Subgroups — #16860404

Order 3968.

958 conjugacy classes of subgroups.

The subgroup lattice has 954 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14521802	C₂	1	1	yes	maximal, characteristic, complemented
2	#14521801	C₂	1	1	yes	maximal, characteristic, complemented
3	#14521800	C₂	1	1	yes	maximal, characteristic, complemented
4	#14521792	C₂	1	1	yes	maximal, characteristic, complemented
5	#14521770	C₂	1	1	yes	maximal, characteristic, complemented
6	#14521769	C₂	1	1	yes	maximal, characteristic, complemented
7	#14521768	C₂	1	1	yes	maximal, characteristic, complemented
8	#14521766	C₂	1	1	yes	maximal, characteristic, complemented
9	#14521766	C₂	1	1	yes	maximal, characteristic, complemented
10	#14521766	C₂	1	1	yes	maximal, characteristic, complemented
11	#14521730	C₂	1	1	yes	maximal, characteristic, complemented
12	#14521729	C₂	1	1	yes	maximal, characteristic, complemented
13	#14521728	C₂	1	1	yes	maximal, characteristic, complemented
14	#14521725	C₂	1	1	yes	maximal, characteristic, complemented
15	#14521725	C₂	1	1	yes	maximal, characteristic, complemented
16	#14521722	C₂	1	1	yes	maximal, characteristic, complemented
17	#14521668	C₂	1	1	yes	maximal, characteristic, complemented
18	#14521667	C₂	1	1	yes	maximal, characteristic, complemented
19	#14521666	C₂	1	1	yes	maximal, characteristic, complemented
20	#14521666	C₂	1	1	yes	maximal, characteristic, complemented
21	#14521664	C₂	1	1	yes	maximal, characteristic, complemented
22	#14521663	C₂	1	1	yes	maximal, characteristic, complemented
23	#14521636	C₂	1	1	yes	maximal, characteristic, complemented
24	#14521634	C₂	1	1	yes	maximal, characteristic, complemented
25	#14521634	C₂	1	1	yes	maximal, characteristic, complemented
26	#14521631	C₂	1	1	yes	maximal, characteristic, complemented
27	#14521631	C₂	1	1	yes	maximal, characteristic, complemented
28	#14521580	C₂	1	1	yes	maximal, characteristic, complemented
29	#14521579	C₂	1	1	yes	maximal, characteristic, complemented
30	#14521576	C₂	1	1	yes	maximal, characteristic, complemented
31	C₃₁×#538	C₂	1	1	yes	maximal, characteristic, complemented
32	C₃₁×#126	C₂²	1	1	yes	characteristic, complemented
33	C₃₁×#126	C₂²	1	1	yes	characteristic, complemented
34	C₃₁×#124	C₂²	1	1	yes	characteristic
35	C₃₁×#124	C₂²	1	1	yes	characteristic, complemented
36	C₃₁×#123	C₂²	1	1	yes	characteristic
37	C₃₁×#123	C₂²	1	1	yes	characteristic, complemented
38	C₃₁×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
39	C₃₁×#121	C₂²	1	1	yes	characteristic
40	C₃₁×#121	C₂²	1	1	yes	characteristic
41	C₃₁×#121	C₂²	1	1	yes	characteristic
42	C₃₁×#120	C₂²	1	1	yes	characteristic
43	C₃₁×#120	C₂²	1	1	yes	characteristic, complemented
44	C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic
45	C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic, complemented
46	C₂×C₂²⋊C₄×C₃₁	C₂²	1	1	yes	characteristic, complemented
47	#11758530	C₂²	1	1	yes	characteristic
48	#11758530	C₂²	1	1	yes	characteristic
49	C₂×C₂²⋊Dic₃₁	C₂²	1	1	yes	characteristic, complemented
50	C₂×C₂²⋊Dic₃₁	C₂²	1	1	yes	characteristic, complemented
51	#11758523	C₂²	1	1	yes	characteristic, complemented
52	#11758523	C₂²	1	1	yes	characteristic, complemented
53	Q₈×Dic₃₁	C₂²	1	1	yes	characteristic, complemented
54	#11758521	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	#11758514	C₂²	1	1	yes	characteristic
64	#11758514	C₂²	1	1	yes	characteristic, complemented
65	#11758513	C₂²	1	1	yes	characteristic
66	#11758513	C₂²	1	1	yes	characteristic
67	#11758513	C₂²	1	1	yes	characteristic
68	#11758513	C₂²	1	1	yes	characteristic
69	#11758513	C₂²	1	1	yes	characteristic, complemented
70	#11758513	C₂²	1	1	yes	characteristic, complemented
71	#11758513	C₂²	1	1	yes	characteristic, complemented
