Subgroups — C₂×C₃₁×#2888 #21516833

Order 7936.

5114 conjugacy classes of subgroups.

The subgroup lattice has 336 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
2	C₂×C₃₁×#568	C₂	1	2	yes	maximal, complemented
3	C₃₁×#2888	C₂	1	16	yes	maximal, direct product factor
4	C₂×C₃₁×#413	C₂	1	6	yes	maximal, complemented
5	C₂²×C₃₁×#100	C₂	1	6	yes	maximal, complemented
6	C₂×C₃₁×H(5,𝔽₂)	—	2	8	no	—
7	C₂×C₃₁×H(5,𝔽₂)	—	2	8	no	—
8	C₂×C₃₁×H(5,𝔽₂)	C₄	1	8	yes	—
9	C₂×C₃₁×H(5,𝔽₂)	C₂²	1	8	yes	—
10	C₂²×#41×C₃₁	C₄	1	2	yes	—
11	C₂²×#41×C₃₁	C₂²	1	3	yes	—
12	C₂²×#41×C₃₁	C₂²	1	1	yes	characteristic
13	C₂³×D₄×C₃₁	C₄	1	6	yes	—
14	C₂³×D₄×C₃₁	C₂²	1	3	yes	—
15	C₃₁×#568	—	2	8	no	—
16	C₃₁×#568	C₂²	1	16	yes	complemented
17	C₂×C₃₁×#131	—	2	8	no	—
18	C₂²×M₁₆×C₃₁	C₂²	1	12	yes	complemented
19	C₃₁×#413	C₂²	1	48	yes	complemented
20	C₂×C₃₁×#101	C₂²	1	4	yes	complemented
21	C₂×C₃₁×#100	C₂²	1	12	yes	complemented
22	C₂×C₃₁×#100	C₂²	1	48	yes	complemented
23	C₂⁵×C₃₁	C₂×C₄	1	6	yes	—
24	C₃₁×H(5,𝔽₂)	—	2	64	no	—
25	C₃₁×H(5,𝔽₂)	—	2	64	no	—
26	C₂×#41×C₃₁	—	2	8	no	—
27	C₂×#41×C₃₁	—	2	8	no	—
28	C₂×#41×C₃₁	—	2	12	no	—
29	C₂×#41×C₃₁	—	2	12	no	—
30	C₂×#41×C₃₁	C₂×C₄	1	16	yes	—
31	C₂×#41×C₃₁	C₂×C₄	1	12	yes	—
32	C₂×#41×C₃₁	C₂×C₄	1	4	yes	—
33	C₂×#41×C₃₁	D₄	1	8	yes	—
34	C₂×#41×C₃₁	D₄	1	8	yes	—
35	C₂×#41×C₃₁	C₂³	1	12	yes	—
36	C₂×#41×C₃₁	C₂³	1	4	yes	—
37	C₂²×Q₈×C₃₁	C₂×C₄	1	1	yes	characteristic
38	C₂²×Q₈×C₃₁	C₂³	1	1	yes	characteristic
39	C₂²×D₄×C₃₁	—	2	24	no	—
40	C₂²×D₄×C₃₁	—	2	24	no	—
41	C₂²×D₄×C₃₁	—	2	12	no	—
42	C₂²×D₄×C₃₁	—	2	12	no	—
43	C₂²×D₄×C₃₁	C₂×C₄	1	6	yes	—
44	C₂²×D₄×C₃₁	C₂×C₄	1	6	yes	—
45	C₂²×D₄×C₃₁	C₂×C₄	1	48	yes	—
46	C₂²×D₄×C₃₁	C₂×C₄	1	12	yes	—
47	C₂²×D₄×C₃₁	C₂×C₄	1	3	yes	—
48	C₂²×D₄×C₃₁	C₂³	1	3	yes	—
49	C₂²×D₄×C₃₁	C₂³	1	12	yes	—
50	C₂³×C₄×C₃₁	C₂×C₄	1	6	yes	—
51	C₂³×C₄×C₃₁	C₂³	1	3	yes	—
52	C₃₁×#131	—	2	64	no	—
53	C₂×M₁₆×C₃₁	—	2	12	no	—
54	C₂×M₁₆×C₃₁	—	2	24	no	—
55	C₂×M₁₆×C₃₁	C₂³	1	8	yes	—
56	C₂×M₁₆×C₃₁	C₂³	1	48	yes	complemented
