Subgroups — C₁₃×#22735 #15709074

Order 3328.

740 conjugacy classes of subgroups.

The subgroup lattice has 422 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#446	C₂	1	1	yes	maximal, characteristic
2	C₂×C₈×Q₈×C₁₃	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#2295	C₂	1	1	yes	maximal, characteristic
4	C₁₃×#1940	C₂	1	2	yes	maximal
5	C₁₃×#1939	C₂	1	1	yes	maximal, characteristic
6	C₁₃×#1939	C₂	1	1	yes	maximal, characteristic
7	C₁₃×#1939	C₂	1	2	yes	maximal
8	C₁₃×#1832	C₂	1	2	yes	maximal
9	C₁₃×#1831	C₂	1	1	yes	maximal, characteristic
10	C₁₃×#1768	C₂	1	2	yes	maximal
11	C₄×C₁₃×C₄⋊C₈	C₂	1	1	yes	maximal, characteristic
12	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
13	C₁₃×#446	—	2	4	no	—
14	C₈×Q₈×C₁₃	—	2	4	no	—
15	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
16	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
17	C₂×C₁₃×C₄⋊C₈	C₂²	1	2	yes	—
18	C₂×C₁₃×C₄⋊C₈	C₂²	1	2	yes	—
19	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
20	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
21	C₂×C₁₃×C₄⋊C₈	C₂²	1	2	yes	—
22	C₂×C₁₃×C₄⋊C₈	C₂²	1	2	yes	—
23	C₂×C₁₃×#97	C₂²	1	2	yes	—
24	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
25	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
26	C₂×C₄×C₈×C₁₃	C₂²	1	2	yes	—
27	C₁₃×#391	C₄	1	1	yes	characteristic
28	C₁₃×#391	C₄	1	1	yes	characteristic
29	C₁₃×#389	C₄	1	1	yes	characteristic
30	C₁₃×#389	C₄	1	1	yes	characteristic
31	C₁₃×#387	C₄	1	2	yes	—
32	C₁₃×#387	C₄	1	2	yes	—
33	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
34	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
35	C₁₃×#376	C₂²	1	2	yes	—
36	C₄³×C₁₃	C₂²	1	1	yes	characteristic
37	C₁₃×#336	C₂²	1	1	yes	characteristic
38	C₁₃×#336	C₂²	1	1	yes	characteristic
39	C₁₃×#336	C₂²	1	2	yes	—
40	C₁₃×#336	C₂²	1	2	yes	—
41	C₁₃×#336	C₂²	1	2	yes	—
42	C₁₃×#336	C₂²	1	2	yes	—
43	C₂²×Q₈×C₁₃	C₂×C₄	1	1	yes	characteristic
44	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
45	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
46	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
47	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
48	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
49	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
50	C₄×Q₈×C₁₃	D₄	1	4	yes	—
51	C₄×Q₈×C₁₃	Q₈	1	4	yes	—
52	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	2	yes	—
53	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
54	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
55	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	2	yes	—
