Subgroups — C₂×C₃₁×#3559 #21519491

Order 7936.

7194 conjugacy classes of subgroups.

The subgroup lattice has 804 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#3559	C₂	1	32	yes	maximal, direct product factor
2	C₂×C₃₁×#563	C₂	1	2	yes	maximal, complemented
3	C₂×C₃₁×#562	C₂	1	2	yes	maximal, complemented
4	C₂×C₃₁×#554	C₂	1	2	yes	maximal, complemented
5	C₂×C₃₁×#553	C₂	1	2	yes	maximal, complemented
6	C₂×C₃₁×#553	C₂	1	2	yes	maximal, complemented
7	C₂×C₃₁×#547	C₂	1	4	yes	maximal, complemented
8	C₂×C₃₁×#547	C₂	1	2	yes	maximal, complemented
9	C₂×C₃₁×#544	C₂	1	2	yes	maximal, complemented
10	C₂×C₃₁×#540	C₂	1	2	yes	maximal, complemented
11	C₂×C₃₁×#539	C₂	1	2	yes	maximal, complemented
12	C₂×C₃₁×#539	C₂	1	4	yes	maximal, complemented
13	C₂×C₃₁×#537	C₂	1	2	yes	maximal, complemented
14	C₂×C₃₁×#532	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×C₃₁×#529	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×C₃₁×#125	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂²×#41×C₃₁	C₂²	1	2	yes	—
18	C₂²×#41×C₃₁	C₂²	1	4	yes	—
19	C₃₁×#563	C₂²	1	32	yes	complemented
20	C₃₁×#562	C₂²	1	32	yes	complemented
21	C₃₁×#554	C₂²	1	32	yes	complemented
22	C₃₁×#553	C₂²	1	32	yes	complemented
23	C₃₁×#553	C₂²	1	32	yes	complemented
24	C₃₁×#547	C₂²	1	64	yes	complemented
25	C₃₁×#547	C₂²	1	32	yes	complemented
26	C₃₁×#544	C₂²	1	32	yes	complemented
27	C₃₁×#540	C₂²	1	32	yes	complemented
28	C₃₁×#539	C₂²	1	32	yes	complemented
29	C₃₁×#539	C₂²	1	64	yes	complemented
30	C₃₁×#537	C₂²	1	32	yes	complemented
31	C₃₁×#532	C₂²	1	16	yes	complemented
32	C₂×C₃₁×C₄⋊Q₈	C₂²	1	1	yes	characteristic
33	C₂×C₃₁×C₄⋊Q₈	C₂²	1	2	yes	—
34	C₂×C₃₁×C₄⋊Q₈	C₂²	1	4	yes	—
35	C₂×C₃₁×#127	C₂²	1	1	yes	characteristic
36	C₃₁×#529	C₂²	1	16	yes	complemented
37	C₂×C₃₁×#126	C₂²	1	2	yes	—
38	C₂×C₃₁×#126	C₂²	1	4	yes	—
39	C₂×C₃₁×#126	C₂²	1	4	yes	—
40	C₂×C₃₁×#125	C₂²	1	2	yes	—
41	C₂×C₃₁×#125	C₂²	1	2	yes	—
42	C₂×C₃₁×#125	C₂²	1	2	yes	—
43	C₂×C₃₁×#125	C₂²	1	2	yes	—
44	C₂×C₃₁×#125	C₂²	1	1	yes	characteristic
45	C₂×C₃₁×#125	C₂²	1	4	yes	—
46	C₂×C₃₁×#125	C₂²	1	2	yes	—
47	C₂×C₃₁×#125	C₂²	1	16	yes	complemented
48	C₂×C₃₁×#124	C₂²	1	1	yes	characteristic
49	C₂×C₃₁×#124	C₂²	1	2	yes	—
50	C₂×C₃₁×#123	C₂²	1	2	yes	—
51	C₂×C₃₁×#123	C₂²	1	4	yes	—
52	C₂×C₃₁×#123	C₂²	1	4	yes	—
53	C₂×C₃₁×#123	C₂²	1	4	yes	—
54	C₂×C₃₁×#123	C₂²	1	4	yes	—
55	C₂×C₃₁×#123	C₂²	1	4	yes	—
56	C₂×C₃₁×#123	C₂²	1	4	yes	—
57	C₂×C₃₁×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
58	C₂×C₃₁×C₂²⋊Q₈	C₂²	1	4	yes	—
59	C₂×C₃₁×C₂²⋊Q₈	C₂²	1	4	yes	—
60	C₂×C₃₁×C₂²⋊Q₈	C₂²	1	4	yes	—
61	C₂×C₃₁×C₂²⋊Q₈	C₂²	1	4	yes	—
62	C₂×C₃₁×C₂²⋊Q₈	C₂²	1	4	yes	—
63	C₂×C₃₁×C₂²⋊Q₈	C₂²	1	4	yes	—
64	C₂×C₃₁×#121	C₂²	1	1	yes	characteristic
65	C₂×C₃₁×#121	C₂²	1	2	yes	—
66	C₂×C₃₁×#121	C₂²	1	2	yes	—
67	C₂×C₃₁×#121	C₂²	1	4	yes	—
68	C₂×C₃₁×#121	C₂²	1	4	yes	—
69	C₂×C₃₁×#121	C₂²	1	4	yes	—
70	C₂×C₃₁×#121	C₂²	1	2	yes	—
71	C₂×C₃₁×#121	C₂²	1	4	yes	—
72	C₂×C₃₁×#121	C₂²	1	2	yes	—
73	C₂×C₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic
74	C₂×C₄×D₄×C₃₁	C₂²	1	2	yes	—
75	C₂×C₄×D₄×C₃₁	C₂²	1	1	yes	characteristic
76	C₂×C₄×D₄×C₃₁	C₂²	1	2	yes	—
77	C₂×C₄×D₄×C₃₁	C₂²	1	2	yes	—
78	C₂×C₄×D₄×C₃₁	C₂²	1	4	yes	—
79	C₂×C₄×D₄×C₃₁	C₂²	1	4	yes	—
80	C₂×C₄×D₄×C₃₁	C₂²	1	2	yes	—
81	C₂×C₄×D₄×C₃₁	C₂²	1	2	yes	—
82	C₂×C₃₁×#117	C₂²	1	2	yes	—
83	C₂×C₃₁×#117	C₂²	1	2	yes	—
84	C₂²×C₄⋊C₄×C₃₁	C₂²	1	2	yes	—
85	C₂²×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
86	C₂²×C₄⋊C₄×C₃₁	C₂²	1	2	yes	—
87	C₂²×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
88	C₂²×C₄⋊C₄×C₃₁	C₂²	1	4	yes	—
89	C₂²×C₄⋊C₄×C₃₁	C₂²	1	2	yes	—
90	C₂²×C₄²×C₃₁	C₂²	1	1	yes	characteristic
91	C₂×#41×C₃₁	—	4	8	no	—
92	C₂×#41×C₃₁	—	4	16	no	—
