Subgroups — C₁₃×#32462 #15718801

Order 3328.

676 conjugacy classes of subgroups.

The subgroup lattice has 390 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#2485	C₂	1	2	yes	maximal
2	C₁₃×#2088	C₂	1	2	yes	maximal, complemented
3	C₁₃×#2076	C₂	1	2	yes	maximal, complemented
4	C₁₃×#2075	C₂	1	2	yes	maximal, complemented
5	C₁₃×#1954	C₂	1	1	yes	maximal, characteristic
6	C₁₃×#1942	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#1942	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#1854	C₂	1	2	yes	maximal, complemented
9	C₁₃×#1854	C₂	1	2	yes	maximal, complemented
10	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
11	C₂×C₁₃×#117	C₂²	1	2	yes	—
12	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
13	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
14	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
15	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
16	C₂×C₁₃×#106	C₂²	1	2	yes	—
17	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
18	C₂×C₁₃×C₂²⋊C₈	C₂²	1	2	yes	—
19	C₂×C₁₃×C₂²⋊C₈	C₂²	1	2	yes	—
20	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
21	C₁₃×#397	—	2	2	no	—
22	C₁₃×#394	—	2	2	no	—
23	C₁₃×#389	C₂²	1	2	yes	—
24	C₁₃×#389	C₂²	1	2	yes	—
25	C₁₃×#388	—	2	2	no	—
26	C₁₃×#387	—	2	2	no	—
27	C₁₃×#380	C₂²	1	2	yes	—
28	C₁₃×#380	C₂²	1	2	yes	—
29	C₁₃×#380	C₂²	1	2	yes	—
30	C₁₃×#340	C₂²	1	2	yes	—
31	C₁₃×#340	C₂²	1	2	yes	—
32	C₁₃×#340	C₂²	1	2	yes	—
33	C₁₃×#340	C₂²	1	2	yes	—
34	C₁₃×#340	C₂²	1	2	yes	—
35	C₂²×D₄×C₁₃	D₄	1	1	yes	characteristic
36	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
37	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
38	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
39	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
40	C₄×D₄×C₁₃	—	4	1	no	—
41	C₄×D₄×C₁₃	—	4	1	no	—
42	C₁₃×#117	—	4	2	no	—
43	C₁₃×#117	—	4	2	no	—
44	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
45	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
46	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
47	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
48	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
49	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
50	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
51	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
52	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
53	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
54	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
55	C₂×C₁₃×C₂²⋊C₄	D₄	1	2	yes	—
56	C₂×C₄²×C₁₃	—	2	2	no	—
57	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
58	C₁₃×#107	—	2	2	no	—
59	C₁₃×#107	—	2	2	no	—
60	C₁₃×#107	—	4	1	no	—
