Subgroups — C₂×C₃₁×#1514 #21474315

Order 7936.

1302 conjugacy classes of subgroups.

The subgroup lattice has 432 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃₁×#532	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃₁×#432	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃₁×#383	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃₁×#1514	C₂	1	8	yes	maximal, direct product factor
5	C₂×C₃₁×#327	C₂	1	4	yes	maximal, complemented
6	C₂²×#41×C₃₁	—	2	1	no	—
7	C₃₁×#532	—	2	2	no	—
8	C₃₁×#532	—	2	2	no	—
9	C₃₁×#532	C₄	1	4	yes	complemented
10	C₃₁×#532	C₂²	1	4	yes	—
11	C₂×C₃₁×C₄⋊Q₈	C₄	1	1	yes	characteristic, complemented
12	C₂×C₃₁×#127	C₄	1	1	yes	characteristic, complemented
13	C₂×C₃₁×#124	—	2	1	no	—
14	C₂×C₃₁×#121	—	2	1	no	—
15	C₂×C₃₁×#121	C₂²	1	2	yes	—
16	C₂×C₄×D₄×C₃₁	—	2	1	no	—
17	C₂×C₄×D₄×C₃₁	C₄	1	2	yes	complemented
18	C₂²×C₄²×C₃₁	C₂²	1	1	yes	characteristic
19	C₃₁×#432	—	2	2	no	—
20	C₃₁×#432	C₂²	1	4	yes	complemented
21	C₂×C₃₁×C₄⋊C₈	—	2	1	no	—
22	C₂×C₃₁×C₂²⋊C₈	C₂²	1	2	yes	—
23	C₂×C₃₁×#97	—	2	1	no	—
24	C₃₁×#383	—	2	2	no	—
25	C₃₁×#383	C₂²	1	4	yes	complemented
26	C₂×C₃₁×#95	—	2	1	no	—
27	C₂×C₃₁×#95	—	2	1	no	—
28	C₂×C₃₁×#95	C₂²	1	2	yes	—
29	C₃₁×#327	C₂²	1	16	yes	complemented
30	C₂×#41×C₃₁	—	2	4	no	—
31	C₂×#41×C₃₁	—	2	4	no	—
32	C₂×#41×C₃₁	—	4	8	no	—
33	C₂²×Q₈×C₃₁	—	2	1	no	—
34	C₂²×D₄×C₃₁	—	2	2	no	—
35	C₂²×D₄×C₃₁	—	2	1	no	—
36	C₂²×D₄×C₃₁	—	2	1	no	—
37	C₂²×D₄×C₃₁	C₂×C₄	1	2	yes	—
38	C₂³×C₄×C₃₁	—	2	2	no	—
39	C₂³×C₄×C₃₁	—	2	2	no	—
40	C₂³×C₄×C₃₁	D₄	1	1	yes	characteristic
41	C₂³×C₄×C₃₁	D₄	1	1	yes	characteristic
42	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
43	C₂²×C₈×C₃₁	—	2	2	no	—
44	C₃₁×C₄⋊Q₈	—	2	2	no	—
45	C₃₁×C₄⋊Q₈	C₂×C₄	1	4	yes	complemented
46	C₃₁×#127	—	2	2	no	—
47	C₃₁×#127	C₂×C₄	1	4	yes	complemented
48	C₃₁×#124	—	2	4	no	—
49	C₃₁×#124	—	2	4	no	—
50	C₃₁×#121	—	2	4	no	—
51	C₃₁×#121	—	2	4	no	—
52	C₃₁×#121	—	2	2	no	—
53	C₃₁×#121	—	2	2	no	—
54	C₃₁×#121	C₂×C₄	1	4	yes	—
55	C₃₁×#121	C₂³	1	4	yes	—
56	C₄×D₄×C₃₁	—	2	4	no	—
57	C₄×D₄×C₃₁	—	2	4	no	—
58	C₄×D₄×C₃₁	—	2	4	no	—
59	C₄×D₄×C₃₁	C₂×C₄	1	8	yes	complemented
