Subgroups — D₄×C₃₁×#137 #21517828

Order 7936.

2746 conjugacy classes of subgroups.

The subgroup lattice has 1014 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃₁×#137	C₂	1	2	yes	maximal, complemented
2	D₄×#41×C₃₁	C₂	1	1	yes	maximal, characteristic
3	C₂×D₄×Q₈×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented
4	D₄×Q₁₆×C₃₁	C₂	1	2	yes	maximal, complemented
5	D₄×SD₁₆×C₃₁	C₂	1	2	yes	maximal, complemented
6	C₃₁×#3278	C₂	1	2	yes	maximal, complemented
7	C₃₁×#3276	C₂	1	2	yes	maximal, complemented
8	C₃₁×#3270	C₂	1	4	yes	maximal, complemented
9	C₃₁×#3266	C₂	1	4	yes	maximal, complemented
10	C₃₁×#3152	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃₁×#3056	C₂	1	2	yes	maximal, complemented
12	C₃₁×#3039	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃₁×#3037	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃₁×#3007	C₂	1	2	yes	maximal, complemented
15	C₃₁×#3004	C₂	1	2	yes	maximal, complemented
16	C₄×C₃₁×#137	C₂	1	1	yes	maximal, characteristic, complemented
17	D₄×M₁₆×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂²×#41×C₃₁	C₂²	1	2	yes	—
19	C₂³×Q₈×C₃₁	C₂²	1	2	yes	complemented
20	C₂×C₃₁×#137	—	2	16	no	—
21	C₂×C₃₁×#137	C₂²	1	2	yes	—
22	C₂×C₃₁×#137	C₂²	1	1	yes	characteristic
23	C₂×C₃₁×#137	C₂²	1	2	yes	complemented
24	C₂×C₃₁×#137	C₂²	1	2	yes	complemented
25	C₂×C₃₁×#137	C₂²	1	4	yes	complemented
26	C₂×C₃₁×#137	C₂²	1	4	yes	complemented
27	C₂×C₃₁×#137	C₂²	1	2	yes	complemented
28	C₂²×Q₁₆×C₃₁	C₂²	1	4	yes	complemented
29	C₂²×SD₁₆×C₃₁	C₂²	1	4	yes	complemented
30	C₂²×M₁₆×C₃₁	C₂²	1	2	yes	complemented
31	C₃₁×#550	C₂²	1	1	yes	characteristic
32	D₄×Q₈×C₃₁	—	2	1	no	—
33	D₄×Q₈×C₃₁	—	2	2	no	—
34	D₄×Q₈×C₃₁	—	2	1	no	—
35	D₄×Q₈×C₃₁	C₂²	1	2	yes	—
36	D₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic
37	D₄×Q₈×C₃₁	C₂²	1	4	yes	complemented
38	D₄×Q₈×C₃₁	C₂²	1	2	yes	complemented
39	C₃₁×#548	C₂²	1	2	yes	—
40	C₃₁×#547	—	2	1	no	—
41	C₃₁×#547	C₂²	1	1	yes	characteristic
42	C₃₁×#546	—	2	2	no	—
43	C₃₁×#546	C₂²	1	2	yes	—
44	D₄²×C₃₁	—	2	1	no	—
45	D₄²×C₃₁	C₂²	1	1	yes	characteristic
46	C₃₁×#532	—	2	1	no	—
47	C₃₁×#532	C₂²	1	1	yes	characteristic
48	C₂×C₃₁×C₄⋊Q₈	—	2	1	no	—
49	C₂×C₃₁×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
50	C₃₁×#525	—	2	2	no	—
51	C₃₁×#525	C₂²	1	2	yes	—
52	C₂×C₃₁×C₂²⋊Q₈	—	2	2	no	—
53	C₂×C₃₁×C₂²⋊Q₈	C₂²	1	2	yes	complemented
54	C₄×#41×C₃₁	C₂²	1	1	yes	characteristic
55	C₂×C₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic, complemented
56	C₂×C₄×D₄×C₃₁	—	2	1	no	—
57	C₂×C₄×D₄×C₃₁	—	2	1	no	—
58	C₂×C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic
59	C₃₁×#497	C₂²	1	4	yes	complemented
60	C₃₁×#494	C₂²	1	2	yes	complemented
61	C₃₁×#492	C₂²	1	2	yes	complemented
62	C₃₁×#470	C₂²	1	4	yes	complemented
63	C₃₁×#468	C₂²	1	4	yes	complemented
64	C₃₁×#467	C₂²	1	4	yes	complemented
65	C₃₁×#465	C₂²	1	4	yes	complemented
66	C₃₁×#464	C₂²	1	4	yes	complemented
67	C₃₁×#462	C₂²	1	2	yes	complemented
68	C₃₁×#462	C₂²	1	2	yes	complemented
69	C₃₁×#462	C₂²	1	2	yes	complemented
70	C₃₁×#461	C₂²	1	2	yes	complemented
71	C₃₁×#461	C₂²	1	2	yes	complemented
72	C₃₁×#460	C₂²	1	2	yes	complemented
73	C₃₁×#452	C₂²	1	4	yes	complemented
74	C₃₁×#452	C₂²	1	4	yes	complemented
75	C₃₁×#451	C₂²	1	4	yes	complemented
76	C₃₁×#451	C₂²	1	4	yes	complemented
77	C₃₁×#451	C₂²	1	4	yes	complemented
78	C₃₁×#450	C₂²	1	4	yes	complemented
79	C₃₁×#448	C₂²	1	4	yes	complemented
80	C₃₁×#448	C₂²	1	4	yes	complemented
81	C₃₁×#441	C₂²	1	2	yes	complemented
82	C₃₁×#440	C₂²	1	2	yes	complemented
83	C₄×Q₁₆×C₃₁	C₂²	1	2	yes	complemented
84	C₄×SD₁₆×C₃₁	C₂²	1	2	yes	complemented
85	C₃₁×#436	C₂²	1	2	yes	complemented
86	C₃₁×#435	C₂²	1	4	yes	complemented
87	C₈×D₄×C₃₁	C₂²	1	2	yes	—
88	C₃₁×#428	C₂²	1	1	yes	characteristic, complemented
89	C₃₁×#423	C₂²	1	1	yes	characteristic, complemented
90	C₃₁×#419	C₂²	1	1	yes	characteristic, complemented
91	C₃₁×#419	C₂²	1	2	yes	complemented
92	C₃₁×#417	C₂²	1	1	yes	characteristic
93	C₃₁×#417	C₂²	1	2	yes	complemented
94	C₃₁×#407	C₂²	1	2	yes	complemented
95	C₄×M₁₆×C₃₁	C₂²	1	1	yes	characteristic, complemented
96	C₂×#41×C₃₁	—	2	2	no	—
97	C₂×#41×C₃₁	—	2	2	no	—
98	C₂×#41×C₃₁	—	2	8	no	—
99	C₂×#41×C₃₁	—	4	4	no	—
100	C₂×#41×C₃₁	C₂³	1	2	yes	—
101	C₂×#41×C₃₁	C₂³	1	2	yes	—
102	C₂×#41×C₃₁	C₂³	1	2	yes	—
103	C₂×#41×C₃₁	C₂³	1	1	yes	characteristic
104	C₂²×Q₈×C₃₁	—	2	2	no	—
105	C₂²×Q₈×C₃₁	—	2	2	no	—
106	C₂²×Q₈×C₃₁	—	2	2	no	—
107	C₂²×Q₈×C₃₁	—	2	8	no	—
108	C₂²×Q₈×C₃₁	—	4	4	no	—
109	C₂²×Q₈×C₃₁	C₂³	1	2	yes	—
110	C₂²×Q₈×C₃₁	C₂³	1	4	yes	—
111	C₂²×Q₈×C₃₁	C₂³	1	4	yes	—
112	C₂²×Q₈×C₃₁	C₂³	1	2	yes	—
113	C₂²×Q₈×C₃₁	C₂³	1	1	yes	characteristic
114	C₂²×D₄×C₃₁	—	2	2	no	—
115	C₂²×D₄×C₃₁	—	2	1	no	—
116	C₂²×D₄×C₃₁	D₄	1	1	yes	characteristic