93	C₂×#41×C₃₁	C₂³	1	16	yes	—
94	C₂×#41×C₃₁	C₂³	1	32	yes	—
95	C₂²×Q₈×C₃₁	C₂³	1	1	yes	characteristic
96	C₂²×Q₈×C₃₁	C₂³	1	4	yes	—
97	C₂²×Q₈×C₃₁	C₂³	1	2	yes	—
98	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
99	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
100	C₂²×D₄×C₃₁	C₂³	1	4	yes	—
101	C₂²×D₄×C₃₁	C₂³	1	4	yes	—
102	C₂²×D₄×C₃₁	C₂³	1	1	yes	characteristic
103	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
104	C₂²×D₄×C₃₁	C₂³	1	4	yes	—
105	C₂²×D₄×C₃₁	C₂³	1	2	yes	—
106	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
107	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
108	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
109	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
110	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
111	C₂³×C₄×C₃₁	C₂³	1	2	yes	—
112	C₂³×C₄×C₃₁	C₂³	1	4	yes	—
113	C₂³×C₄×C₃₁	C₂³	1	4	yes	—
114	C₂³×C₄×C₃₁	C₂³	1	4	yes	—
115	C₂³×C₄×C₃₁	C₂³	1	4	yes	—
116	C₃₁×C₄⋊Q₈	C₂³	1	8	yes	—
117	C₃₁×C₄⋊Q₈	C₂³	1	16	yes	—
118	C₃₁×C₄⋊Q₈	C₂³	1	32	yes	—
119	C₃₁×#127	C₂³	1	8	yes	—
120	C₃₁×#126	C₂³	1	16	yes	—
121	C₃₁×#126	C₂³	1	32	yes	—
122	C₃₁×#126	C₂³	1	32	yes	—
123	C₃₁×#125	C₂³	1	16	yes	—
124	C₃₁×#125	C₂³	1	16	yes	—
125	C₃₁×#125	C₂³	1	16	yes	—
126	C₃₁×#125	C₂³	1	16	yes	—
127	C₃₁×#125	C₂³	1	8	yes	—
128	C₃₁×#125	C₂³	1	32	yes	—
129	C₃₁×#125	C₂³	1	16	yes	—
130	C₃₁×#124	C₂³	1	8	yes	—
131	C₃₁×#124	C₂³	1	16	yes	—
132	C₃₁×#123	C₂³	1	16	yes	—
133	C₃₁×#123	C₂³	1	32	yes	—
134	C₃₁×#123	C₂³	1	32	yes	—
135	C₃₁×#123	C₂³	1	32	yes	—
136	C₃₁×#123	C₂³	1	32	yes	—
137	C₃₁×#123	C₂³	1	32	yes	—
138	C₃₁×#123	C₂³	1	32	yes	—
139	C₃₁×C₂²⋊Q₈	C₂³	1	8	yes	—
140	C₃₁×C₂²⋊Q₈	C₂³	1	32	yes	—
141	C₃₁×C₂²⋊Q₈	C₂³	1	32	yes	—
142	C₃₁×C₂²⋊Q₈	C₂³	1	32	yes	—
143	C₃₁×C₂²⋊Q₈	C₂³	1	32	yes	—
144	C₃₁×C₂²⋊Q₈	C₂³	1	32	yes	—
145	C₃₁×C₂²⋊Q₈	C₂³	1	32	yes	—
146	C₃₁×#121	C₂³	1	8	yes	—
147	C₃₁×#121	C₂³	1	16	yes	—
148	C₃₁×#121	C₂³	1	16	yes	—
149	C₃₁×#121	C₂³	1	32	yes	—
150	C₃₁×#121	C₂³	1	32	yes	—
151	C₃₁×#121	C₂³	1	32	yes	—
152	C₃₁×#121	C₂³	1	16	yes	—
153	C₃₁×#121	C₂³	1	32	yes	—
154	C₃₁×#121	C₂³	1	16	yes	—
155	C₄×Q₈×C₃₁	C₂³	1	8	yes	—
156	C₄×D₄×C₃₁	C₂³	1	16	yes	—
157	C₄×D₄×C₃₁	C₂³	1	8	yes	—
158	C₄×D₄×C₃₁	C₂³	1	16	yes	—
159	C₄×D₄×C₃₁	C₂³	1	16	yes	—
160	C₄×D₄×C₃₁	C₂³	1	32	yes	—
161	C₄×D₄×C₃₁	C₂³	1	32	yes	—
162	C₄×D₄×C₃₁	C₂³	1	16	yes	—
163	C₄×D₄×C₃₁	C₂³	1	16	yes	—
164	C₃₁×#117	C₂³	1	16	yes	—
165	C₃₁×#117	C₂³	1	16	yes	—
166	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
167	C₂×C₄⋊C₄×C₃₁	C₂³	1	4	yes	—
168	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
169	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
170	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
171	C₂×C₄⋊C₄×C₃₁	C₂³	1	4	yes	—
172	C₂×C₄⋊C₄×C₃₁	C₂³	1	4	yes	—
173	C₂×C₄⋊C₄×C₃₁	C₂³	1	4	yes	—
174	C₂×C₄⋊C₄×C₃₁	C₂³	1	4	yes	—
175	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
176	C₂×C₄⋊C₄×C₃₁	C₂³	1	4	yes	—
177	C₂×C₄⋊C₄×C₃₁	C₂³	1	4	yes	—
178	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
179	C₂×C₄⋊C₄×C₃₁	C₂³	1	16	yes	—
180	C₂×C₄⋊C₄×C₃₁	C₂³	1	8	yes	—
181	C₂×C₄⋊C₄×C₃₁	C₂³	1	16	yes	—
182	C₂×C₄⋊C₄×C₃₁	C₂³	1	8	yes	—
183	C₂×C₄⋊C₄×C₃₁	C₂³	1	32	yes	—
184	C₂×C₄⋊C₄×C₃₁	C₂³	1	16	yes	—
185	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
186	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
187	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
188	C₂×C₄⋊C₄×C₃₁	C₂³	1	4	yes	—
189	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
190	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
191	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
192	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
193	C₂×C₂²⋊C₄×C₃₁	C₂³	1	4	yes	—
