Subgroups — #72256271

Order 2048.

At least 14895 conjugacy classes of subgroups; only the 1052 normal subgroups are shown.

The subgroup lattice has 544 nodes (normal subgroups only) — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#72255937	C₂	1	1	yes	maximal, characteristic, complemented
2	#72255932	C₂	1	1	yes	maximal, characteristic, complemented
3	#72255895	C₂	1	4	yes	maximal, complemented
4	#72255890	C₂	1	1	yes	maximal, characteristic, complemented
5	#72255873	C₂	1	4	yes	maximal, complemented
6	#72255866	C₂	1	2	yes	maximal, complemented
7	#72255859	C₂	1	2	yes	maximal, complemented
8	#72251707	C₂	1	1	yes	maximal, characteristic, complemented
9	#72249491	C₂	1	1	yes	maximal, characteristic, complemented
10	#72238545	C₂	1	1	yes	maximal, characteristic, complemented
11	#72237258	C₂	1	1	yes	maximal, characteristic, complemented
12	#72235919	C₂	1	4	yes	maximal, complemented
13	#72235212	C₂	1	2	yes	maximal, complemented
14	#72235210	C₂	1	2	yes	maximal, complemented
15	#72235200	C₂	1	4	yes	maximal, complemented
16	C₂×#62811	C₂²	1	1	yes	characteristic, complemented
17	#10574839	C₂²	1	1	yes	characteristic, complemented
18	#7756445	C₂²	1	2	yes	complemented
19	#7756441	C₂²	1	2	yes	complemented
20	#7722697	C₂²	1	2	yes	—
21	#7722693	C₂²	1	2	yes	—
22	#7710478	C₂²	1	2	yes	complemented
23	#7642350	C₂²	1	2	yes	complemented
24	#7631032	C₂²	1	1	yes	characteristic
25	#7628649	C₂²	1	1	yes	characteristic
26	C₂×#35250	C₂²	1	1	yes	characteristic
27	C₂×#32899	C₂²	1	2	yes	complemented
28	#6628869	C₂²	1	2	yes	complemented
29	#6437448	C₂²	1	2	yes	complemented
30	#6371494	C₂²	1	1	yes	characteristic, complemented
31	#6370728	C₂²	1	1	yes	characteristic, complemented
32	#6370684	C₂²	1	1	yes	characteristic, complemented
33	#6346594	C₂²	1	4	yes	complemented
34	#635987	C₂²	1	2	yes	complemented
35	#393989	C₂²	1	4	yes	complemented
36	#393988	C₂²	1	4	yes	complemented
37	#393988	C₂²	1	4	yes	complemented
38	#393930	C₂²	1	4	yes	complemented
39	#392698	C₂²	1	2	yes	complemented
40	#392659	C₂²	1	2	yes	complemented
41	#392115	C₂²	1	1	yes	characteristic, complemented
42	#392110	C₂²	1	1	yes	characteristic, complemented
43	#359512	C₂²	1	2	yes	complemented
44	#359429	C₂²	1	2	yes	complemented
45	#353295	C₂²	1	1	yes	characteristic, complemented
46	#238058	C₂²	1	4	yes	complemented
47	#234948	C₂²	1	4	yes	complemented
48	#234948	C₂²	1	4	yes	complemented
49	#232528	C₂²	1	4	yes	complemented
50	#202015	C₂²	1	4	yes	complemented
51	#202015	C₂²	1	4	yes	complemented
52	C₂×#9511	C₂²	1	2	yes	complemented
53	C₂×#9511	C₂²	1	2	yes	complemented
54	#201462	C₂²	1	4	yes	complemented
55	#201110	C₂²	1	2	yes	complemented
56	#201110	C₂²	1	2	yes	complemented
57	#190055	C₂²	1	2	yes	complemented
58	#187764	C₂²	1	2	yes	complemented
59	#186948	C₂²	1	2	yes	complemented
60	#185255	C₂²	1	4	yes	complemented
61	#184796	C₂²	1	2	yes	complemented
62	#122111	C₂²	1	4	yes	complemented
