Subgroups — #14270960

Order 1856.

64 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₉×#124	C₂	1	1	yes	maximal, characteristic
2	#11745184	C₂	1	2	yes	maximal, complemented
3	C₂×Q₈×C₂₉	C₂²	1	1	yes	characteristic
4	C₂×D₄×C₂₉	C₄	1	1	yes	characteristic
5	C₂²⋊C₄×C₂₉	—	2	2	no	—
6	C₄²×C₂₉	C₄	1	1	yes	characteristic
7	#90777	—	2	2	no	—
8	C₂³×C₂₉	—	2	1	no	—
9	Q₈×C₂₉	—	4	1	no	—
10	D₄×C₂₉	—	4	1	no	—
11	C₂×C₄×C₂₉	—	2	1	no	—
12	C₂×C₄×C₂₉	C₂×C₄	1	1	yes	characteristic
13	C₂×C₄×C₂₉	D₄	1	2	yes	—
14	#6597	—	4	2	no	—
15	C₂²×C₂₉	—	4	2	no	—
16	C₂²×C₂₉	—	4	1	no	—
17	C₂²×C₂₉	C₂²⋊C₄	1	1	yes	characteristic
18	C₄×C₂₉	—	2	2	no	—
19	C₄×C₂₉	—	2	1	no	—
20	C₄×C₂₉	—	4	1	no	—
21	#355	—	29	1	no	maximal, Sylow
22	C₂×C₂₉	—	2	1	no	—
23	C₂×C₂₉	—	8	1	no	—
24	C₂×C₂₉	#99	1	1	yes	characteristic
25	#124	D₂₉	1	1	yes	characteristic
26	#101	—	29	2	no	—
27	C₂₉	#355	1	1	yes	characteristic, complemented, Sylow
28	C₂×Q₈	C₂×D₂₉	1	1	yes	characteristic
29	C₂×D₄	Dic₂₉	1	1	yes	characteristic
30	M₁₆	—	58	2	no	—
31	C₂²⋊C₄	—	2	2	no	—
32	C₄²	Dic₂₉	1	1	yes	characteristic
33	C₂³	—	2	1	no	—
34	Q₈	—	4	1	no	—
35	D₄	—	4	1	no	—
36	C₂×C₄	—	2	1	no	—
37	C₂×C₄	C₂×Dic₂₉	1	1	yes	characteristic
38	C₂×C₄	C₂²⋊D₂₉	1	2	yes	—
39	C₈	—	116	2	no	—
40	C₂²	—	4	2	no	—
41	C₂²	—	4	1	no	—
42	C₂²	C₂²⋊Dic₂₉	1	1	yes	characteristic
43	C₄	—	2	2	no	—
44	C₄	—	2	1	no	—
45	C₄	—	4	1	no	—
46	C₂	—	2	1	no	—
47	C₂	—	8	1	no	—
48	C₂	#11745182	1	1	yes	characteristic

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

N	H ≅ G/N	type
2. #11745184	C₂	semidirect
27. C₂₉	#355	semidirect

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