Subgroups — #16859126

Order 3968.

1140 conjugacy classes of subgroups.

The subgroup lattice has 680 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14521679	C₂	1	1	yes	maximal, characteristic, complemented
2	#14521670	C₂	1	1	yes	maximal, characteristic, complemented
3	#14521667	C₂	1	2	yes	maximal, complemented
4	#14521664	C₂	1	1	yes	maximal, characteristic, complemented
5	#14521650	C₂	1	1	yes	maximal, characteristic, complemented
6	#14521649	C₂	1	2	yes	maximal, complemented
7	#14521635	C₂	1	2	yes	maximal, complemented
8	#14521631	C₂	1	2	yes	maximal, complemented
9	#14521628	C₂	1	1	yes	maximal, characteristic, complemented
10	#14521615	C₂	1	1	yes	maximal, characteristic, complemented
11	#14521612	C₂	1	1	yes	maximal, characteristic, complemented
12	#14521597	C₂	1	1	yes	maximal, characteristic, complemented
13	#14521594	C₂	1	2	yes	maximal, complemented
14	#14521594	C₂	1	1	yes	maximal, characteristic, complemented
15	#14521584	C₂	1	1	yes	maximal, characteristic, complemented
16	#14521580	C₂	1	1	yes	maximal, characteristic, complemented
17	#14521576	C₂	1	2	yes	maximal, complemented
18	#14521559	C₂	1	2	yes	maximal, complemented
19	#14521557	C₂	1	2	yes	maximal, complemented
20	#14521517	C₂	1	1	yes	maximal, characteristic, complemented
21	C₄×#92497	C₂	1	1	yes	maximal, characteristic, complemented
22	C₄×D₄×D₃₁	C₂	1	1	yes	maximal, characteristic, complemented
23	C₃₁×#540	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#92497	C₂²	1	1	yes	characteristic
25	C₂×#92497	C₂²	1	2	yes	complemented
26	C₂×#92497	C₂²	1	2	yes	complemented
27	C₂×D₄×D₃₁	C₂²	1	1	yes	characteristic
28	C₂×#92495	C₂²	1	1	yes	characteristic
29	C₂²×C₄×D₃₁	C₂²	1	2	yes	—
30	C₃₁×#127	C₂²	1	1	yes	characteristic
31	C₃₁×#125	C₂²	1	1	yes	characteristic, complemented
32	C₃₁×#123	C₂²	1	2	yes	complemented
33	C₃₁×#123	C₂²	1	2	yes	complemented
34	C₃₁×#121	C₂²	1	1	yes	characteristic
35	C₃₁×#121	C₂²	1	1	yes	characteristic, complemented
36	C₃₁×#121	C₂²	1	2	yes	complemented
37	C₃₁×#121	C₂²	1	2	yes	complemented
38	C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic
39	C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic, complemented
40	C₃₁×#117	C₂²	1	1	yes	characteristic, complemented
41	#11758517	C₂²	1	1	yes	characteristic
42	#11758517	C₂²	1	2	yes	—
43	#11758516	C₂²	1	2	yes	—
44	#11758516	C₂²	1	2	yes	—
45	#11758516	C₂²	1	2	yes	complemented
46	#11758516	C₂²	1	2	yes	complemented
47	#11758515	C₂²	1	1	yes	characteristic
48	#11758515	C₂²	1	2	yes	—
49	#11758515	C₂²	1	1	yes	characteristic, complemented
50	#11758515	C₂²	1	2	yes	complemented
51	#11758514	C₂²	1	2	yes	—
52	#11758514	C₂²	1	2	yes	—
53	#11758514	C₂²	1	2	yes	—
54	#11758513	C₂²	1	1	yes	characteristic
55	#11758513	C₂²	1	2	yes	complemented
56	#11758512	C₂²	1	2	yes	complemented
57	D₄×Dic₃₁	C₂²	1	1	yes	characteristic
58	D₄×Dic₃₁	C₂²	1	1	yes	characteristic, complemented
59	D₄×Dic₃₁	C₂²	1	2	yes	complemented
60	D₄×Dic₃₁	C₂²	1	2	yes	complemented
61	#11758507	C₂²	1	1	yes	characteristic