60	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
61	C₂×C₄⋊C₄×C₃₁	C₂×C₄	1	2	yes	—
62	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
63	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
64	C₂×C₄²×C₃₁	C₂×C₄	1	1	yes	characteristic
65	C₂×C₄²×C₃₁	C₂×C₄	1	1	yes	characteristic
66	C₂×C₄²×C₃₁	C₂×C₄	1	2	yes	—
67	C₂×C₄²×C₃₁	D₄	1	2	yes	—
68	C₂×C₄²×C₃₁	D₄	1	1	yes	characteristic
69	C₂×C₄²×C₃₁	D₄	1	1	yes	characteristic
70	C₂×C₄²×C₃₁	D₄	1	2	yes	—
71	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
72	C₃₁×C₄⋊C₈	—	2	4	no	—
73	C₃₁×C₂²⋊C₈	—	2	2	no	—
74	C₃₁×C₂²⋊C₈	C₂³	1	4	yes	—
75	C₃₁×#97	—	2	4	no	—
76	C₃₁×#95	—	2	4	no	—
77	C₃₁×#95	—	2	4	no	—
78	C₃₁×#95	—	2	2	no	—
79	C₃₁×#95	C₂³	1	4	yes	—
80	C₂⁴×C₃₁	—	2	2	no	—
81	C₂⁴×C₃₁	C₂×D₄	1	1	yes	characteristic
82	#41×C₃₁	—	4	16	no	—
83	#41×C₃₁	—	4	16	no	—
84	C₂×Q₈×C₃₁	—	2	4	no	—
85	C₂×Q₈×C₃₁	—	4	4	no	—
86	C₂×D₄×C₃₁	—	2	4	no	—
87	C₂×D₄×C₃₁	—	2	4	no	—
88	C₂×D₄×C₃₁	—	2	2	no	—
89	C₂×D₄×C₃₁	—	2	4	no	—
90	C₂×D₄×C₃₁	—	2	4	no	—
91	C₂×D₄×C₃₁	—	4	4	no	—
92	C₂×D₄×C₃₁	—	4	4	no	—
93	C₂×D₄×C₃₁	—	4	4	no	—
94	C₂×D₄×C₃₁	—	4	8	no	—
95	C₂×D₄×C₃₁	C₂²×C₄	1	4	yes	—
96	C₂²×C₄×C₃₁	—	2	4	no	—
97	C₂²×C₄×C₃₁	—	2	2	no	—
98	C₂²×C₄×C₃₁	—	2	8	no	—
99	C₂²×C₄×C₃₁	—	2	4	no	—
100	C₂²×C₄×C₃₁	—	4	2	no	—
101	C₂²×C₄×C₃₁	—	4	2	no	—
102	C₂²×C₄×C₃₁	—	4	8	no	—
103	C₂²×C₄×C₃₁	—	4	4	no	—
104	C₂²×C₄×C₃₁	—	4	4	no	—
105	C₂²×C₄×C₃₁	—	4	4	no	—
106	C₂²×C₄×C₃₁	C₂²⋊C₄	1	2	yes	—
107	C₂²×C₄×C₃₁	C₂²⋊C₄	1	1	yes	characteristic
108	C₂²×C₄×C₃₁	C₂²⋊C₄	1	1	yes	characteristic
109	C₂²×C₄×C₃₁	C₂²⋊C₄	1	1	yes	characteristic
110	C₂²×C₄×C₃₁	C₂²⋊C₄	1	1	yes	characteristic
111	C₂²×C₄×C₃₁	C₂²⋊C₄	1	2	yes	—
112	C₂²×C₄×C₃₁	C₂²×C₄	1	1	yes	characteristic
113	C₂²×C₄×C₃₁	C₂²×C₄	1	1	yes	characteristic
114	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
115	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
116	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
117	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
118	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
119	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
120	C₂×C₈×C₃₁	—	2	4	no	—
