Subgroups — C₃₁×#21297 #21478056

Order 7936.

738 conjugacy classes of subgroups.

The subgroup lattice has 368 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×#2943	C₂	1	1	yes	maximal, characteristic
2	C₃₁×#2923	C₂	1	2	yes	maximal, complemented
3	C₃₁×#1975	C₂	1	1	yes	maximal, characteristic
4	C₃₁×#1974	C₂	1	1	yes	maximal, characteristic
5	C₃₁×#1946	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃₁×#1945	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃₁×#1938	C₂	1	2	yes	maximal, complemented
8	C₃₁×#1937	C₂	1	2	yes	maximal, complemented
9	C₃₁×#1778	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄×C₃₁×#104	C₂	1	2	yes	maximal, complemented
11	C₄×C₃₁×#97	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₃₁×#135	C₂²	1	1	yes	characteristic
13	C₄×#41×C₃₁	C₂²	1	2	yes	—
14	C₃₁×#442	C₄	1	2	yes	complemented
15	C₃₁×#441	C₄	1	2	yes	complemented
16	C₃₁×#440	C₄	1	4	yes	complemented
17	C₃₁×#433	—	2	4	no	—
18	C₃₁×#432	—	2	4	no	—
19	C₂×C₃₁×#108	C₂²	1	1	yes	characteristic
20	C₂×C₃₁×#108	C₂²	1	1	yes	characteristic
21	C₃₁×#427	C₂²	1	1	yes	characteristic
22	C₃₁×#424	C₂²	1	2	yes	—
23	C₃₁×#424	C₂²	1	2	yes	—
24	C₂×C₃₁×#104	C₂²	1	2	yes	—
25	C₂×C₃₁×#104	C₂²	1	2	yes	—
26	C₃₁×#416	C₂²	1	2	yes	—
27	C₃₁×#408	C₂²	1	2	yes	—
28	C₃₁×#408	C₂²	1	2	yes	—
29	C₄×M₁₆×C₃₁	C₂²	1	2	yes	—
30	C₂×C₃₁×#97	C₂²	1	1	yes	characteristic
31	C₂×C₃₁×#97	C₂²	1	1	yes	characteristic
32	C₂×C₃₁×#97	C₂²	1	1	yes	characteristic
33	C₂×C₃₁×#97	C₂²	1	1	yes	characteristic
34	C₂×C₄×C₈×C₃₁	C₂²	1	1	yes	characteristic
35	C₂×C₄×C₈×C₃₁	C₂²	1	1	yes	characteristic
36	C₄³×C₃₁	C₂²	1	1	yes	characteristic
37	C₃₁×#341	C₂²	1	2	yes	—
38	C₃₁×#339	C₂²	1	2	yes	—
39	C₃₁×#339	C₂²	1	2	yes	—
40	C₂×#41×C₃₁	C₂³	1	2	yes	—
41	C₃₁×#135	—	2	2	no	—
42	C₃₁×#135	—	2	2	no	—
43	C₂×Q₁₆×C₃₁	C₂×C₄	1	1	yes	characteristic
44	C₂×SD₁₆×C₃₁	C₂×C₄	1	2	yes	—
45	C₂×D₈×C₃₁	C₂×C₄	1	1	yes	characteristic
46	C₂×M₁₆×C₃₁	C₂³	1	2	yes	—
47	C₂×M₁₆×C₃₁	C₂³	1	2	yes	—
48	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
49	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
50	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
