Subgroups — D₁₃⋊#1370 #16788674

Order 3328.

286 conjugacy classes of subgroups.

The subgroup lattice has 196 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₁₃⋊(C₄⋊C₁₆)	C₂	1	2	yes	maximal
2	#13129866	C₂	1	2	yes	maximal, complemented
3	#13129865	C₂	1	2	yes	maximal, complemented
4	C₈²×D₁₃	C₂	1	1	yes	maximal, characteristic
5	C₂×D₁₃⋊C₁₆	—	2	2	no	—
6	C₄×C₈×D₁₃	C₄	1	1	yes	characteristic
7	C₄×C₈×D₁₃	C₄	1	1	yes	characteristic
8	C₄×C₈×D₁₃	C₂²	1	1	yes	characteristic
9	#11718260	—	2	2	no	—
10	C₄⋊#6092	C₂²	1	4	yes	—
11	C₈²×C₁₃	C₄	1	1	yes	characteristic
12	C₈×#1055	C₄	1	1	yes	characteristic
13	C₈×#1055	C₂²	1	1	yes	characteristic
14	C₈×#1055	C₂²	1	1	yes	characteristic
15	C₂×C₈×D₁₃	—	2	1	no	—
16	C₂×C₈×D₁₃	C₈	1	1	yes	characteristic
17	C₂×C₈×D₁₃	C₈	1	1	yes	characteristic
18	C₂×C₈×D₁₃	D₄	1	1	yes	characteristic
19	C₂×C₈×D₁₃	Q₈	1	1	yes	characteristic
20	C₄²×D₁₃	C₂×C₄	1	1	yes	characteristic
21	C₂×#6092	—	2	4	no	—
22	D₁₃⋊C₁₆	—	4	4	no	—
23	C₄×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
24	C₄×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
25	C₄×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
26	C₈×Dic₁₃	—	2	1	no	—
27	C₈×Dic₁₃	C₈	1	1	yes	characteristic
28	C₈×Dic₁₃	C₈	1	1	yes	characteristic
29	C₈×Dic₁₃	D₄	1	1	yes	characteristic
30	C₈×Dic₁₃	Q₈	1	1	yes	characteristic
31	C₄×#1055	C₂×C₄	1	1	yes	characteristic
32	C₄×#1055	C₂×C₄	1	1	yes	characteristic
33	C₄×#1055	C₂³	1	1	yes	characteristic
34	C₂×#1370	—	13	1	no	maximal, Sylow
35	C₂×C₄×D₁₃	C₄⋊C₄	1	1	yes	characteristic
36	C₂×C₄×D₁₃	C₂×C₈	1	1	yes	characteristic
37	C₂×C₄×D₁₃	M₁₆	1	1	yes	characteristic
38	C₂×C₈×C₁₃	—	2	1	no	—
39	C₂×C₈×C₁₃	C₄⋊C₄	1	1	yes	characteristic
40	C₂×C₈×C₁₃	C₄⋊C₄	1	1	yes	characteristic
41	C₂×C₈×C₁₃	C₂×C₈	1	1	yes	characteristic
42	C₂×C₈×C₁₃	C₂×C₈	1	1	yes	characteristic
43	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
44	C₄×Dic₁₃	C₄⋊C₄	1	1	yes	characteristic
45	C₄×Dic₁₃	C₂×C₈	1	1	yes	characteristic
46	C₄×Dic₁₃	M₁₆	1	1	yes	characteristic
47	C₂×#1055	—	2	1	no	—
48	C₂×#1055	C₂×C₈	1	1	yes	characteristic
49	C₂×#1055	C₂×C₈	1	1	yes	characteristic
50	C₂×#1055	C₂×D₄	1	1	yes	characteristic
51	C₂×#1055	C₂×Q₈	1	1	yes	characteristic
52	C₈×D₁₃	—	2	4	no	—
53	C₈×D₁₃	—	2	2	no	—
54	C₈×D₁₃	—	2	2	no	—
55	C₈×D₁₃	C₁₆	1	4	yes	complemented
56	C₈×D₁₃	D₈	1	2	yes	—
57	C₈×D₁₃	Q₁₆	1	2	yes	—
58	#6092	—	4	4	no	—
59	C₂×C₄⋊C₁₆	—	13	2	no	—
