Subgroups — C₃₁×#3533 #16843466

Order 3968.

1060 conjugacy classes of subgroups.

The subgroup lattice has 596 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#563	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃₁×#562	C₂	1	2	yes	maximal, complemented
3	C₃₁×#560	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃₁×#559	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃₁×#553	C₂	1	2	yes	maximal, complemented
6	C₃₁×#552	C₂	1	2	yes	maximal, complemented
7	C₃₁×#551	C₂	1	2	yes	maximal, complemented
8	C₃₁×#551	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃₁×#547	C₂	1	2	yes	maximal, complemented
10	C₃₁×#546	C₂	1	2	yes	maximal, complemented
11	C₃₁×#542	C₂	1	2	yes	maximal, complemented
12	C₃₁×#540	C₂	1	2	yes	maximal, complemented
13	C₃₁×#539	C₂	1	2	yes	maximal, complemented
14	C₃₁×#538	C₂	1	2	yes	maximal, complemented
15	C₃₁×#538	C₂	1	2	yes	maximal, complemented
16	C₃₁×#535	C₂	1	1	yes	maximal, characteristic, complemented
17	C₃₁×#534	C₂	1	1	yes	maximal, characteristic, complemented
18	C₃₁×#525	C₂	1	2	yes	maximal, complemented
19	C₂×C₃₁×#123	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×#41×C₃₁	C₂²	1	2	yes	—
21	C₂×#41×C₃₁	C₂²	1	1	yes	characteristic, complemented
22	C₂²×D₄×C₃₁	C₂²	1	1	yes	characteristic
23	C₂²×D₄×C₃₁	C₂²	1	1	yes	characteristic
24	C₂³×C₄×C₃₁	C₂²	1	1	yes	characteristic, complemented
25	C₃₁×C₄⋊Q₈	C₂²	1	2	yes	complemented
26	C₃₁×#127	C₂²	1	1	yes	characteristic
27	C₃₁×#127	C₂²	1	1	yes	characteristic, complemented
28	C₃₁×#126	C₂²	1	2	yes	complemented
29	C₃₁×#126	C₂²	1	2	yes	complemented
30	C₃₁×#126	C₂²	1	2	yes	complemented
31	C₃₁×#126	C₂²	1	2	yes	complemented
32	C₃₁×#126	C₂²	1	2	yes	complemented
33	C₃₁×#126	C₂²	1	2	yes	complemented
34	C₃₁×#125	C₂²	1	2	yes	complemented
35	C₃₁×#125	C₂²	1	2	yes	complemented
36	C₃₁×#125	C₂²	1	2	yes	complemented
37	C₃₁×#124	C₂²	1	1	yes	characteristic
38	C₃₁×#124	C₂²	1	1	yes	characteristic, complemented
39	C₃₁×#124	C₂²	1	2	yes	complemented
40	C₃₁×#124	C₂²	1	2	yes	complemented
41	C₃₁×#124	C₂²	1	2	yes	complemented
42	C₃₁×#124	C₂²	1	2	yes	complemented
43	C₃₁×#123	C₂²	1	2	yes	—
44	C₃₁×#123	C₂²	1	1	yes	characteristic
45	C₃₁×#123	C₂²	1	1	yes	characteristic
46	C₃₁×#123	C₂²	1	2	yes	—
47	C₃₁×#123	C₂²	1	1	yes	characteristic
48	C₃₁×#123	C₂²	1	2	yes	—
49	C₃₁×#123	C₂²	1	1	yes	characteristic
50	C₃₁×#123	C₂²	1	2	yes	complemented
51	C₃₁×#123	C₂²	1	1	yes	characteristic, complemented
52	C₃₁×#123	C₂²	1	1	yes	characteristic, complemented
53	C₃₁×#123	C₂²	1	2	yes	complemented
54	C₃₁×#123	C₂²	1	2	yes	complemented
55	C₃₁×#123	C₂²	1	2	yes	complemented
56	C₃₁×#123	C₂²	1	2	yes	complemented
57	C₃₁×#123	C₂²	1	2	yes	complemented
58	C₃₁×#123	C₂²	1	2	yes	complemented
59	C₃₁×#123	C₂²	1	2	yes	complemented
60	C₃₁×#123	C₂²	1	2	yes	complemented
61	C₃₁×C₂²⋊Q₈	C₂²	1	2	yes	complemented
62	C₃₁×C₂²⋊Q₈	C₂²	1	2	yes	complemented
63	C₃₁×C₂²⋊Q₈	C₂²	1	2	yes	complemented
64	C₃₁×C₂²⋊Q₈	C₂²	1	2	yes	complemented
65	C₃₁×C₂²⋊Q₈	C₂²	1	2	yes	complemented
66	C₃₁×C₂²⋊Q₈	C₂²	1	2	yes	complemented
67	C₃₁×C₂²⋊Q₈	C₂²	1	2	yes	complemented
68	C₃₁×C₂²⋊Q₈	C₂²	1	2	yes	complemented
69	C₃₁×#121	C₂²	1	2	yes	—
70	C₃₁×#121	C₂²	1	2	yes	—
71	C₃₁×#121	C₂²	1	2	yes	—
72	C₃₁×#121	C₂²	1	2	yes	—
73	C₃₁×#121	C₂²	1	2	yes	complemented
74	C₃₁×#121	C₂²	1	2	yes	complemented
75	C₃₁×#121	C₂²	1	2	yes	complemented
76	C₃₁×#121	C₂²	1	2	yes	complemented
77	C₃₁×#121	C₂²	1	2	yes	complemented
78	C₃₁×#121	C₂²	1	2	yes	complemented
79	C₃₁×#121	C₂²	1	2	yes	complemented
