Subgroups — #72266067

Order 2048.

At least 11266 conjugacy classes of subgroups; only the 4580 normal subgroups are shown.

The subgroup lattice has 949 nodes (normal subgroups only) — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#72266066	C₂	1	1	yes	maximal, characteristic, complemented
2	#72266065	C₂	1	2	yes	maximal, complemented
3	#72266057	C₂	1	8	yes	maximal, complemented
4	#72266051	C₂	1	8	yes	maximal, complemented
5	#72266049	C₂	1	8	yes	maximal, complemented
6	#72241143	C₂	1	1	yes	maximal, characteristic, complemented
7	#72240619	C₂	1	2	yes	maximal, complemented
8	#72240617	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×#6370693	C₂	1	1	yes	maximal, characteristic, complemented
10	#72234689	C₂	1	1	yes	maximal, characteristic, complemented
11	#72234668	C₂	1	2	yes	maximal, complemented
12	#72234644	C₂	1	8	yes	maximal, complemented
13	#72234629	C₂	1	2	yes	maximal, complemented
14	C₂×#6628892	C₂	1	1	yes	maximal, characteristic, complemented
15	#72234587	C₂	1	8	yes	maximal, complemented
16	#72225632	C₂	1	8	yes	maximal, complemented
17	C₂²×#32898	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂⁴×H(5,𝔽₂)	C₂²	1	1	yes	characteristic
19	C₂²×#3026	C₂²	1	4	yes	complemented
20	C₂³×B(4,𝔽₂)	C₂²	1	4	yes	complemented
21	C₂²×#2883	C₂²	1	4	yes	complemented
22	#7675443	C₂²	1	4	yes	complemented
23	#7675392	C₂²	1	4	yes	complemented
24	#7670233	C₂²	1	4	yes	complemented
25	#7670206	C₂²	1	4	yes	complemented
26	#7644637	C₂²	1	4	yes	complemented
27	#7641846	C₂²	1	1	yes	characteristic, complemented
28	#7631294	C₂²	1	4	yes	complemented
29	C₂×#34980	C₂²	1	2	yes	—
30	C₂×#34980	C₂²	1	1	yes	characteristic
31	C₂×#34980	C₂²	1	1	yes	characteristic, complemented
32	C₂²×#2403	C₂²	1	2	yes	—
33	C₂²×#2403	C₂²	1	1	yes	characteristic
34	#7626202	C₂²	1	1	yes	characteristic, complemented
35	C₂×#34171	C₂²	1	1	yes	characteristic
36	C₂×#34171	C₂²	1	1	yes	characteristic
37	C₂×#34171	C₂²	1	1	yes	characteristic, complemented
38	#6628892	C₂²	1	8	yes	—
39	#6628892	C₂²	1	4	yes	complemented
40	#6628892	C₂²	1	4	yes	complemented
41	C₂×#32898	C₂²	1	8	yes	—
42	C₂×#32898	C₂²	1	4	yes	complemented
43	C₂×#32898	C₂²	1	4	yes	complemented
44	C₂×#23996	C₂²	1	16	yes	complemented
45	C₂×#21746	C₂²	1	2	yes	complemented
46	C₂×#20609	C₂²	1	4	yes	complemented
47	C₂²×#1790	C₂²	1	4	yes	complemented
48	#6370693	C₂²	1	8	yes	complemented
49	#6370693	C₂²	1	8	yes	complemented
50	C₂×#20585	C₂²	1	4	yes	complemented
51	C₂²×#1781	C₂²	1	2	yes	—
52	C₂²×#1781	C₂²	1	2	yes	—
53	C₂²×#1781	C₂²	1	2	yes	—
54	C₂²×#1781	C₂²	1	1	yes	characteristic
55	C₂²×#1781	C₂²	1	1	yes	characteristic
56	C₂²×#1781	C₂²	1	2	yes	—
57	#517411	C₂²	1	2	yes	complemented
58	#451129	C₂²	1	16	yes	complemented
59	#451128	C₂²	1	16	yes	complemented
60	#449580	C₂²	1	16	yes	complemented
61	#449578	C₂²	1	16	yes	complemented
62	#417973	C₂²	1	16	yes	complemented
63	#417969	C₂²	1	16	yes	complemented
64	#417542	C₂²	1	16	yes	complemented
65	#417538	C₂²	1	16	yes	complemented
66	#405274	C₂²	1	16	yes	complemented
67	#405268	C₂²	1	16	yes	complemented
68	#405104	C₂²	1	8	yes	complemented
69	#405090	C₂²	1	8	yes	complemented
70	#394474	C₂²	1	16	yes	complemented
71	#394470	C₂²	1	16	yes	complemented
72	#394470	C₂²	1	16	yes	complemented
73	#394470	C₂²	1	16	yes	complemented
74	#394273	C₂²	1	16	yes	complemented
75	#394267	C₂²	1	16	yes	complemented
76	#394058	C₂²	1	8	yes	complemented
77	#393929	C₂²	1	8	yes	complemented
78	#392699	C₂²	1	4	yes	complemented
79	#392658	C₂²	1	4	yes	complemented
80	#392231	C₂²	1	4	yes	complemented
81	#382707	C₂²	1	4	yes	complemented
82	#379754	C₂²	1	4	yes	complemented
83	#379733	C₂²	1	4	yes	complemented
84	#374058	C₂²	1	8	yes	complemented
85	#374038	C₂²	1	8	yes	complemented
86	#364545	C₂²	1	16	yes	complemented
87	#364532	C₂²	1	16	yes	complemented
88	#364471	C₂²	1	16	yes	complemented
89	#364471	C₂²	1	16	yes	complemented
90	#364440	C₂²	1	16	yes	complemented
91	#364440	C₂²	1	16	yes	complemented
92	#359892	C₂²	1	8	yes	complemented
93	#359892	C₂²	1	8	yes	complemented
94	#359863	C₂²	1	4	yes	complemented
95	#359811	C₂²	1	4	yes	complemented
96	#359788	C₂²	1	16	yes	complemented
97	#359705	C₂²	1	8	yes	complemented
98	#359695	C₂²	1	8	yes	complemented
99	#359501	C₂²	1	4	yes	complemented
100	#359442	C₂²	1	8	yes	complemented
101	#359442	C₂²	1	4	yes	complemented
102	#359428	C₂²	1	8	yes	complemented
103	#355913	C₂²	1	2	yes	complemented
104	#355913	C₂²	1	2	yes	complemented
105	#355913	C₂²	1	2	yes	complemented
106	#355913	C₂²	1	2	yes	complemented
107	C₂³×H(5,𝔽₂)	C₂³	1	2	yes	—
108	C₂³×H(5,𝔽₂)	C₂³	1	4	yes	—
109	C₂³×H(5,𝔽₂)	C₂³	1	4	yes	—
110	C₂³×H(5,𝔽₂)	C₂³	1	2	yes	—
111	C₂⁵×D₄	C₂³	1	1	yes	characteristic
112	C₂⁵×D₄	C₂³	1	2	yes	—
113	C₂⁵×D₄	C₂³	1	1	yes	characteristic
114	C₂×#3490	C₂³	1	4	yes	complemented
115	C₂²×#534	C₂³	1	4	yes	—
116	C₂²×#534	C₂³	1	2	yes	—
117	C₂³×#120	C₂³	1	4	yes	—
118	C₂³×#120	C₂³	1	2	yes	—
119	C₂³×#120	C₂³	1	1	yes	characteristic
120	C₂²×#518	C₂³	1	2	yes	—