194	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
195	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
196	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
197	C₂×C₂²⋊C₄×C₃₁	C₂³	1	4	yes	—
198	C₂×C₂²⋊C₄×C₃₁	C₂³	1	4	yes	—
199	C₂×C₂²⋊C₄×C₃₁	C₂³	1	4	yes	—
200	C₂×C₂²⋊C₄×C₃₁	C₂³	1	4	yes	—
201	C₂×C₂²⋊C₄×C₃₁	C₂³	1	4	yes	—
202	C₂×C₂²⋊C₄×C₃₁	C₂³	1	4	yes	—
203	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
204	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
205	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
206	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
207	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
208	C₂×C₄²×C₃₁	C₂³	1	8	yes	—
209	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
210	C₂×C₄²×C₃₁	C₂³	1	4	yes	—
211	C₂⁴×C₃₁	C₂⁴	1	2	yes	—
212	C₂⁴×C₃₁	C₂⁴	1	4	yes	—
213	C₂⁴×C₃₁	C₂⁴	1	1	yes	characteristic
214	#41×C₃₁	—	4	32	no	—
215	#41×C₃₁	—	4	64	no	—
216	C₂×Q₈×C₃₁	—	4	2	no	—
217	C₂×Q₈×C₃₁	—	4	8	no	—
218	C₂×Q₈×C₃₁	—	4	4	no	—
219	C₂×Q₈×C₃₁	C₂⁴	1	4	yes	—
220	C₂×Q₈×C₃₁	C₂⁴	1	16	yes	—
221	C₂×Q₈×C₃₁	C₂⁴	1	8	yes	—
222	C₂×D₄×C₃₁	—	2	8	no	—
223	C₂×D₄×C₃₁	—	2	16	no	—
224	C₂×D₄×C₃₁	—	2	8	no	—
225	C₂×D₄×C₃₁	—	4	8	no	—
226	C₂×D₄×C₃₁	—	4	4	no	—
227	C₂×D₄×C₃₁	—	4	2	no	—
228	C₂×D₄×C₃₁	—	4	8	no	—
229	C₂×D₄×C₃₁	—	4	4	no	—
230	C₂×D₄×C₃₁	C₂⁴	1	8	yes	—
231	C₂×D₄×C₃₁	C₂⁴	1	8	yes	—
232	C₂×D₄×C₃₁	C₂⁴	1	16	yes	—
233	C₂×D₄×C₃₁	C₂⁴	1	16	yes	—
234	C₂×D₄×C₃₁	C₂⁴	1	4	yes	—
235	C₂×D₄×C₃₁	C₂⁴	1	8	yes	—
236	C₂×D₄×C₃₁	C₂⁴	1	16	yes	—
237	C₂×D₄×C₃₁	C₂⁴	1	8	yes	—
238	C₂²×C₄×C₃₁	—	2	4	no	—
239	C₂²×C₄×C₃₁	—	2	8	no	—
240	C₂²×C₄×C₃₁	—	2	4	no	—
241	C₂²×C₄×C₃₁	—	2	8	no	—
242	C₂²×C₄×C₃₁	—	4	4	no	—
243	C₂²×C₄×C₃₁	—	4	8	no	—
244	C₂²×C₄×C₃₁	—	4	2	no	—
245	C₂²×C₄×C₃₁	—	4	8	no	—
246	C₂²×C₄×C₃₁	—	4	8	no	—
247	C₂²×C₄×C₃₁	—	4	8	no	—
248	C₂²×C₄×C₃₁	C₂⁴	1	4	yes	—
249	C₂²×C₄×C₃₁	C₂⁴	1	4	yes	—
250	C₂²×C₄×C₃₁	C₂⁴	1	8	yes	—
251	C₂²×C₄×C₃₁	C₂⁴	1	8	yes	—
252	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
253	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
254	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
255	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
256	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
257	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
258	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
259	C₂²×C₄×C₃₁	C₂⁴	1	4	yes	—
260	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
261	C₂²×C₄×C₃₁	C₂⁴	1	4	yes	—
262	C₂²×C₄×C₃₁	C₂⁴	1	4	yes	—
263	C₂²×C₄×C₃₁	C₂⁴	1	4	yes	—
264	C₂²×C₄×C₃₁	C₂⁴	1	8	yes	—
265	C₂²×C₄×C₃₁	C₂⁴	1	16	yes	—
266	C₂²×C₄×C₃₁	C₂⁴	1	16	yes	—
267	C₂²×C₄×C₃₁	C₂⁴	1	16	yes	—
268	C₂²×C₄×C₃₁	C₂⁴	1	16	yes	—
269	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
270	C₄⋊C₄×C₃₁	C₂⁴	1	8	yes	—
271	C₄⋊C₄×C₃₁	C₂⁴	1	16	yes	—
272	C₄⋊C₄×C₃₁	C₂⁴	1	8	yes	—
273	C₄⋊C₄×C₃₁	C₂⁴	1	8	yes	—
274	C₄⋊C₄×C₃₁	C₂⁴	1	8	yes	—
275	C₄⋊C₄×C₃₁	C₂⁴	1	16	yes	—
276	C₄⋊C₄×C₃₁	C₂⁴	1	16	yes	—
277	C₄⋊C₄×C₃₁	C₂⁴	1	16	yes	—
278	C₄⋊C₄×C₃₁	C₂⁴	1	16	yes	—
279	C₄⋊C₄×C₃₁	C₂⁴	1	8	yes	—
280	C₄⋊C₄×C₃₁	C₂⁴	1	16	yes	—
281	C₄⋊C₄×C₃₁	C₂⁴	1	16	yes	—
282	C₄⋊C₄×C₃₁	C₂⁴	1	8	yes	—
283	C₄⋊C₄×C₃₁	C₂⁴	1	8	yes	—
284	C₄⋊C₄×C₃₁	C₂⁴	1	8	yes	—
285	C₄⋊C₄×C₃₁	C₂⁴	1	8	yes	—
286	C₄⋊C₄×C₃₁	C₂⁴	1	16	yes	—
287	C₄⋊C₄×C₃₁	C₂⁴	1	8	yes	—
288	C₄⋊C₄×C₃₁	C₂⁴	1	4	yes	—
289	C₄⋊C₄×C₃₁	C₂⁴	1	4	yes	—
290	C₂²⋊C₄×C₃₁	C₂⁴	1	8	yes	—
291	C₂²⋊C₄×C₃₁	C₂⁴	1	16	yes	—
292	C₂²⋊C₄×C₃₁	C₂⁴	1	8	yes	—
293	C₂²⋊C₄×C₃₁	C₂⁴	1	8	yes	—
294	C₂²⋊C₄×C₃₁	C₂⁴	1	8	yes	—
295	C₂²⋊C₄×C₃₁	C₂⁴	1	16	yes	—
296	C₂²⋊C₄×C₃₁	C₂⁴	1	16	yes	—
297	C₂²⋊C₄×C₃₁	C₂⁴	1	16	yes	—
298	C₂²⋊C₄×C₃₁	C₂⁴	1	16	yes	—
299	C₂²⋊C₄×C₃₁	C₂⁴	1	16	yes	—
300	C₂²⋊C₄×C₃₁	C₂⁴	1	16	yes	—
301	C₂²⋊C₄×C₃₁	C₂⁴	1	8	yes	—
302	C₄²×C₃₁	C₂⁴	1	4	yes	—