80	C₃₁×#121	C₂²	1	2	yes	complemented
81	C₃₁×#120	C₂²	1	2	yes	—
82	C₃₁×#120	C₂²	1	1	yes	characteristic
83	C₃₁×#120	C₂²	1	1	yes	characteristic
84	C₃₁×#120	C₂²	1	2	yes	—
85	C₃₁×#120	C₂²	1	2	yes	complemented
86	C₃₁×#120	C₂²	1	2	yes	complemented
87	C₄×Q₈×C₃₁	C₂²	1	2	yes	complemented
88	C₄×D₄×C₃₁	C₂²	1	2	yes	—
89	C₄×D₄×C₃₁	C₂²	1	2	yes	complemented
90	C₄×D₄×C₃₁	C₂²	1	2	yes	complemented
91	C₄×D₄×C₃₁	C₂²	1	2	yes	complemented
92	C₄×D₄×C₃₁	C₂²	1	2	yes	complemented
93	C₄×D₄×C₃₁	C₂²	1	2	yes	complemented
94	C₄×D₄×C₃₁	C₂²	1	2	yes	complemented
95	C₄×D₄×C₃₁	C₂²	1	2	yes	complemented
96	C₄×D₄×C₃₁	C₂²	1	2	yes	complemented
97	C₃₁×#117	C₂²	1	2	yes	complemented
98	C₃₁×#117	C₂²	1	1	yes	characteristic, complemented
99	C₃₁×#117	C₂²	1	2	yes	complemented
100	C₃₁×#117	C₂²	1	2	yes	complemented
101	C₂×C₄⋊C₄×C₃₁	C₂²	1	2	yes	complemented
102	C₂×C₄⋊C₄×C₃₁	C₂²	1	2	yes	complemented
103	C₂×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	—
104	C₂×C₂²⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
105	C₂×C₂²⋊C₄×C₃₁	C₂²	1	1	yes	characteristic, complemented
106	C₂×C₂²⋊C₄×C₃₁	C₂²	1	2	yes	complemented
107	C₂⁴×C₃₁	C₂³	1	1	yes	characteristic
108	C₂⁴×C₃₁	C₂³	1	1	yes	characteristic
109	C₂⁴×C₃₁	C₂³	1	1	yes	characteristic
110	#41×C₃₁	—	4	4	no	—
111	#41×C₃₁	—	4	2	no	—
112	C₂×Q₈×C₃₁	C₂³	1	2	yes	—
113	C₂×Q₈×C₃₁	C₂³	1	2	yes	—
114	C₂×Q₈×C₃₁	C₂³	1	1	yes	characteristic
115	C₂×D₄×C₃₁	—	4	2	no	—
116	C₂×D₄×C₃₁	—	4	2	no	—
117	C₂×D₄×C₃₁	C₂³	1	2	yes	—
118	C₂×D₄×C₃₁	C₂³	1	2	yes	—
119	C₂×D₄×C₃₁	C₂³	1	2	yes	—
120	C₂×D₄×C₃₁	C₂³	1	2	yes	—
121	C₂×D₄×C₃₁	C₂³	1	2	yes	—
122	C₂×D₄×C₃₁	C₂³	1	2	yes	—
123	C₂×D₄×C₃₁	C₂³	1	2	yes	—
124	C₂×D₄×C₃₁	C₂³	1	2	yes	—
125	C₂×D₄×C₃₁	C₂³	1	2	yes	—
126	C₂×D₄×C₃₁	C₂³	1	1	yes	characteristic
127	C₂×D₄×C₃₁	C₂³	1	1	yes	characteristic
128	C₂×D₄×C₃₁	C₂³	1	2	yes	—
129	C₂×D₄×C₃₁	C₂³	1	1	yes	characteristic
130	C₂×D₄×C₃₁	C₂³	1	2	yes	—
131	C₂×D₄×C₃₁	C₂³	1	1	yes	characteristic
132	C₂×D₄×C₃₁	C₂³	1	1	yes	characteristic
133	C₂²×C₄×C₃₁	—	4	2	no	—
134	C₂²×C₄×C₃₁	C₂³	1	2	yes	—
135	C₂²×C₄×C₃₁	C₂³	1	1	yes	characteristic
136	C₂²×C₄×C₃₁	C₂³	1	2	yes	—
137	C₂²×C₄×C₃₁	C₂³	1	2	yes	—
138	C₂²×C₄×C₃₁	C₂³	1	2	yes	—
139	C₂²×C₄×C₃₁	C₂³	1	2	yes	—
140	C₂²×C₄×C₃₁	C₂³	1	2	yes	—
141	C₂²×C₄×C₃₁	C₂³	1	2	yes	—
142	C₂²×C₄×C₃₁	C₂³	1	2	yes	—
143	C₂²×C₄×C₃₁	C₂³	1	1	yes	characteristic
144	C₂²×C₄×C₃₁	C₂³	1	2	yes	—
145	C₂²×C₄×C₃₁	C₂³	1	1	yes	characteristic
146	C₂²×C₄×C₃₁	C₂³	1	1	yes	characteristic
147	C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
148	C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
149	C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
150	C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
151	C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
152	C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
153	C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
154	C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
155	C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
156	C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
157	C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
158	C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
159	C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
160	C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
161	C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
162	C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
163	C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
164	C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
