Subgroups — C₁₃×#9845 #15696184

Order 3328.

478 conjugacy classes of subgroups.

The subgroup lattice has 234 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3170	C₂	1	1	yes	maximal, characteristic
2	C₁₃×#1994	C₂	1	2	yes	maximal
3	C₄²×C₈×C₁₃	C₂	1	1	yes	maximal, characteristic
4	C₁₃×#1567	C₂	1	1	yes	maximal, characteristic
5	C₁₃×#1493	C₂	1	2	yes	maximal
6	C₁₃×#533	C₂²	1	2	yes	—
7	C₁₃×#500	C₄	1	1	yes	characteristic, complemented
8	C₁₃×#494	C₄	1	1	yes	characteristic, complemented
9	C₁₃×#487	C₄	1	2	yes	complemented
10	C₁₃×#467	—	2	2	no	—
11	C₄×C₁₃×Q₁₆	—	2	2	no	—
12	C₁₃×#423	C₂²	1	2	yes	—
13	C₂×C₄×C₈×C₁₃	—	2	2	no	—
14	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
15	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
16	C₄³×C₁₃	C₂²	1	1	yes	characteristic
17	C₁₃×#339	—	2	4	no	—
18	C₁₃×#335	—	2	2	no	—
19	C₁₃×Q₈⋊C₈	—	2	4	no	—
20	C₂×C₁₃×Q₁₆	—	2	2	no	—
21	C₂×C₁₃×M₁₆	—	2	2	no	—
22	C₂²×C₈×C₁₃	—	2	1	no	—
23	C₂²×C₈×C₁₃	D₄	1	2	yes	—
24	C₁₃×C₄⋊Q₈	C₂×C₄	1	2	yes	—
25	C₁₃×C₄⋊Q₈	C₂×C₄	1	2	yes	—
26	C₁₃×#125	—	2	2	no	—
27	C₁₃×C₂²⋊Q₈	—	2	2	no	—
28	C₁₃×C₂²⋊Q₈	—	2	2	no	—
29	C₄×Q₈×C₁₃	—	2	2	no	—
30	C₄×Q₈×C₁₃	—	2	2	no	—
31	C₁₃×#117	—	2	2	no	—
32	C₂×C₄²×C₁₃	—	2	1	no	—
33	C₂×C₄²×C₁₃	—	2	1	no	—
34	C₂×C₄²×C₁₃	D₄	1	2	yes	—
35	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
36	C₁₃×#107	—	2	2	no	—
37	C₁₃×C₄⋊C₈	—	2	2	no	—
38	C₁₃×C₄⋊C₈	—	2	2	no	—
39	C₁₃×#103	—	2	4	no	—
40	C₄×C₈×C₁₃	—	2	8	no	—
41	C₄×C₈×C₁₃	—	2	1	no	—
42	C₄×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
43	C₄×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
44	C₄×C₈×C₁₃	D₄	1	2	yes	—
45	C₄×C₈×C₁₃	D₄	1	2	yes	—
46	#9845	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
47	C₂×Q₈×C₁₃	—	2	2	no	—
48	C₂×Q₈×C₁₃	—	2	2	no	—
49	C₂²×C₄×C₁₃	—	2	2	no	—
50	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
51	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
52	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
53	C₁₃×Q₁₆	—	4	4	no	—
54	C₁₃×M₁₆	—	4	4	no	—
55	C₂×C₈×C₁₃	—	2	4	no	—
56	C₂×C₈×C₁₃	—	2	2	no	—
57	C₂×C₈×C₁₃	—	2	4	no	—
58	C₂×C₈×C₁₃	—	4	2	no	—
59	C₂×C₈×C₁₃	C₂²⋊C₄	1	2	yes	—
60	C₂×C₈×C₁₃	C₂²⋊C₄	1	2	yes	—
61	C₁₃×C₄⋊C₄	—	2	2	no	—
62	C₁₃×C₄⋊C₄	—	2	2	no	—
63	C₁₃×C₄⋊C₄	—	2	2	no	—
64	C₁₃×C₄⋊C₄	—	2	2	no	—
65	C₁₃×C₄⋊C₄	—	4	2	no	—
66	C₁₃×C₄⋊C₄	—	4	2	no	—
67	C₁₃×C₂²⋊C₄	—	4	2	no	—
68	C₄²×C₁₃	—	2	4	no	—
69	C₄²×C₁₃	—	2	4	no	—
70	C₄²×C₁₃	—	2	2	no	—
71	C₄²×C₁₃	—	4	2	no	—
72	C₄²×C₁₃	Q₁₆	1	4	yes	complemented
73	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
74	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
75	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
76	C₄²×C₁₃	#41	1	1	yes	characteristic
77	#3170	C₂×C₁₃	1	1	yes	characteristic
