Subgroups — C₂×C₃₁×#3488 #21519553

Order 7936.

12366 conjugacy classes of subgroups.

The subgroup lattice has 644 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃₁×H(5,𝔽₂)	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂³×#41×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#3488	C₂	1	32	yes	maximal, direct product factor
4	C₂×C₃₁×#550	C₂	1	2	yes	maximal, complemented
5	C₂×C₃₁×#548	C₂	1	2	yes	maximal, complemented
6	C₂×C₃₁×#546	C₂	1	6	yes	maximal, complemented
7	C₂×D₄²×C₃₁	C₂	1	6	yes	maximal, complemented
8	C₂×C₃₁×#537	C₂	1	3	yes	maximal, complemented
9	C₂×C₃₁×#535	C₂	1	3	yes	maximal, complemented
10	C₂×C₃₁×#525	C₂	1	3	yes	maximal, complemented
11	C₂²×C₃₁×#121	C₂	1	3	yes	maximal, complemented
12	C₂×C₃₁×#520	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×C₃₁×H(5,𝔽₂)	—	2	16	no	—
14	C₂×C₃₁×H(5,𝔽₂)	C₂²	1	16	yes	complemented
15	C₂²×#41×C₃₁	—	2	16	no	—
16	C₂²×#41×C₃₁	C₂²	1	1	yes	characteristic
17	C₂²×#41×C₃₁	C₂²	1	3	yes	complemented
18	C₂²×#41×C₃₁	C₂²	1	3	yes	complemented
19	C₂²×#41×C₃₁	C₂²	1	1	yes	characteristic, complemented
20	C₂²×#41×C₃₁	C₂²	1	3	yes	complemented
21	C₂²×#41×C₃₁	C₂²	1	2	yes	complemented
22	C₂²×#41×C₃₁	C₂²	1	16	yes	complemented
23	C₂³×Q₈×C₃₁	C₂²	1	1	yes	characteristic, complemented
24	C₂³×D₄×C₃₁	C₂²	1	3	yes	complemented
25	C₂³×D₄×C₃₁	C₂²	1	3	yes	complemented
26	C₂³×D₄×C₃₁	C₂²	1	6	yes	complemented
27	C₂³×D₄×C₃₁	C₂²	1	6	yes	complemented
28	C₂⁴×C₄×C₃₁	C₂²	1	3	yes	complemented
29	C₃₁×#550	C₂²	1	32	yes	complemented
30	C₃₁×#548	C₂²	1	32	yes	complemented
31	C₃₁×#546	C₂²	1	96	yes	complemented
32	D₄²×C₃₁	C₂²	1	96	yes	complemented
33	C₃₁×#537	C₂²	1	48	yes	complemented
34	C₃₁×#535	C₂²	1	48	yes	complemented
35	C₂×C₃₁×#127	C₂²	1	6	yes	complemented
36	C₂×C₃₁×#124	C₂²	1	6	yes	complemented
37	C₃₁×#525	C₂²	1	48	yes	complemented
38	C₂×C₃₁×#123	C₂²	1	6	yes	complemented
39	C₂×C₃₁×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
40	C₂×C₃₁×C₂²⋊Q₈	C₂²	1	3	yes	complemented
41	C₂×C₃₁×C₂²⋊Q₈	C₂²	1	6	yes	complemented
42	C₂×C₃₁×#121	C₂²	1	3	yes	complemented
43	C₂×C₃₁×#121	C₂²	1	6	yes	complemented
44	C₂×C₃₁×#121	C₂²	1	6	yes	complemented
45	C₂×C₃₁×#121	C₂²	1	6	yes	complemented
46	C₂×C₃₁×#121	C₂²	1	3	yes	complemented
47	C₂×C₃₁×#121	C₂²	1	12	yes	complemented
48	C₂×C₃₁×#121	C₂²	1	6	yes	complemented
49	C₂×C₃₁×#121	C₂²	1	48	yes	complemented
50	C₂×C₃₁×#120	C₂²	1	6	yes	complemented
51	C₂×C₃₁×#120	C₂²	1	12	yes	complemented
52	C₃₁×#520	C₂²	1	16	yes	complemented
53	C₂×C₄×Q₈×C₃₁	C₂²	1	2	yes	complemented
54	C₂×C₄×D₄×C₃₁	C₂²	1	6	yes	complemented
55	C₂×C₄×D₄×C₃₁	C₂²	1	6	yes	complemented
56	C₂×C₄×D₄×C₃₁	C₂²	1	6	yes	complemented
57	C₂×C₃₁×#117	C₂²	1	3	yes	complemented
58	C₂²×C₄⋊C₄×C₃₁	C₂²	1	3	yes	complemented
59	C₂²×C₂²⋊C₄×C₃₁	C₂²	1	6	yes	complemented
60	C₂⁵×C₃₁	C₂³	1	3	yes	—
61	C₂⁵×C₃₁	C₂³	1	6	yes	—
62	C₃₁×H(5,𝔽₂)	—	2	128	no	—
63	C₂×#41×C₃₁	—	2	128	no	—
64	C₂×#41×C₃₁	—	2	8	no	—
65	C₂×#41×C₃₁	—	2	16	no	—
66	C₂×#41×C₃₁	—	2	24	no	—
67	C₂×#41×C₃₁	—	2	24	no	—
68	C₂×#41×C₃₁	—	2	24	no	—
69	C₂×#41×C₃₁	D₄	1	16	yes	complemented
70	C₂×#41×C₃₁	C₂³	1	8	yes	—
71	C₂×#41×C₃₁	C₂³	1	24	yes	complemented
72	C₂×#41×C₃₁	C₂³	1	24	yes	complemented
73	C₂×#41×C₃₁	C₂³	1	24	yes	complemented
74	C₂×#41×C₃₁	C₂³	1	16	yes	complemented
75	C₂×#41×C₃₁	C₂³	1	8	yes	complemented
76	C₂²×Q₈×C₃₁	—	2	8	no	—
77	C₂²×Q₈×C₃₁	C₂³	1	1	yes	characteristic
78	C₂²×Q₈×C₃₁	C₂³	1	3	yes	—
79	C₂²×Q₈×C₃₁	C₂³	1	1	yes	characteristic
80	C₂²×Q₈×C₃₁	C₂³	1	8	yes	complemented
81	C₂²×D₄×C₃₁	—	2	24	no	—
