Subgroups — C₄×C₃₁×#550 #21490919

Order 7936.

3420 conjugacy classes of subgroups.

The subgroup lattice has 466 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃₁×#550	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×#41×C₃₁	C₂	1	2	yes	maximal, complemented
3	C₃₁×#2366	C₂	1	3	yes	maximal, complemented
4	C₃₁×#2363	C₂	1	6	yes	maximal, complemented
5	C₃₁×#2354	C₂	1	3	yes	maximal, complemented
6	Q₈×C₄⋊C₄×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃₁×#2341	C₂	1	2	yes	maximal, complemented
8	C₄×C₃₁×#127	C₂	1	3	yes	maximal, complemented
9	C₄×C₃₁×#121	C₂	1	6	yes	maximal, complemented
10	C₄²×Q₈×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄²×D₄×C₃₁	C₂	1	3	yes	maximal, complemented
12	C₂²×#41×C₃₁	C₂²	1	2	yes	—
13	C₃₁×#550	C₄	1	16	yes	direct product factor
14	C₂×C₃₁×#127	C₂²	1	3	yes	—
15	C₂×C₃₁×#121	C₂²	1	6	yes	—
16	C₄×#41×C₃₁	—	2	16	no	—
17	C₂×C₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic
18	C₂×C₄×Q₈×C₃₁	C₂²	1	2	yes	—
19	C₂×C₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic
20	C₂×C₄×Q₈×C₃₁	C₂²	1	1	yes	characteristic
21	C₂×C₄×D₄×C₃₁	C₂²	1	6	yes	—
22	C₂×C₄×D₄×C₃₁	C₂²	1	3	yes	—
23	C₂×C₄×D₄×C₃₁	C₂²	1	6	yes	—
24	C₂×C₄×D₄×C₃₁	C₂²	1	3	yes	—
25	C₂×C₄×D₄×C₃₁	C₂²	1	6	yes	—
26	C₂×C₄×D₄×C₃₁	C₂²	1	3	yes	—
27	C₂×C₃₁×#117	C₂²	1	6	yes	—
28	C₂²×C₄²×C₃₁	C₂²	1	6	yes	—
29	C₃₁×#390	C₂²	1	6	yes	—
30	C₃₁×#390	C₂²	1	6	yes	—
31	C₃₁×#390	C₂²	1	6	yes	—
32	C₃₁×#390	C₂²	1	6	yes	—
33	C₃₁×#389	C₂²	1	6	yes	—
34	C₃₁×#388	C₂²	1	12	yes	—
35	C₃₁×#386	C₂²	1	12	yes	—
36	C₃₁×#384	C₂²	1	3	yes	—
37	C₃₁×#380	C₂²	1	6	yes	—
38	C₄×C₄⋊C₄×C₃₁	C₂²	1	3	yes	—
39	C₄×C₄⋊C₄×C₃₁	C₂²	1	3	yes	—
40	C₄×C₄⋊C₄×C₃₁	C₂²	1	3	yes	—
41	C₄×C₄⋊C₄×C₃₁	C₂²	1	3	yes	—
42	C₄×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
43	C₄×C₄⋊C₄×C₃₁	C₂²	1	3	yes	—
44	C₄×C₂²⋊C₄×C₃₁	C₂²	1	6	yes	—
45	C₄×C₂²⋊C₄×C₃₁	C₂²	1	6	yes	—
46	C₄×C₂²⋊C₄×C₃₁	C₂²	1	6	yes	—
47	C₄³×C₃₁	C₂²	1	3	yes	—
48	C₂×#41×C₃₁	—	2	8	no	—
49	C₂×#41×C₃₁	—	2	8	no	—
50	C₂×#41×C₃₁	C₂×C₄	1	16	yes	complemented
51	C₂²×Q₈×C₃₁	C₂³	1	1	yes	characteristic
52	C₂²×D₄×C₃₁	C₂³	1	3	yes	—
53	C₂²×D₄×C₃₁	C₂³	1	6	yes	—
54	C₂²×D₄×C₃₁	C₂³	1	6	yes	—
