Subgroups — #72285111

Order 2048.

At least 6609 conjugacy classes of subgroups; only the 6580 normal subgroups are shown.

The subgroup lattice has 525 nodes (normal subgroups only) — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#72284955	C₂	1	4	yes	maximal, complemented
2	#72284827	C₂	1	4	yes	maximal, complemented
3	C₂²×#8547	C₂	1	1	yes	maximal, characteristic, complemented
4	#72241088	C₂	1	8	yes	maximal, complemented
5	#72241009	C₂	1	1	yes	maximal, characteristic, complemented
6	#72236701	C₂	1	2	yes	maximal, complemented
7	#72236603	C₂	1	2	yes	maximal, complemented
8	#72233045	C₂	1	16	yes	maximal, complemented
9	#72232536	C₂	1	16	yes	maximal, complemented
10	#72231950	C₂	1	8	yes	maximal, complemented
11	C₂²×#62817	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#62817	C₂²	1	8	yes	—
13	C₂×#62817	C₂²	1	16	yes	—
14	C₂²×#3490	C₂²	1	4	yes	—
15	C₂²×#3484	C₂²	1	2	yes	—
16	C₂⁴×#120	C₂²	1	1	yes	characteristic
17	#10575416	C₂²	1	4	yes	complemented
18	C₂×#35222	C₂²	1	1	yes	characteristic, complemented
19	C₂×#35050	C₂²	1	2	yes	complemented
20	#6470020	C₂²	1	16	yes	complemented
21	#6470019	C₂²	1	16	yes	complemented
22	#6440354	C₂²	1	8	yes	complemented
23	#6437445	C₂²	1	8	yes	complemented
24	#6374227	C₂²	1	4	yes	complemented
25	C₂²×#1783	C₂²	1	2	yes	complemented
26	#6347306	C₂²	1	16	yes	complemented
27	#6347305	C₂²	1	16	yes	complemented
28	#6347253	C₂²	1	16	yes	complemented
29	#6347252	C₂²	1	16	yes	complemented
30	#6346602	C₂²	1	16	yes	complemented
31	#6346594	C₂²	1	16	yes	complemented
32	#6343373	C₂²	1	8	yes	complemented
33	C₂²×#1462	C₂²	1	4	yes	complemented
34	#617534	C₂²	1	8	yes	complemented
35	#617359	C₂²	1	8	yes	complemented
36	#617162	C₂²	1	4	yes	complemented
37	#616961	C₂²	1	4	yes	complemented
38	#517573	C₂²	1	2	yes	complemented
39	#517415	C₂²	1	1	yes	characteristic, complemented
40	#346466	C₂²	1	128	yes	complemented
41	#346456	C₂²	1	64	yes	complemented
42	#346446	C₂²	1	64	yes	complemented
43	C₂×#8547	C₂²	1	8	yes	complemented
44	C₂×#8547	C₂²	1	16	yes	complemented
45	#186835	C₂²	1	16	yes	complemented
46	#186808	C₂²	1	32	yes	complemented
47	#185261	C₂²	1	32	yes	complemented
48	#185255	C₂²	1	32	yes	complemented
49	#185249	C₂²	1	32	yes	complemented
50	C₂⁸	D₄	1	1	yes	characteristic
51	C₂³×H(5,𝔽₂)	D₄	1	2	yes	complemented
52	C₂⁵×D₄	D₄	1	2	yes	—
53	C₂⁵×D₄	C₂³	1	1	yes	characteristic
54	#62817	C₂³	1	64	yes	—
55	C₂×#3490	D₄	1	16	yes	complemented
56	C₂×#3490	D₄	1	16	yes	complemented
57	C₂×#3490	D₄	1	16	yes	complemented
58	C₂×#3490	C₂³	1	16	yes	—
59	C₂×#3490	C₂³	1	16	yes	—
60	C₂×#3490	C₂³	1	16	yes	—
61	C₂×#3484	D₄	1	8	yes	complemented
62	C₂×#3484	D₄	1	16	yes	complemented
63	C₂×#3484	C₂³	1	8	yes	—
64	C₂×#3484	C₂³	1	16	yes	—
65	C₂²×#535	D₄	1	4	yes	complemented
