Subgroups — C₅×#11932 #11934652

Order 1280.

398 conjugacy classes of subgroups.

The subgroup lattice has 228 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#494	C₂	1	1	yes	maximal, characteristic
2	C₅×#2150	C₂	1	1	yes	maximal, characteristic
3	C₅×#1564	C₂	1	1	yes	maximal, characteristic
4	C₅×#1362	C₂	1	4	yes	maximal, complemented
5	C₂²×C₅×Q₁₆	—	2	1	no	—
6	C₂²×C₅×Q₁₆	C₄	1	2	yes	—
7	C₂×C₅×C₄⋊Q₈	—	2	1	no	—
8	C₂×C₅×M₃₂	—	2	1	no	—
9	C₅×#494	—	2	1	no	—
10	C₅×#494	—	2	1	no	—
11	C₅×#494	C₄	1	2	yes	—
12	C₅×#494	C₂²	1	2	yes	—
13	C₅×#431	—	2	1	no	—
14	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
15	C₅×C₄⋊C₁₆	—	2	1	no	—
16	C₅×C₄⋊C₁₆	C₂²	1	2	yes	—
17	C₅×#335	C₂²	1	2	yes	—
18	C₅×#334	—	2	1	no	—
19	#11932	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
20	C₂²×C₅×Q₈	—	2	2	no	—
21	C₂×C₅×Q₁₆	—	2	2	no	—
22	C₂×C₅×Q₁₆	—	2	2	no	—
23	C₂×C₅×Q₁₆	—	2	2	no	—
24	C₂×C₅×Q₁₆	—	4	4	no	—
25	C₂×C₅×Q₁₆	—	4	2	no	—
26	C₂×C₅×Q₁₆	—	4	2	no	—
27	C₂×C₅×Q₁₆	C₂×C₄	1	4	yes	—
28	C₂²×C₅×C₈	C₂×C₄	1	1	yes	characteristic
29	C₂²×C₅×C₈	D₄	1	1	yes	characteristic
30	C₅×C₄⋊Q₈	—	2	2	no	—
31	C₅×C₄⋊Q₈	—	2	2	no	—
32	C₅×C₄⋊Q₈	—	4	1	no	—
33	C₅×C₄⋊Q₈	—	4	1	no	—
34	C₂×C₅×C₄⋊C₄	—	4	1	no	—
35	C₂×C₅×C₄⋊C₄	—	4	1	no	—
36	C₂×C₄²×C₅	D₄	1	1	yes	characteristic
37	C₅×M₃₂	—	4	2	no	—
38	C₂×C₅×C₁₆	—	2	2	no	—
39	C₅×C₄⋊C₈	—	2	2	no	—
40	C₅×C₂²⋊C₈	—	4	1	no	—
41	C₄×C₅×C₈	—	4	1	no	—
42	C₄×C₅×C₈	C₂×C₄	1	1	yes	characteristic
43	C₄×C₅×C₈	D₄	1	1	yes	characteristic
44	C₄×C₅×C₈	D₄	1	1	yes	characteristic
45	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
46	C₂×#494	C₂×C₅	1	1	yes	characteristic
47	#2150	C₂×C₅	1	1	yes	characteristic
48	#1564	C₂×C₅	1	1	yes	characteristic
49	#1362	C₂×C₅	1	4	yes	complemented
50	C₂×C₅×Q₈	—	2	4	no	—
51	C₂×C₅×Q₈	—	4	2	no	—
52	C₂×C₅×Q₈	—	4	4	no	—
53	C₂×C₅×Q₈	—	4	4	no	—
54	C₂²×C₄×C₅	—	4	2	no	—
55	C₂²×C₄×C₅	C₂²⋊C₄	1	1	yes	characteristic
56	C₂²×C₄×C₅	D₈	1	1	yes	characteristic
57	C₂²×C₄×C₅	SD₁₆	1	1	yes	characteristic
58	C₅×Q₁₆	—	4	4	no	—
59	C₅×Q₁₆	—	4	4	no	—
60	C₅×Q₁₆	—	4	4	no	—
61	C₅×Q₁₆	—	4	2	no	—
62	C₅×Q₁₆	—	4	2	no	—
63	C₂×C₅×C₈	—	2	2	no	—
64	C₂×C₅×C₈	—	4	2	no	—
65	C₂×C₅×C₈	C₂²⋊C₄	1	1	yes	characteristic
66	C₂×C₅×C₈	C₂²⋊C₄	1	1	yes	characteristic
67	C₂×C₅×C₈	D₈	1	2	yes	—
68	C₂×C₅×C₈	SD₁₆	1	2	yes	—
69	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
70	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
71	C₅×C₄⋊C₄	—	4	2	no	—
72	C₅×C₄⋊C₄	—	4	2	no	—
73	C₅×C₄⋊C₄	—	4	2	no	—
74	C₅×C₄⋊C₄	—	4	2	no	—
75	C₄²×C₅	C₂²⋊C₄	1	1	yes	characteristic
76	C₄²×C₅	D₈	1	1	yes	characteristic
77	C₄²×C₅	SD₁₆	1	1	yes	characteristic
