Subgroups — C₁₃×#32524 #15718863

Order 3328.

720 conjugacy classes of subgroups.

The subgroup lattice has 392 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#2512	C₂	1	2	yes	maximal, complemented
2	C₁₃×#2093	C₂	1	2	yes	maximal, complemented
3	C₁₃×#2067	C₂	1	2	yes	maximal, complemented
4	C₁₃×#2054	C₂	1	2	yes	maximal
5	C₁₃×#1970	C₂	1	1	yes	maximal, characteristic
6	C₁₃×#1947	C₂	1	2	yes	maximal, complemented
7	C₁₃×#1942	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#1939	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#1925	C₂	1	2	yes	maximal, complemented
10	C₂²×C₁₃×D₈	C₂²	1	1	yes	characteristic
11	C₂×C₁₃×#126	—	2	2	no	—
12	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
13	C₂×C₁₃×#107	C₂²	1	2	yes	—
14	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
15	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
16	C₂×C₁₃×C₄⋊C₈	C₂²	1	2	yes	—
17	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
18	C₂×C₁₃×#102	C₂²	1	2	yes	—
19	C₂×C₁₃×#102	C₂²	1	2	yes	—
20	C₂×C₁₃×#102	C₂²	1	2	yes	—
21	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
22	C₁₃×#397	—	2	2	no	—
23	C₁₃×#396	—	2	2	no	—
24	C₁₃×#390	C₂²	1	2	yes	—
25	C₁₃×#390	C₂²	1	2	yes	—
26	C₁₃×#390	C₂²	1	2	yes	—
27	C₁₃×#389	C₂²	1	2	yes	—
28	C₁₃×#388	—	2	2	no	—
29	C₁₃×#384	C₂²	1	2	yes	—
30	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
31	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
32	C₁₃×#340	C₂²	1	2	yes	—
33	C₁₃×#340	C₂²	1	2	yes	—
34	C₁₃×#336	C₂²	1	2	yes	—
35	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
36	C₂×C₁₃×D₈	—	2	2	no	—
37	C₂×C₁₃×D₈	—	4	1	no	—
38	C₂×C₁₃×D₈	—	4	1	no	—
39	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
40	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
41	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
42	C₁₃×#126	—	4	8	no	—
43	C₂×C₁₃×C₄⋊C₄	—	2	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	D₄	1	1	yes	characteristic
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	—	2	2	no	—
56	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
57	C₂×C₄²×C₁₃	—	2	2	no	—
58	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
59	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
60	C₁₃×#107	—	2	2	no	—
61	C₁₃×#107	—	4	1	no	—
62	C₁₃×#107	—	4	2	no	—
63	C₁₃×#107	—	4	1	no	—
64	C₁₃×C₄⋊C₈	—	2	4	no	—
65	C₁₃×C₄⋊C₈	—	4	1	no	—
66	C₁₃×#102	—	2	4	no	—
67	C₁₃×#102	—	4	2	no	—
68	C₁₃×#102	—	4	2	no	—
69	C₄×C₈×C₁₃	—	4	1	no	—
70	C₁₃×#95	—	2	2	no	—
71	C₁₃×#95	—	2	2	no	—
72	C₁₃×#95	D₄	1	2	yes	—
73	#32524	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
74	C₂⁴×C₁₃	—	2	2	no	—
75	C₂×D₄×C₁₃	—	2	2	no	—
76	C₂×D₄×C₁₃	—	2	2	no	—
77	C₂×D₄×C₁₃	—	2	2	no	—
78	C₂×D₄×C₁₃	—	2	2	no	—
79	C₂×D₄×C₁₃	—	2	2	no	—
80	C₂×D₄×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	C₂×D₄	1	1	yes	characteristic
85	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
86	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
87	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
88	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
89	C₁₃×D₈	—	4	4	no	—
90	C₂×C₈×C₁₃	—	2	1	no	—
