Subgroups — C₂×C₃₁×#1979 #21478006

Order 7936.

1438 conjugacy classes of subgroups.

The subgroup lattice has 404 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×Q₁₆×C₃₁	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₃₁×#108	C₂	1	1	yes	maximal, characteristic
3	C₂×C₃₁×#419	C₂	1	2	yes	maximal
4	C₂²×C₃₁×#101	C₂	1	2	yes	maximal
5	C₂×C₃₁×#405	C₂	1	1	yes	maximal, characteristic
6	C₃₁×#1979	C₂	1	8	yes	maximal, direct product factor
7	C₂³×Q₈×C₃₁	C₂²	1	2	yes	—
8	C₂²×Q₁₆×C₃₁	—	2	1	no	—
9	C₂²×Q₁₆×C₃₁	—	2	1	no	—
10	C₂²×Q₁₆×C₃₁	—	2	2	no	—
11	C₂²×Q₁₆×C₃₁	—	2	4	no	—
12	C₂²×Q₁₆×C₃₁	C₄	1	8	yes	complemented
13	C₂²×Q₁₆×C₃₁	C₂²	1	4	yes	—
14	C₂²×M₁₆×C₃₁	C₂²	1	2	yes	—
15	C₂²×M₁₆×C₃₁	C₂²	1	1	yes	characteristic
16	C₂³×C₈×C₃₁	C₂²	1	1	yes	characteristic
17	C₂×C₃₁×#117	C₂²	1	1	yes	characteristic
18	C₂×C₃₁×#108	—	2	4	no	—
19	C₂×C₃₁×#108	C₂²	1	4	yes	—
20	C₃₁×#419	—	2	4	no	—
21	C₃₁×#419	C₂²	1	8	yes	—
22	C₂×C₃₁×#103	—	2	4	no	—
23	C₂×C₃₁×#101	—	2	8	no	—
24	C₂×C₃₁×#101	C₂²	1	8	yes	—
25	C₃₁×#405	—	2	2	no	—
26	C₃₁×#405	C₂²	1	4	yes	—
27	C₂×C₃₁×#97	—	2	1	no	—
28	C₂×C₄×C₈×C₃₁	—	2	1	no	—
29	C₂²×Q₈×C₃₁	—	2	4	no	—
30	C₂²×Q₈×C₃₁	—	2	2	no	—
31	C₂²×Q₈×C₃₁	—	2	2	no	—
32	C₂²×Q₈×C₃₁	—	2	2	no	—
33	C₂²×Q₈×C₃₁	—	2	2	no	—
34	C₂²×Q₈×C₃₁	—	2	2	no	—
35	C₂²×Q₈×C₃₁	—	2	4	no	—
36	C₂²×Q₈×C₃₁	—	2	4	no	—
37	C₂²×Q₈×C₃₁	C₂×C₄	1	8	yes	—
38	C₂²×Q₈×C₃₁	C₂³	1	4	yes	—
39	C₂³×C₄×C₃₁	—	2	2	no	—
40	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
41	C₂×Q₁₆×C₃₁	—	2	8	no	—
42	C₂×Q₁₆×C₃₁	—	2	8	no	—
43	C₂×Q₁₆×C₃₁	—	2	16	no	—
44	C₂×Q₁₆×C₃₁	—	2	4	no	—
45	C₂×Q₁₆×C₃₁	—	2	4	no	—
46	C₂×Q₁₆×C₃₁	—	2	8	no	—
47	C₂×Q₁₆×C₃₁	C₂×C₄	1	16	yes	complemented
48	C₂×M₁₆×C₃₁	—	2	1	no	—
49	C₂×M₁₆×C₃₁	—	2	2	no	—
50	C₂×M₁₆×C₃₁	—	2	2	no	—
51	C₂×M₁₆×C₃₁	—	2	4	no	—
52	C₂×M₁₆×C₃₁	—	2	4	no	—
53	C₂×M₁₆×C₃₁	D₄	1	4	yes	—
54	C₂×M₁₆×C₃₁	C₂³	1	4	yes	—
55	C₂×M₁₆×C₃₁	C₂³	1	2	yes	—
56	C₂²×C₈×C₃₁	—	2	1	no	—
57	C₂²×C₈×C₃₁	—	2	2	no	—
58	C₂²×C₈×C₃₁	C₂×C₄	1	4	yes	—
59	C₂²×C₈×C₃₁	D₄	1	1	yes	characteristic
60	C₂²×C₈×C₃₁	D₄	1	1	yes	characteristic
61	C₂²×C₈×C₃₁	D₄	1	2	yes	—
62	C₂²×C₈×C₃₁	D₄	1	4	yes	—
63	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
64	C₃₁×#117	—	2	1	no	—
65	C₃₁×#117	—	2	1	no	—
66	C₃₁×#117	D₄	1	2	yes	—
