Subgroups — C₁₃×#60623 #15746962

Order 3328.

2042 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3503	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃×#3499	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#3141	C₂	1	3	yes	maximal, complemented
4	C₁₃×#3139	C₂	1	3	yes	maximal, complemented
5	C₁₃×#3137	C₂	1	12	yes	maximal, complemented
6	C₁₃×#3131	C₂	1	3	yes	maximal, complemented
7	C₂×C₁₃×#487	C₂	1	3	yes	maximal, complemented
8	C₁₃×#2898	C₂	1	4	yes	maximal, complemented
9	C₄×C₁₃×#131	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₁₃×2₋¹⁺⁴	C₂²	1	2	yes	—
11	C₂×C₁₃×#131	C₂²	1	2	yes	—
12	Q₈²×C₁₃	—	2	1	no	—
13	C₁₃×#557	—	2	1	no	—
14	C₁₃×#554	—	2	3	no	—
15	D₄×Q₈×C₁₃	—	2	1	no	—
16	D₄×Q₈×C₁₃	—	2	1	no	—
17	D₄×Q₈×C₁₃	—	2	3	no	—
18	C₁₃×#547	—	2	3	no	—
19	C₁₃×#547	—	2	3	no	—
20	C₁₃×#544	C₂²	1	6	yes	—
21	C₁₃×#536	C₂²	1	6	yes	—
22	C₁₃×#533	C₂²	1	3	yes	—
23	C₁₃×#532	C₂²	1	3	yes	—
24	C₂×C₁₃×C₄⋊Q₈	C₂²	1	3	yes	—
25	C₂×C₁₃×C₄⋊Q₈	C₂²	1	3	yes	—
26	C₁₃×#520	C₂²	1	2	yes	—
27	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic
28	C₁₃×#491	C₂²	1	12	yes	—
29	C₁₃×#489	C₂²	1	12	yes	—
30	C₁₃×#488	C₂²	1	12	yes	—
31	C₁₃×#487	C₂²	1	3	yes	—
32	C₁₃×#487	C₂²	1	12	yes	—
33	C₁₃×#487	C₂²	1	6	yes	—
34	C₁₃×#487	C₂²	1	3	yes	—
35	C₁₃×#486	C₂²	1	1	yes	characteristic
36	C₁₃×#486	C₂²	1	3	yes	—
37	C₁₃×#419	C₂²	1	12	yes	—
38	C₁₃×#417	C₂²	1	12	yes	—
39	C₁₃×#416	C₂²	1	12	yes	—
40	C₂×C₁₃×#103	C₂²	1	12	yes	—
41	C₁₃×#405	C₂²	1	6	yes	—
42	C₄×C₁₃×M₁₆	C₂²	1	3	yes	—
43	C₂×C₄×C₈×C₁₃	C₂²	1	3	yes	—
44	C₁₃×2₋¹⁺⁴	—	2	16	no	—
45	C₂×C₁₃×#41	—	2	6	no	—
46	C₂×C₁₃×#41	C₂³	1	6	yes	—
47	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
48	C₂²×Q₈×C₁₃	—	2	2	no	—
49	C₂²×Q₈×C₁₃	—	2	3	no	—
50	C₂²×Q₈×C₁₃	C₂³	1	6	yes	—
51	C₁₃×#131	—	2	8	no	—
52	C₂×C₁₃×M₁₆	C₂³	1	6	yes	—
53	C₂²×C₈×C₁₃	C₂³	1	6	yes	—
54	C₁₃×C₄⋊Q₈	—	2	6	no	—
55	C₁₃×C₄⋊Q₈	—	2	3	no	—
56	C₁₃×C₄⋊Q₈	—	2	3	no	—
57	C₁₃×C₄⋊Q₈	—	2	3	no	—
58	C₁₃×C₄⋊Q₈	—	2	3	no	—
59	C₁₃×C₄⋊Q₈	C₂³	1	3	yes	—
60	C₁₃×C₄⋊Q₈	C₂³	1	6	yes	—
61	C₁₃×C₄⋊Q₈	C₂³	1	3	yes	—
62	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
63	C₁₃×C₄⋊Q₈	C₂³	1	6	yes	—
64	C₁₃×#127	C₂³	1	1	yes	characteristic
