Subgroups — C₁₃×#20822 #15707161

Order 3328.

810 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	C₂×C₁₃×#405	C₂	1	1	yes	maximal, characteristic
2	C₁₃×#2314	C₂	1	2	yes	maximal
3	C₁₃×#1847	C₂	1	2	yes	maximal, complemented
4	C₁₃×#1835	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#1834	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#1809	C₂	1	2	yes	maximal
7	C₁₃×#1808	C₂	1	1	yes	maximal, characteristic
8	C₁₃×#1807	C₂	1	1	yes	maximal, characteristic
9	C₁₃×#1776	C₂	1	2	yes	maximal, complemented
10	C₄×C₁₃×#107	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄×C₁₃×#106	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
13	C₂³×C₈×C₁₃	C₂²	1	1	yes	characteristic
14	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
15	C₂×C₁₃×#107	C₂²	1	2	yes	—
16	C₂×C₁₃×#107	C₂²	1	2	yes	—
17	C₂×C₁₃×#106	C₂²	1	2	yes	—
18	C₂×C₁₃×#106	C₂²	1	2	yes	—
19	C₁₃×#405	C₄	1	8	yes	complemented
20	C₂×C₁₃×#97	C₂²	1	1	yes	characteristic
21	C₂×C₁₃×#97	C₂²	1	1	yes	characteristic
22	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
23	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
24	C₁₃×#388	—	2	2	no	—
25	C₁₃×#388	—	2	2	no	—
26	C₁₃×#387	—	2	2	no	—
27	C₁₃×#387	—	2	2	no	—
28	C₁₃×#384	C₂²	1	2	yes	—
29	C₁₃×#382	C₂²	1	2	yes	—
30	C₁₃×#380	C₂²	1	2	yes	—
31	C₁₃×#380	C₂²	1	2	yes	—
32	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
33	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
34	C₁₃×#340	C₂²	1	1	yes	characteristic
35	C₁₃×#340	C₂²	1	1	yes	characteristic
36	C₁₃×#340	C₂²	1	1	yes	characteristic
37	C₁₃×#340	C₂²	1	1	yes	characteristic
38	C₁₃×#340	C₂²	1	2	yes	—
39	C₁₃×#340	C₂²	1	2	yes	—
40	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
41	C₂×C₁₃×M₁₆	—	2	4	no	—
42	C₂×C₁₃×M₁₆	C₂×C₄	1	4	yes	—
43	C₂²×C₈×C₁₃	—	2	4	no	—
44	C₂²×C₈×C₁₃	C₂×C₄	1	4	yes	—
45	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
46	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
47	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
48	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
49	C₁₃×#117	C₂×C₄	1	4	yes	—
50	C₁₃×#117	Q₈	1	4	yes	—
51	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
52	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
53	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
54	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
55	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
56	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
57	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
58	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
59	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
60	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
61	C₂×C₁₃×C₂²⋊C₄	D₄	1	1	yes	characteristic
62	C₂×C₁₃×C₂²⋊C₄	D₄	1	1	yes	characteristic
63	C₂×C₄²×C₁₃	—	2	2	no	—
64	C₂×C₄²×C₁₃	—	2	2	no	—
65	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
