Subgroups — C₂₉×#1375 #16815089

Order 3712.

140 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₂₉×M₃₂	C₂	1	2	yes	maximal
2	C₂×C₂₉×#97	C₂	1	1	yes	maximal, characteristic
3	C₂²×C₈×C₂₉	C₄	1	1	yes	characteristic
4	C₂²×C₈×C₂₉	C₂²	1	1	yes	characteristic
5	C₂×C₄²×C₂₉	C₄	1	1	yes	characteristic
6	C₂₉×M₃₂	—	2	2	no	—
7	C₂₉×M₃₂	—	2	2	no	—
8	C₂×C₁₆×C₂₉	C₄	1	4	yes	complemented
9	C₂₉×#97	—	2	2	no	—
10	C₂²×C₄×C₂₉	—	2	1	no	—
11	C₂²×C₄×C₂₉	C₂×C₄	1	1	yes	characteristic
12	C₂×C₈×C₂₉	—	2	1	no	—
13	C₂×C₈×C₂₉	—	2	1	no	—
14	C₂×C₈×C₂₉	C₈	1	2	yes	—
15	C₂×C₈×C₂₉	C₂×C₄	1	2	yes	—
16	C₂×C₈×C₂₉	D₄	1	1	yes	characteristic
17	C₂×C₈×C₂₉	D₄	1	2	yes	—
18	C₂×C₈×C₂₉	Q₈	1	1	yes	characteristic
19	C₄²×C₂₉	—	2	1	no	—
20	C₄²×C₂₉	C₈	1	2	yes	—
21	C₁₆×C₂₉	—	2	4	no	—
22	C₂³×C₂₉	M₁₆	1	1	yes	characteristic
23	C₂×C₄×C₂₉	—	2	2	no	—
24	C₂×C₄×C₂₉	—	4	2	no	—
25	C₂×C₄×C₂₉	C₄²	1	1	yes	characteristic
26	C₂×C₄×C₂₉	C₂²⋊C₄	1	1	yes	characteristic
27	C₂×C₄×C₂₉	C₄⋊C₄	1	1	yes	characteristic
28	C₂×C₄×C₂₉	C₂×C₈	1	1	yes	characteristic
29	C₂×C₄×C₂₉	C₂×C₈	1	1	yes	characteristic
30	C₂×C₄×C₂₉	M₁₆	1	1	yes	characteristic
31	C₈×C₂₉	—	2	2	no	—
32	C₈×C₂₉	C₂²⋊C₄	1	2	yes	—
33	C₈×C₂₉	C₄⋊C₄	1	2	yes	—
34	#1375	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
35	C₂²×C₂₉	—	2	2	no	—
36	C₂²×C₂₉	#97	1	1	yes	characteristic
37	C₂²×C₂₉	C₂²⋊C₈	1	1	yes	characteristic
38	C₂²×C₂₉	C₄⋊C₈	1	1	yes	characteristic
39	C₄×C₂₉	—	4	2	no	—
40	C₄×C₂₉	#95	1	1	yes	characteristic
41	C₄×C₂₉	C₄×C₈	1	1	yes	characteristic
42	C₄×C₂₉	C₂²⋊C₈	1	1	yes	characteristic
43	C₄×C₂₉	C₄⋊C₈	1	1	yes	characteristic
44	C₂×M₃₂	C₂×C₂₉	1	2	yes	—
45	C₂×#97	C₂×C₂₉	1	1	yes	characteristic
46	C₂×C₂₉	—	2	1	no	—
47	C₂×C₂₉	—	2	1	no	—
48	C₂×C₂₉	#336	1	1	yes	characteristic
49	C₂×C₂₉	#347	1	2	yes	—
50	C₂²×C₈	C₄×C₂₉	1	1	yes	characteristic
51	C₂²×C₈	C₂²×C₂₉	1	1	yes	characteristic
52	C₂×C₄²	C₄×C₂₉	1	1	yes	characteristic
53	M₃₂	—	2	2	no	—
54	M₃₂	—	2	2	no	—
55	C₂×C₁₆	C₄×C₂₉	1	4	yes	complemented
56	#97	—	2	2	no	—
57	C₂₉	#1375	1	1	yes	characteristic, direct product factor, Sylow
58	C₂²×C₄	—	2	1	no	—
59	C₂²×C₄	C₂×C₄×C₂₉	1	1	yes	characteristic
60	C₂×C₈	—	2	1	no	—
61	C₂×C₈	—	2	1	no	—
62	C₂×C₈	C₈×C₂₉	1	2	yes	—
63	C₂×C₈	C₂×C₄×C₂₉	1	2	yes	—
64	C₂×C₈	D₄×C₂₉	1	1	yes	characteristic
65	C₂×C₈	D₄×C₂₉	1	2	yes	—
66	C₂×C₈	Q₈×C₂₉	1	1	yes	characteristic
67	C₄²	—	2	1	no	—
68	C₄²	C₈×C₂₉	1	2	yes	—
69	C₁₆	—	2	4	no	—
70	C₂³	M₁₆×C₂₉	1	1	yes	characteristic
71	C₂×C₄	—	2	2	no	—
72	C₂×C₄	—	4	2	no	—
73	C₂×C₄	C₄²×C₂₉	1	1	yes	characteristic
74	C₂×C₄	C₂²⋊C₄×C₂₉	1	1	yes	characteristic
75	C₂×C₄	C₄⋊C₄×C₂₉	1	1	yes	characteristic
76	C₂×C₄	C₂×C₈×C₂₉	1	1	yes	characteristic
77	C₂×C₄	C₂×C₈×C₂₉	1	1	yes	characteristic
78	C₂×C₄	M₁₆×C₂₉	1	1	yes	characteristic
79	C₈	—	2	2	no	—
80	C₈	C₂²⋊C₄×C₂₉	1	2	yes	—
81	C₈	C₄⋊C₄×C₂₉	1	2	yes	—
82	C₂²	—	2	2	no	—
83	C₂²	C₂₉×#97	1	1	yes	characteristic
84	C₂²	C₂₉×C₂²⋊C₈	1	1	yes	characteristic
85	C₂²	C₂₉×C₄⋊C₈	1	1	yes	characteristic
86	C₄	—	4	2	no	—
87	C₄	C₂₉×#95	1	1	yes	characteristic
88	C₄	C₄×C₈×C₂₉	1	1	yes	characteristic
89	C₄	C₂₉×C₂²⋊C₈	1	1	yes	characteristic
90	C₄	C₂₉×C₄⋊C₈	1	1	yes	characteristic
91	C₂	—	2	1	no	—
92	C₂	—	2	1	no	—
93	C₂	C₂₉×#336	1	1	yes	characteristic
94	C₂	C₂₉×#347	1	2	yes	—

	subgroup	G/H
center	C₂×C₄×C₂₉	C₄²
commutator	C₄	C₄×C₈×C₂₉
Frattini, cosocle	C₂²×C₈	C₂²×C₂₉
socle	C₂²×C₂₉	#97
prime radical	C₂³×C₂₉	M₁₆
LCS	G ▷ C₄ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₂₉ ◁ G

Complements

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

N	H ≅ G/N	type
8. C₂×C₁₆×C₂₉	C₄	semidirect
34. #1375	C₂₉	direct (N × H)
55. C₂×C₁₆	C₄×C₂₉	semidirect
57. C₂₉	#1375	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×C₂₉×M₃₂	2
C₂×C₂₉×#97	2
#1375	29

Subgroups — C29×#1375 #16815089

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₉×#1375 #16815089