67	C₃₁×#117	C₂³	1	2	yes	—
68	C₂×C₄⋊C₄×C₃₁	D₄	1	2	yes	—
69	C₂×C₂²⋊C₄×C₃₁	—	2	1	no	—
70	C₂×C₄²×C₃₁	—	2	1	no	—
71	C₃₁×#108	—	2	8	no	—
72	C₃₁×#103	—	2	16	no	—
73	C₃₁×#101	—	2	16	no	—
74	C₃₁×#97	—	2	4	no	—
75	C₄×C₈×C₃₁	—	2	4	no	—
76	C₂⁴×C₃₁	#41	1	1	yes	characteristic
77	C₂×Q₈×C₃₁	—	2	8	no	—
78	C₂×Q₈×C₃₁	—	2	4	no	—
79	C₂×Q₈×C₃₁	—	2	8	no	—
80	C₂×Q₈×C₃₁	—	2	8	no	—
81	C₂×Q₈×C₃₁	—	2	8	no	—
82	C₂×Q₈×C₃₁	—	2	8	no	—
83	C₂×Q₈×C₃₁	—	2	4	no	—
84	C₂×Q₈×C₃₁	—	2	4	no	—
85	C₂×Q₈×C₃₁	—	2	4	no	—
86	C₂×Q₈×C₃₁	—	2	4	no	—
87	C₂×Q₈×C₃₁	—	4	2	no	—
88	C₂×Q₈×C₃₁	—	4	2	no	—
89	C₂×Q₈×C₃₁	—	4	4	no	—
90	C₂×Q₈×C₃₁	—	4	4	no	—
91	C₂×Q₈×C₃₁	—	4	4	no	—
92	C₂×Q₈×C₃₁	—	4	4	no	—
93	C₂×Q₈×C₃₁	—	4	4	no	—
94	C₂×Q₈×C₃₁	C₂²×C₄	1	8	yes	—
95	C₂²×C₄×C₃₁	—	2	8	no	—
96	C₂²×C₄×C₃₁	—	2	2	no	—
97	C₂²×C₄×C₃₁	—	2	4	no	—
98	C₂²×C₄×C₃₁	—	4	2	no	—
99	C₂²×C₄×C₃₁	—	4	2	no	—
100	C₂²×C₄×C₃₁	—	4	4	no	—
101	C₂²×C₄×C₃₁	C₂²×C₄	1	2	yes	—
102	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
103	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
104	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
105	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
106	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
107	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
108	C₂²×C₄×C₃₁	#41	1	1	yes	characteristic
109	C₂²×C₄×C₃₁	#41	1	2	yes	—
110	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
111	Q₁₆×C₃₁	—	2	16	no	—
112	Q₁₆×C₃₁	—	2	16	no	—
113	M₁₆×C₃₁	—	2	4	no	—
114	M₁₆×C₃₁	—	2	2	no	—
115	M₁₆×C₃₁	—	2	4	no	—
116	M₁₆×C₃₁	—	2	4	no	—
117	M₁₆×C₃₁	—	4	4	no	—
118	M₁₆×C₃₁	C₂×D₄	1	4	yes	—
119	C₂×C₈×C₃₁	—	2	4	no	—
120	C₂×C₈×C₃₁	—	2	2	no	—
121	C₂×C₈×C₃₁	—	2	4	no	—
122	C₂×C₈×C₃₁	—	4	4	no	—
123	C₂×C₈×C₃₁	C₂²⋊C₄	1	4	yes	—
124	C₂×C₈×C₃₁	C₂²⋊C₄	1	4	yes	—
125	C₂×C₈×C₃₁	C₂²⋊C₄	1	8	yes	—
126	C₂×C₈×C₃₁	C₂²×C₄	1	4	yes	—
127	C₂×C₈×C₃₁	C₂×D₄	1	2	yes	—
128	C₂×C₈×C₃₁	C₂×D₄	1	2	yes	—
129	C₂×C₈×C₃₁	C₂×D₄	1	4	yes	—
130	C₄⋊C₄×C₃₁	—	2	2	no	—
131	C₄⋊C₄×C₃₁	C₂×D₄	1	4	yes	—
132	C₂²⋊C₄×C₃₁	—	2	2	no	—
133	C₂²⋊C₄×C₃₁	—	2	2	no	—
134	C₄²×C₃₁	—	2	2	no	—
135	C₄²×C₃₁	—	2	2	no	—
136	C₂×#1979	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
137	C₂³×C₃₁	—	2	4	no	—
138	C₂³×C₃₁	C₄×D₄	1	2	yes	—
