Subgroups — C₁₃×#13265 #15699604

Order 3328.

338 conjugacy classes of subgroups.

The subgroup lattice has 228 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#2960	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₃×C₄⋊C₁₆	C₂	1	1	yes	maximal, characteristic
3	C₄×C₁₃×M₃₂	C₂	1	1	yes	maximal, characteristic
4	C₁₃×#1379	C₂	1	4	yes	maximal
5	C₁₃×#533	C₄	1	1	yes	characteristic
6	C₂×C₁₃×M₃₂	C₂²	1	2	yes	—
7	C₂²×C₁₃×C₁₆	C₂²	1	2	yes	—
8	C₁₃×#446	—	2	1	no	—
9	C₁₃×#446	—	2	1	no	—
10	C₈×Q₈×C₁₃	—	2	1	no	—
11	C₈×Q₈×C₁₃	—	2	1	no	—
12	C₁₃×#424	C₄	1	2	yes	—
13	C₁₃×#423	C₄	1	1	yes	characteristic
14	C₁₃×#405	C₂²	1	2	yes	—
15	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
16	C₁₃×C₄⋊C₁₆	—	2	1	no	—
17	C₁₃×C₄⋊C₁₆	—	2	1	no	—
18	C₁₃×#346	—	2	1	no	—
19	C₄×C₁₃×C₁₆	—	2	1	no	—
20	C₂×C₁₃×M₁₆	C₂×C₄	1	2	yes	—
21	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
22	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
23	C₁₃×C₄⋊Q₈	C₈	1	1	yes	characteristic
24	C₁₃×C₄⋊Q₈	C₈	1	1	yes	characteristic
25	C₁₃×#125	C₈	1	2	yes	—
26	C₁₃×C₂²⋊Q₈	—	2	1	no	—
27	C₁₃×C₂²⋊Q₈	—	2	1	no	—
28	C₄×Q₈×C₁₃	—	2	1	no	—
29	C₄×Q₈×C₁₃	—	2	1	no	—
30	C₁₃×#117	C₂×C₄	1	2	yes	—
31	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
32	C₁₃×M₃₂	—	2	2	no	—
33	C₁₃×M₃₂	Q₈	1	4	yes	complemented
34	C₂×C₁₃×C₁₆	—	2	2	no	—
35	C₂×C₁₃×C₁₆	—	2	2	no	—
36	C₂×C₁₃×C₁₆	—	2	4	no	—
37	C₁₃×C₄⋊C₈	—	2	2	no	—
38	C₁₃×C₄⋊C₈	—	2	2	no	—
39	C₁₃×C₄⋊C₈	—	2	1	no	—
40	C₁₃×C₄⋊C₈	—	2	1	no	—
41	C₁₃×#97	—	2	2	no	—
42	C₄×C₈×C₁₃	—	2	2	no	—
43	C₄×C₈×C₁₃	D₄	1	1	yes	characteristic
44	C₄×C₈×C₁₃	D₄	1	1	yes	characteristic
45	C₄×C₈×C₁₃	D₄	1	1	yes	characteristic
46	C₄×C₈×C₁₃	D₄	1	1	yes	characteristic
47	#13265	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
48	C₂×Q₈×C₁₃	—	2	1	no	—
49	C₂×Q₈×C₁₃	—	2	1	no	—
50	C₂²×C₄×C₁₃	M₁₆	1	1	yes	characteristic
51	C₂²×C₄×C₁₃	M₁₆	1	1	yes	characteristic
52	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
53	C₁₃×M₁₆	—	2	4	no	—
54	C₂×C₈×C₁₃	—	2	2	no	—
55	C₂×C₈×C₁₃	—	2	2	no	—
56	C₂×C₈×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
57	C₂×C₈×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
58	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
59	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
60	C₂×C₈×C₁₃	C₂×Q₈	1	2	yes	—
61	C₂×C₈×C₁₃	#41	1	2	yes	—
62	C₁₃×C₄⋊C₄	—	2	2	no	—
63	C₁₃×C₄⋊C₄	—	2	2	no	—
64	C₁₃×C₄⋊C₄	—	2	1	no	—
65	C₁₃×C₄⋊C₄	—	2	1	no	—
66	C₁₃×C₄⋊C₄	C₂×C₈	1	2	yes	—
67	C₁₃×C₄⋊C₄	C₂×C₈	1	2	yes	—
68	C₁₃×C₂²⋊C₄	—	2	2	no	—
69	C₄²×C₁₃	—	2	2	no	—
70	C₄²×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
71	C₄²×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
72	C₄²×C₁₃	C₂×C₈	1	1	yes	characteristic
73	C₄²×C₁₃	C₂×C₈	1	1	yes	characteristic
74	C₁₃×C₁₆	—	2	4	no	—