66	C₂²×#535	C₂³	1	2	yes	complemented
67	C₂²×#538	D₄	1	8	yes	complemented
68	C₂²×#543	D₄	1	4	yes	complemented
69	C₂²×#534	D₄	1	4	yes	complemented
70	C₂²×#525	C₂³	1	4	yes	—
71	C₂²×#525	C₂³	1	1	yes	characteristic, complemented
72	C₂³×#120	D₄	1	4	yes	—
73	C₂³×#120	D₄	1	8	yes	—
74	C₂³×#120	C₂³	1	4	yes	—
75	C₂³×#120	C₂³	1	8	yes	—
76	C₂²×#518	D₄	1	2	yes	complemented
77	C₂⁴×C₂²⋊C₄	D₄	1	1	yes	characteristic
78	C₂⁴×C₂²⋊C₄	C₂³	1	2	yes	—
79	#60751	C₂³	1	16	yes	complemented
80	#60750	C₂³	1	16	yes	complemented
81	#60511	C₂³	1	8	yes	complemented
82	#60359	C₂³	1	8	yes	complemented
83	C₂²×#407	C₂³	1	4	yes	complemented
84	C₂×#2561	C₂³	1	4	yes	complemented
85	C₂×#2539	C₂³	1	4	yes	complemented
86	C₂×#2482	C₂³	1	4	yes	complemented
87	C₂×#2404	C₂³	1	4	yes	complemented
88	C₂×#2435	C₂³	1	4	yes	complemented
89	C₂×#2433	C₂³	1	4	yes	complemented
90	C₂×#2626	C₂³	1	4	yes	complemented
91	C₂×#2617	C₂³	1	4	yes	complemented
92	C₂×#2309	C₂³	1	2	yes	complemented
93	C₂×#2280	C₂³	1	2	yes	complemented
94	C₂×#2280	C₂³	1	1	yes	characteristic, complemented
95	#24018	C₂³	1	64	yes	complemented
96	#23907	C₂³	1	32	yes	complemented
97	#23906	C₂³	1	32	yes	complemented
98	#21773	C₂³	1	32	yes	complemented
99	#20979	C₂³	1	16	yes	complemented
100	C₂×#1783	C₂³	1	8	yes	complemented
101	C₂×#1783	C₂³	1	16	yes	complemented
102	#18170	C₂³	1	64	yes	complemented
103	#18169	C₂³	1	64	yes	complemented
104	#18163	C₂³	1	64	yes	complemented
105	#18162	C₂³	1	64	yes	complemented
106	#17592	C₂³	1	32	yes	complemented
107	#17587	C₂³	1	32	yes	complemented
108	#17542	C₂³	1	32	yes	complemented
109	C₂×#1462	C₂³	1	16	yes	complemented
110	C₂×#1462	C₂³	1	16	yes	complemented
111	C₂×#1462	C₂³	1	16	yes	complemented
112	#15283	C₂³	1	32	yes	complemented
113	#15259	C₂³	1	16	yes	complemented
114	#15258	C₂³	1	16	yes	complemented
115	#14335	C₂³	1	4	yes	complemented
116	#13903	C₂³	1	8	yes	complemented
117	#13902	C₂³	1	8	yes	complemented
118	#13868	C₂³	1	8	yes	complemented
119	#13775	C₂³	1	8	yes	complemented
120	#8547	C₂³	1	64	yes	complemented
121	#8453	C₂³	1	128	yes	complemented
122	#8346	C₂³	1	256	yes	complemented
123	C₂⁷	C₂×D₄	1	8	yes	—
124	C₂⁷	C₂×D₄	1	4	yes	—
125	C₂⁷	C₂×D₄	1	2	yes	—
126	C₂⁷	C₂×D₄	1	1	yes	characteristic
127	C₂⁷	C₂×D₄	1	1	yes	characteristic
128	C₂²×H(5,𝔽₂)	C₂×D₄	1	8	yes	—
129	C₂²×H(5,𝔽₂)	C₂×D₄	1	16	yes	—
130	C₂³×#41	C₂×D₄	1	4	yes	—
131	C₂³×#41	C₂⁴	1	1	yes	characteristic, complemented
132	C₂⁴×D₄	C₂×D₄	1	8	yes	—
133	C₂⁴×D₄	C₂×D₄	1	8	yes	—
134	C₂⁴×D₄	C₂×D₄	1	8	yes	—
135	C₂⁴×D₄	C₂×D₄	1	2	yes	—
136	C₂⁴×D₄	C₂×D₄	1	2	yes	—
137	C₂⁴×D₄	C₂×D₄	1	4	yes	—
138	C₂⁴×D₄	C₂×D₄	1	4	yes	—
139	C₂⁴×D₄	C₂×D₄	1	8	yes	—
140	C₂⁴×D₄	C₂×D₄	1	2	yes	—
141	C₂⁴×D₄	C₂⁴	1	2	yes	—
142	C₂⁴×D₄	C₂⁴	1	4	yes	—
143	C₂⁵×C₄	C₂×D₄	1	2	yes	—