121	C₂×C₈×C₃₁	—	4	4	no	—
122	C₄⋊C₄×C₃₁	—	2	4	no	—
123	C₄⋊C₄×C₃₁	—	2	2	no	—
124	C₄⋊C₄×C₃₁	C₂²×C₄	1	4	yes	—
125	C₂²⋊C₄×C₃₁	—	2	4	no	—
126	C₂²⋊C₄×C₃₁	—	2	8	no	—
127	C₂²⋊C₄×C₃₁	—	2	4	no	—
128	C₄²×C₃₁	C₂²⋊C₄	1	2	yes	—
129	C₄²×C₃₁	C₂²⋊C₄	1	2	yes	—
130	C₄²×C₃₁	C₂²⋊C₄	1	2	yes	—
131	C₄²×C₃₁	C₂²⋊C₄	1	2	yes	—
132	C₄²×C₃₁	C₂²×C₄	1	2	yes	—
133	C₄²×C₃₁	C₂²×C₄	1	2	yes	—
134	C₄²×C₃₁	C₂×D₄	1	2	yes	—
135	C₄²×C₃₁	C₂×D₄	1	2	yes	—
136	C₂×#1514	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
137	C₂³×C₃₁	—	2	2	no	—
138	C₂³×C₃₁	—	2	2	no	—
139	C₂³×C₃₁	—	2	4	no	—
140	C₂³×C₃₁	—	4	4	no	—
141	C₂³×C₃₁	—	4	4	no	—
142	C₂³×C₃₁	—	4	4	no	—
143	C₂³×C₃₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
144	C₂³×C₃₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
145	C₂³×C₃₁	AGL(1,ℤ/8)	1	4	yes	—
146	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
147	Q₈×C₃₁	—	4	8	no	—
148	D₄×C₃₁	—	4	4	no	—
149	D₄×C₃₁	—	4	4	no	—
150	D₄×C₃₁	—	4	8	no	—
151	D₄×C₃₁	—	4	8	no	—
152	D₄×C₃₁	—	4	8	no	—
153	D₄×C₃₁	—	4	8	no	—
154	C₂×C₄×C₃₁	—	2	4	no	—
155	C₂×C₄×C₃₁	—	2	2	no	—
156	C₂×C₄×C₃₁	—	2	2	no	—
157	C₂×C₄×C₃₁	—	2	2	no	—
158	C₂×C₄×C₃₁	—	2	2	no	—
159	C₂×C₄×C₃₁	—	2	4	no	—
160	C₂×C₄×C₃₁	—	2	2	no	—
161	C₂×C₄×C₃₁	—	2	2	no	—
162	C₂×C₄×C₃₁	—	2	4	no	—
163	C₂×C₄×C₃₁	—	4	2	no	—
164	C₂×C₄×C₃₁	—	4	1	no	—
165	C₂×C₄×C₃₁	—	4	1	no	—
166	C₂×C₄×C₃₁	—	4	1	no	—
167	C₂×C₄×C₃₁	—	4	2	no	—
168	C₂×C₄×C₃₁	—	4	1	no	—
169	C₂×C₄×C₃₁	—	4	16	no	—
170	C₂×C₄×C₃₁	—	4	4	no	—
171	C₂×C₄×C₃₁	—	4	4	no	—
172	C₂×C₄×C₃₁	—	4	4	no	—
173	C₂×C₄×C₃₁	—	4	4	no	—
174	C₂×C₄×C₃₁	—	8	8	no	—
175	C₂×C₄×C₃₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
176	C₂×C₄×C₃₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
177	C₂×C₄×C₃₁	C₂×C₂²⋊C₄	1	2	yes	—
178	C₂×C₄×C₃₁	C₂×C₂²⋊C₄	1	2	yes	—
179	C₂×C₄×C₃₁	C₂×C₂²⋊C₄	1	2	yes	—
180	C₂×C₄×C₃₁	C₂×C₂²⋊C₄	1	2	yes	—
181	C₂×C₄×C₃₁	C₂³×C₄	1	1	yes	characteristic
182	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
183	C₈×C₃₁	—	4	4	no	—
184	C₂×#532	C₂×C₃₁	1	1	yes	characteristic
185	C₂×#432	C₂×C₃₁	1	1	yes	characteristic, complemented
186	C₂×#383	C₂×C₃₁	1	1	yes	characteristic, complemented