63	#115141	C₂²	1	4	yes	complemented
64	#113288	C₂²	1	4	yes	complemented
65	#112857	C₂²	1	4	yes	complemented
66	#112857	C₂²	1	4	yes	complemented
67	#111959	C₂²	1	4	yes	complemented
68	#111959	C₂²	1	4	yes	complemented
69	#111321	C₂²	1	4	yes	complemented
70	#108255	C₂²	1	2	yes	complemented
71	#108036	C₂²	1	4	yes	complemented
72	#108036	C₂²	1	4	yes	complemented
73	#106326	C₂²	1	4	yes	complemented
74	#105717	C₂²	1	2	yes	complemented
75	C₂²×#585	C₂³	1	1	yes	characteristic
76	C₂⁴×#41	C₂³	1	1	yes	characteristic
77	C₂×#3485	D₄	1	1	yes	characteristic, complemented
78	C₂×#3485	C₂³	1	1	yes	characteristic
79	C₂×#3490	C₂³	1	2	yes	—
80	C₂×#3484	D₄	1	1	yes	characteristic, complemented
81	C₂×#3449	D₄	1	1	yes	characteristic, complemented
82	C₂×#3449	C₂³	1	1	yes	characteristic
83	C₂×#3449	C₂³	1	2	yes	—
84	C₂²×#535	D₄	1	1	yes	characteristic
85	C₂²×#535	D₄	1	1	yes	characteristic
86	C₂²×#525	D₄	1	1	yes	characteristic, complemented
87	C₂²×#525	C₂³	1	2	yes	—
88	C₂³×#121	C₂³	1	1	yes	characteristic
89	C₂×#3428	C₂³	1	1	yes	characteristic
90	#60359	C₂³	1	4	yes	—
91	#60359	C₂³	1	4	yes	—
92	C₂×#2879	C₂³	1	1	yes	characteristic
93	C₂×#2879	C₂³	1	1	yes	characteristic
94	#46430	D₄	1	2	yes	complemented
95	#46427	D₄	1	2	yes	complemented
96	#46425	D₄	1	2	yes	complemented
97	#46424	D₄	1	2	yes	complemented
98	#46357	D₄	1	2	yes	complemented
99	#46356	D₄	1	2	yes	complemented
100	#46355	D₄	1	2	yes	complemented
101	#46354	D₄	1	2	yes	complemented
102	#37479	C₂³	1	2	yes	—
103	#37454	C₂³	1	2	yes	—
104	#36822	D₄	1	2	yes	complemented
105	#36818	D₄	1	2	yes	complemented
106	#36816	D₄	1	2	yes	complemented
107	#36812	D₄	1	2	yes	complemented
108	#36614	D₄	1	2	yes	complemented
109	#36614	C₂³	1	2	yes	—
110	#36614	C₂³	1	2	yes	—
111	#35439	D₄	1	2	yes	complemented
112	#35438	D₄	1	2	yes	complemented
113	#35422	D₄	1	2	yes	complemented
114	#35408	D₄	1	2	yes	complemented
115	#35242	D₄	1	2	yes	complemented
116	#35149	D₄	1	2	yes	complemented
117	#35149	C₂³	1	2	yes	—
118	#35050	C₂³	1	2	yes	—
119	#35050	C₂³	1	2	yes	—
120	C₂×#2404	C₂³	1	2	yes	—
121	C₂×#2404	C₂³	1	4	yes	—
122	C₂×#2404	C₂³	1	2	yes	—
123	C₂×#2403	D₄	1	2	yes	—
124	C₂×#2403	D₄	1	2	yes	—
125	#34632	D₄	1	2	yes	complemented
126	#34632	C₂³	1	2	yes	—
127	#34396	C₂³	1	2	yes	—
128	#34396	C₂³	1	2	yes	—
129	#34176	C₂³	1	2	yes	—
130	#34172	D₄	1	1	yes	characteristic, complemented
131	#34172	C₂³	1	1	yes	characteristic
132	#34171	D₄	1	1	yes	characteristic, complemented
133	#34044	D₄	1	1	yes	characteristic, complemented
134	#34044	C₂³	1	1	yes	characteristic
135	C₂×#2311	D₄	1	1	yes	characteristic
136	C₂×#2311	D₄	1	1	yes	characteristic
137	C₂×#2280	D₄	1	1	yes	characteristic, complemented
138	C₂×#2280	C₂³	1	1	yes	characteristic
139	#20979	C₂³	1	4	yes	—
140	#20979	C₂³	1	4	yes	—
141	#20605	C₂³	1	4	yes	—
142	#20605	C₂³	1	4	yes	—
143	C₂×#1785	C₂³	1	2	yes	—
144	C₂×#1785	C₂³	1	2	yes	—
145	C₂×#1782	C₂³	1	4	yes	—
146	C₂×#1782	C₂³	1	2	yes	—
