Subgroups — #72266149

Order 2048.

At least 6508 conjugacy classes of subgroups; only the 1804 normal subgroups are shown.

The subgroup lattice has 541 nodes (normal subgroups only) — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#72266148	C₂	1	2	yes	maximal, complemented
2	#72266147	C₂	1	2	yes	maximal, complemented
3	#72266146	C₂	1	4	yes	maximal, complemented
4	#72255630	C₂	1	2	yes	maximal, complemented
5	#72241175	C₂	1	4	yes	maximal, complemented
6	#72241167	C₂	1	2	yes	maximal, complemented
7	C₂×#213828	C₂	1	2	yes	maximal, complemented
8	#72240425	C₂	1	4	yes	maximal, complemented
9	C₂×#6370693	C₂	1	1	yes	maximal, characteristic, complemented
10	#72236764	C₂	1	4	yes	maximal, complemented
11	#72233780	C₂	1	1	yes	maximal, characteristic
12	#72225783	C₂	1	1	yes	maximal, characteristic, complemented
13	#72219457	C₂	1	2	yes	maximal, complemented
14	C₂⁴×H(5,𝔽₂)	C₂²	1	1	yes	characteristic
15	C₂×#35346	C₄	1	2	yes	complemented
16	C₂×#35346	C₂²	1	1	yes	characteristic
17	C₂×#35346	C₂²	1	1	yes	characteristic
18	C₂²×#2403	C₄	1	2	yes	complemented
19	C₂²×#2403	C₂²	1	1	yes	characteristic
20	C₂×#34171	C₂²	1	2	yes	complemented
21	C₂×#20586	C₂²	1	2	yes	—
22	C₂×#20586	C₂²	1	2	yes	complemented
23	C₂×#20585	C₂²	1	2	yes	—
24	C₂×#20585	C₂²	1	2	yes	—
25	C₂×#20585	C₂²	1	2	yes	complemented
26	C₂×#20585	C₂²	1	2	yes	complemented
27	C₂²×#1781	C₂²	1	2	yes	—
28	C₂²×#1781	C₂²	1	2	yes	complemented
29	#4928938	C₄	1	4	yes	complemented
30	#4928938	C₂²	1	2	yes	—
31	#4928938	C₂²	1	2	yes	—
32	#613188	C₄	1	4	yes	complemented
33	#612424	C₂²	1	2	yes	—
34	#612424	C₂²	1	2	yes	—
35	#517411	C₄	1	2	yes	complemented
36	#517411	C₂²	1	1	yes	characteristic
37	#517411	C₂²	1	2	yes	complemented
38	#516323	C₄	1	2	yes	complemented
39	#516323	C₂²	1	1	yes	characteristic
40	#516323	C₂²	1	1	yes	characteristic
41	#392111	C₂²	1	2	yes	—
42	#392111	C₂²	1	2	yes	complemented
43	#392109	C₂²	1	2	yes	—
44	#392109	C₂²	1	2	yes	complemented
45	#359428	C₂²	1	8	yes	complemented
46	C₂×#9497	C₂²	1	8	yes	complemented
47	C₂×#9495	C₂²	1	8	yes	complemented
48	C₂×#9495	C₂²	1	8	yes	complemented
49	C₂×#8746	C₂²	1	4	yes	complemented
50	C₂×#8541	C₂²	1	4	yes	complemented
51	#119494	C₂²	1	8	yes	complemented
52	#119484	C₂²	1	8	yes	complemented
53	#115133	C₂²	1	8	yes	complemented
54	#111516	C₂²	1	8	yes	complemented
55	#106543	C₂²	1	8	yes	complemented
56	#106542	C₂²	1	8	yes	complemented
57	#106542	C₂²	1	8	yes	complemented
58	#106132	C₂²	1	4	yes	complemented
59	#105808	C₂²	1	4	yes	complemented
60	C₂²⋊#1304	C₂²	1	8	yes	complemented
61	C₂³×H(5,𝔽₂)	C₂×C₄	1	2	yes	—
62	C₂³×H(5,𝔽₂)	C₂×C₄	1	2	yes	—
63	C₂³×H(5,𝔽₂)	D₄	1	2	yes	—
