Subgroups — C₁₃×#2995 #13112053

Order 1664.

346 conjugacy classes of subgroups.

The subgroup lattice has 230 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#529	C₂	1	1	yes	maximal, characteristic
2	C₁₃×#446	C₂	1	2	yes	maximal, complemented
3	C₁₃×#436	C₂	1	2	yes	maximal, complemented
4	C₁₃×#435	C₂	1	2	yes	maximal, complemented
5	C₁₃×#435	C₂	1	2	yes	maximal, complemented
6	C₁₃×#433	C₂	1	2	yes	maximal, complemented
7	C₁₃×#432	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#424	C₂	1	2	yes	maximal, complemented
9	C₁₃×#423	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
11	C₂×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
12	C₂×C₁₃×M₁₆	C₂²	1	2	yes	—
13	C₂²×C₈×C₁₃	C₂²	1	2	yes	—
14	C₁₃×#126	C₄	1	2	yes	—
15	C₁₃×#125	C₄	1	1	yes	characteristic
16	C₁₃×#124	C₄	1	1	yes	characteristic
17	C₁₃×#123	C₄	1	2	yes	—
18	C₁₃×C₂²⋊Q₈	C₄	1	1	yes	characteristic
19	C₁₃×#121	C₄	1	1	yes	characteristic
20	C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
21	C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
22	C₄×D₄×C₁₃	C₂²	1	2	yes	—
23	C₁₃×#117	C₂²	1	2	yes	—
24	C₂×C₄²×C₁₃	C₂²	1	1	yes	characteristic
25	C₁₃×C₄⋊C₈	C₂²	1	2	yes	—
26	C₁₃×C₄⋊C₈	C₂²	1	2	yes	—
27	C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
28	C₁₃×C₄⋊C₈	C₂²	1	2	yes	—
29	C₁₃×C₄⋊C₈	C₂²	1	2	yes	—
30	C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
31	C₁₃×C₂²⋊C₈	C₂²	1	2	yes	—
32	C₁₃×C₂²⋊C₈	C₂²	1	2	yes	—
33	C₁₃×C₂²⋊C₈	C₂²	1	2	yes	—
34	C₁₃×#97	C₂²	1	2	yes	—
35	C₁₃×#97	C₂²	1	2	yes	—
36	C₄×C₈×C₁₃	C₂²	1	2	yes	—
37	C₂×Q₈×C₁₃	C₂×C₄	1	1	yes	characteristic
38	C₂×D₄×C₁₃	C₂×C₄	1	2	yes	—
39	C₂×D₄×C₁₃	C₂×C₄	1	1	yes	characteristic
40	C₂²×C₄×C₁₃	C₂×C₄	1	1	yes	characteristic
41	C₂²×C₄×C₁₃	C₂×C₄	1	1	yes	characteristic
42	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
43	C₂²×C₄×C₁₃	C₂³	1	2	yes	—
44	C₁₃×M₁₆	—	4	1	no	—
45	C₁₃×M₁₆	—	4	2	no	—
46	C₁₃×M₁₆	—	4	1	no	—
47	C₂×C₈×C₁₃	—	4	2	no	—
48	C₂×C₈×C₁₃	C₂³	1	2	yes	—
49	C₂×C₈×C₁₃	C₂³	1	2	yes	—
50	C₂×C₈×C₁₃	C₂³	1	2	yes	—
51	C₂×C₈×C₁₃	C₂³	1	2	yes	—
52	C₁₃×C₄⋊C₄	C₂×C₄	1	2	yes	—
53	C₁₃×C₄⋊C₄	C₂×C₄	1	2	yes	—
54	C₁₃×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
55	C₁₃×C₄⋊C₄	C₂×C₄	1	2	yes	—
56	C₁₃×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