117	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
118	C₂³×C₄×C₃₁	—	2	2	no	—
119	C₂³×C₄×C₃₁	—	2	2	no	—
120	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
121	C₃₁×#137	—	2	8	no	—
122	C₃₁×#137	—	2	8	no	—
123	C₃₁×#137	—	2	16	no	—
124	C₃₁×#137	—	2	16	no	—
125	C₃₁×#137	—	2	8	no	—
126	C₃₁×#137	—	4	4	no	—
127	C₃₁×#137	D₄	1	8	yes	direct product factor
128	C₂×Q₁₆×C₃₁	—	2	16	no	—
129	C₂×Q₁₆×C₃₁	C₂³	1	4	yes	—
130	C₂×Q₁₆×C₃₁	C₂³	1	4	yes	—
131	C₂×Q₁₆×C₃₁	C₂³	1	4	yes	—
132	C₂×Q₁₆×C₃₁	C₂³	1	4	yes	—
133	C₂×Q₁₆×C₃₁	C₂³	1	2	yes	—
134	C₂×SD₁₆×C₃₁	—	2	16	no	—
135	C₂×SD₁₆×C₃₁	C₂³	1	4	yes	—
136	C₂×SD₁₆×C₃₁	C₂³	1	4	yes	—
137	C₂×SD₁₆×C₃₁	C₂³	1	4	yes	—
138	C₂×SD₁₆×C₃₁	C₂³	1	4	yes	—
139	C₂×SD₁₆×C₃₁	C₂³	1	2	yes	—
140	C₂×M₁₆×C₃₁	—	2	8	no	—
141	C₂×M₁₆×C₃₁	C₂³	1	1	yes	characteristic
142	C₂×M₁₆×C₃₁	C₂³	1	2	yes	—
143	C₂×M₁₆×C₃₁	C₂³	1	4	yes	—
144	C₂×M₁₆×C₃₁	C₂³	1	1	yes	characteristic
145	C₂²×C₈×C₃₁	C₂³	1	4	yes	—
146	C₃₁×C₄⋊Q₈	—	2	2	no	—
147	C₃₁×C₄⋊Q₈	—	2	2	no	—
148	C₃₁×C₄⋊Q₈	—	2	4	no	—
149	C₃₁×C₄⋊Q₈	—	2	1	no	—
150	C₃₁×C₄⋊Q₈	—	2	1	no	—
151	C₃₁×C₄⋊Q₈	—	2	1	no	—
152	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
153	C₃₁×C₄⋊Q₈	C₂³	1	2	yes	—
154	C₃₁×C₄⋊Q₈	C₂³	1	1	yes	characteristic
155	C₃₁×#127	—	2	1	no	—
156	C₃₁×#127	C₂³	1	1	yes	characteristic
157	C₃₁×#124	—	2	2	no	—
158	C₃₁×#124	C₂³	1	2	yes	—
159	C₃₁×#123	—	2	2	no	—
160	C₃₁×#123	—	2	2	no	—
161	C₃₁×#123	—	2	2	no	—
162	C₃₁×C₂²⋊Q₈	—	2	2	no	—
163	C₃₁×C₂²⋊Q₈	—	2	2	no	—
164	C₃₁×C₂²⋊Q₈	—	2	2	no	—
165	C₃₁×C₂²⋊Q₈	—	2	4	no	—
166	C₃₁×C₂²⋊Q₈	—	2	4	no	—
167	C₃₁×C₂²⋊Q₈	—	2	4	no	—
168	C₃₁×C₂²⋊Q₈	—	2	4	no	—
169	C₃₁×C₂²⋊Q₈	—	2	2	no	—
170	C₃₁×C₂²⋊Q₈	C₂³	1	4	yes	—
171	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
172	C₃₁×C₂²⋊Q₈	C₂³	1	2	yes	—
173	C₃₁×C₂²⋊Q₈	C₂³	1	4	yes	—
174	C₃₁×#121	—	2	2	no	—
175	C₃₁×#121	—	2	1	no	—
176	C₃₁×#121	—	2	1	no	—
177	C₃₁×#121	—	2	1	no	—
178	C₃₁×#121	—	2	1	no	—
179	C₃₁×#121	—	2	2	no	—
180	C₃₁×#121	—	2	2	no	—
181	C₃₁×#121	C₂³	1	2	yes	—
182	C₃₁×#121	C₂³	1	2	yes	—
183	C₃₁×#120	—	2	2	no	—
184	C₃₁×#120	—	2	2	no	—
185	C₃₁×#120	—	2	2	no	—
186	C₄×Q₈×C₃₁	—	2	1	no	—
187	C₄×Q₈×C₃₁	—	2	1	no	—
188	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
189	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
190	C₄×Q₈×C₃₁	C₂³	1	2	yes	—
191	C₄×Q₈×C₃₁	C₂³	1	1	yes	characteristic
192	C₄×D₄×C₃₁	—	2	1	no	—
193	C₄×D₄×C₃₁	—	2	2	no	—
194	C₄×D₄×C₃₁	—	2	4	no	—
195	C₄×D₄×C₃₁	—	2	2	no	—
196	C₄×D₄×C₃₁	—	2	2	no	—
197	C₄×D₄×C₃₁	—	2	1	no	—
198	C₄×D₄×C₃₁	—	2	1	no	—
199	C₄×D₄×C₃₁	—	2	2	no	—
200	C₄×D₄×C₃₁	—	2	1	no	—
201	C₄×D₄×C₃₁	—	2	2	no	—
202	C₄×D₄×C₃₁	—	2	1	no	—
203	C₄×D₄×C₃₁	—	2	1	no	—
204	C₄×D₄×C₃₁	D₄	1	1	yes	characteristic
205	C₄×D₄×C₃₁	D₄	1	2	yes	—
206	C₄×D₄×C₃₁	D₄	1	1	yes	characteristic
207	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
208	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
209	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
210	C₄×D₄×C₃₁	C₂³	1	2	yes	—
211	C₄×D₄×C₃₁	C₂³	1	1	yes	characteristic
212	C₃₁×#117	—	2	1	no	—
213	C₃₁×#117	C₂³	1	1	yes	characteristic
214	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
215	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
216	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
217	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
218	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
219	C₂×C₄⋊C₄×C₃₁	D₄	1	1	yes	characteristic
220	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
221	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
222	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
223	C₂×C₂²⋊C₄×C₃₁	D₄	1	2	yes	—
224	C₂×C₄²×C₃₁	—	2	1	no	—
225	C₂×C₄²×C₃₁	—	2	1	no	—
226	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
227	C₃₁×#107	C₂³	1	2	yes	—
228	C₃₁×#106	C₂³	1	2	yes	—
229	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
230	C₃₁×C₄⋊C₈	C₂³	1	2	yes	—
231	C₃₁×#103	C₂³	1	2	yes	—
232	C₃₁×#103	C₂³	1	4	yes	—
233	C₃₁×#103	C₂³	1	2	yes	—
234	C₃₁×#103	C₂³	1	2	yes	—
235	C₃₁×#103	C₂³	1	4	yes	—
236	C₃₁×#103	C₂³	1	4	yes	—
237	C₃₁×#102	C₂³	1	2	yes	—
238	C₃₁×#102	C₂³	1	4	yes	—
239	C₃₁×C₂²⋊C₈	C₂³	1	4	yes	—
240	C₃₁×C₂²⋊C₈	C₂³	1	4	yes	—
241	C₃₁×#97	C₂³	1	2	yes	—
242	C₄×C₈×C₃₁	C₂³	1	2	yes	—
243	C₂⁴×C₃₁	—	2	2	no	—
244	C₂⁴×C₃₁	C₂×D₄	1	2	yes	—
245	#41×C₃₁	—	2	2	no	—
246	#41×C₃₁	—	2	4	no	—
247	#41×C₃₁	—	2	4	no	—
248	#41×C₃₁	—	2	4	no	—
249	#41×C₃₁	—	2	4	no	—
250	#41×C₃₁	—	4	8	no	—
251	#41×C₃₁	—	4	2	no	—
252	#41×C₃₁	—	4	2	no	—
253	#41×C₃₁	—	4	8	no	—
254	#41×C₃₁	C₂×D₄	1	4	yes	—
255	C₂×Q₈×C₃₁	—	2	1	no	—
256	C₂×Q₈×C₃₁	—	2	2	no	—
257	C₂×Q₈×C₃₁	—	2	4	no	—
258	C₂×Q₈×C₃₁	—	2	4	no	—
259	C₂×Q₈×C₃₁	—	2	2	no	—
260	C₂×Q₈×C₃₁	—	2	2	no	—
261	C₂×Q₈×C₃₁	—	2	8	no	—
262	C₂×Q₈×C₃₁	—	2	4	no	—