187	#1514	C₂×C₃₁	1	8	yes	direct product factor
188	C₂×#327	C₂×C₃₁	1	4	yes	complemented
189	C₂²×C₃₁	—	2	1	no	—
190	C₂²×C₃₁	—	2	1	no	—
191	C₂²×C₃₁	—	2	1	no	—
192	C₂²×C₃₁	—	2	1	no	—
193	C₂²×C₃₁	—	2	8	no	—
194	C₂²×C₃₁	—	4	4	no	—
195	C₂²×C₃₁	—	4	4	no	—
196	C₂²×C₃₁	—	4	4	no	—
197	C₂²×C₃₁	—	8	8	no	—
198	C₂²×C₃₁	#410	1	2	yes	—
199	C₂²×C₃₁	#418	1	2	yes	—
200	C₂²×C₃₁	#418	1	2	yes	—
201	C₂²×C₃₁	#421	1	2	yes	—
202	C₂²×C₃₁	C₂²×C₂²⋊C₄	1	1	yes	characteristic
203	C₂²×C₃₁	C₂×AGL(1,ℤ/8)	1	2	yes	—
204	C₄×C₃₁	—	2	1	no	—
205	C₄×C₃₁	—	2	1	no	—
206	C₄×C₃₁	—	2	1	no	—
207	C₄×C₃₁	—	2	1	no	—
208	C₄×C₃₁	—	2	2	no	—
209	C₄×C₃₁	—	2	2	no	—
210	C₄×C₃₁	—	2	2	no	—
211	C₄×C₃₁	—	2	2	no	—
212	C₄×C₃₁	—	4	4	no	—
213	C₄×C₃₁	—	8	4	no	—
214	C₂²×#41	—	2	1	no	—
215	#532	—	2	2	no	—
216	#532	—	2	2	no	—
217	#532	C₄×C₃₁	1	4	yes	complemented
218	#532	C₂²×C₃₁	1	4	yes	—
219	C₂×C₄⋊Q₈	C₄×C₃₁	1	1	yes	characteristic, complemented
220	C₂×#127	C₄×C₃₁	1	1	yes	characteristic, complemented
221	C₂×#124	—	2	1	no	—
222	C₂×#121	—	2	1	no	—
223	C₂×#121	C₂²×C₃₁	1	2	yes	—
224	C₂×C₄×D₄	—	2	1	no	—
225	C₂×C₄×D₄	C₄×C₃₁	1	2	yes	complemented
226	C₂²×C₄²	C₂²×C₃₁	1	1	yes	characteristic
227	#432	—	2	2	no	—
228	#432	C₂²×C₃₁	1	4	yes	complemented
229	C₂×C₄⋊C₈	—	2	1	no	—
230	C₂×C₂²⋊C₈	C₂²×C₃₁	1	2	yes	—
231	C₂×#97	—	2	1	no	—
232	#383	—	2	2	no	—
233	#383	C₂²×C₃₁	1	4	yes	complemented
234	C₂×#95	—	2	1	no	—
235	C₂×#95	—	2	1	no	—
236	C₂×#95	C₂²×C₃₁	1	2	yes	—
237	#327	C₂²×C₃₁	1	16	yes	complemented
238	C₂×C₃₁	—	2	2	no	—
239	C₂×C₃₁	—	2	2	no	—
240	C₂×C₃₁	—	8	4	no	—
241	C₂×C₃₁	#1514	1	4	yes	direct product factor
242	C₂×C₃₁	C₂×#410	1	1	yes	characteristic
243	C₂×C₃₁	C₂×#418	1	1	yes	characteristic
244	C₂×C₃₁	C₂×#421	1	1	yes	characteristic
245	C₂×#41	—	2	4	no	—
246	C₂×#41	—	2	4	no	—
247	C₂×#41	—	4	8	no	—
248	C₂²×Q₈	—	2	1	no	—
249	C₂²×D₄	—	2	2	no	—
250	C₂²×D₄	—	2	1	no	—
251	C₂²×D₄	—	2	1	no	—
252	C₂²×D₄	C₂×C₄×C₃₁	1	2	yes	—
253	C₂³×C₄	—	2	2	no	—
254	C₂³×C₄	—	2	2	no	—
255	C₂³×C₄	D₄×C₃₁	1	1	yes	characteristic
256	C₂³×C₄	D₄×C₃₁	1	1	yes	characteristic
257	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