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	2	no	—
95	C₂×C₈×C₁₃	—	2	2	no	—
96	C₂×C₈×C₁₃	—	2	2	no	—
97	C₂×C₈×C₁₃	#41	1	2	yes	—
98	C₂×C₈×C₁₃	#41	1	2	yes	—
99	C₁₃×C₄⋊C₄	—	2	2	no	—
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	—	4	1	no	—
106	C₁₃×C₄⋊C₄	—	4	4	no	—
107	C₁₃×C₄⋊C₄	—	4	4	no	—
108	C₁₃×C₄⋊C₄	—	8	2	no	—
109	C₁₃×C₄⋊C₄	D₈	1	4	yes	complemented
110	C₁₃×C₂²⋊C₄	—	4	4	no	—
111	C₁₃×C₂²⋊C₄	—	4	4	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	2	no	—
117	C₄²×C₁₃	—	2	1	no	—
118	C₄²×C₁₃	—	2	1	no	—
119	C₄²×C₁₃	—	2	2	no	—
120	C₄²×C₁₃	—	4	4	no	—
121	#2512	C₂×C₁₃	1	2	yes	complemented
122	#2093	C₂×C₁₃	1	2	yes	complemented
123	#2067	C₂×C₁₃	1	2	yes	complemented
124	#2054	C₂×C₁₃	1	2	yes	—
125	#1970	C₂×C₁₃	1	1	yes	characteristic
126	#1947	C₂×C₁₃	1	2	yes	complemented
127	#1942	C₂×C₁₃	1	1	yes	characteristic, complemented
128	#1939	C₂×C₁₃	1	1	yes	characteristic, complemented
129	#1925	C₂×C₁₃	1	2	yes	complemented
130	C₂³×C₁₃	—	4	2	no	—
131	C₂³×C₁₃	—	4	2	no	—
132	C₂³×C₁₃	—	4	2	no	—
133	C₂³×C₁₃	—	4	2	no	—
134	C₂³×C₁₃	—	4	2	no	—
135	C₂³×C₁₃	—	4	2	no	—
136	C₂³×C₁₃	—	4	2	no	—
137	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
138	D₄×C₁₃	—	4	2	no	—
139	D₄×C₁₃	—	4	2	no	—
140	D₄×C₁₃	—	4	2	no	—
141	D₄×C₁₃	—	4	2	no	—
142	C₂×C₄×C₁₃	—	2	1	no	—
143	C₂×C₄×C₁₃	—	2	2	no	—
144	C₂×C₄×C₁₃	—	2	1	no	—
145	C₂×C₄×C₁₃	—	2	2	no	—
146	C₂×C₄×C₁₃	—	2	1	no	—
147	C₂×C₄×C₁₃	—	2	2	no	—
148	C₂×C₄×C₁₃	—	2	2	no	—
149	C₂×C₄×C₁₃	—	2	1	no	—
150	C₂×C₄×C₁₃	—	2	2	no	—
151	C₂×C₄×C₁₃	—	2	1	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	C₂×D₈	1	4	yes	—
162	C₂×C₄×C₁₃	C₂×D₈	1	2	yes	—
163	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
164	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
165	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
166	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
167	C₂×C₄×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
168	C₂×C₄×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
169	C₈×C₁₃	—	2	2	no	—
170	C₈×C₁₃	—	2	2	no	—
171	C₈×C₁₃	—	4	2	no	—
172	C₂²×D₈	C₂²×C₁₃	1	1	yes	characteristic
173	C₂×#126	—	2	2	no	—
174	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
175	C₂×#107	C₂²×C₁₃	1	2	yes	—
176	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
177	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
178	C₂×C₄⋊C₈	C₂²×C₁₃	1	2	yes	—
179	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
180	C₂×#102	C₂²×C₁₃	1	2	yes	—
181	C₂×#102	C₂²×C₁₃	1	2	yes	—
182	C₂×#102	C₂²×C₁₃	1	2	yes	—
183	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
184	#397	—	2	2	no	—
185	#396	—	2	2	no	—
186	#390	C₂²×C₁₃	1	2	yes	—
187	#390	C₂²×C₁₃	1	2	yes	—
188	#390	C₂²×C₁₃	1	2	yes	—
189	#389	C₂²×C₁₃	1	2	yes	—
190	#388	—	2	2	no	—
191	#384	C₂²×C₁₃	1	2	yes	—
192	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
193	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
194	#340	C₂²×C₁₃	1	2	yes	—
195	#340	C₂²×C₁₃	1	2	yes	—
196	#336	C₂²×C₁₃	1	2	yes	—
197	C₂²×C₁₃	—	8	2	no	—
198	C₂²×C₁₃	—	8	2	no	—
199	C₂²×C₁₃	—	8	2	no	—
200	C₂²×C₁₃	—	8	2	no	—
201	C₂²×C₁₃	—	8	2	no	—