147	C₂×#1782	C₂³	1	2	yes	—
148	#20580	C₂³	1	2	yes	—
149	#20579	C₂³	1	2	yes	—
150	#20579	C₂³	1	2	yes	—
151	#17587	C₂³	1	4	yes	—
152	#17587	C₂³	1	4	yes	—
153	#17587	C₂³	1	4	yes	—
154	#17587	C₂³	1	4	yes	—
155	C₂×#1462	C₂³	1	4	yes	—
156	C₂×#1462	C₂³	1	4	yes	—
157	#14681	C₂³	1	2	yes	—
158	#13868	C₂³	1	4	yes	—
159	#10726	C₂³	1	4	yes	—
160	#10716	C₂³	1	4	yes	—
161	#10716	C₂³	1	4	yes	—
162	C₂×#1306	C₂³	1	4	yes	—
163	C₂×#1306	C₂³	1	4	yes	—
164	#7943	C₂³	1	4	yes	—
165	#7943	C₂³	1	4	yes	—
166	#7943	C₂³	1	4	yes	—
167	#7943	C₂³	1	4	yes	—
168	C₂²×H(5,𝔽₂)	C₂×D₄	1	1	yes	characteristic
169	C₂³×#41	C₂×D₄	1	1	yes	characteristic
170	C₂³×#41	C₂×D₄	1	1	yes	characteristic
171	C₂³×#41	C₂×D₄	1	1	yes	characteristic
172	C₂³×#41	C₂×D₄	1	1	yes	characteristic
173	C₂³×#41	C₂×D₄	1	1	yes	characteristic
174	C₂³×#41	C₂×D₄	1	1	yes	characteristic
175	C₂³×#41	C₂×D₄	1	1	yes	characteristic
176	C₂³×#41	C₂⁴	1	2	yes	—
177	C₂³×#41	C₂⁴	1	1	yes	characteristic
178	C₂³×#41	C₂⁴	1	1	yes	characteristic
179	C₂⁴×Q₈	C₂×D₄	1	1	yes	characteristic
180	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
181	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
182	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
183	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
184	C₂⁴×D₄	C₂×D₄	1	2	yes	—
185	C₂⁵×C₄	C₂×D₄	1	1	yes	characteristic
186	C₂⁵×C₄	C₂×D₄	1	1	yes	characteristic
187	C₂⁵×C₄	C₂⁴	1	1	yes	characteristic
188	C₂×#543	C₂×D₄	1	2	yes	complemented
189	C₂×#538	C₂×D₄	1	2	yes	complemented
190	C₂×#538	C₂×D₄	1	2	yes	complemented
191	C₂×#537	C₂×D₄	1	2	yes	—
192	C₂×#537	C₂×D₄	1	2	yes	—
193	C₂×#536	C₂×D₄	1	2	yes	—
194	C₂×#536	C₂×D₄	1	2	yes	—
195	C₂×#536	C₂×D₄	1	2	yes	—
196	C₂×#535	C₂×D₄	1	2	yes	—
197	C₂×#535	C₂×D₄	1	2	yes	—
198	C₂×#534	C₂×D₄	1	2	yes	complemented
199	C₂×#525	C₂×D₄	1	2	yes	—
200	C₂×#525	C₂×D₄	1	2	yes	—
201	C₂×#525	C₂×D₄	1	2	yes	—
202	C₂×#525	C₂×D₄	1	2	yes	—
203	C₂×#525	C₂×D₄	1	2	yes	—
204	C₂×#525	C₂×D₄	1	2	yes	—
205	C₂×#525	C₂×D₄	1	2	yes	—
206	C₂×#525	C₂⁴	1	2	yes	—
207	C₂×#525	C₂⁴	1	2	yes	—
208	C₂²×#120	C₂×D₄	1	2	yes	—
209	C₂²×#120	C₂×D₄	1	2	yes	—
210	C₂²×#120	C₂×D₄	1	2	yes	—
211	C₂²×#120	C₂×D₄	1	2	yes	—
212	C₂×#518	C₂×D₄	1	1	yes	characteristic
213	C₂×#518	C₂×D₄	1	1	yes	characteristic
214	C₂×#518	C₂×D₄	1	1	yes	characteristic
215	C₂²×#117	C₂×D₄	1	1	yes	characteristic
216	C₂²×#117	C₂×D₄	1	1	yes	characteristic
217	C₂²×#117	C₂×D₄	1	1	yes	characteristic
218	C₂²×#117	C₂×D₄	1	1	yes	characteristic
219	C₂²×#117	C₂×D₄	1	1	yes	characteristic
220	C₂²×#117	C₂⁴	1	2	yes	—
221	C₂³×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
222	C₂³×C₂²⋊C₄	C₂⁴	1	2	yes	—
223	C₂×#407	C₂⁴	1	2	yes	—
224	C₂×#407	C₂⁴	1	4	yes	—
225	C₂×#407	C₂⁴	1	2	yes	—
226	#2817	C₂×D₄	1	2	yes	complemented
227	#2816	C₂×D₄	1	2	yes	complemented
228	#2816	C₂×D₄	1	2	yes	complemented
229	#2815	C₂×D₄	1	2	yes	complemented
230	#2608	C₂×D₄	1	2	yes	complemented
231	#2608	C₂×D₄	1	2	yes	complemented
