Subgroups — C₁₃×#36644 #15722983

Order 3328.

4086 conjugacy classes of subgroups.

The subgroup lattice has 210 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#532	C₂	1	6	yes	maximal, complemented
2	C₁₃×#2868	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#2867	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#2858	C₂	1	6	yes	maximal, complemented
5	C₁₃×#2856	C₂	1	8	yes	maximal, complemented
6	C₄×C₁₃×#127	C₂	1	8	yes	maximal, complemented
7	C₂×C₄³×C₁₃	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×C₁₃×#41	C₂²	1	4	yes	—
9	C₁₃×#532	—	2	48	no	—
10	C₂×C₁₃×C₄⋊Q₈	C₂²	1	6	yes	—
11	C₂×C₁₃×#127	C₂²	1	8	yes	—
12	C₂×C₁₃×#127	C₂²	1	6	yes	—
13	C₂×C₁₃×#124	C₂²	1	12	yes	—
14	C₂×C₁₃×#121	C₂²	1	24	yes	—
15	C₂×C₄×D₄×C₁₃	C₂²	1	24	yes	—
16	C₂²×C₄²×C₁₃	C₂²	1	4	yes	—
17	C₂²×C₄²×C₁₃	C₂²	1	3	yes	—
18	C₁₃×#390	C₂²	1	48	yes	—
19	C₁₃×#384	C₂²	1	8	yes	—
20	C₄³×C₁₃	C₂²	1	4	yes	—
21	C₄³×C₁₃	C₂²	1	3	yes	—
22	C₄³×C₁₃	C₂²	1	1	yes	characteristic
23	C₂×C₁₃×#41	—	2	48	no	—
24	C₂²×Q₈×C₁₃	C₂³	1	4	yes	—
25	C₂²×D₄×C₁₃	C₂³	1	24	yes	—
26	C₂²×D₄×C₁₃	C₂³	1	8	yes	—
27	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
28	C₂³×C₄×C₁₃	C₂³	1	8	yes	—
29	C₂³×C₄×C₁₃	C₂³	1	6	yes	—
30	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
31	C₁₃×C₄⋊Q₈	—	2	24	no	—
32	C₁₃×#127	—	2	24	no	—
33	C₁₃×#127	—	2	32	no	—
34	C₁₃×#124	—	2	48	no	—
35	C₁₃×#121	—	2	96	no	—
36	C₄×D₄×C₁₃	—	2	96	no	—
37	C₂×C₁₃×C₄⋊C₄	C₂³	1	24	yes	—
38	C₂×C₁₃×C₂²⋊C₄	C₂³	1	48	yes	—
39	C₂×C₄²×C₁₃	—	2	16	no	—
40	C₂×C₄²×C₁₃	D₄	1	24	yes	complemented
41	C₂×C₄²×C₁₃	C₂³	1	12	yes	—
42	C₂×C₄²×C₁₃	C₂³	1	3	yes	—
43	C₂×C₄²×C₁₃	C₂³	1	3	yes	—
44	C₂×C₄²×C₁₃	C₂³	1	6	yes	—
45	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
46	#36644	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
47	C₂⁴×C₁₃	C₂⁴	1	8	yes	—
48	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
49	C₁₃×#41	—	4	64	no	—
50	C₂×Q₈×C₁₃	—	2	24	no	—
51	C₂×D₄×C₁₃	—	2	48	no	—
52	C₂×D₄×C₁₃	—	2	48	no	—
53	C₂×D₄×C₁₃	—	2	24	no	—
54	C₂×D₄×C₁₃	—	2	96	no	—
55	C₂²×C₄×C₁₃	—	2	24	no	—
56	C₂²×C₄×C₁₃	—	2	48	no	—
57	C₂²×C₄×C₁₃	C₂×D₄	1	24	yes	—
58	C₂²×C₄×C₁₃	C₂×D₄	1	12	yes	—
59	C₂²×C₄×C₁₃	C₂⁴	1	8	yes	—
60	C₂²×C₄×C₁₃	C₂⁴	1	6	yes	—
61	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
62	C₂²×C₄×C₁₃	C₂⁴	1	6	yes	—
63	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
64	C₁₃×C₄⋊C₄	—	2	48	no	—
65	C₁₃×C₂²⋊C₄	—	2	96	no	—
66	C₄²×C₁₃	—	2	24	no	—
67	C₄²×C₁₃	C₂×D₄	1	24	yes	—
68	C₄²×C₁₃	C₂×D₄	1	12	yes	—
69	C₄²×C₁₃	C₂×D₄	1	12	yes	—
70	C₄²×C₁₃	#41	1	16	yes	complemented
71	C₂×#532	C₂×C₁₃	1	6	yes	complemented
72	#2868	C₂×C₁₃	1	1	yes	characteristic, complemented
73	#2867	C₂×C₁₃	1	1	yes	characteristic, complemented
74	#2858	C₂×C₁₃	1	6	yes	complemented
75	#2856	C₂×C₁₃	1	8	yes	complemented
76	C₄×#127	C₂×C₁₃	1	8	yes	complemented
77	C₂×C₄³	C₂×C₁₃	1	1	yes	characteristic, complemented
78	C₂³×C₁₃	—	2	4	no	—
79	C₂³×C₁₃	—	2	24	no	—
80	C₂³×C₁₃	—	2	32	no	—
81	C₂³×C₁₃	C₂²×D₄	1	6	yes	—
82	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
83	Q₈×C₁₃	—	4	16	no	—
84	D₄×C₁₃	—	4	32	no	—
85	D₄×C₁₃	—	4	16	no	—
86	D₄×C₁₃	—	4	96	no	—
87	C₂×C₄×C₁₃	—	2	12	no	—
88	C₂×C₄×C₁₃	—	2	48	no	—
89	C₂×C₄×C₁₃	—	2	24	no	—
90	C₂×C₄×C₁₃	—	4	32	no	—
91	C₂×C₄×C₁₃	#127	1	16	yes	complemented
92	C₂×C₄×C₁₃	C₂²×D₄	1	12	yes	—
93	C₂×C₄×C₁₃	C₂²×D₄	1	6	yes	—
94	C₂×C₄×C₁₃	C₂²×D₄	1	6	yes	—
95	C₂×C₄×C₁₃	C₂²×D₄	1	12	yes	—
