Subgroups — #72286795

Order 2048.

At least 9230 conjugacy classes of subgroups; only the 1244 normal subgroups are shown.

The subgroup lattice has 501 nodes (normal subgroups only) — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#72286785	C₂	1	2	yes	maximal, complemented
2	#72286766	C₂	1	2	yes	maximal, complemented
3	#72286753	C₂	1	2	yes	maximal, complemented
4	#72286743	C₂	1	2	yes	maximal, complemented
5	#72286735	C₂	1	2	yes	maximal, complemented
6	#72286727	C₂	1	2	yes	maximal, complemented
7	#72286719	C₂	1	2	yes	maximal, complemented
8	#72286708	C₂	1	2	yes	maximal, complemented
9	#72286597	C₂	1	2	yes	maximal, complemented
10	#72286549	C₂	1	2	yes	maximal, complemented
11	#72286478	C₂	1	2	yes	maximal, complemented
12	#72286434	C₂	1	2	yes	maximal, complemented
13	#72286278	C₂	1	1	yes	maximal, characteristic, complemented
14	#72286226	C₂	1	1	yes	maximal, characteristic, complemented
15	#72286177	C₂	1	1	yes	maximal, characteristic, complemented
16	#72284814	C₂	1	1	yes	maximal, characteristic, complemented
17	#72284648	C₂	1	1	yes	maximal, characteristic, complemented
18	#72282667	C₂	1	1	yes	maximal, characteristic, complemented
19	#72226694	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×#62862	C₂²	1	1	yes	characteristic
21	C₂³×#535	C₂²	1	1	yes	characteristic
22	C₂×#60806	C₂²	1	1	yes	characteristic, complemented
23	C₂×#60806	C₂²	1	1	yes	characteristic, complemented
24	#7714980	C₂²	1	2	yes	—
25	#7714555	C₂²	1	2	yes	—
26	#7711811	C₂²	1	2	yes	—
27	#7711201	C₂²	1	2	yes	—
28	#7643884	C₂²	1	2	yes	—
29	#7631036	C₂²	1	2	yes	—
30	#7628656	C₂²	1	1	yes	characteristic, complemented
31	#7626355	C₂²	1	1	yes	characteristic
32	#6446630	C₂²	1	1	yes	characteristic
33	#6446630	C₂²	1	1	yes	characteristic, complemented
34	#6446625	C₂²	1	1	yes	characteristic, complemented
35	#6446623	C₂²	1	1	yes	characteristic, complemented
36	#6443103	C₂²	1	1	yes	characteristic
37	#6443103	C₂²	1	1	yes	characteristic, complemented
38	#6443097	C₂²	1	1	yes	characteristic, complemented
39	#6443095	C₂²	1	1	yes	characteristic, complemented
40	#6374281	C₂²	1	1	yes	characteristic, complemented
41	#6374281	C₂²	1	1	yes	characteristic, complemented
42	#6370926	C₂²	1	1	yes	characteristic, complemented
43	#6351566	C₂²	1	2	yes	complemented
44	#6351559	C₂²	1	2	yes	complemented
45	#6348455	C₂²	1	2	yes	complemented
46	#6348447	C₂²	1	2	yes	complemented
47	#6347279	C₂²	1	2	yes	complemented
48	#6347278	C₂²	1	2	yes	complemented
49	#6347126	C₂²	1	4	yes	complemented
50	#236269	C₂²	1	4	yes	complemented
51	#236265	C₂²	1	4	yes	complemented
52	#235528	C₂²	1	4	yes	complemented
53	#235527	C₂²	1	4	yes	complemented
54	#234330	C₂²	1	4	yes	complemented
55	#234329	C₂²	1	4	yes	complemented
56	#201630	C₂²	1	4	yes	complemented
57	#201039	C₂²	1	2	yes	complemented
58	#201037	C₂²	1	2	yes	complemented