139	C₂³×C₃₁	#121	1	1	yes	characteristic
140	C₂³×C₃₁	#121	1	1	yes	characteristic
141	C₂³×C₃₁	#124	1	2	yes	—
142	C₂³×C₃₁	C₂×#41	1	1	yes	characteristic
143	Q₈×C₃₁	—	2	8	no	—
144	Q₈×C₃₁	—	2	8	no	—
145	Q₈×C₃₁	—	4	4	no	—
146	Q₈×C₃₁	—	4	4	no	—
147	Q₈×C₃₁	—	4	8	no	—
148	Q₈×C₃₁	—	4	8	no	—
149	C₂×C₄×C₃₁	—	2	8	no	—
150	C₂×C₄×C₃₁	—	2	4	no	—
151	C₂×C₄×C₃₁	—	4	4	no	—
152	C₂×C₄×C₃₁	—	4	4	no	—
153	C₂×C₄×C₃₁	—	4	8	no	—
154	C₂×C₄×C₃₁	—	4	8	no	—
155	C₂×C₄×C₃₁	—	4	4	no	—
156	C₂×C₄×C₃₁	C₂×C₂²⋊C₄	1	2	yes	—
157	C₂×C₄×C₃₁	C₂×C₂²⋊C₄	1	2	yes	—
158	C₂×C₄×C₃₁	C₄×D₄	1	2	yes	—
159	C₂×C₄×C₃₁	C₄×D₄	1	2	yes	—
160	C₂×C₄×C₃₁	C₄×D₄	1	2	yes	—
161	C₂×C₄×C₃₁	#121	1	2	yes	—
162	C₂×C₄×C₃₁	#121	1	2	yes	—
163	C₂×C₄×C₃₁	#121	1	1	yes	characteristic
164	C₂×C₄×C₃₁	#121	1	1	yes	characteristic
165	C₂×C₄×C₃₁	#124	1	2	yes	—
166	C₂×C₄×C₃₁	#127	1	2	yes	—
167	C₂×C₄×C₃₁	#127	1	2	yes	—
168	C₂×C₄×C₃₁	C₂³×C₄	1	1	yes	characteristic
169	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
170	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
171	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
172	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
173	C₂×C₄×C₃₁	C₂×#41	1	1	yes	characteristic
174	C₈×C₃₁	—	2	4	no	—
175	C₈×C₃₁	—	4	4	no	—
176	C₈×C₃₁	C₂×C₂²⋊C₄	1	4	yes	—
177	C₈×C₃₁	C₂×C₂²⋊C₄	1	4	yes	—
178	C₂³×Q₁₆	C₂×C₃₁	1	1	yes	characteristic
179	C₂²×#108	C₂×C₃₁	1	1	yes	characteristic
180	C₂×#419	C₂×C₃₁	1	2	yes	—
181	C₂²×#101	C₂×C₃₁	1	2	yes	—
182	C₂×#405	C₂×C₃₁	1	1	yes	characteristic
183	#1979	C₂×C₃₁	1	8	yes	direct product factor
184	C₂²×C₃₁	—	2	4	no	—
185	C₂²×C₃₁	—	2	4	no	—
186	C₂²×C₃₁	—	2	2	no	—
187	C₂²×C₃₁	—	2	2	no	—
188	C₂²×C₃₁	#390	1	2	yes	—
189	C₂²×C₃₁	#390	1	2	yes	—
190	C₂²×C₃₁	#473	1	4	yes	—
191	C₂²×C₃₁	C₂×C₄×D₄	1	1	yes	characteristic
192	C₂²×C₃₁	C₂×#121	1	1	yes	characteristic
193	C₂²×C₃₁	C₂×#124	1	1	yes	characteristic
194	C₄×C₃₁	—	4	8	no	—
195	C₄×C₃₁	—	4	4	no	—
196	C₄×C₃₁	#390	1	2	yes	—
197	C₄×C₃₁	#390	1	2	yes	—
198	C₄×C₃₁	C₂²×C₂²⋊C₄	1	1	yes	characteristic
199	C₄×C₃₁	C₂×C₄×D₄	1	1	yes	characteristic
200	C₄×C₃₁	C₂×#121	1	1	yes	characteristic
201	C₄×C₃₁	C₂×#127	1	1	yes	characteristic
202	C₂³×Q₈	C₂²×C₃₁	1	2	yes	—
203	C₂²×Q₁₆	—	2	1	no	—
204	C₂²×Q₁₆	—	2	1	no	—
205	C₂²×Q₁₆	—	2	2	no	—