144	C₂⁵×C₄	C₂⁴	1	1	yes	characteristic
145	#3490	C₂×D₄	1	64	yes	—
146	#3490	C₂×D₄	1	64	yes	—
147	#3490	C₂×D₄	1	64	yes	—
148	#3490	C₂⁴	1	64	yes	—
149	#3484	C₂×D₄	1	64	yes	—
150	#3484	C₂×D₄	1	32	yes	—
151	#3484	C₂⁴	1	32	yes	—
152	C₂×#543	C₂×D₄	1	16	yes	—
153	C₂×#543	C₂×D₄	1	16	yes	—
154	C₂×#543	C₂×D₄	1	16	yes	—
155	C₂×#538	C₂×D₄	1	32	yes	—
156	C₂×#538	C₂×D₄	1	32	yes	—
157	C₂×#538	C₂×D₄	1	32	yes	—
158	C₂×#535	C₂×D₄	1	16	yes	—
159	C₂×#535	C₂×D₄	1	32	yes	—
160	C₂×#534	C₂×D₄	1	16	yes	—
161	C₂×#534	C₂×D₄	1	16	yes	—
162	C₂×#534	C₂×D₄	1	16	yes	—
163	C₂²×#127	C₂⁴	1	4	yes	complemented
164	C₂²×#124	C₂⁴	1	4	yes	complemented
165	C₂×#525	C₂×D₄	1	16	yes	—
166	C₂×#525	C₂×D₄	1	16	yes	—
167	C₂×#525	C₂×D₄	1	16	yes	—
168	C₂×#525	C₂×D₄	1	16	yes	—
169	C₂×#525	C₂×D₄	1	8	yes	—
170	C₂×#525	C₂⁴	1	16	yes	—
171	C₂×#525	C₂⁴	1	8	yes	—
172	C₂²×C₂²⋊Q₈	C₂×D₄	1	8	yes	—
173	C₂²×C₂²⋊Q₈	C₂⁴	1	2	yes	complemented
174	C₂²×#121	C₂×D₄	1	8	yes	—
175	C₂²×#121	C₂⁴	1	2	yes	complemented
176	C₂²×#120	C₂×D₄	1	16	yes	—
177	C₂²×#120	C₂×D₄	1	32	yes	—
178	C₂²×#120	C₂⁴	1	16	yes	—
179	C₂×#518	C₂×D₄	1	8	yes	—
180	C₂×#518	C₂×D₄	1	16	yes	—
181	C₂²×#117	C₂×D₄	1	4	yes	—
182	C₂²×#117	C₂⁴	1	2	yes	complemented
183	C₂²×#117	C₂⁴	1	1	yes	characteristic, complemented
184	C₂³×C₂²⋊C₄	C₂×D₄	1	8	yes	—
185	C₂³×C₂²⋊C₄	C₂×D₄	1	4	yes	—
186	C₂³×C₂²⋊C₄	C₂×D₄	1	4	yes	—
187	C₂³×C₂²⋊C₄	C₂×D₄	1	4	yes	—
188	C₂³×C₂²⋊C₄	C₂×D₄	1	4	yes	—
189	C₂³×C₂²⋊C₄	C₂×D₄	1	8	yes	—
190	C₂³×C₂²⋊C₄	C₂×D₄	1	8	yes	—
191	C₂³×C₂²⋊C₄	C₂×D₄	1	8	yes	—
192	C₂³×C₂²⋊C₄	C₂×D₄	1	4	yes	—
193	C₂³×C₂²⋊C₄	C₂×D₄	1	4	yes	—
194	C₂³×C₂²⋊C₄	C₂⁴	1	4	yes	—
195	C₂³×C₂²⋊C₄	C₂⁴	1	4	yes	—
196	C₂³×C₂²⋊C₄	C₂⁴	1	4	yes	—
197	#3092	C₂⁴	1	32	yes	complemented
198	#3004	C₂⁴	1	16	yes	complemented
199	#3003	C₂⁴	1	16	yes	complemented
200	C₂×#407	C₂⁴	1	16	yes	complemented
201	C₂×#407	C₂⁴	1	8	yes	complemented
202	C₂×#399	C₂⁴	1	8	yes	complemented
203	C₂×#397	C₂⁴	1	8	yes	complemented
204	C₂×#393	C₂⁴	1	8	yes	complemented
205	C₂×#392	C₂⁴	1	8	yes	complemented
206	C₂×#390	C₂⁴	1	8	yes	complemented
207	C₂×#381	C₂⁴	1	4	yes	complemented
208	C₂×#380	C₂⁴	1	4	yes	complemented
209	C₂×C₄×C₂²⋊C₄	C₂⁴	1	4	yes	complemented
210	C₂×C₄×C₂²⋊C₄	C₂⁴	1	4	yes	complemented
211	#1896	C₂⁴	1	64	yes	complemented
212	#1783	C₂⁴	1	32	yes	complemented
213	#1504	C₂⁴	1	128	yes	complemented
214	#1462	C₂⁴	1	64	yes	complemented
215	#1438	C₂⁴	1	16	yes	complemented
216	#1437	C₂⁴	1	32	yes	complemented
217	C₂⁶	#120	1	2	yes	—
218	C₂⁶	#120	1	1	yes	characteristic
219	C₂⁶	#120	1	4	yes	—
220	C₂⁶	#120	1	2	yes	—
221	C₂⁶	#120	1	2	yes	—
222	C₂⁶	#120	1	2	yes	—
223	C₂⁶	#120	1	2	yes	—
224	C₂⁶	#120	1	4	yes	—
225	C₂⁶	#120	1	4	yes	—
226	C₂⁶	#120	1	1	yes	characteristic
227	C₂⁶	#120	1	4	yes	—
228	C₂⁶	#120	1	4	yes	—
229	C₂⁶	C₂²×D₄	1	4	yes	—