303	C₄²×C₃₁	C₂⁴	1	4	yes	—
304	C₄²×C₃₁	C₂⁴	1	4	yes	—
305	C₄²×C₃₁	C₂⁴	1	4	yes	—
306	C₄²×C₃₁	C₂⁴	1	8	yes	—
307	C₄²×C₃₁	C₂⁴	1	16	yes	—
308	C₂×#3559	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
309	C₂³×C₃₁	—	2	2	no	—
310	C₂³×C₃₁	—	2	2	no	—
311	C₂³×C₃₁	—	2	4	no	—
312	C₂³×C₃₁	—	2	8	no	—
313	C₂³×C₃₁	—	2	4	no	—
314	C₂³×C₃₁	—	2	8	no	—
315	C₂³×C₃₁	—	2	8	no	—
316	C₂³×C₃₁	—	2	4	no	—
317	C₂³×C₃₁	H(5,𝔽₂)	1	4	yes	—
318	C₂³×C₃₁	C₂⁵	1	4	yes	—
319	C₂³×C₃₁	C₂⁵	1	8	yes	—
320	C₂³×C₃₁	C₂⁵	1	2	yes	—
321	C₂³×C₃₁	C₂⁵	1	1	yes	characteristic
322	Q₈×C₃₁	—	4	4	no	—
323	Q₈×C₃₁	—	4	16	no	—
324	Q₈×C₃₁	—	4	8	no	—
325	D₄×C₃₁	—	2	16	no	—
326	D₄×C₃₁	—	2	32	no	—
327	D₄×C₃₁	—	2	16	no	—
328	D₄×C₃₁	—	4	16	no	—
329	D₄×C₃₁	—	4	8	no	—
330	D₄×C₃₁	—	4	4	no	—
331	D₄×C₃₁	—	4	16	no	—
332	D₄×C₃₁	—	4	8	no	—
333	C₂×C₄×C₃₁	—	2	2	no	—
334	C₂×C₄×C₃₁	—	2	8	no	—
335	C₂×C₄×C₃₁	—	2	2	no	—
336	C₂×C₄×C₃₁	—	2	8	no	—
337	C₂×C₄×C₃₁	—	2	16	no	—
338	C₂×C₄×C₃₁	—	2	8	no	—
339	C₂×C₄×C₃₁	—	2	4	no	—
340	C₂×C₄×C₃₁	—	2	2	no	—
341	C₂×C₄×C₃₁	—	2	4	no	—
342	C₂×C₄×C₃₁	—	2	8	no	—
343	C₂×C₄×C₃₁	—	2	4	no	—
344	C₂×C₄×C₃₁	—	2	2	no	—
345	C₂×C₄×C₃₁	—	2	2	no	—
346	C₂×C₄×C₃₁	—	2	8	no	—
347	C₂×C₄×C₃₁	—	2	16	no	—
348	C₂×C₄×C₃₁	—	4	8	no	—
349	C₂×C₄×C₃₁	—	4	16	no	—
350	C₂×C₄×C₃₁	—	4	4	no	—
351	C₂×C₄×C₃₁	—	4	16	no	—
352	C₂×C₄×C₃₁	—	4	16	no	—
353	C₂×C₄×C₃₁	—	4	16	no	—
354	C₂×C₄×C₃₁	2₋¹⁺⁴	1	4	yes	—
355	C₂×C₄×C₃₁	C₂⁵	1	2	yes	—
356	C₂×C₄×C₃₁	C₂⁵	1	4	yes	—
357	C₂×C₄×C₃₁	C₂⁵	1	2	yes	—
358	C₂×C₄×C₃₁	C₂⁵	1	2	yes	—
359	C₂×C₄×C₃₁	C₂⁵	1	2	yes	—
360	C₂×C₄×C₃₁	C₂⁵	1	2	yes	—
361	C₂×C₄×C₃₁	C₂⁵	1	4	yes	—
362	C₂×C₄×C₃₁	C₂⁵	1	8	yes	—
363	C₂×C₄×C₃₁	C₂⁵	1	4	yes	—
364	C₂×C₄×C₃₁	C₂⁵	1	8	yes	—
365	C₂×C₄×C₃₁	C₂⁵	1	8	yes	—
366	C₂×C₄×C₃₁	C₂⁵	1	2	yes	—
367	#3559	C₂×C₃₁	1	32	yes	direct product factor
368	C₂×#563	C₂×C₃₁	1	2	yes	complemented
369	C₂×#562	C₂×C₃₁	1	2	yes	complemented
370	C₂×#554	C₂×C₃₁	1	2	yes	complemented
371	C₂×#553	C₂×C₃₁	1	2	yes	complemented
372	C₂×#553	C₂×C₃₁	1	2	yes	complemented
373	C₂×#547	C₂×C₃₁	1	4	yes	complemented
374	C₂×#547	C₂×C₃₁	1	2	yes	complemented
375	C₂×#544	C₂×C₃₁	1	2	yes	complemented
376	C₂×#540	C₂×C₃₁	1	2	yes	complemented
377	C₂×#539	C₂×C₃₁	1	2	yes	complemented
378	C₂×#539	C₂×C₃₁	1	4	yes	complemented
379	C₂×#537	C₂×C₃₁	1	2	yes	complemented
380	C₂×#532	C₂×C₃₁	1	1	yes	characteristic, complemented
381	C₂×#529	C₂×C₃₁	1	1	yes	characteristic, complemented
382	C₂²×#125	C₂×C₃₁	1	1	yes	characteristic, complemented
383	C₂²×C₃₁	—	2	2	no	—
384	C₂²×C₃₁	—	2	2	no	—
385	C₂²×C₃₁	—	2	8	no	—
386	C₂²×C₃₁	—	2	4	no	—
387	C₂²×C₃₁	—	2	8	no	—
388	C₂²×C₃₁	—	2	4	no	—
389	C₂²×C₃₁	—	2	8	no	—
390	C₂²×C₃₁	—	2	8	no	—
391	C₂²×C₃₁	—	2	4	no	—
392	C₂²×C₃₁	—	4	8	no	—
393	C₂²×C₃₁	—	4	16	no	—
394	C₂²×C₃₁	C₂×H(5,𝔽₂)	1	4	yes	—
395	C₂²×C₃₁	C₂×H(5,𝔽₂)	1	2	yes	—
396	C₂²×C₃₁	C₂×2₋¹⁺⁴	1	2	yes	—
397	C₂²×C₃₁	#585	1	2	yes	—
398	C₂²×C₃₁	C₂⁶	1	1	yes	characteristic
399	C₄×C₃₁	—	2	2	no	—
400	C₄×C₃₁	—	2	8	no	—
401	C₄×C₃₁	—	2	2	no	—
402	C₄×C₃₁	—	2	8	no	—
403	C₄×C₃₁	—	2	4	no	—
404	C₄×C₃₁	—	2	2	no	—
405	C₄×C₃₁	—	2	4	no	—
406	C₄×C₃₁	—	2	8	no	—
407	C₄×C₃₁	—	2	4	no	—
408	C₄×C₃₁	—	2	2	no	—
409	C₄×C₃₁	—	2	2	no	—
410	C₄×C₃₁	C₂×2₋¹⁺⁴	1	4	yes	—
411	C₂²×#41	C₂²×C₃₁	1	2	yes	—
412	C₂²×#41	C₂²×C₃₁	1	4	yes	—
413	#563	C₂²×C₃₁	1	32	yes	complemented
414	#562	C₂²×C₃₁	1	32	yes	complemented
415	#554	C₂²×C₃₁	1	32	yes	complemented
416	#553	C₂²×C₃₁	1	32	yes	complemented
417	#553	C₂²×C₃₁	1	32	yes	complemented
418	#547	C₂²×C₃₁	1	64	yes	complemented
419	#547	C₂²×C₃₁	1	32	yes	complemented
420	#544	C₂²×C₃₁	1	32	yes	complemented
421	#540	C₂²×C₃₁	1	32	yes	complemented
422	#539	C₂²×C₃₁	1	32	yes	complemented
423	#539	C₂²×C₃₁	1	64	yes	complemented
424	#537	C₂²×C₃₁	1	32	yes	complemented
