Subgroups — C₂×C₁₃×#3556 #15749099

Order 3328.

6338 conjugacy classes of subgroups.

The subgroup lattice has 164 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3556	C₂	1	32	yes	maximal, direct product factor
2	C₂×C₁₃×#564	C₂	1	4	yes	maximal, complemented
3	C₂×C₁₃×#557	C₂	1	12	yes	maximal, complemented
4	C₂×C₁₃×#541	C₂	1	12	yes	maximal
5	C₂×C₁₃×#533	C₂	1	3	yes	maximal
6	C₁₃×#564	C₂²	1	64	yes	complemented
7	C₁₃×#557	C₂²	1	192	yes	complemented
8	C₁₃×#541	C₂²	1	192	yes	—
9	C₁₃×#533	C₂²	1	48	yes	—
10	C₂×C₁₃×C₄⋊Q₈	C₂²	1	6	yes	—
11	C₂×C₁₃×C₄⋊Q₈	C₂²	1	12	yes	—
12	C₂×C₁₃×#126	C₂²	1	16	yes	—
13	C₂×C₁₃×#125	C₂²	1	6	yes	—
14	C₂×C₁₃×#125	C₂²	1	48	yes	—
15	C₂×C₁₃×#125	C₂²	1	12	yes	—
16	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	12	yes	—
17	C₂×C₄×Q₈×C₁₃	C₂²	1	12	yes	—
18	C₂×C₄×Q₈×C₁₃	C₂²	1	24	yes	—
19	C₂×C₁₃×#117	C₂²	1	6	yes	—
20	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
21	C₂²×Q₈×C₁₃	C₂³	1	12	yes	—
22	C₂³×C₄×C₁₃	C₂³	1	3	yes	—
23	C₁₃×C₄⋊Q₈	C₂³	1	48	yes	—
24	C₁₃×C₄⋊Q₈	C₂³	1	96	yes	—
25	C₁₃×#126	C₂³	1	128	yes	—
26	C₁₃×#125	C₂³	1	48	yes	—
27	C₁₃×#125	C₂³	1	96	yes	—
28	C₁₃×#125	C₂³	1	384	yes	—
29	C₁₃×C₂²⋊Q₈	C₂³	1	96	yes	—
30	C₄×Q₈×C₁₃	C₂³	1	96	yes	—
31	C₄×Q₈×C₁₃	C₂³	1	192	yes	—
32	C₁₃×#117	C₂³	1	48	yes	—
33	C₂×C₁₃×C₄⋊C₄	C₂³	1	12	yes	—
34	C₂×C₁₃×C₄⋊C₄	C₂³	1	12	yes	—
35	C₂×C₁₃×C₄⋊C₄	C₂³	1	24	yes	—
36	C₂×C₁₃×C₄⋊C₄	C₂³	1	48	yes	—
37	C₂×C₁₃×C₂²⋊C₄	C₂³	1	12	yes	—
38	C₂×C₄²×C₁₃	C₂³	1	3	yes	—
39	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
40	C₂×C₄²×C₁₃	C₂³	1	8	yes	—
41	C₂×C₄²×C₁₃	C₂³	1	12	yes	—
42	C₂×C₄²×C₁₃	C₂³	1	16	yes	—
43	C₂×#3556	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
44	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
45	C₂×Q₈×C₁₃	—	2	48	no	—
46	C₂×Q₈×C₁₃	C₂⁴	1	48	yes	—
47	C₂²×C₄×C₁₃	—	2	12	no	—
48	C₂²×C₄×C₁₃	C₂⁴	1	12	yes	—
49	C₂²×C₄×C₁₃	C₂⁴	1	24	yes	—
50	C₂²×C₄×C₁₃	C₂⁴	1	3	yes	—
51	C₂²×C₄×C₁₃	C₂⁴	1	3	yes	—
52	C₁₃×C₄⋊C₄	C₂⁴	1	48	yes	—
53	C₁₃×C₄⋊C₄	C₂⁴	1	48	yes	—
54	C₁₃×C₄⋊C₄	C₂⁴	1	96	yes	—
55	C₁₃×C₄⋊C₄	C₂⁴	1	192	yes	—
56	C₁₃×C₂²⋊C₄	C₂⁴	1	48	yes	—