258	C₂²×C₈	—	2	2	no	—
259	C₄⋊Q₈	—	2	2	no	—
260	C₄⋊Q₈	C₂×C₄×C₃₁	1	4	yes	complemented
261	#127	—	2	2	no	—
262	#127	C₂×C₄×C₃₁	1	4	yes	complemented
263	#124	—	2	4	no	—
264	#124	—	2	4	no	—
265	#121	—	2	4	no	—
266	#121	—	2	4	no	—
267	#121	—	2	2	no	—
268	#121	—	2	2	no	—
269	#121	C₂×C₄×C₃₁	1	4	yes	—
270	#121	C₂³×C₃₁	1	4	yes	—
271	C₄×D₄	—	2	4	no	—
272	C₄×D₄	—	2	4	no	—
273	C₄×D₄	—	2	4	no	—
274	C₄×D₄	C₂×C₄×C₃₁	1	8	yes	complemented
275	C₂×C₄⋊C₄	—	2	1	no	—
276	C₂×C₄⋊C₄	C₂×C₄×C₃₁	1	2	yes	—
277	C₂×C₂²⋊C₄	—	2	2	no	—
278	C₂×C₂²⋊C₄	—	2	2	no	—
279	C₂×C₄²	C₂×C₄×C₃₁	1	1	yes	characteristic
280	C₂×C₄²	C₂×C₄×C₃₁	1	1	yes	characteristic
281	C₂×C₄²	C₂×C₄×C₃₁	1	2	yes	—
282	C₂×C₄²	D₄×C₃₁	1	2	yes	—
283	C₂×C₄²	D₄×C₃₁	1	1	yes	characteristic
284	C₂×C₄²	D₄×C₃₁	1	1	yes	characteristic
285	C₂×C₄²	D₄×C₃₁	1	2	yes	—
286	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
287	C₄⋊C₈	—	2	4	no	—
288	C₂²⋊C₈	—	2	2	no	—
289	C₂²⋊C₈	C₂³×C₃₁	1	4	yes	—
290	#97	—	2	4	no	—
291	#95	—	2	4	no	—
292	#95	—	2	4	no	—
293	#95	—	2	2	no	—
294	#95	C₂³×C₃₁	1	4	yes	—
295	C₃₁	C₂×#1514	1	1	yes	characteristic, direct product factor, Sylow
296	C₂⁴	—	2	2	no	—
297	C₂⁴	C₂×D₄×C₃₁	1	1	yes	characteristic
298	#41	—	4	16	no	—
299	#41	—	4	16	no	—
300	C₂×Q₈	—	2	4	no	—
301	C₂×Q₈	—	4	4	no	—
302	C₂×D₄	—	2	4	no	—
303	C₂×D₄	—	2	4	no	—
304	C₂×D₄	—	2	2	no	—
305	C₂×D₄	—	2	4	no	—
306	C₂×D₄	—	2	4	no	—
307	C₂×D₄	—	4	4	no	—
308	C₂×D₄	—	4	4	no	—
309	C₂×D₄	—	4	4	no	—
310	C₂×D₄	—	4	8	no	—
311	C₂×D₄	C₂²×C₄×C₃₁	1	4	yes	—
312	C₂²×C₄	—	2	4	no	—
313	C₂²×C₄	—	2	2	no	—
314	C₂²×C₄	—	2	8	no	—
315	C₂²×C₄	—	2	4	no	—
316	C₂²×C₄	—	4	2	no	—
317	C₂²×C₄	—	4	2	no	—
318	C₂²×C₄	—	4	8	no	—
319	C₂²×C₄	—	4	4	no	—
320	C₂²×C₄	—	4	4	no	—
321	C₂²×C₄	—	4	4	no	—
322	C₂²×C₄	C₂²⋊C₄×C₃₁	1	1	yes	characteristic
323	C₂²×C₄	C₂²⋊C₄×C₃₁	1	1	yes	characteristic
324	C₂²×C₄	C₂²⋊C₄×C₃₁	1	1	yes	characteristic
325	C₂²×C₄	C₂²⋊C₄×C₃₁	1	1	yes	characteristic
326	C₂²×C₄	C₂²⋊C₄×C₃₁	1	2	yes	—
327	C₂²×C₄	C₂²⋊C₄×C₃₁	1	2	yes	—
328	C₂²×C₄	C₂²×C₄×C₃₁	1	1	yes	characteristic
329	C₂²×C₄	C₂²×C₄×C₃₁	1	1	yes	characteristic
330	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