78	#1994	C₂×C₁₃	1	2	yes	—
79	C₄²×C₈	C₂×C₁₃	1	1	yes	characteristic
80	#1567	C₂×C₁₃	1	1	yes	characteristic
81	#1493	C₂×C₁₃	1	2	yes	—
82	C₂³×C₁₃	#121	1	1	yes	characteristic
83	Q₈×C₁₃	—	4	4	no	—
84	Q₈×C₁₃	—	4	4	no	—
85	C₂×C₄×C₁₃	—	2	4	no	—
86	C₂×C₄×C₁₃	—	2	4	no	—
87	C₂×C₄×C₁₃	—	2	4	no	—
88	C₂×C₄×C₁₃	—	2	2	no	—
89	C₂×C₄×C₁₃	—	2	2	no	—
90	C₂×C₄×C₁₃	—	4	2	no	—
91	C₂×C₄×C₁₃	—	4	2	no	—
92	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
93	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
94	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
95	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
96	C₂×C₄×C₁₃	#124	1	1	yes	characteristic
97	C₂×C₄×C₁₃	#127	1	1	yes	characteristic
98	C₂×C₄×C₁₃	C₂×Q₁₆	1	2	yes	—
99	C₂×C₄×C₁₃	#135	1	2	yes	—
100	C₈×C₁₃	—	2	4	no	—
101	C₈×C₁₃	—	2	2	no	—
102	C₈×C₁₃	—	8	2	no	—
103	C₈×C₁₃	#104	1	4	yes	—
104	#533	C₂²×C₁₃	1	2	yes	—
105	#500	C₄×C₁₃	1	1	yes	characteristic, complemented
106	#494	C₄×C₁₃	1	1	yes	characteristic, complemented
107	#487	C₄×C₁₃	1	2	yes	complemented
108	#467	—	2	2	no	—
109	C₄×Q₁₆	—	2	2	no	—
110	#423	C₂²×C₁₃	1	2	yes	—
111	C₂×C₄×C₈	—	2	2	no	—
112	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
113	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
114	C₄³	C₂²×C₁₃	1	1	yes	characteristic
115	#339	—	2	4	no	—
116	#335	—	2	2	no	—
117	Q₈⋊C₈	—	2	4	no	—
118	C₂²×C₁₃	—	2	1	no	—
119	C₂²×C₁₃	—	2	1	no	—
120	C₂²×C₁₃	#390	1	1	yes	characteristic
121	C₂²×C₁₃	#467	1	2	yes	—
122	C₄×C₁₃	—	2	8	no	—
123	C₄×C₁₃	—	2	1	no	—
124	C₄×C₁₃	—	2	1	no	—
125	C₄×C₁₃	—	8	2	no	—
126	C₄×C₁₃	—	8	2	no	—
127	C₄×C₁₃	C₂×#104	1	2	yes	—
128	C₄×C₁₃	C₄×Q₁₆	1	2	yes	—
129	C₄×C₁₃	#443	1	2	yes	—
130	C₄×C₁₃	#494	1	1	yes	characteristic
131	C₄×C₁₃	#495	1	1	yes	characteristic
132	C₂×Q₁₆	—	2	2	no	—
133	C₂×M₁₆	—	2	2	no	—
134	C₂²×C₈	—	2	1	no	—
135	C₂²×C₈	D₄×C₁₃	1	2	yes	—
136	C₄⋊Q₈	C₂×C₄×C₁₃	1	2	yes	—
137	C₄⋊Q₈	C₂×C₄×C₁₃	1	2	yes	—
138	#125	—	2	2	no	—
139	C₂²⋊Q₈	—	2	2	no	—
140	C₂²⋊Q₈	—	2	2	no	—
141	C₄×Q₈	—	2	2	no	—
142	C₄×Q₈	—	2	2	no	—
143	#117	—	2	2	no	—
144	C₂×C₄²	—	2	1	no	—
145	C₂×C₄²	—	2	1	no	—
146	C₂×C₄²	D₄×C₁₃	1	2	yes	—
147	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
148	#107	—	2	2	no	—
149	C₄⋊C₈	—	2	2	no	—
150	C₄⋊C₈	—	2	2	no	—
151	#103	—	2	4	no	—
152	C₄×C₈	—	2	8	no	—
153	C₄×C₈	—	2	1	no	—
154	C₄×C₈	C₂×C₄×C₁₃	1	1	yes	characteristic
155	C₄×C₈	C₂×C₄×C₁₃	1	1	yes	characteristic
156	C₄×C₈	D₄×C₁₃	1	2	yes	—
157	C₄×C₈	D₄×C₁₃	1	2	yes	—
158	C₂×C₁₃	—	2	2	no	—
159	C₂×C₁₃	#1962	1	1	yes	characteristic
160	C₂×C₁₃	#1969	1	1	yes	characteristic
161	C₂×C₁₃	#1974	1	1	yes	characteristic
162	C₂×Q₈	—	2	2	no	—
163	C₂×Q₈	—	2	2	no	—
164	C₂²×C₄	—	2	2	no	—
165	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