56	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	2	yes	—
57	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
58	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
59	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
60	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
61	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
62	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
63	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
64	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
65	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
66	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
67	C₁₃×C₄⋊C₈	—	2	2	no	—
68	C₁₃×C₄⋊C₈	—	2	2	no	—
69	C₁₃×C₄⋊C₈	—	2	4	no	—
70	C₁₃×C₄⋊C₈	—	2	4	no	—
71	C₁₃×C₄⋊C₈	—	2	2	no	—
72	C₁₃×C₄⋊C₈	—	2	4	no	—
73	C₁₃×C₄⋊C₈	—	2	2	no	—
74	C₁₃×C₄⋊C₈	—	2	4	no	—
75	C₁₃×#97	—	2	4	no	—
76	C₄×C₈×C₁₃	—	2	2	no	—
77	C₄×C₈×C₁₃	—	2	4	no	—
78	C₄×C₈×C₁₃	—	2	2	no	—
79	C₁₃×#95	C₂×C₄	1	2	yes	—
80	C₁₃×#95	C₂×C₄	1	2	yes	—
81	C₁₃×#95	C₂×C₄	1	2	yes	—
82	C₁₃×#95	C₂×C₄	1	2	yes	—
83	C₁₃×#95	C₂×C₄	1	2	yes	—
84	C₁₃×#95	C₂×C₄	1	2	yes	—
85	C₁₃×#95	C₂×C₄	1	2	yes	—
86	#22735	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
87	C₂×Q₈×C₁₃	—	2	2	no	—
88	C₂×Q₈×C₁₃	—	2	2	no	—
89	C₂×Q₈×C₁₃	C₄⋊C₄	1	4	yes	—
90	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
91	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
92	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
93	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
94	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
95	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
96	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
97	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
98	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
99	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
100	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
101	C₂×C₈×C₁₃	—	2	1	no	—
102	C₂×C₈×C₁₃	—	2	1	no	—
103	C₂×C₈×C₁₃	—	2	1	no	—
104	C₂×C₈×C₁₃	—	2	1	no	—
105	C₂×C₈×C₁₃	—	2	1	no	—
106	C₂×C₈×C₁₃	—	2	2	no	—
107	C₂×C₈×C₁₃	—	2	1	no	—
108	C₂×C₈×C₁₃	—	2	2	no	—
109	C₂×C₈×C₁₃	—	2	1	no	—
110	C₂×C₈×C₁₃	—	2	1	no	—
111	C₂×C₈×C₁₃	—	2	2	no	—
112	C₂×C₈×C₁₃	—	2	2	no	—
113	C₂×C₈×C₁₃	—	2	1	no	—
114	C₂×C₈×C₁₃	—	2	1	no	—
115	C₂×C₈×C₁₃	—	2	2	no	—
116	C₂×C₈×C₁₃	—	2	2	no	—
117	C₂×C₈×C₁₃	#41	1	2	yes	—
118	C₂×C₈×C₁₃	#41	1	2	yes	—
119	C₁₃×C₄⋊C₄	—	2	4	no	—
120	C₁₃×C₄⋊C₄	—	2	2	no	—
121	C₁₃×C₄⋊C₄	—	2	2	no	—
122	C₁₃×C₄⋊C₄	—	4	2	no	—
123	C₁₃×C₄⋊C₄	C₄⋊C₄	1	8	yes	—
124	C₁₃×C₄⋊C₄	C₄⋊C₄	1	4	yes	—
