Subgroups — #72340831

Order 2048.

At least 13378 conjugacy classes of subgroups; only the 1050 normal subgroups are shown.

The subgroup lattice has 513 nodes (normal subgroups only) — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#72340830	C₂	1	1	yes	maximal, characteristic, complemented
2	#72340828	C₂	1	1	yes	maximal, characteristic, complemented
3	#72339631	C₂	1	2	yes	maximal, complemented
4	#72338267	C₂	1	2	yes	maximal, complemented
5	#72318321	C₂	1	2	yes	maximal, complemented
6	#72318263	C₂	1	2	yes	maximal, complemented
7	#72317822	C₂	1	2	yes	maximal, complemented
8	#72317685	C₂	1	2	yes	maximal, complemented
9	#72284346	C₂	1	2	yes	maximal, complemented
10	#72284336	C₂	1	2	yes	maximal, complemented
11	#72284236	C₂	1	2	yes	maximal, complemented
12	#72250179	C₂	1	2	yes	maximal, complemented
13	#72235440	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×#499832	C₂	1	2	yes	maximal, complemented
15	C₂×#499787	C₂	1	2	yes	maximal, complemented
16	#72232115	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂×#6628867	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂²×#32898	C₂	1	1	yes	maximal, characteristic, complemented
19	#72219118	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂⁴×H(5,𝔽₂)	C₂²	1	1	yes	characteristic, complemented
21	C₂³×B(4,𝔽₂)	C₂²	1	2	yes	—
22	C₂²×#3019	C₂²	1	2	yes	complemented
23	C₂×#52004	C₂²	1	1	yes	characteristic, complemented
24	C₂×#58990	C₂²	1	1	yes	characteristic, complemented
25	C₂×#35222	C₂²	1	1	yes	characteristic
26	C₂²×#2403	C₂²	1	1	yes	characteristic
27	C₂²×#2196	C₂²	1	4	yes	complemented
28	C₂×#32898	C₂²	1	2	yes	—
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	2	yes	complemented
34	C₂×#32898	C₂²	1	2	yes	complemented
35	C₂×#32891	C₂²	1	2	yes	complemented
36	C₂×#32891	C₂²	1	2	yes	complemented
37	C₂×#32888	C₂²	1	2	yes	—
38	C₂×#32888	C₂²	1	2	yes	complemented
39	C₂×#20616	C₂²	1	2	yes	complemented
40	C₂²×#1790	C₂²	1	2	yes	complemented
41	C₂²×#1783	C₂²	1	1	yes	characteristic, complemented
42	C₂²×#1781	C₂²	1	1	yes	characteristic, complemented
43	#4933776	C₂²	1	1	yes	characteristic, complemented
44	#4932464	C₂²	1	1	yes	characteristic, complemented
45	#4312858	C₂²	1	1	yes	characteristic, complemented
46	#4312055	C₂²	1	1	yes	characteristic, complemented
47	#1425312	C₂²	1	1	yes	characteristic, complemented
48	#1418385	C₂²	1	1	yes	characteristic, complemented
49	#875301	C₂²	1	1	yes	characteristic, complemented
50	#846389	C₂²	1	1	yes	characteristic, complemented
51	#612424	C₂²	1	1	yes	characteristic
52	#570820	C₂²	1	1	yes	characteristic, complemented
53	#557605	C₂²	1	1	yes	characteristic, complemented
54	C₂×#13348	C₂²	1	4	yes	complemented
55	C₂×#13348	C₂²	1	4	yes	complemented
56	C₂×#13348	C₂²	1	4	yes	complemented
57	C₂×#13346	C₂²	1	4	yes	complemented
58	C₂×#13343	C₂²	1	4	yes	complemented
59	C₂×#13090	C₂²	1	2	yes	complemented
60	C₂×#13088	C₂²	1	2	yes	complemented
61	C₂×#13086	C₂²	1	2	yes	complemented
62	C₂×#13082	C₂²	1	2	yes	complemented
63	C₂×#13082	C₂²	1	2	yes	complemented
64	C₂×#13082	C₂²	1	2	yes	complemented
65	C₂×#13049	C₂²	1	4	yes	complemented
66	C₂×#13041	C₂²	1	4	yes	complemented
67	C₂×#12696	C₂²	1	2	yes	complemented
68	C₂×#12687	C₂²	1	2	yes	complemented
69	#392125	C₂²	1	2	yes	complemented
70	#392125	C₂²	1	2	yes	complemented
71	#392125	C₂²	1	2	yes	complemented
72	#392109	C₂²	1	1	yes	characteristic, complemented
73	#148572	C₂²	1	2	yes	complemented