64	C₂³×H(5,𝔽₂)	D₄	1	2	yes	—
65	C₂³×H(5,𝔽₂)	D₄	1	2	yes	—
66	C₂³×H(5,𝔽₂)	D₄	1	2	yes	—
67	C₂³×H(5,𝔽₂)	C₂³	1	1	yes	characteristic
68	C₂³×H(5,𝔽₂)	C₂³	1	1	yes	characteristic
69	C₂³×H(5,𝔽₂)	C₂³	1	1	yes	characteristic
70	C₂³×H(5,𝔽₂)	C₂³	1	1	yes	characteristic
71	C₂⁴×#41	C₂×C₄	1	2	yes	—
72	C₂⁴×#41	D₄	1	2	yes	—
73	C₂⁴×#41	D₄	1	2	yes	—
74	C₂⁵×D₄	C₂×C₄	1	2	yes	—
75	C₂⁵×D₄	C₂×C₄	1	1	yes	characteristic, complemented
76	C₂⁵×D₄	D₄	1	2	yes	—
77	C₂⁵×D₄	D₄	1	2	yes	—
78	C₂⁵×D₄	C₂³	1	1	yes	characteristic
79	C₂⁵×D₄	C₂³	1	1	yes	characteristic
80	C₂⁵×D₄	C₂³	1	1	yes	characteristic
81	C₂³×#120	C₂×C₄	1	2	yes	complemented
82	C₂³×#120	C₂×C₄	1	2	yes	complemented
83	C₂³×#120	C₂×C₄	1	1	yes	characteristic, complemented
84	C₂³×#120	C₂³	1	2	yes	—
85	C₂³×#120	C₂³	1	1	yes	characteristic
86	C₂×#2404	C₂×C₄	1	4	yes	complemented
87	C₂×#2404	C₂×C₄	1	4	yes	complemented
88	C₂×#2404	C₂×C₄	1	4	yes	complemented
89	C₂×#2404	C₂×C₄	1	4	yes	complemented
90	C₂×#2403	C₂×C₄	1	4	yes	complemented
91	C₂×#2403	C₂×C₄	1	4	yes	complemented
92	C₂×#2403	C₂×C₄	1	4	yes	complemented
93	C₂×#2403	C₂×C₄	1	4	yes	complemented
94	C₂×#2403	C₂×C₄	1	4	yes	complemented
95	C₂×#2403	C₂×C₄	1	4	yes	complemented
96	C₂×#2403	C₂³	1	2	yes	—
97	C₂×#2403	C₂³	1	2	yes	—
98	C₂×#2403	C₂³	1	2	yes	—
99	C₂×#2403	C₂³	1	2	yes	—
100	C₂²×#392	C₂×C₄	1	2	yes	complemented
101	C₂²×#392	C₂³	1	2	yes	—
102	C₂×#2309	C₂³	1	4	yes	—
103	C₂×#2308	C₂×C₄	1	2	yes	complemented
104	C₂×#2308	C₂×C₄	1	2	yes	complemented
105	C₂×#2308	C₂×C₄	1	2	yes	complemented
106	C₂×#2308	C₂×C₄	1	2	yes	complemented
107	C₂×#2308	C₂×C₄	1	2	yes	complemented
108	C₂×#2308	C₂³	1	1	yes	characteristic
109	C₂×#2308	C₂³	1	4	yes	—
110	C₂×#2308	C₂³	1	4	yes	—
111	C₂×#2308	C₂³	1	1	yes	characteristic
112	C₂²×#386	C₂×C₄	1	2	yes	complemented
113	C₂²×#386	C₂×C₄	1	2	yes	complemented
114	C₂²×#386	C₂×C₄	1	2	yes	complemented
115	C₂²×#386	C₂×C₄	1	1	yes	characteristic, complemented
116	C₂²×#386	C₂³	1	1	yes	characteristic
117	C₂²×#379	C₂×C₄	1	2	yes	complemented
118	C₂²×#379	C₂×C₄	1	1	yes	characteristic, complemented
119	C₂²×#379	C₂³	1	4	yes	—
120	#20585	D₄	1	16	yes	complemented
121	C₂×#1781	C₂³	1	4	yes	—
122	C₂×#1781	C₂³	1	4	yes	—
123	C₂×#1781	C₂³	1	4	yes	—
124	C₂×#1781	C₂³	1	4	yes	—
125	C₂×#1781	C₂³	1	4	yes	—
126	C₂×#1781	C₂³	1	4	yes	—
127	C₂×#1781	C₂³	1	4	yes	—
128	C₂×#1781	C₂³	1	4	yes	—
129	C₂×#1781	C₂³	1	16	yes	complemented
130	#14681	C₂×C₄	1	2	yes	complemented
131	#14679	C₂³	1	4	yes	—
132	#14679	C₂³	1	2	yes	—
133	#14335	C₂×C₄	1	2	yes	complemented
134	#14335	C₂³	1	2	yes	—
135	#14335	C₂³	1	4	yes	—
136	#13956	C₂×C₄	1	4	yes	complemented
137	#13956	C₂×C₄	1	4	yes	complemented
