Subgroups — C₁₃×#60620 #15746959

Order 3328.

2014 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3458	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₃×#536	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#3140	C₂	1	4	yes	maximal, complemented
4	C₁₃×#3139	C₂	1	4	yes	maximal, complemented
5	C₁₃×#3137	C₂	1	16	yes	maximal, complemented
6	C₁₃×#2896	C₂	1	2	yes	maximal
7	C₂×C₁₃×#419	C₂	1	2	yes	maximal, complemented
8	C₁₃×#2873	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂²×C₁₃×#41	C₂²	1	1	yes	characteristic
10	C₂³×Q₈×C₁₃	C₂²	1	1	yes	characteristic
11	C₂²×C₁₃×M₁₆	C₂²	1	2	yes	—
12	C₁₃×#544	—	2	2	no	—
13	C₁₃×#544	C₂²	1	8	yes	complemented
14	C₁₃×#543	—	2	2	no	—
15	C₁₃×#536	—	2	4	no	—
16	C₁₃×#536	C₂²	1	8	yes	—
17	C₁₃×#533	—	2	4	no	—
18	C₁₃×#533	C₂²	1	4	yes	—
19	C₂×C₁₃×C₄⋊Q₈	C₂²	1	2	yes	—
20	C₂×C₁₃×#124	C₂²	1	2	yes	—
21	C₂×C₁₃×#123	—	2	2	no	—
22	C₂×C₁₃×C₂²⋊Q₈	—	2	2	no	—
23	C₂×C₁₃×#117	C₂²	1	2	yes	—
24	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
25	C₁₃×#491	C₂²	1	16	yes	complemented
26	C₁₃×#489	C₂²	1	16	yes	complemented
27	C₁₃×#488	C₂²	1	16	yes	complemented
28	C₁₃×#487	C₂²	1	16	yes	complemented
29	C₁₃×#419	C₂²	1	4	yes	—
30	C₁₃×#419	C₂²	1	8	yes	—
31	C₁₃×#419	C₂²	1	8	yes	complemented
32	C₁₃×#418	C₂²	1	4	yes	—
33	C₁₃×#417	C₂²	1	8	yes	—
34	C₁₃×#416	C₂²	1	8	yes	—
35	C₂×C₁₃×#103	C₂²	1	8	yes	complemented
36	C₁₃×#405	C₂²	1	8	yes	complemented
37	C₄×C₁₃×M₁₆	C₂²	1	4	yes	—
38	C₂×C₁₃×#41	—	2	2	no	—
39	C₂×C₁₃×#41	—	2	8	no	—
40	C₂×C₁₃×#41	C₂³	1	4	yes	—
41	C₂²×Q₈×C₁₃	—	2	1	no	—
42	C₂²×Q₈×C₁₃	—	2	2	no	—
43	C₂²×Q₈×C₁₃	—	2	8	no	—
44	C₂²×Q₈×C₁₃	C₂³	1	4	yes	—
45	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
46	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
47	C₂²×D₄×C₁₃	—	2	1	no	—
48	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
49	C₂³×C₄×C₁₃	—	2	1	no	—
50	C₂³×C₄×C₁₃	—	2	1	no	—
51	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
52	C₂×C₁₃×M₁₆	—	2	8	no	—
53	C₂×C₁₃×M₁₆	C₂³	1	4	yes	—
54	C₂×C₁₃×M₁₆	C₂³	1	4	yes	—
55	C₂²×C₈×C₁₃	C₂³	1	4	yes	—
56	C₁₃×C₄⋊Q₈	—	2	8	no	—
57	C₁₃×C₄⋊Q₈	—	2	4	no	—
58	C₁₃×C₄⋊Q₈	C₂³	1	8	yes	—
59	C₁₃×C₄⋊Q₈	C₂³	1	8	yes	—
60	C₁₃×#125	—	2	8	no	—
61	C₁₃×#125	C₂³	1	8	yes	—
62	C₁₃×#124	—	2	4	no	—
63	C₁₃×#124	C₂³	1	8	yes	—
