Subgroups — C₁₃×#34552 #15720891

Order 3328.

1962 conjugacy classes of subgroups.

The subgroup lattice has 166 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#2402	C₂	1	6	yes	maximal, complemented
2	C₁₃×#2399	C₂	1	6	yes	maximal, complemented
3	C₁₃×#2396	C₂	1	12	yes	maximal
4	C₄²×Q₈×C₁₃	C₂	1	4	yes	maximal, complemented
5	C₄×C₁₃×#117	C₂	1	3	yes	maximal
6	C₂×C₄×Q₈×C₁₃	C₂²	1	12	yes	—
7	C₂×C₁₃×#117	C₂²	1	6	yes	—
8	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
9	C₁₃×#400	C₂²	1	12	yes	—
10	C₁₃×#399	C₂²	1	4	yes	—
11	C₁₃×#398	C₂²	1	24	yes	—
12	C₁₃×#396	C₂²	1	8	yes	—
13	C₁₃×#395	C₂²	1	12	yes	—
14	C₁₃×#393	C₂²	1	4	yes	—
15	C₄×C₁₃×C₄⋊C₄	C₂²	1	12	yes	—
16	C₄×C₁₃×C₄⋊C₄	C₂²	1	12	yes	—
17	C₄×C₁₃×C₄⋊C₄	C₂²	1	24	yes	—
18	C₄×C₁₃×C₂²⋊C₄	C₂²	1	12	yes	—
19	C₁₃×#376	C₂²	1	3	yes	—
20	C₁₃×#376	C₂²	1	3	yes	—
21	C₄³×C₁₃	C₂²	1	6	yes	—
22	C₂²×Q₈×C₁₃	C₂³	1	4	yes	—
23	C₂³×C₄×C₁₃	C₂³	1	3	yes	—
24	C₄×Q₈×C₁₃	—	2	48	no	—
25	C₁₃×#117	—	2	24	no	—
26	C₂×C₁₃×C₄⋊C₄	C₂³	1	24	yes	—
27	C₂×C₁₃×C₄⋊C₄	C₂³	1	12	yes	—
28	C₂×C₁₃×C₄⋊C₄	C₂³	1	12	yes	—
29	C₂×C₁₃×C₂²⋊C₄	C₂³	1	12	yes	—
30	C₂×C₄²×C₁₃	Q₈	1	8	yes	complemented
31	C₂×C₄²×C₁₃	C₂³	1	24	yes	—
32	C₂×C₄²×C₁₃	C₂³	1	6	yes	—
33	C₂×C₄²×C₁₃	C₂³	1	3	yes	—
34	C₂×C₄²×C₁₃	C₂³	1	6	yes	—
35	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
36	C₁₃×#95	C₂³	1	12	yes	—
37	C₁₃×#95	C₂³	1	12	yes	—
38	C₁₃×#95	C₂³	1	12	yes	—
39	C₁₃×#95	C₂³	1	4	yes	—
40	C₁₃×#95	C₂³	1	8	yes	—
41	#34552	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
42	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
43	C₂×Q₈×C₁₃	—	2	24	no	—
44	C₂²×C₄×C₁₃	—	2	12	no	—
45	C₂²×C₄×C₁₃	C₂×Q₈	1	12	yes	—
46	C₂²×C₄×C₁₃	C₂⁴	1	12	yes	—
47	C₂²×C₄×C₁₃	C₂⁴	1	3	yes	—
48	C₂²×C₄×C₁₃	C₂⁴	1	12	yes	—
49	C₂²×C₄×C₁₃	C₂⁴	1	3	yes	—
50	C₁₃×C₄⋊C₄	—	2	24	no	—
51	C₁₃×C₄⋊C₄	—	2	48	no	—
52	C₁₃×C₄⋊C₄	—	2	24	no	—
53	C₁₃×C₂²⋊C₄	—	2	24	no	—
54	C₄²×C₁₃	—	2	12	no	—
55	C₄²×C₁₃	—	2	48	no	—
56	C₄²×C₁₃	C₂×Q₈	1	12	yes	—
57	C₄²×C₁₃	C₂×Q₈	1	4	yes	—