166	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
167	C₂²×C₄	C₁₃×#41	1	1	yes	characteristic
168	Q₁₆	—	4	4	no	—
169	M₁₆	—	4	4	no	—
170	C₂×C₈	—	2	4	no	—
171	C₂×C₈	—	2	2	no	—
172	C₂×C₈	—	2	4	no	—
173	C₂×C₈	—	4	2	no	—
174	C₂×C₈	C₁₃×C₂²⋊C₄	1	2	yes	—
175	C₂×C₈	C₁₃×C₂²⋊C₄	1	2	yes	—
176	C₄⋊C₄	—	2	2	no	—
177	C₄⋊C₄	—	2	2	no	—
178	C₄⋊C₄	—	2	2	no	—
179	C₄⋊C₄	—	2	2	no	—
180	C₄⋊C₄	—	4	2	no	—
181	C₄⋊C₄	—	4	2	no	—
182	C₂²⋊C₄	—	4	2	no	—
183	C₄²	—	2	4	no	—
184	C₄²	—	2	4	no	—
185	C₄²	—	2	2	no	—
186	C₄²	—	4	2	no	—
187	C₄²	C₁₃×Q₁₆	1	4	yes	complemented
188	C₄²	C₂²×C₄×C₁₃	1	1	yes	characteristic
189	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
190	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
191	C₄²	C₁₃×#41	1	1	yes	characteristic
192	C₁₃	#9845	1	1	yes	characteristic, direct product factor, Sylow
193	C₂³	C₁₃×#121	1	1	yes	characteristic
194	Q₈	—	4	4	no	—
195	Q₈	—	4	4	no	—
196	C₂×C₄	—	2	4	no	—
197	C₂×C₄	—	2	4	no	—
198	C₂×C₄	—	2	4	no	—
199	C₂×C₄	—	2	2	no	—
200	C₂×C₄	—	2	2	no	—
201	C₂×C₄	—	4	2	no	—
202	C₂×C₄	—	4	2	no	—
203	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
204	C₂×C₄	C₄×D₄×C₁₃	1	1	yes	characteristic
205	C₂×C₄	C₄×D₄×C₁₃	1	1	yes	characteristic
206	C₂×C₄	C₁₃×#121	1	1	yes	characteristic
207	C₂×C₄	C₁₃×#124	1	1	yes	characteristic
208	C₂×C₄	C₁₃×#127	1	1	yes	characteristic
209	C₂×C₄	C₂×C₁₃×Q₁₆	1	2	yes	—
210	C₂×C₄	C₁₃×#135	1	2	yes	—
211	C₈	—	2	4	no	—
212	C₈	—	2	2	no	—
213	C₈	—	8	2	no	—
214	C₈	C₁₃×#104	1	4	yes	—
215	C₂²	—	2	1	no	—
216	C₂²	—	2	1	no	—
217	C₂²	C₁₃×#390	1	1	yes	characteristic
218	C₂²	C₁₃×#467	1	2	yes	—
219	C₄	—	2	8	no	—
220	C₄	—	2	1	no	—
221	C₄	—	2	1	no	—
222	C₄	—	8	2	no	—
223	C₄	—	8	2	no	—
224	C₄	C₂×C₁₃×#104	1	2	yes	—
225	C₄	C₄×C₁₃×Q₁₆	1	2	yes	—
226	C₄	C₁₃×#443	1	2	yes	—
227	C₄	C₁₃×#494	1	1	yes	characteristic
228	C₄	C₁₃×#495	1	1	yes	characteristic
229	C₂	—	2	2	no	—
230	C₂	C₁₃×#1962	1	1	yes	characteristic
231	C₂	C₁₃×#1969	1	1	yes	characteristic
232	C₂	C₁₃×#1974	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₁₃	#127
commutator	C₄²	C₂²×C₄×C₁₃
Frattini, cosocle	C₂×C₄²	C₂³×C₁₃
socle	C₂²×C₁₃	#390
prime radical	C₂³×C₁₃	#121
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₃ ◁ C₂×C₄²×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
7. C₁₃×#500	C₄	semidirect
8. C₁₃×#494	C₄	semidirect
9. C₁₃×#487	C₄	semidirect
46. #9845	C₁₃	direct (N × H)
72. C₄²×C₁₃	Q₁₆	semidirect
105. #500	C₄×C₁₃	semidirect
106. #494	C₄×C₁₃	semidirect
107. #487	C₄×C₁₃	semidirect
187. C₄²	C₁₃×Q₁₆	semidirect
192. C₁₃	#9845	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×#3170	2
C₁₃×#1994	2
C₄²×C₈×C₁₃	2
C₁₃×#1567	2
C₁₃×#1493	2
#9845	13

Subgroups — C13×#9845 #15696184

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#9845 #15696184