66	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
67	C₁₃×#107	—	2	4	no	—
68	C₁₃×#107	—	2	4	no	—
69	C₁₃×#106	—	2	4	no	—
70	C₁₃×#106	—	2	4	no	—
71	C₁₃×#97	C₂×C₄	1	4	yes	—
72	C₁₃×#97	C₂×C₄	1	4	yes	—
73	C₄×C₈×C₁₃	C₂×C₄	1	4	yes	—
74	C₄×C₈×C₁₃	C₂×C₄	1	4	yes	—
75	C₁₃×#95	—	2	2	no	—
76	C₁₃×#95	—	2	2	no	—
77	C₁₃×#95	—	2	2	no	—
78	C₁₃×#95	—	2	2	no	—
79	C₁₃×#95	—	2	2	no	—
80	C₁₃×#95	—	2	2	no	—
81	#20822	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
82	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
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	—	2	2	no	—
88	C₂²×C₄×C₁₃	—	2	2	no	—
89	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
90	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
91	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
92	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
93	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
94	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
95	C₂²×C₄×C₁₃	C₂×Q₈	1	2	yes	—
96	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
97	C₁₃×M₁₆	—	2	8	no	—
98	C₂×C₈×C₁₃	—	2	2	no	—
99	C₂×C₈×C₁₃	—	2	2	no	—
100	C₂×C₈×C₁₃	—	2	8	no	—
101	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
102	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
103	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
104	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
105	C₂×C₈×C₁₃	#41	1	4	yes	—
106	C₂×C₈×C₁₃	#41	1	4	yes	—
107	C₁₃×C₄⋊C₄	—	2	2	no	—
108	C₁₃×C₄⋊C₄	—	2	2	no	—
109	C₁₃×C₄⋊C₄	—	2	2	no	—
110	C₁₃×C₄⋊C₄	—	2	2	no	—
111	C₁₃×C₄⋊C₄	—	2	2	no	—
112	C₁₃×C₄⋊C₄	—	2	2	no	—
113	C₁₃×C₄⋊C₄	—	2	2	no	—
114	C₁₃×C₄⋊C₄	—	2	2	no	—
115	C₁₃×C₄⋊C₄	—	8	2	no	—
116	C₁₃×C₄⋊C₄	—	8	2	no	—
117	C₁₃×C₄⋊C₄	C₄⋊C₄	1	4	yes	—
118	C₁₃×C₄⋊C₄	C₄⋊C₄	1	4	yes	—
119	C₁₃×C₂²⋊C₄	—	8	2	no	—
120	C₁₃×C₂²⋊C₄	—	8	2	no	—
121	C₁₃×C₂²⋊C₄	C₄⋊C₄	1	4	yes	—
122	C₁₃×C₂²⋊C₄	C₄⋊C₄	1	4	yes	—
123	C₄²×C₁₃	—	8	2	no	—
124	C₄²×C₁₃	—	8	2	no	—
125	C₄²×C₁₃	C₂²×C₄	1	2	yes	—
126	C₄²×C₁₃	C₂²×C₄	1	2	yes	—
127	C₄²×C₁₃	C₂×Q₈	1	2	yes	—
128	C₄²×C₁₃	C₂×Q₈	1	2	yes	—
129	C₂×#405	C₂×C₁₃	1	1	yes	characteristic
130	#2314	C₂×C₁₃	1	2	yes	—
131	#1847	C₂×C₁₃	1	2	yes	complemented
132	#1835	C₂×C₁₃	1	1	yes	characteristic, complemented
133	#1834	C₂×C₁₃	1	1	yes	characteristic, complemented
134	#1809	C₂×C₁₃	1	2	yes	—
135	#1808	C₂×C₁₃	1	1	yes	characteristic
136	#1807	C₂×C₁₃	1	1	yes	characteristic
137	#1776	C₂×C₁₃	1	2	yes	complemented
138	C₄×#107	C₂×C₁₃	1	1	yes	characteristic, complemented
139	C₄×#106	C₂×C₁₃	1	1	yes	characteristic, complemented
140	C₂³×C₁₃	—	2	2	no	—
141	C₂³×C₁₃	—	2	1	no	—
142	C₂³×C₁₃	—	2	2	no	—
143	C₂³×C₁₃	—	2	1	no	—
144	C₂³×C₁₃	C₂×C₄⋊C₄	1	2	yes	—
145	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
146	C₂×C₄×C₁₃	—	2	2	no	—
147	C₂×C₄×C₁₃	—	2	1	no	—
148	C₂×C₄×C₁₃	—	2	1	no	—
149	C₂×C₄×C₁₃	—	2	2	no	—
150	C₂×C₄×C₁₃	—	2	2	no	—
151	C₂×C₄×C₁₃	—	2	1	no	—
152	C₂×C₄×C₁₃	—	2	1	no	—