165	C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
166	C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
167	C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
168	C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
169	C₂²⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
170	C₂²⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
171	C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
172	C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
173	C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
174	C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
175	C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
176	C₂²⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
177	C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
178	C₂²⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
179	C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
180	C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
181	C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
182	C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
183	C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
184	C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
185	C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
186	C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
187	C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
188	C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
189	C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
190	C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
191	C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
192	C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
193	C₄²×C₃₁	C₂³	1	1	yes	characteristic
194	C₄²×C₃₁	C₂³	1	2	yes	—
195	C₄²×C₃₁	C₂³	1	2	yes	—
196	C₄²×C₃₁	C₂³	1	2	yes	—
197	C₄²×C₃₁	C₂³	1	1	yes	characteristic
198	C₄²×C₃₁	C₂³	1	2	yes	—
199	C₂³×C₃₁	—	2	2	no	—
200	C₂³×C₃₁	—	2	2	no	—
201	C₂³×C₃₁	—	4	2	no	—
202	C₂³×C₃₁	—	4	1	no	—
203	C₂³×C₃₁	—	4	2	no	—
204	C₂³×C₃₁	—	4	2	no	—
205	C₂³×C₃₁	C₂⁴	1	1	yes	characteristic
206	C₂³×C₃₁	C₂⁴	1	1	yes	characteristic
207	C₂³×C₃₁	C₂⁴	1	1	yes	characteristic
208	C₂³×C₃₁	C₂⁴	1	2	yes	—
209	C₂³×C₃₁	C₂⁴	1	1	yes	characteristic
210	C₂³×C₃₁	C₂⁴	1	2	yes	—
211	C₂³×C₃₁	C₂⁴	1	1	yes	characteristic
212	Q₈×C₃₁	—	4	2	no	—
213	Q₈×C₃₁	—	4	2	no	—
214	Q₈×C₃₁	—	4	1	no	—
215	D₄×C₃₁	—	2	4	no	—
216	D₄×C₃₁	—	2	4	no	—
217	D₄×C₃₁	—	4	1	no	—
218	D₄×C₃₁	—	4	1	no	—
219	D₄×C₃₁	—	4	1	no	—
220	D₄×C₃₁	—	4	1	no	—
221	D₄×C₃₁	—	4	2	no	—
222	D₄×C₃₁	—	4	2	no	—
223	D₄×C₃₁	—	4	2	no	—
224	D₄×C₃₁	—	4	2	no	—
225	D₄×C₃₁	—	4	2	no	—
226	D₄×C₃₁	—	4	2	no	—
227	D₄×C₃₁	—	4	2	no	—
228	D₄×C₃₁	—	4	2	no	—
229	D₄×C₃₁	—	4	2	no	—
230	D₄×C₃₁	—	4	1	no	—
231	C₂×C₄×C₃₁	—	2	4	no	—
232	C₂×C₄×C₃₁	—	2	2	no	—
233	C₂×C₄×C₃₁	—	4	1	no	—
234	C₂×C₄×C₃₁	—	4	2	no	—
235	C₂×C₄×C₃₁	—	4	1	no	—
236	C₂×C₄×C₃₁	—	4	2	no	—
237	C₂×C₄×C₃₁	—	4	2	no	—
238	C₂×C₄×C₃₁	—	4	2	no	—
239	C₂×C₄×C₃₁	—	4	2	no	—
240	C₂×C₄×C₃₁	—	4	1	no	—
241	C₂×C₄×C₃₁	—	4	2	no	—
242	C₂×C₄×C₃₁	—	4	2	no	—
243	C₂×C₄×C₃₁	—	4	2	no	—
244	C₂×C₄×C₃₁	C₂⁴	1	2	yes	—
245	C₂×C₄×C₃₁	C₂⁴	1	2	yes	—
246	C₂×C₄×C₃₁	C₂⁴	1	2	yes	—
247	C₂×C₄×C₃₁	C₂⁴	1	2	yes	—
248	C₂×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
249	C₂×C₄×C₃₁	C₂⁴	1	2	yes	—
250	C₂×C₄×C₃₁	C₂⁴	1	2	yes	—
251	C₂×C₄×C₃₁	C₂⁴	1	2	yes	—
252	C₂×C₄×C₃₁	C₂⁴	1	2	yes	—
253	C₂×C₄×C₃₁	C₂⁴	1	2	yes	—
254	C₂×C₄×C₃₁	C₂⁴	1	2	yes	—
255	C₂×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
