Subgroups — C₁₃×#23814 #15710153

Order 3328.

926 conjugacy classes of subgroups.

The subgroup lattice has 212 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#441	C₂	1	2	yes	maximal
2	C₂×C₄×C₁₃×Q₁₆	C₂	1	2	yes	maximal
3	C₁₃×#2327	C₂	1	2	yes	maximal
4	C₁₃×#2097	C₂	1	4	yes	maximal
5	C₁₃×#2016	C₂	1	4	yes	maximal
6	C₁₃×#1746	C₂	1	1	yes	maximal, characteristic
7	C₂²×C₁₃×Q₁₆	C₂²	1	2	yes	—
8	C₂²×C₁₃×Q₁₆	C₂²	1	2	yes	—
9	C₂×C₁₃×C₄⋊Q₈	C₂²	1	2	yes	—
10	C₂×C₄×Q₈×C₁₃	C₂²	1	4	yes	—
11	C₁₃×#441	—	2	8	no	—
12	C₄×C₁₃×Q₁₆	—	2	8	no	—
13	C₂×C₁₃×#107	C₂²	1	2	yes	—
14	C₂×C₁₃×#106	C₂²	1	2	yes	—
15	C₂×C₁₃×#103	C₂²	1	4	yes	—
16	C₂×C₁₃×#103	C₂²	1	4	yes	—
17	C₂×C₁₃×#97	C₂²	1	1	yes	characteristic
18	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
19	C₁₃×#391	C₂²	1	4	yes	—
20	C₁₃×#387	—	2	8	no	—
21	C₁₃×#382	C₂²	1	2	yes	—
22	C₁₃×#376	C₂²	1	1	yes	characteristic
23	C₁₃×#336	C₂²	1	4	yes	—
24	C₂²×Q₈×C₁₃	C₂³	1	4	yes	—
25	C₂×C₁₃×Q₁₆	—	2	8	no	—
26	C₂×C₁₃×Q₁₆	—	2	8	no	—
27	C₂×C₁₃×Q₁₆	—	2	4	no	—
28	C₂×C₁₃×Q₁₆	—	2	4	no	—
29	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
30	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
31	C₁₃×C₄⋊Q₈	—	2	8	no	—
32	C₄×Q₈×C₁₃	—	2	8	no	—
33	C₄×Q₈×C₁₃	—	2	8	no	—
34	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
35	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
36	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
37	C₂×C₄²×C₁₃	—	2	4	no	—
38	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
39	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
40	C₁₃×#107	—	2	4	no	—
41	C₁₃×#106	—	2	4	no	—
42	C₁₃×#103	—	2	8	no	—
43	C₁₃×#103	—	2	8	no	—
44	C₁₃×#97	D₄	1	4	yes	—
45	C₄×C₈×C₁₃	D₄	1	4	yes	—
46	C₁₃×#95	—	2	4	no	—
47	C₁₃×#95	—	2	8	no	—
48	C₁₃×#95	D₄	1	4	yes	—
49	#23814	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
50	C₂×Q₈×C₁₃	—	2	4	no	—
51	C₂×Q₈×C₁₃	—	2	4	no	—
52	C₂×Q₈×C₁₃	—	2	4	no	—
53	C₂×Q₈×C₁₃	—	2	4	no	—
54	C₂×Q₈×C₁₃	—	2	4	no	—
55	C₂×Q₈×C₁₃	#41	1	8	yes	—
56	C₂²×C₄×C₁₃	—	2	4	no	—
57	C₂²×C₄×C₁₃	—	2	4	no	—
58	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
59	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
60	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
61	C₁₃×Q₁₆	—	2	16	no	—
62	C₁₃×Q₁₆	—	2	16	no	—
63	C₂×C₈×C₁₃	—	2	4	no	—
64	C₂×C₈×C₁₃	—	2	4	no	—
65	C₂×C₈×C₁₃	C₂×D₄	1	4	yes	—
66	C₂×C₈×C₁₃	C₂×D₄	1	4	yes	—