59	#200851	C₂²	1	2	yes	complemented
60	#200848	C₂²	1	2	yes	complemented
61	#200466	C₂²	1	4	yes	complemented
62	#197550	C₂²	1	2	yes	complemented
63	#197546	C₂²	1	2	yes	complemented
64	#197531	C₂²	1	4	yes	complemented
65	#187883	C₂²	1	2	yes	complemented
66	#187883	C₂²	1	2	yes	complemented
67	C₂×#8522	C₂²	1	1	yes	characteristic
68	C₂×#8522	C₂²	1	1	yes	characteristic
69	C₂×#8522	C₂²	1	2	yes	complemented
70	C₂×#8522	C₂²	1	2	yes	complemented
71	C₂×#8522	C₂²	1	2	yes	complemented
72	#187463	C₂²	1	2	yes	complemented
73	#187463	C₂²	1	2	yes	complemented
74	#185297	C₂²	1	2	yes	complemented
75	#185297	C₂²	1	2	yes	complemented
76	#185202	C₂²	1	2	yes	complemented
77	#185132	C₂²	1	2	yes	complemented
78	#184776	C₂²	1	2	yes	complemented
79	#113071	C₂²	1	4	yes	complemented
80	#113071	C₂²	1	4	yes	complemented
81	#112067	C₂²	1	4	yes	complemented
82	#112067	C₂²	1	4	yes	complemented
83	#111635	C₂²	1	4	yes	complemented
84	#111635	C₂²	1	4	yes	complemented
85	#108372	C₂²	1	2	yes	complemented
86	#108372	C₂²	1	2	yes	complemented
87	#107339	C₂²	1	2	yes	complemented
88	#107339	C₂²	1	2	yes	complemented
89	#106576	C₂²	1	2	yes	complemented
90	#106576	C₂²	1	2	yes	complemented
91	C₂⁴×#41	D₄	1	1	yes	characteristic
92	C₂⁵×D₄	D₄	1	1	yes	characteristic
93	C₂×#3491	C₂³	1	2	yes	—
94	C₂×#3545	C₂³	1	2	yes	—
95	C₂×#3543	C₂³	1	2	yes	—
96	C₂×#3455	C₂³	1	1	yes	characteristic, complemented
97	C₂²×#535	D₄	1	1	yes	characteristic
98	C₂²×#535	D₄	1	1	yes	characteristic
99	C₂²×#535	D₄	1	1	yes	characteristic
100	C₂²×#535	D₄	1	1	yes	characteristic
101	C₂²×#535	C₂³	1	1	yes	characteristic
102	C₂²×#535	C₂³	1	1	yes	characteristic
103	C₂²×#535	C₂³	1	1	yes	characteristic
104	C₂²×#535	C₂³	1	1	yes	characteristic
105	C₂³×#127	D₄	1	1	yes	characteristic
106	C₂³×#127	C₂³	1	1	yes	characteristic
107	C₂³×#124	D₄	1	1	yes	characteristic
108	C₂³×#124	C₂³	1	1	yes	characteristic
109	C₂³×#117	C₂³	1	1	yes	characteristic
110	#60960	C₂³	1	4	yes	complemented
111	#60958	C₂³	1	4	yes	complemented
112	C₂×#3153	C₂³	1	1	yes	characteristic
113	C₂×#3153	C₂³	1	1	yes	characteristic, complemented
114	C₂×#3151	C₂³	1	1	yes	characteristic
115	C₂×#3151	C₂³	1	1	yes	characteristic, complemented
116	C₂×#3140	C₂³	1	1	yes	characteristic
117	C₂×#3140	C₂³	1	1	yes	characteristic, complemented
118	C₂×#3138	C₂³	1	1	yes	characteristic
119	C₂×#3138	C₂³	1	1	yes	characteristic, complemented
120	C₂×#2921	C₂³	1	1	yes	characteristic, complemented
121	C₂×#2921	C₂³	1	1	yes	characteristic, complemented
122	#52054	D₄	1	4	yes	complemented
123	#52005	D₄	1	8	yes	complemented
124	#52004	D₄	1	4	yes	complemented
125	#51978	D₄	1	4	yes	complemented
126	#51903	D₄	1	8	yes	complemented
127	#51902	D₄	1	4	yes	complemented
128	#37614	C₂³	1	4	yes	—
129	#37606	C₂³	1	4	yes	—
130	#36625	C₂³	1	1	yes	characteristic, complemented
131	#36624	C₂³	1	1	yes	characteristic, complemented