121	C₂²×#518	C₂³	1	2	yes	—
122	C₂×#3026	C₂³	1	16	yes	—
123	C₂×#3026	C₂³	1	16	yes	—
124	C₂²×B(4,𝔽₂)	C₂³	1	16	yes	—
125	C₂²×B(4,𝔽₂)	C₂³	1	16	yes	—
126	C₂×#2883	C₂³	1	16	yes	—
127	C₂×#2883	C₂³	1	16	yes	—
128	C₂³×#99	C₂³	1	4	yes	—
129	C₂³×#99	C₂³	1	8	yes	—
130	C₂³×#99	C₂³	1	4	yes	—
131	C₂³×#99	C₂³	1	8	yes	—
132	C₂³×#99	C₂³	1	8	yes	—
133	C₂³×#99	C₂³	1	8	yes	—
134	C₂×#2849	C₂³	1	2	yes	complemented
135	C₂×#2846	C₂³	1	2	yes	complemented
136	#35370	C₂³	1	4	yes	complemented
137	#35367	C₂³	1	4	yes	complemented
138	#35360	C₂³	1	4	yes	complemented
139	#35360	C₂³	1	4	yes	complemented
140	#35359	C₂³	1	4	yes	complemented
141	#35350	C₂³	1	4	yes	complemented
142	#35348	C₂³	1	4	yes	complemented
143	#35348	C₂³	1	4	yes	complemented
144	#34995	C₂³	1	4	yes	complemented
145	#34993	C₂³	1	4	yes	complemented
146	#34992	C₂³	1	4	yes	complemented
147	#34982	C₂³	1	4	yes	complemented
148	#34982	C₂³	1	4	yes	complemented
149	#34982	C₂³	1	4	yes	complemented
150	#34981	C₂³	1	4	yes	complemented
151	#34980	D₄	1	4	yes	complemented
152	#34980	D₄	1	4	yes	complemented
153	#34980	C₂³	1	8	yes	—
154	#34980	C₂³	1	8	yes	—
155	#34980	C₂³	1	4	yes	—
156	#34980	C₂³	1	2	yes	—
157	#34980	C₂³	1	2	yes	—
158	C₂×#2405	D₄	1	2	yes	complemented
159	C₂×#2405	D₄	1	2	yes	complemented
160	C₂×#2405	C₂³	1	2	yes	complemented
161	C₂×#2410	C₂³	1	4	yes	complemented
162	C₂×#2403	D₄	1	2	yes	complemented
163	C₂×#2403	D₄	1	2	yes	complemented
164	C₂×#2403	D₄	1	2	yes	complemented
165	C₂×#2403	D₄	1	4	yes	complemented
166	C₂×#2403	D₄	1	4	yes	complemented
167	C₂×#2403	D₄	1	2	yes	complemented
168	C₂×#2403	D₄	1	2	yes	complemented
169	C₂×#2403	D₄	1	2	yes	complemented
170	C₂×#2403	C₂³	1	8	yes	—
171	C₂×#2403	C₂³	1	8	yes	—
172	C₂×#2403	C₂³	1	4	yes	—
173	C₂×#2403	C₂³	1	2	yes	—
174	C₂×#2403	C₂³	1	2	yes	—
175	C₂×#2403	C₂³	1	2	yes	complemented
176	#34273	C₂³	1	4	yes	complemented
177	#34251	C₂³	1	4	yes	complemented
178	#34198	C₂³	1	4	yes	complemented
179	#34198	C₂³	1	4	yes	complemented
180	#34198	C₂³	1	4	yes	complemented
181	#34176	C₂³	1	2	yes	complemented
182	#34171	D₄	1	4	yes	complemented
183	#34171	D₄	1	4	yes	complemented
184	#34171	C₂³	1	4	yes	—
185	#34171	C₂³	1	4	yes	—
186	#34171	C₂³	1	4	yes	—
187	#34171	C₂³	1	4	yes	—
188	#34171	C₂³	1	2	yes	complemented
189	C₂×D₄×C₂²⋊C₄	C₂³	1	4	yes	complemented
190	C₂×D₄×C₂²⋊C₄	C₂³	1	4	yes	complemented
191	C₂×#2309	D₄	1	2	yes	complemented
192	C₂×#2308	D₄	1	2	yes	complemented
193	C₂×#2308	C₂³	1	4	yes	—
194	C₂×#2308	C₂³	1	2	yes	—
195	C₂×#2308	C₂³	1	2	yes	—
196	C₂×#2308	C₂³	1	2	yes	—
197	C₂²×#386	C₂³	1	4	yes	—
198	C₂²×#386	C₂³	1	2	yes	—
199	C₂×#2280	D₄	1	2	yes	complemented
200	C₂×#2280	C₂³	1	2	yes	complemented
201	C₂²×#379	D₄	1	2	yes	complemented
202	C₂²×#379	C₂³	1	2	yes	—
203	C₂²×#379	C₂³	1	2	yes	—
204	C₂²×#379	C₂³	1	2	yes	—
205	C₂²×#379	C₂³	1	1	yes	characteristic
206	C₂²×#379	C₂³	1	1	yes	characteristic
207	C₂²×#379	C₂³	1	1	yes	characteristic
208	C₂²×#379	C₂³	1	1	yes	characteristic
209	C₂²×#379	C₂³	1	2	yes	complemented
210	C₂×#2032	C₂³	1	32	yes	complemented
211	C₂×#2021	C₂³	1	32	yes	complemented
212	C₂×#1913	C₂³	1	32	yes	complemented
213	C₂×#1913	C₂³	1	16	yes	complemented
214	C₂×#1898	C₂³	1	32	yes	complemented
215	C₂×#1898	C₂³	1	8	yes	complemented
216	C₂×#1898	C₂³	1	8	yes	complemented
217	C₂×#1889	C₂³	1	16	yes	complemented
218	C₂×#1828	C₂³	1	16	yes	complemented
219	C₂×#1819	C₂³	1	4	yes	complemented
220	#20609	C₂³	1	16	yes	—
221	#20609	C₂³	1	16	yes	—
222	C₂×#1790	C₂³	1	16	yes	—
223	C₂×#1790	C₂³	1	16	yes	—
224	#20585	C₂³	1	16	yes	—
225	#20585	C₂³	1	16	yes	—
226	C₂×#1781	C₂³	1	8	yes	—
227	C₂×#1781	C₂³	1	8	yes	—
228	C₂×#1781	C₂³	1	8	yes	—
229	C₂×#1781	C₂³	1	4	yes	—
230	C₂×#1781	C₂³	1	8	yes	—
231	C₂×#1781	C₂³	1	2	yes	—
232	C₂×#1781	C₂³	1	2	yes	—
233	C₂×#1781	C₂³	1	8	yes	—
234	C₂×#1781	C₂³	1	4	yes	—
235	C₂×#1781	C₂³	1	2	yes	—
236	C₂×#1781	C₂³	1	2	yes	—
237	C₂×#1781	C₂³	1	8	yes	—
238	C₂×#1781	C₂³	1	8	yes	—
239	C₂×#1781	C₂³	1	8	yes	—
240	C₂×#1781	C₂³	1	4	yes	complemented
241	#14681	C₂³	1	4	yes	complemented
242	#14679	C₂³	1	4	yes	complemented
243	#13867	C₂³	1	8	yes	complemented
244	#13867	C₂³	1	8	yes	complemented
245	#11174	C₂³	1	16	yes	complemented
246	#11172	C₂³	1	16	yes	complemented
247	#11169	C₂³	1	16	yes	complemented
248	#11166	C₂³	1	16	yes	complemented
249	#11089	C₂³	1	32	yes	complemented
250	#11089	C₂³	1	32	yes	complemented
251	#11089	C₂³	1	32	yes	complemented
252	#11087	C₂³	1	32	yes	complemented
253	#11046	C₂³	1	32	yes	complemented
254	#11043	C₂³	1	32	yes	complemented
255	#10995	C₂³	1	32	yes	complemented
256	#10991	C₂³	1	16	yes	complemented
257	#10991	C₂³	1	32	yes	complemented
258	#10972	C₂³	1	16	yes	complemented
259	#10972	C₂³	1	32	yes	complemented
260	#10965	C₂³	1	32	yes	complemented
261	#10960	C₂³	1	32	yes	complemented
262	#10938	C₂³	1	32	yes	complemented
263	#10768	C₂³	1	16	yes	complemented
264	#10754	C₂³	1	16	yes	complemented
265	#10745	C₂³	1	16	yes	complemented
266	#10735	C₂³	1	8	yes	complemented
