2	yes	—
619	C₂×#453	#120	1	2	yes	—
620	C₂×#453	#120	1	2	yes	—
621	C₂×#453	#120	1	2	yes	—
622	C₂×#453	#120	1	2	yes	—
623	C₂×#453	#120	1	2	yes	—
624	C₂×#453	#120	1	2	yes	—
625	C₂×#453	#120	1	2	yes	—
626	C₂×#413	C₂²×D₄	1	1	yes	characteristic
627	C₂×#413	C₂²×D₄	1	1	yes	characteristic
628	C₂×#413	C₂²×D₄	1	1	yes	characteristic
629	C₂×#413	C₂²×D₄	1	1	yes	characteristic
630	C₂×#413	C₂²×D₄	1	1	yes	characteristic
631	C₂×#413	C₂²×D₄	1	1	yes	characteristic
632	C₂×#413	C₂²×D₄	1	1	yes	characteristic
633	C₂×#413	C₂²×D₄	1	1	yes	characteristic
634	C₂²×#100	C₂²×D₄	1	2	yes	—
635	C₂²×#100	C₂²×D₄	1	2	yes	—
636	C₂²×#100	C₂²×D₄	1	2	yes	—
637	C₂²×#100	C₂²×D₄	1	2	yes	—
638	C₂²×#100	C₂²×D₄	1	2	yes	—
639	C₂²×#100	C₂²×D₄	1	2	yes	—
640	C₂²×#99	C₂²×D₄	1	2	yes	—
641	C₂²×#99	C₂²×D₄	1	2	yes	—
642	C₂²×#99	C₂²×D₄	1	2	yes	—
643	C₂²×#99	C₂²×D₄	1	2	yes	—
644	C₂²×#99	C₂²×D₄	1	2	yes	—
645	C₂²×#99	C₂²×D₄	1	2	yes	—
646	C₂²×#99	C₂²×D₄	1	2	yes	—
647	C₂²×#99	C₂²×D₄	1	2	yes	—
648	#2310	#120	1	1	yes	characteristic, complemented
649	#2309	#120	1	1	yes	characteristic, complemented
650	#2309	#120	1	1	yes	characteristic, complemented
651	#2309	C₂²×D₄	1	2	yes	—
652	#2309	C₂²×D₄	1	1	yes	characteristic
653	#2308	C₂²×D₄	1	1	yes	characteristic
654	#2308	C₂²×D₄	1	1	yes	characteristic
655	#2308	C₂²×D₄	1	1	yes	characteristic
656	#2308	C₂²×D₄	1	1	yes	characteristic
657	#2308	C₂²×D₄	1	1	yes	characteristic
658	#2308	C₂²×D₄	1	1	yes	characteristic
659	#2308	C₂²×D₄	1	1	yes	characteristic
660	#2308	C₂²×D₄	1	1	yes	characteristic
661	#2308	H(5,𝔽₂)	1	1	yes	characteristic
662	#2308	H(5,𝔽₂)	1	1	yes	characteristic
663	#2308	H(5,𝔽₂)	1	1	yes	characteristic
664	#2308	H(5,𝔽₂)	1	1	yes	characteristic
665	#2297	#120	1	1	yes	characteristic, complemented
666	#2297	#120	1	1	yes	characteristic, complemented
667	#2297	C₂²×D₄	1	1	yes	characteristic
668	#2297	C₂²×D₄	1	1	yes	characteristic
669	#2285	#120	1	1	yes	characteristic, complemented
670	#2285	#120	1	1	yes	characteristic, complemented
671	C₂×#376	#120	1	1	yes	characteristic, complemented
672	C₂⁶	D₄²	1	1	yes	characteristic
673	C₂⁶	D₄²	1	1	yes	characteristic
674	C₂⁶	D₄²	1	1	yes	characteristic
675	C₂×H(5,𝔽₂)	C₂×#120	1	2	yes	—
676	C₂×H(5,𝔽₂)	C₂×#120	1	2	yes	—
677	C₂×H(5,𝔽₂)	C₂×#120	1	2	yes	—
678	C₂×H(5,𝔽₂)	C₂×#120	1	2	yes	—
679	C₂²×#41	C₂×#120	1	1	yes	characteristic
680	C₂²×#41	C₂×#120	1	1	yes	characteristic
681	C₂²×#41	D₄²	1	1	yes	characteristic
682	C₂²×#41	D₄²	1	1	yes	characteristic
683	C₂²×#41	D₄²	1	1	yes	characteristic
684	C₂²×#41	D₄²	1	1	yes	characteristic
685	C₂²×#41	C₂³×D₄	1	1	yes	characteristic
686	C₂²×#41	C₂³×D₄	1	1	yes	characteristic
687	C₂²×#41	C₂×H(5,𝔽₂)	1	1	yes	characteristic