263	C₂×Q₈×C₃₁	—	2	8	no	—
264	C₂×Q₈×C₃₁	—	2	4	no	—
265	C₂×Q₈×C₃₁	—	2	4	no	—
266	C₂×Q₈×C₃₁	—	4	8	no	—
267	C₂×Q₈×C₃₁	—	4	4	no	—
268	C₂×Q₈×C₃₁	—	4	4	no	—
269	C₂×Q₈×C₃₁	—	4	2	no	—
270	C₂×Q₈×C₃₁	—	4	8	no	—
271	C₂×Q₈×C₃₁	—	4	8	no	—
272	C₂×Q₈×C₃₁	C₂×D₄	1	4	yes	complemented
273	C₂×Q₈×C₃₁	C₂⁴	1	2	yes	—
274	C₂×Q₈×C₃₁	C₂⁴	1	4	yes	—
275	C₂×Q₈×C₃₁	C₂⁴	1	2	yes	—
276	C₂×Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
277	C₂×D₄×C₃₁	—	2	1	no	—
278	C₂×D₄×C₃₁	—	2	4	no	—
279	C₂×D₄×C₃₁	—	2	4	no	—
280	C₂×D₄×C₃₁	—	2	2	no	—
281	C₂×D₄×C₃₁	—	2	2	no	—
282	C₂×D₄×C₃₁	—	2	2	no	—
283	C₂×D₄×C₃₁	—	2	2	no	—
284	C₂×D₄×C₃₁	—	2	2	no	—
285	C₂×D₄×C₃₁	—	2	1	no	—
286	C₂×D₄×C₃₁	—	2	2	no	—
287	C₂×D₄×C₃₁	—	2	1	no	—
288	C₂×D₄×C₃₁	—	4	2	no	—
289	C₂×D₄×C₃₁	—	4	8	no	—
290	C₂×D₄×C₃₁	—	4	4	no	—
291	C₂×D₄×C₃₁	C₂×D₄	1	2	yes	—
292	C₂×D₄×C₃₁	C₂×D₄	1	1	yes	characteristic
293	C₂×D₄×C₃₁	C₂×D₄	1	1	yes	characteristic
294	C₂×D₄×C₃₁	C₂⁴	1	2	yes	—
295	C₂×D₄×C₃₁	C₂⁴	1	1	yes	characteristic
296	C₂²×C₄×C₃₁	—	2	1	no	—
297	C₂²×C₄×C₃₁	—	2	1	no	—
298	C₂²×C₄×C₃₁	—	2	4	no	—
299	C₂²×C₄×C₃₁	—	2	4	no	—
300	C₂²×C₄×C₃₁	—	2	1	no	—
301	C₂²×C₄×C₃₁	—	2	2	no	—
302	C₂²×C₄×C₃₁	—	2	2	no	—
303	C₂²×C₄×C₃₁	—	2	4	no	—
304	C₂²×C₄×C₃₁	—	2	4	no	—
305	C₂²×C₄×C₃₁	—	2	1	no	—
306	C₂²×C₄×C₃₁	—	2	2	no	—
307	C₂²×C₄×C₃₁	—	2	2	no	—
308	C₂²×C₄×C₃₁	—	2	2	no	—
309	C₂²×C₄×C₃₁	—	2	1	no	—
310	C₂²×C₄×C₃₁	—	4	8	no	—
311	C₂²×C₄×C₃₁	—	4	8	no	—
312	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
313	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
314	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
315	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
316	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
317	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
318	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
319	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
320	Q₁₆×C₃₁	—	2	8	no	—
321	Q₁₆×C₃₁	—	2	8	no	—
322	Q₁₆×C₃₁	—	2	8	no	—
323	Q₁₆×C₃₁	—	4	4	no	—
324	Q₁₆×C₃₁	C₂×D₄	1	8	yes	complemented
325	SD₁₆×C₃₁	—	2	8	no	—
326	SD₁₆×C₃₁	—	2	8	no	—
327	SD₁₆×C₃₁	—	2	8	no	—
328	SD₁₆×C₃₁	—	4	4	no	—
329	SD₁₆×C₃₁	C₂×D₄	1	8	yes	complemented
330	M₁₆×C₃₁	—	2	4	no	—
331	M₁₆×C₃₁	—	2	2	no	—
332	M₁₆×C₃₁	—	2	8	no	—
333	M₁₆×C₃₁	C₂×D₄	1	4	yes	complemented
334	C₂×C₈×C₃₁	—	2	8	no	—
335	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
336	C₂×C₈×C₃₁	C₂⁴	1	4	yes	—
337	C₂×C₈×C₃₁	C₂⁴	1	2	yes	—
338	C₄⋊C₄×C₃₁	—	2	1	no	—
339	C₄⋊C₄×C₃₁	—	2	2	no	—
340	C₄⋊C₄×C₃₁	—	2	2	no	—
341	C₄⋊C₄×C₃₁	—	2	2	no	—
342	C₄⋊C₄×C₃₁	—	2	2	no	—
343	C₄⋊C₄×C₃₁	—	2	2	no	—
344	C₄⋊C₄×C₃₁	—	2	2	no	—
345	C₄⋊C₄×C₃₁	—	2	2	no	—
346	C₄⋊C₄×C₃₁	—	2	4	no	—
347	C₄⋊C₄×C₃₁	—	2	4	no	—
348	C₄⋊C₄×C₃₁	—	2	1	no	—
349	C₄⋊C₄×C₃₁	—	2	1	no	—
350	C₄⋊C₄×C₃₁	—	2	1	no	—
351	C₄⋊C₄×C₃₁	—	2	1	no	—
352	C₄⋊C₄×C₃₁	—	2	2	no	—
353	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
354	C₄⋊C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
355	C₄⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
356	C₄⋊C₄×C₃₁	C₂⁴	1	2	yes	—
357	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
358	C₄⋊C₄×C₃₁	C₂⁴	1	1	yes	characteristic
359	C₂²⋊C₄×C₃₁	—	2	2	no	—
360	C₂²⋊C₄×C₃₁	—	2	4	no	—
361	C₂²⋊C₄×C₃₁	—	2	4	no	—
362	C₂²⋊C₄×C₃₁	—	2	1	no	—
363	C₂²⋊C₄×C₃₁	—	2	2	no	—
364	C₂²⋊C₄×C₃₁	—	2	2	no	—
365	C₂²⋊C₄×C₃₁	—	2	2	no	—
366	C₂²⋊C₄×C₃₁	—	2	1	no	—
367	C₂²⋊C₄×C₃₁	—	2	1	no	—
368	C₂²⋊C₄×C₃₁	—	2	2	no	—
369	C₂²⋊C₄×C₃₁	—	2	2	no	—
370	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
371	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
372	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
373	C₂²⋊C₄×C₃₁	C₂×D₄	1	2	yes	—
374	C₄²×C₃₁	—	2	1	no	—
375	C₄²×C₃₁	—	2	1	no	—
376	C₄²×C₃₁	—	2	1	no	—
377	C₄²×C₃₁	—	2	2	no	—
378	C₄²×C₃₁	—	2	2	no	—
379	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
380	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
381	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
382	C₄²×C₃₁	C₂⁴	1	1	yes	characteristic
383	D₄×#137	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
384	C₂³×C₃₁	—	2	4	no	—
385	C₂³×C₃₁	—	2	4	no	—
386	C₂³×C₃₁	—	2	1	no	—
387	C₂³×C₃₁	—	2	2	no	—
388	C₂³×C₃₁	—	4	2	no	—
389	C₂³×C₃₁	—	4	4	no	—
390	C₂³×C₃₁	—	4	4	no	—
391	C₂³×C₃₁	—	8	2	no	—
392	C₂³×C₃₁	C₂²×D₄	1	2	yes	—
393	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
394	C₂³×C₃₁	C₂²×D₄	1	2	yes	—
395	Q₈×C₃₁	—	2	4	no	—
396	Q₈×C₃₁	—	2	2	no	—
397	Q₈×C₃₁	—	2	1	no	—
398	Q₈×C₃₁	—	2	4	no	—
399	Q₈×C₃₁	—	2	2	no	—
400	Q₈×C₃₁	—	2	4	no	—
401	Q₈×C₃₁	—	2	2	no	—
402	Q₈×C₃₁	—	4	8	no	—
403	Q₈×C₃₁	—	4	8	no	—
404	Q₈×C₃₁	—	4	4	no	—
405	Q₈×C₃₁	—	4	4	no	—
406	Q₈×C₃₁	C₂²×D₄	1	4	yes	—
407	Q₈×C₃₁	C₂²×D₄	1	2	yes	—
408	D₄×C₃₁	—	2	4	no	—
409	D₄×C₃₁	—	2	4	no	—
