Subgroups — C₂×C₁₃×#1371 #15698345

Order 3328.

262 conjugacy classes of subgroups.

The subgroup lattice has 158 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×C₁₃×C₁₆	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₃×#335	C₂	1	2	yes	maximal
3	C₁₃×#1371	C₂	1	4	yes	maximal, direct product factor
4	C₂²×C₁₃×C₁₆	C₄	1	1	yes	characteristic
5	C₂²×C₁₃×C₁₆	C₄	1	1	yes	characteristic
6	C₂×C₁₃×C₄⋊C₈	—	2	2	no	—
7	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
8	C₄×C₁₃×C₁₆	C₄	1	2	yes	—
9	C₄×C₁₃×C₁₆	C₂²	1	2	yes	—
10	C₁₃×#335	—	2	2	no	—
11	C₁₃×#335	C₂²	1	4	yes	—
12	C₂²×C₈×C₁₃	—	4	2	no	—
13	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
14	C₂²×C₈×C₁₃	Q₈	1	1	yes	characteristic
15	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
16	C₂×C₁₃×C₁₆	—	2	2	no	—
17	C₂×C₁₃×C₁₆	C₈	1	4	yes	complemented
18	C₂×C₁₃×C₁₆	C₂×C₄	1	2	yes	—
19	C₂×C₁₃×C₁₆	C₂×C₄	1	2	yes	—
20	C₁₃×C₄⋊C₈	—	2	4	no	—
21	C₁₃×C₄⋊C₈	—	4	2	no	—
22	C₄×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
23	C₄×C₈×C₁₃	D₄	1	1	yes	characteristic
24	C₄×C₈×C₁₃	Q₈	1	1	yes	characteristic
25	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
26	C₂×#1371	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
27	C₂²×C₄×C₁₃	C₄⋊C₄	1	1	yes	characteristic
28	C₂²×C₄×C₁₃	D₈	1	1	yes	characteristic
29	C₂²×C₄×C₁₃	Q₁₆	1	1	yes	characteristic
30	C₂×C₈×C₁₃	—	2	2	no	—
31	C₂×C₈×C₁₃	—	4	4	no	—
32	C₂×C₈×C₁₃	—	8	4	no	—
33	C₂×C₈×C₁₃	C₄⋊C₄	1	1	yes	characteristic
34	C₂×C₈×C₁₃	C₄⋊C₄	1	1	yes	characteristic
35	C₂×C₈×C₁₃	C₂×C₈	1	2	yes	—
36	C₂×C₈×C₁₃	M₁₆	1	2	yes	—
37	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
38	C₂×C₈×C₁₃	C₂×Q₈	1	1	yes	characteristic
39	C₄²×C₁₃	C₄⋊C₄	1	1	yes	characteristic
40	C₄²×C₁₃	D₈	1	1	yes	characteristic
41	C₄²×C₁₃	Q₁₆	1	1	yes	characteristic
42	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
43	C₁₃×C₁₆	—	2	2	no	—
44	C₁₃×C₁₆	C₂×C₈	1	4	yes	complemented
45	C₂×C₄×C₁₆	C₂×C₁₃	1	1	yes	characteristic
46	C₂×#335	C₂×C₁₃	1	2	yes	—
47	#1371	C₂×C₁₃	1	4	yes	direct product factor
48	C₂³×C₁₃	#107	1	1	yes	characteristic
49	C₂×C₄×C₁₃	—	2	2	no	—
50	C₂×C₄×C₁₃	C₄⋊C₈	1	2	yes	—
51	C₂×C₄×C₁₃	#107	1	1	yes	characteristic
52	C₂×C₄×C₁₃	#107	1	1	yes	characteristic
53	C₂×C₄×C₁₃	#107	1	1	yes	characteristic