202	C₂²×C₁₃	—	8	2	no	—
203	C₂²×C₁₃	—	8	2	no	—
204	C₂²×C₁₃	#537	1	1	yes	characteristic
205	C₂²×C₁₃	#547	1	1	yes	characteristic
206	C₂²×C₁₃	#550	1	1	yes	characteristic
207	C₂²×C₁₃	C₂²×D₈	1	1	yes	characteristic
208	C₂²×C₁₃	#575	1	1	yes	characteristic
209	C₂²×C₁₃	#576	1	1	yes	characteristic
210	C₂²×C₁₃	#578	1	1	yes	characteristic
211	C₄×C₁₃	—	2	4	no	—
212	C₄×C₁₃	—	2	2	no	—
213	C₄×C₁₃	—	4	2	no	—
214	C₄×C₁₃	—	4	1	no	—
215	C₄×C₁₃	—	8	2	no	—
216	C₄×C₁₃	—	8	2	no	—
217	C₄×C₁₃	—	8	2	no	—
218	C₄×C₁₃	#538	1	1	yes	characteristic
219	C₄×C₁₃	#539	1	1	yes	characteristic
220	C₄×C₁₃	#556	1	1	yes	characteristic
221	C₄×C₁₃	#563	1	1	yes	characteristic
222	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
223	C₂×D₈	—	2	2	no	—
224	C₂×D₈	—	4	1	no	—
225	C₂×D₈	—	4	1	no	—
226	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
227	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
228	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
229	#126	—	4	8	no	—
230	C₂×C₄⋊C₄	—	2	2	no	—
231	C₂×C₄⋊C₄	—	2	2	no	—
232	C₂×C₄⋊C₄	—	2	2	no	—
233	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
234	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
235	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
236	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
237	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
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	—	2	2	no	—
242	C₂×C₂²⋊C₄	—	2	2	no	—
243	C₂×C₂²⋊C₄	—	2	2	no	—
244	C₂×C₄²	—	2	2	no	—
245	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
246	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
247	#107	—	2	2	no	—
248	#107	—	4	1	no	—
249	#107	—	4	2	no	—
250	#107	—	4	1	no	—
251	C₄⋊C₈	—	2	4	no	—
252	C₄⋊C₈	—	4	1	no	—
253	#102	—	2	4	no	—
254	#102	—	4	2	no	—
255	#102	—	4	2	no	—
256	C₄×C₈	—	4	1	no	—
257	#95	—	2	2	no	—
258	#95	—	2	2	no	—
259	#95	D₄×C₁₃	1	2	yes	—
260	C₂×C₁₃	—	16	2	no	—
261	C₂×C₁₃	#2727	1	1	yes	characteristic
262	C₂×C₁₃	#3245	1	1	yes	characteristic
263	C₂×C₁₃	#3262	1	1	yes	characteristic
264	C₂×C₁₃	#3334	1	1	yes	characteristic
265	C₂×C₁₃	#3355	1	1	yes	characteristic
266	C₂×C₁₃	#3391	1	1	yes	characteristic
267	C₂×C₁₃	#3402	1	1	yes	characteristic
268	C₂⁴	—	2	2	no	—
269	C₂×D₄	—	2	2	no	—
270	C₂×D₄	—	2	2	no	—
271	C₂×D₄	—	2	2	no	—
272	C₂×D₄	—	2	2	no	—
273	C₂×D₄	—	2	2	no	—
274	C₂×D₄	—	2	2	no	—
275	C₂²×C₄	—	2	2	no	—
276	C₂²×C₄	—	2	2	no	—
277	C₂²×C₄	—	2	2	no	—
278	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
279	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
280	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
281	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
282	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
283	D₈	—	4	4	no	—
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	—	4	1	no	—
300	C₄⋊C₄	—	4	4	no	—
301	C₄⋊C₄	—	4	4	no	—
302	C₄⋊C₄	—	8	2	no	—
303	C₄⋊C₄	C₁₃×D₈	1	4	yes	complemented
304	C₂²⋊C₄	—	4	4	no	—
305	C₂²⋊C₄	—	4	4	no	—
306	C₂²⋊C₄	—	4	4	no	—
307	C₂²⋊C₄	—	4	4	no	—
308	C₂²⋊C₄	—	8	2	no	—
309	C₂²⋊C₄	—	8	2	no	—
310	C₄²	—	2	2	no	—
311	C₄²	—	2	1	no	—
312	C₄²	—	2	1	no	—
313	C₄²	—	2	2	no	—