78	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
79	C₅×C₁₆	—	4	2	no	—
80	C₂²×Q₁₆	—	2	1	no	—
81	C₂²×Q₁₆	C₄×C₅	1	2	yes	—
82	C₂×C₄⋊Q₈	—	2	1	no	—
83	C₂×M₃₂	—	2	1	no	—
84	#494	—	2	1	no	—
85	#494	—	2	1	no	—
86	#494	C₄×C₅	1	2	yes	—
87	#494	C₂²×C₅	1	2	yes	—
88	#431	—	2	1	no	—
89	C₂×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
90	C₄⋊C₁₆	—	2	1	no	—
91	C₄⋊C₁₆	C₂²×C₅	1	2	yes	—
92	#335	C₂²×C₅	1	2	yes	—
93	#334	—	2	1	no	—
94	C₂³×C₅	#102	1	1	yes	characteristic
95	C₅×Q₈	—	4	4	no	—
96	C₅×Q₈	—	4	4	no	—
97	C₅×Q₈	—	8	4	no	—
98	C₂×C₄×C₅	—	2	2	no	—
99	C₂×C₄×C₅	—	2	2	no	—
100	C₂×C₄×C₅	—	4	4	no	—
101	C₂×C₄×C₅	—	8	4	no	—
102	C₂×C₄×C₅	#100	1	2	yes	—
103	C₂×C₄×C₅	#102	1	1	yes	characteristic
104	C₂×C₄×C₅	#102	1	1	yes	characteristic
105	C₂×C₄×C₅	#102	1	2	yes	—
106	C₂×C₄×C₅	#102	1	1	yes	characteristic
107	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
108	C₂×C₄×C₅	C₂×D₈	1	1	yes	characteristic
109	C₂×C₄×C₅	C₂×SD₁₆	1	1	yes	characteristic
110	C₅×C₈	—	2	1	no	—
111	C₅×C₈	—	2	1	no	—
112	C₅×C₈	—	8	2	no	—
113	C₅×C₈	#102	1	2	yes	—
114	C₅×C₈	C₂×D₈	1	1	yes	characteristic
115	C₅×C₈	C₂×SD₁₆	1	1	yes	characteristic
116	C₂²×Q₈	—	2	2	no	—
117	C₂×Q₁₆	—	2	2	no	—
118	C₂×Q₁₆	—	2	2	no	—
119	C₂×Q₁₆	—	2	2	no	—
120	C₂×Q₁₆	—	4	4	no	—
121	C₂×Q₁₆	—	4	2	no	—
122	C₂×Q₁₆	—	4	2	no	—
123	C₂×Q₁₆	C₂×C₄×C₅	1	4	yes	—
124	C₂²×C₈	C₂×C₄×C₅	1	1	yes	characteristic
125	C₂²×C₈	C₅×D₄	1	1	yes	characteristic
126	C₄⋊Q₈	—	2	2	no	—
127	C₄⋊Q₈	—	2	2	no	—
128	C₄⋊Q₈	—	4	1	no	—
129	C₄⋊Q₈	—	4	1	no	—
130	C₂×C₄⋊C₄	—	4	1	no	—
131	C₂×C₄⋊C₄	—	4	1	no	—
132	C₂×C₄²	C₅×D₄	1	1	yes	characteristic
133	M₃₂	—	4	2	no	—
134	C₂×C₁₆	—	2	2	no	—
135	C₄⋊C₈	—	2	2	no	—
136	C₂²⋊C₈	—	4	1	no	—
137	C₄×C₈	—	4	1	no	—
138	C₄×C₈	C₂×C₄×C₅	1	1	yes	characteristic
139	C₄×C₈	C₅×D₄	1	1	yes	characteristic
140	C₄×C₈	C₅×D₄	1	1	yes	characteristic
141	C₄×C₈	C₂³×C₅	1	1	yes	characteristic
142	C₂²×C₅	—	2	1	no	—
143	C₂²×C₅	—	2	1	no	—
144	C₂²×C₅	#331	1	2	yes	—
145	C₂²×C₅	C₂×#102	1	1	yes	characteristic
146	C₄×C₅	—	2	1	no	—
147	C₄×C₅	—	2	1	no	—
148	C₄×C₅	—	8	4	no	—
149	C₄×C₅	#331	1	2	yes	—
150	C₄×C₅	#362	1	2	yes	—
151	C₄×C₅	C₂×#100	1	1	yes	characteristic
152	C₄×C₅	C₂×#102	1	1	yes	characteristic
153	C₄×C₅	#510	1	2	yes	—
154	C₂×Q₈	—	2	4	no	—
155	C₂×Q₈	—	4	2	no	—
156	C₂×Q₈	—	4	4	no	—
157	C₂×Q₈	—	4	4	no	—
158	C₂²×C₄	—	4	2	no	—
159	C₂²×C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
160	C₂²×C₄	C₅×D₈	1	1	yes	characteristic
161	C₂²×C₄	C₅×SD₁₆	1	1	yes	characteristic
162	Q₁₆	—	4	4	no	—
163	Q₁₆	—	4	4	no	—
164	Q₁₆	—	4	2	no	—
165	Q₁₆	—	4	2	no	—
166	Q₁₆	—	4	4	no	—