153	C₂×C₄×C₁₃	—	2	2	no	—
154	C₂×C₄×C₁₃	—	2	2	no	—
155	C₂×C₄×C₁₃	—	2	4	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	—	4	2	no	—
162	C₂×C₄×C₁₃	—	4	2	no	—
163	C₂×C₄×C₁₃	—	4	2	no	—
164	C₂×C₄×C₁₃	—	4	2	no	—
165	C₂×C₄×C₁₃	—	4	2	no	—
166	C₂×C₄×C₁₃	—	4	2	no	—
167	C₂×C₄×C₁₃	—	4	2	no	—
168	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	2	yes	—
169	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	2	yes	—
170	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	2	yes	—
171	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	2	yes	—
172	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	2	yes	—
173	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
174	C₂×C₄×C₁₃	C₂²×Q₈	1	1	yes	characteristic
175	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
176	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
177	C₈×C₁₃	—	2	2	no	—
178	C₈×C₁₃	—	2	2	no	—
179	C₈×C₁₃	#117	1	4	yes	—
180	C₈×C₁₃	#117	1	4	yes	—
181	C₂²×M₁₆	C₂²×C₁₃	1	1	yes	characteristic
182	C₂³×C₈	C₂²×C₁₃	1	1	yes	characteristic
183	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
184	C₂×#107	C₂²×C₁₃	1	2	yes	—
185	C₂×#107	C₂²×C₁₃	1	2	yes	—
186	C₂×#106	C₂²×C₁₃	1	2	yes	—
187	C₂×#106	C₂²×C₁₃	1	2	yes	—
188	#405	C₄×C₁₃	1	8	yes	complemented
189	C₂×#97	C₂²×C₁₃	1	1	yes	characteristic
190	C₂×#97	C₂²×C₁₃	1	1	yes	characteristic
191	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
192	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
193	#388	—	2	2	no	—
194	#388	—	2	2	no	—
195	#387	—	2	2	no	—
196	#387	—	2	2	no	—
197	#384	C₂²×C₁₃	1	2	yes	—
198	#382	C₂²×C₁₃	1	2	yes	—
199	#380	C₂²×C₁₃	1	2	yes	—
200	#380	C₂²×C₁₃	1	2	yes	—
201	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
202	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
203	#340	C₂²×C₁₃	1	1	yes	characteristic
204	#340	C₂²×C₁₃	1	1	yes	characteristic
205	#340	C₂²×C₁₃	1	1	yes	characteristic
206	#340	C₂²×C₁₃	1	1	yes	characteristic
207	#340	C₂²×C₁₃	1	2	yes	—
208	#340	C₂²×C₁₃	1	2	yes	—
209	C₂²×C₁₃	—	2	2	no	—
210	C₂²×C₁₃	—	2	2	no	—
211	C₂²×C₁₃	—	2	2	no	—
212	C₂²×C₁₃	—	4	2	no	—
213	C₂²×C₁₃	—	4	2	no	—
214	C₂²×C₁₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
215	C₂²×C₁₃	#532	1	2	yes	—
216	C₂²×C₁₃	#576	1	1	yes	characteristic
217	C₂²×C₁₃	#577	1	2	yes	—
218	C₂²×C₁₃	#578	1	1	yes	characteristic
219	C₄×C₁₃	—	2	2	no	—
220	C₄×C₁₃	—	2	2	no	—
221	C₄×C₁₃	—	2	2	no	—
222	C₄×C₁₃	—	2	2	no	—
223	C₄×C₁₃	—	2	2	no	—
224	C₄×C₁₃	—	8	2	no	—
225	C₄×C₁₃	—	8	2	no	—
226	C₄×C₁₃	—	8	2	no	—
227	C₄×C₁₃	—	8	2	no	—
228	C₄×C₁₃	C₂×#117	1	1	yes	characteristic
229	C₄×C₁₃	C₂×#117	1	1	yes	characteristic
230	C₄×C₁₃	#533	1	2	yes	—
231	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
232	C₂×M₁₆	—	2	4	no	—
233	C₂×M₁₆	C₂×C₄×C₁₃	1	4	yes	—
234	C₂²×C₈	—	2	4	no	—
235	C₂²×C₈	C₂×C₄×C₁₃	1	4	yes	—
236	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