57	C₂²×C₈×C₃₁	—	2	12	no	—
58	C₃₁×#101	C₂³	1	16	yes	complemented
59	C₃₁×#100	C₂³	1	48	yes	complemented
60	C₂⁴×C₃₁	—	2	12	no	—
61	C₂⁴×C₃₁	—	2	12	no	—
62	C₂⁴×C₃₁	—	8	12	no	—
63	C₂⁴×C₃₁	C₂²×C₄	1	6	yes	—
64	C₂⁴×C₃₁	C₂²×C₄	1	24	yes	—
65	C₂⁴×C₃₁	C₂²×C₄	1	3	yes	—
66	#41×C₃₁	—	2	64	no	—
67	#41×C₃₁	—	2	48	no	—
68	#41×C₃₁	—	2	48	no	—
69	#41×C₃₁	C₂²⋊C₄	1	32	yes	—
70	#41×C₃₁	C₂×D₄	1	32	yes	—
71	C₂×Q₈×C₃₁	—	2	2	no	—
72	C₂×Q₈×C₃₁	—	2	2	no	—
73	C₂×Q₈×C₃₁	C₂²⋊C₄	1	4	yes	—
74	C₂×Q₈×C₃₁	C₂²⋊C₄	1	4	yes	—
75	C₂×Q₈×C₃₁	C₂²×C₄	1	2	yes	—
76	C₂×Q₈×C₃₁	C₂²×C₄	1	4	yes	—
77	C₂×Q₈×C₃₁	C₂⁴	1	2	yes	—
78	C₂×D₄×C₃₁	—	2	12	no	—
79	C₂×D₄×C₃₁	—	2	12	no	—
80	C₂×D₄×C₃₁	—	2	192	no	—
81	C₂×D₄×C₃₁	—	2	12	no	—
82	C₂×D₄×C₃₁	—	2	12	no	—
83	C₂×D₄×C₃₁	—	2	48	no	—
84	C₂×D₄×C₃₁	—	2	6	no	—
85	C₂×D₄×C₃₁	—	2	6	no	—
86	C₂×D₄×C₃₁	—	2	48	no	—
87	C₂×D₄×C₃₁	C₂²⋊C₄	1	12	yes	—
88	C₂×D₄×C₃₁	C₂²⋊C₄	1	12	yes	—
89	C₂×D₄×C₃₁	C₂²×C₄	1	24	yes	—
90	C₂×D₄×C₃₁	C₂²×C₄	1	24	yes	—
91	C₂×D₄×C₃₁	C₂²×C₄	1	6	yes	—
92	C₂×D₄×C₃₁	C₂²×C₄	1	12	yes	—
93	C₂×D₄×C₃₁	C₂⁴	1	6	yes	—
94	C₂²×C₄×C₃₁	—	2	12	no	—
95	C₂²×C₄×C₃₁	—	2	12	no	—
96	C₂²×C₄×C₃₁	C₂²×C₄	1	2	yes	—
97	C₂²×C₄×C₃₁	C₂²×C₄	1	24	yes	—
98	C₂²×C₄×C₃₁	C₂²×C₄	1	3	yes	—
99	C₂²×C₄×C₃₁	C₂²×C₄	1	6	yes	—
100	C₂²×C₄×C₃₁	C₂×D₄	1	12	yes	—
101	C₂²×C₄×C₃₁	C₂×D₄	1	12	yes	—
102	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
103	C₂²×C₄×C₃₁	C₂⁴	1	6	yes	—
104	M₁₆×C₃₁	—	2	8	no	—
105	M₁₆×C₃₁	—	2	48	no	—
106	M₁₆×C₃₁	C₂⁴	1	16	yes	—
107	C₂×C₈×C₃₁	—	2	8	no	—
108	C₂×C₈×C₃₁	—	2	48	no	—
109	C₂×#2888	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
110	C₂³×C₃₁	—	2	6	no	—
111	C₂³×C₃₁	—	2	6	no	—
112	C₂³×C₃₁	—	2	48	no	—
113	C₂³×C₃₁	—	4	6	no	—
114	C₂³×C₃₁	—	4	12	no	—
115	C₂³×C₃₁	—	8	24	no	—
116	C₂³×C₃₁	—	8	24	no	—
117	C₂³×C₃₁	—	8	24	no	—
118	C₂³×C₃₁	C₂×C₂²⋊C₄	1	6	yes	—
119	C₂³×C₃₁	C₂×C₂²⋊C₄	1	6	yes	—
120	C₂³×C₃₁	C₂³×C₄	1	1	yes	characteristic
121	C₂³×C₃₁	C₂³×C₄	1	12	yes	—
122	C₂³×C₃₁	C₂³×C₄	1	6	yes	—