267	#10735	C₂³	1	8	yes	complemented
268	#10735	C₂³	1	8	yes	complemented
269	#10735	C₂³	1	8	yes	complemented
270	#10735	C₂³	1	8	yes	complemented
271	#10735	C₂³	1	8	yes	complemented
272	#10735	C₂³	1	8	yes	complemented
273	#10735	C₂³	1	8	yes	complemented
274	#10725	C₂³	1	8	yes	complemented
275	#10725	C₂³	1	8	yes	complemented
276	#10725	C₂³	1	8	yes	complemented
277	#10725	C₂³	1	8	yes	complemented
278	C₂⁷	C₂×D₄	1	1	yes	characteristic
279	C₂⁷	#41	1	2	yes	complemented
280	C₂⁷	C₂⁴	1	1	yes	characteristic
281	C₂⁷	C₂⁴	1	1	yes	characteristic
282	C₂²×H(5,𝔽₂)	C₂⁴	1	8	yes	—
283	C₂²×H(5,𝔽₂)	C₂⁴	1	8	yes	—
284	C₂⁴×D₄	C₂×D₄	1	2	yes	—
285	C₂⁴×D₄	C₂×D₄	1	2	yes	—
286	C₂⁴×D₄	C₂×D₄	1	2	yes	—
287	C₂⁴×D₄	C₂×D₄	1	2	yes	—
288	C₂⁴×D₄	C₂×D₄	1	2	yes	—
289	C₂⁴×D₄	C₂×D₄	1	2	yes	—
290	C₂⁴×D₄	C₂×D₄	1	2	yes	—
291	C₂⁴×D₄	C₂×D₄	1	2	yes	—
292	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
293	C₂⁴×D₄	C₂×D₄	1	2	yes	—
294	C₂⁴×D₄	C₂×D₄	1	2	yes	—
295	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
296	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
297	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
298	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
299	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
300	C₂⁴×D₄	C₂×D₄	1	2	yes	—
301	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
302	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
303	C₂⁴×D₄	C₂×D₄	1	2	yes	—
304	C₂⁴×D₄	#41	1	4	yes	complemented
305	C₂⁴×D₄	#41	1	4	yes	complemented
306	C₂⁴×D₄	#41	1	4	yes	complemented
307	C₂⁴×D₄	C₂⁴	1	1	yes	characteristic
308	C₂⁴×D₄	C₂⁴	1	2	yes	—
309	C₂⁴×D₄	C₂⁴	1	2	yes	—
310	C₂⁴×D₄	C₂⁴	1	1	yes	characteristic
311	C₂⁴×D₄	C₂⁴	1	1	yes	characteristic
312	C₂⁴×D₄	C₂⁴	1	4	yes	—
313	C₂⁴×D₄	C₂⁴	1	4	yes	—
314	C₂⁴×D₄	C₂⁴	1	4	yes	—
315	C₂⁴×D₄	C₂⁴	1	2	yes	—
316	C₂⁴×D₄	C₂⁴	1	2	yes	—
317	C₂⁵×C₄	C₂×D₄	1	1	yes	characteristic
318	C₂⁵×C₄	#41	1	2	yes	complemented
319	C₂⁵×C₄	C₂⁴	1	1	yes	characteristic
320	C₂×#543	C₂⁴	1	4	yes	complemented
321	C₂×#534	C₂×D₄	1	8	yes	complemented
322	C₂×#534	C₂⁴	1	16	yes	—
323	C₂×#534	C₂⁴	1	4	yes	—
324	C₂×#534	C₂⁴	1	4	yes	—
325	C₂²×#123	C₂×D₄	1	4	yes	complemented
326	C₂²×#120	C₂×D₄	1	2	yes	—
327	C₂²×#120	C₂×D₄	1	2	yes	—
328	C₂²×#120	C₂×D₄	1	4	yes	complemented
329	C₂²×#120	C₂×D₄	1	8	yes	complemented
330	C₂²×#120	C₂×D₄	1	4	yes	complemented
331	C₂²×#120	C₂×D₄	1	4	yes	complemented
332	C₂²×#120	C₂⁴	1	4	yes	—
333	C₂²×#120	C₂⁴	1	16	yes	—
334	C₂²×#120	C₂⁴	1	4	yes	—
335	C₂²×#120	C₂⁴	1	2	yes	—
336	C₂²×#120	C₂⁴	1	2	yes	—
337	C₂²×#120	C₂⁴	1	4	yes	complemented
338	C₂×#518	C₂×D₄	1	4	yes	complemented
339	C₂×#518	C₂×D₄	1	4	yes	complemented
340	C₂×#518	C₂⁴	1	8	yes	—
341	C₂×#518	C₂⁴	1	4	yes	—
342	C₂×#518	C₂⁴	1	4	yes	—
343	C₂×#518	C₂⁴	1	4	yes	complemented
344	C₂²×#117	C₂×D₄	1	4	yes	complemented
345	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
346	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
347	C₂³×C₂²⋊C₄	C₂×D₄	1	4	yes	complemented
348	C₂³×C₂²⋊C₄	C₂⁴	1	1	yes	characteristic
349	C₂³×C₂²⋊C₄	C₂⁴	1	4	yes	—
350	C₂³×C₂²⋊C₄	C₂⁴	1	4	yes	—
351	C₂³×C₂²⋊C₄	C₂⁴	1	4	yes	—
352	C₂³×C₂²⋊C₄	C₂⁴	1	2	yes	—
353	C₂³×C₂²⋊C₄	C₂⁴	1	2	yes	—
354	C₂³×C₂²⋊C₄	C₂⁴	1	2	yes	—
355	C₂³×C₂²⋊C₄	C₂⁴	1	2	yes	—
356	C₂³×C₂²⋊C₄	C₂⁴	1	4	yes	complemented
357	C₂²×#99	C₂⁴	1	8	yes	—
358	C₂²×#99	C₂⁴	1	8	yes	—
359	C₂²×#99	C₂⁴	1	32	yes	—
360	C₂²×#99	C₂⁴	1	32	yes	—
361	C₂²×#99	C₂⁴	1	32	yes	—
362	C₂²×#99	C₂⁴	1	32	yes	—
363	C₂²×#99	C₂⁴	1	8	yes	—
364	C₂²×#99	C₂⁴	1	8	yes	—
365	C₂²×#99	C₂⁴	1	16	yes	complemented
366	#2405	C₂×D₄	1	8	yes	—
367	#2405	C₂×D₄	1	8	yes	—
368	#2405	C₂×D₄	1	4	yes	complemented
369	#2405	C₂×D₄	1	4	yes	complemented
370	#2405	C₂×D₄	1	4	yes	complemented
371	#2405	C₂×D₄	1	4	yes	complemented
372	#2403	C₂×D₄	1	8	yes	—
373	#2403	C₂×D₄	1	8	yes	—
374	#2403	C₂×D₄	1	8	yes	—
375	#2403	C₂×D₄	1	8	yes	—
376	#2403	C₂×D₄	1	8	yes	—
377	#2403	C₂×D₄	1	8	yes	—
378	#2403	C₂×D₄	1	4	yes	complemented
379	#2403	C₂×D₄	1	4	yes	complemented
380	#2403	C₂×D₄	1	4	yes	complemented
381	#2403	C₂×D₄	1	4	yes	complemented
382	#2403	C₂×D₄	1	4	yes	complemented
383	#2403	C₂×D₄	1	4	yes	complemented
384	#2403	C₂×D₄	1	4	yes	complemented
385	#2403	C₂×D₄	1	4	yes	complemented
386	#2403	C₂×D₄	1	4	yes	complemented
387	#2403	C₂×D₄	1	4	yes	complemented
388	#2403	C₂×D₄	1	4	yes	complemented
389	#2403	C₂×D₄	1	4	yes	complemented
390	#2315	C₂⁴	1	4	yes	complemented
391	#2315	C₂⁴	1	4	yes	complemented
392	#2315	C₂⁴	1	4	yes	complemented
393	#2315	C₂⁴	1	4	yes	complemented
394	#2309	C₂×D₄	1	8	yes	complemented
395	#2309	C₂×D₄	1	8	yes	complemented
396	#2308	C₂×D₄	1	8	yes	complemented
397	#2308	C₂×D₄	1	8	yes	complemented
398	#2308	C₂×D₄	1	8	yes	complemented
399	#2308	C₂×D₄	1	4	yes	complemented
400	#2308	C₂×D₄	1	4	yes	complemented
401	#2308	C₂⁴	1	16	yes	—
402	#2308	C₂⁴	1	4	yes	—
403	#2308	C₂⁴	1	4	yes	—
404	#2308	C₂⁴	1	8	yes	—
405	#2308	C₂⁴	1	4	yes	—
406	#2308	C₂⁴	1	4	yes	—
407	#2308	C₂⁴	1	4	yes	complemented
408	C₂×#386	C₂×D₄	1	4	yes	complemented
409	C₂×#386	C₂×D₄	1	8	yes	complemented