688	C₂²×#41	C₂×H(5,𝔽₂)	1	1	yes	characteristic
689	C₂²×#41	C₂×H(5,𝔽₂)	1	1	yes	characteristic
690	C₂²×#41	C₂×H(5,𝔽₂)	1	1	yes	characteristic
691	C₂³×Q₈	C₂×#120	1	1	yes	characteristic
692	C₂³×Q₈	D₄²	1	1	yes	characteristic
693	C₂³×Q₈	D₄²	1	1	yes	characteristic
694	C₂³×D₄	C₂×#120	1	1	yes	characteristic
695	C₂³×D₄	C₂×#120	1	1	yes	characteristic
696	C₂³×D₄	D₄²	1	1	yes	characteristic
697	C₂³×D₄	D₄²	1	1	yes	characteristic
698	C₂³×D₄	C₂³×D₄	1	1	yes	characteristic
699	C₂³×D₄	C₂³×D₄	1	1	yes	characteristic
700	C₂³×D₄	C₂³×D₄	1	1	yes	characteristic
701	C₂³×D₄	C₂³×D₄	1	1	yes	characteristic
702	C₂³×D₄	C₂³×D₄	1	1	yes	characteristic
703	C₂³×D₄	C₂×H(5,𝔽₂)	1	1	yes	characteristic
704	C₂³×D₄	C₂×H(5,𝔽₂)	1	1	yes	characteristic
705	C₂³×D₄	C₂×H(5,𝔽₂)	1	1	yes	characteristic
706	C₂³×D₄	C₂×H(5,𝔽₂)	1	1	yes	characteristic
707	C₂⁴×C₄	D₄²	1	1	yes	characteristic
708	C₂×C₄⋊Q₈	#534	1	1	yes	characteristic
709	C₂×C₄⋊Q₈	#534	1	1	yes	characteristic
710	C₂×C₄⋊Q₈	#534	1	1	yes	characteristic
711	C₂×C₄⋊Q₈	#534	1	1	yes	characteristic
712	C₂×#127	C₂×#120	1	1	yes	characteristic
713	C₂×#127	C₂×#120	1	1	yes	characteristic
714	C₂×#127	C₂×#120	1	1	yes	characteristic
715	C₂×#127	C₂×#120	1	1	yes	characteristic
716	C₂×#127	D₄²	1	1	yes	characteristic
717	C₂×#127	D₄²	1	1	yes	characteristic
718	C₂×#127	D₄²	1	1	yes	characteristic
719	C₂×#127	D₄²	1	1	yes	characteristic
720	C₂×#127	D₄²	1	1	yes	characteristic
721	C₂×#127	D₄²	1	1	yes	characteristic
722	C₂×#127	D₄²	1	1	yes	characteristic
723	C₂×#127	D₄²	1	1	yes	characteristic
724	C₂×#124	C₂×#120	1	1	yes	characteristic
725	C₂×#124	C₂×#120	1	1	yes	characteristic
726	C₂×#124	C₂×#120	1	1	yes	characteristic
727	C₂×#124	C₂×#120	1	1	yes	characteristic
728	C₂×#124	#534	1	1	yes	characteristic
729	C₂×#124	#534	1	1	yes	characteristic
730	C₂×#124	#534	1	1	yes	characteristic
731	C₂×#124	#534	1	1	yes	characteristic
732	C₂×#124	D₄²	1	1	yes	characteristic
733	C₂×#124	D₄²	1	1	yes	characteristic
734	C₂×#124	D₄²	1	1	yes	characteristic
735	C₂×#124	D₄²	1	1	yes	characteristic
736	C₂×#124	D₄²	1	1	yes	characteristic
737	C₂×#124	D₄²	1	1	yes	characteristic
738	C₂×#124	D₄²	1	1	yes	characteristic
739	C₂×#124	D₄²	1	1	yes	characteristic
740	C₂×#117	C₂×#120	1	1	yes	characteristic
741	C₂×#117	C₂×#120	1	1	yes	characteristic
742	C₂×#117	C₂×#120	1	1	yes	characteristic
743	C₂×#117	C₂×#120	1	1	yes	characteristic
744	C₂×#117	D₄²	1	1	yes	characteristic
745	C₂×#117	D₄²	1	1	yes	characteristic
746	C₂×#117	D₄²	1	1	yes	characteristic
747	C₂×#117	D₄²	1	1	yes	characteristic
748	C₂²×C₂²⋊C₄	D₄²	1	1	yes	characteristic
749	C₂²×C₂²⋊C₄	D₄²	1	1	yes	characteristic
750	C₂²×C₂²⋊C₄	D₄²	1	1	yes	characteristic
751	C₂²×C₂²⋊C₄	D₄²	1	1	yes	characteristic
