Subgroups — C₂×C₃₁×#2098 #21480498

Order 7936.

1010 conjugacy classes of subgroups.

The subgroup lattice has 410 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃₁×#430	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃₁×#424	C₂	1	2	yes	maximal, complemented
3	C₂×C₃₁×#421	C₂	1	2	yes	maximal
4	C₂×C₃₁×#408	C₂	1	1	yes	maximal, characteristic
5	C₃₁×#2098	C₂	1	8	yes	maximal, direct product factor
6	C₂×C₃₁×H(3,ℤ/4)	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂²×#41×C₃₁	C₂²	1	1	yes	characteristic
8	C₂²×M₁₆×C₃₁	C₂²	1	2	yes	—
9	C₂²×M₁₆×C₃₁	C₂²	1	1	yes	characteristic
10	C₂³×C₈×C₃₁	C₂²	1	1	yes	characteristic
11	C₂×C₃₁×#117	C₂²	1	2	yes	—
12	C₃₁×#430	—	2	2	no	—
13	C₃₁×#430	C₂²	1	4	yes	complemented
14	C₂×C₃₁×#108	—	2	2	no	—
15	C₃₁×#424	—	2	4	no	—
16	C₃₁×#424	C₂²	1	8	yes	complemented
17	C₂×C₃₁×C₄⋊C₈	—	2	4	no	—
18	C₃₁×#421	—	2	4	no	—
19	C₃₁×#421	C₂²	1	8	yes	—
20	C₂×C₃₁×#104	—	2	4	no	—
21	C₃₁×#408	—	2	2	no	—
22	C₃₁×#408	C₂²	1	4	yes	—
23	C₂×C₃₁×C₂²⋊C₈	—	2	2	no	—
24	C₃₁×H(3,ℤ/4)	C₂²	1	4	yes	complemented
25	C₂×#41×C₃₁	—	2	1	no	—
26	C₂×#41×C₃₁	—	2	1	no	—
27	C₂×#41×C₃₁	—	2	2	no	—
28	C₂×#41×C₃₁	—	2	2	no	—
29	C₂×#41×C₃₁	—	2	2	no	—
30	C₂×#41×C₃₁	—	2	2	no	—
31	C₂×#41×C₃₁	Q₈	1	2	yes	—
32	C₂×#41×C₃₁	C₂³	1	2	yes	—
33	C₂²×Q₈×C₃₁	Q₈	1	1	yes	characteristic
34	C₂²×D₄×C₃₁	—	2	1	no	—
35	C₂²×D₄×C₃₁	Q₈	1	1	yes	characteristic
36	C₂³×C₄×C₃₁	—	2	1	no	—
37	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
38	C₂×M₁₆×C₃₁	—	2	2	no	—
39	C₂×M₁₆×C₃₁	—	2	2	no	—
40	C₂×M₁₆×C₃₁	—	2	2	no	—
41	C₂×M₁₆×C₃₁	—	2	2	no	—
42	C₂×M₁₆×C₃₁	—	2	2	no	—
43	C₂×M₁₆×C₃₁	—	2	2	no	—
44	C₂×M₁₆×C₃₁	—	2	2	no	—
45	C₂×M₁₆×C₃₁	D₄	1	2	yes	—
46	C₂×M₁₆×C₃₁	C₂³	1	4	yes	—
47	C₂×M₁₆×C₃₁	C₂³	1	2	yes	—
48	C₂²×C₈×C₃₁	—	2	1	no	—
49	C₂²×C₈×C₃₁	—	2	1	no	—
50	C₂²×C₈×C₃₁	—	2	2	no	—
51	C₂²×C₈×C₃₁	—	2	2	no	—
52	C₂²×C₈×C₃₁	—	2	2	no	—
53	C₂²×C₈×C₃₁	D₄	1	2	yes	—
54	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
55	C₃₁×#117	—	2	2	no	—
56	C₃₁×#117	—	2	2	no	—
57	C₃₁×#117	D₄	1	4	yes	—
58	C₃₁×#117	C₂³	1	4	yes	—
59	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
60	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
61	C₂×C₄²×C₃₁	D₄	1	4	yes	—
62	C₃₁×#108	—	2	8	no	—
63	C₃₁×C₄⋊C₈	—	2	16	no	—