65	C₁₃×#125	—	2	6	no	—
66	C₁₃×#125	C₂³	1	6	yes	—
67	C₁₃×#124	C₂³	1	6	yes	—
68	C₁₃×#123	—	2	12	no	—
69	C₁₃×C₂²⋊Q₈	—	2	3	no	—
70	C₁₃×C₂²⋊Q₈	—	2	3	no	—
71	C₁₃×C₂²⋊Q₈	—	2	6	no	—
72	C₁₃×C₂²⋊Q₈	—	2	6	no	—
73	C₁₃×C₂²⋊Q₈	—	2	12	no	—
74	C₁₃×#121	—	2	3	no	—
75	C₁₃×#121	—	2	3	no	—
76	C₄×Q₈×C₁₃	—	2	2	no	—
77	C₄×Q₈×C₁₃	—	2	3	no	—
78	C₄×Q₈×C₁₃	—	2	3	no	—
79	C₄×Q₈×C₁₃	D₄	1	1	yes	characteristic
80	C₄×Q₈×C₁₃	D₄	1	1	yes	characteristic
81	C₄×D₄×C₁₃	—	2	6	no	—
82	C₄×D₄×C₁₃	—	2	3	no	—
83	C₄×D₄×C₁₃	—	2	3	no	—
84	C₄×D₄×C₁₃	D₄	1	3	yes	—
85	C₄×D₄×C₁₃	D₄	1	3	yes	—
86	C₁₃×#117	C₂³	1	6	yes	—
87	C₁₃×#117	C₂³	1	3	yes	—
88	C₂×C₁₃×C₄⋊C₄	—	2	3	no	—
89	C₂×C₁₃×C₄⋊C₄	—	2	3	no	—
90	C₂×C₁₃×C₄⋊C₄	—	2	3	no	—
91	C₂×C₁₃×C₄⋊C₄	C₂³	1	6	yes	—
92	C₂×C₄²×C₁₃	C₂³	1	3	yes	—
93	C₁₃×#103	C₂³	1	12	yes	—
94	C₁₃×#103	C₂³	1	24	yes	—
95	C₁₃×#103	C₂³	1	12	yes	—
96	C₁₃×#102	C₂³	1	4	yes	—
97	C₁₃×#102	C₂³	1	12	yes	—
98	C₁₃×#97	C₂³	1	6	yes	—
99	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
100	C₄×C₈×C₁₃	C₂³	1	3	yes	—
101	C₄×C₈×C₁₃	C₂³	1	6	yes	—
102	#60623	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
103	C₁₃×#41	—	2	24	no	—
104	C₁₃×#41	—	4	24	no	—
105	C₁₃×#41	#41	1	8	yes	—
106	C₂×Q₈×C₁₃	—	2	1	no	—
107	C₂×Q₈×C₁₃	—	2	3	no	—
108	C₂×Q₈×C₁₃	—	2	6	no	—
109	C₂×Q₈×C₁₃	—	2	6	no	—
110	C₂×Q₈×C₁₃	—	2	24	no	—
111	C₂×Q₈×C₁₃	—	4	8	no	—
112	C₂×Q₈×C₁₃	—	8	6	no	—
113	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
114	C₂×Q₈×C₁₃	C₂⁴	1	6	yes	—
115	C₂×D₄×C₁₃	—	2	6	no	—
116	C₂×D₄×C₁₃	—	2	1	no	—
117	C₂×D₄×C₁₃	—	2	1	no	—
118	C₂×D₄×C₁₃	C₂×D₄	1	3	yes	—
119	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
120	C₂²×C₄×C₁₃	—	2	6	no	—
121	C₂²×C₄×C₁₃	—	2	6	no	—
122	C₂²×C₄×C₁₃	—	2	6	no	—
123	C₂²×C₄×C₁₃	C₂×D₄	1	3	yes	—
124	C₂²×C₄×C₁₃	C₂×D₄	1	3	yes	—
125	C₂²×C₄×C₁₃	C₂⁴	1	3	yes	—
126	C₁₃×M₁₆	—	2	12	no	—
127	C₂×C₈×C₁₃	—	2	12	no	—
128	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
129	C₂×C₈×C₁₃	C₂⁴	1	6	yes	—
130	C₁₃×C₄⋊C₄	—	2	3	no	—
131	C₁₃×C₄⋊C₄	—	2	3	no	—
132	C₁₃×C₄⋊C₄	—	2	3	no	—
133	C₁₃×C₄⋊C₄	—	2	6	no	—
134	C₁₃×C₄⋊C₄	—	2	6	no	—
135	C₁₃×C₄⋊C₄	—	2	6	no	—
136	C₁₃×C₄⋊C₄	—	2	6	no	—
137	C₁₃×C₄⋊C₄	—	2	1	no	—
138	C₁₃×C₄⋊C₄	—	2	6	no	—