82	C₂²×D₄×C₃₁	—	2	48	no	—
83	C₂²×D₄×C₃₁	—	2	24	no	—
84	C₂²×D₄×C₃₁	—	4	24	no	—
85	C₂²×D₄×C₃₁	C₂³	1	6	yes	—
86	C₂²×D₄×C₃₁	C₂³	1	6	yes	—
87	C₂²×D₄×C₃₁	C₂³	1	6	yes	—
88	C₂²×D₄×C₃₁	C₂³	1	3	yes	—
89	C₂²×D₄×C₃₁	C₂³	1	6	yes	—
90	C₂²×D₄×C₃₁	C₂³	1	3	yes	—
91	C₂²×D₄×C₃₁	C₂³	1	6	yes	—
92	C₂²×D₄×C₃₁	C₂³	1	12	yes	—
93	C₂²×D₄×C₃₁	C₂³	1	3	yes	—
94	C₂²×D₄×C₃₁	C₂³	1	24	yes	complemented
95	C₂²×D₄×C₃₁	C₂³	1	24	yes	complemented
96	C₂²×D₄×C₃₁	C₂³	1	48	yes	complemented
97	C₂²×D₄×C₃₁	C₂³	1	48	yes	complemented
98	C₂³×C₄×C₃₁	—	2	24	no	—
99	C₂³×C₄×C₃₁	C₂³	1	3	yes	—
100	C₂³×C₄×C₃₁	C₂³	1	3	yes	—
101	C₂³×C₄×C₃₁	C₂³	1	3	yes	—
102	C₂³×C₄×C₃₁	C₂³	1	6	yes	—
103	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
104	C₂³×C₄×C₃₁	C₂³	1	3	yes	—
105	C₂³×C₄×C₃₁	C₂³	1	6	yes	—
106	C₂³×C₄×C₃₁	C₂³	1	3	yes	—
107	C₂³×C₄×C₃₁	C₂³	1	24	yes	complemented
108	C₃₁×#127	C₂³	1	48	yes	complemented
109	C₃₁×#124	C₂³	1	48	yes	complemented
110	C₃₁×#123	C₂³	1	48	yes	complemented
111	C₃₁×C₂²⋊Q₈	C₂³	1	8	yes	complemented
112	C₃₁×C₂²⋊Q₈	C₂³	1	24	yes	complemented
113	C₃₁×C₂²⋊Q₈	C₂³	1	48	yes	complemented
114	C₃₁×#121	C₂³	1	24	yes	complemented
115	C₃₁×#121	C₂³	1	48	yes	complemented
116	C₃₁×#121	C₂³	1	48	yes	complemented
117	C₃₁×#121	C₂³	1	48	yes	complemented
118	C₃₁×#121	C₂³	1	24	yes	complemented
119	C₃₁×#121	C₂³	1	96	yes	complemented
120	C₃₁×#121	C₂³	1	48	yes	complemented
121	C₃₁×#120	C₂³	1	48	yes	complemented
122	C₃₁×#120	C₂³	1	96	yes	complemented
123	C₄×Q₈×C₃₁	C₂³	1	16	yes	complemented
124	C₄×D₄×C₃₁	C₂³	1	48	yes	complemented
125	C₄×D₄×C₃₁	C₂³	1	48	yes	complemented
126	C₄×D₄×C₃₁	C₂³	1	48	yes	complemented
127	C₃₁×#117	C₂³	1	24	yes	complemented
128	C₂×C₄⋊C₄×C₃₁	C₂³	1	3	yes	—
129	C₂×C₄⋊C₄×C₃₁	C₂³	1	6	yes	—
130	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
131	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
132	C₂×C₄⋊C₄×C₃₁	C₂³	1	6	yes	—
133	C₂×C₄⋊C₄×C₃₁	C₂³	1	24	yes	complemented
134	C₂×C₂²⋊C₄×C₃₁	C₂³	1	6	yes	—
135	C₂×C₂²⋊C₄×C₃₁	C₂³	1	12	yes	—
136	C₂×C₂²⋊C₄×C₃₁	C₂³	1	6	yes	—
137	C₂×C₂²⋊C₄×C₃₁	C₂³	1	2	yes	—
138	C₂×C₂²⋊C₄×C₃₁	C₂³	1	6	yes	—
139	C₂×C₂²⋊C₄×C₃₁	C₂³	1	6	yes	—
140	C₂×C₂²⋊C₄×C₃₁	C₂³	1	48	yes	complemented
141	C₂×C₄²×C₃₁	C₂³	1	6	yes	—
142	C₂⁴×C₃₁	—	2	12	no	—
143	C₂⁴×C₃₁	—	2	12	no	—
144	C₂⁴×C₃₁	—	2	24	no	—
145	C₂⁴×C₃₁	—	4	6	no	—
146	C₂⁴×C₃₁	—	4	12	no	—
147	C₂⁴×C₃₁	—	4	12	no	—
148	C₂⁴×C₃₁	C₂⁴	1	6	yes	—
149	C₂⁴×C₃₁	C₂⁴	1	3	yes	—
150	C₂⁴×C₃₁	C₂⁴	1	12	yes	—
151	C₂⁴×C₃₁	C₂⁴	1	3	yes	—
152	C₂⁴×C₃₁	C₂⁴	1	1	yes	characteristic
153	C₂⁴×C₃₁	C₂⁴	1	24	yes	—
154	#41×C₃₁	—	2	32	no	—
155	#41×C₃₁	—	2	64	no	—
156	#41×C₃₁	—	2	96	no	—
157	#41×C₃₁	—	2	96	no	—
158	#41×C₃₁	—	2	96	no	—
159	#41×C₃₁	C₂×D₄	1	64	yes	complemented
160	C₂×Q₈×C₃₁	—	2	32	no	—
161	C₂×Q₈×C₃₁	—	2	12	no	—
162	C₂×Q₈×C₃₁	—	2	4	no	—
163	C₂×Q₈×C₃₁	C₂×D₄	1	8	yes	complemented
164	C₂×Q₈×C₃₁	C₂⁴	1	4	yes	—
165	C₂×Q₈×C₃₁	C₂⁴	1	12	yes	—
166	C₂×Q₈×C₃₁	C₂⁴	1	4	yes	—
167	C₂×D₄×C₃₁	—	2	24	no	—
168	C₂×D₄×C₃₁	—	2	24	no	—
169	C₂×D₄×C₃₁	—	2	24	no	—
170	C₂×D₄×C₃₁	—	2	96	no	—
171	C₂×D₄×C₃₁	—	2	192	no	—
172	C₂×D₄×C₃₁	—	2	12	no	—
173	C₂×D₄×C₃₁	—	2	24	no	—
174	C₂×D₄×C₃₁	—	2	12	no	—
175	C₂×D₄×C₃₁	—	2	96	no	—
176	C₂×D₄×C₃₁	—	4	24	no	—
177	C₂×D₄×C₃₁	—	4	12	no	—
178	C₂×D₄×C₃₁	—	4	96	no	—
179	C₂×D₄×C₃₁	C₂×D₄	1	24	yes	complemented
180	C₂×D₄×C₃₁	C₂⁴	1	24	yes	—
181	C₂×D₄×C₃₁	C₂⁴	1	24	yes	—
182	C₂×D₄×C₃₁	C₂⁴	1	24	yes	—
183	C₂×D₄×C₃₁	C₂⁴	1	12	yes	—
184	C₂×D₄×C₃₁	C₂⁴	1	24	yes	—
185	C₂×D₄×C₃₁	C₂⁴	1	12	yes	—
186	C₂×D₄×C₃₁	C₂⁴	1	24	yes	—
187	C₂×D₄×C₃₁	C₂⁴	1	48	yes	—
188	C₂×D₄×C₃₁	C₂⁴	1	12	yes	—
