Group #21467065 — subgroups

Subgroups — C₃₁×#10306 #21467065

Order 7936.

670 conjugacy classes of subgroups; only the 170 normal subgroups are shown.

normal subgroups only

This group has 670 conjugacy classes of subgroups — too many to draw. Only its 170 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃₁×#494	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃₁×#486	C₂	1	2	yes	maximal
3	C₃₁×#1990	C₂	1	2	yes	maximal, complemented
4	C₃₁×#1957	C₂	1	1	yes	maximal, characteristic
5	C₃₁×#1273	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×Q₁₆×C₃₁	—	2	2	no	—
7	C₂×C₃₁×C₄⋊Q₈	C₂²	1	2	yes	—
8	C₂×C₃₁×#127	C₂²	1	1	yes	characteristic
9	C₃₁×#494	—	2	4	no	—
10	C₃₁×#486	—	2	4	no	—
11	C₃₁×#486	—	2	4	no	—
12	C₂×C₃₁×#102	—	2	4	no	—
13	C₂×C₃₁×#102	—	2	2	no	—
14	C₂×C₄×C₈×C₃₁	C₂²	1	2	yes	—
15	C₂×C₄×C₈×C₃₁	C₂²	1	1	yes	characteristic
16	C₃₁×#384	C₂²	1	1	yes	characteristic
17	C₃₁×#340	—	2	4	no	—
18	C₂²×Q₈×C₃₁	—	2	2	no	—
19	C₂²×D₄×C₃₁	—	2	1	no	—
20	C₂²×D₄×C₃₁	—	2	2	no	—
21	C₂×Q₁₆×C₃₁	—	2	8	no	—
22	C₂×Q₁₆×C₃₁	—	4	4	no	—
23	C₂×Q₁₆×C₃₁	—	4	4	no	—
24	C₂²×C₈×C₃₁	D₄	1	4	yes	—
25	C₂²×C₈×C₃₁	D₄	1	2	yes	—
26	C₃₁×C₄⋊Q₈	—	2	2	no	—
27	C₃₁×C₄⋊Q₈	—	2	2	no	—
28	C₃₁×C₄⋊Q₈	—	2	2	no	—
29	C₃₁×C₄⋊Q₈	D₄	1	4	yes	—
30	C₃₁×#127	—	2	2	no	—
31	C₃₁×#127	—	2	1	no	—
32	C₃₁×#127	D₄	1	2	yes	—
33	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
34	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
35	C₂×C₄⋊C₄×C₃₁	—	2	1	no	—
36	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
37	C₂×C₄²×C₃₁	C₂³	1	1	yes	characteristic
38	C₃₁×#102	—	2	16	no	—
39	C₃₁×#102	—	4	4	no	—
40	C₄×C₈×C₃₁	—	2	2	no	—
41	C₄×C₈×C₃₁	—	2	2	no	—
42	C₄×C₈×C₃₁	—	2	2	no	—
43	C₂⁴×C₃₁	—	4	1	no	—
44	C₂×Q₈×C₃₁	—	2	4	no	—
45	C₂×Q₈×C₃₁	—	4	2	no	—
46	C₂×Q₈×C₃₁	—	4	4	no	—
47	C₂×Q₈×C₃₁	—	4	4	no	—
48	C₂×D₄×C₃₁	—	2	4	no	—
49	C₂×D₄×C₃₁	—	2	2	no	—
50	C₂×D₄×C₃₁	—	4	1	no	—
