Subgroups — #72266268

Order 4096.

Only the 1125 normal subgroups are shown; non-normal subgroups are omitted.

The subgroup lattice has 570 nodes (normal subgroups only) — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#72266267	C₂	1	1	yes	maximal, characteristic, complemented
2	#72266256	C₂	1	4	yes	maximal, complemented
3	#72266255	C₂²	1	2	yes	complemented
4	#72266216	C₂	1	2	yes	maximal, complemented
5	#72266151	C₂	1	1	yes	maximal, characteristic, complemented
6	#72266150	C₂	1	2	yes	maximal, complemented
7	#72266143	C₂	1	4	yes	maximal, complemented
8	#72266141	C₂	1	2	yes	maximal, complemented
9	#72266019	C₂	1	2	yes	maximal, complemented
10	#72259040	C₂	1	1	yes	maximal, characteristic, complemented
11	#72259019	C₂²	1	2	yes	complemented
12	#72259016	C₂²	1	2	yes	complemented
13	#72259014	C₂²	1	2	yes	complemented
14	#72258939	C₂	1	1	yes	maximal, characteristic, complemented
15	#72258840	C₂	1	4	yes	maximal, complemented
16	#72258785	C₂	1	4	yes	maximal, complemented
17	#72258752	C₂²	1	4	yes	complemented
18	#72258744	C₂²	1	4	yes	complemented
19	#72258744	C₂²	1	4	yes	complemented
20	#72258744	C₂²	1	4	yes	complemented
21	#72258744	C₂²	1	4	yes	complemented
22	#72258700	C₂²	1	4	yes	complemented
23	#72258693	C₂²	1	4	yes	complemented
24	#72258693	C₂²	1	4	yes	complemented
25	#72258689	C₂²	1	4	yes	complemented
26	#72258662	C₂	1	1	yes	maximal, characteristic, complemented
27	#72258649	C₂²	1	1	yes	characteristic, complemented
28	#72255642	C₂²	1	4	yes	complemented
29	#72255632	C₂²	1	4	yes	complemented
30	#72255630	C₂²	1	2	yes	complemented
31	#72240619	C₂²	1	1	yes	characteristic, complemented
32	#72240427	C₂²	1	4	yes	complemented
33	#72240426	C₂²	1	4	yes	complemented
34	#72240426	C₂²	1	4	yes	complemented
35	#72240425	C₂²	1	2	yes	complemented
36	#72240425	C₂²	1	2	yes	complemented
37	#72238594	C₂²	1	4	yes	complemented
38	#72236821	C₂	1	1	yes	maximal, characteristic, complemented
39	#72236816	C₂²	1	2	yes	complemented
40	#72236815	C₂²	1	2	yes	complemented
41	#72236815	C₂²	1	2	yes	complemented
42	#72236812	C₂²	1	2	yes	complemented
43	#72236800	C₂	1	1	yes	maximal, characteristic, complemented
44	#72236764	C₂²	1	2	yes	complemented
45	#72236756	C₂²	1	4	yes	complemented
46	#72236756	C₂²	1	4	yes	complemented
47	#72236756	C₂²	1	4	yes	complemented
48	#72236756	C₂²	1	4	yes	complemented
49	#72235988	C₂²	1	2	yes	—
50	#72235930	C₂²	1	1	yes	characteristic
51	#72235930	C₂²	1	1	yes	characteristic
52	#72235850	C₂²	1	2	yes	complemented
53	#72235054	C₂²	1	4	yes	complemented
54	C₂×#6628892	C₂²	1	2	yes	complemented
55	#72233780	C₂²	1	1	yes	characteristic, complemented
56	#72232877	C₂²	1	2	yes	—
57	#72225783	C₂²	1	1	yes	characteristic, complemented
58	#72225728	C₂²	1	2	yes	complemented
59	#72225709	C₂²	1	2	yes	complemented
60	#72225665	C₂²	1	1	yes	characteristic
61	#72225643	C₂²	1	4	yes	complemented
62	#72225621	C₂²	1	1	yes	characteristic, complemented
63	#72219457	C₂²	1	2	yes	complemented
64	#72219443	C₂²	1	4	yes	complemented
65	#72219377	C₂²	1	1	yes	characteristic, complemented
66	#72219307	C₂²	1	1	yes	characteristic, complemented
67	C₂×#7631286	C₂²	1	1	yes	characteristic, complemented
68	#72219118	C₂²	1	2	yes	complemented