51	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
52	C₄×Q₈×C₃₁	C₂×C₄	1	4	yes	—
53	C₄×D₄×C₃₁	—	2	4	no	—
54	C₄×D₄×C₃₁	C₂×C₄	1	4	yes	—
55	C₃₁×#117	—	2	2	no	—
56	C₃₁×#117	C₂³	1	2	yes	—
57	C₂×C₄²×C₃₁	—	2	2	no	—
58	C₂×C₄²×C₃₁	—	2	2	no	—
59	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
60	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
61	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
62	C₃₁×#108	—	2	2	no	—
63	C₃₁×#108	—	2	2	no	—
64	C₃₁×#107	C₂×C₄	1	2	yes	—
65	C₃₁×#106	C₂×C₄	1	2	yes	—
66	C₃₁×C₄⋊C₈	—	2	4	no	—
67	C₃₁×C₄⋊C₈	—	2	4	no	—
68	C₃₁×#104	—	2	4	no	—
69	C₃₁×#104	—	2	4	no	—
70	C₃₁×#103	C₂×C₄	1	4	yes	—
71	C₃₁×#102	C₂×C₄	1	4	yes	—
72	C₃₁×C₂²⋊C₈	—	2	4	no	—
73	C₃₁×C₂²⋊C₈	—	2	4	no	—
74	C₃₁×#97	—	2	2	no	—
75	C₃₁×#97	—	2	2	no	—
76	C₃₁×#97	—	2	2	no	—
77	C₃₁×#97	C₂×C₄	1	2	yes	—
78	C₃₁×#97	C₂×C₄	1	2	yes	—
79	C₃₁×#97	D₄	1	4	yes	—
80	C₄×C₈×C₃₁	—	2	2	no	—
81	C₄×C₈×C₃₁	—	2	2	no	—
82	C₄×C₈×C₃₁	—	2	2	no	—
83	#41×C₃₁	—	2	2	no	—
84	#41×C₃₁	—	2	2	no	—
85	#41×C₃₁	—	2	2	no	—
86	#41×C₃₁	—	2	2	no	—
87	C₂×Q₈×C₃₁	C₂²×C₄	1	2	yes	—
88	C₂×D₄×C₃₁	—	2	2	no	—
89	C₂×D₄×C₃₁	C₂²×C₄	1	2	yes	—
90	C₂²×C₄×C₃₁	—	2	1	no	—
91	C₂²×C₄×C₃₁	—	2	1	no	—
92	C₂²×C₄×C₃₁	—	2	2	no	—
93	C₂²×C₄×C₃₁	—	2	4	no	—
94	C₂²×C₄×C₃₁	#41	1	2	yes	—
95	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
96	Q₁₆×C₃₁	—	2	2	no	—
97	SD₁₆×C₃₁	—	2	4	no	—
98	D₈×C₃₁	—	2	2	no	—
99	M₁₆×C₃₁	—	2	2	no	—
100	M₁₆×C₃₁	—	2	2	no	—
101	M₁₆×C₃₁	—	2	2	no	—
102	M₁₆×C₃₁	—	2	2	no	—
103	C₂×C₈×C₃₁	—	2	1	no	—
104	C₂×C₈×C₃₁	—	2	1	no	—
105	C₂×C₈×C₃₁	—	2	1	no	—
106	C₂×C₈×C₃₁	—	2	1	no	—
107	C₂×C₈×C₃₁	—	2	1	no	—
108	C₂×C₈×C₃₁	—	2	1	no	—
109	C₂×C₈×C₃₁	—	2	2	no	—
110	C₂×C₈×C₃₁	—	2	2	no	—
111	C₂×C₈×C₃₁	C₂²×C₄	1	2	yes	—
112	C₂×C₈×C₃₁	C₂²×C₄	1	1	yes	characteristic
113	C₂×C₈×C₃₁	C₂²×C₄	1	1	yes	characteristic
114	C₂×C₈×C₃₁	C₂×D₄	1	2	yes	—
115	C₂×C₈×C₃₁	C₂×D₄	1	2	yes	—
116	C₂×C₈×C₃₁	#41	1	2	yes	—
117	C₂×C₈×C₃₁	#41	1	2	yes	—
118	C₄⋊C₄×C₃₁	—	2	4	no	—
119	C₄⋊C₄×C₃₁	C₂²×C₄	1	4	yes	—
120	C₂²⋊C₄×C₃₁	—	2	2	no	—
121	C₂²⋊C₄×C₃₁	—	2	4	no	—
122	C₄²×C₃₁	—	2	4	no	—
123	C₄²×C₃₁	—	2	2	no	—
124	C₄²×C₃₁	—	2	1	no	—
125	C₄²×C₃₁	—	2	1	no	—
126	C₄²×C₃₁	—	4	4	no	—