410	C₂×#386	C₂×D₄	1	4	yes	complemented
411	C₂×#386	C₂×D₄	1	4	yes	complemented
412	C₂×#386	C₂×D₄	1	4	yes	complemented
413	C₂×#386	C₂⁴	1	16	yes	—
414	C₂×#386	C₂⁴	1	4	yes	—
415	C₂×#386	C₂⁴	1	4	yes	—
416	C₂×#386	C₂⁴	1	4	yes	complemented
417	C₂×#385	C₂⁴	1	4	yes	complemented
418	#2280	C₂×D₄	1	8	yes	complemented
419	#2280	C₂×D₄	1	8	yes	complemented
420	C₂×#381	C₂×D₄	1	4	yes	complemented
421	C₂×#380	C₂⁴	1	4	yes	complemented
422	C₂×#379	C₂×D₄	1	2	yes	—
423	C₂×#379	C₂×D₄	1	2	yes	—
424	C₂×#379	C₂×D₄	1	2	yes	—
425	C₂×#379	C₂×D₄	1	2	yes	—
426	C₂×#379	C₂×D₄	1	2	yes	—
427	C₂×#379	C₂×D₄	1	2	yes	—
428	C₂×#379	C₂×D₄	1	2	yes	—
429	C₂×#379	C₂×D₄	1	2	yes	—
430	C₂×#379	C₂×D₄	1	2	yes	—
431	C₂×#379	C₂×D₄	1	2	yes	—
432	C₂×#379	C₂×D₄	1	2	yes	—
433	C₂×#379	C₂×D₄	1	2	yes	—
434	C₂×#379	C₂×D₄	1	2	yes	—
435	C₂×#379	C₂×D₄	1	2	yes	—
436	C₂×#379	C₂×D₄	1	2	yes	—
437	C₂×#379	C₂×D₄	1	2	yes	—
438	C₂×#379	C₂×D₄	1	4	yes	complemented
439	C₂×#379	C₂×D₄	1	8	yes	complemented
440	C₂×#379	C₂×D₄	1	8	yes	complemented
441	C₂×#379	C₂⁴	1	4	yes	—
442	C₂×#379	C₂⁴	1	4	yes	—
443	C₂×#379	C₂⁴	1	4	yes	—
444	C₂×#379	C₂⁴	1	4	yes	—
445	C₂×#379	C₂⁴	1	4	yes	—
446	C₂×#379	C₂⁴	1	4	yes	—
447	C₂×#379	C₂⁴	1	2	yes	—
448	C₂×#379	C₂⁴	1	2	yes	—
449	C₂×#379	C₂⁴	1	2	yes	—
450	C₂×#379	C₂⁴	1	2	yes	—
451	C₂×#379	C₂⁴	1	2	yes	—
452	C₂×#379	C₂⁴	1	2	yes	—
453	C₂×#379	C₂⁴	1	2	yes	—
454	C₂×#379	C₂⁴	1	2	yes	—
455	C₂×#379	C₂⁴	1	4	yes	complemented
456	C₂×#379	C₂⁴	1	4	yes	complemented
457	C₂×#379	C₂⁴	1	16	yes	complemented
458	#2273	C₂⁴	1	4	yes	complemented
459	C₂×C₄×C₂²⋊C₄	C₂⁴	1	4	yes	complemented
460	C₂×#342	C₂⁴	1	16	yes	complemented
461	C₂×#342	C₂⁴	1	32	yes	complemented
462	C₂×#342	C₂⁴	1	32	yes	complemented
463	C₂×#342	C₂⁴	1	32	yes	complemented
464	C₂×#342	C₂⁴	1	32	yes	complemented
465	C₂²⋊#95	C₂⁴	1	16	yes	complemented
466	C₂⁶	#120	1	2	yes	—
467	C₂⁶	#120	1	2	yes	—
468	C₂⁶	#120	1	2	yes	—
469	C₂⁶	#120	1	2	yes	—
470	C₂⁶	C₂²×D₄	1	1	yes	characteristic
471	C₂⁶	C₂²×D₄	1	2	yes	—
472	C₂⁶	C₂²×D₄	1	2	yes	—
473	C₂⁶	C₂²×D₄	1	1	yes	characteristic
474	C₂⁶	C₂²×D₄	1	2	yes	—
475	C₂⁶	C₂²×D₄	1	1	yes	characteristic
476	C₂⁶	C₂²×D₄	1	1	yes	characteristic
477	C₂⁶	C₂²×D₄	1	1	yes	characteristic
478	C₂⁶	C₂²×D₄	1	1	yes	characteristic
479	C₂⁶	C₂²×D₄	1	1	yes	characteristic
480	C₂⁶	C₂²×D₄	1	1	yes	characteristic
481	C₂⁶	C₂²×D₄	1	1	yes	characteristic
482	C₂⁶	C₂²×D₄	1	1	yes	characteristic
483	C₂⁶	C₂²×D₄	1	1	yes	characteristic
484	C₂⁶	C₂²×D₄	1	1	yes	characteristic
485	C₂⁶	C₂²×D₄	1	1	yes	characteristic
486	C₂⁶	C₂²×D₄	1	1	yes	characteristic
487	C₂⁶	C₂²×D₄	1	1	yes	characteristic
488	C₂⁶	C₂²×D₄	1	1	yes	characteristic
489	C₂⁶	C₂²×D₄	1	1	yes	characteristic
490	C₂⁶	C₂×#41	1	4	yes	—
491	C₂⁶	C₂×#41	1	4	yes	—
492	C₂⁶	C₂×#41	1	4	yes	—
493	C₂⁶	C₂×#41	1	2	yes	—
494	C₂⁶	C₂×#41	1	2	yes	—
495	C₂⁶	C₂×#41	1	2	yes	—
496	C₂⁶	C₂×#41	1	2	yes	—
497	C₂⁶	H(5,𝔽₂)	1	2	yes	—
498	C₂⁶	H(5,𝔽₂)	1	2	yes	—
499	C₂⁶	H(5,𝔽₂)	1	2	yes	—
500	C₂⁶	H(5,𝔽₂)	1	2	yes	—
501	C₂⁶	C₂⁵	1	2	yes	—
502	C₂⁶	C₂⁵	1	1	yes	characteristic
503	C₂⁶	C₂⁵	1	1	yes	characteristic
504	C₂⁶	C₂⁵	1	1	yes	characteristic
505	C₂×H(5,𝔽₂)	H(5,𝔽₂)	1	32	yes	—
506	C₂³×D₄	#120	1	2	yes	—
507	C₂³×D₄	#120	1	2	yes	—
508	C₂³×D₄	#120	1	2	yes	—
509	C₂³×D₄	#120	1	2	yes	—
510	C₂³×D₄	#120	1	4	yes	—
511	C₂³×D₄	#120	1	4	yes	—
512	C₂³×D₄	#120	1	4	yes	—
513	C₂³×D₄	#120	1	4	yes	—
514	C₂³×D₄	#120	1	4	yes	—
515	C₂³×D₄	#120	1	4	yes	—
516	C₂³×D₄	#120	1	4	yes	—
517	C₂³×D₄	#120	1	4	yes	—
518	C₂³×D₄	#120	1	2	yes	—
519	C₂³×D₄	#120	1	2	yes	—
520	C₂³×D₄	#120	1	2	yes	—
521	C₂³×D₄	#120	1	2	yes	—
522	C₂³×D₄	C₂²×D₄	1	2	yes	—
523	C₂³×D₄	C₂²×D₄	1	2	yes	—
524	C₂³×D₄	C₂²×D₄	1	2	yes	—
525	C₂³×D₄	C₂²×D₄	1	2	yes	—
526	C₂³×D₄	C₂²×D₄	1	4	yes	—
527	C₂³×D₄	C₂²×D₄	1	4	yes	—
528	C₂³×D₄	C₂²×D₄	1	4	yes	—
529	C₂³×D₄	C₂²×D₄	1	4	yes	—
530	C₂³×D₄	C₂²×D₄	1	4	yes	—
531	C₂³×D₄	C₂²×D₄	1	4	yes	—
532	C₂³×D₄	C₂²×D₄	1	4	yes	—
533	C₂³×D₄	C₂²×D₄	1	4	yes	—
534	C₂³×D₄	C₂²×D₄	1	2	yes	—
535	C₂³×D₄	C₂²×D₄	1	2	yes	—
536	C₂³×D₄	C₂²×D₄	1	2	yes	—
537	C₂³×D₄	C₂²×D₄	1	2	yes	—
538	C₂³×D₄	C₂²×D₄	1	2	yes	—
539	C₂³×D₄	C₂²×D₄	1	2	yes	—
540	C₂³×D₄	C₂²×D₄	1	2	yes	—
541	C₂³×D₄	C₂²×D₄	1	2	yes	—
542	C₂³×D₄	C₂²×D₄	1	2	yes	—
543	C₂³×D₄	C₂²×D₄	1	2	yes	—
544	C₂³×D₄	C₂²×D₄	1	2	yes	—
545	C₂³×D₄	C₂²×D₄	1	2	yes	—
546	C₂³×D₄	C₂²×D₄	1	2	yes	—
547	C₂³×D₄	C₂²×D₄	1	2	yes	—
548	C₂³×D₄	C₂²×D₄	1	2	yes	—
549	C₂³×D₄	C₂²×D₄	1	2	yes	—
550	C₂³×D₄	C₂²×D₄	1	2	yes	—
551	C₂³×D₄	C₂²×D₄	1	2	yes	—
552	C₂³×D₄	C₂²×D₄	1	2	yes	—
553	C₂³×D₄	C₂²×D₄	1	2	yes	—
554	C₂³×D₄	C₂²×D₄	1	2	yes	—
555	C₂³×D₄	C₂²×D₄	1	2	yes	—
556	C₂³×D₄	C₂²×D₄	1	2	yes	—
557	C₂³×D₄	C₂×#41	1	8	yes	—
558	C₂³×D₄	C₂×#41	1	8	yes	—
559	C₂³×D₄	C₂×#41	1	8	yes	—
560	C₂³×D₄	C₂⁵	1	2	yes	—
561	C₂³×D₄	C₂⁵	1	2	yes	—
562	C₂³×D₄	C₂⁵	1	2	yes	—
563	C₂³×D₄	C₂⁵	1	8	yes	—
564	C₂⁴×C₄	#120	1	2	yes	—
565	C₂⁴×C₄	#120	1	2	yes	—
566	C₂⁴×C₄	#120	1	2	yes	—
567	C₂⁴×C₄	#120	1	2	yes	—
568	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
569	C₂⁴×C₄	C₂²×D₄	1	2	yes	—
570	C₂⁴×C₄	C₂²×D₄	1	2	yes	—
571	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
