Subgroups — #72266019

Order 2048.

At least 10136 conjugacy classes of subgroups; only the 1054 normal subgroups are shown.

The subgroup lattice has 456 nodes (normal subgroups only) — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#72266002	C₂	1	2	yes	maximal, complemented
2	#72265996	C₂	1	2	yes	maximal, complemented
3	#72265994	C₂	1	2	yes	maximal, complemented
4	#72251507	C₂	1	2	yes	maximal, complemented
5	#72241200	C₂	1	2	yes	maximal, complemented
6	#72241188	C₂	1	2	yes	maximal, complemented
7	#72240427	C₂	1	2	yes	maximal, complemented
8	#72240426	C₂	1	2	yes	maximal, complemented
9	#72240425	C₂	1	1	yes	maximal, characteristic, complemented
10	#72238594	C₂	1	2	yes	maximal, complemented
11	#72236815	C₂	1	1	yes	maximal, characteristic, complemented
12	#72236756	C₂	1	2	yes	maximal, complemented
13	C₂×#6628892	C₂	1	1	yes	maximal, characteristic, complemented
14	#72233780	C₂	1	1	yes	maximal, characteristic, complemented
15	#72232877	C₂	1	1	yes	maximal, characteristic, complemented
16	#72219457	C₂	1	1	yes	maximal, characteristic, complemented
17	#72219165	C₂	1	2	yes	maximal, complemented
18	#72219118	C₂	1	1	yes	maximal, characteristic, complemented
19	C₂×#245225	C₂	1	2	yes	maximal, complemented
20	C₂⁴×H(5,𝔽₂)	C₂²	1	1	yes	characteristic, complemented
21	C₂×#35346	C₂²	1	2	yes	—
22	C₂×#35346	C₂²	1	1	yes	characteristic, complemented
23	C₂×#35346	C₂²	1	1	yes	characteristic, complemented
24	C₂×#34980	C₂²	1	1	yes	characteristic
25	C₂×#34980	C₂²	1	2	yes	complemented
26	C₂²×#2403	C₂²	1	1	yes	characteristic
27	C₂×#32900	C₂²	1	2	yes	complemented
28	C₂×#32900	C₂²	1	2	yes	complemented
29	C₂×#32898	C₂²	1	2	yes	—
30	C₂×#32898	C₂²	1	2	yes	—
31	C₂×#32898	C₂²	1	2	yes	complemented
32	C₂×#32898	C₂²	1	2	yes	complemented
33	C₂×#32898	C₂²	1	4	yes	complemented
34	C₂²×#1781	C₂²	1	1	yes	characteristic, complemented
35	C₂²×#1781	C₂²	1	2	yes	complemented
36	#4928938	C₂²	1	2	yes	—
37	#4928938	C₂²	1	2	yes	complemented
38	#4928938	C₂²	1	1	yes	characteristic, complemented
39	#4453260	C₂²	1	1	yes	characteristic, complemented
40	#765934	C₂²	1	1	yes	characteristic, complemented
41	#763548	C₂²	1	1	yes	characteristic, complemented
42	#759288	C₂²	1	1	yes	characteristic, complemented
43	#635984	C₂²	1	1	yes	characteristic, complemented
44	#626258	C₂²	1	1	yes	characteristic, complemented
45	#617161	C₂²	1	1	yes	characteristic, complemented
46	#612424	C₂²	1	1	yes	characteristic
47	#612424	C₂²	1	2	yes	—
48	#612424	C₂²	1	2	yes	complemented
49	#612424	C₂²	1	2	yes	complemented
50	#554236	C₂²	1	1	yes	characteristic, complemented
51	#521311	C₂²	1	1	yes	characteristic, complemented
52	#517411	C₂²	1	1	yes	characteristic, complemented
53	#516323	C₂²	1	2	yes	complemented
54	#405104	C₂²	1	4	yes	complemented
55	#405104	C₂²	1	4	yes	complemented
56	#392125	C₂²	1	2	yes	complemented
57	#392125	C₂²	1	2	yes	complemented
58	#392109	C₂²	1	1	yes	characteristic, complemented
