Subgroups — #16859094

Order 3968.

1040 conjugacy classes of subgroups.

The subgroup lattice has 966 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14521669	C₂	1	1	yes	maximal, characteristic, complemented
2	#14521667	C₂	1	1	yes	maximal, characteristic, complemented
3	#14521665	C₂	1	1	yes	maximal, characteristic, complemented
4	#14521663	C₂	1	1	yes	maximal, characteristic, complemented
5	#14521658	C₂	1	1	yes	maximal, characteristic, complemented
6	#14521656	C₂	1	1	yes	maximal, characteristic, complemented
7	#14521651	C₂	1	1	yes	maximal, characteristic, complemented
8	#14521649	C₂	1	1	yes	maximal, characteristic, complemented
9	#14521647	C₂	1	1	yes	maximal, characteristic, complemented
10	#14521645	C₂	1	1	yes	maximal, characteristic, complemented
11	#14521642	C₂	1	1	yes	maximal, characteristic, complemented
12	#14521640	C₂	1	1	yes	maximal, characteristic, complemented
13	#14521638	C₂	1	1	yes	maximal, characteristic, complemented
14	#14521635	C₂	1	1	yes	maximal, characteristic, complemented
15	#14521633	C₂	1	1	yes	maximal, characteristic, complemented
16	#14521631	C₂	1	1	yes	maximal, characteristic, complemented
17	#14521603	C₂	1	1	yes	maximal, characteristic, complemented
18	#14521596	C₂	1	1	yes	maximal, characteristic, complemented
19	#14521586	C₂	1	1	yes	maximal, characteristic, complemented
20	#14521583	C₂	1	1	yes	maximal, characteristic, complemented
21	#14521581	C₂	1	1	yes	maximal, characteristic, complemented
22	#14521579	C₂	1	1	yes	maximal, characteristic, complemented
23	#14521579	C₂	1	1	yes	maximal, characteristic, complemented
24	#14521577	C₂	1	1	yes	maximal, characteristic, complemented
25	#14521577	C₂	1	1	yes	maximal, characteristic, complemented
26	#14521558	C₂	1	1	yes	maximal, characteristic, complemented
27	#14521558	C₂	1	1	yes	maximal, characteristic, complemented
28	C₄×#92495	C₂	1	1	yes	maximal, characteristic, complemented
29	#14521517	C₂	1	1	yes	maximal, characteristic, complemented
30	#117×D₃₁	C₂	1	1	yes	maximal, characteristic, complemented
31	C₃₁×#529	C₂	1	1	yes	maximal, characteristic, complemented
32	C₂×#92495	C₂²	1	1	yes	characteristic
33	C₂×#92495	C₂²	1	1	yes	characteristic
34	C₂²×C₄×D₃₁	C₂²	1	1	yes	characteristic
35	C₃₁×#126	C₂²	1	1	yes	characteristic
36	C₃₁×#126	C₂²	1	1	yes	characteristic, complemented
37	C₃₁×#125	C₂²	1	1	yes	characteristic, complemented
38	C₃₁×#124	C₂²	1	1	yes	characteristic
39	C₃₁×#123	C₂²	1	1	yes	characteristic
40	C₃₁×#123	C₂²	1	1	yes	characteristic, complemented
41	C₃₁×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
42	C₃₁×#121	C₂²	1	1	yes	characteristic
43	C₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic, complemented
44	C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic
45	C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic
46	C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic, complemented
47	C₃₁×#117	C₂²	1	1	yes	characteristic
48	C₃₁×#117	C₂²	1	1	yes	characteristic, complemented
49	C₂×C₄²×C₃₁	C₂²	1	1	yes	characteristic, complemented
50	#11758524	C₂²	1	1	yes	characteristic
51	#11758523	C₂²	1	1	yes	characteristic
52	#11758523	C₂²	1	1	yes	characteristic, complemented
53	#11758521	C₂²	1	1	yes	characteristic, complemented
54	#11758517	C₂²	1	1	yes	characteristic, complemented
55	#11758516	C₂²	1	1	yes	characteristic
56	#11758516	C₂²	1	1	yes	characteristic
57	#11758516	C₂²	1	1	yes	characteristic
58	#11758516	C₂²	1	1	yes	characteristic
59	#11758515	C₂²	1	1	yes	characteristic
60	#11758515	C₂²	1	1	yes	characteristic
61	#11758514	C₂²	1	1	yes	characteristic
62	#11758514	C₂²	1	1	yes	characteristic
63	#11758513	C₂²	1	1	yes	characteristic
64	#11758512	C₂²	1	1	yes	characteristic
65	#11758512	C₂²	1	1	yes	characteristic, complemented
66	#11758507	C₂²	1	1	yes	characteristic
67	#11758506	C₂²	1	1	yes	characteristic
68	#11758506	C₂²	1	1	yes	characteristic, complemented
69	C₄×C₂²⋊D₃₁	C₂²	1	1	yes	characteristic
70	C₄×C₂²⋊D₃₁	C₂²	1	1	yes	characteristic
71	C₄×C₂²⋊D₃₁	C₂²	1	1	yes	characteristic
72	C₄×C₂²⋊D₃₁	C₂²	1	1	yes	characteristic
73	C₄×C₂²⋊D₃₁	C₂²	1	1	yes	characteristic
74	C₄×C₂²⋊D₃₁	C₂²	1	1	yes	characteristic
75	C₄×C₂²⋊D₃₁	C₂²	1	1	yes	characteristic, complemented
76	C₄×C₂²⋊D₃₁	C₂²	1	1	yes	characteristic, complemented
77	C₄×C₂²⋊D₃₁	C₂²	1	1	yes	characteristic, complemented
78	C₄×C₂²⋊D₃₁	C₂²	1	1	yes	characteristic, complemented
79	#11758503	C₂²	1	1	yes	characteristic
80	#11758503	C₂²	1	1	yes	characteristic, complemented
81	#11758501	C₂²	1	1	yes	characteristic, complemented
82	C₂×C₄×Dic₃₁	C₂²	1	1	yes	characteristic, complemented
