Subgroups — #14272108

Order 1856.

138 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄²×D₂₉	C₂	1	1	yes	maximal, characteristic
2	(C₂×#1181)⋊C₄	C₂	1	6	yes	maximal
3	C₂²×#1181	C₂²	1	4	yes	—
4	C₂×C₄×D₂₉	C₂²	1	3	yes	—
5	C₄²×C₂₉	C₄	1	1	yes	characteristic, complemented
6	C₄×Dic₂₉	C₄	1	3	yes	complemented
7	C₂²×D₂₉	C₂³	1	1	yes	characteristic
8	C₂×#1181	—	2	12	no	—
9	C₂×C₄×C₂₉	C₂×C₄	1	3	yes	—
10	C₂×Dic₂₉	C₂×C₄	1	3	yes	—
11	C₄×D₂₉	—	2	6	no	—
12	C₂²×C₂₉	C₂²×C₄	1	1	yes	characteristic
13	C₂×D₂₉	#41	1	6	yes	—
14	#1181	—	4	4	no	—
15	C₄×C₂₉	—	2	3	no	—
16	Dic₂₉	—	2	3	no	—
17	#383	—	29	1	no	maximal, Sylow
18	C₂×C₂₉	#117	1	3	yes	—
19	D₂₉	#126	1	4	yes	—
20	C₂×C₄²	—	29	1	no	—
21	#95	—	29	6	no	—
22	C₂₉	#383	1	1	yes	characteristic, complemented, Sylow
23	C₂²×C₄	—	29	3	no	—
24	C₂²×C₄	—	29	4	no	—
25	C₄²	—	29	3	no	—
26	C₄²	#1181	1	1	yes	characteristic, complemented
27	C₂³	—	29	1	no	—
28	C₂×C₄	—	29	3	no	—
29	C₂×C₄	—	58	6	no	—
30	C₂×C₄	—	58	12	no	—
31	C₂×C₄	C₂×#1181	1	3	yes	—
32	C₂²	—	29	6	no	—
33	C₂²	C₂²×#1181	1	1	yes	characteristic
34	C₄	—	2	3	no	—
35	C₄	—	58	3	no	—
36	C₄	—	116	4	no	—
37	C₂	—	29	4	no	—
38	C₂	#11745345	1	3	yes	—

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

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