752	C₂²×C₂²⋊C₄	D₄²	1	1	yes	characteristic
753	C₂²×C₂²⋊C₄	D₄²	1	1	yes	characteristic
754	C₂²×C₂²⋊C₄	D₄²	1	1	yes	characteristic
755	C₂²×C₂²⋊C₄	D₄²	1	1	yes	characteristic
756	C₂²×C₂²⋊C₄	D₄²	1	1	yes	characteristic
757	C₂²×C₂²⋊C₄	D₄²	1	1	yes	characteristic
758	C₂²×C₂²⋊C₄	D₄²	1	1	yes	characteristic
759	C₂²×C₂²⋊C₄	D₄²	1	1	yes	characteristic
760	C₂²×C₄²	C₂×#120	1	1	yes	characteristic
761	C₂²×C₄²	C₂×#120	1	1	yes	characteristic
762	C₂²×C₄²	C₂×#120	1	1	yes	characteristic
763	C₂²×C₄²	D₄²	1	1	yes	characteristic
764	C₂²×C₄²	D₄²	1	1	yes	characteristic
765	C₂²×C₄²	D₄²	1	1	yes	characteristic
766	C₂²×C₄²	D₄²	1	1	yes	characteristic
767	#455	B(4,𝔽₂)	1	4	yes	complemented
768	#455	B(4,𝔽₂)	1	4	yes	complemented
769	#453	B(4,𝔽₂)	1	4	yes	complemented
770	#453	B(4,𝔽₂)	1	4	yes	complemented
771	C₂×#100	C₂×#120	1	2	yes	—
772	C₂×#100	C₂×#120	1	2	yes	—
773	C₂×#100	C₂×#120	1	2	yes	—
774	C₂×#100	C₂×#120	1	2	yes	—
775	C₂⁵	C₂×D₄²	1	1	yes	characteristic
776	C₂⁵	C₂×D₄²	1	1	yes	characteristic
777	C₂⁵	C₂×D₄²	1	1	yes	characteristic
778	C₂⁵	C₂×D₄²	1	1	yes	characteristic
779	C₂⁵	#3484	1	1	yes	characteristic
780	C₂⁵	#3484	1	1	yes	characteristic
781	H(5,𝔽₂)	C₂×B(4,𝔽₂)	1	4	yes	—
782	H(5,𝔽₂)	C₂×B(4,𝔽₂)	1	4	yes	—
783	C₂²×Q₈	#2403	1	1	yes	characteristic
784	C₂²×Q₈	#2403	1	1	yes	characteristic
785	C₂²×Q₈	#2403	1	1	yes	characteristic
786	C₂²×Q₈	#2403	1	1	yes	characteristic
787	C₂²×Q₈	C₂×#534	1	1	yes	characteristic
788	C₂²×Q₈	C₂×#534	1	1	yes	characteristic
789	C₂²×D₄	#2403	1	1	yes	characteristic
790	C₂²×D₄	#2403	1	1	yes	characteristic
791	C₂²×D₄	#2403	1	1	yes	characteristic
792	C₂²×D₄	#2403	1	1	yes	characteristic
793	C₂²×D₄	C₂²×#120	1	1	yes	characteristic
794	C₂²×D₄	C₂²×#120	1	1	yes	characteristic
795	C₂²×D₄	C₂×D₄²	1	1	yes	characteristic
796	C₂²×D₄	C₂×D₄²	1	1	yes	characteristic
797	C₂²×D₄	C₂×D₄²	1	1	yes	characteristic
798	C₂²×D₄	C₂×D₄²	1	1	yes	characteristic
799	C₂²×D₄	#3484	1	1	yes	characteristic
800	C₂²×D₄	#3484	1	1	yes	characteristic
801	C₂²×D₄	#3484	1	1	yes	characteristic
802	C₂²×D₄	#3484	1	1	yes	characteristic
803	C₂²×D₄	#3484	1	1	yes	characteristic
804	C₂²×D₄	#3484	1	1	yes	characteristic
805	C₂²×D₄	#3484	1	1	yes	characteristic
806	C₂²×D₄	#3484	1	1	yes	characteristic
807	C₂²×D₄	#3484	1	1	yes	characteristic
808	C₂²×D₄	#3484	1	1	yes	characteristic
809	C₂²×D₄	#3484	1	1	yes	characteristic
810	C₂²×D₄	#3484	1	1	yes	characteristic
811	C₂³×C₄	C₂²×#120	1	1	yes	characteristic
812	C₂³×C₄	C₂×D₄²	1	1	yes	characteristic
813	C₂³×C₄	C₂×D₄²	1	1	yes	characteristic
814	C₂³×C₄	C₂×D₄²	1	1	yes	characteristic
815	C₂³×C₄	C₂×D₄²	1	1	yes	characteristic
816	C₂³×C₄	#3532	1	1	yes	characteristic
817	C₂³×C₄	#3532	1	1	yes	characteristic
818	C₂³×C₄	#3532	1	1	yes	characteristic