256	#3533	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
257	C₂²×C₃₁	—	2	2	no	—
258	C₂²×C₃₁	—	2	2	no	—
259	C₂²×C₃₁	—	2	1	no	—
260	C₂²×C₃₁	—	2	1	no	—
261	C₂²×C₃₁	—	2	2	no	—
262	C₂²×C₃₁	—	2	1	no	—
263	C₂²×C₃₁	—	2	1	no	—
264	C₂²×C₃₁	—	2	2	no	—
265	C₂²×C₃₁	—	2	2	no	—
266	C₂²×C₃₁	—	2	2	no	—
267	C₂²×C₃₁	—	2	2	no	—
268	C₂²×C₃₁	—	2	2	no	—
269	C₂²×C₃₁	—	2	2	no	—
270	C₂²×C₃₁	—	2	2	no	—
271	C₂²×C₃₁	—	2	2	no	—
272	C₂²×C₃₁	—	4	4	no	—
273	C₂²×C₃₁	—	8	2	no	—
274	C₂²×C₃₁	—	8	2	no	—
275	C₂²×C₃₁	H(5,𝔽₂)	1	2	yes	—
276	C₂²×C₃₁	C₂⁵	1	1	yes	characteristic
277	C₄×C₃₁	—	2	2	no	—
278	C₄×C₃₁	—	2	1	no	—
279	C₄×C₃₁	—	2	2	no	—
280	C₄×C₃₁	—	2	1	no	—
281	C₄×C₃₁	—	2	2	no	—
282	C₄×C₃₁	—	2	2	no	—
283	C₄×C₃₁	—	2	2	no	—
284	C₄×C₃₁	—	2	2	no	—
285	C₄×C₃₁	—	2	2	no	—
286	C₄×C₃₁	—	2	2	no	—
287	C₄×C₃₁	—	2	2	no	—
288	C₄×C₃₁	—	2	2	no	—
289	#563	C₂×C₃₁	1	1	yes	characteristic, complemented
290	#562	C₂×C₃₁	1	2	yes	complemented
291	#560	C₂×C₃₁	1	1	yes	characteristic, complemented
292	#559	C₂×C₃₁	1	1	yes	characteristic, complemented
293	#553	C₂×C₃₁	1	2	yes	complemented
294	#552	C₂×C₃₁	1	2	yes	complemented
295	#551	C₂×C₃₁	1	2	yes	complemented
296	#551	C₂×C₃₁	1	1	yes	characteristic, complemented
297	#547	C₂×C₃₁	1	2	yes	complemented
298	#546	C₂×C₃₁	1	2	yes	complemented
299	#542	C₂×C₃₁	1	2	yes	complemented
300	#540	C₂×C₃₁	1	2	yes	complemented
301	#539	C₂×C₃₁	1	2	yes	complemented
302	#538	C₂×C₃₁	1	2	yes	complemented
303	#538	C₂×C₃₁	1	2	yes	complemented
304	#535	C₂×C₃₁	1	1	yes	characteristic, complemented
305	#534	C₂×C₃₁	1	1	yes	characteristic, complemented
306	#525	C₂×C₃₁	1	2	yes	complemented
307	C₂×#123	C₂×C₃₁	1	1	yes	characteristic, complemented
308	C₂×C₃₁	—	2	2	no	—
309	C₂×C₃₁	—	4	2	no	—
310	C₂×C₃₁	—	4	1	no	—
311	C₂×C₃₁	—	4	1	no	—
312	C₂×C₃₁	—	4	2	no	—
313	C₂×C₃₁	—	4	1	no	—
314	C₂×C₃₁	—	4	1	no	—
315	C₂×C₃₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
316	C₂×C₃₁	#585	1	2	yes	—
317	C₂×#41	C₂²×C₃₁	1	2	yes	—
318	C₂×#41	C₂²×C₃₁	1	1	yes	characteristic, complemented
319	C₂²×D₄	C₂²×C₃₁	1	1	yes	characteristic
320	C₂²×D₄	C₂²×C₃₁	1	1	yes	characteristic
321	C₂³×C₄	C₂²×C₃₁	1	1	yes	characteristic, complemented
322	C₄⋊Q₈	C₂²×C₃₁	1	2	yes	complemented
323	#127	C₂²×C₃₁	1	1	yes	characteristic
324	#127	C₂²×C₃₁	1	1	yes	characteristic, complemented
325	#126	C₂²×C₃₁	1	2	yes	complemented
326	#126	C₂²×C₃₁	1	2	yes	complemented
327	#126	C₂²×C₃₁	1	2	yes	complemented
328	#126	C₂²×C₃₁	1	2	yes	complemented
329	#126	C₂²×C₃₁	1	2	yes	complemented
330	#126	C₂²×C₃₁	1	2	yes	complemented
331	#125	C₂²×C₃₁	1	2	yes	complemented
332	#125	C₂²×C₃₁	1	2	yes	complemented
333	#125	C₂²×C₃₁	1	2	yes	complemented
334	#124	C₂²×C₃₁	1	1	yes	characteristic
335	#124	C₂²×C₃₁	1	1	yes	characteristic, complemented
336	#124	C₂²×C₃₁	1	2	yes	complemented
337	#124	C₂²×C₃₁	1	2	yes	complemented
338	#124	C₂²×C₃₁	1	2	yes	complemented
339	#124	C₂²×C₃₁	1	2	yes	complemented
340	#123	C₂²×C₃₁	1	2	yes	—
341	#123	C₂²×C₃₁	1	1	yes	characteristic
342	#123	C₂²×C₃₁	1	1	yes	characteristic
343	#123	C₂²×C₃₁	1	2	yes	—
344	#123	C₂²×C₃₁	1	1	yes	characteristic
345	#123	C₂²×C₃₁	1	2	yes	—
346	#123	C₂²×C₃₁	1	1	yes	characteristic
347	#123	C₂²×C₃₁	1	2	yes	complemented
348	#123	C₂²×C₃₁	1	1	yes	characteristic, complemented
349	#123	C₂²×C₃₁	1	1	yes	characteristic, complemented
350	#123	C₂²×C₃₁	1	2	yes	complemented
351	#123	C₂²×C₃₁	1	2	yes	complemented
352	#123	C₂²×C₃₁	1	2	yes	complemented
353	#123	C₂²×C₃₁	1	2	yes	complemented
354	#123	C₂²×C₃₁	1	2	yes	complemented
355	#123	C₂²×C₃₁	1	2	yes	complemented