123	Q₈×C₃₁	—	2	4	no	—
124	Q₈×C₃₁	—	2	4	no	—
125	Q₈×C₃₁	C₂×C₂²⋊C₄	1	16	yes	—
126	D₄×C₃₁	—	2	48	no	—
127	D₄×C₃₁	—	2	48	no	—
128	D₄×C₃₁	—	2	12	no	—
129	D₄×C₃₁	—	2	12	no	—
130	D₄×C₃₁	C₂×C₂²⋊C₄	1	48	yes	—
131	C₂×C₄×C₃₁	—	2	2	no	—
132	C₂×C₄×C₃₁	—	2	2	no	—
133	C₂×C₄×C₃₁	—	2	48	no	—
134	C₂×C₄×C₃₁	C₂×C₂²⋊C₄	1	6	yes	—
135	C₂×C₄×C₃₁	C₂×C₂²⋊C₄	1	24	yes	—
136	C₂×C₄×C₃₁	C₂×C₂²⋊C₄	1	6	yes	—
137	C₂×C₄×C₃₁	C₂³×C₄	1	4	yes	—
138	C₂×C₄×C₃₁	C₂³×C₄	1	6	yes	—
139	C₂×C₄×C₃₁	C₂³×C₄	1	1	yes	characteristic
140	C₂×C₄×C₃₁	C₂²×D₄	1	24	yes	—
141	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
142	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
143	C₂×C₄×C₃₁	C₂⁵	1	1	yes	characteristic
144	C₈×C₃₁	—	2	16	no	—
145	C₂²×H(5,𝔽₂)	C₂×C₃₁	1	1	yes	characteristic
146	C₂×#568	C₂×C₃₁	1	2	yes	complemented
147	#2888	C₂×C₃₁	1	16	yes	direct product factor
148	C₂×#413	C₂×C₃₁	1	6	yes	complemented
149	C₂²×#100	C₂×C₃₁	1	6	yes	complemented
150	C₂²×C₃₁	—	2	2	no	—
151	C₂²×C₃₁	—	2	12	no	—
152	C₂²×C₃₁	—	2	12	no	—
153	C₂²×C₃₁	—	4	6	no	—
154	C₂²×C₃₁	—	4	6	no	—
155	C₂²×C₃₁	—	4	12	no	—
156	C₂²×C₃₁	—	4	12	no	—
157	C₂²×C₃₁	—	4	12	no	—
158	C₂²×C₃₁	—	8	48	no	—
159	C₂²×C₃₁	C₂²×C₂²⋊C₄	1	1	yes	characteristic
160	C₂²×C₃₁	C₂²×C₂²⋊C₄	1	12	yes	—
161	C₂²×C₃₁	C₂²×C₂²⋊C₄	1	1	yes	characteristic
162	C₂²×C₃₁	C₂⁴×C₄	1	1	yes	characteristic
163	C₄×C₃₁	—	2	4	no	—
164	C₄×C₃₁	C₂²×C₂²⋊C₄	1	12	yes	—
165	C₄×C₃₁	C₂²×C₂²⋊C₄	1	2	yes	—
166	C₄×C₃₁	C₂³×D₄	1	2	yes	—
167	C₂×H(5,𝔽₂)	—	2	8	no	—
168	C₂×H(5,𝔽₂)	—	2	8	no	—
169	C₂×H(5,𝔽₂)	C₄×C₃₁	1	8	yes	—
170	C₂×H(5,𝔽₂)	C₂²×C₃₁	1	8	yes	—
171	C₂²×#41	C₄×C₃₁	1	2	yes	—
172	C₂²×#41	C₂²×C₃₁	1	3	yes	—
173	C₂²×#41	C₂²×C₃₁	1	1	yes	characteristic
174	C₂³×D₄	C₄×C₃₁	1	6	yes	—
175	C₂³×D₄	C₂²×C₃₁	1	3	yes	—
176	#568	—	2	8	no	—
177	#568	C₂²×C₃₁	1	16	yes	complemented
178	C₂×#131	—	2	8	no	—
179	C₂²×M₁₆	C₂²×C₃₁	1	12	yes	complemented
180	#413	C₂²×C₃₁	1	48	yes	complemented
181	C₂×#101	C₂²×C₃₁	1	4	yes	complemented