57	C₄²×C₁₃	C₂⁴	1	12	yes	—
58	C₄²×C₁₃	C₂⁴	1	4	yes	—
59	C₄²×C₁₃	C₂⁴	1	48	yes	—
60	C₄²×C₁₃	C₂⁴	1	64	yes	—
61	#3556	C₂×C₁₃	1	32	yes	direct product factor
62	C₂×#564	C₂×C₁₃	1	4	yes	complemented
63	C₂×#557	C₂×C₁₃	1	12	yes	complemented
64	C₂×#541	C₂×C₁₃	1	12	yes	—
65	C₂×#533	C₂×C₁₃	1	3	yes	—
66	C₂³×C₁₃	—	2	6	no	—
67	C₂³×C₁₃	C₂⁵	1	2	yes	—
68	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
69	Q₈×C₁₃	—	2	96	no	—
70	C₂×C₄×C₁₃	—	2	6	no	—
71	C₂×C₄×C₁₃	—	2	48	no	—
72	C₂×C₄×C₁₃	—	2	24	no	—
73	C₂×C₄×C₁₃	2₋¹⁺⁴	1	12	yes	—
74	C₂×C₄×C₁₃	C₂⁵	1	48	yes	—
75	C₂×C₄×C₁₃	C₂⁵	1	6	yes	—
76	C₂×C₄×C₁₃	C₂⁵	1	6	yes	—
77	#564	C₂²×C₁₃	1	64	yes	complemented
78	#557	C₂²×C₁₃	1	192	yes	complemented
79	#541	C₂²×C₁₃	1	192	yes	—
80	#533	C₂²×C₁₃	1	48	yes	—
81	C₂×C₄⋊Q₈	C₂²×C₁₃	1	6	yes	—
82	C₂×C₄⋊Q₈	C₂²×C₁₃	1	12	yes	—
83	C₂×#126	C₂²×C₁₃	1	16	yes	—
84	C₂×#125	C₂²×C₁₃	1	6	yes	—
85	C₂×#125	C₂²×C₁₃	1	12	yes	—
86	C₂×#125	C₂²×C₁₃	1	48	yes	—
87	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	12	yes	—
88	C₂×C₄×Q₈	C₂²×C₁₃	1	12	yes	—
89	C₂×C₄×Q₈	C₂²×C₁₃	1	24	yes	—
90	C₂×#117	C₂²×C₁₃	1	6	yes	—
91	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
92	C₂²×C₁₃	—	2	6	no	—
93	C₂²×C₁₃	—	4	4	no	—
94	C₂²×C₁₃	C₂×2₋¹⁺⁴	1	6	yes	—
95	C₂²×C₁₃	C₂⁶	1	1	yes	characteristic
96	C₄×C₁₃	—	2	6	no	—
97	C₄×C₁₃	—	2	48	no	—
98	C₄×C₁₃	C₂×2₋¹⁺⁴	1	12	yes	—
99	C₂²×Q₈	C₂³×C₁₃	1	12	yes	—
100	C₂³×C₄	C₂³×C₁₃	1	3	yes	—
101	C₄⋊Q₈	C₂³×C₁₃	1	48	yes	—
102	C₄⋊Q₈	C₂³×C₁₃	1	96	yes	—
103	#126	C₂³×C₁₃	1	128	yes	—
104	#125	C₂³×C₁₃	1	48	yes	—
105	#125	C₂³×C₁₃	1	96	yes	—
106	#125	C₂³×C₁₃	1	384	yes	—
107	C₂²⋊Q₈	C₂³×C₁₃	1	96	yes	—
108	C₄×Q₈	C₂³×C₁₃	1	96	yes	—
109	C₄×Q₈	C₂³×C₁₃	1	192	yes	—
110	#117	C₂³×C₁₃	1	48	yes	—
111	C₂×C₄⋊C₄	C₂³×C₁₃	1	12	yes	—
112	C₂×C₄⋊C₄	C₂³×C₁₃	1	12	yes	—
113	C₂×C₄⋊C₄	C₂³×C₁₃	1	24	yes	—
114	C₂×C₄⋊C₄	C₂³×C₁₃	1	48	yes	—
115	C₂×C₂²⋊C₄	C₂³×C₁₃	1	12	yes	—
116	C₂×C₄²	C₂³×C₁₃	1	12	yes	—
117	C₂×C₄²	C₂³×C₁₃	1	3	yes	—
118	C₂×C₄²	C₂³×C₁₃	1	16	yes	—
119	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
120	C₂×C₄²	C₂³×C₁₃	1	8	yes	—
121	C₂×C₁₃	—	4	2	no	—