61	C₁₃×#107	—	4	1	no	—
62	C₁₃×#106	—	4	2	no	—
63	C₁₃×C₄⋊C₈	—	4	1	no	—
64	C₁₃×C₂²⋊C₈	—	2	4	no	—
65	C₁₃×C₂²⋊C₈	—	2	4	no	—
66	C₄×C₈×C₁₃	—	4	1	no	—
67	C₁₃×#95	—	2	2	no	—
68	C₁₃×#95	—	2	2	no	—
69	C₁₃×#95	—	2	2	no	—
70	C₁₃×#95	—	2	2	no	—
71	C₁₃×#95	—	2	2	no	—
72	#32462	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
73	C₂⁴×C₁₃	C₂×D₄	1	2	yes	—
74	C₂×D₄×C₁₃	—	2	2	no	—
75	C₂×D₄×C₁₃	—	4	1	no	—
76	C₂×D₄×C₁₃	—	4	1	no	—
77	C₂²×C₄×C₁₃	—	2	2	no	—
78	C₂²×C₄×C₁₃	—	2	2	no	—
79	C₂²×C₄×C₁₃	—	2	2	no	—
80	C₂²×C₄×C₁₃	—	2	2	no	—
81	C₂²×C₄×C₁₃	—	2	2	no	—
82	C₂²×C₄×C₁₃	—	2	2	no	—
83	C₂²×C₄×C₁₃	—	2	2	no	—
84	C₂²×C₄×C₁₃	—	2	2	no	—
85	C₂²×C₄×C₁₃	—	2	2	no	—
86	C₂²×C₄×C₁₃	—	2	2	no	—
87	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
88	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
89	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
90	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
91	C₂×C₈×C₁₃	—	2	1	no	—
92	C₂×C₈×C₁₃	—	2	1	no	—
93	C₂×C₈×C₁₃	—	2	1	no	—
94	C₂×C₈×C₁₃	—	2	1	no	—
95	C₂×C₈×C₁₃	—	2	2	no	—
96	C₂×C₈×C₁₃	—	2	2	no	—
97	C₂×C₈×C₁₃	—	2	2	no	—
98	C₂×C₈×C₁₃	#41	1	2	yes	—
99	C₂×C₈×C₁₃	#41	1	2	yes	—
100	C₁₃×C₄⋊C₄	—	2	2	no	—
101	C₁₃×C₄⋊C₄	—	2	2	no	—
102	C₁₃×C₄⋊C₄	—	2	2	no	—
103	C₁₃×C₄⋊C₄	—	2	2	no	—
104	C₁₃×C₄⋊C₄	—	2	2	no	—
105	C₁₃×C₄⋊C₄	—	2	2	no	—
106	C₁₃×C₄⋊C₄	—	2	2	no	—
107	C₁₃×C₄⋊C₄	—	2	2	no	—
108	C₁₃×C₄⋊C₄	—	4	1	no	—
109	C₁₃×C₄⋊C₄	—	4	4	no	—
110	C₁₃×C₄⋊C₄	—	8	2	no	—
111	C₁₃×C₂²⋊C₄	—	4	2	no	—
112	C₁₃×C₂²⋊C₄	—	4	4	no	—
113	C₁₃×C₂²⋊C₄	—	4	4	no	—
114	C₁₃×C₂²⋊C₄	—	8	2	no	—
115	C₁₃×C₂²⋊C₄	—	8	2	no	—
116	C₄²×C₁₃	—	2	1	no	—
117	C₄²×C₁₃	—	2	1	no	—
118	C₄²×C₁₃	—	4	4	no	—
119	#2485	C₂×C₁₃	1	2	yes	—
120	#2088	C₂×C₁₃	1	2	yes	complemented
121	#2076	C₂×C₁₃	1	2	yes	complemented
122	#2075	C₂×C₁₃	1	2	yes	complemented
123	#1954	C₂×C₁₃	1	1	yes	characteristic
124	#1942	C₂×C₁₃	1	1	yes	characteristic, complemented
125	#1942	C₂×C₁₃	1	1	yes	characteristic, complemented
126	#1854	C₂×C₁₃	1	2	yes	complemented
127	#1854	C₂×C₁₃	1	2	yes	complemented
128	C₂³×C₁₃	—	2	2	no	—
129	C₂³×C₁₃	—	2	2	no	—
130	C₂³×C₁₃	—	2	2	no	—
131	C₂³×C₁₃	—	2	2	no	—
132	C₂³×C₁₃	—	2	2	no	—
133	C₂³×C₁₃	—	2	2	no	—
134	C₂³×C₁₃	—	2	2	no	—
135	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
136	D₄×C₁₃	—	4	4	no	—
137	C₂×C₄×C₁₃	—	2	1	no	—
138	C₂×C₄×C₁₃	—	2	1	no	—
139	C₂×C₄×C₁₃	—	2	1	no	—
140	C₂×C₄×C₁₃	—	2	2	no	—
141	C₂×C₄×C₁₃	—	2	2	no	—
142	C₂×C₄×C₁₃	—	2	2	no	—
143	C₂×C₄×C₁₃	—	2	1	no	—
144	C₂×C₄×C₁₃	—	2	1	no	—
145	C₂×C₄×C₁₃	—	4	2	no	—
146	C₂×C₄×C₁₃	—	4	2	no	—
147	C₂×C₄×C₁₃	—	4	2	no	—
148	C₂×C₄×C₁₃	—	4	2	no	—
149	C₂×C₄×C₁₃	—	4	2	no	—
150	C₂×C₄×C₁₃	—	4	2	no	—
151	C₂×C₄×C₁₃	—	4	2	no	—
152	C₂×C₄×C₁₃	—	4	2	no	—
