Subgroups — C₃₁×#3012 #16842945

Order 3968.

764 conjugacy classes of subgroups.

The subgroup lattice has 358 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃₁×H(5,𝔽₂)	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃₁×AGL(1,ℤ/8)	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃₁×#135	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃₁×#537	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃₁×#452	C₂	1	2	yes	maximal, complemented
6	C₃₁×#450	C₂	1	2	yes	maximal, complemented
7	C₃₁×#449	C₂	1	2	yes	maximal, complemented
8	C₃₁×#447	C₂	1	2	yes	maximal, complemented
9	C₃₁×#417	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₃₁×#102	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃₁×#408	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃₁×H(5,𝔽₂)	—	2	4	no	—
13	C₃₁×H(5,𝔽₂)	—	2	4	no	—
14	C₂×#41×C₃₁	—	2	1	no	—
15	C₂×#41×C₃₁	C₂²	1	2	yes	—
16	C₂×#41×C₃₁	C₂²	1	1	yes	characteristic
17	C₂×#41×C₃₁	C₂²	1	1	yes	characteristic
18	C₂×#41×C₃₁	C₂²	1	1	yes	characteristic, complemented
19	C₂²×D₄×C₃₁	—	2	2	no	—
20	C₂²×D₄×C₃₁	—	2	1	no	—
21	C₂²×D₄×C₃₁	C₂²	1	2	yes	—
22	C₂²×D₄×C₃₁	C₂²	1	1	yes	characteristic
23	C₃₁×AGL(1,ℤ/8)	—	2	4	no	—
24	C₃₁×#135	—	2	4	no	—
25	C₂×Q₁₆×C₃₁	C₂²	1	1	yes	characteristic, complemented
26	C₂×SD₁₆×C₃₁	C₂²	1	1	yes	characteristic, complemented
27	C₂×SD₁₆×C₃₁	C₂²	1	1	yes	characteristic, complemented
28	C₂×SD₁₆×C₃₁	C₂²	1	2	yes	complemented
29	C₂×D₈×C₃₁	C₂²	1	1	yes	characteristic, complemented
30	C₂×D₈×C₃₁	C₂²	1	2	yes	complemented
31	C₂×M₁₆×C₃₁	C₂²	1	1	yes	characteristic, complemented
32	C₂²×C₈×C₃₁	C₂²	1	1	yes	characteristic, complemented
33	C₃₁×C₂²⋊Q₈	—	2	1	no	—
34	C₃₁×C₂²⋊Q₈	C₂²	1	2	yes	complemented
35	C₃₁×#121	—	2	1	no	—
36	C₃₁×#121	—	2	2	no	—
37	C₃₁×#121	C₂²	1	2	yes	complemented
38	C₂×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic, complemented
39	C₃₁×#103	C₂²	1	2	yes	complemented
40	C₃₁×#102	C₂²	1	2	yes	complemented
41	C₃₁×#102	C₂²	1	2	yes	complemented
42	C₃₁×#102	C₂²	1	2	yes	complemented
43	C₃₁×C₂²⋊C₈	C₂²	1	2	yes	complemented
44	C₃₁×C₂²⋊C₈	C₂²	1	2	yes	complemented
45	C₂⁴×C₃₁	—	2	2	no	—
46	C₂⁴×C₃₁	—	2	1	no	—
47	#41×C₃₁	—	2	8	no	—
48	#41×C₃₁	—	2	4	no	—
49	#41×C₃₁	—	2	4	no	—
50	#41×C₃₁	—	2	2	no	—
51	#41×C₃₁	—	2	2	no	—