127	C₄²×C₃₁	C₂²×C₄	1	2	yes	—
128	C₄²×C₃₁	C₂×D₄	1	2	yes	—
129	C₄²×C₃₁	#41	1	2	yes	—
130	C₄²×C₃₁	#41	1	2	yes	—
131	#21297	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
132	C₂³×C₃₁	—	2	2	no	—
133	C₂³×C₃₁	C₂×#41	1	1	yes	characteristic
134	Q₈×C₃₁	—	2	2	no	—
135	Q₈×C₃₁	—	2	2	no	—
136	D₄×C₃₁	—	2	2	no	—
137	D₄×C₃₁	—	2	2	no	—
138	D₄×C₃₁	—	4	2	no	—
139	D₄×C₃₁	—	4	2	no	—
140	C₂×C₄×C₃₁	—	2	4	no	—
141	C₂×C₄×C₃₁	—	2	2	no	—
142	C₂×C₄×C₃₁	—	2	4	no	—
143	C₂×C₄×C₃₁	—	2	2	no	—
144	C₂×C₄×C₃₁	—	2	2	no	—
145	C₂×C₄×C₃₁	—	4	2	no	—
146	C₂×C₄×C₃₁	—	4	2	no	—
147	C₂×C₄×C₃₁	—	4	2	no	—
148	C₂×C₄×C₃₁	—	4	2	no	—
149	C₂×C₄×C₃₁	—	8	4	no	—
150	C₂×C₄×C₃₁	C₄×D₄	1	4	yes	—
151	C₂×C₄×C₃₁	C₂³×C₄	1	1	yes	characteristic
152	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
153	C₂×C₄×C₃₁	C₂×#41	1	1	yes	characteristic
154	C₂×C₄×C₃₁	C₂×#41	1	1	yes	characteristic
155	C₂×C₄×C₃₁	C₂×#41	1	1	yes	characteristic
156	C₂×C₄×C₃₁	C₂×#41	1	1	yes	characteristic
157	C₈×C₃₁	—	2	2	no	—
158	C₈×C₃₁	—	2	2	no	—
159	C₈×C₃₁	—	2	2	no	—
160	C₈×C₃₁	—	4	2	no	—
161	C₈×C₃₁	—	4	2	no	—
162	C₈×C₃₁	#117	1	2	yes	—
163	C₈×C₃₁	#117	1	2	yes	—
164	#2943	C₂×C₃₁	1	1	yes	characteristic
165	#2923	C₂×C₃₁	1	2	yes	complemented
166	#1975	C₂×C₃₁	1	1	yes	characteristic
167	#1974	C₂×C₃₁	1	1	yes	characteristic
168	#1946	C₂×C₃₁	1	1	yes	characteristic, complemented
169	#1945	C₂×C₃₁	1	1	yes	characteristic, complemented
170	#1938	C₂×C₃₁	1	2	yes	complemented
171	#1937	C₂×C₃₁	1	2	yes	complemented
172	#1778	C₂×C₃₁	1	1	yes	characteristic, complemented
173	C₄×#104	C₂×C₃₁	1	2	yes	complemented
174	C₄×#97	C₂×C₃₁	1	1	yes	characteristic, complemented
175	C₂²×C₃₁	—	2	2	no	—
176	C₂²×C₃₁	—	4	4	no	—
177	C₂²×C₃₁	—	4	2	no	—
178	C₂²×C₃₁	C₂×C₄×D₄	1	1	yes	characteristic
179	C₂²×C₃₁	#529	1	1	yes	characteristic
180	C₂²×C₃₁	#529	1	1	yes	characteristic
181	C₄×C₃₁	—	2	4	no	—
182	C₄×C₃₁	—	2	4	no	—
183	C₄×C₃₁	—	4	2	no	—
184	C₄×C₃₁	—	4	4	no	—
185	C₄×C₃₁	—	4	2	no	—
186	C₄×C₃₁	C₂×#117	1	1	yes	characteristic
187	C₄×C₃₁	C₄×#41	1	1	yes	characteristic
188	C₄×C₃₁	#532	1	1	yes	characteristic
189	C₄×C₃₁	#532	1	1	yes	characteristic
190	C₂×#135	C₂²×C₃₁	1	1	yes	characteristic