59	#392109	C₂²	1	2	yes	complemented
60	#382422	C₂²	1	2	yes	complemented
61	#379754	C₂²	1	4	yes	complemented
62	#359428	C₂²	1	2	yes	complemented
63	#359428	C₂²	1	2	yes	complemented
64	#359428	C₂²	1	2	yes	complemented
65	C₂×#10337	C₂²	1	4	yes	complemented
66	C₂×#10336	C₂²	1	4	yes	complemented
67	C₂×#10336	C₂²	1	4	yes	complemented
68	C₂×#9499	C₂²	1	2	yes	complemented
69	C₂×#9495	C₂²	1	4	yes	complemented
70	C₂×#9495	C₂²	1	2	yes	complemented
71	C₂×#9495	C₂²	1	2	yes	complemented
72	C₂×#8541	C₂²	1	2	yes	complemented
73	#119494	C₂²	1	2	yes	complemented
74	#116351	C₂²	1	4	yes	complemented
75	#115723	C₂²	1	4	yes	complemented
76	#115135	C₂²	1	2	yes	complemented
77	#115133	C₂²	1	4	yes	complemented
78	#115133	C₂²	1	2	yes	complemented
79	#115133	C₂²	1	2	yes	complemented
80	#111516	C₂²	1	2	yes	complemented
81	#111516	C₂²	1	2	yes	complemented
82	#111459	C₂²	1	4	yes	complemented
83	#111458	C₂²	1	4	yes	complemented
84	#111458	C₂²	1	4	yes	complemented
85	#111458	C₂²	1	4	yes	complemented
86	#110401	C₂²	1	4	yes	complemented
87	#106542	C₂²	1	2	yes	complemented
88	#106132	C₂²	1	2	yes	complemented
89	C₂²⋊#1304	C₂²	1	2	yes	complemented
90	C₂²⋊#1304	C₂²	1	2	yes	complemented
91	C₂³×H(5,𝔽₂)	C₂³	1	2	yes	—
92	C₂³×H(5,𝔽₂)	C₂³	1	2	yes	—
93	C₂³×H(5,𝔽₂)	C₂³	1	1	yes	characteristic, complemented
94	C₂⁵×D₄	D₄	1	1	yes	characteristic, complemented
95	C₂⁵×D₄	C₂³	1	1	yes	characteristic
96	C₂⁵×D₄	C₂³	1	2	yes	—
97	C₂²×#534	D₄	1	2	yes	complemented
98	C₂³×#120	D₄	1	1	yes	characteristic, complemented
99	C₂³×#120	C₂³	1	1	yes	characteristic
100	C₂³×#120	C₂³	1	1	yes	characteristic
101	C₂³×#120	C₂³	1	1	yes	characteristic
102	C₂³×#120	C₂³	1	1	yes	characteristic
103	C₂³×#120	C₂³	1	1	yes	characteristic
104	C₂×#2846	D₄	1	4	yes	complemented
105	C₂×#2405	D₄	1	2	yes	complemented
106	C₂×#2405	C₂³	1	1	yes	characteristic
107	C₂×#2405	C₂³	1	1	yes	characteristic
108	C₂×#2405	C₂³	1	4	yes	—
109	C₂×#2405	C₂³	1	1	yes	characteristic, complemented
110	C₂×#2403	D₄	1	2	yes	complemented
111	C₂×#2403	D₄	1	2	yes	complemented
112	C₂×#2403	D₄	1	2	yes	complemented
113	C₂×#2403	C₂³	1	1	yes	characteristic
114	C₂×#2403	C₂³	1	4	yes	—
115	C₂×#2403	C₂³	1	4	yes	—
116	C₂×#2403	C₂³	1	1	yes	characteristic
117	C₂×#2403	C₂³	1	1	yes	characteristic
118	C₂×#2403	C₂³	1	1	yes	characteristic
119	C₂×#2403	C₂³	1	4	yes	—
120	C₂×#2403	C₂³	1	4	yes	—
121	C₂×#2403	C₂³	1	1	yes	characteristic, complemented
122	C₂×#2403	C₂³	1	1	yes	characteristic, complemented
123	C₂²×#392	D₄	1	1	yes	characteristic, complemented
124	C₂²×#392	D₄	1	1	yes	characteristic, complemented
125	C₂²×#392	C₂³	1	1	yes	characteristic
126	C₂²×#392	C₂³	1	1	yes	characteristic
127	C₂×#2308	D₄	1	2	yes	complemented
128	C₂×#2308	C₂³	1	2	yes	—
129	C₂×#2308	C₂³	1	1	yes	characteristic, complemented
130	C₂×#2308	C₂³	1	1	yes	characteristic, complemented
131	C₂×#2308	C₂³	1	1	yes	characteristic, complemented
132	C₂×#2308	C₂³	1	1	yes	characteristic, complemented
