Subgroups — C₂×D₄×#41×C₃₁ #21519460

Order 7936.

12314 conjugacy classes of subgroups.

The subgroup lattice has 584 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

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

	subgroup	G/H
center	C₂²×C₄×C₃₁	C₂⁴
commutator, Frattini, cosocle	C₂²	C₂⁶×C₃₁
socle	C₂³×C₃₁	C₂⁵
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂³×#41×C₃₁	C₂	semidirect
2. D₄×#41×C₃₁	C₂	direct (N × H)
3. C₂×C₃₁×#550	C₂	semidirect
4. C₂×D₄×Q₈×C₃₁	C₂	semidirect
5. C₂×C₃₁×#548	C₂	semidirect
6. C₂×C₃₁×#547	C₂	semidirect
7. C₂×C₃₁×#546	C₂	semidirect
8. C₂×D₄²×C₃₁	C₂	semidirect
9. C₂×C₃₁×#532	C₂	semidirect
10. C₂×C₃₁×#525	C₂	semidirect
11. C₂×C₄×#41×C₃₁	C₂	semidirect
12. C₂²×C₄×D₄×C₃₁	C₂	semidirect
15. C₂²×#41×C₃₁	C₂²	semidirect
16. C₂²×#41×C₃₁	C₂²	semidirect
17. C₂²×#41×C₃₁	C₂²	semidirect
18. C₂²×#41×C₃₁	C₂²	semidirect
19. C₂³×Q₈×C₃₁	C₂²	semidirect
21. C₂³×D₄×C₃₁	C₂²	semidirect
22. C₂⁴×C₄×C₃₁	C₂²	semidirect
23. C₃₁×#550	C₂²	semidirect
24. D₄×Q₈×C₃₁	C₂²	semidirect
25. C₃₁×#548	C₂²	semidirect
26. C₃₁×#547	C₂²	semidirect
27. C₃₁×#546	C₂²	semidirect
28. D₄²×C₃₁	C₂²	semidirect
29. C₃₁×#532	C₂²	semidirect
30. C₂×C₃₁×C₄⋊Q₈	C₂²	semidirect
31. C₂×C₃₁×#127	C₂²	semidirect
32. C₂×C₃₁×#124	C₂²	semidirect
33. C₃₁×#525	C₂²	semidirect
34. C₂×C₃₁×#123	C₂²	semidirect
35. C₂×C₃₁×C₂²⋊Q₈	C₂²	semidirect
36. C₂×C₃₁×C₂²⋊Q₈	C₂²	semidirect
37. C₂×C₃₁×#121	C₂²	semidirect
38. C₂×C₃₁×#121	C₂²	semidirect
39. C₂×C₃₁×#121	C₂²	semidirect
40. C₂×C₃₁×#121	C₂²	semidirect
41. C₂×C₃₁×#120	C₂²	semidirect
42. C₄×#41×C₃₁	C₂²	semidirect
43. C₂×C₄×Q₈×C₃₁	C₂²	semidirect
44. C₂×C₄×Q₈×C₃₁	C₂²	semidirect
47. C₂×C₄×D₄×C₃₁	C₂²	semidirect
48. C₂×C₄×D₄×C₃₁	C₂²	semidirect
49. C₂×C₄×D₄×C₃₁	C₂²	semidirect
50. C₂×C₄×D₄×C₃₁	C₂²	semidirect
51. C₂×C₄×D₄×C₃₁	C₂²	semidirect
52. C₂×C₄×D₄×C₃₁	C₂²	semidirect
53. C₂×C₄×D₄×C₃₁	C₂²	semidirect
54. C₂×C₄×D₄×C₃₁	C₂²	semidirect
55. C₂×C₃₁×#117	C₂²	semidirect
56. C₂²×C₄⋊C₄×C₃₁	C₂²	semidirect
57. C₂²×C₂²⋊C₄×C₃₁	C₂²	semidirect
58. C₂²×C₄²×C₃₁	C₂²	semidirect
64. C₂×#41×C₃₁	D₄	direct (N × H)
66. C₂×#41×C₃₁	C₂³	semidirect
67. C₂×#41×C₃₁	C₂³	semidirect
68. C₂×#41×C₃₁	C₂³	semidirect
72. C₂²×Q₈×C₃₁	C₂³	semidirect
83. C₂²×D₄×C₃₁	C₂³	semidirect
93. C₂³×C₄×C₃₁	C₂³	semidirect
94. C₃₁×C₄⋊Q₈	C₂³	semidirect
95. C₃₁×#127	C₂³	semidirect
96. C₃₁×#124	C₂³	semidirect
