Subgroups — C₁₃×#22736 #15709075

Order 3328.

812 conjugacy classes of subgroups.

The subgroup lattice has 356 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	2	yes	maximal
2	C₄²×Q₈×C₁₃	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#1940	C₂	1	4	yes	maximal
4	C₁₃×#1939	C₂	1	2	yes	maximal
5	C₁₃×#1831	C₂	1	2	yes	maximal
6	C₁₃×#1831	C₂	1	1	yes	maximal, characteristic
7	C₁₃×#1767	C₂	1	2	yes	maximal
8	C₄×C₁₃×C₄⋊C₈	C₂	1	1	yes	maximal, characteristic
9	C₂×C₄×Q₈×C₁₃	C₄	1	1	yes	characteristic
10	C₂×C₄×Q₈×C₁₃	C₄	1	1	yes	characteristic
11	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
12	C₁₃×#446	—	2	8	no	—
13	C₂×C₁₃×C₄⋊C₈	C₂²	1	2	yes	—
14	C₂×C₁₃×C₄⋊C₈	C₂²	1	4	yes	—
15	C₂×C₁₃×C₄⋊C₈	C₂²	1	2	yes	—
16	C₂×C₁₃×C₄⋊C₈	C₂²	1	4	yes	—
17	C₂×C₁₃×#97	C₂²	1	4	yes	—
18	C₂×C₄×C₈×C₁₃	C₂²	1	2	yes	—
19	C₄×C₁₃×C₄⋊C₄	C₄	1	1	yes	characteristic
20	C₄×C₁₃×C₄⋊C₄	C₄	1	2	yes	—
21	C₄×C₁₃×C₄⋊C₄	C₄	1	2	yes	—
22	C₄×C₁₃×C₄⋊C₄	C₄	1	1	yes	characteristic
23	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
24	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
25	C₄³×C₁₃	C₂²	1	1	yes	characteristic
26	C₄³×C₁₃	C₂²	1	2	yes	—
27	C₁₃×#336	C₂²	1	1	yes	characteristic
28	C₁₃×#336	C₂²	1	1	yes	characteristic
29	C₁₃×#336	C₂²	1	2	yes	—
30	C₁₃×#336	C₂²	1	4	yes	—
31	C₁₃×#336	C₂²	1	2	yes	—
32	C₂²×Q₈×C₁₃	C₂×C₄	1	1	yes	characteristic
33	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
34	C₂²×C₈×C₁₃	C₂³	1	4	yes	—
35	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
36	C₄×Q₈×C₁₃	—	2	4	no	—
37	C₄×Q₈×C₁₃	—	2	4	no	—
38	C₄×Q₈×C₁₃	D₄	1	4	yes	—
39	C₄×Q₈×C₁₃	Q₈	1	4	yes	—
40	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
41	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	2	yes	—
42	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	2	yes	—
43	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	2	yes	—
44	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
45	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
46	C₂×C₄²×C₁₃	C₂×C₄	1	2	yes	—
47	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
48	C₂×C₄²×C₁₃	C₂×C₄	1	2	yes	—
49	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
50	C₂×C₄²×C₁₃	C₂×C₄	1	2	yes	—
51	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
52	C₂×C₄²×C₁₃	C₂×C₄	1	2	yes	—
53	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
54	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
55	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
56	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
57	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
58	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
59	C₁₃×C₄⋊C₈	—	2	4	no	—
60	C₁₃×C₄⋊C₈	—	2	8	no	—
61	C₁₃×C₄⋊C₈	—	2	4	no	—
62	C₁₃×C₄⋊C₈	—	2	8	no	—
63	C₁₃×#97	—	2	8	no	—
64	C₄×C₈×C₁₃	—	2	4	no	—
65	C₁₃×#95	C₂×C₄	1	2	yes	—
66	C₁₃×#95	C₂×C₄	1	2	yes	—
67	C₁₃×#95	C₂×C₄	1	2	yes	—
68	#22736	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
69	C₂×Q₈×C₁₃	—	2	2	no	—
70	C₂×Q₈×C₁₃	—	2	2	no	—
71	C₂×Q₈×C₁₃	C₄⋊C₄	1	4	yes	—
72	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
73	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
74	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
75	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
76	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