572	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
573	C₂⁴×C₄	C₂²×D₄	1	2	yes	—
574	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
575	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
576	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
577	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
578	C₂⁴×C₄	C₂×#41	1	4	yes	—
579	C₂⁴×C₄	C₂×#41	1	4	yes	—
580	C₂⁴×C₄	C₂×#41	1	4	yes	—
581	C₂⁴×C₄	C₂⁵	1	2	yes	—
582	C₂×#123	C₂²×D₄	1	8	yes	—
583	C₂×#123	C₂²×D₄	1	8	yes	—
584	C₂×#120	C₂²×D₄	1	8	yes	—
585	C₂×#120	C₂²×D₄	1	8	yes	—
586	C₂×#120	C₂²×D₄	1	8	yes	—
587	C₂×#120	C₂²×D₄	1	8	yes	—
588	C₂×#120	C₂²×D₄	1	8	yes	—
589	C₂×#120	C₂²×D₄	1	8	yes	—
590	C₂×#117	C₂²×D₄	1	8	yes	—
591	C₂×#117	C₂²×D₄	1	8	yes	—
592	C₂²×C₂²⋊C₄	C₂²×D₄	1	2	yes	—
593	C₂²×C₂²⋊C₄	C₂²×D₄	1	2	yes	—
594	C₂²×C₂²⋊C₄	C₂²×D₄	1	2	yes	—
595	C₂²×C₂²⋊C₄	C₂²×D₄	1	2	yes	—
596	C₂²×C₂²⋊C₄	C₂²×D₄	1	2	yes	—
597	C₂²×C₂²⋊C₄	C₂²×D₄	1	8	yes	—
598	C₂²×C₂²⋊C₄	C₂²×D₄	1	4	yes	—
599	C₂²×C₂²⋊C₄	C₂²×D₄	1	4	yes	—
600	C₂²×C₂²⋊C₄	C₂²×D₄	1	8	yes	—
601	C₂²×C₂²⋊C₄	C₂²×D₄	1	4	yes	—
602	C₂²×C₂²⋊C₄	C₂²×D₄	1	4	yes	—
603	C₂²×C₂²⋊C₄	C₂²×D₄	1	4	yes	—
604	C₂²×C₂²⋊C₄	C₂²×D₄	1	4	yes	—
605	C₂²×C₂²⋊C₄	C₂²×D₄	1	4	yes	—
606	C₂²×C₂²⋊C₄	C₂²×D₄	1	4	yes	—
607	C₂²×C₂²⋊C₄	C₂⁵	1	8	yes	—
608	C₂²×C₂²⋊C₄	C₂⁵	1	8	yes	—
609	C₂²×C₂²⋊C₄	C₂⁵	1	8	yes	—
610	C₂²×C₂²⋊C₄	C₂⁵	1	2	yes	—
611	C₂²×C₂²⋊C₄	C₂⁵	1	4	yes	—
612	C₂²×C₂²⋊C₄	C₂⁵	1	4	yes	—
613	C₂²×C₂²⋊C₄	C₂⁵	1	4	yes	—
614	C₂²×C₂²⋊C₄	C₂⁵	1	4	yes	—
615	#386	C₂²×D₄	1	8	yes	—
616	#386	C₂²×D₄	1	8	yes	—
617	#386	C₂²×D₄	1	8	yes	—
618	#386	C₂²×D₄	1	8	yes	—
619	#386	C₂²×D₄	1	8	yes	—
620	#386	C₂²×D₄	1	8	yes	—
621	#386	C₂²×D₄	1	8	yes	—
622	#386	C₂²×D₄	1	8	yes	—
623	#381	C₂²×D₄	1	8	yes	—
624	#381	C₂²×D₄	1	8	yes	—
625	#379	C₂²×D₄	1	4	yes	—
626	#379	C₂²×D₄	1	4	yes	—
627	#379	C₂²×D₄	1	4	yes	—
628	#379	C₂²×D₄	1	4	yes	—
629	#379	C₂²×D₄	1	8	yes	—
630	#379	C₂²×D₄	1	8	yes	—
631	#379	C₂²×D₄	1	4	yes	—
632	#379	C₂²×D₄	1	4	yes	—
633	#379	C₂²×D₄	1	4	yes	—
634	#379	C₂²×D₄	1	4	yes	—
635	#379	C₂²×D₄	1	4	yes	—
636	#379	C₂²×D₄	1	4	yes	—
637	#379	C₂²×D₄	1	4	yes	—
638	#379	C₂²×D₄	1	4	yes	—
639	#379	C₂²×D₄	1	4	yes	—
640	#379	C₂²×D₄	1	4	yes	—
641	#379	C₂²×D₄	1	4	yes	—
642	#379	C₂²×D₄	1	4	yes	—
643	C₂⁵	C₂×#120	1	2	yes	—
644	C₂⁵	C₂×#120	1	2	yes	—
645	C₂⁵	C₂×#120	1	4	yes	—
646	C₂⁵	C₂×#120	1	4	yes	—
647	C₂⁵	C₂×#120	1	4	yes	—
648	C₂⁵	C₂×#120	1	1	yes	characteristic
649	C₂⁵	C₂×#120	1	4	yes	—
650	C₂⁵	C₂×#120	1	2	yes	—
651	C₂⁵	C₂×#120	1	2	yes	—
652	C₂⁵	C₂×#120	1	1	yes	characteristic
653	C₂⁵	C₂×#120	1	1	yes	characteristic
654	C₂⁵	C₂×#120	1	1	yes	characteristic
655	C₂⁵	C₂×#120	1	1	yes	characteristic
656	C₂⁵	C₂×#120	1	1	yes	characteristic
657	C₂⁵	C₂×#120	1	1	yes	characteristic
658	C₂⁵	C₂×#120	1	1	yes	characteristic
659	C₂⁵	C₂×#120	1	1	yes	characteristic
660	C₂⁵	C₂×#120	1	1	yes	characteristic
661	C₂⁵	C₂×#120	1	1	yes	characteristic
662	C₂⁵	C₂×#120	1	1	yes	characteristic
663	C₂⁵	C₂×#120	1	1	yes	characteristic
664	C₂⁵	C₂×#120	1	1	yes	characteristic
665	C₂⁵	C₂×#120	1	1	yes	characteristic
666	C₂⁵	C₂×#120	1	1	yes	characteristic
667	C₂⁵	#525	1	1	yes	characteristic
668	C₂⁵	#525	1	1	yes	characteristic
669	C₂⁵	#525	1	2	yes	—
670	C₂⁵	#525	1	1	yes	characteristic
671	C₂⁵	#525	1	1	yes	characteristic
672	C₂⁵	#525	1	2	yes	—
673	C₂⁵	#525	1	2	yes	—
674	C₂⁵	#525	1	2	yes	—
675	C₂⁵	#525	1	2	yes	—
676	C₂⁵	#525	1	2	yes	—
677	C₂⁵	#535	1	1	yes	characteristic
678	C₂⁵	#535	1	1	yes	characteristic
679	C₂⁵	#535	1	1	yes	characteristic
680	C₂⁵	#535	1	2	yes	—
681	C₂⁵	#535	1	2	yes	—
682	C₂⁵	#535	1	2	yes	—
683	C₂⁵	#535	1	2	yes	—
684	C₂⁵	#535	1	1	yes	characteristic
685	C₂⁵	#535	1	2	yes	—
686	C₂⁵	#535	1	2	yes	—
687	C₂⁵	#546	1	2	yes	—
688	C₂⁵	#546	1	2	yes	—
689	C₂⁵	#546	1	2	yes	—
690	C₂⁵	#546	1	2	yes	—
691	C₂⁵	#546	1	2	yes	—
692	C₂⁵	#546	1	2	yes	—
693	C₂⁵	#546	1	2	yes	—
694	C₂⁵	#546	1	2	yes	—
695	C₂⁵	#546	1	2	yes	—
696	C₂⁵	#546	1	2	yes	—
697	C₂⁵	#546	1	2	yes	—
698	C₂⁵	#546	1	2	yes	—
699	C₂⁵	#546	1	2	yes	—
700	C₂⁵	#546	1	2	yes	—
701	C₂⁵	#546	1	2	yes	—
702	C₂⁵	#546	1	2	yes	—
703	C₂⁵	#546	1	2	yes	—
704	C₂⁵	#546	1	2	yes	—
705	C₂⁵	#546	1	2	yes	—
706	C₂⁵	#546	1	2	yes	—
707	C₂⁵	#546	1	2	yes	—
708	C₂⁵	#546	1	2	yes	—
709	C₂⁵	#546	1	2	yes	—
710	C₂⁵	#546	1	2	yes	—
711	C₂⁵	#546	1	2	yes	—
712	C₂⁵	#546	1	2	yes	—
713	C₂⁵	#546	1	2	yes	—
714	C₂⁵	#546	1	2	yes	—
715	C₂⁵	#546	1	2	yes	—
716	C₂⁵	#546	1	2	yes	—
717	C₂⁵	#546	1	2	yes	—
718	C₂⁵	#546	1	2	yes	—
719	C₂⁵	C₂³×D₄	1	2	yes	—
720	C₂⁵	C₂³×D₄	1	2	yes	—
721	C₂⁵	C₂³×D₄	1	2	yes	—
722	C₂⁵	C₂³×D₄	1	2	yes	—
723	C₂⁵	C₂³×D₄	1	1	yes	characteristic
724	C₂⁵	C₂³×D₄	1	1	yes	characteristic
725	C₂⁵	C₂³×D₄	1	1	yes	characteristic
726	C₂⁵	C₂³×D₄	1	1	yes	characteristic
727	C₂⁵	C₂³×D₄	1	1	yes	characteristic
728	C₂⁵	C₂³×D₄	1	1	yes	characteristic
729	C₂⁵	C₂³×D₄	1	1	yes	characteristic
730	C₂⁵	C₂³×D₄	1	1	yes	characteristic
731	C₂⁵	C₂³×D₄	1	1	yes	characteristic
732	C₂⁵	C₂³×D₄	1	1	yes	characteristic
733	C₂⁵	C₂³×D₄	1	1	yes	characteristic