74	#148170	C₂²	1	4	yes	complemented
75	#148167	C₂²	1	4	yes	complemented
76	#147771	C₂²	1	4	yes	complemented
77	#147770	C₂²	1	4	yes	complemented
78	#147749	C₂²	1	4	yes	complemented
79	#147749	C₂²	1	4	yes	complemented
80	#147749	C₂²	1	4	yes	complemented
81	#147561	C₂²	1	2	yes	complemented
82	#147559	C₂²	1	2	yes	complemented
83	#147555	C₂²	1	2	yes	complemented
84	#147555	C₂²	1	2	yes	complemented
85	#147555	C₂²	1	2	yes	complemented
86	#147489	C₂²	1	4	yes	complemented
87	#146566	C₂²	1	2	yes	complemented
88	#146564	C₂²	1	2	yes	complemented
89	#146467	C₂²	1	2	yes	complemented
90	#146457	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	2	yes	—
94	C₂⁵×D₄	D₄	1	1	yes	characteristic, complemented
95	C₂⁵×D₄	C₂³	1	1	yes	characteristic
96	C₂²×D₄²	C₂³	1	1	yes	characteristic, complemented
97	C₂²×#535	D₄	1	1	yes	characteristic, complemented
98	C₂²×#535	C₂³	1	1	yes	characteristic
99	C₂²×#525	D₄	1	1	yes	characteristic, complemented
100	C₂³×#120	D₄	1	1	yes	characteristic, complemented
101	C₂³×#120	D₄	1	1	yes	characteristic, complemented
102	C₂³×#120	C₂³	1	1	yes	characteristic
103	C₂²×B(4,𝔽₂)	C₂³	1	4	yes	—
104	C₂²×B(4,𝔽₂)	C₂³	1	4	yes	—
105	C₂²×B(4,𝔽₂)	C₂³	1	4	yes	—
106	C₂²×#455	C₂³	1	4	yes	—
107	C₂²×#453	C₂³	1	4	yes	—
108	C₂³×#100	C₂³	1	2	yes	—
109	C₂³×#99	C₂³	1	2	yes	—
110	C₂×#2684	C₂³	1	1	yes	characteristic, complemented
111	C₂×#2684	C₂³	1	1	yes	characteristic, complemented
112	C₂×#2684	C₂³	1	1	yes	characteristic, complemented
113	C₂×#2679	C₂³	1	1	yes	characteristic, complemented
114	C₂×#2669	C₂³	1	1	yes	characteristic, complemented
115	C₂×#2435	D₄	1	1	yes	characteristic, complemented
116	C₂×#2435	D₄	1	1	yes	characteristic, complemented
117	C₂×#2435	C₂³	1	1	yes	characteristic
118	C₂×#2435	C₂³	1	1	yes	characteristic
119	C₂×#2433	D₄	1	1	yes	characteristic, complemented
120	C₂×#2433	D₄	1	1	yes	characteristic, complemented
121	C₂×#2433	C₂³	1	1	yes	characteristic
122	C₂×#2433	C₂³	1	1	yes	characteristic
123	C₂×#2403	D₄	1	1	yes	characteristic, complemented
124	C₂×#2403	D₄	1	1	yes	characteristic, complemented
125	C₂×#2403	D₄	1	1	yes	characteristic, complemented
126	C₂×#2403	D₄	1	1	yes	characteristic, complemented
127	C₂×#2403	D₄	1	1	yes	characteristic, complemented
128	C₂×#2403	D₄	1	1	yes	characteristic, complemented
129	C₂×#2403	D₄	1	1	yes	characteristic, complemented
130	C₂×#2403	C₂³	1	1	yes	characteristic
131	C₂×#2403	C₂³	1	1	yes	characteristic
132	C₂×#2403	C₂³	1	1	yes	characteristic
133	C₂×#2403	C₂³	1	1	yes	characteristic
134	C₂×#2403	C₂³	1	1	yes	characteristic
135	C₂×#2403	C₂³	1	1	yes	characteristic
136	C₂×#2403	C₂³	1	1	yes	characteristic
137	C₂×#2380	C₂³	1	1	yes	characteristic, complemented
138	C₂×#2358	C₂³	1	1	yes	characteristic, complemented
139	C₂×#2309	D₄	1	1	yes	characteristic, complemented
140	C₂×#2309	C₂³	1	1	yes	characteristic
141	C₂²×#386	D₄	1	1	yes	characteristic, complemented
142	C₂²×#386	C₂³	1	1	yes	characteristic
143	C₂×#2280	D₄	1	1	yes	characteristic, complemented
144	C₂²×#379	D₄	1	1	yes	characteristic, complemented
145	C₂²×#354	C₂³	1	4	yes	complemented
146	C₂²×#353	C₂³	1	4	yes	complemented
147	C₂²×AΣL(1,𝔽₁₆)	C₂³	1	4	yes	complemented
148	C₂²×AΣL(1,𝔽₁₆)	C₂³	1	4	yes	complemented
149	C₂²×AΣL(1,𝔽₁₆)	C₂³	1	4	yes	complemented
150	#32898	D₄	1	16	yes	complemented
151	#32888	D₄	1	16	yes	complemented
152	C₂×#1792	C₂³	1	4	yes	—
153	C₂×#1792	C₂³	1	4	yes	—
154	C₂×#1790	C₂³	1	4	yes	—
155	C₂×#1790	C₂³	1	4	yes	—
