Subgroups — C₅×#9635 #11932355

Order 1280.

260 conjugacy classes of subgroups.

The subgroup lattice has 184 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#1574	C₂	1	2	yes	maximal
2	C₅×#1566	C₂	1	1	yes	maximal, characteristic
3	C₅×#1564	C₂	1	1	yes	maximal, characteristic
4	C₅×#1451	C₂	1	1	yes	maximal, characteristic
5	C₅×#1299	C₂	1	2	yes	maximal
6	C₅×#431	C₂²	1	2	yes	—
7	C₅×#431	C₂²	1	1	yes	characteristic
8	C₅×#423	C₂²	1	2	yes	—
9	C₄×C₅×M₁₆	C₂²	1	1	yes	characteristic
10	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
11	C₅×#335	—	2	2	no	—
12	C₅×#335	C₄	1	2	yes	—
13	C₅×#334	—	2	2	no	—
14	C₅×#334	—	2	1	no	—
15	C₅×#334	—	2	1	no	—
16	C₅×#334	C₄	1	2	yes	—
17	C₅×#322	—	2	1	no	—
18	C₅×#322	—	2	1	no	—
19	#9635	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
20	C₂×C₅×M₁₆	—	2	1	no	—
21	C₂×C₅×M₁₆	—	2	2	no	—
22	C₂²×C₅×C₈	Q₈	1	1	yes	characteristic
23	C₂²×C₅×C₈	Q₈	1	1	yes	characteristic
24	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
25	C₅×C₄⋊C₈	—	2	2	no	—
26	C₅×C₄⋊C₈	—	2	2	no	—
27	C₅×C₄⋊C₈	C₂×C₄	1	4	yes	—
28	C₅×C₄⋊C₈	D₄	1	2	yes	—
29	C₅×C₂²⋊C₈	—	2	2	no	—
30	C₅×C₂²⋊C₈	—	2	1	no	—
31	C₅×#97	Q₈	1	2	yes	—
32	C₄×C₅×C₈	—	2	1	no	—
33	C₄×C₅×C₈	—	2	1	no	—
34	C₄×C₅×C₈	—	2	2	no	—
35	C₄×C₅×C₈	C₂×C₄	1	1	yes	characteristic
36	C₄×C₅×C₈	C₂×C₄	1	1	yes	characteristic
37	C₄×C₅×C₈	D₄	1	1	yes	characteristic
38	C₄×C₅×C₈	D₄	1	1	yes	characteristic
39	#1574	C₂×C₅	1	2	yes	—
40	#1566	C₂×C₅	1	1	yes	characteristic
41	#1564	C₂×C₅	1	1	yes	characteristic
42	#1451	C₂×C₅	1	1	yes	characteristic
43	#1299	C₂×C₅	1	2	yes	—
44	C₂²×C₄×C₅	C₂×Q₈	1	1	yes	characteristic
45	C₂²×C₄×C₅	#41	1	1	yes	characteristic
46	C₂²×C₄×C₅	#41	1	1	yes	characteristic
47	C₅×M₁₆	—	4	2	no	—
48	C₅×M₁₆	—	8	2	no	—
49	C₂×C₅×C₈	—	2	2	no	—
50	C₂×C₅×C₈	—	2	4	no	—
51	C₂×C₅×C₈	—	2	2	no	—
52	C₂×C₅×C₈	—	2	2	no	—
53	C₂×C₅×C₈	—	4	1	no	—
54	C₂×C₅×C₈	—	4	2	no	—
55	C₂×C₅×C₈	C₄⋊C₄	1	1	yes	characteristic
56	C₂×C₅×C₈	C₄⋊C₄	1	1	yes	characteristic
57	C₂×C₅×C₈	C₄⋊C₄	1	1	yes	characteristic
58	C₂×C₅×C₈	C₄⋊C₄	1	1	yes	characteristic
59	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
60	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