69	#72218854	C₂²	1	2	yes	complemented
70	#72218846	C₂²	1	2	yes	complemented
71	#72218467	C₂²	1	2	yes	complemented
72	#72218387	C₂²	1	4	yes	complemented
73	#72214832	C₂²	1	2	yes	complemented
74	#72214549	C₂²	1	4	yes	complemented
75	C₂⁴×H(5,𝔽₂)	C₂³	1	1	yes	characteristic
76	C₂²×#3484	D₄	1	1	yes	characteristic, complemented
77	C₂²×#3484	C₂³	1	1	yes	characteristic
78	C₂³×D₄²	C₂³	1	1	yes	characteristic
79	C₂×#46996	D₄	1	2	yes	complemented
80	C₂×#35347	D₄	1	1	yes	characteristic, complemented
81	C₂×#35347	D₄	1	1	yes	characteristic, complemented
82	C₂×#35346	D₄	1	1	yes	characteristic, complemented
83	C₂×#35346	D₄	1	2	yes	complemented
84	C₂×#35346	C₂³	1	2	yes	—
85	C₂×#35346	C₂³	1	1	yes	characteristic
86	C₂×#34980	D₄	1	1	yes	characteristic, complemented
87	C₂×#34980	C₂³	1	2	yes	—
88	C₂×#34980	C₂³	1	4	yes	—
89	C₂×#34980	C₂³	1	2	yes	—
90	C₂²×#2403	D₄	1	1	yes	characteristic, complemented
91	C₂²×#2403	C₂³	1	1	yes	characteristic
92	C₂²×#2403	C₂³	1	2	yes	—
93	C₂×#34171	C₂³	1	1	yes	characteristic
94	C₂²×#1781	C₂³	1	2	yes	—
95	C₂²×#1781	C₂³	1	4	yes	—
96	#5955303	D₄	1	2	yes	complemented
97	#4928938	D₄	1	2	yes	complemented
98	#4453260	D₄	1	2	yes	complemented
99	#4414129	C₂³	1	2	yes	—
100	#4388020	D₄	1	2	yes	complemented
101	#4388002	D₄	1	2	yes	complemented
102	#4387621	D₄	1	2	yes	complemented
103	#4387617	D₄	1	2	yes	complemented
104	#4387617	D₄	1	2	yes	complemented
105	#4387585	D₄	1	2	yes	complemented
106	#765934	D₄	1	2	yes	complemented
107	#763548	D₄	1	2	yes	complemented
108	#759288	C₂³	1	2	yes	—
109	#636791	D₄	1	2	yes	complemented
110	#635984	C₂³	1	2	yes	—
111	#635984	C₂³	1	2	yes	—
112	#635984	C₂³	1	2	yes	—
113	#635984	C₂³	1	2	yes	—
114	#626258	D₄	1	2	yes	complemented
115	#617710	D₄	1	2	yes	complemented
116	#617161	D₄	1	2	yes	complemented
117	#616964	D₄	1	2	yes	complemented
118	#613191	D₄	1	2	yes	complemented
119	#612424	C₂³	1	2	yes	—
120	#612424	C₂³	1	2	yes	—
121	#612424	C₂³	1	4	yes	—
122	#612424	C₂³	1	4	yes	—
123	C₂×#14715	C₂³	1	2	yes	—
124	#576599	D₄	1	2	yes	complemented
125	#556752	D₄	1	1	yes	characteristic, complemented
126	#555894	C₂³	1	2	yes	—
127	#554236	D₄	1	2	yes	complemented
128	#521311	C₂³	1	2	yes	—
129	#521311	C₂³	1	2	yes	—
130	#517411	D₄	1	1	yes	characteristic, complemented
131	#517411	D₄	1	1	yes	characteristic, complemented
132	#517411	C₂³	1	1	yes	characteristic
133	#517411	C₂³	1	1	yes	characteristic
134	#517411	C₂³	1	1	yes	characteristic
135	#517411	C₂³	1	1	yes	characteristic
136	#516577	D₄	1	2	yes	complemented
137	#515362	D₄	1	1	yes	characteristic, complemented
138	#515362	D₄	1	1	yes	characteristic, complemented
139	#515285	D₄	1	1	yes	characteristic, complemented
140	#515285	C₂³	1	1	yes	characteristic
141	#392109	C₂³	1	2	yes	—
142	#392109	C₂³	1	2	yes	—
143	#392109	C₂³	1	2	yes	—
144	#392109	C₂³	1	4	yes	—
145	#392109	C₂³	1	4	yes	—
146	#382422	C₂³	1	4	yes	—
147	#382422	C₂³	1	4	yes	—
148	#382422	C₂³	1	2	yes	—
149	#382422	C₂³	1	2	yes	—
150	#359428	C₂³	1	4	yes	—
151	#359428	C₂³	1	4	yes	—
152	#359428	C₂³	1	4	yes	—
153	#359428	C₂³	1	4	yes	—
154	#359428	C₂³	1	4	yes	—
155	#359428	C₂³	1	4	yes	—
156	C₂×#10965	C₂³	1	4	yes	—
157	C₂×#10965	C₂³	1	2	yes	—
158	#154094	C₂³	1	2	yes	—
159	#123513	C₂³	1	4	yes	—
160	C₂²⋊#1304	C₂³	1	4	yes	—