156	C₂×#1790	C₂³	1	4	yes	—
157	C₂×#1790	C₂³	1	4	yes	—
158	C₂×#1790	C₂³	1	4	yes	—
159	C₂×#1783	C₂³	1	2	yes	—
160	C₂×#1783	C₂³	1	2	yes	—
161	C₂×#1781	C₂³	1	2	yes	—
162	C₂×#1781	C₂³	1	2	yes	—
163	C₂×#1781	C₂³	1	2	yes	—
164	C₂×#1781	C₂³	1	2	yes	—
165	C₂×#1781	C₂³	1	2	yes	—
166	#14679	D₄	1	1	yes	characteristic, complemented
167	#14513	C₂³	1	1	yes	characteristic, complemented
168	#14486	C₂³	1	1	yes	characteristic, complemented
169	#14473	C₂³	1	1	yes	characteristic, complemented
170	#14419	C₂³	1	1	yes	characteristic, complemented
171	#14357	C₂³	1	1	yes	characteristic, complemented
172	#14357	C₂³	1	1	yes	characteristic, complemented
173	#14357	C₂³	1	1	yes	characteristic, complemented
174	#13867	D₄	1	1	yes	characteristic, complemented
175	#13867	D₄	1	1	yes	characteristic, complemented
176	#13867	D₄	1	1	yes	characteristic, complemented
177	#13867	C₂³	1	1	yes	characteristic
178	#13867	C₂³	1	1	yes	characteristic
179	#13867	C₂³	1	1	yes	characteristic
180	#13832	C₂³	1	1	yes	characteristic, complemented
181	C₂×#1393	C₂³	1	4	yes	complemented
182	C₂×#1393	C₂³	1	4	yes	complemented
183	C₂×#1390	C₂³	1	4	yes	complemented
184	C₂×#1390	C₂³	1	4	yes	complemented
185	C₂×#1390	C₂³	1	4	yes	complemented
186	C₂×#1390	C₂³	1	4	yes	complemented
187	C₂×#1390	C₂³	1	4	yes	complemented
188	C₂⁷	C₂×D₄	1	1	yes	characteristic
189	C₂⁷	C₂×D₄	1	1	yes	characteristic
190	C₂⁷	C₂×D₄	1	1	yes	characteristic
191	C₂²×H(5,𝔽₂)	C₂×D₄	1	8	yes	—
192	C₂²×H(5,𝔽₂)	C₂×D₄	1	8	yes	complemented
193	C₂²×H(5,𝔽₂)	C₂⁴	1	4	yes	—
194	C₂³×#41	C₂×D₄	1	1	yes	characteristic, complemented
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	1	yes	characteristic
200	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
201	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
202	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
203	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
204	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
205	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
206	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
207	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
208	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
209	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic, complemented
210	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic, complemented
211	C₂⁴×D₄	C₂⁴	1	1	yes	characteristic
212	C₂⁴×D₄	C₂⁴	1	1	yes	characteristic
213	C₂⁴×D₄	C₂⁴	1	1	yes	characteristic
214	C₂⁵×C₄	C₂×D₄	1	1	yes	characteristic
215	C₂⁵×C₄	C₂×D₄	1	1	yes	characteristic
216	C₂²×#127	C₂×D₄	1	1	yes	characteristic
217	C₂²×#127	C₂×D₄	1	1	yes	characteristic, complemented
218	C₂²×#127	C₂×D₄	1	1	yes	characteristic, complemented
219	C₂²×#127	C₂⁴	1	1	yes	characteristic
220	C₂²×#124	C₂×D₄	1	1	yes	characteristic
221	C₂²×#124	C₂×D₄	1	1	yes	characteristic, complemented
222	C₂²×#124	C₂×D₄	1	1	yes	characteristic, complemented
223	C₂²×#124	C₂⁴	1	1	yes	characteristic
224	C₂²×C₂²⋊Q₈	C₂×D₄	1	1	yes	characteristic
225	C₂²×C₂²⋊Q₈	C₂×D₄	1	1	yes	characteristic, complemented
226	C₂²×#121	C₂×D₄	1	1	yes	characteristic
227	C₂²×#121	C₂×D₄	1	1	yes	characteristic, complemented
228	C₂²×#120	C₂×D₄	1	1	yes	characteristic
229	C₂²×#120	C₂×D₄	1	1	yes	characteristic
230	C₂²×#120	C₂×D₄	1	1	yes	characteristic
231	C₂²×#120	C₂×D₄	1	1	yes	characteristic
232	C₂²×#120	C₂×D₄	1	1	yes	characteristic
233	C₂²×#120	C₂×D₄	1	1	yes	characteristic
234	C₂²×#120	C₂×D₄	1	1	yes	characteristic