819	C₂³×C₄	#3532	1	1	yes	characteristic
820	#127	C₂×B(4,𝔽₂)	1	2	yes	—
821	#127	C₂×B(4,𝔽₂)	1	2	yes	—
822	#124	C₂×B(4,𝔽₂)	1	2	yes	—
823	#124	C₂×B(4,𝔽₂)	1	2	yes	—
824	C₂×C₄²	#2403	1	1	yes	characteristic
825	C₂×C₄²	#2403	1	1	yes	characteristic
826	C₂×C₄²	#2403	1	1	yes	characteristic
827	C₂×C₄²	#2403	1	1	yes	characteristic
828	C₂×C₄²	#2403	1	1	yes	characteristic
829	C₂×C₄²	#2403	1	1	yes	characteristic
830	C₂×C₄²	#2403	1	1	yes	characteristic
831	C₂×C₄²	#2403	1	1	yes	characteristic
832	#100	C₂×B(4,𝔽₂)	1	4	yes	—
833	#100	C₂×B(4,𝔽₂)	1	4	yes	—
834	C₂⁴	#35346	1	1	yes	characteristic
835	C₂⁴	D₄×#120	1	1	yes	characteristic
836	C₂⁴	D₄×#120	1	1	yes	characteristic
837	C₂⁴	D₄×#120	1	1	yes	characteristic
838	C₂⁴	D₄×#120	1	1	yes	characteristic
839	C₂⁴	#58990	1	1	yes	characteristic
840	C₂⁴	#58990	1	1	yes	characteristic
841	C₂⁴	#58990	1	1	yes	characteristic
842	C₂⁴	#58990	1	1	yes	characteristic
843	C₂×Q₈	#23900	1	2	yes	—
844	C₂×D₄	#23900	1	2	yes	—
845	C₂×D₄	C₂²×B(4,𝔽₂)	1	2	yes	—
846	C₂×D₄	C₂²×B(4,𝔽₂)	1	2	yes	—
847	C₂×D₄	#60399	1	2	yes	—
848	C₂×D₄	#60399	1	2	yes	—
849	C₂²×C₄	C₂×#2403	1	1	yes	characteristic
850	C₂²×C₄	C₂×#2403	1	1	yes	characteristic
851	C₂²×C₄	#37644	1	1	yes	characteristic
852	C₂²×C₄	#37644	1	1	yes	characteristic
853	C₂²×C₄	#37644	1	1	yes	characteristic
854	C₂²×C₄	#37644	1	1	yes	characteristic
855	C₄²	#23900	1	1	yes	characteristic
856	C₄²	#23900	1	1	yes	characteristic
857	C₄²	#23900	1	1	yes	characteristic
858	C₄²	#23900	1	1	yes	characteristic
859	C₂³	#647656	1	1	yes	characteristic
860	C₂³	#6499874	1	2	yes	—
861	C₂³	D₄×B(4,𝔽₂)	1	2	yes	—
862	C₂³	D₄×B(4,𝔽₂)	1	2	yes	—
863	C₂³	D₄×B(4,𝔽₂)	1	2	yes	—
864	C₂³	D₄×B(4,𝔽₂)	1	2	yes	—
865	C₂×C₄	C₂×#23900	1	1	yes	characteristic
866	C₂×C₄	C₂×#23900	1	1	yes	characteristic
867	C₂×C₄	#6437632	1	1	yes	characteristic
868	C₂×C₄	#6437632	1	1	yes	characteristic
869	C₂²	#72216646	1	1	yes	characteristic
870	C₂²	#72216660	1	1	yes	characteristic
871	C₂²	#72216660	1	1	yes	characteristic
872	C₂	#72216662	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂	#72216662
commutator, Frattini, cosocle	C₂²×H(5,𝔽₂)	C₂⁵
LCS	G ▷ C₂²×H(5,𝔽₂) ▷ C₂³ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂ ◁ C₂³ ◁ C₂²×H(5,𝔽₂) ◁ G
LECS	G ▷ C₂²×H(5,𝔽₂) ▷ C₂³ ▷ C₂ ▷ C₁

Complements

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

N	H ≅ G/N	type
1. #72341541	C₂	semidirect
2. #72341530	C₂	semidirect
3. #72341502	C₂	semidirect
4. #72341499	C₂	semidirect
6. #72341478	C₂	semidirect
7. #72341475	C₂²	semidirect
8. #72341474	C₂	semidirect
9. #72341473	C₂²	semidirect
10. #72341472	C₂	semidirect
12. #72341469	C₂	semidirect
13. #72341467	C₂	semidirect
14. #72341466	C₂²	semidirect