55	C₂³×C₄×C₃₁	C₂³	1	6	yes	—
56	C₂³×C₄×C₃₁	C₂³	1	6	yes	—
57	C₂³×C₄×C₃₁	C₂³	1	6	yes	—
58	C₃₁×#127	C₂×C₄	1	24	yes	complemented
59	C₃₁×#121	C₂×C₄	1	48	yes	complemented
60	C₄×Q₈×C₃₁	—	2	8	no	—
61	C₄×Q₈×C₃₁	—	2	4	no	—
62	C₄×Q₈×C₃₁	C₂×C₄	1	8	yes	complemented
63	C₄×Q₈×C₃₁	D₄	1	8	yes	complemented
64	C₄×D₄×C₃₁	—	2	24	no	—
65	C₄×D₄×C₃₁	—	2	12	no	—
66	C₄×D₄×C₃₁	—	2	24	no	—
67	C₄×D₄×C₃₁	—	2	12	no	—
68	C₄×D₄×C₃₁	—	4	12	no	—
69	C₄×D₄×C₃₁	C₂×C₄	1	24	yes	complemented
70	C₃₁×#117	—	2	24	no	—
71	C₂×C₄⋊C₄×C₃₁	C₂³	1	6	yes	—
72	C₂×C₄⋊C₄×C₃₁	C₂³	1	3	yes	—
73	C₂×C₄⋊C₄×C₃₁	C₂³	1	3	yes	—
74	C₂×C₄⋊C₄×C₃₁	C₂³	1	6	yes	—
75	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
76	C₂×C₄⋊C₄×C₃₁	C₂³	1	3	yes	—
77	C₂×C₄⋊C₄×C₃₁	C₂³	1	3	yes	—
78	C₂×C₄⋊C₄×C₃₁	C₂³	1	1	yes	characteristic
79	C₂×C₂²⋊C₄×C₃₁	C₂³	1	12	yes	—
80	C₂×C₂²⋊C₄×C₃₁	C₂³	1	6	yes	—
81	C₂×C₂²⋊C₄×C₃₁	C₂³	1	6	yes	—
82	C₂×C₂²⋊C₄×C₃₁	C₂³	1	12	yes	—
83	C₂×C₂²⋊C₄×C₃₁	C₂³	1	6	yes	—
84	C₂×C₄²×C₃₁	—	2	24	no	—
85	C₂×C₄²×C₃₁	C₂³	1	6	yes	—
86	C₂×C₄²×C₃₁	C₂³	1	6	yes	—
87	C₂×C₄²×C₃₁	C₂³	1	3	yes	—
88	C₂×C₄²×C₃₁	C₂³	1	3	yes	—
89	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
90	C₂×C₄²×C₃₁	C₂³	1	3	yes	—
91	C₂×C₄²×C₃₁	C₂³	1	3	yes	—
92	C₂×C₄²×C₃₁	C₂³	1	3	yes	—
93	C₂×C₄²×C₃₁	C₂³	1	3	yes	—
94	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
95	C₃₁×#95	C₂³	1	2	yes	—
96	C₃₁×#95	C₂³	1	6	yes	—
97	C₃₁×#95	C₂³	1	6	yes	—
98	C₃₁×#95	C₂³	1	6	yes	—
99	C₂⁴×C₃₁	C₂⁴	1	6	yes	—
100	#41×C₃₁	—	2	64	no	—
101	C₂×Q₈×C₃₁	C₂²×C₄	1	4	yes	—
102	C₂×Q₈×C₃₁	C₂×D₄	1	4	yes	—
103	C₂×Q₈×C₃₁	#41	1	4	yes	—
104	C₂×D₄×C₃₁	—	2	12	no	—
105	C₂×D₄×C₃₁	—	2	6	no	—
106	C₂×D₄×C₃₁	—	2	6	no	—
107	C₂×D₄×C₃₁	—	2	12	no	—
108	C₂×D₄×C₃₁	—	4	6	no	—
109	C₂×D₄×C₃₁	—	4	6	no	—
110	C₂×D₄×C₃₁	C₂²×C₄	1	12	yes	—
111	C₂×D₄×C₃₁	C₂²×C₄	1	24	yes	—
112	C₂×D₄×C₃₁	C₂²×C₄	1	24	yes	—
113	C₂²×C₄×C₃₁	—	2	12	no	—
114	C₂²×C₄×C₃₁	—	2	12	no	—
115	C₂²×C₄×C₃₁	—	2	12	no	—
116	C₂²×C₄×C₃₁	—	2	12	no	—
117	C₂²×C₄×C₃₁	—	2	12	no	—
118	C₂²×C₄×C₃₁	—	2	12	no	—
119	C₂²×C₄×C₃₁	—	2	12	no	—
120	C₂²×C₄×C₃₁	—	4	6	no	—
121	C₂²×C₄×C₃₁	C₂²×C₄	1	24	yes	—
122	C₂²×C₄×C₃₁	C₂⁴	1	3	yes	—
123	C₂²×C₄×C₃₁	C₂⁴	1	6	yes	—