64	C₃₁×#104	—	2	16	no	—
65	C₃₁×C₂²⋊C₈	—	2	8	no	—
66	C₂⁴×C₃₁	—	2	1	no	—
67	C₂⁴×C₃₁	#41	1	1	yes	characteristic
68	#41×C₃₁	—	2	4	no	—
69	#41×C₃₁	—	2	4	no	—
70	#41×C₃₁	—	2	4	no	—
71	#41×C₃₁	—	2	4	no	—
72	#41×C₃₁	—	4	2	no	—
73	#41×C₃₁	—	4	2	no	—
74	#41×C₃₁	—	4	2	no	—
75	#41×C₃₁	—	4	2	no	—
76	C₂×Q₈×C₃₁	—	2	1	no	—
77	C₂×Q₈×C₃₁	—	2	2	no	—
78	C₂×Q₈×C₃₁	—	2	2	no	—
79	C₂×Q₈×C₃₁	C₂×Q₈	1	2	yes	—
80	C₂×D₄×C₃₁	—	2	2	no	—
81	C₂×D₄×C₃₁	—	2	2	no	—
82	C₂×D₄×C₃₁	—	2	2	no	—
83	C₂×D₄×C₃₁	—	2	2	no	—
84	C₂×D₄×C₃₁	—	2	1	no	—
85	C₂×D₄×C₃₁	—	4	2	no	—
86	C₂×D₄×C₃₁	—	4	2	no	—
87	C₂×D₄×C₃₁	C₂×Q₈	1	2	yes	—
88	C₂²×C₄×C₃₁	—	2	1	no	—
89	C₂²×C₄×C₃₁	—	2	4	no	—
90	C₂²×C₄×C₃₁	—	2	2	no	—
91	C₂²×C₄×C₃₁	—	2	2	no	—
92	C₂²×C₄×C₃₁	—	4	1	no	—
93	C₂²×C₄×C₃₁	—	4	1	no	—
94	C₂²×C₄×C₃₁	—	4	1	no	—
95	C₂²×C₄×C₃₁	—	4	1	no	—
96	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
97	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
98	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
99	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
100	C₂²×C₄×C₃₁	C₂×Q₈	1	1	yes	characteristic
101	C₂²×C₄×C₃₁	C₂×Q₈	1	1	yes	characteristic
102	C₂²×C₄×C₃₁	#41	1	1	yes	characteristic
103	C₂²×C₄×C₃₁	#41	1	2	yes	—
104	C₂²×C₄×C₃₁	#41	1	2	yes	—
105	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
106	M₁₆×C₃₁	—	2	4	no	—
107	M₁₆×C₃₁	—	2	4	no	—
108	M₁₆×C₃₁	—	2	4	no	—
109	M₁₆×C₃₁	—	2	4	no	—
110	M₁₆×C₃₁	—	4	2	no	—
111	M₁₆×C₃₁	—	4	2	no	—
112	C₂×C₈×C₃₁	—	2	2	no	—
113	C₂×C₈×C₃₁	—	2	2	no	—
114	C₂×C₈×C₃₁	—	2	2	no	—
115	C₂×C₈×C₃₁	—	2	4	no	—
116	C₂×C₈×C₃₁	—	2	4	no	—
117	C₂×C₈×C₃₁	—	4	2	no	—
118	C₂×C₈×C₃₁	—	4	1	no	—
119	C₂×C₈×C₃₁	—	4	2	no	—
120	C₂×C₈×C₃₁	—	4	1	no	—
121	C₂×C₈×C₃₁	—	4	2	no	—
122	C₂×C₈×C₃₁	C₂×D₄	1	4	yes	—
123	C₄⋊C₄×C₃₁	—	2	4	no	—
124	C₄⋊C₄×C₃₁	—	2	4	no	—
125	C₂²⋊C₄×C₃₁	—	2	4	no	—
126	C₂²⋊C₄×C₃₁	—	2	4	no	—
127	C₄²×C₃₁	—	2	4	no	—
128	C₄²×C₃₁	C₂×D₄	1	8	yes	—
129	C₂×#2098	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
130	C₂³×C₃₁	—	2	2	no	—
131	C₂³×C₃₁	—	4	2	no	—
132	C₂³×C₃₁	—	4	4	no	—
133	C₂³×C₃₁	—	4	1	no	—
134	C₂³×C₃₁	—	4	1	no	—
135	C₂³×C₃₁	C₂²⋊Q₈	1	1	yes	characteristic
136	C₂³×C₃₁	C₂²⋊Q₈	1	1	yes	characteristic
137	C₂³×C₃₁	#123	1	2	yes	—
138	C₂³×C₃₁	#123	1	2	yes	—
