Subgroups — C₁₃×#2923 #13111981

Order 1664.

384 conjugacy classes of subgroups.

The subgroup lattice has 156 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×C₁₃×#41	C₂	1	1	yes	maximal, characteristic
2	C₁₃×#433	C₂	1	4	yes	maximal, complemented
3	C₁₃×#432	C₂	1	4	yes	maximal, complemented
4	C₁₃×#424	C₂	1	2	yes	maximal, complemented
5	C₁₃×#408	C₂	1	2	yes	maximal
6	C₄×C₁₃×M₁₆	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₁₃×#97	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₁₃×#41	C₂²	1	1	yes	characteristic
9	C₂×C₁₃×M₁₆	C₂²	1	2	yes	—
10	C₂²×C₈×C₁₃	C₂²	1	2	yes	—
11	C₄×Q₈×C₁₃	C₄	1	2	yes	—
12	C₄×D₄×C₁₃	C₄	1	4	yes	—
13	C₄×D₄×C₁₃	C₄	1	2	yes	—
14	C₁₃×#117	C₂²	1	1	yes	characteristic
15	C₁₃×#117	C₂²	1	2	yes	—
16	C₂×C₄²×C₁₃	C₂²	1	1	yes	characteristic
17	C₂×C₄²×C₁₃	C₂²	1	2	yes	—
18	C₁₃×C₄⋊C₈	C₂²	1	8	yes	—
19	C₁₃×C₂²⋊C₈	C₂²	1	8	yes	—
20	C₁₃×#97	C₂²	1	2	yes	—
21	C₁₃×#97	C₂²	1	2	yes	—
22	C₁₃×#97	C₂²	1	2	yes	—
23	C₄×C₈×C₁₃	C₂²	1	2	yes	—
24	C₁₃×#41	—	2	4	no	—
25	C₂×Q₈×C₁₃	C₂×C₄	1	1	yes	characteristic
26	C₂×D₄×C₁₃	C₂×C₄	1	2	yes	—
27	C₂×D₄×C₁₃	C₂×C₄	1	1	yes	characteristic
28	C₂²×C₄×C₁₃	C₂×C₄	1	4	yes	—
29	C₂²×C₄×C₁₃	C₂×C₄	1	2	yes	—
30	C₂²×C₄×C₁₃	C₂³	1	2	yes	—
31	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
32	C₁₃×M₁₆	—	2	4	no	—
33	C₂×C₈×C₁₃	—	2	4	no	—
34	C₂×C₈×C₁₃	C₂³	1	4	yes	—
35	C₂×C₈×C₁₃	C₂³	1	4	yes	—
36	C₁₃×C₄⋊C₄	C₂×C₄	1	4	yes	—
37	C₁₃×C₄⋊C₄	C₂×C₄	1	2	yes	—
38	C₁₃×C₂²⋊C₄	C₂×C₄	1	4	yes	—
39	C₁₃×C₂²⋊C₄	C₂×C₄	1	2	yes	—
40	C₄²×C₁₃	C₂×C₄	1	4	yes	—
41	C₄²×C₁₃	C₂×C₄	1	2	yes	—
42	C₄²×C₁₃	C₂³	1	1	yes	characteristic
43	C₄²×C₁₃	C₂³	1	1	yes	characteristic
44	C₄²×C₁₃	C₂³	1	2	yes	—
45	#2923	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
46	C₂³×C₁₃	C₂²×C₄	1	2	yes	—
47	C₂³×C₁₃	C₂²×C₄	1	1	yes	characteristic
48	Q₈×C₁₃	—	2	2	no	—
49	D₄×C₁₃	—	2	4	no	—
50	D₄×C₁₃	—	2	2	no	—
51	C₂×C₄×C₁₃	—	2	4	no	—
52	C₂×C₄×C₁₃	—	4	2	no	—
53	C₂×C₄×C₁₃	—	4	4	no	—
54	C₂×C₄×C₁₃	C₂²×C₄	1	2	yes	—
55	C₂×C₄×C₁₃	C₂²×C₄	1	2	yes	—
56	C₂×C₄×C₁₃	C₂²×C₄	1	2	yes	—
57	C₂×C₄×C₁₃	C₂²×C₄	1	4	yes	—
58	C₂×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
59	C₂×C₄×C₁₃	#41	1	4	yes	—
60	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
61	C₈×C₁₃	—	2	4	no	—
62	C₈×C₁₃	—	2	4	no	—
63	C₄×#41	C₂×C₁₃	1	1	yes	characteristic
64	#433	C₂×C₁₃	1	4	yes	complemented
65	#432	C₂×C₁₃	1	4	yes	complemented
66	#424	C₂×C₁₃	1	2	yes	complemented
67	#408	C₂×C₁₃	1	2	yes	—
68	C₄×M₁₆	C₂×C₁₃	1	1	yes	characteristic, complemented
69	C₂×#97	C₂×C₁₃	1	1	yes	characteristic, complemented