132	#36621	C₂³	1	4	yes	—
133	#35118	C₂³	1	4	yes	—
134	#35094	D₄	1	4	yes	—
135	#35090	D₄	1	2	yes	—
136	#35089	D₄	1	2	yes	—
137	#34989	D₄	1	4	yes	—
138	#34982	D₄	1	2	yes	—
139	#34981	D₄	1	2	yes	—
140	#34634	C₂³	1	1	yes	characteristic
141	#34633	C₂³	1	1	yes	characteristic
142	#34366	C₂³	1	2	yes	—
143	#34364	C₂³	1	2	yes	—
144	#34177	C₂³	1	2	yes	—
145	#34048	C₂³	1	1	yes	characteristic, complemented
146	#25865	D₄	1	8	yes	complemented
147	#25734	D₄	1	4	yes	complemented
148	#25732	D₄	1	4	yes	complemented
149	#21204	C₂³	1	1	yes	characteristic
150	#21204	C₂³	1	1	yes	characteristic
151	#21204	C₂³	1	1	yes	characteristic, complemented
152	#21204	C₂³	1	1	yes	characteristic, complemented
153	#21203	C₂³	1	1	yes	characteristic
154	#21203	C₂³	1	1	yes	characteristic
155	#21203	C₂³	1	1	yes	characteristic, complemented
156	#21203	C₂³	1	1	yes	characteristic, complemented
157	#20715	C₂³	1	4	yes	complemented
158	#20377	C₂³	1	1	yes	characteristic
159	#20377	C₂³	1	1	yes	characteristic
160	C₄×#407	C₂³	1	1	yes	characteristic, complemented
161	C₄×#407	C₂³	1	1	yes	characteristic, complemented
162	C₂×#1555	C₂³	1	2	yes	—
163	C₂×#1555	C₂³	1	2	yes	—
164	C₂×#1555	C₂³	1	4	yes	complemented
165	C₂×#1533	C₂³	1	2	yes	—
166	C₂×#1533	C₂³	1	2	yes	—
167	C₂×#1533	C₂³	1	4	yes	complemented
168	#17650	C₂³	1	4	yes	complemented
169	#17650	C₂³	1	4	yes	complemented
170	#17596	C₂³	1	4	yes	complemented
171	#17595	C₂³	1	4	yes	complemented
172	#17581	C₂³	1	4	yes	complemented
173	#17581	C₂³	1	4	yes	complemented
174	#17502	C₂³	1	4	yes	complemented
175	#17502	C₂³	1	4	yes	complemented
176	C₂×#1464	C₂³	1	2	yes	—
177	C₂×#1464	C₂³	1	2	yes	—
178	C₂×#1464	C₂³	1	4	yes	complemented
179	#8073	C₂³	1	4	yes	complemented
180	#8073	C₂³	1	4	yes	complemented
181	#7984	C₂³	1	4	yes	complemented
182	#7984	C₂³	1	4	yes	complemented
183	#7972	C₂³	1	4	yes	complemented
184	#7972	C₂³	1	4	yes	complemented
185	C₂³×#41	C₂×D₄	1	1	yes	characteristic
186	C₂³×#41	C₂×D₄	1	1	yes	characteristic
187	C₂³×#41	C₂×D₄	1	1	yes	characteristic
188	C₂³×#41	C₂×D₄	1	1	yes	characteristic
189	C₂⁴×Q₈	C₂×D₄	1	1	yes	characteristic
190	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
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	C₂⁵×C₄	C₂×D₄	1	1	yes	characteristic
198	C₂×#563	C₂×D₄	1	2	yes	—
199	C₂×#562	C₂×D₄	1	4	yes	—
200	C₂×H(3,𝔽₄)	C₂×D₄	1	2	yes	—
201	C₂×#559	C₂×D₄	1	2	yes	—
202	C₂×#550	C₂×D₄	1	4	yes	—
203	C₂×D₄²	C₂×D₄	1	2	yes	—
204	C₂×#543	C₂×D₄	1	2	yes	—
205	C₂×#539	C₂×D₄	1	4	yes	—
206	C₂×#535	C₂×D₄	1	4	yes	—
207	C₂×#535	C₂×D₄	1	4	yes	—
208	C₂×#535	C₂×D₄	1	4	yes	—
209	C₂×#535	C₂×D₄	1	4	yes	—
210	C₂×#535	C₂×D₄	1	4	yes	—
211	C₂×#535	C₂×D₄	1	4	yes	—
212	C₂×#534	C₂×D₄	1	2	yes	—
213	C₂×#533	C₂⁴	1	1	yes	characteristic
214	C₂×#532	C₂⁴	1	1	yes	characteristic
215	C₂²×#127	C₂×D₄	1	1	yes	characteristic
216	C₂²×#127	C₂×D₄	1	1	yes	characteristic