67	C₁₃×C₄⋊C₄	—	2	16	no	—
68	C₁₃×C₄⋊C₄	—	2	4	no	—
69	C₁₃×C₄⋊C₄	—	2	4	no	—
70	C₁₃×C₄⋊C₄	—	4	8	no	—
71	C₄²×C₁₃	—	2	4	no	—
72	C₄²×C₁₃	—	4	8	no	—
73	C₄²×C₁₃	C₂×D₄	1	2	yes	—
74	C₄²×C₁₃	C₂×D₄	1	2	yes	—
75	C₂×#441	C₂×C₁₃	1	2	yes	—
76	C₂×C₄×Q₁₆	C₂×C₁₃	1	2	yes	—
77	#2327	C₂×C₁₃	1	2	yes	—
78	#2097	C₂×C₁₃	1	4	yes	—
79	#2016	C₂×C₁₃	1	4	yes	—
80	#1746	C₂×C₁₃	1	1	yes	characteristic
81	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
82	Q₈×C₁₃	—	2	8	no	—
83	Q₈×C₁₃	—	2	8	no	—
84	Q₈×C₁₃	—	4	4	no	—
85	Q₈×C₁₃	—	4	4	no	—
86	C₂×C₄×C₁₃	—	2	4	no	—
87	C₂×C₄×C₁₃	—	2	4	no	—
88	C₂×C₄×C₁₃	—	2	8	no	—
89	C₂×C₄×C₁₃	—	2	8	no	—
90	C₂×C₄×C₁₃	—	4	4	no	—
91	C₂×C₄×C₁₃	—	4	4	no	—
92	C₂×C₄×C₁₃	—	4	4	no	—
93	C₂×C₄×C₁₃	—	4	8	no	—
94	C₂×C₄×C₁₃	#127	1	4	yes	—
95	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
96	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
97	C₂×C₄×C₁₃	C₂×#41	1	4	yes	—
98	C₈×C₁₃	—	2	4	no	—
99	C₈×C₁₃	—	2	4	no	—
100	C₂²×Q₁₆	C₂²×C₁₃	1	2	yes	—
101	C₂²×Q₁₆	C₂²×C₁₃	1	2	yes	—
102	C₂×C₄⋊Q₈	C₂²×C₁₃	1	2	yes	—
103	C₂×C₄×Q₈	C₂²×C₁₃	1	4	yes	—
104	#441	—	2	8	no	—
105	C₄×Q₁₆	—	2	8	no	—
106	C₂×#107	C₂²×C₁₃	1	2	yes	—
107	C₂×#106	C₂²×C₁₃	1	2	yes	—
108	C₂×#103	C₂²×C₁₃	1	4	yes	—
109	C₂×#103	C₂²×C₁₃	1	4	yes	—
110	C₂×#97	C₂²×C₁₃	1	1	yes	characteristic
111	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
112	#391	C₂²×C₁₃	1	4	yes	—
113	#387	—	2	8	no	—
114	#382	C₂²×C₁₃	1	2	yes	—
115	#376	C₂²×C₁₃	1	1	yes	characteristic
116	#336	C₂²×C₁₃	1	4	yes	—
117	C₂²×C₁₃	#525	1	2	yes	—
118	C₂²×C₁₃	C₂×#127	1	1	yes	characteristic
119	C₂²×C₁₃	#578	1	4	yes	—
120	C₄×C₁₃	—	2	4	no	—
121	C₄×C₁₃	—	4	4	no	—
122	C₄×C₁₃	—	4	8	no	—
123	C₄×C₁₃	—	8	4	no	—
124	C₄×C₁₃	#525	1	2	yes	—
125	C₄×C₁₃	#525	1	2	yes	—
126	C₂²×Q₈	C₂³×C₁₃	1	4	yes	—
127	C₂×Q₁₆	—	2	8	no	—
128	C₂×Q₁₆	—	2	8	no	—
129	C₂×Q₁₆	—	2	4	no	—
130	C₂×Q₁₆	—	2	4	no	—
131	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
132	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
133	C₄⋊Q₈	—	2	8	no	—
134	C₄×Q₈	—	2	8	no	—
135	C₄×Q₈	—	2	8	no	—
136	C₂×C₄⋊C₄	—	2	4	no	—
137	C₂×C₄⋊C₄	—	2	4	no	—
138	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
139	C₂×C₄²	—	2	4	no	—
140	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
141	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
142	#107	—	2	4	no	—
143	#106	—	2	4	no	—
144	#103	—	2	8	no	—