60	C₂×C₈²	—	13	1	no	—
61	#1370	—	13	2	no	—
62	#1370	—	13	2	no	—
63	C₂²×D₁₃	C₄⋊C₈	1	1	yes	characteristic
64	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
65	C₂×C₄×C₁₃	C₂²×C₈	1	1	yes	characteristic
66	C₂×C₄×C₁₃	C₂×M₁₆	1	1	yes	characteristic
67	C₂×Dic₁₃	C₄⋊C₈	1	1	yes	characteristic
68	C₂×Dic₁₃	C₄⋊C₈	1	1	yes	characteristic
69	C₂×Dic₁₃	C₄⋊C₈	1	1	yes	characteristic
70	C₄×D₁₃	—	2	2	no	—
71	C₄×D₁₃	#107	1	2	yes	—
72	C₄×D₁₃	#108	1	2	yes	—
73	C₄×D₁₃	C₂×C₁₆	1	2	yes	—
74	C₄×D₁₃	M₃₂	1	2	yes	—
75	C₈×C₁₃	—	2	2	no	—
76	C₈×C₁₃	—	2	1	no	—
77	C₈×C₁₃	—	2	1	no	—
78	C₈×C₁₃	#107	1	2	yes	—
79	C₈×C₁₃	C₂×C₁₆	1	2	yes	complemented
80	#1055	—	2	2	no	—
81	#1055	—	2	1	no	—
82	#1055	—	2	1	no	—
83	#1055	C₂×C₁₆	1	2	yes	complemented
84	#1055	C₂×D₈	1	1	yes	characteristic
85	#1055	C₂×Q₁₆	1	1	yes	characteristic
86	C₂²×C₁₆	—	26	2	no	—
87	C₂×C₄×C₈	—	13	1	no	—
88	C₂×C₄×C₈	—	13	1	no	—
89	C₂×C₄×C₈	—	13	1	no	—
90	C₄⋊C₁₆	—	13	4	no	—
91	C₄⋊C₁₆	—	26	2	no	—
92	C₈²	—	13	1	no	—
93	C₈²	—	13	1	no	—
94	C₈²	—	13	1	no	—
95	C₈²	#261	1	1	yes	characteristic
96	C₂²×C₁₃	C₂×C₄⋊C₈	1	1	yes	characteristic
97	C₂×D₁₃	#335	1	2	yes	—
98	C₂×D₁₃	C₄⋊C₁₆	1	2	yes	—
99	C₂×D₁₃	#364	1	2	yes	—
100	C₄×C₁₃	—	2	1	no	—
101	C₄×C₁₃	C₂×#107	1	1	yes	characteristic
102	C₄×C₁₃	C₂×#108	1	1	yes	characteristic
103	C₄×C₁₃	C₂²×C₁₆	1	1	yes	characteristic
104	C₄×C₁₃	C₂×M₃₂	1	1	yes	characteristic
105	Dic₁₃	—	2	1	no	—
106	Dic₁₃	#335	1	2	yes	—
107	Dic₁₃	C₄⋊C₁₆	1	2	yes	—
108	C₂²×C₈	—	13	1	no	—
109	C₂²×C₈	—	13	1	no	—
110	C₂²×C₈	—	13	1	no	—
111	C₂²×C₈	—	13	1	no	—
112	C₂²×C₈	—	26	1	no	—
113	C₂×C₄²	—	13	1	no	—
114	C₂×C₁₆	—	26	4	no	—
115	C₂×C₁₆	—	52	4	no	—
116	C₄×C₈	—	13	1	no	—
117	C₄×C₈	—	13	1	no	—
118	C₄×C₈	—	13	1	no	—
119	C₄×C₈	—	13	1	no	—
120	C₄×C₈	—	13	1	no	—
121	C₄×C₈	—	13	1	no	—
122	C₄×C₈	—	13	1	no	—
123	C₄×C₈	—	26	1	no	—
124	C₄×C₈	C₂×#261	1	1	yes	characteristic
125	C₄×C₈	C₂×#261	1	1	yes	characteristic
126	C₄×C₈	C₂×#261	1	1	yes	characteristic
127	C₂×C₁₃	C₂×#335	1	1	yes	characteristic
128	C₂×C₁₃	C₂×C₄⋊C₁₆	1	1	yes	characteristic
129	C₂×C₁₃	C₂×#364	1	1	yes	characteristic
130	D₁₃	#1370	1	4	yes	complemented
131	C₂²×C₄	—	13	1	no	—
132	C₂²×C₄	—	13	1	no	—
133	C₂²×C₄	—	13	1	no	—
134	C₂×C₈	—	2	1	no	—
135	C₂×C₈	—	13	1	no	—
136	C₂×C₈	—	13	1	no	—
137	C₂×C₈	—	13	4	no	—
138	C₂×C₈	—	13	2	no	—
139	C₂×C₈	—	13	2	no	—
140	C₂×C₈	—	13	1	no	—
141	C₂×C₈	—	13	1	no	—
