Subgroups — C₁₃×#33499 #15719838

Order 3328.

452 conjugacy classes of subgroups.

The subgroup lattice has 238 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	C₁₃×#2183	C₂	1	2	yes	maximal, complemented
3	C₁₃×#2183	C₂	1	4	yes	maximal, complemented
4	Q₈×C₁₃×C₁₆	C₂	1	2	yes	maximal, complemented
5	C₁₃×#2164	C₂	1	4	yes	maximal
6	C₁₃×#2163	C₂	1	1	yes	maximal, characteristic
7	C₁₃×#2162	C₂	1	1	yes	maximal, characteristic
8	C₁₃×#533	C₄	1	1	yes	characteristic
9	C₁₃×#446	C₄	1	2	yes	—
10	C₁₃×#446	C₄	1	2	yes	—
11	C₈×Q₈×C₁₃	C₂²	1	2	yes	—
12	C₈×Q₈×C₁₃	C₂²	1	2	yes	—
13	C₁₃×#424	C₄	1	2	yes	—
14	C₁₃×#423	C₄	1	1	yes	characteristic
15	C₁₃×#405	C₂²	1	2	yes	—
16	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
17	C₁₃×C₄⋊C₁₆	C₂²	1	2	yes	—
18	C₁₃×C₄⋊C₁₆	C₂²	1	2	yes	—
19	C₁₃×C₄⋊C₁₆	C₂²	1	4	yes	—
20	C₁₃×C₄⋊C₁₆	C₂²	1	4	yes	—
21	C₁₃×C₂²⋊C₁₆	C₂²	1	2	yes	—
22	C₁₃×C₂²⋊C₁₆	C₂²	1	2	yes	—
23	C₁₃×#346	C₂²	1	2	yes	—
24	C₁₃×#346	C₂²	1	4	yes	—
25	C₄×C₁₃×C₁₆	C₂²	1	1	yes	characteristic
26	C₄×C₁₃×C₁₆	C₂²	1	1	yes	characteristic
27	C₄×C₁₃×C₁₆	C₂²	1	4	yes	—
28	C₂×C₁₃×M₁₆	C₂×C₄	1	2	yes	—
29	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
30	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
31	C₁₃×C₄⋊Q₈	C₈	1	1	yes	characteristic
32	C₁₃×C₄⋊Q₈	C₈	1	1	yes	characteristic
33	C₁₃×#125	C₈	1	2	yes	—
34	C₁₃×C₂²⋊Q₈	C₈	1	2	yes	—
35	C₁₃×C₂²⋊Q₈	C₈	1	2	yes	—
36	C₄×Q₈×C₁₃	C₂×C₄	1	2	yes	—
37	C₄×Q₈×C₁₃	C₂×C₄	1	2	yes	—
38	C₁₃×#117	C₂×C₄	1	2	yes	—
39	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
40	C₂×C₁₃×C₁₆	C₂³	1	2	yes	—
41	C₂×C₁₃×C₁₆	C₂³	1	2	yes	—
42	C₂×C₁₃×C₁₆	C₂³	1	4	yes	—
43	C₁₃×C₄⋊C₈	C₂×C₄	1	2	yes	—
44	C₁₃×C₄⋊C₈	C₂×C₄	1	2	yes	—
45	C₁₃×C₄⋊C₈	C₂×C₄	1	4	yes	—
46	C₁₃×C₄⋊C₈	C₂×C₄	1	4	yes	—
47	C₁₃×#97	C₂×C₄	1	4	yes	—
48	C₄×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
49	C₄×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
50	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
51	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
52	C₄×C₈×C₁₃	C₂³	1	4	yes	—
53	#33499	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
54	C₂×Q₈×C₁₃	C₂×C₈	1	2	yes	—
55	C₂×Q₈×C₁₃	C₂×C₈	1	2	yes	—
56	C₂²×C₄×C₁₃	C₂×C₈	1	1	yes	characteristic
57	C₂²×C₄×C₁₃	C₂×C₈	1	1	yes	characteristic
