Subgroups — C₅×#9634 #11932354

Order 1280.

268 conjugacy classes of subgroups.

The subgroup lattice has 194 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×#1567	C₂	1	1	yes	maximal, characteristic
3	C₅×#1564	C₂	1	1	yes	maximal, characteristic
4	C₅×C₈×M₁₆	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	—	2	1	no	—
13	C₅×#335	—	2	1	no	—
14	C₅×#335	C₄	1	2	yes	—
15	C₅×#334	—	2	2	no	—
16	C₅×#334	C₄	1	2	yes	—
17	C₅×#322	—	2	1	no	—
18	C₅×C₈²	—	2	1	no	—
19	#9634	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	1	yes	characteristic
29	C₅×C₄⋊C₈	D₄	1	1	yes	characteristic
30	C₅×C₂²⋊C₈	—	2	2	no	—
31	C₅×C₂²⋊C₈	—	2	1	no	—
32	C₅×#97	Q₈	1	2	yes	—
33	C₄×C₅×C₈	—	2	1	no	—
34	C₄×C₅×C₈	—	2	1	no	—
35	C₄×C₅×C₈	—	2	2	no	—
36	C₄×C₅×C₈	C₂×C₄	1	1	yes	characteristic
37	C₄×C₅×C₈	C₂×C₄	1	1	yes	characteristic
38	C₄×C₅×C₈	D₄	1	1	yes	characteristic
39	C₄×C₅×C₈	D₄	1	1	yes	characteristic
40	#1574	C₂×C₅	1	2	yes	—
41	#1567	C₂×C₅	1	1	yes	characteristic
42	#1564	C₂×C₅	1	1	yes	characteristic
43	C₈×M₁₆	C₂×C₅	1	1	yes	characteristic
44	#1299	C₂×C₅	1	2	yes	—
45	C₂²×C₄×C₅	C₂×Q₈	1	1	yes	characteristic
46	C₂²×C₄×C₅	#41	1	1	yes	characteristic
47	C₂²×C₄×C₅	#41	1	1	yes	characteristic
48	C₅×M₁₆	—	2	4	no	—
49	C₅×M₁₆	—	8	2	no	—
50	C₂×C₅×C₈	—	2	2	no	—
51	C₂×C₅×C₈	—	2	2	no	—
52	C₂×C₅×C₈	—	2	4	no	—
53	C₂×C₅×C₈	—	2	1	no	—
54	C₂×C₅×C₈	—	2	1	no	—
55	C₂×C₅×C₈	—	4	1	no	—
56	C₂×C₅×C₈	—	4	2	no	—
57	C₂×C₅×C₈	C₄⋊C₄	1	1	yes	characteristic
58	C₂×C₅×C₈	C₄⋊C₄	1	1	yes	characteristic
59	C₂×C₅×C₈	C₄⋊C₄	1	1	yes	characteristic
60	C₂×C₅×C₈	C₄⋊C₄	1	1	yes	characteristic
61	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
62	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
63	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
64	C₄²×C₅	C₂×Q₈	1	1	yes	characteristic
65	#431	C₂²×C₅	1	2	yes	—
66	#431	C₂²×C₅	1	1	yes	characteristic
67	#423	C₂²×C₅	1	2	yes	—
68	C₄×M₁₆	C₂²×C₅	1	1	yes	characteristic
69	C₂×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
70	#335	—	2	2	no	—
71	#335	—	2	1	no	—
72	#335	—	2	1	no	—
73	#335	C₄×C₅	1	2	yes	—
74	#334	—	2	2	no	—
75	#334	C₄×C₅	1	2	yes	—
76	#322	—	2	1	no	—
77	C₈²	—	2	1	no	—
78	C₂³×C₅	#125	1	1	yes	characteristic
79	C₂×C₄×C₅	—	2	1	no	—
80	C₂×C₄×C₅	—	2	1	no	—
81	C₂×C₄×C₅	—	2	2	no	—
82	C₂×C₄×C₅	—	2	1	no	—
83	C₂×C₄×C₅	—	2	1	no	—
84	C₂×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
85	C₂×C₄×C₅	C₄×D₄	1	1	yes	characteristic
86	C₂×C₄×C₅	C₄×Q₈	1	1	yes	characteristic
87	C₂×C₄×C₅	#121	1	1	yes	characteristic
88	C₂×C₄×C₅	C₂²⋊Q₈	1	1	yes	characteristic
89	C₂×C₄×C₅	C₄⋊Q₈	1	1	yes	characteristic
90	C₅×C₈	—	2	4	no	—
91	C₅×C₈	—	2	1	no	—
92	C₅×C₈	—	2	1	no	—
93	C₅×C₈	—	2	1	no	—
94	C₅×C₈	—	4	4	no	—
95	C₅×C₈	—	4	1	no	—
96	C₅×C₈	—	4	1	no	—
97	C₅×C₈	—	8	2	no	—
98	C₅×C₈	#108	1	2	yes	—
99	C₂×M₁₆	—	2	1	no	—
100	C₂×M₁₆	—	2	2	no	—
101	C₂²×C₈	C₅×Q₈	1	1	yes	characteristic
102	C₂²×C₈	C₅×Q₈	1	1	yes	characteristic
103	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
104	C₄⋊C₈	—	2	2	no	—
105	C₄⋊C₈	—	2	2	no	—