425	#532	C₂²×C₃₁	1	16	yes	complemented
426	C₂×C₄⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic
427	C₂×C₄⋊Q₈	C₂²×C₃₁	1	2	yes	—
428	C₂×C₄⋊Q₈	C₂²×C₃₁	1	4	yes	—
429	C₂×#127	C₂²×C₃₁	1	1	yes	characteristic
430	#529	C₂²×C₃₁	1	16	yes	complemented
431	C₂×#126	C₂²×C₃₁	1	2	yes	—
432	C₂×#126	C₂²×C₃₁	1	4	yes	—
433	C₂×#126	C₂²×C₃₁	1	4	yes	—
434	C₂×#125	C₂²×C₃₁	1	2	yes	—
435	C₂×#125	C₂²×C₃₁	1	2	yes	—
436	C₂×#125	C₂²×C₃₁	1	2	yes	—
437	C₂×#125	C₂²×C₃₁	1	2	yes	—
438	C₂×#125	C₂²×C₃₁	1	1	yes	characteristic
439	C₂×#125	C₂²×C₃₁	1	4	yes	—
440	C₂×#125	C₂²×C₃₁	1	2	yes	—
441	C₂×#125	C₂²×C₃₁	1	16	yes	complemented
442	C₂×#124	C₂²×C₃₁	1	1	yes	characteristic
443	C₂×#124	C₂²×C₃₁	1	2	yes	—
444	C₂×#123	C₂²×C₃₁	1	2	yes	—
445	C₂×#123	C₂²×C₃₁	1	4	yes	—
446	C₂×#123	C₂²×C₃₁	1	4	yes	—
447	C₂×#123	C₂²×C₃₁	1	4	yes	—
448	C₂×#123	C₂²×C₃₁	1	4	yes	—
449	C₂×#123	C₂²×C₃₁	1	4	yes	—
450	C₂×#123	C₂²×C₃₁	1	4	yes	—
451	C₂×C₂²⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic
452	C₂×C₂²⋊Q₈	C₂²×C₃₁	1	4	yes	—
453	C₂×C₂²⋊Q₈	C₂²×C₃₁	1	4	yes	—
454	C₂×C₂²⋊Q₈	C₂²×C₃₁	1	4	yes	—
455	C₂×C₂²⋊Q₈	C₂²×C₃₁	1	4	yes	—
456	C₂×C₂²⋊Q₈	C₂²×C₃₁	1	4	yes	—
457	C₂×C₂²⋊Q₈	C₂²×C₃₁	1	4	yes	—
458	C₂×#121	C₂²×C₃₁	1	1	yes	characteristic
459	C₂×#121	C₂²×C₃₁	1	2	yes	—
460	C₂×#121	C₂²×C₃₁	1	2	yes	—
461	C₂×#121	C₂²×C₃₁	1	4	yes	—
462	C₂×#121	C₂²×C₃₁	1	4	yes	—
463	C₂×#121	C₂²×C₃₁	1	4	yes	—
464	C₂×#121	C₂²×C₃₁	1	2	yes	—
465	C₂×#121	C₂²×C₃₁	1	4	yes	—
466	C₂×#121	C₂²×C₃₁	1	2	yes	—
467	C₂×C₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic
468	C₂×C₄×D₄	C₂²×C₃₁	1	2	yes	—
469	C₂×C₄×D₄	C₂²×C₃₁	1	1	yes	characteristic
470	C₂×C₄×D₄	C₂²×C₃₁	1	2	yes	—
471	C₂×C₄×D₄	C₂²×C₃₁	1	2	yes	—
472	C₂×C₄×D₄	C₂²×C₃₁	1	4	yes	—
473	C₂×C₄×D₄	C₂²×C₃₁	1	4	yes	—
474	C₂×C₄×D₄	C₂²×C₃₁	1	2	yes	—
475	C₂×C₄×D₄	C₂²×C₃₁	1	2	yes	—
476	C₂×#117	C₂²×C₃₁	1	2	yes	—
477	C₂×#117	C₂²×C₃₁	1	2	yes	—
478	C₂²×C₄⋊C₄	C₂²×C₃₁	1	2	yes	—
479	C₂²×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
480	C₂²×C₄⋊C₄	C₂²×C₃₁	1	2	yes	—
481	C₂²×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
482	C₂²×C₄⋊C₄	C₂²×C₃₁	1	4	yes	—
483	C₂²×C₄⋊C₄	C₂²×C₃₁	1	2	yes	—
484	C₂²×C₄²	C₂²×C₃₁	1	1	yes	characteristic
485	C₂×C₃₁	—	2	4	no	—
486	C₂×C₃₁	—	4	4	no	—
487	C₂×C₃₁	—	4	8	no	—
488	C₂×C₃₁	#3559	1	4	yes	direct product factor
489	C₂×C₃₁	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
490	C₂×C₃₁	C₂²×2₋¹⁺⁴	1	1	yes	characteristic
491	C₂×C₃₁	C₂×#585	1	1	yes	characteristic
492	C₂×#41	—	4	8	no	—
493	C₂×#41	—	4	16	no	—
494	C₂×#41	C₂³×C₃₁	1	16	yes	—
495	C₂×#41	C₂³×C₃₁	1	32	yes	—
496	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
497	C₂²×Q₈	C₂³×C₃₁	1	4	yes	—
498	C₂²×Q₈	C₂³×C₃₁	1	2	yes	—
499	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
500	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
501	C₂²×D₄	C₂³×C₃₁	1	4	yes	—
502	C₂²×D₄	C₂³×C₃₁	1	4	yes	—
503	C₂²×D₄	C₂³×C₃₁	1	1	yes	characteristic
504	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
505	C₂²×D₄	C₂³×C₃₁	1	4	yes	—
506	C₂²×D₄	C₂³×C₃₁	1	2	yes	—
507	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
508	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
509	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
510	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
511	C₂³×C₄	C₂³×C₃₁	1	2	yes	—
512	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
513	C₂³×C₄	C₂³×C₃₁	1	4	yes	—
514	C₂³×C₄	C₂³×C₃₁	1	4	yes	—
515	C₂³×C₄	C₂³×C₃₁	1	4	yes	—
516	C₂³×C₄	C₂³×C₃₁	1	4	yes	—
517	C₄⋊Q₈	C₂³×C₃₁	1	8	yes	—
518	C₄⋊Q₈	C₂³×C₃₁	1	16	yes	—
519	C₄⋊Q₈	C₂³×C₃₁	1	32	yes	—
520	#127	C₂³×C₃₁	1	8	yes	—
521	#126	C₂³×C₃₁	1	16	yes	—
522	#126	C₂³×C₃₁	1	32	yes	—
523	#126	C₂³×C₃₁	1	32	yes	—
