Subgroups — #14271533

Order 1856.

90 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₉×#125	C₂	1	1	yes	maximal, characteristic
2	#11745231	C₂	1	1	yes	maximal, characteristic
3	#11745158	C₂	1	4	yes	maximal
4	#11745151	C₂	1	1	yes	maximal, characteristic
5	C₂×Dic₅₈	C₂²	1	2	yes	—
6	C₄⋊C₄×C₂₉	—	2	2	no	—
7	C₄⋊C₄×C₂₉	C₂²	1	2	yes	—
8	C₄²×C₂₉	C₂²	1	1	yes	characteristic
9	C₄⋊Dic₂₉	—	2	2	no	—
10	C₂×#6597	C₂²	1	2	yes	—
11	C₂×C₄×C₂₉	—	2	2	no	—
12	C₂×C₄×C₂₉	D₄	1	2	yes	—
13	C₂×C₄×C₂₉	C₂³	1	1	yes	characteristic
14	C₂×Dic₂₉	—	2	2	no	—
15	Dic₅₈	—	2	4	no	—
16	#6597	—	2	2	no	—
17	C₂²×C₂₉	C₂×D₄	1	1	yes	characteristic
18	C₄×C₂₉	—	2	2	no	—
19	C₄×C₂₉	—	4	2	no	—
20	C₄×C₂₉	#41	1	2	yes	—
21	Dic₂₉	—	4	2	no	—
22	#491	—	29	1	no	maximal, Sylow
23	C₂×C₂₉	#124	1	1	yes	characteristic
24	C₂×C₂₉	#137	1	2	yes	—
25	C₄⋊Q₈	—	29	1	no	—
26	#125	D₂₉	1	1	yes	characteristic
27	#103	—	29	4	no	—
28	#97	—	29	1	no	—
29	C₂₉	#491	1	1	yes	characteristic, complemented, Sylow
30	C₂×Q₈	—	29	2	no	—
31	C₂×C₈	—	29	2	no	—
32	C₄⋊C₄	—	2	2	no	—
33	C₄⋊C₄	—	58	2	no	—
34	C₄⋊C₄	C₂×D₂₉	1	2	yes	—
35	C₄²	C₂×D₂₉	1	1	yes	characteristic
36	Q₈	—	58	4	no	—
37	C₂×C₄	—	2	2	no	—
38	C₂×C₄	—	58	2	no	—
39	C₂×C₄	C₂²⋊D₂₉	1	2	yes	—
40	C₂×C₄	C₂²×D₂₉	1	1	yes	characteristic
41	C₈	—	58	2	no	—
42	C₂²	C₂×C₂²⋊D₂₉	1	1	yes	characteristic
43	C₄	—	2	2	no	—
44	C₄	—	4	2	no	—
45	C₄	—	116	2	no	—
46	C₄	#90809	1	2	yes	—
47	C₂	#11745309	1	1	yes	characteristic
48	C₂	#11745313	1	2	yes	—

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

N	H ≅ G/N	type
29. C₂₉	#491	semidirect

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