Subgroups — C₂×Q₈×C₂²⋊D₁₃ #13128308

Order 1664.

1568 conjugacy classes of subgroups.

The subgroup lattice has 212 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×Q₈×C₁₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×Q₈×D₁₃	C₂	1	1	yes	maximal, characteristic, complemented
3	Q₈×C₂²⋊D₁₃	C₂	1	16	yes	maximal, direct product factor
4	C₂×#88200	C₂	1	3	yes	maximal, complemented
5	C₂×Q₈×Dic₁₃	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#88198	C₂	1	3	yes	maximal, complemented
7	C₂×C₄×C₂²⋊D₁₃	C₂	1	3	yes	maximal
8	C₂×#88178	C₂	1	3	yes	maximal, complemented
9	C₂²×Q₈×C₁₃	—	2	8	no	—
10	C₂²×Q₈×C₁₃	C₂²	1	3	yes	—
11	C₂²×Q₈×C₁₃	C₂²	1	1	yes	characteristic
12	C₂²×Q₈×C₁₃	C₂²	1	8	yes	complemented
13	C₂³×C₄×C₁₃	C₂²	1	3	yes	—
14	C₂²×C₂²⋊D₁₃	C₂²	1	1	yes	characteristic
15	C₂×Q₈×D₁₃	—	2	8	no	—
16	C₂×Q₈×D₁₃	C₂²	1	8	yes	complemented
17	C₂²×C₄×D₁₃	C₂²	1	3	yes	—
18	C₂²×Dic₂₆	C₂²	1	3	yes	—
19	C₂×C₂²⋊Dic₁₃	C₂²	1	3	yes	—
20	#88200	C₂²	1	24	yes	complemented
21	Q₈×Dic₁₃	C₂²	1	8	yes	complemented
22	#88198	C₂²	1	24	yes	complemented
23	C₄×C₂²⋊D₁₃	C₂²	1	24	yes	—
24	C₂×#6103	C₂²	1	3	yes	—
25	C₂×C₄⋊Dic₁₃	C₂²	1	3	yes	—
26	#88178	C₂²	1	24	yes	complemented
27	C₂×#6101	C₂²	1	6	yes	—
28	C₂×#6101	C₂²	1	3	yes	—
29	C₂×C₄×Dic₁₃	C₂²	1	3	yes	—
30	C₂⁴×C₁₃	C₂³	1	1	yes	characteristic
31	C₂³×D₁₃	C₂³	1	1	yes	characteristic
32	C₂×Q₈×C₁₃	—	2	32	no	—
33	C₂×Q₈×C₁₃	—	2	12	no	—
34	C₂×Q₈×C₁₃	D₄	1	8	yes	complemented
35	C₂×Q₈×C₁₃	C₂³	1	12	yes	—
36	C₂×Q₈×C₁₃	C₂³	1	4	yes	—
37	C₂²×C₄×C₁₃	—	2	12	no	—
38	C₂²×C₄×C₁₃	C₂³	1	3	yes	—
39	C₂²×C₄×C₁₃	C₂³	1	12	yes	—
40	C₂²×C₄×C₁₃	C₂³	1	3	yes	—
41	C₂×C₂²⋊D₁₃	Q₈	1	8	yes	direct product factor
42	C₂×C₂²⋊D₁₃	C₂³	1	4	yes	—
43	C₂²×Dic₁₃	C₂³	1	3	yes	—
44	C₂²×Dic₁₃	C₂³	1	3	yes	—
45	C₂²×Dic₁₃	C₂³	1	1	yes	characteristic
46	Q₈×D₁₃	—	2	32	no	—
47	C₂×C₄×D₁₃	—	2	12	no	—
48	C₂×C₄×D₁₃	C₂³	1	12	yes	—
49	C₂×Dic₂₆	—	2	12	no	—
50	C₂×Dic₂₆	C₂³	1	12	yes	—
51	C₂²⋊Dic₁₃	C₂³	1	12	yes	—
52	#6103	C₂³	1	12	yes	—
53	C₄⋊Dic₁₃	C₂³	1	12	yes	—
54	#6101	C₂³	1	24	yes	—
55	#6101	C₂³	1	12	yes	—
56	C₄×Dic₁₃	C₂³	1	12	yes	—
57	C₂×D₄×Q₈	—	13	1	no	maximal, Sylow
58	C₂³×C₁₃	—	2	2	no	—
59	C₂³×C₁₃	—	2	2	no	—
60	C₂³×C₁₃	C₂×Q₈	1	4	yes	complemented
61	C₂³×C₁₃	C₂⁴	1	2	yes	—