206	C₂²×Q₁₆	—	2	4	no	—
207	C₂²×Q₁₆	C₄×C₃₁	1	8	yes	complemented
208	C₂²×Q₁₆	C₂²×C₃₁	1	4	yes	—
209	C₂²×M₁₆	C₂²×C₃₁	1	2	yes	—
210	C₂²×M₁₆	C₂²×C₃₁	1	1	yes	characteristic
211	C₂³×C₈	C₂²×C₃₁	1	1	yes	characteristic
212	C₂×#117	C₂²×C₃₁	1	1	yes	characteristic
213	C₂×#108	—	2	4	no	—
214	C₂×#108	C₂²×C₃₁	1	4	yes	—
215	#419	—	2	4	no	—
216	#419	C₂²×C₃₁	1	8	yes	—
217	C₂×#103	—	2	4	no	—
218	C₂×#101	—	2	8	no	—
219	C₂×#101	C₂²×C₃₁	1	8	yes	—
220	#405	—	2	2	no	—
221	#405	C₂²×C₃₁	1	4	yes	—
222	C₂×#97	—	2	1	no	—
223	C₂×C₄×C₈	—	2	1	no	—
224	C₂×C₃₁	—	2	1	no	—
225	C₂×C₃₁	—	2	1	no	—
226	C₂×C₃₁	—	2	2	no	—
227	C₂×C₃₁	#1979	1	4	yes	direct product factor
228	C₂×C₃₁	C₂×#390	1	1	yes	characteristic
229	C₂×C₃₁	C₂×#473	1	2	yes	—
230	C₂²×Q₈	—	2	4	no	—
231	C₂²×Q₈	—	2	2	no	—
232	C₂²×Q₈	—	2	2	no	—
233	C₂²×Q₈	—	2	2	no	—
234	C₂²×Q₈	—	2	4	no	—
235	C₂²×Q₈	—	2	2	no	—
236	C₂²×Q₈	—	2	2	no	—
237	C₂²×Q₈	—	2	4	no	—
238	C₂²×Q₈	C₂×C₄×C₃₁	1	8	yes	—
239	C₂²×Q₈	C₂³×C₃₁	1	4	yes	—
240	C₂³×C₄	—	2	2	no	—
241	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
242	C₂×Q₁₆	—	2	8	no	—
243	C₂×Q₁₆	—	2	8	no	—
244	C₂×Q₁₆	—	2	16	no	—
245	C₂×Q₁₆	—	2	4	no	—
246	C₂×Q₁₆	—	2	4	no	—
247	C₂×Q₁₆	—	2	8	no	—
248	C₂×Q₁₆	C₂×C₄×C₃₁	1	16	yes	complemented
249	C₂×M₁₆	—	2	1	no	—
250	C₂×M₁₆	—	2	2	no	—
251	C₂×M₁₆	—	2	2	no	—
252	C₂×M₁₆	—	2	4	no	—
253	C₂×M₁₆	—	2	4	no	—
254	C₂×M₁₆	D₄×C₃₁	1	4	yes	—
255	C₂×M₁₆	C₂³×C₃₁	1	4	yes	—
256	C₂×M₁₆	C₂³×C₃₁	1	2	yes	—
257	C₂²×C₈	—	2	1	no	—
258	C₂²×C₈	—	2	2	no	—
259	C₂²×C₈	C₂×C₄×C₃₁	1	4	yes	—
260	C₂²×C₈	D₄×C₃₁	1	1	yes	characteristic
261	C₂²×C₈	D₄×C₃₁	1	1	yes	characteristic
262	C₂²×C₈	D₄×C₃₁	1	2	yes	—
263	C₂²×C₈	D₄×C₃₁	1	4	yes	—
264	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
265	#117	—	2	1	no	—
266	#117	—	2	1	no	—
267	#117	D₄×C₃₁	1	2	yes	—
268	#117	C₂³×C₃₁	1	2	yes	—
269	C₂×C₄⋊C₄	D₄×C₃₁	1	2	yes	—
270	C₂×C₂²⋊C₄	—	2	1	no	—
271	C₂×C₄²	—	2	1	no	—
272	#108	—	2	8	no	—
273	#103	—	2	16	no	—
274	#101	—	2	16	no	—
275	#97	—	2	4	no	—
276	C₄×C₈	—	2	4	no	—
277	C₃₁	C₂×#1979	1	1	yes	characteristic, direct product factor, Sylow
278	C₂⁴	#41×C₃₁	1	1	yes	characteristic
279	C₂×Q₈	—	2	8	no	—
280	C₂×Q₈	—	2	4	no	—
281	C₂×Q₈	—	2	8	no	—
282	C₂×Q₈	—	2	8	no	—
283	C₂×Q₈	—	2	8	no	—