524	#125	C₂³×C₃₁	1	16	yes	—
525	#125	C₂³×C₃₁	1	16	yes	—
526	#125	C₂³×C₃₁	1	16	yes	—
527	#125	C₂³×C₃₁	1	16	yes	—
528	#125	C₂³×C₃₁	1	8	yes	—
529	#125	C₂³×C₃₁	1	32	yes	—
530	#125	C₂³×C₃₁	1	16	yes	—
531	#124	C₂³×C₃₁	1	8	yes	—
532	#124	C₂³×C₃₁	1	16	yes	—
533	#123	C₂³×C₃₁	1	16	yes	—
534	#123	C₂³×C₃₁	1	32	yes	—
535	#123	C₂³×C₃₁	1	32	yes	—
536	#123	C₂³×C₃₁	1	32	yes	—
537	#123	C₂³×C₃₁	1	32	yes	—
538	#123	C₂³×C₃₁	1	32	yes	—
539	#123	C₂³×C₃₁	1	32	yes	—
540	C₂²⋊Q₈	C₂³×C₃₁	1	8	yes	—
541	C₂²⋊Q₈	C₂³×C₃₁	1	32	yes	—
542	C₂²⋊Q₈	C₂³×C₃₁	1	32	yes	—
543	C₂²⋊Q₈	C₂³×C₃₁	1	32	yes	—
544	C₂²⋊Q₈	C₂³×C₃₁	1	32	yes	—
545	C₂²⋊Q₈	C₂³×C₃₁	1	32	yes	—
546	C₂²⋊Q₈	C₂³×C₃₁	1	32	yes	—
547	#121	C₂³×C₃₁	1	8	yes	—
548	#121	C₂³×C₃₁	1	16	yes	—
549	#121	C₂³×C₃₁	1	16	yes	—
550	#121	C₂³×C₃₁	1	32	yes	—
551	#121	C₂³×C₃₁	1	32	yes	—
552	#121	C₂³×C₃₁	1	32	yes	—
553	#121	C₂³×C₃₁	1	16	yes	—
554	#121	C₂³×C₃₁	1	32	yes	—
555	#121	C₂³×C₃₁	1	16	yes	—
556	C₄×Q₈	C₂³×C₃₁	1	8	yes	—
557	C₄×D₄	C₂³×C₃₁	1	16	yes	—
558	C₄×D₄	C₂³×C₃₁	1	8	yes	—
559	C₄×D₄	C₂³×C₃₁	1	16	yes	—
560	C₄×D₄	C₂³×C₃₁	1	16	yes	—
561	C₄×D₄	C₂³×C₃₁	1	32	yes	—
562	C₄×D₄	C₂³×C₃₁	1	32	yes	—
563	C₄×D₄	C₂³×C₃₁	1	16	yes	—
564	C₄×D₄	C₂³×C₃₁	1	16	yes	—
565	#117	C₂³×C₃₁	1	16	yes	—
566	#117	C₂³×C₃₁	1	16	yes	—
567	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
568	C₂×C₄⋊C₄	C₂³×C₃₁	1	4	yes	—
569	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
570	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
571	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
572	C₂×C₄⋊C₄	C₂³×C₃₁	1	4	yes	—
573	C₂×C₄⋊C₄	C₂³×C₃₁	1	4	yes	—
574	C₂×C₄⋊C₄	C₂³×C₃₁	1	4	yes	—
575	C₂×C₄⋊C₄	C₂³×C₃₁	1	4	yes	—
576	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
577	C₂×C₄⋊C₄	C₂³×C₃₁	1	4	yes	—
578	C₂×C₄⋊C₄	C₂³×C₃₁	1	4	yes	—
579	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
580	C₂×C₄⋊C₄	C₂³×C₃₁	1	16	yes	—
581	C₂×C₄⋊C₄	C₂³×C₃₁	1	8	yes	—
582	C₂×C₄⋊C₄	C₂³×C₃₁	1	16	yes	—
583	C₂×C₄⋊C₄	C₂³×C₃₁	1	8	yes	—
584	C₂×C₄⋊C₄	C₂³×C₃₁	1	32	yes	—
585	C₂×C₄⋊C₄	C₂³×C₃₁	1	16	yes	—
586	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
587	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
588	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
589	C₂×C₄⋊C₄	C₂³×C₃₁	1	4	yes	—
590	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
591	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
592	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
593	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
594	C₂×C₂²⋊C₄	C₂³×C₃₁	1	4	yes	—
595	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
596	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
597	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
598	C₂×C₂²⋊C₄	C₂³×C₃₁	1	4	yes	—
599	C₂×C₂²⋊C₄	C₂³×C₃₁	1	4	yes	—
600	C₂×C₂²⋊C₄	C₂³×C₃₁	1	4	yes	—
601	C₂×C₂²⋊C₄	C₂³×C₃₁	1	4	yes	—
602	C₂×C₂²⋊C₄	C₂³×C₃₁	1	4	yes	—
603	C₂×C₂²⋊C₄	C₂³×C₃₁	1	4	yes	—
604	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
605	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
606	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
607	C₂×C₄²	C₂³×C₃₁	1	4	yes	—
608	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
609	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
610	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
611	C₂×C₄²	C₂³×C₃₁	1	8	yes	—
612	C₃₁	C₂×#3559	1	1	yes	characteristic, direct product factor, Sylow
613	C₂⁴	C₂⁴×C₃₁	1	2	yes	—
614	C₂⁴	C₂⁴×C₃₁	1	4	yes	—
615	C₂⁴	C₂⁴×C₃₁	1	1	yes	characteristic
616	#41	—	4	32	no	—
617	#41	—	4	64	no	—
618	C₂×Q₈	—	4	2	no	—
619	C₂×Q₈	—	4	8	no	—
620	C₂×Q₈	—	4	4	no	—
621	C₂×Q₈	C₂⁴×C₃₁	1	4	yes	—
622	C₂×Q₈	C₂⁴×C₃₁	1	16	yes	—
623	C₂×Q₈	C₂⁴×C₃₁	1	8	yes	—
624	C₂×D₄	—	2	8	no	—
