Subgroups — C₂×C₁₃×#1370 #15698342

Order 3328.

286 conjugacy classes of subgroups.

The subgroup lattice has 172 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×C₄⋊C₁₆	C₂	1	2	yes	maximal
2	C₂×C₈²×C₁₃	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#1370	C₂	1	4	yes	maximal, direct product factor
4	C₂²×C₁₃×C₁₆	—	2	2	no	—
5	C₂×C₄×C₈×C₁₃	C₄	1	1	yes	characteristic
6	C₂×C₄×C₈×C₁₃	C₄	1	1	yes	characteristic
7	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
8	C₁₃×C₄⋊C₁₆	—	2	2	no	—
9	C₁₃×C₄⋊C₁₆	C₂²	1	4	yes	—
10	C₈²×C₁₃	C₄	1	2	yes	—
11	C₈²×C₁₃	C₂²	1	2	yes	—
12	C₂²×C₈×C₁₃	—	2	1	no	—
13	C₂²×C₈×C₁₃	C₈	1	1	yes	characteristic
14	C₂²×C₈×C₁₃	C₈	1	1	yes	characteristic
15	C₂²×C₈×C₁₃	D₄	1	1	yes	characteristic
16	C₂²×C₈×C₁₃	Q₈	1	1	yes	characteristic
17	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
18	C₂×C₁₃×C₁₆	—	2	4	no	—
19	C₂×C₁₃×C₁₆	—	4	4	no	—
20	C₄×C₈×C₁₃	—	2	1	no	—
21	C₄×C₈×C₁₃	C₈	1	2	yes	—
22	C₄×C₈×C₁₃	C₂×C₄	1	2	yes	—
23	C₄×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
24	C₄×C₈×C₁₃	C₂×C₄	1	2	yes	—
25	C₄×C₈×C₁₃	D₄	1	1	yes	characteristic
26	C₄×C₈×C₁₃	Q₈	1	1	yes	characteristic
27	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
28	C₂×#1370	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
29	C₂²×C₄×C₁₃	C₄⋊C₄	1	1	yes	characteristic
30	C₂²×C₄×C₁₃	C₂×C₈	1	1	yes	characteristic
31	C₂²×C₄×C₁₃	M₁₆	1	1	yes	characteristic
32	C₂×C₈×C₁₃	—	2	4	no	—
33	C₂×C₈×C₁₃	—	2	2	no	—
34	C₂×C₈×C₁₃	—	2	2	no	—
35	C₂×C₈×C₁₃	—	2	2	no	—
36	C₂×C₈×C₁₃	C₁₆	1	4	yes	complemented
37	C₂×C₈×C₁₃	C₄⋊C₄	1	1	yes	characteristic
38	C₂×C₈×C₁₃	C₄⋊C₄	1	1	yes	characteristic
39	C₂×C₈×C₁₃	C₂×C₈	1	2	yes	—
40	C₂×C₈×C₁₃	C₂×C₈	1	2	yes	—
41	C₂×C₈×C₁₃	D₈	1	2	yes	—
42	C₂×C₈×C₁₃	Q₁₆	1	2	yes	—
43	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
44	C₂×C₈×C₁₃	C₂×Q₈	1	1	yes	characteristic
45	C₄²×C₁₃	C₄⋊C₄	1	1	yes	characteristic
46	C₄²×C₁₃	C₂×C₈	1	1	yes	characteristic
47	C₄²×C₁₃	M₁₆	1	1	yes	characteristic
48	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
49	C₁₃×C₁₆	—	4	4	no	—
50	C₂×C₄⋊C₁₆	C₂×C₁₃	1	2	yes	—
51	C₂×C₈²	C₂×C₁₃	1	1	yes	characteristic
52	#1370	C₂×C₁₃	1	4	yes	direct product factor
53	C₂³×C₁₃	C₄⋊C₈	1	1	yes	characteristic
54	C₂×C₄×C₁₃	—	2	2	no	—
55	C₂×C₄×C₁₃	C₄⋊C₈	1	1	yes	characteristic
56	C₂×C₄×C₁₃	C₄⋊C₈	1	1	yes	characteristic
57	C₂×C₄×C₁₃	C₄⋊C₈	1	1	yes	characteristic
58	C₂×C₄×C₁₃	#107	1	2	yes	—