58	C₄²×C₁₃	#41	1	24	yes	—
59	#2402	C₂×C₁₃	1	6	yes	complemented
60	#2399	C₂×C₁₃	1	6	yes	complemented
61	#2396	C₂×C₁₃	1	12	yes	—
62	C₄²×Q₈	C₂×C₁₃	1	4	yes	complemented
63	C₄×#117	C₂×C₁₃	1	3	yes	—
64	C₂³×C₁₃	—	2	6	no	—
65	C₂³×C₁₃	C₂²×Q₈	1	2	yes	—
66	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
67	Q₈×C₁₃	—	2	32	no	—
68	C₂×C₄×C₁₃	—	2	24	no	—
69	C₂×C₄×C₁₃	—	2	6	no	—
70	C₂×C₄×C₁₃	—	2	24	no	—
71	C₂×C₄×C₁₃	—	2	12	no	—
72	C₂×C₄×C₁₃	—	2	24	no	—
73	C₂×C₄×C₁₃	C₂²×Q₈	1	6	yes	—
74	C₂×C₄×C₁₃	C₂²×Q₈	1	6	yes	—
75	C₂×C₄×C₁₃	C₂×#41	1	24	yes	—
76	C₂×C₄×C₁₃	C₂×#41	1	12	yes	—
77	C₂×C₄×Q₈	C₂²×C₁₃	1	12	yes	—
78	C₂×#117	C₂²×C₁₃	1	6	yes	—
79	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
80	#400	C₂²×C₁₃	1	12	yes	—
81	#399	C₂²×C₁₃	1	4	yes	—
82	#398	C₂²×C₁₃	1	24	yes	—
83	#396	C₂²×C₁₃	1	8	yes	—
84	#395	C₂²×C₁₃	1	12	yes	—
85	#393	C₂²×C₁₃	1	4	yes	—
86	C₄×C₄⋊C₄	C₂²×C₁₃	1	12	yes	—
87	C₄×C₄⋊C₄	C₂²×C₁₃	1	24	yes	—
88	C₄×C₄⋊C₄	C₂²×C₁₃	1	12	yes	—
89	C₄×C₂²⋊C₄	C₂²×C₁₃	1	12	yes	—
90	#376	C₂²×C₁₃	1	3	yes	—
91	#376	C₂²×C₁₃	1	3	yes	—
92	C₄³	C₂²×C₁₃	1	6	yes	—
93	C₂²×C₁₃	—	2	6	no	—
94	C₂²×C₁₃	—	4	4	no	—
95	C₂²×C₁₃	C₂³×Q₈	1	1	yes	characteristic
96	C₂²×C₁₃	C₂²×#41	1	6	yes	—
97	C₄×C₁₃	—	2	6	no	—
98	C₄×C₁₃	—	2	24	no	—
99	C₄×C₁₃	—	4	12	no	—
100	C₄×C₁₃	#533	1	12	yes	—
101	C₂²×Q₈	C₂³×C₁₃	1	4	yes	—
102	C₂³×C₄	C₂³×C₁₃	1	3	yes	—
103	C₄×Q₈	—	2	48	no	—
104	#117	—	2	24	no	—
105	C₂×C₄⋊C₄	C₂³×C₁₃	1	12	yes	—
106	C₂×C₄⋊C₄	C₂³×C₁₃	1	24	yes	—
107	C₂×C₄⋊C₄	C₂³×C₁₃	1	12	yes	—
108	C₂×C₂²⋊C₄	C₂³×C₁₃	1	12	yes	—
109	C₂×C₄²	Q₈×C₁₃	1	8	yes	complemented
110	C₂×C₄²	C₂³×C₁₃	1	6	yes	—
111	C₂×C₄²	C₂³×C₁₃	1	24	yes	—
112	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
113	C₂×C₄²	C₂³×C₁₃	1	3	yes	—
114	C₂×C₄²	C₂³×C₁₃	1	6	yes	—
115	#95	C₂³×C₁₃	1	12	yes	—
116	#95	C₂³×C₁₃	1	12	yes	—
117	#95	C₂³×C₁₃	1	12	yes	—
118	#95	C₂³×C₁₃	1	4	yes	—
119	#95	C₂³×C₁₃	1	8	yes	—
120	C₂×C₁₃	—	4	2	no	—
121	C₂×C₁₃	C₂×#533	1	3	yes	—
122	C₂×C₁₃	#3444	1	4	yes	—