139	C₂³×C₃₁	C₂×#41	1	1	yes	characteristic
140	Q₈×C₃₁	—	2	4	no	—
141	Q₈×C₃₁	—	4	2	no	—
142	D₄×C₃₁	—	2	4	no	—
143	D₄×C₃₁	—	4	4	no	—
144	D₄×C₃₁	—	4	4	no	—
145	D₄×C₃₁	—	4	2	no	—
146	C₂×C₄×C₃₁	—	2	2	no	—
147	C₂×C₄×C₃₁	—	2	8	no	—
148	C₂×C₄×C₃₁	—	4	8	no	—
149	C₂×C₄×C₃₁	—	4	1	no	—
150	C₂×C₄×C₃₁	—	4	1	no	—
151	C₂×C₄×C₃₁	—	4	2	no	—
152	C₂×C₄×C₃₁	—	4	2	no	—
153	C₂×C₄×C₃₁	—	4	2	no	—
154	C₂×C₄×C₃₁	—	4	2	no	—
155	C₂×C₄×C₃₁	C₂²⋊Q₈	1	2	yes	—
156	C₂×C₄×C₃₁	C₂²⋊Q₈	1	2	yes	—
157	C₂×C₄×C₃₁	C₂²⋊Q₈	1	2	yes	—
158	C₂×C₄×C₃₁	C₂²⋊Q₈	1	2	yes	—
159	C₂×C₄×C₃₁	C₂²⋊Q₈	1	1	yes	characteristic
160	C₂×C₄×C₃₁	C₂²⋊Q₈	1	1	yes	characteristic
161	C₂×C₄×C₃₁	#123	1	1	yes	characteristic
162	C₂×C₄×C₃₁	#123	1	1	yes	characteristic
163	C₂×C₄×C₃₁	#123	1	2	yes	—
164	C₂×C₄×C₃₁	#123	1	2	yes	—
165	C₂×C₄×C₃₁	#123	1	2	yes	—
166	C₂×C₄×C₃₁	#127	1	2	yes	—
167	C₂×C₄×C₃₁	#127	1	1	yes	characteristic
168	C₂×C₄×C₃₁	#127	1	1	yes	characteristic
169	C₂×C₄×C₃₁	C₂²×D₄	1	2	yes	—
170	C₂×C₄×C₃₁	C₂²×D₄	1	1	yes	characteristic
171	C₂×C₄×C₃₁	C₂²×Q₈	1	1	yes	characteristic
172	C₂×C₄×C₃₁	C₂×#41	1	2	yes	—
173	C₈×C₃₁	—	2	4	no	—
174	C₈×C₃₁	—	4	2	no	—
175	C₈×C₃₁	—	4	4	no	—
176	C₂×#430	C₂×C₃₁	1	1	yes	characteristic, complemented
177	C₂×#424	C₂×C₃₁	1	2	yes	complemented
178	C₂×#421	C₂×C₃₁	1	2	yes	—
179	C₂×#408	C₂×C₃₁	1	1	yes	characteristic
180	#2098	C₂×C₃₁	1	8	yes	direct product factor
181	C₂×H(3,ℤ/4)	C₂×C₃₁	1	1	yes	characteristic, complemented
182	C₂²×C₃₁	—	2	4	no	—
183	C₂²×C₃₁	—	2	2	no	—
184	C₂²×C₃₁	—	4	1	no	—
185	C₂²×C₃₁	—	4	2	no	—
186	C₂²×C₃₁	—	4	1	no	—
187	C₂²×C₃₁	—	4	4	no	—
188	C₂²×C₃₁	—	4	2	no	—
189	C₂²×C₃₁	—	8	2	no	—
190	C₂²×C₃₁	—	8	2	no	—
191	C₂²×C₃₁	#399	1	1	yes	characteristic
192	C₂²×C₃₁	#399	1	2	yes	—
193	C₂²×C₃₁	#399	1	1	yes	characteristic
194	C₂²×C₃₁	C₂×C₂²⋊Q₈	1	1	yes	characteristic
195	C₂²×C₃₁	C₂×#123	1	2	yes	—
196	C₄×C₃₁	—	4	8	no	—
197	C₄×C₃₁	—	4	2	no	—
198	C₄×C₃₁	#399	1	1	yes	characteristic
199	C₄×C₃₁	#399	1	1	yes	characteristic
200	C₄×C₃₁	#399	1	2	yes	—
201	C₄×C₃₁	C₂×C₂²⋊Q₈	1	2	yes	—
202	C₄×C₃₁	C₂×#123	1	1	yes	characteristic
203	C₄×C₃₁	C₂×#127	1	1	yes	characteristic
204	C₂²×#41	C₂²×C₃₁	1	1	yes	characteristic
205	C₂²×M₁₆	C₂²×C₃₁	1	2	yes	—
206	C₂²×M₁₆	C₂²×C₃₁	1	1	yes	characteristic