125	C₄²×C₁₃	—	2	2	no	—
126	C₄²×C₁₃	—	2	2	no	—
127	C₄²×C₁₃	—	2	2	no	—
128	C₄²×C₁₃	—	2	1	no	—
129	C₄²×C₁₃	—	2	1	no	—
130	C₄²×C₁₃	—	2	2	no	—
131	C₄²×C₁₃	—	2	2	no	—
132	C₄²×C₁₃	—	2	1	no	—
133	C₄²×C₁₃	—	2	1	no	—
134	C₄²×C₁₃	—	4	1	no	—
135	C₄²×C₁₃	C₂×D₄	1	2	yes	—
136	C₄²×C₁₃	C₂×D₄	1	4	yes	—
137	C₄²×C₁₃	C₂×Q₈	1	4	yes	—
138	C₄²×C₁₃	C₂×Q₈	1	2	yes	—
139	C₂×#446	C₂×C₁₃	1	1	yes	characteristic
140	C₂×C₈×Q₈	C₂×C₁₃	1	1	yes	characteristic
141	#2295	C₂×C₁₃	1	1	yes	characteristic
142	#1940	C₂×C₁₃	1	2	yes	—
143	#1939	C₂×C₁₃	1	2	yes	—
144	#1939	C₂×C₁₃	1	1	yes	characteristic
145	#1939	C₂×C₁₃	1	1	yes	characteristic
146	#1832	C₂×C₁₃	1	2	yes	—
147	#1831	C₂×C₁₃	1	1	yes	characteristic
148	#1768	C₂×C₁₃	1	2	yes	—
149	C₄×C₄⋊C₈	C₂×C₁₃	1	1	yes	characteristic
150	C₂³×C₁₃	C₂³×C₄	1	1	yes	characteristic
151	Q₈×C₁₃	—	2	8	no	—
152	C₂×C₄×C₁₃	—	2	1	no	—
153	C₂×C₄×C₁₃	—	2	1	no	—
154	C₂×C₄×C₁₃	—	2	1	no	—
155	C₂×C₄×C₁₃	—	2	2	no	—
156	C₂×C₄×C₁₃	—	2	2	no	—
157	C₂×C₄×C₁₃	—	2	2	no	—
158	C₂×C₄×C₁₃	—	2	1	no	—
159	C₂×C₄×C₁₃	—	2	2	no	—
160	C₂×C₄×C₁₃	—	2	2	no	—
161	C₂×C₄×C₁₃	—	2	2	no	—
162	C₂×C₄×C₁₃	—	2	1	no	—
163	C₂×C₄×C₁₃	—	2	1	no	—
164	C₂×C₄×C₁₃	—	2	1	no	—
165	C₂×C₄×C₁₃	—	2	1	no	—
166	C₂×C₄×C₁₃	—	2	1	no	—
167	C₂×C₄×C₁₃	—	2	1	no	—
168	C₂×C₄×C₁₃	—	2	1	no	—
169	C₂×C₄×C₁₃	—	2	2	no	—
170	C₂×C₄×C₁₃	—	2	2	no	—
171	C₂×C₄×C₁₃	—	2	2	no	—
172	C₂×C₄×C₁₃	—	2	1	no	—
173	C₂×C₄×C₁₃	—	2	1	no	—
174	C₂×C₄×C₁₃	—	2	2	no	—
175	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	2	yes	—
176	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	4	yes	—
177	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	4	yes	—
178	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	2	yes	—
179	C₂×C₄×C₁₃	#131	1	2	yes	—
180	C₂×C₄×C₁₃	#131	1	2	yes	—
181	C₂×C₄×C₁₃	#131	1	2	yes	—
182	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
183	C₂×C₄×C₁₃	C₂²×Q₈	1	1	yes	characteristic
184	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
185	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
186	C₂×C₄×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
187	C₂×C₄×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
188	C₈×C₁₃	—	2	2	no	—
189	C₈×C₁₃	—	2	2	no	—
190	C₈×C₁₃	—	4	1	no	—
191	C₈×C₁₃	—	4	2	no	—
192	C₈×C₁₃	—	4	1	no	—
193	C₈×C₁₃	—	4	2	no	—
194	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
195	#446	—	2	4	no	—
196	C₈×Q₈	—	2	4	no	—
197	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
198	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
199	C₂×C₄⋊C₈	C₂²×C₁₃	1	2	yes	—
200	C₂×C₄⋊C₈	C₂²×C₁₃	1	2	yes	—