217	C₂²×#127	C₂×D₄	1	1	yes	characteristic
218	C₂²×#127	C₂×D₄	1	1	yes	characteristic
219	C₂²×#127	C₂×D₄	1	1	yes	characteristic
220	C₂²×#127	C₂×D₄	1	1	yes	characteristic
221	C₂²×#127	C₂⁴	1	1	yes	characteristic
222	C₂²×#127	C₂⁴	1	1	yes	characteristic
223	C₂×#529	C₂⁴	1	4	yes	—
224	C₂²×#124	C₂×D₄	1	1	yes	characteristic
225	C₂²×#124	C₂×D₄	1	1	yes	characteristic
226	C₂²×#124	C₂×D₄	1	1	yes	characteristic
227	C₂²×#124	C₂×D₄	1	1	yes	characteristic
228	C₂²×#124	C₂×D₄	1	1	yes	characteristic
229	C₂²×#124	C₂×D₄	1	1	yes	characteristic
230	C₂²×#124	C₂⁴	1	1	yes	characteristic
231	C₂²×#124	C₂⁴	1	1	yes	characteristic
232	C₂²×#117	C₂×D₄	1	1	yes	characteristic
233	C₂²×#117	C₂×D₄	1	1	yes	characteristic
234	C₂²×#117	C₂×D₄	1	2	yes	—
235	C₂²×#117	C₂×D₄	1	2	yes	—
236	C₂²×#117	C₂⁴	1	1	yes	characteristic
237	C₂²×#117	C₂⁴	1	1	yes	characteristic
238	C₂³×C₄⋊C₄	C₂×D₄	1	2	yes	—
239	C₂³×C₂²⋊C₄	C₂×D₄	1	2	yes	—
240	C₂³×C₄²	C₂×D₄	1	1	yes	characteristic
241	C₂³×C₄²	C₂⁴	1	1	yes	characteristic
242	C₂×#497	C₂×D₄	1	2	yes	complemented
243	C₂×#496	C₂×D₄	1	2	yes	complemented
244	C₂×#493	C₂×D₄	1	2	yes	complemented
245	C₂×#492	C₂×D₄	1	2	yes	complemented
246	C₂×#489	C₂×D₄	1	4	yes	complemented
247	C₂×#486	C₂×D₄	1	4	yes	complemented
248	C₂×#432	C₂⁴	1	4	yes	—
249	C₂×#432	C₂⁴	1	4	yes	—
250	C₂×C₄×M₁₆	C₂⁴	1	1	yes	characteristic
251	C₂×C₄×M₁₆	C₂⁴	1	1	yes	characteristic
252	C₂×C₄×M₁₆	C₂⁴	1	1	yes	characteristic
253	C₂×C₄×M₁₆	C₂⁴	1	1	yes	characteristic
254	#2855	C₂×D₄	1	4	yes	—
255	#2854	C₂×D₄	1	4	yes	—
256	#2848	C₂×D₄	1	4	yes	—
257	#2847	C₂×D₄	1	4	yes	—
258	#2657	C₂×D₄	1	8	yes	—
259	#2641	C₂×D₄	1	8	yes	—
260	#2632	C₂×D₄	1	8	yes	—
261	#2631	C₂×D₄	1	8	yes	—
262	#2628	C₂×D₄	1	4	yes	complemented
263	#2627	C₂×D₄	1	4	yes	—
264	#2626	C₂×D₄	1	4	yes	—
265	#2621	C₂×D₄	1	2	yes	complemented
266	#2619	C₂×D₄	1	2	yes	complemented
267	#2618	C₂×D₄	1	4	yes	—
268	#2617	C₂×D₄	1	4	yes	—
269	#2611	C₂×D₄	1	8	yes	—
270	#2610	C₂×D₄	1	8	yes	—
271	#2599	C₂×D₄	1	8	yes	—
272	#2598	C₂×D₄	1	8	yes	—
273	#2380	C₂×D₄	1	4	yes	—
274	#2380	C₂×D₄	1	4	yes	—
275	#2372	C₂×D₄	1	4	yes	—
276	#2372	C₂×D₄	1	4	yes	—
277	#2315	C₂×D₄	1	2	yes	—
278	#2315	C₂×D₄	1	2	yes	—
279	#2313	C₂×D₄	1	4	yes	—
280	#2285	C₂⁴	1	1	yes	characteristic
281	#2285	C₂⁴	1	1	yes	characteristic
282	#2283	C₂⁴	1	4	yes	—
283	#1961	C₂×D₄	1	4	yes	complemented
284	#1961	C₂×D₄	1	4	yes	complemented
285	#1958	C₂×D₄	1	4	yes	complemented
286	#1958	C₂×D₄	1	4	yes	complemented
287	#1750	C₂×D₄	1	4	yes	complemented
288	#1750	C₂×D₄	1	4	yes	complemented
289	C₂⁶	#120	1	1	yes	characteristic
290	C₂²×#41	#120	1	4	yes	—
291	C₂²×#41	#120	1	4	yes	—
292	C₂²×#41	#120	1	4	yes	—
293	C₂³×Q₈	C₂²×D₄	1	1	yes	characteristic
294	C₂³×Q₈	C₂²×D₄	1	1	yes	characteristic
295	C₂³×D₄	#120	1	4	yes	—
296	C₂³×D₄	#120	1	2	yes	—
297	C₂³×D₄	#120	1	2	yes	—
298	C₂³×D₄	#120	1	2	yes	—
299	C₂³×D₄	#120	1	2	yes	—