314	C₄²	—	4	4	no	—
315	C₁₃	#32524	1	1	yes	characteristic, direct product factor, Sylow
316	C₂³	—	4	2	no	—
317	C₂³	—	4	2	no	—
318	C₂³	—	4	2	no	—
319	C₂³	—	4	2	no	—
320	C₂³	—	4	2	no	—
321	C₂³	—	4	2	no	—
322	C₂³	—	4	2	no	—
323	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
324	D₄	—	4	2	no	—
325	D₄	—	4	2	no	—
326	D₄	—	4	2	no	—
327	D₄	—	4	2	no	—
328	C₂×C₄	—	2	1	no	—
329	C₂×C₄	—	2	2	no	—
330	C₂×C₄	—	2	1	no	—
331	C₂×C₄	—	2	2	no	—
332	C₂×C₄	—	2	1	no	—
333	C₂×C₄	—	2	2	no	—
334	C₂×C₄	—	2	2	no	—
335	C₂×C₄	—	2	1	no	—
336	C₂×C₄	—	2	2	no	—
337	C₂×C₄	—	2	1	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	—	4	2	no	—
347	C₂×C₄	C₂×C₁₃×D₈	1	4	yes	—
348	C₂×C₄	C₂×C₁₃×D₈	1	2	yes	—
349	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
350	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
351	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
352	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
353	C₂×C₄	C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
354	C₂×C₄	C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
355	C₈	—	2	2	no	—
356	C₈	—	2	2	no	—
357	C₈	—	4	2	no	—
358	C₂²	—	8	2	no	—
359	C₂²	—	8	2	no	—
360	C₂²	—	8	2	no	—
361	C₂²	—	8	2	no	—
362	C₂²	—	8	2	no	—
363	C₂²	—	8	2	no	—
364	C₂²	—	8	2	no	—
365	C₂²	C₁₃×#537	1	1	yes	characteristic
366	C₂²	C₁₃×#547	1	1	yes	characteristic
367	C₂²	C₁₃×#550	1	1	yes	characteristic
368	C₂²	C₂²×C₁₃×D₈	1	1	yes	characteristic
369	C₂²	C₁₃×#575	1	1	yes	characteristic
370	C₂²	C₁₃×#576	1	1	yes	characteristic
371	C₂²	C₁₃×#578	1	1	yes	characteristic
372	C₄	—	2	4	no	—
373	C₄	—	2	2	no	—
374	C₄	—	4	1	no	—
375	C₄	—	4	2	no	—
376	C₄	—	8	2	no	—
377	C₄	—	8	2	no	—
378	C₄	—	8	2	no	—
379	C₄	C₁₃×#538	1	1	yes	characteristic
380	C₄	C₁₃×#539	1	1	yes	characteristic
381	C₄	C₁₃×#556	1	1	yes	characteristic
382	C₄	C₁₃×#563	1	1	yes	characteristic
383	C₂	—	16	2	no	—
384	C₂	C₁₃×#2727	1	1	yes	characteristic
385	C₂	C₁₃×#3245	1	1	yes	characteristic
386	C₂	C₁₃×#3262	1	1	yes	characteristic
387	C₂	C₁₃×#3334	1	1	yes	characteristic
388	C₂	C₁₃×#3355	1	1	yes	characteristic
389	C₂	C₁₃×#3391	1	1	yes	characteristic
390	C₂	C₁₃×#3402	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
prime radical	C₂²×C₁₃×D₈	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ C₄×C₁₃×C₄⋊C₄ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₃×#2512	C₂	semidirect
2. C₁₃×#2093	C₂	semidirect
3. C₁₃×#2067	C₂	semidirect
6. C₁₃×#1947	C₂	semidirect
7. C₁₃×#1942	C₂	semidirect
8. C₁₃×#1939	C₂	semidirect
9. C₁₃×#1925	C₂	semidirect
73. #32524	C₁₃	direct (N × H)
109. C₁₃×C₄⋊C₄	D₈	semidirect
121. #2512	C₂×C₁₃	semidirect
122. #2093	C₂×C₁₃	semidirect
123. #2067	C₂×C₁₃	semidirect
126. #1947	C₂×C₁₃	semidirect
127. #1942	C₂×C₁₃	semidirect
128. #1939	C₂×C₁₃	semidirect
129. #1925	C₂×C₁₃	semidirect
303. C₄⋊C₄	C₁₃×D₈	semidirect
315. C₁₃	#32524	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×#2512	2
C₁₃×#2093	2
C₁₃×#2067	2
C₁₃×#2054	2
C₁₃×#1970	2
C₁₃×#1947	2
C₁₃×#1942	2
C₁₃×#1939	2
C₁₃×#1925	2
#32524	13

Subgroups — C13×#32524 #15718863

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#32524 #15718863