237	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
238	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
239	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
240	#117	C₂×C₄×C₁₃	1	4	yes	—
241	#117	Q₈×C₁₃	1	4	yes	—
242	C₂×C₄⋊C₄	—	2	2	no	—
243	C₂×C₄⋊C₄	—	2	2	no	—
244	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
245	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
246	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
247	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
248	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
249	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
250	C₂×C₂²⋊C₄	—	2	2	no	—
251	C₂×C₂²⋊C₄	—	2	2	no	—
252	C₂×C₂²⋊C₄	D₄×C₁₃	1	1	yes	characteristic
253	C₂×C₂²⋊C₄	D₄×C₁₃	1	1	yes	characteristic
254	C₂×C₄²	—	2	2	no	—
255	C₂×C₄²	—	2	2	no	—
256	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
257	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
258	#107	—	2	4	no	—
259	#107	—	2	4	no	—
260	#106	—	2	4	no	—
261	#106	—	2	4	no	—
262	#97	C₂×C₄×C₁₃	1	4	yes	—
263	#97	C₂×C₄×C₁₃	1	4	yes	—
264	C₄×C₈	C₂×C₄×C₁₃	1	4	yes	—
265	C₄×C₈	C₂×C₄×C₁₃	1	4	yes	—
266	#95	—	2	2	no	—
267	#95	—	2	2	no	—
268	#95	—	2	2	no	—
269	#95	—	2	2	no	—
270	#95	—	2	2	no	—
271	#95	—	2	2	no	—
272	C₂×C₁₃	—	4	2	no	—
273	C₂×C₁₃	#2285	1	1	yes	characteristic
274	C₂×C₁₃	#2912	1	1	yes	characteristic
275	C₂×C₁₃	#2913	1	1	yes	characteristic
276	C₂×C₁₃	#3178	1	2	yes	—
277	C₂×C₁₃	#3179	1	2	yes	—
278	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
279	C₂²×C₄	—	2	2	no	—
280	C₂²×C₄	—	2	2	no	—
281	C₂²×C₄	—	2	2	no	—
282	C₂²×C₄	—	2	2	no	—
283	C₂²×C₄	—	2	2	no	—
284	C₂²×C₄	—	2	2	no	—
285	C₂²×C₄	C₂²×C₄×C₁₃	1	2	yes	—
286	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
287	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
288	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
289	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
290	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
291	C₂²×C₄	C₂×Q₈×C₁₃	1	2	yes	—
292	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
293	M₁₆	—	2	8	no	—
294	C₂×C₈	—	2	2	no	—
295	C₂×C₈	—	2	2	no	—
296	C₂×C₈	—	2	8	no	—
297	C₂×C₈	C₂²×C₄×C₁₃	1	2	yes	—
298	C₂×C₈	C₂²×C₄×C₁₃	1	2	yes	—
299	C₂×C₈	C₂²×C₄×C₁₃	1	2	yes	—
300	C₂×C₈	C₂²×C₄×C₁₃	1	2	yes	—
301	C₂×C₈	C₁₃×#41	1	4	yes	—
302	C₂×C₈	C₁₃×#41	1	4	yes	—
303	C₄⋊C₄	—	2	2	no	—
304	C₄⋊C₄	—	2	2	no	—
305	C₄⋊C₄	—	2	2	no	—
306	C₄⋊C₄	—	2	2	no	—
307	C₄⋊C₄	—	2	2	no	—
308	C₄⋊C₄	—	2	2	no	—
309	C₄⋊C₄	—	2	2	no	—
310	C₄⋊C₄	—	2	2	no	—
311	C₄⋊C₄	—	8	2	no	—
312	C₄⋊C₄	—	8	2	no	—
313	C₄⋊C₄	C₁₃×C₄⋊C₄	1	4	yes	—
314	C₄⋊C₄	C₁₃×C₄⋊C₄	1	4	yes	—
315	C₂²⋊C₄	—	8	2	no	—
316	C₂²⋊C₄	—	8	2	no	—
317	C₂²⋊C₄	C₁₃×C₄⋊C₄	1	4	yes	—
318	C₂²⋊C₄	C₁₃×C₄⋊C₄	1	4	yes	—
319	C₄²	—	8	2	no	—
320	C₄²	—	8	2	no	—
321	C₄²	C₂²×C₄×C₁₃	1	2	yes	—
322	C₄²	C₂²×C₄×C₁₃	1	2	yes	—
323	C₄²	C₂×Q₈×C₁₃	1	2	yes	—
324	C₄²	C₂×Q₈×C₁₃	1	2	yes	—