410	D₄×C₃₁	—	2	2	no	—
411	D₄×C₃₁	—	2	2	no	—
412	D₄×C₃₁	—	2	1	no	—
413	D₄×C₃₁	—	2	2	no	—
414	D₄×C₃₁	—	4	4	no	—
415	D₄×C₃₁	—	4	4	no	—
416	D₄×C₃₁	—	4	4	no	—
417	D₄×C₃₁	—	4	4	no	—
418	D₄×C₃₁	—	4	4	no	—
419	D₄×C₃₁	—	4	2	no	—
420	D₄×C₃₁	—	8	1	no	—
421	D₄×C₃₁	—	8	2	no	—
422	D₄×C₃₁	#137	1	4	yes	direct product factor
423	D₄×C₃₁	C₂²×D₄	1	2	yes	—
424	C₂×C₄×C₃₁	—	2	4	no	—
425	C₂×C₄×C₃₁	—	2	4	no	—
426	C₂×C₄×C₃₁	—	2	1	no	—
427	C₂×C₄×C₃₁	—	2	2	no	—
428	C₂×C₄×C₃₁	—	2	4	no	—
429	C₂×C₄×C₃₁	—	2	4	no	—
430	C₂×C₄×C₃₁	—	2	4	no	—
431	C₂×C₄×C₃₁	—	2	2	no	—
432	C₂×C₄×C₃₁	—	2	2	no	—
433	C₂×C₄×C₃₁	—	2	2	no	—
434	C₂×C₄×C₃₁	—	2	2	no	—
435	C₂×C₄×C₃₁	—	2	2	no	—
436	C₂×C₄×C₃₁	—	2	1	no	—
437	C₂×C₄×C₃₁	—	2	1	no	—
438	C₂×C₄×C₃₁	—	2	2	no	—
439	C₂×C₄×C₃₁	—	2	2	no	—
440	C₂×C₄×C₃₁	—	2	4	no	—
441	C₂×C₄×C₃₁	—	4	1	no	—
442	C₂×C₄×C₃₁	—	4	4	no	—
443	C₂×C₄×C₃₁	—	4	4	no	—
444	C₂×C₄×C₃₁	—	4	8	no	—
445	C₂×C₄×C₃₁	—	4	8	no	—
446	C₂×C₄×C₃₁	—	4	4	no	—
447	C₂×C₄×C₃₁	—	4	2	no	—
448	C₂×C₄×C₃₁	—	4	4	no	—
449	C₂×C₄×C₃₁	—	4	4	no	—
450	C₂×C₄×C₃₁	—	4	2	no	—
451	C₂×C₄×C₃₁	—	8	1	no	—
452	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
453	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
454	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
455	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
456	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
457	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
458	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
459	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
460	C₂×C₄×C₃₁	H(5,𝔽₂)	1	2	yes	—
461	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
462	C₈×C₃₁	—	2	4	no	—
463	C₈×C₃₁	—	2	2	no	—
464	C₈×C₃₁	C₂²×D₄	1	4	yes	—
465	C₂²×#137	C₂×C₃₁	1	2	yes	complemented
466	D₄×#41	C₂×C₃₁	1	1	yes	characteristic
467	C₂×D₄×Q₈	C₂×C₃₁	1	1	yes	characteristic, complemented
468	D₄×Q₁₆	C₂×C₃₁	1	2	yes	complemented
469	D₄×SD₁₆	C₂×C₃₁	1	2	yes	complemented
470	#3278	C₂×C₃₁	1	2	yes	complemented
471	#3276	C₂×C₃₁	1	2	yes	complemented
472	#3270	C₂×C₃₁	1	4	yes	complemented
473	#3266	C₂×C₃₁	1	4	yes	complemented
474	#3152	C₂×C₃₁	1	1	yes	characteristic, complemented
475	#3056	C₂×C₃₁	1	2	yes	complemented
476	#3039	C₂×C₃₁	1	1	yes	characteristic, complemented
477	#3037	C₂×C₃₁	1	1	yes	characteristic, complemented
478	#3007	C₂×C₃₁	1	2	yes	complemented
479	#3004	C₂×C₃₁	1	2	yes	complemented
480	C₄×#137	C₂×C₃₁	1	1	yes	characteristic, complemented
481	D₄×M₁₆	C₂×C₃₁	1	1	yes	characteristic, complemented
482	C₂²×C₃₁	—	2	1	no	—
483	C₂²×C₃₁	—	2	2	no	—
484	C₂²×C₃₁	—	2	2	no	—
485	C₂²×C₃₁	—	2	1	no	—
486	C₂²×C₃₁	—	2	2	no	—
487	C₂²×C₃₁	—	2	2	no	—
488	C₂²×C₃₁	—	2	2	no	—
489	C₂²×C₃₁	—	2	2	no	—
490	C₂²×C₃₁	—	4	8	no	—
491	C₂²×C₃₁	—	4	1	no	—
492	C₂²×C₃₁	—	4	1	no	—
493	C₂²×C₃₁	—	4	2	no	—
494	C₂²×C₃₁	—	4	2	no	—
495	C₂²×C₃₁	—	4	2	no	—
496	C₂²×C₃₁	—	8	8	no	—
497	C₂²×C₃₁	D₄²	1	2	yes	—
498	C₂²×C₃₁	C₂×#137	1	4	yes	complemented
499	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
500	C₄×C₃₁	—	2	1	no	—
501	C₄×C₃₁	—	2	1	no	—
502	C₄×C₃₁	—	2	2	no	—
503	C₄×C₃₁	—	2	2	no	—
504	C₄×C₃₁	—	2	2	no	—
505	C₄×C₃₁	—	2	4	no	—
506	C₄×C₃₁	—	2	1	no	—
507	C₄×C₃₁	—	4	2	no	—
508	C₄×C₃₁	—	4	1	no	—
509	C₄×C₃₁	—	4	2	no	—
510	C₄×C₃₁	—	4	4	no	—
511	C₄×C₃₁	—	4	1	no	—
512	C₄×C₃₁	D₄²	1	2	yes	—
513	C₄×C₃₁	C₂×#137	1	2	yes	complemented
514	C₄×C₃₁	C₂³×D₄	1	1	yes	characteristic
515	C₄×C₃₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
516	C₂²×#41	C₂²×C₃₁	1	2	yes	—
517	C₂³×Q₈	C₂²×C₃₁	1	2	yes	complemented
518	C₂×#137	—	2	16	no	—
519	C₂×#137	C₂²×C₃₁	1	2	yes	—
520	C₂×#137	C₂²×C₃₁	1	1	yes	characteristic
521	C₂×#137	C₂²×C₃₁	1	2	yes	complemented
522	C₂×#137	C₂²×C₃₁	1	2	yes	complemented
523	C₂×#137	C₂²×C₃₁	1	4	yes	complemented
524	C₂×#137	C₂²×C₃₁	1	4	yes	complemented
525	C₂×#137	C₂²×C₃₁	1	2	yes	complemented
526	C₂²×Q₁₆	C₂²×C₃₁	1	4	yes	complemented
527	C₂²×SD₁₆	C₂²×C₃₁	1	4	yes	complemented
528	C₂²×M₁₆	C₂²×C₃₁	1	2	yes	complemented
529	#550	C₂²×C₃₁	1	1	yes	characteristic
530	D₄×Q₈	—	2	1	no	—
531	D₄×Q₈	—	2	2	no	—
532	D₄×Q₈	—	2	1	no	—
533	D₄×Q₈	C₂²×C₃₁	1	2	yes	—
534	D₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic
535	D₄×Q₈	C₂²×C₃₁	1	4	yes	complemented
536	D₄×Q₈	C₂²×C₃₁	1	2	yes	complemented
537	#548	C₂²×C₃₁	1	2	yes	—
538	#547	—	2	1	no	—
539	#547	C₂²×C₃₁	1	1	yes	characteristic
540	#546	—	2	2	no	—
541	#546	C₂²×C₃₁	1	2	yes	—
542	D₄²	—	2	1	no	—
543	D₄²	C₂²×C₃₁	1	1	yes	characteristic
544	#532	—	2	1	no	—
545	#532	C₂²×C₃₁	1	1	yes	characteristic
546	C₂×C₄⋊Q₈	—	2	1	no	—
547	C₂×C₄⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
548	#525	—	2	2	no	—
549	#525	C₂²×C₃₁	1	2	yes	—
550	C₂×C₂²⋊Q₈	—	2	2	no	—
551	C₂×C₂²⋊Q₈	C₂²×C₃₁	1	2	yes	complemented