133	C₂²×#386	D₄	1	1	yes	characteristic, complemented
134	C₂²×#386	D₄	1	1	yes	characteristic, complemented
135	C₂²×#386	D₄	1	1	yes	characteristic, complemented
136	C₂²×#386	C₂³	1	1	yes	characteristic
137	C₂²×#379	D₄	1	1	yes	characteristic, complemented
138	C₂²×#379	C₂³	1	2	yes	—
139	C₂²×#379	C₂³	1	1	yes	characteristic
140	#32898	D₄	1	16	yes	complemented
141	C₂×#1819	C₂³	1	4	yes	complemented
142	C₂×#1781	C₂³	1	4	yes	—
143	C₂×#1781	C₂³	1	2	yes	—
144	C₂×#1781	C₂³	1	2	yes	—
145	C₂×#1781	C₂³	1	4	yes	—
146	C₂×#1781	C₂³	1	4	yes	—
147	C₂×#1781	C₂³	1	2	yes	—
148	C₂×#1781	C₂³	1	4	yes	—
149	C₂×#1781	C₂³	1	2	yes	—
150	C₂×#1781	C₂³	1	4	yes	complemented
151	C₂×#1781	C₂³	1	4	yes	complemented
152	C₂×#1781	C₂³	1	4	yes	complemented
153	C₂×#1781	C₂³	1	4	yes	complemented
154	#14715	D₄	1	8	yes	complemented
155	#14694	D₄	1	4	yes	complemented
156	#14679	C₂³	1	2	yes	—
157	#14679	C₂³	1	2	yes	—
158	#14679	C₂³	1	1	yes	characteristic
159	#14338	C₂³	1	1	yes	characteristic, complemented
160	#14335	C₂³	1	2	yes	—
161	#14335	C₂³	1	1	yes	characteristic, complemented
162	#14127	C₂³	1	1	yes	characteristic, complemented
163	#13869	C₂³	1	1	yes	characteristic, complemented
164	#13867	D₄	1	2	yes	complemented
165	#13867	D₄	1	2	yes	complemented
166	#13867	C₂³	1	4	yes	—
167	#13867	C₂³	1	1	yes	characteristic
168	#13867	C₂³	1	1	yes	characteristic
169	#13867	C₂³	1	4	yes	—
170	#13867	C₂³	1	4	yes	—
171	#13867	C₂³	1	1	yes	characteristic, complemented
172	#13867	C₂³	1	1	yes	characteristic, complemented
173	#13867	C₂³	1	1	yes	characteristic, complemented
174	#13775	C₂³	1	1	yes	characteristic, complemented
175	#10725	C₂³	1	4	yes	complemented
176	#10725	C₂³	1	4	yes	complemented
177	#10725	C₂³	1	4	yes	complemented
178	C₂×#1304	C₂³	1	4	yes	complemented
179	C₂×#1304	C₂³	1	4	yes	complemented
180	C₂×#1304	C₂³	1	4	yes	complemented
181	C₂×#1304	C₂³	1	4	yes	complemented
182	C₂⁷	C₂×D₄	1	1	yes	characteristic
183	C₂⁷	C₂×D₄	1	1	yes	characteristic
184	C₂⁷	C₂×D₄	1	2	yes	complemented
185	C₂⁷	C₂⁴	1	1	yes	characteristic
186	C₂²×H(5,𝔽₂)	C₂×D₄	1	8	yes	—
187	C₂⁴×D₄	C₂×D₄	1	2	yes	—
188	C₂⁴×D₄	C₂×D₄	1	2	yes	—
189	C₂⁴×D₄	C₂×D₄	1	2	yes	—
190	C₂⁴×D₄	C₂×D₄	1	2	yes	—
191	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
192	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
193	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
194	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
195	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
196	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
197	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
198	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
199	C₂⁴×D₄	C₂×D₄	1	4	yes	complemented
200	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic, complemented
201	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic, complemented
202	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic, complemented