70	C₂²×C₁₃	—	2	2	no	—
71	C₂²×C₁₃	—	2	2	no	—
72	C₂²×C₁₃	—	2	4	no	—
73	C₂²×C₁₃	#117	1	2	yes	—
74	C₂²×C₁₃	C₂³×C₄	1	1	yes	characteristic
75	C₄×C₁₃	—	2	2	no	—
76	C₄×C₁₃	—	2	2	no	—
77	C₄×C₁₃	—	2	2	no	—
78	C₄×C₁₃	—	2	4	no	—
79	C₄×C₁₃	#117	1	2	yes	—
80	C₄×C₁₃	C₂×#41	1	2	yes	—
81	C₂×#41	C₂²×C₁₃	1	1	yes	characteristic
82	C₂×M₁₆	C₂²×C₁₃	1	2	yes	—
83	C₂²×C₈	C₂²×C₁₃	1	2	yes	—
84	C₄×Q₈	C₄×C₁₃	1	2	yes	—
85	C₄×D₄	C₄×C₁₃	1	4	yes	—
86	C₄×D₄	C₄×C₁₃	1	2	yes	—
87	#117	C₂²×C₁₃	1	1	yes	characteristic
88	#117	C₂²×C₁₃	1	2	yes	—
89	C₂×C₄²	C₂²×C₁₃	1	1	yes	characteristic
90	C₂×C₄²	C₂²×C₁₃	1	2	yes	—
91	C₄⋊C₈	C₂²×C₁₃	1	8	yes	—
92	C₂²⋊C₈	C₂²×C₁₃	1	8	yes	—
93	#97	C₂²×C₁₃	1	2	yes	—
94	#97	C₂²×C₁₃	1	2	yes	—
95	#97	C₂²×C₁₃	1	2	yes	—
96	C₄×C₈	C₂²×C₁₃	1	2	yes	—
97	C₂×C₁₃	—	2	2	no	—
98	C₂×C₁₃	—	4	2	no	—
99	C₂×C₁₃	C₂×#117	1	1	yes	characteristic
100	C₂×C₁₃	#568	1	2	yes	—
101	#41	—	2	4	no	—
102	C₂×Q₈	C₂×C₄×C₁₃	1	1	yes	characteristic
103	C₂×D₄	C₂×C₄×C₁₃	1	2	yes	—
104	C₂×D₄	C₂×C₄×C₁₃	1	1	yes	characteristic
105	C₂²×C₄	C₂×C₄×C₁₃	1	4	yes	—
106	C₂²×C₄	C₂×C₄×C₁₃	1	2	yes	—
107	C₂²×C₄	C₂³×C₁₃	1	2	yes	—
108	C₂²×C₄	C₂³×C₁₃	1	1	yes	characteristic
109	M₁₆	—	2	4	no	—
110	C₂×C₈	—	2	4	no	—
111	C₂×C₈	C₂³×C₁₃	1	4	yes	—
112	C₂×C₈	C₂³×C₁₃	1	4	yes	—
113	C₄⋊C₄	C₂×C₄×C₁₃	1	4	yes	—
114	C₄⋊C₄	C₂×C₄×C₁₃	1	2	yes	—
115	C₂²⋊C₄	C₂×C₄×C₁₃	1	4	yes	—
116	C₂²⋊C₄	C₂×C₄×C₁₃	1	2	yes	—
117	C₄²	C₂×C₄×C₁₃	1	4	yes	—
118	C₄²	C₂×C₄×C₁₃	1	2	yes	—
119	C₄²	C₂³×C₁₃	1	1	yes	characteristic
120	C₄²	C₂³×C₁₃	1	1	yes	characteristic
121	C₄²	C₂³×C₁₃	1	2	yes	—
122	C₁₃	#2923	1	1	yes	characteristic, direct product factor, Sylow
123	C₂³	C₂²×C₄×C₁₃	1	2	yes	—
124	C₂³	C₂²×C₄×C₁₃	1	1	yes	characteristic
125	Q₈	—	2	2	no	—
126	D₄	—	2	4	no	—
127	D₄	—	2	2	no	—
128	C₂×C₄	—	2	4	no	—
129	C₂×C₄	—	4	2	no	—
130	C₂×C₄	—	4	4	no	—
131	C₂×C₄	C₂²×C₄×C₁₃	1	2	yes	—
132	C₂×C₄	C₂²×C₄×C₁₃	1	2	yes	—
133	C₂×C₄	C₂²×C₄×C₁₃	1	2	yes	—
134	C₂×C₄	C₂²×C₄×C₁₃	1	4	yes	—
135	C₂×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
136	C₂×C₄	C₁₃×#41	1	4	yes	—
137	C₂×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
138	C₈	—	2	4	no	—
139	C₈	—	2	4	no	—
140	C₂²	—	2	2	no	—
141	C₂²	—	2	2	no	—
142	C₂²	—	2	4	no	—
143	C₂²	C₁₃×#117	1	2	yes	—
144	C₂²	C₂³×C₄×C₁₃	1	1	yes	characteristic
145	C₄	—	2	2	no	—
146	C₄	—	2	2	no	—
147	C₄	—	2	2	no	—
148	C₄	—	2	4	no	—
149	C₄	C₁₃×#117	1	2	yes	—
150	C₄	C₂×C₁₃×#41	1	2	yes	—
151	C₂	—	2	2	no	—
152	C₂	—	4	2	no	—
153	C₂	C₂×C₁₃×#117	1	1	yes	characteristic
154	C₂	C₁₃×#568	1	2	yes	—

