Subgroups — C₁₃×#32932 #15719271

Order 3328.

1436 conjugacy classes of subgroups.

The subgroup lattice has 298 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₁₃×#131	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₃×#465	C₂	1	3	yes	maximal, complemented
3	C₁₃×#2616	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#2615	C₂	1	1	yes	maximal, characteristic
5	C₁₃×#1895	C₂	1	3	yes	maximal, complemented
6	C₁₃×#1894	C₂	1	3	yes	maximal, complemented
7	C₁₃×#1807	C₂	1	3	yes	maximal, complemented
8	C₂²×C₁₃×#41	C₂²	1	1	yes	characteristic
9	C₂²×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic
10	C₂×C₁₃×#131	—	2	12	no	—
11	C₂²×C₁₃×M₁₆	C₂²	1	3	yes	—
12	C₂³×C₈×C₁₃	C₂²	1	3	yes	—
13	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	3	yes	—
14	C₂×C₁₃×#121	C₂²	1	3	yes	—
15	C₁₃×#465	—	2	12	no	—
16	C₂×C₁₃×#106	C₂²	1	3	yes	—
17	C₂×C₁₃×#103	C₂²	1	3	yes	—
18	C₂×C₁₃×#102	C₂²	1	3	yes	—
19	C₁₃×#395	—	2	1	no	—
20	C₁₃×#394	—	2	3	no	—
21	C₁₃×#393	—	2	1	no	—
22	C₁₃×#392	—	2	3	no	—
23	C₁₃×#380	C₂²	1	3	yes	—
24	C₁₃×#380	C₂²	1	3	yes	—
25	C₁₃×#340	C₂²	1	6	yes	—
26	C₂×C₁₃×#41	—	2	6	no	—
27	C₂×C₁₃×#41	—	2	6	no	—
28	C₂²×Q₈×C₁₃	D₄	1	1	yes	characteristic
29	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
30	C₂²×D₄×C₁₃	—	2	3	no	—
31	C₂²×D₄×C₁₃	D₄	1	3	yes	—
32	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
33	C₂³×C₄×C₁₃	C₂³	1	3	yes	—
34	C₂×C₁₃×SD₁₆	—	2	6	no	—
35	C₁₃×#131	—	2	32	no	—
36	C₂×C₁₃×M₁₆	—	2	6	no	—
37	C₂×C₁₃×M₁₆	—	2	12	no	—
38	C₂²×C₈×C₁₃	—	2	12	no	—
39	C₂²×C₈×C₁₃	D₄	1	12	yes	complemented
40	C₂²×C₈×C₁₃	C₂³	1	3	yes	—
41	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
42	C₁₃×C₂²⋊Q₈	—	2	6	no	—
43	C₁₃×C₂²⋊Q₈	—	2	6	no	—
44	C₁₃×#121	—	2	6	no	—
45	C₁₃×#121	—	2	6	no	—
46	C₂×C₁₃×C₄⋊C₄	—	2	3	no	—
47	C₂×C₁₃×C₄⋊C₄	C₂³	1	3	yes	—
48	C₂×C₁₃×C₄⋊C₄	C₂³	1	3	yes	—
49	C₂×C₁₃×C₂²⋊C₄	—	2	3	no	—
50	C₂×C₁₃×C₂²⋊C₄	—	2	3	no	—
51	C₂×C₁₃×C₂²⋊C₄	—	2	3	no	—
52	C₂×C₁₃×C₂²⋊C₄	—	2	3	no	—
53	C₁₃×#106	—	2	6	no	—
54	C₁₃×#103	—	2	6	no	—
55	C₁₃×#102	—	2	6	no	—
56	C₁₃×#95	—	2	3	no	—
57	C₁₃×#95	—	2	3	no	—
58	#32932	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
59	C₂⁴×C₁₃	—	2	1	no	—
60	C₂⁴×C₁₃	C₂×D₄	1	3	yes	—
61	C₁₃×#41	—	2	8	no	—
62	C₁₃×#41	—	2	24	no	—
63	C₂×Q₈×C₁₃	—	2	6	no	—
64	C₂×Q₈×C₁₃	—	2	3	no	—
65	C₂×Q₈×C₁₃	—	2	3	no	—
66	C₂×D₄×C₁₃	—	2	12	no	—
67	C₂×D₄×C₁₃	—	2	6	no	—