203	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic, complemented
204	C₂⁴×D₄	C₂⁴	1	1	yes	characteristic
205	C₂⁴×D₄	C₂⁴	1	1	yes	characteristic
206	C₂⁴×D₄	C₂⁴	1	1	yes	characteristic
207	C₂⁴×D₄	C₂⁴	1	4	yes	—
208	C₂⁴×D₄	C₂⁴	1	1	yes	characteristic
209	C₂⁴×D₄	C₂⁴	1	1	yes	characteristic
210	C₂⁴×D₄	C₂⁴	1	1	yes	characteristic
211	C₂⁵×C₄	C₂×D₄	1	1	yes	characteristic
212	C₂⁵×C₄	C₂×D₄	1	1	yes	characteristic
213	C₂⁵×C₄	C₂×D₄	1	2	yes	complemented
214	C₂²×#123	C₂×D₄	1	2	yes	—
215	C₂²×#123	C₂×D₄	1	2	yes	complemented
216	C₂²×#120	C₂×D₄	1	2	yes	—
217	C₂²×#120	C₂×D₄	1	2	yes	—
218	C₂²×#120	C₂×D₄	1	8	yes	—
219	C₂²×#120	C₂×D₄	1	4	yes	—
220	C₂²×#120	C₂×D₄	1	4	yes	—
221	C₂²×#120	C₂×D₄	1	2	yes	complemented
222	C₂²×#120	C₂×D₄	1	2	yes	complemented
223	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
224	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
225	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
226	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
227	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
228	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
229	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
230	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
231	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
232	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
233	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
234	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
235	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic, complemented
236	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic, complemented
237	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic, complemented
238	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic, complemented
239	C₂³×C₂²⋊C₄	C₂×D₄	1	2	yes	complemented
240	C₂³×C₂²⋊C₄	C₂⁴	1	1	yes	characteristic
241	C₂³×C₂²⋊C₄	C₂⁴	1	1	yes	characteristic
242	C₂³×C₂²⋊C₄	C₂⁴	1	1	yes	characteristic
243	C₂³×C₂²⋊C₄	C₂⁴	1	1	yes	characteristic
244	#2403	C₂×D₄	1	8	yes	—
245	#2403	C₂×D₄	1	16	yes	complemented
246	C₂×#386	C₂×D₄	1	2	yes	—
247	C₂×#386	C₂×D₄	1	2	yes	—
248	C₂×#386	C₂×D₄	1	8	yes	—
249	C₂×#386	C₂×D₄	1	2	yes	—
250	C₂×#386	C₂×D₄	1	2	yes	—
251	C₂×#386	C₂×D₄	1	2	yes	—
252	C₂×#386	C₂×D₄	1	2	yes	complemented
253	C₂×#386	C₂×D₄	1	2	yes	complemented
254	C₂×#386	C₂×D₄	1	2	yes	complemented
255	C₂×#386	C₂×D₄	1	2	yes	complemented
256	C₂×#386	C₂×D₄	1	2	yes	complemented
257	C₂×#379	C₂×D₄	1	2	yes	complemented
258	C₂×#379	C₂×D₄	1	2	yes	complemented
259	C₂×#379	C₂×D₄	1	2	yes	complemented
260	C₂×#379	C₂×D₄	1	8	yes	complemented
261	C₂×#379	C₂×D₄	1	4	yes	complemented
262	C₂×#379	C₂×D₄	1	4	yes	complemented
263	C₂×#379	C₂⁴	1	4	yes	—
264	C₂×#379	C₂⁴	1	4	yes	—
265	C₂×#379	C₂⁴	1	1	yes	characteristic
266	C₂×#379	C₂⁴	1	1	yes	characteristic
267	C₂×#379	C₂⁴	1	4	yes	—
268	C₂×#379	C₂⁴	1	1	yes	characteristic
269	C₂×#379	C₂⁴	1	1	yes	characteristic