83	#11758475	C₂²	1	1	yes	characteristic
84	#11758475	C₂²	1	1	yes	characteristic
85	#11758475	C₂²	1	1	yes	characteristic
86	#11758475	C₂²	1	1	yes	characteristic, complemented
87	#11758475	C₂²	1	1	yes	characteristic, complemented
88	#11758475	C₂²	1	1	yes	characteristic, complemented
89	#11758474	C₂²	1	1	yes	characteristic
90	#11758474	C₂²	1	1	yes	characteristic, complemented
91	#11758473	C₂²	1	1	yes	characteristic
92	#11758473	C₂²	1	1	yes	characteristic
93	#11758473	C₂²	1	1	yes	characteristic
94	#11758473	C₂²	1	1	yes	characteristic
95	#11758473	C₂²	1	1	yes	characteristic, complemented
96	#11758473	C₂²	1	1	yes	characteristic, complemented
97	#11758472	C₂²	1	1	yes	characteristic
98	#11758472	C₂²	1	1	yes	characteristic
99	#11758471	C₂²	1	1	yes	characteristic
100	#11758471	C₂²	1	1	yes	characteristic
101	#11758471	C₂²	1	1	yes	characteristic
102	#11758471	C₂²	1	1	yes	characteristic
103	#11758471	C₂²	1	1	yes	characteristic, complemented
104	#11758471	C₂²	1	1	yes	characteristic, complemented
105	#11758470	C₂²	1	1	yes	characteristic
106	#11758470	C₂²	1	1	yes	characteristic
107	#11758469	C₂²	1	1	yes	characteristic
108	#11758469	C₂²	1	1	yes	characteristic
109	C₄⋊C₄×D₃₁	C₂²	1	1	yes	characteristic
110	C₄⋊C₄×D₃₁	C₂²	1	1	yes	characteristic
111	#11758467	C₂²	1	1	yes	characteristic, complemented
112	#11758467	C₂²	1	1	yes	characteristic, complemented
113	#11758466	C₂²	1	1	yes	characteristic, complemented
114	#11758466	C₂²	1	1	yes	characteristic, complemented
115	#11758466	C₂²	1	1	yes	characteristic, complemented
116	#11758466	C₂²	1	1	yes	characteristic, complemented
117	#11758466	C₂²	1	1	yes	characteristic, complemented
118	#11758466	C₂²	1	1	yes	characteristic, complemented
119	#11758465	C₂²	1	1	yes	characteristic, complemented
120	#11758465	C₂²	1	1	yes	characteristic, complemented
121	#11758464	C₂²	1	1	yes	characteristic, complemented
122	#11758464	C₂²	1	1	yes	characteristic, complemented
123	#11758463	C₂²	1	1	yes	characteristic
124	#11758463	C₂²	1	1	yes	characteristic, complemented
125	#11758462	C₂²	1	1	yes	characteristic
126	#11758462	C₂²	1	1	yes	characteristic
127	#11758462	C₂²	1	1	yes	characteristic
128	#11758462	C₂²	1	1	yes	characteristic
129	#11758462	C₂²	1	1	yes	characteristic, complemented
130	#11758462	C₂²	1	1	yes	characteristic, complemented
131	#11758461	C₂²	1	1	yes	characteristic
132	#11758461	C₂²	1	1	yes	characteristic
133	#11758461	C₂²	1	1	yes	characteristic
134	#11758461	C₂²	1	1	yes	characteristic
135	#11758461	C₂²	1	1	yes	characteristic
136	#11758461	C₂²	1	1	yes	characteristic
137	#11758460	C₂²	1	1	yes	characteristic
138	#11758460	C₂²	1	1	yes	characteristic
139	#11758460	C₂²	1	1	yes	characteristic
140	#11758460	C₂²	1	1	yes	characteristic
141	#11758460	C₂²	1	1	yes	characteristic, complemented
142	#11758460	C₂²	1	1	yes	characteristic, complemented
143	#11758459	C₂²	1	1	yes	characteristic
144	#11758459	C₂²	1	1	yes	characteristic
145	(C₂²⋊D₃₁)⋊C₄	C₂²	1	1	yes	characteristic
146	(C₂²⋊D₃₁)⋊C₄	C₂²	1	1	yes	characteristic
147	(C₂²⋊D₃₁)⋊C₄	C₂²	1	1	yes	characteristic, complemented
148	(C₂²⋊D₃₁)⋊C₄	C₂²	1	1	yes	characteristic, complemented
149	C₂²⋊C₄×D₃₁	C₂²	1	1	yes	characteristic
150	C₂²⋊C₄×D₃₁	C₂²	1	1	yes	characteristic
151	#11758456	C₂²	1	1	yes	characteristic
152	#11758456	C₂²	1	1	yes	characteristic
153	#11758456	C₂²	1	1	yes	characteristic
154	#11758456	C₂²	1	1	yes	characteristic, complemented
155	#11758456	C₂²	1	1	yes	characteristic, complemented
156	#11758456	C₂²	1	1	yes	characteristic, complemented
157	#11758455	C₂²	1	1	yes	characteristic
158	#11758455	C₂²	1	1	yes	characteristic
159	#11758455	C₂²	1	1	yes	characteristic, complemented
160	#11758455	C₂²	1	1	yes	characteristic, complemented
161	#11758454	C₂²	1	1	yes	characteristic
162	#11758454	C₂²	1	1	yes	characteristic
163	#11758453	C₂²	1	1	yes	characteristic
164	#11758453	C₂²	1	1	yes	characteristic, complemented
165	#11758452	C₂²	1	1	yes	characteristic
166	C₄×D₁₂₄	C₂²	1	1	yes	characteristic
167	C₄×D₁₂₄	C₂²	1	1	yes	characteristic
168	C₄×D₁₂₄	C₂²	1	1	yes	characteristic
169	C₄×D₁₂₄	C₂²	1	1	yes	characteristic
170	C₄×D₁₂₄	C₂²	1	1	yes	characteristic, complemented
171	#11758449	C₂²	1	1	yes	characteristic
172	#11758449	C₂²	1	1	yes	characteristic
173	#11758449	C₂²	1	1	yes	characteristic
174	#11758449	C₂²	1	1	yes	characteristic
175	#11758449	C₂²	1	1	yes	characteristic, complemented
176	#11758449	C₂²	1	1	yes	characteristic, complemented
177	C₄²×D₃₁	C₂²	1	1	yes	characteristic
178	C₄²×D₃₁	C₂²	1	1	yes	characteristic