72	#11758512	C₂²	1	1	yes	characteristic
73	#11758512	C₂²	1	1	yes	characteristic
74	#11758512	C₂²	1	1	yes	characteristic
75	#11758512	C₂²	1	1	yes	characteristic, complemented
76	#11758512	C₂²	1	1	yes	characteristic, complemented
77	#11758512	C₂²	1	1	yes	characteristic, complemented
78	D₄×Dic₃₁	C₂²	1	1	yes	characteristic
79	D₄×Dic₃₁	C₂²	1	1	yes	characteristic
80	D₄×Dic₃₁	C₂²	1	1	yes	characteristic, complemented
81	D₄×Dic₃₁	C₂²	1	1	yes	characteristic, complemented
82	D₄×Dic₃₁	C₂²	1	1	yes	characteristic, complemented
83	#11758506	C₂²	1	1	yes	characteristic
84	#11758506	C₂²	1	1	yes	characteristic
85	#11758506	C₂²	1	1	yes	characteristic, complemented
86	C₄×C₂²⋊D₃₁	C₂²	1	1	yes	characteristic
87	C₄×C₂²⋊D₃₁	C₂²	1	1	yes	characteristic
88	C₄×C₂²⋊D₃₁	C₂²	1	1	yes	characteristic, complemented
89	C₂×(C₂×D₃₁)⋊C₄	C₂²	1	1	yes	characteristic, complemented
90	#11758503	C₂²	1	1	yes	characteristic, complemented
91	#11758503	C₂²	1	1	yes	characteristic, complemented
92	#11758503	C₂²	1	1	yes	characteristic, complemented
93	#11758501	C₂²	1	1	yes	characteristic, complemented
94	#11758501	C₂²	1	1	yes	characteristic, complemented
95	#11758501	C₂²	1	1	yes	characteristic, complemented
96	#11758501	C₂²	1	1	yes	characteristic, complemented
97	#11758501	C₂²	1	1	yes	characteristic, complemented
98	C₂×C₄×Dic₃₁	C₂²	1	1	yes	characteristic, complemented
99	#11758475	C₂²	1	1	yes	characteristic, complemented
100	#11758475	C₂²	1	1	yes	characteristic, complemented
101	#11758475	C₂²	1	1	yes	characteristic, complemented
102	#11758475	C₂²	1	1	yes	characteristic, complemented
103	#11758475	C₂²	1	1	yes	characteristic, complemented
104	#11758475	C₂²	1	1	yes	characteristic, complemented
105	#11758475	C₂²	1	1	yes	characteristic, complemented
106	#11758474	C₂²	1	1	yes	characteristic, complemented
107	#11758473	C₂²	1	1	yes	characteristic, complemented
108	#11758473	C₂²	1	1	yes	characteristic, complemented
109	#11758473	C₂²	1	1	yes	characteristic, complemented
110	#11758469	C₂²	1	1	yes	characteristic, complemented
111	#11758467	C₂²	1	1	yes	characteristic, complemented
112	#11758466	C₂²	1	1	yes	characteristic, complemented
113	#11758466	C₂²	1	1	yes	characteristic, complemented
114	#11758465	C₂²	1	1	yes	characteristic, complemented
115	#11758465	C₂²	1	1	yes	characteristic, complemented
116	#11758465	C₂²	1	1	yes	characteristic, complemented
117	#11758465	C₂²	1	1	yes	characteristic, complemented
118	#11758464	C₂²	1	1	yes	characteristic, complemented
119	#11758464	C₂²	1	1	yes	characteristic, complemented
120	#11758464	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
125	#11758463	C₂²	1	1	yes	characteristic, complemented
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
130	#11758462	C₂²	1	1	yes	characteristic
131	#11758462	C₂²	1	1	yes	characteristic
132	#11758462	C₂²	1	1	yes	characteristic
133	#11758462	C₂²	1	1	yes	characteristic
134	#11758462	C₂²	1	1	yes	characteristic
135	#11758462	C₂²	1	1	yes	characteristic
136	#11758462	C₂²	1	1	yes	characteristic, complemented
137	#11758462	C₂²	1	1	yes	characteristic, complemented
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
142	(C₂²⋊D₃₁)⋊C₄	C₂²	1	1	yes	characteristic
143	(C₂²⋊D₃₁)⋊C₄	C₂²	1	1	yes	characteristic
144	(C₂²⋊D₃₁)⋊C₄	C₂²	1	1	yes	characteristic
145	(C₂²⋊D₃₁)⋊C₄	C₂²	1	1	yes	characteristic
146	(C₂²⋊D₃₁)⋊C₄	C₂²	1	1	yes	characteristic, complemented
147	C₂²⋊C₄×D₃₁	C₂²	1	1	yes	characteristic, complemented
148	C₂²⋊C₄×D₃₁	C₂²	1	1	yes	characteristic, complemented
149	#11758456	C₂²	1	1	yes	characteristic, complemented
150	#11758456	C₂²	1	1	yes	characteristic, complemented
151	#11758456	C₂²	1	1	yes	characteristic, complemented
152	#11758456	C₂²	1	1	yes	characteristic, complemented