331	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
332	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
333	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
334	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
335	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
336	C₂×C₈	—	2	4	no	—
337	C₂×C₈	—	4	4	no	—
338	C₄⋊C₄	—	2	4	no	—
339	C₄⋊C₄	—	2	2	no	—
340	C₄⋊C₄	C₂²×C₄×C₃₁	1	4	yes	—
341	C₂²⋊C₄	—	2	4	no	—
342	C₂²⋊C₄	—	2	8	no	—
343	C₂²⋊C₄	—	2	4	no	—
344	C₄²	C₂²⋊C₄×C₃₁	1	2	yes	—
345	C₄²	C₂²⋊C₄×C₃₁	1	2	yes	—
346	C₄²	C₂²⋊C₄×C₃₁	1	2	yes	—
347	C₄²	C₂²⋊C₄×C₃₁	1	2	yes	—
348	C₄²	C₂²×C₄×C₃₁	1	2	yes	—
349	C₄²	C₂²×C₄×C₃₁	1	2	yes	—
350	C₄²	C₂×D₄×C₃₁	1	2	yes	—
351	C₄²	C₂×D₄×C₃₁	1	2	yes	—
352	C₂³	—	2	2	no	—
353	C₂³	—	2	2	no	—
354	C₂³	—	2	4	no	—
355	C₂³	—	4	4	no	—
356	C₂³	—	4	4	no	—
357	C₂³	—	4	4	no	—
358	C₂³	C₂×C₂²⋊C₄×C₃₁	1	1	yes	characteristic
359	C₂³	C₂×C₂²⋊C₄×C₃₁	1	1	yes	characteristic
360	C₂³	C₃₁×AGL(1,ℤ/8)	1	4	yes	—
361	C₂³	C₂²×D₄×C₃₁	1	1	yes	characteristic
362	Q₈	—	4	8	no	—
363	D₄	—	4	4	no	—
364	D₄	—	4	4	no	—
365	D₄	—	4	8	no	—
366	D₄	—	4	8	no	—
367	D₄	—	4	8	no	—
368	D₄	—	4	8	no	—
369	C₂×C₄	—	2	2	no	—
370	C₂×C₄	—	2	2	no	—
371	C₂×C₄	—	2	2	no	—
372	C₂×C₄	—	2	2	no	—
373	C₂×C₄	—	2	4	no	—
374	C₂×C₄	—	2	2	no	—
375	C₂×C₄	—	2	2	no	—
376	C₂×C₄	—	2	4	no	—
377	C₂×C₄	—	2	4	no	—
378	C₂×C₄	—	4	2	no	—
379	C₂×C₄	—	4	1	no	—
380	C₂×C₄	—	4	1	no	—
381	C₂×C₄	—	4	1	no	—
382	C₂×C₄	—	4	2	no	—
383	C₂×C₄	—	4	1	no	—
384	C₂×C₄	—	4	16	no	—
385	C₂×C₄	—	4	4	no	—
386	C₂×C₄	—	4	4	no	—
387	C₂×C₄	—	4	4	no	—
388	C₂×C₄	—	4	4	no	—
389	C₂×C₄	—	8	8	no	—
390	C₂×C₄	C₂×C₂²⋊C₄×C₃₁	1	1	yes	characteristic
391	C₂×C₄	C₂×C₂²⋊C₄×C₃₁	1	1	yes	characteristic
392	C₂×C₄	C₂×C₂²⋊C₄×C₃₁	1	2	yes	—
393	C₂×C₄	C₂×C₂²⋊C₄×C₃₁	1	2	yes	—
394	C₂×C₄	C₂×C₂²⋊C₄×C₃₁	1	2	yes	—
395	C₂×C₄	C₂×C₂²⋊C₄×C₃₁	1	2	yes	—
396	C₂×C₄	C₂³×C₄×C₃₁	1	1	yes	characteristic
397	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
398	C₈	—	4	4	no	—
399	C₂²	—	2	1	no	—
400	C₂²	—	2	1	no	—
401	C₂²	—	2	1	no	—
402	C₂²	—	2	1	no	—
403	C₂²	—	2	8	no	—
404	C₂²	—	4	4	no	—
405	C₂²	—	4	4	no	—
406	C₂²	—	4	4	no	—
407	C₂²	—	8	8	no	—