270	C₂²×#95	C₂×D₄	1	1	yes	characteristic
271	C₂²×#95	C₂×D₄	1	1	yes	characteristic
272	C₂²×#95	C₂×D₄	1	1	yes	characteristic
273	C₂²×#95	C₂×D₄	1	1	yes	characteristic
274	#1781	C₂×D₄	1	8	yes	—
275	#1781	C₂×D₄	1	16	yes	complemented
276	C₂²⋊#95	C₂×D₄	1	8	yes	complemented
277	C₂⁶	#120	1	2	yes	—
278	C₂⁶	#120	1	2	yes	—
279	C₂⁶	C₂²×D₄	1	1	yes	characteristic
280	C₂⁶	C₂²×D₄	1	1	yes	characteristic
281	C₂⁶	C₂²×D₄	1	1	yes	characteristic
282	C₂⁶	C₂²×D₄	1	1	yes	characteristic
283	C₂⁶	C₂²×D₄	1	1	yes	characteristic
284	C₂⁶	C₂²×D₄	1	1	yes	characteristic
285	C₂⁶	C₂²×D₄	1	1	yes	characteristic
286	C₂⁶	C₂²×D₄	1	1	yes	characteristic
287	C₂⁶	C₂²×D₄	1	1	yes	characteristic
288	C₂⁶	C₂²×D₄	1	1	yes	characteristic
289	C₂⁶	C₂²×D₄	1	4	yes	—
290	C₂⁶	C₂²×D₄	1	1	yes	characteristic
291	C₂⁶	C₂²×D₄	1	2	yes	—
292	C₂⁶	C₂²×D₄	1	2	yes	—
293	C₂⁶	C₂²×D₄	1	1	yes	characteristic
294	C₂⁶	H(5,𝔽₂)	1	2	yes	—
295	C₂⁶	H(5,𝔽₂)	1	2	yes	—
296	C₂⁶	C₂⁵	1	1	yes	characteristic
297	C₂³×D₄	#120	1	2	yes	—
298	C₂³×D₄	#120	1	2	yes	—
299	C₂³×D₄	#120	1	2	yes	—
300	C₂³×D₄	#120	1	2	yes	—
301	C₂³×D₄	#120	1	2	yes	—
302	C₂³×D₄	#120	1	2	yes	—
303	C₂³×D₄	#120	1	4	yes	—
304	C₂³×D₄	C₂²×D₄	1	2	yes	—
305	C₂³×D₄	C₂²×D₄	1	2	yes	—
306	C₂³×D₄	C₂²×D₄	1	4	yes	—
307	C₂³×D₄	C₂²×D₄	1	2	yes	—
308	C₂³×D₄	C₂²×D₄	1	2	yes	—
309	C₂³×D₄	C₂²×D₄	1	4	yes	—
310	C₂³×D₄	C₂²×D₄	1	8	yes	—
311	C₂³×D₄	C₂²×D₄	1	4	yes	—
312	C₂³×D₄	H(5,𝔽₂)	1	8	yes	—
313	C₂³×D₄	H(5,𝔽₂)	1	4	yes	—
314	C₂⁴×C₄	#120	1	2	yes	—
315	C₂⁴×C₄	#120	1	2	yes	—
316	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
317	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
318	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
319	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
320	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
321	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
322	C₂⁴×C₄	C₂²×D₄	1	4	yes	—
323	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
324	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
325	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
326	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
327	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
328	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
329	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
330	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
331	C₂×#120	#120	1	8	yes	complemented
332	C₂²×C₂²⋊C₄	#120	1	4	yes	—
333	C₂²×C₂²⋊C₄	#120	1	2	yes	—
334	C₂²×C₂²⋊C₄	#120	1	2	yes	—
335	C₂²×C₂²⋊C₄	C₂²×D₄	1	2	yes	—
336	C₂²×C₂²⋊C₄	C₂²×D₄	1	2	yes	—
337	C₂²×C₂²⋊C₄	C₂²×D₄	1	2	yes	—
338	C₂²×C₂²⋊C₄	C₂²×D₄	1	8	yes	—
339	C₂²×C₂²⋊C₄	C₂²×D₄	1	4	yes	—
340	C₂²×C₂²⋊C₄	C₂²×D₄	1	2	yes	—
341	#386	#120	1	8	yes	complemented
342	#379	C₂²×D₄	1	8	yes	—
343	#379	C₂²×D₄	1	4	yes	—
344	C₂⁵	B(4,𝔽₂)	1	8	yes	complemented
345	C₂⁵	C₂×#120	1	1	yes	characteristic
346	C₂⁵	C₂×#120	1	1	yes	characteristic
347	C₂⁵	C₂×#120	1	2	yes	—