153	#11758456	C₂²	1	1	yes	characteristic, complemented
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	#11758456	C₂²	1	1	yes	characteristic, complemented
158	#11758456	C₂²	1	1	yes	characteristic, complemented
159	#11758456	C₂²	1	1	yes	characteristic, complemented
160	#11758456	C₂²	1	1	yes	characteristic, complemented
161	#11758456	C₂²	1	1	yes	characteristic, complemented
162	#11758456	C₂²	1	1	yes	characteristic, complemented
163	#11758456	C₂²	1	1	yes	characteristic, complemented
164	#11758456	C₂²	1	1	yes	characteristic, complemented
165	#11758455	C₂²	1	1	yes	characteristic, complemented
166	#11758455	C₂²	1	1	yes	characteristic, complemented
167	#11758455	C₂²	1	1	yes	characteristic, complemented
168	#11758455	C₂²	1	1	yes	characteristic, complemented
169	#11758455	C₂²	1	1	yes	characteristic, complemented
170	#11758455	C₂²	1	1	yes	characteristic, complemented
171	#11758455	C₂²	1	1	yes	characteristic, complemented
172	#11758455	C₂²	1	1	yes	characteristic, complemented
173	#11758455	C₂²	1	1	yes	characteristic, complemented
174	#11758454	C₂²	1	1	yes	characteristic, complemented
175	#11758454	C₂²	1	1	yes	characteristic, complemented
176	#11758454	C₂²	1	1	yes	characteristic, complemented
177	#11758454	C₂²	1	1	yes	characteristic, complemented
178	#11758454	C₂²	1	1	yes	characteristic, complemented
179	#11758453	C₂²	1	1	yes	characteristic, complemented
180	#11758449	C₂²	1	1	yes	characteristic, complemented
181	#11758449	C₂²	1	1	yes	characteristic, complemented
182	#11758449	C₂²	1	1	yes	characteristic, complemented
183	#11758446	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	C₂⁴×C₃₁	C₂³	1	1	yes	characteristic
188	C₂³×D₃₁	C₂³	1	1	yes	characteristic
189	C₂×Q₈×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	C₂×D₄×C₃₁	C₂³	1	1	yes	characteristic
193	C₂×D₄×C₃₁	C₂³	1	1	yes	characteristic
194	C₂×D₄×C₃₁	C₂³	1	1	yes	characteristic
195	C₂×D₄×C₃₁	C₂³	1	1	yes	characteristic
196	C₂×D₄×C₃₁	C₂³	1	1	yes	characteristic
197	C₂²×C₄×C₃₁	C₂³	1	1	yes	characteristic
198	C₂²×C₄×C₃₁	C₂³	1	1	yes	characteristic
199	C₂²×C₄×C₃₁	C₂³	1	1	yes	characteristic
200	C₂²×C₄×C₃₁	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	C₂×C₂²⋊D₃₁	C₂³	1	1	yes	characteristic
208	C₂×C₂²⋊D₃₁	C₂³	1	1	yes	characteristic
209	C₂²×Dic₃₁	C₂³	1	1	yes	characteristic
210	C₂²×Dic₃₁	C₂³	1	1	yes	characteristic
211	C₂²×Dic₃₁	C₂³	1	1	yes	characteristic
212	C₂²×Dic₃₁	C₂³	1	1	yes	characteristic
213	C₂²×Dic₃₁	C₂³	1	1	yes	characteristic
214	C₂²×Dic₃₁	C₂³	1	1	yes	characteristic
215	C₂²×Dic₃₁	C₂³	1	1	yes	characteristic
216	C₂×C₄×D₃₁	C₂³	1	1	yes	characteristic
217	C₂×C₄×D₃₁	C₂³	1	1	yes	characteristic
218	C₂×C₄×D₃₁	C₂³	1	1	yes	characteristic
219	C₂×C₄×D₃₁	C₂³	1	1	yes	characteristic
220	C₂×Dic₆₂	C₂³	1	1	yes	characteristic
221	C₂×Dic₆₂	C₂³	1	1	yes	characteristic
222	C₂×Dic₆₂	C₂³	1	1	yes	characteristic
223	C₂×Dic₆₂	C₂³	1	1	yes	characteristic
224	C₂×Dic₆₂	C₂³	1	1	yes	characteristic
225	C₂×Dic₆₂	C₂³	1	1	yes	characteristic
226	C₂×Dic₆₂	C₂³	1	1	yes	characteristic
227	C₂×Dic₆₂	C₂³	1	1	yes	characteristic
228	C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
229	C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
230	C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
231	C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
232	C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
233	C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
234	C₂²⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
235	C₂²⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
236	C₂²⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
237	C₂²⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
238	C₂²⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