284	C₂×Q₈	—	2	8	no	—
285	C₂×Q₈	—	2	4	no	—
286	C₂×Q₈	—	2	4	no	—
287	C₂×Q₈	—	2	4	no	—
288	C₂×Q₈	—	2	4	no	—
289	C₂×Q₈	—	4	2	no	—
290	C₂×Q₈	—	4	2	no	—
291	C₂×Q₈	—	4	4	no	—
292	C₂×Q₈	—	4	4	no	—
293	C₂×Q₈	—	4	4	no	—
294	C₂×Q₈	—	4	4	no	—
295	C₂×Q₈	—	4	4	no	—
296	C₂×Q₈	C₂²×C₄×C₃₁	1	8	yes	—
297	C₂²×C₄	—	2	8	no	—
298	C₂²×C₄	—	2	2	no	—
299	C₂²×C₄	—	2	4	no	—
300	C₂²×C₄	—	4	2	no	—
301	C₂²×C₄	—	4	2	no	—
302	C₂²×C₄	—	4	4	no	—
303	C₂²×C₄	C₂²×C₄×C₃₁	1	2	yes	—
304	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
305	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
306	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
307	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
308	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
309	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
310	C₂²×C₄	#41×C₃₁	1	1	yes	characteristic
311	C₂²×C₄	#41×C₃₁	1	2	yes	—
312	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
313	Q₁₆	—	2	16	no	—
314	Q₁₆	—	2	16	no	—
315	M₁₆	—	2	4	no	—
316	M₁₆	—	2	2	no	—
317	M₁₆	—	2	4	no	—
318	M₁₆	—	2	4	no	—
319	M₁₆	—	4	4	no	—
320	M₁₆	C₂×D₄×C₃₁	1	4	yes	—
321	C₂×C₈	—	2	4	no	—
322	C₂×C₈	—	2	2	no	—
323	C₂×C₈	—	2	4	no	—
324	C₂×C₈	—	4	4	no	—
325	C₂×C₈	C₂²⋊C₄×C₃₁	1	4	yes	—
326	C₂×C₈	C₂²⋊C₄×C₃₁	1	4	yes	—
327	C₂×C₈	C₂²⋊C₄×C₃₁	1	8	yes	—
328	C₂×C₈	C₂²×C₄×C₃₁	1	4	yes	—
329	C₂×C₈	C₂×D₄×C₃₁	1	2	yes	—
330	C₂×C₈	C₂×D₄×C₃₁	1	2	yes	—
331	C₂×C₈	C₂×D₄×C₃₁	1	4	yes	—
332	C₄⋊C₄	—	2	2	no	—
333	C₄⋊C₄	C₂×D₄×C₃₁	1	4	yes	—
334	C₂²⋊C₄	—	2	2	no	—
335	C₂²⋊C₄	—	2	2	no	—
336	C₄²	—	2	2	no	—
337	C₄²	—	2	2	no	—
338	C₂³	—	2	4	no	—
339	C₂³	C₄×D₄×C₃₁	1	2	yes	—
340	C₂³	C₃₁×#121	1	1	yes	characteristic
341	C₂³	C₃₁×#121	1	1	yes	characteristic
342	C₂³	C₃₁×#124	1	2	yes	—
343	C₂³	C₂×#41×C₃₁	1	1	yes	characteristic
344	Q₈	—	2	8	no	—
345	Q₈	—	2	8	no	—
346	Q₈	—	4	4	no	—
347	Q₈	—	4	4	no	—
348	Q₈	—	4	8	no	—
349	Q₈	—	4	8	no	—
350	C₂×C₄	—	2	8	no	—
351	C₂×C₄	—	2	4	no	—
352	C₂×C₄	—	4	4	no	—
353	C₂×C₄	—	4	4	no	—
354	C₂×C₄	—	4	4	no	—
355	C₂×C₄	—	4	8	no	—
356	C₂×C₄	—	4	8	no	—
357	C₂×C₄	C₂×C₂²⋊C₄×C₃₁	1	2	yes	—
358	C₂×C₄	C₂×C₂²⋊C₄×C₃₁	1	2	yes	—
359	C₂×C₄	C₄×D₄×C₃₁	1	2	yes	—
360	C₂×C₄	C₄×D₄×C₃₁	1	2	yes	—
361	C₂×C₄	C₄×D₄×C₃₁	1	2	yes	—
362	C₂×C₄	C₃₁×#121	1	2	yes	—