138	#13956	C₂×C₄	1	4	yes	complemented
139	#13956	C₂×C₄	1	4	yes	complemented
140	#13867	C₂×C₄	1	4	yes	complemented
141	#13867	C₂×C₄	1	4	yes	complemented
142	#13867	C₂×C₄	1	4	yes	complemented
143	#13867	C₂×C₄	1	4	yes	complemented
144	#13867	C₂×C₄	1	4	yes	complemented
145	#13867	C₂×C₄	1	4	yes	complemented
146	#13867	C₂³	1	2	yes	—
147	#13867	C₂³	1	2	yes	—
148	#13867	C₂³	1	2	yes	—
149	#13867	C₂³	1	2	yes	—
150	#10725	C₂³	1	16	yes	complemented
151	C₂×#1304	C₂³	1	16	yes	complemented
152	C₂×#1304	C₂³	1	16	yes	complemented
153	C₂⁷	C₂²⋊C₄	1	2	yes	—
154	C₂⁷	C₂²×C₄	1	1	yes	characteristic
155	C₂⁷	C₂²×C₄	1	1	yes	characteristic
156	C₂⁷	C₂×D₄	1	1	yes	characteristic
157	C₂⁷	C₂×D₄	1	1	yes	characteristic
158	C₂⁷	C₂⁴	1	1	yes	characteristic
159	C₂²×H(5,𝔽₂)	C₂×D₄	1	8	yes	—
160	C₂²×H(5,𝔽₂)	#41	1	8	yes	—
161	C₂³×#41	C₂²⋊C₄	1	2	yes	—
162	C₂³×#41	C₂²⋊C₄	1	2	yes	—
163	C₂³×#41	C₂²⋊C₄	1	2	yes	—
164	C₂³×#41	C₂²⋊C₄	1	2	yes	—
165	C₂³×#41	C₂²⋊C₄	1	2	yes	—
166	C₂³×#41	C₂²⋊C₄	1	2	yes	—
167	C₂³×#41	C₂²⋊C₄	1	2	yes	—
168	C₂³×#41	C₂²⋊C₄	1	2	yes	—
169	C₂³×#41	C₂²⋊C₄	1	2	yes	—
170	C₂³×#41	C₂²⋊C₄	1	2	yes	—
171	C₂³×#41	C₂²⋊C₄	1	2	yes	—
172	C₂³×#41	C₂²⋊C₄	1	2	yes	—
173	C₂³×#41	C₂²×C₄	1	2	yes	—
174	C₂³×#41	C₂²×C₄	1	2	yes	—
175	C₂³×#41	C₂²×C₄	1	2	yes	—
176	C₂³×#41	C₂²×C₄	1	2	yes	—
177	C₂³×#41	C₂×D₄	1	2	yes	—
178	C₂³×#41	C₂×D₄	1	2	yes	—
179	C₂³×#41	C₂×D₄	1	2	yes	—
180	C₂³×#41	C₂×D₄	1	2	yes	—
181	C₂³×#41	C₂×D₄	1	2	yes	—
182	C₂³×#41	C₂×D₄	1	2	yes	—
183	C₂³×#41	C₂×D₄	1	2	yes	—
184	C₂³×#41	C₂×D₄	1	2	yes	—
185	C₂⁴×Q₈	C₂²⋊C₄	1	2	yes	—
186	C₂⁴×D₄	C₂²⋊C₄	1	2	yes	—
187	C₂⁴×D₄	C₂²⋊C₄	1	2	yes	—
188	C₂⁴×D₄	C₂²⋊C₄	1	2	yes	—
189	C₂⁴×D₄	C₂²⋊C₄	1	2	yes	—
190	C₂⁴×D₄	C₂²⋊C₄	1	2	yes	—
191	C₂⁴×D₄	C₂²⋊C₄	1	2	yes	—
192	C₂⁴×D₄	C₂²⋊C₄	1	2	yes	—
193	C₂⁴×D₄	C₂²⋊C₄	1	2	yes	—
194	C₂⁴×D₄	C₂²⋊C₄	1	2	yes	—
195	C₂⁴×D₄	C₂²⋊C₄	1	2	yes	—
196	C₂⁴×D₄	C₂²⋊C₄	1	2	yes	—
197	C₂⁴×D₄	C₂²⋊C₄	1	2	yes	—
198	C₂⁴×D₄	C₂²⋊C₄	1	2	yes	—
199	C₂⁴×D₄	C₂²⋊C₄	1	2	yes	—
200	C₂⁴×D₄	C₂²⋊C₄	1	2	yes	—
201	C₂⁴×D₄	C₂²×C₄	1	2	yes	—
202	C₂⁴×D₄	C₂²×C₄	1	2	yes	—
203	C₂⁴×D₄	C₂²×C₄	1	2	yes	—
204	C₂⁴×D₄	C₂²×C₄	1	2	yes	—
205	C₂⁴×D₄	C₂²×C₄	1	2	yes	—
206	C₂⁴×D₄	C₂²×C₄	1	2	yes	—
207	C₂⁴×D₄	C₂²×C₄	1	2	yes	—
208	C₂⁴×D₄	C₂²×C₄	1	2	yes	—
209	C₂⁴×D₄	C₂²×C₄	1	1	yes	characteristic
210	C₂⁴×D₄	C₂²×C₄	1	1	yes	characteristic
211	C₂⁴×D₄	C₂²×C₄	1	2	yes	—
212	C₂⁴×D₄	C₂²×C₄	1	2	yes	—
213	C₂⁴×D₄	C₂²×C₄	1	2	yes	—
214	C₂⁴×D₄	C₂×D₄	1	2	yes	—
215	C₂⁴×D₄	C₂×D₄	1	2	yes	—
216	C₂⁴×D₄	C₂×D₄	1	2	yes	—
217	C₂⁴×D₄	C₂×D₄	1	2	yes	—
218	C₂⁴×D₄	C₂×D₄	1	2	yes	—
219	C₂⁴×D₄	C₂×D₄	1	2	yes	—
220	C₂⁴×D₄	C₂×D₄	1	2	yes	—
221	C₂⁴×D₄	C₂×D₄	1	2	yes	—
222	C₂⁴×D₄	C₂×D₄	1	2	yes	—
223	C₂⁴×D₄	C₂×D₄	1	2	yes	—