15. #72341465	C₂²	semidirect
16. #72341382	C₂	semidirect
17. #72341374	C₂	semidirect
18. #72341363	C₂²	semidirect
19. #72341362	C₂²	semidirect
20. #72341347	C₂	semidirect
21. #72341322	C₂	semidirect
22. #72341322	C₂	semidirect
23. #72341320	C₂²	semidirect
24. #72341315	C₂	semidirect
25. #72341312	C₂²	semidirect
26. #72341305	C₂	semidirect
27. #72341286	C₂²	semidirect
28. #72341286	C₂²	semidirect
29. #72337584	C₂	semidirect
30. #72311323	C₂	semidirect
31. #72311315	C₂²	semidirect
32. #72311295	C₂²	semidirect
33. #72311270	C₂	semidirect
34. #72311266	C₂²	semidirect
35. #72311264	C₂²	semidirect
37. #72311253	C₂	semidirect
38. #72311246	C₂²	semidirect
39. #72311237	C₂²	semidirect
40. #72311231	C₂²	semidirect
41. #72311231	C₂²	semidirect
42. #72311163	C₂	semidirect
43. #72311157	C₂²	semidirect
44. #72311152	C₂²	semidirect
45. #72311152	C₂²	semidirect
46. #72311150	C₂²	semidirect
47. #72311147	C₂²	semidirect
48. #72311145	C₂²	semidirect
49. #72311145	C₂²	semidirect
50. #72311145	C₂²	semidirect
51. #72311145	C₂²	semidirect
52. #72311140	C₂²	semidirect
53. #72311140	C₂²	semidirect
54. #72311115	C₂²	semidirect
56. #72306419	C₂²	semidirect
58. #72306417	C₂²	semidirect
60. #72306415	C₂²	semidirect
61. #72303101	C₂	semidirect
62. #72303095	C₂²	semidirect
63. #72303091	C₂²	semidirect
64. #72303086	C₂²	semidirect
65. #72303086	C₂²	semidirect
66. #72303081	C₂²	semidirect
67. #72303066	C₂²	semidirect
68. #72303066	C₂²	semidirect
69. #72303055	C₂²	semidirect
70. #72303055	C₂²	semidirect
71. #72302998	C₂²	semidirect
72. #72302950	C₂²	semidirect
73. #72302950	C₂²	semidirect
74. #72285520	C₂	semidirect
75. #72285500	C₂²	semidirect
76. #72285500	C₂²	semidirect
77. #72285407	C₂²	semidirect
78. #72285407	C₂²	semidirect
79. #72285407	C₂²	semidirect
80. #72285407	C₂²	semidirect
81. #72284823	C₂²	semidirect
82. #72283936	C₂²	semidirect
83. #72283640	C₂²	semidirect
84. #72260657	C₂²	semidirect
85. #72260657	C₂²	semidirect
86. #72241340	C₂	semidirect
87. #72241339	C₂	semidirect
88. #72241339	C₂	semidirect
89. #72241338	C₂	semidirect
90. #72241337	C₂²	semidirect
91. #72241337	C₂²	semidirect
92. #72241337	C₂²	semidirect
93. #72241337	C₂²	semidirect
94. #72241337	C₂²	semidirect
95. #72241337	C₂²	semidirect
96. #72241334	C₂	semidirect
97. #72241333	C₂²	semidirect
98. #72241333	C₂²	semidirect
99. #72241332	C₂²	semidirect
100. #72241332	C₂²	semidirect
101. #72241332	C₂²	semidirect
102. #72241332	C₂²	semidirect
103. #72241332	C₂²	semidirect
104. #72241332	C₂²	semidirect
105. #72241316	C₂²	semidirect
106. #72241316	C₂²	semidirect
107. #72241315	C₂²	semidirect
108. #72241315	C₂²	semidirect
109. #72241315	C₂²	semidirect