96	C₂×C₄×C₁₃	C₂×#41	1	24	yes	—
97	C₂²×#41	C₂²×C₁₃	1	4	yes	—
98	#532	—	2	48	no	—
99	C₂×C₄⋊Q₈	C₂²×C₁₃	1	6	yes	—
100	C₂×#127	C₂²×C₁₃	1	8	yes	—
101	C₂×#127	C₂²×C₁₃	1	6	yes	—
102	C₂×#124	C₂²×C₁₃	1	12	yes	—
103	C₂×#121	C₂²×C₁₃	1	24	yes	—
104	C₂×C₄×D₄	C₂²×C₁₃	1	24	yes	—
105	C₂²×C₄²	C₂²×C₁₃	1	4	yes	—
106	C₂²×C₄²	C₂²×C₁₃	1	3	yes	—
107	#390	C₂²×C₁₃	1	48	yes	—
108	#384	C₂²×C₁₃	1	8	yes	—
109	C₄³	C₂²×C₁₃	1	4	yes	—
110	C₄³	C₂²×C₁₃	1	3	yes	—
111	C₄³	C₂²×C₁₃	1	1	yes	characteristic
112	C₂²×C₁₃	—	2	12	no	—
113	C₂²×C₁₃	—	4	8	no	—
114	C₂²×C₁₃	—	4	48	no	—
115	C₂²×C₁₃	C₂×#127	1	4	yes	—
116	C₂²×C₁₃	C₂³×D₄	1	3	yes	—
117	C₂²×C₁₃	C₂²×#41	1	4	yes	—
118	C₄×C₁₃	—	2	12	no	—
119	C₄×C₁₃	—	4	8	no	—
120	C₄×C₁₃	C₂×#127	1	4	yes	—
121	C₄×C₁₃	C₂×#127	1	4	yes	—
122	C₄×C₁₃	#532	1	24	yes	complemented
123	C₂×#41	—	2	48	no	—
124	C₂²×Q₈	C₂³×C₁₃	1	4	yes	—
125	C₂²×D₄	C₂³×C₁₃	1	24	yes	—
126	C₂²×D₄	C₂³×C₁₃	1	8	yes	—
127	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
128	C₂³×C₄	C₂³×C₁₃	1	8	yes	—
129	C₂³×C₄	C₂³×C₁₃	1	6	yes	—
130	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
131	C₄⋊Q₈	—	2	24	no	—
132	#127	—	2	24	no	—
133	#127	—	2	32	no	—
134	#124	—	2	48	no	—
135	#121	—	2	96	no	—
136	C₄×D₄	—	2	96	no	—
137	C₂×C₄⋊C₄	C₂³×C₁₃	1	24	yes	—
138	C₂×C₂²⋊C₄	C₂³×C₁₃	1	48	yes	—
139	C₂×C₄²	—	2	16	no	—
140	C₂×C₄²	D₄×C₁₃	1	24	yes	complemented
141	C₂×C₄²	C₂³×C₁₃	1	12	yes	—
142	C₂×C₄²	C₂³×C₁₃	1	6	yes	—
143	C₂×C₄²	C₂³×C₁₃	1	3	yes	—
144	C₂×C₄²	C₂³×C₁₃	1	3	yes	—
145	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
146	C₂×C₁₃	—	2	4	no	—
147	C₂×C₁₃	—	8	8	no	—
148	C₂×C₁₃	C₂²×#127	1	1	yes	characteristic
149	C₂×C₁₃	C₂×#532	1	6	yes	—
150	C₂⁴	C₂⁴×C₁₃	1	8	yes	—
151	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
152	#41	—	4	64	no	—
153	C₂×Q₈	—	2	24	no	—
154	C₂×D₄	—	2	48	no	—
155	C₂×D₄	—	2	48	no	—
156	C₂×D₄	—	2	24	no	—
157	C₂×D₄	—	2	96	no	—
158	C₂²×C₄	—	2	24	no	—
159	C₂²×C₄	—	2	48	no	—
160	C₂²×C₄	C₂×D₄×C₁₃	1	24	yes	—
161	C₂²×C₄	C₂×D₄×C₁₃	1	12	yes	—
162	C₂²×C₄	C₂⁴×C₁₃	1	8	yes	—
163	C₂²×C₄	C₂⁴×C₁₃	1	6	yes	—
164	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
165	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
166	C₂²×C₄	C₂⁴×C₁₃	1	6	yes	—
167	C₄⋊C₄	—	2	48	no	—
168	C₂²⋊C₄	—	2	96	no	—
169	C₄²	—	2	24	no	—
170	C₄²	C₂×D₄×C₁₃	1	24	yes	—
171	C₄²	C₂×D₄×C₁₃	1	12	yes	—
172	C₄²	C₂×D₄×C₁₃	1	12	yes	—
173	C₄²	C₁₃×#41	1	16	yes	complemented
174	C₁₃	#36644	1	1	yes	characteristic, direct product factor, Sylow
175	C₂³	—	2	4	no	—
176	C₂³	—	2	24	no	—
177	C₂³	—	2	32	no	—
178	C₂³	C₂²×D₄×C₁₃	1	6	yes	—
179	C₂³	C₂⁵×C₁₃	1	1	yes	characteristic
180	Q₈	—	4	16	no	—
181	D₄	—	4	32	no	—
182	D₄	—	4	16	no	—
183	D₄	—	4	96	no	—
184	C₂×C₄	—	2	12	no	—
185	C₂×C₄	—	2	48	no	—
186	C₂×C₄	—	2	24	no	—
187	C₂×C₄	—	4	32	no	—
188	C₂×C₄	C₁₃×#127	1	16	yes	complemented
189	C₂×C₄	C₂²×D₄×C₁₃	1	12	yes	—
190	C₂×C₄	C₂²×D₄×C₁₃	1	6	yes	—
191	C₂×C₄	C₂²×D₄×C₁₃	1	6	yes	—
192	C₂×C₄	C₂²×D₄×C₁₃	1	12	yes	—
193	C₂×C₄	C₂×C₁₃×#41	1	24	yes	—
194	C₂²	—	2	12	no	—
195	C₂²	—	4	8	no	—
196	C₂²	—	4	48	no	—
197	C₂²	C₂×C₁₃×#127	1	4	yes	—
198	C₂²	C₂³×D₄×C₁₃	1	3	yes	—
199	C₂²	C₂²×C₁₃×#41	1	4	yes	—
200	C₄	—	2	12	no	—
201	C₄	—	4	8	no	—
202	C₄	C₂×C₁₃×#127	1	4	yes	—
203	C₄	C₂×C₁₃×#127	1	4	yes	—
204	C₄	C₁₃×#532	1	24	yes	complemented
205	C₂	—	2	4	no	—
206	C₂	—	8	8	no	—
207	C₂	C₂²×C₁₃×#127	1	1	yes	characteristic
208	C₂	C₂×C₁₃×#532	1	6	yes	—