230	C₂⁶	C₂²×D₄	1	2	yes	—
231	C₂⁶	C₂²×D₄	1	16	yes	—
232	C₂⁶	C₂²×D₄	1	4	yes	—
233	C₂⁶	C₂²×D₄	1	4	yes	—
234	C₂⁶	C₂²×D₄	1	4	yes	—
235	C₂⁶	C₂²×D₄	1	2	yes	—
236	C₂⁶	C₂²×D₄	1	4	yes	—
237	C₂⁶	C₂²×D₄	1	1	yes	characteristic
238	C₂×H(5,𝔽₂)	C₂²×D₄	1	32	yes	—
239	C₂²×#41	#120	1	16	yes	complemented
240	C₂²×#41	#120	1	8	yes	complemented
241	C₂²×#41	C₂²×D₄	1	8	yes	—
242	C₂²×#41	C₂²×D₄	1	16	yes	—
243	C₂³×Q₈	#120	1	4	yes	complemented
244	C₂³×Q₈	C₂⁵	1	1	yes	characteristic, complemented
245	C₂³×D₄	#120	1	4	yes	—
246	C₂³×D₄	#120	1	8	yes	—
247	C₂³×D₄	#120	1	4	yes	—
248	C₂³×D₄	#120	1	8	yes	—
249	C₂³×D₄	#120	1	16	yes	—
250	C₂³×D₄	#120	1	8	yes	—
251	C₂³×D₄	#120	1	4	yes	complemented
252	C₂³×D₄	C₂²×D₄	1	4	yes	—
253	C₂³×D₄	C₂²×D₄	1	32	yes	—
254	C₂³×D₄	C₂²×D₄	1	4	yes	—
255	C₂³×D₄	C₂²×D₄	1	8	yes	—
256	C₂³×D₄	C₂²×D₄	1	8	yes	—
257	C₂³×D₄	C₂²×D₄	1	4	yes	—
258	C₂³×D₄	C₂²×D₄	1	8	yes	—
259	C₂³×D₄	C₂²×D₄	1	16	yes	—
260	C₂³×D₄	C₂²×D₄	1	8	yes	—
261	C₂³×D₄	C₂⁵	1	4	yes	—
262	C₂³×D₄	C₂⁵	1	1	yes	characteristic, complemented
263	C₂⁴×C₄	#120	1	4	yes	—
264	C₂⁴×C₄	#120	1	4	yes	—
265	C₂⁴×C₄	#120	1	4	yes	—
266	C₂⁴×C₄	#120	1	4	yes	—
267	C₂⁴×C₄	C₂²×D₄	1	4	yes	—
268	C₂⁴×C₄	C₂²×D₄	1	4	yes	—
269	C₂⁴×C₄	C₂²×D₄	1	4	yes	—
270	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
271	C₂⁴×C₄	C₂²×D₄	1	2	yes	—
272	C₂⁴×C₄	C₂²×D₄	1	2	yes	—
273	C₂⁴×C₄	C₂²×D₄	1	2	yes	—
274	C₂⁴×C₄	C₂²×D₄	1	4	yes	—
275	C₂⁴×C₄	C₂²×D₄	1	4	yes	—
276	C₂⁴×C₄	C₂²×D₄	1	4	yes	—
277	C₂⁴×C₄	C₂²×D₄	1	4	yes	—
278	C₂⁴×C₄	C₂²×D₄	1	4	yes	—
279	C₂⁴×C₄	C₂⁵	1	1	yes	characteristic
280	C₂⁴×C₄	C₂⁵	1	2	yes	—
281	#543	C₂²×D₄	1	64	yes	—
282	#538	C₂²×D₄	1	128	yes	—
283	#535	C₂²×D₄	1	64	yes	—
284	#534	C₂²×D₄	1	64	yes	—
285	#525	#120	1	32	yes	complemented
286	#525	#120	1	32	yes	complemented
287	#525	#120	1	16	yes	complemented
288	#525	#120	1	16	yes	complemented
289	#525	C₂²×D₄	1	32	yes	—
290	#525	C₂²×D₄	1	32	yes	—
291	#525	C₂²×D₄	1	32	yes	—
292	#525	C₂²×D₄	1	16	yes	—
293	#525	C₂²×D₄	1	32	yes	—
294	#525	C₂⁵	1	16	yes	—
295	C₂×C₂²⋊Q₈	#120	1	16	yes	complemented
296	C₂×C₂²⋊Q₈	#120	1	16	yes	complemented
297	C₂×C₂²⋊Q₈	#120	1	16	yes	complemented
298	C₂×C₂²⋊Q₈	C₂²×D₄	1	16	yes	—
299	C₂×C₂²⋊Q₈	C₂²×D₄	1	16	yes	—
300	C₂×C₂²⋊Q₈	C₂²×D₄	1	16	yes	—
301	C₂×#121	#120	1	16	yes	complemented
302	C₂×#121	#120	1	16	yes	complemented
303	C₂×#121	#120	1	16	yes	complemented
304	C₂×#121	C₂²×D₄	1	16	yes	—
305	C₂×#121	C₂²×D₄	1	16	yes	—
306	C₂×#121	C₂²×D₄	1	16	yes	—
307	#518	C₂²×D₄	1	32	yes	—
308	C₂×#117	#120	1	16	yes	complemented
309	C₂×#117	#120	1	8	yes	complemented
310	C₂×#117	C₂²×D₄	1	16	yes	—
311	C₂×#117	C₂²×D₄	1	8	yes	—
312	C₂²×C₄⋊C₄	#120	1	8	yes	complemented
313	C₂²×C₄⋊C₄	C₂⁵	1	2	yes	complemented
314	C₂²×C₂²⋊C₄	#120	1	8	yes	—
315	C₂²×C₂²⋊C₄	#120	1	8	yes	—
