Subgroups — #72234749

Order 2048.

At least 9851 conjugacy classes of subgroups; only the 5268 normal subgroups are shown.

The subgroup lattice has 752 nodes (normal subgroups only) — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#72234689	C₂	1	2	yes	maximal, complemented
2	#72234675	C₂	1	1	yes	maximal, characteristic, complemented
3	#72234668	C₂	1	2	yes	maximal, complemented
4	#72234645	C₂	1	16	yes	maximal, complemented
5	#72234629	C₂	1	4	yes	maximal, complemented
6	#72234625	C₂	1	2	yes	maximal, complemented
7	#72234616	C₂	1	4	yes	maximal, complemented
8	C₂×#6628892	C₂	1	2	yes	maximal, complemented
9	#72234586	C₂	1	4	yes	maximal, complemented
10	#72233069	C₂	1	16	yes	maximal, complemented
11	#72225733	C₂	1	4	yes	maximal, complemented
12	#72219307	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×#7631286	C₂	1	1	yes	maximal, characteristic, complemented
14	#72213862	C₂	1	4	yes	maximal, complemented
15	C₂⁴×H(5,𝔽₂)	C₂²	1	1	yes	characteristic, complemented
16	C₂×#62817	C₂²	1	1	yes	characteristic, complemented
17	C₂²×#3484	C₂²	1	2	yes	complemented
18	C₂³×D₄²	C₂²	1	1	yes	characteristic
19	C₂²×#3026	C₂²	1	8	yes	complemented
20	#7675416	C₂²	1	8	yes	complemented
21	#7675391	C₂²	1	8	yes	complemented
22	#7642273	C₂²	1	2	yes	complemented
23	#7642257	C₂²	1	2	yes	complemented
24	#7631286	C₂²	1	16	yes	complemented
25	#7630945	C₂²	1	2	yes	complemented
26	#7630939	C₂²	1	2	yes	complemented
27	C₂×#35347	C₂²	1	2	yes	complemented
28	C₂×#35346	C₂²	1	2	yes	complemented
29	C₂×#34980	C₂²	1	2	yes	—
30	C₂×#34980	C₂²	1	2	yes	—
31	C₂×#34980	C₂²	1	4	yes	complemented
32	C₂×#34980	C₂²	1	2	yes	complemented
33	C₂²×#2403	C₂²	1	2	yes	complemented
34	#7626202	C₂²	1	1	yes	characteristic, complemented
35	C₂×#34256	C₂²	1	2	yes	complemented
36	C₂×#34171	C₂²	1	1	yes	characteristic, complemented
37	#6628892	C₂²	1	8	yes	complemented
38	#6628892	C₂²	1	8	yes	complemented
39	#6628892	C₂²	1	16	yes	complemented
40	#6451874	C₂²	1	8	yes	complemented
41	#6451874	C₂²	1	16	yes	complemented
42	C₂×#23895	C₂²	1	16	yes	complemented
43	#6437621	C₂²	1	8	yes	complemented
44	#6437621	C₂²	1	16	yes	complemented
45	C₂×#21746	C₂²	1	4	yes	complemented
46	C₂×#21746	C₂²	1	2	yes	complemented
47	C₂×#20609	C₂²	1	8	yes	complemented
48	C₂²×#1781	C₂²	1	2	yes	complemented
49	C₂²×#1781	C₂²	1	4	yes	complemented
50	#517411	C₂²	1	2	yes	complemented
51	#449505	C₂²	1	16	yes	complemented
52	#449469	C₂²	1	16	yes	complemented
53	#417896	C₂²	1	16	yes	complemented
54	#417824	C₂²	1	16	yes	complemented
55	#417532	C₂²	1	32	yes	complemented
56	#417499	C₂²	1	32	yes	complemented
57	#405104	C₂²	1	16	yes	complemented
58	#405090	C₂²	1	16	yes	complemented
59	#394418	C₂²	1	16	yes	complemented
60	#394267	C₂²	1	32	yes	complemented
61	#394173	C₂²	1	16	yes	complemented
62	#394064	C₂²	1	32	yes	complemented
63	#394058	C₂²	1	16	yes	complemented
64	#393929	C₂²	1	16	yes	complemented
65	#392699	C₂²	1	8	yes	complemented
66	#392245	C₂²	1	2	yes	complemented
67	#392109	C₂²	1	2	yes	complemented
68	#382422	C₂²	1	2	yes	complemented
69	#382390	C₂²	1	2	yes	complemented
70	#379733	C₂²	1	8	yes	complemented
71	#374058	C₂²	1	16	yes	complemented
72	#364500	C₂²	1	32	yes	complemented
73	#364440	C₂²	1	32	yes	complemented
74	#359811	C₂²	1	8	yes	complemented
75	#359705	C₂²	1	8	yes	complemented
76	#359579	C₂²	1	16	yes	complemented
77	#359549	C₂²	1	16	yes	complemented
78	#359442	C₂²	1	8	yes	complemented
79	#359442	C₂²	1	8	yes	complemented
80	#355913	C₂²	1	4	yes	complemented
81	C₂³×H(5,𝔽₂)	C₂³	1	2	yes	—
82	C₂³×H(5,𝔽₂)	C₂³	1	8	yes	—
83	C₂³×H(5,𝔽₂)	C₂³	1	2	yes	—
84	C₂⁵×D₄	D₄	1	1	yes	characteristic, complemented
85	C₂⁵×D₄	C₂³	1	1	yes	characteristic
86	C₂⁵×D₄	C₂³	1	2	yes	—
87	C₂⁵×D₄	C₂³	1	1	yes	characteristic
88	C₂⁵×D₄	C₂³	1	1	yes	characteristic
89	C₂×#3490	C₂³	1	4	yes	complemented
90	C₂×#3490	C₂³	1	2	yes	complemented
91	C₂×#3484	C₂³	1	16	yes	—
92	C₂×#3484	C₂³	1	2	yes	complemented
93	C₂×#3484	C₂³	1	4	yes	complemented
94	C₂×#3484	C₂³	1	4	yes	complemented
95	C₂²×D₄²	D₄	1	8	yes	complemented
96	C₂²×D₄²	C₂³	1	8	yes	—
97	C₂²×#534	C₂³	1	4	yes	—
98	C₂²×#534	C₂³	1	4	yes	—
99	C₂²×#534	C₂³	1	8	yes	complemented
100	C₂³×#127	D₄	1	1	yes	characteristic, complemented
101	C₂³×#121	D₄	1	1	yes	characteristic, complemented
102	C₂³×#121	D₄	1	1	yes	characteristic, complemented