189	C₂²×C₄×C₃₁	—	2	12	no	—
190	C₂²×C₄×C₃₁	—	2	4	no	—
191	C₂²×C₄×C₃₁	—	2	12	no	—
192	C₂²×C₄×C₃₁	—	2	12	no	—
193	C₂²×C₄×C₃₁	—	2	12	no	—
194	C₂²×C₄×C₃₁	—	2	24	no	—
195	C₂²×C₄×C₃₁	—	2	96	no	—
196	C₂²×C₄×C₃₁	—	4	12	no	—
197	C₂²×C₄×C₃₁	C₂×D₄	1	24	yes	complemented
198	C₂²×C₄×C₃₁	C₂⁴	1	12	yes	—
199	C₂²×C₄×C₃₁	C₂⁴	1	12	yes	—
200	C₂²×C₄×C₃₁	C₂⁴	1	12	yes	—
201	C₂²×C₄×C₃₁	C₂⁴	1	24	yes	—
202	C₂²×C₄×C₃₁	C₂⁴	1	4	yes	—
203	C₂²×C₄×C₃₁	C₂⁴	1	12	yes	—
204	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
205	C₂²×C₄×C₃₁	C₂⁴	1	6	yes	—
206	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
207	C₂²×C₄×C₃₁	C₂⁴	1	3	yes	—
208	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
209	C₂²×C₄×C₃₁	C₂⁴	1	24	yes	—
210	C₂²×C₄×C₃₁	C₂⁴	1	3	yes	—
211	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
212	C₂²×C₄×C₃₁	C₂⁴	1	12	yes	—
213	C₄⋊C₄×C₃₁	C₂⁴	1	12	yes	—
214	C₄⋊C₄×C₃₁	C₂⁴	1	24	yes	—
215	C₄⋊C₄×C₃₁	C₂⁴	1	4	yes	—
216	C₄⋊C₄×C₃₁	C₂⁴	1	8	yes	—
217	C₄⋊C₄×C₃₁	C₂⁴	1	24	yes	—
218	C₂²⋊C₄×C₃₁	C₂⁴	1	24	yes	—
219	C₂²⋊C₄×C₃₁	C₂⁴	1	48	yes	—
220	C₂²⋊C₄×C₃₁	C₂⁴	1	24	yes	—
221	C₂²⋊C₄×C₃₁	C₂⁴	1	8	yes	—
222	C₂²⋊C₄×C₃₁	C₂⁴	1	24	yes	—
223	C₂²⋊C₄×C₃₁	C₂⁴	1	24	yes	—
224	C₄²×C₃₁	C₂⁴	1	24	yes	—
225	C₂×#3488	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
226	C₂³×C₃₁	—	2	2	no	—
227	C₂³×C₃₁	—	2	6	no	—
228	C₂³×C₃₁	—	2	2	no	—
229	C₂³×C₃₁	—	2	6	no	—
230	C₂³×C₃₁	—	2	24	no	—
231	C₂³×C₃₁	—	2	6	no	—
232	C₂³×C₃₁	—	2	12	no	—
233	C₂³×C₃₁	—	2	12	no	—
234	C₂³×C₃₁	—	2	6	no	—
235	C₂³×C₃₁	—	2	24	no	—
236	C₂³×C₃₁	—	2	6	no	—
237	C₂³×C₃₁	—	2	12	no	—
238	C₂³×C₃₁	—	2	48	no	—
239	C₂³×C₃₁	—	4	12	no	—
240	C₂³×C₃₁	—	4	24	no	—
241	C₂³×C₃₁	—	4	24	no	—
242	C₂³×C₃₁	—	4	48	no	—
243	C₂³×C₃₁	—	8	48	no	—
244	C₂³×C₃₁	C₂²×D₄	1	12	yes	—
245	C₂³×C₃₁	H(5,𝔽₂)	1	4	yes	complemented
246	C₂³×C₃₁	C₂⁵	1	12	yes	—
247	C₂³×C₃₁	C₂⁵	1	6	yes	—
248	C₂³×C₃₁	C₂⁵	1	6	yes	—
249	C₂³×C₃₁	C₂⁵	1	2	yes	—
250	C₂³×C₃₁	C₂⁵	1	1	yes	characteristic
251	Q₈×C₃₁	—	2	24	no	—
252	Q₈×C₃₁	—	2	8	no	—
253	Q₈×C₃₁	C₂²×D₄	1	16	yes	complemented
254	D₄×C₃₁	—	2	48	no	—
255	D₄×C₃₁	—	2	48	no	—
256	D₄×C₃₁	—	2	48	no	—
257	D₄×C₃₁	—	2	24	no	—
258	D₄×C₃₁	—	2	48	no	—
259	D₄×C₃₁	—	2	24	no	—
260	D₄×C₃₁	—	4	48	no	—
261	D₄×C₃₁	—	4	24	no	—
262	D₄×C₃₁	C₂²×D₄	1	48	yes	complemented
263	C₂×C₄×C₃₁	—	2	2	no	—
264	C₂×C₄×C₃₁	—	2	4	no	—
265	C₂×C₄×C₃₁	—	2	6	no	—
266	C₂×C₄×C₃₁	—	2	24	no	—
267	C₂×C₄×C₃₁	—	2	12	no	—
268	C₂×C₄×C₃₁	—	2	4	no	—
269	C₂×C₄×C₃₁	—	2	8	no	—
270	C₂×C₄×C₃₁	—	2	24	no	—
271	C₂×C₄×C₃₁	—	2	24	no	—
272	C₂×C₄×C₃₁	—	2	24	no	—
273	C₂×C₄×C₃₁	—	2	48	no	—
274	C₂×C₄×C₃₁	—	4	24	no	—
275	C₂×C₄×C₃₁	C₂²×D₄	1	4	yes	—
276	C₂×C₄×C₃₁	C₂²×D₄	1	12	yes	—
277	C₂×C₄×C₃₁	C₂²×D₄	1	48	yes	complemented
278	C₂×C₄×C₃₁	C₂⁵	1	4	yes	—
279	C₂×C₄×C₃₁	C₂⁵	1	12	yes	—
280	C₂×C₄×C₃₁	C₂⁵	1	2	yes	—
281	C₂×C₄×C₃₁	C₂⁵	1	6	yes	—
282	C₂×C₄×C₃₁	C₂⁵	1	4	yes	—
283	C₂×C₄×C₃₁	C₂⁵	1	6	yes	—
284	C₂×C₄×C₃₁	C₂⁵	1	2	yes	—
285	C₂²×H(5,𝔽₂)	C₂×C₃₁	1	1	yes	characteristic, complemented
286	C₂³×#41	C₂×C₃₁	1	1	yes	characteristic, complemented
287	#3488	C₂×C₃₁	1	32	yes	direct product factor
288	C₂×#550	C₂×C₃₁	1	2	yes	complemented
289	C₂×#548	C₂×C₃₁	1	2	yes	complemented
290	C₂×#546	C₂×C₃₁	1	6	yes	complemented
291	C₂×D₄²	C₂×C₃₁	1	6	yes	complemented
292	C₂×#537	C₂×C₃₁	1	3	yes	complemented
293	C₂×#535	C₂×C₃₁	1	3	yes	complemented
294	C₂×#525	C₂×C₃₁	1	3	yes	complemented
295	C₂²×#121	C₂×C₃₁	1	3	yes	complemented
296	C₂×#520	C₂×C₃₁	1	1	yes	characteristic, complemented
297	C₂²×C₃₁	—	2	2	no	—
298	C₂²×C₃₁	—	2	6	no	—
299	C₂²×C₃₁	—	2	2	no	—