232	#2607	C₂×D₄	1	2	yes	complemented
233	#2607	C₂×D₄	1	2	yes	complemented
234	#2561	C₂×D₄	1	2	yes	complemented
235	#2561	C₂×D₄	1	2	yes	complemented
236	#2561	C₂×D₄	1	2	yes	complemented
237	#2561	C₂×D₄	1	2	yes	complemented
238	#2539	C₂×D₄	1	2	yes	complemented
239	#2539	C₂×D₄	1	2	yes	complemented
240	#2539	C₂×D₄	1	2	yes	complemented
241	#2539	C₂×D₄	1	2	yes	complemented
242	#2432	C₂×D₄	1	2	yes	—
243	#2432	C₂×D₄	1	2	yes	—
244	#2432	C₂×D₄	1	2	yes	—
245	#2432	C₂×D₄	1	2	yes	—
246	#2431	C₂×D₄	1	2	yes	—
247	#2431	C₂×D₄	1	2	yes	—
248	#2431	C₂×D₄	1	2	yes	—
249	#2431	C₂×D₄	1	2	yes	—
250	#2404	C₂×D₄	1	2	yes	—
251	#2404	C₂×D₄	1	2	yes	—
252	#2404	C₂×D₄	1	2	yes	—
253	#2404	C₂×D₄	1	2	yes	—
254	#2404	C₂×D₄	1	2	yes	—
255	#2404	C₂×D₄	1	2	yes	—
256	#2404	C₂×D₄	1	2	yes	—
257	#2404	C₂×D₄	1	2	yes	—
258	#2333	C₂×D₄	1	2	yes	complemented
259	#2333	C₂×D₄	1	2	yes	complemented
260	#2333	C₂×D₄	1	2	yes	complemented
261	#2333	C₂×D₄	1	2	yes	complemented
262	#2332	C₂×D₄	1	2	yes	complemented
263	#2332	C₂×D₄	1	2	yes	complemented
264	#2332	C₂×D₄	1	2	yes	complemented
265	#2332	C₂×D₄	1	2	yes	complemented
266	#2312	C₂×D₄	1	2	yes	complemented
267	#2312	C₂×D₄	1	2	yes	complemented
268	#2310	C₂×D₄	1	2	yes	—
269	#2310	C₂×D₄	1	2	yes	—
270	#2309	C₂×D₄	1	2	yes	—
271	#2297	C₂×D₄	1	2	yes	—
272	#2297	C₂×D₄	1	2	yes	—
273	#2297	C₂×D₄	1	2	yes	—
274	#2297	C₂×D₄	1	2	yes	—
275	C₂×#386	C₂×D₄	1	2	yes	—
276	C₂×#386	C₂×D₄	1	2	yes	—
277	C₂×#386	C₂×D₄	1	2	yes	—
278	C₂×#386	C₂×D₄	1	2	yes	—
279	#2280	C₂×D₄	1	2	yes	—
280	#2280	C₂×D₄	1	2	yes	—
281	#2280	C₂×D₄	1	2	yes	—
282	#2280	C₂×D₄	1	2	yes	—
283	#2280	C₂×D₄	1	2	yes	—
284	#2280	C₂×D₄	1	2	yes	—
285	#2280	C₂×D₄	1	2	yes	—
286	#2280	C₂⁴	1	2	yes	—
287	#2280	C₂⁴	1	2	yes	—
288	C₂×#381	C₂⁴	1	4	yes	—
289	C₂×#381	C₂⁴	1	2	yes	—
290	C₂×#379	C₂×D₄	1	2	yes	—
291	#2273	C₂×D₄	1	2	yes	complemented
292	#2273	C₂×D₄	1	2	yes	complemented
293	C₂⁶	#120	1	1	yes	characteristic
294	C₂⁶	#120	1	1	yes	characteristic
295	C₂⁶	C₂²×D₄	1	1	yes	characteristic
296	C₂⁶	C₂²×D₄	1	2	yes	—
297	C₂²×#41	#120	1	2	yes	—
298	C₂²×#41	C₂²×D₄	1	2	yes	—
299	C₂²×#41	C₂²×D₄	1	2	yes	—
300	C₂²×#41	C₂²×D₄	1	2	yes	—
301	C₂²×#41	C₂²×D₄	1	2	yes	—
302	C₂²×#41	C₂²×D₄	1	2	yes	—
303	C₂²×#41	C₂²×D₄	1	2	yes	—
304	C₂³×Q₈	#120	1	1	yes	characteristic
305	C₂³×Q₈	#120	1	1	yes	characteristic
306	C₂³×Q₈	#120	1	1	yes	characteristic
307	C₂³×Q₈	C₂²×D₄	1	1	yes	characteristic
308	C₂³×Q₈	C₂²×D₄	1	1	yes	characteristic
309	C₂³×Q₈	H(5,𝔽₂)	1	2	yes	—
310	C₂³×D₄	#120	1	1	yes	characteristic
311	C₂³×D₄	#120	1	1	yes	characteristic
312	C₂³×D₄	#120	1	1	yes	characteristic
313	C₂³×D₄	#120	1	1	yes	characteristic
314	C₂³×D₄	#120	1	1	yes	characteristic
315	C₂³×D₄	#120	1	1	yes	characteristic
316	C₂³×D₄	#120	1	1	yes	characteristic
317	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
318	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
319	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
320	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