68	C₂×D₄×C₁₃	—	2	3	no	—
69	C₂×D₄×C₁₃	—	2	3	no	—
70	C₂×D₄×C₁₃	—	4	6	no	—
71	C₂×D₄×C₁₃	—	8	6	no	—
72	C₂²×C₄×C₁₃	—	2	6	no	—
73	C₂²×C₄×C₁₃	—	2	6	no	—
74	C₂²×C₄×C₁₃	—	2	3	no	—
75	C₂²×C₄×C₁₃	—	2	3	no	—
76	C₂²×C₄×C₁₃	—	2	1	no	—
77	C₂²×C₄×C₁₃	C₂×D₄	1	3	yes	—
78	C₂²×C₄×C₁₃	C₂×D₄	1	6	yes	—
79	C₂²×C₄×C₁₃	#41	1	6	yes	—
80	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
81	C₁₃×SD₁₆	—	4	4	no	—
82	C₁₃×M₁₆	—	2	24	no	—
83	C₂×C₈×C₁₃	—	2	6	no	—
84	C₂×C₈×C₁₃	—	2	24	no	—
85	C₂×C₈×C₁₃	C₂×D₄	1	6	yes	—
86	C₂×C₈×C₁₃	C₂×D₄	1	6	yes	—
87	C₁₃×C₄⋊C₄	—	2	3	no	—
88	C₁₃×C₄⋊C₄	—	2	3	no	—
89	C₁₃×C₄⋊C₄	—	2	3	no	—
90	C₁₃×C₄⋊C₄	—	2	3	no	—
91	C₁₃×C₄⋊C₄	—	4	6	no	—
92	C₁₃×C₂²⋊C₄	—	4	6	no	—
93	C₁₃×C₂²⋊C₄	—	4	6	no	—
94	C₁₃×C₂²⋊C₄	—	8	3	no	—
95	C₁₃×C₂²⋊C₄	—	8	3	no	—
96	C₂²×#131	C₂×C₁₃	1	1	yes	characteristic, complemented
97	C₂×#465	C₂×C₁₃	1	3	yes	complemented
98	#2616	C₂×C₁₃	1	1	yes	characteristic, complemented
99	#2615	C₂×C₁₃	1	1	yes	characteristic
100	#1895	C₂×C₁₃	1	3	yes	complemented
101	#1894	C₂×C₁₃	1	3	yes	complemented
102	#1807	C₂×C₁₃	1	3	yes	complemented
103	C₂³×C₁₃	—	2	6	no	—
104	C₂³×C₁₃	—	2	3	no	—
105	C₂³×C₁₃	—	2	3	no	—
106	C₂³×C₁₃	—	2	6	no	—
107	C₂³×C₁₃	—	4	3	no	—
108	C₂³×C₁₃	—	4	3	no	—
109	C₂³×C₁₃	—	4	1	no	—
110	C₂³×C₁₃	#121	1	6	yes	—
111	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
112	Q₈×C₁₃	—	2	8	no	—
113	Q₈×C₁₃	—	4	1	no	—
114	Q₈×C₁₃	—	4	3	no	—
115	D₄×C₁₃	—	2	24	no	—
116	D₄×C₁₃	—	4	1	no	—
117	D₄×C₁₃	—	4	3	no	—
118	D₄×C₁₃	—	8	12	no	—
119	C₂×C₄×C₁₃	—	2	6	no	—
120	C₂×C₄×C₁₃	—	2	6	no	—
121	C₂×C₄×C₁₃	—	2	6	no	—
122	C₂×C₄×C₁₃	—	2	12	no	—
123	C₂×C₄×C₁₃	—	4	3	no	—
124	C₂×C₄×C₁₃	—	4	3	no	—
125	C₂×C₄×C₁₃	—	4	3	no	—
126	C₂×C₄×C₁₃	—	4	3	no	—
127	C₂×C₄×C₁₃	—	4	6	no	—
128	C₂×C₄×C₁₃	—	4	3	no	—
129	C₂×C₄×C₁₃	#121	1	6	yes	—
130	C₂×C₄×C₁₃	C₂²×D₄	1	3	yes	—
131	C₂×C₄×C₁₃	C₂×#41	1	3	yes	—
132	C₈×C₁₃	—	2	6	no	—
133	C₈×C₁₃	#120	1	4	yes	—
134	C₂²×#41	C₂²×C₁₃	1	1	yes	characteristic
135	C₂²×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic
136	C₂×#131	—	2	12	no	—
137	C₂²×M₁₆	C₂²×C₁₃	1	3	yes	—
138	C₂³×C₈	C₂²×C₁₃	1	3	yes	—
139	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	3	yes	—
140	C₂×#121	C₂²×C₁₃	1	3	yes	—
141	#465	—	2	12	no	—
142	C₂×#106	C₂²×C₁₃	1	3	yes	—
143	C₂×#103	C₂²×C₁₃	1	3	yes	—
144	C₂×#102	C₂²×C₁₃	1	3	yes	—
145	#395	—	2	1	no	—
146	#394	—	2	3	no	—
147	#393	—	2	1	no	—