300	C₂²×C₃₁	—	2	6	no	—
301	C₂²×C₃₁	—	2	8	no	—
302	C₂²×C₃₁	—	2	24	no	—
303	C₂²×C₃₁	—	2	6	no	—
304	C₂²×C₃₁	—	2	12	no	—
305	C₂²×C₃₁	—	2	12	no	—
306	C₂²×C₃₁	—	2	6	no	—
307	C₂²×C₃₁	—	2	6	no	—
308	C₂²×C₃₁	—	2	12	no	—
309	C₂²×C₃₁	—	4	48	no	—
310	C₂²×C₃₁	—	4	12	no	—
311	C₂²×C₃₁	—	4	24	no	—
312	C₂²×C₃₁	—	8	48	no	—
313	C₂²×C₃₁	C₂³×D₄	1	12	yes	—
314	C₂²×C₃₁	C₂³×D₄	1	2	yes	—
315	C₂²×C₃₁	C₂×H(5,𝔽₂)	1	2	yes	—
316	C₂²×C₃₁	C₂×H(5,𝔽₂)	1	4	yes	complemented
317	C₂²×C₃₁	#585	1	2	yes	—
318	C₂²×C₃₁	C₂⁶	1	1	yes	characteristic
319	C₄×C₃₁	—	2	2	no	—
320	C₄×C₃₁	—	2	4	no	—
321	C₄×C₃₁	—	2	6	no	—
322	C₄×C₃₁	—	2	12	no	—
323	C₄×C₃₁	—	2	4	no	—
324	C₄×C₃₁	C₂³×D₄	1	4	yes	—
325	C₄×C₃₁	C₂³×D₄	1	12	yes	—
326	C₂×H(5,𝔽₂)	—	2	16	no	—
327	C₂×H(5,𝔽₂)	C₂²×C₃₁	1	16	yes	complemented
328	C₂²×#41	—	2	16	no	—
329	C₂²×#41	C₂²×C₃₁	1	1	yes	characteristic
330	C₂²×#41	C₂²×C₃₁	1	3	yes	complemented
331	C₂²×#41	C₂²×C₃₁	1	3	yes	complemented
332	C₂²×#41	C₂²×C₃₁	1	1	yes	characteristic, complemented
333	C₂²×#41	C₂²×C₃₁	1	3	yes	complemented
334	C₂²×#41	C₂²×C₃₁	1	2	yes	complemented
335	C₂²×#41	C₂²×C₃₁	1	16	yes	complemented
336	C₂³×Q₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
337	C₂³×D₄	C₂²×C₃₁	1	3	yes	complemented
338	C₂³×D₄	C₂²×C₃₁	1	3	yes	complemented
339	C₂³×D₄	C₂²×C₃₁	1	6	yes	complemented
340	C₂³×D₄	C₂²×C₃₁	1	6	yes	complemented
341	C₂⁴×C₄	C₂²×C₃₁	1	3	yes	complemented
342	#550	C₂²×C₃₁	1	32	yes	complemented
343	#548	C₂²×C₃₁	1	32	yes	complemented
344	#546	C₂²×C₃₁	1	96	yes	complemented
345	D₄²	C₂²×C₃₁	1	96	yes	complemented
346	#537	C₂²×C₃₁	1	48	yes	complemented
347	#535	C₂²×C₃₁	1	48	yes	complemented
348	C₂×#127	C₂²×C₃₁	1	6	yes	complemented
349	C₂×#124	C₂²×C₃₁	1	6	yes	complemented
350	#525	C₂²×C₃₁	1	48	yes	complemented
351	C₂×#123	C₂²×C₃₁	1	6	yes	complemented
352	C₂×C₂²⋊Q₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
353	C₂×C₂²⋊Q₈	C₂²×C₃₁	1	3	yes	complemented
354	C₂×C₂²⋊Q₈	C₂²×C₃₁	1	6	yes	complemented
355	C₂×#121	C₂²×C₃₁	1	3	yes	complemented
356	C₂×#121	C₂²×C₃₁	1	6	yes	complemented
357	C₂×#121	C₂²×C₃₁	1	6	yes	complemented
358	C₂×#121	C₂²×C₃₁	1	6	yes	complemented
359	C₂×#121	C₂²×C₃₁	1	3	yes	complemented
360	C₂×#121	C₂²×C₃₁	1	12	yes	complemented
361	C₂×#121	C₂²×C₃₁	1	6	yes	complemented
362	C₂×#121	C₂²×C₃₁	1	48	yes	complemented
363	C₂×#120	C₂²×C₃₁	1	6	yes	complemented
364	C₂×#120	C₂²×C₃₁	1	12	yes	complemented
365	#520	C₂²×C₃₁	1	16	yes	complemented
366	C₂×C₄×Q₈	C₂²×C₃₁	1	2	yes	complemented
367	C₂×C₄×D₄	C₂²×C₃₁	1	6	yes	complemented
368	C₂×C₄×D₄	C₂²×C₃₁	1	6	yes	complemented
369	C₂×C₄×D₄	C₂²×C₃₁	1	6	yes	complemented
370	C₂×#117	C₂²×C₃₁	1	3	yes	complemented
371	C₂²×C₄⋊C₄	C₂²×C₃₁	1	3	yes	complemented
372	C₂²×C₂²⋊C₄	C₂²×C₃₁	1	6	yes	complemented
373	C₂×C₃₁	—	2	4	no	—
374	C₂×C₃₁	—	2	12	no	—
375	C₂×C₃₁	—	4	6	no	—
376	C₂×C₃₁	—	4	12	no	—
377	C₂×C₃₁	#3488	1	4	yes	direct product factor
378	C₂×C₃₁	C₂⁴×D₄	1	1	yes	characteristic
379	C₂×C₃₁	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
380	C₂×C₃₁	C₂×#585	1	1	yes	characteristic
381	C₂⁵	C₂³×C₃₁	1	3	yes	—
382	C₂⁵	C₂³×C₃₁	1	6	yes	—
383	H(5,𝔽₂)	—	2	128	no	—
384	C₂×#41	—	2	128	no	—
385	C₂×#41	—	2	8	no	—
386	C₂×#41	—	2	16	no	—
387	C₂×#41	—	2	24	no	—
388	C₂×#41	—	2	24	no	—
389	C₂×#41	—	2	24	no	—
390	C₂×#41	D₄×C₃₁	1	16	yes	complemented
391	C₂×#41	C₂³×C₃₁	1	8	yes	—
392	C₂×#41	C₂³×C₃₁	1	24	yes	complemented
393	C₂×#41	C₂³×C₃₁	1	24	yes	complemented
394	C₂×#41	C₂³×C₃₁	1	24	yes	complemented
395	C₂×#41	C₂³×C₃₁	1	16	yes	complemented
396	C₂×#41	C₂³×C₃₁	1	8	yes	complemented