145	#103	—	2	8	no	—
146	#97	D₄×C₁₃	1	4	yes	—
147	C₄×C₈	D₄×C₁₃	1	4	yes	—
148	#95	—	2	4	no	—
149	#95	—	2	8	no	—
150	#95	D₄×C₁₃	1	4	yes	—
151	C₂×C₁₃	#2397	1	1	yes	characteristic
152	C₂×C₁₃	#3127	1	4	yes	—
153	C₂×C₁₃	#3156	1	2	yes	—
154	C₂×Q₈	—	2	4	no	—
155	C₂×Q₈	—	2	4	no	—
156	C₂×Q₈	—	2	4	no	—
157	C₂×Q₈	—	2	4	no	—
158	C₂×Q₈	—	2	4	no	—
159	C₂×Q₈	C₁₃×#41	1	8	yes	—
160	C₂²×C₄	—	2	4	no	—
161	C₂²×C₄	—	2	4	no	—
162	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
163	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
164	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
165	Q₁₆	—	2	16	no	—
166	Q₁₆	—	2	16	no	—
167	C₂×C₈	—	2	4	no	—
168	C₂×C₈	—	2	4	no	—
169	C₂×C₈	C₂×D₄×C₁₃	1	4	yes	—
170	C₂×C₈	C₂×D₄×C₁₃	1	4	yes	—
171	C₄⋊C₄	—	2	16	no	—
172	C₄⋊C₄	—	2	4	no	—
173	C₄⋊C₄	—	2	4	no	—
174	C₄⋊C₄	—	4	8	no	—
175	C₄²	—	2	4	no	—
176	C₄²	—	4	8	no	—
177	C₄²	C₂×D₄×C₁₃	1	2	yes	—
178	C₄²	C₂×D₄×C₁₃	1	2	yes	—
179	C₁₃	#23814	1	1	yes	characteristic, direct product factor, Sylow
180	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
181	Q₈	—	2	8	no	—
182	Q₈	—	2	8	no	—
183	Q₈	—	4	4	no	—
184	Q₈	—	4	4	no	—
185	C₂×C₄	—	2	4	no	—
186	C₂×C₄	—	2	4	no	—
187	C₂×C₄	—	2	8	no	—
188	C₂×C₄	—	2	8	no	—
189	C₂×C₄	—	4	4	no	—
190	C₂×C₄	—	4	4	no	—
191	C₂×C₄	—	4	4	no	—
192	C₂×C₄	—	4	8	no	—
193	C₂×C₄	C₁₃×#127	1	4	yes	—
194	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
195	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
196	C₂×C₄	C₂×C₁₃×#41	1	4	yes	—
197	C₈	—	2	4	no	—
198	C₈	—	2	4	no	—
199	C₂²	C₁₃×#525	1	2	yes	—
200	C₂²	C₂×C₁₃×#127	1	1	yes	characteristic
201	C₂²	C₁₃×#578	1	4	yes	—
202	C₄	—	2	4	no	—
203	C₄	—	4	4	no	—
204	C₄	—	4	8	no	—
205	C₄	—	8	4	no	—
206	C₄	C₁₃×#525	1	2	yes	—
207	C₄	C₁₃×#525	1	2	yes	—
208	C₂	C₁₃×#2397	1	1	yes	characteristic
209	C₂	C₁₃×#3127	1	4	yes	—
210	C₂	C₁₃×#3156	1	2	yes	—

	subgroup	G/H
center, socle, prime radical	C₂³×C₁₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ C₁₃×#376 ◁ G

Complements

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

N	H ≅ G/N	type
49. #23814	C₁₃	direct (N × H)
179. C₁₃	#23814	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×C₁₃×#441	2
C₂×C₄×C₁₃×Q₁₆	2
C₁₃×#2327	2
C₁₃×#2097	2
C₁₃×#2016	2
C₁₃×#1746	2
#23814	13

Subgroups — C13×#23814 #15710153

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#23814 #15710153