161	C₂²⋊#1304	C₂³	1	4	yes	—
162	C₂²⋊#1304	C₂³	1	4	yes	—
163	C₂²⋊#1304	C₂³	1	4	yes	—
164	C₂²⋊#1304	C₂³	1	4	yes	—
165	C₂²⋊#1304	C₂³	1	4	yes	—
166	C₂²⋊#1304	C₂³	1	4	yes	—
167	C₂²⋊#1304	C₂³	1	4	yes	—
168	C₂³×H(5,𝔽₂)	C₂×D₄	1	1	yes	characteristic, complemented
169	C₂³×H(5,𝔽₂)	C₂×D₄	1	1	yes	characteristic, complemented
170	C₂³×H(5,𝔽₂)	C₂×D₄	1	2	yes	complemented
171	C₂⁵×D₄	C₂×D₄	1	1	yes	characteristic
172	C₂⁵×D₄	C₂×D₄	1	1	yes	characteristic
173	C₂⁵×D₄	C₂×D₄	1	1	yes	characteristic
174	C₂⁵×D₄	C₂⁴	1	1	yes	characteristic
175	C₂⁵×D₄	C₂⁴	1	1	yes	characteristic
176	C₂⁵×D₄	C₂⁴	1	2	yes	—
177	C₂²×#534	C₂×D₄	1	2	yes	—
178	C₂²×#534	C₂×D₄	1	2	yes	—
179	C₂²×#534	C₂×D₄	1	2	yes	complemented
180	C₂³×#127	C₂×D₄	1	1	yes	characteristic
181	C₂³×#121	C₂×D₄	1	1	yes	characteristic
182	C₂³×#121	C₂×D₄	1	1	yes	characteristic
183	C₂³×#121	C₂×D₄	1	1	yes	characteristic
184	C₂³×#121	C₂×D₄	1	1	yes	characteristic
185	C₂³×#120	C₂×D₄	1	1	yes	characteristic
186	C₂³×#120	C₂×D₄	1	1	yes	characteristic
187	C₂³×#120	C₂×D₄	1	2	yes	—
188	C₂³×#120	C₂×D₄	1	1	yes	characteristic
189	C₂³×#120	C₂×D₄	1	2	yes	complemented
190	C₂³×#120	C₂⁴	1	2	yes	—
191	C₂³×#120	C₂⁴	1	2	yes	—
192	C₂³×#120	C₂⁴	1	1	yes	characteristic
193	C₂³×#120	C₂⁴	1	2	yes	—
194	C₂²×#518	C₂×D₄	1	1	yes	characteristic, complemented
195	C₂²×#518	C₂×D₄	1	1	yes	characteristic, complemented
196	C₂³×C₄×D₄	C₂×D₄	1	1	yes	characteristic
197	C₂³×C₄×D₄	C₂×D₄	1	1	yes	characteristic
198	C₂×#2840	C₂×D₄	1	2	yes	complemented
199	C₂×#2405	C₂×D₄	1	2	yes	—
200	C₂×#2405	C₂×D₄	1	2	yes	—
201	C₂×#2405	C₂×D₄	1	2	yes	—
202	C₂×#2405	C₂×D₄	1	2	yes	—
203	C₂×#2405	C₂×D₄	1	2	yes	—
204	C₂×#2405	C₂×D₄	1	2	yes	complemented
205	C₂×#2405	C₂×D₄	1	2	yes	complemented
206	C₂×#2405	C₂×D₄	1	2	yes	complemented
207	C₂×#2403	C₂×D₄	1	2	yes	—
208	C₂×#2403	C₂×D₄	1	2	yes	—
209	C₂×#2403	C₂×D₄	1	2	yes	—
210	C₂×#2403	C₂×D₄	1	2	yes	—
211	C₂×#2403	C₂×D₄	1	2	yes	—
212	C₂×#2403	C₂×D₄	1	2	yes	—
213	C₂×#2403	C₂×D₄	1	2	yes	—
214	C₂×#2403	C₂×D₄	1	2	yes	—
215	C₂×#2403	C₂×D₄	1	2	yes	—
216	C₂×#2403	C₂×D₄	1	2	yes	—
217	C₂×#2403	C₂×D₄	1	2	yes	—
218	C₂×#2403	C₂×D₄	1	2	yes	—
219	C₂×#2403	C₂×D₄	1	2	yes	—
220	C₂×#2403	C₂×D₄	1	2	yes	complemented
221	C₂×#2403	C₂×D₄	1	2	yes	complemented
222	C₂×#2403	C₂×D₄	1	2	yes	complemented
223	C₂×#2403	C₂×D₄	1	2	yes	complemented
224	C₂²×#392	C₂×D₄	1	2	yes	—
225	C₂²×#392	C₂×D₄	1	2	yes	—
226	C₂×#2309	C₂×D₄	1	2	yes	complemented
227	C₂×#2308	C₂×D₄	1	2	yes	—
228	C₂×#2308	C₂×D₄	1	2	yes	—
229	C₂×#2308	C₂×D₄	1	2	yes	—
230	C₂×#2308	C₂×D₄	1	2	yes	—
231	C₂×#2308	C₂×D₄	1	1	yes	characteristic, complemented
232	C₂×#2308	C₂×D₄	1	1	yes	characteristic, complemented
233	C₂×#2308	C₂×D₄	1	2	yes	complemented
234	C₂×#2308	C₂×D₄	1	2	yes	complemented
235	C₂×#2308	C₂×D₄	1	2	yes	complemented
236	C₂×#2308	C₂×D₄	1	2	yes	complemented
237	C₂×#2308	C₂×D₄	1	2	yes	complemented
238	C₂×#2308	C₂×D₄	1	1	yes	characteristic, complemented
239	C₂×#2308	C₂×D₄	1	1	yes	characteristic, complemented
240	C₂×#2308	C₂×D₄	1	2	yes	complemented
241	C₂×#2308	C₂×D₄	1	2	yes	complemented
242	C₂²×#386	C₂×D₄	1	2	yes	—
243	C₂²×#386	C₂×D₄	1	2	yes	—
244	C₂²×#386	C₂×D₄	1	2	yes	complemented
245	C₂²×#379	C₂×D₄	1	1	yes	characteristic
246	C₂²×#379	C₂×D₄	1	1	yes	characteristic