148	#392	—	2	3	no	—
149	#380	C₂²×C₁₃	1	3	yes	—
150	#380	C₂²×C₁₃	1	3	yes	—
151	#340	C₂²×C₁₃	1	6	yes	—
152	C₂²×C₁₃	—	2	6	no	—
153	C₂²×C₁₃	—	2	6	no	—
154	C₂²×C₁₃	—	2	6	no	—
155	C₂²×C₁₃	—	4	6	no	—
156	C₂²×C₁₃	—	4	6	no	—
157	C₂²×C₁₃	—	8	1	no	—
158	C₂²×C₁₃	—	8	3	no	—
159	C₂²×C₁₃	—	8	3	no	—
160	C₂²×C₁₃	C₂×#121	1	3	yes	—
161	C₂²×C₁₃	#577	1	3	yes	—
162	C₂²×C₁₃	#577	1	1	yes	characteristic
163	C₄×C₁₃	—	2	6	no	—
164	C₄×C₁₃	—	8	1	no	—
165	C₄×C₁₃	—	8	3	no	—
166	C₄×C₁₃	—	8	3	no	—
167	C₄×C₁₃	C₂×#120	1	1	yes	characteristic
168	C₄×C₁₃	#525	1	3	yes	—
169	C₂×#41	—	2	6	no	—
170	C₂×#41	—	2	6	no	—
171	C₂²×Q₈	D₄×C₁₃	1	1	yes	characteristic
172	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
173	C₂²×D₄	—	2	3	no	—
174	C₂²×D₄	D₄×C₁₃	1	3	yes	—
175	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
176	C₂³×C₄	C₂³×C₁₃	1	3	yes	—
177	C₂×SD₁₆	—	2	6	no	—
178	#131	—	2	32	no	—
179	C₂×M₁₆	—	2	6	no	—
180	C₂×M₁₆	—	2	12	no	—
181	C₂²×C₈	—	2	12	no	—
182	C₂²×C₈	D₄×C₁₃	1	12	yes	complemented
183	C₂²×C₈	C₂³×C₁₃	1	3	yes	—
184	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
185	C₂²⋊Q₈	—	2	6	no	—
186	C₂²⋊Q₈	—	2	6	no	—
187	#121	—	2	6	no	—
188	#121	—	2	6	no	—
189	C₂×C₄⋊C₄	—	2	3	no	—
190	C₂×C₄⋊C₄	C₂³×C₁₃	1	3	yes	—
191	C₂×C₄⋊C₄	C₂³×C₁₃	1	3	yes	—
192	C₂×C₂²⋊C₄	—	2	3	no	—
193	C₂×C₂²⋊C₄	—	2	3	no	—
194	C₂×C₂²⋊C₄	—	2	3	no	—
195	C₂×C₂²⋊C₄	—	2	3	no	—
196	#106	—	2	6	no	—
197	#103	—	2	6	no	—
198	#102	—	2	6	no	—
199	#95	—	2	3	no	—
200	#95	—	2	3	no	—
201	C₂×C₁₃	—	4	6	no	—
202	C₂×C₁₃	—	16	1	no	—
203	C₂×C₁₃	#2847	1	1	yes	characteristic
204	C₂×C₁₃	#3057	1	3	yes	—
205	C₂×C₁₃	#3060	1	3	yes	—
206	C₂⁴	—	2	1	no	—
207	C₂⁴	C₂×D₄×C₁₃	1	3	yes	—
208	#41	—	2	8	no	—
209	#41	—	2	24	no	—
210	C₂×Q₈	—	2	6	no	—
211	C₂×Q₈	—	2	3	no	—
212	C₂×Q₈	—	2	3	no	—
213	C₂×D₄	—	2	12	no	—
214	C₂×D₄	—	2	6	no	—
215	C₂×D₄	—	2	3	no	—
216	C₂×D₄	—	2	3	no	—
217	C₂×D₄	—	4	6	no	—
218	C₂×D₄	—	8	6	no	—
219	C₂²×C₄	—	2	6	no	—
220	C₂²×C₄	—	2	6	no	—
221	C₂²×C₄	—	2	3	no	—
222	C₂²×C₄	—	2	3	no	—
223	C₂²×C₄	—	2	1	no	—
224	C₂²×C₄	C₂×D₄×C₁₃	1	3	yes	—
225	C₂²×C₄	C₂×D₄×C₁₃	1	6	yes	—
226	C₂²×C₄	C₁₃×#41	1	6	yes	—
227	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
228	SD₁₆	—	4	4	no	—
229	M₁₆	—	2	24	no	—
230	C₂×C₈	—	2	6	no	—
231	C₂×C₈	—	2	24	no	—
232	C₂×C₈	C₂×D₄×C₁₃	1	6	yes	—
233	C₂×C₈	C₂×D₄×C₁₃	1	6	yes	—
234	C₄⋊C₄	—	2	3	no	—
235	C₄⋊C₄	—	2	3	no	—
236	C₄⋊C₄	—	2	3	no	—