103	C₂³×#121	D₄	1	1	yes	characteristic, complemented
104	C₂³×#121	C₂³	1	1	yes	characteristic
105	C₂³×#120	D₄	1	1	yes	characteristic, complemented
106	C₂³×#120	D₄	1	1	yes	characteristic, complemented
107	C₂³×#120	C₂³	1	4	yes	—
108	C₂³×#120	C₂³	1	1	yes	characteristic
109	C₂³×#120	C₂³	1	1	yes	characteristic
110	C₂³×#120	C₂³	1	2	yes	—
111	C₂²×#518	C₂³	1	2	yes	—
112	C₂³×C₄×D₄	D₄	1	1	yes	characteristic, complemented
113	C₂³×C₄×D₄	C₂³	1	1	yes	characteristic
114	C₂×#3026	C₂³	1	32	yes	—
115	C₂×#3026	C₂³	1	32	yes	complemented
116	C₂×#3026	C₂³	1	16	yes	complemented
117	C₂³×#99	C₂³	1	8	yes	—
118	C₂³×#99	C₂³	1	16	yes	complemented
119	C₂×#2849	D₄	1	4	yes	complemented
120	C₂×#2849	C₂³	1	4	yes	complemented
121	C₂×#2846	D₄	1	4	yes	complemented
122	C₂×#2846	C₂³	1	4	yes	complemented
123	#35390	C₂³	1	4	yes	complemented
124	#35367	C₂³	1	4	yes	complemented
125	#35358	C₂³	1	8	yes	complemented
126	#35351	C₂³	1	4	yes	complemented
127	#35348	C₂³	1	8	yes	complemented
128	#35347	C₂³	1	16	yes	—
129	#35347	C₂³	1	4	yes	complemented
130	#35346	C₂³	1	16	yes	—
131	#34985	C₂³	1	4	yes	complemented
132	#34984	C₂³	1	4	yes	complemented
133	#34980	D₄	1	8	yes	complemented
134	#34980	D₄	1	8	yes	complemented
135	#34980	D₄	1	16	yes	complemented
136	#34980	C₂³	1	16	yes	—
137	#34980	C₂³	1	8	yes	—
138	#34980	C₂³	1	4	yes	—
139	#34980	C₂³	1	4	yes	—
140	#34980	C₂³	1	16	yes	—
141	#34980	C₂³	1	16	yes	complemented
142	#34980	C₂³	1	8	yes	complemented
143	C₂×#2405	D₄	1	4	yes	complemented
144	C₂×#2405	D₄	1	4	yes	complemented
145	C₂×#2405	C₂³	1	4	yes	complemented
146	C₂×#2410	C₂³	1	8	yes	complemented
147	C₂×#2403	D₄	1	4	yes	complemented
148	C₂×#2403	D₄	1	4	yes	complemented
149	C₂×#2403	C₂³	1	16	yes	—
150	C₂×#2403	C₂³	1	4	yes	complemented
151	C₂×#2613	D₄	1	8	yes	complemented
152	#34264	C₂³	1	8	yes	complemented
153	#34256	C₂³	1	16	yes	—
154	#34198	C₂³	1	8	yes	complemented
155	#34176	C₂³	1	2	yes	complemented
156	#34171	C₂³	1	8	yes	—
157	#34171	C₂³	1	4	yes	complemented
158	#34171	C₂³	1	2	yes	complemented
159	C₂×#2308	C₂³	1	2	yes	—
160	C₂×#2308	C₂³	1	4	yes	—
161	C₂×#2308	C₂³	1	4	yes	—
162	C₂×#2308	C₂³	1	8	yes	complemented
163	C₂²×#386	C₂³	1	4	yes	—
164	C₂²×#379	C₂³	1	4	yes	—
165	C₂²×#379	C₂³	1	2	yes	—
166	C₂²×#379	C₂³	1	2	yes	—
167	#23468	C₂³	1	16	yes	complemented
168	#23444	C₂³	1	16	yes	complemented
169	#23444	C₂³	1	32	yes	complemented
170	C₂×#2021	C₂³	1	64	yes	complemented
171	C₂×#1913	C₂³	1	32	yes	complemented
172	C₂×#1913	C₂³	1	32	yes	complemented
173	C₂×#1898	C₂³	1	16	yes	complemented
174	C₂×#1898	C₂³	1	16	yes	complemented
175	C₂×#1898	C₂³	1	16	yes	complemented
176	#20960	C₂³	1	16	yes	complemented
177	#20960	C₂³	1	32	yes	complemented
178	C₂×#1819	C₂³	1	4	yes	complemented
179	C₂×#1819	C₂³	1	8	yes	complemented
180	#20609	C₂³	1	32	yes	—
181	#20609	C₂³	1	32	yes	complemented
182	C₂×#1781	C₂³	1	16	yes	—
183	C₂×#1781	C₂³	1	8	yes	—
184	C₂×#1781	C₂³	1	4	yes	—
185	C₂×#1781	C₂³	1	4	yes	—
186	C₂×#1781	C₂³	1	16	yes	complemented
187	C₂×#1781	C₂³	1	16	yes	complemented
188	C₂×#1781	C₂³	1	4	yes	complemented
189	C₂×#1781	C₂³	1	8	yes	complemented
190	#14681	C₂³	1	4	yes	complemented
191	#14679	C₂³	1	4	yes	complemented
192	#13867	C₂³	1	16	yes	complemented
193	#11172	C₂³	1	32	yes	complemented
194	#11087	C₂³	1	64	yes	complemented
195	#11046	C₂³	1	32	yes	complemented
196	#10995	C₂³	1	64	yes	complemented
197	#10991	C₂³	1	64	yes	complemented
198	#10980	C₂³	1	16	yes	complemented
199	#10972	C₂³	1	32	yes	complemented
200	#10972	C₂³	1	32	yes	complemented
201	#10965	C₂³	1	16	yes	complemented
202	#10938	C₂³	1	32	yes	complemented
203	#10761	C₂³	1	16	yes	complemented
204	#10754	C₂³	1	32	yes	complemented
205	#10735	C₂³	1	16	yes	complemented
206	#10735	C₂³	1	16	yes	complemented
207	#10725	C₂³	1	16	yes	complemented
208	C₂⁷	C₂×D₄	1	1	yes	characteristic
209	C₂⁷	C₂×D₄	1	2	yes	complemented
210	C₂⁷	C₂×D₄	1	1	yes	characteristic, complemented
211	C₂⁷	C₂⁴	1	1	yes	characteristic
212	C₂⁷	C₂⁴	1	1	yes	characteristic
213	C₂²×H(5,𝔽₂)	C₂⁴	1	8	yes	—
214	C₂²×H(5,𝔽₂)	C₂⁴	1	8	yes	—
215	C₂²×H(5,𝔽₂)	C₂⁴	1	2	yes	complemented
216	C₂⁴×D₄	C₂×D₄	1	4	yes	—
217	C₂⁴×D₄	C₂×D₄	1	4	yes	—
218	C₂⁴×D₄	C₂×D₄	1	4	yes	—
219	C₂⁴×D₄	C₂×D₄	1	4	yes	—
220	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
221	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
