Subgroups — C₁₃×#3233 #13112291

Order 1664.

332 conjugacy classes of subgroups.

The subgroup lattice has 260 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#533	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃×#529	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#499	C₂	1	2	yes	maximal, complemented
4	C₁₃×#488	C₂	1	2	yes	maximal, complemented
5	C₁₃×#485	C₂	1	2	yes	maximal, complemented
6	C₁₃×#482	C₂	1	2	yes	maximal
7	C₁₃×#477	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#476	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#475	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#474	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#431	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
13	C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
14	C₁₃×#126	—	2	1	no	—
15	C₁₃×#125	C₂²	1	2	yes	—
16	C₁₃×#125	C₂²	1	1	yes	characteristic
17	C₁₃×#124	C₂²	1	1	yes	characteristic
18	C₁₃×#123	—	2	1	no	—
19	C₁₃×C₂²⋊Q₈	—	2	1	no	—
20	C₁₃×C₂²⋊Q₈	—	2	1	no	—
21	C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
22	C₁₃×#121	C₂²	1	1	yes	characteristic
23	C₄×Q₈×C₁₃	—	2	1	no	—
24	C₄×Q₈×C₁₃	—	2	1	no	—
25	C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
26	C₄×D₄×C₁₃	—	2	1	no	—
27	C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
28	C₁₃×#117	—	2	1	no	—
29	C₁₃×#117	C₂²	1	2	yes	—
30	C₂×C₄²×C₁₃	C₂²	1	1	yes	characteristic
31	C₁₃×#107	C₂²	1	2	yes	—
32	C₁₃×#107	C₂²	1	2	yes	—
33	C₁₃×#106	C₂²	1	2	yes	—
34	C₁₃×#106	C₂²	1	2	yes	—
35	C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
36	C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
37	C₁₃×#103	C₂²	1	2	yes	—
38	C₁₃×#103	C₂²	1	2	yes	—
39	C₁₃×#102	C₂²	1	2	yes	—
40	C₁₃×#102	C₂²	1	2	yes	—
41	C₁₃×C₂²⋊C₈	C₂²	1	2	yes	—
42	C₄×C₈×C₁₃	C₂²	1	2	yes	—
43	C₂×Q₈×C₁₃	—	2	1	no	—
44	C₂×Q₈×C₁₃	—	2	1	no	—
45	C₂×Q₈×C₁₃	C₂³	1	1	yes	characteristic
46	C₂×D₄×C₁₃	—	2	1	no	—
47	C₂×D₄×C₁₃	C₂³	1	1	yes	characteristic
48	C₂²×C₄×C₁₃	—	2	1	no	—
49	C₂²×C₄×C₁₃	D₄	1	1	yes	characteristic
50	C₂²×C₄×C₁₃	D₄	1	1	yes	characteristic
51	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
52	C₂×C₈×C₁₃	C₂³	1	2	yes	—
53	C₂×C₈×C₁₃	C₂³	1	2	yes	—
54	C₁₃×C₄⋊C₄	—	2	1	no	—
55	C₁₃×C₄⋊C₄	—	2	1	no	—
56	C₁₃×C₄⋊C₄	—	2	1	no	—
57	C₁₃×C₄⋊C₄	—	2	2	no	—
58	C₁₃×C₄⋊C₄	—	2	2	no	—
59	C₁₃×C₄⋊C₄	—	2	1	no	—
60	C₁₃×C₄⋊C₄	—	2	1	no	—
61	C₁₃×C₄⋊C₄	—	2	1	no	—
62	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
63	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
64	C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
65	C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
66	C₁₃×C₂²⋊C₄	—	2	2	no	—
67	C₁₃×C₂²⋊C₄	—	2	1	no	—
68	C₁₃×C₂²⋊C₄	—	2	1	no	—
69	C₁₃×C₂²⋊C₄	—	2	1	no	—
70	C₁₃×C₂²⋊C₄	—	2	1	no	—
71	C₁₃×C₂²⋊C₄	—	2	1	no	—
72	C₄²×C₁₃	—	2	1	no	—
73	C₄²×C₁₃	—	2	2	no	—
74	C₄²×C₁₃	D₄	1	1	yes	characteristic
75	C₄²×C₁₃	D₄	1	1	yes	characteristic
76	C₄²×C₁₃	C₂³	1	1	yes	characteristic
77	C₄²×C₁₃	C₂³	1	1	yes	characteristic
78	#3233	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
79	C₂³×C₁₃	—	2	1	no	—
80	C₂³×C₁₃	C₂×D₄	1	1	yes	characteristic
81	Q₈×C₁₃	—	2	1	no	—
82	Q₈×C₁₃	—	2	1	no	—
83	Q₈×C₁₃	—	4	2	no	—
84	Q₈×C₁₃	—	4	2	no	—
85	D₄×C₁₃	—	2	1	no	—
86	D₄×C₁₃	—	2	1	no	—
87	D₄×C₁₃	—	4	2	no	—
88	C₂×C₄×C₁₃	—	2	2	no	—
89	C₂×C₄×C₁₃	—	2	1	no	—