62	#11758507	C₂²	1	2	yes	complemented
63	#11758506	C₂²	1	2	yes	complemented
64	#11758506	C₂²	1	2	yes	complemented
65	C₄×C₂²⋊D₃₁	C₂²	1	2	yes	—
66	C₄×C₂²⋊D₃₁	C₂²	1	2	yes	—
67	#11758501	C₂²	1	1	yes	characteristic, complemented
68	#11758501	C₂²	1	2	yes	complemented
69	C₂×C₄×Dic₃₁	C₂²	1	2	yes	complemented
70	C₂×C₄×Dic₃₁	C₂²	1	1	yes	characteristic, complemented
71	#11758475	C₂²	1	2	yes	complemented
72	#11758475	C₂²	1	2	yes	complemented
73	#11758474	C₂²	1	2	yes	—
74	#11758474	C₂²	1	1	yes	characteristic, complemented
75	#11758473	C₂²	1	2	yes	—
76	#11758473	C₂²	1	2	yes	complemented
77	#11758472	C₂²	1	1	yes	characteristic
78	#11758471	C₂²	1	2	yes	complemented
79	#11758470	C₂²	1	1	yes	characteristic
80	#11758470	C₂²	1	1	yes	characteristic
81	#11758470	C₂²	1	1	yes	characteristic
82	#11758470	C₂²	1	2	yes	complemented
83	#11758469	C₂²	1	1	yes	characteristic
84	#11758469	C₂²	1	2	yes	complemented
85	C₄⋊C₄×D₃₁	C₂²	1	1	yes	characteristic
86	#11758467	C₂²	1	1	yes	characteristic, complemented
87	#11758466	C₂²	1	2	yes	complemented
88	#11758465	C₂²	1	1	yes	characteristic, complemented
89	#11758465	C₂²	1	2	yes	complemented
90	#11758464	C₂²	1	1	yes	characteristic, complemented
91	#11758464	C₂²	1	1	yes	characteristic, complemented
92	#11758464	C₂²	1	1	yes	characteristic, complemented
93	#11758462	C₂²	1	2	yes	—
94	#11758462	C₂²	1	2	yes	complemented
95	#11758462	C₂²	1	2	yes	complemented
96	#11758462	C₂²	1	2	yes	complemented
97	#11758461	C₂²	1	2	yes	—
98	#11758461	C₂²	1	2	yes	complemented
99	#11758460	C₂²	1	2	yes	complemented
100	#11758460	C₂²	1	2	yes	complemented
101	#11758459	C₂²	1	2	yes	—
102	(C₂²⋊D₃₁)⋊C₄	C₂²	1	1	yes	characteristic
103	(C₂²⋊D₃₁)⋊C₄	C₂²	1	2	yes	—
104	(C₂²⋊D₃₁)⋊C₄	C₂²	1	2	yes	—
105	(C₂²⋊D₃₁)⋊C₄	C₂²	1	1	yes	characteristic
106	(C₂²⋊D₃₁)⋊C₄	C₂²	1	1	yes	characteristic, complemented
107	(C₂²⋊D₃₁)⋊C₄	C₂²	1	1	yes	characteristic, complemented
108	(C₂²⋊D₃₁)⋊C₄	C₂²	1	2	yes	complemented
109	C₂²⋊C₄×D₃₁	C₂²	1	2	yes	—
110	#11758456	C₂²	1	2	yes	complemented
111	#11758456	C₂²	1	2	yes	complemented
112	#11758455	C₂²	1	2	yes	complemented
113	#11758454	C₂²	1	2	yes	complemented
114	#11758454	C₂²	1	2	yes	complemented
115	#11758452	C₂²	1	1	yes	characteristic
116	C₄×D₁₂₄	C₂²	1	1	yes	characteristic
117	#11758449	C₂²	1	1	yes	characteristic
118	#11758449	C₂²	1	1	yes	characteristic, complemented
119	C₄²×D₃₁	C₂²	1	1	yes	characteristic
120	C₄²×D₃₁	C₂²	1	1	yes	characteristic, complemented
121	#11758446	C₂²	1	1	yes	characteristic, complemented
122	C₄×Dic₆₂	C₂²	1	1	yes	characteristic, complemented
123	C₂³×D₃₁	C₂³	1	2	yes	—
124	C₂×D₄×C₃₁	C₂³	1	1	yes	characteristic
125	C₂×D₄×C₃₁	C₂³	1	1	yes	characteristic
126	C₂×D₄×C₃₁	C₂³	1	2	yes	—
127	C₂×D₄×C₃₁	C₂³	1	2	yes	—
128	C₂×D₄×C₃₁	C₂³	1	2	yes	—
129	C₂×D₄×C₃₁	C₂³	1	2	yes	—
130	C₂²×C₄×C₃₁	C₂³	1	1	yes	characteristic
131	C₂²×C₄×C₃₁	C₂³	1	2	yes	—
132	C₂²×C₄×C₃₁	C₂³	1	2	yes	—
133	C₂×C₂²⋊D₃₁	C₂³	1	1	yes	characteristic
134	C₂×C₂²⋊D₃₁	C₂³	1	2	yes	—
135	C₂×C₂²⋊D₃₁	C₂³	1	2	yes	—
136	C₂×C₂²⋊D₃₁	C₂³	1	1	yes	characteristic