182	C₂×#100	C₂²×C₃₁	1	12	yes	complemented
183	C₂×#100	C₂²×C₃₁	1	48	yes	complemented
184	C₂×C₃₁	—	2	1	no	—
185	C₂×C₃₁	—	2	1	no	—
186	C₂×C₃₁	—	2	12	no	—
187	C₂×C₃₁	—	4	12	no	—
188	C₂×C₃₁	#2888	1	2	yes	direct product factor
189	C₂×C₃₁	C₂³×C₂²⋊C₄	1	1	yes	characteristic
190	C₂⁵	C₂×C₄×C₃₁	1	6	yes	—
191	H(5,𝔽₂)	—	2	64	no	—
192	H(5,𝔽₂)	—	2	64	no	—
193	C₂×#41	—	2	8	no	—
194	C₂×#41	—	2	8	no	—
195	C₂×#41	—	2	12	no	—
196	C₂×#41	—	2	12	no	—
197	C₂×#41	C₂×C₄×C₃₁	1	16	yes	—
198	C₂×#41	C₂×C₄×C₃₁	1	12	yes	—
199	C₂×#41	C₂×C₄×C₃₁	1	4	yes	—
200	C₂×#41	D₄×C₃₁	1	8	yes	—
201	C₂×#41	D₄×C₃₁	1	8	yes	—
202	C₂×#41	C₂³×C₃₁	1	12	yes	—
203	C₂×#41	C₂³×C₃₁	1	4	yes	—
204	C₂²×Q₈	C₂×C₄×C₃₁	1	1	yes	characteristic
205	C₂²×Q₈	C₂³×C₃₁	1	1	yes	characteristic
206	C₂²×D₄	—	2	24	no	—
207	C₂²×D₄	—	2	24	no	—
208	C₂²×D₄	—	2	12	no	—
209	C₂²×D₄	—	2	12	no	—
210	C₂²×D₄	C₂×C₄×C₃₁	1	6	yes	—
211	C₂²×D₄	C₂×C₄×C₃₁	1	6	yes	—
212	C₂²×D₄	C₂×C₄×C₃₁	1	48	yes	—
213	C₂²×D₄	C₂×C₄×C₃₁	1	12	yes	—
214	C₂²×D₄	C₂×C₄×C₃₁	1	3	yes	—
215	C₂²×D₄	C₂³×C₃₁	1	3	yes	—
216	C₂²×D₄	C₂³×C₃₁	1	12	yes	—
217	C₂³×C₄	C₂×C₄×C₃₁	1	6	yes	—
218	C₂³×C₄	C₂³×C₃₁	1	3	yes	—
219	#131	—	2	64	no	—
220	C₂×M₁₆	—	2	12	no	—
221	C₂×M₁₆	—	2	24	no	—
222	C₂×M₁₆	C₂³×C₃₁	1	8	yes	—
223	C₂×M₁₆	C₂³×C₃₁	1	48	yes	complemented
224	C₂²×C₈	—	2	12	no	—
225	#101	C₂³×C₃₁	1	16	yes	complemented
226	#100	C₂³×C₃₁	1	48	yes	complemented
227	C₃₁	C₂×#2888	1	1	yes	characteristic, direct product factor, Sylow
228	C₂⁴	—	2	12	no	—
229	C₂⁴	—	2	12	no	—
230	C₂⁴	—	8	12	no	—
231	C₂⁴	C₂²×C₄×C₃₁	1	6	yes	—
232	C₂⁴	C₂²×C₄×C₃₁	1	24	yes	—
233	C₂⁴	C₂²×C₄×C₃₁	1	3	yes	—
234	#41	—	2	64	no	—
235	#41	—	2	48	no	—
236	#41	—	2	48	no	—
237	#41	C₂²⋊C₄×C₃₁	1	32	yes	—
238	#41	C₂×D₄×C₃₁	1	32	yes	—
239	C₂×Q₈	—	2	2	no	—
240	C₂×Q₈	—	2	2	no	—
241	C₂×Q₈	C₂²⋊C₄×C₃₁	1	4	yes	—
242	C₂×Q₈	C₂²⋊C₄×C₃₁	1	4	yes	—
243	C₂×Q₈	C₂²×C₄×C₃₁	1	2	yes	—
244	C₂×Q₈	C₂²×C₄×C₃₁	1	4	yes	—
245	C₂×Q₈	C₂⁴×C₃₁	1	2	yes	—
246	C₂×D₄	—	2	12	no	—
247	C₂×D₄	—	2	12	no	—