325	C₁₃	#20822	1	1	yes	characteristic, direct product factor, Sylow
326	C₂³	—	2	2	no	—
327	C₂³	—	2	1	no	—
328	C₂³	—	2	2	no	—
329	C₂³	—	2	1	no	—
330	C₂³	C₂×C₁₃×C₄⋊C₄	1	2	yes	—
331	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
332	C₂×C₄	—	2	2	no	—
333	C₂×C₄	—	2	1	no	—
334	C₂×C₄	—	2	1	no	—
335	C₂×C₄	—	2	2	no	—
336	C₂×C₄	—	2	2	no	—
337	C₂×C₄	—	2	1	no	—
338	C₂×C₄	—	2	1	no	—
339	C₂×C₄	—	2	2	no	—
340	C₂×C₄	—	2	2	no	—
341	C₂×C₄	—	2	4	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	—	4	2	no	—
348	C₂×C₄	—	4	2	no	—
349	C₂×C₄	—	4	2	no	—
350	C₂×C₄	—	4	2	no	—
351	C₂×C₄	—	4	2	no	—
352	C₂×C₄	—	4	2	no	—
353	C₂×C₄	—	4	2	no	—
354	C₂×C₄	C₂×C₁₃×C₄⋊C₄	1	2	yes	—
355	C₂×C₄	C₂×C₁₃×C₄⋊C₄	1	2	yes	—
356	C₂×C₄	C₂×C₁₃×C₄⋊C₄	1	2	yes	—
357	C₂×C₄	C₂×C₁₃×C₄⋊C₄	1	2	yes	—
358	C₂×C₄	C₂×C₁₃×C₄⋊C₄	1	2	yes	—
359	C₂×C₄	C₂³×C₄×C₁₃	1	1	yes	characteristic
360	C₂×C₄	C₂²×Q₈×C₁₃	1	1	yes	characteristic
361	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
362	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
363	C₈	—	2	2	no	—
364	C₈	—	2	2	no	—
365	C₈	C₁₃×#117	1	4	yes	—
366	C₈	C₁₃×#117	1	4	yes	—
367	C₂²	—	2	2	no	—
368	C₂²	—	2	2	no	—
369	C₂²	—	2	2	no	—
370	C₂²	—	4	2	no	—
371	C₂²	—	4	2	no	—
372	C₂²	C₂²×C₁₃×C₄⋊C₄	1	1	yes	characteristic
373	C₂²	C₁₃×#532	1	2	yes	—
374	C₂²	C₁₃×#576	1	1	yes	characteristic
375	C₂²	C₁₃×#577	1	2	yes	—
376	C₂²	C₁₃×#578	1	1	yes	characteristic
377	C₄	—	2	2	no	—
378	C₄	—	2	2	no	—
379	C₄	—	2	2	no	—
380	C₄	—	2	2	no	—
381	C₄	—	2	2	no	—
382	C₄	—	8	2	no	—
383	C₄	—	8	2	no	—
384	C₄	—	8	2	no	—
385	C₄	—	8	2	no	—
386	C₄	C₂×C₁₃×#117	1	1	yes	characteristic
387	C₄	C₂×C₁₃×#117	1	1	yes	characteristic
388	C₄	C₁₃×#533	1	2	yes	—
389	C₂	—	4	2	no	—
390	C₂	C₁₃×#2285	1	1	yes	characteristic
391	C₂	C₁₃×#2912	1	1	yes	characteristic
392	C₂	C₁₃×#2913	1	1	yes	characteristic
393	C₂	C₁₃×#3178	1	2	yes	—
394	C₂	C₁₃×#3179	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₁₃
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
prime radical	C₂⁴×C₁₃	C₂×D₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ C₂×C₁₃×#117 ◁ G

Complements

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

N	H ≅ G/N	type
3. C₁₃×#1847	C₂	semidirect
4. C₁₃×#1835	C₂	semidirect
5. C₁₃×#1834	C₂	semidirect
9. C₁₃×#1776	C₂	semidirect
10. C₄×C₁₃×#107	C₂	semidirect
11. C₄×C₁₃×#106	C₂	semidirect
19. C₁₃×#405	C₄	semidirect
81. #20822	C₁₃	direct (N × H)
131. #1847	C₂×C₁₃	semidirect
132. #1835	C₂×C₁₃	semidirect
133. #1834	C₂×C₁₃	semidirect
137. #1776	C₂×C₁₃	semidirect
138. C₄×#107	C₂×C₁₃	semidirect
139. C₄×#106	C₂×C₁₃	semidirect
188. #405	C₄×C₁₃	semidirect
325. C₁₃	#20822	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×C₁₃×#405	2
C₁₃×#2314	2
C₁₃×#1847	2
C₁₃×#1835	2
C₁₃×#1834	2
C₁₃×#1809	2
C₁₃×#1808	2
C₁₃×#1807	2
C₁₃×#1776	2
C₄×C₁₃×#107	2
C₄×C₁₃×#106	2
#20822	13

Subgroups — C13×#20822 #15707161

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#20822 #15707161