191	C₄×#41	C₂²×C₃₁	1	2	yes	—
192	#442	C₄×C₃₁	1	2	yes	complemented
193	#441	C₄×C₃₁	1	2	yes	complemented
194	#440	C₄×C₃₁	1	4	yes	complemented
195	#433	—	2	4	no	—
196	#432	—	2	4	no	—
197	C₂×#108	C₂²×C₃₁	1	1	yes	characteristic
198	C₂×#108	C₂²×C₃₁	1	1	yes	characteristic
199	#427	C₂²×C₃₁	1	1	yes	characteristic
200	#424	C₂²×C₃₁	1	2	yes	—
201	#424	C₂²×C₃₁	1	2	yes	—
202	C₂×#104	C₂²×C₃₁	1	2	yes	—
203	C₂×#104	C₂²×C₃₁	1	2	yes	—
204	#416	C₂²×C₃₁	1	2	yes	—
205	#408	C₂²×C₃₁	1	2	yes	—
206	#408	C₂²×C₃₁	1	2	yes	—
207	C₄×M₁₆	C₂²×C₃₁	1	2	yes	—
208	C₂×#97	C₂²×C₃₁	1	1	yes	characteristic
209	C₂×#97	C₂²×C₃₁	1	1	yes	characteristic
210	C₂×#97	C₂²×C₃₁	1	1	yes	characteristic
211	C₂×#97	C₂²×C₃₁	1	1	yes	characteristic
212	C₂×C₄×C₈	C₂²×C₃₁	1	1	yes	characteristic
213	C₂×C₄×C₈	C₂²×C₃₁	1	1	yes	characteristic
214	C₄³	C₂²×C₃₁	1	1	yes	characteristic
215	#341	C₂²×C₃₁	1	2	yes	—
216	#339	C₂²×C₃₁	1	2	yes	—
217	#339	C₂²×C₃₁	1	2	yes	—
218	C₂×C₃₁	—	2	1	no	—
219	C₂×C₃₁	—	2	1	no	—
220	C₂×C₃₁	—	8	2	no	—
221	C₂×C₃₁	#2293	1	1	yes	characteristic
222	C₂×C₃₁	#2956	1	2	yes	—
223	C₂×#41	C₂³×C₃₁	1	2	yes	—
224	#135	—	2	2	no	—
225	#135	—	2	2	no	—
226	C₂×Q₁₆	C₂×C₄×C₃₁	1	1	yes	characteristic
227	C₂×SD₁₆	C₂×C₄×C₃₁	1	2	yes	—
228	C₂×D₈	C₂×C₄×C₃₁	1	1	yes	characteristic
229	C₂×M₁₆	C₂³×C₃₁	1	2	yes	—
230	C₂×M₁₆	C₂³×C₃₁	1	2	yes	—
231	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
232	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
233	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
234	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
235	C₄×Q₈	C₂×C₄×C₃₁	1	4	yes	—
236	C₄×D₄	—	2	4	no	—
237	C₄×D₄	C₂×C₄×C₃₁	1	4	yes	—
238	#117	—	2	2	no	—
239	#117	C₂³×C₃₁	1	2	yes	—
240	C₂×C₄²	—	2	2	no	—
241	C₂×C₄²	—	2	2	no	—
242	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
243	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
244	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
245	#108	—	2	2	no	—
246	#108	—	2	2	no	—
247	#107	C₂×C₄×C₃₁	1	2	yes	—
248	#106	C₂×C₄×C₃₁	1	2	yes	—
249	C₄⋊C₈	—	2	4	no	—
250	C₄⋊C₈	—	2	4	no	—
251	#104	—	2	4	no	—
252	#104	—	2	4	no	—
253	#103	C₂×C₄×C₃₁	1	4	yes	—
254	#102	C₂×C₄×C₃₁	1	4	yes	—
