Subgroups — C₁₃×#7162 #15693501

Order 3328.

200 conjugacy classes of subgroups.

The subgroup lattice has 176 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#364	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₃×#364	C₂	1	1	yes	maximal, characteristic
3	C₄×C₁₃×M₃₂	C₂	1	1	yes	maximal, characteristic
4	C₂×C₁₃×M₃₂	—	2	1	no	—
5	C₂×C₁₃×M₃₂	—	2	1	no	—
6	C₂×C₁₃×M₃₂	C₄	1	1	yes	characteristic
7	C₂×C₁₃×M₃₂	C₄	1	1	yes	characteristic
8	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
9	C₁₃×#364	—	2	1	no	—
10	C₁₃×#364	—	2	1	no	—
11	C₁₃×#364	C₄	1	2	yes	—
12	C₁₃×#364	C₄	1	2	yes	—
13	C₁₃×#346	—	2	1	no	—
14	C₄×C₁₃×C₁₆	—	2	1	no	—
15	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
16	C₂²×C₈×C₁₃	D₄	1	1	yes	characteristic
17	C₂×C₄²×C₁₃	Q₈	1	1	yes	characteristic
18	C₁₃×M₃₂	—	2	1	no	—
19	C₁₃×M₃₂	—	2	1	no	—
20	C₁₃×M₃₂	—	2	2	no	—
21	C₁₃×M₃₂	—	2	2	no	—
22	C₁₃×M₃₂	—	4	1	no	—
23	C₁₃×M₃₂	—	4	1	no	—
24	C₁₃×M₃₂	C₈	1	2	yes	—
25	C₁₃×M₃₂	C₈	1	2	yes	—
26	C₂×C₁₃×C₁₆	—	2	1	no	—
27	C₂×C₁₃×C₁₆	—	2	1	no	—
28	C₂×C₁₃×C₁₆	—	4	1	no	—
29	C₂×C₁₃×C₁₆	—	4	1	no	—
30	C₄×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
31	C₄×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
32	C₄×C₈×C₁₃	D₄	1	1	yes	characteristic
33	C₄×C₈×C₁₃	D₄	1	1	yes	characteristic
34	#7162	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
35	C₂²×C₄×C₁₃	—	2	1	no	—
36	C₂²×C₄×C₁₃	C₄⋊C₄	1	1	yes	characteristic
37	C₂×C₈×C₁₃	C₄²	1	1	yes	characteristic
38	C₂×C₈×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
39	C₂×C₈×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
40	C₂×C₈×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
41	C₂×C₈×C₁₃	C₂×C₈	1	1	yes	characteristic
42	C₂×C₈×C₁₃	C₂×C₈	1	1	yes	characteristic
43	C₂×C₈×C₁₃	M₁₆	1	1	yes	characteristic
44	C₂×C₈×C₁₃	M₁₆	1	1	yes	characteristic
45	C₂×C₈×C₁₃	D₈	1	1	yes	characteristic
46	C₂×C₈×C₁₃	SD₁₆	1	1	yes	characteristic
47	C₂×C₈×C₁₃	SD₁₆	1	1	yes	characteristic
48	C₂×C₈×C₁₃	Q₁₆	1	1	yes	characteristic
49	C₄²×C₁₃	—	2	1	no	—
50	C₄²×C₁₃	C₄⋊C₄	1	1	yes	characteristic
51	C₄²×C₁₃	C₄⋊C₄	1	1	yes	characteristic
52	C₁₃×C₁₆	—	2	2	no	—
53	C₁₃×C₁₆	—	2	2	no	—
54	C₁₃×C₁₆	—	4	2	no	—
55	C₁₃×C₁₆	—	4	2	no	—
56	C₂×#364	C₂×C₁₃	1	1	yes	characteristic
57	C₂×#364	C₂×C₁₃	1	1	yes	characteristic
58	C₄×M₃₂	C₂×C₁₃	1	1	yes	characteristic