348	C₂⁵	C₂×#120	1	1	yes	characteristic
349	C₂⁵	C₂×#120	1	1	yes	characteristic
350	C₂⁵	C₂×#120	1	2	yes	—
351	C₂⁵	C₂×#120	1	2	yes	—
352	C₂⁵	C₂×#120	1	2	yes	—
353	C₂⁵	C₂×#120	1	1	yes	characteristic
354	C₂⁵	C₂×#120	1	1	yes	characteristic
355	C₂⁵	C₂×#120	1	2	yes	complemented
356	C₂⁵	#534	1	1	yes	characteristic
357	C₂⁵	#534	1	1	yes	characteristic
358	C₂⁵	#534	1	2	yes	—
359	C₂⁵	D₄²	1	2	yes	—
360	C₂⁵	D₄²	1	2	yes	—
361	C₂⁵	D₄²	1	2	yes	—
362	C₂⁵	D₄²	1	4	yes	—
363	C₂⁵	D₄²	1	2	yes	—
364	C₂⁵	D₄²	1	2	yes	—
365	C₂⁵	D₄²	1	2	yes	—
366	C₂⁵	D₄²	1	2	yes	—
367	C₂⁵	D₄²	1	8	yes	—
368	C₂⁵	D₄²	1	2	yes	—
369	C₂⁵	C₂³×D₄	1	1	yes	characteristic
370	C₂⁵	C₂³×D₄	1	1	yes	characteristic
371	C₂⁵	C₂³×D₄	1	2	yes	—
372	C₂⁵	C₂³×D₄	1	1	yes	characteristic
373	C₂⁵	C₂³×D₄	1	2	yes	—
374	C₂⁵	C₂×H(5,𝔽₂)	1	2	yes	—
375	C₂⁵	C₂×H(5,𝔽₂)	1	2	yes	—
376	C₂⁵	C₂×H(5,𝔽₂)	1	4	yes	—
377	C₂²×D₄	B(4,𝔽₂)	1	8	yes	complemented
378	C₂²×D₄	C₂×#120	1	4	yes	—
379	C₂²×D₄	#534	1	4	yes	—
380	C₂²×D₄	D₄²	1	8	yes	—
381	C₂³×C₄	C₂×#120	1	2	yes	—
382	C₂³×C₄	C₂×#120	1	2	yes	—
383	C₂³×C₄	C₂×#120	1	2	yes	—
384	C₂³×C₄	C₂×#120	1	2	yes	—
385	C₂³×C₄	C₂×#120	1	2	yes	—
386	C₂³×C₄	C₂×#120	1	2	yes	complemented
387	C₂³×C₄	D₄²	1	8	yes	—
388	C₂³×C₄	D₄²	1	4	yes	—
389	C₂×C₂²⋊C₄	C₂×#120	1	4	yes	complemented
390	C₂⁴	#2403	1	1	yes	characteristic
391	C₂⁴	#2403	1	2	yes	—
392	C₂⁴	#2403	1	1	yes	characteristic
393	C₂⁴	#2403	1	1	yes	characteristic
394	C₂⁴	#2403	1	1	yes	characteristic
395	C₂⁴	#2403	1	2	yes	—
396	C₂⁴	#2403	1	4	yes	—
397	C₂⁴	C₂×B(4,𝔽₂)	1	4	yes	—
398	C₂⁴	C₂×B(4,𝔽₂)	1	4	yes	—
399	C₂⁴	C₂×B(4,𝔽₂)	1	4	yes	—
400	C₂⁴	C₂×B(4,𝔽₂)	1	4	yes	—
401	C₂⁴	C₂×B(4,𝔽₂)	1	4	yes	—
402	C₂⁴	#3026	1	4	yes	complemented
403	C₂⁴	C₂²×#120	1	1	yes	characteristic
404	C₂⁴	C₂²×#120	1	1	yes	characteristic
405	C₂⁴	C₂²×#120	1	1	yes	characteristic
406	C₂⁴	C₂×#534	1	1	yes	characteristic
407	C₂⁴	C₂×#534	1	1	yes	characteristic
408	C₂⁴	C₂×D₄²	1	2	yes	—
409	C₂⁴	C₂×D₄²	1	2	yes	—
410	C₂⁴	C₂×D₄²	1	2	yes	—
411	C₂⁴	C₂×D₄²	1	2	yes	—
412	C₂⁴	C₂×D₄²	1	4	yes	—
413	C₂⁴	#3484	1	2	yes	—
414	C₂⁴	#3484	1	2	yes	—
415	C₂⁴	#3484	1	4	yes	—
416	C₂⁴	#3484	1	2	yes	—
417	C₂⁴	#3484	1	4	yes	—
418	C₂⁴	#3532	1	4	yes	—
419	C₂²×C₄	#2403	1	4	yes	—
420	C₂²×C₄	C₂×B(4,𝔽₂)	1	4	yes	—
421	C₂³	#23895	1	2	yes	—
422	C₂³	#23900	1	2	yes	—
423	C₂³	#23900	1	4	yes	—
424	C₂³	#23900	1	2	yes	—
425	C₂³	#23900	1	8	yes	—
426	C₂³	C₂×#2403	1	1	yes	characteristic
427	C₂³	C₂×#2403	1	1	yes	characteristic
428	C₂³	#35346	1	1	yes	characteristic
429	C₂³	D₄×#120	1	2	yes	—
430	C₂³	D₄×#120	1	2	yes	—
431	C₂³	#37644	1	2	yes	—
432	C₂³	#37644	1	2	yes	—
433	C₂³	#58990	1	4	yes	—
434	C₂³	C₂²×B(4,𝔽₂)	1	2	yes	—
435	C₂³	C₂²×B(4,𝔽₂)	1	2	yes	—
436	C₂³	C₂×#3026	1	2	yes	—
437	C₂³	#60399	1	2	yes	—
438	C₂²	#647656	1	1	yes	characteristic
439	C₂²	C₂×#23900	1	2	yes	—
440	C₂²	C₂×#23900	1	1	yes	characteristic
441	C₂²	C₂×#23900	1	1	yes	characteristic
442	C₂²	#6437621	1	1	yes	characteristic
443	C₂²	C₂×#23895	1	1	yes	characteristic