248	C₂×D₄	—	2	192	no	—
249	C₂×D₄	—	2	12	no	—
250	C₂×D₄	—	2	12	no	—
251	C₂×D₄	—	2	48	no	—
252	C₂×D₄	—	2	6	no	—
253	C₂×D₄	—	2	6	no	—
254	C₂×D₄	—	2	48	no	—
255	C₂×D₄	C₂²⋊C₄×C₃₁	1	12	yes	—
256	C₂×D₄	C₂²⋊C₄×C₃₁	1	12	yes	—
257	C₂×D₄	C₂²×C₄×C₃₁	1	24	yes	—
258	C₂×D₄	C₂²×C₄×C₃₁	1	24	yes	—
259	C₂×D₄	C₂²×C₄×C₃₁	1	6	yes	—
260	C₂×D₄	C₂²×C₄×C₃₁	1	12	yes	—
261	C₂×D₄	C₂⁴×C₃₁	1	6	yes	—
262	C₂²×C₄	—	2	12	no	—
263	C₂²×C₄	—	2	12	no	—
264	C₂²×C₄	C₂²×C₄×C₃₁	1	2	yes	—
265	C₂²×C₄	C₂²×C₄×C₃₁	1	24	yes	—
266	C₂²×C₄	C₂²×C₄×C₃₁	1	3	yes	—
267	C₂²×C₄	C₂²×C₄×C₃₁	1	6	yes	—
268	C₂²×C₄	C₂×D₄×C₃₁	1	12	yes	—
269	C₂²×C₄	C₂×D₄×C₃₁	1	12	yes	—
270	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
271	C₂²×C₄	C₂⁴×C₃₁	1	6	yes	—
272	M₁₆	—	2	8	no	—
273	M₁₆	—	2	48	no	—
274	M₁₆	C₂⁴×C₃₁	1	16	yes	—
275	C₂×C₈	—	2	8	no	—
276	C₂×C₈	—	2	48	no	—
277	C₂³	—	2	6	no	—
278	C₂³	—	2	6	no	—
279	C₂³	—	2	48	no	—
280	C₂³	—	4	6	no	—
281	C₂³	—	4	12	no	—
282	C₂³	—	8	24	no	—
283	C₂³	—	8	24	no	—
284	C₂³	—	8	24	no	—
285	C₂³	C₂×C₂²⋊C₄×C₃₁	1	6	yes	—
286	C₂³	C₂×C₂²⋊C₄×C₃₁	1	6	yes	—
287	C₂³	C₂³×C₄×C₃₁	1	1	yes	characteristic
288	C₂³	C₂³×C₄×C₃₁	1	12	yes	—
289	C₂³	C₂³×C₄×C₃₁	1	6	yes	—
290	Q₈	—	2	4	no	—
291	Q₈	—	2	4	no	—
292	Q₈	C₂×C₂²⋊C₄×C₃₁	1	16	yes	—
293	D₄	—	2	48	no	—
294	D₄	—	2	48	no	—
295	D₄	—	2	12	no	—
296	D₄	—	2	12	no	—
297	D₄	C₂×C₂²⋊C₄×C₃₁	1	48	yes	—
298	C₂×C₄	—	2	2	no	—
299	C₂×C₄	—	2	2	no	—
300	C₂×C₄	—	2	48	no	—
301	C₂×C₄	C₂×C₂²⋊C₄×C₃₁	1	6	yes	—
302	C₂×C₄	C₂×C₂²⋊C₄×C₃₁	1	6	yes	—
303	C₂×C₄	C₂×C₂²⋊C₄×C₃₁	1	24	yes	—
304	C₂×C₄	C₂³×C₄×C₃₁	1	4	yes	—
305	C₂×C₄	C₂³×C₄×C₃₁	1	6	yes	—
306	C₂×C₄	C₂³×C₄×C₃₁	1	1	yes	characteristic
307	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
308	C₂×C₄	C₂²×D₄×C₃₁	1	24	yes	—
309	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
310	C₂×C₄	C₂⁵×C₃₁	1	1	yes	characteristic
311	C₈	—	2	16	no	—
312	C₂²	—	2	2	no	—
313	C₂²	—	2	12	no	—
314	C₂²	—	2	12	no	—
315	C₂²	—	4	6	no	—
316	C₂²	—	4	6	no	—
317	C₂²	—	4	12	no	—