54	C₂×C₄×C₁₃	#108	1	2	yes	—
55	C₂×C₄×C₁₃	D₁₆	1	2	yes	—
56	C₂×C₄×C₁₃	Q₃₂	1	2	yes	—
57	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
58	C₂×C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
59	C₂×C₄×C₁₃	C₂×Q₁₆	1	1	yes	characteristic
60	C₈×C₁₃	—	2	1	no	—
61	C₈×C₁₃	—	2	1	no	—
62	C₈×C₁₃	—	8	4	no	—
63	C₈×C₁₃	C₄⋊C₈	1	2	yes	—
64	C₈×C₁₃	C₂²×C₈	1	1	yes	characteristic
65	C₈×C₁₃	C₂×M₁₆	1	1	yes	characteristic
66	C₂²×C₁₆	C₄×C₁₃	1	1	yes	characteristic
67	C₂²×C₁₆	C₄×C₁₃	1	1	yes	characteristic
68	C₂×C₄⋊C₈	—	2	2	no	—
69	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
70	C₄×C₁₆	C₄×C₁₃	1	2	yes	—
71	C₄×C₁₆	C₂²×C₁₃	1	2	yes	—
72	#335	—	2	2	no	—
73	#335	C₂²×C₁₃	1	4	yes	—
74	C₂²×C₁₃	#335	1	2	yes	—
75	C₂²×C₁₃	#366	1	2	yes	—
76	C₂²×C₁₃	#368	1	2	yes	—
77	C₂²×C₁₃	C₂×#107	1	1	yes	characteristic
78	C₄×C₁₃	—	2	1	no	—
79	C₄×C₁₃	—	2	1	no	—
80	C₄×C₁₃	#335	1	2	yes	—
81	C₄×C₁₃	#366	1	2	yes	—
82	C₄×C₁₃	C₂×C₄⋊C₈	1	1	yes	characteristic
83	C₄×C₁₃	C₂×#108	1	1	yes	characteristic
84	C₄×C₁₃	C₂×D₁₆	1	1	yes	characteristic
85	C₄×C₁₃	C₂×Q₃₂	1	1	yes	characteristic
86	C₂²×C₈	—	4	2	no	—
87	C₂²×C₈	C₂×C₄×C₁₃	1	1	yes	characteristic
88	C₂²×C₈	Q₈×C₁₃	1	1	yes	characteristic
89	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
90	C₂×C₁₆	—	2	2	no	—
91	C₂×C₁₆	C₈×C₁₃	1	4	yes	complemented
92	C₂×C₁₆	C₂×C₄×C₁₃	1	2	yes	—
93	C₂×C₁₆	C₂×C₄×C₁₃	1	2	yes	—
94	C₄⋊C₈	—	2	4	no	—
95	C₄⋊C₈	—	4	2	no	—
96	C₄×C₈	C₂×C₄×C₁₃	1	1	yes	characteristic
97	C₄×C₈	D₄×C₁₃	1	1	yes	characteristic
98	C₄×C₈	Q₈×C₁₃	1	1	yes	characteristic
99	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
100	C₂×C₁₃	#1371	1	4	yes	direct product factor
101	C₂×C₁₃	C₂×#335	1	1	yes	characteristic
102	C₂×C₁₃	C₂×#366	1	1	yes	characteristic
103	C₂×C₁₃	C₂×#368	1	1	yes	characteristic
104	C₂²×C₄	C₁₃×C₄⋊C₄	1	1	yes	characteristic
105	C₂²×C₄	C₁₃×D₈	1	1	yes	characteristic
106	C₂²×C₄	C₁₃×Q₁₆	1	1	yes	characteristic
107	C₂×C₈	—	2	2	no	—
108	C₂×C₈	—	4	4	no	—
109	C₂×C₈	—	8	4	no	—
110	C₂×C₈	C₁₃×C₄⋊C₄	1	1	yes	characteristic
111	C₂×C₈	C₁₃×C₄⋊C₄	1	1	yes	characteristic
112	C₂×C₈	C₂×C₈×C₁₃	1	2	yes	—
113	C₂×C₈	C₁₃×M₁₆	1	2	yes	—
114	C₂×C₈	C₂²×C₄×C₁₃	1	1	yes	characteristic
115	C₂×C₈	C₂×Q₈×C₁₃	1	1	yes	characteristic
116	C₄²	C₁₃×C₄⋊C₄	1	1	yes	characteristic