75	C₁₃×C₁₆	—	4	2	no	—
76	#2960	C₂×C₁₃	1	1	yes	characteristic
77	C₂×C₄⋊C₁₆	C₂×C₁₃	1	1	yes	characteristic
78	C₄×M₃₂	C₂×C₁₃	1	1	yes	characteristic
79	#1379	C₂×C₁₃	1	4	yes	—
80	C₂³×C₁₃	C₂×M₁₆	1	1	yes	characteristic
81	Q₈×C₁₃	—	4	2	no	—
82	Q₈×C₁₃	—	4	2	no	—
83	C₂×C₄×C₁₃	—	2	2	no	—
84	C₂×C₄×C₁₃	—	2	2	no	—
85	C₂×C₄×C₁₃	—	2	2	no	—
86	C₂×C₄×C₁₃	—	4	1	no	—
87	C₂×C₄×C₁₃	C₂²⋊C₈	1	1	yes	characteristic
88	C₂×C₄×C₁₃	C₂²⋊C₈	1	1	yes	characteristic
89	C₂×C₄×C₁₃	C₂²⋊C₈	1	1	yes	characteristic
90	C₂×C₄×C₁₃	C₂²⋊C₈	1	1	yes	characteristic
91	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
92	C₂×C₄×C₁₃	C₄×Q₈	1	2	yes	—
93	C₂×C₄×C₁₃	C₂²×C₈	1	1	yes	characteristic
94	C₂×C₄×C₁₃	#131	1	2	yes	—
95	C₈×C₁₃	—	2	1	no	—
96	C₈×C₁₃	—	2	1	no	—
97	C₈×C₁₃	—	4	2	no	—
98	C₈×C₁₃	C₂²⋊Q₈	1	2	yes	—
99	C₈×C₁₃	#124	1	1	yes	characteristic
100	C₈×C₁₃	C₄⋊Q₈	1	1	yes	characteristic
101	#533	C₄×C₁₃	1	1	yes	characteristic
102	C₂×M₃₂	C₂²×C₁₃	1	2	yes	—
103	C₂²×C₁₆	C₂²×C₁₃	1	2	yes	—
104	#446	—	2	1	no	—
105	#446	—	2	1	no	—
106	C₈×Q₈	—	2	1	no	—
107	C₈×Q₈	—	2	1	no	—
108	#424	C₄×C₁₃	1	2	yes	—
109	#423	C₄×C₁₃	1	1	yes	characteristic
110	#405	C₂²×C₁₃	1	2	yes	—
111	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
112	C₄⋊C₁₆	—	2	1	no	—
113	C₄⋊C₁₆	—	2	1	no	—
114	#346	—	2	1	no	—
115	C₄×C₁₆	—	2	1	no	—
116	C₂²×C₁₃	—	2	1	no	—
117	C₂²×C₁₃	—	2	1	no	—
118	C₂²×C₁₃	C₂×C₂²⋊C₈	1	1	yes	characteristic
119	C₂²×C₁₃	#446	1	2	yes	—
120	C₄×C₁₃	—	2	1	no	—
121	C₄×C₁₃	—	2	1	no	—
122	C₄×C₁₃	—	2	1	no	—
123	C₄×C₁₃	—	4	2	no	—
124	C₄×C₁₃	—	4	2	no	—
125	C₄×C₁₃	#350	1	2	yes	—
126	C₄×C₁₃	#391	1	1	yes	characteristic
127	C₄×C₁₃	#408	1	1	yes	characteristic
128	C₄×C₁₃	C₈×Q₈	1	2	yes	—
129	C₂×M₁₆	C₂×C₄×C₁₃	1	2	yes	—
130	C₂²×C₈	C₂×C₄×C₁₃	1	1	yes	characteristic
131	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
132	C₄⋊Q₈	C₈×C₁₃	1	1	yes	characteristic
133	C₄⋊Q₈	C₈×C₁₃	1	1	yes	characteristic
134	#125	C₈×C₁₃	1	2	yes	—
135	C₂²⋊Q₈	—	2	1	no	—
136	C₂²⋊Q₈	—	2	1	no	—
137	C₄×Q₈	—	2	1	no	—
138	C₄×Q₈	—	2	1	no	—
139	#117	C₂×C₄×C₁₃	1	2	yes	—
140	C₂×C₄²	C₂×C₄×C₁₃	1	1	yes	characteristic
141	M₃₂	—	2	2	no	—
142	M₃₂	Q₈×C₁₃	1	4	yes	complemented
143	C₂×C₁₆	—	2	2	no	—
144	C₂×C₁₆	—	2	2	no	—
145	C₂×C₁₆	—	2	4	no	—
146	C₄⋊C₈	—	2	2	no	—
147	C₄⋊C₈	—	2	2	no	—
148	C₄⋊C₈	—	2	1	no	—
149	C₄⋊C₈	—	2	1	no	—
150	#97	—	2	2	no	—
151	C₄×C₈	—	2	2	no	—
152	C₄×C₈	D₄×C₁₃	1	1	yes	characteristic
153	C₄×C₈	D₄×C₁₃	1	1	yes	characteristic
154	C₄×C₈	D₄×C₁₃	1	1	yes	characteristic
155	C₄×C₈	D₄×C₁₃	1	1	yes	characteristic
156	C₂×C₁₃	—	2	2	no	—
157	C₂×C₁₃	#1984	1	1	yes	characteristic
158	C₂×C₁₃	C₂×#350	1	1	yes	characteristic
159	C₂×C₁₃	#2117	1	1	yes	characteristic
160	C₂×Q₈	—	2	1	no	—
161	C₂×Q₈	—	2	1	no	—
162	C₂²×C₄	C₁₃×M₁₆	1	1	yes	characteristic