397	C₂²×Q₈	—	2	8	no	—
398	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
399	C₂²×Q₈	C₂³×C₃₁	1	3	yes	—
400	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
401	C₂²×Q₈	C₂³×C₃₁	1	8	yes	complemented
402	C₂²×D₄	—	2	24	no	—
403	C₂²×D₄	—	2	48	no	—
404	C₂²×D₄	—	2	24	no	—
405	C₂²×D₄	—	4	24	no	—
406	C₂²×D₄	C₂³×C₃₁	1	6	yes	—
407	C₂²×D₄	C₂³×C₃₁	1	6	yes	—
408	C₂²×D₄	C₂³×C₃₁	1	6	yes	—
409	C₂²×D₄	C₂³×C₃₁	1	3	yes	—
410	C₂²×D₄	C₂³×C₃₁	1	6	yes	—
411	C₂²×D₄	C₂³×C₃₁	1	3	yes	—
412	C₂²×D₄	C₂³×C₃₁	1	6	yes	—
413	C₂²×D₄	C₂³×C₃₁	1	12	yes	—
414	C₂²×D₄	C₂³×C₃₁	1	3	yes	—
415	C₂²×D₄	C₂³×C₃₁	1	24	yes	complemented
416	C₂²×D₄	C₂³×C₃₁	1	24	yes	complemented
417	C₂²×D₄	C₂³×C₃₁	1	48	yes	complemented
418	C₂²×D₄	C₂³×C₃₁	1	48	yes	complemented
419	C₂³×C₄	—	2	24	no	—
420	C₂³×C₄	C₂³×C₃₁	1	3	yes	—
421	C₂³×C₄	C₂³×C₃₁	1	3	yes	—
422	C₂³×C₄	C₂³×C₃₁	1	3	yes	—
423	C₂³×C₄	C₂³×C₃₁	1	6	yes	—
424	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
425	C₂³×C₄	C₂³×C₃₁	1	3	yes	—
426	C₂³×C₄	C₂³×C₃₁	1	6	yes	—
427	C₂³×C₄	C₂³×C₃₁	1	3	yes	—
428	C₂³×C₄	C₂³×C₃₁	1	24	yes	complemented
429	#127	C₂³×C₃₁	1	48	yes	complemented
430	#124	C₂³×C₃₁	1	48	yes	complemented
431	#123	C₂³×C₃₁	1	48	yes	complemented
432	C₂²⋊Q₈	C₂³×C₃₁	1	8	yes	complemented
433	C₂²⋊Q₈	C₂³×C₃₁	1	24	yes	complemented
434	C₂²⋊Q₈	C₂³×C₃₁	1	48	yes	complemented
435	#121	C₂³×C₃₁	1	24	yes	complemented
436	#121	C₂³×C₃₁	1	48	yes	complemented
437	#121	C₂³×C₃₁	1	48	yes	complemented
438	#121	C₂³×C₃₁	1	48	yes	complemented
439	#121	C₂³×C₃₁	1	24	yes	complemented
440	#121	C₂³×C₃₁	1	96	yes	complemented
441	#121	C₂³×C₃₁	1	48	yes	complemented
442	#120	C₂³×C₃₁	1	48	yes	complemented
443	#120	C₂³×C₃₁	1	96	yes	complemented
444	C₄×Q₈	C₂³×C₃₁	1	16	yes	complemented
445	C₄×D₄	C₂³×C₃₁	1	48	yes	complemented
446	C₄×D₄	C₂³×C₃₁	1	48	yes	complemented
447	C₄×D₄	C₂³×C₃₁	1	48	yes	complemented
448	#117	C₂³×C₃₁	1	24	yes	complemented
449	C₂×C₄⋊C₄	C₂³×C₃₁	1	3	yes	—
450	C₂×C₄⋊C₄	C₂³×C₃₁	1	6	yes	—
451	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
452	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
453	C₂×C₄⋊C₄	C₂³×C₃₁	1	6	yes	—
454	C₂×C₄⋊C₄	C₂³×C₃₁	1	24	yes	complemented
455	C₂×C₂²⋊C₄	C₂³×C₃₁	1	6	yes	—
456	C₂×C₂²⋊C₄	C₂³×C₃₁	1	12	yes	—
457	C₂×C₂²⋊C₄	C₂³×C₃₁	1	6	yes	—
458	C₂×C₂²⋊C₄	C₂³×C₃₁	1	2	yes	—
459	C₂×C₂²⋊C₄	C₂³×C₃₁	1	6	yes	—
460	C₂×C₂²⋊C₄	C₂³×C₃₁	1	6	yes	—
461	C₂×C₂²⋊C₄	C₂³×C₃₁	1	48	yes	complemented
462	C₂×C₄²	C₂³×C₃₁	1	6	yes	—
463	C₃₁	C₂×#3488	1	1	yes	characteristic, direct product factor, Sylow
464	C₂⁴	—	2	12	no	—
465	C₂⁴	—	2	12	no	—
466	C₂⁴	—	2	24	no	—
467	C₂⁴	—	4	6	no	—
468	C₂⁴	—	4	12	no	—
469	C₂⁴	—	4	12	no	—
470	C₂⁴	C₂⁴×C₃₁	1	6	yes	—
471	C₂⁴	C₂⁴×C₃₁	1	3	yes	—
472	C₂⁴	C₂⁴×C₃₁	1	12	yes	—
473	C₂⁴	C₂⁴×C₃₁	1	3	yes	—
474	C₂⁴	C₂⁴×C₃₁	1	1	yes	characteristic
475	C₂⁴	C₂⁴×C₃₁	1	24	yes	—
476	#41	—	2	32	no	—
477	#41	—	2	64	no	—
478	#41	—	2	96	no	—
479	#41	—	2	96	no	—
480	#41	—	2	96	no	—
481	#41	C₂×D₄×C₃₁	1	64	yes	complemented
482	C₂×Q₈	—	2	32	no	—
483	C₂×Q₈	—	2	12	no	—
484	C₂×Q₈	—	2	4	no	—
485	C₂×Q₈	C₂×D₄×C₃₁	1	8	yes	complemented
486	C₂×Q₈	C₂⁴×C₃₁	1	4	yes	—
487	C₂×Q₈	C₂⁴×C₃₁	1	12	yes	—
488	C₂×Q₈	C₂⁴×C₃₁	1	4	yes	—
489	C₂×D₄	—	2	24	no	—
490	C₂×D₄	—	2	24	no	—
491	C₂×D₄	—	2	24	no	—
492	C₂×D₄	—	2	96	no	—
493	C₂×D₄	—	2	192	no	—
494	C₂×D₄	—	2	12	no	—
495	C₂×D₄	—	2	24	no	—
496	C₂×D₄	—	2	12	no	—
497	C₂×D₄	—	2	96	no	—
498	C₂×D₄	—	4	24	no	—
499	C₂×D₄	—	4	12	no	—
500	C₂×D₄	—	4	96	no	—
501	C₂×D₄	C₂×D₄×C₃₁	1	24	yes	complemented
502	C₂×D₄	C₂⁴×C₃₁	1	24	yes	—
503	C₂×D₄	C₂⁴×C₃₁	1	24	yes	—