321	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
322	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
323	C₂³×D₄	H(5,𝔽₂)	1	2	yes	—
324	C₂⁴×C₄	#120	1	1	yes	characteristic
325	C₂⁴×C₄	#120	1	1	yes	characteristic
326	C₂⁴×C₄	#120	1	1	yes	characteristic
327	C₂⁴×C₄	#120	1	1	yes	characteristic
328	C₂⁴×C₄	#120	1	1	yes	characteristic
329	C₂⁴×C₄	#120	1	1	yes	characteristic
330	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
331	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
332	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
333	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
334	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
335	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
336	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
337	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
338	C₂⁴×C₄	C₂²×D₄	1	2	yes	—
339	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
340	C₂⁴×C₄	C₂⁵	1	1	yes	characteristic
341	C₂×C₄⋊Q₈	#120	1	2	yes	—
342	C₂×C₄⋊Q₈	#120	1	2	yes	—
343	C₂×#127	#120	1	2	yes	—
344	C₂×#127	#120	1	2	yes	—
345	C₂×#124	#120	1	2	yes	—
346	C₂×#124	#120	1	2	yes	—
347	C₂×#124	#120	1	2	yes	—
348	C₂×#124	#120	1	2	yes	—
349	C₂×C₂²⋊Q₈	#120	1	2	yes	—
350	C₂×C₂²⋊Q₈	#120	1	2	yes	—
351	C₂×C₂²⋊Q₈	C₂²×D₄	1	2	yes	—
352	C₂×C₂²⋊Q₈	C₂²×D₄	1	2	yes	—
353	C₂×C₂²⋊Q₈	C₂²×D₄	1	2	yes	—
354	C₂×C₂²⋊Q₈	C₂²×D₄	1	2	yes	—
355	C₂×#121	#120	1	2	yes	—
356	C₂×#121	#120	1	2	yes	—
357	C₂×#121	C₂²×D₄	1	2	yes	—
358	C₂×#121	C₂²×D₄	1	2	yes	—
359	C₂×#121	C₂²×D₄	1	2	yes	—
360	C₂×#121	C₂²×D₄	1	2	yes	—
361	C₂×#120	#120	1	2	yes	—
362	C₂×#120	#120	1	2	yes	—
363	C₂×#120	#120	1	2	yes	—
364	C₂×#120	#120	1	2	yes	—
365	C₂×#120	#120	1	2	yes	—
366	C₂×#120	#120	1	2	yes	—
367	C₂×#120	#120	1	2	yes	—
368	C₂×#120	#120	1	2	yes	—
369	C₂×#117	#120	1	2	yes	—
370	C₂×#117	#120	1	1	yes	characteristic
371	C₂×#117	#120	1	1	yes	characteristic
372	C₂×#117	#120	1	1	yes	characteristic
373	C₂×#117	#120	1	1	yes	characteristic
374	C₂×#117	C₂²×D₄	1	2	yes	—
375	C₂×#117	C₂²×D₄	1	2	yes	—
376	C₂×#117	C₂²×D₄	1	2	yes	—
377	C₂×#117	C₂²×D₄	1	2	yes	—
378	C₂×#117	C₂²×D₄	1	2	yes	—
379	C₂×#117	C₂²×D₄	1	2	yes	—
380	C₂²×C₄⋊C₄	#120	1	1	yes	characteristic
381	C₂²×C₄⋊C₄	#120	1	1	yes	characteristic
382	C₂²×C₂²⋊C₄	C₂²×D₄	1	2	yes	—
383	C₂²×C₂²⋊C₄	C₂²×D₄	1	2	yes	—
384	C₂²×C₂²⋊C₄	C₂²×D₄	1	2	yes	—
385	C₂²×C₂²⋊C₄	C₂²×D₄	1	2	yes	—
386	C₂²×C₂²⋊C₄	C₂²×D₄	1	2	yes	—
387	C₂²×C₂²⋊C₄	C₂²×D₄	1	2	yes	—
388	C₂²×C₄²	#120	1	2	yes	—
389	C₂²×C₄²	#120	1	2	yes	—
390	C₂²×C₄²	H(5,𝔽₂)	1	4	yes	—
391	C₂×C₂²⋊C₈	H(5,𝔽₂)	1	4	yes	—
392	#391	#120	1	2	yes	—
393	#391	#120	1	2	yes	—
394	#391	#120	1	2	yes	—
395	#391	#120	1	2	yes	—
396	#390	#120	1	2	yes	—
397	#390	#120	1	2	yes	—
398	#390	#120	1	2	yes	—
399	#390	#120	1	2	yes	—
400	#386	#120	1	2	yes	—
401	#386	#120	1	2	yes	—
402	#386	#120	1	2	yes	—
403	#386	#120	1	2	yes	—
404	#386	#120	1	2	yes	—
405	#386	#120	1	2	yes	—
