Finite Group Databasebeta

Subgroups — #13102593

Order 1600.

496 conjugacy classes of subgroups; only the 149 normal subgroups are shown.

normal subgroups only

This group has 496 conjugacy classes of subgroups — too many to draw. Only its 149 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×C₂²⋊(C₅⋊D₅)	C₂	1	1	yes	maximal, characteristic
2	C₂²×#6029	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#87799	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅²×C₂²⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
5	#11716687	C₂	1	1	yes	maximal, characteristic, complemented
6	#11716682	C₂	1	1	yes	maximal, characteristic, complemented
7	#11716681	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×C₄×C₅²	C₂²	1	1	yes	characteristic
9	C₂×C₂²⋊(C₅⋊D₅)	C₄	1	1	yes	characteristic
10	C₂×C₄×C₅⋊D₅	C₂²	1	1	yes	characteristic
11	C₂×C₅²×C₈	C₂²	1	1	yes	characteristic
12	C₂×C₅²×C₈	C₂²	1	1	yes	characteristic
13	C₂²⋊#1039	C₄	1	1	yes	characteristic
14	#87808	C₄	1	1	yes	characteristic
15	#87806	C₄	1	1	yes	characteristic
16	C₄×#1039	C₂²	1	1	yes	characteristic
17	C₂×#6029	—	2	2	no	—
18	C₂×#6029	C₂²	1	1	yes	characteristic
19	C₂×#6029	C₂²	1	1	yes	characteristic
20	#87799	—	2	2	no	—
21	#65019	—	5	6	no	maximal
22	C₂³×C₅²	C₂×C₄	1	1	yes	characteristic
23	C₂²×C₅⋊D₅	C₂×C₄	1	1	yes	characteristic
24	C₂×C₄×C₅²	—	2	1	no	—
25	C₂×C₄×C₅²	—	2	1	no	—
26	C₂×C₄×C₅²	C₂×C₄	1	1	yes	characteristic
27	C₂×C₄×C₅²	C₂³	1	1	yes	characteristic
28	C₂²⋊(C₅⋊D₅)	—	2	2	no	—
29	C₂×#1039	C₂×C₄	1	1	yes	characteristic
30	C₂×#1039	C₂×C₄	1	1	yes	characteristic
31	C₂×#1039	C₂×C₄	1	1	yes	characteristic
32	C₄×C₅⋊D₅	—	2	1	no	—
33	C₄×C₅⋊D₅	—	2	1	no	—
34	C₅²×C₈	—	2	1	no	—
35	C₅²×C₈	—	2	1	no	—
36	#6029	—	2	1	no	—
37	#6029	D₄	1	2	yes	complemented
38	C₄×C₂²⋊D₅	—	5	6	no	—
39	C₂²×#168	—	5	6	no	—
40	C₂×#676	—	5	6	no	—
41	C₅×C₂²⋊C₈	D₅	1	6	yes	complemented
42	#3952	—	5	6	no	—
43	#3947	—	5	6	no	—
44	#3946	—	5	6	no	—
45	C₂²×C₅²	—	2	1	no	—
46	C₂²×C₅²	—	2	1	no	—
47	C₂²×C₅²	M₁₆	1	2	yes	complemented
48	C₂²×C₅²	C₂²×C₄	1	1	yes	characteristic
49	C₂×C₅⋊D₅	—	2	1	no	—
50	C₂×C₅⋊D₅	—	2	1	no	—
51	C₂×C₅⋊D₅	—	2	1	no	—
52	C₄×C₅²	—	2	1	no	—
53	C₄×C₅²	C₂×D₄	1	1	yes	characteristic
54	C₄×C₅²	#41	1	1	yes	characteristic
55	#1039	—	2	1	no	—
56	#1039	—	2	1	no	—
57	#1039	—	2	1	no	—
58	C₂²×C₄×C₅	C₂×D₅	1	6	yes	—
59	C₂×C₂²⋊D₅	—	5	6	no	—
60	C₂×C₄×D₅	—	5	6	no	—
61	C₂×C₅×C₈	C₂×D₅	1	6	yes	—
62	C₂×C₅×C₈	C₂×D₅	1	6	yes	—
63	C₂²⋊Dic₅	—	5	6	no	—
64	#685	—	5	6	no	—
65	#683	—	5	6	no	—
66	C₄×Dic₅	—	5	6	no	—
67	C₂×#168	—	5	6	no	—
68	C₂×#168	—	5	6	no	—
69	C₂×#168	—	10	12	no	—
70	#676	—	10	12	no	—
71	#435	—	25	1	no	Sylow
72	C₂×C₅²	—	2	2	no	—
73	C₂×C₅²	C₄×D₄	1	1	yes	characteristic
74	C₂×C₅²	C₂×M₁₆	1	1	yes	characteristic
75	C₂×C₅²	#131	1	1	yes	characteristic
76	C₅⋊D₅	—	4	1	no	—
77	C₂³×C₅	C₄×D₅	1	6	yes	—
78	C₂²×D₅	—	5	6	no	—
79	C₂×C₄×C₅	—	2	6	no	—
80	C₂×C₄×C₅	—	2	6	no	—
81	C₂×C₄×C₅	C₄×D₅	1	6	yes	—