207	C₂³×C₈	C₂²×C₃₁	1	1	yes	characteristic
208	C₂×#117	C₂²×C₃₁	1	2	yes	—
209	#430	—	2	2	no	—
210	#430	C₂²×C₃₁	1	4	yes	complemented
211	C₂×#108	—	2	2	no	—
212	#424	—	2	4	no	—
213	#424	C₂²×C₃₁	1	8	yes	complemented
214	C₂×C₄⋊C₈	—	2	4	no	—
215	#421	—	2	4	no	—
216	#421	C₂²×C₃₁	1	8	yes	—
217	C₂×#104	—	2	4	no	—
218	#408	—	2	2	no	—
219	#408	C₂²×C₃₁	1	4	yes	—
220	C₂×C₂²⋊C₈	—	2	2	no	—
221	H(3,ℤ/4)	C₂²×C₃₁	1	4	yes	complemented
222	C₂×C₃₁	—	2	2	no	—
223	C₂×C₃₁	—	2	1	no	—
224	C₂×C₃₁	—	2	1	no	—
225	C₂×C₃₁	—	2	2	no	—
226	C₂×C₃₁	—	8	2	no	—
227	C₂×C₃₁	#2098	1	2	yes	direct product factor
228	C₂×C₃₁	C₂×#399	1	1	yes	characteristic
229	C₂×#41	—	2	1	no	—
230	C₂×#41	—	2	1	no	—
231	C₂×#41	—	2	2	no	—
232	C₂×#41	—	2	2	no	—
233	C₂×#41	—	2	2	no	—
234	C₂×#41	—	2	2	no	—
235	C₂×#41	Q₈×C₃₁	1	2	yes	—
236	C₂×#41	C₂³×C₃₁	1	2	yes	—
237	C₂²×Q₈	Q₈×C₃₁	1	1	yes	characteristic
238	C₂²×D₄	—	2	1	no	—
239	C₂²×D₄	Q₈×C₃₁	1	1	yes	characteristic
240	C₂³×C₄	—	2	1	no	—
241	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
242	C₂×M₁₆	—	2	2	no	—
243	C₂×M₁₆	—	2	2	no	—
244	C₂×M₁₆	—	2	2	no	—
245	C₂×M₁₆	—	2	2	no	—
246	C₂×M₁₆	—	2	2	no	—
247	C₂×M₁₆	—	2	2	no	—
248	C₂×M₁₆	—	2	2	no	—
249	C₂×M₁₆	D₄×C₃₁	1	2	yes	—
250	C₂×M₁₆	C₂³×C₃₁	1	4	yes	—
251	C₂×M₁₆	C₂³×C₃₁	1	2	yes	—
252	C₂²×C₈	—	2	1	no	—
253	C₂²×C₈	—	2	1	no	—
254	C₂²×C₈	—	2	2	no	—
255	C₂²×C₈	—	2	2	no	—
256	C₂²×C₈	—	2	2	no	—
257	C₂²×C₈	D₄×C₃₁	1	2	yes	—
258	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
259	#117	—	2	2	no	—
260	#117	—	2	2	no	—
261	#117	D₄×C₃₁	1	4	yes	—
262	#117	C₂³×C₃₁	1	4	yes	—
263	C₂×C₄⋊C₄	—	2	2	no	—
264	C₂×C₂²⋊C₄	—	2	2	no	—
265	C₂×C₄²	D₄×C₃₁	1	4	yes	—
266	#108	—	2	8	no	—
267	C₄⋊C₈	—	2	16	no	—
268	#104	—	2	16	no	—
269	C₂²⋊C₈	—	2	8	no	—
270	C₃₁	C₂×#2098	1	1	yes	characteristic, direct product factor, Sylow
271	C₂⁴	—	2	1	no	—
272	C₂⁴	#41×C₃₁	1	1	yes	characteristic
273	#41	—	2	4	no	—
274	#41	—	2	4	no	—
275	#41	—	2	4	no	—
276	#41	—	2	4	no	—
277	#41	—	4	2	no	—
278	#41	—	4	2	no	—
279	#41	—	4	2	no	—
280	#41	—	4	2	no	—
281	C₂×Q₈	—	2	1	no	—
282	C₂×Q₈	—	2	2	no	—
283	C₂×Q₈	—	2	2	no	—
284	C₂×Q₈	C₂×Q₈×C₃₁	1	2	yes	—
285	C₂×D₄	—	2	2	no	—
286	C₂×D₄	—	2	2	no	—
287	C₂×D₄	—	2	2	no	—
288	C₂×D₄	—	2	2	no	—
289	C₂×D₄	—	2	1	no	—