64	C₁₃×#123	—	2	16	no	—
65	C₁₃×C₂²⋊Q₈	—	2	8	no	—
66	C₁₃×C₂²⋊Q₈	—	2	16	no	—
67	C₁₃×C₂²⋊Q₈	—	2	16	no	—
68	C₄×Q₈×C₁₃	—	2	8	no	—
69	C₁₃×#117	—	2	2	no	—
70	C₁₃×#117	—	2	2	no	—
71	C₁₃×#117	D₄	1	4	yes	—
72	C₁₃×#117	C₂³	1	4	yes	—
73	C₁₃×#117	C₂³	1	4	yes	—
74	C₁₃×#117	C₂³	1	4	yes	—
75	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
76	C₂×C₁₃×C₄⋊C₄	D₄	1	2	yes	—
77	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
78	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
79	C₂×C₁₃×C₂²⋊C₄	—	2	4	no	—
80	C₂×C₁₃×C₂²⋊C₄	D₄	1	2	yes	—
81	C₂×C₄²×C₁₃	—	2	2	no	—
82	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
83	C₁₃×#103	C₂³	1	32	yes	—
84	C₁₃×#103	C₂³	1	16	yes	—
85	C₁₃×#102	C₂³	1	16	yes	—
86	C₁₃×#97	C₂³	1	8	yes	—
87	C₄×C₈×C₁₃	C₂³	1	8	yes	—
88	#60620	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
89	C₂⁴×C₁₃	—	2	1	no	—
90	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
91	C₁₃×#41	—	2	8	no	—
92	C₁₃×#41	—	2	8	no	—
93	C₁₃×#41	—	4	8	no	—
94	C₂×Q₈×C₁₃	—	2	4	no	—
95	C₂×Q₈×C₁₃	—	2	2	no	—
96	C₂×Q₈×C₁₃	—	2	1	no	—
97	C₂×Q₈×C₁₃	—	2	8	no	—
98	C₂×Q₈×C₁₃	—	2	8	no	—
99	C₂×Q₈×C₁₃	—	2	8	no	—
100	C₂×Q₈×C₁₃	—	2	8	no	—
101	C₂×Q₈×C₁₃	—	2	4	no	—
102	C₂×Q₈×C₁₃	—	4	4	no	—
103	C₂×Q₈×C₁₃	—	4	8	no	—
104	C₂×Q₈×C₁₃	C₂⁴	1	4	yes	—
105	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
106	C₂×D₄×C₁₃	—	2	4	no	—
107	C₂×D₄×C₁₃	—	2	1	no	—
108	C₂×D₄×C₁₃	—	2	4	no	—
109	C₂×D₄×C₁₃	—	4	4	no	—
110	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
111	C₂²×C₄×C₁₃	—	2	2	no	—
112	C₂²×C₄×C₁₃	—	2	1	no	—
113	C₂²×C₄×C₁₃	—	2	4	no	—
114	C₂²×C₄×C₁₃	—	2	4	no	—
115	C₂²×C₄×C₁₃	—	2	4	no	—
116	C₂²×C₄×C₁₃	—	4	4	no	—
117	C₂²×C₄×C₁₃	—	4	4	no	—
118	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
119	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
120	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
121	C₂²×C₄×C₁₃	#41	1	8	yes	—
122	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
123	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
124	C₁₃×M₁₆	—	2	8	no	—
125	C₁₃×M₁₆	—	2	8	no	—
126	C₂×C₈×C₁₃	—	2	8	no	—
127	C₂×C₈×C₁₃	C₂⁴	1	8	yes	—
128	C₁₃×C₄⋊C₄	—	2	16	no	—
129	C₁₃×C₄⋊C₄	—	2	4	no	—
130	C₁₃×C₄⋊C₄	—	2	8	no	—
131	C₁₃×C₄⋊C₄	—	2	16	no	—
132	C₁₃×C₄⋊C₄	C₂×D₄	1	8	yes	—
133	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