61	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
62	C₄²×C₅	C₂×Q₈	1	1	yes	characteristic
63	#431	C₂²×C₅	1	2	yes	—
64	#431	C₂²×C₅	1	1	yes	characteristic
65	#423	C₂²×C₅	1	2	yes	—
66	C₄×M₁₆	C₂²×C₅	1	1	yes	characteristic
67	C₂×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
68	#335	—	2	2	no	—
69	#335	C₄×C₅	1	2	yes	—
70	#334	—	2	2	no	—
71	#334	—	2	1	no	—
72	#334	—	2	1	no	—
73	#334	C₄×C₅	1	2	yes	—
74	#322	—	2	1	no	—
75	#322	—	2	1	no	—
76	C₂³×C₅	#125	1	1	yes	characteristic
77	C₂×C₄×C₅	—	2	1	no	—
78	C₂×C₄×C₅	—	2	1	no	—
79	C₂×C₄×C₅	—	2	2	no	—
80	C₂×C₄×C₅	—	2	2	no	—
81	C₂×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
82	C₂×C₄×C₅	C₄×D₄	1	1	yes	characteristic
83	C₂×C₄×C₅	C₄×Q₈	1	1	yes	characteristic
84	C₂×C₄×C₅	#121	1	1	yes	characteristic
85	C₂×C₄×C₅	C₂²⋊Q₈	1	1	yes	characteristic
86	C₂×C₄×C₅	C₄⋊Q₈	1	1	yes	characteristic
87	C₅×C₈	—	2	1	no	—
88	C₅×C₈	—	2	1	no	—
89	C₅×C₈	—	2	1	no	—
90	C₅×C₈	—	4	2	no	—
91	C₅×C₈	—	4	4	no	—
92	C₅×C₈	—	4	2	no	—
93	C₅×C₈	—	8	2	no	—
94	C₅×C₈	#108	1	2	yes	—
95	C₂×M₁₆	—	2	1	no	—
96	C₂×M₁₆	—	2	2	no	—
97	C₂²×C₈	C₅×Q₈	1	1	yes	characteristic
98	C₂²×C₈	C₅×Q₈	1	1	yes	characteristic
99	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
100	C₄⋊C₈	—	2	2	no	—
101	C₄⋊C₈	—	2	2	no	—
102	C₄⋊C₈	C₂×C₄×C₅	1	4	yes	—
103	C₄⋊C₈	C₅×D₄	1	2	yes	—
104	C₂²⋊C₈	—	2	2	no	—
105	C₂²⋊C₈	—	2	1	no	—
106	#97	C₅×Q₈	1	2	yes	—
107	C₄×C₈	—	2	1	no	—
108	C₄×C₈	—	2	1	no	—
109	C₄×C₈	—	2	2	no	—
110	C₄×C₈	C₂×C₄×C₅	1	1	yes	characteristic
111	C₄×C₈	C₂×C₄×C₅	1	1	yes	characteristic
112	C₄×C₈	C₅×D₄	1	1	yes	characteristic
113	C₄×C₈	C₅×D₄	1	1	yes	characteristic
114	C₂²×C₅	—	2	1	no	—
115	C₂²×C₅	—	2	1	no	—
116	C₂²×C₅	—	2	1	no	—
117	C₂²×C₅	#389	1	1	yes	characteristic
118	C₄×C₅	—	2	1	no	—
119	C₄×C₅	—	2	1	no	—
120	C₄×C₅	—	2	1	no	—
121	C₄×C₅	C₂×#108	1	1	yes	characteristic
122	C₄×C₅	#430	1	1	yes	characteristic
123	C₄×C₅	#444	1	2	yes	—
124	C₄×C₅	#471	1	2	yes	—
125	C₂²×C₄	C₂×C₅×Q₈	1	1	yes	characteristic
126	C₂²×C₄	C₅×#41	1	1	yes	characteristic
127	C₂²×C₄	C₅×#41	1	1	yes	characteristic
128	M₁₆	—	4	2	no	—
129	M₁₆	—	8	2	no	—
130	C₂×C₈	—	2	2	no	—
131	C₂×C₈	—	2	4	no	—
132	C₂×C₈	—	2	2	no	—
133	C₂×C₈	—	2	2	no	—
134	C₂×C₈	—	4	1	no	—
135	C₂×C₈	—	4	2	no	—