153	C₂×C₄×C₁₃	—	4	2	no	—
154	C₂×C₄×C₁₃	—	4	2	no	—
155	C₂×C₄×C₁₃	—	4	2	no	—
156	C₂×C₄×C₁₃	—	4	2	no	—
157	C₂×C₄×C₁₃	—	4	2	no	—
158	C₂×C₄×C₁₃	—	4	2	no	—
159	C₂×C₄×C₁₃	—	4	2	no	—
160	C₂×C₄×C₁₃	—	4	2	no	—
161	C₂×C₄×C₁₃	#135	1	2	yes	—
162	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
163	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
164	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
165	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
166	C₂×C₄×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
167	C₂×C₄×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
168	C₈×C₁₃	—	2	2	no	—
169	C₈×C₁₃	—	2	2	no	—
170	C₈×C₁₃	—	4	2	no	—
171	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
172	C₂×#117	C₂²×C₁₃	1	2	yes	—
173	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
174	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
175	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
176	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
177	C₂×#106	C₂²×C₁₃	1	2	yes	—
178	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
179	C₂×C₂²⋊C₈	C₂²×C₁₃	1	2	yes	—
180	C₂×C₂²⋊C₈	C₂²×C₁₃	1	2	yes	—
181	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
182	#397	—	2	2	no	—
183	#394	—	2	2	no	—
184	#389	C₂²×C₁₃	1	2	yes	—
185	#389	C₂²×C₁₃	1	2	yes	—
186	#388	—	2	2	no	—
187	#387	—	2	2	no	—
188	#380	C₂²×C₁₃	1	2	yes	—
189	#380	C₂²×C₁₃	1	2	yes	—
190	#380	C₂²×C₁₃	1	2	yes	—
191	#340	C₂²×C₁₃	1	2	yes	—
192	#340	C₂²×C₁₃	1	2	yes	—
193	#340	C₂²×C₁₃	1	2	yes	—
194	#340	C₂²×C₁₃	1	2	yes	—
195	#340	C₂²×C₁₃	1	2	yes	—
196	C₂²×C₁₃	—	4	2	no	—
197	C₂²×C₁₃	—	4	2	no	—
198	C₂²×C₁₃	—	4	2	no	—
199	C₂²×C₁₃	—	4	2	no	—
200	C₂²×C₁₃	—	4	2	no	—
201	C₂²×C₁₃	—	4	2	no	—
202	C₂²×C₁₃	—	4	2	no	—
203	C₂²×C₁₃	#534	1	1	yes	characteristic
204	C₂²×C₁₃	#547	1	1	yes	characteristic
205	C₂²×C₁₃	#547	1	1	yes	characteristic
206	C₂²×C₁₃	C₂×#135	1	1	yes	characteristic
207	C₂²×C₁₃	#575	1	1	yes	characteristic
208	C₂²×C₁₃	#576	1	1	yes	characteristic
209	C₂²×C₁₃	#578	1	1	yes	characteristic
210	C₄×C₁₃	—	2	2	no	—
211	C₄×C₁₃	—	4	1	no	—
212	C₄×C₁₃	—	4	2	no	—
213	C₄×C₁₃	—	8	2	no	—
214	C₄×C₁₃	—	8	2	no	—
215	C₄×C₁₃	—	8	2	no	—
216	C₄×C₁₃	—	8	2	no	—
217	C₄×C₁₃	#539	1	1	yes	characteristic
218	C₄×C₁₃	#539	1	1	yes	characteristic
219	C₄×C₁₃	#559	1	1	yes	characteristic
220	C₄×C₁₃	#563	1	1	yes	characteristic
221	C₂²×D₄	D₄×C₁₃	1	1	yes	characteristic
222	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
223	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
224	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
225	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
226	C₄×D₄	—	4	1	no	—
227	C₄×D₄	—	4	1	no	—
228	#117	—	4	2	no	—