62	C₂³×C₁₃	C₂⁴	1	1	yes	characteristic
63	C₂²×D₁₃	—	2	2	no	—
64	C₂²×D₁₃	—	2	2	no	—
65	C₂²×D₁₃	C₂×Q₈	1	4	yes	complemented
66	C₂²×D₁₃	C₂⁴	1	2	yes	—
67	Q₈×C₁₃	—	2	24	no	—
68	Q₈×C₁₃	C₂×D₄	1	16	yes	complemented
69	C₂×C₄×C₁₃	—	2	6	no	—
70	C₂×C₄×C₁₃	—	2	24	no	—
71	C₂×C₄×C₁₃	C₂×D₄	1	12	yes	—
72	C₂×C₄×C₁₃	C₂⁴	1	6	yes	—
73	C₂×C₄×C₁₃	C₂⁴	1	6	yes	—
74	C₂²⋊D₁₃	C₂×Q₈	1	16	yes	direct product factor
75	C₂×Dic₁₃	—	2	6	no	—
76	C₂×Dic₁₃	—	2	6	no	—
77	C₂×Dic₁₃	C₂×Q₈	1	4	yes	complemented
78	C₂×Dic₁₃	C₂⁴	1	6	yes	—
79	C₂×Dic₁₃	C₂⁴	1	6	yes	—
80	C₂×Dic₁₃	C₂⁴	1	2	yes	—
81	C₄×D₁₃	—	2	24	no	—
82	Dic₂₆	—	2	24	no	—
83	C₂³×Q₈	—	13	1	no	—
84	C₂³×Q₈	D₁₃	1	1	yes	characteristic, complemented
85	D₄×Q₈	—	13	16	no	—
86	C₂×C₄⋊Q₈	—	13	3	no	—
87	C₂×C₂²⋊Q₈	—	13	3	no	—
88	C₂×C₂²⋊Q₈	—	13	3	no	—
89	C₂×C₄×Q₈	—	13	1	no	—
90	C₂×C₄×D₄	—	13	3	no	—
91	C₂²×C₁₃	—	2	8	no	—
92	C₂²×C₁₃	—	2	2	no	—
93	C₂²×C₁₃	—	2	2	no	—
94	C₂²×C₁₃	C₂²×D₄	1	2	yes	—
95	C₂²×C₁₃	C₂²×Q₈	1	2	yes	—
96	C₂²×C₁₃	C₂²×Q₈	1	4	yes	complemented
97	C₂²×C₁₃	2₋¹⁺⁴	1	2	yes	—
98	C₂²×C₁₃	C₂⁵	1	1	yes	characteristic
99	C₂×D₁₃	—	2	8	no	—
100	C₂×D₁₃	—	2	2	no	—
101	C₂×D₁₃	—	2	2	no	—
102	C₂×D₁₃	C₂²×Q₈	1	4	yes	complemented
103	C₄×C₁₃	—	2	6	no	—
104	C₄×C₁₃	C₂²×D₄	1	12	yes	—
105	Dic₁₃	—	2	6	no	—
106	Dic₁₃	—	2	6	no	—
107	Dic₁₃	C₂²×Q₈	1	4	yes	complemented
108	C₂²×Q₈	—	2	8	no	—
109	C₂²×Q₈	—	13	8	no	—
110	C₂²×Q₈	—	13	3	no	—
111	C₂²×Q₈	—	26	8	no	—
112	C₂²×Q₈	C₂×D₁₃	1	3	yes	—
113	C₂²×Q₈	C₂×D₁₃	1	1	yes	characteristic
114	C₂²×Q₈	C₂×D₁₃	1	8	yes	complemented
115	C₂²×D₄	—	13	1	no	—
116	C₂³×C₄	—	13	3	no	—
117	C₂³×C₄	C₂×D₁₃	1	3	yes	—
118	C₄⋊Q₈	—	13	24	no	—
119	C₂²⋊Q₈	—	13	24	no	—
120	C₂²⋊Q₈	—	13	24	no	—
121	C₄×Q₈	—	13	8	no	—
122	C₄×D₄	—	13	24	no	—
123	C₂×C₄⋊C₄	—	13	3	no	—
124	C₂×C₄⋊C₄	—	13	3	no	—
125	C₂×C₄⋊C₄	—	13	6	no	—
126	C₂×C₂²⋊C₄	—	13	3	no	—
127	C₂×C₂²⋊C₄	—	13	3	no	—
128	C₂×C₄²	—	13	3	no	—
129	C₂×C₁₃	—	2	4	no	—
130	C₂×C₁₃	D₄×Q₈	1	4	yes	complemented
131	C₂×C₁₃	C₂³×D₄	1	1	yes	characteristic
132	C₂×C₁₃	C₂³×Q₈	1	1	yes	characteristic
133	C₂×C₁₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
134	D₁₃	—	2	4	no	—
135	C₂⁴	—	13	1	no	—
136	C₂⁴	C₂²×D₁₃	1	1	yes	characteristic
137	C₂×Q₈	—	2	32	no	—
138	C₂×Q₈	—	2	12	no	—