82	C₂×C₄×C₅	C₂²×D₅	1	6	yes	—
83	C₂²⋊D₅	—	10	12	no	—
84	C₂×Dic₅	—	5	6	no	—
85	C₂×Dic₅	—	5	6	no	—
86	C₂×Dic₅	—	5	6	no	—
87	C₄×D₅	—	10	6	no	—
88	C₄×D₅	—	10	6	no	—
89	C₅×C₈	—	2	6	no	—
90	C₅×C₈	—	2	6	no	—
91	#168	—	5	12	no	—
92	#168	—	10	6	no	—
93	C₂×M₁₆	—	25	1	no	—
94	C₂²×C₈	—	25	1	no	—
95	C₄×D₄	—	25	1	no	—
96	C₄⋊C₈	—	25	1	no	—
97	C₂²⋊C₈	—	25	1	no	—
98	C₂²⋊C₈	C₅⋊D₅	1	1	yes	characteristic, complemented
99	#97	—	25	1	no	—
100	C₅²	#435	1	1	yes	characteristic, complemented, Sylow
101	C₂²×C₅	—	2	6	no	—
102	C₂²×C₅	—	2	6	no	—
103	C₂²×C₅	#676	1	12	yes	complemented
104	C₂²×C₅	C₂×C₄×D₅	1	6	yes	—
105	C₂×D₅	—	10	6	no	—
106	C₂×D₅	—	10	6	no	—
107	C₂×D₅	—	10	6	no	—
108	C₄×C₅	—	2	6	no	—
109	C₄×C₅	D₄×D₅	1	6	yes	—
110	C₄×C₅	#711	1	6	yes	—
111	Dic₅	—	10	6	no	—
112	Dic₅	—	10	6	no	—
113	Dic₅	—	10	6	no	—
114	C₂×D₄	—	25	1	no	—
115	C₂²×C₄	—	25	1	no	—
116	C₂²×C₄	C₂×C₅⋊D₅	1	1	yes	characteristic
117	M₁₆	—	50	2	no	—
118	C₂×C₈	—	25	1	no	—
119	C₂×C₈	—	25	1	no	—
120	C₂×C₈	—	50	2	no	—
121	C₂×C₈	C₂×C₅⋊D₅	1	1	yes	characteristic
122	C₂×C₈	C₂×C₅⋊D₅	1	1	yes	characteristic
123	C₄⋊C₄	—	25	1	no	—
124	C₂²⋊C₄	—	25	1	no	—
125	C₂²⋊C₄	—	25	1	no	—
126	C₄²	—	25	1	no	—
127	C₂×C₅	—	2	12	no	—
128	C₂×C₅	#4027	1	6	yes	—
129	C₂×C₅	C₂×#676	1	6	yes	—
130	C₂×C₅	#4053	1	6	yes	—
131	D₅	—	20	6	no	—
132	C₂³	—	25	1	no	—
133	C₂³	C₄×C₅⋊D₅	1	1	yes	characteristic
134	D₄	—	50	2	no	—
135	C₂×C₄	—	2	1	no	—
136	C₂×C₄	—	2	1	no	—
137	C₂×C₄	—	25	1	no	—
138	C₂×C₄	—	25	1	no	—
139	C₂×C₄	—	25	1	no	—
140	C₂×C₄	—	50	1	no	—
141	C₂×C₄	—	50	1	no	—
142	C₂×C₄	C₄×C₅⋊D₅	1	1	yes	characteristic
143	C₂×C₄	C₂²×C₅⋊D₅	1	1	yes	characteristic
144	C₈	—	2	1	no	—
145	C₈	—	2	1	no	—
146	C₈	—	25	2	no	—
147	C₈	—	50	1	no	—
148	C₅	#65019	1	6	yes	complemented
149	C₂²	—	2	1	no	—
150	C₂²	—	2	1	no	—
151	C₂²	—	50	1	no	—
152	C₂²	—	50	1	no	—
153	C₂²	—	50	1	no	—
154	C₂²	#87799	1	2	yes	complemented
155	C₂²	C₂×C₄×C₅⋊D₅	1	1	yes	characteristic
156	C₄	—	2	1	no	—
157	C₄	—	50	1	no	—
158	C₄	—	50	1	no	—
159	C₄	—	50	1	no	—
160	C₄	D₄×C₅⋊D₅	1	1	yes	characteristic
161	C₄	#87902	1	1	yes	characteristic
162	C₂	—	2	2	no	—
163	C₂	—	100	1	no	—
164	C₂	#11717201	1	1	yes	characteristic
165	C₂	C₂×#87799	1	1	yes	characteristic
166	C₂	#11717227	1	1	yes	characteristic

Complements

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

N	H ≅ G/N	type
2. C₂²×#6029	C₂	semidirect
3. C₂×#87799	C₂	semidirect
4. C₅²×C₂²⋊C₈	C₂	semidirect
5. #11716687	C₂	semidirect
6. #11716682	C₂	semidirect
7. #11716681	C₂	semidirect
37. #6029	D₄	semidirect
41. C₅×C₂²⋊C₈	D₅	semidirect
47. C₂²×C₅²	M₁₆	semidirect
98. C₂²⋊C₈	C₅⋊D₅	semidirect
100. C₅²	#435	semidirect
103. C₂²×C₅	#676	semidirect
148. C₅	#65019	semidirect
154. C₂²	#87799	semidirect

Maximal subgroups

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

subgroup	index
C₄×C₂²⋊(C₅⋊D₅)	2
C₂²×#6029	2
C₂×#87799	2
C₅²×C₂²⋊C₈	2
#11716687	2
#11716682	2
#11716681	2
#65019	5