124	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
125	C₂²×C₄×C₃₁	C₂⁴	1	3	yes	—
126	C₂²×C₄×C₃₁	C₂⁴	1	3	yes	—
127	C₂²×C₄×C₃₁	C₂⁴	1	2	yes	—
128	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
129	C₂²×C₄×C₃₁	C₂⁴	1	3	yes	—
130	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
131	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
132	C₄⋊C₄×C₃₁	—	2	12	no	—
133	C₄⋊C₄×C₃₁	—	2	6	no	—
134	C₄⋊C₄×C₃₁	—	2	6	no	—
135	C₄⋊C₄×C₃₁	—	4	6	no	—
136	C₄⋊C₄×C₃₁	C₂²×C₄	1	4	yes	—
137	C₄⋊C₄×C₃₁	C₂²×C₄	1	12	yes	—
138	C₄⋊C₄×C₃₁	C₂×D₄	1	12	yes	—
139	C₄⋊C₄×C₃₁	#41	1	4	yes	complemented
140	C₂²⋊C₄×C₃₁	—	2	24	no	—
141	C₂²⋊C₄×C₃₁	—	2	12	no	—
142	C₂²⋊C₄×C₃₁	—	2	12	no	—
143	C₂²⋊C₄×C₃₁	—	4	12	no	—
144	C₂²⋊C₄×C₃₁	C₂²×C₄	1	24	yes	—
145	C₄²×C₃₁	—	2	4	no	—
146	C₄²×C₃₁	—	2	12	no	—
147	C₄²×C₃₁	—	2	12	no	—
148	C₄²×C₃₁	—	2	6	no	—
149	C₄²×C₃₁	—	2	6	no	—
150	C₄²×C₃₁	—	2	6	no	—
151	C₄²×C₃₁	—	4	3	no	—
152	C₄²×C₃₁	C₂²×C₄	1	12	yes	—
153	C₄²×C₃₁	C₂×D₄	1	12	yes	—
154	C₄²×C₃₁	#41	1	4	yes	complemented
155	C₄×#550	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
156	C₂³×C₃₁	—	2	6	no	—
157	C₂³×C₃₁	—	2	6	no	—
158	C₂³×C₃₁	—	2	6	no	—
159	C₂³×C₃₁	—	2	6	no	—
160	C₂³×C₃₁	—	2	6	no	—
161	C₂³×C₃₁	—	2	6	no	—
162	C₂³×C₃₁	C₂³×C₄	1	12	yes	—
163	C₂³×C₃₁	C₂⁵	1	1	yes	characteristic
164	Q₈×C₃₁	C₄×D₄	1	16	yes	complemented
165	D₄×C₃₁	—	2	48	no	—
166	D₄×C₃₁	—	2	24	no	—
167	D₄×C₃₁	—	4	24	no	—
168	C₂×C₄×C₃₁	—	2	2	no	—
169	C₂×C₄×C₃₁	—	2	2	no	—
170	C₂×C₄×C₃₁	—	2	1	no	—
171	C₂×C₄×C₃₁	—	2	3	no	—
172	C₂×C₄×C₃₁	—	2	2	no	—
173	C₂×C₄×C₃₁	—	2	3	no	—
174	C₂×C₄×C₃₁	—	2	1	no	—
175	C₂×C₄×C₃₁	—	2	3	no	—
176	C₂×C₄×C₃₁	—	2	3	no	—
177	C₂×C₄×C₃₁	—	2	2	no	—
178	C₂×C₄×C₃₁	—	2	48	no	—
179	C₂×C₄×C₃₁	—	2	6	no	—
180	C₂×C₄×C₃₁	—	2	3	no	—
181	C₂×C₄×C₃₁	—	2	3	no	—
182	C₂×C₄×C₃₁	—	2	6	no	—
183	C₂×C₄×C₃₁	—	2	3	no	—
184	C₂×C₄×C₃₁	—	2	6	no	—
185	C₂×C₄×C₃₁	—	4	24	no	—
186	C₂×C₄×C₃₁	—	4	24	no	—
187	C₂×C₄×C₃₁	C₂³×C₄	1	6	yes	—
188	C₂×C₄×C₃₁	C₂³×C₄	1	4	yes	—
189	C₂×C₄×C₃₁	C₂³×C₄	1	6	yes	—
190	C₂×C₄×C₃₁	C₂³×C₄	1	2	yes	—
191	C₂×C₄×C₃₁	C₂²×D₄	1	6	yes	—
192	C₂×C₄×C₃₁	C₂²×D₄	1	6	yes	—
193	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