255	C₂²⋊C₈	—	2	4	no	—
256	C₂²⋊C₈	—	2	4	no	—
257	#97	—	2	2	no	—
258	#97	—	2	2	no	—
259	#97	—	2	2	no	—
260	#97	C₂×C₄×C₃₁	1	2	yes	—
261	#97	C₂×C₄×C₃₁	1	2	yes	—
262	#97	D₄×C₃₁	1	4	yes	—
263	C₄×C₈	—	2	2	no	—
264	C₄×C₈	—	2	2	no	—
265	C₄×C₈	—	2	2	no	—
266	C₃₁	#21297	1	1	yes	characteristic, direct product factor, Sylow
267	#41	—	2	2	no	—
268	#41	—	2	2	no	—
269	#41	—	2	2	no	—
270	#41	—	2	2	no	—
271	C₂×Q₈	C₂²×C₄×C₃₁	1	2	yes	—
272	C₂×D₄	—	2	2	no	—
273	C₂×D₄	C₂²×C₄×C₃₁	1	2	yes	—
274	C₂²×C₄	—	2	1	no	—
275	C₂²×C₄	—	2	1	no	—
276	C₂²×C₄	—	2	2	no	—
277	C₂²×C₄	—	2	4	no	—
278	C₂²×C₄	#41×C₃₁	1	2	yes	—
279	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
280	Q₁₆	—	2	2	no	—
281	SD₁₆	—	2	4	no	—
282	D₈	—	2	2	no	—
283	M₁₆	—	2	2	no	—
284	M₁₆	—	2	2	no	—
285	M₁₆	—	2	2	no	—
286	M₁₆	—	2	2	no	—
287	C₂×C₈	—	2	1	no	—
288	C₂×C₈	—	2	1	no	—
289	C₂×C₈	—	2	1	no	—
290	C₂×C₈	—	2	1	no	—
291	C₂×C₈	—	2	1	no	—
292	C₂×C₈	—	2	1	no	—
293	C₂×C₈	—	2	2	no	—
294	C₂×C₈	—	2	2	no	—
295	C₂×C₈	C₂²×C₄×C₃₁	1	2	yes	—
296	C₂×C₈	C₂²×C₄×C₃₁	1	1	yes	characteristic
297	C₂×C₈	C₂²×C₄×C₃₁	1	1	yes	characteristic
298	C₂×C₈	C₂×D₄×C₃₁	1	2	yes	—
299	C₂×C₈	C₂×D₄×C₃₁	1	2	yes	—
300	C₂×C₈	#41×C₃₁	1	2	yes	—
301	C₂×C₈	#41×C₃₁	1	2	yes	—
302	C₄⋊C₄	—	2	4	no	—
303	C₄⋊C₄	C₂²×C₄×C₃₁	1	4	yes	—
304	C₂²⋊C₄	—	2	2	no	—
305	C₂²⋊C₄	—	2	4	no	—
306	C₄²	—	2	4	no	—
307	C₄²	—	2	2	no	—
308	C₄²	—	2	1	no	—
309	C₄²	—	2	1	no	—
310	C₄²	—	4	4	no	—
311	C₄²	C₂²×C₄×C₃₁	1	2	yes	—
312	C₄²	C₂×D₄×C₃₁	1	2	yes	—
313	C₄²	#41×C₃₁	1	2	yes	—
314	C₄²	#41×C₃₁	1	2	yes	—
315	C₂³	—	2	2	no	—
316	C₂³	C₂×#41×C₃₁	1	1	yes	characteristic
317	Q₈	—	2	2	no	—
318	Q₈	—	2	2	no	—
319	D₄	—	2	2	no	—
320	D₄	—	2	2	no	—
321	D₄	—	4	2	no	—
322	D₄	—	4	2	no	—
323	C₂×C₄	—	2	4	no	—
324	C₂×C₄	—	2	2	no	—
325	C₂×C₄	—	2	4	no	—
326	C₂×C₄	—	2	2	no	—
327	C₂×C₄	—	2	2	no	—
328	C₂×C₄	—	4	2	no	—
329	C₂×C₄	—	4	2	no	—
330	C₂×C₄	—	4	2	no	—
331	C₂×C₄	—	4	2	no	—
332	C₂×C₄	—	8	4	no	—
333	C₂×C₄	C₄×D₄×C₃₁	1	4	yes	—
334	C₂×C₄	C₂³×C₄×C₃₁	1	1	yes	characteristic
335	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
336	C₂×C₄	C₂×#41×C₃₁	1	1	yes	characteristic
337	C₂×C₄	C₂×#41×C₃₁	1	1	yes	characteristic