300	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
301	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
302	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
303	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
304	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
305	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
306	C₂⁴×C₄	#120	1	1	yes	characteristic
307	C₂⁴×C₄	#120	1	1	yes	characteristic
308	C₂⁴×C₄	#120	1	1	yes	characteristic
309	C₂⁴×C₄	#120	1	2	yes	—
310	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
311	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
312	C₂⁴×C₄	C₂²×D₄	1	2	yes	—
313	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
314	C₂×C₄⋊Q₈	C₂²×D₄	1	2	yes	complemented
315	C₂×C₄⋊Q₈	C₂²×D₄	1	1	yes	characteristic, complemented
316	C₂×#127	#120	1	4	yes	—
317	C₂×#127	#120	1	2	yes	—
318	C₂×#127	#120	1	4	yes	—
319	C₂×#127	#120	1	2	yes	—
320	C₂×#127	C₂²×D₄	1	4	yes	—
321	C₂×#127	C₂²×D₄	1	2	yes	—
322	C₂×#127	C₂²×D₄	1	2	yes	—
323	C₂×#127	C₂²×D₄	1	2	yes	—
324	C₂×#127	C₂²×D₄	1	2	yes	—
325	C₂×#127	C₂²×D₄	1	1	yes	characteristic, complemented
326	C₂×#127	H(5,𝔽₂)	1	4	yes	—
327	C₂×#125	C₂²×D₄	1	4	yes	—
328	C₂×#124	#120	1	4	yes	—
329	C₂×#124	#120	1	2	yes	—
330	C₂×#124	#120	1	2	yes	—
331	C₂×#124	#120	1	4	yes	—
332	C₂×#124	C₂²×D₄	1	4	yes	—
333	C₂×#124	C₂²×D₄	1	4	yes	—
334	C₂×#124	C₂²×D₄	1	2	yes	—
335	C₂×#124	C₂²×D₄	1	2	yes	—
336	C₂×#124	C₂²×D₄	1	2	yes	—
337	C₂×#124	C₂²×D₄	1	2	yes	—
338	C₂×#124	H(5,𝔽₂)	1	4	yes	—
339	C₂×C₂²⋊Q₈	C₂²×D₄	1	4	yes	—
340	C₂×#121	C₂²×D₄	1	4	yes	—
341	C₂×C₄×Q₈	C₂²×D₄	1	4	yes	—
342	C₂×C₄×D₄	C₂²×D₄	1	4	yes	—
343	C₂×#117	C₂²×D₄	1	4	yes	—
344	C₂×#117	C₂²×D₄	1	4	yes	—
345	C₂×#117	C₂²×D₄	1	2	yes	—
346	C₂×#117	C₂²×D₄	1	2	yes	—
347	C₂×#117	H(5,𝔽₂)	1	4	yes	—
348	C₂²×C₄⋊C₄	#120	1	2	yes	—
349	C₂²×C₄⋊C₄	#120	1	2	yes	—
350	C₂²×C₄⋊C₄	C₂²×D₄	1	2	yes	—
351	C₂²×C₄⋊C₄	C₂²×D₄	1	2	yes	—
352	C₂²×C₂²⋊C₄	#120	1	2	yes	—
353	C₂²×C₂²⋊C₄	#120	1	2	yes	—
354	C₂²×C₂²⋊C₄	C₂²×D₄	1	2	yes	—
355	C₂²×C₂²⋊C₄	C₂²×D₄	1	2	yes	—
356	C₂²×C₄²	#120	1	2	yes	—
357	C₂²×C₄²	C₂²×D₄	1	2	yes	—
358	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
359	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
360	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
361	C₂²×C₄²	C₂⁵	1	1	yes	characteristic
362	C₂×#97	C₂²×D₄	1	2	yes	complemented
363	C₂×#97	C₂²×D₄	1	2	yes	complemented
364	C₂×C₄×C₈	C₂²×D₄	1	2	yes	complemented
365	C₂×C₄×C₈	C₂²×D₄	1	2	yes	complemented
366	#400	#120	1	8	yes	—
367	#399	#120	1	8	yes	—
368	#398	#120	1	8	yes	—
369	#397	#120	1	8	yes	—
370	#395	#120	1	8	yes	—
371	#394	#120	1	8	yes	—
372	#393	#120	1	8	yes	—
373	#392	#120	1	8	yes	—
374	#383	C₂²×D₄	1	8	yes	—
375	#382	C₂²×D₄	1	2	yes	complemented
376	#382	C₂²×D₄	1	2	yes	complemented
377	#380	C₂²×D₄	1	4	yes	—
378	#380	C₂²×D₄	1	4	yes	—
379	#376	C₂²×D₄	1	8	yes	—
380	C₂⁵	C₂×#120	1	1	yes	characteristic