222	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
223	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
224	C₂⁴×D₄	C₂×D₄	1	4	yes	—
225	C₂⁴×D₄	C₂×D₄	1	4	yes	—
226	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
227	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
228	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
229	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
230	C₂⁴×D₄	C₂×D₄	1	8	yes	complemented
231	C₂⁴×D₄	C₂×D₄	1	4	yes	complemented
232	C₂⁴×D₄	C₂×D₄	1	4	yes	complemented
233	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic, complemented
234	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic, complemented
235	C₂⁴×D₄	C₂×D₄	1	8	yes	complemented
236	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic, complemented
237	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic, complemented
238	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic, complemented
239	C₂⁴×D₄	C₂×D₄	1	2	yes	complemented
240	C₂⁴×D₄	C₂×D₄	1	2	yes	complemented
241	C₂⁴×D₄	C₂⁴	1	1	yes	characteristic
242	C₂⁴×D₄	C₂⁴	1	8	yes	—
243	C₂⁴×D₄	C₂⁴	1	4	yes	—
244	C₂⁴×D₄	C₂⁴	1	4	yes	—
245	C₂⁴×D₄	C₂⁴	1	4	yes	—
246	C₂⁴×D₄	C₂⁴	1	1	yes	characteristic
247	C₂⁴×D₄	C₂⁴	1	1	yes	characteristic
248	C₂⁴×D₄	C₂⁴	1	2	yes	—
249	C₂⁴×D₄	C₂⁴	1	4	yes	—
250	C₂⁵×C₄	C₂×D₄	1	1	yes	characteristic
251	C₂⁵×C₄	C₂×D₄	1	2	yes	complemented
252	C₂⁵×C₄	C₂×D₄	1	1	yes	characteristic, complemented
253	C₂⁵×C₄	C₂×D₄	1	1	yes	characteristic, complemented
254	C₂⁵×C₄	C₂⁴	1	1	yes	characteristic
255	C₂×#543	C₂⁴	1	2	yes	complemented
256	C₂×#534	C₂×D₄	1	16	yes	complemented
257	C₂×#534	C₂×D₄	1	16	yes	complemented
258	C₂×#534	C₂⁴	1	32	yes	—
259	C₂×#534	C₂⁴	1	8	yes	—
260	C₂×#534	C₂⁴	1	16	yes	—
261	C₂×#534	C₂⁴	1	8	yes	—
262	C₂×#534	C₂⁴	1	4	yes	complemented
263	C₂×#534	C₂⁴	1	2	yes	complemented
264	C₂²×#127	C₂×D₄	1	8	yes	complemented
265	C₂²×#123	C₂×D₄	1	8	yes	complemented
266	C₂²×#123	C₂×D₄	1	8	yes	complemented
267	C₂²×#121	C₂×D₄	1	8	yes	complemented
268	C₂²×#121	C₂×D₄	1	8	yes	complemented
269	C₂²×#121	C₂×D₄	1	4	yes	complemented
270	C₂²×#121	C₂×D₄	1	8	yes	complemented
271	C₂²×#121	C₂⁴	1	4	yes	—
272	C₂²×#120	C₂×D₄	1	4	yes	—
273	C₂²×#120	C₂×D₄	1	4	yes	—
274	C₂²×#120	C₂×D₄	1	8	yes	—
275	C₂²×#120	C₂×D₄	1	4	yes	—
276	C₂²×#120	C₂×D₄	1	8	yes	complemented
277	C₂²×#120	C₂×D₄	1	8	yes	complemented
278	C₂²×#120	C₂×D₄	1	8	yes	complemented
279	C₂²×#120	C₂×D₄	1	8	yes	complemented
280	C₂²×#120	C₂×D₄	1	4	yes	complemented
281	C₂²×#120	C₂×D₄	1	4	yes	complemented
282	C₂²×#120	C₂×D₄	1	4	yes	complemented
283	C₂²×#120	C₂⁴	1	16	yes	—
284	C₂²×#120	C₂⁴	1	4	yes	—
285	C₂²×#120	C₂⁴	1	4	yes	—
286	C₂²×#120	C₂⁴	1	4	yes	—
287	C₂²×#120	C₂⁴	1	4	yes	—
288	C₂²×#120	C₂⁴	1	8	yes	complemented
289	C₂×#518	C₂⁴	1	8	yes	—
290	C₂×#518	C₂⁴	1	4	yes	complemented
291	C₂×#518	C₂⁴	1	2	yes	complemented
292	C₂×#518	C₂⁴	1	4	yes	complemented
293	C₂²×C₄×D₄	C₂×D₄	1	8	yes	complemented
294	C₂²×C₄×D₄	C₂×D₄	1	4	yes	complemented
295	C₂²×C₄×D₄	C₂⁴	1	4	yes	—
296	C₂³×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic, complemented
297	C₂³×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic, complemented
298	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
299	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
300	C₂³×C₂²⋊C₄	C₂×D₄	1	2	yes	complemented
301	C₂³×C₂²⋊C₄	C₂×D₄	1	2	yes	complemented
302	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic, complemented
303	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic, complemented
304	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic, complemented
305	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic, complemented
306	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic, complemented
307	C₂³×C₂²⋊C₄	C₂⁴	1	2	yes	—
308	C₂³×C₂²⋊C₄	C₂⁴	1	1	yes	characteristic
309	C₂³×C₂²⋊C₄	C₂⁴	1	8	yes	—
310	C₂³×C₂²⋊C₄	C₂⁴	1	4	yes	—
311	C₂³×C₂²⋊C₄	C₂⁴	1	4	yes	—
312	C₂³×C₄²	C₂×D₄	1	1	yes	characteristic, complemented
313	C₂²×#99	C₂⁴	1	16	yes	—
314	C₂²×#99	C₂⁴	1	64	yes	—
315	C₂²×#99	C₂⁴	1	16	yes	—
316	C₂²×#99	C₂⁴	1	16	yes	complemented
317	C₂²×#99	C₂⁴	1	32	yes	complemented
318	#2849	C₂×D₄	1	32	yes	complemented
319	#2846	C₂×D₄	1	32	yes	complemented
320	#2613	C₂×D₄	1	64	yes	complemented
321	#2405	C₂×D₄	1	8	yes	complemented
322	#2405	C₂×D₄	1	8	yes	complemented
323	#2405	C₂×D₄	1	8	yes	complemented