51	C₂×D₄×C₃₁	—	4	2	no	—
52	C₂×D₄×C₃₁	—	4	2	no	—
53	C₂×D₄×C₃₁	—	4	4	no	—
54	C₂×D₄×C₃₁	—	4	2	no	—
55	C₂×D₄×C₃₁	—	4	4	no	—
56	C₂²×C₄×C₃₁	—	4	2	no	—
57	C₂²×C₄×C₃₁	—	4	1	no	—
58	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
59	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
60	Q₁₆×C₃₁	—	4	16	no	—
61	C₂×C₈×C₃₁	—	2	2	no	—
62	C₂×C₈×C₃₁	—	2	2	no	—
63	C₂×C₈×C₃₁	—	2	4	no	—
64	C₂×C₈×C₃₁	—	2	4	no	—
65	C₂×C₈×C₃₁	—	2	4	no	—
66	C₂×C₈×C₃₁	D₈	1	4	yes	—
67	C₄⋊C₄×C₃₁	—	2	4	no	—
68	C₄⋊C₄×C₃₁	—	2	4	no	—
69	C₄⋊C₄×C₃₁	—	4	2	no	—
70	C₄⋊C₄×C₃₁	—	4	2	no	—
71	C₄⋊C₄×C₃₁	—	4	2	no	—
72	C₄⋊C₄×C₃₁	—	4	4	no	—
73	C₄²×C₃₁	C₂×D₄	1	2	yes	—
74	C₄²×C₃₁	C₂×D₄	1	1	yes	characteristic
75	C₄²×C₃₁	#41	1	1	yes	characteristic
76	#10306	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
77	C₂³×C₃₁	—	4	2	no	—
78	C₂³×C₃₁	—	8	1	no	—
79	C₂³×C₃₁	—	8	2	no	—
80	C₂³×C₃₁	—	8	1	no	—
81	C₂³×C₃₁	—	8	2	no	—
82	C₂³×C₃₁	#127	1	1	yes	characteristic
83	Q₈×C₃₁	—	4	8	no	—
84	Q₈×C₃₁	—	8	4	no	—
85	D₄×C₃₁	—	4	8	no	—
86	D₄×C₃₁	—	4	4	no	—
87	D₄×C₃₁	—	8	2	no	—
88	D₄×C₃₁	—	8	4	no	—
89	C₂×C₄×C₃₁	—	4	4	no	—
90	C₂×C₄×C₃₁	—	8	2	no	—
91	C₂×C₄×C₃₁	—	8	2	no	—
92	C₂×C₄×C₃₁	—	8	1	no	—
93	C₂×C₄×C₃₁	—	8	2	no	—
94	C₂×C₄×C₃₁	#120	1	1	yes	characteristic
95	C₂×C₄×C₃₁	#120	1	2	yes	—
96	C₂×C₄×C₃₁	#121	1	1	yes	characteristic
97	C₂×C₄×C₃₁	#121	1	2	yes	—
98	C₂×C₄×C₃₁	C₂×D₈	1	2	yes	—
99	C₂×C₄×C₃₁	#135	1	4	yes	—
100	C₂×C₄×C₃₁	AGL(1,ℤ/8)	1	2	yes	—
101	C₂×C₄×C₃₁	#137	1	4	yes	—
102	C₈×C₃₁	—	2	4	no	—
103	C₈×C₃₁	—	4	4	no	—
104	C₂×#494	C₂×C₃₁	1	1	yes	characteristic, complemented
105	C₂×#486	C₂×C₃₁	1	2	yes	—
106	#1990	C₂×C₃₁	1	2	yes	complemented
107	#1957	C₂×C₃₁	1	1	yes	characteristic
108	#1273	C₂×C₃₁	1	1	yes	characteristic, complemented
109	C₂²×C₃₁	—	8	2	no	—
110	C₂²×C₃₁	—	8	4	no	—
111	C₂²×C₃₁	—	16	1	no	—
112	C₂²×C₃₁	—	16	2	no	—
113	C₂²×C₃₁	—	16	1	no	—
