Subgroups — C₁₃×#3377 #13112435

Order 1664.

332 conjugacy classes of subgroups.

The subgroup lattice has 318 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#557	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃×#556	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#491	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#489	C₂	1	1	yes	maximal, characteristic
5	C₁₃×#488	C₂	1	1	yes	maximal, characteristic
6	C₁₃×#479	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#478	C₂	1	1	yes	maximal, characteristic
8	C₁₃×#477	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#464	C₂	1	1	yes	maximal, characteristic
10	C₁₃×#464	C₂	1	1	yes	maximal, characteristic
11	C₁₃×#462	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#446	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#441	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₃×#440	C₂	1	1	yes	maximal, characteristic
15	C₄×C₁₃×Q₁₆	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic
17	C₂×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic
18	C₂×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic
19	C₁₃×C₄⋊Q₈	—	2	1	no	—
20	C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
21	C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
22	C₁₃×#126	—	2	1	no	—
23	C₁₃×#126	—	2	1	no	—
24	C₁₃×#125	—	2	1	no	—
25	C₁₃×#125	—	2	1	no	—
26	C₁₃×#125	C₂²	1	1	yes	characteristic
27	C₁₃×#125	C₂²	1	1	yes	characteristic
28	C₁₃×#124	C₂²	1	1	yes	characteristic
29	C₁₃×#124	C₂²	1	1	yes	characteristic
30	C₁₃×C₂²⋊Q₈	—	2	1	no	—
31	C₄×Q₈×C₁₃	—	2	1	no	—
32	C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
33	C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
34	C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
35	C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
36	C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
37	C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
38	C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
39	C₁₃×#117	—	2	1	no	—
40	C₁₃×#107	C₂²	1	1	yes	characteristic
41	C₁₃×#107	C₂²	1	1	yes	characteristic
42	C₁₃×#106	C₂²	1	1	yes	characteristic
43	C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
44	C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
45	C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
46	C₁₃×#103	C₂²	1	1	yes	characteristic
47	C₁₃×#103	C₂²	1	1	yes	characteristic
48	C₁₃×#103	C₂²	1	1	yes	characteristic
49	C₁₃×#103	C₂²	1	1	yes	characteristic
50	C₁₃×#103	C₂²	1	1	yes	characteristic
51	C₁₃×#103	C₂²	1	1	yes	characteristic
52	C₁₃×#103	C₂²	1	1	yes	characteristic
53	C₁₃×#102	C₂²	1	1	yes	characteristic
54	C₁₃×#102	C₂²	1	1	yes	characteristic
55	C₁₃×#102	C₂²	1	1	yes	characteristic
56	C₁₃×#97	C₂²	1	1	yes	characteristic
57	C₁₃×#97	C₂²	1	1	yes	characteristic
58	C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
59	C₂×Q₈×C₁₃	—	2	1	no	—
60	C₂×Q₈×C₁₃	D₄	1	1	yes	characteristic
61	C₂×Q₈×C₁₃	C₂³	1	1	yes	characteristic
62	C₂×Q₈×C₁₃	C₂³	1	1	yes	characteristic
63	C₂×Q₈×C₁₃	C₂³	1	1	yes	characteristic
64	C₂×D₄×C₁₃	C₂³	1	1	yes	characteristic
65	C₂²×C₄×C₁₃	—	2	1	no	—
66	C₁₃×Q₁₆	—	2	2	no	—
67	C₁₃×Q₁₆	—	2	2	no	—
68	C₁₃×SD₁₆	—	2	2	no	—
69	C₂×C₈×C₁₃	C₂³	1	1	yes	characteristic