229	#117	—	4	2	no	—
230	C₂×C₄⋊C₄	—	2	2	no	—
231	C₂×C₄⋊C₄	—	2	2	no	—
232	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
233	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
234	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
235	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
236	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
237	C₂×C₂²⋊C₄	—	2	2	no	—
238	C₂×C₂²⋊C₄	—	2	2	no	—
239	C₂×C₂²⋊C₄	—	2	2	no	—
240	C₂×C₂²⋊C₄	—	2	2	no	—
241	C₂×C₂²⋊C₄	D₄×C₁₃	1	2	yes	—
242	C₂×C₄²	—	2	2	no	—
243	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
244	#107	—	2	2	no	—
245	#107	—	2	2	no	—
246	#107	—	4	1	no	—
247	#107	—	4	1	no	—
248	#106	—	4	2	no	—
249	C₄⋊C₈	—	4	1	no	—
250	C₂²⋊C₈	—	2	4	no	—
251	C₂²⋊C₈	—	2	4	no	—
252	C₄×C₈	—	4	1	no	—
253	#95	—	2	2	no	—
254	#95	—	2	2	no	—
255	#95	—	2	2	no	—
256	#95	—	2	2	no	—
257	#95	—	2	2	no	—
258	C₂×C₁₃	—	8	2	no	—
259	C₂×C₁₃	#2724	1	1	yes	characteristic
260	C₂×C₁₃	#3191	1	1	yes	characteristic
261	C₂×C₁₃	#3203	1	1	yes	characteristic
262	C₂×C₁₃	#3341	1	1	yes	characteristic
263	C₂×C₁₃	#3342	1	1	yes	characteristic
264	C₂×C₁₃	#3352	1	1	yes	characteristic
265	C₂×C₁₃	#3355	1	1	yes	characteristic
266	C₂⁴	C₂×D₄×C₁₃	1	2	yes	—
267	C₂×D₄	—	2	2	no	—
268	C₂×D₄	—	4	1	no	—
269	C₂×D₄	—	4	1	no	—
270	C₂²×C₄	—	2	2	no	—
271	C₂²×C₄	—	2	2	no	—
272	C₂²×C₄	—	2	2	no	—
273	C₂²×C₄	—	2	2	no	—
274	C₂²×C₄	—	2	2	no	—
275	C₂²×C₄	—	2	2	no	—
276	C₂²×C₄	—	2	2	no	—
277	C₂²×C₄	—	2	2	no	—
278	C₂²×C₄	—	2	2	no	—
279	C₂²×C₄	—	2	2	no	—
280	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
281	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
282	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
283	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
284	C₂×C₈	—	2	1	no	—
285	C₂×C₈	—	2	1	no	—
286	C₂×C₈	—	2	1	no	—
287	C₂×C₈	—	2	1	no	—
288	C₂×C₈	—	2	2	no	—
289	C₂×C₈	—	2	2	no	—
290	C₂×C₈	—	2	2	no	—
291	C₂×C₈	C₁₃×#41	1	2	yes	—
292	C₂×C₈	C₁₃×#41	1	2	yes	—
293	C₄⋊C₄	—	2	2	no	—
294	C₄⋊C₄	—	2	2	no	—
295	C₄⋊C₄	—	2	2	no	—
296	C₄⋊C₄	—	2	2	no	—
297	C₄⋊C₄	—	2	2	no	—
298	C₄⋊C₄	—	2	2	no	—
299	C₄⋊C₄	—	2	2	no	—
300	C₄⋊C₄	—	2	2	no	—
301	C₄⋊C₄	—	4	1	no	—
302	C₄⋊C₄	—	4	4	no	—
303	C₄⋊C₄	—	8	2	no	—
304	C₂²⋊C₄	—	4	2	no	—
305	C₂²⋊C₄	—	4	4	no	—
306	C₂²⋊C₄	—	4	4	no	—
307	C₂²⋊C₄	—	8	2	no	—
308	C₂²⋊C₄	—	8	2	no	—
309	C₄²	—	2	1	no	—
310	C₄²	—	2	1	no	—
311	C₄²	—	4	4	no	—
312	C₁₃	#32462	1	1	yes	characteristic, direct product factor, Sylow
313	C₂³	—	2	2	no	—
314	C₂³	—	2	2	no	—
315	C₂³	—	2	2	no	—
316	C₂³	—	2	2	no	—
317	C₂³	—	2	2	no	—
318	C₂³	—	2	2	no	—
319	C₂³	—	2	2	no	—
320	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
321	D₄	—	4	4	no	—
322	C₂×C₄	—	2	1	no	—
323	C₂×C₄	—	2	1	no	—