316	C₂²×C₂²⋊C₄	#120	1	16	yes	—
317	C₂²×C₂²⋊C₄	#120	1	8	yes	—
318	C₂²×C₂²⋊C₄	#120	1	8	yes	—
319	C₂²×C₂²⋊C₄	#120	1	8	yes	—
320	C₂²×C₂²⋊C₄	#120	1	16	yes	—
321	C₂²×C₂²⋊C₄	#120	1	8	yes	—
322	C₂²×C₂²⋊C₄	#120	1	16	yes	—
323	C₂²×C₂²⋊C₄	C₂²×D₄	1	16	yes	—
324	C₂²×C₂²⋊C₄	C₂²×D₄	1	8	yes	—
325	C₂²×C₂²⋊C₄	C₂²×D₄	1	8	yes	—
326	C₂²×C₂²⋊C₄	C₂²×D₄	1	8	yes	—
327	C₂²×C₂²⋊C₄	C₂²×D₄	1	8	yes	—
328	C₂²×C₂²⋊C₄	C₂²×D₄	1	8	yes	—
329	C₂²×C₂²⋊C₄	C₂²×D₄	1	16	yes	—
330	C₂²×C₂²⋊C₄	C₂²×D₄	1	8	yes	—
331	C₂²×C₂²⋊C₄	C₂²×D₄	1	8	yes	—
332	C₂²×C₂²⋊C₄	C₂²×D₄	1	16	yes	—
333	C₂²×C₂²⋊C₄	C₂²×D₄	1	8	yes	—
334	C₂²×C₂²⋊C₄	C₂²×D₄	1	8	yes	—
335	C₂²×C₂²⋊C₄	C₂²×D₄	1	16	yes	—
336	C₂²×C₂²⋊C₄	C₂⁵	1	8	yes	—
337	C₂²×C₄²	C₂⁵	1	4	yes	complemented
338	#407	C₂⁵	1	16	yes	complemented
339	C₂×#95	C₂⁵	1	8	yes	complemented
340	C₂⁵	C₂×#120	1	4	yes	—
341	C₂⁵	C₂×#120	1	4	yes	—
342	C₂⁵	C₂×#120	1	4	yes	—
343	C₂⁵	C₂×#120	1	2	yes	—
344	C₂⁵	C₂×#120	1	4	yes	—
345	C₂⁵	C₂×#120	1	4	yes	—
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	2	yes	—
350	C₂⁵	C₂×#120	1	8	yes	—
351	C₂⁵	C₂×#120	1	8	yes	—
352	C₂⁵	C₂×#120	1	8	yes	—
353	C₂⁵	C₂×#120	1	4	yes	—
354	C₂⁵	C₂×#120	1	8	yes	—
355	C₂⁵	C₂×#120	1	4	yes	—
356	C₂⁵	C₂×#120	1	2	yes	—
357	C₂⁵	C₂×#120	1	4	yes	—
358	C₂⁵	C₂×#120	1	8	yes	—
359	C₂⁵	C₂×#120	1	4	yes	—
360	C₂⁵	C₂×#120	1	4	yes	—
361	C₂⁵	C₂×#120	1	8	yes	—
362	C₂⁵	C₂×#120	1	4	yes	—
363	C₂⁵	C₂×#120	1	2	yes	—
364	C₂⁵	C₂×#120	1	2	yes	—
365	C₂⁵	C₂×#120	1	2	yes	—
366	C₂⁵	C₂³×D₄	1	4	yes	—
367	C₂⁵	C₂³×D₄	1	8	yes	—
368	C₂⁵	C₂³×D₄	1	2	yes	—
369	C₂⁵	C₂³×D₄	1	1	yes	characteristic
370	C₂⁵	C₂³×D₄	1	4	yes	—
371	C₂×#41	C₂×#120	1	16	yes	—
372	C₂×#41	C₂×#120	1	32	yes	—
373	C₂×#41	C₂³×D₄	1	16	yes	—
374	C₂²×Q₈	C₂×#120	1	8	yes	—
375	C₂²×Q₈	C₂×#120	1	16	yes	—
376	C₂²×D₄	C₂×#120	1	8	yes	—
377	C₂²×D₄	C₂×#120	1	16	yes	—
378	C₂²×D₄	C₂×#120	1	8	yes	—
379	C₂²×D₄	C₂×#120	1	16	yes	—
380	C₂²×D₄	C₂×#120	1	8	yes	—
381	C₂²×D₄	C₂×#120	1	16	yes	—
382	C₂²×D₄	C₂³×D₄	1	8	yes	—
383	C₂²×D₄	C₂³×D₄	1	8	yes	—
384	C₂³×C₄	C₂×#120	1	2	yes	—
385	C₂³×C₄	C₂×#120	1	8	yes	—
386	C₂³×C₄	C₂×#120	1	8	yes	—
387	C₂³×C₄	C₂×#120	1	8	yes	—
388	C₂³×C₄	C₂×#120	1	8	yes	—
389	C₂³×C₄	C₂×#120	1	8	yes	—
390	C₂³×C₄	C₂×#120	1	8	yes	—
391	C₂³×C₄	C₂×#120	1	4	yes	—
392	C₂³×C₄	C₂×#120	1	4	yes	—
393	C₂³×C₄	C₂×#120	1	2	yes	—
394	C₂³×C₄	C₂×#120	1	4	yes	—
395	C₂³×C₄	C₂×#120	1	4	yes	—
396	C₂³×C₄	C₂×#120	1	4	yes	—
397	C₂³×C₄	C₂×#120	1	8	yes	—
398	C₂³×C₄	C₂×#120	1	4	yes	—
399	C₂³×C₄	C₂×#120	1	8	yes	—
400	C₂³×C₄	C₂×#120	1	4	yes	—
401	C₂³×C₄	C₂×#120	1	4	yes	—
402	C₂³×C₄	C₂×#120	1	4	yes	—
403	C₂³×C₄	C₂×#120	1	4	yes	—
404	C₂³×C₄	C₂×#120	1	4	yes	—
405	C₂³×C₄	C₂×#120	1	4	yes	—
406	C₂³×C₄	C₂×#120	1	8	yes	—
407	C₂³×C₄	C₂×#120	1	8	yes	—
408	C₂³×C₄	C₂×#120	1	8	yes	—
409	C₂³×C₄	C₂×#120	1	8	yes	—
410	C₂³×C₄	C₂³×D₄	1	2	yes	—