235	C₂²×#120	C₂×D₄	1	1	yes	characteristic, complemented
236	C₂²×#120	C₂×D₄	1	1	yes	characteristic, complemented
237	C₂²×#120	C₂⁴	1	1	yes	characteristic
238	C₂²×#120	C₂⁴	1	1	yes	characteristic
239	C₂²×#120	C₂⁴	1	1	yes	characteristic
240	C₂²×#117	C₂×D₄	1	1	yes	characteristic, complemented
241	C₂²×#117	C₂×D₄	1	1	yes	characteristic, complemented
242	C₂²×#117	C₂×D₄	1	1	yes	characteristic, complemented
243	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
244	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
245	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
246	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic, complemented
247	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic, complemented
248	C₂×B(4,𝔽₂)	C₂×D₄	1	16	yes	—
249	C₂×#453	C₂×D₄	1	16	yes	complemented
250	C₂²×#100	C₂⁴	1	4	yes	—
251	C₂²×#99	C₂⁴	1	4	yes	—
252	C₂²×#99	C₂⁴	1	4	yes	—
253	#2433	C₂×D₄	1	8	yes	—
254	#2403	C₂×D₄	1	8	yes	—
255	C₂×#390	C₂×D₄	1	1	yes	characteristic
256	C₂×#390	C₂×D₄	1	1	yes	characteristic
257	C₂×#390	C₂×D₄	1	1	yes	characteristic, complemented
258	C₂×#390	C₂×D₄	1	1	yes	characteristic, complemented
259	C₂×#390	C₂×D₄	1	1	yes	characteristic, complemented
260	C₂×#390	C₂×D₄	1	1	yes	characteristic, complemented
261	C₂×#390	C₂⁴	1	1	yes	characteristic
262	C₂×#390	C₂⁴	1	1	yes	characteristic
263	C₂×#386	C₂×D₄	1	1	yes	characteristic
264	C₂×#386	C₂×D₄	1	1	yes	characteristic
265	C₂×#386	C₂×D₄	1	1	yes	characteristic
266	C₂×#386	C₂×D₄	1	1	yes	characteristic
267	C₂×#386	C₂×D₄	1	1	yes	characteristic
268	C₂×#386	C₂×D₄	1	1	yes	characteristic
269	C₂×#386	C₂×D₄	1	1	yes	characteristic
270	C₂×#386	C₂×D₄	1	1	yes	characteristic
271	C₂×#386	C₂×D₄	1	1	yes	characteristic
272	C₂×#386	C₂×D₄	1	1	yes	characteristic, complemented
273	C₂×#386	C₂×D₄	1	1	yes	characteristic, complemented
274	C₂×#386	C₂×D₄	1	1	yes	characteristic, complemented
275	C₂×#386	C₂×D₄	1	1	yes	characteristic, complemented
276	C₂×#386	C₂×D₄	1	1	yes	characteristic, complemented
277	C₂×#386	C₂×D₄	1	1	yes	characteristic, complemented
278	C₂×#386	C₂⁴	1	1	yes	characteristic
279	C₂×#386	C₂⁴	1	1	yes	characteristic
280	C₂×#386	C₂⁴	1	1	yes	characteristic
281	C₂×#386	C₂⁴	1	1	yes	characteristic
282	C₂×#386	C₂⁴	1	1	yes	characteristic
283	C₂×#379	C₂×D₄	1	1	yes	characteristic
284	C₂×#379	C₂×D₄	1	1	yes	characteristic
285	C₂×#379	C₂×D₄	1	1	yes	characteristic
286	C₂×#379	C₂×D₄	1	1	yes	characteristic
287	C₂×#379	C₂×D₄	1	1	yes	characteristic
288	C₂×#379	C₂×D₄	1	1	yes	characteristic
289	C₂×#379	C₂×D₄	1	1	yes	characteristic, complemented
290	C₂×#379	C₂×D₄	1	1	yes	characteristic, complemented
291	C₂×#379	C₂×D₄	1	1	yes	characteristic, complemented
292	C₂×#379	C₂×D₄	1	1	yes	characteristic, complemented
293	C₂×C₄×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
294	C₂×C₄×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
295	C₂×C₄×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic, complemented
296	C₂×C₄×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic, complemented
297	#1792	C₂×D₄	1	16	yes	complemented
298	#1790	C₂×D₄	1	16	yes	complemented
299	#1783	C₂×D₄	1	8	yes	—
300	#1781	C₂×D₄	1	8	yes	complemented
301	C₂⁶	#120	1	1	yes	characteristic
302	C₂⁶	#120	1	1	yes	characteristic
303	C₂⁶	#120	1	1	yes	characteristic
304	C₂⁶	#120	1	1	yes	characteristic
305	C₂⁶	#120	1	1	yes	characteristic
306	C₂⁶	#120	1	1	yes	characteristic