324	C₂×C₄	—	2	1	no	—
325	C₂×C₄	—	2	2	no	—
326	C₂×C₄	—	2	2	no	—
327	C₂×C₄	—	2	2	no	—
328	C₂×C₄	—	2	1	no	—
329	C₂×C₄	—	2	1	no	—
330	C₂×C₄	—	4	2	no	—
331	C₂×C₄	—	4	2	no	—
332	C₂×C₄	—	4	2	no	—
333	C₂×C₄	—	4	2	no	—
334	C₂×C₄	—	4	2	no	—
335	C₂×C₄	—	4	2	no	—
336	C₂×C₄	—	4	2	no	—
337	C₂×C₄	—	4	2	no	—
338	C₂×C₄	—	4	2	no	—
339	C₂×C₄	—	4	2	no	—
340	C₂×C₄	—	4	2	no	—
341	C₂×C₄	—	4	2	no	—
342	C₂×C₄	—	4	2	no	—
343	C₂×C₄	—	4	2	no	—
344	C₂×C₄	—	4	2	no	—
345	C₂×C₄	—	4	2	no	—
346	C₂×C₄	C₁₃×#135	1	2	yes	—
347	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
348	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
349	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
350	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
351	C₂×C₄	C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
352	C₂×C₄	C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
353	C₈	—	2	2	no	—
354	C₈	—	2	2	no	—
355	C₈	—	4	2	no	—
356	C₂²	—	4	2	no	—
357	C₂²	—	4	2	no	—
358	C₂²	—	4	2	no	—
359	C₂²	—	4	2	no	—
360	C₂²	—	4	2	no	—
361	C₂²	—	4	2	no	—
362	C₂²	—	4	2	no	—
363	C₂²	C₁₃×#534	1	1	yes	characteristic
364	C₂²	C₁₃×#547	1	1	yes	characteristic
365	C₂²	C₁₃×#547	1	1	yes	characteristic
366	C₂²	C₂×C₁₃×#135	1	1	yes	characteristic
367	C₂²	C₁₃×#575	1	1	yes	characteristic
368	C₂²	C₁₃×#576	1	1	yes	characteristic
369	C₂²	C₁₃×#578	1	1	yes	characteristic
370	C₄	—	2	2	no	—
371	C₄	—	4	1	no	—
372	C₄	—	4	2	no	—
373	C₄	—	8	2	no	—
374	C₄	—	8	2	no	—
375	C₄	—	8	2	no	—
376	C₄	—	8	2	no	—
377	C₄	C₁₃×#539	1	1	yes	characteristic
378	C₄	C₁₃×#539	1	1	yes	characteristic
379	C₄	C₁₃×#559	1	1	yes	characteristic
380	C₄	C₁₃×#563	1	1	yes	characteristic
381	C₂	—	8	2	no	—
382	C₂	C₁₃×#2724	1	1	yes	characteristic
383	C₂	C₁₃×#3191	1	1	yes	characteristic
384	C₂	C₁₃×#3203	1	1	yes	characteristic
385	C₂	C₁₃×#3341	1	1	yes	characteristic
386	C₂	C₁₃×#3342	1	1	yes	characteristic
387	C₂	C₁₃×#3352	1	1	yes	characteristic
388	C₂	C₁₃×#3355	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
2. C₁₃×#2088	C₂	semidirect
3. C₁₃×#2076	C₂	semidirect
4. C₁₃×#2075	C₂	semidirect
6. C₁₃×#1942	C₂	semidirect
7. C₁₃×#1942	C₂	semidirect
8. C₁₃×#1854	C₂	semidirect
9. C₁₃×#1854	C₂	semidirect
72. #32462	C₁₃	direct (N × H)
120. #2088	C₂×C₁₃	semidirect
121. #2076	C₂×C₁₃	semidirect
122. #2075	C₂×C₁₃	semidirect
124. #1942	C₂×C₁₃	semidirect
125. #1942	C₂×C₁₃	semidirect
126. #1854	C₂×C₁₃	semidirect
127. #1854	C₂×C₁₃	semidirect
312. C₁₃	#32462	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×#2485	2
C₁₃×#2088	2
C₁₃×#2076	2
C₁₃×#2075	2
C₁₃×#1954	2
C₁₃×#1942	2
C₁₃×#1854	2
#32462	13

Subgroups — C13×#32462 #15718801

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#32462 #15718801