70	C₂×C₈×C₁₃	C₂³	1	1	yes	characteristic
71	C₂×C₈×C₁₃	C₂³	1	1	yes	characteristic
72	C₂×C₈×C₁₃	C₂³	1	1	yes	characteristic
73	C₁₃×C₄⋊C₄	—	2	1	no	—
74	C₁₃×C₄⋊C₄	—	2	1	no	—
75	C₁₃×C₄⋊C₄	—	2	1	no	—
76	C₁₃×C₄⋊C₄	—	2	1	no	—
77	C₁₃×C₄⋊C₄	—	2	1	no	—
78	C₁₃×C₄⋊C₄	—	2	1	no	—
79	C₁₃×C₄⋊C₄	—	2	1	no	—
80	C₁₃×C₄⋊C₄	—	2	1	no	—
81	C₁₃×C₄⋊C₄	—	2	1	no	—
82	C₁₃×C₄⋊C₄	—	2	1	no	—
83	C₁₃×C₄⋊C₄	—	2	1	no	—
84	C₁₃×C₄⋊C₄	—	2	1	no	—
85	C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
86	C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
87	C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
88	C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
89	C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
90	C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
91	C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
92	C₁₃×C₂²⋊C₄	—	2	1	no	—
93	C₁₃×C₂²⋊C₄	—	2	1	no	—
94	C₁₃×C₂²⋊C₄	—	2	1	no	—
95	C₁₃×C₂²⋊C₄	—	2	1	no	—
96	C₁₃×C₂²⋊C₄	—	2	1	no	—
97	C₄²×C₁₃	—	2	1	no	—
98	C₄²×C₁₃	—	2	1	no	—
99	C₄²×C₁₃	—	2	1	no	—
100	C₄²×C₁₃	—	2	1	no	—
101	C₄²×C₁₃	—	2	1	no	—
102	C₄²×C₁₃	C₂³	1	1	yes	characteristic
103	C₄²×C₁₃	C₂³	1	1	yes	characteristic
104	C₄²×C₁₃	C₂³	1	1	yes	characteristic
105	#3377	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
106	C₂³×C₁₃	—	2	1	no	—
107	Q₈×C₁₃	—	2	1	no	—
108	Q₈×C₁₃	—	2	1	no	—
109	Q₈×C₁₃	—	2	1	no	—
110	Q₈×C₁₃	—	2	1	no	—
111	Q₈×C₁₃	—	2	1	no	—
112	Q₈×C₁₃	—	4	1	no	—
113	Q₈×C₁₃	—	4	2	no	—
114	Q₈×C₁₃	#41	1	2	yes	—
115	D₄×C₁₃	—	2	1	no	—
116	D₄×C₁₃	—	2	1	no	—
117	C₂×C₄×C₁₃	—	2	1	no	—
118	C₂×C₄×C₁₃	—	2	1	no	—
119	C₂×C₄×C₁₃	—	2	1	no	—
120	C₂×C₄×C₁₃	—	2	1	no	—
121	C₂×C₄×C₁₃	—	2	1	no	—
122	C₂×C₄×C₁₃	—	2	1	no	—
123	C₂×C₄×C₁₃	—	2	1	no	—
124	C₂×C₄×C₁₃	—	4	2	no	—
125	C₂×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
126	C₂×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
127	C₂×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
128	C₂×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
129	C₂×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
130	C₂×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
131	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
132	C₈×C₁₃	—	2	1	no	—
133	C₈×C₁₃	—	2	1	no	—
134	C₈×C₁₃	—	2	1	no	—
135	C₈×C₁₃	—	2	1	no	—
136	#557	C₂×C₁₃	1	1	yes	characteristic, complemented
137	#556	C₂×C₁₃	1	1	yes	characteristic
138	#491	C₂×C₁₃	1	1	yes	characteristic, complemented
139	#489	C₂×C₁₃	1	1	yes	characteristic
140	#488	C₂×C₁₃	1	1	yes	characteristic
141	#479	C₂×C₁₃	1	1	yes	characteristic, complemented
142	#478	C₂×C₁₃	1	1	yes	characteristic
143	#477	C₂×C₁₃	1	1	yes	characteristic, complemented
144	#464	C₂×C₁₃	1	1	yes	characteristic
145	#464	C₂×C₁₃	1	1	yes	characteristic
146	#462	C₂×C₁₃	1	1	yes	characteristic, complemented
147	#446	C₂×C₁₃	1	1	yes	characteristic, complemented
148	#441	C₂×C₁₃	1	1	yes	characteristic, complemented
149	#440	C₂×C₁₃	1	1	yes	characteristic
150	C₄×Q₁₆	C₂×C₁₃	1	1	yes	characteristic, complemented
151	C₂²×C₁₃	—	4	1	no	—
152	C₂²×C₁₃	—	4	1	no	—
153	C₂²×C₁₃	—	4	1	no	—
154	C₂²×C₁₃	C₂²×D₄	1	1	yes	characteristic
155	C₄×C₁₃	—	2	2	no	—
156	C₄×C₁₃	—	2	1	no	—
157	C₄×C₁₃	—	2	1	no	—
158	C₄×C₁₃	—	2	1	no	—
159	C₄×C₁₃	—	2	1	no	—