97. C₃₁×#123	C₂³	semidirect
98. C₃₁×C₂²⋊Q₈	C₂³	semidirect
99. C₃₁×C₂²⋊Q₈	C₂³	semidirect
100. C₃₁×#121	C₂³	semidirect
101. C₃₁×#121	C₂³	semidirect
102. C₃₁×#121	C₂³	semidirect
103. C₃₁×#121	C₂³	semidirect
104. C₃₁×#120	C₂³	semidirect
105. C₄×Q₈×C₃₁	C₂³	semidirect
106. C₄×Q₈×C₃₁	C₂³	semidirect
109. C₄×D₄×C₃₁	C₂³	semidirect
110. C₄×D₄×C₃₁	C₂³	semidirect
111. C₄×D₄×C₃₁	C₂³	semidirect
112. C₄×D₄×C₃₁	C₂³	semidirect
113. C₄×D₄×C₃₁	C₂³	semidirect
114. C₄×D₄×C₃₁	C₂³	semidirect
115. C₄×D₄×C₃₁	C₂³	semidirect
116. C₃₁×#117	C₂³	semidirect
123. C₂×C₄⋊C₄×C₃₁	C₂³	semidirect
130. C₂×C₂²⋊C₄×C₃₁	C₂³	semidirect
135. C₂×C₄²×C₃₁	C₂³	semidirect
146. #41×C₃₁	C₂×D₄	direct (N × H)
149. C₂×Q₈×C₃₁	C₂×D₄	semidirect
159. C₂×D₄×C₃₁	C₂×D₄	semidirect
160. C₂×D₄×C₃₁	#41	direct (N × H)
176. C₂²×C₄×C₃₁	C₂×D₄	semidirect
209. C₂×D₄×#41	C₃₁	direct (N × H)
222. C₂³×C₃₁	C₂×#41	semidirect
228. Q₈×C₃₁	C₂²×D₄	semidirect
234. D₄×C₃₁	C₂²×D₄	semidirect
235. D₄×C₃₁	C₂×#41	direct (N × H)
250. C₂×C₄×C₃₁	C₂²×D₄	semidirect
251. C₂×C₄×C₃₁	C₂×#41	semidirect
260. C₂³×#41	C₂×C₃₁	semidirect
261. D₄×#41	C₂×C₃₁	direct (N × H)
262. C₂×#550	C₂×C₃₁	semidirect
263. C₂×D₄×Q₈	C₂×C₃₁	semidirect
264. C₂×#548	C₂×C₃₁	semidirect
265. C₂×#547	C₂×C₃₁	semidirect
266. C₂×#546	C₂×C₃₁	semidirect
267. C₂×D₄²	C₂×C₃₁	semidirect
268. C₂×#532	C₂×C₃₁	semidirect
269. C₂×#525	C₂×C₃₁	semidirect
270. C₂×C₄×#41	C₂×C₃₁	semidirect
271. C₂²×C₄×D₄	C₂×C₃₁	semidirect
286. C₂²×C₃₁	C₂²×#41	semidirect
296. C₄×C₃₁	C₂²×#41	semidirect
299. C₂²×#41	C₂²×C₃₁	semidirect
300. C₂²×#41	C₂²×C₃₁	semidirect
301. C₂²×#41	C₂²×C₃₁	semidirect
302. C₂²×#41	C₂²×C₃₁	semidirect
303. C₂³×Q₈	C₂²×C₃₁	semidirect
305. C₂³×D₄	C₂²×C₃₁	semidirect
306. C₂⁴×C₄	C₂²×C₃₁	semidirect
307. #550	C₂²×C₃₁	semidirect
308. D₄×Q₈	C₂²×C₃₁	semidirect
309. #548	C₂²×C₃₁	semidirect
310. #547	C₂²×C₃₁	semidirect
311. #546	C₂²×C₃₁	semidirect
312. D₄²	C₂²×C₃₁	semidirect
313. #532	C₂²×C₃₁	semidirect
314. C₂×C₄⋊Q₈	C₂²×C₃₁	semidirect
315. C₂×#127	C₂²×C₃₁	semidirect
316. C₂×#124	C₂²×C₃₁	semidirect
317. #525	C₂²×C₃₁	semidirect
318. C₂×#123	C₂²×C₃₁	semidirect
319. C₂×C₂²⋊Q₈	C₂²×C₃₁	semidirect
320. C₂×C₂²⋊Q₈	C₂²×C₃₁	semidirect
321. C₂×#121	C₂²×C₃₁	semidirect
322. C₂×#121	C₂²×C₃₁	semidirect
323. C₂×#121	C₂²×C₃₁	semidirect
324. C₂×#121	C₂²×C₃₁	semidirect
325. C₂×#120	C₂²×C₃₁	semidirect