324	#2405	C₂×D₄	1	8	yes	complemented
325	#2405	C₂×D₄	1	16	yes	complemented
326	#2405	C₂×D₄	1	16	yes	complemented
327	#2403	C₂×D₄	1	8	yes	complemented
328	#2403	C₂×D₄	1	8	yes	complemented
329	#2403	C₂×D₄	1	16	yes	complemented
330	#2403	C₂×D₄	1	16	yes	complemented
331	#2403	C₂×D₄	1	8	yes	complemented
332	#2403	C₂×D₄	1	8	yes	complemented
333	#2315	C₂⁴	1	4	yes	complemented
334	#2308	C₂×D₄	1	16	yes	complemented
335	#2308	C₂×D₄	1	16	yes	complemented
336	#2308	C₂⁴	1	8	yes	—
337	#2308	C₂⁴	1	32	yes	—
338	#2308	C₂⁴	1	8	yes	—
339	#2308	C₂⁴	1	8	yes	—
340	#2308	C₂⁴	1	16	yes	—
341	#2308	C₂⁴	1	4	yes	complemented
342	C₂×#386	C₂×D₄	1	8	yes	complemented
343	C₂×#386	C₂×D₄	1	8	yes	complemented
344	C₂×#386	C₂⁴	1	16	yes	—
345	C₂×#386	C₂⁴	1	8	yes	complemented
346	C₂×#385	C₂⁴	1	8	yes	complemented
347	C₂×#381	C₂×D₄	1	8	yes	complemented
348	C₂×#379	C₂×D₄	1	4	yes	complemented
349	C₂×#379	C₂×D₄	1	8	yes	complemented
350	C₂×#379	C₂×D₄	1	4	yes	complemented
351	C₂×#379	C₂×D₄	1	8	yes	complemented
352	C₂×#379	C₂×D₄	1	4	yes	complemented
353	C₂×#379	C₂×D₄	1	4	yes	complemented
354	C₂×#379	C₂×D₄	1	4	yes	complemented
355	C₂×#379	C₂×D₄	1	4	yes	complemented
356	C₂×#379	C₂⁴	1	8	yes	—
357	C₂×#379	C₂⁴	1	8	yes	—
358	C₂×#379	C₂⁴	1	4	yes	—
359	C₂×#379	C₂⁴	1	8	yes	—
360	C₂×#379	C₂⁴	1	4	yes	—
361	C₂×#379	C₂⁴	1	8	yes	complemented
362	C₂×#379	C₂⁴	1	16	yes	complemented
363	#2273	C₂⁴	1	4	yes	complemented
364	C₂×#342	C₂⁴	1	32	yes	complemented
365	C₂×#342	C₂⁴	1	16	yes	complemented
366	C₂×#342	C₂⁴	1	64	yes	complemented
367	C₂²⋊#95	C₂⁴	1	16	yes	complemented
368	C₂⁶	#120	1	2	yes	—
369	C₂⁶	#120	1	4	yes	—
370	C₂⁶	#120	1	2	yes	—
371	C₂⁶	C₂²×D₄	1	1	yes	characteristic
372	C₂⁶	C₂²×D₄	1	4	yes	—
373	C₂⁶	C₂²×D₄	1	8	yes	—
374	C₂⁶	C₂²×D₄	1	4	yes	—
375	C₂⁶	C₂²×D₄	1	4	yes	—
376	C₂⁶	C₂²×D₄	1	1	yes	characteristic
377	C₂⁶	C₂²×D₄	1	1	yes	characteristic
378	C₂⁶	C₂²×D₄	1	2	yes	—
379	C₂⁶	C₂²×D₄	1	1	yes	characteristic
380	C₂⁶	C₂²×D₄	1	1	yes	characteristic
381	C₂⁶	C₂²×D₄	1	1	yes	characteristic
382	C₂⁶	C₂²×D₄	1	2	yes	—
383	C₂⁶	C₂²×D₄	1	2	yes	—
384	C₂⁶	C₂²×D₄	1	1	yes	characteristic
385	C₂⁶	C₂²×D₄	1	2	yes	—
386	C₂⁶	C₂²×D₄	1	2	yes	—
387	C₂⁶	C₂²×D₄	1	2	yes	—
388	C₂⁶	C₂²×D₄	1	2	yes	—
389	C₂⁶	C₂²×D₄	1	2	yes	—
390	C₂⁶	C₂²×D₄	1	4	yes	—
391	C₂⁶	C₂²×D₄	1	2	yes	complemented
392	C₂⁶	H(5,𝔽₂)	1	2	yes	—
393	C₂⁶	H(5,𝔽₂)	1	4	yes	—
394	C₂⁶	H(5,𝔽₂)	1	2	yes	—
395	C₂⁶	C₂⁵	1	2	yes	—
396	C₂⁶	C₂⁵	1	1	yes	characteristic
397	C₂⁶	C₂⁵	1	2	yes	—
398	C₂×H(5,𝔽₂)	H(5,𝔽₂)	1	32	yes	complemented
399	C₂³×D₄	#120	1	2	yes	—
400	C₂³×D₄	#120	1	8	yes	—
401	C₂³×D₄	#120	1	8	yes	—
402	C₂³×D₄	#120	1	8	yes	—
403	C₂³×D₄	#120	1	8	yes	—
404	C₂³×D₄	#120	1	2	yes	—
405	C₂³×D₄	#120	1	2	yes	—
406	C₂³×D₄	#120	1	4	yes	—
407	C₂³×D₄	#120	1	4	yes	—
408	C₂³×D₄	#120	1	2	yes	—
409	C₂³×D₄	#120	1	2	yes	—
410	C₂³×D₄	#120	1	2	yes	—
411	C₂³×D₄	#120	1	4	yes	—
412	C₂³×D₄	#120	1	4	yes	—
413	C₂³×D₄	#120	1	4	yes	—
414	C₂³×D₄	C₂²×D₄	1	4	yes	—
415	C₂³×D₄	C₂²×D₄	1	4	yes	—
416	C₂³×D₄	C₂²×D₄	1	8	yes	—
417	C₂³×D₄	C₂²×D₄	1	8	yes	—
418	C₂³×D₄	C₂²×D₄	1	8	yes	—
419	C₂³×D₄	C₂²×D₄	1	8	yes	—
420	C₂³×D₄	C₂²×D₄	1	4	yes	—
421	C₂³×D₄	C₂²×D₄	1	4	yes	—
422	C₂³×D₄	C₂²×D₄	1	4	yes	—
423	C₂³×D₄	C₂²×D₄	1	4	yes	—
424	C₂³×D₄	C₂²×D₄	1	2	yes	—
425	C₂³×D₄	C₂²×D₄	1	16	yes	—
426	C₂³×D₄	C₂²×D₄	1	8	yes	—
427	C₂³×D₄	C₂²×D₄	1	4	yes	—
428	C₂³×D₄	C₂²×D₄	1	4	yes	—
429	C₂³×D₄	C₂²×D₄	1	4	yes	—
430	C₂³×D₄	C₂²×D₄	1	4	yes	—
431	C₂³×D₄	C₂²×D₄	1	4	yes	—
432	C₂³×D₄	C₂²×D₄	1	4	yes	—
433	C₂³×D₄	C₂²×D₄	1	4	yes	—
434	C₂³×D₄	C₂²×D₄	1	4	yes	—
435	C₂³×D₄	C₂²×D₄	1	4	yes	—
436	C₂³×D₄	C₂²×D₄	1	4	yes	—
437	C₂³×D₄	C₂²×D₄	1	2	yes	—
438	C₂³×D₄	C₂²×D₄	1	2	yes	—
439	C₂³×D₄	C₂²×D₄	1	4	yes	—
440	C₂³×D₄	C₂²×D₄	1	4	yes	—
441	C₂³×D₄	C₂²×D₄	1	4	yes	—
442	C₂³×D₄	C₂²×D₄	1	4	yes	—
443	C₂³×D₄	C₂²×D₄	1	4	yes	—
444	C₂³×D₄	C₂²×D₄	1	4	yes	complemented
445	C₂³×D₄	C₂²×D₄	1	4	yes	complemented
446	C₂³×D₄	C₂²×D₄	1	4	yes	complemented
447	C₂³×D₄	C₂⁵	1	4	yes	—
448	C₂³×D₄	C₂⁵	1	2	yes	—
449	C₂³×D₄	C₂⁵	1	2	yes	—
450	C₂³×D₄	C₂⁵	1	8	yes	—
451	C₂³×D₄	C₂⁵	1	2	yes	—
452	C₂⁴×C₄	#120	1	2	yes	—
453	C₂⁴×C₄	#120	1	4	yes	—
454	C₂⁴×C₄	#120	1	2	yes	—
455	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
456	C₂⁴×C₄	C₂²×D₄	1	4	yes	—
457	C₂⁴×C₄	C₂²×D₄	1	8	yes	—
458	C₂⁴×C₄	C₂²×D₄	1	4	yes	—
459	C₂⁴×C₄	C₂²×D₄	1	4	yes	—
460	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