137	C₂×C₂²⋊D₃₁	C₂³	1	2	yes	—
138	C₂×C₂²⋊D₃₁	C₂³	1	2	yes	—
139	C₂×C₂²⋊D₃₁	C₂³	1	2	yes	—
140	C₂×C₂²⋊D₃₁	C₂³	1	2	yes	—
141	C₂×C₂²⋊D₃₁	C₂³	1	2	yes	—
142	C₂²×Dic₃₁	C₂³	1	2	yes	—
143	C₂²×Dic₃₁	C₂³	1	2	yes	—
144	C₂²×Dic₃₁	C₂³	1	2	yes	—
145	C₂²×Dic₃₁	C₂³	1	1	yes	characteristic
146	C₂²×Dic₃₁	C₂³	1	1	yes	characteristic
147	#92497	—	2	4	no	—
148	#92497	—	4	4	no	—
149	#92497	—	4	4	no	—
150	D₄×D₃₁	—	2	4	no	—
151	#92495	—	2	4	no	—
152	C₂×D₁₂₄	C₂³	1	1	yes	characteristic
153	C₂×D₁₂₄	C₂³	1	1	yes	characteristic
154	C₂×D₁₂₄	C₂³	1	2	yes	—
155	C₂×C₄×D₃₁	—	4	4	no	—
156	C₂×C₄×D₃₁	C₂³	1	1	yes	characteristic
157	C₂×C₄×D₃₁	C₂³	1	1	yes	characteristic
158	C₂×C₄×D₃₁	C₂³	1	1	yes	characteristic
159	C₂×C₄×D₃₁	C₂³	1	2	yes	—
160	C₂×C₄×D₃₁	C₂³	1	1	yes	characteristic
161	C₂×C₄×D₃₁	C₂³	1	1	yes	characteristic
162	C₂×C₄×D₃₁	C₂³	1	2	yes	—
163	C₂×C₄×D₃₁	C₂³	1	2	yes	—
164	C₂×C₄×D₃₁	C₂³	1	1	yes	characteristic
165	C₂×Dic₆₂	C₂³	1	1	yes	characteristic
166	C₂×Dic₆₂	C₂³	1	1	yes	characteristic
167	C₂×Dic₆₂	C₂³	1	2	yes	—
168	C₂×Dic₆₂	C₂³	1	2	yes	—
169	C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
170	C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
171	C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
172	C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
173	C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
174	C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
175	C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
176	C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
177	C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
178	C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
179	C₂²⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
180	C₂²⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
181	C₄²×C₃₁	C₂³	1	1	yes	characteristic
182	C₄²×C₃₁	C₂³	1	1	yes	characteristic
183	C₂²⋊Dic₃₁	C₂³	1	2	yes	—
184	C₂²⋊Dic₃₁	C₂³	1	2	yes	—
185	C₂²⋊Dic₃₁	C₂³	1	2	yes	—
186	C₂²⋊Dic₃₁	C₂³	1	2	yes	—
187	C₂²⋊Dic₃₁	C₂³	1	2	yes	—
188	C₂²⋊Dic₃₁	C₂³	1	2	yes	—
189	C₂²⋊Dic₃₁	C₂³	1	2	yes	—
190	(C₂×D₃₁)⋊C₄	C₂³	1	1	yes	characteristic
191	(C₂×D₃₁)⋊C₄	C₂³	1	1	yes	characteristic
192	(C₂×D₃₁)⋊C₄	C₂³	1	1	yes	characteristic
193	(C₂×D₃₁)⋊C₄	C₂³	1	1	yes	characteristic
194	(C₂×D₃₁)⋊C₄	C₂³	1	2	yes	—
195	(C₂×D₃₁)⋊C₄	C₂³	1	2	yes	—
196	(C₂×D₃₁)⋊C₄	C₂³	1	2	yes	—
197	(C₂×D₃₁)⋊C₄	C₂³	1	2	yes	—
198	(C₂×D₃₁)⋊C₄	C₂³	1	2	yes	—
199	(C₂×D₃₁)⋊C₄	C₂³	1	2	yes	—
200	(C₂×D₃₁)⋊C₄	C₂³	1	2	yes	—
201	(C₂×D₃₁)⋊C₄	C₂³	1	2	yes	—
202	C₄⋊Dic₃₁	C₂³	1	1	yes	characteristic
203	C₄⋊Dic₃₁	C₂³	1	1	yes	characteristic
204	C₄⋊Dic₃₁	C₂³	1	2	yes	—
205	C₄⋊Dic₃₁	C₂³	1	2	yes	—
206	C₄⋊Dic₃₁	C₂³	1	2	yes	—
207	Dic₃₁⋊C₄	C₂³	1	2	yes	—
208	Dic₃₁⋊C₄	C₂³	1	1	yes	characteristic
209	Dic₃₁⋊C₄	C₂³	1	1	yes	characteristic
210	Dic₃₁⋊C₄	C₂³	1	1	yes	characteristic
211	Dic₃₁⋊C₄	C₂³	1	1	yes	characteristic
212	Dic₃₁⋊C₄	C₂³	1	2	yes	—
213	Dic₃₁⋊C₄	C₂³	1	2	yes	—
214	Dic₃₁⋊C₄	C₂³	1	2	yes	—
215	Dic₃₁⋊C₄	C₂³	1	2	yes	—
216	Dic₃₁⋊C₄	C₂³	1	2	yes	—
217	C₄×Dic₃₁	C₂³	1	2	yes	—