247	C₂²×#379	C₂×D₄	1	1	yes	characteristic
248	C₂²×#379	C₂×D₄	1	2	yes	complemented
249	C₂²×#379	C₂⁴	1	4	yes	—
250	C₂²×#379	C₂⁴	1	2	yes	—
251	C₂²×#379	C₂⁴	1	2	yes	—
252	#14681	C₂×D₄	1	2	yes	—
253	#14679	C₂⁴	1	2	yes	—
254	#14679	C₂⁴	1	4	yes	—
255	#14679	C₂⁴	1	2	yes	—
256	#14679	C₂⁴	1	2	yes	—
257	#14679	C₂⁴	1	2	yes	—
258	#14673	C₂×D₄	1	2	yes	complemented
259	#14673	C₂×D₄	1	2	yes	complemented
260	#14673	C₂×D₄	1	2	yes	complemented
261	#14341	C₂×D₄	1	2	yes	complemented
262	#14341	C₂×D₄	1	2	yes	complemented
263	#14338	C₂×D₄	1	2	yes	complemented
264	#14338	C₂×D₄	1	2	yes	complemented
265	#14335	C₂×D₄	1	2	yes	—
266	#14335	C₂×D₄	1	2	yes	—
267	#14335	C₂×D₄	1	2	yes	complemented
268	#14335	C₂×D₄	1	2	yes	complemented
269	#14335	C₂×D₄	1	2	yes	complemented
270	#14127	C₂×D₄	1	2	yes	complemented
271	#13869	C₂×D₄	1	2	yes	—
272	#13869	C₂×D₄	1	2	yes	complemented
273	#13869	C₂×D₄	1	2	yes	complemented
274	#13869	C₂×D₄	1	2	yes	complemented
275	#13867	C₂×D₄	1	2	yes	—
276	#13867	C₂×D₄	1	2	yes	—
277	#13867	C₂×D₄	1	2	yes	—
278	#13867	C₂×D₄	1	2	yes	—
279	#13867	C₂×D₄	1	2	yes	—
280	#13867	C₂×D₄	1	2	yes	—
281	#13867	C₂×D₄	1	2	yes	—
282	#13867	C₂×D₄	1	2	yes	—
283	#13867	C₂×D₄	1	2	yes	—
284	#13867	C₂×D₄	1	2	yes	complemented
285	#13867	C₂×D₄	1	2	yes	complemented
286	#13867	C₂×D₄	1	2	yes	complemented
287	#13867	C₂×D₄	1	2	yes	complemented
288	#13867	C₂×D₄	1	2	yes	complemented
289	#13794	C₂×D₄	1	2	yes	complemented
290	#13775	C₂×D₄	1	2	yes	complemented
291	#13775	C₂×D₄	1	2	yes	complemented
292	C₂×C₂²⋊#95	C₂×D₄	1	2	yes	complemented
293	C₂⁷	#120	1	1	yes	characteristic
294	C₂⁷	#120	1	1	yes	characteristic
295	C₂⁷	C₂²×D₄	1	1	yes	characteristic
296	C₂⁷	C₂²×D₄	1	1	yes	characteristic
297	C₂⁷	H(5,𝔽₂)	1	2	yes	complemented
298	C₂⁷	C₂⁵	1	1	yes	characteristic
299	C₂⁴×D₄	#120	1	1	yes	characteristic
300	C₂⁴×D₄	#120	1	1	yes	characteristic
301	C₂⁴×D₄	#120	1	1	yes	characteristic
302	C₂⁴×D₄	#120	1	1	yes	characteristic
303	C₂⁴×D₄	#120	1	2	yes	—
304	C₂⁴×D₄	#120	1	1	yes	characteristic
305	C₂⁴×D₄	C₂²×D₄	1	1	yes	characteristic
306	C₂⁴×D₄	C₂²×D₄	1	1	yes	characteristic
307	C₂⁴×D₄	C₂²×D₄	1	2	yes	—
308	C₂⁴×D₄	C₂²×D₄	1	2	yes	—
309	C₂⁴×D₄	C₂²×D₄	1	2	yes	—
310	C₂⁴×D₄	C₂²×D₄	1	2	yes	—
311	C₂⁴×D₄	C₂²×D₄	1	1	yes	characteristic
312	C₂⁴×D₄	C₂²×D₄	1	1	yes	characteristic
313	C₂⁴×D₄	C₂²×D₄	1	1	yes	characteristic
314	C₂⁴×D₄	C₂²×D₄	1	1	yes	characteristic
315	C₂⁴×D₄	C₂²×D₄	1	1	yes	characteristic
316	C₂⁴×D₄	C₂²×D₄	1	1	yes	characteristic
317	C₂⁴×D₄	C₂²×D₄	1	2	yes	—
318	C₂⁴×D₄	C₂²×D₄	1	2	yes	—
319	C₂⁴×D₄	C₂²×D₄	1	2	yes	—
320	C₂⁴×D₄	C₂²×D₄	1	2	yes	—
321	C₂⁴×D₄	C₂²×D₄	1	2	yes	—
322	C₂⁴×D₄	C₂²×D₄	1	2	yes	—
323	C₂⁴×D₄	C₂²×D₄	1	2	yes	—
324	C₂⁴×D₄	C₂²×D₄	1	1	yes	characteristic
325	C₂⁴×D₄	C₂²×D₄	1	1	yes	characteristic
326	C₂⁴×D₄	C₂²×D₄	1	1	yes	characteristic
327	C₂⁴×D₄	C₂²×D₄	1	2	yes	—
328	C₂⁴×D₄	C₂²×D₄	1	2	yes	—
329	C₂⁵×C₄	#120	1	1	yes	characteristic
330	C₂⁵×C₄	#120	1	1	yes	characteristic
331	C₂⁵×C₄	#120	1	1	yes	characteristic
332	C₂⁵×C₄	C₂²×D₄	1	1	yes	characteristic
333	C₂⁵×C₄	C₂²×D₄	1	1	yes	characteristic
334	C₂⁵×C₄	H(5,𝔽₂)	1	2	yes	complemented
335	C₂²×#123	#120	1	2	yes	—
336	C₂²×#123	#120	1	2	yes	—
337	C₂²×#123	#120	1	2	yes	—
338	C₂²×#123	#120	1	2	yes	—
339	C₂²×#120	#120	1	2	yes	—
340	C₂²×#120	#120	1	2	yes	—