	subgroup	G/H
center	C₂×C₄×C₁₃	C₂⁴
commutator	C₂²	C₂³×C₄×C₁₃
Frattini, cosocle	C₂×C₄	C₂⁴×C₁₃
socle	C₂²×C₁₃	C₂³×C₄
prime radical	C₂×C₁₃×#41	C₂²
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₃×#433	C₂	semidirect
3. C₁₃×#432	C₂	semidirect
4. C₁₃×#424	C₂	semidirect
6. C₄×C₁₃×M₁₆	C₂	semidirect
7. C₂×C₁₃×#97	C₂	semidirect
45. #2923	C₁₃	direct (N × H)
64. #433	C₂×C₁₃	semidirect
65. #432	C₂×C₁₃	semidirect
66. #424	C₂×C₁₃	semidirect
68. C₄×M₁₆	C₂×C₁₃	semidirect
69. C₂×#97	C₂×C₁₃	semidirect
122. C₁₃	#2923	direct (N × H)

Maximal subgroups

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

subgroup	index
C₄×C₁₃×#41	2
C₁₃×#433	2
C₁₃×#432	2
C₁₃×#424	2
C₁₃×#408	2
C₄×C₁₃×M₁₆	2
C₂×C₁₃×#97	2
#2923	13

Subgroups — C13×#2923 #13111981

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#2923 #13111981