356	#123	C₂²×C₃₁	1	2	yes	complemented
357	#123	C₂²×C₃₁	1	2	yes	complemented
358	C₂²⋊Q₈	C₂²×C₃₁	1	2	yes	complemented
359	C₂²⋊Q₈	C₂²×C₃₁	1	2	yes	complemented
360	C₂²⋊Q₈	C₂²×C₃₁	1	2	yes	complemented
361	C₂²⋊Q₈	C₂²×C₃₁	1	2	yes	complemented
362	C₂²⋊Q₈	C₂²×C₃₁	1	2	yes	complemented
363	C₂²⋊Q₈	C₂²×C₃₁	1	2	yes	complemented
364	C₂²⋊Q₈	C₂²×C₃₁	1	2	yes	complemented
365	C₂²⋊Q₈	C₂²×C₃₁	1	2	yes	complemented
366	#121	C₂²×C₃₁	1	2	yes	—
367	#121	C₂²×C₃₁	1	2	yes	—
368	#121	C₂²×C₃₁	1	2	yes	—
369	#121	C₂²×C₃₁	1	2	yes	—
370	#121	C₂²×C₃₁	1	2	yes	complemented
371	#121	C₂²×C₃₁	1	2	yes	complemented
372	#121	C₂²×C₃₁	1	2	yes	complemented
373	#121	C₂²×C₃₁	1	2	yes	complemented
374	#121	C₂²×C₃₁	1	2	yes	complemented
375	#121	C₂²×C₃₁	1	2	yes	complemented
376	#121	C₂²×C₃₁	1	2	yes	complemented
377	#121	C₂²×C₃₁	1	2	yes	complemented
378	#120	C₂²×C₃₁	1	2	yes	—
379	#120	C₂²×C₃₁	1	1	yes	characteristic
380	#120	C₂²×C₃₁	1	1	yes	characteristic
381	#120	C₂²×C₃₁	1	2	yes	—
382	#120	C₂²×C₃₁	1	2	yes	complemented
383	#120	C₂²×C₃₁	1	2	yes	complemented
384	C₄×Q₈	C₂²×C₃₁	1	2	yes	complemented
385	C₄×D₄	C₂²×C₃₁	1	2	yes	—
386	C₄×D₄	C₂²×C₃₁	1	2	yes	complemented
387	C₄×D₄	C₂²×C₃₁	1	2	yes	complemented
388	C₄×D₄	C₂²×C₃₁	1	2	yes	complemented
389	C₄×D₄	C₂²×C₃₁	1	2	yes	complemented
390	C₄×D₄	C₂²×C₃₁	1	2	yes	complemented
391	C₄×D₄	C₂²×C₃₁	1	2	yes	complemented
392	C₄×D₄	C₂²×C₃₁	1	2	yes	complemented
393	C₄×D₄	C₂²×C₃₁	1	2	yes	complemented
394	#117	C₂²×C₃₁	1	2	yes	complemented
395	#117	C₂²×C₃₁	1	1	yes	characteristic, complemented
396	#117	C₂²×C₃₁	1	2	yes	complemented
397	#117	C₂²×C₃₁	1	2	yes	complemented
398	C₂×C₄⋊C₄	C₂²×C₃₁	1	2	yes	complemented
399	C₂×C₄⋊C₄	C₂²×C₃₁	1	2	yes	complemented
400	C₂×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	—
401	C₂×C₂²⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
402	C₂×C₂²⋊C₄	C₂²×C₃₁	1	1	yes	characteristic, complemented
403	C₂×C₂²⋊C₄	C₂²×C₃₁	1	2	yes	complemented
404	C₃₁	#3533	1	1	yes	characteristic, direct product factor, Sylow
405	C₂⁴	C₂³×C₃₁	1	1	yes	characteristic
406	C₂⁴	C₂³×C₃₁	1	1	yes	characteristic
407	C₂⁴	C₂³×C₃₁	1	1	yes	characteristic
408	#41	—	4	4	no	—
409	#41	—	4	2	no	—
410	C₂×Q₈	C₂³×C₃₁	1	2	yes	—
411	C₂×Q₈	C₂³×C₃₁	1	2	yes	—
412	C₂×Q₈	C₂³×C₃₁	1	1	yes	characteristic
413	C₂×D₄	—	4	2	no	—
414	C₂×D₄	—	4	2	no	—
415	C₂×D₄	C₂³×C₃₁	1	2	yes	—
416	C₂×D₄	C₂³×C₃₁	1	2	yes	—
417	C₂×D₄	C₂³×C₃₁	1	2	yes	—
418	C₂×D₄	C₂³×C₃₁	1	2	yes	—
419	C₂×D₄	C₂³×C₃₁	1	2	yes	—
420	C₂×D₄	C₂³×C₃₁	1	2	yes	—
421	C₂×D₄	C₂³×C₃₁	1	2	yes	—
422	C₂×D₄	C₂³×C₃₁	1	2	yes	—
423	C₂×D₄	C₂³×C₃₁	1	2	yes	—
424	C₂×D₄	C₂³×C₃₁	1	1	yes	characteristic
425	C₂×D₄	C₂³×C₃₁	1	1	yes	characteristic
426	C₂×D₄	C₂³×C₃₁	1	2	yes	—
427	C₂×D₄	C₂³×C₃₁	1	1	yes	characteristic
428	C₂×D₄	C₂³×C₃₁	1	2	yes	—
429	C₂×D₄	C₂³×C₃₁	1	1	yes	characteristic
430	C₂×D₄	C₂³×C₃₁	1	1	yes	characteristic
431	C₂²×C₄	—	4	2	no	—
432	C₂²×C₄	C₂³×C₃₁	1	2	yes	—
433	C₂²×C₄	C₂³×C₃₁	1	1	yes	characteristic
434	C₂²×C₄	C₂³×C₃₁	1	2	yes	—
435	C₂²×C₄	C₂³×C₃₁	1	2	yes	—
436	C₂²×C₄	C₂³×C₃₁	1	2	yes	—
437	C₂²×C₄	C₂³×C₃₁	1	2	yes	—
438	C₂²×C₄	C₂³×C₃₁	1	2	yes	—
439	C₂²×C₄	C₂³×C₃₁	1	2	yes	—
440	C₂²×C₄	C₂³×C₃₁	1	2	yes	—
441	C₂²×C₄	C₂³×C₃₁	1	1	yes	characteristic
442	C₂²×C₄	C₂³×C₃₁	1	2	yes	—
443	C₂²×C₄	C₂³×C₃₁	1	1	yes	characteristic
444	C₂²×C₄	C₂³×C₃₁	1	1	yes	characteristic
445	C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
446	C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
447	C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