461	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
462	C₂⁴×C₄	C₂²×D₄	1	2	yes	—
463	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
464	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
465	C₂⁴×C₄	C₂²×D₄	1	4	yes	—
466	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
467	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
468	C₂⁴×C₄	C₂²×D₄	1	2	yes	complemented
469	C₂⁴×C₄	C₂²×D₄	1	2	yes	complemented
470	C₂⁴×C₄	C₂²×D₄	1	2	yes	complemented
471	C₂⁴×C₄	C₂⁵	1	2	yes	—
472	C₂×#123	C₂²×D₄	1	16	yes	—
473	C₂×#123	C₂²×D₄	1	32	yes	—
474	C₂×#123	C₂²×D₄	1	16	yes	complemented
475	C₂×#120	#120	1	16	yes	—
476	C₂×#120	#120	1	16	yes	—
477	C₂×#120	C₂²×D₄	1	16	yes	—
478	C₂×#120	C₂²×D₄	1	32	yes	—
479	C₂×#120	C₂²×D₄	1	16	yes	—
480	C₂×#120	C₂²×D₄	1	16	yes	—
481	C₂×#120	C₂²×D₄	1	16	yes	complemented
482	C₂²×C₄⋊C₄	C₂²×D₄	1	4	yes	—
483	C₂²×C₄⋊C₄	C₂²×D₄	1	4	yes	—
484	C₂²×C₂²⋊C₄	#120	1	2	yes	—
485	C₂²×C₂²⋊C₄	#120	1	4	yes	—
486	C₂²×C₂²⋊C₄	#120	1	4	yes	—
487	C₂²×C₂²⋊C₄	#120	1	2	yes	—
488	C₂²×C₂²⋊C₄	#120	1	4	yes	—
489	C₂²×C₂²⋊C₄	C₂²×D₄	1	4	yes	—
490	C₂²×C₂²⋊C₄	C₂²×D₄	1	4	yes	—
491	C₂²×C₂²⋊C₄	C₂²×D₄	1	4	yes	—
492	C₂²×C₂²⋊C₄	C₂²×D₄	1	4	yes	—
493	C₂²×C₂²⋊C₄	C₂²×D₄	1	4	yes	—
494	C₂²×C₂²⋊C₄	C₂²×D₄	1	4	yes	—
495	C₂²×C₂²⋊C₄	C₂²×D₄	1	4	yes	—
496	C₂²×C₂²⋊C₄	C₂²×D₄	1	2	yes	—
497	C₂²×C₂²⋊C₄	C₂²×D₄	1	4	yes	—
498	C₂²×C₂²⋊C₄	C₂²×D₄	1	4	yes	—
499	C₂²×C₂²⋊C₄	C₂²×D₄	1	4	yes	—
500	C₂²×C₂²⋊C₄	C₂²×D₄	1	4	yes	—
501	C₂²×C₂²⋊C₄	C₂²×D₄	1	8	yes	—
502	C₂²×C₂²⋊C₄	C₂²×D₄	1	8	yes	—
503	C₂²×C₂²⋊C₄	C₂²×D₄	1	4	yes	complemented
504	C₂²×C₂²⋊C₄	C₂²×D₄	1	4	yes	complemented
505	C₂²×C₂²⋊C₄	C₂²×D₄	1	4	yes	complemented
506	C₂²×C₂²⋊C₄	C₂²×D₄	1	8	yes	complemented
507	C₂²×C₂²⋊C₄	C₂²×D₄	1	8	yes	complemented
508	C₂²×C₂²⋊C₄	C₂⁵	1	16	yes	—
509	C₂²×C₂²⋊C₄	C₂⁵	1	4	yes	—
510	C₂²×C₂²⋊C₄	C₂⁵	1	8	yes	—
511	C₂²×C₂²⋊C₄	C₂⁵	1	8	yes	—
512	C₂²×C₂²⋊C₄	C₂⁵	1	2	yes	—
513	C₂²×C₄²	C₂²×D₄	1	4	yes	—
514	#386	C₂²×D₄	1	16	yes	—
515	#386	C₂²×D₄	1	16	yes	—
516	#386	C₂²×D₄	1	16	yes	complemented
517	#386	C₂²×D₄	1	16	yes	complemented
518	#381	C₂²×D₄	1	32	yes	—
519	#379	C₂²×D₄	1	32	yes	—
520	#379	C₂²×D₄	1	16	yes	—
521	#379	C₂²×D₄	1	16	yes	—
522	#379	C₂²×D₄	1	8	yes	—
523	#379	C₂²×D₄	1	8	yes	—
524	#379	C₂²×D₄	1	8	yes	complemented
525	#379	C₂²×D₄	1	8	yes	complemented
526	C₂⁵	C₂×#120	1	2	yes	—
527	C₂⁵	C₂×#120	1	2	yes	—
528	C₂⁵	C₂×#120	1	1	yes	characteristic
529	C₂⁵	C₂×#120	1	8	yes	—
530	C₂⁵	C₂×#120	1	1	yes	characteristic
531	C₂⁵	C₂×#120	1	8	yes	—
532	C₂⁵	C₂×#120	1	2	yes	—
533	C₂⁵	C₂×#120	1	2	yes	—
534	C₂⁵	C₂×#120	1	2	yes	—
535	C₂⁵	C₂×#120	1	2	yes	—
536	C₂⁵	C₂×#120	1	1	yes	characteristic
537	C₂⁵	C₂×#120	1	2	yes	—
538	C₂⁵	C₂×#120	1	2	yes	—
539	C₂⁵	C₂×#120	1	1	yes	characteristic
540	C₂⁵	C₂×#120	1	2	yes	—
541	C₂⁵	C₂×#120	1	2	yes	—
542	C₂⁵	C₂×#120	1	2	yes	—
543	C₂⁵	C₂×#120	1	1	yes	characteristic
544	C₂⁵	C₂×#120	1	4	yes	—
545	C₂⁵	C₂×#120	1	1	yes	characteristic
546	C₂⁵	C₂×#120	1	2	yes	—
547	C₂⁵	C₂×#120	1	2	yes	—
548	C₂⁵	C₂×#120	1	4	yes	—
549	C₂⁵	C₂×#120	1	2	yes	—
550	C₂⁵	C₂×#120	1	2	yes	—
551	C₂⁵	#534	1	1	yes	characteristic
552	C₂⁵	#534	1	2	yes	—
553	C₂⁵	#534	1	1	yes	characteristic
554	C₂⁵	#534	1	2	yes	—
555	C₂⁵	#534	1	2	yes	—
556	C₂⁵	#534	1	4	yes	—
557	C₂⁵	#534	1	4	yes	—
558	C₂⁵	D₄²	1	4	yes	—
559	C₂⁵	D₄²	1	4	yes	—
560	C₂⁵	D₄²	1	4	yes	—
561	C₂⁵	D₄²	1	4	yes	—
562	C₂⁵	D₄²	1	4	yes	—
563	C₂⁵	D₄²	1	4	yes	—
564	C₂⁵	D₄²	1	4	yes	—
565	C₂⁵	D₄²	1	4	yes	—
566	C₂⁵	D₄²	1	4	yes	—
567	C₂⁵	D₄²	1	4	yes	—
568	C₂⁵	D₄²	1	4	yes	—
569	C₂⁵	D₄²	1	4	yes	—
570	C₂⁵	D₄²	1	4	yes	—
571	C₂⁵	D₄²	1	4	yes	—
572	C₂⁵	D₄²	1	4	yes	—
573	C₂⁵	D₄²	1	4	yes	—
574	C₂⁵	C₂³×D₄	1	2	yes	—
575	C₂⁵	C₂³×D₄	1	4	yes	—
576	C₂⁵	C₂³×D₄	1	2	yes	—
577	C₂⁵	C₂³×D₄	1	2	yes	—
578	C₂⁵	C₂³×D₄	1	2	yes	—
579	C₂⁵	C₂³×D₄	1	8	yes	—
580	C₂⁵	C₂³×D₄	1	1	yes	characteristic
581	C₂⁵	C₂³×D₄	1	2	yes	—
582	C₂⁵	C₂³×D₄	1	2	yes	—
583	C₂⁵	C₂³×D₄	1	2	yes	—
584	C₂⁵	C₂³×D₄	1	4	yes	—
585	C₂⁵	C₂³×D₄	1	2	yes	—
586	C₂⁵	C₂³×D₄	1	2	yes	—
587	C₂⁵	C₂³×D₄	1	2	yes	—
588	C₂⁵	C₂³×D₄	1	1	yes	characteristic
589	C₂⁵	C₂³×D₄	1	2	yes	—
590	C₂⁵	C₂³×D₄	1	2	yes	—
591	C₂⁵	C₂³×D₄	1	4	yes	—
592	C₂⁵	C₂³×D₄	1	2	yes	—
593	C₂⁵	C₂³×D₄	1	2	yes	—
594	C₂⁵	C₂³×D₄	1	2	yes	—
595	C₂⁵	C₂×H(5,𝔽₂)	1	2	yes	—
596	C₂⁵	C₂×H(5,𝔽₂)	1	2	yes	—
597	C₂⁵	C₂×H(5,𝔽₂)	1	4	yes	—
598	C₂⁵	C₂×H(5,𝔽₂)	1	4	yes	—
599	C₂⁵	C₂⁶	1	1	yes	characteristic
600	C₂²×D₄	C₂×#120	1	8	yes	—