106	C₄⋊C₈	C₂×C₄×C₅	1	4	yes	—
107	C₄⋊C₈	C₅×D₄	1	1	yes	characteristic
108	C₄⋊C₈	C₅×D₄	1	1	yes	characteristic
109	C₂²⋊C₈	—	2	2	no	—
110	C₂²⋊C₈	—	2	1	no	—
111	#97	C₅×Q₈	1	2	yes	—
112	C₄×C₈	—	2	1	no	—
113	C₄×C₈	—	2	1	no	—
114	C₄×C₈	—	2	2	no	—
115	C₄×C₈	C₂×C₄×C₅	1	1	yes	characteristic
116	C₄×C₈	C₂×C₄×C₅	1	1	yes	characteristic
117	C₄×C₈	C₅×D₄	1	1	yes	characteristic
118	C₄×C₈	C₅×D₄	1	1	yes	characteristic
119	C₂²×C₅	—	2	1	no	—
120	C₂²×C₅	—	2	1	no	—
121	C₂²×C₅	—	2	1	no	—
122	C₂²×C₅	#389	1	1	yes	characteristic
123	C₄×C₅	—	2	1	no	—
124	C₄×C₅	—	2	1	no	—
125	C₄×C₅	—	2	1	no	—
126	C₄×C₅	C₂×#108	1	1	yes	characteristic
127	C₄×C₅	#430	1	1	yes	characteristic
128	C₄×C₅	#443	1	2	yes	—
129	C₄×C₅	#472	1	1	yes	characteristic
130	C₄×C₅	#473	1	1	yes	characteristic
131	C₂²×C₄	C₂×C₅×Q₈	1	1	yes	characteristic
132	C₂²×C₄	C₅×#41	1	1	yes	characteristic
133	C₂²×C₄	C₅×#41	1	1	yes	characteristic
134	M₁₆	—	2	4	no	—
135	M₁₆	—	8	2	no	—
136	C₂×C₈	—	2	2	no	—
137	C₂×C₈	—	2	2	no	—
138	C₂×C₈	—	2	4	no	—
139	C₂×C₈	—	2	1	no	—
140	C₂×C₈	—	2	1	no	—
141	C₂×C₈	—	4	1	no	—
142	C₂×C₈	—	4	2	no	—
143	C₂×C₈	C₅×C₄⋊C₄	1	1	yes	characteristic
144	C₂×C₈	C₅×C₄⋊C₄	1	1	yes	characteristic
145	C₂×C₈	C₅×C₄⋊C₄	1	1	yes	characteristic
146	C₂×C₈	C₅×C₄⋊C₄	1	1	yes	characteristic
147	C₄²	C₂²×C₄×C₅	1	1	yes	characteristic
148	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
149	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
150	C₄²	C₂×C₅×Q₈	1	1	yes	characteristic
151	C₂×C₅	—	4	1	no	—
152	C₂×C₅	#1945	1	1	yes	characteristic
153	C₂×C₅	#1950	1	1	yes	characteristic
154	C₂×C₅	#1952	1	1	yes	characteristic
155	C₂³	C₅×#125	1	1	yes	characteristic
156	C₂×C₄	—	2	1	no	—
157	C₂×C₄	—	2	1	no	—
158	C₂×C₄	—	2	2	no	—
159	C₂×C₄	—	2	1	no	—
160	C₂×C₄	—	2	1	no	—
161	C₂×C₄	C₂×C₅×C₄⋊C₄	1	1	yes	characteristic
162	C₂×C₄	C₄×C₅×D₄	1	1	yes	characteristic
163	C₂×C₄	C₄×C₅×Q₈	1	1	yes	characteristic
164	C₂×C₄	C₅×#121	1	1	yes	characteristic
165	C₂×C₄	C₅×C₂²⋊Q₈	1	1	yes	characteristic
166	C₂×C₄	C₅×C₄⋊Q₈	1	1	yes	characteristic
167	C₈	—	2	4	no	—
168	C₈	—	2	1	no	—
169	C₈	—	2	1	no	—
170	C₈	—	2	1	no	—
171	C₈	—	4	4	no	—
172	C₈	—	4	1	no	—
173	C₈	—	4	1	no	—
174	C₈	—	8	2	no	—
175	C₈	C₅×#108	1	2	yes	—
176	C₅	#9634	1	1	yes	characteristic, direct product factor, Sylow
177	C₂²	—	2	1	no	—
178	C₂²	—	2	1	no	—
179	C₂²	—	2	1	no	—
180	C₂²	C₅×#389	1	1	yes	characteristic
181	C₄	—	2	1	no	—
182	C₄	—	2	1	no	—
183	C₄	—	2	1	no	—
184	C₄	C₂×C₅×#108	1	1	yes	characteristic
185	C₄	C₅×#430	1	1	yes	characteristic
186	C₄	C₅×#443	1	2	yes	—
187	C₄	C₅×#472	1	1	yes	characteristic
188	C₄	C₅×#473	1	1	yes	characteristic
189	C₂	—	4	1	no	—
190	C₂	C₅×#1945	1	1	yes	characteristic
191	C₂	C₅×#1950	1	1	yes	characteristic
192	C₂	C₅×#1952	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. #9634	C₅	direct (N × H)
176. C₅	#9634	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×#1567	2
C₅×#1564	2
C₅×C₈×M₁₆	2
C₅×#1299	2
#9634	5

Subgroups — C5×#9634 #11932354

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#9634 #11932354