448	C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
449	C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
450	C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
451	C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
452	C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
453	C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
454	C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
455	C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
456	C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
457	C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
458	C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
459	C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
460	C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
461	C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
462	C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
463	C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
464	C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
465	C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
466	C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
467	C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
468	C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
469	C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
470	C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
471	C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
472	C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
473	C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
474	C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
475	C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
476	C₂²⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
477	C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
478	C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
479	C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
480	C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
481	C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
482	C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
483	C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
484	C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
485	C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
486	C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
487	C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
488	C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
489	C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
490	C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
491	C₄²	C₂³×C₃₁	1	1	yes	characteristic
492	C₄²	C₂³×C₃₁	1	2	yes	—
493	C₄²	C₂³×C₃₁	1	2	yes	—
494	C₄²	C₂³×C₃₁	1	2	yes	—
495	C₄²	C₂³×C₃₁	1	1	yes	characteristic
496	C₄²	C₂³×C₃₁	1	2	yes	—
497	C₂³	—	2	2	no	—
498	C₂³	—	2	2	no	—
499	C₂³	—	4	2	no	—
500	C₂³	—	4	1	no	—
501	C₂³	—	4	2	no	—
502	C₂³	—	4	2	no	—
503	C₂³	C₂⁴×C₃₁	1	1	yes	characteristic
504	C₂³	C₂⁴×C₃₁	1	1	yes	characteristic
505	C₂³	C₂⁴×C₃₁	1	1	yes	characteristic
506	C₂³	C₂⁴×C₃₁	1	2	yes	—
507	C₂³	C₂⁴×C₃₁	1	1	yes	characteristic
508	C₂³	C₂⁴×C₃₁	1	2	yes	—
509	C₂³	C₂⁴×C₃₁	1	1	yes	characteristic
510	Q₈	—	4	2	no	—
511	Q₈	—	4	2	no	—
512	Q₈	—	4	1	no	—
513	D₄	—	2	4	no	—
514	D₄	—	2	4	no	—
515	D₄	—	4	1	no	—
516	D₄	—	4	1	no	—
517	D₄	—	4	1	no	—
518	D₄	—	4	1	no	—
519	D₄	—	4	2	no	—
520	D₄	—	4	2	no	—
521	D₄	—	4	2	no	—
522	D₄	—	4	2	no	—
523	D₄	—	4	2	no	—
524	D₄	—	4	2	no	—
525	D₄	—	4	2	no	—
526	D₄	—	4	2	no	—
527	D₄	—	4	2	no	—
528	D₄	—	4	1	no	—
529	C₂×C₄	—	2	4	no	—