224	C₂⁴×D₄	C₂×D₄	1	2	yes	—
225	C₂⁴×D₄	C₂×D₄	1	2	yes	—
226	C₂⁴×D₄	C₂×D₄	1	2	yes	—
227	C₂⁴×D₄	C₂×D₄	1	2	yes	—
228	C₂⁴×D₄	C₂×D₄	1	2	yes	—
229	C₂⁴×D₄	C₂×D₄	1	2	yes	—
230	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
231	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
232	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
233	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
234	C₂⁴×D₄	C₂⁴	1	2	yes	—
235	C₂⁴×D₄	C₂⁴	1	1	yes	characteristic
236	C₂⁴×D₄	C₂⁴	1	1	yes	characteristic
237	C₂⁴×D₄	C₂⁴	1	1	yes	characteristic
238	C₂⁴×D₄	C₂⁴	1	1	yes	characteristic
239	C₂⁴×D₄	C₂⁴	1	1	yes	characteristic
240	C₂⁴×D₄	C₂⁴	1	1	yes	characteristic
241	C₂⁵×C₄	C₂²⋊C₄	1	2	yes	—
242	C₂⁵×C₄	C₂²⋊C₄	1	2	yes	—
243	C₂⁵×C₄	C₂²⋊C₄	1	2	yes	—
244	C₂⁵×C₄	C₂²×C₄	1	1	yes	characteristic
245	C₂⁵×C₄	C₂²×C₄	1	1	yes	characteristic
246	C₂⁵×C₄	C₂×D₄	1	1	yes	characteristic
247	C₂⁵×C₄	C₂×D₄	1	1	yes	characteristic
248	C₂²×#120	C₂²×C₄	1	4	yes	—
249	C₂²×#120	C₂²×C₄	1	4	yes	—
250	C₂²×#120	C₂²×C₄	1	4	yes	—
251	C₂²×#120	C₂²×C₄	1	4	yes	—
252	C₂³×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
253	C₂³×C₂²⋊C₄	C₂²×C₄	1	1	yes	characteristic
254	C₂³×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
255	C₂³×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
256	C₂³×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
257	C₂³×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
258	C₂³×C₂²⋊C₄	C₂²×C₄	1	1	yes	characteristic
259	C₂³×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
260	C₂³×C₂²⋊C₄	C₂²×C₄	1	2	yes	—
261	C₂³×C₂²⋊C₄	C₂⁴	1	2	yes	—
262	#2308	C₂×D₄	1	16	yes	complemented
263	C₂×#386	C₂²×C₄	1	4	yes	—
264	C₂×#386	C₂²×C₄	1	4	yes	—
265	C₂×#386	C₂²×C₄	1	4	yes	—
266	C₂×#386	C₂²×C₄	1	4	yes	—
267	C₂×#386	C₂²×C₄	1	4	yes	—
268	C₂×#386	C₂²×C₄	1	4	yes	—
269	C₂×#386	C₂²×C₄	1	4	yes	—
270	C₂×#386	C₂²×C₄	1	4	yes	—
271	C₂×#386	C₂²×C₄	1	4	yes	—
272	C₂×#386	C₂²×C₄	1	4	yes	—
273	C₂×#386	C₂²×C₄	1	4	yes	—
274	C₂×#386	C₂²×C₄	1	4	yes	—
275	C₂×#381	C₂²×C₄	1	2	yes	—
276	C₂×#381	C₂²×C₄	1	4	yes	—
277	C₂×#381	C₂²×C₄	1	2	yes	—
278	C₂×#379	C₂²×C₄	1	4	yes	—
279	C₂×#379	C₂²×C₄	1	4	yes	—
280	C₂×#379	C₂²×C₄	1	4	yes	—
281	C₂×#379	C₂⁴	1	8	yes	—
282	C₂×#379	C₂⁴	1	8	yes	—
283	C₂×#379	C₂⁴	1	2	yes	—
284	C₂×#379	C₂⁴	1	2	yes	—
285	C₂²×#95	C₂²×C₄	1	2	yes	—
286	C₂²×#95	C₂²×C₄	1	2	yes	—
287	#1781	C₂×D₄	1	16	yes	—
288	#1781	C₂×D₄	1	16	yes	complemented
289	C₂⁶	C₂×C₂²⋊C₄	1	2	yes	—
290	C₂⁶	C₂×C₂²⋊C₄	1	2	yes	—
291	C₂⁶	C₂×C₂²⋊C₄	1	2	yes	—
292	C₂⁶	C₂×C₂²⋊C₄	1	2	yes	—
293	C₂⁶	C₂×C₂²⋊C₄	1	2	yes	—
294	C₂⁶	C₂×C₂²⋊C₄	1	2	yes	—
295	C₂⁶	C₂×C₂²⋊C₄	1	2	yes	—
296	C₂⁶	C₂×C₂²⋊C₄	1	2	yes	—
297	C₂⁶	C₂×C₂²⋊C₄	1	2	yes	—