139	C₁₃×C₄⋊C₄	—	2	6	no	—
140	C₁₃×C₄⋊C₄	C₂×D₄	1	3	yes	—
141	C₁₃×C₄⋊C₄	C₂×D₄	1	3	yes	—
142	C₁₃×C₄⋊C₄	C₂⁴	1	6	yes	—
143	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
144	C₁₃×C₂²⋊C₄	—	2	6	no	—
145	C₁₃×C₂²⋊C₄	—	2	6	no	—
146	C₁₃×C₂²⋊C₄	—	2	6	no	—
147	C₁₃×C₂²⋊C₄	C₂×D₄	1	6	yes	—
148	C₄²×C₁₃	—	2	6	no	—
149	C₄²×C₁₃	C₂×D₄	1	3	yes	—
150	C₄²×C₁₃	C₂×D₄	1	3	yes	—
151	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
152	C₄²×C₁₃	C₂⁴	1	3	yes	—
153	#3503	C₂×C₁₃	1	1	yes	characteristic, complemented
154	#3499	C₂×C₁₃	1	1	yes	characteristic
155	#3141	C₂×C₁₃	1	3	yes	complemented
156	#3139	C₂×C₁₃	1	3	yes	complemented
157	#3137	C₂×C₁₃	1	12	yes	complemented
158	#3131	C₂×C₁₃	1	3	yes	complemented
159	C₂×#487	C₂×C₁₃	1	3	yes	complemented
160	#2898	C₂×C₁₃	1	4	yes	complemented
161	C₄×#131	C₂×C₁₃	1	1	yes	characteristic, complemented
162	C₂³×C₁₃	—	2	2	no	—
163	C₂³×C₁₃	C₂²×D₄	1	3	yes	—
164	Q₈×C₁₃	—	2	12	no	—
165	Q₈×C₁₃	—	4	12	no	—
166	Q₈×C₁₃	—	4	6	no	—
167	Q₈×C₁₃	—	4	2	no	—
168	Q₈×C₁₃	—	8	6	no	—
169	Q₈×C₁₃	#124	1	4	yes	—
170	D₄×C₁₃	—	2	4	no	—
171	D₄×C₁₃	—	4	12	no	—
172	D₄×C₁₃	—	4	2	no	—
173	D₄×C₁₃	—	4	2	no	—
174	D₄×C₁₃	#124	1	12	yes	—
175	C₂×C₄×C₁₃	—	2	6	no	—
176	C₂×C₄×C₁₃	—	2	6	no	—
177	C₂×C₄×C₁₃	—	2	2	no	—
178	C₂×C₄×C₁₃	—	2	6	no	—
179	C₂×C₄×C₁₃	—	2	6	no	—
180	C₂×C₄×C₁₃	—	4	12	no	—
181	C₂×C₄×C₁₃	—	4	12	no	—
182	C₂×C₄×C₁₃	—	8	6	no	—
183	C₂×C₄×C₁₃	C₂²×D₄	1	3	yes	—
184	C₂×C₄×C₁₃	C₂²×D₄	1	3	yes	—
185	C₂×C₄×C₁₃	C₂²×D₄	1	3	yes	—
186	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
187	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
188	C₂×C₄×C₁₃	C₂×#41	1	12	yes	—
189	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
190	C₈×C₁₃	—	2	2	no	—
191	C₈×C₁₃	—	2	6	no	—
192	C₂×2₋¹⁺⁴	C₂²×C₁₃	1	2	yes	—
193	C₂×#131	C₂²×C₁₃	1	2	yes	—
194	Q₈²	—	2	1	no	—
195	#557	—	2	1	no	—
196	#554	—	2	3	no	—
197	D₄×Q₈	—	2	1	no	—
198	D₄×Q₈	—	2	1	no	—
199	D₄×Q₈	—	2	3	no	—
200	#547	—	2	3	no	—
201	#547	—	2	3	no	—
202	#544	C₂²×C₁₃	1	6	yes	—
203	#536	C₂²×C₁₃	1	6	yes	—
204	#533	C₂²×C₁₃	1	3	yes	—
205	#532	C₂²×C₁₃	1	3	yes	—
206	C₂×C₄⋊Q₈	C₂²×C₁₃	1	3	yes	—
207	C₂×C₄⋊Q₈	C₂²×C₁₃	1	3	yes	—
208	#520	C₂²×C₁₃	1	2	yes	—
