Subgroups — C₅×#13279 #11935999

Order 1280.

366 conjugacy classes of subgroups.

The subgroup lattice has 216 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#500	C₂	1	1	yes	maximal, characteristic
2	C₅×#2150	C₂	1	1	yes	maximal, characteristic
3	C₄×C₅×#108	C₂	1	1	yes	maximal, characteristic
4	C₅×#1387	C₂	1	4	yes	maximal
5	C₂×C₅×C₄⋊Q₈	—	2	1	no	—
6	C₂×C₅×M₃₂	C₂²	1	2	yes	—
7	C₅×#500	—	2	1	no	—
8	C₅×#500	—	2	1	no	—
9	C₅×#500	C₄	1	2	yes	—
10	C₅×#500	C₄	1	2	yes	—
11	C₂×C₅×#108	C₂²	1	2	yes	—
12	C₂×C₅×#107	—	2	1	no	—
13	C₂×C₅×#107	C₂²	1	2	yes	—
14	C₄×C₅×M₁₆	—	2	1	no	—
15	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
16	C₅×C₄⋊C₁₆	—	2	1	no	—
17	C₅×C₄⋊C₁₆	—	2	1	no	—
18	C₅×#341	—	2	1	no	—
19	#13279	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
20	C₂²×C₅×Q₈	—	4	1	no	—
21	C₂×C₅×M₁₆	—	2	2	no	—
22	C₂²×C₅×C₈	D₄	1	1	yes	characteristic
23	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
24	C₅×C₄⋊Q₈	—	2	2	no	—
25	C₅×C₄⋊Q₈	—	2	2	no	—
26	C₅×C₄⋊Q₈	—	4	1	no	—
27	C₅×C₄⋊Q₈	—	4	1	no	—
28	C₂×C₅×C₄⋊C₄	—	2	2	no	—
29	C₂×C₅×C₄⋊C₄	—	4	1	no	—
30	C₂×C₄²×C₅	D₄	1	1	yes	characteristic
31	C₅×M₃₂	—	2	4	no	—
32	C₂×C₅×C₁₆	—	2	2	no	—
33	C₅×#108	—	2	2	no	—
34	C₅×#108	Q₈	1	4	yes	complemented
35	C₅×#107	—	2	2	no	—
36	C₅×#107	—	2	2	no	—
37	C₅×#107	—	2	2	no	—
38	C₅×#107	C₂×C₄	1	4	yes	—
39	C₅×#97	—	4	1	no	—
40	C₄×C₅×C₈	—	4	1	no	—
41	C₄×C₅×C₈	C₂×C₄	1	1	yes	characteristic
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	C₂×#500	C₂×C₅	1	1	yes	characteristic
46	#2150	C₂×C₅	1	1	yes	characteristic
47	C₄×#108	C₂×C₅	1	1	yes	characteristic
48	#1387	C₂×C₅	1	4	yes	—
49	C₂×C₅×Q₈	—	4	2	no	—
50	C₂×C₅×Q₈	—	4	2	no	—
51	C₂×C₅×Q₈	—	8	4	no	—
52	C₂²×C₄×C₅	—	4	2	no	—
53	C₂²×C₄×C₅	SD₁₆	1	1	yes	characteristic
54	C₂²×C₄×C₅	SD₁₆	1	1	yes	characteristic
55	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
56	C₅×M₁₆	—	2	4	no	—
57	C₅×M₁₆	—	4	2	no	—
58	C₂×C₅×C₈	—	2	2	no	—
59	C₂×C₅×C₈	—	4	2	no	—
60	C₂×C₅×C₈	C₂²⋊C₄	1	1	yes	characteristic
61	C₂×C₅×C₈	C₂²⋊C₄	1	1	yes	characteristic
62	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
63	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
64	C₂×C₅×C₈	C₂×Q₈	1	2	yes	—
65	C₂×C₅×C₈	#41	1	2	yes	—
66	C₅×C₄⋊C₄	—	2	4	no	—
67	C₅×C₄⋊C₄	—	4	2	no	—
68	C₅×C₄⋊C₄	—	4	2	no	—
69	C₅×C₄⋊C₄	—	4	2	no	—
70	C₄²×C₅	C₂²⋊C₄	1	1	yes	characteristic
71	C₄²×C₅	C₂²⋊C₄	1	1	yes	characteristic
72	C₄²×C₅	D₈	1	1	yes	characteristic
