Subgroups — C₁₃×#32792 #15719131

Order 3328.

600 conjugacy classes of subgroups.

The subgroup lattice has 246 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#2628	C₂	1	2	yes	maximal
2	C₁₃×#2101	C₂	1	4	yes	maximal, complemented
3	C₁₃×#2076	C₂	1	2	yes	maximal
4	C₁₃×#2075	C₂	1	2	yes	maximal
5	C₁₃×#2057	C₂	1	4	yes	maximal, complemented
6	C₁₃×#1818	C₂	1	1	yes	maximal, characteristic
7	C₂×C₁₃×C₄⋊Q₈	C₂²	1	2	yes	—
8	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
9	C₂×C₁₃×#107	C₂²	1	2	yes	—
10	C₂×C₁₃×#107	C₂²	1	2	yes	—
11	C₂×C₁₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
12	C₂×C₁₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
13	C₁₃×#400	—	2	2	no	—
14	C₁₃×#399	—	2	2	no	—
15	C₁₃×#395	—	2	2	no	—
16	C₁₃×#393	—	2	2	no	—
17	C₁₃×#389	C₂²	1	4	yes	—
18	C₁₃×#382	C₂²	1	2	yes	—
19	C₁₃×#380	C₂²	1	4	yes	—
20	C₁₃×#340	C₂²	1	4	yes	—
21	C₁₃×#340	C₂²	1	4	yes	—
22	C₁₃×#340	C₂²	1	2	yes	—
23	C₁₃×#340	C₂²	1	2	yes	—
24	C₁₃×#336	C₂²	1	4	yes	—
25	C₂²×Q₈×C₁₃	—	2	2	no	—
26	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
27	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
28	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
29	C₁₃×C₄⋊Q₈	—	4	2	no	—
30	C₁₃×C₄⋊Q₈	—	4	2	no	—
31	C₁₃×#117	—	4	1	no	—
32	C₁₃×#117	—	4	1	no	—
33	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
34	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
35	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
36	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
37	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
38	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
39	C₂×C₁₃×C₂²⋊C₄	—	2	4	no	—
40	C₂×C₁₃×C₂²⋊C₄	D₄	1	2	yes	—
41	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
42	C₁₃×#107	—	4	2	no	—
43	C₁₃×#107	—	4	2	no	—
44	C₁₃×C₂²⋊C₈	—	4	1	no	—
45	C₁₃×C₂²⋊C₈	—	4	1	no	—
46	C₁₃×#95	—	2	4	no	—
47	C₁₃×#95	—	2	2	no	—
48	C₁₃×#95	—	2	2	no	—
49	C₁₃×#95	—	2	4	no	—
50	#32792	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
51	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
52	C₂×Q₈×C₁₃	—	4	4	no	—
53	C₂×Q₈×C₁₃	—	8	4	no	—
54	C₂²×C₄×C₁₃	—	2	1	no	—
55	C₂²×C₄×C₁₃	—	2	1	no	—
56	C₂²×C₄×C₁₃	—	2	4	no	—
57	C₂²×C₄×C₁₃	—	2	4	no	—
58	C₂²×C₄×C₁₃	—	2	4	no	—
59	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
60	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
61	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
62	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
63	C₂×C₈×C₁₃	—	2	2	no	—
64	C₂×C₈×C₁₃	—	2	2	no	—
65	C₂×C₈×C₁₃	—	2	4	no	—
66	C₂×C₈×C₁₃	—	2	4	no	—
67	C₁₃×C₄⋊C₄	—	2	4	no	—
68	C₁₃×C₄⋊C₄	—	2	4	no	—
69	C₁₃×C₄⋊C₄	—	2	8	no	—
70	C₁₃×C₄⋊C₄	—	4	1	no	—
71	C₁₃×C₄⋊C₄	—	4	1	no	—
72	C₁₃×C₄⋊C₄	—	4	4	no	—
73	C₁₃×C₄⋊C₄	—	8	4	no	—
74	C₁₃×C₂²⋊C₄	—	4	2	no	—
75	C₁₃×C₂²⋊C₄	—	8	4	no	—