218	C₄×Dic₃₁	C₂³	1	1	yes	characteristic
219	C₄×Dic₃₁	C₂³	1	1	yes	characteristic
220	C₄×Dic₃₁	C₂³	1	1	yes	characteristic
221	C₄×Dic₃₁	C₂³	1	1	yes	characteristic
222	C₄×Dic₃₁	C₂³	1	1	yes	characteristic
223	C₄×Dic₃₁	C₂³	1	1	yes	characteristic
224	C₄×Dic₃₁	C₂³	1	1	yes	characteristic
225	C₄×Dic₃₁	C₂³	1	2	yes	—
226	C₄×Dic₃₁	C₂³	1	2	yes	—
227	C₄×Dic₃₁	C₂³	1	1	yes	characteristic
228	C₂³×C₃₁	C₂⁴	1	2	yes	—
229	C₂³×C₃₁	C₂⁴	1	2	yes	—
230	C₂³×C₃₁	C₂⁴	1	1	yes	characteristic
231	C₂²×D₃₁	—	2	4	no	—
232	C₂²×D₃₁	—	4	2	no	—
233	C₂²×D₃₁	—	4	2	no	—
234	C₂²×D₃₁	C₂⁴	1	2	yes	—
235	C₂²×D₃₁	C₂⁴	1	1	yes	characteristic
236	C₂²×D₃₁	C₂⁴	1	1	yes	characteristic
237	D₄×C₃₁	—	2	2	no	—
238	D₄×C₃₁	—	2	2	no	—
239	D₄×C₃₁	—	4	2	no	—
240	D₄×C₃₁	—	4	2	no	—
241	D₄×C₃₁	—	4	2	no	—
242	D₄×C₃₁	—	4	2	no	—
243	C₂×C₄×C₃₁	—	2	2	no	—
244	C₂×C₄×C₃₁	—	4	2	no	—
245	C₂×C₄×C₃₁	—	4	2	no	—
246	C₂×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
247	C₂×C₄×C₃₁	C₂⁴	1	2	yes	—
248	C₂×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
249	C₂×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
250	C₂×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
251	C₂×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
252	C₂×C₄×C₃₁	C₂⁴	1	2	yes	—
253	C₂×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
254	C₂²⋊D₃₁	—	2	2	no	—
255	C₂²⋊D₃₁	—	2	4	no	—
256	C₂²⋊D₃₁	—	2	2	no	—
257	C₂²⋊D₃₁	—	2	4	no	—
258	C₂²⋊D₃₁	—	4	2	no	—
259	C₂²⋊D₃₁	—	4	2	no	—
260	C₂²⋊D₃₁	—	4	2	no	—
261	C₂²⋊D₃₁	—	4	2	no	—
262	C₂²⋊D₃₁	—	4	2	no	—
263	C₂×Dic₃₁	—	2	4	no	—
264	C₂×Dic₃₁	—	2	4	no	—
265	C₂×Dic₃₁	—	2	2	no	—
266	C₂×Dic₃₁	—	2	4	no	—
267	C₂×Dic₃₁	—	4	1	no	—
268	C₂×Dic₃₁	C₂⁴	1	1	yes	characteristic
269	C₂×Dic₃₁	C₂⁴	1	1	yes	characteristic
270	C₂×Dic₃₁	C₂⁴	1	2	yes	—
271	C₂×Dic₃₁	C₂⁴	1	1	yes	characteristic
272	C₂×Dic₃₁	C₂⁴	1	2	yes	—
273	C₂×Dic₃₁	C₂⁴	1	1	yes	characteristic
274	C₂×Dic₃₁	C₂⁴	1	2	yes	—
275	C₂×Dic₃₁	C₂⁴	1	1	yes	characteristic
276	C₂×Dic₃₁	C₂⁴	1	1	yes	characteristic
277	D₁₂₄	—	2	2	no	—
278	D₁₂₄	—	2	2	no	—
279	D₁₂₄	—	4	2	no	—
280	C₄×D₃₁	—	2	2	no	—
281	C₄×D₃₁	—	2	2	no	—
282	C₄×D₃₁	—	2	4	no	—
283	C₄×D₃₁	—	2	2	no	—
284	C₄×D₃₁	—	4	2	no	—
285	C₄×D₃₁	—	4	2	no	—
286	C₄×D₃₁	—	4	1	no	—
287	C₄×D₃₁	—	4	1	no	—
288	C₄×D₃₁	#41	1	4	yes	complemented
289	Dic₆₂	—	2	2	no	—
290	Dic₆₂	—	2	2	no	—
291	Dic₆₂	—	4	2	no	—
292	Dic₆₂	—	4	2	no	—
293	#3460	—	31	1	no	maximal, Sylow
294	C₂²×C₃₁	—	2	2	no	—
295	C₂²×C₃₁	—	2	1	no	—
296	C₂²×C₃₁	—	2	2	no	—
297	C₂²×C₃₁	—	2	2	no	—
298	C₂²×C₃₁	—	2	1	no	—
299	C₂²×C₃₁	—	2	2	no	—
300	C₂²×C₃₁	—	2	1	no	—
301	C₂²×C₃₁	—	2	2	no	—
302	C₂²×C₃₁	—	2	2	no	—
303	C₂²×C₃₁	C₂⁵	1	1	yes	characteristic
304	C₂×D₃₁	—	2	1	no	—
305	C₂×D₃₁	—	2	1	no	—
306	C₂×D₃₁	—	2	1	no	—
307	C₂×D₃₁	—	2	2	no	—
308	C₂×D₃₁	—	2	2	no	—
309	C₂×D₃₁	—	2	1	no	—
310	C₂×D₃₁	—	2	1	no	—
311	C₂×D₃₁	—	2	2	no	—
312	C₂×D₃₁	—	4	8	no	—
313	C₂×D₃₁	C₂×#41	1	2	yes	—
314	C₄×C₃₁	—	2	1	no	—
315	C₄×C₃₁	—	2	1	no	—
316	C₄×C₃₁	—	2	2	no	—
317	C₄×C₃₁	—	2	1	no	—
318	C₄×C₃₁	—	2	1	no	—
319	C₄×C₃₁	—	2	1	no	—
320	C₄×C₃₁	—	2	2	no	—
321	C₄×C₃₁	C₂×#41	1	2	yes	—
