Subgroups — C₇₁×#1453 #22584015

Order 9088.

190 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#431×C₇₁	C₂	1	2	yes	maximal
2	C₄×M₁₆×C₇₁	C₂	1	1	yes	maximal, characteristic
3	#322×C₇₁	C₂	1	2	yes	maximal, complemented
4	#322×C₇₁	C₂	1	1	yes	maximal, characteristic, complemented
5	C₈²×C₇₁	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×M₁₆×C₇₁	C₄	1	2	yes	—
7	C₂×C₄²×C₇₁	C₂²	1	1	yes	characteristic
8	C₄⋊C₈×C₇₁	C₄	1	4	yes	—
9	C₂²⋊C₈×C₇₁	C₄	1	4	yes	—
10	#97×C₇₁	C₄	1	2	yes	—
11	C₄×C₈×C₇₁	C₂²	1	2	yes	—
12	C₄×C₈×C₇₁	C₂²	1	2	yes	—
13	C₄×C₈×C₇₁	C₂²	1	1	yes	characteristic
14	C₄×C₈×C₇₁	C₂²	1	1	yes	characteristic
15	C₂²×C₄×C₇₁	C₂×C₄	1	2	yes	—
16	C₂²×C₄×C₇₁	C₂×C₄	1	1	yes	characteristic
17	M₁₆×C₇₁	—	2	4	no	—
18	C₂×C₈×C₇₁	C₂×C₄	1	2	yes	—
19	C₂×C₈×C₇₁	C₂×C₄	1	4	yes	—
20	C₂×C₈×C₇₁	C₂×C₄	1	4	yes	—
21	C₂×C₈×C₇₁	C₂×C₄	1	2	yes	—
22	C₄²×C₇₁	C₂×C₄	1	1	yes	characteristic
23	C₄²×C₇₁	C₂×C₄	1	2	yes	—
24	C₄²×C₇₁	C₂³	1	1	yes	characteristic
25	C₂³×C₇₁	C₄²	1	1	yes	characteristic
26	C₂×C₄×C₇₁	—	2	2	no	—
27	C₂×C₄×C₇₁	—	2	4	no	—
28	C₂×C₄×C₇₁	C₄²	1	1	yes	characteristic
29	C₂×C₄×C₇₁	C₄²	1	2	yes	—
30	C₂×C₄×C₇₁	C₂²×C₄	1	1	yes	characteristic
31	C₂×C₄×C₇₁	C₂²×C₄	1	2	yes	—
32	C₈×C₇₁	—	2	2	no	—
33	C₈×C₇₁	—	2	4	no	—
34	C₈×C₇₁	—	2	4	no	—
35	C₈×C₇₁	M₁₆	1	4	yes	—
36	C₂²×C₇₁	—	2	1	no	—
37	C₂²×C₇₁	—	2	2	no	—
38	C₂²×C₇₁	C₂×C₄²	1	1	yes	characteristic
39	C₄×C₇₁	—	2	1	no	—
40	C₄×C₇₁	—	2	2	no	—
41	C₄×C₇₁	C₂×M₁₆	1	2	yes	—
42	C₄×C₇₁	#131	1	4	yes	—
43	C₂×C₇₁	—	4	1	no	—
44	C₂×C₇₁	C₄×M₁₆	1	1	yes	characteristic
45	C₂×C₇₁	#405	1	2	yes	—
46	#1453	C₇₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
47	C₇₁	#1453	1	1	yes	characteristic, direct product factor, Sylow
48	#431	C₂×C₇₁	1	2	yes	—
49	C₄×M₁₆	C₂×C₇₁	1	1	yes	characteristic
50	#322	C₂×C₇₁	1	1	yes	characteristic, complemented
51	#322	C₂×C₇₁	1	2	yes	complemented
52	C₈²	C₂×C₇₁	1	1	yes	characteristic, complemented
53	C₂×M₁₆	C₄×C₇₁	1	2	yes	—
54	C₂×C₄²	C₂²×C₇₁	1	1	yes	characteristic
55	C₄⋊C₈	C₄×C₇₁	1	4	yes	—
56	C₂²⋊C₈	C₄×C₇₁	1	4	yes	—
57	#97	C₄×C₇₁	1	2	yes	—
58	C₄×C₈	C₂²×C₇₁	1	1	yes	characteristic
59	C₄×C₈	C₂²×C₇₁	1	2	yes	—
60	C₄×C₈	C₂²×C₇₁	1	1	yes	characteristic
61	C₄×C₈	C₂²×C₇₁	1	2	yes	—
62	C₂²×C₄	C₂×C₄×C₇₁	1	2	yes	—
63	C₂²×C₄	C₂×C₄×C₇₁	1	1	yes	characteristic
64	M₁₆	—	2	4	no	—
65	C₂×C₈	C₂×C₄×C₇₁	1	2	yes	—
66	C₂×C₈	C₂×C₄×C₇₁	1	4	yes	—
67	C₂×C₈	C₂×C₄×C₇₁	1	4	yes	—
68	C₂×C₈	C₂×C₄×C₇₁	1	2	yes	—
69	C₄²	C₂×C₄×C₇₁	1	1	yes	characteristic
70	C₄²	C₂×C₄×C₇₁	1	2	yes	—
71	C₄²	C₂³×C₇₁	1	1	yes	characteristic
72	C₂³	C₄²×C₇₁	1	1	yes	characteristic
73	C₂×C₄	—	2	2	no	—
74	C₂×C₄	—	2	4	no	—
75	C₂×C₄	C₄²×C₇₁	1	2	yes	—
76	C₂×C₄	C₄²×C₇₁	1	1	yes	characteristic
77	C₂×C₄	C₂²×C₄×C₇₁	1	1	yes	characteristic
78	C₂×C₄	C₂²×C₄×C₇₁	1	2	yes	—
79	C₈	—	2	2	no	—
80	C₈	—	2	4	no	—
81	C₈	—	2	4	no	—
82	C₈	M₁₆×C₇₁	1	4	yes	—
83	C₂²	—	2	2	no	—
84	C₂²	—	2	1	no	—
85	C₂²	C₂×C₄²×C₇₁	1	1	yes	characteristic
86	C₄	—	2	2	no	—
87	C₄	—	2	1	no	—
88	C₄	C₂×M₁₆×C₇₁	1	2	yes	—
89	C₄	#131×C₇₁	1	4	yes	—
90	C₂	—	4	1	no	—
91	C₂	C₄×M₁₆×C₇₁	1	1	yes	characteristic
92	C₂	#405×C₇₁	1	2	yes	—

	subgroup	G/H
center	C₄²×C₇₁	C₂³
commutator	C₂²	C₂×C₄²×C₇₁
Frattini, cosocle	C₄²	C₂³×C₇₁
socle	C₂²×C₇₁	C₂×C₄²
prime radical	C₂³×C₇₁	C₄²
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₄²×C₇₁ ◁ G

Complements

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

N	H ≅ G/N	type
3. #322×C₇₁	C₂	semidirect
4. #322×C₇₁	C₂	semidirect
5. C₈²×C₇₁	C₂	semidirect
46. #1453	C₇₁	direct (N × H)
47. C₇₁	#1453	direct (N × H)
50. #322	C₂×C₇₁	semidirect
51. #322	C₂×C₇₁	semidirect
52. C₈²	C₂×C₇₁	semidirect

Maximal subgroups

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

subgroup	index
#431×C₇₁	2
C₄×M₁₆×C₇₁	2
#322×C₇₁	2
C₈²×C₇₁	2
#1453	71

Subgroups — C71×#1453 #22584015

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₁×#1453 #22584015