552	C₄×#41	C₂²×C₃₁	1	1	yes	characteristic
553	C₂×C₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
554	C₂×C₄×D₄	—	2	1	no	—
555	C₂×C₄×D₄	—	2	1	no	—
556	C₂×C₄×D₄	C₂²×C₃₁	1	1	yes	characteristic
557	#497	C₂²×C₃₁	1	4	yes	complemented
558	#494	C₂²×C₃₁	1	2	yes	complemented
559	#492	C₂²×C₃₁	1	2	yes	complemented
560	#470	C₂²×C₃₁	1	4	yes	complemented
561	#468	C₂²×C₃₁	1	4	yes	complemented
562	#467	C₂²×C₃₁	1	4	yes	complemented
563	#465	C₂²×C₃₁	1	4	yes	complemented
564	#464	C₂²×C₃₁	1	4	yes	complemented
565	#462	C₂²×C₃₁	1	2	yes	complemented
566	#462	C₂²×C₃₁	1	2	yes	complemented
567	#462	C₂²×C₃₁	1	2	yes	complemented
568	#461	C₂²×C₃₁	1	2	yes	complemented
569	#461	C₂²×C₃₁	1	2	yes	complemented
570	#460	C₂²×C₃₁	1	2	yes	complemented
571	#452	C₂²×C₃₁	1	4	yes	complemented
572	#452	C₂²×C₃₁	1	4	yes	complemented
573	#451	C₂²×C₃₁	1	4	yes	complemented
574	#451	C₂²×C₃₁	1	4	yes	complemented
575	#451	C₂²×C₃₁	1	4	yes	complemented
576	#450	C₂²×C₃₁	1	4	yes	complemented
577	#448	C₂²×C₃₁	1	4	yes	complemented
578	#448	C₂²×C₃₁	1	4	yes	complemented
579	#441	C₂²×C₃₁	1	2	yes	complemented
580	#440	C₂²×C₃₁	1	2	yes	complemented
581	C₄×Q₁₆	C₂²×C₃₁	1	2	yes	complemented
582	C₄×SD₁₆	C₂²×C₃₁	1	2	yes	complemented
583	#436	C₂²×C₃₁	1	2	yes	complemented
584	#435	C₂²×C₃₁	1	4	yes	complemented
585	C₈×D₄	C₂²×C₃₁	1	2	yes	—
586	#428	C₂²×C₃₁	1	1	yes	characteristic, complemented
587	#423	C₂²×C₃₁	1	1	yes	characteristic, complemented
588	#419	C₂²×C₃₁	1	1	yes	characteristic, complemented
589	#419	C₂²×C₃₁	1	2	yes	complemented
590	#417	C₂²×C₃₁	1	1	yes	characteristic
591	#417	C₂²×C₃₁	1	2	yes	complemented
592	#407	C₂²×C₃₁	1	2	yes	complemented
593	C₄×M₁₆	C₂²×C₃₁	1	1	yes	characteristic, complemented
594	C₂×C₃₁	—	2	2	no	—
595	C₂×C₃₁	—	2	4	no	—
596	C₂×C₃₁	—	4	2	no	—
597	C₂×C₃₁	—	4	2	no	—
598	C₂×C₃₁	—	8	2	no	—
599	C₂×C₃₁	C₂×D₄²	1	1	yes	characteristic
600	C₂×C₃₁	C₂²×#137	1	1	yes	characteristic
601	C₂×C₃₁	#3586	1	1	yes	characteristic
602	C₂×#41	—	2	2	no	—
603	C₂×#41	—	2	2	no	—
604	C₂×#41	—	2	8	no	—
605	C₂×#41	—	4	4	no	—
606	C₂×#41	C₂³×C₃₁	1	2	yes	—
607	C₂×#41	C₂³×C₃₁	1	2	yes	—
608	C₂×#41	C₂³×C₃₁	1	2	yes	—
609	C₂×#41	C₂³×C₃₁	1	1	yes	characteristic
610	C₂²×Q₈	—	2	2	no	—
611	C₂²×Q₈	—	2	2	no	—
612	C₂²×Q₈	—	2	2	no	—
613	C₂²×Q₈	—	2	8	no	—
614	C₂²×Q₈	—	4	4	no	—
615	C₂²×Q₈	C₂³×C₃₁	1	2	yes	—
616	C₂²×Q₈	C₂³×C₃₁	1	2	yes	—
617	C₂²×Q₈	C₂³×C₃₁	1	4	yes	—
618	C₂²×Q₈	C₂³×C₃₁	1	4	yes	—
619	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
620	C₂²×D₄	—	2	2	no	—
621	C₂²×D₄	—	2	1	no	—
622	C₂²×D₄	D₄×C₃₁	1	1	yes	characteristic
623	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
624	C₂³×C₄	—	2	2	no	—
625	C₂³×C₄	—	2	2	no	—
626	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
627	#137	—	2	8	no	—
628	#137	—	2	8	no	—
629	#137	—	2	16	no	—
630	#137	—	2	16	no	—
631	#137	—	2	8	no	—
632	#137	—	4	4	no	—
633	#137	D₄×C₃₁	1	8	yes	direct product factor
634	C₂×Q₁₆	—	2	16	no	—
635	C₂×Q₁₆	C₂³×C₃₁	1	4	yes	—
636	C₂×Q₁₆	C₂³×C₃₁	1	4	yes	—
637	C₂×Q₁₆	C₂³×C₃₁	1	4	yes	—
638	C₂×Q₁₆	C₂³×C₃₁	1	4	yes	—
639	C₂×Q₁₆	C₂³×C₃₁	1	2	yes	—
640	C₂×SD₁₆	—	2	16	no	—
641	C₂×SD₁₆	C₂³×C₃₁	1	4	yes	—
642	C₂×SD₁₆	C₂³×C₃₁	1	4	yes	—
643	C₂×SD₁₆	C₂³×C₃₁	1	4	yes	—
644	C₂×SD₁₆	C₂³×C₃₁	1	4	yes	—
645	C₂×SD₁₆	C₂³×C₃₁	1	2	yes	—
646	C₂×M₁₆	—	2	8	no	—
647	C₂×M₁₆	C₂³×C₃₁	1	2	yes	—
648	C₂×M₁₆	C₂³×C₃₁	1	4	yes	—
649	C₂×M₁₆	C₂³×C₃₁	1	1	yes	characteristic
650	C₂×M₁₆	C₂³×C₃₁	1	1	yes	characteristic
651	C₂²×C₈	C₂³×C₃₁	1	4	yes	—
652	C₄⋊Q₈	—	2	2	no	—
653	C₄⋊Q₈	—	2	2	no	—
654	C₄⋊Q₈	—	2	4	no	—
655	C₄⋊Q₈	—	2	1	no	—
656	C₄⋊Q₈	—	2	1	no	—
657	C₄⋊Q₈	—	2	1	no	—
658	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
659	C₄⋊Q₈	C₂³×C₃₁	1	2	yes	—
660	C₄⋊Q₈	C₂³×C₃₁	1	1	yes	characteristic
661	#127	—	2	1	no	—
662	#127	C₂³×C₃₁	1	1	yes	characteristic
663	#124	—	2	2	no	—
664	#124	C₂³×C₃₁	1	2	yes	—
665	#123	—	2	2	no	—
666	#123	—	2	2	no	—
667	#123	—	2	2	no	—
668	C₂²⋊Q₈	—	2	2	no	—
669	C₂²⋊Q₈	—	2	2	no	—
670	C₂²⋊Q₈	—	2	2	no	—
671	C₂²⋊Q₈	—	2	4	no	—
672	C₂²⋊Q₈	—	2	4	no	—
673	C₂²⋊Q₈	—	2	4	no	—
674	C₂²⋊Q₈	—	2	4	no	—
675	C₂²⋊Q₈	—	2	2	no	—
676	C₂²⋊Q₈	C₂³×C₃₁	1	4	yes	—
677	C₂²⋊Q₈	C₂³×C₃₁	1	4	yes	—
678	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
679	C₂²⋊Q₈	C₂³×C₃₁	1	2	yes	—
680	#121	—	2	2	no	—
681	#121	—	2	1	no	—
682	#121	—	2	1	no	—
683	#121	—	2	1	no	—
684	#121	—	2	1	no	—
685	#121	—	2	2	no	—
686	#121	—	2	2	no	—
687	#121	C₂³×C₃₁	1	2	yes	—
688	#121	C₂³×C₃₁	1	2	yes	—
689	#120	—	2	2	no	—
690	#120	—	2	2	no	—
691	#120	—	2	2	no	—
692	C₄×Q₈	—	2	1	no	—
693	C₄×Q₈	—	2	1	no	—
694	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
695	C₄×Q₈	C₂³×C₃₁	1	2	yes	—
696	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
697	C₄×Q₈	C₂³×C₃₁	1	1	yes	characteristic