290	C₂×D₄	—	4	2	no	—
291	C₂×D₄	—	4	2	no	—
292	C₂×D₄	C₂×Q₈×C₃₁	1	2	yes	—
293	C₂²×C₄	—	2	1	no	—
294	C₂²×C₄	—	2	4	no	—
295	C₂²×C₄	—	2	2	no	—
296	C₂²×C₄	—	2	2	no	—
297	C₂²×C₄	—	4	1	no	—
298	C₂²×C₄	—	4	1	no	—
299	C₂²×C₄	—	4	1	no	—
300	C₂²×C₄	—	4	1	no	—
301	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
302	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
303	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
304	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
305	C₂²×C₄	C₂×Q₈×C₃₁	1	1	yes	characteristic
306	C₂²×C₄	C₂×Q₈×C₃₁	1	1	yes	characteristic
307	C₂²×C₄	#41×C₃₁	1	1	yes	characteristic
308	C₂²×C₄	#41×C₃₁	1	2	yes	—
309	C₂²×C₄	#41×C₃₁	1	2	yes	—
310	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
311	M₁₆	—	2	4	no	—
312	M₁₆	—	2	4	no	—
313	M₁₆	—	2	4	no	—
314	M₁₆	—	2	4	no	—
315	M₁₆	—	4	2	no	—
316	M₁₆	—	4	2	no	—
317	C₂×C₈	—	2	2	no	—
318	C₂×C₈	—	2	2	no	—
319	C₂×C₈	—	2	2	no	—
320	C₂×C₈	—	2	4	no	—
321	C₂×C₈	—	2	4	no	—
322	C₂×C₈	—	4	2	no	—
323	C₂×C₈	—	4	1	no	—
324	C₂×C₈	—	4	1	no	—
325	C₂×C₈	—	4	2	no	—
326	C₂×C₈	—	4	2	no	—
327	C₂×C₈	C₂×D₄×C₃₁	1	4	yes	—
328	C₄⋊C₄	—	2	4	no	—
329	C₄⋊C₄	—	2	4	no	—
330	C₂²⋊C₄	—	2	4	no	—
331	C₂²⋊C₄	—	2	4	no	—
332	C₄²	—	2	4	no	—
333	C₄²	C₂×D₄×C₃₁	1	8	yes	—
334	C₂³	—	2	2	no	—
335	C₂³	—	4	2	no	—
336	C₂³	—	4	4	no	—
337	C₂³	—	4	1	no	—
338	C₂³	—	4	1	no	—
339	C₂³	C₃₁×C₂²⋊Q₈	1	1	yes	characteristic
340	C₂³	C₃₁×C₂²⋊Q₈	1	1	yes	characteristic
341	C₂³	C₃₁×#123	1	2	yes	—
342	C₂³	C₃₁×#123	1	2	yes	—
343	C₂³	C₂×#41×C₃₁	1	1	yes	characteristic
344	Q₈	—	2	4	no	—
345	Q₈	—	4	2	no	—
346	D₄	—	2	4	no	—
347	D₄	—	4	4	no	—
348	D₄	—	4	4	no	—
349	D₄	—	4	2	no	—
350	C₂×C₄	—	2	2	no	—
351	C₂×C₄	—	2	8	no	—
352	C₂×C₄	—	4	8	no	—
353	C₂×C₄	—	4	1	no	—
354	C₂×C₄	—	4	1	no	—
355	C₂×C₄	—	4	2	no	—
356	C₂×C₄	—	4	2	no	—
357	C₂×C₄	—	4	2	no	—
358	C₂×C₄	—	4	2	no	—
359	C₂×C₄	C₃₁×C₂²⋊Q₈	1	1	yes	characteristic
360	C₂×C₄	C₃₁×C₂²⋊Q₈	1	1	yes	characteristic
361	C₂×C₄	C₃₁×C₂²⋊Q₈	1	2	yes	—
362	C₂×C₄	C₃₁×C₂²⋊Q₈	1	2	yes	—
363	C₂×C₄	C₃₁×C₂²⋊Q₈	1	2	yes	—
364	C₂×C₄	C₃₁×C₂²⋊Q₈	1	2	yes	—
365	C₂×C₄	C₃₁×#123	1	2	yes	—
366	C₂×C₄	C₃₁×#123	1	2	yes	—
367	C₂×C₄	C₃₁×#123	1	1	yes	characteristic
368	C₂×C₄	C₃₁×#123	1	1	yes	characteristic
369	C₂×C₄	C₃₁×#123	1	2	yes	—