411	C₂³×C₄	C₂³×D₄	1	8	yes	—
412	C₂³×C₄	C₂³×D₄	1	2	yes	—
413	C₂³×C₄	C₂³×D₄	1	4	yes	—
414	C₂³×C₄	C₂³×D₄	1	4	yes	—
415	C₂³×C₄	C₂³×D₄	1	4	yes	—
416	C₂³×C₄	C₂³×D₄	1	4	yes	—
417	C₂³×C₄	C₂³×D₄	1	2	yes	—
418	C₂³×C₄	C₂³×D₄	1	1	yes	characteristic
419	C₂³×C₄	C₂³×D₄	1	4	yes	—
420	C₂³×C₄	C₂³×D₄	1	4	yes	—
421	C₂³×C₄	C₂³×D₄	1	4	yes	—
422	C₂³×C₄	C₂³×D₄	1	4	yes	—
423	C₂³×C₄	C₂⁶	1	1	yes	characteristic
424	C₂²⋊Q₈	C₂×#120	1	32	yes	—
425	C₂²⋊Q₈	C₂×#120	1	32	yes	—
426	C₂²⋊Q₈	C₂×#120	1	32	yes	—
427	C₂²⋊Q₈	C₂³×D₄	1	32	yes	—
428	#121	C₂×#120	1	32	yes	—
429	#121	C₂×#120	1	32	yes	—
430	#121	C₂×#120	1	32	yes	—
431	#121	C₂³×D₄	1	32	yes	—
432	#117	C₂×#120	1	16	yes	—
433	#117	C₂×#120	1	32	yes	—
434	#117	C₂³×D₄	1	16	yes	—
435	C₂×C₄⋊C₄	C₂×#120	1	16	yes	—
436	C₂×C₄⋊C₄	C₂×#120	1	16	yes	—
437	C₂×C₄⋊C₄	C₂×#120	1	16	yes	—
438	C₂×C₂²⋊C₄	C₂×#120	1	16	yes	—
439	C₂×C₂²⋊C₄	C₂×#120	1	16	yes	—
440	C₂×C₂²⋊C₄	C₂×#120	1	16	yes	—
441	C₂×C₂²⋊C₄	C₂×#120	1	16	yes	—
442	C₂×C₂²⋊C₄	C₂×#120	1	16	yes	—
443	C₂×C₂²⋊C₄	C₂×#120	1	16	yes	—
444	C₂×C₂²⋊C₄	C₂³×D₄	1	16	yes	—
445	C₂×C₂²⋊C₄	C₂³×D₄	1	16	yes	—
446	C₂⁴	#2846	1	1	yes	characteristic
447	C₂⁴	#2846	1	1	yes	characteristic
448	C₂⁴	#2846	1	2	yes	—
449	C₂⁴	#2846	1	2	yes	—
450	C₂⁴	#2846	1	2	yes	—
451	C₂⁴	#2846	1	2	yes	—
452	C₂⁴	#2846	1	1	yes	characteristic
453	C₂⁴	#2846	1	2	yes	—
454	C₂⁴	#2846	1	1	yes	characteristic
455	C₂⁴	#2846	1	2	yes	—
456	C₂⁴	#3019	1	16	yes	complemented
457	C₂⁴	#3026	1	8	yes	—
458	C₂⁴	C₂²×#120	1	2	yes	—
459	C₂⁴	C₂²×#120	1	2	yes	—
460	C₂⁴	C₂²×#120	1	2	yes	—
461	C₂⁴	C₂²×#120	1	2	yes	—
462	C₂⁴	C₂²×#120	1	2	yes	—
463	C₂⁴	C₂²×#120	1	2	yes	—
464	C₂⁴	C₂²×#120	1	4	yes	—
465	C₂⁴	C₂²×#120	1	8	yes	—
466	C₂⁴	C₂²×#120	1	8	yes	—
467	C₂⁴	C₂²×#120	1	1	yes	characteristic
468	C₂⁴	C₂²×#120	1	2	yes	—
469	C₂⁴	C₂²×#120	1	8	yes	—
470	C₂⁴	C₂²×#120	1	4	yes	—
471	C₂⁴	C₂²×#120	1	2	yes	—
472	C₂⁴	C₂²×#120	1	1	yes	characteristic
473	C₂⁴	C₂⁴×D₄	1	1	yes	characteristic
474	C₂×Q₈	C₂²×#120	1	16	yes	—
475	C₂×D₄	C₂²×#120	1	16	yes	—
476	C₂²×C₄	#2846	1	4	yes	—
477	C₂²×C₄	#2846	1	4	yes	—
478	C₂²×C₄	#2846	1	8	yes	—
479	C₂²×C₄	#2846	1	8	yes	—
480	C₂²×C₄	#2846	1	8	yes	—
481	C₂²×C₄	#2846	1	8	yes	—
482	C₂²×C₄	#2846	1	8	yes	—
483	C₂²×C₄	C₂²×#120	1	4	yes	—
484	C₂²×C₄	C₂²×#120	1	2	yes	—
485	C₂²×C₄	C₂²×#120	1	4	yes	—
486	C₂²×C₄	C₂²×#120	1	4	yes	—
487	C₂²×C₄	C₂²×#120	1	16	yes	—
488	C₂²×C₄	C₂²×#120	1	4	yes	—
489	C₂²×C₄	C₂²×#120	1	4	yes	—
490	C₂²×C₄	C₂²×#120	1	4	yes	—
491	C₂²×C₄	C₂²×#120	1	8	yes	—
492	C₂²×C₄	C₂²×#120	1	8	yes	—
493	C₂²×C₄	C₂²×#120	1	8	yes	—
494	C₂²×C₄	C₂²×#120	1	8	yes	—
495	C₂²×C₄	C₂²×#120	1	8	yes	—
496	C₂²×C₄	C₂⁴×D₄	1	2	yes	—
497	C₂²×C₄	C₂⁴×D₄	1	4	yes	—
498	C₄⋊C₄	C₂²×#120	1	32	yes	—
499	C₂³	C₂×#2846	1	2	yes	—
500	C₂³	C₂×#2846	1	2	yes	—
501	C₂³	C₂×#2846	1	2	yes	—