381	C₂⁵	C₂×#120	1	1	yes	characteristic
382	C₂⁵	C₂×#120	1	1	yes	characteristic
383	C₂²×Q₈	C₂×#120	1	2	yes	—
384	C₂²×Q₈	C₂×#120	1	4	yes	—
385	C₂²×Q₈	C₂×#120	1	2	yes	—
386	C₂²×Q₈	C₂×#120	1	2	yes	—
387	C₂²×Q₈	#534	1	2	yes	—
388	C₂²×D₄	C₂×#120	1	2	yes	—
389	C₂²×D₄	C₂×#120	1	2	yes	—
390	C₂²×D₄	C₂×#120	1	2	yes	—
391	C₂²×D₄	C₂×#120	1	4	yes	—
392	C₂²×D₄	C₂×#120	1	1	yes	characteristic
393	C₂²×D₄	C₂×#120	1	1	yes	characteristic
394	C₂²×D₄	C₂×#120	1	2	yes	—
395	C₂²×D₄	C₂×#120	1	1	yes	characteristic
396	C₂²×D₄	C₂×#120	1	1	yes	characteristic
397	C₂²×D₄	C₂×#120	1	2	yes	—
398	C₂²×D₄	C₂×#120	1	2	yes	—
399	C₂²×D₄	C₂×#120	1	2	yes	—
400	C₂²×D₄	#534	1	2	yes	—
401	C₂²×D₄	#534	1	2	yes	—
402	C₂²×D₄	#534	1	2	yes	—
403	C₂³×C₄	C₂×#120	1	1	yes	characteristic
404	C₂³×C₄	C₂×#120	1	1	yes	characteristic
405	C₂³×C₄	C₂×#120	1	1	yes	characteristic
406	C₂³×C₄	C₂×#120	1	2	yes	—
407	C₂³×C₄	C₂×#120	1	2	yes	—
408	C₂³×C₄	C₂×#120	1	2	yes	—
409	C₂³×C₄	C₂×#120	1	2	yes	—
410	C₂³×C₄	C₂×#120	1	2	yes	—
411	C₂³×C₄	C₂×#120	1	2	yes	—
412	C₂³×C₄	#534	1	2	yes	—
413	C₂³×C₄	C₂³×D₄	1	1	yes	characteristic
414	C₂³×C₄	C₂³×D₄	1	2	yes	—
415	#127	D₄²	1	4	yes	—
416	#127	D₄²	1	4	yes	—
417	#127	D₄²	1	4	yes	—
418	#127	D₄²	1	4	yes	—
419	#124	D₄²	1	4	yes	—
420	#124	D₄²	1	4	yes	—
421	#124	D₄²	1	4	yes	—
422	#124	D₄²	1	4	yes	—
423	C₂×C₄⋊C₄	C₂×#120	1	4	yes	—
424	C₂×C₄⋊C₄	C₂×#120	1	4	yes	—
425	C₂×C₄⋊C₄	C₂×#120	1	8	yes	—
426	C₂×C₄⋊C₄	D₄²	1	4	yes	—
427	C₂×C₄⋊C₄	D₄²	1	4	yes	—
428	C₂×C₂²⋊C₄	C₂×#120	1	8	yes	—
429	C₂×C₂²⋊C₄	D₄²	1	4	yes	—
430	C₂×C₂²⋊C₄	D₄²	1	4	yes	—
431	C₂×C₄²	C₂×#120	1	2	yes	—
432	C₂×C₄²	C₂×#120	1	2	yes	—
433	C₂×C₄²	C₂×#120	1	2	yes	—
434	C₂×C₄²	#534	1	2	yes	—
435	C₂×C₄²	C₂³×D₄	1	1	yes	characteristic
436	C₂×C₄²	C₂³×D₄	1	1	yes	characteristic
437	C₂×C₄²	C₂³×D₄	1	2	yes	—
438	C₂×C₄²	C₂³×D₄	1	2	yes	—
439	C₂×C₄²	C₂×H(5,𝔽₂)	1	2	yes	—
440	C₂×C₄²	C₂×H(5,𝔽₂)	1	2	yes	—
441	C₂×C₄²	C₂×H(5,𝔽₂)	1	2	yes	—
442	#95	C₂×#120	1	8	yes	—
443	#95	C₂×#120	1	8	yes	—
444	C₂⁴	#2403	1	2	yes	—
445	C₂⁴	#2846	1	2	yes	—
446	C₂⁴	#3019	1	2	yes	—
447	C₂⁴	#3019	1	2	yes	—
448	C₂⁴	#3019	1	2	yes	—
449	C₂⁴	C₂²×#120	1	1	yes	characteristic
450	C₂×Q₈	#2403	1	4	yes	—
451	C₂×D₄	#2403	1	2	yes	—
452	C₂×D₄	#2403	1	2	yes	—
453	C₂×D₄	#2403	1	4	yes	—
454	C₂×D₄	#2403	1	2	yes	—
455	C₂×D₄	#2403	1	2	yes	—
456	C₂²×C₄	#2403	1	2	yes	—
457	C₂²×C₄	#2403	1	4	yes	—
458	C₂²×C₄	#2846	1	2	yes	—
459	C₂²×C₄	#2846	1	4	yes	—
460	C₂²×C₄	#3019	1	2	yes	—
461	C₂²×C₄	C₂²×#120	1	1	yes	characteristic
462	C₂²×C₄	C₂²×#120	1	1	yes	characteristic
463	C₂²×C₄	C₂²×#120	1	1	yes	characteristic
464	C₂²×C₄	C₂²×#120	1	4	yes	—
465	C₂²×C₄	C₂×#534	1	1	yes	characteristic
466	C₂²×C₄	C₂×#534	1	1	yes	characteristic
467	C₂²×C₄	C₂×#534	1	1	yes	characteristic
468	C₂²×C₄	C₂×D₄²	1	2	yes	—
469	C₂²×C₄	C₂×D₄²	1	2	yes	—
470	C₂²×C₄	#3484	1	4	yes	—
471	C₄²	C₂×D₄²	1	2	yes	—
472	C₄²	C₂×D₄²	1	2	yes	—
473	C₄²	C₂×D₄²	1	2	yes	—