239	C₂²⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
240	C₂²⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
241	C₂²⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
242	C₂²⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
243	C₂²⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
244	C₂²⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
245	C₂²⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
246	C₂²⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
247	C₂²⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
248	C₄²×C₃₁	C₂³	1	1	yes	characteristic
249	C₄²×C₃₁	C₂³	1	1	yes	characteristic
250	C₂²⋊Dic₃₁	C₂³	1	1	yes	characteristic
251	C₂²⋊Dic₃₁	C₂³	1	1	yes	characteristic
252	C₂²⋊Dic₃₁	C₂³	1	1	yes	characteristic
253	C₂²⋊Dic₃₁	C₂³	1	1	yes	characteristic
254	C₂²⋊Dic₃₁	C₂³	1	1	yes	characteristic
255	C₂²⋊Dic₃₁	C₂³	1	1	yes	characteristic
256	C₂²⋊Dic₃₁	C₂³	1	1	yes	characteristic
257	C₂²⋊Dic₃₁	C₂³	1	1	yes	characteristic
258	C₂²⋊Dic₃₁	C₂³	1	1	yes	characteristic
259	C₂²⋊Dic₃₁	C₂³	1	1	yes	characteristic
260	C₂²⋊Dic₃₁	C₂³	1	1	yes	characteristic
261	C₂²⋊Dic₃₁	C₂³	1	1	yes	characteristic
262	C₂²⋊Dic₃₁	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	C₂²⋊Dic₃₁	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	C₄⋊Dic₃₁	C₂³	1	1	yes	characteristic
291	C₄⋊Dic₃₁	C₂³	1	1	yes	characteristic
292	C₄⋊Dic₃₁	C₂³	1	1	yes	characteristic
293	C₄⋊Dic₃₁	C₂³	1	1	yes	characteristic
294	C₄⋊Dic₃₁	C₂³	1	1	yes	characteristic
295	C₄⋊Dic₃₁	C₂³	1	1	yes	characteristic
296	C₄⋊Dic₃₁	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	Dic₃₁⋊C₄	C₂³	1	1	yes	characteristic
303	Dic₃₁⋊C₄	C₂³	1	1	yes	characteristic
304	Dic₃₁⋊C₄	C₂³	1	1	yes	characteristic
305	Dic₃₁⋊C₄	C₂³	1	1	yes	characteristic
306	Dic₃₁⋊C₄	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	C₄×Dic₃₁	C₂³	1	1	yes	characteristic
327	C₄×Dic₃₁	C₂³	1	1	yes	characteristic
328	C₄×Dic₃₁	C₂³	1	1	yes	characteristic
329	C₄×Dic₃₁	C₂³	1	1	yes	characteristic
330	C₄×Dic₃₁	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	C₂³×C₃₁	—	4	1	no	—
343	C₂³×C₃₁	—	4	1	no	—
344	C₂³×C₃₁	—	4	1	no	—
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	C₂³×C₃₁	C₂⁴	1	1	yes	characteristic
349	C₂³×C₃₁	C₂⁴	1	1	yes	characteristic
350	C₂²×D₃₁	—	4	1	no	—
351	C₂²×D₃₁	—	4	1	no	—
352	C₂²×D₃₁	—	4	1	no	—
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	D₄×C₃₁	—	4	1	no	—
360	D₄×C₃₁	—	4	1	no	—
361	D₄×C₃₁	—	4	1	no	—
362	D₄×C₃₁	—	4	1	no	—
363	C₂×C₄×C₃₁	—	4	1	no	—
364	C₂×C₄×C₃₁	—	4	1	no	—
365	C₂×C₄×C₃₁	—	4	1	no	—
366	C₂×C₄×C₃₁	—	4	1	no	—
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	C₂×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
377	C₂²⋊D₃₁	—	4	1	no	—
378	C₂²⋊D₃₁	—	4	1	no	—
379	C₂²⋊D₃₁	—	4	1	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	C₂×Dic₃₁	—	4	1	no	—
386	C₂×Dic₃₁	—	4	1	no	—
387	C₂×Dic₃₁	—	4	1	no	—
388	C₂×Dic₃₁	—	4	1	no	—
389	C₂×Dic₃₁	—	4	1	no	—
390	C₂×Dic₃₁	—	4	1	no	—
391	C₂×Dic₃₁	—	4	1	no	—
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	C₂×Dic₃₁	C₂⁴	1	1	yes	characteristic
402	C₂×Dic₃₁	C₂⁴	1	1	yes	characteristic
403	C₂×Dic₃₁	C₂⁴	1	1	yes	characteristic
404	C₂×Dic₃₁	C₂⁴	1	1	yes	characteristic
405	C₂×Dic₃₁	C₂⁴	1	1	yes	characteristic
406	C₄×D₃₁	—	4	1	no	—
407	C₄×D₃₁	—	4	1	no	—
408	C₄×D₃₁	—	4	1	no	—
409	C₄×D₃₁	—	4	1	no	—
410	Dic₆₂	—	4	1	no	—
411	Dic₆₂	—	4	1	no	—
412	Dic₆₂	—	4	1	no	—
413	Dic₆₂	—	4	1	no	—
414	Dic₆₂	—	4	1	no	—
415	Dic₆₂	—	4	1	no	—
416	Dic₆₂	—	4	1	no	—
417	Dic₆₂	—	4	1	no	—
418	#3568	—	31	1	no	maximal, Sylow
419	C₂²×C₃₁	—	2	1	no	—
420	C₂²×C₃₁	—	2	1	no	—
421	C₂²×C₃₁	—	2	1	no	—
422	C₂²×C₃₁	—	2	1	no	—
423	C₂²×C₃₁	—	2	1	no	—
424	C₂²×C₃₁	—	2	1	no	—
425	C₂²×C₃₁	—	2	1	no	—
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	—	8	2	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	—	8	2	no	—