52	#41×C₃₁	—	2	2	no	—
53	#41×C₃₁	—	2	2	no	—
54	#41×C₃₁	—	2	2	no	—
55	#41×C₃₁	D₄	1	4	yes	complemented
56	C₂×Q₈×C₃₁	D₄	1	1	yes	characteristic
57	C₂×Q₈×C₃₁	C₂³	1	1	yes	characteristic
58	C₂×Q₈×C₃₁	C₂³	1	1	yes	characteristic
59	C₂×D₄×C₃₁	—	2	16	no	—
60	C₂×D₄×C₃₁	—	2	8	no	—
61	C₂×D₄×C₃₁	—	2	2	no	—
62	C₂×D₄×C₃₁	—	2	1	no	—
63	C₂×D₄×C₃₁	—	2	4	no	—
64	C₂×D₄×C₃₁	—	2	4	no	—
65	C₂×D₄×C₃₁	—	2	1	no	—
66	C₂×D₄×C₃₁	—	2	2	no	—
67	C₂×D₄×C₃₁	—	2	2	no	—
68	C₂×D₄×C₃₁	—	2	1	no	—
69	C₂×D₄×C₃₁	—	2	2	no	—
70	C₂×D₄×C₃₁	D₄	1	2	yes	—
71	C₂×D₄×C₃₁	D₄	1	1	yes	characteristic
72	C₂×D₄×C₃₁	D₄	1	4	yes	complemented
73	C₂×D₄×C₃₁	C₂³	1	1	yes	characteristic
74	C₂×D₄×C₃₁	C₂³	1	1	yes	characteristic
75	C₂×D₄×C₃₁	C₂³	1	2	yes	—
76	C₂²×C₄×C₃₁	—	2	2	no	—
77	C₂²×C₄×C₃₁	—	2	1	no	—
78	C₂²×C₄×C₃₁	—	2	1	no	—
79	C₂²×C₄×C₃₁	—	2	1	no	—
80	C₂²×C₄×C₃₁	C₂³	1	2	yes	—
81	C₂²×C₄×C₃₁	C₂³	1	1	yes	characteristic
82	Q₁₆×C₃₁	—	2	2	no	—
83	SD₁₆×C₃₁	—	2	2	no	—
84	SD₁₆×C₃₁	—	2	2	no	—
85	SD₁₆×C₃₁	—	2	4	no	—
86	D₈×C₃₁	—	2	2	no	—
87	D₈×C₃₁	—	2	4	no	—
88	M₁₆×C₃₁	—	2	2	no	—
89	C₂×C₈×C₃₁	—	2	2	no	—
90	C₂×C₈×C₃₁	C₂³	1	1	yes	characteristic
91	C₂×C₈×C₃₁	C₂³	1	1	yes	characteristic
92	C₂×C₈×C₃₁	C₂³	1	2	yes	—
93	C₄⋊C₄×C₃₁	—	2	1	no	—
94	C₄⋊C₄×C₃₁	—	2	2	no	—
95	C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
96	C₂²⋊C₄×C₃₁	—	2	2	no	—
97	C₂²⋊C₄×C₃₁	—	2	2	no	—
98	C₂³×C₃₁	—	2	8	no	—
99	C₂³×C₃₁	—	2	2	no	—
100	C₂³×C₃₁	—	2	1	no	—
101	C₂³×C₃₁	—	2	4	no	—
102	C₂³×C₃₁	—	2	1	no	—
103	C₂³×C₃₁	—	8	1	no	—
104	C₂³×C₃₁	—	8	1	no	—
105	C₂³×C₃₁	—	8	2	no	—
106	C₂³×C₃₁	—	8	2	no	—
107	C₂³×C₃₁	C₂×D₄	1	2	yes	—
108	C₂³×C₃₁	C₂×D₄	1	1	yes	characteristic
109	Q₈×C₃₁	—	2	2	no	—
110	Q₈×C₃₁	—	2	1	no	—
111	Q₈×C₃₁	—	2	1	no	—
112	Q₈×C₃₁	—	2	1	no	—
113	Q₈×C₃₁	C₂×D₄	1	2	yes	—
114	D₄×C₃₁	—	2	8	no	—
115	D₄×C₃₁	—	2	8	no	—
116	D₄×C₃₁	—	2	4	no	—
117	D₄×C₃₁	—	2	4	no	—
118	D₄×C₃₁	—	2	2	no	—
119	D₄×C₃₁	—	2	4	no	—
120	D₄×C₃₁	—	2	2	no	—
121	D₄×C₃₁	—	2	1	no	—
122	D₄×C₃₁	—	2	1	no	—
123	D₄×C₃₁	—	2	1	no	—
124	D₄×C₃₁	—	4	2	no	—
125	D₄×C₃₁	—	8	2	no	—
126	D₄×C₃₁	C₂×D₄	1	2	yes	—
127	D₄×C₃₁	C₂×D₄	1	4	yes	—
128	C₂×C₄×C₃₁	—	2	8	no	—
129	C₂×C₄×C₃₁	—	2	1	no	—
130	C₂×C₄×C₃₁	—	2	4	no	—
131	C₂×C₄×C₃₁	—	2	2	no	—
132	C₂×C₄×C₃₁	—	2	2	no	—
133	C₂×C₄×C₃₁	—	2	2	no	—
134	C₂×C₄×C₃₁	—	2	1	no	—