114	C₂²×C₃₁	#392	1	1	yes	characteristic
115	C₂²×C₃₁	#493	1	1	yes	characteristic
116	C₂²×C₃₁	#495	1	2	yes	—
117	C₂²×C₃₁	#496	1	1	yes	characteristic
118	C₂²×C₃₁	#497	1	2	yes	—
119	C₄×C₃₁	—	8	4	no	—
120	C₄×C₃₁	—	16	1	no	—
121	C₄×C₃₁	#447	1	2	yes	—
122	C₄×C₃₁	#452	1	4	yes	—
123	C₄×C₃₁	#459	1	2	yes	—
124	C₄×C₃₁	#464	1	4	yes	—
125	C₂²×Q₁₆	—	2	2	no	—
126	C₂×C₄⋊Q₈	C₂²×C₃₁	1	2	yes	—
127	C₂×#127	C₂²×C₃₁	1	1	yes	characteristic
128	#494	—	2	4	no	—
129	#486	—	2	4	no	—
130	#486	—	2	4	no	—
131	C₂×#102	—	2	4	no	—
132	C₂×#102	—	2	2	no	—
133	C₂×C₄×C₈	C₂²×C₃₁	1	2	yes	—
134	C₂×C₄×C₈	C₂²×C₃₁	1	1	yes	characteristic
135	#384	C₂²×C₃₁	1	1	yes	characteristic
136	#340	—	2	4	no	—
137	C₂×C₃₁	—	16	2	no	—
138	C₂×C₃₁	#1709	1	1	yes	characteristic
139	C₂×C₃₁	#1720	1	2	yes	—
140	C₂×C₃₁	#1722	1	1	yes	characteristic
141	C₂×C₃₁	#2011	1	1	yes	characteristic
142	C₂×C₃₁	#2015	1	2	yes	—
143	C₂²×Q₈	—	2	2	no	—
144	C₂²×D₄	—	2	1	no	—
145	C₂²×D₄	—	2	2	no	—
146	C₂×Q₁₆	—	2	8	no	—
147	C₂×Q₁₆	—	4	4	no	—
148	C₂×Q₁₆	—	4	4	no	—
149	C₂²×C₈	D₄×C₃₁	1	4	yes	—
150	C₂²×C₈	D₄×C₃₁	1	2	yes	—
151	C₄⋊Q₈	—	2	2	no	—
152	C₄⋊Q₈	—	2	2	no	—
153	C₄⋊Q₈	—	2	2	no	—
154	C₄⋊Q₈	D₄×C₃₁	1	4	yes	—
155	#127	—	2	2	no	—
156	#127	—	2	1	no	—
157	#127	D₄×C₃₁	1	2	yes	—
158	C₂×C₄⋊C₄	—	2	2	no	—
159	C₂×C₄⋊C₄	—	2	2	no	—
160	C₂×C₄⋊C₄	—	2	2	no	—
161	C₂×C₄⋊C₄	—	2	1	no	—
162	C₂×C₄²	C₂³×C₃₁	1	1	yes	characteristic
163	#102	—	2	16	no	—
164	#102	—	4	4	no	—
165	C₄×C₈	—	2	2	no	—
166	C₄×C₈	—	2	2	no	—
167	C₄×C₈	—	2	2	no	—
168	C₃₁	#10306	1	1	yes	characteristic, direct product factor, Sylow
169	C₂⁴	—	4	1	no	—
170	C₂×Q₈	—	2	4	no	—
171	C₂×Q₈	—	4	2	no	—
172	C₂×Q₈	—	4	4	no	—
173	C₂×Q₈	—	4	4	no	—
174	C₂×D₄	—	2	4	no	—
175	C₂×D₄	—	2	2	no	—
176	C₂×D₄	—	4	1	no	—
177	C₂×D₄	—	4	2	no	—
178	C₂×D₄	—	4	2	no	—
179	C₂×D₄	—	4	4	no	—
180	C₂×D₄	—	4	2	no	—
181	C₂×D₄	—	4	4	no	—
182	C₂²×C₄	—	4	2	no	—
183	C₂²×C₄	—	4	1	no	—