502	C₂³	C₂×#2846	1	2	yes	—
503	C₂³	C₂×#2846	1	2	yes	—
504	C₂³	C₂×#2846	1	1	yes	characteristic
505	C₂³	C₂×#2846	1	1	yes	characteristic
506	C₂³	C₂×#3019	1	16	yes	—
507	C₂³	C₂×#3019	1	8	yes	—
508	C₂³	C₂×#3026	1	8	yes	—
509	C₂³	C₂×#3026	1	4	yes	—
510	C₂³	C₂³×#120	1	1	yes	characteristic
511	C₂³	C₂³×#120	1	2	yes	—
512	C₂×C₄	C₂×#2846	1	4	yes	—
513	C₂×C₄	C₂×#2846	1	8	yes	—
514	C₂×C₄	C₂³×#120	1	4	yes	—
515	C₂²	#6628867	1	4	yes	—
516	C₂²	#6628867	1	4	yes	—
517	C₂²	#6628892	1	2	yes	—
518	C₂²	#6628892	1	2	yes	—
519	C₂²	C₂²×#2846	1	1	yes	characteristic
520	C₂²	C₂²×#3019	1	4	yes	—
521	C₂²	C₂²×#3026	1	2	yes	—
522	C₂	C₂×#6628867	1	2	yes	—
523	C₂	C₂×#6628892	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²	C₂²×#2846
commutator, Frattini, cosocle	C₂³×C₄	C₂⁶
LCS	G ▷ C₂³×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂² ◁ C₂⁵×C₄ ◁ G
LECS	G ▷ C₂³×C₄ ▷ C₂² ▷ C₁

Complements

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

N	H ≅ G/N	type
1. #72284955	C₂	semidirect
2. #72284827	C₂	semidirect
3. C₂²×#8547	C₂	semidirect
4. #72241088	C₂	semidirect
5. #72241009	C₂	semidirect
6. #72236701	C₂	semidirect
7. #72236603	C₂	semidirect
8. #72233045	C₂	semidirect
9. #72232536	C₂	semidirect
10. #72231950	C₂	semidirect
11. C₂²×#62817	C₂	semidirect
17. #10575416	C₂²	semidirect
18. C₂×#35222	C₂²	semidirect
19. C₂×#35050	C₂²	semidirect
20. #6470020	C₂²	semidirect
21. #6470019	C₂²	semidirect
22. #6440354	C₂²	semidirect
23. #6437445	C₂²	semidirect
24. #6374227	C₂²	semidirect
25. C₂²×#1783	C₂²	semidirect
26. #6347306	C₂²	semidirect
27. #6347305	C₂²	semidirect
28. #6347253	C₂²	semidirect
29. #6347252	C₂²	semidirect
30. #6346602	C₂²	semidirect
31. #6346594	C₂²	semidirect
32. #6343373	C₂²	semidirect
33. C₂²×#1462	C₂²	semidirect
34. #617534	C₂²	semidirect
35. #617359	C₂²	semidirect
36. #617162	C₂²	semidirect
37. #616961	C₂²	semidirect
38. #517573	C₂²	semidirect
39. #517415	C₂²	semidirect
40. #346466	C₂²	semidirect
41. #346456	C₂²	semidirect
42. #346446	C₂²	semidirect
43. C₂×#8547	C₂²	semidirect
44. C₂×#8547	C₂²	semidirect
45. #186835	C₂²	semidirect
46. #186808	C₂²	semidirect
47. #185261	C₂²	semidirect
48. #185255	C₂²	semidirect
49. #185249	C₂²	semidirect
51. C₂³×H(5,𝔽₂)	D₄	semidirect
55. C₂×#3490	D₄	semidirect
56. C₂×#3490	D₄	semidirect
57. C₂×#3490	D₄	semidirect
61. C₂×#3484	D₄	semidirect
62. C₂×#3484	D₄	semidirect
65. C₂²×#535	D₄	semidirect
66. C₂²×#535	C₂³	semidirect
67. C₂²×#538	D₄	semidirect
68. C₂²×#543	D₄	semidirect
69. C₂²×#534	D₄	semidirect
71. C₂²×#525	C₂³	semidirect
76. C₂²×#518	D₄	semidirect
79. #60751	C₂³	semidirect
80. #60750	C₂³	semidirect
81. #60511	C₂³	semidirect
82. #60359	C₂³	semidirect
83. C₂²×#407	C₂³	semidirect
84. C₂×#2561	C₂³	semidirect