322	Dic₃₁	—	2	1	no	—
323	Dic₃₁	—	2	2	no	—
324	Dic₃₁	—	2	1	no	—
325	Dic₃₁	—	2	2	no	—
326	Dic₃₁	—	2	2	no	—
327	Dic₃₁	—	2	1	no	—
328	Dic₃₁	—	2	1	no	—
329	Dic₃₁	C₂×#41	1	2	yes	—
330	Dic₃₁	H(5,𝔽₂)	1	2	yes	—
331	#544	—	31	1	no	—
332	#542	—	31	2	no	—
333	#542	—	31	1	no	—
334	#542	—	31	1	no	—
335	#540	—	31	2	no	—
336	#540	—	31	1	no	—
337	#540	D₃₁	1	1	yes	characteristic, complemented
338	#538	—	31	2	no	—
339	#538	—	31	2	no	—
340	#537	—	31	1	no	—
341	#535	—	31	1	no	—
342	#535	—	31	1	no	—
343	#532	—	31	1	no	—
344	#532	—	31	1	no	—
345	#532	—	31	2	no	—
346	#529	—	31	1	no	—
347	#529	—	31	2	no	—
348	#529	—	31	1	no	—
349	#525	—	31	2	no	—
350	#525	—	31	2	no	—
351	C₄×#41	—	31	1	no	—
352	C₄×#41	—	31	1	no	—
353	C₂×C₄×D₄	—	31	1	no	—
354	C₂×C₃₁	—	4	2	no	—
355	C₂×C₃₁	—	4	2	no	—
356	C₂×C₃₁	—	4	1	no	—
357	C₂×C₃₁	C₂²×#41	1	1	yes	characteristic
358	C₂×C₃₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
359	C₂×C₃₁	#585	1	1	yes	characteristic
360	D₃₁	—	2	2	no	—
361	D₃₁	—	4	1	no	—
362	D₃₁	—	4	2	no	—
363	C₂×#41	—	31	1	no	—
364	C₂×#41	—	31	2	no	—
365	C₂×#41	—	31	2	no	—
366	C₂×#41	—	31	1	no	—
367	C₂²×D₄	—	31	1	no	—
368	C₂³×C₄	—	31	2	no	—
369	C₄⋊Q₈	—	31	2	no	—
370	C₄⋊Q₈	—	31	1	no	—
371	C₄⋊Q₈	—	31	1	no	—
372	#127	—	31	2	no	—
373	#127	—	31	1	no	—
374	#127	C₂×D₃₁	1	1	yes	characteristic
375	#126	—	31	2	no	—
376	#126	—	31	2	no	—
377	#126	—	31	2	no	—
378	#126	—	31	2	no	—
379	#125	—	31	2	no	—
380	#125	—	31	1	no	—
381	#125	C₂×D₃₁	1	1	yes	characteristic, complemented
382	#124	—	31	1	no	—
383	#124	—	31	2	no	—
384	#124	—	31	2	no	—
385	#124	—	31	2	no	—
386	#124	—	31	2	no	—
387	#124	—	31	2	no	—
388	#124	—	31	1	no	—
389	#123	—	31	2	no	—
390	#123	—	31	2	no	—
391	#123	—	31	2	no	—
392	#123	—	31	2	no	—
393	#123	—	31	2	no	—
394	#123	—	31	2	no	—
395	#123	C₂×D₃₁	1	2	yes	complemented
396	#123	C₂×D₃₁	1	2	yes	complemented
397	C₂²⋊Q₈	—	31	2	no	—
398	C₂²⋊Q₈	—	31	1	no	—
399	C₂²⋊Q₈	—	31	2	no	—
400	C₂²⋊Q₈	—	31	2	no	—
401	C₂²⋊Q₈	—	31	2	no	—
402	C₂²⋊Q₈	—	31	1	no	—
403	C₂²⋊Q₈	—	31	2	no	—
404	#121	—	31	2	no	—
405	#121	—	31	2	no	—
406	#121	—	31	1	no	—
407	#121	—	31	2	no	—
408	#121	—	31	1	no	—
409	#121	—	31	2	no	—
410	#121	—	31	2	no	—
411	#121	—	31	2	no	—
412	#121	—	31	1	no	—
413	#121	—	31	2	no	—
414	#121	—	31	1	no	—
415	#121	—	31	2	no	—
416	#121	—	31	2	no	—
417	#121	C₂×D₃₁	1	1	yes	characteristic
418	#121	C₂×D₃₁	1	2	yes	complemented
419	#121	C₂×D₃₁	1	1	yes	characteristic, complemented
420	#121	C₂×D₃₁	1	2	yes	complemented
421	#120	—	31	2	no	—
422	#120	—	31	2	no	—
423	#120	—	31	2	no	—
424	#120	—	31	2	no	—
425	C₄×Q₈	—	31	1	no	—
426	C₄×Q₈	—	31	1	no	—
427	C₄×Q₈	—	31	1	no	—
428	C₄×Q₈	—	31	1	no	—
429	C₄×D₄	—	31	1	no	—
430	C₄×D₄	—	31	1	no	—
431	C₄×D₄	—	31	2	no	—
432	C₄×D₄	—	31	2	no	—
433	C₄×D₄	—	31	2	no	—
434	C₄×D₄	—	31	2	no	—
435	C₄×D₄	—	31	1	no	—
436	C₄×D₄	—	31	1	no	—
437	C₄×D₄	—	31	1	no	—
438	C₄×D₄	—	31	2	no	—
439	C₄×D₄	—	31	2	no	—
440	C₄×D₄	—	31	2	no	—
441	C₄×D₄	—	31	1	no	—
442	C₄×D₄	—	31	1	no	—
443	C₄×D₄	—	31	1	no	—
444	C₄×D₄	—	31	1	no	—
445	C₄×D₄	—	31	2	no	—