179	C₄²×D₃₁	C₂²	1	1	yes	characteristic, complemented
180	C₄²×D₃₁	C₂²	1	1	yes	characteristic, complemented
181	#11758447	C₂²	1	1	yes	characteristic, complemented
182	C₄×Dic₆₂	C₂²	1	1	yes	characteristic, complemented
183	C₄×Dic₆₂	C₂²	1	1	yes	characteristic, complemented
184	C₄×Dic₆₂	C₂²	1	1	yes	characteristic, complemented
185	C₄×Dic₆₂	C₂²	1	1	yes	characteristic, complemented
186	C₄×Dic₆₂	C₂²	1	1	yes	characteristic, complemented
187	C₂³×D₃₁	C₂³	1	1	yes	characteristic
188	C₂×Q₈×C₃₁	C₂³	1	1	yes	characteristic
189	C₂×D₄×C₃₁	C₂³	1	1	yes	characteristic
190	C₂×D₄×C₃₁	C₂³	1	1	yes	characteristic
191	C₂×D₄×C₃₁	C₂³	1	1	yes	characteristic
192	C₂²×C₄×C₃₁	C₂³	1	1	yes	characteristic
193	C₂²×C₄×C₃₁	C₂³	1	1	yes	characteristic
194	C₂²×C₄×C₃₁	C₂³	1	1	yes	characteristic
195	C₂²×C₄×C₃₁	C₂³	1	1	yes	characteristic
196	C₂²×C₄×C₃₁	C₂³	1	1	yes	characteristic
197	C₂×C₂²⋊D₃₁	C₂³	1	1	yes	characteristic
198	C₂×C₂²⋊D₃₁	C₂³	1	1	yes	characteristic
199	C₂×C₂²⋊D₃₁	C₂³	1	1	yes	characteristic
200	C₂×C₂²⋊D₃₁	C₂³	1	1	yes	characteristic
201	C₂×C₂²⋊D₃₁	C₂³	1	1	yes	characteristic
202	C₂×C₂²⋊D₃₁	C₂³	1	1	yes	characteristic
203	C₂×C₂²⋊D₃₁	C₂³	1	1	yes	characteristic
204	C₂×C₂²⋊D₃₁	C₂³	1	1	yes	characteristic
205	C₂×C₂²⋊D₃₁	C₂³	1	1	yes	characteristic
206	C₂×C₂²⋊D₃₁	C₂³	1	1	yes	characteristic
207	C₂²×Dic₃₁	C₂³	1	1	yes	characteristic
208	C₂²×Dic₃₁	C₂³	1	1	yes	characteristic
209	C₂²×Dic₃₁	C₂³	1	1	yes	characteristic
210	#92495	—	2	4	no	—
211	#92495	—	2	4	no	—
212	C₂×D₁₂₄	C₂³	1	1	yes	characteristic
213	C₂×D₁₂₄	C₂³	1	1	yes	characteristic
214	C₂×D₁₂₄	C₂³	1	1	yes	characteristic
215	C₂×D₁₂₄	C₂³	1	1	yes	characteristic
216	C₂×D₁₂₄	C₂³	1	1	yes	characteristic
217	C₂×C₄×D₃₁	—	2	4	no	—
218	C₂×C₄×D₃₁	C₂³	1	1	yes	characteristic
219	C₂×C₄×D₃₁	C₂³	1	1	yes	characteristic
220	C₂×C₄×D₃₁	C₂³	1	1	yes	characteristic
221	C₂×C₄×D₃₁	C₂³	1	1	yes	characteristic
222	C₂×C₄×D₃₁	C₂³	1	1	yes	characteristic
223	C₂×C₄×D₃₁	C₂³	1	1	yes	characteristic
224	C₂×C₄×D₃₁	C₂³	1	1	yes	characteristic
225	C₂×C₄×D₃₁	C₂³	1	1	yes	characteristic
226	C₂×C₄×D₃₁	C₂³	1	1	yes	characteristic
227	C₂×C₄×D₃₁	C₂³	1	1	yes	characteristic
228	C₂×C₄×D₃₁	C₂³	1	1	yes	characteristic
229	C₂×C₄×D₃₁	C₂³	1	1	yes	characteristic
230	C₂×C₄×D₃₁	C₂³	1	1	yes	characteristic
231	C₂×C₄×D₃₁	C₂³	1	1	yes	characteristic
232	C₂×Dic₆₂	C₂³	1	1	yes	characteristic
233	C₂×Dic₆₂	C₂³	1	1	yes	characteristic
234	C₂×Dic₆₂	C₂³	1	1	yes	characteristic
235	C₂×Dic₆₂	C₂³	1	1	yes	characteristic
236	C₂×Dic₆₂	C₂³	1	1	yes	characteristic
237	C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
238	C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
239	C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
240	C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
241	C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
242	C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
243	C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
244	C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
245	C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
246	C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
247	C₂²⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
248	C₂²⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
249	C₂²⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
250	C₂²⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
251	C₂²⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
252	C₂²⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
253	C₂²⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
254	C₂²⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
255	C₂²⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
256	C₂²⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
257	C₄²×C₃₁	C₂³	1	1	yes	characteristic
258	C₄²×C₃₁	C₂³	1	1	yes	characteristic
259	C₄²×C₃₁	C₂³	1	1	yes	characteristic
260	C₄²×C₃₁	C₂³	1	1	yes	characteristic
261	C₄²×C₃₁	C₂³	1	1	yes	characteristic
262	C₄²×C₃₁	C₂³	1	1	yes	characteristic
263	C₂²⋊Dic₃₁	C₂³	1	1	yes	characteristic
264	C₂²⋊Dic₃₁	C₂³	1	1	yes	characteristic
265	C₂²⋊Dic₃₁	C₂³	1	1	yes	characteristic
266	C₂²⋊Dic₃₁	C₂³	1	1	yes	characteristic
267	C₂²⋊Dic₃₁	C₂³	1	1	yes	characteristic
268	C₂²⋊Dic₃₁	C₂³	1	1	yes	characteristic
269	C₂²⋊Dic₃₁	C₂³	1	1	yes	characteristic
270	C₂²⋊Dic₃₁	C₂³	1	1	yes	characteristic
271	C₂²⋊Dic₃₁	C₂³	1	1	yes	characteristic
272	C₂²⋊Dic₃₁	C₂³	1	1	yes	characteristic
273	(C₂×D₃₁)⋊C₄	C₂³	1	1	yes	characteristic
274	(C₂×D₃₁)⋊C₄	C₂³	1	1	yes	characteristic
275	(C₂×D₃₁)⋊C₄	C₂³	1	1	yes	characteristic
276	(C₂×D₃₁)⋊C₄	C₂³	1	1	yes	characteristic