444	C₂²	#6437629	1	1	yes	characteristic
445	C₂²	#6437632	1	1	yes	characteristic
446	C₂²	#6499867	1	2	yes	—
447	C₂²	#6573715	1	4	yes	—
448	C₂	#72217546	1	1	yes	characteristic
449	C₂	#72225689	1	1	yes	characteristic
450	C₂	#72233042	1	1	yes	characteristic
451	C₂	#72233065	1	1	yes	characteristic
452	C₂	#72233069	1	1	yes	characteristic
453	C₂	#72236720	1	1	yes	characteristic
454	C₂	#72237496	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³	C₂×#2403
commutator, Frattini, cosocle	C₂⁶	C₂⁵
LCS	G ▷ C₂⁶ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³ ◁ C₂⁷ ◁ G
LECS	G ▷ C₂⁶ ▷ C₂² ▷ C₁

Complements

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

N	H ≅ G/N	type
1. #72266002	C₂	semidirect
2. #72265996	C₂	semidirect
3. #72265994	C₂	semidirect
4. #72251507	C₂	semidirect
5. #72241200	C₂	semidirect
6. #72241188	C₂	semidirect
7. #72240427	C₂	semidirect
8. #72240426	C₂	semidirect
9. #72240425	C₂	semidirect
10. #72238594	C₂	semidirect
11. #72236815	C₂	semidirect
12. #72236756	C₂	semidirect
13. C₂×#6628892	C₂	semidirect
14. #72233780	C₂	semidirect
15. #72232877	C₂	semidirect
16. #72219457	C₂	semidirect
17. #72219165	C₂	semidirect
18. #72219118	C₂	semidirect
19. C₂×#245225	C₂	semidirect
20. C₂⁴×H(5,𝔽₂)	C₂²	semidirect
22. C₂×#35346	C₂²	semidirect
23. C₂×#35346	C₂²	semidirect
25. C₂×#34980	C₂²	semidirect
27. C₂×#32900	C₂²	semidirect
28. C₂×#32900	C₂²	semidirect
31. C₂×#32898	C₂²	semidirect
32. C₂×#32898	C₂²	semidirect
33. C₂×#32898	C₂²	semidirect
34. C₂²×#1781	C₂²	semidirect
35. C₂²×#1781	C₂²	semidirect
37. #4928938	C₂²	semidirect
38. #4928938	C₂²	semidirect
39. #4453260	C₂²	semidirect
40. #765934	C₂²	semidirect
41. #763548	C₂²	semidirect
42. #759288	C₂²	semidirect
43. #635984	C₂²	semidirect
44. #626258	C₂²	semidirect
45. #617161	C₂²	semidirect
48. #612424	C₂²	semidirect
49. #612424	C₂²	semidirect
50. #554236	C₂²	semidirect
51. #521311	C₂²	semidirect
52. #517411	C₂²	semidirect
53. #516323	C₂²	semidirect
54. #405104	C₂²	semidirect
55. #405104	C₂²	semidirect
56. #392125	C₂²	semidirect
57. #392125	C₂²	semidirect
58. #392109	C₂²	semidirect
59. #392109	C₂²	semidirect
60. #382422	C₂²	semidirect
61. #379754	C₂²	semidirect
62. #359428	C₂²	semidirect
63. #359428	C₂²	semidirect
64. #359428	C₂²	semidirect
65. C₂×#10337	C₂²	semidirect
66. C₂×#10336	C₂²	semidirect
67. C₂×#10336	C₂²	semidirect
68. C₂×#9499	C₂²	semidirect
69. C₂×#9495	C₂²	semidirect
70. C₂×#9495	C₂²	semidirect
71. C₂×#9495	C₂²	semidirect
72. C₂×#8541	C₂²	semidirect
73. #119494	C₂²	semidirect
74. #116351	C₂²	semidirect
75. #115723	C₂²	semidirect
76. #115135	C₂²	semidirect
77. #115133	C₂²	semidirect
78. #115133	C₂²	semidirect
79. #115133	C₂²	semidirect
80. #111516	C₂²	semidirect
81. #111516	C₂²	semidirect
82. #111459	C₂²	semidirect
83. #111458	C₂²	semidirect
84. #111458	C₂²	semidirect
85. #111458	C₂²	semidirect
86. #110401	C₂²	semidirect
87. #106542	C₂²	semidirect