698	C₄×D₄	—	2	1	no	—
699	C₄×D₄	—	2	2	no	—
700	C₄×D₄	—	2	4	no	—
701	C₄×D₄	—	2	2	no	—
702	C₄×D₄	—	2	2	no	—
703	C₄×D₄	—	2	1	no	—
704	C₄×D₄	—	2	1	no	—
705	C₄×D₄	—	2	2	no	—
706	C₄×D₄	—	2	1	no	—
707	C₄×D₄	—	2	2	no	—
708	C₄×D₄	—	2	1	no	—
709	C₄×D₄	—	2	1	no	—
710	C₄×D₄	D₄×C₃₁	1	1	yes	characteristic
711	C₄×D₄	D₄×C₃₁	1	2	yes	—
712	C₄×D₄	D₄×C₃₁	1	1	yes	characteristic
713	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
714	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
715	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
716	C₄×D₄	C₂³×C₃₁	1	2	yes	—
717	C₄×D₄	C₂³×C₃₁	1	1	yes	characteristic
718	#117	—	2	1	no	—
719	#117	C₂³×C₃₁	1	1	yes	characteristic
720	C₂×C₄⋊C₄	—	2	1	no	—
721	C₂×C₄⋊C₄	—	2	1	no	—
722	C₂×C₄⋊C₄	—	2	1	no	—
723	C₂×C₄⋊C₄	—	2	2	no	—
724	C₂×C₄⋊C₄	—	2	1	no	—
725	C₂×C₄⋊C₄	D₄×C₃₁	1	1	yes	characteristic
726	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
727	C₂×C₂²⋊C₄	—	2	2	no	—
728	C₂×C₂²⋊C₄	—	2	2	no	—
729	C₂×C₂²⋊C₄	D₄×C₃₁	1	2	yes	—
730	C₂×C₄²	—	2	1	no	—
731	C₂×C₄²	—	2	1	no	—
732	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
733	#107	C₂³×C₃₁	1	2	yes	—
734	#106	C₂³×C₃₁	1	2	yes	—
735	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
736	C₄⋊C₈	C₂³×C₃₁	1	2	yes	—
737	#103	C₂³×C₃₁	1	2	yes	—
738	#103	C₂³×C₃₁	1	4	yes	—
739	#103	C₂³×C₃₁	1	2	yes	—
740	#103	C₂³×C₃₁	1	2	yes	—
741	#103	C₂³×C₃₁	1	4	yes	—
742	#103	C₂³×C₃₁	1	4	yes	—
743	#102	C₂³×C₃₁	1	2	yes	—
744	#102	C₂³×C₃₁	1	4	yes	—
745	C₂²⋊C₈	C₂³×C₃₁	1	4	yes	—
746	C₂²⋊C₈	C₂³×C₃₁	1	4	yes	—
747	#97	C₂³×C₃₁	1	2	yes	—
748	C₄×C₈	C₂³×C₃₁	1	2	yes	—
749	C₃₁	D₄×#137	1	1	yes	characteristic, direct product factor, Sylow
750	C₂⁴	—	2	2	no	—
751	C₂⁴	C₂×D₄×C₃₁	1	2	yes	—
752	#41	—	2	2	no	—
753	#41	—	2	4	no	—
754	#41	—	2	4	no	—
755	#41	—	2	4	no	—
756	#41	—	2	4	no	—
757	#41	—	4	8	no	—
758	#41	—	4	2	no	—
759	#41	—	4	2	no	—
760	#41	—	4	8	no	—
761	#41	C₂×D₄×C₃₁	1	4	yes	—
762	C₂×Q₈	—	2	1	no	—
763	C₂×Q₈	—	2	2	no	—
764	C₂×Q₈	—	2	4	no	—
765	C₂×Q₈	—	2	4	no	—
766	C₂×Q₈	—	2	2	no	—
767	C₂×Q₈	—	2	2	no	—
768	C₂×Q₈	—	2	8	no	—
769	C₂×Q₈	—	2	4	no	—
770	C₂×Q₈	—	2	8	no	—
771	C₂×Q₈	—	2	4	no	—
772	C₂×Q₈	—	2	4	no	—
773	C₂×Q₈	—	4	8	no	—
774	C₂×Q₈	—	4	4	no	—
775	C₂×Q₈	—	4	4	no	—
776	C₂×Q₈	—	4	2	no	—
777	C₂×Q₈	—	4	8	no	—
778	C₂×Q₈	—	4	8	no	—
779	C₂×Q₈	C₂×D₄×C₃₁	1	4	yes	complemented
780	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
781	C₂×Q₈	C₂⁴×C₃₁	1	4	yes	—
782	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
783	C₂×Q₈	C₂⁴×C₃₁	1	1	yes	characteristic
784	C₂×D₄	—	2	1	no	—
785	C₂×D₄	—	2	4	no	—
786	C₂×D₄	—	2	4	no	—
787	C₂×D₄	—	2	2	no	—
788	C₂×D₄	—	2	2	no	—
789	C₂×D₄	—	2	2	no	—
790	C₂×D₄	—	2	2	no	—
791	C₂×D₄	—	2	2	no	—
792	C₂×D₄	—	2	1	no	—
793	C₂×D₄	—	2	2	no	—
794	C₂×D₄	—	2	1	no	—
795	C₂×D₄	—	4	2	no	—
796	C₂×D₄	—	4	8	no	—
797	C₂×D₄	—	4	4	no	—
798	C₂×D₄	C₂×D₄×C₃₁	1	2	yes	—
799	C₂×D₄	C₂×D₄×C₃₁	1	1	yes	characteristic
800	C₂×D₄	C₂×D₄×C₃₁	1	1	yes	characteristic
801	C₂×D₄	C₂⁴×C₃₁	1	2	yes	—
802	C₂×D₄	C₂⁴×C₃₁	1	1	yes	characteristic
803	C₂²×C₄	—	2	1	no	—
804	C₂²×C₄	—	2	1	no	—
805	C₂²×C₄	—	2	4	no	—
806	C₂²×C₄	—	2	4	no	—
807	C₂²×C₄	—	2	1	no	—
808	C₂²×C₄	—	2	2	no	—
809	C₂²×C₄	—	2	2	no	—
810	C₂²×C₄	—	2	4	no	—
811	C₂²×C₄	—	2	4	no	—
812	C₂²×C₄	—	2	1	no	—
813	C₂²×C₄	—	2	2	no	—
814	C₂²×C₄	—	2	2	no	—
815	C₂²×C₄	—	2	2	no	—
816	C₂²×C₄	—	2	1	no	—
817	C₂²×C₄	—	4	8	no	—
818	C₂²×C₄	—	4	8	no	—
819	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
820	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
821	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
822	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
823	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
824	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
825	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
826	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
827	Q₁₆	—	2	8	no	—
828	Q₁₆	—	2	8	no	—
829	Q₁₆	—	2	8	no	—
830	Q₁₆	—	4	4	no	—
831	Q₁₆	C₂×D₄×C₃₁	1	8	yes	complemented
832	SD₁₆	—	2	8	no	—
833	SD₁₆	—	2	8	no	—
834	SD₁₆	—	2	8	no	—
835	SD₁₆	—	4	4	no	—
836	SD₁₆	C₂×D₄×C₃₁	1	8	yes	complemented
837	M₁₆	—	2	4	no	—
838	M₁₆	—	2	2	no	—
839	M₁₆	—	2	8	no	—
840	M₁₆	C₂×D₄×C₃₁	1	4	yes	complemented
841	C₂×C₈	—	2	8	no	—
842	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
843	C₂×C₈	C₂⁴×C₃₁	1	4	yes	—
844	C₂×C₈	C₂⁴×C₃₁	1	2	yes	—
845	C₄⋊C₄	—	2	1	no	—
846	C₄⋊C₄	—	2	2	no	—
847	C₄⋊C₄	—	2	2	no	—
848	C₄⋊C₄	—	2	2	no	—
849	C₄⋊C₄	—	2	2	no	—
850	C₄⋊C₄	—	2	2	no	—
851	C₄⋊C₄	—	2	2	no	—
852	C₄⋊C₄	—	2	2	no	—
853	C₄⋊C₄	—	2	4	no	—
854	C₄⋊C₄	—	2	4	no	—
855	C₄⋊C₄	—	2	1	no	—
856	C₄⋊C₄	—	2	1	no	—
857	C₄⋊C₄	—	2	1	no	—
858	C₄⋊C₄	—	2	1	no	—
859	C₄⋊C₄	—	2	2	no	—
860	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