298	C₂⁶	C₂×C₂²⋊C₄	1	2	yes	—
299	C₂⁶	C₂³×C₄	1	1	yes	characteristic
300	C₂⁶	C₂³×C₄	1	1	yes	characteristic
301	C₂⁶	C₂³×C₄	1	1	yes	characteristic
302	C₂⁶	C₂³×C₄	1	1	yes	characteristic
303	C₂⁶	C₂³×C₄	1	2	yes	—
304	C₂⁶	C₂²×D₄	1	1	yes	characteristic
305	C₂⁶	C₂²×D₄	1	1	yes	characteristic
306	C₂⁶	C₂²×D₄	1	1	yes	characteristic
307	C₂⁶	C₂²×D₄	1	1	yes	characteristic
308	C₂⁶	C₂²×D₄	1	1	yes	characteristic
309	C₂⁶	C₂²×D₄	1	1	yes	characteristic
310	C₂⁶	C₂²×D₄	1	1	yes	characteristic
311	C₂⁶	C₂²×D₄	1	1	yes	characteristic
312	C₂⁶	H(5,𝔽₂)	1	8	yes	—
313	C₂⁶	C₂⁵	1	1	yes	characteristic
314	C₂²×#41	C₄×D₄	1	16	yes	—
315	C₂²×#41	#120	1	8	yes	—
316	C₂²×#41	#121	1	16	yes	—
317	C₂²×#41	#123	1	8	yes	—
318	C₂³×Q₈	C₂×C₂²⋊C₄	1	2	yes	—
319	C₂³×Q₈	C₂×C₂²⋊C₄	1	2	yes	—
320	C₂³×Q₈	C₂×C₂²⋊C₄	1	2	yes	—
321	C₂³×Q₈	C₂×C₂²⋊C₄	1	2	yes	—
322	C₂³×D₄	#99	1	16	yes	complemented
323	C₂³×D₄	#99	1	16	yes	complemented
324	C₂³×D₄	C₂×C₂²⋊C₄	1	2	yes	—
325	C₂³×D₄	C₂×C₂²⋊C₄	1	2	yes	—
326	C₂³×D₄	C₂×C₂²⋊C₄	1	2	yes	—
327	C₂³×D₄	C₂×C₂²⋊C₄	1	2	yes	—
328	C₂³×D₄	C₂×C₂²⋊C₄	1	2	yes	—
329	C₂³×D₄	C₂×C₂²⋊C₄	1	2	yes	—
330	C₂³×D₄	C₂×C₂²⋊C₄	1	2	yes	—
331	C₂³×D₄	C₂×C₂²⋊C₄	1	2	yes	—
332	C₂³×D₄	C₂×C₂²⋊C₄	1	2	yes	—
333	C₂³×D₄	C₂×C₂²⋊C₄	1	2	yes	—
334	C₂³×D₄	C₂×C₂²⋊C₄	1	2	yes	—
335	C₂³×D₄	C₂×C₂²⋊C₄	1	2	yes	—
336	C₂³×D₄	C₂×C₂²⋊C₄	1	2	yes	—
337	C₂³×D₄	C₂×C₂²⋊C₄	1	2	yes	—
338	C₂³×D₄	C₂×C₂²⋊C₄	1	2	yes	—
339	C₂³×D₄	C₂×C₂²⋊C₄	1	2	yes	—
340	C₂³×D₄	C₂×C₂²⋊C₄	1	2	yes	—
341	C₂³×D₄	C₂×C₂²⋊C₄	1	2	yes	—
342	C₂³×D₄	C₂×C₂²⋊C₄	1	2	yes	—
343	C₂³×D₄	C₂×C₂²⋊C₄	1	2	yes	—
344	C₂³×D₄	C₂×C₂²⋊C₄	1	2	yes	—
345	C₂³×D₄	C₂×C₂²⋊C₄	1	2	yes	—
346	C₂³×D₄	C₂×C₂²⋊C₄	1	2	yes	—
347	C₂³×D₄	C₂×C₂²⋊C₄	1	2	yes	—
348	C₂³×D₄	C₄×D₄	1	16	yes	—
349	C₂³×D₄	#120	1	8	yes	—
350	C₂³×D₄	#121	1	16	yes	—
351	C₂³×D₄	#123	1	8	yes	—
352	C₂³×D₄	C₂³×C₄	1	2	yes	—
353	C₂³×D₄	C₂³×C₄	1	2	yes	—
354	C₂³×D₄	C₂³×C₄	1	2	yes	—
355	C₂³×D₄	C₂³×C₄	1	2	yes	—
356	C₂³×D₄	C₂²×D₄	1	2	yes	—
357	C₂³×D₄	C₂²×D₄	1	2	yes	—
358	C₂³×D₄	C₂²×D₄	1	2	yes	—
359	C₂³×D₄	C₂²×D₄	1	2	yes	—
360	C₂³×D₄	C₂²×D₄	1	2	yes	—
361	C₂³×D₄	C₂²×D₄	1	2	yes	—
362	C₂³×D₄	C₂²×D₄	1	2	yes	—
363	C₂³×D₄	C₂²×D₄	1	2	yes	—
364	C₂³×D₄	C₂²×D₄	1	4	yes	—
365	C₂³×D₄	C₂²×D₄	1	4	yes	—
366	C₂³×D₄	C₂²×D₄	1	4	yes	—
367	C₂³×D₄	C₂×#41	1	4	yes	—
368	C₂³×D₄	C₂×#41	1	4	yes	—
369	C₂³×D₄	C₂×#41	1	4	yes	—
370	C₂³×D₄	H(5,𝔽₂)	1	8	yes	—
371	C₂⁴×C₄	C₂×C₂²⋊C₄	1	2	yes	—
372	C₂⁴×C₄	C₂×C₂²⋊C₄	1	2	yes	—
373	C₂⁴×C₄	C₂×C₂²⋊C₄	1	2	yes	—
374	C₂⁴×C₄	C₂×C₂²⋊C₄	1	2	yes	—
375	C₂⁴×C₄	C₂×C₂²⋊C₄	1	2	yes	—
376	C₂⁴×C₄	C₂×C₂²⋊C₄	1	2	yes	—
377	C₂⁴×C₄	C₂×C₂²⋊C₄	1	2	yes	—
378	C₂⁴×C₄	C₂×C₂²⋊C₄	1	2	yes	—
379	C₂⁴×C₄	C₂×C₂²⋊C₄	1	2	yes	—
380	C₂⁴×C₄	C₂×C₂²⋊C₄	1	2	yes	—