277	(C₂×D₃₁)⋊C₄	C₂³	1	1	yes	characteristic
278	(C₂×D₃₁)⋊C₄	C₂³	1	1	yes	characteristic
279	(C₂×D₃₁)⋊C₄	C₂³	1	1	yes	characteristic
280	(C₂×D₃₁)⋊C₄	C₂³	1	1	yes	characteristic
281	(C₂×D₃₁)⋊C₄	C₂³	1	1	yes	characteristic
282	(C₂×D₃₁)⋊C₄	C₂³	1	1	yes	characteristic
283	(C₂×D₃₁)⋊C₄	C₂³	1	1	yes	characteristic
284	(C₂×D₃₁)⋊C₄	C₂³	1	1	yes	characteristic
285	(C₂×D₃₁)⋊C₄	C₂³	1	1	yes	characteristic
286	(C₂×D₃₁)⋊C₄	C₂³	1	1	yes	characteristic
287	(C₂×D₃₁)⋊C₄	C₂³	1	1	yes	characteristic
288	(C₂×D₃₁)⋊C₄	C₂³	1	1	yes	characteristic
289	(C₂×D₃₁)⋊C₄	C₂³	1	1	yes	characteristic
290	(C₂×D₃₁)⋊C₄	C₂³	1	1	yes	characteristic
291	(C₂×D₃₁)⋊C₄	C₂³	1	1	yes	characteristic
292	(C₂×D₃₁)⋊C₄	C₂³	1	1	yes	characteristic
293	(C₂×D₃₁)⋊C₄	C₂³	1	1	yes	characteristic
294	(C₂×D₃₁)⋊C₄	C₂³	1	1	yes	characteristic
295	(C₂×D₃₁)⋊C₄	C₂³	1	1	yes	characteristic
296	(C₂×D₃₁)⋊C₄	C₂³	1	1	yes	characteristic
297	C₄⋊Dic₃₁	C₂³	1	1	yes	characteristic
298	C₄⋊Dic₃₁	C₂³	1	1	yes	characteristic
299	C₄⋊Dic₃₁	C₂³	1	1	yes	characteristic
300	C₄⋊Dic₃₁	C₂³	1	1	yes	characteristic
301	C₄⋊Dic₃₁	C₂³	1	1	yes	characteristic
302	C₄⋊Dic₃₁	C₂³	1	1	yes	characteristic
303	C₄⋊Dic₃₁	C₂³	1	1	yes	characteristic
304	C₄⋊Dic₃₁	C₂³	1	1	yes	characteristic
305	C₄⋊Dic₃₁	C₂³	1	1	yes	characteristic
306	C₄⋊Dic₃₁	C₂³	1	1	yes	characteristic
307	Dic₃₁⋊C₄	C₂³	1	1	yes	characteristic
308	Dic₃₁⋊C₄	C₂³	1	1	yes	characteristic
309	Dic₃₁⋊C₄	C₂³	1	1	yes	characteristic
310	Dic₃₁⋊C₄	C₂³	1	1	yes	characteristic
311	Dic₃₁⋊C₄	C₂³	1	1	yes	characteristic
312	Dic₃₁⋊C₄	C₂³	1	1	yes	characteristic
313	Dic₃₁⋊C₄	C₂³	1	1	yes	characteristic
314	Dic₃₁⋊C₄	C₂³	1	1	yes	characteristic
315	Dic₃₁⋊C₄	C₂³	1	1	yes	characteristic
316	Dic₃₁⋊C₄	C₂³	1	1	yes	characteristic
317	Dic₃₁⋊C₄	C₂³	1	1	yes	characteristic
318	Dic₃₁⋊C₄	C₂³	1	1	yes	characteristic
319	Dic₃₁⋊C₄	C₂³	1	1	yes	characteristic
320	Dic₃₁⋊C₄	C₂³	1	1	yes	characteristic
321	Dic₃₁⋊C₄	C₂³	1	1	yes	characteristic
322	Dic₃₁⋊C₄	C₂³	1	1	yes	characteristic
323	Dic₃₁⋊C₄	C₂³	1	1	yes	characteristic
324	Dic₃₁⋊C₄	C₂³	1	1	yes	characteristic
325	Dic₃₁⋊C₄	C₂³	1	1	yes	characteristic
326	Dic₃₁⋊C₄	C₂³	1	1	yes	characteristic
327	Dic₃₁⋊C₄	C₂³	1	1	yes	characteristic
328	Dic₃₁⋊C₄	C₂³	1	1	yes	characteristic
329	Dic₃₁⋊C₄	C₂³	1	1	yes	characteristic
330	Dic₃₁⋊C₄	C₂³	1	1	yes	characteristic
331	C₄×Dic₃₁	C₂³	1	1	yes	characteristic
332	C₄×Dic₃₁	C₂³	1	1	yes	characteristic
333	C₄×Dic₃₁	C₂³	1	1	yes	characteristic
334	C₄×Dic₃₁	C₂³	1	1	yes	characteristic
335	C₄×Dic₃₁	C₂³	1	1	yes	characteristic
336	C₄×Dic₃₁	C₂³	1	1	yes	characteristic
337	C₄×Dic₃₁	C₂³	1	1	yes	characteristic
338	C₄×Dic₃₁	C₂³	1	1	yes	characteristic
339	C₄×Dic₃₁	C₂³	1	1	yes	characteristic
340	C₄×Dic₃₁	C₂³	1	1	yes	characteristic
341	C₄×Dic₃₁	C₂³	1	1	yes	characteristic
342	C₄×Dic₃₁	C₂³	1	1	yes	characteristic
343	C₄×Dic₃₁	C₂³	1	1	yes	characteristic
344	C₄×Dic₃₁	C₂³	1	1	yes	characteristic
345	C₂³×C₃₁	C₂⁴	1	1	yes	characteristic
346	C₂³×C₃₁	C₂⁴	1	1	yes	characteristic
347	C₂³×C₃₁	C₂⁴	1	1	yes	characteristic
348	C₂²×D₃₁	—	2	2	no	—
349	C₂²×D₃₁	—	4	1	no	—
350	C₂²×D₃₁	—	4	1	no	—
351	C₂²×D₃₁	C₂⁴	1	1	yes	characteristic
352	C₂²×D₃₁	C₂⁴	1	1	yes	characteristic
353	C₂²×D₃₁	C₂⁴	1	1	yes	characteristic
354	C₂²×D₃₁	C₂⁴	1	1	yes	characteristic
355	Q₈×C₃₁	—	4	1	no	—
356	D₄×C₃₁	—	4	1	no	—
357	D₄×C₃₁	—	4	1	no	—
358	D₄×C₃₁	—	4	1	no	—
359	C₂×C₄×C₃₁	—	2	2	no	—
360	C₂×C₄×C₃₁	—	2	2	no	—
361	C₂×C₄×C₃₁	—	2	2	no	—
362	C₂×C₄×C₃₁	—	4	1	no	—
363	C₂×C₄×C₃₁	—	4	1	no	—
364	C₂×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
365	C₂×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
366	C₂×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
367	C₂×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
368	C₂×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
369	C₂×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
370	C₂×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
371	C₂×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
372	C₂×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
373	C₂×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
374	C₂×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
375	C₂×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
376	C₂²⋊D₃₁	—	2	2	no	—
377	C₂²⋊D₃₁	—	2	2	no	—
378	C₂²⋊D₃₁	—	2	2	no	—
379	C₂²⋊D₃₁	—	2	2	no	—
380	C₂²⋊D₃₁	—	4	1	no	—
381	C₂²⋊D₃₁	—	4	1	no	—
382	C₂²⋊D₃₁	—	4	1	no	—
383	C₂²⋊D₃₁	—	4	1	no	—
384	C₂²⋊D₃₁	—	4	1	no	—
385	C₂²⋊D₃₁	—	4	1	no	—
386	C₂×Dic₃₁	—	2	2	no	—
387	C₂×Dic₃₁	—	4	1	no	—
388	C₂×Dic₃₁	—	4	1	no	—
389	C₂×Dic₃₁	C₂⁴	1	1	yes	characteristic
390	C₂×Dic₃₁	C₂⁴	1	1	yes	characteristic