601	C₂²×D₄	C₂×#120	1	8	yes	—
602	C₂²×D₄	C₂×#120	1	8	yes	—
603	C₂²×D₄	C₂×#120	1	8	yes	—
604	C₂²×D₄	C₂×#120	1	8	yes	—
605	C₂²×D₄	C₂×#120	1	8	yes	—
606	C₂²×D₄	C₂×#120	1	8	yes	—
607	C₂²×D₄	C₂×#120	1	8	yes	—
608	C₂²×D₄	C₂×#120	1	16	yes	—
609	C₂²×D₄	C₂×#120	1	8	yes	—
610	C₂²×D₄	C₂³×D₄	1	8	yes	—
611	C₂²×D₄	C₂³×D₄	1	8	yes	—
612	C₂²×D₄	C₂³×D₄	1	8	yes	—
613	C₂²×D₄	C₂×H(5,𝔽₂)	1	16	yes	—
614	C₂²×D₄	C₂×H(5,𝔽₂)	1	32	yes	—
615	C₂³×C₄	C₂×#120	1	2	yes	—
616	C₂³×C₄	C₂×#120	1	2	yes	—
617	C₂³×C₄	C₂×#120	1	8	yes	—
618	C₂³×C₄	C₂×#120	1	8	yes	—
619	C₂³×C₄	C₂×#120	1	2	yes	—
620	C₂³×C₄	C₂×#120	1	2	yes	—
621	C₂³×C₄	C₂×#120	1	2	yes	—
622	C₂³×C₄	C₂×#120	1	2	yes	—
623	C₂³×C₄	C₂×#120	1	2	yes	—
624	C₂³×C₄	C₂×#120	1	2	yes	—
625	C₂³×C₄	C₂×#120	1	2	yes	—
626	C₂³×C₄	C₂×#120	1	2	yes	—
627	C₂³×C₄	C₂³×D₄	1	4	yes	—
628	C₂³×C₄	C₂³×D₄	1	2	yes	—
629	C₂³×C₄	C₂³×D₄	1	2	yes	—
630	C₂³×C₄	C₂³×D₄	1	8	yes	—
631	C₂³×C₄	C₂³×D₄	1	2	yes	—
632	C₂³×C₄	C₂³×D₄	1	2	yes	—
633	C₂³×C₄	C₂³×D₄	1	4	yes	—
634	C₂³×C₄	C₂³×D₄	1	4	yes	—
635	C₂³×C₄	C₂³×D₄	1	2	yes	—
636	C₂³×C₄	C₂³×D₄	1	2	yes	—
637	C₂³×C₄	C₂³×D₄	1	2	yes	—
638	C₂×C₂²⋊C₄	C₂×#120	1	8	yes	—
639	C₂×C₂²⋊C₄	C₂×#120	1	8	yes	—
640	C₂×C₂²⋊C₄	C₂×#120	1	16	yes	—
641	C₂×C₂²⋊C₄	C₂×#120	1	8	yes	—
642	C₂×C₂²⋊C₄	C₂³×D₄	1	16	yes	—
643	C₂×C₂²⋊C₄	C₂³×D₄	1	16	yes	—
644	C₂×C₂²⋊C₄	C₂³×D₄	1	8	yes	—
645	C₂⁴	#2403	1	2	yes	—
646	C₂⁴	#2403	1	1	yes	characteristic
647	C₂⁴	#2403	1	2	yes	—
648	C₂⁴	#2403	1	2	yes	—
649	C₂⁴	#2403	1	2	yes	—
650	C₂⁴	#2403	1	2	yes	—
651	C₂⁴	#2403	1	4	yes	—
652	C₂⁴	#2403	1	1	yes	characteristic
653	C₂⁴	#2403	1	1	yes	characteristic
654	C₂⁴	#2403	1	2	yes	—
655	C₂⁴	#2403	1	4	yes	—
656	C₂⁴	#2403	1	4	yes	—
657	C₂⁴	#2403	1	2	yes	—
658	C₂⁴	#2403	1	2	yes	—
659	C₂⁴	#2403	1	4	yes	—
660	C₂⁴	#2403	1	2	yes	—
661	C₂⁴	#2403	1	2	yes	—
662	C₂⁴	#2403	1	4	yes	—
663	C₂⁴	#2403	1	4	yes	—
664	C₂⁴	#2403	1	4	yes	—
665	C₂⁴	#2403	1	4	yes	—
666	C₂⁴	#2403	1	4	yes	—
667	C₂⁴	#2403	1	4	yes	—
668	C₂⁴	#2403	1	1	yes	characteristic
669	C₂⁴	C₂²×#120	1	1	yes	characteristic
670	C₂⁴	C₂²×#120	1	1	yes	characteristic
671	C₂⁴	C₂²×#120	1	1	yes	characteristic
672	C₂⁴	C₂²×#120	1	2	yes	—
673	C₂⁴	C₂²×#120	1	2	yes	—
674	C₂⁴	C₂²×#120	1	4	yes	—
675	C₂⁴	C₂²×#120	1	4	yes	—
676	C₂⁴	C₂²×#120	1	4	yes	—
677	C₂⁴	C₂²×#120	1	2	yes	—
678	C₂⁴	C₂²×#120	1	2	yes	—
679	C₂⁴	C₂²×#120	1	2	yes	—
680	C₂⁴	C₂²×#120	1	2	yes	—
681	C₂⁴	C₂²×#120	1	2	yes	—
682	C₂⁴	C₂²×#120	1	4	yes	—
683	C₂⁴	C₂²×#120	1	1	yes	characteristic
684	C₂⁴	C₂²×#120	1	2	yes	—
685	C₂⁴	C₂×#534	1	2	yes	—
686	C₂⁴	C₂×#534	1	1	yes	characteristic
687	C₂⁴	C₂×#534	1	1	yes	characteristic
688	C₂⁴	C₂×#534	1	2	yes	—
689	C₂⁴	C₂×#534	1	4	yes	—
690	C₂⁴	C₂×#534	1	2	yes	—
691	C₂⁴	C₂×D₄²	1	4	yes	—
692	C₂⁴	C₂×D₄²	1	4	yes	—
693	C₂⁴	C₂×D₄²	1	4	yes	—
694	C₂⁴	C₂×D₄²	1	4	yes	—
695	C₂⁴	C₂×D₄²	1	4	yes	—
696	C₂⁴	C₂×D₄²	1	4	yes	—
697	C₂⁴	C₂×D₄²	1	4	yes	—
698	C₂⁴	C₂×D₄²	1	4	yes	—
699	C₂⁴	C₂×D₄²	1	4	yes	—
700	C₂⁴	C₂×D₄²	1	4	yes	—
701	C₂⁴	C₂×D₄²	1	4	yes	—
702	C₂⁴	C₂×D₄²	1	4	yes	—
703	C₂⁴	#3484	1	8	yes	—
704	C₂⁴	#3484	1	16	yes	complemented
705	C₂⁴	C₂⁴×D₄	1	1	yes	characteristic
706	C₂⁴	C₂⁴×D₄	1	2	yes	—
707	C₂⁴	C₂⁴×D₄	1	2	yes	—
708	C₂⁴	C₂²×H(5,𝔽₂)	1	2	yes	—
709	C₂⁴	C₂²×H(5,𝔽₂)	1	8	yes	—
710	C₂×D₄	#3484	1	32	yes	—
711	C₂²×C₄	C₂²×#120	1	4	yes	—
712	C₂²×C₄	C₂²×#120	1	4	yes	—
713	C₂²×C₄	C₂²×#120	1	4	yes	—
714	C₂²×C₄	C₂²×#120	1	4	yes	—
715	C₂²×C₄	C₂²×#120	1	4	yes	—
716	C₂²×C₄	#3484	1	8	yes	—
717	C₂²×C₄	#3484	1	16	yes	complemented
718	C₂³	#23895	1	4	yes	complemented
719	C₂³	C₂×#2403	1	2	yes	—
720	C₂³	C₂×#2403	1	2	yes	—
721	C₂³	C₂×#2403	1	4	yes	—
722	C₂³	C₂×#2403	1	4	yes	—
723	C₂³	C₂×#2403	1	2	yes	—
724	C₂³	C₂×#2403	1	4	yes	—
725	C₂³	C₂×#2403	1	1	yes	characteristic
726	C₂³	C₂×#2403	1	1	yes	characteristic
727	C₂³	C₂×#2403	1	2	yes	—
728	C₂³	C₂×#2403	1	1	yes	characteristic
729	C₂³	C₂×#2403	1	1	yes	characteristic
730	C₂³	#35346	1	8	yes	—
731	C₂³	C₂³×#120	1	1	yes	characteristic
732	C₂³	C₂³×#120	1	1	yes	characteristic
733	C₂³	C₂²×#534	1	1	yes	characteristic
734	C₂³	C₂²×D₄²	1	4	yes	—
735	C₂³	C₂×#3484	1	4	yes	—
736	C₂³	C₂×#3484	1	8	yes	—
737	C₂³	C₂×#3484	1	8	yes	—
738	C₂³	#62817	1	8	yes	—
739	C₂×C₄	#35346	1	8	yes	—
740	C₂²	C₂×#23895	1	2	yes	—
741	C₂²	C₂×#23895	1	4	yes	—
742	C₂²	#6437629	1	2	yes	—
743	C₂²	C₂²×#2403	1	1	yes	characteristic
744	C₂²	C₂×#35346	1	2	yes	—
745	C₂²	#7630939	1	2	yes	—