136	C₂×C₈	C₅×C₄⋊C₄	1	1	yes	characteristic
137	C₂×C₈	C₅×C₄⋊C₄	1	1	yes	characteristic
138	C₂×C₈	C₅×C₄⋊C₄	1	1	yes	characteristic
139	C₂×C₈	C₅×C₄⋊C₄	1	1	yes	characteristic
140	C₄²	C₂²×C₄×C₅	1	1	yes	characteristic
141	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
142	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
143	C₄²	C₂×C₅×Q₈	1	1	yes	characteristic
144	C₂×C₅	—	4	1	no	—
145	C₂×C₅	#1946	1	1	yes	characteristic
146	C₂×C₅	#1950	1	1	yes	characteristic
147	C₂×C₅	#1951	1	1	yes	characteristic
148	C₂³	C₅×#125	1	1	yes	characteristic
149	C₂×C₄	—	2	1	no	—
150	C₂×C₄	—	2	1	no	—
151	C₂×C₄	—	2	2	no	—
152	C₂×C₄	—	2	2	no	—
153	C₂×C₄	C₂×C₅×C₄⋊C₄	1	1	yes	characteristic
154	C₂×C₄	C₄×C₅×D₄	1	1	yes	characteristic
155	C₂×C₄	C₄×C₅×Q₈	1	1	yes	characteristic
156	C₂×C₄	C₅×#121	1	1	yes	characteristic
157	C₂×C₄	C₅×C₂²⋊Q₈	1	1	yes	characteristic
158	C₂×C₄	C₅×C₄⋊Q₈	1	1	yes	characteristic
159	C₈	—	2	1	no	—
160	C₈	—	2	1	no	—
161	C₈	—	2	1	no	—
162	C₈	—	4	2	no	—
163	C₈	—	4	4	no	—
164	C₈	—	4	2	no	—
165	C₈	—	8	2	no	—
166	C₈	C₅×#108	1	2	yes	—
167	C₅	#9635	1	1	yes	characteristic, direct product factor, Sylow
168	C₂²	—	2	1	no	—
169	C₂²	—	2	1	no	—
170	C₂²	—	2	1	no	—
171	C₂²	C₅×#389	1	1	yes	characteristic
172	C₄	—	2	1	no	—
173	C₄	—	2	1	no	—
174	C₄	—	2	1	no	—
175	C₄	C₂×C₅×#108	1	1	yes	characteristic
176	C₄	C₅×#430	1	1	yes	characteristic
177	C₄	C₅×#444	1	2	yes	—
178	C₄	C₅×#471	1	2	yes	—
179	C₂	—	4	1	no	—
180	C₂	C₅×#1946	1	1	yes	characteristic
181	C₂	C₅×#1950	1	1	yes	characteristic
182	C₂	C₅×#1951	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₅	#121
commutator	C₄²	C₂²×C₄×C₅
Frattini, cosocle	C₂×C₄²	C₂³×C₅
socle	C₂²×C₅	#389
prime radical	C₂³×C₅	#125
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₅ ◁ C₂×C₄²×C₅ ◁ G

Complements

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

N	H ≅ G/N	type
19. #9635	C₅	direct (N × H)
167. C₅	#9635	direct (N × H)

Maximal subgroups

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

subgroup	index
C₅×#1574	2
C₅×#1566	2
C₅×#1564	2
C₅×#1451	2
C₅×#1299	2
#9635	5

Subgroups — C5×#9635 #11932355

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#9635 #11932355