391	C₂×Dic₃₁	C₂⁴	1	1	yes	characteristic
392	C₂×Dic₃₁	C₂⁴	1	1	yes	characteristic
393	C₂×Dic₃₁	C₂⁴	1	1	yes	characteristic
394	C₂×Dic₃₁	C₂⁴	1	1	yes	characteristic
395	C₂×Dic₃₁	C₂⁴	1	1	yes	characteristic
396	C₂×Dic₃₁	C₂⁴	1	1	yes	characteristic
397	C₂×Dic₃₁	C₂⁴	1	1	yes	characteristic
398	C₂×Dic₃₁	C₂⁴	1	1	yes	characteristic
399	C₂×Dic₃₁	C₂⁴	1	1	yes	characteristic
400	C₂×Dic₃₁	C₂⁴	1	1	yes	characteristic
401	D₁₂₄	—	2	2	no	—
402	D₁₂₄	—	2	2	no	—
403	D₁₂₄	—	4	1	no	—
404	D₁₂₄	—	4	1	no	—
405	D₁₂₄	—	4	1	no	—
406	C₄×D₃₁	—	2	2	no	—
407	C₄×D₃₁	—	2	2	no	—
408	C₄×D₃₁	—	2	2	no	—
409	C₄×D₃₁	—	2	2	no	—
410	C₄×D₃₁	—	2	2	no	—
411	C₄×D₃₁	—	4	1	no	—
412	C₄×D₃₁	—	4	1	no	—
413	C₄×D₃₁	—	4	1	no	—
414	C₄×D₃₁	—	4	1	no	—
415	C₄×D₃₁	—	4	1	no	—
416	C₄×D₃₁	—	4	1	no	—
417	C₄×D₃₁	—	4	1	no	—
418	C₄×D₃₁	—	4	1	no	—
419	C₄×D₃₁	#41	1	4	yes	—
420	Dic₆₂	—	2	2	no	—
421	Dic₆₂	—	2	2	no	—
422	Dic₆₂	—	4	1	no	—
423	Dic₆₂	—	4	1	no	—
424	Dic₆₂	—	4	1	no	—
425	#3455	—	31	1	no	maximal, Sylow
426	C₂²×C₃₁	—	2	1	no	—
427	C₂²×C₃₁	—	2	1	no	—
428	C₂²×C₃₁	—	2	1	no	—
429	C₂²×C₃₁	—	2	1	no	—
430	C₂²×C₃₁	—	2	1	no	—
431	C₂²×C₃₁	—	2	1	no	—
432	C₂²×C₃₁	—	2	1	no	—
433	C₂²×C₃₁	—	2	1	no	—
434	C₂²×C₃₁	—	2	1	no	—
435	C₂²×C₃₁	C₂⁵	1	1	yes	characteristic
436	C₂×D₃₁	—	2	1	no	—
437	C₂×D₃₁	—	2	1	no	—
438	C₂×D₃₁	—	2	1	no	—
439	C₂×D₃₁	—	2	1	no	—
440	C₂×D₃₁	—	2	1	no	—
441	C₂×D₃₁	—	2	1	no	—
442	C₂×D₃₁	—	2	1	no	—
443	C₂×D₃₁	—	2	1	no	—
444	C₂×D₃₁	—	2	1	no	—
445	C₂×D₃₁	—	2	1	no	—
446	C₂×D₃₁	—	2	1	no	—
447	C₂×D₃₁	—	4	4	no	—
448	C₂×D₃₁	C₂×#41	1	2	yes	—
449	C₄×C₃₁	—	2	1	no	—
450	C₄×C₃₁	—	2	1	no	—
451	C₄×C₃₁	—	2	1	no	—
452	C₄×C₃₁	—	2	1	no	—
453	C₄×C₃₁	—	2	1	no	—
454	C₄×C₃₁	—	2	1	no	—
455	C₄×C₃₁	—	2	1	no	—
456	C₄×C₃₁	—	2	1	no	—
457	C₄×C₃₁	—	2	1	no	—
458	C₄×C₃₁	—	2	1	no	—
459	C₄×C₃₁	—	2	1	no	—
460	C₄×C₃₁	C₂×#41	1	2	yes	—
461	Dic₃₁	—	2	1	no	—
462	Dic₃₁	—	2	1	no	—
463	Dic₃₁	—	2	1	no	—
464	Dic₃₁	—	2	1	no	—
465	Dic₃₁	—	2	1	no	—
466	Dic₃₁	—	2	1	no	—
467	Dic₃₁	—	2	1	no	—
468	Dic₃₁	—	2	1	no	—
469	Dic₃₁	—	2	1	no	—
470	Dic₃₁	—	2	1	no	—
471	Dic₃₁	—	2	1	no	—
472	Dic₃₁	C₂×#41	1	2	yes	—
473	#542	—	31	1	no	—
474	#542	—	31	1	no	—
475	#542	—	31	1	no	—
476	#542	—	31	1	no	—
477	#541	—	31	1	no	—
478	#541	—	31	1	no	—
479	#540	—	31	1	no	—
480	#540	—	31	1	no	—
481	#539	—	31	1	no	—
482	#539	—	31	1	no	—
483	#539	—	31	1	no	—
484	#539	—	31	1	no	—
485	#538	—	31	1	no	—
486	#538	—	31	1	no	—
487	#538	—	31	1	no	—
488	#538	—	31	1	no	—
489	#533	—	31	1	no	—
490	#532	—	31	1	no	—
491	#529	—	31	1	no	—
492	#529	—	31	1	no	—
493	#529	—	31	1	no	—
494	#529	—	31	1	no	—
495	#529	—	31	1	no	—
496	#529	—	31	1	no	—
497	#529	—	31	1	no	—
498	#529	D₃₁	1	1	yes	characteristic, complemented
499	#525	—	31	1	no	—
500	#525	—	31	1	no	—
501	C₄×#41	—	31	1	no	—
502	C₄×#41	—	31	1	no	—
503	C₂×#117	—	31	1	no	—
504	C₂×C₃₁	—	4	1	no	—
505	C₂×C₃₁	—	4	1	no	—
506	C₂×C₃₁	—	4	1	no	—
507	C₂×C₃₁	C₂²×#41	1	1	yes	characteristic
508	C₂×C₃₁	#585	1	1	yes	characteristic
509	C₂×C₃₁	#585	1	1	yes	characteristic
510	D₃₁	—	2	2	no	—
511	D₃₁	—	4	1	no	—
512	D₃₁	—	4	1	no	—
513	D₃₁	—	4	1	no	—
514	C₂×#41	—	31	1	no	—
515	C₂×#41	—	31	1	no	—
516	C₂³×C₄	—	31	1	no	—
517	C₄⋊Q₈	—	31	1	no	—
518	C₄⋊Q₈	—	31	1	no	—
519	C₄⋊Q₈	—	31	1	no	—
520	#127	—	31	1	no	—
521	#126	—	31	1	no	—
522	#126	—	31	1	no	—
523	#126	—	31	1	no	—
524	#126	—	31	1	no	—
525	#126	—	31	1	no	—
526	#126	—	31	1	no	—
527	#126	—	31	1	no	—
528	#126	—	31	1	no	—
529	#126	—	31	1	no	—
530	#126	—	31	1	no	—
531	#126	—	31	1	no	—
532	#126	—	31	1	no	—
533	#126	—	31	1	no	—
534	#126	—	31	1	no	—
535	#126	C₂×D₃₁	1	1	yes	characteristic
536	#126	C₂×D₃₁	1	1	yes	characteristic, complemented
537	#125	—	31	1	no	—
538	#125	—	31	1	no	—
539	#125	—	31	1	no	—
540	#125	—	31	1	no	—
541	#125	—	31	1	no	—
542	#125	—	31	1	no	—
543	#125	—	31	1	no	—
544	#125	—	31	1	no	—
545	#125	—	31	1	no	—
546	#125	C₂×D₃₁	1	1	yes	characteristic, complemented
547	#124	—	31	1	no	—
548	#124	—	31	1	no	—
549	#124	—	31	1	no	—
550	#124	—	31	1	no	—
551	#124	—	31	1	no	—
552	#124	—	31	1	no	—
553	#124	—	31	1	no	—
554	#124	—	31	1	no	—
555	#124	—	31	1	no	—
556	#124	C₂×D₃₁	1	1	yes	characteristic
557	#123	—	31	1	no	—
558	#123	—	31	1	no	—
559	#123	—	31	1	no	—
560	#123	—	31	1	no	—
561	#123	—	31	1	no	—
562	#123	—	31	1	no	—
563	#123	—	31	1	no	—
564	#123	—	31	1	no	—
565	#123	—	31	1	no	—
566	#123	—	31	1	no	—
567	#123	—	31	1	no	—
568	#123	—	31	1	no	—
569	#123	—	31	1	no	—
570	#123	—	31	1	no	—
571	#123	—	31	1	no	—
572	#123	—	31	1	no	—
573	#123	—	31	1	no	—
574	#123	—	31	1	no	—
575	#123	C₂×D₃₁	1	1	yes	characteristic
576	#123	C₂×D₃₁	1	1	yes	characteristic, complemented
577	C₂²⋊Q₈	—	31	1	no	—
