Subgroups — C₂×C₁₃×#2247 #15720049

Order 3328.

814 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	C₂²×C₁₃×Q₃₂	C₂	1	4	yes	maximal
2	C₂×C₁₃×#494	C₂	1	2	yes	maximal
3	C₁₃×#2247	C₂	1	8	yes	maximal, direct product factor
4	C₂×C₄×C₁₃×C₁₆	C₂	1	1	yes	maximal, characteristic
5	C₂²×C₁₃×Q₁₆	—	2	2	no	—
6	C₂²×C₁₃×Q₁₆	C₂²	1	4	yes	—
7	C₂×C₁₃×C₄⋊Q₈	—	2	2	no	—
8	C₂×C₁₃×Q₃₂	—	2	16	no	—
9	C₂×C₁₃×Q₃₂	C₂²	1	16	yes	—
10	C₂²×C₁₃×C₁₆	C₂²	1	2	yes	—
11	C₁₃×#494	—	2	4	no	—
12	C₁₃×#494	C₂²	1	8	yes	—
13	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
14	C₄×C₁₃×C₁₆	C₂²	1	4	yes	—
15	C₂²×Q₈×C₁₃	—	2	4	no	—
16	C₂×C₁₃×Q₁₆	—	2	16	no	—
17	C₂×C₁₃×Q₁₆	—	2	4	no	—
18	C₂×C₁₃×Q₁₆	—	2	8	no	—
19	C₂×C₁₃×Q₁₆	—	4	8	no	—
20	C₂×C₁₃×Q₁₆	C₂³	1	8	yes	—
21	C₂²×C₈×C₁₃	D₄	1	1	yes	characteristic
22	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
23	C₁₃×C₄⋊Q₈	—	2	8	no	—
24	C₁₃×C₄⋊Q₈	—	4	4	no	—
25	C₂×C₁₃×C₄⋊C₄	—	4	4	no	—
26	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
27	C₁₃×Q₃₂	—	2	32	no	—
28	C₂×C₁₃×C₁₆	D₄	1	8	yes	—
29	C₂×C₁₃×C₁₆	C₂³	1	4	yes	—
30	C₄×C₈×C₁₃	D₄	1	2	yes	—
31	C₄×C₈×C₁₃	C₂³	1	2	yes	—
32	C₂×#2247	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
33	C₂×Q₈×C₁₃	—	2	8	no	—
34	C₂×Q₈×C₁₃	—	4	4	no	—
35	C₂×Q₈×C₁₃	—	4	8	no	—
36	C₂×Q₈×C₁₃	—	4	8	no	—
37	C₂²×C₄×C₁₃	—	4	4	no	—
38	C₂²×C₄×C₁₃	D₈	1	2	yes	—
39	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
40	C₁₃×Q₁₆	—	2	16	no	—
41	C₁₃×Q₁₆	—	4	8	no	—
42	C₁₃×Q₁₆	—	4	16	no	—
43	C₂×C₈×C₁₃	D₈	1	4	yes	—
44	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
45	C₂×C₈×C₁₃	C₂×D₄	1	4	yes	—
46	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
47	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
48	C₁₃×C₄⋊C₄	—	4	16	no	—
49	C₄²×C₁₃	D₈	1	2	yes	—
50	C₄²×C₁₃	C₂×D₄	1	2	yes	—
51	C₁₃×C₁₆	C₂×D₄	1	8	yes	—
52	C₂²×Q₃₂	C₂×C₁₃	1	4	yes	—
53	C₂×#494	C₂×C₁₃	1	2	yes	—
54	#2247	C₂×C₁₃	1	8	yes	direct product factor
55	C₂×C₄×C₁₆	C₂×C₁₃	1	1	yes	characteristic
56	C₂³×C₁₃	C₂×D₈	1	1	yes	characteristic
57	Q₈×C₁₃	—	4	8	no	—
58	Q₈×C₁₃	—	4	8	no	—
59	Q₈×C₁₃	—	8	8	no	—
60	C₂×C₄×C₁₃	—	4	8	no	—
61	C₂×C₄×C₁₃	—	8	8	no	—
62	C₂×C₄×C₁₃	Q₃₂	1	8	yes	complemented
63	C₂×C₄×C₁₃	#127	1	2	yes	—
64	C₂×C₄×C₁₃	C₂×D₈	1	2	yes	—
65	C₂×C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
66	C₂×C₄×C₁₃	C₂×D₈	1	4	yes	—
67	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
68	C₈×C₁₃	#127	1	2	yes	—
69	C₈×C₁₃	C₂×D₈	1	4	yes	—
70	C₈×C₁₃	C₂²×D₄	1	2	yes	—
71	C₂²×Q₁₆	—	2	2	no	—
72	C₂²×Q₁₆	C₂²×C₁₃	1	4	yes	—
73	C₂×C₄⋊Q₈	—	2	2	no	—
74	C₂×Q₃₂	—	2	16	no	—
75	C₂×Q₃₂	C₂²×C₁₃	1	16	yes	—
76	C₂²×C₁₆	C₂²×C₁₃	1	2	yes	—
77	#494	—	2	4	no	—
78	#494	C₂²×C₁₃	1	8	yes	—
79	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
80	C₄×C₁₆	C₂²×C₁₃	1	4	yes	—
81	C₂²×C₁₃	#493	1	2	yes	—
82	C₂²×C₁₃	C₂×Q₃₂	1	4	yes	—
83	C₂²×C₁₃	C₂²×D₈	1	1	yes	characteristic
84	C₄×C₁₃	—	8	8	no	—
85	C₄×C₁₃	#493	1	2	yes	—
86	C₄×C₁₃	C₂×Q₃₂	1	8	yes	complemented
87	C₄×C₁₃	C₂×#127	1	1	yes	characteristic