446	C₄×D₄	—	31	1	no	—
447	C₄×D₄	C₂×D₃₁	1	1	yes	characteristic
448	C₄×D₄	C₂×D₃₁	1	1	yes	characteristic, complemented
449	#117	—	31	1	no	—
450	#117	—	31	2	no	—
451	#117	—	31	2	no	—
452	#117	—	31	2	no	—
453	#117	—	31	1	no	—
454	#117	—	31	1	no	—
455	#117	C₂×D₃₁	1	1	yes	characteristic, complemented
456	C₂×C₄⋊C₄	—	31	1	no	—
457	C₂×C₂²⋊C₄	—	31	2	no	—
458	C₂×C₄²	—	31	2	no	—
459	C₂×C₄²	—	31	1	no	—
460	C₂×C₄²	—	31	1	no	—
461	C₂×C₄²	—	31	1	no	—
462	C₃₁	#3460	1	1	yes	characteristic, complemented, Sylow
463	C₂⁴	—	31	2	no	—
464	#41	—	62	4	no	—
465	#41	—	62	4	no	—
466	#41	—	124	4	no	—
467	#41	—	124	4	no	—
468	C₂×Q₈	—	31	1	no	—
469	C₂×Q₈	—	31	1	no	—
470	C₂×Q₈	—	31	2	no	—
471	C₂×Q₈	—	31	2	no	—
472	C₂×D₄	—	31	1	no	—
473	C₂×D₄	—	31	2	no	—
474	C₂×D₄	—	31	2	no	—
475	C₂×D₄	—	31	1	no	—
476	C₂×D₄	—	31	2	no	—
477	C₂×D₄	—	31	2	no	—
478	C₂×D₄	—	31	2	no	—
479	C₂×D₄	—	31	2	no	—
480	C₂×D₄	—	31	2	no	—
481	C₂×D₄	—	31	1	no	—
482	C₂×D₄	—	31	1	no	—
483	C₂×D₄	—	31	2	no	—
484	C₂×D₄	—	62	4	no	—
485	C₂×D₄	C₂²×D₃₁	1	1	yes	characteristic
486	C₂×D₄	C₂²×D₃₁	1	1	yes	characteristic
487	C₂×D₄	C₂²×D₃₁	1	2	yes	—
488	C₂×D₄	C₂²×D₃₁	1	2	yes	—
489	C₂×D₄	C₂²×D₃₁	1	2	yes	—
490	C₂×D₄	C₂²×D₃₁	1	2	yes	—
491	C₂²×C₄	—	31	1	no	—
492	C₂²×C₄	—	31	2	no	—
493	C₂²×C₄	—	31	2	no	—
494	C₂²×C₄	—	31	1	no	—
495	C₂²×C₄	—	31	2	no	—
496	C₂²×C₄	—	31	1	no	—
497	C₂²×C₄	—	31	1	no	—
498	C₂²×C₄	—	31	1	no	—
499	C₂²×C₄	—	31	1	no	—
500	C₂²×C₄	—	31	2	no	—
501	C₂²×C₄	—	31	1	no	—
502	C₂²×C₄	—	31	1	no	—
503	C₂²×C₄	—	31	2	no	—
504	C₂²×C₄	—	31	2	no	—
505	C₂²×C₄	—	124	4	no	—
506	C₂²×C₄	C₂²×D₃₁	1	1	yes	characteristic
507	C₂²×C₄	C₂²×D₃₁	1	2	yes	—
508	C₂²×C₄	C₂²×D₃₁	1	2	yes	—
509	C₄⋊C₄	—	31	2	no	—
510	C₄⋊C₄	—	31	1	no	—
511	C₄⋊C₄	—	31	1	no	—
512	C₄⋊C₄	—	31	2	no	—
513	C₄⋊C₄	—	31	1	no	—
514	C₄⋊C₄	—	31	2	no	—
515	C₄⋊C₄	—	31	1	no	—
516	C₄⋊C₄	—	31	2	no	—
517	C₄⋊C₄	—	31	2	no	—
518	C₄⋊C₄	—	31	2	no	—
519	C₄⋊C₄	—	31	1	no	—
520	C₄⋊C₄	—	31	1	no	—
521	C₄⋊C₄	—	31	2	no	—
522	C₄⋊C₄	—	31	2	no	—
523	C₄⋊C₄	—	31	2	no	—
524	C₄⋊C₄	C₂²×D₃₁	1	1	yes	characteristic
525	C₄⋊C₄	C₂²×D₃₁	1	1	yes	characteristic
526	C₄⋊C₄	C₂²×D₃₁	1	2	yes	—
527	C₄⋊C₄	C₂²×D₃₁	1	1	yes	characteristic
528	C₄⋊C₄	C₂²×D₃₁	1	1	yes	characteristic
529	C₄⋊C₄	C₂²×D₃₁	1	2	yes	—
530	C₂²⋊C₄	—	31	2	no	—
531	C₂²⋊C₄	—	31	2	no	—
532	C₂²⋊C₄	—	31	2	no	—
533	C₂²⋊C₄	—	31	2	no	—
534	C₂²⋊C₄	—	31	2	no	—
535	C₂²⋊C₄	—	31	2	no	—
536	C₂²⋊C₄	—	31	2	no	—
537	C₂²⋊C₄	—	31	2	no	—
538	C₂²⋊C₄	—	31	2	no	—
539	C₂²⋊C₄	—	31	1	no	—
540	C₂²⋊C₄	—	31	2	no	—
541	C₂²⋊C₄	—	31	1	no	—
542	C₂²⋊C₄	—	31	1	no	—
543	C₂²⋊C₄	—	31	1	no	—
544	C₂²⋊C₄	—	31	2	no	—
545	C₂²⋊C₄	—	31	2	no	—
546	C₂²⋊C₄	—	31	2	no	—
547	C₂²⋊C₄	—	31	2	no	—
548	C₂²⋊C₄	—	31	2	no	—
549	C₂²⋊C₄	C₂²×D₃₁	1	2	yes	—
550	C₂²⋊C₄	C₂²×D₃₁	1	2	yes	—
551	C₂²⋊C₄	C₂²×D₃₁	1	2	yes	—
552	C₂²⋊C₄	C₂²×D₃₁	1	1	yes	characteristic
553	C₂²⋊C₄	C₂²×D₃₁	1	1	yes	characteristic
554	C₂²⋊C₄	C₂²×D₃₁	1	2	yes	—
555	C₄²	—	31	1	no	—
556	C₄²	—	31	1	no	—
557	C₄²	—	31	2	no	—
558	C₄²	—	31	1	no	—
559	C₄²	—	31	1	no	—
560	C₄²	—	31	1	no	—
561	C₄²	—	31	2	no	—