504	C₂×D₄	C₂⁴×C₃₁	1	24	yes	—
505	C₂×D₄	C₂⁴×C₃₁	1	12	yes	—
506	C₂×D₄	C₂⁴×C₃₁	1	24	yes	—
507	C₂×D₄	C₂⁴×C₃₁	1	12	yes	—
508	C₂×D₄	C₂⁴×C₃₁	1	24	yes	—
509	C₂×D₄	C₂⁴×C₃₁	1	48	yes	—
510	C₂×D₄	C₂⁴×C₃₁	1	12	yes	—
511	C₂²×C₄	—	2	12	no	—
512	C₂²×C₄	—	2	4	no	—
513	C₂²×C₄	—	2	12	no	—
514	C₂²×C₄	—	2	12	no	—
515	C₂²×C₄	—	2	12	no	—
516	C₂²×C₄	—	2	24	no	—
517	C₂²×C₄	—	2	96	no	—
518	C₂²×C₄	—	4	12	no	—
519	C₂²×C₄	C₂×D₄×C₃₁	1	24	yes	complemented
520	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
521	C₂²×C₄	C₂⁴×C₃₁	1	6	yes	—
522	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
523	C₂²×C₄	C₂⁴×C₃₁	1	3	yes	—
524	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
525	C₂²×C₄	C₂⁴×C₃₁	1	12	yes	—
526	C₂²×C₄	C₂⁴×C₃₁	1	12	yes	—
527	C₂²×C₄	C₂⁴×C₃₁	1	12	yes	—
528	C₂²×C₄	C₂⁴×C₃₁	1	24	yes	—
529	C₂²×C₄	C₂⁴×C₃₁	1	4	yes	—
530	C₂²×C₄	C₂⁴×C₃₁	1	12	yes	—
531	C₂²×C₄	C₂⁴×C₃₁	1	24	yes	—
532	C₂²×C₄	C₂⁴×C₃₁	1	3	yes	—
533	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
534	C₂²×C₄	C₂⁴×C₃₁	1	12	yes	—
535	C₄⋊C₄	C₂⁴×C₃₁	1	12	yes	—
536	C₄⋊C₄	C₂⁴×C₃₁	1	24	yes	—
537	C₄⋊C₄	C₂⁴×C₃₁	1	4	yes	—
538	C₄⋊C₄	C₂⁴×C₃₁	1	8	yes	—
539	C₄⋊C₄	C₂⁴×C₃₁	1	24	yes	—
540	C₂²⋊C₄	C₂⁴×C₃₁	1	24	yes	—
541	C₂²⋊C₄	C₂⁴×C₃₁	1	48	yes	—
542	C₂²⋊C₄	C₂⁴×C₃₁	1	24	yes	—
543	C₂²⋊C₄	C₂⁴×C₃₁	1	8	yes	—
544	C₂²⋊C₄	C₂⁴×C₃₁	1	24	yes	—
545	C₂²⋊C₄	C₂⁴×C₃₁	1	24	yes	—
546	C₄²	C₂⁴×C₃₁	1	24	yes	—
547	C₂³	—	2	2	no	—
548	C₂³	—	2	6	no	—
549	C₂³	—	2	2	no	—
550	C₂³	—	2	6	no	—
551	C₂³	—	2	24	no	—
552	C₂³	—	2	6	no	—
553	C₂³	—	2	12	no	—
554	C₂³	—	2	12	no	—
555	C₂³	—	2	6	no	—
556	C₂³	—	2	24	no	—
557	C₂³	—	2	6	no	—
558	C₂³	—	2	12	no	—
559	C₂³	—	2	48	no	—
560	C₂³	—	4	12	no	—
561	C₂³	—	4	24	no	—
562	C₂³	—	4	24	no	—
563	C₂³	—	4	48	no	—
564	C₂³	—	8	48	no	—
565	C₂³	C₂²×D₄×C₃₁	1	12	yes	—
566	C₂³	C₃₁×H(5,𝔽₂)	1	4	yes	complemented
567	C₂³	C₂⁵×C₃₁	1	12	yes	—
568	C₂³	C₂⁵×C₃₁	1	6	yes	—
569	C₂³	C₂⁵×C₃₁	1	6	yes	—
570	C₂³	C₂⁵×C₃₁	1	2	yes	—
571	C₂³	C₂⁵×C₃₁	1	1	yes	characteristic
572	Q₈	—	2	24	no	—
573	Q₈	—	2	8	no	—
574	Q₈	C₂²×D₄×C₃₁	1	16	yes	complemented
575	D₄	—	2	48	no	—
576	D₄	—	2	48	no	—
577	D₄	—	2	48	no	—
578	D₄	—	2	24	no	—
579	D₄	—	2	48	no	—
580	D₄	—	2	24	no	—
581	D₄	—	4	48	no	—
582	D₄	—	4	24	no	—
583	D₄	C₂²×D₄×C₃₁	1	48	yes	complemented
584	C₂×C₄	—	2	2	no	—
585	C₂×C₄	—	2	4	no	—
586	C₂×C₄	—	2	6	no	—
587	C₂×C₄	—	2	24	no	—
588	C₂×C₄	—	2	12	no	—
589	C₂×C₄	—	2	4	no	—
590	C₂×C₄	—	2	8	no	—
591	C₂×C₄	—	2	24	no	—
592	C₂×C₄	—	2	24	no	—
593	C₂×C₄	—	2	24	no	—
594	C₂×C₄	—	2	48	no	—
595	C₂×C₄	—	4	24	no	—
596	C₂×C₄	C₂²×D₄×C₃₁	1	4	yes	—
597	C₂×C₄	C₂²×D₄×C₃₁	1	12	yes	—
598	C₂×C₄	C₂²×D₄×C₃₁	1	48	yes	complemented
599	C₂×C₄	C₂⁵×C₃₁	1	4	yes	—
600	C₂×C₄	C₂⁵×C₃₁	1	12	yes	—
601	C₂×C₄	C₂⁵×C₃₁	1	2	yes	—
602	C₂×C₄	C₂⁵×C₃₁	1	6	yes	—
603	C₂×C₄	C₂⁵×C₃₁	1	4	yes	—
604	C₂×C₄	C₂⁵×C₃₁	1	6	yes	—
605	C₂×C₄	C₂⁵×C₃₁	1	2	yes	—
606	C₂²	—	2	2	no	—
607	C₂²	—	2	6	no	—
608	C₂²	—	2	2	no	—
609	C₂²	—	2	6	no	—
610	C₂²	—	2	8	no	—
611	C₂²	—	2	24	no	—
612	C₂²	—	2	6	no	—
613	C₂²	—	2	12	no	—
614	C₂²	—	2	12	no	—
615	C₂²	—	2	6	no	—
616	C₂²	—	2	6	no	—
617	C₂²	—	2	12	no	—
618	C₂²	—	4	48	no	—
619	C₂²	—	4	12	no	—
620	C₂²	—	4	24	no	—
621	C₂²	—	8	48	no	—
622	C₂²	C₂³×D₄×C₃₁	1	12	yes	—
623	C₂²	C₂³×D₄×C₃₁	1	2	yes	—
624	C₂²	C₂×C₃₁×H(5,𝔽₂)	1	2	yes	—
625	C₂²	C₂×C₃₁×H(5,𝔽₂)	1	4	yes	complemented
626	C₂²	C₃₁×#585	1	2	yes	—
627	C₂²	C₂⁶×C₃₁	1	1	yes	characteristic
628	C₄	—	2	2	no	—
629	C₄	—	2	4	no	—
630	C₄	—	2	6	no	—
631	C₄	—	2	12	no	—
632	C₄	—	2	4	no	—
633	C₄	C₂³×D₄×C₃₁	1	4	yes	—
634	C₄	C₂³×D₄×C₃₁	1	12	yes	—