76	C₄²×C₁₃	—	2	2	no	—
77	C₄²×C₁₃	—	2	2	no	—
78	#2628	C₂×C₁₃	1	2	yes	—
79	#2101	C₂×C₁₃	1	4	yes	complemented
80	#2076	C₂×C₁₃	1	2	yes	—
81	#2075	C₂×C₁₃	1	2	yes	—
82	#2057	C₂×C₁₃	1	4	yes	complemented
83	#1818	C₂×C₁₃	1	1	yes	characteristic
84	C₂³×C₁₃	—	2	1	no	—
85	C₂³×C₁₃	—	2	2	no	—
86	C₂³×C₁₃	—	2	2	no	—
87	C₂³×C₁₃	—	2	2	no	—
88	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
89	Q₈×C₁₃	—	8	8	no	—
90	C₂×C₄×C₁₃	—	2	2	no	—
91	C₂×C₄×C₁₃	—	2	2	no	—
92	C₂×C₄×C₁₃	—	2	1	no	—
93	C₂×C₄×C₁₃	—	2	2	no	—
94	C₂×C₄×C₁₃	—	2	4	no	—
95	C₂×C₄×C₁₃	—	2	4	no	—
96	C₂×C₄×C₁₃	—	4	2	no	—
97	C₂×C₄×C₁₃	—	4	2	no	—
98	C₂×C₄×C₁₃	—	4	4	no	—
99	C₂×C₄×C₁₃	—	4	4	no	—
100	C₂×C₄×C₁₃	—	4	4	no	—
101	C₂×C₄×C₁₃	—	4	4	no	—
102	C₂×C₄×C₁₃	—	4	4	no	—
103	C₂×C₄×C₁₃	—	4	4	no	—
104	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
105	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
106	C₂×C₄×C₁₃	2₋¹⁺⁴	1	4	yes	—
107	C₈×C₁₃	—	4	2	no	—
108	C₈×C₁₃	—	4	2	no	—
109	C₂×C₄⋊Q₈	C₂²×C₁₃	1	2	yes	—
110	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
111	C₂×#107	C₂²×C₁₃	1	2	yes	—
112	C₂×#107	C₂²×C₁₃	1	2	yes	—
113	C₂×C₂²⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
114	C₂×C₂²⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
115	#400	—	2	2	no	—
116	#399	—	2	2	no	—
117	#395	—	2	2	no	—
118	#393	—	2	2	no	—
119	#389	C₂²×C₁₃	1	4	yes	—
120	#382	C₂²×C₁₃	1	2	yes	—
121	#380	C₂²×C₁₃	1	4	yes	—
122	#340	C₂²×C₁₃	1	4	yes	—
123	#340	C₂²×C₁₃	1	4	yes	—
124	#340	C₂²×C₁₃	1	2	yes	—
125	#340	C₂²×C₁₃	1	2	yes	—
126	#336	C₂²×C₁₃	1	4	yes	—
127	C₂²×C₁₃	—	4	1	no	—
128	C₂²×C₁₃	—	4	1	no	—
129	C₂²×C₁₃	—	4	1	no	—
130	C₂²×C₁₃	—	4	4	no	—
131	C₂²×C₁₃	#534	1	1	yes	characteristic
132	C₂²×C₁₃	#536	1	2	yes	—
133	C₂²×C₁₃	#576	1	2	yes	—
134	C₂²×C₁₃	#578	1	2	yes	—
135	C₄×C₁₃	—	4	1	no	—
136	C₄×C₁₃	—	4	2	no	—
137	C₄×C₁₃	—	4	2	no	—
138	C₄×C₁₃	—	8	4	no	—
139	C₄×C₁₃	—	8	4	no	—
140	C₄×C₁₃	#563	1	2	yes	—
141	C₄×C₁₃	#563	1	2	yes	—
142	C₂²×Q₈	—	2	2	no	—
143	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
144	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
145	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
146	C₄⋊Q₈	—	4	2	no	—
147	C₄⋊Q₈	—	4	2	no	—
148	#117	—	4	1	no	—
149	#117	—	4	1	no	—
150	C₂×C₄⋊C₄	—	2	2	no	—
151	C₂×C₄⋊C₄	—	2	4	no	—
152	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
153	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
154	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
155	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
156	C₂×C₂²⋊C₄	—	2	4	no	—
157	C₂×C₂²⋊C₄	D₄×C₁₃	1	2	yes	—
158	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
159	#107	—	4	2	no	—
160	#107	—	4	2	no	—
161	C₂²⋊C₈	—	4	1	no	—
162	C₂²⋊C₈	—	4	1	no	—
163	#95	—	2	4	no	—
164	#95	—	2	2	no	—
165	#95	—	2	2	no	—
166	#95	—	2	4	no	—