58	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
59	C₁₃×M₁₆	—	4	2	no	—
60	C₂×C₈×C₁₃	—	2	2	no	—
61	C₂×C₈×C₁₃	—	4	1	no	—
62	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
63	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
64	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
65	C₂×C₈×C₁₃	C₂²×C₄	1	4	yes	—
66	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
67	C₁₃×C₄⋊C₄	C₂×C₈	1	2	yes	—
68	C₁₃×C₄⋊C₄	C₂×C₈	1	2	yes	—
69	C₁₃×C₄⋊C₄	C₂×C₈	1	4	yes	—
70	C₁₃×C₄⋊C₄	C₂×C₈	1	4	yes	—
71	C₁₃×C₄⋊C₄	C₂×C₈	1	2	yes	—
72	C₁₃×C₄⋊C₄	C₂×C₈	1	2	yes	—
73	C₁₃×C₂²⋊C₄	C₂×C₈	1	4	yes	—
74	C₄²×C₁₃	C₂×C₈	1	1	yes	characteristic
75	C₄²×C₁₃	C₂×C₈	1	1	yes	characteristic
76	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
77	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
78	C₄²×C₁₃	C₂²×C₄	1	4	yes	—
79	C₁₃×C₁₆	—	2	2	no	—
80	C₁₃×C₁₆	—	2	2	no	—
81	C₁₃×C₁₆	—	2	4	no	—
82	#2960	C₂×C₁₃	1	1	yes	characteristic
83	#2183	C₂×C₁₃	1	2	yes	complemented
84	#2183	C₂×C₁₃	1	4	yes	complemented
85	Q₈×C₁₆	C₂×C₁₃	1	2	yes	complemented
86	#2164	C₂×C₁₃	1	4	yes	—
87	#2163	C₂×C₁₃	1	1	yes	characteristic
88	#2162	C₂×C₁₃	1	1	yes	characteristic
89	C₂³×C₁₃	C₂²×C₈	1	1	yes	characteristic
90	Q₈×C₁₃	—	2	4	no	—
91	Q₈×C₁₃	—	4	2	no	—
92	C₂×C₄×C₁₃	—	2	1	no	—
93	C₂×C₄×C₁₃	—	2	1	no	—
94	C₂×C₄×C₁₃	—	2	2	no	—
95	C₂×C₄×C₁₃	—	4	1	no	—
96	C₂×C₄×C₁₃	C₂²×C₈	1	1	yes	characteristic
97	C₂×C₄×C₁₃	C₂²×C₈	1	1	yes	characteristic
98	C₂×C₄×C₁₃	C₂²×C₈	1	1	yes	characteristic
99	C₂×C₄×C₁₃	C₂²×C₈	1	1	yes	characteristic
100	C₂×C₄×C₁₃	C₂²×C₈	1	4	yes	—
101	C₂×C₄×C₁₃	C₂²×C₈	1	4	yes	—
102	C₂×C₄×C₁₃	C₂²×C₈	1	1	yes	characteristic
103	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
104	C₈×C₁₃	—	2	1	no	—
105	C₈×C₁₃	—	2	1	no	—
106	C₈×C₁₃	—	2	1	no	—
107	C₈×C₁₃	—	2	4	no	—
108	C₈×C₁₃	2₋¹⁺⁴	1	2	yes	—
109	#533	C₄×C₁₃	1	1	yes	characteristic
110	#446	C₄×C₁₃	1	2	yes	—
111	#446	C₄×C₁₃	1	2	yes	—
112	C₈×Q₈	C₂²×C₁₃	1	2	yes	—
113	C₈×Q₈	C₂²×C₁₃	1	2	yes	—
114	#424	C₄×C₁₃	1	2	yes	—
115	#423	C₄×C₁₃	1	1	yes	characteristic
116	#405	C₂²×C₁₃	1	2	yes	—
117	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
118	C₄⋊C₁₆	C₂²×C₁₃	1	2	yes	—
119	C₄⋊C₁₆	C₂²×C₁₃	1	2	yes	—
120	C₄⋊C₁₆	C₂²×C₁₃	1	4	yes	—
121	C₄⋊C₁₆	C₂²×C₁₃	1	4	yes	—