318	C₂²	—	4	12	no	—
319	C₂²	—	4	12	no	—
320	C₂²	—	8	48	no	—
321	C₂²	C₂²×C₂²⋊C₄×C₃₁	1	1	yes	characteristic
322	C₂²	C₂²×C₂²⋊C₄×C₃₁	1	12	yes	—
323	C₂²	C₂²×C₂²⋊C₄×C₃₁	1	1	yes	characteristic
324	C₂²	C₂⁴×C₄×C₃₁	1	1	yes	characteristic
325	C₄	—	2	4	no	—
326	C₄	C₂²×C₂²⋊C₄×C₃₁	1	12	yes	—
327	C₄	C₂²×C₂²⋊C₄×C₃₁	1	2	yes	—
328	C₄	C₂³×D₄×C₃₁	1	2	yes	—
329	C₂	—	2	1	no	—
330	C₂	—	2	1	no	—
331	C₂	—	2	12	no	—
332	C₂	—	4	12	no	—
333	C₂	C₃₁×#2888	1	2	yes	direct product factor
334	C₂	C₂³×C₂²⋊C₄×C₃₁	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₃₁	C₂²×C₂²⋊C₄
commutator	C₂²	C₂⁴×C₄×C₃₁
Frattini, cosocle	C₂×C₄	C₂⁵×C₃₁
prime radical	C₂²×C₃₁×H(5,𝔽₂)	C₂
LCS	G ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃₁ ◁ C₂²×#41×C₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₃₁×#568	C₂	semidirect
3. C₃₁×#2888	C₂	direct (N × H)
4. C₂×C₃₁×#413	C₂	semidirect
5. C₂²×C₃₁×#100	C₂	semidirect
16. C₃₁×#568	C₂²	semidirect
18. C₂²×M₁₆×C₃₁	C₂²	semidirect
19. C₃₁×#413	C₂²	semidirect
20. C₂×C₃₁×#101	C₂²	semidirect
21. C₂×C₃₁×#100	C₂²	semidirect
22. C₂×C₃₁×#100	C₂²	semidirect
56. C₂×M₁₆×C₃₁	C₂³	semidirect
58. C₃₁×#101	C₂³	semidirect
59. C₃₁×#100	C₂³	semidirect
109. C₂×#2888	C₃₁	direct (N × H)
146. C₂×#568	C₂×C₃₁	semidirect
147. #2888	C₂×C₃₁	direct (N × H)
148. C₂×#413	C₂×C₃₁	semidirect
149. C₂²×#100	C₂×C₃₁	semidirect
177. #568	C₂²×C₃₁	semidirect
179. C₂²×M₁₆	C₂²×C₃₁	semidirect
180. #413	C₂²×C₃₁	semidirect
181. C₂×#101	C₂²×C₃₁	semidirect
182. C₂×#100	C₂²×C₃₁	semidirect
183. C₂×#100	C₂²×C₃₁	semidirect
188. C₂×C₃₁	#2888	direct (N × H)
223. C₂×M₁₆	C₂³×C₃₁	semidirect
225. #101	C₂³×C₃₁	semidirect
226. #100	C₂³×C₃₁	semidirect
227. C₃₁	C₂×#2888	direct (N × H)
333. C₂	C₃₁×#2888	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
C₂×C₃₁×#568	2
C₃₁×#2888	2
C₂×C₃₁×#413	2
C₂²×C₃₁×#100	2
C₂×#2888	31

Subgroups — C2×C31×#2888 #21516833

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃₁×#2888 #21516833