90	C₂×C₄×C₁₃	—	2	1	no	—
91	C₂×C₄×C₁₃	—	2	1	no	—
92	C₂×C₄×C₁₃	—	2	1	no	—
93	C₂×C₄×C₁₃	—	2	2	no	—
94	C₂×C₄×C₁₃	—	2	2	no	—
95	C₂×C₄×C₁₃	—	2	1	no	—
96	C₂×C₄×C₁₃	—	4	1	no	—
97	C₂×C₄×C₁₃	—	4	2	no	—
98	C₂×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
99	C₂×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
100	C₂×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
101	C₂×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
102	C₂×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
103	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
104	C₈×C₁₃	—	2	2	no	—
105	C₈×C₁₃	—	2	2	no	—
106	#533	C₂×C₁₃	1	1	yes	characteristic, complemented
107	#529	C₂×C₁₃	1	1	yes	characteristic
108	#499	C₂×C₁₃	1	2	yes	complemented
109	#488	C₂×C₁₃	1	2	yes	complemented
110	#485	C₂×C₁₃	1	2	yes	complemented
111	#482	C₂×C₁₃	1	2	yes	—
112	#477	C₂×C₁₃	1	1	yes	characteristic, complemented
113	#476	C₂×C₁₃	1	1	yes	characteristic, complemented
114	#475	C₂×C₁₃	1	1	yes	characteristic, complemented
115	#474	C₂×C₁₃	1	1	yes	characteristic, complemented
116	#431	C₂×C₁₃	1	1	yes	characteristic, complemented
117	C₂²×C₁₃	—	2	1	no	—
118	C₂²×C₁₃	—	2	1	no	—
119	C₂²×C₁₃	—	2	1	no	—
120	C₂²×C₁₃	—	4	1	no	—
121	C₂²×C₁₃	—	4	1	no	—
122	C₂²×C₁₃	—	4	1	no	—
123	C₂²×C₁₃	C₂²×D₄	1	1	yes	characteristic
124	C₄×C₁₃	—	2	1	no	—
125	C₄×C₁₃	—	2	1	no	—
126	C₄×C₁₃	—	2	1	no	—
127	C₄×C₁₃	—	2	1	no	—
128	C₄×C₁₃	—	4	1	no	—
129	C₄×C₁₃	—	4	1	no	—
130	C₄×C₁₃	—	4	2	no	—
131	C₄×C₁₃	—	4	1	no	—
132	C₄×C₁₃	—	4	2	no	—
133	C₄×C₁₃	#135	1	2	yes	—
134	C₄×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
135	C₄×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
136	C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
137	C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
138	#126	—	2	1	no	—
139	#125	C₂²×C₁₃	1	1	yes	characteristic
140	#125	C₂²×C₁₃	1	2	yes	—
141	#124	C₂²×C₁₃	1	1	yes	characteristic
142	#123	—	2	1	no	—
143	C₂²⋊Q₈	—	2	1	no	—
144	C₂²⋊Q₈	—	2	1	no	—
145	C₂²⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
146	#121	C₂²×C₁₃	1	1	yes	characteristic
147	C₄×Q₈	—	2	1	no	—
148	C₄×Q₈	—	2	1	no	—
149	C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
150	C₄×D₄	—	2	1	no	—
151	C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
152	#117	—	2	1	no	—
153	#117	C₂²×C₁₃	1	2	yes	—
154	C₂×C₄²	C₂²×C₁₃	1	1	yes	characteristic
155	#107	C₂²×C₁₃	1	2	yes	—
156	#107	C₂²×C₁₃	1	2	yes	—
157	#106	C₂²×C₁₃	1	2	yes	—
158	#106	C₂²×C₁₃	1	2	yes	—
159	C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
160	C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
161	#103	C₂²×C₁₃	1	2	yes	—
162	#103	C₂²×C₁₃	1	2	yes	—
163	#102	C₂²×C₁₃	1	2	yes	—
164	#102	C₂²×C₁₃	1	2	yes	—
165	C₂²⋊C₈	C₂²×C₁₃	1	2	yes	—
166	C₄×C₈	C₂²×C₁₃	1	2	yes	—
167	C₂×C₁₃	—	4	1	no	—
168	C₂×C₁₃	—	8	1	no	—
169	C₂×C₁₃	#536	1	1	yes	characteristic
170	C₂×C₁₃	C₂×#135	1	1	yes	characteristic
171	C₂×C₁₃	#575	1	1	yes	characteristic
172	C₂×Q₈	—	2	1	no	—
173	C₂×Q₈	—	2	1	no	—
174	C₂×Q₈	C₂³×C₁₃	1	1	yes	characteristic
175	C₂×D₄	—	2	1	no	—
176	C₂×D₄	C₂³×C₁₃	1	1	yes	characteristic
177	C₂²×C₄	—	2	1	no	—
178	C₂²×C₄	D₄×C₁₃	1	1	yes	characteristic
179	C₂²×C₄	D₄×C₁₃	1	1	yes	characteristic
180	C₂²×C₄	C₂³×C₁₃	1	1	yes	characteristic
181	C₂×C₈	C₂³×C₁₃	1	2	yes	—
182	C₂×C₈	C₂³×C₁₃	1	2	yes	—