381	C₂⁴×C₄	C₂×C₂²⋊C₄	1	2	yes	—
382	C₂⁴×C₄	C₂×C₂²⋊C₄	1	2	yes	—
383	C₂⁴×C₄	C₂×C₂²⋊C₄	1	2	yes	—
384	C₂⁴×C₄	C₂×C₂²⋊C₄	1	2	yes	—
385	C₂⁴×C₄	C₂×C₂²⋊C₄	1	2	yes	—
386	C₂⁴×C₄	C₂×C₂²⋊C₄	1	2	yes	—
387	C₂⁴×C₄	C₂×C₂²⋊C₄	1	2	yes	—
388	C₂⁴×C₄	C₂×C₂²⋊C₄	1	2	yes	—
389	C₂⁴×C₄	C₂³×C₄	1	1	yes	characteristic
390	C₂⁴×C₄	C₂³×C₄	1	2	yes	—
391	C₂⁴×C₄	C₂³×C₄	1	1	yes	characteristic
392	C₂⁴×C₄	C₂³×C₄	1	2	yes	—
393	C₂⁴×C₄	C₂³×C₄	1	2	yes	—
394	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
395	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
396	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
397	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
398	C₂²×C₂²⋊C₄	C₂³×C₄	1	4	yes	—
399	C₂²×C₂²⋊C₄	C₂³×C₄	1	4	yes	—
400	#379	C₂²×D₄	1	16	yes	—
401	C₂⁵	#386	1	8	yes	—
402	C₂⁵	C₂×#99	1	8	yes	—
403	C₂⁵	C₂×#99	1	8	yes	—
404	C₂⁵	C₂×#99	1	8	yes	—
405	C₂⁵	C₂×#99	1	8	yes	—
406	C₂⁵	C₂²×C₂²⋊C₄	1	1	yes	characteristic
407	C₂⁵	C₂²×C₂²⋊C₄	1	1	yes	characteristic
408	C₂⁵	C₂²×C₂²⋊C₄	1	2	yes	—
409	C₂⁵	C₂²×C₂²⋊C₄	1	2	yes	—
410	C₂⁵	C₂²×C₂²⋊C₄	1	2	yes	—
411	C₂⁵	C₂²×C₂²⋊C₄	1	1	yes	characteristic
412	C₂⁵	C₂²×C₂²⋊C₄	1	1	yes	characteristic
413	C₂⁵	C₂²×C₂²⋊C₄	1	2	yes	—
414	C₂⁵	C₂²×C₂²⋊C₄	1	2	yes	—
415	C₂⁵	C₂²×C₂²⋊C₄	1	2	yes	—
416	C₂⁵	C₂×C₄×D₄	1	4	yes	—
417	C₂⁵	#518	1	4	yes	—
418	C₂⁵	#518	1	4	yes	—
419	C₂⁵	C₂×#120	1	2	yes	—
420	C₂⁵	C₂×#121	1	4	yes	—
421	C₂⁵	C₂×#123	1	2	yes	—
422	C₂⁵	#534	1	4	yes	—
423	C₂⁵	#534	1	4	yes	—
424	C₂⁵	#534	1	4	yes	—
425	C₂⁵	#534	1	4	yes	—
426	C₂⁵	#534	1	4	yes	—
427	C₂⁵	C₂⁴×C₄	1	1	yes	characteristic
428	C₂⁵	C₂³×D₄	1	1	yes	characteristic
429	C₂⁵	C₂³×D₄	1	1	yes	characteristic
430	C₂⁵	C₂³×D₄	1	2	yes	—
431	C₂⁵	C₂²×#41	1	2	yes	—
432	C₂⁵	C₂×H(5,𝔽₂)	1	4	yes	—
433	C₂⁵	C₂×H(5,𝔽₂)	1	4	yes	—
434	C₂²×Q₈	#386	1	8	yes	—
435	C₂²×D₄	#386	1	8	yes	—
436	C₂²×D₄	#386	1	8	yes	—
437	C₂²×D₄	#386	1	8	yes	—
438	C₂²×D₄	C₂×#99	1	8	yes	—
439	C₂²×D₄	C₂×#99	1	8	yes	—
440	C₂²×D₄	C₂×#99	1	8	yes	—
441	C₂²×D₄	C₂×#99	1	8	yes	—
442	C₂²×D₄	C₂×#99	1	8	yes	—
443	C₂²×D₄	C₂×#99	1	8	yes	—
444	C₂²×D₄	C₂×#99	1	8	yes	—
445	C₂²×D₄	C₂×#99	1	8	yes	—
446	C₂²×D₄	C₂×C₄×D₄	1	8	yes	—
447	C₂²×D₄	C₂×C₄×D₄	1	8	yes	—
448	C₂²×D₄	#518	1	8	yes	—
449	C₂²×D₄	C₂×#120	1	4	yes	—
450	C₂²×D₄	C₂×#120	1	4	yes	—
451	C₂²×D₄	C₂×#121	1	8	yes	—
452	C₂²×D₄	C₂×#121	1	8	yes	—
453	C₂²×D₄	C₂×#123	1	4	yes	—
454	C₂²×D₄	C₂×#123	1	4	yes	—
455	C₂²×D₄	#534	1	8	yes	—
456	C₂³×C₄	#386	1	8	yes	—
457	C₂³×C₄	#386	1	8	yes	—
458	C₂³×C₄	#386	1	8	yes	—
459	C₂³×C₄	C₂×#99	1	8	yes	—
460	C₂³×C₄	C₂×#99	1	8	yes	—
461	C₂³×C₄	C₂²×C₂²⋊C₄	1	2	yes	—
462	C₂³×C₄	C₂²×C₂²⋊C₄	1	2	yes	—
463	C₂³×C₄	C₂²×C₂²⋊C₄	1	2	yes	—
464	C₂³×C₄	C₂²×C₂²⋊C₄	1	2	yes	—
465	C₂³×C₄	C₂²×C₂²⋊C₄	1	2	yes	—