110. #72241315	C₂²	semidirect
111. #72241305	C₂²	semidirect
112. #72241305	C₂²	semidirect
113. #72241304	C₂²	semidirect
114. #72241303	C₂²	semidirect
115. #72241301	C₂²	semidirect
116. #72241085	C₂	semidirect
117. #72241079	C₂²	semidirect
118. #72241079	C₂²	semidirect
119. #72241079	C₂²	semidirect
120. #72241079	C₂²	semidirect
121. #72238017	C₂	semidirect
122. #72238016	C₂²	semidirect
123. #72238016	C₂²	semidirect
124. #72238015	C₂²	semidirect
125. #72238015	C₂²	semidirect
126. #72238015	C₂²	semidirect
127. #72238015	C₂²	semidirect
128. #72238015	C₂²	semidirect
129. #72238015	C₂²	semidirect
130. #72238014	C₂²	semidirect
131. #72238014	C₂²	semidirect
132. #72238013	C₂²	semidirect
133. #72238013	C₂²	semidirect
134. #72238013	C₂²	semidirect
135. #72238013	C₂²	semidirect
136. #72238013	C₂²	semidirect
137. #72238013	C₂²	semidirect
138. #72238012	C₂²	semidirect
139. #72238010	C₂²	semidirect
140. #72238010	C₂²	semidirect
141. #72236975	C₂²	semidirect
142. #72236925	C₂²	semidirect
143. #72236925	C₂²	semidirect
144. #72236925	C₂²	semidirect
145. #72236711	C₂²	semidirect
146. #72236702	C₂²	semidirect
147. #72236680	C₂²	semidirect
148. #72236680	C₂²	semidirect
149. #72236657	C₂²	semidirect
151. #72234146	C₂²	semidirect
152. #72233917	C₂²	semidirect
153. #72227588	C₂²	semidirect
154. #72213565	C₂	semidirect
155. #72213523	C₂²	semidirect
156. #72213523	C₂²	semidirect
157. #72213523	C₂²	semidirect
158. #72213513	C₂²	semidirect
159. #72213513	C₂²	semidirect
160. #72213513	C₂²	semidirect
161. #72213504	C₂²	semidirect
162. #72213504	C₂²	semidirect
163. #72213504	C₂²	semidirect
164. #72213504	C₂²	semidirect
165. #72213504	C₂²	semidirect
166. #72213504	C₂²	semidirect
167. #72213504	C₂²	semidirect
168. #72213504	C₂²	semidirect
169. #72213504	C₂²	semidirect
170. #72213504	C₂²	semidirect
171. #72213504	C₂²	semidirect
172. #72213504	C₂²	semidirect
173. #72213462	C₂²	semidirect
174. #72213462	C₂²	semidirect
175. #72213435	C₂²	semidirect
176. #72213435	C₂²	semidirect
177. #72213435	C₂²	semidirect
178. #72213435	C₂²	semidirect
179. #72213423	C₂²	semidirect
180. #72213210	C₂²	semidirect
181. #72213210	C₂²	semidirect
182. #72210439	C₂²	semidirect
183. #72210035	C₂²	semidirect
184. #72210025	C₂²	semidirect
185. #72210025	C₂²	semidirect
186. #72210025	C₂²	semidirect
196. C₂×#60390	D₄	semidirect
197. C₂×#60388	D₄	semidirect
209. C₂²×#2200	D₄	semidirect
210. C₂²×#2199	D₄	semidirect
211. C₂²×#2197	D₄	semidirect
212. C₂²×#2196	D₄	semidirect
213. #6628972	D₄	semidirect
214. #6628970	D₄	semidirect
228. #6628874	D₄	semidirect
229. #6628873	D₄	semidirect
240. #6443332	D₄	semidirect
241. #6443331	D₄	semidirect