443	C₄×C₃₁	—	2	1	no	—
444	C₄×C₃₁	—	2	1	no	—
445	C₄×C₃₁	—	2	1	no	—
446	C₄×C₃₁	—	2	1	no	—
447	C₄×C₃₁	—	2	1	no	—
448	C₄×C₃₁	—	2	1	no	—
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	Dic₃₁	—	2	1	no	—
454	Dic₃₁	—	2	1	no	—
455	Dic₃₁	—	2	1	no	—
456	Dic₃₁	—	2	1	no	—
457	Dic₃₁	—	2	1	no	—
458	Dic₃₁	—	2	1	no	—
459	Dic₃₁	—	2	1	no	—
460	Dic₃₁	—	2	1	no	—
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	#563	—	31	1	no	—
468	#563	—	31	1	no	—
469	#563	—	31	1	no	—
470	H(3,𝔽₄)	—	31	1	no	—
471	#556	—	31	1	no	—
472	#556	—	31	1	no	—
473	#556	—	31	1	no	—
474	#556	—	31	1	no	—
475	#556	—	31	1	no	—
476	#556	—	31	1	no	—
477	#551	—	31	1	no	—
478	#551	—	31	1	no	—
479	#551	—	31	1	no	—
480	#551	—	31	1	no	—
481	#551	—	31	1	no	—
482	#551	—	31	1	no	—
483	#542	—	31	1	no	—
484	#542	—	31	1	no	—
485	#542	—	31	1	no	—
486	#542	—	31	1	no	—
487	#542	—	31	1	no	—
488	#542	—	31	1	no	—
489	#538	—	31	1	no	—
490	#538	—	31	1	no	—
491	#538	—	31	1	no	—
492	#538	—	31	1	no	—
493	#538	—	31	1	no	—
494	#538	D₃₁	1	1	yes	characteristic, complemented
495	#529	—	31	1	no	—
496	#529	—	31	1	no	—
497	#529	—	31	1	no	—
498	C₂×C₃₁	—	4	1	no	—
499	C₂×C₃₁	—	4	1	no	—
500	C₂×C₃₁	—	4	1	no	—
501	C₂×C₃₁	—	4	1	no	—
502	C₂×C₃₁	—	4	1	no	—
503	C₂×C₃₁	#585	1	1	yes	characteristic
504	C₂×C₃₁	#585	1	1	yes	characteristic
505	C₂×C₃₁	#585	1	1	yes	characteristic
506	D₃₁	—	4	1	no	—
507	D₃₁	—	4	1	no	—
508	C₄⋊Q₈	—	31	1	no	—
509	C₄⋊Q₈	—	31	1	no	—
510	C₄⋊Q₈	—	31	1	no	—
511	C₄⋊Q₈	—	31	1	no	—
512	C₄⋊Q₈	—	31	1	no	—
513	C₄⋊Q₈	—	31	1	no	—
514	#126	—	31	1	no	—
515	#126	—	31	1	no	—
516	#126	—	31	1	no	—
517	#126	—	31	1	no	—
518	#126	—	31	1	no	—
519	#126	—	31	1	no	—
520	#126	—	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	—	31	1	no	—
536	#126	—	31	1	no	—
537	#126	—	31	1	no	—
538	#126	C₂×D₃₁	1	1	yes	characteristic, complemented
539	#126	C₂×D₃₁	1	1	yes	characteristic, complemented
540	#125	—	31	1	no	—
541	#125	—	31	1	no	—
542	#125	—	31	1	no	—
543	#124	—	31	1	no	—
544	#124	—	31	1	no	—
545	#124	—	31	1	no	—
546	#124	—	31	1	no	—
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	—	31	1	no	—
557	#124	—	31	1	no	—
558	#124	—	31	1	no	—
559	#124	—	31	1	no	—
560	#124	—	31	1	no	—
561	#124	—	31	1	no	—
562	#124	C₂×D₃₁	1	1	yes	characteristic
563	#124	C₂×D₃₁	1	1	yes	characteristic, complemented
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	—	31	1	no	—
576	#123	—	31	1	no	—
577	#123	—	31	1	no	—
578	#123	—	31	1	no	—
579	#123	—	31	1	no	—
580	#123	C₂×D₃₁	1	1	yes	characteristic
581	#123	C₂×D₃₁	1	1	yes	characteristic, complemented
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	—	31	1	no	—
593	C₂²⋊Q₈	—	31	1	no	—
594	C₂²⋊Q₈	—	31	1	no	—
595	C₂²⋊Q₈	—	31	1	no	—
596	C₂²⋊Q₈	—	31	1	no	—
597	C₂²⋊Q₈	—	31	1	no	—
598	C₂²⋊Q₈	—	31	1	no	—
599	C₂²⋊Q₈	—	31	1	no	—
600	C₂²⋊Q₈	—	31	1	no	—
601	C₂²⋊Q₈	—	31	1	no	—
602	C₂²⋊Q₈	C₂×D₃₁	1	1	yes	characteristic, complemented
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	—	31	1	no	—
609	#121	C₂×D₃₁	1	1	yes	characteristic
610	#121	C₂×D₃₁	1	1	yes	characteristic
611	#121	C₂×D₃₁	1	1	yes	characteristic
612	#120	—	31	1	no	—
613	#120	—	31	1	no	—
614	#120	—	31	1	no	—
615	#120	—	31	1	no	—
616	#120	—	31	1	no	—
617	#120	—	31	1	no	—
618	#120	C₂×D₃₁	1	1	yes	characteristic
619	#120	C₂×D₃₁	1	1	yes	characteristic, complemented
620	C₄×Q₈	—	31	1	no	—
621	C₄×Q₈	—	31	1	no	—
622	C₄×Q₈	—	31	1	no	—
623	C₄×Q₈	—	31	1	no	—
624	C₄×Q₈	—	31	1	no	—
625	C₄×Q₈	—	31	1	no	—
626	C₄×Q₈	—	31	1	no	—
627	C₄×Q₈	—	31	1	no	—
628	C₄×Q₈	—	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, complemented
644	#117	—	31	1	no	—
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	C₂×C₂²⋊C₄	—	31	1	no	—
657	C₂×C₂²⋊C₄	—	31	1	no	—
658	C₂×C₂²⋊C₄	—	31	1	no	—