466	C₂³×C₄	C₂²×C₂²⋊C₄	1	2	yes	—
467	C₂³×C₄	C₂×C₄×D₄	1	4	yes	—
468	C₂³×C₄	C₂×#120	1	2	yes	—
469	C₂³×C₄	C₂×#121	1	4	yes	—
470	C₂³×C₄	C₂×#123	1	2	yes	—
471	C₂³×C₄	#534	1	4	yes	—
472	C₂⁴	#1898	1	32	yes	complemented
473	C₂⁴	C₂×#386	1	4	yes	—
474	C₂⁴	C₂×#386	1	4	yes	—
475	C₂⁴	C₂×#386	1	4	yes	—
476	C₂⁴	#2308	1	2	yes	—
477	C₂⁴	#2308	1	2	yes	—
478	C₂⁴	#2308	1	2	yes	—
479	C₂⁴	#2308	1	2	yes	—
480	C₂⁴	#2308	1	4	yes	—
481	C₂⁴	C₂²×#99	1	4	yes	—
482	C₂⁴	C₂²×#99	1	4	yes	—
483	C₂⁴	C₂²×#99	1	4	yes	—
484	C₂⁴	C₂²×#99	1	4	yes	—
485	C₂⁴	C₂²×#99	1	4	yes	—
486	C₂⁴	C₂²×#99	1	4	yes	—
487	C₂⁴	C₂²×#99	1	4	yes	—
488	C₂⁴	C₂²×#99	1	4	yes	—
489	C₂⁴	C₂²×#99	1	4	yes	—
490	C₂⁴	C₂²×#99	1	4	yes	—
491	C₂⁴	C₂³×C₂²⋊C₄	1	1	yes	characteristic
492	C₂⁴	C₂²×C₄×D₄	1	2	yes	—
493	C₂⁴	C₂×#518	1	2	yes	—
494	C₂⁴	C₂×#518	1	2	yes	—
495	C₂⁴	C₂²×#120	1	1	yes	characteristic
496	C₂⁴	C₂²×#121	1	2	yes	—
497	C₂⁴	C₂²×#123	1	1	yes	characteristic
498	C₂⁴	C₂×#534	1	2	yes	—
499	C₂⁴	C₂×#534	1	2	yes	—
500	C₂⁴	C₂×#534	1	2	yes	—
501	C₂⁴	C₂×#534	1	2	yes	—
502	C₂⁴	#3484	1	8	yes	—
503	C₂⁴	#3490	1	8	yes	—
504	C₂²×C₄	C₂×#386	1	4	yes	—
505	C₂²×C₄	C₂×#386	1	4	yes	—
506	C₂²×C₄	C₂×#386	1	4	yes	—
507	C₂²×C₄	#2308	1	4	yes	—
508	C₂²×C₄	C₂²×#99	1	4	yes	—
509	C₂²×C₄	C₂²×#99	1	4	yes	—
510	C₂²×C₄	C₂²×#99	1	4	yes	—
511	C₂²×C₄	C₂²×#99	1	4	yes	—
512	C₂³	C₂×#1898	1	8	yes	—
513	C₂³	C₂×#1898	1	8	yes	—
514	C₂³	C₂×#1898	1	8	yes	—
515	C₂³	#21746	1	4	yes	—
516	C₂³	#21746	1	4	yes	—
517	C₂³	#21776	1	4	yes	—
518	C₂³	C₂²×#386	1	1	yes	characteristic
519	C₂³	C₂×#2308	1	1	yes	characteristic
520	C₂³	C₂×#2308	1	1	yes	characteristic
521	C₂³	#34198	1	4	yes	—
522	C₂³	#34980	1	2	yes	—
523	C₂³	#34981	1	4	yes	—
524	C₂³	#34992	1	2	yes	—
525	C₂³	C₂³×#99	1	2	yes	—
526	C₂³	C₂³×#99	1	2	yes	—
527	C₂×C₄	#21746	1	8	yes	—
528	C₂²	#516383	1	1	yes	characteristic
529	C₂²	C₂²×#1898	1	2	yes	—
530	C₂²	C₂×#21746	1	2	yes	—
531	C₂²	C₂×#21746	1	1	yes	characteristic
532	C₂²	C₂×#21746	1	1	yes	characteristic
533	C₂²	C₂×#21776	1	2	yes	—
534	C₂²	#6374187	1	2	yes	—
535	C₂	#72217666	1	1	yes	characteristic
536	C₂	#72225776	1	1	yes	characteristic
537	C₂	#72234690	1	2	yes	—
538	C₂	#72241025	1	2	yes	—
539	C₂	#72265918	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³	C₂×#2308
commutator	C₂⁵	C₂⁴×C₄
Frattini, cosocle	C₂⁶	C₂⁵
prime radical	#72233780	C₂
LCS	G ▷ C₂⁵ ▷ 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. #72266148	C₂	semidirect
2. #72266147	C₂	semidirect
3. #72266146	C₂	semidirect
4. #72255630	C₂	semidirect
5. #72241175	C₂	semidirect
6. #72241167	C₂	semidirect
7. C₂×#213828	C₂	semidirect
8. #72240425	C₂	semidirect
9. C₂×#6370693	C₂	semidirect