578	C₂²⋊Q₈	—	31	1	no	—
579	C₂²⋊Q₈	—	31	1	no	—
580	C₂²⋊Q₈	—	31	1	no	—
581	C₂²⋊Q₈	—	31	1	no	—
582	C₂²⋊Q₈	—	31	1	no	—
583	C₂²⋊Q₈	—	31	1	no	—
584	C₂²⋊Q₈	—	31	1	no	—
585	C₂²⋊Q₈	—	31	1	no	—
586	C₂²⋊Q₈	—	31	1	no	—
587	C₂²⋊Q₈	—	31	1	no	—
588	C₂²⋊Q₈	—	31	1	no	—
589	C₂²⋊Q₈	—	31	1	no	—
590	C₂²⋊Q₈	—	31	1	no	—
591	C₂²⋊Q₈	—	31	1	no	—
592	C₂²⋊Q₈	C₂×D₃₁	1	1	yes	characteristic, complemented
593	#121	—	31	1	no	—
594	#121	—	31	1	no	—
595	#121	—	31	1	no	—
596	#121	—	31	1	no	—
597	#121	—	31	1	no	—
598	#121	—	31	1	no	—
599	#121	—	31	1	no	—
600	#121	—	31	1	no	—
601	#121	—	31	1	no	—
602	#121	—	31	1	no	—
603	#121	—	31	1	no	—
604	#121	—	31	1	no	—
605	#121	—	31	1	no	—
606	#121	—	31	1	no	—
607	#121	—	31	1	no	—
608	#121	C₂×D₃₁	1	1	yes	characteristic
609	#120	—	31	1	no	—
610	#120	—	31	1	no	—
611	#120	—	31	1	no	—
612	#120	—	31	1	no	—
613	C₄×Q₈	—	31	1	no	—
614	C₄×Q₈	—	31	1	no	—
615	C₄×Q₈	—	31	1	no	—
616	C₄×Q₈	—	31	1	no	—
617	C₄×Q₈	—	31	1	no	—
618	C₄×Q₈	—	31	1	no	—
619	C₄×Q₈	—	31	1	no	—
620	C₄×Q₈	C₂×D₃₁	1	1	yes	characteristic, complemented
621	C₄×D₄	—	31	1	no	—
622	C₄×D₄	—	31	1	no	—
623	C₄×D₄	—	31	1	no	—
624	C₄×D₄	—	31	1	no	—
625	C₄×D₄	—	31	1	no	—
626	C₄×D₄	—	31	1	no	—
627	C₄×D₄	—	31	1	no	—
628	C₄×D₄	—	31	1	no	—
629	C₄×D₄	—	31	1	no	—
630	C₄×D₄	—	31	1	no	—
631	C₄×D₄	—	31	1	no	—
632	C₄×D₄	—	31	1	no	—
633	C₄×D₄	—	31	1	no	—
634	C₄×D₄	—	31	1	no	—
635	C₄×D₄	—	31	1	no	—
636	C₄×D₄	—	31	1	no	—
637	C₄×D₄	—	31	1	no	—
638	C₄×D₄	—	31	1	no	—
639	C₄×D₄	—	31	1	no	—
640	C₄×D₄	—	31	1	no	—
641	C₄×D₄	—	31	1	no	—
642	C₄×D₄	C₂×D₃₁	1	1	yes	characteristic
643	C₄×D₄	C₂×D₃₁	1	1	yes	characteristic
644	C₄×D₄	C₂×D₃₁	1	1	yes	characteristic, complemented
645	#117	—	31	1	no	—
646	#117	—	31	1	no	—
647	#117	—	31	1	no	—
648	#117	—	31	1	no	—
649	#117	—	31	1	no	—
650	#117	—	31	1	no	—
651	#117	—	31	1	no	—
652	#117	—	31	1	no	—
653	#117	—	31	1	no	—
654	#117	—	31	1	no	—
655	#117	—	31	1	no	—
656	#117	—	31	1	no	—
657	#117	C₂×D₃₁	1	1	yes	characteristic
658	#117	C₂×D₃₁	1	1	yes	characteristic, complemented
659	C₂×C₄⋊C₄	—	31	1	no	—
660	C₂×C₄⋊C₄	—	31	1	no	—
661	C₂×C₂²⋊C₄	—	31	1	no	—
662	C₂×C₂²⋊C₄	—	31	1	no	—
663	C₂×C₄²	—	31	1	no	—
664	C₂×C₄²	—	31	1	no	—
665	C₂×C₄²	—	31	1	no	—
666	C₂×C₄²	—	31	1	no	—
667	C₂×C₄²	—	31	1	no	—
668	C₂×C₄²	C₂×D₃₁	1	1	yes	characteristic, complemented
669	C₃₁	#3455	1	1	yes	characteristic, complemented, Sylow
670	C₂⁴	—	31	1	no	—
671	#41	—	62	4	no	—
672	#41	—	62	4	no	—
673	C₂×Q₈	—	31	1	no	—
674	C₂×Q₈	—	31	1	no	—
675	C₂×Q₈	—	31	1	no	—
676	C₂×Q₈	—	31	1	no	—
677	C₂×Q₈	—	31	1	no	—
678	C₂×Q₈	C₂²×D₃₁	1	1	yes	characteristic
679	C₂×D₄	—	31	1	no	—
680	C₂×D₄	—	31	1	no	—
681	C₂×D₄	—	31	1	no	—
682	C₂×D₄	—	31	1	no	—
683	C₂×D₄	—	31	1	no	—
684	C₂×D₄	—	31	1	no	—
685	C₂×D₄	—	31	1	no	—
686	C₂×D₄	—	31	1	no	—
687	C₂×D₄	—	31	1	no	—
688	C₂×D₄	—	31	1	no	—
689	C₂×D₄	—	31	1	no	—
690	C₂×D₄	—	31	1	no	—
691	C₂×D₄	—	31	1	no	—
692	C₂×D₄	—	31	1	no	—
693	C₂×D₄	—	31	1	no	—
694	C₂×D₄	C₂²×D₃₁	1	1	yes	characteristic
695	C₂×D₄	C₂²×D₃₁	1	1	yes	characteristic
696	C₂×D₄	C₂²×D₃₁	1	1	yes	characteristic
697	C₂²×C₄	—	31	1	no	—
698	C₂²×C₄	—	31	1	no	—
699	C₂²×C₄	—	31	1	no	—
700	C₂²×C₄	—	31	1	no	—
701	C₂²×C₄	—	31	1	no	—
702	C₂²×C₄	—	31	1	no	—
703	C₂²×C₄	—	31	1	no	—
704	C₂²×C₄	—	31	1	no	—
705	C₂²×C₄	—	31	1	no	—
706	C₂²×C₄	—	31	1	no	—
707	C₂²×C₄	—	31	1	no	—
708	C₂²×C₄	—	31	1	no	—
709	C₂²×C₄	—	31	1	no	—
710	C₂²×C₄	—	31	1	no	—
711	C₂²×C₄	—	31	1	no	—
712	C₂²×C₄	—	31	1	no	—
713	C₂²×C₄	—	31	1	no	—
714	C₂²×C₄	—	62	4	no	—
715	C₂²×C₄	C₂²×D₃₁	1	1	yes	characteristic
716	C₂²×C₄	C₂²×D₃₁	1	1	yes	characteristic
717	C₂²×C₄	C₂²×D₃₁	1	1	yes	characteristic
718	C₂²×C₄	C₂²×D₃₁	1	1	yes	characteristic
719	C₂²×C₄	C₂²×D₃₁	1	1	yes	characteristic
720	C₄⋊C₄	—	31	1	no	—
721	C₄⋊C₄	—	31	1	no	—
722	C₄⋊C₄	—	31	1	no	—
723	C₄⋊C₄	—	31	1	no	—
724	C₄⋊C₄	—	31	1	no	—
725	C₄⋊C₄	—	31	1	no	—
726	C₄⋊C₄	—	31	1	no	—
727	C₄⋊C₄	—	31	1	no	—
728	C₄⋊C₄	—	31	1	no	—
729	C₄⋊C₄	—	31	1	no	—
730	C₄⋊C₄	—	31	1	no	—
731	C₄⋊C₄	—	31	1	no	—
732	C₄⋊C₄	—	31	1	no	—
733	C₄⋊C₄	—	31	1	no	—
734	C₄⋊C₄	—	31	1	no	—
735	C₄⋊C₄	—	31	1	no	—
736	C₄⋊C₄	—	31	1	no	—
737	C₄⋊C₄	—	31	1	no	—
738	C₄⋊C₄	—	31	1	no	—
739	C₄⋊C₄	—	31	1	no	—
740	C₄⋊C₄	—	31	1	no	—
741	C₄⋊C₄	—	31	1	no	—
742	C₄⋊C₄	—	31	1	no	—
743	C₄⋊C₄	—	31	1	no	—
744	C₄⋊C₄	—	31	1	no	—
745	C₄⋊C₄	—	31	1	no	—
746	C₄⋊C₄	—	31	1	no	—
747	C₄⋊C₄	—	31	1	no	—
748	C₄⋊C₄	—	31	1	no	—
749	C₄⋊C₄	—	31	1	no	—
750	C₄⋊C₄	—	31	1	no	—
751	C₄⋊C₄	—	31	1	no	—
752	C₄⋊C₄	—	31	1	no	—
753	C₄⋊C₄	—	31	1	no	—
754	C₄⋊C₄	C₂²×D₃₁	1	1	yes	characteristic
755	C₄⋊C₄	C₂²×D₃₁	1	1	yes	characteristic
756	C₄⋊C₄	C₂²×D₃₁	1	1	yes	characteristic