635	C₂	—	2	4	no	—
636	C₂	—	2	12	no	—
637	C₂	—	4	6	no	—
638	C₂	—	4	12	no	—
639	C₂	C₃₁×#3488	1	4	yes	direct product factor
640	C₂	C₂⁴×D₄×C₃₁	1	1	yes	characteristic
641	C₂	C₂²×C₃₁×H(5,𝔽₂)	1	1	yes	characteristic
642	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. C₂²×C₃₁×H(5,𝔽₂)	C₂	semidirect
2. C₂³×#41×C₃₁	C₂	semidirect
3. C₃₁×#3488	C₂	direct (N × H)
4. C₂×C₃₁×#550	C₂	semidirect
5. C₂×C₃₁×#548	C₂	semidirect
6. C₂×C₃₁×#546	C₂	semidirect
7. C₂×D₄²×C₃₁	C₂	semidirect
8. C₂×C₃₁×#537	C₂	semidirect
9. C₂×C₃₁×#535	C₂	semidirect
10. C₂×C₃₁×#525	C₂	semidirect
11. C₂²×C₃₁×#121	C₂	semidirect
12. C₂×C₃₁×#520	C₂	semidirect
14. C₂×C₃₁×H(5,𝔽₂)	C₂²	semidirect
17. C₂²×#41×C₃₁	C₂²	semidirect
18. C₂²×#41×C₃₁	C₂²	semidirect
19. C₂²×#41×C₃₁	C₂²	semidirect
20. C₂²×#41×C₃₁	C₂²	semidirect
21. C₂²×#41×C₃₁	C₂²	semidirect
22. C₂²×#41×C₃₁	C₂²	semidirect
23. C₂³×Q₈×C₃₁	C₂²	semidirect
24. C₂³×D₄×C₃₁	C₂²	semidirect
25. C₂³×D₄×C₃₁	C₂²	semidirect
26. C₂³×D₄×C₃₁	C₂²	semidirect
27. C₂³×D₄×C₃₁	C₂²	semidirect
28. C₂⁴×C₄×C₃₁	C₂²	semidirect
29. C₃₁×#550	C₂²	semidirect
30. C₃₁×#548	C₂²	semidirect
31. C₃₁×#546	C₂²	semidirect
32. D₄²×C₃₁	C₂²	semidirect
33. C₃₁×#537	C₂²	semidirect
34. C₃₁×#535	C₂²	semidirect
35. C₂×C₃₁×#127	C₂²	semidirect
36. C₂×C₃₁×#124	C₂²	semidirect
37. C₃₁×#525	C₂²	semidirect
38. C₂×C₃₁×#123	C₂²	semidirect
39. C₂×C₃₁×C₂²⋊Q₈	C₂²	semidirect
40. C₂×C₃₁×C₂²⋊Q₈	C₂²	semidirect
41. C₂×C₃₁×C₂²⋊Q₈	C₂²	semidirect
42. C₂×C₃₁×#121	C₂²	semidirect
43. C₂×C₃₁×#121	C₂²	semidirect
44. C₂×C₃₁×#121	C₂²	semidirect
45. C₂×C₃₁×#121	C₂²	semidirect
46. C₂×C₃₁×#121	C₂²	semidirect
47. C₂×C₃₁×#121	C₂²	semidirect
48. C₂×C₃₁×#121	C₂²	semidirect
49. C₂×C₃₁×#121	C₂²	semidirect
50. C₂×C₃₁×#120	C₂²	semidirect
51. C₂×C₃₁×#120	C₂²	semidirect
52. C₃₁×#520	C₂²	semidirect
53. C₂×C₄×Q₈×C₃₁	C₂²	semidirect
54. C₂×C₄×D₄×C₃₁	C₂²	semidirect
55. C₂×C₄×D₄×C₃₁	C₂²	semidirect
56. C₂×C₄×D₄×C₃₁	C₂²	semidirect
57. C₂×C₃₁×#117	C₂²	semidirect
58. C₂²×C₄⋊C₄×C₃₁	C₂²	semidirect
59. C₂²×C₂²⋊C₄×C₃₁	C₂²	semidirect
69. C₂×#41×C₃₁	D₄	semidirect
71. C₂×#41×C₃₁	C₂³	semidirect
72. C₂×#41×C₃₁	C₂³	semidirect
73. C₂×#41×C₃₁	C₂³	semidirect
74. C₂×#41×C₃₁	C₂³	semidirect
75. C₂×#41×C₃₁	C₂³	semidirect
80. C₂²×Q₈×C₃₁	C₂³	semidirect
94. C₂²×D₄×C₃₁	C₂³	semidirect
95. C₂²×D₄×C₃₁	C₂³	semidirect
96. C₂²×D₄×C₃₁	C₂³	semidirect
97. C₂²×D₄×C₃₁	C₂³	semidirect
107. C₂³×C₄×C₃₁	C₂³	semidirect
108. C₃₁×#127	C₂³	semidirect
109. C₃₁×#124	C₂³	semidirect
110. C₃₁×#123	C₂³	semidirect
111. C₃₁×C₂²⋊Q₈	C₂³	semidirect
112. C₃₁×C₂²⋊Q₈	C₂³	semidirect
113. C₃₁×C₂²⋊Q₈	C₂³	semidirect
114. C₃₁×#121	C₂³	semidirect
115. C₃₁×#121	C₂³	semidirect
116. C₃₁×#121	C₂³	semidirect
117. C₃₁×#121	C₂³	semidirect
118. C₃₁×#121	C₂³	semidirect
119. C₃₁×#121	C₂³	semidirect
120. C₃₁×#121	C₂³	semidirect
121. C₃₁×#120	C₂³	semidirect
122. C₃₁×#120	C₂³	semidirect
123. C₄×Q₈×C₃₁	C₂³	semidirect
124. C₄×D₄×C₃₁	C₂³	semidirect
125. C₄×D₄×C₃₁	C₂³	semidirect
126. C₄×D₄×C₃₁	C₂³	semidirect
127. C₃₁×#117	C₂³	semidirect
133. C₂×C₄⋊C₄×C₃₁	C₂³	semidirect
140. C₂×C₂²⋊C₄×C₃₁	C₂³	semidirect
159. #41×C₃₁	C₂×D₄	semidirect
163. C₂×Q₈×C₃₁	C₂×D₄	semidirect
179. C₂×D₄×C₃₁	C₂×D₄	semidirect
197. C₂²×C₄×C₃₁	C₂×D₄	semidirect
225. C₂×#3488	C₃₁	direct (N × H)
245. C₂³×C₃₁	H(5,𝔽₂)	semidirect
253. Q₈×C₃₁	C₂²×D₄	semidirect
262. D₄×C₃₁	C₂²×D₄	semidirect
277. C₂×C₄×C₃₁	C₂²×D₄	semidirect
285. C₂²×H(5,𝔽₂)	C₂×C₃₁	semidirect
286. C₂³×#41	C₂×C₃₁	semidirect
287. #3488	C₂×C₃₁	direct (N × H)
288. C₂×#550	C₂×C₃₁	semidirect