163	C₂²×C₄	C₁₃×M₁₆	1	1	yes	characteristic
164	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
165	M₁₆	—	2	4	no	—
166	C₂×C₈	—	2	2	no	—
167	C₂×C₈	—	2	2	no	—
168	C₂×C₈	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
169	C₂×C₈	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
170	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
171	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
172	C₂×C₈	C₂×Q₈×C₁₃	1	2	yes	—
173	C₂×C₈	C₁₃×#41	1	2	yes	—
174	C₄⋊C₄	—	2	2	no	—
175	C₄⋊C₄	—	2	2	no	—
176	C₄⋊C₄	—	2	1	no	—
177	C₄⋊C₄	—	2	1	no	—
178	C₄⋊C₄	C₂×C₈×C₁₃	1	2	yes	—
179	C₄⋊C₄	C₂×C₈×C₁₃	1	2	yes	—
180	C₂²⋊C₄	—	2	2	no	—
181	C₄²	—	2	2	no	—
182	C₄²	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
183	C₄²	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
184	C₄²	C₂×C₈×C₁₃	1	1	yes	characteristic
185	C₄²	C₂×C₈×C₁₃	1	1	yes	characteristic
186	C₁₆	—	2	4	no	—
187	C₁₆	—	4	2	no	—
188	C₁₃	#13265	1	1	yes	characteristic, direct product factor, Sylow
189	C₂³	C₂×C₁₃×M₁₆	1	1	yes	characteristic
190	Q₈	—	4	2	no	—
191	Q₈	—	4	2	no	—
192	C₂×C₄	—	2	2	no	—
193	C₂×C₄	—	2	2	no	—
194	C₂×C₄	—	2	2	no	—
195	C₂×C₄	—	4	1	no	—
196	C₂×C₄	C₁₃×C₂²⋊C₈	1	1	yes	characteristic
197	C₂×C₄	C₁₃×C₂²⋊C₈	1	1	yes	characteristic
198	C₂×C₄	C₁₃×C₂²⋊C₈	1	1	yes	characteristic
199	C₂×C₄	C₁₃×C₂²⋊C₈	1	1	yes	characteristic
200	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
201	C₂×C₄	C₄×Q₈×C₁₃	1	2	yes	—
202	C₂×C₄	C₂²×C₈×C₁₃	1	1	yes	characteristic
203	C₂×C₄	C₁₃×#131	1	2	yes	—
204	C₈	—	2	1	no	—
205	C₈	—	2	1	no	—
206	C₈	—	4	2	no	—
207	C₈	C₁₃×C₂²⋊Q₈	1	2	yes	—
208	C₈	C₁₃×#124	1	1	yes	characteristic
209	C₈	C₁₃×C₄⋊Q₈	1	1	yes	characteristic
210	C₂²	—	2	1	no	—
211	C₂²	—	2	1	no	—
212	C₂²	C₂×C₁₃×C₂²⋊C₈	1	1	yes	characteristic
213	C₂²	C₁₃×#446	1	2	yes	—
214	C₄	—	2	1	no	—
215	C₄	—	2	1	no	—
216	C₄	—	2	1	no	—
217	C₄	—	4	2	no	—
218	C₄	—	4	2	no	—
219	C₄	C₁₃×#350	1	2	yes	—
220	C₄	C₁₃×#391	1	1	yes	characteristic
221	C₄	C₁₃×#408	1	1	yes	characteristic
222	C₄	C₈×Q₈×C₁₃	1	2	yes	—
223	C₂	—	2	2	no	—
224	C₂	C₁₃×#1984	1	1	yes	characteristic
225	C₂	C₂×C₁₃×#350	1	1	yes	characteristic
226	C₂	C₁₃×#2117	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₈×C₁₃	C₂×D₄
commutator	C₂×C₄	C₂²×C₈×C₁₃
Frattini, cosocle	C₂²×C₈	C₂³×C₁₃
socle	C₂²×C₁₃	C₂×C₂²⋊C₈
prime radical	C₂³×C₁₃	C₂×M₁₆
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₈×C₁₃ ◁ C₂×C₄×C₈×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
33. C₁₃×M₃₂	Q₈	semidirect
47. #13265	C₁₃	direct (N × H)
142. M₃₂	Q₈×C₁₃	semidirect
188. C₁₃	#13265	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×#2960	2
C₂×C₁₃×C₄⋊C₁₆	2
C₄×C₁₃×M₃₂	2
C₁₃×#1379	2
#13265	13

Subgroups — C13×#13265 #15699604

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#13265 #15699604