625	C₂×D₄	—	2	16	no	—
626	C₂×D₄	—	2	8	no	—
627	C₂×D₄	—	4	8	no	—
628	C₂×D₄	—	4	4	no	—
629	C₂×D₄	—	4	2	no	—
630	C₂×D₄	—	4	8	no	—
631	C₂×D₄	—	4	4	no	—
632	C₂×D₄	C₂⁴×C₃₁	1	8	yes	—
633	C₂×D₄	C₂⁴×C₃₁	1	8	yes	—
634	C₂×D₄	C₂⁴×C₃₁	1	16	yes	—
635	C₂×D₄	C₂⁴×C₃₁	1	16	yes	—
636	C₂×D₄	C₂⁴×C₃₁	1	4	yes	—
637	C₂×D₄	C₂⁴×C₃₁	1	8	yes	—
638	C₂×D₄	C₂⁴×C₃₁	1	16	yes	—
639	C₂×D₄	C₂⁴×C₃₁	1	8	yes	—
640	C₂²×C₄	—	2	4	no	—
641	C₂²×C₄	—	2	8	no	—
642	C₂²×C₄	—	2	4	no	—
643	C₂²×C₄	—	2	8	no	—
644	C₂²×C₄	—	4	4	no	—
645	C₂²×C₄	—	4	8	no	—
646	C₂²×C₄	—	4	2	no	—
647	C₂²×C₄	—	4	8	no	—
648	C₂²×C₄	—	4	8	no	—
649	C₂²×C₄	—	4	8	no	—
650	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
651	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
652	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
653	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
654	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
655	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
656	C₂²×C₄	C₂⁴×C₃₁	1	4	yes	—
657	C₂²×C₄	C₂⁴×C₃₁	1	4	yes	—
658	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
659	C₂²×C₄	C₂⁴×C₃₁	1	4	yes	—
660	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
661	C₂²×C₄	C₂⁴×C₃₁	1	4	yes	—
662	C₂²×C₄	C₂⁴×C₃₁	1	4	yes	—
663	C₂²×C₄	C₂⁴×C₃₁	1	8	yes	—
664	C₂²×C₄	C₂⁴×C₃₁	1	8	yes	—
665	C₂²×C₄	C₂⁴×C₃₁	1	4	yes	—
666	C₂²×C₄	C₂⁴×C₃₁	1	8	yes	—
667	C₂²×C₄	C₂⁴×C₃₁	1	16	yes	—
668	C₂²×C₄	C₂⁴×C₃₁	1	16	yes	—
669	C₂²×C₄	C₂⁴×C₃₁	1	16	yes	—
670	C₂²×C₄	C₂⁴×C₃₁	1	16	yes	—
671	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
672	C₄⋊C₄	C₂⁴×C₃₁	1	8	yes	—
673	C₄⋊C₄	C₂⁴×C₃₁	1	16	yes	—
674	C₄⋊C₄	C₂⁴×C₃₁	1	8	yes	—
675	C₄⋊C₄	C₂⁴×C₃₁	1	8	yes	—
676	C₄⋊C₄	C₂⁴×C₃₁	1	8	yes	—
677	C₄⋊C₄	C₂⁴×C₃₁	1	16	yes	—
678	C₄⋊C₄	C₂⁴×C₃₁	1	16	yes	—
679	C₄⋊C₄	C₂⁴×C₃₁	1	16	yes	—
680	C₄⋊C₄	C₂⁴×C₃₁	1	16	yes	—
681	C₄⋊C₄	C₂⁴×C₃₁	1	8	yes	—
682	C₄⋊C₄	C₂⁴×C₃₁	1	16	yes	—
683	C₄⋊C₄	C₂⁴×C₃₁	1	16	yes	—
684	C₄⋊C₄	C₂⁴×C₃₁	1	8	yes	—
685	C₄⋊C₄	C₂⁴×C₃₁	1	8	yes	—
686	C₄⋊C₄	C₂⁴×C₃₁	1	8	yes	—
687	C₄⋊C₄	C₂⁴×C₃₁	1	8	yes	—
688	C₄⋊C₄	C₂⁴×C₃₁	1	16	yes	—
689	C₄⋊C₄	C₂⁴×C₃₁	1	8	yes	—
690	C₄⋊C₄	C₂⁴×C₃₁	1	4	yes	—
691	C₄⋊C₄	C₂⁴×C₃₁	1	4	yes	—
692	C₂²⋊C₄	C₂⁴×C₃₁	1	8	yes	—
693	C₂²⋊C₄	C₂⁴×C₃₁	1	16	yes	—
694	C₂²⋊C₄	C₂⁴×C₃₁	1	8	yes	—
695	C₂²⋊C₄	C₂⁴×C₃₁	1	8	yes	—
696	C₂²⋊C₄	C₂⁴×C₃₁	1	8	yes	—
697	C₂²⋊C₄	C₂⁴×C₃₁	1	16	yes	—
698	C₂²⋊C₄	C₂⁴×C₃₁	1	16	yes	—
699	C₂²⋊C₄	C₂⁴×C₃₁	1	16	yes	—
700	C₂²⋊C₄	C₂⁴×C₃₁	1	16	yes	—
701	C₂²⋊C₄	C₂⁴×C₃₁	1	16	yes	—
702	C₂²⋊C₄	C₂⁴×C₃₁	1	16	yes	—
703	C₂²⋊C₄	C₂⁴×C₃₁	1	8	yes	—
704	C₄²	C₂⁴×C₃₁	1	4	yes	—
705	C₄²	C₂⁴×C₃₁	1	4	yes	—
706	C₄²	C₂⁴×C₃₁	1	4	yes	—
707	C₄²	C₂⁴×C₃₁	1	4	yes	—
708	C₄²	C₂⁴×C₃₁	1	8	yes	—
709	C₄²	C₂⁴×C₃₁	1	16	yes	—
710	C₂³	—	2	2	no	—
711	C₂³	—	2	2	no	—
712	C₂³	—	2	4	no	—
713	C₂³	—	2	8	no	—
714	C₂³	—	2	4	no	—
715	C₂³	—	2	8	no	—
716	C₂³	—	2	8	no	—
717	C₂³	—	2	4	no	—
718	C₂³	C₃₁×H(5,𝔽₂)	1	4	yes	—
719	C₂³	C₂⁵×C₃₁	1	4	yes	—
720	C₂³	C₂⁵×C₃₁	1	8	yes	—
721	C₂³	C₂⁵×C₃₁	1	2	yes	—
722	C₂³	C₂⁵×C₃₁	1	1	yes	characteristic
723	Q₈	—	4	4	no	—
724	Q₈	—	4	16	no	—
725	Q₈	—	4	8	no	—
726	D₄	—	2	16	no	—
727	D₄	—	2	32	no	—
728	D₄	—	2	16	no	—
729	D₄	—	4	16	no	—
730	D₄	—	4	8	no	—
731	D₄	—	4	4	no	—
732	D₄	—	4	16	no	—
733	D₄	—	4	8	no	—
734	C₂×C₄	—	2	2	no	—
735	C₂×C₄	—	2	8	no	—
736	C₂×C₄	—	2	2	no	—
737	C₂×C₄	—	2	8	no	—
738	C₂×C₄	—	2	16	no	—
739	C₂×C₄	—	2	8	no	—
740	C₂×C₄	—	2	4	no	—
741	C₂×C₄	—	2	2	no	—
742	C₂×C₄	—	2	4	no	—
743	C₂×C₄	—	2	8	no	—
744	C₂×C₄	—	2	4	no	—
745	C₂×C₄	—	2	2	no	—
746	C₂×C₄	—	2	2	no	—
747	C₂×C₄	—	2	8	no	—
748	C₂×C₄	—	2	16	no	—
749	C₂×C₄	—	4	8	no	—
750	C₂×C₄	—	4	16	no	—
751	C₂×C₄	—	4	4	no	—
752	C₂×C₄	—	4	16	no	—
753	C₂×C₄	—	4	16	no	—
754	C₂×C₄	—	4	16	no	—
755	C₂×C₄	C₃₁×2₋¹⁺⁴	1	4	yes	—
756	C₂×C₄	C₂⁵×C₃₁	1	2	yes	—