746	C₂²	#7642244	1	2	yes	—
747	C₂²	#7670203	1	8	yes	—
748	C₂	#72217875	1	1	yes	characteristic
749	C₂	C₂²×#23895	1	1	yes	characteristic
750	C₂	C₂×#6437629	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²	C₂²×#2403
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. #72234689	C₂	semidirect
2. #72234675	C₂	semidirect
3. #72234668	C₂	semidirect
4. #72234645	C₂	semidirect
5. #72234629	C₂	semidirect
6. #72234625	C₂	semidirect
7. #72234616	C₂	semidirect
8. C₂×#6628892	C₂	semidirect
9. #72234586	C₂	semidirect
10. #72233069	C₂	semidirect
11. #72225733	C₂	semidirect
12. #72219307	C₂	semidirect
13. C₂×#7631286	C₂	semidirect
14. #72213862	C₂	semidirect
15. C₂⁴×H(5,𝔽₂)	C₂²	semidirect
16. C₂×#62817	C₂²	semidirect
17. C₂²×#3484	C₂²	semidirect
19. C₂²×#3026	C₂²	semidirect
20. #7675416	C₂²	semidirect
21. #7675391	C₂²	semidirect
22. #7642273	C₂²	semidirect
23. #7642257	C₂²	semidirect
24. #7631286	C₂²	semidirect
25. #7630945	C₂²	semidirect
26. #7630939	C₂²	semidirect
27. C₂×#35347	C₂²	semidirect
28. C₂×#35346	C₂²	semidirect
31. C₂×#34980	C₂²	semidirect
32. C₂×#34980	C₂²	semidirect
33. C₂²×#2403	C₂²	semidirect
34. #7626202	C₂²	semidirect
35. C₂×#34256	C₂²	semidirect
36. C₂×#34171	C₂²	semidirect
37. #6628892	C₂²	semidirect
38. #6628892	C₂²	semidirect
39. #6628892	C₂²	semidirect
40. #6451874	C₂²	semidirect
41. #6451874	C₂²	semidirect
42. C₂×#23895	C₂²	semidirect
43. #6437621	C₂²	semidirect
44. #6437621	C₂²	semidirect
45. C₂×#21746	C₂²	semidirect
46. C₂×#21746	C₂²	semidirect
47. C₂×#20609	C₂²	semidirect
48. C₂²×#1781	C₂²	semidirect
49. C₂²×#1781	C₂²	semidirect
50. #517411	C₂²	semidirect
51. #449505	C₂²	semidirect
52. #449469	C₂²	semidirect
53. #417896	C₂²	semidirect
54. #417824	C₂²	semidirect
55. #417532	C₂²	semidirect
56. #417499	C₂²	semidirect
57. #405104	C₂²	semidirect
58. #405090	C₂²	semidirect
59. #394418	C₂²	semidirect
60. #394267	C₂²	semidirect
61. #394173	C₂²	semidirect
62. #394064	C₂²	semidirect
63. #394058	C₂²	semidirect
64. #393929	C₂²	semidirect
65. #392699	C₂²	semidirect
66. #392245	C₂²	semidirect
67. #392109	C₂²	semidirect
68. #382422	C₂²	semidirect
69. #382390	C₂²	semidirect
70. #379733	C₂²	semidirect
71. #374058	C₂²	semidirect
72. #364500	C₂²	semidirect
73. #364440	C₂²	semidirect
74. #359811	C₂²	semidirect
75. #359705	C₂²	semidirect
76. #359579	C₂²	semidirect
77. #359549	C₂²	semidirect
78. #359442	C₂²	semidirect
79. #359442	C₂²	semidirect
80. #355913	C₂²	semidirect
84. C₂⁵×D₄	D₄	semidirect
89. C₂×#3490	C₂³	semidirect
90. C₂×#3490	C₂³	semidirect
92. C₂×#3484	C₂³	semidirect
93. C₂×#3484	C₂³	semidirect
94. C₂×#3484	C₂³	semidirect
95. C₂²×D₄²	D₄	semidirect
99. C₂²×#534	C₂³	semidirect
100. C₂³×#127	D₄	semidirect
101. C₂³×#121	D₄	semidirect
102. C₂³×#121	D₄	semidirect
103. C₂³×#121	D₄	semidirect
105. C₂³×#120	D₄	semidirect
106. C₂³×#120	D₄	semidirect
112. C₂³×C₄×D₄	D₄	semidirect
115. C₂×#3026	C₂³	semidirect
116. C₂×#3026	C₂³	semidirect
118. C₂³×#99	C₂³	semidirect
119. C₂×#2849	D₄	semidirect
120. C₂×#2849	C₂³	semidirect
121. C₂×#2846	D₄	semidirect
122. C₂×#2846	C₂³	semidirect
123. #35390	C₂³	semidirect
124. #35367	C₂³	semidirect
125. #35358	C₂³	semidirect
126. #35351	C₂³	semidirect
127. #35348	C₂³	semidirect
129. #35347	C₂³	semidirect
131. #34985	C₂³	semidirect
132. #34984	C₂³	semidirect
133. #34980	D₄	semidirect
134. #34980	D₄	semidirect
135. #34980	D₄	semidirect
141. #34980	C₂³	semidirect
142. #34980	C₂³	semidirect
143. C₂×#2405	D₄	semidirect
144. C₂×#2405	D₄	semidirect
145. C₂×#2405	C₂³	semidirect
146. C₂×#2410	C₂³	semidirect
147. C₂×#2403	D₄	semidirect
148. C₂×#2403	D₄	semidirect
150. C₂×#2403	C₂³	semidirect
151. C₂×#2613	D₄	semidirect
152. #34264	C₂³	semidirect
154. #34198	C₂³	semidirect
155. #34176	C₂³	semidirect
157. #34171	C₂³	semidirect
158. #34171	C₂³	semidirect
162. C₂×#2308	C₂³	semidirect
167. #23468	C₂³	semidirect
168. #23444	C₂³	semidirect
169. #23444	C₂³	semidirect
170. C₂×#2021	C₂³	semidirect
171. C₂×#1913	C₂³	semidirect
172. C₂×#1913	C₂³	semidirect
173. C₂×#1898	C₂³	semidirect
174. C₂×#1898	C₂³	semidirect
175. C₂×#1898	C₂³	semidirect
176. #20960	C₂³	semidirect
177. #20960	C₂³	semidirect
178. C₂×#1819	C₂³	semidirect
179. C₂×#1819	C₂³	semidirect
181. #20609	C₂³	semidirect
186. C₂×#1781	C₂³	semidirect
187. C₂×#1781	C₂³	semidirect