861	C₄⋊C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
862	C₄⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
863	C₄⋊C₄	C₂⁴×C₃₁	1	2	yes	—
864	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
865	C₄⋊C₄	C₂⁴×C₃₁	1	1	yes	characteristic
866	C₂²⋊C₄	—	2	2	no	—
867	C₂²⋊C₄	—	2	4	no	—
868	C₂²⋊C₄	—	2	4	no	—
869	C₂²⋊C₄	—	2	1	no	—
870	C₂²⋊C₄	—	2	2	no	—
871	C₂²⋊C₄	—	2	2	no	—
872	C₂²⋊C₄	—	2	2	no	—
873	C₂²⋊C₄	—	2	1	no	—
874	C₂²⋊C₄	—	2	1	no	—
875	C₂²⋊C₄	—	2	2	no	—
876	C₂²⋊C₄	—	2	2	no	—
877	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
878	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
879	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
880	C₂²⋊C₄	C₂×D₄×C₃₁	1	2	yes	—
881	C₄²	—	2	1	no	—
882	C₄²	—	2	1	no	—
883	C₄²	—	2	1	no	—
884	C₄²	—	2	2	no	—
885	C₄²	—	2	2	no	—
886	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
887	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
888	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
889	C₄²	C₂⁴×C₃₁	1	1	yes	characteristic
890	C₂³	—	2	4	no	—
891	C₂³	—	2	4	no	—
892	C₂³	—	2	1	no	—
893	C₂³	—	2	2	no	—
894	C₂³	—	4	2	no	—
895	C₂³	—	4	4	no	—
896	C₂³	—	4	4	no	—
897	C₂³	—	8	2	no	—
898	C₂³	C₂²×D₄×C₃₁	1	2	yes	—
899	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
900	C₂³	C₂²×D₄×C₃₁	1	2	yes	—
901	Q₈	—	2	4	no	—
902	Q₈	—	2	2	no	—
903	Q₈	—	2	1	no	—
904	Q₈	—	2	4	no	—
905	Q₈	—	2	2	no	—
906	Q₈	—	2	4	no	—
907	Q₈	—	2	2	no	—
908	Q₈	—	4	8	no	—
909	Q₈	—	4	8	no	—
910	Q₈	—	4	4	no	—
911	Q₈	—	4	4	no	—
912	Q₈	C₂²×D₄×C₃₁	1	4	yes	—
913	Q₈	C₂²×D₄×C₃₁	1	2	yes	—
914	D₄	—	2	4	no	—
915	D₄	—	2	4	no	—
916	D₄	—	2	2	no	—
917	D₄	—	2	2	no	—
918	D₄	—	2	1	no	—
919	D₄	—	2	2	no	—
920	D₄	—	4	4	no	—
921	D₄	—	4	4	no	—
922	D₄	—	4	4	no	—
923	D₄	—	4	4	no	—
924	D₄	—	4	4	no	—
925	D₄	—	4	2	no	—
926	D₄	—	8	1	no	—
927	D₄	—	8	2	no	—
928	D₄	C₃₁×#137	1	4	yes	direct product factor
929	D₄	C₂²×D₄×C₃₁	1	2	yes	—
930	C₂×C₄	—	2	4	no	—
931	C₂×C₄	—	2	4	no	—
932	C₂×C₄	—	2	1	no	—
933	C₂×C₄	—	2	2	no	—
934	C₂×C₄	—	2	4	no	—
935	C₂×C₄	—	2	4	no	—
936	C₂×C₄	—	2	4	no	—
937	C₂×C₄	—	2	2	no	—
938	C₂×C₄	—	2	2	no	—
939	C₂×C₄	—	2	2	no	—
940	C₂×C₄	—	2	2	no	—
941	C₂×C₄	—	2	2	no	—
942	C₂×C₄	—	2	1	no	—
943	C₂×C₄	—	2	1	no	—
944	C₂×C₄	—	2	2	no	—
945	C₂×C₄	—	2	2	no	—
946	C₂×C₄	—	2	4	no	—
947	C₂×C₄	—	4	1	no	—
948	C₂×C₄	—	4	4	no	—
949	C₂×C₄	—	4	4	no	—
950	C₂×C₄	—	4	8	no	—
951	C₂×C₄	—	4	8	no	—
952	C₂×C₄	—	4	4	no	—
953	C₂×C₄	—	4	2	no	—
954	C₂×C₄	—	4	4	no	—
955	C₂×C₄	—	4	4	no	—
956	C₂×C₄	—	4	2	no	—
957	C₂×C₄	—	8	1	no	—
958	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
959	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
960	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
961	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
962	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
963	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
964	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
965	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
966	C₂×C₄	C₃₁×H(5,𝔽₂)	1	2	yes	—
967	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
968	C₈	—	2	4	no	—
969	C₈	—	2	2	no	—
970	C₈	C₂²×D₄×C₃₁	1	4	yes	—
971	C₂²	—	2	2	no	—
972	C₂²	—	2	1	no	—
973	C₂²	—	2	1	no	—
974	C₂²	—	2	2	no	—
975	C₂²	—	2	2	no	—
976	C₂²	—	2	2	no	—
977	C₂²	—	2	2	no	—
978	C₂²	—	2	2	no	—
979	C₂²	—	4	8	no	—
980	C₂²	—	4	1	no	—
981	C₂²	—	4	1	no	—
982	C₂²	—	4	2	no	—
983	C₂²	—	4	2	no	—
984	C₂²	—	4	2	no	—
985	C₂²	—	8	8	no	—
986	C₂²	D₄²×C₃₁	1	2	yes	—
987	C₂²	C₂×C₃₁×#137	1	4	yes	complemented
988	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
989	C₄	—	2	2	no	—
990	C₄	—	2	2	no	—
991	C₄	—	2	2	no	—
992	C₄	—	2	4	no	—
993	C₄	—	2	1	no	—
994	C₄	—	2	1	no	—
995	C₄	—	2	1	no	—
996	C₄	—	4	2	no	—
997	C₄	—	4	4	no	—
998	C₄	—	4	1	no	—
999	C₄	—	4	2	no	—
1000	C₄	—	4	1	no	—
1001	C₄	D₄²×C₃₁	1	2	yes	—
1002	C₄	C₂×C₃₁×#137	1	2	yes	complemented
1003	C₄	C₂³×D₄×C₃₁	1	1	yes	characteristic
1004	C₄	C₂×C₃₁×H(5,𝔽₂)	1	1	yes	characteristic
1005	C₂	—	2	2	no	—
1006	C₂	—	2	4	no	—
1007	C₂	—	4	2	no	—
1008	C₂	—	4	2	no	—
1009	C₂	—	8	2	no	—
1010	C₂	C₂×D₄²×C₃₁	1	1	yes	characteristic
1011	C₂	C₂²×C₃₁×#137	1	1	yes	characteristic
1012	C₂	C₃₁×#3586	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₃₁	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₃₁
prime radical	D₄×#41×C₃₁	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃₁ ◁ C₂×C₄×D₄×C₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂²×C₃₁×#137	C₂	semidirect
3. C₂×D₄×Q₈×C₃₁	C₂	semidirect
4. D₄×Q₁₆×C₃₁	C₂	semidirect
5. D₄×SD₁₆×C₃₁	C₂	semidirect
6. C₃₁×#3278	C₂	semidirect
7. C₃₁×#3276	C₂	semidirect
8. C₃₁×#3270	C₂	semidirect
9. C₃₁×#3266	C₂	semidirect
10. C₃₁×#3152	C₂	semidirect