307	C₂⁶	#120	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	C₂²×D₄	1	1	yes	characteristic
313	C₂⁶	C₂²×D₄	1	1	yes	characteristic
314	C₂⁶	C₂²×D₄	1	1	yes	characteristic
315	C₂⁶	C₂²×D₄	1	1	yes	characteristic
316	C₂⁶	C₂²×D₄	1	1	yes	characteristic
317	C₂×H(5,𝔽₂)	C₂²×D₄	1	8	yes	—
318	C₂×H(5,𝔽₂)	C₂²×D₄	1	8	yes	—
319	C₂×H(5,𝔽₂)	H(5,𝔽₂)	1	8	yes	—
320	C₂³×Q₈	C₂²×D₄	1	1	yes	characteristic
321	C₂³×D₄	#120	1	1	yes	characteristic
322	C₂³×D₄	#120	1	1	yes	characteristic
323	C₂³×D₄	#120	1	1	yes	characteristic
324	C₂³×D₄	#120	1	1	yes	characteristic
325	C₂³×D₄	#120	1	1	yes	characteristic
326	C₂³×D₄	#120	1	1	yes	characteristic
327	C₂³×D₄	#120	1	4	yes	complemented
328	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
329	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
330	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
331	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
332	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
333	C₂³×D₄	C₂²×D₄	1	4	yes	—
334	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
335	C₂³×D₄	C₂²×D₄	1	4	yes	—
336	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
337	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
338	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
339	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
340	C₂³×D₄	H(5,𝔽₂)	1	4	yes	—
341	C₂³×D₄	H(5,𝔽₂)	1	4	yes	—
342	C₂³×D₄	C₂⁵	1	1	yes	characteristic
343	C₂⁴×C₄	#120	1	1	yes	characteristic
344	C₂⁴×C₄	#120	1	1	yes	characteristic
345	C₂⁴×C₄	#120	1	1	yes	characteristic
346	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
347	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
348	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
349	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
350	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
351	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
352	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
353	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
354	C₂×#127	#120	1	4	yes	complemented
355	C₂×#127	C₂²×D₄	1	4	yes	—
356	C₂×#121	#120	1	4	yes	complemented
357	C₂×#120	#120	1	4	yes	complemented
358	C₂×#120	C₂²×D₄	1	4	yes	—
359	C₂²×C₄⋊C₄	C₂²×D₄	1	1	yes	characteristic
360	C₂²×C₄⋊C₄	C₂²×D₄	1	1	yes	characteristic
361	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
362	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
363	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
364	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
365	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
366	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
367	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
368	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
369	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
370	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
371	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
372	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
373	C₂×#100	C₂²×D₄	1	8	yes	—
374	C₂×#99	C₂²×D₄	1	8	yes	—
375	#390	#120	1	4	yes	complemented
376	#390	C₂²×D₄	1	4	yes	—
377	#386	#120	1	4	yes	complemented
378	#386	C₂²×D₄	1	4	yes	—
379	#379	#120	1	4	yes	complemented
380	C₄×C₂²⋊C₄	#120	1	4	yes	complemented
381	C₂⁵	B(4,𝔽₂)	1	1	yes	characteristic
382	C₂⁵	B(4,𝔽₂)	1	1	yes	characteristic
383	C₂⁵	B(4,𝔽₂)	1	1	yes	characteristic
384	C₂⁵	B(4,𝔽₂)	1	1	yes	characteristic
385	C₂⁵	B(4,𝔽₂)	1	4	yes	—
386	C₂⁵	C₂×#120	1	1	yes	characteristic