	subgroup	G/H
center	C₂²×C₄×C₁₃	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁵×C₁₃
socle	C₂³×C₁₃	C₂⁵
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₃×#532	C₂	semidirect
2. C₁₃×#2868	C₂	semidirect
3. C₁₃×#2867	C₂	semidirect
4. C₁₃×#2858	C₂	semidirect
5. C₁₃×#2856	C₂	semidirect
6. C₄×C₁₃×#127	C₂	semidirect
7. C₂×C₄³×C₁₃	C₂	semidirect
40. C₂×C₄²×C₁₃	D₄	semidirect
46. #36644	C₁₃	direct (N × H)
70. C₄²×C₁₃	#41	semidirect
71. C₂×#532	C₂×C₁₃	semidirect
72. #2868	C₂×C₁₃	semidirect
73. #2867	C₂×C₁₃	semidirect
74. #2858	C₂×C₁₃	semidirect
75. #2856	C₂×C₁₃	semidirect
76. C₄×#127	C₂×C₁₃	semidirect
77. C₂×C₄³	C₂×C₁₃	semidirect
91. C₂×C₄×C₁₃	#127	semidirect
122. C₄×C₁₃	#532	semidirect
140. C₂×C₄²	D₄×C₁₃	semidirect
173. C₄²	C₁₃×#41	semidirect
174. C₁₃	#36644	direct (N × H)
188. C₂×C₄	C₁₃×#127	semidirect
204. C₄	C₁₃×#532	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₁₃×#532	2
C₁₃×#2868	2
C₁₃×#2867	2
C₁₃×#2858	2
C₁₃×#2856	2
C₄×C₁₃×#127	2
C₂×C₄³×C₁₃	2
#36644	13

Subgroups — C13×#36644 #15722983

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#36644 #15722983