135	C₂×C₄×C₃₁	—	4	2	no	—
136	C₂×C₄×C₃₁	—	8	1	no	—
137	C₂×C₄×C₃₁	C₂×D₄	1	2	yes	—
138	C₂×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
139	C₂×C₄×C₃₁	C₂×D₄	1	2	yes	—
140	C₂×C₄×C₃₁	C₂×D₄	1	2	yes	—
141	C₂×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
142	C₈×C₃₁	—	2	1	no	—
143	C₈×C₃₁	—	2	1	no	—
144	C₈×C₃₁	—	2	2	no	—
145	#3012	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
146	C₂²×C₃₁	—	2	1	no	—
147	C₂²×C₃₁	—	2	1	no	—
148	C₂²×C₃₁	—	2	2	no	—
149	C₂²×C₃₁	—	2	4	no	—
150	C₂²×C₃₁	—	2	2	no	—
151	C₂²×C₃₁	—	2	2	no	—
152	C₂²×C₃₁	—	2	2	no	—
153	C₂²×C₃₁	—	4	2	no	—
154	C₂²×C₃₁	—	4	1	no	—
155	C₂²×C₃₁	—	4	2	no	—
156	C₂²×C₃₁	—	4	1	no	—
157	C₂²×C₃₁	—	4	1	no	—
158	C₂²×C₃₁	—	4	1	no	—
159	C₂²×C₃₁	—	4	1	no	—
160	C₂²×C₃₁	—	8	4	no	—
161	C₂²×C₃₁	—	8	8	no	—
162	C₂²×C₃₁	#120	1	2	yes	—
163	C₂²×C₃₁	C₂²×D₄	1	1	yes	characteristic
164	C₄×C₃₁	—	2	2	no	—
165	C₄×C₃₁	—	2	2	no	—
166	C₄×C₃₁	—	4	1	no	—
167	C₄×C₃₁	—	4	2	no	—
168	C₄×C₃₁	#120	1	2	yes	—
169	C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
170	C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
171	C₂×H(5,𝔽₂)	C₂×C₃₁	1	1	yes	characteristic, complemented
172	C₂×AGL(1,ℤ/8)	C₂×C₃₁	1	1	yes	characteristic, complemented
173	C₂×#135	C₂×C₃₁	1	1	yes	characteristic, complemented
174	#537	C₂×C₃₁	1	1	yes	characteristic, complemented
175	#452	C₂×C₃₁	1	2	yes	complemented
176	#450	C₂×C₃₁	1	2	yes	complemented
177	#449	C₂×C₃₁	1	2	yes	complemented
178	#447	C₂×C₃₁	1	2	yes	complemented
179	#417	C₂×C₃₁	1	1	yes	characteristic, complemented
180	C₂×#102	C₂×C₃₁	1	1	yes	characteristic, complemented
181	#408	C₂×C₃₁	1	1	yes	characteristic, complemented
182	C₂×C₃₁	—	2	2	no	—
183	C₂×C₃₁	—	4	2	no	—
184	C₂×C₃₁	—	4	4	no	—
185	C₂×C₃₁	—	4	2	no	—
186	C₂×C₃₁	—	8	1	no	—
187	C₂×C₃₁	C₂×#120	1	1	yes	characteristic
188	C₂×C₃₁	#576	1	1	yes	characteristic
189	C₂×C₃₁	#577	1	1	yes	characteristic
190	H(5,𝔽₂)	—	2	4	no	—
191	H(5,𝔽₂)	—	2	4	no	—
192	C₂×#41	—	2	1	no	—
193	C₂×#41	C₂²×C₃₁	1	2	yes	—
194	C₂×#41	C₂²×C₃₁	1	1	yes	characteristic
195	C₂×#41	C₂²×C₃₁	1	1	yes	characteristic
196	C₂×#41	C₂²×C₃₁	1	1	yes	characteristic, complemented
197	C₂²×D₄	—	2	2	no	—
198	C₂²×D₄	—	2	1	no	—
199	C₂²×D₄	C₂²×C₃₁	1	2	yes	—
200	C₂²×D₄	C₂²×C₃₁	1	1	yes	characteristic