184	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
185	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
186	Q₁₆	—	4	16	no	—
187	C₂×C₈	—	2	2	no	—
188	C₂×C₈	—	2	2	no	—
189	C₂×C₈	—	2	4	no	—
190	C₂×C₈	—	2	4	no	—
191	C₂×C₈	—	2	4	no	—
192	C₂×C₈	D₈×C₃₁	1	4	yes	—
193	C₄⋊C₄	—	2	4	no	—
194	C₄⋊C₄	—	2	4	no	—
195	C₄⋊C₄	—	4	2	no	—
196	C₄⋊C₄	—	4	2	no	—
197	C₄⋊C₄	—	4	2	no	—
198	C₄⋊C₄	—	4	4	no	—
199	C₄²	C₂×D₄×C₃₁	1	2	yes	—
200	C₄²	C₂×D₄×C₃₁	1	1	yes	characteristic
201	C₄²	#41×C₃₁	1	1	yes	characteristic
202	C₂³	—	4	2	no	—
203	C₂³	—	8	1	no	—
204	C₂³	—	8	2	no	—
205	C₂³	—	8	1	no	—
206	C₂³	—	8	2	no	—
207	C₂³	C₃₁×#127	1	1	yes	characteristic
208	Q₈	—	4	8	no	—
209	Q₈	—	8	4	no	—
210	D₄	—	4	8	no	—
211	D₄	—	4	4	no	—
212	D₄	—	8	2	no	—
213	D₄	—	8	4	no	—
214	C₂×C₄	—	4	4	no	—
215	C₂×C₄	—	8	2	no	—
216	C₂×C₄	—	8	2	no	—
217	C₂×C₄	—	8	1	no	—
218	C₂×C₄	—	8	2	no	—
219	C₂×C₄	C₃₁×#120	1	1	yes	characteristic
220	C₂×C₄	C₃₁×#120	1	2	yes	—
221	C₂×C₄	C₃₁×#121	1	1	yes	characteristic
222	C₂×C₄	C₃₁×#121	1	2	yes	—
223	C₂×C₄	C₂×D₈×C₃₁	1	2	yes	—
224	C₂×C₄	C₃₁×#135	1	4	yes	—
225	C₂×C₄	C₃₁×AGL(1,ℤ/8)	1	2	yes	—
226	C₂×C₄	C₃₁×#137	1	4	yes	—
227	C₈	—	2	4	no	—
228	C₈	—	4	4	no	—
229	C₂²	—	8	2	no	—
230	C₂²	—	8	4	no	—
231	C₂²	—	16	1	no	—
232	C₂²	—	16	2	no	—
233	C₂²	—	16	1	no	—
234	C₂²	C₃₁×#392	1	1	yes	characteristic
235	C₂²	C₃₁×#493	1	1	yes	characteristic
236	C₂²	C₃₁×#495	1	2	yes	—
237	C₂²	C₃₁×#496	1	1	yes	characteristic
238	C₂²	C₃₁×#497	1	2	yes	—
239	C₄	—	8	4	no	—
240	C₄	—	16	1	no	—
241	C₄	C₃₁×#447	1	2	yes	—
242	C₄	C₃₁×#452	1	4	yes	—
243	C₄	C₃₁×#459	1	2	yes	—
244	C₄	C₃₁×#464	1	4	yes	—
245	C₂	—	16	2	no	—
246	C₂	C₃₁×#1709	1	1	yes	characteristic
247	C₂	C₃₁×#1720	1	2	yes	—
248	C₂	C₃₁×#1722	1	1	yes	characteristic
249	C₂	C₃₁×#2011	1	1	yes	characteristic
250	C₂	C₃₁×#2015	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×C₃₁×#494