194	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
195	C₂×C₄×C₃₁	C₂×#41	1	4	yes	—
196	C₂×C₄×C₃₁	C₂×#41	1	6	yes	—
197	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
198	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
199	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
200	C₂×C₄×C₃₁	H(5,𝔽₂)	1	2	yes	—
201	C₂×#550	C₂×C₃₁	1	1	yes	characteristic
202	C₂×C₄×#41	C₂×C₃₁	1	2	yes	complemented
203	#2366	C₂×C₃₁	1	3	yes	complemented
204	#2363	C₂×C₃₁	1	6	yes	complemented
205	#2354	C₂×C₃₁	1	3	yes	complemented
206	Q₈×C₄⋊C₄	C₂×C₃₁	1	1	yes	characteristic, complemented
207	#2341	C₂×C₃₁	1	2	yes	complemented
208	C₄×#127	C₂×C₃₁	1	3	yes	complemented
209	C₄×#121	C₂×C₃₁	1	6	yes	complemented
210	C₄²×Q₈	C₂×C₃₁	1	1	yes	characteristic, complemented
211	C₄²×D₄	C₂×C₃₁	1	3	yes	complemented
212	C₂²×C₃₁	—	2	12	no	—
213	C₂²×C₃₁	—	2	12	no	—
214	C₂²×C₃₁	—	2	12	no	—
215	C₂²×C₃₁	—	4	6	no	—
216	C₂²×C₃₁	—	4	6	no	—
217	C₂²×C₃₁	—	4	6	no	—
218	C₂²×C₃₁	—	4	6	no	—
219	C₂²×C₃₁	C₂⁴×C₄	1	1	yes	characteristic
220	C₂²×C₃₁	C₂³×D₄	1	1	yes	characteristic
221	C₂²×C₃₁	C₂²×#41	1	1	yes	characteristic
222	C₂²×C₃₁	C₂²×#41	1	1	yes	characteristic
223	C₂²×C₃₁	C₂²×#41	1	1	yes	characteristic
224	C₂²×C₃₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
225	C₂²×C₃₁	#585	1	1	yes	characteristic
226	C₄×C₃₁	—	2	4	no	—
227	C₄×C₃₁	—	2	6	no	—
228	C₄×C₃₁	—	2	4	no	—
229	C₄×C₃₁	—	2	6	no	—
230	C₄×C₃₁	—	2	2	no	—
231	C₄×C₃₁	—	4	6	no	—
232	C₄×C₃₁	—	4	3	no	—
233	C₄×C₃₁	C₂×C₄×D₄	1	12	yes	—
234	C₄×C₃₁	C₄×#41	1	4	yes	complemented
235	C₄×C₃₁	#550	1	4	yes	direct product factor
236	C₂²×#41	C₂²×C₃₁	1	2	yes	—
237	#550	C₄×C₃₁	1	16	yes	direct product factor
238	C₂×#127	C₂²×C₃₁	1	3	yes	—
239	C₂×#121	C₂²×C₃₁	1	6	yes	—
240	C₄×#41	—	2	16	no	—
241	C₂×C₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic
242	C₂×C₄×Q₈	C₂²×C₃₁	1	2	yes	—
243	C₂×C₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic
244	C₂×C₄×Q₈	C₂²×C₃₁	1	1	yes	characteristic
245	C₂×C₄×D₄	C₂²×C₃₁	1	3	yes	—
246	C₂×C₄×D₄	C₂²×C₃₁	1	6	yes	—
247	C₂×C₄×D₄	C₂²×C₃₁	1	6	yes	—
248	C₂×C₄×D₄	C₂²×C₃₁	1	3	yes	—
249	C₂×C₄×D₄	C₂²×C₃₁	1	6	yes	—
250	C₂×C₄×D₄	C₂²×C₃₁	1	3	yes	—