530	C₂×C₄	—	2	2	no	—
531	C₂×C₄	—	4	1	no	—
532	C₂×C₄	—	4	2	no	—
533	C₂×C₄	—	4	1	no	—
534	C₂×C₄	—	4	2	no	—
535	C₂×C₄	—	4	2	no	—
536	C₂×C₄	—	4	2	no	—
537	C₂×C₄	—	4	2	no	—
538	C₂×C₄	—	4	1	no	—
539	C₂×C₄	—	4	2	no	—
540	C₂×C₄	—	4	2	no	—
541	C₂×C₄	—	4	2	no	—
542	C₂×C₄	C₂⁴×C₃₁	1	2	yes	—
543	C₂×C₄	C₂⁴×C₃₁	1	2	yes	—
544	C₂×C₄	C₂⁴×C₃₁	1	2	yes	—
545	C₂×C₄	C₂⁴×C₃₁	1	2	yes	—
546	C₂×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
547	C₂×C₄	C₂⁴×C₃₁	1	2	yes	—
548	C₂×C₄	C₂⁴×C₃₁	1	2	yes	—
549	C₂×C₄	C₂⁴×C₃₁	1	2	yes	—
550	C₂×C₄	C₂⁴×C₃₁	1	2	yes	—
551	C₂×C₄	C₂⁴×C₃₁	1	2	yes	—
552	C₂×C₄	C₂⁴×C₃₁	1	2	yes	—
553	C₂×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
554	C₂²	—	2	2	no	—
555	C₂²	—	2	2	no	—
556	C₂²	—	2	1	no	—
557	C₂²	—	2	1	no	—
558	C₂²	—	2	2	no	—
559	C₂²	—	2	1	no	—
560	C₂²	—	2	1	no	—
561	C₂²	—	2	2	no	—
562	C₂²	—	2	2	no	—
563	C₂²	—	2	2	no	—
564	C₂²	—	2	2	no	—
565	C₂²	—	2	2	no	—
566	C₂²	—	2	2	no	—
567	C₂²	—	2	2	no	—
568	C₂²	—	2	2	no	—
569	C₂²	—	4	4	no	—
570	C₂²	—	8	2	no	—
571	C₂²	—	8	2	no	—
572	C₂²	C₃₁×H(5,𝔽₂)	1	2	yes	—
573	C₂²	C₂⁵×C₃₁	1	1	yes	characteristic
574	C₄	—	2	2	no	—
575	C₄	—	2	1	no	—
576	C₄	—	2	2	no	—
577	C₄	—	2	1	no	—
578	C₄	—	2	2	no	—
579	C₄	—	2	2	no	—
580	C₄	—	2	2	no	—
581	C₄	—	2	2	no	—
582	C₄	—	2	2	no	—
583	C₄	—	2	2	no	—
584	C₄	—	2	2	no	—
585	C₄	—	2	2	no	—
586	C₂	—	2	2	no	—
587	C₂	—	4	1	no	—
588	C₂	—	4	1	no	—
589	C₂	—	4	1	no	—
590	C₂	—	4	2	no	—
591	C₂	—	4	1	no	—
592	C₂	—	4	2	no	—
593	C₂	C₂×C₃₁×H(5,𝔽₂)	1	1	yes	characteristic
594	C₂	C₃₁×#585	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₃₁	C₂⁵
commutator, Frattini, cosocle	C₂²	C₂⁵×C₃₁
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃₁×#563	C₂	semidirect
2. C₃₁×#562	C₂	semidirect
3. C₃₁×#560	C₂	semidirect
4. C₃₁×#559	C₂	semidirect
5. C₃₁×#553	C₂	semidirect
6. C₃₁×#552	C₂	semidirect
7. C₃₁×#551	C₂	semidirect
8. C₃₁×#551	C₂	semidirect
9. C₃₁×#547	C₂	semidirect
10. C₃₁×#546	C₂	semidirect
11. C₃₁×#542	C₂	semidirect
12. C₃₁×#540	C₂	semidirect
13. C₃₁×#539	C₂	semidirect
14. C₃₁×#538	C₂	semidirect
15. C₃₁×#538	C₂	semidirect
16. C₃₁×#535	C₂	semidirect
17. C₃₁×#534	C₂	semidirect
18. C₃₁×#525	C₂	semidirect
19. C₂×C₃₁×#123	C₂	semidirect
21. C₂×#41×C₃₁	C₂²	semidirect
24. C₂³×C₄×C₃₁	C₂²	semidirect
25. C₃₁×C₄⋊Q₈	C₂²	semidirect
27. C₃₁×#127	C₂²	semidirect
28. C₃₁×#126	C₂²	semidirect
29. C₃₁×#126	C₂²	semidirect
30. C₃₁×#126	C₂²	semidirect
31. C₃₁×#126	C₂²	semidirect
32. C₃₁×#126	C₂²	semidirect
33. C₃₁×#126	C₂²	semidirect
34. C₃₁×#125	C₂²	semidirect
35. C₃₁×#125	C₂²	semidirect
36. C₃₁×#125	C₂²	semidirect
38. C₃₁×#124	C₂²	semidirect
39. C₃₁×#124	C₂²	semidirect
40. C₃₁×#124	C₂²	semidirect
41. C₃₁×#124	C₂²	semidirect
42. C₃₁×#124	C₂²	semidirect
50. C₃₁×#123	C₂²	semidirect
51. C₃₁×#123	C₂²	semidirect
52. C₃₁×#123	C₂²	semidirect
53. C₃₁×#123	C₂²	semidirect
54. C₃₁×#123	C₂²	semidirect
55. C₃₁×#123	C₂²	semidirect
56. C₃₁×#123	C₂²	semidirect
57. C₃₁×#123	C₂²	semidirect
58. C₃₁×#123	C₂²	semidirect
59. C₃₁×#123	C₂²	semidirect
60. C₃₁×#123	C₂²	semidirect
61. C₃₁×C₂²⋊Q₈	C₂²	semidirect
62. C₃₁×C₂²⋊Q₈	C₂²	semidirect
63. C₃₁×C₂²⋊Q₈	C₂²	semidirect
64. C₃₁×C₂²⋊Q₈	C₂²	semidirect
65. C₃₁×C₂²⋊Q₈	C₂²	semidirect
66. C₃₁×C₂²⋊Q₈	C₂²	semidirect
67. C₃₁×C₂²⋊Q₈	C₂²	semidirect
68. C₃₁×C₂²⋊Q₈	C₂²	semidirect
73. C₃₁×#121	C₂²	semidirect
74. C₃₁×#121	C₂²	semidirect
75. C₃₁×#121	C₂²	semidirect
76. C₃₁×#121	C₂²	semidirect
77. C₃₁×#121	C₂²	semidirect
78. C₃₁×#121	C₂²	semidirect
79. C₃₁×#121	C₂²	semidirect
80. C₃₁×#121	C₂²	semidirect