201	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
202	C₂×C₄⋊C₈	C₂²×C₁₃	1	2	yes	—
203	C₂×C₄⋊C₈	C₂²×C₁₃	1	2	yes	—
204	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
205	C₂×#97	C₂²×C₁₃	1	2	yes	—
206	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
207	C₂×C₄×C₈	C₂²×C₁₃	1	2	yes	—
208	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
209	#391	C₄×C₁₃	1	1	yes	characteristic
210	#391	C₄×C₁₃	1	1	yes	characteristic
211	#389	C₄×C₁₃	1	1	yes	characteristic
212	#389	C₄×C₁₃	1	1	yes	characteristic
213	#387	C₄×C₁₃	1	2	yes	—
214	#387	C₄×C₁₃	1	2	yes	—
215	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
216	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
217	#376	C₂²×C₁₃	1	2	yes	—
218	C₄³	C₂²×C₁₃	1	1	yes	characteristic
219	#336	C₂²×C₁₃	1	2	yes	—
220	#336	C₂²×C₁₃	1	2	yes	—
221	#336	C₂²×C₁₃	1	1	yes	characteristic
222	#336	C₂²×C₁₃	1	2	yes	—
223	#336	C₂²×C₁₃	1	2	yes	—
224	#336	C₂²×C₁₃	1	1	yes	characteristic
225	C₂²×C₁₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
226	C₂²×C₁₃	C₄×#41	1	1	yes	characteristic
227	C₂²×C₁₃	#519	1	1	yes	characteristic
228	C₂²×C₁₃	C₂×#131	1	1	yes	characteristic
229	C₂²×C₁₃	C₂×#131	1	1	yes	characteristic
230	C₂²×C₁₃	C₂×#131	1	1	yes	characteristic
231	C₂²×C₁₃	#568	1	1	yes	characteristic
232	C₄×C₁₃	—	2	4	no	—
233	C₄×C₁₃	—	2	2	no	—
234	C₄×C₁₃	—	2	4	no	—
235	C₄×C₁₃	—	2	2	no	—
236	C₄×C₁₃	—	4	2	no	—
237	C₄×C₁₃	—	4	1	no	—
238	C₄×C₁₃	—	4	2	no	—
239	C₄×C₁₃	—	4	1	no	—
240	C₄×C₁₃	—	4	1	no	—
241	C₄×C₁₃	#424	1	4	yes	—
242	C₄×C₁₃	#548	1	1	yes	characteristic
243	C₄×C₁₃	#548	1	1	yes	characteristic
244	C₄×C₁₃	#557	1	1	yes	characteristic
245	C₄×C₁₃	#557	1	1	yes	characteristic
246	C₂²×Q₈	C₂×C₄×C₁₃	1	1	yes	characteristic
247	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
248	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
249	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
250	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
251	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
252	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
253	C₄×Q₈	D₄×C₁₃	1	4	yes	—
254	C₄×Q₈	Q₈×C₁₃	1	4	yes	—
255	C₂×C₄⋊C₄	C₂×C₄×C₁₃	1	2	yes	—
256	C₂×C₄⋊C₄	C₂×C₄×C₁₃	1	1	yes	characteristic
257	C₂×C₄⋊C₄	C₂×C₄×C₁₃	1	1	yes	characteristic
258	C₂×C₄⋊C₄	C₂×C₄×C₁₃	1	2	yes	—
259	C₂×C₄⋊C₄	C₂×C₄×C₁₃	1	2	yes	—
260	C₂×C₄⋊C₄	C₂×C₄×C₁₃	1	1	yes	characteristic
261	C₂×C₄²	C₂×C₄×C₁₃	1	1	yes	characteristic
262	C₂×C₄²	C₂×C₄×C₁₃	1	1	yes	characteristic
263	C₂×C₄²	C₂×C₄×C₁₃	1	1	yes	characteristic
264	C₂×C₄²	C₂×C₄×C₁₃	1	1	yes	characteristic