142	C₂×C₈	—	26	2	no	—
143	C₂×C₈	—	26	2	no	—
144	C₂×C₈	—	26	4	no	—
145	C₂×C₈	—	26	1	no	—
146	C₂×C₈	D₁₃⋊C₈	1	1	yes	characteristic
147	C₂×C₈	D₁₃⋊C₈	1	1	yes	characteristic
148	C₂×C₈	C₄⋊#261	1	1	yes	characteristic
149	C₂×C₈	C₄⋊#261	1	1	yes	characteristic
150	C₄²	—	13	1	no	—
151	C₄²	—	13	1	no	—
152	C₄²	—	13	1	no	—
153	C₄²	C₂²×#261	1	1	yes	characteristic
154	C₁₆	—	52	4	no	—
155	C₁₃	C₂×#1370	1	1	yes	characteristic, complemented, Sylow
156	C₂³	—	13	1	no	—
157	C₂×C₄	—	13	1	no	—
158	C₂×C₄	—	13	1	no	—
159	C₂×C₄	—	13	2	no	—
160	C₂×C₄	—	13	2	no	—
161	C₂×C₄	—	13	2	no	—
162	C₂×C₄	—	13	2	no	—
163	C₂×C₄	—	13	1	no	—
164	C₂×C₄	—	26	2	no	—
165	C₂×C₄	C₂×D₁₃⋊C₈	1	1	yes	characteristic
166	C₂×C₄	D₁₃⋊M₁₆	1	1	yes	characteristic
167	C₂×C₄	C₂×C₄⋊#261	1	1	yes	characteristic
168	C₈	—	2	2	no	—
169	C₈	—	2	1	no	—
170	C₈	—	2	1	no	—
171	C₈	—	13	2	no	—
172	C₈	—	13	1	no	—
173	C₈	—	13	1	no	—
174	C₈	—	26	2	no	—
175	C₈	—	26	1	no	—
176	C₈	—	26	1	no	—
177	C₈	D₁₃⋊C₁₆	1	2	yes	complemented
178	C₈	#88102	1	2	yes	—
179	C₂²	—	13	2	no	—
180	C₂²	—	13	2	no	—
181	C₂²	—	13	2	no	—
182	C₂²	D₁₃⋊(C₄⋊C₈)	1	1	yes	characteristic
183	C₄	—	2	1	no	—
184	C₄	—	13	2	no	—
185	C₄	—	13	2	no	—
186	C₄	—	26	1	no	—
187	C₄	C₂×D₁₃⋊C₁₆	1	1	yes	characteristic
188	C₄	D₁₃⋊M₃₂	1	1	yes	characteristic
189	C₄	C₂×#88102	1	1	yes	characteristic
190	C₄	D₁₃⋊#108	1	1	yes	characteristic
191	C₂	—	13	4	no	—
192	C₂	D₁₃⋊#335	1	1	yes	characteristic
193	C₂	D₁₃⋊(C₄⋊C₁₆)	1	1	yes	characteristic
194	C₂	D₁₃⋊#364	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₈	C₄⋊#261
commutator	C₄×C₁₃	C₂²×C₁₆
Frattini	C₄²	C₂²×#261
Fitting	C₈²×C₁₃	C₄
socle	C₂²×C₁₃	C₂×C₄⋊C₈
prime radical	C₂²×D₁₃	C₄⋊C₈
cosocle	C₄×#1055	C₂³
hypercenter	C₈²	#261
hypocenter	C₁₃	C₂×#1370
LCS	G ▷ C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₈ ◁ C₄×C₈ ◁ C₈²

Complements

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

N	H ≅ G/N	type
2. #13129866	C₂	semidirect
3. #13129865	C₂	semidirect
55. C₈×D₁₃	C₁₆	semidirect
79. C₈×C₁₃	C₂×C₁₆	semidirect
83. #1055	C₂×C₁₆	semidirect
130. D₁₃	#1370	semidirect
155. C₁₃	C₂×#1370	semidirect
177. C₈	D₁₃⋊C₁₆	semidirect

Maximal subgroups

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

subgroup	index
D₁₃⋊(C₄⋊C₁₆)	2
#13129866	2
#13129865	2
C₈²×D₁₃	2
C₂×#1370	13

Subgroups — D13⋊#1370 #16788674

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₁₃⋊#1370 #16788674