59	C₂³×C₁₃	#108	1	1	yes	characteristic
60	C₂×C₄×C₁₃	—	2	1	no	—
61	C₂×C₄×C₁₃	—	2	1	no	—
62	C₂×C₄×C₁₃	—	4	2	no	—
63	C₂×C₄×C₁₃	#95	1	1	yes	characteristic
64	C₂×C₄×C₁₃	C₄⋊C₈	1	1	yes	characteristic
65	C₂×C₄×C₁₃	C₄⋊C₈	1	1	yes	characteristic
66	C₂×C₄×C₁₃	#106	1	1	yes	characteristic
67	C₂×C₄×C₁₃	#107	1	1	yes	characteristic
68	C₂×C₄×C₁₃	#108	1	1	yes	characteristic
69	C₈×C₁₃	C₄×C₈	1	1	yes	characteristic
70	C₈×C₁₃	#97	1	1	yes	characteristic
71	C₈×C₁₃	C₂²⋊C₈	1	1	yes	characteristic
72	C₈×C₁₃	C₂²⋊C₈	1	1	yes	characteristic
73	C₈×C₁₃	#102	1	1	yes	characteristic
74	C₈×C₁₃	#102	1	1	yes	characteristic
75	C₈×C₁₃	#103	1	1	yes	characteristic
76	C₈×C₁₃	#103	1	1	yes	characteristic
77	C₂×M₃₂	—	2	1	no	—
78	C₂×M₃₂	—	2	1	no	—
79	C₂×M₃₂	C₄×C₁₃	1	1	yes	characteristic
80	C₂×M₃₂	C₄×C₁₃	1	1	yes	characteristic
81	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
82	#364	—	2	1	no	—
83	#364	—	2	1	no	—
84	#364	C₄×C₁₃	1	2	yes	—
85	#364	C₄×C₁₃	1	2	yes	—
86	#346	—	2	1	no	—
87	C₄×C₁₆	—	2	1	no	—
88	C₂²×C₁₃	—	4	1	no	—
89	C₂²×C₁₃	#334	1	1	yes	characteristic
90	C₂²×C₁₃	#335	1	1	yes	characteristic
91	C₂²×C₁₃	#341	1	1	yes	characteristic
92	C₄×C₁₃	—	2	2	no	—
93	C₄×C₁₃	—	4	1	no	—
94	C₄×C₁₃	#334	1	1	yes	characteristic
95	C₄×C₁₃	#335	1	1	yes	characteristic
96	C₄×C₁₃	#336	1	1	yes	characteristic
97	C₄×C₁₃	#340	1	1	yes	characteristic
98	C₂²×C₈	C₂×C₄×C₁₃	1	1	yes	characteristic
99	C₂²×C₈	D₄×C₁₃	1	1	yes	characteristic
100	C₂×C₄²	Q₈×C₁₃	1	1	yes	characteristic
101	M₃₂	—	2	1	no	—
102	M₃₂	—	2	1	no	—
103	M₃₂	—	2	2	no	—
104	M₃₂	—	2	2	no	—
105	M₃₂	—	4	1	no	—
106	M₃₂	—	4	1	no	—
107	M₃₂	C₈×C₁₃	1	2	yes	—
108	M₃₂	C₈×C₁₃	1	2	yes	—
109	C₂×C₁₆	—	2	1	no	—
110	C₂×C₁₆	—	2	1	no	—
111	C₂×C₁₆	—	4	1	no	—
112	C₂×C₁₆	—	4	1	no	—
113	C₄×C₈	C₂×C₄×C₁₃	1	1	yes	characteristic
114	C₄×C₈	C₂×C₄×C₁₃	1	1	yes	characteristic
115	C₄×C₈	D₄×C₁₃	1	1	yes	characteristic
116	C₄×C₈	D₄×C₁₃	1	1	yes	characteristic
117	C₂×C₁₃	—	2	1	no	—
118	C₂×C₁₃	—	2	1	no	—
119	C₂×C₁₃	—	2	1	no	—
120	C₂×C₁₃	#1277	1	1	yes	characteristic
121	C₂²×C₄	—	2	1	no	—
122	C₂²×C₄	C₁₃×C₄⋊C₄	1	1	yes	characteristic
123	C₂×C₈	C₄²×C₁₃	1	1	yes	characteristic
124	C₂×C₈	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
125	C₂×C₈	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