341	C₂²×#120	#120	1	2	yes	—
342	C₂²×#120	#120	1	2	yes	—
343	C₂²×#120	#120	1	2	yes	—
344	C₂²×#120	#120	1	2	yes	—
345	C₂²×#120	#120	1	2	yes	—
346	C₂²×#120	#120	1	2	yes	—
347	C₂³×C₄⋊C₄	#120	1	1	yes	characteristic
348	C₂³×C₄⋊C₄	#120	1	1	yes	characteristic
349	C₂³×C₂²⋊C₄	#120	1	1	yes	characteristic
350	C₂³×C₂²⋊C₄	#120	1	1	yes	characteristic
351	C₂³×C₂²⋊C₄	#120	1	2	yes	—
352	C₂³×C₂²⋊C₄	#120	1	1	yes	characteristic
353	C₂³×C₂²⋊C₄	#120	1	1	yes	characteristic
354	C₂³×C₂²⋊C₄	#120	1	1	yes	characteristic
355	C₂³×C₂²⋊C₄	#120	1	1	yes	characteristic
356	C₂³×C₂²⋊C₄	#120	1	1	yes	characteristic
357	C₂³×C₂²⋊C₄	#120	1	2	yes	—
358	C₂³×C₂²⋊C₄	#120	1	2	yes	—
359	C₂³×C₂²⋊C₄	#120	1	2	yes	—
360	C₂³×C₂²⋊C₄	#120	1	1	yes	characteristic
361	C₂³×C₂²⋊C₄	#120	1	1	yes	characteristic
362	C₂³×C₂²⋊C₄	C₂²×D₄	1	2	yes	—
363	C₂³×C₂²⋊C₄	C₂²×D₄	1	2	yes	—
364	C₂³×C₂²⋊C₄	C₂²×D₄	1	2	yes	—
365	C₂³×C₂²⋊C₄	C₂²×D₄	1	2	yes	—
366	C₂³×C₂²⋊C₄	C₂²×D₄	1	2	yes	—
367	C₂³×C₂²⋊C₄	C₂²×D₄	1	2	yes	—
368	C₂³×C₂²⋊C₄	C₂²×D₄	1	2	yes	—
369	C₂³×C₂²⋊C₄	C₂²×D₄	1	2	yes	—
370	C₂³×C₂²⋊C₄	C₂²×D₄	1	2	yes	—
371	C₂³×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
372	C₂³×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
373	C₂³×C₂²⋊C₄	C₂²×D₄	1	2	yes	—
374	C₂³×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
375	C₂³×C₂²⋊C₄	C₂²×D₄	1	2	yes	—
376	C₂³×C₄²	#120	1	1	yes	characteristic
377	C₂×#386	#120	1	2	yes	—
378	C₂×#386	#120	1	2	yes	—
379	C₂×#386	#120	1	2	yes	—
380	C₂×#386	#120	1	2	yes	—
381	C₂×#386	#120	1	2	yes	—
382	C₂×#386	#120	1	2	yes	—
383	C₂×#386	#120	1	2	yes	—
384	C₂×#386	#120	1	2	yes	—
385	C₂×#386	#120	1	2	yes	—
386	C₂×#386	#120	1	2	yes	—
387	C₂×#386	#120	1	2	yes	—
388	C₂×#386	#120	1	2	yes	—
389	C₂×#386	#120	1	2	yes	—
390	C₂×#386	#120	1	2	yes	—
391	C₂×#386	#120	1	2	yes	—
392	C₂×#386	#120	1	2	yes	—
393	C₂×#386	#120	1	2	yes	—
394	C₂×#386	#120	1	2	yes	—
395	C₂×#386	#120	1	2	yes	—
396	C₂×#386	#120	1	2	yes	—
397	C₂×#381	#120	1	2	yes	—
398	C₂×#381	#120	1	2	yes	—
399	C₂×#381	#120	1	2	yes	—
400	C₂×#381	#120	1	2	yes	—
401	C₂×#379	#120	1	2	yes	—
402	C₂×#379	#120	1	1	yes	characteristic
403	C₂×#379	#120	1	1	yes	characteristic
404	C₂×#379	C₂²×D₄	1	2	yes	—
405	C₂×#379	C₂²×D₄	1	2	yes	—
406	C₂×#379	C₂²×D₄	1	2	yes	—
407	C₂×#379	C₂²×D₄	1	2	yes	—
408	C₂×#379	C₂²×D₄	1	2	yes	—
409	C₂×#379	C₂²×D₄	1	2	yes	—
410	C₂×#379	C₂²×D₄	1	2	yes	—
411	C₂×#379	C₂²×D₄	1	2	yes	—
412	C₂×#379	C₂²×D₄	1	2	yes	—
413	C₂×#379	C₂²×D₄	1	2	yes	—
414	C₂×#379	C₂²×D₄	1	2	yes	—
415	C₂×#379	C₂²×D₄	1	2	yes	—
416	C₂×#379	C₂²×D₄	1	2	yes	—
417	C₂×#379	C₂²×D₄	1	2	yes	—
418	C₂×#379	C₂²×D₄	1	2	yes	—
419	C₂×#379	C₂²×D₄	1	2	yes	—
420	C₂×#379	H(5,𝔽₂)	1	4	yes	complemented
421	C₂×#379	H(5,𝔽₂)	1	4	yes	complemented
422	C₂²×#95	#120	1	2	yes	—
423	C₂²×#95	#120	1	2	yes	—
424	C₂⁶	B(4,𝔽₂)	1	4	yes	complemented
425	C₂⁶	C₂×#120	1	1	yes	characteristic
426	C₂⁶	C₂×#120	1	1	yes	characteristic
427	C₂⁶	C₂×#120	1	1	yes	characteristic
428	C₂⁶	C₂×#120	1	1	yes	characteristic
429	C₂⁶	C₂×#120	1	1	yes	characteristic
430	C₂⁶	C₂×#120	1	1	yes	characteristic
431	C₂⁶	C₂×#120	1	1	yes	characteristic
432	C₂⁶	C₂×#120	1	2	yes	—
433	C₂⁶	C₂×#120	1	2	yes	—
434	C₂⁶	C₂×#120	1	1	yes	characteristic
435	C₂⁶	C₂×#120	1	1	yes	characteristic
436	C₂⁶	C₂×#120	1	2	yes	—