73	C₄²×C₅	D₈	1	1	yes	characteristic
74	C₅×C₁₆	—	4	2	no	—
75	C₂×C₄⋊Q₈	—	2	1	no	—
76	C₂×M₃₂	C₂²×C₅	1	2	yes	—
77	#500	—	2	1	no	—
78	#500	—	2	1	no	—
79	#500	C₄×C₅	1	2	yes	—
80	#500	C₄×C₅	1	2	yes	—
81	C₂×#108	C₂²×C₅	1	2	yes	—
82	C₂×#107	—	2	1	no	—
83	C₂×#107	C₂²×C₅	1	2	yes	—
84	C₄×M₁₆	—	2	1	no	—
85	C₂×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
86	C₄⋊C₁₆	—	2	1	no	—
87	C₄⋊C₁₆	—	2	1	no	—
88	#341	—	2	1	no	—
89	C₂³×C₅	C₂×SD₁₆	1	1	yes	characteristic
90	C₅×Q₈	—	8	4	no	—
91	C₅×Q₈	—	8	4	no	—
92	C₂×C₄×C₅	—	2	2	no	—
93	C₂×C₄×C₅	—	2	2	no	—
94	C₂×C₄×C₅	—	4	4	no	—
95	C₂×C₄×C₅	—	8	4	no	—
96	C₂×C₄×C₅	#102	1	1	yes	characteristic
97	C₂×C₄×C₅	#102	1	1	yes	characteristic
98	C₂×C₄×C₅	#102	1	1	yes	characteristic
99	C₂×C₄×C₅	#102	1	1	yes	characteristic
100	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
101	C₂×C₄×C₅	C₂²⋊Q₈	1	2	yes	—
102	C₂×C₄×C₅	C₂×D₈	1	1	yes	characteristic
103	C₂×C₄×C₅	#137	1	2	yes	—
104	C₅×C₈	—	2	1	no	—
105	C₅×C₈	—	2	1	no	—
106	C₅×C₈	—	4	4	no	—
107	C₅×C₈	C₄×Q₈	1	2	yes	—
108	C₅×C₈	#124	1	1	yes	characteristic
109	C₅×C₈	C₄⋊Q₈	1	1	yes	characteristic
110	C₂²×Q₈	—	4	1	no	—
111	C₂×M₁₆	—	2	2	no	—
112	C₂²×C₈	C₅×D₄	1	1	yes	characteristic
113	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
114	C₄⋊Q₈	—	2	2	no	—
115	C₄⋊Q₈	—	2	2	no	—
116	C₄⋊Q₈	—	4	1	no	—
117	C₄⋊Q₈	—	4	1	no	—
118	C₂×C₄⋊C₄	—	2	2	no	—
119	C₂×C₄⋊C₄	—	4	1	no	—
120	C₂×C₄²	C₅×D₄	1	1	yes	characteristic
121	M₃₂	—	2	4	no	—
122	C₂×C₁₆	—	2	2	no	—
123	#108	—	2	2	no	—
124	#108	C₅×Q₈	1	4	yes	complemented
125	#107	—	2	2	no	—
126	#107	—	2	2	no	—
127	#107	—	2	2	no	—
128	#107	C₂×C₄×C₅	1	4	yes	—
129	#97	—	4	1	no	—
130	C₄×C₈	—	4	1	no	—
131	C₄×C₈	C₂×C₄×C₅	1	1	yes	characteristic
132	C₄×C₈	C₂×C₄×C₅	1	1	yes	characteristic
133	C₄×C₈	C₅×D₄	1	1	yes	characteristic
134	C₄×C₈	C₅×D₄	1	1	yes	characteristic
135	C₂²×C₅	—	2	1	no	—
136	C₂²×C₅	—	2	1	no	—
137	C₂²×C₅	C₂×#102	1	1	yes	characteristic
138	C₂²×C₅	#475	1	2	yes	—
139	C₄×C₅	—	2	1	no	—
140	C₄×C₅	—	2	1	no	—
141	C₄×C₅	—	8	4	no	—
142	C₄×C₅	#361	1	2	yes	—
143	C₄×C₅	#362	1	2	yes	—
144	C₄×C₅	#391	1	1	yes	characteristic
145	C₄×C₅	#419	1	1	yes	characteristic
146	C₄×C₅	#474	1	2	yes	—
147	C₂×Q₈	—	4	2	no	—
148	C₂×Q₈	—	4	2	no	—
149	C₂×Q₈	—	8	4	no	—
150	C₂²×C₄	—	4	2	no	—
151	C₂²×C₄	C₅×SD₁₆	1	1	yes	characteristic
152	C₂²×C₄	C₅×SD₁₆	1	1	yes	characteristic
153	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