134	C₁₃×C₂²⋊C₄	—	2	4	no	—
135	C₁₃×C₂²⋊C₄	—	2	4	no	—
136	C₁₃×C₂²⋊C₄	—	2	16	no	—
137	C₁₃×C₂²⋊C₄	C₂×D₄	1	8	yes	—
138	C₄²×C₁₃	—	2	4	no	—
139	C₄²×C₁₃	—	2	4	no	—
140	C₄²×C₁₃	C₂×D₄	1	4	yes	—
141	C₄²×C₁₃	C₂⁴	1	4	yes	—
142	#3458	C₂×C₁₃	1	1	yes	characteristic, complemented
143	C₂×#536	C₂×C₁₃	1	1	yes	characteristic
144	#3140	C₂×C₁₃	1	4	yes	complemented
145	#3139	C₂×C₁₃	1	4	yes	complemented
146	#3137	C₂×C₁₃	1	16	yes	complemented
147	#2896	C₂×C₁₃	1	2	yes	—
148	C₂×#419	C₂×C₁₃	1	2	yes	complemented
149	#2873	C₂×C₁₃	1	1	yes	characteristic, complemented
150	C₂³×C₁₃	—	2	2	no	—
151	C₂³×C₁₃	—	4	2	no	—
152	C₂³×C₁₃	—	4	4	no	—
153	C₂³×C₁₃	—	4	2	no	—
154	C₂³×C₁₃	#124	1	4	yes	—
155	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
156	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
157	Q₈×C₁₃	—	2	8	no	—
158	Q₈×C₁₃	—	2	4	no	—
159	Q₈×C₁₃	—	4	8	no	—
160	Q₈×C₁₃	—	4	4	no	—
161	Q₈×C₁₃	—	4	2	no	—
162	Q₈×C₁₃	—	8	8	no	—
163	D₄×C₁₃	—	2	4	no	—
164	D₄×C₁₃	—	4	8	no	—
165	D₄×C₁₃	—	4	2	no	—
166	C₂×C₄×C₁₃	—	2	8	no	—
167	C₂×C₄×C₁₃	—	2	4	no	—
168	C₂×C₄×C₁₃	—	2	2	no	—
169	C₂×C₄×C₁₃	—	4	4	no	—
170	C₂×C₄×C₁₃	—	4	2	no	—
171	C₂×C₄×C₁₃	—	4	4	no	—
172	C₂×C₄×C₁₃	—	4	8	no	—
173	C₂×C₄×C₁₃	—	4	8	no	—
174	C₂×C₄×C₁₃	—	8	4	no	—
175	C₂×C₄×C₁₃	#124	1	4	yes	—
176	C₂×C₄×C₁₃	#124	1	8	yes	—
177	C₂×C₄×C₁₃	C₂²×D₄	1	8	yes	—
178	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
179	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
180	C₂×C₄×C₁₃	C₂×#41	1	4	yes	—
181	C₂×C₄×C₁₃	C₂×#41	1	4	yes	—
182	C₂×C₄×C₁₃	C₂×#41	1	4	yes	—
183	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
184	C₈×C₁₃	—	2	8	no	—
185	C₂²×#41	C₂²×C₁₃	1	1	yes	characteristic
186	C₂³×Q₈	C₂²×C₁₃	1	1	yes	characteristic
187	C₂²×M₁₆	C₂²×C₁₃	1	2	yes	—
188	#544	—	2	2	no	—
189	#544	C₂²×C₁₃	1	8	yes	complemented
190	#543	—	2	2	no	—
191	#536	—	2	4	no	—
192	#536	C₂²×C₁₃	1	8	yes	—
193	#533	—	2	4	no	—
194	#533	C₂²×C₁₃	1	4	yes	—
195	C₂×C₄⋊Q₈	C₂²×C₁₃	1	2	yes	—
196	C₂×#124	C₂²×C₁₃	1	2	yes	—
197	C₂×#123	—	2	2	no	—
198	C₂×C₂²⋊Q₈	—	2	2	no	—
199	C₂×#117	C₂²×C₁₃	1	2	yes	—
200	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
201	#491	C₂²×C₁₃	1	16	yes	complemented
202	#489	C₂²×C₁₃	1	16	yes	complemented
203	#488	C₂²×C₁₃	1	16	yes	complemented