757	C₂×C₄	C₂⁵×C₃₁	1	4	yes	—
758	C₂×C₄	C₂⁵×C₃₁	1	2	yes	—
759	C₂×C₄	C₂⁵×C₃₁	1	2	yes	—
760	C₂×C₄	C₂⁵×C₃₁	1	2	yes	—
761	C₂×C₄	C₂⁵×C₃₁	1	2	yes	—
762	C₂×C₄	C₂⁵×C₃₁	1	4	yes	—
763	C₂×C₄	C₂⁵×C₃₁	1	8	yes	—
764	C₂×C₄	C₂⁵×C₃₁	1	4	yes	—
765	C₂×C₄	C₂⁵×C₃₁	1	8	yes	—
766	C₂×C₄	C₂⁵×C₃₁	1	8	yes	—
767	C₂×C₄	C₂⁵×C₃₁	1	2	yes	—
768	C₂²	—	2	2	no	—
769	C₂²	—	2	2	no	—
770	C₂²	—	2	8	no	—
771	C₂²	—	2	4	no	—
772	C₂²	—	2	8	no	—
773	C₂²	—	2	4	no	—
774	C₂²	—	2	8	no	—
775	C₂²	—	2	8	no	—
776	C₂²	—	2	4	no	—
777	C₂²	—	4	8	no	—
778	C₂²	—	4	16	no	—
779	C₂²	C₂×C₃₁×H(5,𝔽₂)	1	4	yes	—
780	C₂²	C₂×C₃₁×H(5,𝔽₂)	1	2	yes	—
781	C₂²	C₂×C₃₁×2₋¹⁺⁴	1	2	yes	—
782	C₂²	C₃₁×#585	1	2	yes	—
783	C₂²	C₂⁶×C₃₁	1	1	yes	characteristic
784	C₄	—	2	2	no	—
785	C₄	—	2	8	no	—
786	C₄	—	2	2	no	—
787	C₄	—	2	8	no	—
788	C₄	—	2	4	no	—
789	C₄	—	2	2	no	—
790	C₄	—	2	4	no	—
791	C₄	—	2	8	no	—
792	C₄	—	2	4	no	—
793	C₄	—	2	2	no	—
794	C₄	—	2	2	no	—
795	C₄	C₂×C₃₁×2₋¹⁺⁴	1	4	yes	—
796	C₂	—	2	4	no	—
797	C₂	—	4	4	no	—
798	C₂	—	4	8	no	—
799	C₂	C₃₁×#3559	1	4	yes	direct product factor
800	C₂	C₂²×C₃₁×H(5,𝔽₂)	1	1	yes	characteristic
801	C₂	C₂²×C₃₁×2₋¹⁺⁴	1	1	yes	characteristic
802	C₂	C₂×C₃₁×#585	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₃₁	C₂⁵
commutator, Frattini, cosocle	C₂²	C₂⁶×C₃₁
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃₁×#3559	C₂	direct (N × H)
2. C₂×C₃₁×#563	C₂	semidirect
3. C₂×C₃₁×#562	C₂	semidirect
4. C₂×C₃₁×#554	C₂	semidirect
5. C₂×C₃₁×#553	C₂	semidirect
6. C₂×C₃₁×#553	C₂	semidirect
7. C₂×C₃₁×#547	C₂	semidirect
8. C₂×C₃₁×#547	C₂	semidirect
9. C₂×C₃₁×#544	C₂	semidirect
10. C₂×C₃₁×#540	C₂	semidirect
11. C₂×C₃₁×#539	C₂	semidirect
12. C₂×C₃₁×#539	C₂	semidirect
13. C₂×C₃₁×#537	C₂	semidirect
14. C₂×C₃₁×#532	C₂	semidirect
15. C₂×C₃₁×#529	C₂	semidirect
16. C₂²×C₃₁×#125	C₂	semidirect
19. C₃₁×#563	C₂²	semidirect
20. C₃₁×#562	C₂²	semidirect
21. C₃₁×#554	C₂²	semidirect
22. C₃₁×#553	C₂²	semidirect
23. C₃₁×#553	C₂²	semidirect
24. C₃₁×#547	C₂²	semidirect
25. C₃₁×#547	C₂²	semidirect
26. C₃₁×#544	C₂²	semidirect
27. C₃₁×#540	C₂²	semidirect
28. C₃₁×#539	C₂²	semidirect
29. C₃₁×#539	C₂²	semidirect
30. C₃₁×#537	C₂²	semidirect
31. C₃₁×#532	C₂²	semidirect
36. C₃₁×#529	C₂²	semidirect
47. C₂×C₃₁×#125	C₂²	semidirect
308. C₂×#3559	C₃₁	direct (N × H)
367. #3559	C₂×C₃₁	direct (N × H)
368. C₂×#563	C₂×C₃₁	semidirect
369. C₂×#562	C₂×C₃₁	semidirect
370. C₂×#554	C₂×C₃₁	semidirect
371. C₂×#553	C₂×C₃₁	semidirect
372. C₂×#553	C₂×C₃₁	semidirect
373. C₂×#547	C₂×C₃₁	semidirect
374. C₂×#547	C₂×C₃₁	semidirect
375. C₂×#544	C₂×C₃₁	semidirect
376. C₂×#540	C₂×C₃₁	semidirect
377. C₂×#539	C₂×C₃₁	semidirect
378. C₂×#539	C₂×C₃₁	semidirect
379. C₂×#537	C₂×C₃₁	semidirect
380. C₂×#532	C₂×C₃₁	semidirect
381. C₂×#529	C₂×C₃₁	semidirect
382. C₂²×#125	C₂×C₃₁	semidirect
413. #563	C₂²×C₃₁	semidirect
414. #562	C₂²×C₃₁	semidirect
415. #554	C₂²×C₃₁	semidirect
416. #553	C₂²×C₃₁	semidirect
417. #553	C₂²×C₃₁	semidirect
418. #547	C₂²×C₃₁	semidirect
419. #547	C₂²×C₃₁	semidirect
420. #544	C₂²×C₃₁	semidirect
421. #540	C₂²×C₃₁	semidirect
422. #539	C₂²×C₃₁	semidirect
423. #539	C₂²×C₃₁	semidirect
424. #537	C₂²×C₃₁	semidirect
425. #532	C₂²×C₃₁	semidirect
430. #529	C₂²×C₃₁	semidirect
441. C₂×#125	C₂²×C₃₁	semidirect
488. C₂×C₃₁	#3559	direct (N × H)
612. C₃₁	C₂×#3559	direct (N × H)
799. C₂	C₃₁×#3559	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×#3559	2
C₂×C₃₁×#563	2
C₂×C₃₁×#562	2
C₂×C₃₁×#554	2
C₂×C₃₁×#553	2
C₂×C₃₁×#547	2
C₂×C₃₁×#544	2
C₂×C₃₁×#540	2
C₂×C₃₁×#539	2
C₂×C₃₁×#537	2
C₂×C₃₁×#532	2
C₂×C₃₁×#529	2
C₂²×C₃₁×#125	2
C₂×#3559	31

Subgroups — C2×C31×#3559 #21519491

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃₁×#3559 #21519491