370	C₂×C₄	C₃₁×#127	1	2	yes	—
371	C₂×C₄	C₃₁×#127	1	1	yes	characteristic
372	C₂×C₄	C₃₁×#127	1	1	yes	characteristic
373	C₂×C₄	C₂²×D₄×C₃₁	1	2	yes	—
374	C₂×C₄	C₂²×D₄×C₃₁	1	1	yes	characteristic
375	C₂×C₄	C₂²×Q₈×C₃₁	1	1	yes	characteristic
376	C₂×C₄	C₂×#41×C₃₁	1	2	yes	—
377	C₈	—	2	4	no	—
378	C₈	—	4	2	no	—
379	C₈	—	4	4	no	—
380	C₂²	—	2	4	no	—
381	C₂²	—	2	2	no	—
382	C₂²	—	4	1	no	—
383	C₂²	—	4	2	no	—
384	C₂²	—	4	1	no	—
385	C₂²	—	4	4	no	—
386	C₂²	—	4	2	no	—
387	C₂²	—	8	2	no	—
388	C₂²	—	8	2	no	—
389	C₂²	C₃₁×#399	1	1	yes	characteristic
390	C₂²	C₃₁×#399	1	2	yes	—
391	C₂²	C₃₁×#399	1	1	yes	characteristic
392	C₂²	C₂×C₃₁×C₂²⋊Q₈	1	1	yes	characteristic
393	C₂²	C₂×C₃₁×#123	1	2	yes	—
394	C₄	—	4	8	no	—
395	C₄	—	4	2	no	—
396	C₄	C₃₁×#399	1	1	yes	characteristic
397	C₄	C₃₁×#399	1	1	yes	characteristic
398	C₄	C₃₁×#399	1	2	yes	—
399	C₄	C₂×C₃₁×C₂²⋊Q₈	1	2	yes	—
400	C₄	C₂×C₃₁×#123	1	1	yes	characteristic
401	C₄	C₂×C₃₁×#127	1	1	yes	characteristic
402	C₂	—	2	2	no	—
403	C₂	—	2	1	no	—
404	C₂	—	2	1	no	—
405	C₂	—	2	2	no	—
406	C₂	—	8	2	no	—
407	C₂	C₃₁×#2098	1	2	yes	direct product factor
408	C₂	C₂×C₃₁×#399	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₃₁	#127
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₃₁
socle	C₂²×C₃₁	#399
prime radical	C₂²×#41×C₃₁	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₃₁ ◁ C₂³×C₄×C₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₃₁×#430	C₂	semidirect
2. C₂×C₃₁×#424	C₂	semidirect
5. C₃₁×#2098	C₂	direct (N × H)
6. C₂×C₃₁×H(3,ℤ/4)	C₂	semidirect
13. C₃₁×#430	C₂²	semidirect
16. C₃₁×#424	C₂²	semidirect
24. C₃₁×H(3,ℤ/4)	C₂²	semidirect
129. C₂×#2098	C₃₁	direct (N × H)
176. C₂×#430	C₂×C₃₁	semidirect
177. C₂×#424	C₂×C₃₁	semidirect
180. #2098	C₂×C₃₁	direct (N × H)
181. C₂×H(3,ℤ/4)	C₂×C₃₁	semidirect
210. #430	C₂²×C₃₁	semidirect
213. #424	C₂²×C₃₁	semidirect
221. H(3,ℤ/4)	C₂²×C₃₁	semidirect
227. C₂×C₃₁	#2098	direct (N × H)
270. C₃₁	C₂×#2098	direct (N × H)
407. C₂	C₃₁×#2098	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×#430	2
C₂×C₃₁×#424	2
C₂×C₃₁×#421	2
C₂×C₃₁×#408	2
C₃₁×#2098	2
C₂×C₃₁×H(3,ℤ/4)	2
C₂×#2098	31

Subgroups — C2×C31×#2098 #21480498

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃₁×#2098 #21480498