167	C₂×C₁₃	—	8	1	no	—
168	C₂×C₁₃	#2817	1	1	yes	characteristic
169	C₂×C₁₃	#3199	1	1	yes	characteristic
170	C₂×C₁₃	#3202	1	1	yes	characteristic
171	C₂×C₁₃	#3243	1	4	yes	—
172	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
173	C₂×Q₈	—	4	4	no	—
174	C₂×Q₈	—	8	4	no	—
175	C₂²×C₄	—	2	1	no	—
176	C₂²×C₄	—	2	1	no	—
177	C₂²×C₄	—	2	4	no	—
178	C₂²×C₄	—	2	4	no	—
179	C₂²×C₄	—	2	4	no	—
180	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
181	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
182	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
183	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
184	C₂×C₈	—	2	2	no	—
185	C₂×C₈	—	2	2	no	—
186	C₂×C₈	—	2	4	no	—
187	C₂×C₈	—	2	4	no	—
188	C₄⋊C₄	—	2	4	no	—
189	C₄⋊C₄	—	2	4	no	—
190	C₄⋊C₄	—	2	8	no	—
191	C₄⋊C₄	—	4	1	no	—
192	C₄⋊C₄	—	4	1	no	—
193	C₄⋊C₄	—	4	4	no	—
194	C₄⋊C₄	—	8	4	no	—
195	C₂²⋊C₄	—	4	2	no	—
196	C₂²⋊C₄	—	8	4	no	—
197	C₄²	—	2	2	no	—
198	C₄²	—	2	2	no	—
199	C₁₃	#32792	1	1	yes	characteristic, direct product factor, Sylow
200	C₂³	—	2	1	no	—
201	C₂³	—	2	2	no	—
202	C₂³	—	2	2	no	—
203	C₂³	—	2	2	no	—
204	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
205	Q₈	—	8	8	no	—
206	C₂×C₄	—	2	2	no	—
207	C₂×C₄	—	2	2	no	—
208	C₂×C₄	—	2	1	no	—
209	C₂×C₄	—	2	2	no	—
210	C₂×C₄	—	2	4	no	—
211	C₂×C₄	—	2	4	no	—
212	C₂×C₄	—	4	2	no	—
213	C₂×C₄	—	4	2	no	—
214	C₂×C₄	—	4	4	no	—
215	C₂×C₄	—	4	4	no	—
216	C₂×C₄	—	4	4	no	—
217	C₂×C₄	—	4	4	no	—
218	C₂×C₄	—	4	4	no	—
219	C₂×C₄	—	4	4	no	—
220	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
221	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
222	C₂×C₄	C₁₃×2₋¹⁺⁴	1	4	yes	—
223	C₈	—	4	2	no	—
224	C₈	—	4	2	no	—
225	C₂²	—	4	1	no	—
226	C₂²	—	4	1	no	—
227	C₂²	—	4	1	no	—
228	C₂²	—	4	4	no	—
229	C₂²	C₁₃×#534	1	1	yes	characteristic
230	C₂²	C₁₃×#536	1	2	yes	—
231	C₂²	C₁₃×#576	1	2	yes	—
232	C₂²	C₁₃×#578	1	2	yes	—
233	C₄	—	4	1	no	—
234	C₄	—	4	2	no	—
235	C₄	—	4	2	no	—
236	C₄	—	8	4	no	—
237	C₄	—	8	4	no	—
238	C₄	C₁₃×#563	1	2	yes	—
239	C₄	C₁₃×#563	1	2	yes	—
240	C₂	—	8	1	no	—
241	C₂	C₁₃×#2817	1	1	yes	characteristic
242	C₂	C₁₃×#3199	1	1	yes	characteristic
243	C₂	C₁₃×#3202	1	1	yes	characteristic
244	C₂	C₁₃×#3243	1	4	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
prime radical	C₂⁴×C₁₃	C₂×D₄
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ C₂×C₁₃×#117 ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₃×#2101	C₂	semidirect
5. C₁₃×#2057	C₂	semidirect
50. #32792	C₁₃	direct (N × H)
79. #2101	C₂×C₁₃	semidirect
82. #2057	C₂×C₁₃	semidirect
199. C₁₃	#32792	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×#2628	2
C₁₃×#2101	2
C₁₃×#2076	2
C₁₃×#2075	2
C₁₃×#2057	2
C₁₃×#1818	2
#32792	13

Subgroups — C13×#32792 #15719131

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#32792 #15719131