Subgroups — C₁₃×#3203 #13112261

Order 1664.

402 conjugacy classes of subgroups.

The subgroup lattice has 240 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#537	C₂	1	2	yes	maximal, complemented
2	C₁₃×#484	C₂	1	2	yes	maximal, complemented
3	C₁₃×#480	C₂	1	2	yes	maximal, complemented
4	C₁₃×#468	C₂	1	2	yes	maximal, complemented
5	C₁₃×#467	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#466	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#452	C₂	1	2	yes	maximal, complemented
8	C₁₃×#449	C₂	1	2	yes	maximal, complemented
9	C₁₃×#408	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₁₃×#41	C₂²	1	2	yes	—
11	C₂×C₁₃×#41	C₂²	1	1	yes	characteristic
12	C₂×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic
13	C₂×C₁₃×SD₁₆	C₂²	1	2	yes	—
14	C₂×C₁₃×D₈	C₂²	1	1	yes	characteristic
15	C₂×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
16	C₂²×C₈×C₁₃	C₂²	1	1	yes	characteristic
17	C₁₃×C₂²⋊Q₈	—	2	2	no	—
18	C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	—
19	C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	—
20	C₁₃×#121	—	2	2	no	—
21	C₁₃×#121	—	2	2	no	—
22	C₁₃×#121	—	2	2	no	—
23	C₁₃×#121	C₂²	1	2	yes	—
24	C₁₃×#121	C₂²	1	2	yes	—
25	C₂×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
26	C₁₃×#107	C₂²	1	1	yes	characteristic
27	C₁₃×#107	C₂²	1	1	yes	characteristic
28	C₁₃×#107	C₂²	1	2	yes	—
29	C₁₃×#103	C₂²	1	2	yes	—
30	C₁₃×#103	C₂²	1	2	yes	—
31	C₁₃×#102	C₂²	1	2	yes	—
32	C₁₃×#102	C₂²	1	2	yes	—
33	C₁₃×C₂²⋊C₈	C₂²	1	2	yes	—
34	C₁₃×C₂²⋊C₈	C₂²	1	2	yes	—
35	C₁₃×#41	—	4	1	no	—
36	C₁₃×#41	—	4	1	no	—
37	C₁₃×#41	—	4	2	no	—
38	C₁₃×#41	—	4	2	no	—
39	C₂×Q₈×C₁₃	D₄	1	1	yes	characteristic
40	C₂×Q₈×C₁₃	C₂³	1	2	yes	—
41	C₂×D₄×C₁₃	—	2	2	no	—
42	C₂×D₄×C₁₃	—	2	2	no	—
43	C₂×D₄×C₁₃	—	2	2	no	—
44	C₂×D₄×C₁₃	D₄	1	1	yes	characteristic
45	C₂×D₄×C₁₃	D₄	1	2	yes	—
46	C₂×D₄×C₁₃	C₂³	1	2	yes	—
47	C₂²×C₄×C₁₃	—	2	2	no	—
48	C₂²×C₄×C₁₃	—	2	2	no	—
49	C₂²×C₄×C₁₃	C₂³	1	2	yes	—
50	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
51	C₁₃×Q₁₆	—	4	1	no	—
52	C₁₃×SD₁₆	—	4	2	no	—
53	C₁₃×D₈	—	4	1	no	—
54	C₁₃×M₁₆	—	4	1	no	—
55	C₂×C₈×C₁₃	—	4	1	no	—
56	C₂×C₈×C₁₃	C₂³	1	1	yes	characteristic
57	C₂×C₈×C₁₃	C₂³	1	2	yes	—
58	C₂×C₈×C₁₃	C₂³	1	1	yes	characteristic
59	C₁₃×C₄⋊C₄	—	2	2	no	—
60	C₁₃×C₄⋊C₄	—	2	2	no	—
61	C₁₃×C₄⋊C₄	—	2	2	no	—
62	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
63	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
64	C₁₃×C₂²⋊C₄	—	2	2	no	—
65	C₁₃×C₂²⋊C₄	—	2	2	no	—
66	C₁₃×C₂²⋊C₄	—	2	2	no	—
67	C₁₃×C₂²⋊C₄	—	2	2	no	—
68	#3203	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
69	C₂³×C₁₃	—	2	2	no	—
70	C₂³×C₁₃	C₂×D₄	1	1	yes	characteristic
71	C₂³×C₁₃	C₂×D₄	1	2	yes	—
72	Q₈×C₁₃	—	2	2	no	—
73	Q₈×C₁₃	—	2	2	no	—
74	Q₈×C₁₃	—	4	1	no	—
75	D₄×C₁₃	—	2	2	no	—
76	D₄×C₁₃	—	2	2	no	—
77	D₄×C₁₃	—	4	2	no	—
78	D₄×C₁₃	—	4	1	no	—
79	D₄×C₁₃	—	4	4	no	—
80	D₄×C₁₃	—	8	2	no	—