251	C₂×#117	C₂²×C₃₁	1	6	yes	—
252	C₂²×C₄²	C₂²×C₃₁	1	6	yes	—
253	#390	C₂²×C₃₁	1	6	yes	—
254	#390	C₂²×C₃₁	1	6	yes	—
255	#390	C₂²×C₃₁	1	6	yes	—
256	#390	C₂²×C₃₁	1	6	yes	—
257	#389	C₂²×C₃₁	1	6	yes	—
258	#388	C₂²×C₃₁	1	12	yes	—
259	#386	C₂²×C₃₁	1	12	yes	—
260	#384	C₂²×C₃₁	1	3	yes	—
261	#380	C₂²×C₃₁	1	6	yes	—
262	C₄×C₄⋊C₄	C₂²×C₃₁	1	3	yes	—
263	C₄×C₄⋊C₄	C₂²×C₃₁	1	3	yes	—
264	C₄×C₄⋊C₄	C₂²×C₃₁	1	3	yes	—
265	C₄×C₄⋊C₄	C₂²×C₃₁	1	3	yes	—
266	C₄×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic
267	C₄×C₄⋊C₄	C₂²×C₃₁	1	3	yes	—
268	C₄×C₂²⋊C₄	C₂²×C₃₁	1	6	yes	—
269	C₄×C₂²⋊C₄	C₂²×C₃₁	1	6	yes	—
270	C₄×C₂²⋊C₄	C₂²×C₃₁	1	6	yes	—
271	C₄³	C₂²×C₃₁	1	3	yes	—
272	C₂×C₃₁	—	4	12	no	—
273	C₂×C₃₁	C₂²×C₄×D₄	1	1	yes	characteristic
274	C₂×C₃₁	C₂×C₄×#41	1	1	yes	characteristic
275	C₂×C₃₁	C₄×H(5,𝔽₂)	1	1	yes	characteristic
276	C₂×C₃₁	C₂×#550	1	1	yes	characteristic
277	C₂×C₃₁	D₄×#41	1	1	yes	characteristic
278	C₂×C₃₁	#3480	1	1	yes	characteristic
279	C₂×C₃₁	#3483	1	1	yes	characteristic
280	C₂×#41	—	2	8	no	—
281	C₂×#41	—	2	8	no	—
282	C₂×#41	C₂×C₄×C₃₁	1	16	yes	complemented
283	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
284	C₂²×D₄	C₂³×C₃₁	1	3	yes	—
285	C₂²×D₄	C₂³×C₃₁	1	6	yes	—
286	C₂²×D₄	C₂³×C₃₁	1	6	yes	—
287	C₂³×C₄	C₂³×C₃₁	1	6	yes	—
288	C₂³×C₄	C₂³×C₃₁	1	6	yes	—
289	C₂³×C₄	C₂³×C₃₁	1	6	yes	—
290	#127	C₂×C₄×C₃₁	1	24	yes	complemented
291	#121	C₂×C₄×C₃₁	1	48	yes	complemented
292	C₄×Q₈	—	2	8	no	—
293	C₄×Q₈	—	2	4	no	—
294	C₄×Q₈	C₂×C₄×C₃₁	1	8	yes	complemented
295	C₄×Q₈	D₄×C₃₁	1	8	yes	complemented
296	C₄×D₄	—	2	24	no	—
297	C₄×D₄	—	2	12	no	—
298	C₄×D₄	—	2	24	no	—
299	C₄×D₄	—	2	12	no	—
300	C₄×D₄	—	4	12	no	—
301	C₄×D₄	C₂×C₄×C₃₁	1	24	yes	complemented
302	#117	—	2	24	no	—
303	C₂×C₄⋊C₄	C₂³×C₃₁	1	6	yes	—
304	C₂×C₄⋊C₄	C₂³×C₃₁	1	3	yes	—
305	C₂×C₄⋊C₄	C₂³×C₃₁	1	3	yes	—
306	C₂×C₄⋊C₄	C₂³×C₃₁	1	6	yes	—
307	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
308	C₂×C₄⋊C₄	C₂³×C₃₁	1	3	yes	—
309	C₂×C₄⋊C₄	C₂³×C₃₁	1	3	yes	—
310	C₂×C₄⋊C₄	C₂³×C₃₁	1	1	yes	characteristic
311	C₂×C₂²⋊C₄	C₂³×C₃₁	1	12	yes	—
312	C₂×C₂²⋊C₄	C₂³×C₃₁	1	6	yes	—
313	C₂×C₂²⋊C₄	C₂³×C₃₁	1	6	yes	—
314	C₂×C₂²⋊C₄	C₂³×C₃₁	1	12	yes	—