562	C₄²	—	31	1	no	—
563	C₄²	—	31	1	no	—
564	C₄²	—	31	1	no	—
565	C₄²	—	31	2	no	—
566	C₄²	C₂²×D₃₁	1	1	yes	characteristic
567	C₄²	C₂²×D₃₁	1	1	yes	characteristic
568	C₂³	—	31	1	no	—
569	C₂³	—	31	2	no	—
570	C₂³	—	31	1	no	—
571	C₂³	—	62	4	no	—
572	C₂³	—	124	2	no	—
573	C₂³	—	124	2	no	—
574	C₂³	C₂³×D₃₁	1	2	yes	—
575	C₂³	C₂³×D₃₁	1	1	yes	characteristic
576	C₂³	C₂³×D₃₁	1	2	yes	—
577	Q₈	—	62	2	no	—
578	Q₈	—	62	2	no	—
579	Q₈	—	124	2	no	—
580	Q₈	—	124	2	no	—
581	D₄	—	2	2	no	—
582	D₄	—	2	2	no	—
583	D₄	—	4	2	no	—
584	D₄	—	4	2	no	—
585	D₄	—	4	2	no	—
586	D₄	—	4	2	no	—
587	D₄	—	62	2	no	—
588	D₄	—	62	4	no	—
589	D₄	—	62	2	no	—
590	D₄	—	62	2	no	—
591	D₄	—	62	4	no	—
592	D₄	—	62	2	no	—
593	D₄	—	124	2	no	—
594	D₄	—	124	2	no	—
595	D₄	—	124	2	no	—
596	D₄	—	124	2	no	—
597	D₄	—	124	2	no	—
598	D₄	—	124	2	no	—
599	C₂×C₄	—	2	2	no	—
600	C₂×C₄	—	4	2	no	—
601	C₂×C₄	—	4	2	no	—
602	C₂×C₄	—	31	1	no	—
603	C₂×C₄	—	31	1	no	—
604	C₂×C₄	—	31	4	no	—
605	C₂×C₄	—	31	1	no	—
606	C₂×C₄	—	31	2	no	—
607	C₂×C₄	—	31	1	no	—
608	C₂×C₄	—	31	1	no	—
609	C₂×C₄	—	31	2	no	—
610	C₂×C₄	—	31	1	no	—
611	C₂×C₄	—	31	2	no	—
612	C₂×C₄	—	62	2	no	—
613	C₂×C₄	—	62	4	no	—
614	C₂×C₄	—	62	2	no	—
615	C₂×C₄	—	62	4	no	—
616	C₂×C₄	—	62	4	no	—
617	C₂×C₄	—	62	4	no	—
618	C₂×C₄	—	62	2	no	—
619	C₂×C₄	—	62	2	no	—
620	C₂×C₄	—	124	1	no	—
621	C₂×C₄	—	124	1	no	—
622	C₂×C₄	—	124	2	no	—
623	C₂×C₄	—	124	2	no	—
624	C₂×C₄	—	124	1	no	—
625	C₂×C₄	C₂³×D₃₁	1	1	yes	characteristic
626	C₂×C₄	C₂³×D₃₁	1	1	yes	characteristic
627	C₂×C₄	C₂³×D₃₁	1	2	yes	—
628	C₂×C₄	C₂³×D₃₁	1	1	yes	characteristic
629	C₂×C₄	C₂³×D₃₁	1	1	yes	characteristic
630	C₂×C₄	C₂³×D₃₁	1	1	yes	characteristic
631	C₂×C₄	C₂³×D₃₁	1	2	yes	—
632	C₂×C₄	C₂³×D₃₁	1	1	yes	characteristic
633	C₂²	—	2	1	no	—
634	C₂²	—	2	2	no	—
635	C₂²	—	2	2	no	—
636	C₂²	—	2	2	no	—
637	C₂²	—	2	1	no	—
638	C₂²	—	2	2	no	—
639	C₂²	—	2	2	no	—
640	C₂²	—	2	1	no	—
641	C₂²	—	2	2	no	—
642	C₂²	—	31	2	no	—
643	C₂²	—	62	1	no	—
644	C₂²	—	62	1	no	—
645	C₂²	—	62	1	no	—
646	C₂²	—	62	2	no	—
647	C₂²	—	62	2	no	—
648	C₂²	—	62	1	no	—
649	C₂²	—	62	1	no	—
650	C₂²	—	62	2	no	—
651	C₂²	—	124	8	no	—
652	C₂²	C₂⁴×D₃₁	1	1	yes	characteristic
653	C₄	—	2	1	no	—
654	C₄	—	2	1	no	—
655	C₄	—	2	2	no	—
656	C₄	—	2	1	no	—
657	C₄	—	2	1	no	—
658	C₄	—	2	2	no	—
659	C₄	—	2	1	no	—
660	C₄	—	31	2	no	—
661	C₄	—	31	2	no	—
662	C₄	—	62	2	no	—
663	C₄	—	62	1	no	—
664	C₄	—	62	2	no	—
665	C₄	—	62	2	no	—
666	C₄	—	62	1	no	—
667	C₄	—	62	1	no	—
668	C₄	—	62	1	no	—
669	C₄	#41×D₃₁	1	2	yes	—
670	C₂	—	4	2	no	—
671	C₂	—	4	1	no	—
672	C₂	—	4	2	no	—
673	C₂	—	62	2	no	—
674	C₂	—	124	2	no	—
675	C₂	—	124	1	no	—
676	C₂	C₂×#41×D₃₁	1	1	yes	characteristic
677	C₂	H(5,𝔽₂)×D₃₁	1	1	yes	characteristic
678	C₂	#14521884	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₃₁
commutator, socle, cosocle	C₂²×C₃₁	C₂⁵
Fitting	C₃₁×#540	C₂
hypercenter	#540	D₃₁
hypocenter	C₃₁	#3460
LCS	G ▷ C₂²×C₃₁ ▷ C₃₁
UCS	C₁ ◁ C₂² ◁ #540

Complements

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

N	H ≅ G/N	type
1. #14521679	C₂	semidirect
2. #14521670	C₂	semidirect