139	C₂×Q₈	—	13	12	no	—
140	C₂×Q₈	—	26	32	no	—
141	C₂×Q₈	—	26	12	no	—
142	C₂×Q₈	C₂²⋊D₁₃	1	8	yes	direct product factor
143	C₂×Q₈	C₂²×D₁₃	1	12	yes	—
144	C₂×Q₈	C₂²×D₁₃	1	4	yes	—
145	C₂×D₄	—	13	8	no	—
146	C₂×D₄	—	13	4	no	—
147	C₂²×C₄	—	2	12	no	—
148	C₂²×C₄	—	13	1	no	—
149	C₂²×C₄	—	13	3	no	—
150	C₂²×C₄	—	13	3	no	—
151	C₂²×C₄	—	13	12	no	—
152	C₂²×C₄	—	26	12	no	—
153	C₂²×C₄	C₂²×D₁₃	1	12	yes	—
154	C₂²×C₄	C₂²×D₁₃	1	3	yes	—
155	C₂²×C₄	C₂²×D₁₃	1	3	yes	—
156	C₄⋊C₄	—	13	12	no	—
157	C₄⋊C₄	—	13	12	no	—
158	C₄⋊C₄	—	13	24	no	—
159	C₂²⋊C₄	—	13	12	no	—
160	C₂²⋊C₄	—	13	12	no	—
161	C₄²	—	13	12	no	—
162	C₁₃	C₂×D₄×Q₈	1	1	yes	characteristic, complemented, Sylow
163	C₂³	—	2	2	no	—
164	C₂³	—	2	2	no	—
165	C₂³	—	13	4	no	—
166	C₂³	—	13	2	no	—
167	C₂³	—	26	2	no	—
168	C₂³	—	26	2	no	—
169	C₂³	Q₈×D₁₃	1	4	yes	complemented
170	C₂³	C₂³×D₁₃	1	2	yes	—
171	C₂³	C₂³×D₁₃	1	1	yes	characteristic
172	Q₈	—	2	24	no	—
173	Q₈	—	26	24	no	—
174	Q₈	C₂×C₂²⋊D₁₃	1	16	yes	direct product factor
175	D₄	—	13	16	no	—
176	C₂×C₄	—	2	6	no	—
177	C₂×C₄	—	2	24	no	—
178	C₂×C₄	—	13	4	no	—
179	C₂×C₄	—	13	2	no	—
180	C₂×C₄	—	13	6	no	—
181	C₂×C₄	—	13	6	no	—
182	C₂×C₄	—	26	6	no	—
183	C₂×C₄	—	26	6	no	—
184	C₂×C₄	—	26	24	no	—
185	C₂×C₄	C₂×C₂²⋊D₁₃	1	12	yes	—
186	C₂×C₄	C₂³×D₁₃	1	6	yes	—
187	C₂×C₄	C₂³×D₁₃	1	6	yes	—
188	C₂²	—	2	8	no	—
189	C₂²	—	2	2	no	—
190	C₂²	—	2	2	no	—
191	C₂²	—	13	4	no	—
192	C₂²	—	26	8	no	—
193	C₂²	—	26	2	no	—
194	C₂²	—	26	2	no	—
195	C₂²	C₂×Q₈×D₁₃	1	2	yes	—
196	C₂²	C₂×Q₈×D₁₃	1	4	yes	complemented
197	C₂²	#88254	1	2	yes	—
198	C₂²	C₂²×C₂²⋊D₁₃	1	2	yes	—
199	C₂²	C₂⁴×D₁₃	1	1	yes	characteristic
200	C₄	—	2	6	no	—
201	C₄	—	13	4	no	—
202	C₄	—	26	6	no	—
203	C₄	—	26	6	no	—
204	C₄	C₂²×C₂²⋊D₁₃	1	12	yes	—
205	C₂	—	2	4	no	—
206	C₂	—	26	4	no	—
207	C₂	Q₈×C₂²⋊D₁₃	1	4	yes	direct product factor
208	C₂	C₂²×Q₈×D₁₃	1	1	yes	characteristic
209	C₂	C₂×#88254	1	1	yes	characteristic
210	C₂	C₂³×C₂²⋊D₁₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂³×D₁₃
commutator, cosocle	C₂²×C₁₃	C₂⁵
Frattini	C₂²	C₂⁴×D₁₃
Fitting	C₂³×Q₈×C₁₃	C₂
socle	C₂³×C₁₃	C₂⁴
prime radical	C₂²×C₂²⋊D₁₃	C₂²
hypercenter	C₂³×Q₈	D₁₃
hypocenter	C₁₃	C₂×D₄×Q₈
LCS	G ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂³ ◁ C₂³×Q₈