154	M₁₆	—	2	4	no	—
155	M₁₆	—	4	2	no	—
156	C₂×C₈	—	2	2	no	—
157	C₂×C₈	—	4	2	no	—
158	C₂×C₈	C₅×C₂²⋊C₄	1	1	yes	characteristic
159	C₂×C₈	C₅×C₂²⋊C₄	1	1	yes	characteristic
160	C₂×C₈	C₂²×C₄×C₅	1	1	yes	characteristic
161	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
162	C₂×C₈	C₂×C₅×Q₈	1	2	yes	—
163	C₂×C₈	C₅×#41	1	2	yes	—
164	C₄⋊C₄	—	2	4	no	—
165	C₄⋊C₄	—	4	2	no	—
166	C₄⋊C₄	—	4	2	no	—
167	C₄⋊C₄	—	4	2	no	—
168	C₄²	C₅×C₂²⋊C₄	1	1	yes	characteristic
169	C₄²	C₅×C₂²⋊C₄	1	1	yes	characteristic
170	C₄²	C₅×D₈	1	1	yes	characteristic
171	C₄²	C₅×D₈	1	1	yes	characteristic
172	C₁₆	—	4	2	no	—
173	C₂×C₅	—	2	2	no	—
174	C₂×C₅	#1988	1	1	yes	characteristic
175	C₂×C₅	C₂×#361	1	1	yes	characteristic
176	C₂×C₅	C₂×#362	1	1	yes	characteristic
177	C₂³	C₂×C₅×SD₁₆	1	1	yes	characteristic
178	Q₈	—	8	4	no	—
179	Q₈	—	8	4	no	—
180	C₂×C₄	—	2	2	no	—
181	C₂×C₄	—	2	2	no	—
182	C₂×C₄	—	4	4	no	—
183	C₂×C₄	—	8	4	no	—
184	C₂×C₄	C₅×#102	1	1	yes	characteristic
185	C₂×C₄	C₅×#102	1	1	yes	characteristic
186	C₂×C₄	C₅×#102	1	1	yes	characteristic
187	C₂×C₄	C₅×#102	1	1	yes	characteristic
188	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
189	C₂×C₄	C₅×C₂²⋊Q₈	1	2	yes	—
190	C₂×C₄	C₂×C₅×D₈	1	1	yes	characteristic
191	C₂×C₄	C₅×#137	1	2	yes	—
192	C₈	—	2	1	no	—
193	C₈	—	2	1	no	—
194	C₈	—	4	4	no	—
195	C₈	C₄×C₅×Q₈	1	2	yes	—
196	C₈	C₅×#124	1	1	yes	characteristic
197	C₈	C₅×C₄⋊Q₈	1	1	yes	characteristic
198	C₅	#13279	1	1	yes	characteristic, direct product factor, Sylow
199	C₂²	—	2	1	no	—
200	C₂²	—	2	1	no	—
201	C₂²	C₂×C₅×#102	1	1	yes	characteristic
202	C₂²	C₅×#475	1	2	yes	—
203	C₄	—	2	1	no	—
204	C₄	—	2	1	no	—
205	C₄	—	8	4	no	—
206	C₄	C₅×#361	1	2	yes	—
207	C₄	C₅×#362	1	2	yes	—
208	C₄	C₅×#391	1	1	yes	characteristic
209	C₄	C₅×#419	1	1	yes	characteristic
210	C₄	C₅×#474	1	2	yes	—
211	C₂	—	2	2	no	—
212	C₂	C₅×#1988	1	1	yes	characteristic
213	C₂	C₂×C₅×#361	1	1	yes	characteristic
214	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	C₂²×C₈	C₂³×C₅
prime radical	C₂³×C₅	C₂×SD₁₆
LCS	G ▷ C₂×C₈ ▷ 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
19. #13279	C₅	direct (N × H)
34. C₅×#108	Q₈	semidirect
124. #108	C₅×Q₈	semidirect
198. C₅	#13279	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×#500	2
C₅×#2150	2
C₄×C₅×#108	2
C₅×#1387	2
#13279	5

Subgroups — C5×#13279 #11935999

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#13279 #11935999