408	C₂²	C₃₁×#410	1	2	yes	—
409	C₂²	C₃₁×#418	1	2	yes	—
410	C₂²	C₃₁×#418	1	2	yes	—
411	C₂²	C₃₁×#421	1	2	yes	—
412	C₂²	C₂²×C₂²⋊C₄×C₃₁	1	1	yes	characteristic
413	C₂²	C₂×C₃₁×AGL(1,ℤ/8)	1	2	yes	—
414	C₄	—	2	1	no	—
415	C₄	—	2	1	no	—
416	C₄	—	2	1	no	—
417	C₄	—	2	1	no	—
418	C₄	—	2	2	no	—
419	C₄	—	2	2	no	—
420	C₄	—	2	2	no	—
421	C₄	—	2	2	no	—
422	C₄	—	4	4	no	—
423	C₄	—	8	4	no	—
424	C₂	—	2	2	no	—
425	C₂	—	2	2	no	—
426	C₂	—	8	4	no	—
427	C₂	C₃₁×#1514	1	4	yes	direct product factor
428	C₂	C₂×C₃₁×#410	1	1	yes	characteristic
429	C₂	C₂×C₃₁×#418	1	1	yes	characteristic
430	C₂	C₂×C₃₁×#421	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₃₁	C₂×C₂²⋊C₄
commutator	C₂×C₄	C₂³×C₄×C₃₁
Frattini, cosocle	C₂²×C₄	C₂⁴×C₃₁
prime radical	C₂×C₃₁×#532	C₂
LCS	G ▷ C₂×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₃₁ ◁ C₂²×C₄²×C₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₃₁×#432	C₂	semidirect
3. C₂×C₃₁×#383	C₂	semidirect
4. C₃₁×#1514	C₂	direct (N × H)
5. C₂×C₃₁×#327	C₂	semidirect
9. C₃₁×#532	C₄	semidirect
11. C₂×C₃₁×C₄⋊Q₈	C₄	semidirect
12. C₂×C₃₁×#127	C₄	semidirect
17. C₂×C₄×D₄×C₃₁	C₄	semidirect
20. C₃₁×#432	C₂²	semidirect
25. C₃₁×#383	C₂²	semidirect
29. C₃₁×#327	C₂²	semidirect
45. C₃₁×C₄⋊Q₈	C₂×C₄	semidirect
47. C₃₁×#127	C₂×C₄	semidirect
59. C₄×D₄×C₃₁	C₂×C₄	semidirect
136. C₂×#1514	C₃₁	direct (N × H)
185. C₂×#432	C₂×C₃₁	semidirect
186. C₂×#383	C₂×C₃₁	semidirect
187. #1514	C₂×C₃₁	direct (N × H)
188. C₂×#327	C₂×C₃₁	semidirect
217. #532	C₄×C₃₁	semidirect
219. C₂×C₄⋊Q₈	C₄×C₃₁	semidirect
220. C₂×#127	C₄×C₃₁	semidirect
225. C₂×C₄×D₄	C₄×C₃₁	semidirect
228. #432	C₂²×C₃₁	semidirect
233. #383	C₂²×C₃₁	semidirect
237. #327	C₂²×C₃₁	semidirect
241. C₂×C₃₁	#1514	direct (N × H)
260. C₄⋊Q₈	C₂×C₄×C₃₁	semidirect
262. #127	C₂×C₄×C₃₁	semidirect
274. C₄×D₄	C₂×C₄×C₃₁	semidirect
295. C₃₁	C₂×#1514	direct (N × H)
427. C₂	C₃₁×#1514	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₃₁×#532	2
C₂×C₃₁×#432	2
C₂×C₃₁×#383	2
C₃₁×#1514	2
C₂×C₃₁×#327	2
C₂×#1514	31

Subgroups — C2×C31×#1514 #21474315

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃₁×#1514 #21474315