437	C₂⁶	C₂³×D₄	1	1	yes	characteristic
438	C₂⁶	C₂³×D₄	1	1	yes	characteristic
439	C₂⁶	C₂³×D₄	1	1	yes	characteristic
440	C₂⁶	C₂³×D₄	1	2	yes	—
441	C₂⁶	C₂³×D₄	1	2	yes	—
442	C₂⁶	C₂×H(5,𝔽₂)	1	2	yes	—
443	C₂⁶	C₂×H(5,𝔽₂)	1	2	yes	—
444	C₂⁶	C₂×H(5,𝔽₂)	1	2	yes	—
445	C₂⁶	#585	1	2	yes	—
446	C₂³×D₄	C₂×#120	1	2	yes	—
447	C₂³×D₄	C₂×#120	1	2	yes	—
448	C₂³×D₄	C₂×#120	1	2	yes	—
449	C₂³×D₄	C₂×#120	1	2	yes	—
450	C₂³×D₄	C₂×#120	1	2	yes	—
451	C₂³×D₄	C₂×#120	1	2	yes	—
452	C₂³×D₄	C₂×#120	1	2	yes	—
453	C₂³×D₄	C₂×#120	1	2	yes	—
454	C₂⁴×C₄	C₂×#120	1	1	yes	characteristic
455	C₂⁴×C₄	C₂×#120	1	1	yes	characteristic
456	C₂⁴×C₄	C₂×#120	1	2	yes	—
457	C₂⁴×C₄	C₂×#120	1	2	yes	—
458	C₂⁴×C₄	C₂×#120	1	1	yes	characteristic
459	C₂⁴×C₄	C₂×#120	1	1	yes	characteristic
460	C₂⁴×C₄	C₂×#120	1	1	yes	characteristic
461	C₂⁴×C₄	C₂×#120	1	1	yes	characteristic
462	C₂⁴×C₄	C₂×#120	1	2	yes	—
463	C₂⁴×C₄	C₂×#120	1	1	yes	characteristic
464	C₂⁴×C₄	C₂×#120	1	2	yes	—
465	C₂⁴×C₄	C₂×#120	1	2	yes	—
466	C₂⁴×C₄	C₂×#120	1	2	yes	—
467	C₂⁴×C₄	C₂×#120	1	2	yes	—
468	C₂⁴×C₄	C₂×#120	1	2	yes	—
469	C₂⁴×C₄	C₂×#120	1	2	yes	—
470	C₂⁴×C₄	C₂×#120	1	2	yes	—
471	C₂⁴×C₄	C₂×#120	1	2	yes	—
472	C₂×#120	B(4,𝔽₂)	1	8	yes	complemented
473	C₂²×C₂²⋊C₄	B(4,𝔽₂)	1	4	yes	complemented
474	C₂²×C₂²⋊C₄	C₂×#120	1	2	yes	—
475	C₂²×C₂²⋊C₄	C₂×#120	1	2	yes	—
476	C₂²×C₂²⋊C₄	C₂×#120	1	2	yes	—
477	C₂²×C₂²⋊C₄	C₂×#120	1	2	yes	—
478	C₂²×C₂²⋊C₄	C₂×#120	1	2	yes	—
479	C₂²×C₂²⋊C₄	C₂×#120	1	2	yes	—
480	C₂²×C₂²⋊C₄	C₂×#120	1	2	yes	—
481	C₂²×C₂²⋊C₄	C₂×#120	1	2	yes	—
482	C₂²×C₂²⋊C₄	C₂×#120	1	2	yes	—
483	C₂²×C₂²⋊C₄	C₂×#120	1	2	yes	—
484	C₂²×C₂²⋊C₄	C₂×#120	1	2	yes	—
485	C₂²×C₂²⋊C₄	C₂×#120	1	2	yes	—
486	C₂⁵	#2846	1	1	yes	characteristic
487	C₂⁵	#2846	1	1	yes	characteristic
488	C₂⁵	#2846	1	1	yes	characteristic
489	C₂⁵	#2846	1	1	yes	characteristic
490	C₂⁵	C₂×B(4,𝔽₂)	1	2	yes	—
491	C₂⁵	C₂×B(4,𝔽₂)	1	2	yes	—
492	C₂⁵	C₂×B(4,𝔽₂)	1	4	yes	—
493	C₂⁵	C₂×B(4,𝔽₂)	1	2	yes	—
494	C₂⁵	C₂×B(4,𝔽₂)	1	2	yes	—
495	C₂⁵	#3026	1	2	yes	—
496	C₂⁵	#3026	1	2	yes	—
497	C₂⁵	C₂²×#120	1	1	yes	characteristic
498	C₂⁵	C₂²×#120	1	1	yes	characteristic
499	C₂⁵	C₂²×#120	1	2	yes	—
500	C₂⁵	C₂²×#120	1	2	yes	—
501	C₂⁵	C₂²×#120	1	1	yes	characteristic
502	C₂⁵	#3484	1	1	yes	characteristic
503	C₂⁵	#3484	1	1	yes	characteristic
504	C₂⁵	#3484	1	1	yes	characteristic
505	C₂⁵	#3484	1	2	yes	—
506	C₂⁵	#3484	1	2	yes	—
507	C₂⁵	#3484	1	4	yes	—
508	C₂⁵	#3485	1	1	yes	characteristic
509	C₂⁵	#3488	1	4	yes	—
510	C₂⁵	#3496	1	2	yes	—
511	C₂⁵	#3496	1	2	yes	—
512	C₂⁵	#3496	1	4	yes	—
513	C₂⁵	#3498	1	4	yes	—
514	C₂²×D₄	C₂×B(4,𝔽₂)	1	4	yes	—
515	C₂²×D₄	#3026	1	4	yes	—
516	C₂³×C₄	#2846	1	2	yes	—
517	C₂³×C₄	#2846	1	2	yes	—
518	C₂³×C₄	C₂×B(4,𝔽₂)	1	2	yes	—
519	C₂³×C₄	C₂×B(4,𝔽₂)	1	2	yes	—
520	C₂×C₂²⋊C₄	C₂×B(4,𝔽₂)	1	4	yes	—
521	C₂⁴	#32898	1	2	yes	—
522	C₂⁴	#32898	1	2	yes	—
523	C₂⁴	#32898	1	2	yes	—
524	C₂⁴	#32898	1	4	yes	—
525	C₂⁴	#32898	1	2	yes	—
526	C₂⁴	#35346	1	1	yes	characteristic
527	C₂⁴	#35346	1	1	yes	characteristic
528	C₂⁴	#35347	1	1	yes	characteristic
529	C₂⁴	#35347	1	1	yes	characteristic
530	C₂⁴	#35512	1	1	yes	characteristic
531	C₂⁴	#35527	1	1	yes	characteristic
532	C₂⁴	#35680	1	4	yes	—
533	C₂⁴	#35680	1	4	yes	—
534	C₂⁴	C₂×#2846	1	1	yes	characteristic
535	C₂⁴	C₂²×B(4,𝔽₂)	1	2	yes	—
536	C₂⁴	C₂²×B(4,𝔽₂)	1	1	yes	characteristic