85. C₂×#2539	C₂³	semidirect
86. C₂×#2482	C₂³	semidirect
87. C₂×#2404	C₂³	semidirect
88. C₂×#2435	C₂³	semidirect
89. C₂×#2433	C₂³	semidirect
90. C₂×#2626	C₂³	semidirect
91. C₂×#2617	C₂³	semidirect
92. C₂×#2309	C₂³	semidirect
93. C₂×#2280	C₂³	semidirect
94. C₂×#2280	C₂³	semidirect
95. #24018	C₂³	semidirect
96. #23907	C₂³	semidirect
97. #23906	C₂³	semidirect
98. #21773	C₂³	semidirect
99. #20979	C₂³	semidirect
100. C₂×#1783	C₂³	semidirect
101. C₂×#1783	C₂³	semidirect
102. #18170	C₂³	semidirect
103. #18169	C₂³	semidirect
104. #18163	C₂³	semidirect
105. #18162	C₂³	semidirect
106. #17592	C₂³	semidirect
107. #17587	C₂³	semidirect
108. #17542	C₂³	semidirect
109. C₂×#1462	C₂³	semidirect
110. C₂×#1462	C₂³	semidirect
111. C₂×#1462	C₂³	semidirect
112. #15283	C₂³	semidirect
113. #15259	C₂³	semidirect
114. #15258	C₂³	semidirect
115. #14335	C₂³	semidirect
116. #13903	C₂³	semidirect
117. #13902	C₂³	semidirect
118. #13868	C₂³	semidirect
119. #13775	C₂³	semidirect
120. #8547	C₂³	semidirect
121. #8453	C₂³	semidirect
122. #8346	C₂³	semidirect
131. C₂³×#41	C₂⁴	semidirect
163. C₂²×#127	C₂⁴	semidirect
164. C₂²×#124	C₂⁴	semidirect
173. C₂²×C₂²⋊Q₈	C₂⁴	semidirect
175. C₂²×#121	C₂⁴	semidirect
182. C₂²×#117	C₂⁴	semidirect
183. C₂²×#117	C₂⁴	semidirect
197. #3092	C₂⁴	semidirect
198. #3004	C₂⁴	semidirect
199. #3003	C₂⁴	semidirect
200. C₂×#407	C₂⁴	semidirect
201. C₂×#407	C₂⁴	semidirect
202. C₂×#399	C₂⁴	semidirect
203. C₂×#397	C₂⁴	semidirect
204. C₂×#393	C₂⁴	semidirect
205. C₂×#392	C₂⁴	semidirect
206. C₂×#390	C₂⁴	semidirect
207. C₂×#381	C₂⁴	semidirect
208. C₂×#380	C₂⁴	semidirect
209. C₂×C₄×C₂²⋊C₄	C₂⁴	semidirect
210. C₂×C₄×C₂²⋊C₄	C₂⁴	semidirect
211. #1896	C₂⁴	semidirect
212. #1783	C₂⁴	semidirect
213. #1504	C₂⁴	semidirect
214. #1462	C₂⁴	semidirect
215. #1438	C₂⁴	semidirect
216. #1437	C₂⁴	semidirect
239. C₂²×#41	#120	semidirect
240. C₂²×#41	#120	semidirect
243. C₂³×Q₈	#120	semidirect
244. C₂³×Q₈	C₂⁵	semidirect
251. C₂³×D₄	#120	semidirect
262. C₂³×D₄	C₂⁵	semidirect
285. #525	#120	semidirect
286. #525	#120	semidirect
287. #525	#120	semidirect
288. #525	#120	semidirect
295. C₂×C₂²⋊Q₈	#120	semidirect
296. C₂×C₂²⋊Q₈	#120	semidirect
297. C₂×C₂²⋊Q₈	#120	semidirect
301. C₂×#121	#120	semidirect
302. C₂×#121	#120	semidirect
303. C₂×#121	#120	semidirect
308. C₂×#117	#120	semidirect
309. C₂×#117	#120	semidirect
312. C₂²×C₄⋊C₄	#120	semidirect
313. C₂²×C₄⋊C₄	C₂⁵	semidirect
337. C₂²×C₄²	C₂⁵	semidirect
338. #407	C₂⁵	semidirect
339. C₂×#95	C₂⁵	semidirect
456. C₂⁴	#3019	semidirect

Maximal subgroups

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

subgroup	index
#72284955	2
#72284827	2
C₂²×#8547	2
#72241088	2
#72241009	2
#72236701	2
#72236603	2
#72233045	2
#72232536	2
#72231950	2
C₂²×#62817	2