C₂

yes

maximal, characteristic, complemented

C₂×C₃₁×#486

C₂

yes

maximal

C₃₁×#1990

C₂

yes

maximal, complemented

C₃₁×#1957

C₂

yes

maximal, characteristic

C₃₁×#1273

C₂

yes

maximal, characteristic, complemented

C₂²×Q₁₆×C₃₁

—

C₂×C₃₁×C₄⋊Q₈

C₂²

yes

—

C₂×C₃₁×#127

C₂²

yes

characteristic

C₃₁×#494

—

C₃₁×#486

—

C₃₁×#486

—

C₂×C₃₁×#102

—

C₂×C₃₁×#102

—

C₂×C₄×C₈×C₃₁

C₂²

yes

—

C₂×C₄×C₈×C₃₁

C₂²

yes

characteristic

C₃₁×#384

C₂²

yes

characteristic

C₃₁×#340

—

C₂²×Q₈×C₃₁

—

C₂²×D₄×C₃₁

—

C₂²×D₄×C₃₁

—

C₂×Q₁₆×C₃₁

—

C₂×Q₁₆×C₃₁

—

C₂×Q₁₆×C₃₁

—

C₂²×C₈×C₃₁

D₄

yes

—

C₂²×C₈×C₃₁

D₄

yes

—

C₃₁×C₄⋊Q₈

—

C₃₁×C₄⋊Q₈

—

C₃₁×C₄⋊Q₈

—

C₃₁×C₄⋊Q₈

D₄

yes

—

C₃₁×#127

—

C₃₁×#127

—

C₃₁×#127

D₄

yes

—

C₂×C₄⋊C₄×C₃₁

—

C₂×C₄⋊C₄×C₃₁

—

C₂×C₄⋊C₄×C₃₁

—

C₂×C₄⋊C₄×C₃₁

—

C₂×C₄²×C₃₁

C₂³

yes

characteristic

C₃₁×#102

—

C₃₁×#102

—

C₄×C₈×C₃₁

—

C₄×C₈×C₃₁

—

C₄×C₈×C₃₁

—

C₂⁴×C₃₁

—

C₂×Q₈×C₃₁

—

C₂×Q₈×C₃₁

—

C₂×Q₈×C₃₁

—

C₂×Q₈×C₃₁

—

C₂×D₄×C₃₁

—

C₂×D₄×C₃₁

—

C₂×D₄×C₃₁

—

C₂×D₄×C₃₁

—

C₂×D₄×C₃₁

—

C₂×D₄×C₃₁

—

C₂×D₄×C₃₁

—

C₂×D₄×C₃₁

—

C₂²×C₄×C₃₁

—

C₂²×C₄×C₃₁

—

C₂²×C₄×C₃₁

C₂×D₄

yes

characteristic

C₂²×C₄×C₃₁

C₂×D₄

yes

—

Q₁₆×C₃₁

—

C₂×C₈×C₃₁

—

C₂×C₈×C₃₁

—

C₂×C₈×C₃₁

—

C₂×C₈×C₃₁

—

C₂×C₈×C₃₁

—

C₂×C₈×C₃₁

D₈

yes

—

C₄⋊C₄×C₃₁

—

C₄⋊C₄×C₃₁

—

C₄⋊C₄×C₃₁

—

C₄⋊C₄×C₃₁

—

C₄⋊C₄×C₃₁

—

C₄⋊C₄×C₃₁

—

C₄²×C₃₁

C₂×D₄

yes

—

C₄²×C₃₁

C₂×D₄

yes

C₄²×C₃₁

yes

C₃₁

yes

maximal, characteristic, direct product factor, Sylow

C₂³×C₃₁

—

C₂³×C₃₁

—

C₂³×C₃₁

—

C₂³×C₃₁

—

C₂³×C₃₁

—

C₂³×C₃₁

#127

yes

characteristic

Q₈×C₃₁

—

Q₈×C₃₁

—

D₄×C₃₁

—

D₄×C₃₁

—

D₄×C₃₁

—

D₄×C₃₁

—

C₂×C₄×C₃₁

—

C₂×C₄×C₃₁

—

C₂×C₄×C₃₁

—

C₂×C₄×C₃₁

—

C₂×C₄×C₃₁

—

C₂×C₄×C₃₁

#120

yes

characteristic

C₂×C₄×C₃₁

#120

yes

—

C₂×C₄×C₃₁

#121

yes

characteristic

C₂×C₄×C₃₁

#121

yes

—

C₂×C₄×C₃₁

C₂×D₈

yes

—

C₂×C₄×C₃₁

#135

yes

—

100

C₂×C₄×C₃₁

AGL(1,ℤ/8)