659	C₂×C₂²⋊C₄	—	31	1	no	—
660	C₂×C₂²⋊C₄	—	31	1	no	—
661	C₂×C₂²⋊C₄	C₂×D₃₁	1	1	yes	characteristic, complemented
662	C₂×C₄²	—	31	1	no	—
663	C₃₁	#3568	1	1	yes	characteristic, complemented, Sylow
664	C₂⁴	—	31	1	no	—
665	C₂⁴	C₂²×D₃₁	1	1	yes	characteristic
666	C₂×Q₈	—	31	1	no	—
667	C₂×Q₈	—	31	1	no	—
668	C₂×Q₈	—	31	1	no	—
669	C₂×Q₈	—	31	1	no	—
670	C₂×Q₈	—	31	1	no	—
671	C₂×Q₈	—	31	1	no	—
672	C₂×Q₈	—	31	1	no	—
673	C₂×Q₈	—	31	1	no	—
674	C₂×Q₈	C₂²×D₃₁	1	1	yes	characteristic
675	C₂×D₄	—	31	1	no	—
676	C₂×D₄	—	31	1	no	—
677	C₂×D₄	—	31	1	no	—
678	C₂×D₄	—	31	1	no	—
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	C₂²×D₃₁	1	1	yes	characteristic
684	C₂×D₄	C₂²×D₃₁	1	1	yes	characteristic
685	C₂×D₄	C₂²×D₃₁	1	1	yes	characteristic
686	C₂×D₄	C₂²×D₃₁	1	1	yes	characteristic
687	C₂×D₄	C₂²×D₃₁	1	1	yes	characteristic
688	C₂×D₄	C₂²×D₃₁	1	1	yes	characteristic
689	C₂×D₄	C₂²×D₃₁	1	1	yes	characteristic
690	C₂²×C₄	—	31	1	no	—
691	C₂²×C₄	—	31	1	no	—
692	C₂²×C₄	—	31	1	no	—
693	C₂²×C₄	—	31	1	no	—
694	C₂²×C₄	—	31	1	no	—
695	C₂²×C₄	—	31	1	no	—
696	C₂²×C₄	—	31	1	no	—
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	C₂²×D₃₁	1	1	yes	characteristic
702	C₂²×C₄	C₂²×D₃₁	1	1	yes	characteristic
703	C₂²×C₄	C₂²×D₃₁	1	1	yes	characteristic
704	C₂²×C₄	C₂²×D₃₁	1	1	yes	characteristic
705	C₄⋊C₄	—	31	1	no	—
706	C₄⋊C₄	—	31	1	no	—
707	C₄⋊C₄	—	31	1	no	—
708	C₄⋊C₄	—	31	1	no	—
709	C₄⋊C₄	—	31	1	no	—
710	C₄⋊C₄	—	31	1	no	—
711	C₄⋊C₄	—	31	1	no	—
712	C₄⋊C₄	—	31	1	no	—
713	C₄⋊C₄	—	31	1	no	—
714	C₄⋊C₄	—	31	1	no	—
715	C₄⋊C₄	—	31	1	no	—
716	C₄⋊C₄	—	31	1	no	—
717	C₄⋊C₄	—	31	1	no	—
718	C₄⋊C₄	—	31	1	no	—
719	C₄⋊C₄	—	31	1	no	—
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	C₂²×D₃₁	1	1	yes	characteristic
742	C₄⋊C₄	C₂²×D₃₁	1	1	yes	characteristic
743	C₄⋊C₄	C₂²×D₃₁	1	1	yes	characteristic
744	C₄⋊C₄	C₂²×D₃₁	1	1	yes	characteristic
745	C₄⋊C₄	C₂²×D₃₁	1	1	yes	characteristic
746	C₄⋊C₄	C₂²×D₃₁	1	1	yes	characteristic
747	C₂²⋊C₄	—	31	1	no	—
748	C₂²⋊C₄	—	31	1	no	—
749	C₂²⋊C₄	—	31	1	no	—
750	C₂²⋊C₄	—	31	1	no	—
751	C₂²⋊C₄	—	31	1	no	—
752	C₂²⋊C₄	—	31	1	no	—
753	C₂²⋊C₄	—	31	1	no	—
754	C₂²⋊C₄	—	31	1	no	—
755	C₂²⋊C₄	—	31	1	no	—
756	C₂²⋊C₄	—	31	1	no	—
757	C₂²⋊C₄	—	31	1	no	—
758	C₂²⋊C₄	—	31	1	no	—
759	C₂²⋊C₄	—	31	1	no	—
760	C₂²⋊C₄	—	31	1	no	—
761	C₂²⋊C₄	—	31	1	no	—
762	C₂²⋊C₄	—	31	1	no	—
763	C₂²⋊C₄	—	31	1	no	—
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	C₂²×D₃₁	1	1	yes	characteristic
788	C₂²⋊C₄	C₂²×D₃₁	1	1	yes	characteristic
789	C₂²⋊C₄	C₂²×D₃₁	1	1	yes	characteristic
790	C₂²⋊C₄	C₂²×D₃₁	1	1	yes	characteristic
791	C₂²⋊C₄	C₂²×D₃₁	1	1	yes	characteristic
792	C₂²⋊C₄	C₂²×D₃₁	1	1	yes	characteristic
793	C₂²⋊C₄	C₂²×D₃₁	1	1	yes	characteristic
794	C₂²⋊C₄	C₂²×D₃₁	1	1	yes	characteristic
795	C₂²⋊C₄	C₂²×D₃₁	1	1	yes	characteristic
796	C₂²⋊C₄	C₂²×D₃₁	1	1	yes	characteristic
797	C₂²⋊C₄	C₂²×D₃₁	1	1	yes	characteristic
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	C₄²	—	31	1	no	—
802	C₄²	—	31	1	no	—
803	C₄²	—	31	1	no	—
804	C₄²	—	31	1	no	—
805	C₄²	—	31	1	no	—
806	C₄²	—	31	1	no	—
807	C₄²	—	31	1	no	—
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	C₂²×D₃₁	1	1	yes	characteristic
818	C₄²	C₂²×D₃₁	1	1	yes	characteristic
819	C₂³	—	4	1	no	—
820	C₂³	—	4	1	no	—
821	C₂³	—	4	1	no	—
822	C₂³	—	31	1	no	—
823	C₂³	—	31	1	no	—
824	C₂³	—	124	1	no	—
825	C₂³	—	124	1	no	—
826	C₂³	—	124	1	no	—
827	C₂³	C₂³×D₃₁	1	1	yes	characteristic
828	C₂³	C₂³×D₃₁	1	1	yes	characteristic
829	C₂³	C₂³×D₃₁	1	1	yes	characteristic
830	C₂³	C₂³×D₃₁	1	1	yes	characteristic
831	C₂³	C₂³×D₃₁	1	1	yes	characteristic
832	Q₈	—	4	1	no	—
833	Q₈	—	124	1	no	—
834	Q₈	—	124	1	no	—
835	Q₈	—	124	1	no	—
836	Q₈	—	124	1	no	—
837	Q₈	—	124	1	no	—
838	Q₈	—	124	1	no	—
839	Q₈	—	124	1	no	—
840	Q₈	—	124	1	no	—
841	D₄	—	4	1	no	—
842	D₄	—	4	1	no	—