10. #72236764	C₂	semidirect
12. #72225783	C₂	semidirect
13. #72219457	C₂	semidirect
15. C₂×#35346	C₄	semidirect
18. C₂²×#2403	C₄	semidirect
20. C₂×#34171	C₂²	semidirect
22. C₂×#20586	C₂²	semidirect
25. C₂×#20585	C₂²	semidirect
26. C₂×#20585	C₂²	semidirect
28. C₂²×#1781	C₂²	semidirect
29. #4928938	C₄	semidirect
32. #613188	C₄	semidirect
35. #517411	C₄	semidirect
37. #517411	C₂²	semidirect
38. #516323	C₄	semidirect
42. #392111	C₂²	semidirect
44. #392109	C₂²	semidirect
45. #359428	C₂²	semidirect
46. C₂×#9497	C₂²	semidirect
47. C₂×#9495	C₂²	semidirect
48. C₂×#9495	C₂²	semidirect
49. C₂×#8746	C₂²	semidirect
50. C₂×#8541	C₂²	semidirect
51. #119494	C₂²	semidirect
52. #119484	C₂²	semidirect
53. #115133	C₂²	semidirect
54. #111516	C₂²	semidirect
55. #106543	C₂²	semidirect
56. #106542	C₂²	semidirect
57. #106542	C₂²	semidirect
58. #106132	C₂²	semidirect
59. #105808	C₂²	semidirect
60. C₂²⋊#1304	C₂²	semidirect
75. C₂⁵×D₄	C₂×C₄	semidirect
81. C₂³×#120	C₂×C₄	semidirect
82. C₂³×#120	C₂×C₄	semidirect
83. C₂³×#120	C₂×C₄	semidirect
86. C₂×#2404	C₂×C₄	semidirect
87. C₂×#2404	C₂×C₄	semidirect
88. C₂×#2404	C₂×C₄	semidirect
89. C₂×#2404	C₂×C₄	semidirect
90. C₂×#2403	C₂×C₄	semidirect
91. C₂×#2403	C₂×C₄	semidirect
92. C₂×#2403	C₂×C₄	semidirect
93. C₂×#2403	C₂×C₄	semidirect
94. C₂×#2403	C₂×C₄	semidirect
95. C₂×#2403	C₂×C₄	semidirect
100. C₂²×#392	C₂×C₄	semidirect
103. C₂×#2308	C₂×C₄	semidirect
104. C₂×#2308	C₂×C₄	semidirect
105. C₂×#2308	C₂×C₄	semidirect
106. C₂×#2308	C₂×C₄	semidirect
107. C₂×#2308	C₂×C₄	semidirect
112. C₂²×#386	C₂×C₄	semidirect
113. C₂²×#386	C₂×C₄	semidirect
114. C₂²×#386	C₂×C₄	semidirect
115. C₂²×#386	C₂×C₄	semidirect
117. C₂²×#379	C₂×C₄	semidirect
118. C₂²×#379	C₂×C₄	semidirect
120. #20585	D₄	semidirect
129. C₂×#1781	C₂³	semidirect
130. #14681	C₂×C₄	semidirect
133. #14335	C₂×C₄	semidirect
136. #13956	C₂×C₄	semidirect
137. #13956	C₂×C₄	semidirect
138. #13956	C₂×C₄	semidirect
139. #13956	C₂×C₄	semidirect
140. #13867	C₂×C₄	semidirect
141. #13867	C₂×C₄	semidirect
142. #13867	C₂×C₄	semidirect
143. #13867	C₂×C₄	semidirect
144. #13867	C₂×C₄	semidirect
145. #13867	C₂×C₄	semidirect
150. #10725	C₂³	semidirect
151. C₂×#1304	C₂³	semidirect
152. C₂×#1304	C₂³	semidirect
262. #2308	C₂×D₄	semidirect
288. #1781	C₂×D₄	semidirect
322. C₂³×D₄	#99	semidirect
323. C₂³×D₄	#99	semidirect
472. C₂⁴	#1898	semidirect

Maximal subgroups

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

subgroup	index
#72266148	2
#72266147	2
#72266146	2
#72255630	2
#72241175	2
#72241167	2
C₂×#213828	2
#72240425	2
C₂×#6370693	2
#72236764	2
#72233780	2
#72225783	2
#72219457	2