387	C₂⁵	C₂×#120	1	1	yes	characteristic
388	C₂⁵	C₂×#120	1	1	yes	characteristic
389	C₂⁵	C₂×#120	1	1	yes	characteristic
390	C₂⁵	C₂×#120	1	1	yes	characteristic
391	C₂⁵	C₂×#120	1	1	yes	characteristic
392	C₂⁵	C₂×#120	1	1	yes	characteristic
393	C₂⁵	C₂×#120	1	1	yes	characteristic
394	C₂⁵	C₂×#120	1	1	yes	characteristic
395	C₂⁵	C₂×#120	1	2	yes	—
396	C₂⁵	C₂×#120	1	2	yes	—
397	C₂⁵	#534	1	2	yes	—
398	C₂⁵	D₄²	1	4	yes	—
399	C₂⁵	D₄²	1	4	yes	—
400	C₂⁵	D₄²	1	4	yes	—
401	C₂⁵	C₂³×D₄	1	1	yes	characteristic
402	C₂⁵	C₂³×D₄	1	1	yes	characteristic
403	H(5,𝔽₂)	D₄²	1	16	yes	—
404	C₂²×D₄	B(4,𝔽₂)	1	4	yes	—
405	C₂²×D₄	C₂×#120	1	2	yes	—
406	C₂²×D₄	C₂×#120	1	2	yes	—
407	C₂²×D₄	C₂×#120	1	2	yes	complemented
408	C₂²×D₄	#534	1	2	yes	—
409	C₂²×D₄	#534	1	2	yes	—
410	C₂²×D₄	D₄²	1	4	yes	—
411	C₂²×D₄	D₄²	1	4	yes	—
412	C₂²×D₄	D₄²	1	4	yes	—
413	C₂²×D₄	D₄²	1	4	yes	—
414	C₂²×D₄	C₂³×D₄	1	2	yes	—
415	C₂²×D₄	C₂³×D₄	1	2	yes	—
416	C₂²×D₄	C₂×H(5,𝔽₂)	1	2	yes	—
417	C₂²×D₄	C₂×H(5,𝔽₂)	1	2	yes	—
418	C₂²×D₄	C₂×H(5,𝔽₂)	1	4	yes	—
419	C₂³×C₄	B(4,𝔽₂)	1	4	yes	—
420	C₂³×C₄	C₂×#120	1	1	yes	characteristic
421	C₂³×C₄	C₂×#120	1	1	yes	characteristic
422	C₂³×C₄	C₂×#120	1	2	yes	—
423	C₂³×C₄	C₂×#120	1	1	yes	characteristic
424	C₂³×C₄	C₂×#120	1	2	yes	—
425	C₂³×C₄	#534	1	2	yes	—
426	C₂³×C₄	D₄²	1	4	yes	—
427	C₂³×C₄	C₂³×D₄	1	1	yes	characteristic
428	C₂×C₄⋊C₄	C₂×#120	1	2	yes	complemented
429	C₂×C₂²⋊C₄	C₂×#120	1	2	yes	—
430	C₂×C₂²⋊C₄	C₂×#120	1	2	yes	—
431	C₂×C₄²	C₂×#120	1	2	yes	complemented
432	C₂×C₄²	C₂×#120	1	2	yes	complemented
433	C₂⁴	#2403	1	2	yes	—
434	C₂⁴	#2403	1	2	yes	—
435	C₂⁴	#2403	1	2	yes	—
436	C₂⁴	#2403	1	2	yes	—
437	C₂⁴	#2403	1	2	yes	—
438	C₂⁴	#2403	1	2	yes	—
439	C₂⁴	C₂×B(4,𝔽₂)	1	1	yes	characteristic
440	C₂⁴	C₂×B(4,𝔽₂)	1	1	yes	characteristic
441	C₂⁴	C₂×B(4,𝔽₂)	1	1	yes	characteristic
442	C₂⁴	C₂×B(4,𝔽₂)	1	1	yes	characteristic
443	C₂⁴	C₂×B(4,𝔽₂)	1	1	yes	characteristic
444	C₂⁴	C₂×B(4,𝔽₂)	1	2	yes	—
445	C₂⁴	C₂×B(4,𝔽₂)	1	1	yes	characteristic
446	C₂⁴	C₂×B(4,𝔽₂)	1	2	yes	—
447	C₂⁴	C₂×B(4,𝔽₂)	1	2	yes	—
448	C₂⁴	C₂×B(4,𝔽₂)	1	2	yes	—
449	C₂⁴	C₂×B(4,𝔽₂)	1	2	yes	—
450	C₂⁴	C₂×B(4,𝔽₂)	1	2	yes	—
451	C₂⁴	C₂²×#120	1	1	yes	characteristic
452	C₂⁴	C₂²×#120	1	1	yes	characteristic
453	C₂⁴	C₂×#534	1	1	yes	characteristic
454	C₂⁴	C₂×D₄²	1	2	yes	—
455	C₂⁴	C₂×D₄²	1	2	yes	—
456	C₂⁴	C₂×D₄²	1	2	yes	—
457	C₂⁴	#3484	1	2	yes	—
458	C₂⁴	#3484	1	2	yes	—
459	C₂×D₄	C₂×D₄²	1	4	yes	—
460	C₂×D₄	#3484	1	4	yes	—
461	C₂×D₄	#3484	1	4	yes	—
462	C₂×D₄	#3532	1	4	yes	—
463	C₂²×C₄	#2403	1	2	yes	—
464	C₂²×C₄	#2403	1	2	yes	—
465	C₂²×C₄	C₂×B(4,𝔽₂)	1	2	yes	—
466	C₂²×C₄	C₂×B(4,𝔽₂)	1	2	yes	—
467	C₂²×C₄	C₂×B(4,𝔽₂)	1	2	yes	—
468	C₂²×C₄	C₂²×#120	1	1	yes	characteristic
469	C₂²×C₄	C₂×#534	1	1	yes	characteristic
470	C₂²×C₄	C₂×D₄²	1	2	yes	—
471	C₂²×C₄	#3484	1	2	yes	—
472	C₂³	#23900	1	2	yes	—
473	C₂³	#23900	1	2	yes	—
474	C₂³	#23900	1	2	yes	—
475	C₂³	#23900	1	2	yes	—
476	C₂³	#23900	1	4	yes	—
477	C₂³	#33551	1	2	yes	—
478	C₂³	#33551	1	2	yes	—
479	C₂³	#33551	1	2	yes	—
480	C₂³	C₂×#2403	1	1	yes	characteristic
481	C₂³	C₂×#2403	1	1	yes	characteristic
482	C₂³	#35346	1	1	yes	characteristic
483	C₂³	D₄×#120	1	2	yes	—
484	C₂³	#37644	1	2	yes	—
485	C₂³	#58990	1	4	yes	—
486	C₂³	C₂²×B(4,𝔽₂)	1	1	yes	characteristic
487	C₂³	C₂²×B(4,𝔽₂)	1	1	yes	characteristic
488	C₂³	C₂²×B(4,𝔽₂)	1	1	yes	characteristic
489	C₂³	C₂²×B(4,𝔽₂)	1	1	yes	characteristic
490	C₂×C₄	#23900	1	4	yes	—
491	C₂×C₄	D₄×#120	1	2	yes	—
492	C₂×C₄	#37644	1	2	yes	—