Complements

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

N	H ≅ G/N	type
1. C₂³×Q₈×C₁₃	C₂	semidirect
2. C₂²×Q₈×D₁₃	C₂	semidirect
3. Q₈×C₂²⋊D₁₃	C₂	direct (N × H)
4. C₂×#88200	C₂	semidirect
5. C₂×Q₈×Dic₁₃	C₂	semidirect
6. C₂×#88198	C₂	semidirect
8. C₂×#88178	C₂	semidirect
12. C₂²×Q₈×C₁₃	C₂²	semidirect
16. C₂×Q₈×D₁₃	C₂²	semidirect
20. #88200	C₂²	semidirect
21. Q₈×Dic₁₃	C₂²	semidirect
22. #88198	C₂²	semidirect
26. #88178	C₂²	semidirect
34. C₂×Q₈×C₁₃	D₄	semidirect
41. C₂×C₂²⋊D₁₃	Q₈	direct (N × H)
60. C₂³×C₁₃	C₂×Q₈	semidirect
65. C₂²×D₁₃	C₂×Q₈	semidirect
68. Q₈×C₁₃	C₂×D₄	semidirect
74. C₂²⋊D₁₃	C₂×Q₈	direct (N × H)
77. C₂×Dic₁₃	C₂×Q₈	semidirect
84. C₂³×Q₈	D₁₃	semidirect
96. C₂²×C₁₃	C₂²×Q₈	semidirect
102. C₂×D₁₃	C₂²×Q₈	semidirect
107. Dic₁₃	C₂²×Q₈	semidirect
114. C₂²×Q₈	C₂×D₁₃	semidirect
130. C₂×C₁₃	D₄×Q₈	semidirect
142. C₂×Q₈	C₂²⋊D₁₃	direct (N × H)
162. C₁₃	C₂×D₄×Q₈	semidirect
169. C₂³	Q₈×D₁₃	semidirect
174. Q₈	C₂×C₂²⋊D₁₃	direct (N × H)
196. C₂²	C₂×Q₈×D₁₃	semidirect
207. C₂	Q₈×C₂²⋊D₁₃	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂³×Q₈×C₁₃	2
C₂²×Q₈×D₁₃	2
Q₈×C₂²⋊D₁₃	2
C₂×#88200	2
C₂×Q₈×Dic₁₃	2
C₂×#88198	2
C₂×C₄×C₂²⋊D₁₃	2
C₂×#88178	2
C₂×D₄×Q₈	13

Subgroups — C2×Q8×C22⋊D13 #13128308

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×Q₈×C₂²⋊D₁₃ #13128308