88	C₄×C₁₃	C₂²×D₈	1	1	yes	characteristic
89	C₂²×Q₈	—	2	4	no	—
90	C₂×Q₁₆	—	2	16	no	—
91	C₂×Q₁₆	—	2	8	no	—
92	C₂×Q₁₆	—	2	4	no	—
93	C₂×Q₁₆	—	4	8	no	—
94	C₂×Q₁₆	C₂³×C₁₃	1	8	yes	—
95	C₂²×C₈	D₄×C₁₃	1	1	yes	characteristic
96	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
97	C₄⋊Q₈	—	2	8	no	—
98	C₄⋊Q₈	—	4	4	no	—
99	C₂×C₄⋊C₄	—	4	4	no	—
100	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
101	Q₃₂	—	2	32	no	—
102	C₂×C₁₆	D₄×C₁₃	1	8	yes	—
103	C₂×C₁₆	C₂³×C₁₃	1	4	yes	—
104	C₄×C₈	D₄×C₁₃	1	2	yes	—
105	C₄×C₈	C₂³×C₁₃	1	2	yes	—
106	C₂×C₁₃	#2247	1	4	yes	direct product factor
107	C₂×C₁₃	C₂×#493	1	1	yes	characteristic
108	C₂×C₁₃	C₂²×Q₃₂	1	2	yes	—
109	C₂×Q₈	—	2	8	no	—
110	C₂×Q₈	—	4	4	no	—
111	C₂×Q₈	—	4	8	no	—
112	C₂×Q₈	—	4	8	no	—
113	C₂²×C₄	—	4	4	no	—
114	C₂²×C₄	C₁₃×D₈	1	2	yes	—
115	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
116	Q₁₆	—	2	16	no	—
117	Q₁₆	—	4	8	no	—
118	Q₁₆	—	4	16	no	—
119	C₂×C₈	C₁₃×D₈	1	4	yes	—
120	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
121	C₂×C₈	C₂×D₄×C₁₃	1	4	yes	—
122	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
123	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
124	C₄⋊C₄	—	4	16	no	—
125	C₄²	C₁₃×D₈	1	2	yes	—
126	C₄²	C₂×D₄×C₁₃	1	2	yes	—
127	C₁₆	C₂×D₄×C₁₃	1	8	yes	—
128	C₁₃	C₂×#2247	1	1	yes	characteristic, direct product factor, Sylow
129	C₂³	C₂×C₁₃×D₈	1	1	yes	characteristic
130	Q₈	—	4	8	no	—
131	Q₈	—	4	8	no	—
132	Q₈	—	8	8	no	—
133	C₂×C₄	—	4	8	no	—
134	C₂×C₄	—	8	8	no	—
135	C₂×C₄	C₁₃×Q₃₂	1	8	yes	complemented
136	C₂×C₄	C₁₃×#127	1	2	yes	—
137	C₂×C₄	C₂×C₁₃×D₈	1	1	yes	characteristic
138	C₂×C₄	C₂×C₁₃×D₈	1	2	yes	—
139	C₂×C₄	C₂×C₁₃×D₈	1	4	yes	—
140	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
141	C₈	C₁₃×#127	1	2	yes	—
142	C₈	C₂×C₁₃×D₈	1	4	yes	—
143	C₈	C₂²×D₄×C₁₃	1	2	yes	—
144	C₂²	C₁₃×#493	1	2	yes	—
145	C₂²	C₂×C₁₃×Q₃₂	1	4	yes	—
146	C₂²	C₂²×C₁₃×D₈	1	1	yes	characteristic
147	C₄	—	8	8	no	—
148	C₄	C₁₃×#493	1	2	yes	—
149	C₄	C₂×C₁₃×Q₃₂	1	8	yes	complemented
150	C₄	C₂×C₁₃×#127	1	1	yes	characteristic
151	C₄	C₂²×C₁₃×D₈	1	1	yes	characteristic
152	C₂	C₁₃×#2247	1	4	yes	direct product factor
153	C₂	C₂×C₁₃×#493	1	1	yes	characteristic
154	C₂	C₂²×C₁₃×Q₃₂	1	2	yes	—

	subgroup	G/H
center, socle, prime radical	C₂³×C₁₃	C₂×D₈
commutator, Frattini, cosocle	C₂×C₈	C₂⁴×C₁₃
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ C₂×C₄²×C₁₃ ◁ C₂×C₄×C₈×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₁₃×#2247	C₂	direct (N × H)
32. C₂×#2247	C₁₃	direct (N × H)
54. #2247	C₂×C₁₃	direct (N × H)
62. C₂×C₄×C₁₃	Q₃₂	semidirect
86. C₄×C₁₃	C₂×Q₃₂	semidirect
106. C₂×C₁₃	#2247	direct (N × H)
128. C₁₃	C₂×#2247	direct (N × H)
135. C₂×C₄	C₁₃×Q₃₂	semidirect
149. C₄	C₂×C₁₃×Q₃₂	semidirect
152. C₂	C₁₃×#2247	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₁₃×Q₃₂	2
C₂×C₁₃×#494	2
C₁₃×#2247	2
C₂×C₄×C₁₃×C₁₆	2
C₂×#2247	13

Subgroups — C2×C13×#2247 #15720049

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₃×#2247 #15720049