315	C₂×C₂²⋊C₄	C₂³×C₃₁	1	6	yes	—
316	C₂×C₄²	—	2	24	no	—
317	C₂×C₄²	C₂³×C₃₁	1	6	yes	—
318	C₂×C₄²	C₂³×C₃₁	1	3	yes	—
319	C₂×C₄²	C₂³×C₃₁	1	6	yes	—
320	C₂×C₄²	C₂³×C₃₁	1	3	yes	—
321	C₂×C₄²	C₂³×C₃₁	1	3	yes	—
322	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
323	C₂×C₄²	C₂³×C₃₁	1	3	yes	—
324	C₂×C₄²	C₂³×C₃₁	1	3	yes	—
325	C₂×C₄²	C₂³×C₃₁	1	3	yes	—
326	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
327	#95	C₂³×C₃₁	1	2	yes	—
328	#95	C₂³×C₃₁	1	6	yes	—
329	#95	C₂³×C₃₁	1	6	yes	—
330	#95	C₂³×C₃₁	1	6	yes	—
331	C₃₁	C₄×#550	1	1	yes	characteristic, direct product factor, Sylow
332	C₂⁴	C₂⁴×C₃₁	1	6	yes	—
333	#41	—	2	64	no	—
334	C₂×Q₈	C₂²×C₄×C₃₁	1	4	yes	—
335	C₂×Q₈	C₂×D₄×C₃₁	1	4	yes	—
336	C₂×Q₈	#41×C₃₁	1	4	yes	—
337	C₂×D₄	—	2	12	no	—
338	C₂×D₄	—	2	6	no	—
339	C₂×D₄	—	2	6	no	—
340	C₂×D₄	—	2	12	no	—
341	C₂×D₄	—	4	6	no	—
342	C₂×D₄	—	4	6	no	—
343	C₂×D₄	C₂²×C₄×C₃₁	1	12	yes	—
344	C₂×D₄	C₂²×C₄×C₃₁	1	24	yes	—
345	C₂×D₄	C₂²×C₄×C₃₁	1	24	yes	—
346	C₂²×C₄	—	2	12	no	—
347	C₂²×C₄	—	2	12	no	—
348	C₂²×C₄	—	2	12	no	—
349	C₂²×C₄	—	2	12	no	—
350	C₂²×C₄	—	2	12	no	—
351	C₂²×C₄	—	2	12	no	—
352	C₂²×C₄	—	2	12	no	—
353	C₂²×C₄	—	4	6	no	—
354	C₂²×C₄	C₂²×C₄×C₃₁	1	24	yes	—
355	C₂²×C₄	C₂⁴×C₃₁	1	3	yes	—
356	C₂²×C₄	C₂⁴×C₃₁	1	6	yes	—
357	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
358	C₂²×C₄	C₂⁴×C₃₁	1	3	yes	—
359	C₂²×C₄	C₂⁴×C₃₁	1	3	yes	—
360	C₂²×C₄	C₂⁴×C₃₁	1	2	yes	—
361	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
362	C₂²×C₄	C₂⁴×C₃₁	1	3	yes	—
363	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
364	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
365	C₄⋊C₄	—	2	12	no	—
366	C₄⋊C₄	—	2	6	no	—
367	C₄⋊C₄	—	2	6	no	—
368	C₄⋊C₄	—	4	6	no	—
369	C₄⋊C₄	C₂²×C₄×C₃₁	1	4	yes	—
370	C₄⋊C₄	C₂²×C₄×C₃₁	1	12	yes	—
371	C₄⋊C₄	C₂×D₄×C₃₁	1	12	yes	—
372	C₄⋊C₄	#41×C₃₁	1	4	yes	complemented
373	C₂²⋊C₄	—	2	24	no	—
374	C₂²⋊C₄	—	2	12	no	—
375	C₂²⋊C₄	—	2	12	no	—
376	C₂²⋊C₄	—	4	12	no	—
377	C₂²⋊C₄	C₂²×C₄×C₃₁	1	24	yes	—
378	C₄²	—	2	4	no	—
379	C₄²	—	2	12	no	—
380	C₄²	—	2	12	no	—
381	C₄²	—	2	6	no	—
382	C₄²	—	2	6	no	—
383	C₄²	—	2	6	no	—
384	C₄²	—	4	3	no	—
385	C₄²	C₂²×C₄×C₃₁	1	12	yes	—
386	C₄²	C₂×D₄×C₃₁	1	12	yes	—