59	C₂×C₄×C₁₃	#108	1	2	yes	—
60	C₂×C₄×C₁₃	C₂×C₁₆	1	2	yes	—
61	C₂×C₄×C₁₃	M₃₂	1	2	yes	—
62	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
63	C₂×C₄×C₁₃	C₂²×C₈	1	1	yes	characteristic
64	C₂×C₄×C₁₃	C₂×M₁₆	1	1	yes	characteristic
65	C₈×C₁₃	—	2	4	no	—
66	C₈×C₁₃	—	2	1	no	—
67	C₈×C₁₃	—	2	1	no	—
68	C₈×C₁₃	—	2	2	no	—
69	C₈×C₁₃	#107	1	2	yes	—
70	C₈×C₁₃	C₂×C₁₆	1	4	yes	complemented
71	C₈×C₁₃	C₂×D₈	1	1	yes	characteristic
72	C₈×C₁₃	C₂×Q₁₆	1	1	yes	characteristic
73	C₂²×C₁₆	—	2	2	no	—
74	C₂×C₄×C₈	C₄×C₁₃	1	1	yes	characteristic
75	C₂×C₄×C₈	C₄×C₁₃	1	1	yes	characteristic
76	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
77	C₄⋊C₁₆	—	2	2	no	—
78	C₄⋊C₁₆	C₂²×C₁₃	1	4	yes	—
79	C₈²	C₄×C₁₃	1	2	yes	—
80	C₈²	C₂²×C₁₃	1	2	yes	—
81	C₂²×C₁₃	#335	1	2	yes	—
82	C₂²×C₁₃	C₄⋊C₁₆	1	2	yes	—
83	C₂²×C₁₃	#364	1	2	yes	—
84	C₂²×C₁₃	C₂×C₄⋊C₈	1	1	yes	characteristic
85	C₄×C₁₃	—	2	1	no	—
86	C₄×C₁₃	—	2	1	no	—
87	C₄×C₁₃	#335	1	2	yes	—
88	C₄×C₁₃	C₄⋊C₁₆	1	2	yes	—
89	C₄×C₁₃	C₂×#107	1	1	yes	characteristic
90	C₄×C₁₃	C₂×#108	1	1	yes	characteristic
91	C₄×C₁₃	C₂²×C₁₆	1	1	yes	characteristic
92	C₄×C₁₃	C₂×M₃₂	1	1	yes	characteristic
93	C₂²×C₈	—	2	1	no	—
94	C₂²×C₈	C₈×C₁₃	1	1	yes	characteristic
95	C₂²×C₈	C₈×C₁₃	1	1	yes	characteristic
96	C₂²×C₈	D₄×C₁₃	1	1	yes	characteristic
97	C₂²×C₈	Q₈×C₁₃	1	1	yes	characteristic
98	C₂×C₄²	C₂×C₄×C₁₃	1	1	yes	characteristic
99	C₂×C₁₆	—	2	4	no	—
100	C₂×C₁₆	—	4	4	no	—
101	C₄×C₈	—	2	1	no	—
102	C₄×C₈	C₈×C₁₃	1	2	yes	—
103	C₄×C₈	C₂×C₄×C₁₃	1	2	yes	—
104	C₄×C₈	C₂×C₄×C₁₃	1	1	yes	characteristic
105	C₄×C₈	C₂×C₄×C₁₃	1	2	yes	—
106	C₄×C₈	D₄×C₁₃	1	1	yes	characteristic
107	C₄×C₈	Q₈×C₁₃	1	1	yes	characteristic
108	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
109	C₂×C₁₃	#1370	1	4	yes	direct product factor
110	C₂×C₁₃	C₂×#335	1	1	yes	characteristic
111	C₂×C₁₃	C₂×C₄⋊C₁₆	1	1	yes	characteristic
112	C₂×C₁₃	C₂×#364	1	1	yes	characteristic
113	C₂²×C₄	C₁₃×C₄⋊C₄	1	1	yes	characteristic
114	C₂²×C₄	C₂×C₈×C₁₃	1	1	yes	characteristic
115	C₂²×C₄	C₁₃×M₁₆	1	1	yes	characteristic
116	C₂×C₈	—	2	4	no	—
117	C₂×C₈	—	2	2	no	—
118	C₂×C₈	—	2	2	no	—
119	C₂×C₈	—	2	2	no	—
120	C₂×C₈	C₁₃×C₁₆	1	4	yes	complemented
121	C₂×C₈	C₁₃×C₄⋊C₄	1	1	yes	characteristic
122	C₂×C₈	C₁₃×C₄⋊C₄	1	1	yes	characteristic
123	C₂×C₈	C₂×C₈×C₁₃	1	2	yes	—
124	C₂×C₈	C₂×C₈×C₁₃	1	2	yes	—
125	C₂×C₈	C₁₃×D₈	1	2	yes	—
126	C₂×C₈	C₁₃×Q₁₆	1	2	yes	—