122	C₂²⋊C₁₆	C₂²×C₁₃	1	2	yes	—
123	C₂²⋊C₁₆	C₂²×C₁₃	1	2	yes	—
124	#346	C₂²×C₁₃	1	2	yes	—
125	#346	C₂²×C₁₃	1	4	yes	—
126	C₄×C₁₆	C₂²×C₁₃	1	1	yes	characteristic
127	C₄×C₁₆	C₂²×C₁₃	1	1	yes	characteristic
128	C₄×C₁₆	C₂²×C₁₃	1	4	yes	—
129	C₂²×C₁₃	—	2	1	no	—
130	C₂²×C₁₃	—	2	1	no	—
131	C₂²×C₁₃	—	2	1	no	—
132	C₂²×C₁₃	C₂³×C₈	1	1	yes	characteristic
133	C₄×C₁₃	—	2	1	no	—
134	C₄×C₁₃	—	2	4	no	—
135	C₄×C₁₃	—	2	1	no	—
136	C₄×C₁₃	—	2	1	no	—
137	C₄×C₁₃	—	2	4	no	—
138	C₄×C₁₃	—	2	1	no	—
139	C₄×C₁₃	#504	1	2	yes	—
140	C₄×C₁₃	#519	1	1	yes	characteristic
141	C₄×C₁₃	#568	1	1	yes	characteristic
142	C₂×M₁₆	C₂×C₄×C₁₃	1	2	yes	—
143	C₂²×C₈	C₂×C₄×C₁₃	1	1	yes	characteristic
144	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
145	C₄⋊Q₈	C₈×C₁₃	1	1	yes	characteristic
146	C₄⋊Q₈	C₈×C₁₃	1	1	yes	characteristic
147	#125	C₈×C₁₃	1	2	yes	—
148	C₂²⋊Q₈	C₈×C₁₃	1	2	yes	—
149	C₂²⋊Q₈	C₈×C₁₃	1	2	yes	—
150	C₄×Q₈	C₂×C₄×C₁₃	1	2	yes	—
151	C₄×Q₈	C₂×C₄×C₁₃	1	2	yes	—
152	#117	C₂×C₄×C₁₃	1	2	yes	—
153	C₂×C₄²	C₂×C₄×C₁₃	1	1	yes	characteristic
154	C₂×C₁₆	C₂³×C₁₃	1	2	yes	—
155	C₂×C₁₆	C₂³×C₁₃	1	2	yes	—
156	C₂×C₁₆	C₂³×C₁₃	1	4	yes	—
157	C₄⋊C₈	C₂×C₄×C₁₃	1	2	yes	—
158	C₄⋊C₈	C₂×C₄×C₁₃	1	2	yes	—
159	C₄⋊C₈	C₂×C₄×C₁₃	1	4	yes	—
160	C₄⋊C₈	C₂×C₄×C₁₃	1	4	yes	—
161	#97	C₂×C₄×C₁₃	1	4	yes	—
162	C₄×C₈	C₂×C₄×C₁₃	1	1	yes	characteristic
163	C₄×C₈	C₂×C₄×C₁₃	1	1	yes	characteristic
164	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
165	C₄×C₈	C₂³×C₁₃	1	4	yes	—
166	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
167	C₂×C₁₃	—	4	1	no	—
168	C₂×C₁₃	#2982	1	1	yes	characteristic
169	C₂×C₁₃	C₂×#504	1	1	yes	characteristic
170	C₂×C₁₃	#3407	1	1	yes	characteristic
171	C₂×Q₈	C₂×C₈×C₁₃	1	2	yes	—
172	C₂×Q₈	C₂×C₈×C₁₃	1	2	yes	—
173	C₂²×C₄	C₂×C₈×C₁₃	1	1	yes	characteristic
174	C₂²×C₄	C₂×C₈×C₁₃	1	1	yes	characteristic
175	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
176	M₁₆	—	4	2	no	—
177	C₂×C₈	—	2	2	no	—
178	C₂×C₈	—	4	1	no	—
179	C₂×C₈	C₂²×C₄×C₁₃	1	1	yes	characteristic
180	C₂×C₈	C₂²×C₄×C₁₃	1	1	yes	characteristic
181	C₂×C₈	C₂²×C₄×C₁₃	1	1	yes	characteristic
182	C₂×C₈	C₂²×C₄×C₁₃	1	4	yes	—
183	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
184	C₄⋊C₄	C₂×C₈×C₁₃	1	2	yes	—
185	C₄⋊C₄	C₂×C₈×C₁₃	1	2	yes	—
186	C₄⋊C₄	C₂×C₈×C₁₃	1	4	yes	—
