Subgroups — C₄×C₁₃×#368 #15699014

Order 3328.

314 conjugacy classes of subgroups.

The subgroup lattice has 136 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#368	C₂	1	2	yes	maximal
2	C₂×C₄×C₁₃×C₁₆	C₂	1	1	yes	maximal, characteristic
3	C₄×C₁₃×#108	C₂	1	2	yes	maximal
4	C₁₃×#1381	C₂	1	2	yes	maximal
5	C₂²×C₁₃×C₁₆	C₂²	1	1	yes	characteristic
6	C₂²×C₁₃×C₁₆	C₂²	1	1	yes	characteristic
7	C₂×C₁₃×#108	C₂²	1	4	yes	—
8	C₄×C₁₃×M₁₆	—	2	2	no	—
9	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
10	C₁₃×#368	C₄	1	8	yes	direct product factor
11	C₄×C₁₃×C₁₆	C₄	1	4	yes	—
12	C₁₃×#341	—	2	2	no	—
13	C₂×C₁₃×M₁₆	—	2	4	no	—
14	C₂²×C₈×C₁₃	D₄	1	1	yes	characteristic
15	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
16	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
17	C₂×C₁₃×C₁₆	—	2	2	no	—
18	C₂×C₁₃×C₁₆	C₂×C₄	1	2	yes	—
19	C₂×C₁₃×C₁₆	C₂×C₄	1	2	yes	—
20	C₂×C₁₃×C₁₆	C₂×C₄	1	4	yes	—
21	C₁₃×#108	—	2	4	no	—
22	C₁₃×#108	C₂×C₄	1	8	yes	—
23	C₁₃×#97	—	4	2	no	—
24	C₄×C₈×C₁₃	—	4	2	no	—
25	C₄×C₈×C₁₃	C₂×C₄	1	2	yes	—
26	C₄×C₈×C₁₃	Q₈	1	2	yes	—
27	C₄×#368	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
28	C₂²×C₄×C₁₃	Q₁₆	1	2	yes	—
29	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
30	C₁₃×M₁₆	—	2	8	no	—
31	C₁₃×M₁₆	—	4	4	no	—
32	C₂×C₈×C₁₃	—	2	2	no	—
33	C₂×C₈×C₁₃	—	4	4	no	—
34	C₂×C₈×C₁₃	C₄⋊C₄	1	2	yes	—
35	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
36	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
37	C₂×C₈×C₁₃	C₂×Q₈	1	1	yes	characteristic
38	C₂×C₈×C₁₃	#41	1	2	yes	—
39	C₄²×C₁₃	C₄⋊C₄	1	2	yes	—
40	C₄²×C₁₃	D₈	1	1	yes	characteristic
41	C₄²×C₁₃	D₈	1	1	yes	characteristic
42	C₁₃×C₁₆	—	2	2	no	—
43	C₁₃×C₁₆	C₄²	1	4	yes	—
44	C₂×#368	C₂×C₁₃	1	2	yes	—
45	C₂×C₄×C₁₆	C₂×C₁₃	1	1	yes	characteristic
46	C₄×#108	C₂×C₁₃	1	2	yes	—
47	#1381	C₂×C₁₃	1	2	yes	—
48	C₂³×C₁₃	C₂×Q₁₆	1	1	yes	characteristic
49	C₂×C₄×C₁₃	—	2	4	no	—
50	C₂×C₄×C₁₃	#107	1	2	yes	—
51	C₂×C₄×C₁₃	#107	1	2	yes	—
52	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
53	C₂×C₄×C₁₃	C₄×D₄	1	2	yes	—
54	C₂×C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
55	C₂×C₄×C₁₃	#135	1	2	yes	—
56	C₈×C₁₃	—	2	2	no	—
57	C₈×C₁₃	—	4	8	no	—
58	C₈×C₁₃	C₂×C₄²	1	1	yes	characteristic
59	C₈×C₁₃	#117	1	1	yes	characteristic
60	C₈×C₁₃	C₄×Q₈	1	2	yes	—
61	C₂²×C₁₆	C₂²×C₁₃	1	1	yes	characteristic
62	C₂²×C₁₆	C₂²×C₁₃	1	1	yes	characteristic
63	C₂×#108	C₂²×C₁₃	1	4	yes	—
64	C₄×M₁₆	—	2	2	no	—
65	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
66	#368	C₄×C₁₃	1	8	yes	direct product factor
67	C₄×C₁₆	C₄×C₁₃	1	4	yes	—
68	#341	—	2	2	no	—
69	C₂²×C₁₃	—	2	2	no	—
70	C₂²×C₁₃	C₂×#107	1	1	yes	characteristic
71	C₂²×C₁₃	C₄×Q₁₆	1	2	yes	—
72	C₄×C₁₃	—	2	2	no	—