81	D₄×C₁₃	—	8	2	no	—
82	C₂×C₄×C₁₃	—	2	1	no	—
83	C₂×C₄×C₁₃	—	2	1	no	—
84	C₂×C₄×C₁₃	—	2	2	no	—
85	C₂×C₄×C₁₃	—	2	2	no	—
86	C₂×C₄×C₁₃	—	2	2	no	—
87	C₂×C₄×C₁₃	—	2	2	no	—
88	C₂×C₄×C₁₃	—	2	2	no	—
89	C₂×C₄×C₁₃	—	4	4	no	—
90	C₂×C₄×C₁₃	—	8	2	no	—
91	C₂×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
92	C₂×C₄×C₁₃	C₂×D₄	1	2	yes	—
93	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
94	C₈×C₁₃	—	2	1	no	—
95	C₈×C₁₃	—	2	1	no	—
96	C₈×C₁₃	—	2	2	no	—
97	#537	C₂×C₁₃	1	2	yes	complemented
98	#484	C₂×C₁₃	1	2	yes	complemented
99	#480	C₂×C₁₃	1	2	yes	complemented
100	#468	C₂×C₁₃	1	2	yes	complemented
101	#467	C₂×C₁₃	1	1	yes	characteristic, complemented
102	#466	C₂×C₁₃	1	1	yes	characteristic, complemented
103	#452	C₂×C₁₃	1	2	yes	complemented
104	#449	C₂×C₁₃	1	2	yes	complemented
105	#408	C₂×C₁₃	1	1	yes	characteristic, complemented
106	C₂²×C₁₃	—	2	2	no	—
107	C₂²×C₁₃	—	2	1	no	—
108	C₂²×C₁₃	—	2	2	no	—
109	C₂²×C₁₃	—	2	1	no	—
110	C₂²×C₁₃	—	2	1	no	—
111	C₂²×C₁₃	—	2	2	no	—
112	C₂²×C₁₃	—	4	2	no	—
113	C₂²×C₁₃	—	4	2	no	—
114	C₂²×C₁₃	—	4	2	no	—
115	C₂²×C₁₃	C₂²×D₄	1	1	yes	characteristic
116	C₄×C₁₃	—	2	2	no	—
117	C₄×C₁₃	—	2	1	no	—
118	C₄×C₁₃	—	4	2	no	—
119	C₄×C₁₃	—	4	2	no	—
120	C₄×C₁₃	—	4	2	no	—
121	C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
122	C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
123	C₂×#41	C₂²×C₁₃	1	2	yes	—
124	C₂×#41	C₂²×C₁₃	1	1	yes	characteristic
125	C₂×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic
126	C₂×SD₁₆	C₂²×C₁₃	1	2	yes	—
127	C₂×D₈	C₂²×C₁₃	1	1	yes	characteristic
128	C₂×M₁₆	C₂²×C₁₃	1	1	yes	characteristic
129	C₂²×C₈	C₂²×C₁₃	1	1	yes	characteristic
130	C₂²⋊Q₈	—	2	2	no	—
131	C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	—
132	C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	—
133	#121	—	2	2	no	—
134	#121	—	2	2	no	—
135	#121	—	2	2	no	—
136	#121	C₂²×C₁₃	1	2	yes	—
137	#121	C₂²×C₁₃	1	2	yes	—
138	C₂×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
139	#107	C₂²×C₁₃	1	1	yes	characteristic
140	#107	C₂²×C₁₃	1	1	yes	characteristic
141	#107	C₂²×C₁₃	1	2	yes	—
142	#103	C₂²×C₁₃	1	2	yes	—
143	#103	C₂²×C₁₃	1	2	yes	—
144	#102	C₂²×C₁₃	1	2	yes	—
145	#102	C₂²×C₁₃	1	2	yes	—
146	C₂²⋊C₈	C₂²×C₁₃	1	2	yes	—
147	C₂²⋊C₈	C₂²×C₁₃	1	2	yes	—
148	C₂×C₁₃	—	4	2	no	—
149	C₂×C₁₃	—	4	1	no	—
150	C₂×C₁₃	—	8	2	no	—
151	C₂×C₁₃	#534	1	1	yes	characteristic
152	C₂×C₁₃	#576	1	1	yes	characteristic
153	C₂×C₁₃	#578	1	1	yes	characteristic
154	#41	—	4	1	no	—
155	#41	—	4	1	no	—
156	#41	—	4	2	no	—
157	#41	—	4	2	no	—
158	C₂×Q₈	D₄×C₁₃	1	1	yes	characteristic
159	C₂×Q₈	C₂³×C₁₃	1	2	yes	—
160	C₂×D₄	—	2	2	no	—
161	C₂×D₄	—	2	2	no	—
162	C₂×D₄	—	2	2	no	—
163	C₂×D₄	D₄×C₁₃	1	1	yes	characteristic
164	C₂×D₄	D₄×C₁₃	1	2	yes	—
165	C₂×D₄	C₂³×C₁₃	1	2	yes	—
166	C₂²×C₄	—	2	2	no	—
167	C₂²×C₄	—	2	2	no	—
168	C₂²×C₄	C₂³×C₁₃	1	2	yes	—
169	C₂²×C₄	C₂³×C₁₃	1	1	yes	characteristic