474	C₄²	C₂×D₄²	1	2	yes	—
475	C₄²	#3484	1	4	yes	—
476	C₄²	#3484	1	4	yes	—
477	C₂³	#23912	1	4	yes	—
478	C₂³	C₂×#2403	1	1	yes	characteristic
479	C₂³	#34980	1	1	yes	characteristic
480	C₂³	C₂×#2846	1	1	yes	characteristic
481	C₂³	C₂×#3019	1	1	yes	characteristic
482	C₂³	C₂×#3019	1	1	yes	characteristic
483	C₂³	C₂×#3019	1	1	yes	characteristic
484	C₂³	C₂×#3019	1	1	yes	characteristic
485	C₂×C₄	C₂×#2403	1	1	yes	characteristic
486	C₂×C₄	C₂×#2403	1	1	yes	characteristic
487	C₂×C₄	#34980	1	1	yes	characteristic
488	C₂×C₄	#34980	1	1	yes	characteristic
489	C₂×C₄	D₄×#120	1	4	yes	—
490	C₂×C₄	D₄×#120	1	4	yes	—
491	C₂²	#612424	1	1	yes	characteristic
492	C₂²	C₂×#23912	1	1	yes	characteristic
493	C₂²	#6437445	1	1	yes	characteristic
494	C₂²	#6470032	1	1	yes	characteristic
495	C₂²	#6470032	1	1	yes	characteristic
496	C₂²	#6628867	1	1	yes	characteristic
497	C₂²	#6628867	1	1	yes	characteristic
498	C₂	#72233775	1	2	yes	—
499	C₂	#72284465	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²	#612424
commutator, Frattini, cosocle	C₂²×C₄²	C₂⁵
LCS	G ▷ C₂²×C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂² ◁ C₂²×C₄² ◁ G
LECS	G ▷ C₂²×C₄² ▷ C₂² ▷ C₁

Complements

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

N	H ≅ G/N	type
1. #72286785	C₂	semidirect
2. #72286766	C₂	semidirect
3. #72286753	C₂	semidirect
4. #72286743	C₂	semidirect
5. #72286735	C₂	semidirect
6. #72286727	C₂	semidirect
7. #72286719	C₂	semidirect
8. #72286708	C₂	semidirect
9. #72286597	C₂	semidirect
10. #72286549	C₂	semidirect
11. #72286478	C₂	semidirect
12. #72286434	C₂	semidirect
13. #72286278	C₂	semidirect
14. #72286226	C₂	semidirect
15. #72286177	C₂	semidirect
16. #72284814	C₂	semidirect
17. #72284648	C₂	semidirect
18. #72282667	C₂	semidirect
19. #72226694	C₂	semidirect
22. C₂×#60806	C₂²	semidirect
23. C₂×#60806	C₂²	semidirect
30. #7628656	C₂²	semidirect
33. #6446630	C₂²	semidirect
34. #6446625	C₂²	semidirect
35. #6446623	C₂²	semidirect
37. #6443103	C₂²	semidirect
38. #6443097	C₂²	semidirect
39. #6443095	C₂²	semidirect
40. #6374281	C₂²	semidirect
41. #6374281	C₂²	semidirect
42. #6370926	C₂²	semidirect
43. #6351566	C₂²	semidirect
44. #6351559	C₂²	semidirect
45. #6348455	C₂²	semidirect
46. #6348447	C₂²	semidirect
47. #6347279	C₂²	semidirect
48. #6347278	C₂²	semidirect
49. #6347126	C₂²	semidirect
50. #236269	C₂²	semidirect
51. #236265	C₂²	semidirect
52. #235528	C₂²	semidirect
53. #235527	C₂²	semidirect
54. #234330	C₂²	semidirect
55. #234329	C₂²	semidirect
56. #201630	C₂²	semidirect
57. #201039	C₂²	semidirect
58. #201037	C₂²	semidirect
59. #200851	C₂²	semidirect
60. #200848	C₂²	semidirect
61. #200466	C₂²	semidirect
62. #197550	C₂²	semidirect
63. #197546	C₂²	semidirect
64. #197531	C₂²	semidirect
65. #187883	C₂²	semidirect
66. #187883	C₂²	semidirect
69. C₂×#8522	C₂²	semidirect
70. C₂×#8522	C₂²	semidirect