183	C₄⋊C₄	—	2	1	no	—
184	C₄⋊C₄	—	2	1	no	—
185	C₄⋊C₄	—	2	1	no	—
186	C₄⋊C₄	—	2	2	no	—
187	C₄⋊C₄	—	2	2	no	—
188	C₄⋊C₄	—	2	1	no	—
189	C₄⋊C₄	—	2	1	no	—
190	C₄⋊C₄	—	2	1	no	—
191	C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
192	C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
193	C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
194	C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
195	C₂²⋊C₄	—	2	2	no	—
196	C₂²⋊C₄	—	2	1	no	—
197	C₂²⋊C₄	—	2	1	no	—
198	C₂²⋊C₄	—	2	1	no	—
199	C₂²⋊C₄	—	2	1	no	—
200	C₂²⋊C₄	—	2	1	no	—
201	C₄²	—	2	1	no	—
202	C₄²	—	2	2	no	—
203	C₄²	D₄×C₁₃	1	1	yes	characteristic
204	C₄²	D₄×C₁₃	1	1	yes	characteristic
205	C₄²	C₂³×C₁₃	1	1	yes	characteristic
206	C₄²	C₂³×C₁₃	1	1	yes	characteristic
207	C₁₃	#3233	1	1	yes	characteristic, direct product factor, Sylow
208	C₂³	—	2	1	no	—
209	C₂³	C₂×D₄×C₁₃	1	1	yes	characteristic
210	Q₈	—	2	1	no	—
211	Q₈	—	2	1	no	—
212	Q₈	—	4	2	no	—
213	Q₈	—	4	2	no	—
214	D₄	—	2	1	no	—
215	D₄	—	2	1	no	—
216	D₄	—	4	2	no	—
217	C₂×C₄	—	2	2	no	—
218	C₂×C₄	—	2	1	no	—
219	C₂×C₄	—	2	1	no	—
220	C₂×C₄	—	2	1	no	—
221	C₂×C₄	—	2	1	no	—
222	C₂×C₄	—	2	2	no	—
223	C₂×C₄	—	2	2	no	—
224	C₂×C₄	—	2	1	no	—
225	C₂×C₄	—	4	1	no	—
226	C₂×C₄	—	4	2	no	—
227	C₂×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
228	C₂×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
229	C₂×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
230	C₂×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
231	C₂×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
232	C₂×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
233	C₈	—	2	2	no	—
234	C₈	—	2	2	no	—
235	C₂²	—	2	1	no	—
236	C₂²	—	2	1	no	—
237	C₂²	—	2	1	no	—
238	C₂²	—	4	1	no	—
239	C₂²	—	4	1	no	—
240	C₂²	—	4	1	no	—
241	C₂²	C₂²×D₄×C₁₃	1	1	yes	characteristic
242	C₄	—	2	1	no	—
243	C₄	—	2	1	no	—
244	C₄	—	2	1	no	—
245	C₄	—	2	1	no	—
246	C₄	—	4	1	no	—
247	C₄	—	4	1	no	—
248	C₄	—	4	2	no	—
249	C₄	—	4	1	no	—
250	C₄	—	4	2	no	—
251	C₄	C₁₃×#135	1	2	yes	—
252	C₄	C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
253	C₄	C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
254	C₂	—	4	1	no	—
255	C₂	—	8	1	no	—
256	C₂	C₁₃×#536	1	1	yes	characteristic
257	C₂	C₂×C₁₃×#135	1	1	yes	characteristic
258	C₂	C₁₃×#575	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁴×C₁₃
prime radical	C₁₃×#121	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₂×C₄²×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₃×#533	C₂	semidirect
3. C₁₃×#499	C₂	semidirect
4. C₁₃×#488	C₂	semidirect
5. C₁₃×#485	C₂	semidirect
7. C₁₃×#477	C₂	semidirect
8. C₁₃×#476	C₂	semidirect
9. C₁₃×#475	C₂	semidirect
10. C₁₃×#474	C₂	semidirect
11. C₁₃×#431	C₂	semidirect
78. #3233	C₁₃	direct (N × H)
106. #533	C₂×C₁₃	semidirect
108. #499	C₂×C₁₃	semidirect
109. #488	C₂×C₁₃	semidirect
110. #485	C₂×C₁₃	semidirect
112. #477	C₂×C₁₃	semidirect
113. #476	C₂×C₁₃	semidirect
114. #475	C₂×C₁₃	semidirect
115. #474	C₂×C₁₃	semidirect
116. #431	C₂×C₁₃	semidirect
207. C₁₃	#3233	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×#533	2
C₁₃×#529	2
C₁₃×#499	2
C₁₃×#488	2
C₁₃×#485	2
C₁₃×#482	2
C₁₃×#477	2
C₁₃×#476	2
C₁₃×#475	2
C₁₃×#474	2
C₁₃×#431	2
#3233	13

Subgroups — C13×#3233 #13112291

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#3233 #13112291