204	#487	C₂²×C₁₃	1	16	yes	complemented
205	#419	C₂²×C₁₃	1	4	yes	—
206	#419	C₂²×C₁₃	1	8	yes	—
207	#419	C₂²×C₁₃	1	8	yes	complemented
208	#418	C₂²×C₁₃	1	4	yes	—
209	#417	C₂²×C₁₃	1	8	yes	—
210	#416	C₂²×C₁₃	1	8	yes	—
211	C₂×#103	C₂²×C₁₃	1	8	yes	complemented
212	#405	C₂²×C₁₃	1	8	yes	complemented
213	C₄×M₁₆	C₂²×C₁₃	1	4	yes	—
214	C₂²×C₁₃	—	2	2	no	—
215	C₂²×C₁₃	—	2	4	no	—
216	C₂²×C₁₃	—	4	4	no	—
217	C₂²×C₁₃	—	4	4	no	—
218	C₂²×C₁₃	—	4	2	no	—
219	C₂²×C₁₃	—	8	4	no	—
220	C₂²×C₁₃	C₂×#124	1	2	yes	—
221	C₂²×C₁₃	C₂×#124	1	4	yes	—
222	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
223	C₄×C₁₃	—	2	8	no	—
224	C₄×C₁₃	—	4	8	no	—
225	C₄×C₁₃	—	4	2	no	—
226	C₄×C₁₃	—	4	4	no	—
227	C₄×C₁₃	C₂×#124	1	4	yes	—
228	C₄×C₁₃	C₂×#124	1	2	yes	—
229	C₄×C₁₃	C₂²×#41	1	2	yes	—
230	C₂×#41	—	2	2	no	—
231	C₂×#41	—	2	8	no	—
232	C₂×#41	C₂³×C₁₃	1	4	yes	—
233	C₂²×Q₈	—	2	1	no	—
234	C₂²×Q₈	—	2	2	no	—
235	C₂²×Q₈	—	2	8	no	—
236	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
237	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
238	C₂²×Q₈	C₂³×C₁₃	1	4	yes	—
239	C₂²×D₄	—	2	1	no	—
240	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
241	C₂³×C₄	—	2	1	no	—
242	C₂³×C₄	—	2	1	no	—
243	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
244	C₂×M₁₆	—	2	8	no	—
245	C₂×M₁₆	C₂³×C₁₃	1	4	yes	—
246	C₂×M₁₆	C₂³×C₁₃	1	4	yes	—
247	C₂²×C₈	C₂³×C₁₃	1	4	yes	—
248	C₄⋊Q₈	—	2	8	no	—
249	C₄⋊Q₈	—	2	4	no	—
250	C₄⋊Q₈	C₂³×C₁₃	1	8	yes	—
251	C₄⋊Q₈	C₂³×C₁₃	1	8	yes	—
252	#125	—	2	8	no	—
253	#125	C₂³×C₁₃	1	8	yes	—
254	#124	—	2	4	no	—
255	#124	C₂³×C₁₃	1	8	yes	—
256	#123	—	2	16	no	—
257	C₂²⋊Q₈	—	2	8	no	—
258	C₂²⋊Q₈	—	2	16	no	—
259	C₂²⋊Q₈	—	2	16	no	—
260	C₄×Q₈	—	2	8	no	—
261	#117	—	2	2	no	—
262	#117	—	2	2	no	—
263	#117	D₄×C₁₃	1	4	yes	—
264	#117	C₂³×C₁₃	1	4	yes	—
265	#117	C₂³×C₁₃	1	4	yes	—
266	#117	C₂³×C₁₃	1	4	yes	—
267	C₂×C₄⋊C₄	—	2	4	no	—
268	C₂×C₄⋊C₄	D₄×C₁₃	1	2	yes	—
269	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
270	C₂×C₂²⋊C₄	—	2	2	no	—
271	C₂×C₂²⋊C₄	—	2	4	no	—
272	C₂×C₂²⋊C₄	D₄×C₁₃	1	2	yes	—
273	C₂×C₄²	—	2	2	no	—
274	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
275	#103	C₂³×C₁₃	1	32	yes	—
276	#103	C₂³×C₁₃	1	16	yes	—
277	#102	C₂³×C₁₃	1	16	yes	—
278	#97	C₂³×C₁₃	1	8	yes	—
279	C₄×C₈	C₂³×C₁₃	1	8	yes	—
280	C₂×C₁₃	—	2	2	no	—