3. #14521667	C₂	semidirect
4. #14521664	C₂	semidirect
5. #14521650	C₂	semidirect
6. #14521649	C₂	semidirect
7. #14521635	C₂	semidirect
8. #14521631	C₂	semidirect
9. #14521628	C₂	semidirect
10. #14521615	C₂	semidirect
11. #14521612	C₂	semidirect
12. #14521597	C₂	semidirect
13. #14521594	C₂	semidirect
14. #14521594	C₂	semidirect
15. #14521584	C₂	semidirect
16. #14521580	C₂	semidirect
17. #14521576	C₂	semidirect
18. #14521559	C₂	semidirect
19. #14521557	C₂	semidirect
20. #14521517	C₂	semidirect
21. C₄×#92497	C₂	semidirect
22. C₄×D₄×D₃₁	C₂	semidirect
23. C₃₁×#540	C₂	semidirect
25. C₂×#92497	C₂²	semidirect
26. C₂×#92497	C₂²	semidirect
31. C₃₁×#125	C₂²	semidirect
32. C₃₁×#123	C₂²	semidirect
33. C₃₁×#123	C₂²	semidirect
35. C₃₁×#121	C₂²	semidirect
36. C₃₁×#121	C₂²	semidirect
37. C₃₁×#121	C₂²	semidirect
39. C₄×D₄×C₃₁	C₂²	semidirect
40. C₃₁×#117	C₂²	semidirect
45. #11758516	C₂²	semidirect
46. #11758516	C₂²	semidirect
49. #11758515	C₂²	semidirect
50. #11758515	C₂²	semidirect
55. #11758513	C₂²	semidirect
56. #11758512	C₂²	semidirect
58. D₄×Dic₃₁	C₂²	semidirect
59. D₄×Dic₃₁	C₂²	semidirect
60. D₄×Dic₃₁	C₂²	semidirect
62. #11758507	C₂²	semidirect
63. #11758506	C₂²	semidirect
64. #11758506	C₂²	semidirect
67. #11758501	C₂²	semidirect
68. #11758501	C₂²	semidirect
69. C₂×C₄×Dic₃₁	C₂²	semidirect
70. C₂×C₄×Dic₃₁	C₂²	semidirect
71. #11758475	C₂²	semidirect
72. #11758475	C₂²	semidirect
74. #11758474	C₂²	semidirect
76. #11758473	C₂²	semidirect
78. #11758471	C₂²	semidirect
82. #11758470	C₂²	semidirect
84. #11758469	C₂²	semidirect
86. #11758467	C₂²	semidirect
87. #11758466	C₂²	semidirect
88. #11758465	C₂²	semidirect
89. #11758465	C₂²	semidirect
90. #11758464	C₂²	semidirect
91. #11758464	C₂²	semidirect
92. #11758464	C₂²	semidirect
94. #11758462	C₂²	semidirect
95. #11758462	C₂²	semidirect
96. #11758462	C₂²	semidirect
98. #11758461	C₂²	semidirect
99. #11758460	C₂²	semidirect
100. #11758460	C₂²	semidirect
106. (C₂²⋊D₃₁)⋊C₄	C₂²	semidirect
107. (C₂²⋊D₃₁)⋊C₄	C₂²	semidirect
108. (C₂²⋊D₃₁)⋊C₄	C₂²	semidirect
110. #11758456	C₂²	semidirect
111. #11758456	C₂²	semidirect
112. #11758455	C₂²	semidirect
113. #11758454	C₂²	semidirect
114. #11758454	C₂²	semidirect
118. #11758449	C₂²	semidirect
120. C₄²×D₃₁	C₂²	semidirect
121. #11758446	C₂²	semidirect
122. C₄×Dic₆₂	C₂²	semidirect
288. C₄×D₃₁	#41	semidirect
337. #540	D₃₁	semidirect
381. #125	C₂×D₃₁	semidirect
395. #123	C₂×D₃₁	semidirect
396. #123	C₂×D₃₁	semidirect
418. #121	C₂×D₃₁	semidirect
419. #121	C₂×D₃₁	semidirect
420. #121	C₂×D₃₁	semidirect
448. C₄×D₄	C₂×D₃₁	semidirect
455. #117	C₂×D₃₁	semidirect
462. C₃₁	#3460	semidirect

Maximal subgroups

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

subgroup	index
#14521679	2
#14521670	2
#14521667	2
#14521664	2
#14521650	2
#14521649	2
#14521635	2
#14521631	2
#14521628	2
#14521615	2
#14521612	2
#14521597	2
#14521594	2
#14521584	2
#14521580	2
#14521576	2
#14521559	2
#14521557	2
#14521517	2
C₄×#92497	2
C₄×D₄×D₃₁	2
C₃₁×#540	2
#3460	31