57	C₁₃×C₄⋊C₄	C₂×C₄	1	2	yes	—
58	C₁₃×C₂²⋊C₄	C₂×C₄	1	2	yes	—
59	C₁₃×C₂²⋊C₄	C₂×C₄	1	2	yes	—
60	C₁₃×C₂²⋊C₄	C₂×C₄	1	2	yes	—
61	C₁₃×C₂²⋊C₄	C₂×C₄	1	2	yes	—
62	C₁₃×C₂²⋊C₄	C₂×C₄	1	2	yes	—
63	C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
64	C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
65	C₄²×C₁₃	C₂³	1	2	yes	—
66	C₄²×C₁₃	C₂³	1	1	yes	characteristic
67	C₄²×C₁₃	C₂³	1	1	yes	characteristic
68	#2995	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
69	C₂³×C₁₃	C₂²×C₄	1	2	yes	—
70	C₂³×C₁₃	C₂²×C₄	1	1	yes	characteristic
71	Q₈×C₁₃	—	4	1	no	—
72	D₄×C₁₃	—	4	1	no	—
73	D₄×C₁₃	—	4	2	no	—
74	C₂×C₄×C₁₃	—	2	2	no	—
75	C₂×C₄×C₁₃	—	2	1	no	—
76	C₂×C₄×C₁₃	—	2	1	no	—
77	C₂×C₄×C₁₃	—	2	2	no	—
78	C₂×C₄×C₁₃	—	4	1	no	—
79	C₂×C₄×C₁₃	—	4	1	no	—
80	C₂×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
81	C₂×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
82	C₂×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
83	C₂×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
84	C₂×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
85	C₂×C₄×C₁₃	C₂²×C₄	1	2	yes	—
86	C₂×C₄×C₁₃	C₂²×C₄	1	2	yes	—
87	C₂×C₄×C₁₃	C₂²×C₄	1	2	yes	—
88	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
89	C₈×C₁₃	—	2	2	no	—
90	C₈×C₁₃	—	2	2	no	—
91	C₈×C₁₃	—	2	2	no	—
92	C₈×C₁₃	—	2	2	no	—
93	#529	C₂×C₁₃	1	1	yes	characteristic
94	#446	C₂×C₁₃	1	2	yes	complemented
95	#436	C₂×C₁₃	1	2	yes	complemented
96	#435	C₂×C₁₃	1	2	yes	complemented
97	#435	C₂×C₁₃	1	2	yes	complemented
98	#433	C₂×C₁₃	1	2	yes	complemented
99	#432	C₂×C₁₃	1	1	yes	characteristic, complemented
100	#424	C₂×C₁₃	1	2	yes	complemented
101	#423	C₂×C₁₃	1	1	yes	characteristic, complemented
102	C₂²×C₁₃	—	2	2	no	—
103	C₂²×C₁₃	—	2	1	no	—
104	C₂²×C₁₃	—	2	1	no	—
105	C₂²×C₁₃	—	2	1	no	—
106	C₂²×C₁₃	—	2	2	no	—
107	C₂²×C₁₃	—	2	2	no	—
108	C₂²×C₁₃	C₂³×C₄	1	1	yes	characteristic
109	C₄×C₁₃	—	2	2	no	—
110	C₄×C₁₃	—	2	1	no	—
111	C₄×C₁₃	—	2	1	no	—
112	C₄×C₁₃	—	2	1	no	—
113	C₄×C₁₃	—	2	1	no	—
114	C₄×C₁₃	—	2	1	no	—
115	C₄×C₁₃	—	2	2	no	—
116	C₄×C₁₃	—	2	2	no	—
117	C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
118	C₄×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
119	C₂×M₁₆	C₂²×C₁₃	1	1	yes	characteristic
120	C₂×M₁₆	C₂²×C₁₃	1	1	yes	characteristic