289. C₂×#548	C₂×C₃₁	semidirect
290. C₂×#546	C₂×C₃₁	semidirect
291. C₂×D₄²	C₂×C₃₁	semidirect
292. C₂×#537	C₂×C₃₁	semidirect
293. C₂×#535	C₂×C₃₁	semidirect
294. C₂×#525	C₂×C₃₁	semidirect
295. C₂²×#121	C₂×C₃₁	semidirect
296. C₂×#520	C₂×C₃₁	semidirect
316. C₂²×C₃₁	C₂×H(5,𝔽₂)	semidirect
327. C₂×H(5,𝔽₂)	C₂²×C₃₁	semidirect
330. C₂²×#41	C₂²×C₃₁	semidirect
331. C₂²×#41	C₂²×C₃₁	semidirect
332. C₂²×#41	C₂²×C₃₁	semidirect
333. C₂²×#41	C₂²×C₃₁	semidirect
334. C₂²×#41	C₂²×C₃₁	semidirect
335. C₂²×#41	C₂²×C₃₁	semidirect
336. C₂³×Q₈	C₂²×C₃₁	semidirect
337. C₂³×D₄	C₂²×C₃₁	semidirect
338. C₂³×D₄	C₂²×C₃₁	semidirect
339. C₂³×D₄	C₂²×C₃₁	semidirect
340. C₂³×D₄	C₂²×C₃₁	semidirect
341. C₂⁴×C₄	C₂²×C₃₁	semidirect
342. #550	C₂²×C₃₁	semidirect
343. #548	C₂²×C₃₁	semidirect
344. #546	C₂²×C₃₁	semidirect
345. D₄²	C₂²×C₃₁	semidirect
346. #537	C₂²×C₃₁	semidirect
347. #535	C₂²×C₃₁	semidirect
348. C₂×#127	C₂²×C₃₁	semidirect
349. C₂×#124	C₂²×C₃₁	semidirect
350. #525	C₂²×C₃₁	semidirect
351. C₂×#123	C₂²×C₃₁	semidirect
352. C₂×C₂²⋊Q₈	C₂²×C₃₁	semidirect
353. C₂×C₂²⋊Q₈	C₂²×C₃₁	semidirect
354. C₂×C₂²⋊Q₈	C₂²×C₃₁	semidirect
355. C₂×#121	C₂²×C₃₁	semidirect
356. C₂×#121	C₂²×C₃₁	semidirect
357. C₂×#121	C₂²×C₃₁	semidirect
358. C₂×#121	C₂²×C₃₁	semidirect
359. C₂×#121	C₂²×C₃₁	semidirect
360. C₂×#121	C₂²×C₃₁	semidirect
361. C₂×#121	C₂²×C₃₁	semidirect
362. C₂×#121	C₂²×C₃₁	semidirect
363. C₂×#120	C₂²×C₃₁	semidirect
364. C₂×#120	C₂²×C₃₁	semidirect
365. #520	C₂²×C₃₁	semidirect
366. C₂×C₄×Q₈	C₂²×C₃₁	semidirect
367. C₂×C₄×D₄	C₂²×C₃₁	semidirect
368. C₂×C₄×D₄	C₂²×C₃₁	semidirect
369. C₂×C₄×D₄	C₂²×C₃₁	semidirect
370. C₂×#117	C₂²×C₃₁	semidirect
371. C₂²×C₄⋊C₄	C₂²×C₃₁	semidirect
372. C₂²×C₂²⋊C₄	C₂²×C₃₁	semidirect
377. C₂×C₃₁	#3488	direct (N × H)
390. C₂×#41	D₄×C₃₁	semidirect
392. C₂×#41	C₂³×C₃₁	semidirect
393. C₂×#41	C₂³×C₃₁	semidirect
394. C₂×#41	C₂³×C₃₁	semidirect
395. C₂×#41	C₂³×C₃₁	semidirect
396. C₂×#41	C₂³×C₃₁	semidirect
401. C₂²×Q₈	C₂³×C₃₁	semidirect
415. C₂²×D₄	C₂³×C₃₁	semidirect
416. C₂²×D₄	C₂³×C₃₁	semidirect
417. C₂²×D₄	C₂³×C₃₁	semidirect
418. C₂²×D₄	C₂³×C₃₁	semidirect
428. C₂³×C₄	C₂³×C₃₁	semidirect
429. #127	C₂³×C₃₁	semidirect
430. #124	C₂³×C₃₁	semidirect
431. #123	C₂³×C₃₁	semidirect
432. C₂²⋊Q₈	C₂³×C₃₁	semidirect
433. C₂²⋊Q₈	C₂³×C₃₁	semidirect
434. C₂²⋊Q₈	C₂³×C₃₁	semidirect
435. #121	C₂³×C₃₁	semidirect
436. #121	C₂³×C₃₁	semidirect
437. #121	C₂³×C₃₁	semidirect
438. #121	C₂³×C₃₁	semidirect
439. #121	C₂³×C₃₁	semidirect
440. #121	C₂³×C₃₁	semidirect
441. #121	C₂³×C₃₁	semidirect
442. #120	C₂³×C₃₁	semidirect
443. #120	C₂³×C₃₁	semidirect
444. C₄×Q₈	C₂³×C₃₁	semidirect
445. C₄×D₄	C₂³×C₃₁	semidirect
446. C₄×D₄	C₂³×C₃₁	semidirect
447. C₄×D₄	C₂³×C₃₁	semidirect
448. #117	C₂³×C₃₁	semidirect
454. C₂×C₄⋊C₄	C₂³×C₃₁	semidirect
461. C₂×C₂²⋊C₄	C₂³×C₃₁	semidirect
463. C₃₁	C₂×#3488	direct (N × H)
481. #41	C₂×D₄×C₃₁	semidirect
485. C₂×Q₈	C₂×D₄×C₃₁	semidirect
501. C₂×D₄	C₂×D₄×C₃₁	semidirect
519. C₂²×C₄	C₂×D₄×C₃₁	semidirect
566. C₂³	C₃₁×H(5,𝔽₂)	semidirect
574. Q₈	C₂²×D₄×C₃₁	semidirect
583. D₄	C₂²×D₄×C₃₁	semidirect
598. C₂×C₄	C₂²×D₄×C₃₁	semidirect
625. C₂²	C₂×C₃₁×H(5,𝔽₂)	semidirect
639. C₂	C₃₁×#3488	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₃₁×H(5,𝔽₂)	2
C₂³×#41×C₃₁	2
C₃₁×#3488	2
C₂×C₃₁×#550	2
C₂×C₃₁×#548	2
C₂×C₃₁×#546	2
C₂×D₄²×C₃₁	2
C₂×C₃₁×#537	2
C₂×C₃₁×#535	2
C₂×C₃₁×#525	2
C₂²×C₃₁×#121	2
C₂×C₃₁×#520	2
C₂×#3488	31

Subgroups — C2×C31×#3488 #21519553

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃₁×#3488 #21519553