281	C₂×C₁₃	—	2	4	no	—
282	C₂×C₁₃	—	8	2	no	—
283	C₂×C₁₃	C₂²×#124	1	1	yes	characteristic
284	C₂×C₁₃	#3586	1	2	yes	—
285	C₂⁴	—	2	1	no	—
286	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
287	#41	—	2	8	no	—
288	#41	—	2	8	no	—
289	#41	—	4	8	no	—
290	C₂×Q₈	—	2	4	no	—
291	C₂×Q₈	—	2	2	no	—
292	C₂×Q₈	—	2	1	no	—
293	C₂×Q₈	—	2	8	no	—
294	C₂×Q₈	—	2	8	no	—
295	C₂×Q₈	—	2	8	no	—
296	C₂×Q₈	—	2	8	no	—
297	C₂×Q₈	—	2	4	no	—
298	C₂×Q₈	—	4	4	no	—
299	C₂×Q₈	—	4	8	no	—
300	C₂×Q₈	C₂⁴×C₁₃	1	4	yes	—
301	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
302	C₂×D₄	—	2	4	no	—
303	C₂×D₄	—	2	1	no	—
304	C₂×D₄	—	2	4	no	—
305	C₂×D₄	—	4	4	no	—
306	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
307	C₂²×C₄	—	2	2	no	—
308	C₂²×C₄	—	2	1	no	—
309	C₂²×C₄	—	2	4	no	—
310	C₂²×C₄	—	2	4	no	—
311	C₂²×C₄	—	2	4	no	—
312	C₂²×C₄	—	4	4	no	—
313	C₂²×C₄	—	4	4	no	—
314	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
315	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
316	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
317	C₂²×C₄	C₁₃×#41	1	8	yes	—
318	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
319	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
320	M₁₆	—	2	8	no	—
321	M₁₆	—	2	8	no	—
322	C₂×C₈	—	2	8	no	—
323	C₂×C₈	C₂⁴×C₁₃	1	8	yes	—
324	C₄⋊C₄	—	2	16	no	—
325	C₄⋊C₄	—	2	4	no	—
326	C₄⋊C₄	—	2	8	no	—
327	C₄⋊C₄	—	2	16	no	—
328	C₄⋊C₄	C₂×D₄×C₁₃	1	8	yes	—
329	C₄⋊C₄	C₂⁴×C₁₃	1	8	yes	—
330	C₂²⋊C₄	—	2	4	no	—
331	C₂²⋊C₄	—	2	4	no	—
332	C₂²⋊C₄	—	2	16	no	—
333	C₂²⋊C₄	C₂×D₄×C₁₃	1	8	yes	—
334	C₄²	—	2	4	no	—
335	C₄²	—	2	4	no	—
336	C₄²	C₂×D₄×C₁₃	1	4	yes	—
337	C₄²	C₂⁴×C₁₃	1	4	yes	—
338	C₁₃	#60620	1	1	yes	characteristic, direct product factor, Sylow
339	C₂³	—	2	2	no	—
340	C₂³	—	4	2	no	—
341	C₂³	—	4	4	no	—
342	C₂³	—	4	2	no	—
343	C₂³	C₁₃×#124	1	4	yes	—
344	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
345	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
346	Q₈	—	2	8	no	—
347	Q₈	—	2	4	no	—
348	Q₈	—	4	8	no	—
349	Q₈	—	4	4	no	—
350	Q₈	—	4	2	no	—
351	Q₈	—	8	8	no	—
352	D₄	—	2	4	no	—
353	D₄	—	4	8	no	—
354	D₄	—	4	2	no	—
355	C₂×C₄	—	2	8	no	—
356	C₂×C₄	—	2	4	no	—
357	C₂×C₄	—	2	2	no	—
358	C₂×C₄	—	4	4	no	—
359	C₂×C₄	—	4	2	no	—
360	C₂×C₄	—	4	4	no	—
361	C₂×C₄	—	4	8	no	—
362	C₂×C₄	—	4	8	no	—