123	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
124	C₂×Q₈	—	2	24	no	—
125	C₂²×C₄	—	2	12	no	—
126	C₂²×C₄	C₂×Q₈×C₁₃	1	12	yes	—
127	C₂²×C₄	C₂⁴×C₁₃	1	12	yes	—
128	C₂²×C₄	C₂⁴×C₁₃	1	3	yes	—
129	C₂²×C₄	C₂⁴×C₁₃	1	12	yes	—
130	C₂²×C₄	C₂⁴×C₁₃	1	3	yes	—
131	C₄⋊C₄	—	2	24	no	—
132	C₄⋊C₄	—	2	48	no	—
133	C₄⋊C₄	—	2	24	no	—
134	C₂²⋊C₄	—	2	24	no	—
135	C₄²	—	2	12	no	—
136	C₄²	—	2	48	no	—
137	C₄²	C₂×Q₈×C₁₃	1	12	yes	—
138	C₄²	C₂×Q₈×C₁₃	1	4	yes	—
139	C₄²	C₁₃×#41	1	24	yes	—
140	C₁₃	#34552	1	1	yes	characteristic, direct product factor, Sylow
141	C₂³	—	2	6	no	—
142	C₂³	C₂²×Q₈×C₁₃	1	2	yes	—
143	C₂³	C₂⁵×C₁₃	1	1	yes	characteristic
144	Q₈	—	2	32	no	—
145	C₂×C₄	—	2	24	no	—
146	C₂×C₄	—	2	6	no	—
147	C₂×C₄	—	2	24	no	—
148	C₂×C₄	—	2	12	no	—
149	C₂×C₄	—	2	24	no	—
150	C₂×C₄	C₂²×Q₈×C₁₃	1	6	yes	—
151	C₂×C₄	C₂²×Q₈×C₁₃	1	6	yes	—
152	C₂×C₄	C₂×C₁₃×#41	1	24	yes	—
153	C₂×C₄	C₂×C₁₃×#41	1	12	yes	—
154	C₂²	—	2	6	no	—
155	C₂²	—	4	4	no	—
156	C₂²	C₂³×Q₈×C₁₃	1	1	yes	characteristic
157	C₂²	C₂²×C₁₃×#41	1	6	yes	—
158	C₄	—	2	6	no	—
159	C₄	—	2	24	no	—
160	C₄	—	4	12	no	—
161	C₄	C₁₃×#533	1	12	yes	—
162	C₂	—	4	2	no	—
163	C₂	C₂×C₁₃×#533	1	3	yes	—
164	C₂	C₁₃×#3444	1	4	yes	—

	subgroup	G/H
center	C₂×C₄²×C₁₃	C₂³
commutator, Frattini, cosocle	C₂³	C₂⁵×C₁₃
socle	C₂³×C₁₃	C₂⁵
prime radical	C₂⁴×C₁₃	C₂⁴
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂×C₄²×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₃×#2402	C₂	semidirect
2. C₁₃×#2399	C₂	semidirect
4. C₄²×Q₈×C₁₃	C₂	semidirect
30. C₂×C₄²×C₁₃	Q₈	semidirect
41. #34552	C₁₃	direct (N × H)
59. #2402	C₂×C₁₃	semidirect
60. #2399	C₂×C₁₃	semidirect
62. C₄²×Q₈	C₂×C₁₃	semidirect
109. C₂×C₄²	Q₈×C₁₃	semidirect
140. C₁₃	#34552	direct (N × H)

Maximal subgroups

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

subgroup	index
C₁₃×#2402	2
C₁₃×#2399	2
C₁₃×#2396	2
C₄²×Q₈×C₁₃	2
C₄×C₁₃×#117	2
#34552	13

Subgroups — C13×#34552 #15720891

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#34552 #15720891