201	AGL(1,ℤ/8)	—	2	4	no	—
202	#135	—	2	4	no	—
203	C₂×Q₁₆	C₂²×C₃₁	1	1	yes	characteristic, complemented
204	C₂×SD₁₆	C₂²×C₃₁	1	1	yes	characteristic, complemented
205	C₂×SD₁₆	C₂²×C₃₁	1	1	yes	characteristic, complemented
206	C₂×SD₁₆	C₂²×C₃₁	1	2	yes	complemented
207	C₂×D₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
208	C₂×D₈	C₂²×C₃₁	1	2	yes	complemented
209	C₂×M₁₆	C₂²×C₃₁	1	1	yes	characteristic, complemented
210	C₂²×C₈	C₂²×C₃₁	1	1	yes	characteristic, complemented
211	C₂²⋊Q₈	—	2	1	no	—
212	C₂²⋊Q₈	C₂²×C₃₁	1	2	yes	complemented
213	#121	—	2	1	no	—
214	#121	—	2	2	no	—
215	#121	C₂²×C₃₁	1	2	yes	complemented
216	C₂×C₄⋊C₄	C₂²×C₃₁	1	1	yes	characteristic, complemented
217	#103	C₂²×C₃₁	1	2	yes	complemented
218	#102	C₂²×C₃₁	1	2	yes	complemented
219	#102	C₂²×C₃₁	1	2	yes	complemented
220	#102	C₂²×C₃₁	1	2	yes	complemented
221	C₂²⋊C₈	C₂²×C₃₁	1	2	yes	complemented
222	C₂²⋊C₈	C₂²×C₃₁	1	2	yes	complemented
223	C₃₁	#3012	1	1	yes	characteristic, direct product factor, Sylow
224	C₂⁴	—	2	2	no	—
225	C₂⁴	—	2	1	no	—
226	#41	—	2	8	no	—
227	#41	—	2	4	no	—
228	#41	—	2	4	no	—
229	#41	—	2	2	no	—
230	#41	—	2	2	no	—
231	#41	—	2	2	no	—
232	#41	—	2	2	no	—
233	#41	—	2	2	no	—
234	#41	D₄×C₃₁	1	4	yes	complemented
235	C₂×Q₈	D₄×C₃₁	1	1	yes	characteristic
236	C₂×Q₈	C₂³×C₃₁	1	1	yes	characteristic
237	C₂×Q₈	C₂³×C₃₁	1	1	yes	characteristic
238	C₂×D₄	—	2	16	no	—
239	C₂×D₄	—	2	8	no	—
240	C₂×D₄	—	2	2	no	—
241	C₂×D₄	—	2	1	no	—
242	C₂×D₄	—	2	4	no	—
243	C₂×D₄	—	2	4	no	—
244	C₂×D₄	—	2	1	no	—
245	C₂×D₄	—	2	2	no	—
246	C₂×D₄	—	2	2	no	—
247	C₂×D₄	—	2	1	no	—
248	C₂×D₄	—	2	2	no	—
249	C₂×D₄	D₄×C₃₁	1	2	yes	—
250	C₂×D₄	D₄×C₃₁	1	1	yes	characteristic
251	C₂×D₄	D₄×C₃₁	1	4	yes	complemented
252	C₂×D₄	C₂³×C₃₁	1	1	yes	characteristic
253	C₂×D₄	C₂³×C₃₁	1	1	yes	characteristic
254	C₂×D₄	C₂³×C₃₁	1	2	yes	—
255	C₂²×C₄	—	2	2	no	—
256	C₂²×C₄	—	2	1	no	—
257	C₂²×C₄	—	2	1	no	—
258	C₂²×C₄	—	2	1	no	—
259	C₂²×C₄	C₂³×C₃₁	1	2	yes	—
260	C₂²×C₄	C₂³×C₃₁	1	1	yes	characteristic
261	Q₁₆	—	2	2	no	—
262	SD₁₆	—	2	2	no	—
263	SD₁₆	—	2	2	no	—
264	SD₁₆	—	2	4	no	—
265	D₈	—	2	2	no	—
266	D₈	—	2	4	no	—
267	M₁₆	—	2	2	no	—
268	C₂×C₈	—	2	2	no	—
269	C₂×C₈	C₂³×C₃₁	1	1	yes	characteristic
270	C₂×C₈	C₂³×C₃₁	1	1	yes	characteristic
271	C₂×C₈	C₂³×C₃₁	1	2	yes	—
272	C₄⋊C₄	—	2	1	no	—