734	C₂⁵	C₂³×D₄	1	1	yes	characteristic
735	C₂⁵	C₂³×D₄	1	1	yes	characteristic
736	C₂⁵	C₂³×D₄	1	1	yes	characteristic
737	C₂⁵	C₂³×D₄	1	1	yes	characteristic
738	C₂⁵	C₂³×D₄	1	1	yes	characteristic
739	C₂⁵	C₂³×D₄	1	1	yes	characteristic
740	C₂⁵	C₂³×D₄	1	1	yes	characteristic
741	C₂⁵	C₂³×D₄	1	2	yes	—
742	C₂⁵	C₂²×#41	1	8	yes	—
743	C₂⁵	C₂²×#41	1	2	yes	—
744	C₂⁵	C₂²×#41	1	2	yes	—
745	C₂⁵	C₂²×#41	1	2	yes	—
746	C₂⁵	C₂²×#41	1	2	yes	—
747	C₂⁵	C₂²×#41	1	2	yes	—
748	C₂⁵	C₂²×#41	1	2	yes	—
749	C₂⁵	C₂×H(5,𝔽₂)	1	2	yes	—
750	C₂⁵	C₂×H(5,𝔽₂)	1	2	yes	—
751	C₂⁵	C₂×H(5,𝔽₂)	1	2	yes	—
752	C₂⁵	C₂×H(5,𝔽₂)	1	2	yes	—
753	C₂⁵	C₂×H(5,𝔽₂)	1	2	yes	—
754	C₂⁵	C₂×H(5,𝔽₂)	1	2	yes	—
755	C₂⁵	C₂⁶	1	1	yes	characteristic
756	C₂²×D₄	C₂×#120	1	4	yes	—
757	C₂²×D₄	C₂×#120	1	4	yes	—
758	C₂²×D₄	C₂×#120	1	4	yes	—
759	C₂²×D₄	C₂×#120	1	4	yes	—
760	C₂²×D₄	C₂×#120	1	4	yes	—
761	C₂²×D₄	C₂×#120	1	4	yes	—
762	C₂²×D₄	C₂×#120	1	4	yes	—
763	C₂²×D₄	C₂×#120	1	4	yes	—
764	C₂²×D₄	C₂×#120	1	4	yes	—
765	C₂²×D₄	C₂×#120	1	4	yes	—
766	C₂²×D₄	C₂×#120	1	4	yes	—
767	C₂²×D₄	C₂×#120	1	4	yes	—
768	C₂²×D₄	C₂³×D₄	1	4	yes	—
769	C₂²×D₄	C₂³×D₄	1	4	yes	—
770	C₂²×D₄	C₂³×D₄	1	4	yes	—
771	C₂²×D₄	C₂³×D₄	1	4	yes	—
772	C₂²×D₄	C₂×H(5,𝔽₂)	1	16	yes	—
773	C₂²×D₄	C₂×H(5,𝔽₂)	1	32	yes	—
774	C₂³×C₄	C₂×#120	1	2	yes	—
775	C₂³×C₄	C₂×#120	1	2	yes	—
776	C₂³×C₄	C₂×#120	1	4	yes	—
777	C₂³×C₄	C₂×#120	1	4	yes	—
778	C₂³×C₄	C₂×#120	1	4	yes	—
779	C₂³×C₄	C₂×#120	1	4	yes	—
780	C₂³×C₄	C₂×#120	1	2	yes	—
781	C₂³×C₄	C₂×#120	1	2	yes	—
782	C₂³×C₄	C₂³×D₄	1	2	yes	—
783	C₂³×C₄	C₂³×D₄	1	2	yes	—
784	C₂³×C₄	C₂³×D₄	1	2	yes	—
785	C₂³×C₄	C₂³×D₄	1	2	yes	—
786	C₂³×C₄	C₂³×D₄	1	2	yes	—
787	C₂³×C₄	C₂³×D₄	1	2	yes	—
788	C₂³×C₄	C₂³×D₄	1	2	yes	—
789	C₂³×C₄	C₂²×#41	1	8	yes	—
790	C₂×C₂²⋊C₄	C₂³×D₄	1	8	yes	—
791	C₂×C₂²⋊C₄	C₂³×D₄	1	8	yes	—
792	C₂×C₂²⋊C₄	C₂³×D₄	1	8	yes	—
793	C₂×C₂²⋊C₄	C₂³×D₄	1	8	yes	—
794	C₂⁴	#2404	1	1	yes	characteristic
795	C₂⁴	#2404	1	1	yes	characteristic
796	C₂⁴	#2404	1	1	yes	characteristic
797	C₂⁴	#2404	1	1	yes	characteristic
798	C₂⁴	#2404	1	1	yes	characteristic
799	C₂⁴	#2404	1	1	yes	characteristic
800	C₂⁴	#2404	1	1	yes	characteristic
801	C₂⁴	#2404	1	2	yes	—
802	C₂⁴	#2404	1	2	yes	—
803	C₂⁴	#2404	1	2	yes	—
804	C₂⁴	#2404	1	2	yes	—
805	C₂⁴	#2404	1	2	yes	—
806	C₂⁴	#2404	1	1	yes	characteristic
807	C₂⁴	#2404	1	1	yes	characteristic
808	C₂⁴	#2404	1	1	yes	characteristic
809	C₂⁴	#2404	1	1	yes	characteristic
810	C₂⁴	#2404	1	2	yes	—
811	C₂⁴	#2404	1	2	yes	—
812	C₂⁴	#2404	1	2	yes	—
813	C₂⁴	#2404	1	1	yes	characteristic
814	C₂⁴	#2404	1	2	yes	—
815	C₂⁴	#2404	1	2	yes	—
816	C₂⁴	#2404	1	2	yes	—
817	C₂⁴	#2404	1	2	yes	—
818	C₂⁴	#2404	1	2	yes	—
819	C₂⁴	#2404	1	2	yes	—
820	C₂⁴	#2404	1	2	yes	—
821	C₂⁴	#2404	1	1	yes	characteristic
822	C₂⁴	#2404	1	1	yes	characteristic
823	C₂⁴	#2404	1	1	yes	characteristic
824	C₂⁴	#2404	1	2	yes	—
825	C₂⁴	#2404	1	2	yes	—
826	C₂⁴	#2404	1	2	yes	—
827	C₂⁴	#2404	1	2	yes	—
828	C₂⁴	#2404	1	2	yes	—
829	C₂⁴	#2404	1	2	yes	—
830	C₂⁴	#2404	1	2	yes	—
831	C₂⁴	#2404	1	2	yes	—
832	C₂⁴	#2404	1	2	yes	—
833	C₂⁴	#2404	1	1	yes	characteristic
834	C₂⁴	C₂²×#120	1	1	yes	characteristic
835	C₂⁴	C₂²×#120	1	1	yes	characteristic
836	C₂⁴	C₂²×#120	1	1	yes	characteristic
837	C₂⁴	C₂²×#120	1	1	yes	characteristic
838	C₂⁴	C₂²×#120	1	4	yes	—
839	C₂⁴	C₂²×#120	1	4	yes	—
840	C₂⁴	C₂²×#120	1	1	yes	characteristic
841	C₂⁴	C₂²×#120	1	1	yes	characteristic
842	C₂⁴	C₂²×#120	1	1	yes	characteristic
843	C₂⁴	C₂²×#120	1	1	yes	characteristic
844	C₂⁴	C₂²×#120	1	1	yes	characteristic
845	C₂⁴	C₂²×#120	1	1	yes	characteristic
846	C₂⁴	C₂²×#120	1	1	yes	characteristic
847	C₂⁴	C₂²×#120	1	1	yes	characteristic
848	C₂⁴	C₂×#525	1	1	yes	characteristic
849	C₂⁴	C₂×#525	1	1	yes	characteristic
850	C₂⁴	C₂×#525	1	1	yes	characteristic
851	C₂⁴	C₂×#525	1	1	yes	characteristic
852	C₂⁴	C₂×#525	1	2	yes	—
853	C₂⁴	C₂×#525	1	1	yes	characteristic
854	C₂⁴	C₂×#525	1	2	yes	—
855	C₂⁴	C₂×#525	1	1	yes	characteristic
856	C₂⁴	C₂×#525	1	2	yes	—
857	C₂⁴	C₂×#535	1	1	yes	characteristic
858	C₂⁴	C₂×#535	1	1	yes	characteristic
859	C₂⁴	C₂×#535	1	1	yes	characteristic
860	C₂⁴	C₂×#535	1	1	yes	characteristic
861	C₂⁴	C₂×#535	1	1	yes	characteristic
862	C₂⁴	C₂×#535	1	2	yes	—
863	C₂⁴	C₂×#535	1	1	yes	characteristic
864	C₂⁴	C₂×#535	1	2	yes	—
865	C₂⁴	C₂×#535	1	2	yes	—
866	C₂⁴	C₂×#546	1	2	yes	—
867	C₂⁴	C₂×#546	1	2	yes	—
868	C₂⁴	C₂×#546	1	2	yes	—
869	C₂⁴	C₂×#546	1	2	yes	—
870	C₂⁴	C₂×#546	1	2	yes	—
871	C₂⁴	C₂×#546	1	2	yes	—
872	C₂⁴	C₂×#546	1	2	yes	—
873	C₂⁴	C₂×#546	1	2	yes	—
874	C₂⁴	C₂×#546	1	2	yes	—
875	C₂⁴	C₂×#546	1	2	yes	—
876	C₂⁴	C₂×#546	1	2	yes	—
877	C₂⁴	C₂×#546	1	2	yes	—
878	C₂⁴	C₂×#546	1	2	yes	—
879	C₂⁴	C₂×#546	1	2	yes	—
880	C₂⁴	C₂×#546	1	2	yes	—
881	C₂⁴	C₂×#546	1	2	yes	—
882	C₂⁴	C₂×#546	1	2	yes	—
883	C₂⁴	C₂×#546	1	2	yes	—
884	C₂⁴	C₂×#546	1	2	yes	—
885	C₂⁴	C₂×#546	1	2	yes	—
886	C₂⁴	C₂×#546	1	2	yes	—
887	C₂⁴	C₂×#546	1	2	yes	—
888	C₂⁴	C₂×#546	1	2	yes	—
889	C₂⁴	C₂×#546	1	2	yes	—
890	C₂⁴	#3484	1	8	yes	—
891	C₂⁴	#3490	1	16	yes	complemented
892	C₂⁴	C₂⁴×D₄	1	1	yes	characteristic
893	C₂⁴	C₂⁴×D₄	1	1	yes	characteristic