188. C₂×#1781	C₂³	semidirect
189. C₂×#1781	C₂³	semidirect
190. #14681	C₂³	semidirect
191. #14679	C₂³	semidirect
192. #13867	C₂³	semidirect
193. #11172	C₂³	semidirect
194. #11087	C₂³	semidirect
195. #11046	C₂³	semidirect
196. #10995	C₂³	semidirect
197. #10991	C₂³	semidirect
198. #10980	C₂³	semidirect
199. #10972	C₂³	semidirect
200. #10972	C₂³	semidirect
201. #10965	C₂³	semidirect
202. #10938	C₂³	semidirect
203. #10761	C₂³	semidirect
204. #10754	C₂³	semidirect
205. #10735	C₂³	semidirect
206. #10735	C₂³	semidirect
207. #10725	C₂³	semidirect
209. C₂⁷	C₂×D₄	semidirect
210. C₂⁷	C₂×D₄	semidirect
215. C₂²×H(5,𝔽₂)	C₂⁴	semidirect
230. C₂⁴×D₄	C₂×D₄	semidirect
231. C₂⁴×D₄	C₂×D₄	semidirect
232. C₂⁴×D₄	C₂×D₄	semidirect
233. C₂⁴×D₄	C₂×D₄	semidirect
234. C₂⁴×D₄	C₂×D₄	semidirect
235. C₂⁴×D₄	C₂×D₄	semidirect
236. C₂⁴×D₄	C₂×D₄	semidirect
237. C₂⁴×D₄	C₂×D₄	semidirect
238. C₂⁴×D₄	C₂×D₄	semidirect
239. C₂⁴×D₄	C₂×D₄	semidirect
240. C₂⁴×D₄	C₂×D₄	semidirect
251. C₂⁵×C₄	C₂×D₄	semidirect
252. C₂⁵×C₄	C₂×D₄	semidirect
253. C₂⁵×C₄	C₂×D₄	semidirect
255. C₂×#543	C₂⁴	semidirect
256. C₂×#534	C₂×D₄	semidirect
257. C₂×#534	C₂×D₄	semidirect
262. C₂×#534	C₂⁴	semidirect
263. C₂×#534	C₂⁴	semidirect
264. C₂²×#127	C₂×D₄	semidirect
265. C₂²×#123	C₂×D₄	semidirect
266. C₂²×#123	C₂×D₄	semidirect
267. C₂²×#121	C₂×D₄	semidirect
268. C₂²×#121	C₂×D₄	semidirect
269. C₂²×#121	C₂×D₄	semidirect
270. C₂²×#121	C₂×D₄	semidirect
276. C₂²×#120	C₂×D₄	semidirect
277. C₂²×#120	C₂×D₄	semidirect
278. C₂²×#120	C₂×D₄	semidirect
279. C₂²×#120	C₂×D₄	semidirect
280. C₂²×#120	C₂×D₄	semidirect
281. C₂²×#120	C₂×D₄	semidirect
282. C₂²×#120	C₂×D₄	semidirect
288. C₂²×#120	C₂⁴	semidirect
290. C₂×#518	C₂⁴	semidirect
291. C₂×#518	C₂⁴	semidirect
292. C₂×#518	C₂⁴	semidirect
293. C₂²×C₄×D₄	C₂×D₄	semidirect
294. C₂²×C₄×D₄	C₂×D₄	semidirect
296. C₂³×C₄⋊C₄	C₂×D₄	semidirect
297. C₂³×C₄⋊C₄	C₂×D₄	semidirect
300. C₂³×C₂²⋊C₄	C₂×D₄	semidirect
301. C₂³×C₂²⋊C₄	C₂×D₄	semidirect
302. C₂³×C₂²⋊C₄	C₂×D₄	semidirect
303. C₂³×C₂²⋊C₄	C₂×D₄	semidirect
304. C₂³×C₂²⋊C₄	C₂×D₄	semidirect
305. C₂³×C₂²⋊C₄	C₂×D₄	semidirect
306. C₂³×C₂²⋊C₄	C₂×D₄	semidirect
312. C₂³×C₄²	C₂×D₄	semidirect
316. C₂²×#99	C₂⁴	semidirect
317. C₂²×#99	C₂⁴	semidirect
318. #2849	C₂×D₄	semidirect
319. #2846	C₂×D₄	semidirect
320. #2613	C₂×D₄	semidirect
321. #2405	C₂×D₄	semidirect
322. #2405	C₂×D₄	semidirect
323. #2405	C₂×D₄	semidirect
324. #2405	C₂×D₄	semidirect
325. #2405	C₂×D₄	semidirect
326. #2405	C₂×D₄	semidirect
327. #2403	C₂×D₄	semidirect
328. #2403	C₂×D₄	semidirect
329. #2403	C₂×D₄	semidirect
330. #2403	C₂×D₄	semidirect
331. #2403	C₂×D₄	semidirect
332. #2403	C₂×D₄	semidirect
333. #2315	C₂⁴	semidirect
334. #2308	C₂×D₄	semidirect
335. #2308	C₂×D₄	semidirect
341. #2308	C₂⁴	semidirect
342. C₂×#386	C₂×D₄	semidirect
343. C₂×#386	C₂×D₄	semidirect
345. C₂×#386	C₂⁴	semidirect
346. C₂×#385	C₂⁴	semidirect
347. C₂×#381	C₂×D₄	semidirect
348. C₂×#379	C₂×D₄	semidirect
349. C₂×#379	C₂×D₄	semidirect
350. C₂×#379	C₂×D₄	semidirect
351. C₂×#379	C₂×D₄	semidirect
352. C₂×#379	C₂×D₄	semidirect
353. C₂×#379	C₂×D₄	semidirect
354. C₂×#379	C₂×D₄	semidirect
355. C₂×#379	C₂×D₄	semidirect
361. C₂×#379	C₂⁴	semidirect
362. C₂×#379	C₂⁴	semidirect
363. #2273	C₂⁴	semidirect
364. C₂×#342	C₂⁴	semidirect
365. C₂×#342	C₂⁴	semidirect
366. C₂×#342	C₂⁴	semidirect
367. C₂²⋊#95	C₂⁴	semidirect
391. C₂⁶	C₂²×D₄	semidirect
398. C₂×H(5,𝔽₂)	H(5,𝔽₂)	semidirect
444. C₂³×D₄	C₂²×D₄	semidirect
445. C₂³×D₄	C₂²×D₄	semidirect
446. C₂³×D₄	C₂²×D₄	semidirect
468. C₂⁴×C₄	C₂²×D₄	semidirect
469. C₂⁴×C₄	C₂²×D₄	semidirect
470. C₂⁴×C₄	C₂²×D₄	semidirect
474. C₂×#123	C₂²×D₄	semidirect
481. C₂×#120	C₂²×D₄	semidirect
503. C₂²×C₂²⋊C₄	C₂²×D₄	semidirect
504. C₂²×C₂²⋊C₄	C₂²×D₄	semidirect
505. C₂²×C₂²⋊C₄	C₂²×D₄	semidirect
506. C₂²×C₂²⋊C₄	C₂²×D₄	semidirect
507. C₂²×C₂²⋊C₄	C₂²×D₄	semidirect
516. #386	C₂²×D₄	semidirect
517. #386	C₂²×D₄	semidirect
524. #379	C₂²×D₄	semidirect
525. #379	C₂²×D₄	semidirect
704. C₂⁴	#3484	semidirect
717. C₂²×C₄	#3484	semidirect
718. C₂³	#23895	semidirect

Maximal subgroups

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

subgroup	index
#72234689	2
#72234675	2
#72234668	2
#72234645	2
#72234629	2
#72234625	2
#72234616	2
C₂×#6628892	2
#72234586	2
#72233069	2
#72225733	2
#72219307	2
C₂×#7631286	2
#72213862	2