363	C₂×C₄	—	8	4	no	—
364	C₂×C₄	C₁₃×#124	1	4	yes	—
365	C₂×C₄	C₁₃×#124	1	8	yes	—
366	C₂×C₄	C₂²×D₄×C₁₃	1	8	yes	—
367	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
368	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
369	C₂×C₄	C₂×C₁₃×#41	1	4	yes	—
370	C₂×C₄	C₂×C₁₃×#41	1	4	yes	—
371	C₂×C₄	C₂×C₁₃×#41	1	4	yes	—
372	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
373	C₈	—	2	8	no	—
374	C₂²	—	2	2	no	—
375	C₂²	—	2	4	no	—
376	C₂²	—	4	4	no	—
377	C₂²	—	4	4	no	—
378	C₂²	—	4	2	no	—
379	C₂²	—	8	4	no	—
380	C₂²	C₂×C₁₃×#124	1	2	yes	—
381	C₂²	C₂×C₁₃×#124	1	4	yes	—
382	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
383	C₄	—	2	8	no	—
384	C₄	—	4	8	no	—
385	C₄	—	4	2	no	—
386	C₄	—	4	4	no	—
387	C₄	C₂×C₁₃×#124	1	4	yes	—
388	C₄	C₂×C₁₃×#124	1	2	yes	—
389	C₄	C₂²×C₁₃×#41	1	2	yes	—
390	C₂	—	2	2	no	—
391	C₂	—	2	4	no	—
392	C₂	—	8	2	no	—
393	C₂	C₂²×C₁₃×#124	1	1	yes	characteristic
394	C₂	C₁₃×#3586	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₃
prime radical	C₂²×C₁₃×#41	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₂×C₁₃×#117 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₃×#3458	C₂	semidirect
3. C₁₃×#3140	C₂	semidirect
4. C₁₃×#3139	C₂	semidirect
5. C₁₃×#3137	C₂	semidirect
7. C₂×C₁₃×#419	C₂	semidirect
8. C₁₃×#2873	C₂	semidirect
13. C₁₃×#544	C₂²	semidirect
25. C₁₃×#491	C₂²	semidirect
26. C₁₃×#489	C₂²	semidirect
27. C₁₃×#488	C₂²	semidirect
28. C₁₃×#487	C₂²	semidirect
31. C₁₃×#419	C₂²	semidirect
35. C₂×C₁₃×#103	C₂²	semidirect
36. C₁₃×#405	C₂²	semidirect
88. #60620	C₁₃	direct (N × H)
142. #3458	C₂×C₁₃	semidirect
144. #3140	C₂×C₁₃	semidirect
145. #3139	C₂×C₁₃	semidirect
146. #3137	C₂×C₁₃	semidirect
148. C₂×#419	C₂×C₁₃	semidirect
149. #2873	C₂×C₁₃	semidirect
189. #544	C₂²×C₁₃	semidirect
201. #491	C₂²×C₁₃	semidirect
202. #489	C₂²×C₁₃	semidirect
203. #488	C₂²×C₁₃	semidirect
204. #487	C₂²×C₁₃	semidirect
207. #419	C₂²×C₁₃	semidirect
211. C₂×#103	C₂²×C₁₃	semidirect
212. #405	C₂²×C₁₃	semidirect
338. C₁₃	#60620	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×#3458	2
C₂×C₁₃×#536	2
C₁₃×#3140	2
C₁₃×#3139	2
C₁₃×#3137	2
C₁₃×#2896	2
C₂×C₁₃×#419	2
C₁₃×#2873	2
#60620	13

Subgroups — C13×#60620 #15746959

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#60620 #15746959