73	C₄×C₁₃	#368	1	4	yes	direct product factor
74	C₄×C₁₃	C₄×C₄⋊C₄	1	1	yes	characteristic
75	C₄×C₁₃	#427	1	1	yes	characteristic
76	C₄×C₁₃	C₄×D₈	1	2	yes	—
77	C₂×M₁₆	—	2	4	no	—
78	C₂²×C₈	D₄×C₁₃	1	1	yes	characteristic
79	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
80	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
81	C₂×C₁₆	—	2	2	no	—
82	C₂×C₁₆	C₂×C₄×C₁₃	1	2	yes	—
83	C₂×C₁₆	C₂×C₄×C₁₃	1	2	yes	—
84	C₂×C₁₆	C₂×C₄×C₁₃	1	4	yes	—
85	#108	—	2	4	no	—
86	#108	C₂×C₄×C₁₃	1	8	yes	—
87	#97	—	4	2	no	—
88	C₄×C₈	—	4	2	no	—
89	C₄×C₈	C₂×C₄×C₁₃	1	2	yes	—
90	C₄×C₈	Q₈×C₁₃	1	2	yes	—
91	C₂×C₁₃	—	2	2	no	—
92	C₂×C₁₃	C₄×#107	1	1	yes	characteristic
93	C₂×C₁₃	C₂×#368	1	2	yes	—
94	C₂²×C₄	C₁₃×Q₁₆	1	2	yes	—
95	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
96	M₁₆	—	2	8	no	—
97	M₁₆	—	4	4	no	—
98	C₂×C₈	—	2	2	no	—
99	C₂×C₈	—	4	4	no	—
100	C₂×C₈	C₁₃×C₄⋊C₄	1	2	yes	—
101	C₂×C₈	C₂²×C₄×C₁₃	1	1	yes	characteristic
102	C₂×C₈	C₂²×C₄×C₁₃	1	2	yes	—
103	C₂×C₈	C₂×Q₈×C₁₃	1	1	yes	characteristic
104	C₂×C₈	C₁₃×#41	1	2	yes	—
105	C₄²	C₁₃×C₄⋊C₄	1	2	yes	—
106	C₄²	C₁₃×D₈	1	1	yes	characteristic
107	C₄²	C₁₃×D₈	1	1	yes	characteristic
108	C₁₆	—	2	2	no	—
109	C₁₆	C₄²×C₁₃	1	4	yes	—
110	C₁₃	C₄×#368	1	1	yes	characteristic, direct product factor, Sylow
111	C₂³	C₂×C₁₃×Q₁₆	1	1	yes	characteristic
112	C₂×C₄	—	2	4	no	—
113	C₂×C₄	C₁₃×#107	1	2	yes	—
114	C₂×C₄	C₁₃×#107	1	2	yes	—
115	C₂×C₄	C₂×C₁₃×C₄⋊C₄	1	1	yes	characteristic
116	C₂×C₄	C₄×D₄×C₁₃	1	2	yes	—
117	C₂×C₄	C₂×C₁₃×D₈	1	1	yes	characteristic
118	C₂×C₄	C₁₃×#135	1	2	yes	—
119	C₈	—	2	2	no	—
120	C₈	—	4	8	no	—
121	C₈	C₂×C₄²×C₁₃	1	1	yes	characteristic
122	C₈	C₁₃×#117	1	1	yes	characteristic
123	C₈	C₄×Q₈×C₁₃	1	2	yes	—
124	C₂²	—	2	2	no	—
125	C₂²	C₂×C₁₃×#107	1	1	yes	characteristic
126	C₂²	C₄×C₁₃×Q₁₆	1	2	yes	—
127	C₄	—	2	2	no	—
128	C₄	C₁₃×#368	1	4	yes	direct product factor
129	C₄	C₄×C₁₃×C₄⋊C₄	1	1	yes	characteristic
130	C₄	C₁₃×#427	1	1	yes	characteristic
131	C₄	C₄×C₁₃×D₈	1	2	yes	—
132	C₂	—	2	2	no	—
133	C₂	C₄×C₁₃×#107	1	1	yes	characteristic
134	C₂	C₂×C₁₃×#368	1	2	yes	—

	subgroup	G/H
center	C₄²×C₁₃	D₈
commutator	C₈	C₂×C₄²×C₁₃
Frattini, cosocle	C₂²×C₈	C₂³×C₁₃
socle	C₂²×C₁₃	C₂×#107
prime radical	C₂³×C₁₃	C₂×Q₁₆
LCS	G ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄²×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
10. C₁₃×#368	C₄	direct (N × H)
27. C₄×#368	C₁₃	direct (N × H)
66. #368	C₄×C₁₃	direct (N × H)
73. C₄×C₁₃	#368	direct (N × H)
110. C₁₃	C₄×#368	direct (N × H)
128. C₄	C₁₃×#368	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×#368	2
C₂×C₄×C₁₃×C₁₆	2
C₄×C₁₃×#108	2
C₁₃×#1381	2
C₄×#368	13

Subgroups — C4×C13×#368 #15699014

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×C₁₃×#368 #15699014