11. C₃₁×#3056	C₂	semidirect
12. C₃₁×#3039	C₂	semidirect
13. C₃₁×#3037	C₂	semidirect
14. C₃₁×#3007	C₂	semidirect
15. C₃₁×#3004	C₂	semidirect
16. C₄×C₃₁×#137	C₂	semidirect
17. D₄×M₁₆×C₃₁	C₂	semidirect
19. C₂³×Q₈×C₃₁	C₂²	semidirect
23. C₂×C₃₁×#137	C₂²	semidirect
24. C₂×C₃₁×#137	C₂²	semidirect
25. C₂×C₃₁×#137	C₂²	semidirect
26. C₂×C₃₁×#137	C₂²	semidirect
27. C₂×C₃₁×#137	C₂²	semidirect
28. C₂²×Q₁₆×C₃₁	C₂²	semidirect
29. C₂²×SD₁₆×C₃₁	C₂²	semidirect
30. C₂²×M₁₆×C₃₁	C₂²	semidirect
37. D₄×Q₈×C₃₁	C₂²	semidirect
38. D₄×Q₈×C₃₁	C₂²	semidirect
49. C₂×C₃₁×C₄⋊Q₈	C₂²	semidirect
53. C₂×C₃₁×C₂²⋊Q₈	C₂²	semidirect
55. C₂×C₄×Q₈×C₃₁	C₂²	semidirect
59. C₃₁×#497	C₂²	semidirect
60. C₃₁×#494	C₂²	semidirect
61. C₃₁×#492	C₂²	semidirect
62. C₃₁×#470	C₂²	semidirect
63. C₃₁×#468	C₂²	semidirect
64. C₃₁×#467	C₂²	semidirect
65. C₃₁×#465	C₂²	semidirect
66. C₃₁×#464	C₂²	semidirect
67. C₃₁×#462	C₂²	semidirect
68. C₃₁×#462	C₂²	semidirect
69. C₃₁×#462	C₂²	semidirect
70. C₃₁×#461	C₂²	semidirect
71. C₃₁×#461	C₂²	semidirect
72. C₃₁×#460	C₂²	semidirect
73. C₃₁×#452	C₂²	semidirect
74. C₃₁×#452	C₂²	semidirect
75. C₃₁×#451	C₂²	semidirect
76. C₃₁×#451	C₂²	semidirect
77. C₃₁×#451	C₂²	semidirect
78. C₃₁×#450	C₂²	semidirect
79. C₃₁×#448	C₂²	semidirect
80. C₃₁×#448	C₂²	semidirect
81. C₃₁×#441	C₂²	semidirect
82. C₃₁×#440	C₂²	semidirect
83. C₄×Q₁₆×C₃₁	C₂²	semidirect
84. C₄×SD₁₆×C₃₁	C₂²	semidirect
85. C₃₁×#436	C₂²	semidirect
86. C₃₁×#435	C₂²	semidirect
88. C₃₁×#428	C₂²	semidirect
89. C₃₁×#423	C₂²	semidirect
90. C₃₁×#419	C₂²	semidirect
91. C₃₁×#419	C₂²	semidirect
93. C₃₁×#417	C₂²	semidirect
94. C₃₁×#407	C₂²	semidirect
95. C₄×M₁₆×C₃₁	C₂²	semidirect
127. C₃₁×#137	D₄	direct (N × H)
272. C₂×Q₈×C₃₁	C₂×D₄	semidirect
324. Q₁₆×C₃₁	C₂×D₄	semidirect
329. SD₁₆×C₃₁	C₂×D₄	semidirect
333. M₁₆×C₃₁	C₂×D₄	semidirect
383. D₄×#137	C₃₁	direct (N × H)
422. D₄×C₃₁	#137	direct (N × H)
465. C₂²×#137	C₂×C₃₁	semidirect
467. C₂×D₄×Q₈	C₂×C₃₁	semidirect
468. D₄×Q₁₆	C₂×C₃₁	semidirect
469. D₄×SD₁₆	C₂×C₃₁	semidirect
470. #3278	C₂×C₃₁	semidirect
471. #3276	C₂×C₃₁	semidirect
472. #3270	C₂×C₃₁	semidirect
473. #3266	C₂×C₃₁	semidirect
474. #3152	C₂×C₃₁	semidirect
475. #3056	C₂×C₃₁	semidirect
476. #3039	C₂×C₃₁	semidirect
477. #3037	C₂×C₃₁	semidirect
478. #3007	C₂×C₃₁	semidirect
479. #3004	C₂×C₃₁	semidirect
480. C₄×#137	C₂×C₃₁	semidirect
481. D₄×M₁₆	C₂×C₃₁	semidirect
498. C₂²×C₃₁	C₂×#137	semidirect
513. C₄×C₃₁	C₂×#137	semidirect
517. C₂³×Q₈	C₂²×C₃₁	semidirect
521. C₂×#137	C₂²×C₃₁	semidirect
522. C₂×#137	C₂²×C₃₁	semidirect
523. C₂×#137	C₂²×C₃₁	semidirect
524. C₂×#137	C₂²×C₃₁	semidirect
525. C₂×#137	C₂²×C₃₁	semidirect
526. C₂²×Q₁₆	C₂²×C₃₁	semidirect
527. C₂²×SD₁₆	C₂²×C₃₁	semidirect
528. C₂²×M₁₆	C₂²×C₃₁	semidirect
535. D₄×Q₈	C₂²×C₃₁	semidirect
536. D₄×Q₈	C₂²×C₃₁	semidirect
547. C₂×C₄⋊Q₈	C₂²×C₃₁	semidirect
551. C₂×C₂²⋊Q₈	C₂²×C₃₁	semidirect
553. C₂×C₄×Q₈	C₂²×C₃₁	semidirect
557. #497	C₂²×C₃₁	semidirect
558. #494	C₂²×C₃₁	semidirect
559. #492	C₂²×C₃₁	semidirect
560. #470	C₂²×C₃₁	semidirect
561. #468	C₂²×C₃₁	semidirect
562. #467	C₂²×C₃₁	semidirect
563. #465	C₂²×C₃₁	semidirect
564. #464	C₂²×C₃₁	semidirect
565. #462	C₂²×C₃₁	semidirect
566. #462	C₂²×C₃₁	semidirect
567. #462	C₂²×C₃₁	semidirect
568. #461	C₂²×C₃₁	semidirect
569. #461	C₂²×C₃₁	semidirect
570. #460	C₂²×C₃₁	semidirect
571. #452	C₂²×C₃₁	semidirect
572. #452	C₂²×C₃₁	semidirect
573. #451	C₂²×C₃₁	semidirect
574. #451	C₂²×C₃₁	semidirect
575. #451	C₂²×C₃₁	semidirect
576. #450	C₂²×C₃₁	semidirect
577. #448	C₂²×C₃₁	semidirect
578. #448	C₂²×C₃₁	semidirect
579. #441	C₂²×C₃₁	semidirect
580. #440	C₂²×C₃₁	semidirect
581. C₄×Q₁₆	C₂²×C₃₁	semidirect
582. C₄×SD₁₆	C₂²×C₃₁	semidirect
583. #436	C₂²×C₃₁	semidirect
584. #435	C₂²×C₃₁	semidirect
586. #428	C₂²×C₃₁	semidirect
587. #423	C₂²×C₃₁	semidirect
588. #419	C₂²×C₃₁	semidirect
589. #419	C₂²×C₃₁	semidirect
591. #417	C₂²×C₃₁	semidirect
592. #407	C₂²×C₃₁	semidirect
593. C₄×M₁₆	C₂²×C₃₁	semidirect
633. #137	D₄×C₃₁	direct (N × H)
749. C₃₁	D₄×#137	direct (N × H)
779. C₂×Q₈	C₂×D₄×C₃₁	semidirect
831. Q₁₆	C₂×D₄×C₃₁	semidirect
836. SD₁₆	C₂×D₄×C₃₁	semidirect
840. M₁₆	C₂×D₄×C₃₁	semidirect
928. D₄	C₃₁×#137	direct (N × H)
987. C₂²	C₂×C₃₁×#137	semidirect
1002. C₄	C₂×C₃₁×#137	semidirect

Maximal subgroups

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

subgroup	index
C₂²×C₃₁×#137	2
D₄×#41×C₃₁	2
C₂×D₄×Q₈×C₃₁	2
D₄×Q₁₆×C₃₁	2
D₄×SD₁₆×C₃₁	2
C₃₁×#3278	2
C₃₁×#3276	2
C₃₁×#3270	2
C₃₁×#3266	2
C₃₁×#3152	2
C₃₁×#3056	2
C₃₁×#3039	2
C₃₁×#3037	2
C₃₁×#3007	2
C₃₁×#3004	2
C₄×C₃₁×#137	2
D₄×M₁₆×C₃₁	2
D₄×#137	31

Subgroups — D4×C31×#137 #21517828

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₄×C₃₁×#137 #21517828