265	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
266	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
267	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
268	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
269	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
270	C₄⋊C₈	—	2	2	no	—
271	C₄⋊C₈	—	2	4	no	—
272	C₄⋊C₈	—	2	4	no	—
273	C₄⋊C₈	—	2	2	no	—
274	C₄⋊C₈	—	2	2	no	—
275	C₄⋊C₈	—	2	4	no	—
276	C₄⋊C₈	—	2	2	no	—
277	C₄⋊C₈	—	2	4	no	—
278	#97	—	2	4	no	—
279	C₄×C₈	—	2	2	no	—
280	C₄×C₈	—	2	4	no	—
281	C₄×C₈	—	2	2	no	—
282	#95	C₂×C₄×C₁₃	1	2	yes	—
283	#95	C₂×C₄×C₁₃	1	2	yes	—
284	#95	C₂×C₄×C₁₃	1	2	yes	—
285	#95	C₂×C₄×C₁₃	1	2	yes	—
286	#95	C₂×C₄×C₁₃	1	2	yes	—
287	#95	C₂×C₄×C₁₃	1	2	yes	—
288	#95	C₂×C₄×C₁₃	1	2	yes	—
289	C₂×C₁₃	#2351	1	1	yes	characteristic
290	C₂×C₁₃	C₂×#424	1	1	yes	characteristic
291	C₂×C₁₃	#2906	1	1	yes	characteristic
292	C₂×C₁₃	#2966	1	1	yes	characteristic
293	C₂×C₁₃	#2969	1	1	yes	characteristic
294	C₂×C₁₃	#2985	1	1	yes	characteristic
295	C₂×C₁₃	#2986	1	1	yes	characteristic
296	C₂×Q₈	—	2	2	no	—
297	C₂×Q₈	—	2	2	no	—
298	C₂×Q₈	C₁₃×C₄⋊C₄	1	4	yes	—
299	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
300	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
301	C₂²×C₄	C₂²×C₄×C₁₃	1	2	yes	—
302	C₂²×C₄	C₂²×C₄×C₁₃	1	2	yes	—
303	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
304	C₂²×C₄	C₂²×C₄×C₁₃	1	2	yes	—
305	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
306	C₂²×C₄	C₂²×C₄×C₁₃	1	2	yes	—
307	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
308	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
309	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
310	C₂×C₈	—	2	1	no	—
311	C₂×C₈	—	2	1	no	—
312	C₂×C₈	—	2	1	no	—
313	C₂×C₈	—	2	1	no	—
314	C₂×C₈	—	2	1	no	—
315	C₂×C₈	—	2	2	no	—
316	C₂×C₈	—	2	1	no	—
317	C₂×C₈	—	2	2	no	—
318	C₂×C₈	—	2	1	no	—
319	C₂×C₈	—	2	2	no	—
320	C₂×C₈	—	2	1	no	—
321	C₂×C₈	—	2	2	no	—
322	C₂×C₈	—	2	2	no	—
323	C₂×C₈	—	2	1	no	—
324	C₂×C₈	—	2	1	no	—
325	C₂×C₈	—	2	2	no	—
326	C₂×C₈	C₁₃×#41	1	2	yes	—
327	C₂×C₈	C₁₃×#41	1	2	yes	—
328	C₄⋊C₄	—	2	4	no	—
329	C₄⋊C₄	—	2	2	no	—
330	C₄⋊C₄	—	2	2	no	—
331	C₄⋊C₄	—	4	2	no	—
332	C₄⋊C₄	C₁₃×C₄⋊C₄	1	8	yes	—
333	C₄⋊C₄	C₁₃×C₄⋊C₄	1	4	yes	—
334	C₄²	—	2	2	no	—
335	C₄²	—	2	2	no	—
336	C₄²	—	2	2	no	—
337	C₄²	—	2	1	no	—
338	C₄²	—	2	1	no	—
339	C₄²	—	2	2	no	—
340	C₄²	—	2	2	no	—
341	C₄²	—	2	1	no	—
342	C₄²	—	2	1	no	—
343	C₄²	—	4	1	no	—
344	C₄²	C₂×D₄×C₁₃	1	2	yes	—
345	C₄²	C₂×D₄×C₁₃	1	4	yes	—
346	C₄²	C₂×Q₈×C₁₃	1	4	yes	—
347	C₄²	C₂×Q₈×C₁₃	1	2	yes	—
348	C₁₃	#22735	1	1	yes	characteristic, direct product factor, Sylow