338	C₂×C₄	C₂×#41×C₃₁	1	1	yes	characteristic
339	C₂×C₄	C₂×#41×C₃₁	1	1	yes	characteristic
340	C₈	—	2	2	no	—
341	C₈	—	2	2	no	—
342	C₈	—	2	2	no	—
343	C₈	—	4	2	no	—
344	C₈	—	4	2	no	—
345	C₈	C₃₁×#117	1	2	yes	—
346	C₈	C₃₁×#117	1	2	yes	—
347	C₂²	—	2	2	no	—
348	C₂²	—	4	4	no	—
349	C₂²	—	4	2	no	—
350	C₂²	C₂×C₄×D₄×C₃₁	1	1	yes	characteristic
351	C₂²	C₃₁×#529	1	1	yes	characteristic
352	C₂²	C₃₁×#529	1	1	yes	characteristic
353	C₄	—	2	4	no	—
354	C₄	—	2	4	no	—
355	C₄	—	4	2	no	—
356	C₄	—	4	4	no	—
357	C₄	—	4	2	no	—
358	C₄	C₂×C₃₁×#117	1	1	yes	characteristic
359	C₄	C₄×#41×C₃₁	1	1	yes	characteristic
360	C₄	C₃₁×#532	1	1	yes	characteristic
361	C₄	C₃₁×#532	1	1	yes	characteristic
362	C₂	—	2	1	no	—
363	C₂	—	2	1	no	—
364	C₂	—	8	2	no	—
365	C₂	C₃₁×#2293	1	1	yes	characteristic
366	C₂	C₃₁×#2956	1	2	yes	—

	subgroup	G/H
center	C₂×C₄×C₃₁	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₃₁
Frattini, cosocle	C₂²×C₄	C₂⁴×C₃₁
socle	C₂²×C₃₁	C₂×C₄×D₄
prime radical	C₂×C₃₁×#135	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₃₁ ◁ C₂×C₃₁×#97 ◁ G

Complements

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

N	H ≅ G/N	type
2. C₃₁×#2923	C₂	semidirect
5. C₃₁×#1946	C₂	semidirect
6. C₃₁×#1945	C₂	semidirect
7. C₃₁×#1938	C₂	semidirect
8. C₃₁×#1937	C₂	semidirect
9. C₃₁×#1778	C₂	semidirect
10. C₄×C₃₁×#104	C₂	semidirect
11. C₄×C₃₁×#97	C₂	semidirect
14. C₃₁×#442	C₄	semidirect
15. C₃₁×#441	C₄	semidirect
16. C₃₁×#440	C₄	semidirect
131. #21297	C₃₁	direct (N × H)
165. #2923	C₂×C₃₁	semidirect
168. #1946	C₂×C₃₁	semidirect
169. #1945	C₂×C₃₁	semidirect
170. #1938	C₂×C₃₁	semidirect
171. #1937	C₂×C₃₁	semidirect
172. #1778	C₂×C₃₁	semidirect
173. C₄×#104	C₂×C₃₁	semidirect
174. C₄×#97	C₂×C₃₁	semidirect
192. #442	C₄×C₃₁	semidirect
193. #441	C₄×C₃₁	semidirect
194. #440	C₄×C₃₁	semidirect
266. C₃₁	#21297	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃₁×#2943	2
C₃₁×#2923	2
C₃₁×#1975	2
C₃₁×#1974	2
C₃₁×#1946	2
C₃₁×#1945	2
C₃₁×#1938	2
C₃₁×#1937	2
C₃₁×#1778	2
C₄×C₃₁×#104	2
C₄×C₃₁×#97	2
#21297	31

Subgroups — C31×#21297 #21478056

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#21297 #21478056