894	C₂⁴	C₂⁴×D₄	1	1	yes	characteristic
895	C₂⁴	C₂³×#41	1	2	yes	—
896	C₂⁴	C₂²×H(5,𝔽₂)	1	2	yes	—
897	C₂⁴	C₂²×H(5,𝔽₂)	1	8	yes	—
898	C₂×D₄	#3484	1	16	yes	—
899	C₂×D₄	#3484	1	16	yes	—
900	C₂²×C₄	C₂²×#120	1	4	yes	—
901	C₂²×C₄	C₂²×#120	1	4	yes	—
902	C₂²×C₄	#3484	1	8	yes	—
903	C₂²×C₄	#3490	1	16	yes	complemented
904	C₂³	#23996	1	4	yes	complemented
905	C₂³	C₂×#2404	1	1	yes	characteristic
906	C₂³	C₂×#2404	1	1	yes	characteristic
907	C₂³	C₂×#2404	1	1	yes	characteristic
908	C₂³	C₂×#2404	1	1	yes	characteristic
909	C₂³	C₂×#2404	1	1	yes	characteristic
910	C₂³	C₂×#2404	1	1	yes	characteristic
911	C₂³	C₂×#2404	1	1	yes	characteristic
912	C₂³	C₂×#2404	1	2	yes	—
913	C₂³	C₂×#2404	1	2	yes	—
914	C₂³	C₂×#2404	1	2	yes	—
915	C₂³	C₂×#2404	1	2	yes	—
916	C₂³	C₂×#2404	1	2	yes	—
917	C₂³	C₂×#2404	1	1	yes	characteristic
918	C₂³	C₂×#2404	1	2	yes	—
919	C₂³	C₂×#2404	1	1	yes	characteristic
920	C₂³	C₂×#2404	1	1	yes	characteristic
921	C₂³	C₂×#2404	1	1	yes	characteristic
922	C₂³	C₂×#2404	1	1	yes	characteristic
923	C₂³	#35346	1	8	yes	—
924	C₂³	C₂³×#120	1	1	yes	characteristic
925	C₂³	C₂²×#525	1	1	yes	characteristic
926	C₂³	C₂²×#535	1	1	yes	characteristic
927	C₂³	C₂²×#546	1	2	yes	—
928	C₂³	C₂²×#546	1	2	yes	—
929	C₂³	C₂×#3484	1	4	yes	—
930	C₂³	C₂×#3484	1	4	yes	—
931	C₂³	C₂×#3484	1	4	yes	—
932	C₂³	C₂×#3490	1	8	yes	—
933	C₂³	#62817	1	8	yes	—
934	C₂×C₄	#35346	1	8	yes	—
935	C₂²	C₂×#23996	1	2	yes	—
936	C₂²	C₂×#23996	1	2	yes	—
937	C₂²	C₂×#23996	1	2	yes	—
938	C₂²	#6451863	1	2	yes	—
939	C₂²	C₂²×#2404	1	1	yes	characteristic
940	C₂²	C₂×#35346	1	2	yes	—
941	C₂²	#7630944	1	2	yes	—
942	C₂²	#7642273	1	2	yes	—
943	C₂²	#7670206	1	4	yes	—
944	C₂²	#7670206	1	4	yes	—
945	C₂	C₂²×#23996	1	1	yes	characteristic
946	C₂	#72259101	1	1	yes	characteristic
947	C₂	C₂×#6451863	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²	C₂²×#2404
commutator, Frattini, cosocle	C₂⁵	C₂⁶
LCS	G ▷ C₂⁵ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂² ◁ C₂⁷ ◁ G
LECS	G ▷ C₂⁵ ▷ C₂ ▷ C₁

Complements

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

N	H ≅ G/N	type
1. #72266066	C₂	semidirect
2. #72266065	C₂	semidirect
3. #72266057	C₂	semidirect
4. #72266051	C₂	semidirect
5. #72266049	C₂	semidirect
6. #72241143	C₂	semidirect
7. #72240619	C₂	semidirect
8. #72240617	C₂	semidirect
9. C₂×#6370693	C₂	semidirect
10. #72234689	C₂	semidirect
11. #72234668	C₂	semidirect
12. #72234644	C₂	semidirect
13. #72234629	C₂	semidirect
14. C₂×#6628892	C₂	semidirect
15. #72234587	C₂	semidirect
16. #72225632	C₂	semidirect
17. C₂²×#32898	C₂	semidirect
19. C₂²×#3026	C₂²	semidirect
20. C₂³×B(4,𝔽₂)	C₂²	semidirect
21. C₂²×#2883	C₂²	semidirect
22. #7675443	C₂²	semidirect
23. #7675392	C₂²	semidirect
24. #7670233	C₂²	semidirect
25. #7670206	C₂²	semidirect
26. #7644637	C₂²	semidirect
27. #7641846	C₂²	semidirect
28. #7631294	C₂²	semidirect
31. C₂×#34980	C₂²	semidirect
34. #7626202	C₂²	semidirect
37. C₂×#34171	C₂²	semidirect
39. #6628892	C₂²	semidirect
40. #6628892	C₂²	semidirect
42. C₂×#32898	C₂²	semidirect
43. C₂×#32898	C₂²	semidirect
44. C₂×#23996	C₂²	semidirect
45. C₂×#21746	C₂²	semidirect
46. C₂×#20609	C₂²	semidirect
47. C₂²×#1790	C₂²	semidirect
48. #6370693	C₂²	semidirect
49. #6370693	C₂²	semidirect
50. C₂×#20585	C₂²	semidirect
57. #517411	C₂²	semidirect
58. #451129	C₂²	semidirect
59. #451128	C₂²	semidirect
60. #449580	C₂²	semidirect
61. #449578	C₂²	semidirect
62. #417973	C₂²	semidirect
63. #417969	C₂²	semidirect
64. #417542	C₂²	semidirect
65. #417538	C₂²	semidirect
66. #405274	C₂²	semidirect
67. #405268	C₂²	semidirect
68. #405104	C₂²	semidirect
69. #405090	C₂²	semidirect
70. #394474	C₂²	semidirect
71. #394470	C₂²	semidirect
72. #394470	C₂²	semidirect
73. #394470	C₂²	semidirect
74. #394273	C₂²	semidirect
75. #394267	C₂²	semidirect
76. #394058	C₂²	semidirect
77. #393929	C₂²	semidirect
78. #392699	C₂²	semidirect
79. #392658	C₂²	semidirect
80. #392231	C₂²	semidirect
81. #382707	C₂²	semidirect
82. #379754	C₂²	semidirect
83. #379733	C₂²	semidirect
84. #374058	C₂²	semidirect
85. #374038	C₂²	semidirect
86. #364545	C₂²	semidirect
87. #364532	C₂²	semidirect
88. #364471	C₂²	semidirect
89. #364471	C₂²	semidirect
90. #364440	C₂²	semidirect
91. #364440	C₂²	semidirect
92. #359892	C₂²	semidirect
93. #359892	C₂²	semidirect
94. #359863	C₂²	semidirect
95. #359811	C₂²	semidirect
96. #359788	C₂²	semidirect
97. #359705	C₂²	semidirect
98. #359695	C₂²	semidirect
99. #359501	C₂²	semidirect
100. #359442	C₂²	semidirect
101. #359442	C₂²	semidirect
102. #359428	C₂²	semidirect
103. #355913	C₂²	semidirect
104. #355913	C₂²	semidirect
105. #355913	C₂²	semidirect
106. #355913	C₂²	semidirect
114. C₂×#3490	C₂³	semidirect
134. C₂×#2849	C₂³	semidirect
135. C₂×#2846	C₂³	semidirect
136. #35370	C₂³	semidirect
137. #35367	C₂³	semidirect
138. #35360	C₂³	semidirect
139. #35360	C₂³	semidirect
140. #35359	C₂³	semidirect
141. #35350	C₂³	semidirect
142. #35348	C₂³	semidirect
143. #35348	C₂³	semidirect