122	C₂×C₁₃	#3556	1	4	yes	direct product factor
123	C₂×C₁₃	C₂²×2₋¹⁺⁴	1	3	yes	—
124	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
125	C₂×Q₈	—	2	48	no	—
126	C₂×Q₈	C₂⁴×C₁₃	1	48	yes	—
127	C₂²×C₄	—	2	12	no	—
128	C₂²×C₄	C₂⁴×C₁₃	1	24	yes	—
129	C₂²×C₄	C₂⁴×C₁₃	1	3	yes	—
130	C₂²×C₄	C₂⁴×C₁₃	1	12	yes	—
131	C₂²×C₄	C₂⁴×C₁₃	1	3	yes	—
132	C₄⋊C₄	C₂⁴×C₁₃	1	48	yes	—
133	C₄⋊C₄	C₂⁴×C₁₃	1	48	yes	—
134	C₄⋊C₄	C₂⁴×C₁₃	1	96	yes	—
135	C₄⋊C₄	C₂⁴×C₁₃	1	192	yes	—
136	C₂²⋊C₄	C₂⁴×C₁₃	1	48	yes	—
137	C₄²	C₂⁴×C₁₃	1	12	yes	—
138	C₄²	C₂⁴×C₁₃	1	4	yes	—
139	C₄²	C₂⁴×C₁₃	1	48	yes	—
140	C₄²	C₂⁴×C₁₃	1	64	yes	—
141	C₁₃	C₂×#3556	1	1	yes	characteristic, direct product factor, Sylow
142	C₂³	—	2	6	no	—
143	C₂³	C₂⁵×C₁₃	1	2	yes	—
144	C₂³	C₂⁵×C₁₃	1	1	yes	characteristic
145	Q₈	—	2	96	no	—
146	C₂×C₄	—	2	6	no	—
147	C₂×C₄	—	2	48	no	—
148	C₂×C₄	—	2	24	no	—
149	C₂×C₄	C₁₃×2₋¹⁺⁴	1	12	yes	—
150	C₂×C₄	C₂⁵×C₁₃	1	48	yes	—
151	C₂×C₄	C₂⁵×C₁₃	1	6	yes	—
152	C₂×C₄	C₂⁵×C₁₃	1	6	yes	—
153	C₂²	—	2	6	no	—
154	C₂²	—	4	4	no	—
155	C₂²	C₂×C₁₃×2₋¹⁺⁴	1	6	yes	—
156	C₂²	C₂⁶×C₁₃	1	1	yes	characteristic
157	C₄	—	2	6	no	—
158	C₄	—	2	48	no	—
159	C₄	C₂×C₁₃×2₋¹⁺⁴	1	12	yes	—
160	C₂	—	4	2	no	—
161	C₂	C₁₃×#3556	1	4	yes	direct product factor
162	C₂	C₂²×C₁₃×2₋¹⁺⁴	1	3	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂⁵
commutator, Frattini, cosocle	C₂²	C₂⁶×C₁₃
prime radical	C₂⁴×C₁₃	C₂⁴
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₃×#3556	C₂	direct (N × H)
2. C₂×C₁₃×#564	C₂	semidirect
3. C₂×C₁₃×#557	C₂	semidirect
6. C₁₃×#564	C₂²	semidirect
7. C₁₃×#557	C₂²	semidirect
43. C₂×#3556	C₁₃	direct (N × H)
61. #3556	C₂×C₁₃	direct (N × H)
62. C₂×#564	C₂×C₁₃	semidirect
63. C₂×#557	C₂×C₁₃	semidirect
77. #564	C₂²×C₁₃	semidirect
78. #557	C₂²×C₁₃	semidirect
122. C₂×C₁₃	#3556	direct (N × H)
141. C₁₃	C₂×#3556	direct (N × H)
161. C₂	C₁₃×#3556	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×#3556	2
C₂×C₁₃×#564	2
C₂×C₁₃×#557	2
C₂×C₁₃×#541	2
C₂×C₁₃×#533	2
C₂×#3556	13

Subgroups — C2×C13×#3556 #15749099

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₃×#3556 #15749099