406	#386	#120	1	2	yes	—
407	#386	#120	1	2	yes	—
408	#381	C₂²×D₄	1	2	yes	—
409	#381	C₂²×D₄	1	2	yes	—
410	#381	C₂²×D₄	1	2	yes	—
411	#381	C₂²×D₄	1	2	yes	—
412	C₄×C₂²⋊C₄	#120	1	2	yes	—
413	C₄×C₂²⋊C₄	#120	1	2	yes	—
414	C₄×C₂²⋊C₄	#120	1	2	yes	—
415	C₄×C₂²⋊C₄	#120	1	2	yes	—
416	C₄×C₂²⋊C₄	C₂²×D₄	1	2	yes	—
417	C₄×C₂²⋊C₄	C₂²×D₄	1	2	yes	—
418	C₄×C₂²⋊C₄	C₂²×D₄	1	2	yes	—
419	C₄×C₂²⋊C₄	C₂²×D₄	1	2	yes	—
420	C₄×C₂²⋊C₄	C₂²×D₄	1	2	yes	—
421	C₄×C₂²⋊C₄	C₂²×D₄	1	2	yes	—
422	C₄×C₂²⋊C₄	C₂²×D₄	1	2	yes	—
423	C₄×C₂²⋊C₄	C₂²×D₄	1	2	yes	—
424	C₂⁵	C₂×#120	1	1	yes	characteristic
425	C₂⁵	C₂×#120	1	1	yes	characteristic
426	C₂⁵	C₂×#120	1	1	yes	characteristic
427	C₂⁵	C₂×#120	1	1	yes	characteristic
428	C₂⁵	C₂×#120	1	1	yes	characteristic
429	C₂⁵	C₂×#120	1	1	yes	characteristic
430	C₂⁵	C₂×#120	1	2	yes	—
431	C₂⁵	C₂×#120	1	2	yes	—
432	C₂⁵	C₂³×D₄	1	1	yes	characteristic
433	C₂²×Q₈	C₂×#120	1	2	yes	—
434	C₂²×Q₈	C₂×#120	1	2	yes	—
435	C₂²×Q₈	C₂×#120	1	2	yes	—
436	C₂²×Q₈	C₂×#120	1	2	yes	—
437	C₂²×D₄	B(4,𝔽₂)	1	4	yes	—
438	C₂²×D₄	C₂×#120	1	2	yes	—
439	C₂²×D₄	C₂×#120	1	2	yes	—
440	C₂²×D₄	C₂×#120	1	2	yes	—
441	C₂²×D₄	C₂×#120	1	2	yes	—
442	C₂²×D₄	C₂×#120	1	2	yes	—
443	C₂²×D₄	C₂×#120	1	2	yes	—
444	C₂²×D₄	C₂×#120	1	2	yes	—
445	C₂²×D₄	C₂×#120	1	2	yes	—
446	C₂³×C₄	B(4,𝔽₂)	1	4	yes	—
447	C₂³×C₄	C₂×#120	1	1	yes	characteristic
448	C₂³×C₄	C₂×#120	1	1	yes	characteristic
449	C₂³×C₄	C₂×#120	1	1	yes	characteristic
450	C₂³×C₄	C₂×#120	1	1	yes	characteristic
451	C₂³×C₄	C₂×#120	1	1	yes	characteristic
452	C₂³×C₄	C₂×#120	1	1	yes	characteristic
453	C₂³×C₄	C₂×#120	1	1	yes	characteristic
454	C₂³×C₄	C₂×#120	1	1	yes	characteristic
455	C₂³×C₄	C₂×#120	1	1	yes	characteristic
456	C₂³×C₄	C₂×#120	1	1	yes	characteristic
457	C₂³×C₄	C₂×#120	1	2	yes	—
458	C₂³×C₄	C₂×#120	1	2	yes	—
459	C₂³×C₄	C₂×#120	1	2	yes	—
460	C₂³×C₄	C₂×#120	1	2	yes	—
461	C₂³×C₄	C₂³×D₄	1	1	yes	characteristic
462	C₂³×C₄	C₂³×D₄	1	1	yes	characteristic
463	C₂³×C₄	C₂³×D₄	1	2	yes	—
464	C₂³×C₄	C₂³×D₄	1	2	yes	—
465	C₂³×C₄	C₂×H(5,𝔽₂)	1	2	yes	—
466	C₂³×C₄	C₂×H(5,𝔽₂)	1	2	yes	—
467	C₂³×C₄	C₂×H(5,𝔽₂)	1	2	yes	—
468	C₂³×C₄	#585	1	2	yes	—
469	C₂×C₄⋊C₄	C₂×#120	1	2	yes	—
470	C₂×C₄⋊C₄	C₂×#120	1	2	yes	—
471	C₂×C₄⋊C₄	C₂×#120	1	2	yes	—
472	C₂×C₄⋊C₄	C₂×#120	1	2	yes	—
473	C₂×C₂²⋊C₄	C₂×#120	1	2	yes	—
474	C₂×C₂²⋊C₄	C₂×#120	1	2	yes	—
475	C₂×C₂²⋊C₄	C₂×#120	1	2	yes	—
476	C₂×C₂²⋊C₄	C₂×#120	1	2	yes	—
477	C₂×C₄²	C₂×#120	1	2	yes	—
478	C₂×C₄²	C₂×#120	1	2	yes	—
479	C₂×C₄²	C₂×#120	1	2	yes	—
480	C₂×C₄²	C₂×#120	1	2	yes	—
481	C₂×C₄²	C₂×#120	1	2	yes	—
482	C₂×C₄²	C₂×#120	1	2	yes	—
483	C₂×C₄²	C₂×#120	1	2	yes	—
484	C₂×C₄²	C₂×#120	1	2	yes	—
485	C₂⁴	#2846	1	2	yes	—
486	C₂⁴	#2846	1	1	yes	characteristic
487	C₂⁴	#2846	1	1	yes	characteristic
488	C₂⁴	C₂×B(4,𝔽₂)	1	2	yes	—
489	C₂⁴	C₂×B(4,𝔽₂)	1	2	yes	—
490	C₂⁴	C₂×B(4,𝔽₂)	1	2	yes	—
491	C₂⁴	#3026	1	2	yes	—
492	C₂⁴	C₂²×#120	1	2	yes	—
493	C₂⁴	C₂²×#120	1	1	yes	characteristic
494	C₂⁴	#3484	1	2	yes	—
495	C₂⁴	#3496	1	2	yes	—