237	C₄⋊C₄	—	2	3	no	—
238	C₄⋊C₄	—	4	6	no	—
239	C₂²⋊C₄	—	4	6	no	—
240	C₂²⋊C₄	—	4	6	no	—
241	C₂²⋊C₄	—	8	3	no	—
242	C₂²⋊C₄	—	8	3	no	—
243	C₁₃	#32932	1	1	yes	characteristic, direct product factor, Sylow
244	C₂³	—	2	6	no	—
245	C₂³	—	2	3	no	—
246	C₂³	—	2	3	no	—
247	C₂³	—	2	6	no	—
248	C₂³	—	4	3	no	—
249	C₂³	—	4	3	no	—
250	C₂³	—	4	1	no	—
251	C₂³	C₁₃×#121	1	6	yes	—
252	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
253	Q₈	—	2	8	no	—
254	Q₈	—	4	1	no	—
255	Q₈	—	4	3	no	—
256	D₄	—	2	24	no	—
257	D₄	—	4	1	no	—
258	D₄	—	4	3	no	—
259	D₄	—	8	12	no	—
260	C₂×C₄	—	2	6	no	—
261	C₂×C₄	—	2	6	no	—
262	C₂×C₄	—	2	6	no	—
263	C₂×C₄	—	2	12	no	—
264	C₂×C₄	—	4	3	no	—
265	C₂×C₄	—	4	3	no	—
266	C₂×C₄	—	4	3	no	—
267	C₂×C₄	—	4	3	no	—
268	C₂×C₄	—	4	6	no	—
269	C₂×C₄	—	4	3	no	—
270	C₂×C₄	C₁₃×#121	1	6	yes	—
271	C₂×C₄	C₂²×D₄×C₁₃	1	3	yes	—
272	C₂×C₄	C₂×C₁₃×#41	1	3	yes	—
273	C₈	—	2	6	no	—
274	C₈	C₁₃×#120	1	4	yes	—
275	C₂²	—	2	6	no	—
276	C₂²	—	2	6	no	—
277	C₂²	—	2	6	no	—
278	C₂²	—	4	6	no	—
279	C₂²	—	4	6	no	—
280	C₂²	—	8	3	no	—
281	C₂²	—	8	3	no	—
282	C₂²	—	8	1	no	—
283	C₂²	C₂×C₁₃×#121	1	3	yes	—
284	C₂²	C₁₃×#577	1	3	yes	—
285	C₂²	C₁₃×#577	1	1	yes	characteristic
286	C₄	—	2	6	no	—
287	C₄	—	8	3	no	—
288	C₄	—	8	3	no	—
289	C₄	—	8	1	no	—
290	C₄	C₂×C₁₃×#120	1	1	yes	characteristic
291	C₄	C₁₃×#525	1	3	yes	—
292	C₂	—	4	6	no	—
293	C₂	—	16	1	no	—
294	C₂	C₁₃×#2847	1	1	yes	characteristic
295	C₂	C₁₃×#3057	1	3	yes	—
296	C₂	C₁₃×#3060	1	3	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
prime radical	C₁₃×#2615	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ C₂²×C₁₃×#41 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂²×C₁₃×#131	C₂	semidirect
2. C₂×C₁₃×#465	C₂	semidirect
3. C₁₃×#2616	C₂	semidirect
5. C₁₃×#1895	C₂	semidirect
6. C₁₃×#1894	C₂	semidirect
7. C₁₃×#1807	C₂	semidirect
39. C₂²×C₈×C₁₃	D₄	semidirect
58. #32932	C₁₃	direct (N × H)
96. C₂²×#131	C₂×C₁₃	semidirect
97. C₂×#465	C₂×C₁₃	semidirect
98. #2616	C₂×C₁₃	semidirect
100. #1895	C₂×C₁₃	semidirect
101. #1894	C₂×C₁₃	semidirect
102. #1807	C₂×C₁₃	semidirect
182. C₂²×C₈	D₄×C₁₃	semidirect
243. C₁₃	#32932	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₁₃×#131	2
C₂×C₁₃×#465	2
C₁₃×#2616	2
C₁₃×#2615	2
C₁₃×#1895	2
C₁₃×#1894	2
C₁₃×#1807	2
#32932	13

Subgroups — C13×#32932 #15719271

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#32932 #15719271