843	D₄	—	4	1	no	—
844	D₄	—	4	1	no	—
845	D₄	—	4	1	no	—
846	D₄	—	4	1	no	—
847	D₄	—	4	1	no	—
848	D₄	—	124	1	no	—
849	D₄	—	124	1	no	—
850	D₄	—	124	1	no	—
851	D₄	—	124	1	no	—
852	D₄	—	124	1	no	—
853	D₄	—	124	1	no	—
854	D₄	—	124	1	no	—
855	D₄	—	124	1	no	—
856	C₂×C₄	—	4	1	no	—
857	C₂×C₄	—	4	1	no	—
858	C₂×C₄	—	4	1	no	—
859	C₂×C₄	—	4	1	no	—
860	C₂×C₄	—	31	1	no	—
861	C₂×C₄	—	31	1	no	—
862	C₂×C₄	—	31	1	no	—
863	C₂×C₄	—	31	1	no	—
864	C₂×C₄	—	31	1	no	—
865	C₂×C₄	—	31	1	no	—
866	C₂×C₄	—	31	1	no	—
867	C₂×C₄	—	31	1	no	—
868	C₂×C₄	—	31	1	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	—	124	1	no	—
875	C₂×C₄	—	124	1	no	—
876	C₂×C₄	—	124	1	no	—
877	C₂×C₄	—	124	1	no	—
878	C₂×C₄	—	124	1	no	—
879	C₂×C₄	—	124	1	no	—
880	C₂×C₄	—	124	1	no	—
881	C₂×C₄	—	124	1	no	—
882	C₂×C₄	—	124	1	no	—
883	C₂×C₄	—	124	1	no	—
884	C₂×C₄	—	124	1	no	—
885	C₂×C₄	C₂³×D₃₁	1	1	yes	characteristic
886	C₂×C₄	C₂³×D₃₁	1	1	yes	characteristic
887	C₂×C₄	C₂³×D₃₁	1	1	yes	characteristic
888	C₂×C₄	C₂³×D₃₁	1	1	yes	characteristic
889	C₂×C₄	C₂³×D₃₁	1	1	yes	characteristic
890	C₂×C₄	C₂³×D₃₁	1	1	yes	characteristic
891	C₂×C₄	C₂³×D₃₁	1	1	yes	characteristic
892	C₂×C₄	C₂³×D₃₁	1	1	yes	characteristic
893	C₂×C₄	C₂³×D₃₁	1	1	yes	characteristic
894	C₂×C₄	C₂³×D₃₁	1	1	yes	characteristic
895	C₂²	—	2	1	no	—
896	C₂²	—	2	1	no	—
897	C₂²	—	2	1	no	—
898	C₂²	—	2	1	no	—
899	C₂²	—	2	1	no	—
900	C₂²	—	2	1	no	—
901	C₂²	—	2	1	no	—
902	C₂²	—	2	1	no	—
903	C₂²	—	2	1	no	—
904	C₂²	—	2	1	no	—
905	C₂²	—	2	1	no	—
906	C₂²	—	2	1	no	—
907	C₂²	—	2	1	no	—
908	C₂²	—	2	1	no	—
909	C₂²	—	2	1	no	—
910	C₂²	—	8	2	no	—
911	C₂²	—	62	1	no	—
912	C₂²	—	62	1	no	—
913	C₂²	—	62	1	no	—
914	C₂²	—	62	1	no	—
915	C₂²	—	62	1	no	—
916	C₂²	—	62	1	no	—
917	C₂²	—	248	2	no	—
918	C₂²	C₂⁴×D₃₁	1	1	yes	characteristic
919	C₄	—	2	1	no	—
920	C₄	—	2	1	no	—
921	C₄	—	2	1	no	—
922	C₄	—	2	1	no	—
923	C₄	—	2	1	no	—
924	C₄	—	2	1	no	—
925	C₄	—	2	1	no	—
926	C₄	—	2	1	no	—
927	C₄	—	2	1	no	—
928	C₄	—	2	1	no	—
929	C₄	—	62	1	no	—
930	C₄	—	62	1	no	—
931	C₄	—	62	1	no	—
932	C₄	—	62	1	no	—
933	C₄	—	62	1	no	—
934	C₄	—	62	1	no	—
935	C₄	—	62	1	no	—
936	C₄	—	62	1	no	—
937	C₄	—	62	1	no	—
938	C₄	—	62	1	no	—
939	C₄	—	62	1	no	—
940	C₄	—	62	1	no	—
941	C₄	—	62	1	no	—
942	C₄	—	62	1	no	—
943	C₂	—	4	1	no	—
944	C₂	—	4	1	no	—
945	C₂	—	4	1	no	—
946	C₂	—	4	1	no	—
947	C₂	—	4	1	no	—
948	C₂	—	124	1	no	—
949	C₂	—	124	1	no	—
950	C₂	#14521884	1	1	yes	characteristic
951	C₂	#14521884	1	1	yes	characteristic
952	C₂	#14521885	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₃₁
commutator, socle, cosocle	C₂²×C₃₁	C₂⁵
Fitting	C₃₁×#538	C₂
hypercenter	#538	D₃₁
hypocenter	C₃₁	#3568
LCS	G ▷ C₂²×C₃₁ ▷ C₃₁
UCS	C₁ ◁ C₂² ◁ #538

Complements

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

N	H ≅ G/N	type
1. #14521802	C₂	semidirect
2. #14521801	C₂	semidirect
3. #14521800	C₂	semidirect
4. #14521792	C₂	semidirect
5. #14521770	C₂	semidirect
6. #14521769	C₂	semidirect
7. #14521768	C₂	semidirect
8. #14521766	C₂	semidirect
9. #14521766	C₂	semidirect
10. #14521766	C₂	semidirect
11. #14521730	C₂	semidirect
12. #14521729	C₂	semidirect
13. #14521728	C₂	semidirect
14. #14521725	C₂	semidirect
15. #14521725	C₂	semidirect
16. #14521722	C₂	semidirect
17. #14521668	C₂	semidirect
18. #14521667	C₂	semidirect
19. #14521666	C₂	semidirect
20. #14521666	C₂	semidirect
21. #14521664	C₂	semidirect
22. #14521663	C₂	semidirect
23. #14521636	C₂	semidirect
24. #14521634	C₂	semidirect
25. #14521634	C₂	semidirect
26. #14521631	C₂	semidirect
27. #14521631	C₂	semidirect
28. #14521580	C₂	semidirect
29. #14521579	C₂	semidirect
30. #14521576	C₂	semidirect
31. C₃₁×#538	C₂	semidirect
32. C₃₁×#126	C₂²	semidirect
33. C₃₁×#126	C₂²	semidirect
35. C₃₁×#124	C₂²	semidirect
37. C₃₁×#123	C₂²	semidirect