496	C₂²×C₄	#2846	1	2	yes	—
497	C₂²×C₄	#2846	1	1	yes	characteristic
498	C₂²×C₄	#2846	1	1	yes	characteristic
499	C₂²×C₄	C₂×B(4,𝔽₂)	1	2	yes	—
500	C₂²×C₄	C₂×B(4,𝔽₂)	1	2	yes	—
501	C₂²×C₄	C₂×B(4,𝔽₂)	1	2	yes	—
502	C₂²×C₄	#3026	1	2	yes	—
503	C₂²×C₄	C₂²×#120	1	1	yes	characteristic
504	C₂²×C₄	C₂²×#120	1	2	yes	—
505	C₂²×C₄	C₂²×#120	1	1	yes	characteristic
506	C₂²×C₄	#3484	1	1	yes	characteristic
507	C₂²×C₄	#3484	1	1	yes	characteristic
508	C₂²×C₄	#3484	1	1	yes	characteristic
509	C₂²×C₄	#3484	1	2	yes	—
510	C₂²×C₄	#3484	1	4	yes	—
511	C₂²×C₄	#3485	1	1	yes	characteristic
512	C₂²×C₄	#3488	1	4	yes	—
513	C₂²×C₄	#3496	1	2	yes	—
514	C₂²×C₄	#3496	1	4	yes	—
515	C₂²×C₄	#3498	1	4	yes	—
516	C₂³	#32898	1	2	yes	—
517	C₂³	#32898	1	2	yes	—
518	C₂³	#35346	1	1	yes	characteristic
519	C₂³	#35347	1	1	yes	characteristic
520	C₂³	#35680	1	4	yes	—
521	C₂³	C₂×#2846	1	1	yes	characteristic
522	C₂³	C₂²×B(4,𝔽₂)	1	1	yes	characteristic
523	C₂³	C₂²×B(4,𝔽₂)	1	1	yes	characteristic
524	C₂³	C₂×#3026	1	1	yes	characteristic
525	C₂³	C₂×#3026	1	1	yes	characteristic
526	C₂×C₄	#32898	1	2	yes	—
527	C₂×C₄	#32898	1	2	yes	—
528	C₂×C₄	#35346	1	1	yes	characteristic
529	C₂×C₄	#35347	1	1	yes	characteristic
530	C₂×C₄	#35512	1	1	yes	characteristic
531	C₂×C₄	#35527	1	1	yes	characteristic
532	C₂×C₄	#35680	1	4	yes	—
533	C₂²	#4928938	1	1	yes	characteristic
534	C₂²	#6499867	1	1	yes	characteristic
535	C₂²	#6499870	1	1	yes	characteristic
536	C₂²	#6500010	1	1	yes	characteristic
537	C₂²	#6500010	1	1	yes	characteristic
538	C₂²	C₂×#32898	1	1	yes	characteristic
539	C₂²	C₂×#32898	1	1	yes	characteristic
540	C₂	#72239296	1	1	yes	characteristic
541	C₂	#72240103	1	1	yes	characteristic
542	C₂	#72251427	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²	#4928938
commutator, Frattini, cosocle	C₂⁴×C₄	C₂⁵
LCS	G ▷ C₂⁴×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂² ◁ C₂⁴×C₄ ◁ G
LECS	G ▷ C₂⁴×C₄ ▷ C₂² ▷ C₁

Complements

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

N	H ≅ G/N	type
1. #72255937	C₂	semidirect
2. #72255932	C₂	semidirect
3. #72255895	C₂	semidirect
4. #72255890	C₂	semidirect
5. #72255873	C₂	semidirect
6. #72255866	C₂	semidirect
7. #72255859	C₂	semidirect
8. #72251707	C₂	semidirect
9. #72249491	C₂	semidirect
10. #72238545	C₂	semidirect
11. #72237258	C₂	semidirect
12. #72235919	C₂	semidirect
13. #72235212	C₂	semidirect
14. #72235210	C₂	semidirect
15. #72235200	C₂	semidirect
16. C₂×#62811	C₂²	semidirect
17. #10574839	C₂²	semidirect
18. #7756445	C₂²	semidirect
19. #7756441	C₂²	semidirect
22. #7710478	C₂²	semidirect
23. #7642350	C₂²	semidirect
27. C₂×#32899	C₂²	semidirect
28. #6628869	C₂²	semidirect
29. #6437448	C₂²	semidirect
30. #6371494	C₂²	semidirect
31. #6370728	C₂²	semidirect
32. #6370684	C₂²	semidirect
33. #6346594	C₂²	semidirect
34. #635987	C₂²	semidirect
35. #393989	C₂²	semidirect
36. #393988	C₂²	semidirect
37. #393988	C₂²	semidirect
38. #393930	C₂²	semidirect