88. #106132	C₂²	semidirect
89. C₂²⋊#1304	C₂²	semidirect
90. C₂²⋊#1304	C₂²	semidirect
93. C₂³×H(5,𝔽₂)	C₂³	semidirect
94. C₂⁵×D₄	D₄	semidirect
97. C₂²×#534	D₄	semidirect
98. C₂³×#120	D₄	semidirect
104. C₂×#2846	D₄	semidirect
105. C₂×#2405	D₄	semidirect
109. C₂×#2405	C₂³	semidirect
110. C₂×#2403	D₄	semidirect
111. C₂×#2403	D₄	semidirect
112. C₂×#2403	D₄	semidirect
121. C₂×#2403	C₂³	semidirect
122. C₂×#2403	C₂³	semidirect
123. C₂²×#392	D₄	semidirect
124. C₂²×#392	D₄	semidirect
127. C₂×#2308	D₄	semidirect
129. C₂×#2308	C₂³	semidirect
130. C₂×#2308	C₂³	semidirect
131. C₂×#2308	C₂³	semidirect
132. C₂×#2308	C₂³	semidirect
133. C₂²×#386	D₄	semidirect
134. C₂²×#386	D₄	semidirect
135. C₂²×#386	D₄	semidirect
137. C₂²×#379	D₄	semidirect
140. #32898	D₄	semidirect
141. C₂×#1819	C₂³	semidirect
150. C₂×#1781	C₂³	semidirect
151. C₂×#1781	C₂³	semidirect
152. C₂×#1781	C₂³	semidirect
153. C₂×#1781	C₂³	semidirect
154. #14715	D₄	semidirect
155. #14694	D₄	semidirect
159. #14338	C₂³	semidirect
161. #14335	C₂³	semidirect
162. #14127	C₂³	semidirect
163. #13869	C₂³	semidirect
164. #13867	D₄	semidirect
165. #13867	D₄	semidirect
171. #13867	C₂³	semidirect
172. #13867	C₂³	semidirect
173. #13867	C₂³	semidirect
174. #13775	C₂³	semidirect
175. #10725	C₂³	semidirect
176. #10725	C₂³	semidirect
177. #10725	C₂³	semidirect
178. C₂×#1304	C₂³	semidirect
179. C₂×#1304	C₂³	semidirect
180. C₂×#1304	C₂³	semidirect
181. C₂×#1304	C₂³	semidirect
184. C₂⁷	C₂×D₄	semidirect
199. C₂⁴×D₄	C₂×D₄	semidirect
200. C₂⁴×D₄	C₂×D₄	semidirect
201. C₂⁴×D₄	C₂×D₄	semidirect
202. C₂⁴×D₄	C₂×D₄	semidirect
203. C₂⁴×D₄	C₂×D₄	semidirect
213. C₂⁵×C₄	C₂×D₄	semidirect
215. C₂²×#123	C₂×D₄	semidirect
221. C₂²×#120	C₂×D₄	semidirect
222. C₂²×#120	C₂×D₄	semidirect
235. C₂³×C₂²⋊C₄	C₂×D₄	semidirect
236. C₂³×C₂²⋊C₄	C₂×D₄	semidirect
237. C₂³×C₂²⋊C₄	C₂×D₄	semidirect
238. C₂³×C₂²⋊C₄	C₂×D₄	semidirect
239. C₂³×C₂²⋊C₄	C₂×D₄	semidirect
245. #2403	C₂×D₄	semidirect
252. C₂×#386	C₂×D₄	semidirect
253. C₂×#386	C₂×D₄	semidirect
254. C₂×#386	C₂×D₄	semidirect
255. C₂×#386	C₂×D₄	semidirect
256. C₂×#386	C₂×D₄	semidirect
257. C₂×#379	C₂×D₄	semidirect
258. C₂×#379	C₂×D₄	semidirect
259. C₂×#379	C₂×D₄	semidirect
260. C₂×#379	C₂×D₄	semidirect
261. C₂×#379	C₂×D₄	semidirect
262. C₂×#379	C₂×D₄	semidirect
275. #1781	C₂×D₄	semidirect
276. C₂²⋊#95	C₂×D₄	semidirect
331. C₂×#120	#120	semidirect
341. #386	#120	semidirect
344. C₂⁵	B(4,𝔽₂)	semidirect
355. C₂⁵	C₂×#120	semidirect
377. C₂²×D₄	B(4,𝔽₂)	semidirect
386. C₂³×C₄	C₂×#120	semidirect
389. C₂×C₂²⋊C₄	C₂×#120	semidirect
402. C₂⁴	#3026	semidirect

Maximal subgroups

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

subgroup	index
#72266002	2
#72265996	2
#72265994	2
#72251507	2
#72241200	2
#72241188	2
#72240427	2
#72240426	2
#72240425	2
#72238594	2
#72236815	2
#72236756	2
C₂×#6628892	2
#72233780	2
#72232877	2
#72219457	2
#72219165	2
#72219118	2
C₂×#245225	2