242. #6442560	D₄	semidirect
243. #6442560	D₄	semidirect
244. #6437971	D₄	semidirect
245. #6437970	D₄	semidirect
249. #6437454	D₄	semidirect
251. #6437452	D₄	semidirect
259. #6372704	D₄	semidirect
260. #6372704	D₄	semidirect
261. #498928	D₄	semidirect
262. #498928	D₄	semidirect
263. #498927	D₄	semidirect
264. #498927	D₄	semidirect
265. #498927	D₄	semidirect
266. #498927	D₄	semidirect
267. #498927	D₄	semidirect
268. #498927	D₄	semidirect
297. #494597	D₄	semidirect
298. #494597	D₄	semidirect
299. #494596	D₄	semidirect
300. #494596	D₄	semidirect
317. #449492	D₄	semidirect
318. #417813	D₄	semidirect
319. #417568	D₄	semidirect
320. #417566	D₄	semidirect
378. C₂×2₋¹⁺⁶	C₂×D₄	semidirect
383. #62859	C₂×D₄	semidirect
388. #62812	C₂×D₄	semidirect
398. C₄×#585	C₂×D₄	semidirect
400. C₂²×#458	C₂×D₄	semidirect
406. C₂²×B(4,𝔽₂)	C₂×D₄	semidirect
416. C₂×#3021	C₂×D₄	semidirect
417. C₂×#3021	C₂×D₄	semidirect
418. C₂×#3021	C₂×D₄	semidirect
424. C₂×#3019	C₂×D₄	semidirect
433. C₂²×#455	C₂×D₄	semidirect
437. C₂×#2889	C₂×D₄	semidirect
454. #35527	C₂×D₄	semidirect
480. C₂²×#352	C₂×D₄	semidirect
486. C₂²×AΣL(1,𝔽₁₆)	C₂×D₄	semidirect
489. #20956	C₂×D₄	semidirect
494. #20855	C₂×D₄	semidirect
496. #20637	C₂×D₄	semidirect
500. #20615	C₂×D₄	semidirect
501. #20615	C₂×D₄	semidirect
502. #20615	C₂×D₄	semidirect
509. #20609	C₂×D₄	semidirect
510. #20609	C₂×D₄	semidirect
511. #20593	C₂×D₄	semidirect
515. #20586	C₂×D₄	semidirect
530. C₄×#413	C₂×D₄	semidirect
537. #12574	C₂×D₄	semidirect
538. #12574	C₂×D₄	semidirect
539. #11167	C₂×D₄	semidirect
541. #10989	C₂×D₄	semidirect
542. #10981	C₂×D₄	semidirect
543. #10977	C₂×D₄	semidirect
552. C₂²×H(5,𝔽₂)	#120	semidirect
560. C₂×#536	#120	semidirect
564. C₂×#535	#120	semidirect
582. C₂²×#127	#120	semidirect
587. C₂²×#124	#120	semidirect
588. C₂²×#124	#120	semidirect
606. C₂×C₄×#41	#120	semidirect
607. C₂×C₄×#41	#120	semidirect
648. #2310	#120	semidirect
649. #2309	#120	semidirect
650. #2309	#120	semidirect
665. #2297	#120	semidirect
666. #2297	#120	semidirect
669. #2285	#120	semidirect
670. #2285	#120	semidirect
671. C₂×#376	#120	semidirect
767. #455	B(4,𝔽₂)	semidirect
768. #455	B(4,𝔽₂)	semidirect
769. #453	B(4,𝔽₂)	semidirect
770. #453	B(4,𝔽₂)	semidirect

Maximal subgroups

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

subgroup	index
#72341541	2
#72341530	2
#72341502	2
#72341499	2
#72341478	2
#72341474	2
#72341472	2
#72341469	2
#72341467	2
#72341382	2
#72341374	2
#72341347	2
#72341322	2
#72341315	2
#72341305	2
#72337584	2
#72311323	2
#72311270	2
#72311253	2
#72311163	2
#72303101	2
#72285520	2
#72241340	2
#72241339	2
#72241338	2
#72241334	2
#72241085	2
#72238017	2
#72213565	2