757	C₄⋊C₄	C₂²×D₃₁	1	1	yes	characteristic
758	C₄⋊C₄	C₂²×D₃₁	1	1	yes	characteristic
759	C₄⋊C₄	C₂²×D₃₁	1	1	yes	characteristic
760	C₄⋊C₄	C₂²×D₃₁	1	1	yes	characteristic
761	C₄⋊C₄	C₂²×D₃₁	1	1	yes	characteristic
762	C₄⋊C₄	C₂²×D₃₁	1	1	yes	characteristic
763	C₄⋊C₄	C₂²×D₃₁	1	1	yes	characteristic
764	C₂²⋊C₄	—	31	1	no	—
765	C₂²⋊C₄	—	31	1	no	—
766	C₂²⋊C₄	—	31	1	no	—
767	C₂²⋊C₄	—	31	1	no	—
768	C₂²⋊C₄	—	31	1	no	—
769	C₂²⋊C₄	—	31	1	no	—
770	C₂²⋊C₄	—	31	1	no	—
771	C₂²⋊C₄	—	31	1	no	—
772	C₂²⋊C₄	—	31	1	no	—
773	C₂²⋊C₄	—	31	1	no	—
774	C₂²⋊C₄	—	31	1	no	—
775	C₂²⋊C₄	—	31	1	no	—
776	C₂²⋊C₄	—	31	1	no	—
777	C₂²⋊C₄	—	31	1	no	—
778	C₂²⋊C₄	—	31	1	no	—
779	C₂²⋊C₄	—	31	1	no	—
780	C₂²⋊C₄	—	31	1	no	—
781	C₂²⋊C₄	—	31	1	no	—
782	C₂²⋊C₄	—	31	1	no	—
783	C₂²⋊C₄	—	31	1	no	—
784	C₂²⋊C₄	—	31	1	no	—
785	C₂²⋊C₄	—	31	1	no	—
786	C₂²⋊C₄	—	31	1	no	—
787	C₂²⋊C₄	—	31	1	no	—
788	C₂²⋊C₄	—	31	1	no	—
789	C₂²⋊C₄	—	31	1	no	—
790	C₂²⋊C₄	—	31	1	no	—
791	C₂²⋊C₄	—	31	1	no	—
792	C₂²⋊C₄	—	31	1	no	—
793	C₂²⋊C₄	—	31	1	no	—
794	C₂²⋊C₄	—	31	1	no	—
795	C₂²⋊C₄	—	31	1	no	—
796	C₂²⋊C₄	—	31	1	no	—
797	C₂²⋊C₄	—	31	1	no	—
798	C₂²⋊C₄	C₂²×D₃₁	1	1	yes	characteristic
799	C₂²⋊C₄	C₂²×D₃₁	1	1	yes	characteristic
800	C₂²⋊C₄	C₂²×D₃₁	1	1	yes	characteristic
801	C₂²⋊C₄	C₂²×D₃₁	1	1	yes	characteristic
802	C₂²⋊C₄	C₂²×D₃₁	1	1	yes	characteristic
803	C₂²⋊C₄	C₂²×D₃₁	1	1	yes	characteristic
804	C₂²⋊C₄	C₂²×D₃₁	1	1	yes	characteristic
805	C₂²⋊C₄	C₂²×D₃₁	1	1	yes	characteristic
806	C₂²⋊C₄	C₂²×D₃₁	1	1	yes	characteristic
807	C₂²⋊C₄	C₂²×D₃₁	1	1	yes	characteristic
808	C₄²	—	31	1	no	—
809	C₄²	—	31	1	no	—
810	C₄²	—	31	1	no	—
811	C₄²	—	31	1	no	—
812	C₄²	—	31	1	no	—
813	C₄²	—	31	1	no	—
814	C₄²	—	31	1	no	—
815	C₄²	—	31	1	no	—
816	C₄²	—	31	1	no	—
817	C₄²	—	31	1	no	—
818	C₄²	—	31	1	no	—
819	C₄²	—	31	1	no	—
820	C₄²	—	31	1	no	—
821	C₄²	—	31	1	no	—
822	C₄²	C₂²×D₃₁	1	1	yes	characteristic
823	C₄²	C₂²×D₃₁	1	1	yes	characteristic
824	C₄²	C₂²×D₃₁	1	1	yes	characteristic
825	C₄²	C₂²×D₃₁	1	1	yes	characteristic
826	C₄²	C₂²×D₃₁	1	1	yes	characteristic
827	C₄²	C₂²×D₃₁	1	1	yes	characteristic
828	C₂³	—	31	1	no	—
829	C₂³	—	31	1	no	—
830	C₂³	—	31	1	no	—
831	C₂³	—	31	1	no	—
832	C₂³	—	62	2	no	—
833	C₂³	—	124	1	no	—
834	C₂³	—	124	1	no	—
835	C₂³	C₂³×D₃₁	1	1	yes	characteristic
836	C₂³	C₂³×D₃₁	1	1	yes	characteristic
837	C₂³	C₂³×D₃₁	1	1	yes	characteristic
838	Q₈	—	4	1	no	—
839	Q₈	—	62	2	no	—
840	Q₈	—	62	2	no	—
841	Q₈	—	124	1	no	—
842	Q₈	—	124	1	no	—
843	Q₈	—	124	1	no	—
844	D₄	—	4	1	no	—
845	D₄	—	4	1	no	—
846	D₄	—	4	1	no	—
847	D₄	—	62	2	no	—
848	D₄	—	62	2	no	—
849	D₄	—	62	2	no	—
850	D₄	—	62	2	no	—
851	D₄	—	62	2	no	—
852	D₄	—	62	2	no	—
853	D₄	—	124	1	no	—
854	D₄	—	124	1	no	—
855	D₄	—	124	1	no	—
856	D₄	—	124	1	no	—
857	D₄	—	124	1	no	—
858	D₄	—	124	1	no	—
859	D₄	—	124	1	no	—
860	D₄	—	124	1	no	—
861	D₄	—	124	1	no	—
862	C₂×C₄	—	2	2	no	—
863	C₂×C₄	—	2	2	no	—
864	C₂×C₄	—	2	2	no	—
865	C₂×C₄	—	4	1	no	—
866	C₂×C₄	—	4	1	no	—
867	C₂×C₄	—	31	1	no	—
868	C₂×C₄	—	31	4	no	—
869	C₂×C₄	—	31	1	no	—
870	C₂×C₄	—	31	1	no	—
871	C₂×C₄	—	31	1	no	—
872	C₂×C₄	—	31	1	no	—
873	C₂×C₄	—	31	1	no	—
874	C₂×C₄	—	31	1	no	—
875	C₂×C₄	—	31	1	no	—
876	C₂×C₄	—	31	1	no	—
877	C₂×C₄	—	31	1	no	—
878	C₂×C₄	—	31	1	no	—
879	C₂×C₄	—	31	1	no	—
880	C₂×C₄	—	62	2	no	—
881	C₂×C₄	—	62	2	no	—
882	C₂×C₄	—	62	2	no	—
883	C₂×C₄	—	62	2	no	—
884	C₂×C₄	—	62	2	no	—
885	C₂×C₄	—	62	2	no	—
886	C₂×C₄	—	124	1	no	—
887	C₂×C₄	—	124	1	no	—
888	C₂×C₄	—	124	1	no	—
889	C₂×C₄	—	124	1	no	—
890	C₂×C₄	—	124	1	no	—
891	C₂×C₄	—	124	1	no	—
892	C₂×C₄	—	124	1	no	—
893	C₂×C₄	—	124	1	no	—
894	C₂×C₄	—	124	1	no	—
895	C₂×C₄	—	124	1	no	—
896	C₂×C₄	C₂³×D₃₁	1	1	yes	characteristic
897	C₂×C₄	C₂³×D₃₁	1	1	yes	characteristic
898	C₂×C₄	C₂³×D₃₁	1	1	yes	characteristic
899	C₂×C₄	C₂³×D₃₁	1	1	yes	characteristic
900	C₂×C₄	C₂³×D₃₁	1	1	yes	characteristic
901	C₂×C₄	C₂³×D₃₁	1	1	yes	characteristic
902	C₂×C₄	C₂³×D₃₁	1	1	yes	characteristic
903	C₂×C₄	C₂³×D₃₁	1	1	yes	characteristic
904	C₂×C₄	C₂³×D₃₁	1	1	yes	characteristic
905	C₂×C₄	C₂³×D₃₁	1	1	yes	characteristic
906	C₂×C₄	C₂³×D₃₁	1	1	yes	characteristic
907	C₂×C₄	C₂³×D₃₁	1	1	yes	characteristic
908	C₂²	—	2	1	no	—
909	C₂²	—	2	1	no	—
910	C₂²	—	2	1	no	—
911	C₂²	—	2	1	no	—
912	C₂²	—	2	1	no	—
913	C₂²	—	2	1	no	—
914	C₂²	—	2	1	no	—
915	C₂²	—	2	1	no	—
916	C₂²	—	2	1	no	—
917	C₂²	—	31	2	no	—
918	C₂²	—	62	1	no	—
919	C₂²	—	62	1	no	—
920	C₂²	—	62	1	no	—
921	C₂²	—	62	1	no	—
922	C₂²	—	62	1	no	—
923	C₂²	—	62	1	no	—
924	C₂²	—	62	1	no	—
925	C₂²	—	62	1	no	—
926	C₂²	—	62	1	no	—
927	C₂²	—	62	1	no	—
928	C₂²	—	62	1	no	—
929	C₂²	—	124	4	no	—
930	C₂²	C₂⁴×D₃₁	1	1	yes	characteristic