326. C₄×#41	C₂²×C₃₁	semidirect
327. C₂×C₄×Q₈	C₂²×C₃₁	semidirect
328. C₂×C₄×Q₈	C₂²×C₃₁	semidirect
331. C₂×C₄×D₄	C₂²×C₃₁	semidirect
332. C₂×C₄×D₄	C₂²×C₃₁	semidirect
333. C₂×C₄×D₄	C₂²×C₃₁	semidirect
334. C₂×C₄×D₄	C₂²×C₃₁	semidirect
335. C₂×C₄×D₄	C₂²×C₃₁	semidirect
336. C₂×C₄×D₄	C₂²×C₃₁	semidirect
337. C₂×C₄×D₄	C₂²×C₃₁	semidirect
338. C₂×C₄×D₄	C₂²×C₃₁	semidirect
339. C₂×#117	C₂²×C₃₁	semidirect
340. C₂²×C₄⋊C₄	C₂²×C₃₁	semidirect
341. C₂²×C₂²⋊C₄	C₂²×C₃₁	semidirect
342. C₂²×C₄²	C₂²×C₃₁	semidirect
346. C₂×C₃₁	D₄×#41	direct (N × H)
355. C₂×#41	D₄×C₃₁	direct (N × H)
357. C₂×#41	C₂³×C₃₁	semidirect
358. C₂×#41	C₂³×C₃₁	semidirect
359. C₂×#41	C₂³×C₃₁	semidirect
363. C₂²×Q₈	C₂³×C₃₁	semidirect
374. C₂²×D₄	C₂³×C₃₁	semidirect
384. C₂³×C₄	C₂³×C₃₁	semidirect
385. C₄⋊Q₈	C₂³×C₃₁	semidirect
386. #127	C₂³×C₃₁	semidirect
387. #124	C₂³×C₃₁	semidirect
388. #123	C₂³×C₃₁	semidirect
389. C₂²⋊Q₈	C₂³×C₃₁	semidirect
390. C₂²⋊Q₈	C₂³×C₃₁	semidirect
391. #121	C₂³×C₃₁	semidirect
392. #121	C₂³×C₃₁	semidirect
393. #121	C₂³×C₃₁	semidirect
394. #121	C₂³×C₃₁	semidirect
395. #120	C₂³×C₃₁	semidirect
396. C₄×Q₈	C₂³×C₃₁	semidirect
397. C₄×Q₈	C₂³×C₃₁	semidirect
400. C₄×D₄	C₂³×C₃₁	semidirect
401. C₄×D₄	C₂³×C₃₁	semidirect
402. C₄×D₄	C₂³×C₃₁	semidirect
403. C₄×D₄	C₂³×C₃₁	semidirect
404. C₄×D₄	C₂³×C₃₁	semidirect
405. C₄×D₄	C₂³×C₃₁	semidirect
406. C₄×D₄	C₂³×C₃₁	semidirect
407. #117	C₂³×C₃₁	semidirect
414. C₂×C₄⋊C₄	C₂³×C₃₁	semidirect
421. C₂×C₂²⋊C₄	C₂³×C₃₁	semidirect
426. C₂×C₄²	C₂³×C₃₁	semidirect
427. C₃₁	C₂×D₄×#41	direct (N × H)
438. #41	C₂×D₄×C₃₁	direct (N × H)
441. C₂×Q₈	C₂×D₄×C₃₁	semidirect
451. C₂×D₄	C₂×D₄×C₃₁	semidirect
452. C₂×D₄	#41×C₃₁	direct (N × H)
468. C₂²×C₄	C₂×D₄×C₃₁	semidirect
513. C₂³	C₂×#41×C₃₁	semidirect
519. Q₈	C₂²×D₄×C₃₁	semidirect
525. D₄	C₂²×D₄×C₃₁	semidirect
526. D₄	C₂×#41×C₃₁	direct (N × H)
541. C₂×C₄	C₂²×D₄×C₃₁	semidirect
542. C₂×C₄	C₂×#41×C₃₁	semidirect
565. C₂²	C₂²×#41×C₃₁	semidirect
575. C₄	C₂²×#41×C₃₁	semidirect
579. C₂	D₄×#41×C₃₁	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×#41×C₃₁	2
D₄×#41×C₃₁	2
C₂×C₃₁×#550	2
C₂×D₄×Q₈×C₃₁	2
C₂×C₃₁×#548	2
C₂×C₃₁×#547	2
C₂×C₃₁×#546	2
C₂×D₄²×C₃₁	2
C₂×C₃₁×#532	2
C₂×C₃₁×#525	2
C₂×C₄×#41×C₃₁	2
C₂²×C₄×D₄×C₃₁	2
C₂×D₄×#41	31

Subgroups — C2×D4×#41×C31 #21519460

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×D₄×#41×C₃₁ #21519460