363	C₂×C₄	C₃₁×#121	1	2	yes	—
364	C₂×C₄	C₃₁×#121	1	1	yes	characteristic
365	C₂×C₄	C₃₁×#121	1	1	yes	characteristic
366	C₂×C₄	C₃₁×#124	1	2	yes	—
367	C₂×C₄	C₃₁×#127	1	2	yes	—
368	C₂×C₄	C₃₁×#127	1	2	yes	—
369	C₂×C₄	C₂³×C₄×C₃₁	1	1	yes	characteristic
370	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
371	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
372	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
373	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
374	C₂×C₄	C₂×#41×C₃₁	1	1	yes	characteristic
375	C₈	—	2	4	no	—
376	C₈	—	4	4	no	—
377	C₈	C₂×C₂²⋊C₄×C₃₁	1	4	yes	—
378	C₈	C₂×C₂²⋊C₄×C₃₁	1	4	yes	—
379	C₂²	—	2	4	no	—
380	C₂²	—	2	4	no	—
381	C₂²	—	2	2	no	—
382	C₂²	—	2	2	no	—
383	C₂²	C₃₁×#390	1	2	yes	—
384	C₂²	C₃₁×#390	1	2	yes	—
385	C₂²	C₃₁×#473	1	4	yes	—
386	C₂²	C₂×C₄×D₄×C₃₁	1	1	yes	characteristic
387	C₂²	C₂×C₃₁×#121	1	1	yes	characteristic
388	C₂²	C₂×C₃₁×#124	1	1	yes	characteristic
389	C₄	—	4	8	no	—
390	C₄	—	4	4	no	—
391	C₄	C₃₁×#390	1	2	yes	—
392	C₄	C₃₁×#390	1	2	yes	—
393	C₄	C₂²×C₂²⋊C₄×C₃₁	1	1	yes	characteristic
394	C₄	C₂×C₄×D₄×C₃₁	1	1	yes	characteristic
395	C₄	C₂×C₃₁×#121	1	1	yes	characteristic
396	C₄	C₂×C₃₁×#127	1	1	yes	characteristic
397	C₂	—	2	1	no	—
398	C₂	—	2	1	no	—
399	C₂	—	2	2	no	—
400	C₂	C₃₁×#1979	1	4	yes	direct product factor
401	C₂	C₂×C₃₁×#390	1	1	yes	characteristic
402	C₂	C₂×C₃₁×#473	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₃₁	#121
commutator	C₂×C₄	C₂³×C₄×C₃₁
Frattini, cosocle	C₂²×C₄	C₂⁴×C₃₁
prime radical	C₂⁴×C₃₁	#41
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₃₁ ◁ C₂³×C₄×C₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
6. C₃₁×#1979	C₂	direct (N × H)
12. C₂²×Q₁₆×C₃₁	C₄	semidirect
47. C₂×Q₁₆×C₃₁	C₂×C₄	semidirect
136. C₂×#1979	C₃₁	direct (N × H)
183. #1979	C₂×C₃₁	direct (N × H)
207. C₂²×Q₁₆	C₄×C₃₁	semidirect
227. C₂×C₃₁	#1979	direct (N × H)
248. C₂×Q₁₆	C₂×C₄×C₃₁	semidirect
277. C₃₁	C₂×#1979	direct (N × H)
400. C₂	C₃₁×#1979	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂³×Q₁₆×C₃₁	2
C₂²×C₃₁×#108	2
C₂×C₃₁×#419	2
C₂²×C₃₁×#101	2
C₂×C₃₁×#405	2
C₃₁×#1979	2
C₂×#1979	31

Subgroups — C2×C31×#1979 #21478006

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃₁×#1979 #21478006