39. #392698	C₂²	semidirect
40. #392659	C₂²	semidirect
41. #392115	C₂²	semidirect
42. #392110	C₂²	semidirect
43. #359512	C₂²	semidirect
44. #359429	C₂²	semidirect
45. #353295	C₂²	semidirect
46. #238058	C₂²	semidirect
47. #234948	C₂²	semidirect
48. #234948	C₂²	semidirect
49. #232528	C₂²	semidirect
50. #202015	C₂²	semidirect
51. #202015	C₂²	semidirect
52. C₂×#9511	C₂²	semidirect
53. C₂×#9511	C₂²	semidirect
54. #201462	C₂²	semidirect
55. #201110	C₂²	semidirect
56. #201110	C₂²	semidirect
57. #190055	C₂²	semidirect
58. #187764	C₂²	semidirect
59. #186948	C₂²	semidirect
60. #185255	C₂²	semidirect
61. #184796	C₂²	semidirect
62. #122111	C₂²	semidirect
63. #115141	C₂²	semidirect
64. #113288	C₂²	semidirect
65. #112857	C₂²	semidirect
66. #112857	C₂²	semidirect
67. #111959	C₂²	semidirect
68. #111959	C₂²	semidirect
69. #111321	C₂²	semidirect
70. #108255	C₂²	semidirect
71. #108036	C₂²	semidirect
72. #108036	C₂²	semidirect
73. #106326	C₂²	semidirect
74. #105717	C₂²	semidirect
77. C₂×#3485	D₄	semidirect
80. C₂×#3484	D₄	semidirect
81. C₂×#3449	D₄	semidirect
86. C₂²×#525	D₄	semidirect
94. #46430	D₄	semidirect
95. #46427	D₄	semidirect
96. #46425	D₄	semidirect
97. #46424	D₄	semidirect
98. #46357	D₄	semidirect
99. #46356	D₄	semidirect
100. #46355	D₄	semidirect
101. #46354	D₄	semidirect
104. #36822	D₄	semidirect
105. #36818	D₄	semidirect
106. #36816	D₄	semidirect
107. #36812	D₄	semidirect
108. #36614	D₄	semidirect
111. #35439	D₄	semidirect
112. #35438	D₄	semidirect
113. #35422	D₄	semidirect
114. #35408	D₄	semidirect
115. #35242	D₄	semidirect
116. #35149	D₄	semidirect
125. #34632	D₄	semidirect
130. #34172	D₄	semidirect
132. #34171	D₄	semidirect
133. #34044	D₄	semidirect
137. C₂×#2280	D₄	semidirect
188. C₂×#543	C₂×D₄	semidirect
189. C₂×#538	C₂×D₄	semidirect
190. C₂×#538	C₂×D₄	semidirect
198. C₂×#534	C₂×D₄	semidirect
226. #2817	C₂×D₄	semidirect
227. #2816	C₂×D₄	semidirect
228. #2816	C₂×D₄	semidirect
229. #2815	C₂×D₄	semidirect
230. #2608	C₂×D₄	semidirect
231. #2608	C₂×D₄	semidirect
232. #2607	C₂×D₄	semidirect
233. #2607	C₂×D₄	semidirect
234. #2561	C₂×D₄	semidirect
235. #2561	C₂×D₄	semidirect
236. #2561	C₂×D₄	semidirect
237. #2561	C₂×D₄	semidirect
238. #2539	C₂×D₄	semidirect
239. #2539	C₂×D₄	semidirect
240. #2539	C₂×D₄	semidirect
241. #2539	C₂×D₄	semidirect
258. #2333	C₂×D₄	semidirect
259. #2333	C₂×D₄	semidirect
260. #2333	C₂×D₄	semidirect
261. #2333	C₂×D₄	semidirect
262. #2332	C₂×D₄	semidirect
263. #2332	C₂×D₄	semidirect
264. #2332	C₂×D₄	semidirect
265. #2332	C₂×D₄	semidirect
266. #2312	C₂×D₄	semidirect
267. #2312	C₂×D₄	semidirect
291. #2273	C₂×D₄	semidirect
292. #2273	C₂×D₄	semidirect

Maximal subgroups

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

subgroup	index
#72255937	2
#72255932	2
#72255895	2
#72255890	2
#72255873	2
#72255866	2
#72255859	2
#72251707	2
#72249491	2
#72238545	2
#72237258	2
#72235919	2
#72235212	2
#72235210	2
#72235200	2