144. #34995	C₂³	semidirect
145. #34993	C₂³	semidirect
146. #34992	C₂³	semidirect
147. #34982	C₂³	semidirect
148. #34982	C₂³	semidirect
149. #34982	C₂³	semidirect
150. #34981	C₂³	semidirect
151. #34980	D₄	semidirect
152. #34980	D₄	semidirect
158. C₂×#2405	D₄	semidirect
159. C₂×#2405	D₄	semidirect
160. C₂×#2405	C₂³	semidirect
161. C₂×#2410	C₂³	semidirect
162. C₂×#2403	D₄	semidirect
163. C₂×#2403	D₄	semidirect
164. C₂×#2403	D₄	semidirect
165. C₂×#2403	D₄	semidirect
166. C₂×#2403	D₄	semidirect
167. C₂×#2403	D₄	semidirect
168. C₂×#2403	D₄	semidirect
169. C₂×#2403	D₄	semidirect
175. C₂×#2403	C₂³	semidirect
176. #34273	C₂³	semidirect
177. #34251	C₂³	semidirect
178. #34198	C₂³	semidirect
179. #34198	C₂³	semidirect
180. #34198	C₂³	semidirect
181. #34176	C₂³	semidirect
182. #34171	D₄	semidirect
183. #34171	D₄	semidirect
188. #34171	C₂³	semidirect
189. C₂×D₄×C₂²⋊C₄	C₂³	semidirect
190. C₂×D₄×C₂²⋊C₄	C₂³	semidirect
191. C₂×#2309	D₄	semidirect
192. C₂×#2308	D₄	semidirect
199. C₂×#2280	D₄	semidirect
200. C₂×#2280	C₂³	semidirect
201. C₂²×#379	D₄	semidirect
209. C₂²×#379	C₂³	semidirect
210. C₂×#2032	C₂³	semidirect
211. C₂×#2021	C₂³	semidirect
212. C₂×#1913	C₂³	semidirect
213. C₂×#1913	C₂³	semidirect
214. C₂×#1898	C₂³	semidirect
215. C₂×#1898	C₂³	semidirect
216. C₂×#1898	C₂³	semidirect
217. C₂×#1889	C₂³	semidirect
218. C₂×#1828	C₂³	semidirect
219. C₂×#1819	C₂³	semidirect
240. C₂×#1781	C₂³	semidirect
241. #14681	C₂³	semidirect
242. #14679	C₂³	semidirect
243. #13867	C₂³	semidirect
244. #13867	C₂³	semidirect
245. #11174	C₂³	semidirect
246. #11172	C₂³	semidirect
247. #11169	C₂³	semidirect
248. #11166	C₂³	semidirect
249. #11089	C₂³	semidirect
250. #11089	C₂³	semidirect
251. #11089	C₂³	semidirect
252. #11087	C₂³	semidirect
253. #11046	C₂³	semidirect
254. #11043	C₂³	semidirect
255. #10995	C₂³	semidirect
256. #10991	C₂³	semidirect
257. #10991	C₂³	semidirect
258. #10972	C₂³	semidirect
259. #10972	C₂³	semidirect
260. #10965	C₂³	semidirect
261. #10960	C₂³	semidirect
262. #10938	C₂³	semidirect
263. #10768	C₂³	semidirect
264. #10754	C₂³	semidirect
265. #10745	C₂³	semidirect
266. #10735	C₂³	semidirect
267. #10735	C₂³	semidirect
268. #10735	C₂³	semidirect
269. #10735	C₂³	semidirect
270. #10735	C₂³	semidirect
271. #10735	C₂³	semidirect
272. #10735	C₂³	semidirect
273. #10735	C₂³	semidirect
274. #10725	C₂³	semidirect
275. #10725	C₂³	semidirect
276. #10725	C₂³	semidirect
277. #10725	C₂³	semidirect
279. C₂⁷	#41	semidirect
304. C₂⁴×D₄	#41	semidirect
305. C₂⁴×D₄	#41	semidirect
306. C₂⁴×D₄	#41	semidirect
318. C₂⁵×C₄	#41	semidirect
320. C₂×#543	C₂⁴	semidirect
321. C₂×#534	C₂×D₄	semidirect
325. C₂²×#123	C₂×D₄	semidirect
328. C₂²×#120	C₂×D₄	semidirect
329. C₂²×#120	C₂×D₄	semidirect
330. C₂²×#120	C₂×D₄	semidirect
331. C₂²×#120	C₂×D₄	semidirect
337. C₂²×#120	C₂⁴	semidirect
338. C₂×#518	C₂×D₄	semidirect
339. C₂×#518	C₂×D₄	semidirect
343. C₂×#518	C₂⁴	semidirect
344. C₂²×#117	C₂×D₄	semidirect
347. C₂³×C₂²⋊C₄	C₂×D₄	semidirect
356. C₂³×C₂²⋊C₄	C₂⁴	semidirect
365. C₂²×#99	C₂⁴	semidirect
368. #2405	C₂×D₄	semidirect
369. #2405	C₂×D₄	semidirect
370. #2405	C₂×D₄	semidirect
371. #2405	C₂×D₄	semidirect
378. #2403	C₂×D₄	semidirect
379. #2403	C₂×D₄	semidirect
380. #2403	C₂×D₄	semidirect
381. #2403	C₂×D₄	semidirect
382. #2403	C₂×D₄	semidirect
383. #2403	C₂×D₄	semidirect
384. #2403	C₂×D₄	semidirect
385. #2403	C₂×D₄	semidirect
386. #2403	C₂×D₄	semidirect
387. #2403	C₂×D₄	semidirect
388. #2403	C₂×D₄	semidirect
389. #2403	C₂×D₄	semidirect
390. #2315	C₂⁴	semidirect
391. #2315	C₂⁴	semidirect
392. #2315	C₂⁴	semidirect
393. #2315	C₂⁴	semidirect
394. #2309	C₂×D₄	semidirect
395. #2309	C₂×D₄	semidirect
396. #2308	C₂×D₄	semidirect
397. #2308	C₂×D₄	semidirect
398. #2308	C₂×D₄	semidirect
399. #2308	C₂×D₄	semidirect
400. #2308	C₂×D₄	semidirect
407. #2308	C₂⁴	semidirect
408. C₂×#386	C₂×D₄	semidirect
409. C₂×#386	C₂×D₄	semidirect
410. C₂×#386	C₂×D₄	semidirect
411. C₂×#386	C₂×D₄	semidirect
412. C₂×#386	C₂×D₄	semidirect
416. C₂×#386	C₂⁴	semidirect
417. C₂×#385	C₂⁴	semidirect
418. #2280	C₂×D₄	semidirect
419. #2280	C₂×D₄	semidirect
420. C₂×#381	C₂×D₄	semidirect
421. C₂×#380	C₂⁴	semidirect
438. C₂×#379	C₂×D₄	semidirect
439. C₂×#379	C₂×D₄	semidirect
440. C₂×#379	C₂×D₄	semidirect
455. C₂×#379	C₂⁴	semidirect
456. C₂×#379	C₂⁴	semidirect
457. C₂×#379	C₂⁴	semidirect
458. #2273	C₂⁴	semidirect
459. C₂×C₄×C₂²⋊C₄	C₂⁴	semidirect
460. C₂×#342	C₂⁴	semidirect
461. C₂×#342	C₂⁴	semidirect
462. C₂×#342	C₂⁴	semidirect
463. C₂×#342	C₂⁴	semidirect
464. C₂×#342	C₂⁴	semidirect
465. C₂²⋊#95	C₂⁴	semidirect
891. C₂⁴	#3490	semidirect
903. C₂²×C₄	#3490	semidirect
904. C₂³	#23996	semidirect

Maximal subgroups

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

subgroup	index
#72266066	2
#72266065	2
#72266057	2
#72266051	2
#72266049	2
#72241143	2
#72240619	2
#72240617	2
C₂×#6370693	2
#72234689	2
#72234668	2
#72234644	2
#72234629	2
C₂×#6628892	2
#72234587	2
#72225632	2
C₂²×#32898	2