387	C₄²	#41×C₃₁	1	4	yes	complemented
388	C₂³	—	2	6	no	—
389	C₂³	—	2	6	no	—
390	C₂³	—	2	6	no	—
391	C₂³	—	2	6	no	—
392	C₂³	—	2	6	no	—
393	C₂³	—	2	6	no	—
394	C₂³	C₂³×C₄×C₃₁	1	12	yes	—
395	C₂³	C₂⁵×C₃₁	1	1	yes	characteristic
396	Q₈	C₄×D₄×C₃₁	1	16	yes	complemented
397	D₄	—	2	48	no	—
398	D₄	—	2	24	no	—
399	D₄	—	4	24	no	—
400	C₂×C₄	—	2	2	no	—
401	C₂×C₄	—	2	2	no	—
402	C₂×C₄	—	2	1	no	—
403	C₂×C₄	—	2	3	no	—
404	C₂×C₄	—	2	2	no	—
405	C₂×C₄	—	2	3	no	—
406	C₂×C₄	—	2	1	no	—
407	C₂×C₄	—	2	3	no	—
408	C₂×C₄	—	2	3	no	—
409	C₂×C₄	—	2	2	no	—
410	C₂×C₄	—	2	48	no	—
411	C₂×C₄	—	2	6	no	—
412	C₂×C₄	—	2	3	no	—
413	C₂×C₄	—	2	3	no	—
414	C₂×C₄	—	2	6	no	—
415	C₂×C₄	—	2	3	no	—
416	C₂×C₄	—	2	6	no	—
417	C₂×C₄	—	4	24	no	—
418	C₂×C₄	—	4	24	no	—
419	C₂×C₄	C₂³×C₄×C₃₁	1	6	yes	—
420	C₂×C₄	C₂³×C₄×C₃₁	1	4	yes	—
421	C₂×C₄	C₂³×C₄×C₃₁	1	6	yes	—
422	C₂×C₄	C₂³×C₄×C₃₁	1	2	yes	—
423	C₂×C₄	C₂²×D₄×C₃₁	1	6	yes	—
424	C₂×C₄	C₂²×D₄×C₃₁	1	6	yes	—
425	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
426	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
427	C₂×C₄	C₂×#41×C₃₁	1	4	yes	—
428	C₂×C₄	C₂×#41×C₃₁	1	6	yes	—
429	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
430	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
431	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
432	C₂×C₄	C₃₁×H(5,𝔽₂)	1	2	yes	—
433	C₂²	—	2	12	no	—
434	C₂²	—	2	12	no	—
435	C₂²	—	2	12	no	—
436	C₂²	—	4	6	no	—
437	C₂²	—	4	6	no	—
438	C₂²	—	4	6	no	—
439	C₂²	—	4	6	no	—
440	C₂²	C₂⁴×C₄×C₃₁	1	1	yes	characteristic
441	C₂²	C₂³×D₄×C₃₁	1	1	yes	characteristic
442	C₂²	C₂²×#41×C₃₁	1	1	yes	characteristic
443	C₂²	C₂²×#41×C₃₁	1	1	yes	characteristic
444	C₂²	C₂²×#41×C₃₁	1	1	yes	characteristic
445	C₂²	C₂×C₃₁×H(5,𝔽₂)	1	1	yes	characteristic
446	C₂²	C₃₁×#585	1	1	yes	characteristic
447	C₄	—	2	4	no	—
448	C₄	—	2	6	no	—
449	C₄	—	2	4	no	—
450	C₄	—	2	6	no	—
451	C₄	—	2	2	no	—
452	C₄	—	4	6	no	—
453	C₄	—	4	3	no	—
454	C₄	C₂×C₄×D₄×C₃₁	1	12	yes	—
455	C₄	C₄×#41×C₃₁	1	4	yes	complemented
456	C₄	C₃₁×#550	1	4	yes	direct product factor
457	C₂	—	4	12	no	—
458	C₂	C₂²×C₄×D₄×C₃₁	1	1	yes	characteristic
459	C₂	C₂×C₄×#41×C₃₁	1	1	yes	characteristic