167	C₂×C₈	—	2	2	no	—
168	C₂×C₈	—	4	2	no	—
169	C₂×C₈	C₅×C₂²⋊C₄	1	1	yes	characteristic
170	C₂×C₈	C₅×C₂²⋊C₄	1	1	yes	characteristic
171	C₂×C₈	C₅×D₈	1	2	yes	—
172	C₂×C₈	C₅×SD₁₆	1	2	yes	—
173	C₂×C₈	C₂²×C₄×C₅	1	1	yes	characteristic
174	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
175	C₄⋊C₄	—	4	2	no	—
176	C₄⋊C₄	—	4	2	no	—
177	C₄⋊C₄	—	4	2	no	—
178	C₄⋊C₄	—	4	2	no	—
179	C₄²	C₅×C₂²⋊C₄	1	1	yes	characteristic
180	C₄²	C₅×D₈	1	1	yes	characteristic
181	C₄²	C₅×SD₁₆	1	1	yes	characteristic
182	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
183	C₁₆	—	4	2	no	—
184	C₂×C₅	—	2	2	no	—
185	C₂×C₅	C₂×#331	1	1	yes	characteristic
186	C₂×C₅	#2141	1	1	yes	characteristic
187	C₂×C₅	C₂×#362	1	1	yes	characteristic
188	C₂³	C₅×#102	1	1	yes	characteristic
189	Q₈	—	4	4	no	—
190	Q₈	—	4	4	no	—
191	Q₈	—	8	4	no	—
192	C₂×C₄	—	2	2	no	—
193	C₂×C₄	—	2	2	no	—
194	C₂×C₄	—	4	4	no	—
195	C₂×C₄	—	8	4	no	—
196	C₂×C₄	C₅×#100	1	2	yes	—
197	C₂×C₄	C₅×#102	1	1	yes	characteristic
198	C₂×C₄	C₅×#102	1	1	yes	characteristic
199	C₂×C₄	C₅×#102	1	2	yes	—
200	C₂×C₄	C₅×#102	1	1	yes	characteristic
201	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
202	C₂×C₄	C₂×C₅×D₈	1	1	yes	characteristic
203	C₂×C₄	C₂×C₅×SD₁₆	1	1	yes	characteristic
204	C₈	—	2	1	no	—
205	C₈	—	2	1	no	—
206	C₈	—	8	2	no	—
207	C₈	C₅×#102	1	2	yes	—
208	C₈	C₂×C₅×D₈	1	1	yes	characteristic
209	C₈	C₂×C₅×SD₁₆	1	1	yes	characteristic
210	C₅	#11932	1	1	yes	characteristic, direct product factor, Sylow
211	C₂²	—	2	1	no	—
212	C₂²	—	2	1	no	—
213	C₂²	C₅×#331	1	2	yes	—
214	C₂²	C₂×C₅×#102	1	1	yes	characteristic
215	C₄	—	2	1	no	—
216	C₄	—	2	1	no	—
217	C₄	—	8	4	no	—
218	C₄	C₅×#331	1	2	yes	—
219	C₄	C₅×#362	1	2	yes	—
220	C₄	C₂×C₅×#100	1	1	yes	characteristic
221	C₄	C₂×C₅×#102	1	1	yes	characteristic
222	C₄	C₅×#510	1	2	yes	—
223	C₂	—	2	2	no	—
224	C₂	C₂×C₅×#331	1	1	yes	characteristic
225	C₂	C₅×#2141	1	1	yes	characteristic
226	C₂	C₂×C₅×#362	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₅	C₂×#102
commutator	C₂×C₈	C₂²×C₄×C₅
Frattini, cosocle	C₄×C₈	C₂³×C₅
prime radical	C₂³×C₅	#102
LCS	G ▷ C₂×C₈ ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₅ ◁ C₂×C₄²×C₅ ◁ C₂×C₄×C₅×C₈ ◁ G

Complements

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

N	H ≅ G/N	type
4. C₅×#1362	C₂	semidirect
19. #11932	C₅	direct (N × H)
49. #1362	C₂×C₅	semidirect
210. C₅	#11932	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₅×#494	2
C₅×#2150	2
C₅×#1564	2
C₅×#1362	2
#11932	5

Subgroups — C5×#11932 #11934652

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#11932 #11934652