160	C₄×C₁₃	—	2	1	no	—
161	C₄×C₁₃	—	2	1	no	—
162	C₄×C₁₃	—	4	1	no	—
163	C₄×C₁₃	—	4	1	no	—
164	C₄×C₁₃	—	4	1	no	—
165	C₄×C₁₃	—	4	1	no	—
166	C₄×C₁₃	—	4	1	no	—
167	C₄×C₁₃	—	4	1	no	—
168	C₄×C₁₃	C₂×#41	1	1	yes	characteristic
169	C₄×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
170	C₂×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic
171	C₂×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic
172	C₂×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic
173	C₄⋊Q₈	—	2	1	no	—
174	C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
175	C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
176	#126	—	2	1	no	—
177	#126	—	2	1	no	—
178	#125	—	2	1	no	—
179	#125	—	2	1	no	—
180	#125	C₂²×C₁₃	1	1	yes	characteristic
181	#125	C₂²×C₁₃	1	1	yes	characteristic
182	#124	C₂²×C₁₃	1	1	yes	characteristic
183	#124	C₂²×C₁₃	1	1	yes	characteristic
184	C₂²⋊Q₈	—	2	1	no	—
185	C₄×Q₈	—	2	1	no	—
186	C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
187	C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
188	C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
189	C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
190	C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
191	C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
192	C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
193	#117	—	2	1	no	—
194	#107	C₂²×C₁₃	1	1	yes	characteristic
195	#107	C₂²×C₁₃	1	1	yes	characteristic
196	#106	C₂²×C₁₃	1	1	yes	characteristic
197	C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
198	C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
199	C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
200	#103	C₂²×C₁₃	1	1	yes	characteristic
201	#103	C₂²×C₁₃	1	1	yes	characteristic
202	#103	C₂²×C₁₃	1	1	yes	characteristic
203	#103	C₂²×C₁₃	1	1	yes	characteristic
204	#103	C₂²×C₁₃	1	1	yes	characteristic
205	#103	C₂²×C₁₃	1	1	yes	characteristic
206	#103	C₂²×C₁₃	1	1	yes	characteristic
207	#102	C₂²×C₁₃	1	1	yes	characteristic
208	#102	C₂²×C₁₃	1	1	yes	characteristic
209	#102	C₂²×C₁₃	1	1	yes	characteristic
210	#97	C₂²×C₁₃	1	1	yes	characteristic
211	#97	C₂²×C₁₃	1	1	yes	characteristic
212	C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
213	C₂×C₁₃	—	8	1	no	—
214	C₂×C₁₃	#548	1	1	yes	characteristic
215	C₂×C₁₃	#575	1	1	yes	characteristic
216	C₂×C₁₃	#578	1	1	yes	characteristic
217	C₂×Q₈	—	2	1	no	—
218	C₂×Q₈	D₄×C₁₃	1	1	yes	characteristic
219	C₂×Q₈	C₂³×C₁₃	1	1	yes	characteristic
220	C₂×Q₈	C₂³×C₁₃	1	1	yes	characteristic
221	C₂×Q₈	C₂³×C₁₃	1	1	yes	characteristic
222	C₂×D₄	C₂³×C₁₃	1	1	yes	characteristic
223	C₂²×C₄	—	2	1	no	—
224	Q₁₆	—	2	2	no	—
225	Q₁₆	—	2	2	no	—
226	SD₁₆	—	2	2	no	—
227	C₂×C₈	C₂³×C₁₃	1	1	yes	characteristic
228	C₂×C₈	C₂³×C₁₃	1	1	yes	characteristic
229	C₂×C₈	C₂³×C₁₃	1	1	yes	characteristic
230	C₂×C₈	C₂³×C₁₃	1	1	yes	characteristic
231	C₄⋊C₄	—	2	1	no	—
232	C₄⋊C₄	—	2	1	no	—
233	C₄⋊C₄	—	2	1	no	—
234	C₄⋊C₄	—	2	1	no	—
235	C₄⋊C₄	—	2	1	no	—
236	C₄⋊C₄	—	2	1	no	—
237	C₄⋊C₄	—	2	1	no	—
238	C₄⋊C₄	—	2	1	no	—
239	C₄⋊C₄	—	2	1	no	—
240	C₄⋊C₄	—	2	1	no	—
241	C₄⋊C₄	—	2	1	no	—
242	C₄⋊C₄	—	2	1	no	—
243	C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
244	C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