209	C₄×#41	C₂²×C₁₃	1	1	yes	characteristic
210	#491	C₂²×C₁₃	1	12	yes	—
211	#489	C₂²×C₁₃	1	12	yes	—
212	#488	C₂²×C₁₃	1	12	yes	—
213	#487	C₂²×C₁₃	1	3	yes	—
214	#487	C₂²×C₁₃	1	12	yes	—
215	#487	C₂²×C₁₃	1	6	yes	—
216	#487	C₂²×C₁₃	1	3	yes	—
217	#486	C₂²×C₁₃	1	1	yes	characteristic
218	#486	C₂²×C₁₃	1	3	yes	—
219	#419	C₂²×C₁₃	1	12	yes	—
220	#417	C₂²×C₁₃	1	12	yes	—
221	#416	C₂²×C₁₃	1	12	yes	—
222	C₂×#103	C₂²×C₁₃	1	12	yes	—
223	#405	C₂²×C₁₃	1	6	yes	—
224	C₄×M₁₆	C₂²×C₁₃	1	3	yes	—
225	C₂×C₄×C₈	C₂²×C₁₃	1	3	yes	—
226	C₂²×C₁₃	—	2	3	no	—
227	C₂²×C₁₃	—	2	3	no	—
228	C₂²×C₁₃	—	4	2	no	—
229	C₂²×C₁₃	—	4	2	no	—
230	C₂²×C₁₃	—	4	2	no	—
231	C₂²×C₁₃	C₂×#124	1	6	yes	—
232	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
233	C₄×C₁₃	—	2	3	no	—
234	C₄×C₁₃	—	2	3	no	—
235	C₄×C₁₃	—	4	6	no	—
236	C₄×C₁₃	—	4	6	no	—
237	C₄×C₁₃	—	4	2	no	—
238	C₄×C₁₃	C₂×#124	1	6	yes	—
239	C₄×C₁₃	#577	1	2	yes	—
240	C₄×C₁₃	#578	1	2	yes	—
241	C₄×C₁₃	C₂²×#41	1	2	yes	—
242	2₋¹⁺⁴	—	2	16	no	—
243	C₂×#41	—	2	6	no	—
244	C₂×#41	C₂³×C₁₃	1	6	yes	—
245	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
246	C₂²×Q₈	—	2	2	no	—
247	C₂²×Q₈	—	2	3	no	—
248	C₂²×Q₈	C₂³×C₁₃	1	6	yes	—
249	#131	—	2	8	no	—
250	C₂×M₁₆	C₂³×C₁₃	1	6	yes	—
251	C₂²×C₈	C₂³×C₁₃	1	6	yes	—
252	C₄⋊Q₈	—	2	6	no	—
253	C₄⋊Q₈	—	2	3	no	—
254	C₄⋊Q₈	—	2	3	no	—
255	C₄⋊Q₈	—	2	3	no	—
256	C₄⋊Q₈	—	2	3	no	—
257	C₄⋊Q₈	C₂³×C₁₃	1	3	yes	—
258	C₄⋊Q₈	C₂³×C₁₃	1	6	yes	—
259	C₄⋊Q₈	C₂³×C₁₃	1	3	yes	—
260	C₄⋊Q₈	C₂³×C₁₃	1	6	yes	—
261	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
262	#127	C₂³×C₁₃	1	1	yes	characteristic
263	#125	—	2	6	no	—
264	#125	C₂³×C₁₃	1	6	yes	—
265	#124	C₂³×C₁₃	1	6	yes	—
266	#123	—	2	12	no	—
267	C₂²⋊Q₈	—	2	3	no	—
268	C₂²⋊Q₈	—	2	3	no	—
269	C₂²⋊Q₈	—	2	6	no	—
270	C₂²⋊Q₈	—	2	6	no	—
271	C₂²⋊Q₈	—	2	12	no	—
272	#121	—	2	3	no	—
273	#121	—	2	3	no	—
274	C₄×Q₈	—	2	2	no	—
275	C₄×Q₈	—	2	3	no	—
276	C₄×Q₈	—	2	3	no	—
277	C₄×Q₈	D₄×C₁₃	1	1	yes	characteristic
278	C₄×Q₈	D₄×C₁₃	1	1	yes	characteristic
279	C₄×D₄	—	2	6	no	—
280	C₄×D₄	—	2	3	no	—
281	C₄×D₄	—	2	3	no	—
282	C₄×D₄	D₄×C₁₃	1	3	yes	—
283	C₄×D₄	D₄×C₁₃	1	3	yes	—
284	#117	C₂³×C₁₃	1	6	yes	—
285	#117	C₂³×C₁₃	1	3	yes	—
286	C₂×C₄⋊C₄	—	2	3	no	—
287	C₂×C₄⋊C₄	—	2	3	no	—