121	C₂×M₁₆	C₂²×C₁₃	1	2	yes	—
122	C₂²×C₈	C₂²×C₁₃	1	2	yes	—
123	#126	C₄×C₁₃	1	2	yes	—
124	#125	C₄×C₁₃	1	1	yes	characteristic
125	#124	C₄×C₁₃	1	1	yes	characteristic
126	#123	C₄×C₁₃	1	2	yes	—
127	C₂²⋊Q₈	C₄×C₁₃	1	1	yes	characteristic
128	#121	C₄×C₁₃	1	1	yes	characteristic
129	C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
130	C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
131	C₄×D₄	C₂²×C₁₃	1	2	yes	—
132	#117	C₂²×C₁₃	1	2	yes	—
133	C₂×C₄²	C₂²×C₁₃	1	1	yes	characteristic
134	C₄⋊C₈	C₂²×C₁₃	1	2	yes	—
135	C₄⋊C₈	C₂²×C₁₃	1	2	yes	—
136	C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
137	C₄⋊C₈	C₂²×C₁₃	1	2	yes	—
138	C₄⋊C₈	C₂²×C₁₃	1	2	yes	—
139	C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
140	C₂²⋊C₈	C₂²×C₁₃	1	2	yes	—
141	C₂²⋊C₈	C₂²×C₁₃	1	2	yes	—
142	C₂²⋊C₈	C₂²×C₁₃	1	2	yes	—
143	#97	C₂²×C₁₃	1	2	yes	—
144	#97	C₂²×C₁₃	1	2	yes	—
145	C₄×C₈	C₂²×C₁₃	1	2	yes	—
146	C₂×C₁₃	—	4	1	no	—
147	C₂×C₁₃	—	4	2	no	—
148	C₂×C₁₃	#520	1	1	yes	characteristic
149	C₂×C₁₃	#568	1	1	yes	characteristic
150	C₂×C₁₃	#568	1	1	yes	characteristic
151	C₂×Q₈	C₂×C₄×C₁₃	1	1	yes	characteristic
152	C₂×D₄	C₂×C₄×C₁₃	1	2	yes	—
153	C₂×D₄	C₂×C₄×C₁₃	1	1	yes	characteristic
154	C₂²×C₄	C₂×C₄×C₁₃	1	1	yes	characteristic
155	C₂²×C₄	C₂×C₄×C₁₃	1	1	yes	characteristic
156	C₂²×C₄	C₂³×C₁₃	1	1	yes	characteristic
157	C₂²×C₄	C₂³×C₁₃	1	2	yes	—
158	M₁₆	—	4	1	no	—
159	M₁₆	—	4	2	no	—
160	M₁₆	—	4	1	no	—
161	C₂×C₈	—	4	2	no	—
162	C₂×C₈	C₂³×C₁₃	1	2	yes	—
163	C₂×C₈	C₂³×C₁₃	1	2	yes	—
164	C₂×C₈	C₂³×C₁₃	1	2	yes	—
165	C₂×C₈	C₂³×C₁₃	1	2	yes	—
166	C₄⋊C₄	C₂×C₄×C₁₃	1	2	yes	—
167	C₄⋊C₄	C₂×C₄×C₁₃	1	2	yes	—
168	C₄⋊C₄	C₂×C₄×C₁₃	1	1	yes	characteristic
169	C₄⋊C₄	C₂×C₄×C₁₃	1	2	yes	—
170	C₄⋊C₄	C₂×C₄×C₁₃	1	1	yes	characteristic
171	C₄⋊C₄	C₂×C₄×C₁₃	1	2	yes	—
172	C₂²⋊C₄	C₂×C₄×C₁₃	1	2	yes	—
173	C₂²⋊C₄	C₂×C₄×C₁₃	1	2	yes	—
174	C₂²⋊C₄	C₂×C₄×C₁₃	1	2	yes	—
175	C₂²⋊C₄	C₂×C₄×C₁₃	1	2	yes	—
176	C₂²⋊C₄	C₂×C₄×C₁₃	1	2	yes	—
177	C₄²	C₂×C₄×C₁₃	1	1	yes	characteristic
178	C₄²	C₂×C₄×C₁₃	1	1	yes	characteristic
179	C₄²	C₂³×C₁₃	1	2	yes	—
180	C₄²	C₂³×C₁₃	1	1	yes	characteristic
181	C₄²	C₂³×C₁₃	1	1	yes	characteristic
182	C₁₃	#2995	1	1	yes	characteristic, direct product factor, Sylow
183	C₂³	C₂²×C₄×C₁₃	1	2	yes	—
184	C₂³	C₂²×C₄×C₁₃	1	1	yes	characteristic