245	C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
246	C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
247	C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
248	C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
249	C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
250	C₂²⋊C₄	—	2	1	no	—
251	C₂²⋊C₄	—	2	1	no	—
252	C₂²⋊C₄	—	2	1	no	—
253	C₂²⋊C₄	—	2	1	no	—
254	C₂²⋊C₄	—	2	1	no	—
255	C₄²	—	2	1	no	—
256	C₄²	—	2	1	no	—
257	C₄²	—	2	1	no	—
258	C₄²	—	2	1	no	—
259	C₄²	—	2	1	no	—
260	C₄²	C₂³×C₁₃	1	1	yes	characteristic
261	C₄²	C₂³×C₁₃	1	1	yes	characteristic
262	C₄²	C₂³×C₁₃	1	1	yes	characteristic
263	C₁₃	#3377	1	1	yes	characteristic, direct product factor, Sylow
264	C₂³	—	2	1	no	—
265	Q₈	—	2	1	no	—
266	Q₈	—	2	1	no	—
267	Q₈	—	2	1	no	—
268	Q₈	—	2	1	no	—
269	Q₈	—	2	1	no	—
270	Q₈	—	4	1	no	—
271	Q₈	—	4	2	no	—
272	Q₈	C₁₃×#41	1	2	yes	—
273	D₄	—	2	1	no	—
274	D₄	—	2	1	no	—
275	C₂×C₄	—	2	1	no	—
276	C₂×C₄	—	2	1	no	—
277	C₂×C₄	—	2	1	no	—
278	C₂×C₄	—	2	1	no	—
279	C₂×C₄	—	2	1	no	—
280	C₂×C₄	—	2	1	no	—
281	C₂×C₄	—	2	1	no	—
282	C₂×C₄	—	4	2	no	—
283	C₂×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
284	C₂×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
285	C₂×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
286	C₂×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
287	C₂×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
288	C₂×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
289	C₂×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
290	C₈	—	2	1	no	—
291	C₈	—	2	1	no	—
292	C₈	—	2	1	no	—
293	C₈	—	2	1	no	—
294	C₂²	—	4	1	no	—
295	C₂²	—	4	1	no	—
296	C₂²	—	4	1	no	—
297	C₂²	C₂²×D₄×C₁₃	1	1	yes	characteristic
298	C₄	—	2	2	no	—
299	C₄	—	2	1	no	—
300	C₄	—	2	1	no	—
301	C₄	—	2	1	no	—
302	C₄	—	2	1	no	—
303	C₄	—	2	1	no	—
304	C₄	—	2	1	no	—
305	C₄	—	4	1	no	—
306	C₄	—	4	1	no	—
307	C₄	—	4	1	no	—
308	C₄	—	4	1	no	—
309	C₄	—	4	1	no	—
310	C₄	—	4	1	no	—
311	C₄	C₂×C₁₃×#41	1	1	yes	characteristic
312	C₄	C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
313	C₂	—	8	1	no	—
314	C₂	C₁₃×#548	1	1	yes	characteristic
315	C₂	C₁₃×#575	1	1	yes	characteristic
316	C₂	C₁₃×#578	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁴×C₁₃
prime radical	C₂×D₄×C₁₃	C₂³
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₄×Q₈×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₃×#557	C₂	semidirect
3. C₁₃×#491	C₂	semidirect
6. C₁₃×#479	C₂	semidirect
8. C₁₃×#477	C₂	semidirect
11. C₁₃×#462	C₂	semidirect
12. C₁₃×#446	C₂	semidirect
13. C₁₃×#441	C₂	semidirect
15. C₄×C₁₃×Q₁₆	C₂	semidirect
105. #3377	C₁₃	direct (N × H)
136. #557	C₂×C₁₃	semidirect
138. #491	C₂×C₁₃	semidirect
141. #479	C₂×C₁₃	semidirect
143. #477	C₂×C₁₃	semidirect
146. #462	C₂×C₁₃	semidirect
147. #446	C₂×C₁₃	semidirect
148. #441	C₂×C₁₃	semidirect
150. C₄×Q₁₆	C₂×C₁₃	semidirect
263. C₁₃	#3377	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×#557	2
C₁₃×#556	2
C₁₃×#491	2
C₁₃×#489	2
C₁₃×#488	2
C₁₃×#479	2
C₁₃×#478	2
C₁₃×#477	2
C₁₃×#464	2
C₁₃×#462	2
C₁₃×#446	2
C₁₃×#441	2
C₁₃×#440	2
C₄×C₁₃×Q₁₆	2
#3377	13

Subgroups — C13×#3377 #13112435

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#3377 #13112435