493	C₂²	#499832	1	4	yes	complemented
494	C₂²	#647656	1	1	yes	characteristic
495	C₂²	C₂×#23900	1	1	yes	characteristic
496	C₂²	C₂×#23900	1	1	yes	characteristic
497	C₂²	C₂×#23900	1	1	yes	characteristic
498	C₂²	C₂×#23900	1	1	yes	characteristic
499	C₂²	#6499867	1	1	yes	characteristic
500	C₂²	#6499867	1	1	yes	characteristic
501	C₂²	C₂×#33551	1	1	yes	characteristic
502	C₂²	C₂×#33551	1	1	yes	characteristic
503	C₂²	C₂×#33551	1	1	yes	characteristic
504	C₂²	#7622875	1	1	yes	characteristic
505	C₂	#72217546	1	1	yes	characteristic
506	C₂	#72218077	1	1	yes	characteristic
507	C₂	#72233116	1	1	yes	characteristic
508	C₂	#72233499	1	1	yes	characteristic
509	C₂	C₂×#499832	1	1	yes	characteristic
510	C₂	#72235270	1	1	yes	characteristic
511	C₂	#72238471	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³	C₂²×B(4,𝔽₂)
commutator, Frattini, cosocle	C₂³×D₄	C₂⁵
LCS	G ▷ C₂³×D₄ ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³ ◁ C₂⁶ ◁ C₂⁵×D₄ ◁ G
LECS	G ▷ C₂³×D₄ ▷ C₂² ▷ C₂ ▷ C₁

Complements

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

N	H ≅ G/N	type
1. #72340830	C₂	semidirect
2. #72340828	C₂	semidirect
3. #72339631	C₂	semidirect
4. #72338267	C₂	semidirect
5. #72318321	C₂	semidirect
6. #72318263	C₂	semidirect
7. #72317822	C₂	semidirect
8. #72317685	C₂	semidirect
9. #72284346	C₂	semidirect
10. #72284336	C₂	semidirect
11. #72284236	C₂	semidirect
12. #72250179	C₂	semidirect
13. #72235440	C₂	semidirect
14. C₂×#499832	C₂	semidirect
15. C₂×#499787	C₂	semidirect
16. #72232115	C₂	semidirect
17. C₂×#6628867	C₂	semidirect
18. C₂²×#32898	C₂	semidirect
19. #72219118	C₂	semidirect
20. C₂⁴×H(5,𝔽₂)	C₂²	semidirect
22. C₂²×#3019	C₂²	semidirect
23. C₂×#52004	C₂²	semidirect
24. C₂×#58990	C₂²	semidirect
27. C₂²×#2196	C₂²	semidirect
31. C₂×#32898	C₂²	semidirect
32. C₂×#32898	C₂²	semidirect
33. C₂×#32898	C₂²	semidirect
34. C₂×#32898	C₂²	semidirect
35. C₂×#32891	C₂²	semidirect
36. C₂×#32891	C₂²	semidirect
38. C₂×#32888	C₂²	semidirect
39. C₂×#20616	C₂²	semidirect
40. C₂²×#1790	C₂²	semidirect
41. C₂²×#1783	C₂²	semidirect
42. C₂²×#1781	C₂²	semidirect
43. #4933776	C₂²	semidirect
44. #4932464	C₂²	semidirect
45. #4312858	C₂²	semidirect
46. #4312055	C₂²	semidirect
47. #1425312	C₂²	semidirect
48. #1418385	C₂²	semidirect
49. #875301	C₂²	semidirect
50. #846389	C₂²	semidirect
52. #570820	C₂²	semidirect
53. #557605	C₂²	semidirect
54. C₂×#13348	C₂²	semidirect
55. C₂×#13348	C₂²	semidirect
56. C₂×#13348	C₂²	semidirect
57. C₂×#13346	C₂²	semidirect
58. C₂×#13343	C₂²	semidirect
59. C₂×#13090	C₂²	semidirect
60. C₂×#13088	C₂²	semidirect
61. C₂×#13086	C₂²	semidirect
62. C₂×#13082	C₂²	semidirect
63. C₂×#13082	C₂²	semidirect
64. C₂×#13082	C₂²	semidirect
65. C₂×#13049	C₂²	semidirect
66. C₂×#13041	C₂²	semidirect
67. C₂×#12696	C₂²	semidirect
68. C₂×#12687	C₂²	semidirect
69. #392125	C₂²	semidirect
70. #392125	C₂²	semidirect
71. #392125	C₂²	semidirect
72. #392109	C₂²	semidirect
73. #148572	C₂²	semidirect
74. #148170	C₂²	semidirect
75. #148167	C₂²	semidirect
76. #147771	C₂²	semidirect
77. #147770	C₂²	semidirect
78. #147749	C₂²	semidirect
79. #147749	C₂²	semidirect
80. #147749	C₂²	semidirect
81. #147561	C₂²	semidirect
82. #147559	C₂²	semidirect
83. #147555	C₂²	semidirect
84. #147555	C₂²	semidirect
85. #147555	C₂²	semidirect
86. #147489	C₂²	semidirect
87. #146566	C₂²	semidirect
88. #146564	C₂²	semidirect
89. #146467	C₂²	semidirect
90. #146457	C₂²	semidirect