yes

—

101

C₂×C₄×C₃₁

#137

yes

—

102

C₈×C₃₁

—

103

C₈×C₃₁

—

104

C₂×#494

C₂×C₃₁

yes

characteristic, complemented

105

C₂×#486

C₂×C₃₁

yes

—

106

#1990

C₂×C₃₁

yes

complemented

107

#1957

C₂×C₃₁

yes

characteristic

108

#1273

C₂×C₃₁

yes

characteristic, complemented

109

C₂²×C₃₁

—

110

C₂²×C₃₁

—

111

C₂²×C₃₁

—

112

C₂²×C₃₁

—

113

C₂²×C₃₁

—

114

C₂²×C₃₁

#392

yes

characteristic

115

C₂²×C₃₁

#493

yes

characteristic

116

C₂²×C₃₁

#495

yes

—

117

C₂²×C₃₁

#496

yes

characteristic

118

C₂²×C₃₁

#497

yes

—

119

C₄×C₃₁

—

120

C₄×C₃₁

—

121

C₄×C₃₁

#447

yes

—

122

C₄×C₃₁

#452

yes

—

123

C₄×C₃₁

#459

yes

—

124

C₄×C₃₁

#464

yes

—

125

C₂²×Q₁₆

—

126

C₂×C₄⋊Q₈

C₂²×C₃₁

yes

—

127

C₂×#127

C₂²×C₃₁

yes

characteristic

128

#494

—

129

#486

—

130

#486

—

131

C₂×#102

—

132

C₂×#102

—

133

C₂×C₄×C₈

C₂²×C₃₁

yes

—

134

C₂×C₄×C₈

C₂²×C₃₁

yes

characteristic

135

#384

C₂²×C₃₁

yes

characteristic

136

#340

—

137

C₂×C₃₁

—

138

C₂×C₃₁

#1709

yes

characteristic

139

C₂×C₃₁

#1720

yes

—

140

C₂×C₃₁

#1722

yes

characteristic

141

C₂×C₃₁

#2011

yes

characteristic

142

C₂×C₃₁

#2015

yes

—

143

C₂²×Q₈

—

144

C₂²×D₄

—

145

C₂²×D₄

—

146

C₂×Q₁₆

—

147

C₂×Q₁₆

—

148

C₂×Q₁₆

—

149

C₂²×C₈

D₄×C₃₁

yes

—

150

C₂²×C₈

D₄×C₃₁

yes

—

151

C₄⋊Q₈

—

152

C₄⋊Q₈

—

153

C₄⋊Q₈

—

154

C₄⋊Q₈

D₄×C₃₁

yes

—

155

#127

—

156

#127

—

157

#127

D₄×C₃₁

yes

—

158

C₂×C₄⋊C₄

—

159

C₂×C₄⋊C₄

—

160

C₂×C₄⋊C₄

—

161

C₂×C₄⋊C₄

—

162

C₂×C₄²

C₂³×C₃₁

yes

characteristic

163

#102

—

164

#102

—

165

C₄×C₈

—

166

C₄×C₈

—

167

C₄×C₈

—

168

C₃₁

#10306

yes

characteristic, direct product factor, Sylow

169

C₂⁴

—

170

C₂×Q₈

—

171

C₂×Q₈

—

172

C₂×Q₈

—

173

C₂×Q₈

—

174

C₂×D₄

—

175

C₂×D₄

—

176

C₂×D₄

—

177

C₂×D₄

—

178

C₂×D₄

—

179

C₂×D₄

—

180

C₂×D₄

—

181

C₂×D₄

—

182

C₂²×C₄

—

183

C₂²×C₄

—

184

C₂²×C₄

C₂×D₄×C₃₁

yes

characteristic

185

C₂²×C₄

C₂×D₄×C₃₁

yes

—

186

Q₁₆

—

187

C₂×C₈

—

188

C₂×C₈

—

189

C₂×C₈

—

190

C₂×C₈

—

191

C₂×C₈

—

192

C₂×C₈

D₈×C₃₁

yes

—

193

C₄⋊C₄

—

194

C₄⋊C₄

—

195

C₄⋊C₄

—

196

C₄⋊C₄

—

197

C₄⋊C₄

—

198

C₄⋊C₄

—

199

C₄²

C₂×D₄×C₃₁

yes

—

200

C₄²

C₂×D₄×C₃₁

yes

characteristic

201

C₄²

#41×C₃₁

yes

characteristic

202

C₂³

—

203

C₂³

—

204

C₂³

—

205