273	C₄⋊C₄	—	2	2	no	—
274	C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
275	C₂²⋊C₄	—	2	2	no	—
276	C₂²⋊C₄	—	2	2	no	—
277	C₂³	—	2	8	no	—
278	C₂³	—	2	2	no	—
279	C₂³	—	2	1	no	—
280	C₂³	—	2	4	no	—
281	C₂³	—	2	1	no	—
282	C₂³	—	8	1	no	—
283	C₂³	—	8	1	no	—
284	C₂³	—	8	2	no	—
285	C₂³	—	8	2	no	—
286	C₂³	C₂×D₄×C₃₁	1	2	yes	—
287	C₂³	C₂×D₄×C₃₁	1	1	yes	characteristic
288	Q₈	—	2	2	no	—
289	Q₈	—	2	1	no	—
290	Q₈	—	2	1	no	—
291	Q₈	—	2	1	no	—
292	Q₈	C₂×D₄×C₃₁	1	2	yes	—
293	D₄	—	2	8	no	—
294	D₄	—	2	8	no	—
295	D₄	—	2	4	no	—
296	D₄	—	2	4	no	—
297	D₄	—	2	2	no	—
298	D₄	—	2	4	no	—
299	D₄	—	2	2	no	—
300	D₄	—	2	1	no	—
301	D₄	—	2	1	no	—
302	D₄	—	2	1	no	—
303	D₄	—	4	2	no	—
304	D₄	—	8	2	no	—
305	D₄	C₂×D₄×C₃₁	1	2	yes	—
306	D₄	C₂×D₄×C₃₁	1	4	yes	—
307	C₂×C₄	—	2	8	no	—
308	C₂×C₄	—	2	1	no	—
309	C₂×C₄	—	2	4	no	—
310	C₂×C₄	—	2	2	no	—
311	C₂×C₄	—	2	2	no	—
312	C₂×C₄	—	2	2	no	—
313	C₂×C₄	—	2	1	no	—
314	C₂×C₄	—	4	2	no	—
315	C₂×C₄	—	8	1	no	—
316	C₂×C₄	C₂×D₄×C₃₁	1	2	yes	—
317	C₂×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
318	C₂×C₄	C₂×D₄×C₃₁	1	2	yes	—
319	C₂×C₄	C₂×D₄×C₃₁	1	2	yes	—
320	C₂×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
321	C₈	—	2	1	no	—
322	C₈	—	2	1	no	—
323	C₈	—	2	2	no	—
324	C₂²	—	2	1	no	—
325	C₂²	—	2	1	no	—
326	C₂²	—	2	2	no	—
327	C₂²	—	2	4	no	—
328	C₂²	—	2	2	no	—
329	C₂²	—	2	2	no	—
330	C₂²	—	2	2	no	—
331	C₂²	—	4	2	no	—
332	C₂²	—	4	1	no	—
333	C₂²	—	4	2	no	—
334	C₂²	—	4	1	no	—
335	C₂²	—	4	1	no	—
336	C₂²	—	4	1	no	—
337	C₂²	—	4	1	no	—
338	C₂²	—	8	4	no	—
339	C₂²	—	8	8	no	—
340	C₂²	C₃₁×#120	1	2	yes	—
341	C₂²	C₂²×D₄×C₃₁	1	1	yes	characteristic
342	C₄	—	2	2	no	—
343	C₄	—	2	2	no	—
344	C₄	—	4	1	no	—
345	C₄	—	4	2	no	—
346	C₄	C₃₁×#120	1	2	yes	—
347	C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
348	C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
349	C₂	—	2	2	no	—
350	C₂	—	4	2	no	—
351	C₂	—	4	4	no	—
352	C₂	—	4	2	no	—
353	C₂	—	8	1	no	—
354	C₂	C₂×C₃₁×#120	1	1	yes	characteristic
355	C₂	C₃₁×#576	1	1	yes	characteristic
356	C₂	C₃₁×#577	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₃₁	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁴×C₃₁
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃₁ ◁ C₂×#41×C₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₃₁×H(5,𝔽₂)	C₂	semidirect