288	C₂×C₄⋊C₄	—	2	3	no	—
289	C₂×C₄⋊C₄	C₂³×C₁₃	1	6	yes	—
290	C₂×C₄²	C₂³×C₁₃	1	3	yes	—
291	#103	C₂³×C₁₃	1	12	yes	—
292	#103	C₂³×C₁₃	1	24	yes	—
293	#103	C₂³×C₁₃	1	12	yes	—
294	#102	C₂³×C₁₃	1	4	yes	—
295	#102	C₂³×C₁₃	1	12	yes	—
296	#97	C₂³×C₁₃	1	6	yes	—
297	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
298	C₄×C₈	C₂³×C₁₃	1	3	yes	—
299	C₄×C₈	C₂³×C₁₃	1	6	yes	—
300	C₂×C₁₃	—	2	6	no	—
301	C₂×C₁₃	—	8	2	no	—
302	C₂×C₁₃	C₂²×#124	1	1	yes	characteristic
303	C₂×C₁₃	C₂×#577	1	1	yes	characteristic
304	C₂×C₁₃	C₂×#578	1	1	yes	characteristic
305	#41	—	2	24	no	—
306	#41	—	4	24	no	—
307	#41	C₁₃×#41	1	8	yes	—
308	C₂×Q₈	—	2	1	no	—
309	C₂×Q₈	—	2	3	no	—
310	C₂×Q₈	—	2	6	no	—
311	C₂×Q₈	—	2	6	no	—
312	C₂×Q₈	—	2	24	no	—
313	C₂×Q₈	—	4	8	no	—
314	C₂×Q₈	—	8	6	no	—
315	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
316	C₂×Q₈	C₂⁴×C₁₃	1	6	yes	—
317	C₂×D₄	—	2	6	no	—
318	C₂×D₄	—	2	1	no	—
319	C₂×D₄	—	2	1	no	—
320	C₂×D₄	C₂×D₄×C₁₃	1	3	yes	—
321	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
322	C₂²×C₄	—	2	6	no	—
323	C₂²×C₄	—	2	6	no	—
324	C₂²×C₄	—	2	6	no	—
325	C₂²×C₄	C₂×D₄×C₁₃	1	3	yes	—
326	C₂²×C₄	C₂×D₄×C₁₃	1	3	yes	—
327	C₂²×C₄	C₂⁴×C₁₃	1	3	yes	—
328	M₁₆	—	2	12	no	—
329	C₂×C₈	—	2	12	no	—
330	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
331	C₂×C₈	C₂⁴×C₁₃	1	6	yes	—
332	C₄⋊C₄	—	2	3	no	—
333	C₄⋊C₄	—	2	3	no	—
334	C₄⋊C₄	—	2	3	no	—
335	C₄⋊C₄	—	2	6	no	—
336	C₄⋊C₄	—	2	6	no	—
337	C₄⋊C₄	—	2	6	no	—
338	C₄⋊C₄	—	2	6	no	—
339	C₄⋊C₄	—	2	1	no	—
340	C₄⋊C₄	—	2	6	no	—
341	C₄⋊C₄	—	2	6	no	—
342	C₄⋊C₄	C₂×D₄×C₁₃	1	3	yes	—
343	C₄⋊C₄	C₂×D₄×C₁₃	1	3	yes	—
344	C₄⋊C₄	C₂⁴×C₁₃	1	6	yes	—
345	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
346	C₂²⋊C₄	—	2	6	no	—
347	C₂²⋊C₄	—	2	6	no	—
348	C₂²⋊C₄	—	2	6	no	—
349	C₂²⋊C₄	C₂×D₄×C₁₃	1	6	yes	—
350	C₄²	—	2	6	no	—
351	C₄²	C₂×D₄×C₁₃	1	3	yes	—
352	C₄²	C₂×D₄×C₁₃	1	3	yes	—
353	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
354	C₄²	C₂⁴×C₁₃	1	3	yes	—
355	C₁₃	#60623	1	1	yes	characteristic, direct product factor, Sylow
356	C₂³	—	2	2	no	—
357	C₂³	C₂²×D₄×C₁₃	1	3	yes	—
358	Q₈	—	2	12	no	—
359	Q₈	—	4	12	no	—
360	Q₈	—	4	6	no	—
361	Q₈	—	4	2	no	—
362	Q₈	—	8	6	no	—
363	Q₈	C₁₃×#124	1	4	yes	—