C₂³

—

206

C₂³

—

207

C₂³

C₃₁×#127

yes

characteristic

208

Q₈

—

209

Q₈

—

210

D₄

—

211

D₄

—

212

D₄

—

213

D₄

—

214

C₂×C₄

—

215

C₂×C₄

—

216

C₂×C₄

—

217

C₂×C₄

—

218

C₂×C₄

—

219

C₂×C₄

C₃₁×#120

yes

characteristic

220

C₂×C₄

C₃₁×#120

yes

—

221

C₂×C₄

C₃₁×#121

yes

characteristic

222

C₂×C₄

C₃₁×#121

yes

—

223

C₂×C₄

C₂×D₈×C₃₁

yes

—

224

C₂×C₄

C₃₁×#135

yes

—

225

C₂×C₄

C₃₁×AGL(1,ℤ/8)

yes

—

226

C₂×C₄

C₃₁×#137

yes

—

227

C₈

—

228

C₈

—

229

C₂²

—

230

C₂²

—

231

C₂²

—

232

C₂²

—

233

C₂²

—

234

C₂²

C₃₁×#392

yes

characteristic

235

C₂²

C₃₁×#493

yes

characteristic

236

C₂²

C₃₁×#495

yes

—

237

C₂²

C₃₁×#496

yes

characteristic

238

C₂²

C₃₁×#497

yes

—

239

C₄

—

240

C₄

—

241

C₄

C₃₁×#447

yes

—

242

C₄

C₃₁×#452

yes

—

243

C₄

C₃₁×#459

yes

—

244

C₄

C₃₁×#464

yes

—

245

C₂

—

246

C₂

C₃₁×#1709

yes

characteristic

247

C₂

C₃₁×#1720

yes

—

248

C₂

C₃₁×#1722

yes

characteristic

249

C₂

C₃₁×#2011

yes

characteristic

250

C₂

C₃₁×#2015

yes

—

	subgroup	G/H
center, socle	C₂³×C₃₁	#127
commutator, Frattini, cosocle	C₂×C₄²	C₂³×C₃₁
prime radical	C₂×C₃₁×#127	C₂²
LCS	G ▷ C₂×C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₃₁ ◁ C₂×C₄²×C₃₁ ◁ G

subgroup

G/H

center, socle

C₂³×C₃₁

#127

commutator, Frattini, cosocle

C₂×C₄²

C₂³×C₃₁

prime radical

C₂×C₃₁×#127

C₂²

LCS

G ▷ C₂×C₄² ▷ C₂² ▷ C₁

UCS

C₁ ◁ C₂³×C₃₁ ◁ C₂×C₄²×C₃₁ ◁ G

N	H ≅ G/N	type
1. C₂×C₃₁×#494	C₂	semidirect
3. C₃₁×#1990	C₂	semidirect
5. C₃₁×#1273	C₂	semidirect
76. #10306	C₃₁	direct (N × H)
104. C₂×#494	C₂×C₃₁	semidirect
106. #1990	C₂×C₃₁	semidirect
108. #1273	C₂×C₃₁	semidirect
168. C₃₁	#10306	direct (N × H)

H ≅ G/N

type

1. C₂×C₃₁×#494

C₂

semidirect

3. C₃₁×#1990

C₂

semidirect

5. C₃₁×#1273

C₂

semidirect

76. #10306

C₃₁

direct (N × H)

104. C₂×#494

C₂×C₃₁

semidirect

106. #1990

C₂×C₃₁

semidirect

108. #1273

C₂×C₃₁

semidirect

168. C₃₁

#10306

direct (N × H)

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

subgroup	index
C₂×C₃₁×#494	2
C₂×C₃₁×#486	2
C₃₁×#1990	2
C₃₁×#1957	2
C₃₁×#1273	2
#10306	31

subgroup

index

C₂×C₃₁×#494

C₂×C₃₁×#486

C₃₁×#1990

C₃₁×#1957

C₃₁×#1273

#10306

Subgroups — C₃₁×#10306 #21467065

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C31×#10306 #21467065

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#10306 #21467065