931	C₄	—	2	1	no	—
932	C₄	—	2	1	no	—
933	C₄	—	2	1	no	—
934	C₄	—	2	1	no	—
935	C₄	—	2	1	no	—
936	C₄	—	2	1	no	—
937	C₄	—	2	1	no	—
938	C₄	—	2	1	no	—
939	C₄	—	2	1	no	—
940	C₄	—	2	1	no	—
941	C₄	—	2	1	no	—
942	C₄	—	31	2	no	—
943	C₄	—	62	1	no	—
944	C₄	—	62	1	no	—
945	C₄	—	62	1	no	—
946	C₄	—	62	1	no	—
947	C₄	—	62	1	no	—
948	C₄	—	62	1	no	—
949	C₄	—	62	1	no	—
950	C₄	—	62	1	no	—
951	C₄	—	62	1	no	—
952	C₄	—	62	1	no	—
953	C₄	—	62	1	no	—
954	C₄	#41×D₃₁	1	2	yes	—
955	C₂	—	4	1	no	—
956	C₂	—	4	1	no	—
957	C₂	—	4	1	no	—
958	C₂	—	62	2	no	—
959	C₂	—	124	1	no	—
960	C₂	—	124	1	no	—
961	C₂	—	124	1	no	—
962	C₂	C₂×#41×D₃₁	1	1	yes	characteristic
963	C₂	#14521885	1	1	yes	characteristic
964	C₂	#14521885	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂³×D₃₁
commutator, socle, cosocle	C₂²×C₃₁	C₂⁵
Frattini	C₂²	C₂⁴×D₃₁
Fitting	C₃₁×#529	C₂
hypercenter	#529	D₃₁
hypocenter	C₃₁	#3455
LCS	G ▷ C₂²×C₃₁ ▷ C₃₁
UCS	C₁ ◁ C₂×C₄ ◁ #529

Complements

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

N	H ≅ G/N	type
1. #14521669	C₂	semidirect
2. #14521667	C₂	semidirect
3. #14521665	C₂	semidirect
4. #14521663	C₂	semidirect
5. #14521658	C₂	semidirect
6. #14521656	C₂	semidirect
7. #14521651	C₂	semidirect
8. #14521649	C₂	semidirect
9. #14521647	C₂	semidirect
10. #14521645	C₂	semidirect
11. #14521642	C₂	semidirect
12. #14521640	C₂	semidirect
13. #14521638	C₂	semidirect
14. #14521635	C₂	semidirect
15. #14521633	C₂	semidirect
16. #14521631	C₂	semidirect
17. #14521603	C₂	semidirect
18. #14521596	C₂	semidirect
19. #14521586	C₂	semidirect
20. #14521583	C₂	semidirect
21. #14521581	C₂	semidirect
22. #14521579	C₂	semidirect
23. #14521579	C₂	semidirect
24. #14521577	C₂	semidirect
25. #14521577	C₂	semidirect
26. #14521558	C₂	semidirect
27. #14521558	C₂	semidirect
28. C₄×#92495	C₂	semidirect
29. #14521517	C₂	semidirect
30. #117×D₃₁	C₂	semidirect
31. C₃₁×#529	C₂	semidirect
36. C₃₁×#126	C₂²	semidirect
37. C₃₁×#125	C₂²	semidirect
40. C₃₁×#123	C₂²	semidirect
41. C₃₁×C₂²⋊Q₈	C₂²	semidirect
43. C₄×Q₈×C₃₁	C₂²	semidirect
46. C₄×D₄×C₃₁	C₂²	semidirect
48. C₃₁×#117	C₂²	semidirect
49. C₂×C₄²×C₃₁	C₂²	semidirect
52. #11758523	C₂²	semidirect
53. #11758521	C₂²	semidirect
54. #11758517	C₂²	semidirect
65. #11758512	C₂²	semidirect
68. #11758506	C₂²	semidirect
75. C₄×C₂²⋊D₃₁	C₂²	semidirect
76. C₄×C₂²⋊D₃₁	C₂²	semidirect
77. C₄×C₂²⋊D₃₁	C₂²	semidirect
78. C₄×C₂²⋊D₃₁	C₂²	semidirect
80. #11758503	C₂²	semidirect
81. #11758501	C₂²	semidirect
82. C₂×C₄×Dic₃₁	C₂²	semidirect
86. #11758475	C₂²	semidirect
87. #11758475	C₂²	semidirect
88. #11758475	C₂²	semidirect
90. #11758474	C₂²	semidirect
95. #11758473	C₂²	semidirect
96. #11758473	C₂²	semidirect
103. #11758471	C₂²	semidirect
104. #11758471	C₂²	semidirect
111. #11758467	C₂²	semidirect
112. #11758467	C₂²	semidirect
113. #11758466	C₂²	semidirect
114. #11758466	C₂²	semidirect
115. #11758466	C₂²	semidirect
116. #11758466	C₂²	semidirect
117. #11758466	C₂²	semidirect
118. #11758466	C₂²	semidirect
119. #11758465	C₂²	semidirect
120. #11758465	C₂²	semidirect
121. #11758464	C₂²	semidirect
122. #11758464	C₂²	semidirect
124. #11758463	C₂²	semidirect
129. #11758462	C₂²	semidirect
130. #11758462	C₂²	semidirect
141. #11758460	C₂²	semidirect
142. #11758460	C₂²	semidirect
147. (C₂²⋊D₃₁)⋊C₄	C₂²	semidirect
148. (C₂²⋊D₃₁)⋊C₄	C₂²	semidirect
154. #11758456	C₂²	semidirect
155. #11758456	C₂²	semidirect
156. #11758456	C₂²	semidirect
159. #11758455	C₂²	semidirect
160. #11758455	C₂²	semidirect
164. #11758453	C₂²	semidirect
170. C₄×D₁₂₄	C₂²	semidirect
175. #11758449	C₂²	semidirect
176. #11758449	C₂²	semidirect
179. C₄²×D₃₁	C₂²	semidirect
180. C₄²×D₃₁	C₂²	semidirect
181. #11758447	C₂²	semidirect
182. C₄×Dic₆₂	C₂²	semidirect
183. C₄×Dic₆₂	C₂²	semidirect
184. C₄×Dic₆₂	C₂²	semidirect
185. C₄×Dic₆₂	C₂²	semidirect
186. C₄×Dic₆₂	C₂²	semidirect
498. #529	D₃₁	semidirect
536. #126	C₂×D₃₁	semidirect
546. #125	C₂×D₃₁	semidirect
576. #123	C₂×D₃₁	semidirect
592. C₂²⋊Q₈	C₂×D₃₁	semidirect
620. C₄×Q₈	C₂×D₃₁	semidirect
644. C₄×D₄	C₂×D₃₁	semidirect
658. #117	C₂×D₃₁	semidirect
668. C₂×C₄²	C₂×D₃₁	semidirect
669. C₃₁	#3455	semidirect

Maximal subgroups

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

subgroup	index
#14521669	2
#14521667	2
#14521665	2
#14521663	2
#14521658	2
#14521656	2
#14521651	2
#14521649	2
#14521647	2
#14521645	2
#14521642	2
#14521640	2
#14521638	2
#14521635	2
#14521633	2
#14521631	2
#14521603	2
#14521596	2
#14521586	2
#14521583	2
#14521581	2
#14521579	2
#14521577	2
#14521558	2
C₄×#92495	2
#14521517	2
#117×D₃₁	2
C₃₁×#529	2
#3455	31