117	C₄²	C₁₃×D₈	1	1	yes	characteristic
118	C₄²	C₁₃×Q₁₆	1	1	yes	characteristic
119	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
120	C₁₆	—	2	2	no	—
121	C₁₆	C₂×C₈×C₁₃	1	4	yes	complemented
122	C₁₃	C₂×#1371	1	1	yes	characteristic, direct product factor, Sylow
123	C₂³	C₁₃×#107	1	1	yes	characteristic
124	C₂×C₄	—	2	2	no	—
125	C₂×C₄	C₁₃×C₄⋊C₈	1	2	yes	—
126	C₂×C₄	C₁₃×#107	1	1	yes	characteristic
127	C₂×C₄	C₁₃×#107	1	1	yes	characteristic
128	C₂×C₄	C₁₃×#107	1	1	yes	characteristic
129	C₂×C₄	C₁₃×#108	1	2	yes	—
130	C₂×C₄	C₁₃×D₁₆	1	2	yes	—
131	C₂×C₄	C₁₃×Q₃₂	1	2	yes	—
132	C₂×C₄	C₂×C₁₃×C₄⋊C₄	1	1	yes	characteristic
133	C₂×C₄	C₂×C₁₃×D₈	1	1	yes	characteristic
134	C₂×C₄	C₂×C₁₃×Q₁₆	1	1	yes	characteristic
135	C₈	—	2	1	no	—
136	C₈	—	2	1	no	—
137	C₈	—	8	4	no	—
138	C₈	C₁₃×C₄⋊C₈	1	2	yes	—
139	C₈	C₂²×C₈×C₁₃	1	1	yes	characteristic
140	C₈	C₂×C₁₃×M₁₆	1	1	yes	characteristic
141	C₂²	C₁₃×#335	1	2	yes	—
142	C₂²	C₁₃×#366	1	2	yes	—
143	C₂²	C₁₃×#368	1	2	yes	—
144	C₂²	C₂×C₁₃×#107	1	1	yes	characteristic
145	C₄	—	2	1	no	—
146	C₄	—	2	1	no	—
147	C₄	C₁₃×#335	1	2	yes	—
148	C₄	C₁₃×#366	1	2	yes	—
149	C₄	C₂×C₁₃×C₄⋊C₈	1	1	yes	characteristic
150	C₄	C₂×C₁₃×#108	1	1	yes	characteristic
151	C₄	C₂×C₁₃×D₁₆	1	1	yes	characteristic
152	C₄	C₂×C₁₃×Q₃₂	1	1	yes	characteristic
153	C₂	C₁₃×#1371	1	4	yes	direct product factor
154	C₂	C₂×C₁₃×#335	1	1	yes	characteristic
155	C₂	C₂×C₁₃×#366	1	1	yes	characteristic
156	C₂	C₂×C₁₃×#368	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄×C₁₃	D₈
commutator	C₈	C₂²×C₈×C₁₃
Frattini, cosocle	C₄×C₈	C₂³×C₁₃
socle, prime radical	C₂³×C₁₃	#107
LCS	G ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×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×#1371	C₂	direct (N × H)
17. C₂×C₁₃×C₁₆	C₈	semidirect
26. C₂×#1371	C₁₃	direct (N × H)
44. C₁₃×C₁₆	C₂×C₈	semidirect
47. #1371	C₂×C₁₃	direct (N × H)
91. C₂×C₁₆	C₈×C₁₃	semidirect
100. C₂×C₁₃	#1371	direct (N × H)
121. C₁₆	C₂×C₈×C₁₃	semidirect
122. C₁₃	C₂×#1371	direct (N × H)
153. C₂	C₁₃×#1371	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×C₄×C₁₃×C₁₆	2
C₂×C₁₃×#335	2
C₁₃×#1371	2
C₂×#1371	13

Subgroups — C2×C13×#1371 #15698345

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₃×#1371 #15698345