170	Q₁₆	—	4	1	no	—
171	SD₁₆	—	4	2	no	—
172	D₈	—	4	1	no	—
173	M₁₆	—	4	1	no	—
174	C₂×C₈	—	4	1	no	—
175	C₂×C₈	C₂³×C₁₃	1	1	yes	characteristic
176	C₂×C₈	C₂³×C₁₃	1	2	yes	—
177	C₂×C₈	C₂³×C₁₃	1	1	yes	characteristic
178	C₄⋊C₄	—	2	2	no	—
179	C₄⋊C₄	—	2	2	no	—
180	C₄⋊C₄	—	2	2	no	—
181	C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
182	C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
183	C₂²⋊C₄	—	2	2	no	—
184	C₂²⋊C₄	—	2	2	no	—
185	C₂²⋊C₄	—	2	2	no	—
186	C₂²⋊C₄	—	2	2	no	—
187	C₁₃	#3203	1	1	yes	characteristic, direct product factor, Sylow
188	C₂³	—	2	2	no	—
189	C₂³	C₂×D₄×C₁₃	1	1	yes	characteristic
190	C₂³	C₂×D₄×C₁₃	1	2	yes	—
191	Q₈	—	2	2	no	—
192	Q₈	—	2	2	no	—
193	Q₈	—	4	1	no	—
194	D₄	—	2	2	no	—
195	D₄	—	2	2	no	—
196	D₄	—	4	2	no	—
197	D₄	—	4	1	no	—
198	D₄	—	4	4	no	—
199	D₄	—	8	2	no	—
200	D₄	—	8	2	no	—
201	C₂×C₄	—	2	1	no	—
202	C₂×C₄	—	2	1	no	—
203	C₂×C₄	—	2	2	no	—
204	C₂×C₄	—	2	2	no	—
205	C₂×C₄	—	2	2	no	—
206	C₂×C₄	—	2	2	no	—
207	C₂×C₄	—	2	2	no	—
208	C₂×C₄	—	4	4	no	—
209	C₂×C₄	—	8	2	no	—
210	C₂×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
211	C₂×C₄	C₂×D₄×C₁₃	1	2	yes	—
212	C₂×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
213	C₈	—	2	1	no	—
214	C₈	—	2	1	no	—
215	C₈	—	2	2	no	—
216	C₂²	—	2	2	no	—
217	C₂²	—	2	1	no	—
218	C₂²	—	2	2	no	—
219	C₂²	—	2	1	no	—
220	C₂²	—	2	1	no	—
221	C₂²	—	2	2	no	—
222	C₂²	—	4	2	no	—
223	C₂²	—	4	2	no	—
224	C₂²	—	4	2	no	—
225	C₂²	C₂²×D₄×C₁₃	1	1	yes	characteristic
226	C₄	—	2	2	no	—
227	C₄	—	2	1	no	—
228	C₄	—	4	2	no	—
229	C₄	—	4	2	no	—
230	C₄	—	4	2	no	—
231	C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
232	C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
233	C₂	—	4	2	no	—
234	C₂	—	4	1	no	—
235	C₂	—	8	2	no	—
236	C₂	C₁₃×#534	1	1	yes	characteristic
237	C₂	C₁₃×#576	1	1	yes	characteristic
238	C₂	C₁₃×#578	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁴×C₁₃
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₂×C₁₃×#41 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₃×#537	C₂	semidirect
2. C₁₃×#484	C₂	semidirect
3. C₁₃×#480	C₂	semidirect
4. C₁₃×#468	C₂	semidirect
5. C₁₃×#467	C₂	semidirect
6. C₁₃×#466	C₂	semidirect
7. C₁₃×#452	C₂	semidirect
8. C₁₃×#449	C₂	semidirect
9. C₁₃×#408	C₂	semidirect
68. #3203	C₁₃	direct (N × H)
97. #537	C₂×C₁₃	semidirect
98. #484	C₂×C₁₃	semidirect
99. #480	C₂×C₁₃	semidirect
100. #468	C₂×C₁₃	semidirect
101. #467	C₂×C₁₃	semidirect
102. #466	C₂×C₁₃	semidirect
103. #452	C₂×C₁₃	semidirect
104. #449	C₂×C₁₃	semidirect
105. #408	C₂×C₁₃	semidirect
187. C₁₃	#3203	direct (N × H)

Maximal subgroups

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

subgroup	index
C₁₃×#537	2
C₁₃×#484	2
C₁₃×#480	2
C₁₃×#468	2
C₁₃×#467	2
C₁₃×#466	2
C₁₃×#452	2
C₁₃×#449	2
C₁₃×#408	2
#3203	13

Subgroups — C13×#3203 #13112261

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#3203 #13112261