127	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
128	C₂×C₈	C₂×Q₈×C₁₃	1	1	yes	characteristic
129	C₄²	C₁₃×C₄⋊C₄	1	1	yes	characteristic
130	C₄²	C₂×C₈×C₁₃	1	1	yes	characteristic
131	C₄²	C₁₃×M₁₆	1	1	yes	characteristic
132	C₄²	C₂²×C₄×C₁₃	1	1	yes	characteristic
133	C₁₆	—	4	4	no	—
134	C₁₃	C₂×#1370	1	1	yes	characteristic, direct product factor, Sylow
135	C₂³	C₁₃×C₄⋊C₈	1	1	yes	characteristic
136	C₂×C₄	—	2	2	no	—
137	C₂×C₄	C₁₃×C₄⋊C₈	1	1	yes	characteristic
138	C₂×C₄	C₁₃×C₄⋊C₈	1	1	yes	characteristic
139	C₂×C₄	C₁₃×C₄⋊C₈	1	1	yes	characteristic
140	C₂×C₄	C₁₃×#107	1	2	yes	—
141	C₂×C₄	C₁₃×#108	1	2	yes	—
142	C₂×C₄	C₂×C₁₃×C₁₆	1	2	yes	—
143	C₂×C₄	C₁₃×M₃₂	1	2	yes	—
144	C₂×C₄	C₂×C₁₃×C₄⋊C₄	1	1	yes	characteristic
145	C₂×C₄	C₂²×C₈×C₁₃	1	1	yes	characteristic
146	C₂×C₄	C₂×C₁₃×M₁₆	1	1	yes	characteristic
147	C₈	—	2	4	no	—
148	C₈	—	2	1	no	—
149	C₈	—	2	1	no	—
150	C₈	—	2	2	no	—
151	C₈	C₁₃×#107	1	2	yes	—
152	C₈	C₂×C₁₃×C₁₆	1	4	yes	complemented
153	C₈	C₂×C₁₃×D₈	1	1	yes	characteristic
154	C₈	C₂×C₁₃×Q₁₆	1	1	yes	characteristic
155	C₂²	C₁₃×#335	1	2	yes	—
156	C₂²	C₁₃×C₄⋊C₁₆	1	2	yes	—
157	C₂²	C₁₃×#364	1	2	yes	—
158	C₂²	C₂×C₁₃×C₄⋊C₈	1	1	yes	characteristic
159	C₄	—	2	1	no	—
160	C₄	—	2	1	no	—
161	C₄	C₁₃×#335	1	2	yes	—
162	C₄	C₁₃×C₄⋊C₁₆	1	2	yes	—
163	C₄	C₂×C₁₃×#107	1	1	yes	characteristic
164	C₄	C₂×C₁₃×#108	1	1	yes	characteristic
165	C₄	C₂²×C₁₃×C₁₆	1	1	yes	characteristic
166	C₄	C₂×C₁₃×M₃₂	1	1	yes	characteristic
167	C₂	C₁₃×#1370	1	4	yes	direct product factor
168	C₂	C₂×C₁₃×#335	1	1	yes	characteristic
169	C₂	C₂×C₁₃×C₄⋊C₁₆	1	1	yes	characteristic
170	C₂	C₂×C₁₃×#364	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₈×C₁₃	D₄
commutator	C₄	C₂²×C₁₃×C₁₆
Frattini, cosocle	C₄×C₈	C₂³×C₁₃
socle, prime radical	C₂³×C₁₃	C₄⋊C₈
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₈×C₁₃ ◁ C₂×C₄×C₈×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₁₃×#1370	C₂	direct (N × H)
28. C₂×#1370	C₁₃	direct (N × H)
36. C₂×C₈×C₁₃	C₁₆	semidirect
52. #1370	C₂×C₁₃	direct (N × H)
70. C₈×C₁₃	C₂×C₁₆	semidirect
109. C₂×C₁₃	#1370	direct (N × H)
120. C₂×C₈	C₁₃×C₁₆	semidirect
134. C₁₃	C₂×#1370	direct (N × H)
152. C₈	C₂×C₁₃×C₁₆	semidirect
167. C₂	C₁₃×#1370	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×C₄⋊C₁₆	2
C₂×C₈²×C₁₃	2
C₁₃×#1370	2
C₂×#1370	13

Subgroups — C2×C13×#1370 #15698342

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₃×#1370 #15698342