126	C₂×C₈	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
127	C₂×C₈	C₂×C₈×C₁₃	1	1	yes	characteristic
128	C₂×C₈	C₂×C₈×C₁₃	1	1	yes	characteristic
129	C₂×C₈	C₁₃×M₁₆	1	1	yes	characteristic
130	C₂×C₈	C₁₃×M₁₆	1	1	yes	characteristic
131	C₂×C₈	C₁₃×D₈	1	1	yes	characteristic
132	C₂×C₈	C₁₃×SD₁₆	1	1	yes	characteristic
133	C₂×C₈	C₁₃×SD₁₆	1	1	yes	characteristic
134	C₂×C₈	C₁₃×Q₁₆	1	1	yes	characteristic
135	C₄²	—	2	1	no	—
136	C₄²	C₁₃×C₄⋊C₄	1	1	yes	characteristic
137	C₄²	C₁₃×C₄⋊C₄	1	1	yes	characteristic
138	C₁₆	—	2	2	no	—
139	C₁₆	—	2	2	no	—
140	C₁₆	—	4	2	no	—
141	C₁₆	—	4	2	no	—
142	C₁₃	#7162	1	1	yes	characteristic, direct product factor, Sylow
143	C₂³	C₁₃×#108	1	1	yes	characteristic
144	C₂×C₄	—	2	1	no	—
145	C₂×C₄	—	2	1	no	—
146	C₂×C₄	—	4	2	no	—
147	C₂×C₄	C₁₃×#95	1	1	yes	characteristic
148	C₂×C₄	C₁₃×C₄⋊C₈	1	1	yes	characteristic
149	C₂×C₄	C₁₃×C₄⋊C₈	1	1	yes	characteristic
150	C₂×C₄	C₁₃×#106	1	1	yes	characteristic
151	C₂×C₄	C₁₃×#107	1	1	yes	characteristic
152	C₂×C₄	C₁₃×#108	1	1	yes	characteristic
153	C₈	C₄×C₈×C₁₃	1	1	yes	characteristic
154	C₈	C₁₃×#97	1	1	yes	characteristic
155	C₈	C₁₃×C₂²⋊C₈	1	1	yes	characteristic
156	C₈	C₁₃×C₂²⋊C₈	1	1	yes	characteristic
157	C₈	C₁₃×#102	1	1	yes	characteristic
158	C₈	C₁₃×#102	1	1	yes	characteristic
159	C₈	C₁₃×#103	1	1	yes	characteristic
160	C₈	C₁₃×#103	1	1	yes	characteristic
161	C₂²	—	4	1	no	—
162	C₂²	C₁₃×#334	1	1	yes	characteristic
163	C₂²	C₁₃×#335	1	1	yes	characteristic
164	C₂²	C₁₃×#341	1	1	yes	characteristic
165	C₄	—	2	2	no	—
166	C₄	—	4	1	no	—
167	C₄	C₁₃×#334	1	1	yes	characteristic
168	C₄	C₁₃×#335	1	1	yes	characteristic
169	C₄	C₁₃×#336	1	1	yes	characteristic
170	C₄	C₁₃×#340	1	1	yes	characteristic
171	C₂	—	2	1	no	—
172	C₂	—	2	1	no	—
173	C₂	—	2	1	no	—
174	C₂	C₁₃×#1277	1	1	yes	characteristic

	subgroup	G/H
center	C₈×C₁₃	#102
commutator	C₈	C₄×C₈×C₁₃
Frattini, cosocle	C₂×C₄×C₈	C₂²×C₁₃
socle	C₂×C₁₃	#1277
prime radical	C₂³×C₁₃	#108
LCS	G ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₈×C₁₃ ◁ C₂²×C₈×C₁₃ ◁ C₂×C₄×C₈×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
34. #7162	C₁₃	direct (N × H)
142. C₁₃	#7162	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×C₁₃×#364	2
C₄×C₁₃×M₃₂	2
#7162	13

Subgroups — C13×#7162 #15693501

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#7162 #15693501