185	Q₈	—	4	1	no	—
186	D₄	—	4	1	no	—
187	D₄	—	4	2	no	—
188	C₂×C₄	—	2	2	no	—
189	C₂×C₄	—	2	1	no	—
190	C₂×C₄	—	2	1	no	—
191	C₂×C₄	—	2	2	no	—
192	C₂×C₄	—	4	1	no	—
193	C₂×C₄	—	4	1	no	—
194	C₂×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
195	C₂×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
196	C₂×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
197	C₂×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
198	C₂×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
199	C₂×C₄	C₂²×C₄×C₁₃	1	2	yes	—
200	C₂×C₄	C₂²×C₄×C₁₃	1	2	yes	—
201	C₂×C₄	C₂²×C₄×C₁₃	1	2	yes	—
202	C₂×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
203	C₈	—	2	2	no	—
204	C₈	—	2	2	no	—
205	C₈	—	2	2	no	—
206	C₈	—	2	2	no	—
207	C₂²	—	2	2	no	—
208	C₂²	—	2	1	no	—
209	C₂²	—	2	1	no	—
210	C₂²	—	2	1	no	—
211	C₂²	—	2	2	no	—
212	C₂²	—	2	2	no	—
213	C₂²	C₂³×C₄×C₁₃	1	1	yes	characteristic
214	C₄	—	2	2	no	—
215	C₄	—	2	1	no	—
216	C₄	—	2	1	no	—
217	C₄	—	2	1	no	—
218	C₄	—	2	1	no	—
219	C₄	—	2	1	no	—
220	C₄	—	2	2	no	—
221	C₄	—	2	2	no	—
222	C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
223	C₄	C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
224	C₂	—	4	1	no	—
225	C₂	—	4	2	no	—
226	C₂	C₁₃×#520	1	1	yes	characteristic
227	C₂	C₁₃×#568	1	1	yes	characteristic
228	C₂	C₁₃×#568	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₁₃	C₂⁴
commutator	C₂²	C₂³×C₄×C₁₃
Frattini, cosocle	C₂×C₄	C₂⁴×C₁₃
socle	C₂²×C₁₃	C₂³×C₄
prime radical	C₁₃×#121	C₄
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₃×#446	C₂	semidirect
3. C₁₃×#436	C₂	semidirect
4. C₁₃×#435	C₂	semidirect
5. C₁₃×#435	C₂	semidirect
6. C₁₃×#433	C₂	semidirect
7. C₁₃×#432	C₂	semidirect
8. C₁₃×#424	C₂	semidirect
9. C₁₃×#423	C₂	semidirect
68. #2995	C₁₃	direct (N × H)
94. #446	C₂×C₁₃	semidirect
95. #436	C₂×C₁₃	semidirect
96. #435	C₂×C₁₃	semidirect
97. #435	C₂×C₁₃	semidirect
98. #433	C₂×C₁₃	semidirect
99. #432	C₂×C₁₃	semidirect
100. #424	C₂×C₁₃	semidirect
101. #423	C₂×C₁₃	semidirect
182. C₁₃	#2995	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×#529	2
C₁₃×#446	2
C₁₃×#436	2
C₁₃×#435	2
C₁₃×#433	2
C₁₃×#432	2
C₁₃×#424	2
C₁₃×#423	2
#2995	13

Subgroups — C13×#2995 #13112053

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#2995 #13112053