38. C₃₁×C₂²⋊Q₈	C₂²	semidirect
43. C₃₁×#120	C₂²	semidirect
45. C₄×D₄×C₃₁	C₂²	semidirect
46. C₂×C₂²⋊C₄×C₃₁	C₂²	semidirect
49. C₂×C₂²⋊Dic₃₁	C₂²	semidirect
50. C₂×C₂²⋊Dic₃₁	C₂²	semidirect
51. #11758523	C₂²	semidirect
52. #11758523	C₂²	semidirect
53. Q₈×Dic₃₁	C₂²	semidirect
54. #11758521	C₂²	semidirect
64. #11758514	C₂²	semidirect
69. #11758513	C₂²	semidirect
70. #11758513	C₂²	semidirect
71. #11758513	C₂²	semidirect
75. #11758512	C₂²	semidirect
76. #11758512	C₂²	semidirect
77. #11758512	C₂²	semidirect
80. D₄×Dic₃₁	C₂²	semidirect
81. D₄×Dic₃₁	C₂²	semidirect
82. D₄×Dic₃₁	C₂²	semidirect
85. #11758506	C₂²	semidirect
88. C₄×C₂²⋊D₃₁	C₂²	semidirect
89. C₂×(C₂×D₃₁)⋊C₄	C₂²	semidirect
90. #11758503	C₂²	semidirect
91. #11758503	C₂²	semidirect
92. #11758503	C₂²	semidirect
93. #11758501	C₂²	semidirect
94. #11758501	C₂²	semidirect
95. #11758501	C₂²	semidirect
96. #11758501	C₂²	semidirect
97. #11758501	C₂²	semidirect
98. C₂×C₄×Dic₃₁	C₂²	semidirect
99. #11758475	C₂²	semidirect
100. #11758475	C₂²	semidirect
101. #11758475	C₂²	semidirect
102. #11758475	C₂²	semidirect
103. #11758475	C₂²	semidirect
104. #11758475	C₂²	semidirect
105. #11758475	C₂²	semidirect
106. #11758474	C₂²	semidirect
107. #11758473	C₂²	semidirect
108. #11758473	C₂²	semidirect
109. #11758473	C₂²	semidirect
110. #11758469	C₂²	semidirect
111. #11758467	C₂²	semidirect
112. #11758466	C₂²	semidirect
113. #11758466	C₂²	semidirect
114. #11758465	C₂²	semidirect
115. #11758465	C₂²	semidirect
116. #11758465	C₂²	semidirect
117. #11758465	C₂²	semidirect
118. #11758464	C₂²	semidirect
119. #11758464	C₂²	semidirect
120. #11758464	C₂²	semidirect
121. #11758464	C₂²	semidirect
122. #11758464	C₂²	semidirect
125. #11758463	C₂²	semidirect
136. #11758462	C₂²	semidirect
137. #11758462	C₂²	semidirect
146. (C₂²⋊D₃₁)⋊C₄	C₂²	semidirect
147. C₂²⋊C₄×D₃₁	C₂²	semidirect
148. C₂²⋊C₄×D₃₁	C₂²	semidirect
149. #11758456	C₂²	semidirect
150. #11758456	C₂²	semidirect
151. #11758456	C₂²	semidirect
152. #11758456	C₂²	semidirect
153. #11758456	C₂²	semidirect
154. #11758456	C₂²	semidirect
155. #11758456	C₂²	semidirect
156. #11758456	C₂²	semidirect
157. #11758456	C₂²	semidirect
158. #11758456	C₂²	semidirect
159. #11758456	C₂²	semidirect
160. #11758456	C₂²	semidirect
161. #11758456	C₂²	semidirect
162. #11758456	C₂²	semidirect
163. #11758456	C₂²	semidirect
164. #11758456	C₂²	semidirect
165. #11758455	C₂²	semidirect
166. #11758455	C₂²	semidirect
167. #11758455	C₂²	semidirect
168. #11758455	C₂²	semidirect
169. #11758455	C₂²	semidirect
170. #11758455	C₂²	semidirect
171. #11758455	C₂²	semidirect
172. #11758455	C₂²	semidirect
173. #11758455	C₂²	semidirect
174. #11758454	C₂²	semidirect
175. #11758454	C₂²	semidirect
176. #11758454	C₂²	semidirect
177. #11758454	C₂²	semidirect
178. #11758454	C₂²	semidirect
179. #11758453	C₂²	semidirect
180. #11758449	C₂²	semidirect
181. #11758449	C₂²	semidirect
182. #11758449	C₂²	semidirect
183. #11758446	C₂²	semidirect
184. C₄×Dic₆₂	C₂²	semidirect
185. C₄×Dic₆₂	C₂²	semidirect
186. C₄×Dic₆₂	C₂²	semidirect
494. #538	D₃₁	semidirect
538. #126	C₂×D₃₁	semidirect
539. #126	C₂×D₃₁	semidirect
563. #124	C₂×D₃₁	semidirect
581. #123	C₂×D₃₁	semidirect
602. C₂²⋊Q₈	C₂×D₃₁	semidirect
619. #120	C₂×D₃₁	semidirect
643. C₄×D₄	C₂×D₃₁	semidirect
661. C₂×C₂²⋊C₄	C₂×D₃₁	semidirect
663. C₃₁	#3568	semidirect

Maximal subgroups

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

subgroup	index
#14521802	2
#14521801	2
#14521800	2
#14521792	2
#14521770	2
#14521769	2
#14521768	2
#14521766	2
#14521730	2
#14521729	2
#14521728	2
#14521725	2
#14521722	2
#14521668	2
#14521667	2
#14521666	2
#14521664	2
#14521663	2
#14521636	2
#14521634	2
#14521631	2
#14521580	2
#14521579	2
#14521576	2
C₃₁×#538	2
#3568	31