71. C₂×#8522	C₂²	semidirect
72. #187463	C₂²	semidirect
73. #187463	C₂²	semidirect
74. #185297	C₂²	semidirect
75. #185297	C₂²	semidirect
76. #185202	C₂²	semidirect
77. #185132	C₂²	semidirect
78. #184776	C₂²	semidirect
79. #113071	C₂²	semidirect
80. #113071	C₂²	semidirect
81. #112067	C₂²	semidirect
82. #112067	C₂²	semidirect
83. #111635	C₂²	semidirect
84. #111635	C₂²	semidirect
85. #108372	C₂²	semidirect
86. #108372	C₂²	semidirect
87. #107339	C₂²	semidirect
88. #107339	C₂²	semidirect
89. #106576	C₂²	semidirect
90. #106576	C₂²	semidirect
96. C₂×#3455	C₂³	semidirect
110. #60960	C₂³	semidirect
111. #60958	C₂³	semidirect
113. C₂×#3153	C₂³	semidirect
115. C₂×#3151	C₂³	semidirect
117. C₂×#3140	C₂³	semidirect
119. C₂×#3138	C₂³	semidirect
120. C₂×#2921	C₂³	semidirect
121. C₂×#2921	C₂³	semidirect
122. #52054	D₄	semidirect
123. #52005	D₄	semidirect
124. #52004	D₄	semidirect
125. #51978	D₄	semidirect
126. #51903	D₄	semidirect
127. #51902	D₄	semidirect
130. #36625	C₂³	semidirect
131. #36624	C₂³	semidirect
145. #34048	C₂³	semidirect
146. #25865	D₄	semidirect
147. #25734	D₄	semidirect
148. #25732	D₄	semidirect
151. #21204	C₂³	semidirect
152. #21204	C₂³	semidirect
155. #21203	C₂³	semidirect
156. #21203	C₂³	semidirect
157. #20715	C₂³	semidirect
160. C₄×#407	C₂³	semidirect
161. C₄×#407	C₂³	semidirect
164. C₂×#1555	C₂³	semidirect
167. C₂×#1533	C₂³	semidirect
168. #17650	C₂³	semidirect
169. #17650	C₂³	semidirect
170. #17596	C₂³	semidirect
171. #17595	C₂³	semidirect
172. #17581	C₂³	semidirect
173. #17581	C₂³	semidirect
174. #17502	C₂³	semidirect
175. #17502	C₂³	semidirect
178. C₂×#1464	C₂³	semidirect
179. #8073	C₂³	semidirect
180. #8073	C₂³	semidirect
181. #7984	C₂³	semidirect
182. #7984	C₂³	semidirect
183. #7972	C₂³	semidirect
184. #7972	C₂³	semidirect
242. C₂×#497	C₂×D₄	semidirect
243. C₂×#496	C₂×D₄	semidirect
244. C₂×#493	C₂×D₄	semidirect
245. C₂×#492	C₂×D₄	semidirect
246. C₂×#489	C₂×D₄	semidirect
247. C₂×#486	C₂×D₄	semidirect
262. #2628	C₂×D₄	semidirect
265. #2621	C₂×D₄	semidirect
266. #2619	C₂×D₄	semidirect
283. #1961	C₂×D₄	semidirect
284. #1961	C₂×D₄	semidirect
285. #1958	C₂×D₄	semidirect
286. #1958	C₂×D₄	semidirect
287. #1750	C₂×D₄	semidirect
288. #1750	C₂×D₄	semidirect
314. C₂×C₄⋊Q₈	C₂²×D₄	semidirect
315. C₂×C₄⋊Q₈	C₂²×D₄	semidirect
325. C₂×#127	C₂²×D₄	semidirect
362. C₂×#97	C₂²×D₄	semidirect
363. C₂×#97	C₂²×D₄	semidirect
364. C₂×C₄×C₈	C₂²×D₄	semidirect
365. C₂×C₄×C₈	C₂²×D₄	semidirect
375. #382	C₂²×D₄	semidirect
376. #382	C₂²×D₄	semidirect

Maximal subgroups

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

subgroup	index
#72286785	2
#72286766	2
#72286753	2
#72286743	2
#72286735	2
#72286727	2
#72286719	2
#72286708	2
#72286597	2
#72286549	2
#72286478	2
#72286434	2
#72286278	2
#72286226	2
#72286177	2
#72284814	2
#72284648	2
#72282667	2
#72226694	2