460	C₂	C₄×C₃₁×H(5,𝔽₂)	1	1	yes	characteristic
461	C₂	C₂×C₃₁×#550	1	1	yes	characteristic
462	C₂	D₄×#41×C₃₁	1	1	yes	characteristic
463	C₂	C₃₁×#3480	1	1	yes	characteristic
464	C₂	C₃₁×#3483	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄×C₃₁	C₂⁴
commutator	C₂²	C₂⁴×C₄×C₃₁
Frattini, cosocle	C₂³	C₂⁵×C₃₁
socle	C₂³×C₃₁	C₂⁵
prime radical	C₂×C₃₁×#550	C₂
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
2. C₂×C₄×#41×C₃₁	C₂	semidirect
3. C₃₁×#2366	C₂	semidirect
4. C₃₁×#2363	C₂	semidirect
5. C₃₁×#2354	C₂	semidirect
6. Q₈×C₄⋊C₄×C₃₁	C₂	semidirect
7. C₃₁×#2341	C₂	semidirect
8. C₄×C₃₁×#127	C₂	semidirect
9. C₄×C₃₁×#121	C₂	semidirect
10. C₄²×Q₈×C₃₁	C₂	semidirect
11. C₄²×D₄×C₃₁	C₂	semidirect
13. C₃₁×#550	C₄	direct (N × H)
50. C₂×#41×C₃₁	C₂×C₄	semidirect
58. C₃₁×#127	C₂×C₄	semidirect
59. C₃₁×#121	C₂×C₄	semidirect
62. C₄×Q₈×C₃₁	C₂×C₄	semidirect
63. C₄×Q₈×C₃₁	D₄	semidirect
69. C₄×D₄×C₃₁	C₂×C₄	semidirect
139. C₄⋊C₄×C₃₁	#41	semidirect
154. C₄²×C₃₁	#41	semidirect
155. C₄×#550	C₃₁	direct (N × H)
164. Q₈×C₃₁	C₄×D₄	semidirect
202. C₂×C₄×#41	C₂×C₃₁	semidirect
203. #2366	C₂×C₃₁	semidirect
204. #2363	C₂×C₃₁	semidirect
205. #2354	C₂×C₃₁	semidirect
206. Q₈×C₄⋊C₄	C₂×C₃₁	semidirect
207. #2341	C₂×C₃₁	semidirect
208. C₄×#127	C₂×C₃₁	semidirect
209. C₄×#121	C₂×C₃₁	semidirect
210. C₄²×Q₈	C₂×C₃₁	semidirect
211. C₄²×D₄	C₂×C₃₁	semidirect
234. C₄×C₃₁	C₄×#41	semidirect
235. C₄×C₃₁	#550	direct (N × H)
237. #550	C₄×C₃₁	direct (N × H)
282. C₂×#41	C₂×C₄×C₃₁	semidirect
290. #127	C₂×C₄×C₃₁	semidirect
291. #121	C₂×C₄×C₃₁	semidirect
294. C₄×Q₈	C₂×C₄×C₃₁	semidirect
295. C₄×Q₈	D₄×C₃₁	semidirect
301. C₄×D₄	C₂×C₄×C₃₁	semidirect
331. C₃₁	C₄×#550	direct (N × H)
372. C₄⋊C₄	#41×C₃₁	semidirect
387. C₄²	#41×C₃₁	semidirect
396. Q₈	C₄×D₄×C₃₁	semidirect
455. C₄	C₄×#41×C₃₁	semidirect
456. C₄	C₃₁×#550	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×#550	2
C₂×C₄×#41×C₃₁	2
C₃₁×#2366	2
C₃₁×#2363	2
C₃₁×#2354	2
Q₈×C₄⋊C₄×C₃₁	2
C₃₁×#2341	2
C₄×C₃₁×#127	2
C₄×C₃₁×#121	2
C₄²×Q₈×C₃₁	2
C₄²×D₄×C₃₁	2
C₄×#550	31

Subgroups — C4×C31×#550 #21490919

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×C₃₁×#550 #21490919