537	C₂⁴	C₂²×B(4,𝔽₂)	1	1	yes	characteristic
538	C₂⁴	C₂×#3026	1	1	yes	characteristic
539	C₂⁴	C₂×#3026	1	1	yes	characteristic
540	C₂⁴	C₂×#3026	1	2	yes	—
541	C₂⁴	#60399	1	4	yes	—
542	C₂²×C₄	#32898	1	4	yes	—
543	C₂³	#347042	1	4	yes	—
544	C₂³	#4928938	1	1	yes	characteristic
545	C₂³	#6499867	1	1	yes	characteristic
546	C₂³	#6499870	1	1	yes	characteristic
547	C₂³	#6499874	1	2	yes	—
548	C₂³	#6500010	1	1	yes	characteristic
549	C₂³	#6500010	1	1	yes	characteristic
550	C₂³	#6533135	1	4	yes	—
551	C₂³	#6533339	1	4	yes	—
552	C₂³	C₂×#32898	1	1	yes	characteristic
553	C₂³	C₂×#32898	1	2	yes	—
554	C₂³	C₂×#32898	1	1	yes	characteristic
555	C₂³	#6628896	1	2	yes	—
556	C₂²	C₂×#347042	1	1	yes	characteristic
557	C₂²	#72216323	1	2	yes	—
558	C₂²	#72219157	1	1	yes	characteristic
559	C₂²	#72225712	1	1	yes	characteristic
560	C₂²	#72233203	1	2	yes	—
561	C₂²	#72234953	1	2	yes	—
562	C₂²	#72234953	1	1	yes	characteristic
563	C₂²	#72240103	1	1	yes	characteristic
564	C₂	#72234961	1	2	yes	—
565	C₂	#72240117	1	1	yes	characteristic
566	C₂	#72258426	1	1	yes	characteristic
567	C₂	#72265925	1	1	yes	characteristic
568	C₂	#72265974	1	2	yes	—

	subgroup	G/H
center, socle	C₂³	#4928938
commutator, Frattini, cosocle	C₂⁷	C₂⁵
LCS	G ▷ C₂⁷ ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³ ◁ C₂⁷ ◁ G
LECS	G ▷ C₂⁷ ▷ C₂³ ▷ C₁

Complements

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

N	H ≅ G/N	type
1. #72266267	C₂	semidirect
2. #72266256	C₂	semidirect
3. #72266255	C₂²	semidirect
4. #72266216	C₂	semidirect
5. #72266151	C₂	semidirect
6. #72266150	C₂	semidirect
7. #72266143	C₂	semidirect
8. #72266141	C₂	semidirect
9. #72266019	C₂	semidirect
10. #72259040	C₂	semidirect
11. #72259019	C₂²	semidirect
12. #72259016	C₂²	semidirect
13. #72259014	C₂²	semidirect
14. #72258939	C₂	semidirect
15. #72258840	C₂	semidirect
16. #72258785	C₂	semidirect
17. #72258752	C₂²	semidirect
18. #72258744	C₂²	semidirect
19. #72258744	C₂²	semidirect
20. #72258744	C₂²	semidirect
21. #72258744	C₂²	semidirect
22. #72258700	C₂²	semidirect
23. #72258693	C₂²	semidirect
24. #72258693	C₂²	semidirect
25. #72258689	C₂²	semidirect
26. #72258662	C₂	semidirect
27. #72258649	C₂²	semidirect
28. #72255642	C₂²	semidirect
29. #72255632	C₂²	semidirect
30. #72255630	C₂²	semidirect
31. #72240619	C₂²	semidirect
32. #72240427	C₂²	semidirect
33. #72240426	C₂²	semidirect
34. #72240426	C₂²	semidirect
35. #72240425	C₂²	semidirect
36. #72240425	C₂²	semidirect
37. #72238594	C₂²	semidirect
38. #72236821	C₂	semidirect
39. #72236816	C₂²	semidirect
40. #72236815	C₂²	semidirect
41. #72236815	C₂²	semidirect
42. #72236812	C₂²	semidirect
43. #72236800	C₂	semidirect
44. #72236764	C₂²	semidirect
45. #72236756	C₂²	semidirect
46. #72236756	C₂²	semidirect
47. #72236756	C₂²	semidirect
48. #72236756	C₂²	semidirect
52. #72235850	C₂²	semidirect
53. #72235054	C₂²	semidirect
54. C₂×#6628892	C₂²	semidirect
55. #72233780	C₂²	semidirect
57. #72225783	C₂²	semidirect
58. #72225728	C₂²	semidirect
59. #72225709	C₂²	semidirect
61. #72225643	C₂²	semidirect
62. #72225621	C₂²	semidirect
63. #72219457	C₂²	semidirect
64. #72219443	C₂²	semidirect
65. #72219377	C₂²	semidirect
66. #72219307	C₂²	semidirect
67. C₂×#7631286	C₂²	semidirect