85. C₃₁×#120	C₂²	semidirect
86. C₃₁×#120	C₂²	semidirect
87. C₄×Q₈×C₃₁	C₂²	semidirect
89. C₄×D₄×C₃₁	C₂²	semidirect
90. C₄×D₄×C₃₁	C₂²	semidirect
91. C₄×D₄×C₃₁	C₂²	semidirect
92. C₄×D₄×C₃₁	C₂²	semidirect
93. C₄×D₄×C₃₁	C₂²	semidirect
94. C₄×D₄×C₃₁	C₂²	semidirect
95. C₄×D₄×C₃₁	C₂²	semidirect
96. C₄×D₄×C₃₁	C₂²	semidirect
97. C₃₁×#117	C₂²	semidirect
98. C₃₁×#117	C₂²	semidirect
99. C₃₁×#117	C₂²	semidirect
100. C₃₁×#117	C₂²	semidirect
101. C₂×C₄⋊C₄×C₃₁	C₂²	semidirect
102. C₂×C₄⋊C₄×C₃₁	C₂²	semidirect
105. C₂×C₂²⋊C₄×C₃₁	C₂²	semidirect
106. C₂×C₂²⋊C₄×C₃₁	C₂²	semidirect
256. #3533	C₃₁	direct (N × H)
289. #563	C₂×C₃₁	semidirect
290. #562	C₂×C₃₁	semidirect
291. #560	C₂×C₃₁	semidirect
292. #559	C₂×C₃₁	semidirect
293. #553	C₂×C₃₁	semidirect
294. #552	C₂×C₃₁	semidirect
295. #551	C₂×C₃₁	semidirect
296. #551	C₂×C₃₁	semidirect
297. #547	C₂×C₃₁	semidirect
298. #546	C₂×C₃₁	semidirect
299. #542	C₂×C₃₁	semidirect
300. #540	C₂×C₃₁	semidirect
301. #539	C₂×C₃₁	semidirect
302. #538	C₂×C₃₁	semidirect
303. #538	C₂×C₃₁	semidirect
304. #535	C₂×C₃₁	semidirect
305. #534	C₂×C₃₁	semidirect
306. #525	C₂×C₃₁	semidirect
307. C₂×#123	C₂×C₃₁	semidirect
318. C₂×#41	C₂²×C₃₁	semidirect
321. C₂³×C₄	C₂²×C₃₁	semidirect
322. C₄⋊Q₈	C₂²×C₃₁	semidirect
324. #127	C₂²×C₃₁	semidirect
325. #126	C₂²×C₃₁	semidirect
326. #126	C₂²×C₃₁	semidirect
327. #126	C₂²×C₃₁	semidirect
328. #126	C₂²×C₃₁	semidirect
329. #126	C₂²×C₃₁	semidirect
330. #126	C₂²×C₃₁	semidirect
331. #125	C₂²×C₃₁	semidirect
332. #125	C₂²×C₃₁	semidirect
333. #125	C₂²×C₃₁	semidirect
335. #124	C₂²×C₃₁	semidirect
336. #124	C₂²×C₃₁	semidirect
337. #124	C₂²×C₃₁	semidirect
338. #124	C₂²×C₃₁	semidirect
339. #124	C₂²×C₃₁	semidirect
347. #123	C₂²×C₃₁	semidirect
348. #123	C₂²×C₃₁	semidirect
349. #123	C₂²×C₃₁	semidirect
350. #123	C₂²×C₃₁	semidirect
351. #123	C₂²×C₃₁	semidirect
352. #123	C₂²×C₃₁	semidirect
353. #123	C₂²×C₃₁	semidirect
354. #123	C₂²×C₃₁	semidirect
355. #123	C₂²×C₃₁	semidirect
356. #123	C₂²×C₃₁	semidirect
357. #123	C₂²×C₃₁	semidirect
358. C₂²⋊Q₈	C₂²×C₃₁	semidirect
359. C₂²⋊Q₈	C₂²×C₃₁	semidirect
360. C₂²⋊Q₈	C₂²×C₃₁	semidirect
361. C₂²⋊Q₈	C₂²×C₃₁	semidirect
362. C₂²⋊Q₈	C₂²×C₃₁	semidirect
363. C₂²⋊Q₈	C₂²×C₃₁	semidirect
364. C₂²⋊Q₈	C₂²×C₃₁	semidirect
365. C₂²⋊Q₈	C₂²×C₃₁	semidirect
370. #121	C₂²×C₃₁	semidirect
371. #121	C₂²×C₃₁	semidirect
372. #121	C₂²×C₃₁	semidirect
373. #121	C₂²×C₃₁	semidirect
374. #121	C₂²×C₃₁	semidirect
375. #121	C₂²×C₃₁	semidirect
376. #121	C₂²×C₃₁	semidirect
377. #121	C₂²×C₃₁	semidirect
382. #120	C₂²×C₃₁	semidirect
383. #120	C₂²×C₃₁	semidirect
384. C₄×Q₈	C₂²×C₃₁	semidirect
386. C₄×D₄	C₂²×C₃₁	semidirect
387. C₄×D₄	C₂²×C₃₁	semidirect
388. C₄×D₄	C₂²×C₃₁	semidirect
389. C₄×D₄	C₂²×C₃₁	semidirect
390. C₄×D₄	C₂²×C₃₁	semidirect
391. C₄×D₄	C₂²×C₃₁	semidirect
392. C₄×D₄	C₂²×C₃₁	semidirect
393. C₄×D₄	C₂²×C₃₁	semidirect
394. #117	C₂²×C₃₁	semidirect
395. #117	C₂²×C₃₁	semidirect
396. #117	C₂²×C₃₁	semidirect
397. #117	C₂²×C₃₁	semidirect
398. C₂×C₄⋊C₄	C₂²×C₃₁	semidirect
399. C₂×C₄⋊C₄	C₂²×C₃₁	semidirect
402. C₂×C₂²⋊C₄	C₂²×C₃₁	semidirect
403. C₂×C₂²⋊C₄	C₂²×C₃₁	semidirect
404. C₃₁	#3533	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃₁×#563	2
C₃₁×#562	2
C₃₁×#560	2
C₃₁×#559	2
C₃₁×#553	2
C₃₁×#552	2
C₃₁×#551	2
C₃₁×#547	2
C₃₁×#546	2
C₃₁×#542	2
C₃₁×#540	2
C₃₁×#539	2
C₃₁×#538	2
C₃₁×#535	2
C₃₁×#534	2
C₃₁×#525	2
C₂×C₃₁×#123	2
#3533	31

Subgroups — C31×#3533 #16843466

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#3533 #16843466