2. C₂×C₃₁×AGL(1,ℤ/8)	C₂	semidirect
3. C₂×C₃₁×#135	C₂	semidirect
4. C₃₁×#537	C₂	semidirect
5. C₃₁×#452	C₂	semidirect
6. C₃₁×#450	C₂	semidirect
7. C₃₁×#449	C₂	semidirect
8. C₃₁×#447	C₂	semidirect
9. C₃₁×#417	C₂	semidirect
10. C₂×C₃₁×#102	C₂	semidirect
11. C₃₁×#408	C₂	semidirect
18. C₂×#41×C₃₁	C₂²	semidirect
25. C₂×Q₁₆×C₃₁	C₂²	semidirect
26. C₂×SD₁₆×C₃₁	C₂²	semidirect
27. C₂×SD₁₆×C₃₁	C₂²	semidirect
28. C₂×SD₁₆×C₃₁	C₂²	semidirect
29. C₂×D₈×C₃₁	C₂²	semidirect
30. C₂×D₈×C₃₁	C₂²	semidirect
31. C₂×M₁₆×C₃₁	C₂²	semidirect
32. C₂²×C₈×C₃₁	C₂²	semidirect
34. C₃₁×C₂²⋊Q₈	C₂²	semidirect
37. C₃₁×#121	C₂²	semidirect
38. C₂×C₄⋊C₄×C₃₁	C₂²	semidirect
39. C₃₁×#103	C₂²	semidirect
40. C₃₁×#102	C₂²	semidirect
41. C₃₁×#102	C₂²	semidirect
42. C₃₁×#102	C₂²	semidirect
43. C₃₁×C₂²⋊C₈	C₂²	semidirect
44. C₃₁×C₂²⋊C₈	C₂²	semidirect
55. #41×C₃₁	D₄	semidirect
72. C₂×D₄×C₃₁	D₄	semidirect
145. #3012	C₃₁	direct (N × H)
171. C₂×H(5,𝔽₂)	C₂×C₃₁	semidirect
172. C₂×AGL(1,ℤ/8)	C₂×C₃₁	semidirect
173. C₂×#135	C₂×C₃₁	semidirect
174. #537	C₂×C₃₁	semidirect
175. #452	C₂×C₃₁	semidirect
176. #450	C₂×C₃₁	semidirect
177. #449	C₂×C₃₁	semidirect
178. #447	C₂×C₃₁	semidirect
179. #417	C₂×C₃₁	semidirect
180. C₂×#102	C₂×C₃₁	semidirect
181. #408	C₂×C₃₁	semidirect
196. C₂×#41	C₂²×C₃₁	semidirect
203. C₂×Q₁₆	C₂²×C₃₁	semidirect
204. C₂×SD₁₆	C₂²×C₃₁	semidirect
205. C₂×SD₁₆	C₂²×C₃₁	semidirect
206. C₂×SD₁₆	C₂²×C₃₁	semidirect
207. C₂×D₈	C₂²×C₃₁	semidirect
208. C₂×D₈	C₂²×C₃₁	semidirect
209. C₂×M₁₆	C₂²×C₃₁	semidirect
210. C₂²×C₈	C₂²×C₃₁	semidirect
212. C₂²⋊Q₈	C₂²×C₃₁	semidirect
215. #121	C₂²×C₃₁	semidirect
216. C₂×C₄⋊C₄	C₂²×C₃₁	semidirect
217. #103	C₂²×C₃₁	semidirect
218. #102	C₂²×C₃₁	semidirect
219. #102	C₂²×C₃₁	semidirect
220. #102	C₂²×C₃₁	semidirect
221. C₂²⋊C₈	C₂²×C₃₁	semidirect
222. C₂²⋊C₈	C₂²×C₃₁	semidirect
223. C₃₁	#3012	direct (N × H)
234. #41	D₄×C₃₁	semidirect
251. C₂×D₄	D₄×C₃₁	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃₁×H(5,𝔽₂)	2
C₂×C₃₁×AGL(1,ℤ/8)	2
C₂×C₃₁×#135	2
C₃₁×#537	2
C₃₁×#452	2
C₃₁×#450	2
C₃₁×#449	2
C₃₁×#447	2
C₃₁×#417	2
C₂×C₃₁×#102	2
C₃₁×#408	2
#3012	31

Subgroups — C31×#3012 #16842945

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#3012 #16842945