187	C₄⋊C₄	C₂×C₈×C₁₃	1	4	yes	—
188	C₄⋊C₄	C₂×C₈×C₁₃	1	2	yes	—
189	C₄⋊C₄	C₂×C₈×C₁₃	1	2	yes	—
190	C₂²⋊C₄	C₂×C₈×C₁₃	1	4	yes	—
191	C₄²	C₂×C₈×C₁₃	1	1	yes	characteristic
192	C₄²	C₂×C₈×C₁₃	1	1	yes	characteristic
193	C₄²	C₂²×C₄×C₁₃	1	1	yes	characteristic
194	C₄²	C₂²×C₄×C₁₃	1	1	yes	characteristic
195	C₄²	C₂²×C₄×C₁₃	1	4	yes	—
196	C₁₆	—	2	2	no	—
197	C₁₆	—	2	2	no	—
198	C₁₆	—	2	4	no	—
199	C₁₃	#33499	1	1	yes	characteristic, direct product factor, Sylow
200	C₂³	C₂²×C₈×C₁₃	1	1	yes	characteristic
201	Q₈	—	2	4	no	—
202	Q₈	—	4	2	no	—
203	C₂×C₄	—	2	2	no	—
204	C₂×C₄	—	2	1	no	—
205	C₂×C₄	—	2	1	no	—
206	C₂×C₄	—	4	1	no	—
207	C₂×C₄	C₂²×C₈×C₁₃	1	1	yes	characteristic
208	C₂×C₄	C₂²×C₈×C₁₃	1	1	yes	characteristic
209	C₂×C₄	C₂²×C₈×C₁₃	1	1	yes	characteristic
210	C₂×C₄	C₂²×C₈×C₁₃	1	1	yes	characteristic
211	C₂×C₄	C₂²×C₈×C₁₃	1	4	yes	—
212	C₂×C₄	C₂²×C₈×C₁₃	1	4	yes	—
213	C₂×C₄	C₂²×C₈×C₁₃	1	1	yes	characteristic
214	C₂×C₄	C₂³×C₄×C₁₃	1	1	yes	characteristic
215	C₈	—	2	1	no	—
216	C₈	—	2	1	no	—
217	C₈	—	2	1	no	—
218	C₈	—	2	4	no	—
219	C₈	C₁₃×2₋¹⁺⁴	1	2	yes	—
220	C₂²	—	2	1	no	—
221	C₂²	—	2	1	no	—
222	C₂²	—	2	1	no	—
223	C₂²	C₂³×C₈×C₁₃	1	1	yes	characteristic
224	C₄	—	2	1	no	—
225	C₄	—	2	4	no	—
226	C₄	—	2	1	no	—
227	C₄	—	2	1	no	—
228	C₄	—	2	4	no	—
229	C₄	—	2	1	no	—
230	C₄	C₁₃×#504	1	2	yes	—
231	C₄	C₁₃×#519	1	1	yes	characteristic
232	C₄	C₁₃×#568	1	1	yes	characteristic
233	C₂	—	4	1	no	—
234	C₂	C₁₃×#2982	1	1	yes	characteristic
235	C₂	C₂×C₁₃×#504	1	1	yes	characteristic
236	C₂	C₁₃×#3407	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₈×C₁₃	C₂⁴
commutator	C₂²	C₂³×C₈×C₁₃
Frattini, cosocle	C₂×C₈	C₂⁴×C₁₃
socle	C₂²×C₁₃	C₂³×C₈
prime radical	C₂³×C₁₃	C₂²×C₈
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₈×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₃×#2183	C₂	semidirect
3. C₁₃×#2183	C₂	semidirect
4. Q₈×C₁₃×C₁₆	C₂	semidirect
53. #33499	C₁₃	direct (N × H)
83. #2183	C₂×C₁₃	semidirect
84. #2183	C₂×C₁₃	semidirect
85. Q₈×C₁₆	C₂×C₁₃	semidirect
199. C₁₃	#33499	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
C₁₃×#2183	2
Q₈×C₁₃×C₁₆	2
C₁₃×#2164	2
C₁₃×#2163	2
C₁₃×#2162	2
#33499	13

Subgroups — C13×#33499 #15719838

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#33499 #15719838