364	D₄	—	2	4	no	—
365	D₄	—	4	12	no	—
366	D₄	—	4	2	no	—
367	D₄	—	4	2	no	—
368	D₄	C₁₃×#124	1	12	yes	—
369	C₂×C₄	—	2	6	no	—
370	C₂×C₄	—	2	6	no	—
371	C₂×C₄	—	2	2	no	—
372	C₂×C₄	—	2	6	no	—
373	C₂×C₄	—	2	6	no	—
374	C₂×C₄	—	4	12	no	—
375	C₂×C₄	—	4	12	no	—
376	C₂×C₄	—	8	6	no	—
377	C₂×C₄	C₂²×D₄×C₁₃	1	3	yes	—
378	C₂×C₄	C₂²×D₄×C₁₃	1	3	yes	—
379	C₂×C₄	C₂²×D₄×C₁₃	1	3	yes	—
380	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
381	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
382	C₂×C₄	C₂×C₁₃×#41	1	12	yes	—
383	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
384	C₈	—	2	2	no	—
385	C₈	—	2	6	no	—
386	C₂²	—	2	3	no	—
387	C₂²	—	2	3	no	—
388	C₂²	—	4	2	no	—
389	C₂²	—	4	2	no	—
390	C₂²	—	4	2	no	—
391	C₂²	C₂×C₁₃×#124	1	6	yes	—
392	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
393	C₄	—	2	3	no	—
394	C₄	—	2	3	no	—
395	C₄	—	4	6	no	—
396	C₄	—	4	2	no	—
397	C₄	—	4	6	no	—
398	C₄	C₂×C₁₃×#124	1	6	yes	—
399	C₄	C₁₃×#577	1	2	yes	—
400	C₄	C₁₃×#578	1	2	yes	—
401	C₄	C₂²×C₁₃×#41	1	2	yes	—
402	C₂	—	2	6	no	—
403	C₂	—	8	2	no	—
404	C₂	C₂²×C₁₃×#124	1	1	yes	characteristic
405	C₂	C₂×C₁₃×#577	1	1	yes	characteristic
406	C₂	C₂×C₁₃×#578	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₃
prime radical	C₁₃×#3499	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₄×C₁₃×#41 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₃×#3503	C₂	semidirect
3. C₁₃×#3141	C₂	semidirect
4. C₁₃×#3139	C₂	semidirect
5. C₁₃×#3137	C₂	semidirect
6. C₁₃×#3131	C₂	semidirect
7. C₂×C₁₃×#487	C₂	semidirect
8. C₁₃×#2898	C₂	semidirect
9. C₄×C₁₃×#131	C₂	semidirect
102. #60623	C₁₃	direct (N × H)
153. #3503	C₂×C₁₃	semidirect
155. #3141	C₂×C₁₃	semidirect
156. #3139	C₂×C₁₃	semidirect
157. #3137	C₂×C₁₃	semidirect
158. #3131	C₂×C₁₃	semidirect
159. C₂×#487	C₂×C₁₃	semidirect
160. #2898	C₂×C₁₃	semidirect
161. C₄×#131	C₂×C₁₃	semidirect
355. C₁₃	#60623	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×#3503	2
C₁₃×#3499	2
C₁₃×#3141	2
C₁₃×#3139	2
C₁₃×#3137	2
C₁₃×#3131	2
C₂×C₁₃×#487	2
C₁₃×#2898	2
C₄×C₁₃×#131	2
#60623	13

Subgroups — C13×#60623 #15746962

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#60623 #15746962