94. C₂⁵×D₄	D₄	semidirect
96. C₂²×D₄²	C₂³	semidirect
97. C₂²×#535	D₄	semidirect
99. C₂²×#525	D₄	semidirect
100. C₂³×#120	D₄	semidirect
101. C₂³×#120	D₄	semidirect
110. C₂×#2684	C₂³	semidirect
111. C₂×#2684	C₂³	semidirect
112. C₂×#2684	C₂³	semidirect
113. C₂×#2679	C₂³	semidirect
114. C₂×#2669	C₂³	semidirect
115. C₂×#2435	D₄	semidirect
116. C₂×#2435	D₄	semidirect
119. C₂×#2433	D₄	semidirect
120. C₂×#2433	D₄	semidirect
123. C₂×#2403	D₄	semidirect
124. C₂×#2403	D₄	semidirect
125. C₂×#2403	D₄	semidirect
126. C₂×#2403	D₄	semidirect
127. C₂×#2403	D₄	semidirect
128. C₂×#2403	D₄	semidirect
129. C₂×#2403	D₄	semidirect
137. C₂×#2380	C₂³	semidirect
138. C₂×#2358	C₂³	semidirect
139. C₂×#2309	D₄	semidirect
141. C₂²×#386	D₄	semidirect
143. C₂×#2280	D₄	semidirect
144. C₂²×#379	D₄	semidirect
145. C₂²×#354	C₂³	semidirect
146. C₂²×#353	C₂³	semidirect
147. C₂²×AΣL(1,𝔽₁₆)	C₂³	semidirect
148. C₂²×AΣL(1,𝔽₁₆)	C₂³	semidirect
149. C₂²×AΣL(1,𝔽₁₆)	C₂³	semidirect
150. #32898	D₄	semidirect
151. #32888	D₄	semidirect
166. #14679	D₄	semidirect
167. #14513	C₂³	semidirect
168. #14486	C₂³	semidirect
169. #14473	C₂³	semidirect
170. #14419	C₂³	semidirect
171. #14357	C₂³	semidirect
172. #14357	C₂³	semidirect
173. #14357	C₂³	semidirect
174. #13867	D₄	semidirect
175. #13867	D₄	semidirect
176. #13867	D₄	semidirect
180. #13832	C₂³	semidirect
181. C₂×#1393	C₂³	semidirect
182. C₂×#1393	C₂³	semidirect
183. C₂×#1390	C₂³	semidirect
184. C₂×#1390	C₂³	semidirect
185. C₂×#1390	C₂³	semidirect
186. C₂×#1390	C₂³	semidirect
187. C₂×#1390	C₂³	semidirect
192. C₂²×H(5,𝔽₂)	C₂×D₄	semidirect
194. C₂³×#41	C₂×D₄	semidirect
209. C₂⁴×D₄	C₂×D₄	semidirect
210. C₂⁴×D₄	C₂×D₄	semidirect
217. C₂²×#127	C₂×D₄	semidirect
218. C₂²×#127	C₂×D₄	semidirect
221. C₂²×#124	C₂×D₄	semidirect
222. C₂²×#124	C₂×D₄	semidirect
225. C₂²×C₂²⋊Q₈	C₂×D₄	semidirect
227. C₂²×#121	C₂×D₄	semidirect
235. C₂²×#120	C₂×D₄	semidirect
236. C₂²×#120	C₂×D₄	semidirect
240. C₂²×#117	C₂×D₄	semidirect
241. C₂²×#117	C₂×D₄	semidirect
242. C₂²×#117	C₂×D₄	semidirect
246. C₂³×C₂²⋊C₄	C₂×D₄	semidirect
247. C₂³×C₂²⋊C₄	C₂×D₄	semidirect
249. C₂×#453	C₂×D₄	semidirect
257. C₂×#390	C₂×D₄	semidirect
258. C₂×#390	C₂×D₄	semidirect
259. C₂×#390	C₂×D₄	semidirect
260. C₂×#390	C₂×D₄	semidirect
272. C₂×#386	C₂×D₄	semidirect
273. C₂×#386	C₂×D₄	semidirect
274. C₂×#386	C₂×D₄	semidirect
275. C₂×#386	C₂×D₄	semidirect
276. C₂×#386	C₂×D₄	semidirect
277. C₂×#386	C₂×D₄	semidirect
289. C₂×#379	C₂×D₄	semidirect
290. C₂×#379	C₂×D₄	semidirect
291. C₂×#379	C₂×D₄	semidirect
292. C₂×#379	C₂×D₄	semidirect
295. C₂×C₄×C₂²⋊C₄	C₂×D₄	semidirect
296. C₂×C₄×C₂²⋊C₄	C₂×D₄	semidirect
297. #1792	C₂×D₄	semidirect
298. #1790	C₂×D₄	semidirect
300. #1781	C₂×D₄	semidirect
327. C₂³×D₄	#120	semidirect
354. C₂×#127	#120	semidirect
356. C₂×#121	#120	semidirect
357. C₂×#120	#120	semidirect
375. #390	#120	semidirect
377. #386	#120	semidirect
379. #379	#120	semidirect
380. C₄×C₂²⋊C₄	#120	semidirect
407. C₂²×D₄	C₂×#120	semidirect
428. C₂×C₄⋊C₄	C₂×#120	semidirect
431. C₂×C₄²	C₂×#120	semidirect
432. C₂×C₄²	C₂×#120	semidirect
493. C₂²	#499832	semidirect

Maximal subgroups

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

subgroup	index
#72340830	2
#72340828	2
#72339631	2
#72338267	2
#72318321	2
#72318263	2
#72317822	2
#72317685	2
#72284346	2
#72284336	2
#72284236	2
#72250179	2
#72235440	2
C₂×#499832	2
C₂×#499787	2
#72232115	2
C₂×#6628867	2
C₂²×#32898	2
#72219118	2