349	C₂³	C₂³×C₄×C₁₃	1	1	yes	characteristic
350	Q₈	—	2	8	no	—
351	C₂×C₄	—	2	1	no	—
352	C₂×C₄	—	2	1	no	—
353	C₂×C₄	—	2	1	no	—
354	C₂×C₄	—	2	2	no	—
355	C₂×C₄	—	2	2	no	—
356	C₂×C₄	—	2	2	no	—
357	C₂×C₄	—	2	1	no	—
358	C₂×C₄	—	2	2	no	—
359	C₂×C₄	—	2	2	no	—
360	C₂×C₄	—	2	2	no	—
361	C₂×C₄	—	2	1	no	—
362	C₂×C₄	—	2	1	no	—
363	C₂×C₄	—	2	1	no	—
364	C₂×C₄	—	2	1	no	—
365	C₂×C₄	—	2	1	no	—
366	C₂×C₄	—	2	1	no	—
367	C₂×C₄	—	2	1	no	—
368	C₂×C₄	—	2	2	no	—
369	C₂×C₄	—	2	2	no	—
370	C₂×C₄	—	2	2	no	—
371	C₂×C₄	—	2	1	no	—
372	C₂×C₄	—	2	1	no	—
373	C₂×C₄	—	2	2	no	—
374	C₂×C₄	C₂×C₁₃×C₄⋊C₄	1	2	yes	—
375	C₂×C₄	C₂×C₁₃×C₄⋊C₄	1	4	yes	—
376	C₂×C₄	C₂×C₁₃×C₄⋊C₄	1	4	yes	—
377	C₂×C₄	C₂×C₁₃×C₄⋊C₄	1	2	yes	—
378	C₂×C₄	C₁₃×#131	1	2	yes	—
379	C₂×C₄	C₁₃×#131	1	2	yes	—
380	C₂×C₄	C₁₃×#131	1	2	yes	—
381	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
382	C₂×C₄	C₂²×Q₈×C₁₃	1	1	yes	characteristic
383	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
384	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
385	C₂×C₄	C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
386	C₂×C₄	C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
387	C₈	—	2	2	no	—
388	C₈	—	2	2	no	—
389	C₈	—	4	1	no	—
390	C₈	—	4	2	no	—
391	C₈	—	4	1	no	—
392	C₈	—	4	2	no	—
393	C₂²	C₂²×C₁₃×C₄⋊C₄	1	1	yes	characteristic
394	C₂²	C₄×C₁₃×#41	1	1	yes	characteristic
395	C₂²	C₁₃×#519	1	1	yes	characteristic
396	C₂²	C₂×C₁₃×#131	1	1	yes	characteristic
397	C₂²	C₂×C₁₃×#131	1	1	yes	characteristic
398	C₂²	C₂×C₁₃×#131	1	1	yes	characteristic
399	C₂²	C₁₃×#568	1	1	yes	characteristic
400	C₄	—	2	4	no	—
401	C₄	—	2	2	no	—
402	C₄	—	2	4	no	—
403	C₄	—	2	2	no	—
404	C₄	—	4	2	no	—
405	C₄	—	4	1	no	—
406	C₄	—	4	2	no	—
407	C₄	—	4	1	no	—
408	C₄	—	4	1	no	—
409	C₄	C₁₃×#424	1	4	yes	—
410	C₄	C₁₃×#548	1	1	yes	characteristic
411	C₄	C₁₃×#548	1	1	yes	characteristic
412	C₄	C₁₃×#557	1	1	yes	characteristic
413	C₄	C₁₃×#557	1	1	yes	characteristic
414	C₂	C₁₃×#2351	1	1	yes	characteristic
415	C₂	C₂×C₁₃×#424	1	1	yes	characteristic
416	C₂	C₁₃×#2906	1	1	yes	characteristic
417	C₂	C₁₃×#2966	1	1	yes	characteristic
418	C₂	C₁₃×#2969	1	1	yes	characteristic
419	C₂	C₁₃×#2985	1	1	yes	characteristic
420	C₂	C₁₃×#2986	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
86. #22735	C₁₃	direct (N × H)
348. C₁₃	#22735	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×#446	2
C₂×C₈×Q₈×C₁₃	2
C₁₃×#2295	2
C₁₃×#1940	2
C₁₃×#1939	2
C₁₃×#1832	2
C₁₃×#1831	2
C₁₃×#1768	2
C₄×C₁₃×C₄⋊C₈	2
#22735	13

Subgroups — C13×#22735 #15709074

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#22735 #15709074