68. #72219118	C₂²	semidirect
69. #72218854	C₂²	semidirect
70. #72218846	C₂²	semidirect
71. #72218467	C₂²	semidirect
72. #72218387	C₂²	semidirect
73. #72214832	C₂²	semidirect
74. #72214549	C₂²	semidirect
76. C₂²×#3484	D₄	semidirect
79. C₂×#46996	D₄	semidirect
80. C₂×#35347	D₄	semidirect
81. C₂×#35347	D₄	semidirect
82. C₂×#35346	D₄	semidirect
83. C₂×#35346	D₄	semidirect
86. C₂×#34980	D₄	semidirect
90. C₂²×#2403	D₄	semidirect
96. #5955303	D₄	semidirect
97. #4928938	D₄	semidirect
98. #4453260	D₄	semidirect
100. #4388020	D₄	semidirect
101. #4388002	D₄	semidirect
102. #4387621	D₄	semidirect
103. #4387617	D₄	semidirect
104. #4387617	D₄	semidirect
105. #4387585	D₄	semidirect
106. #765934	D₄	semidirect
107. #763548	D₄	semidirect
109. #636791	D₄	semidirect
114. #626258	D₄	semidirect
115. #617710	D₄	semidirect
116. #617161	D₄	semidirect
117. #616964	D₄	semidirect
118. #613191	D₄	semidirect
124. #576599	D₄	semidirect
125. #556752	D₄	semidirect
127. #554236	D₄	semidirect
130. #517411	D₄	semidirect
131. #517411	D₄	semidirect
136. #516577	D₄	semidirect
137. #515362	D₄	semidirect
138. #515362	D₄	semidirect
139. #515285	D₄	semidirect
168. C₂³×H(5,𝔽₂)	C₂×D₄	semidirect
169. C₂³×H(5,𝔽₂)	C₂×D₄	semidirect
170. C₂³×H(5,𝔽₂)	C₂×D₄	semidirect
179. C₂²×#534	C₂×D₄	semidirect
189. C₂³×#120	C₂×D₄	semidirect
194. C₂²×#518	C₂×D₄	semidirect
195. C₂²×#518	C₂×D₄	semidirect
198. C₂×#2840	C₂×D₄	semidirect
204. C₂×#2405	C₂×D₄	semidirect
205. C₂×#2405	C₂×D₄	semidirect
206. C₂×#2405	C₂×D₄	semidirect
220. C₂×#2403	C₂×D₄	semidirect
221. C₂×#2403	C₂×D₄	semidirect
222. C₂×#2403	C₂×D₄	semidirect
223. C₂×#2403	C₂×D₄	semidirect
226. C₂×#2309	C₂×D₄	semidirect
231. C₂×#2308	C₂×D₄	semidirect
232. C₂×#2308	C₂×D₄	semidirect
233. C₂×#2308	C₂×D₄	semidirect
234. C₂×#2308	C₂×D₄	semidirect
235. C₂×#2308	C₂×D₄	semidirect
236. C₂×#2308	C₂×D₄	semidirect
237. C₂×#2308	C₂×D₄	semidirect
238. C₂×#2308	C₂×D₄	semidirect
239. C₂×#2308	C₂×D₄	semidirect
240. C₂×#2308	C₂×D₄	semidirect
241. C₂×#2308	C₂×D₄	semidirect
244. C₂²×#386	C₂×D₄	semidirect
248. C₂²×#379	C₂×D₄	semidirect
258. #14673	C₂×D₄	semidirect
259. #14673	C₂×D₄	semidirect
260. #14673	C₂×D₄	semidirect
261. #14341	C₂×D₄	semidirect
262. #14341	C₂×D₄	semidirect
263. #14338	C₂×D₄	semidirect
264. #14338	C₂×D₄	semidirect
267. #14335	C₂×D₄	semidirect
268. #14335	C₂×D₄	semidirect
269. #14335	C₂×D₄	semidirect
270. #14127	C₂×D₄	semidirect
272. #13869	C₂×D₄	semidirect
273. #13869	C₂×D₄	semidirect
274. #13869	C₂×D₄	semidirect
284. #13867	C₂×D₄	semidirect
285. #13867	C₂×D₄	semidirect
286. #13867	C₂×D₄	semidirect
287. #13867	C₂×D₄	semidirect
288. #13867	C₂×D₄	semidirect
289. #13794	C₂×D₄	semidirect
290. #13775	C₂×D₄	semidirect
291. #13775	C₂×D₄	semidirect
292. C₂×C₂²⋊#95	C₂×D₄	semidirect
297. C₂⁷	H(5,𝔽₂)	semidirect
334. C₂⁵×C₄	H(5,𝔽₂)	semidirect
420. C₂×#379	H(5,𝔽₂)	semidirect
421. C₂×#379	H(5,𝔽₂)	semidirect
424. C₂⁶	B(4,𝔽₂)	semidirect
472. C₂×#120	B(4,𝔽₂)	semidirect
473. C₂²×C₂²⋊C₄	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
#72266267	2
#72266256	2
#72266216	2
#72266151	2
#72266150	2
#72266143	2
#72266141	2
#72266019	2
#72259040	2
#72258939	2
#72258840	2
#72258785	2
#72258662	2
#72236821	2
#72236800	2