77	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
78	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
79	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
80	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
81	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
82	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
83	C₂×C₈×C₁₃	—	2	2	no	—
84	C₂×C₈×C₁₃	—	2	2	no	—
85	C₂×C₈×C₁₃	—	2	2	no	—
86	C₂×C₈×C₁₃	—	2	4	no	—
87	C₂×C₈×C₁₃	—	2	2	no	—
88	C₂×C₈×C₁₃	—	2	4	no	—
89	C₂×C₈×C₁₃	—	2	2	no	—
90	C₂×C₈×C₁₃	—	2	4	no	—
91	C₂×C₈×C₁₃	#41	1	4	yes	—
92	C₁₃×C₄⋊C₄	—	2	4	no	—
93	C₁₃×C₄⋊C₄	—	2	4	no	—
94	C₁₃×C₄⋊C₄	—	2	2	no	—
95	C₁₃×C₄⋊C₄	C₄⋊C₄	1	8	yes	—
96	C₁₃×C₄⋊C₄	C₄⋊C₄	1	4	yes	—
97	C₁₃×C₄⋊C₄	M₁₆	1	4	yes	—
98	C₄²×C₁₃	—	2	4	no	—
99	C₄²×C₁₃	—	2	2	no	—
100	C₄²×C₁₃	—	2	4	no	—
101	C₄²×C₁₃	—	2	2	no	—
102	C₄²×C₁₃	—	2	4	no	—
103	C₄²×C₁₃	—	2	2	no	—
104	C₄²×C₁₃	—	2	4	no	—
105	C₄²×C₁₃	—	2	2	no	—
106	C₄²×C₁₃	—	4	2	no	—
107	C₄²×C₁₃	—	4	1	no	—
108	C₄²×C₁₃	M₁₆	1	4	yes	—
109	C₄²×C₁₃	C₂×D₄	1	2	yes	—
110	C₄²×C₁₃	C₂×D₄	1	4	yes	—
111	C₄²×C₁₃	C₂×Q₈	1	4	yes	—
112	C₄²×C₁₃	C₂×Q₈	1	2	yes	—
113	C₂×#446	C₂×C₁₃	1	2	yes	—
114	C₄²×Q₈	C₂×C₁₃	1	1	yes	characteristic
115	#1940	C₂×C₁₃	1	4	yes	—
116	#1939	C₂×C₁₃	1	2	yes	—
117	#1831	C₂×C₁₃	1	2	yes	—
118	#1831	C₂×C₁₃	1	1	yes	characteristic
119	#1767	C₂×C₁₃	1	2	yes	—
120	C₄×C₄⋊C₈	C₂×C₁₃	1	1	yes	characteristic
121	C₂³×C₁₃	C₂³×C₄	1	1	yes	characteristic
122	Q₈×C₁₃	—	2	8	no	—
123	C₂×C₄×C₁₃	—	2	1	no	—
124	C₂×C₄×C₁₃	—	2	2	no	—
125	C₂×C₄×C₁₃	—	2	1	no	—
126	C₂×C₄×C₁₃	—	2	1	no	—
127	C₂×C₄×C₁₃	—	2	1	no	—
128	C₂×C₄×C₁₃	—	2	2	no	—
129	C₂×C₄×C₁₃	—	2	2	no	—
130	C₂×C₄×C₁₃	—	2	1	no	—
131	C₂×C₄×C₁₃	—	2	2	no	—
132	C₂×C₄×C₁₃	—	2	1	no	—
133	C₂×C₄×C₁₃	—	2	1	no	—
134	C₂×C₄×C₁₃	—	2	2	no	—
135	C₂×C₄×C₁₃	—	2	1	no	—
136	C₂×C₄×C₁₃	—	2	2	no	—
137	C₂×C₄×C₁₃	—	2	2	no	—
138	C₂×C₄×C₁₃	—	2	1	no	—
139	C₂×C₄×C₁₃	—	2	2	no	—
140	C₂×C₄×C₁₃	—	2	1	no	—
141	C₂×C₄×C₁₃	—	2	2	no	—
142	C₂×C₄×C₁₃	—	2	1	no	—
143	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	2	yes	—
144	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	4	yes	—
145	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	4	yes	—
146	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	2	yes	—
147	C₂×C₄×C₁₃	C₂×M₁₆	1	2	yes	—
148	C₂×C₄×C₁₃	C₂×M₁₆	1	4	yes	—
149	C₂×C₄×C₁₃	C₂×M₁₆	1	2	yes	—
150	C₂×C₄×C₁₃	C₂×M₁₆	1	2	yes	—
151	C₂×C₄×C₁₃	C₂×M₁₆	1	2	yes	—
152	C₂×C₄×C₁₃	#131	1	2	yes	—
153	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
154	C₂×C₄×C₁₃	C₂²×Q₈	1	1	yes	characteristic
155	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
156	C₂×C₄×C₁₃	2₋¹⁺⁴	1	2	yes	—
157	C₈×C₁₃	—	2	4	no	—
158	C₈×C₁₃	—	4	2	no	—
159	C₈×C₁₃	—	4	4	no	—
160	C₂×C₄×Q₈	C₄×C₁₃	1	1	yes	characteristic
161	C₂×C₄×Q₈	C₄×C₁₃	1	1	yes	characteristic
162	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
163	#446	—	2	8	no	—
164	C₂×C₄⋊C₈	C₂²×C₁₃	1	2	yes	—
165	C₂×C₄⋊C₈	C₂²×C₁₃	1	4	yes	—
166	C₂×C₄⋊C₈	C₂²×C₁₃	1	4	yes	—
167	C₂×C₄⋊C₈	C₂²×C₁₃	1	2	yes	—
168	C₂×#97	C₂²×C₁₃	1	4	yes	—
169	C₂×C₄×C₈	C₂²×C₁₃	1	2	yes	—
170	C₄×C₄⋊C₄	C₄×C₁₃	1	1	yes	characteristic
171	C₄×C₄⋊C₄	C₄×C₁₃	1	2	yes	—
172	C₄×C₄⋊C₄	C₄×C₁₃	1	2	yes	—
173	C₄×C₄⋊C₄	C₄×C₁₃	1	1	yes	characteristic
174	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
175	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
176	C₄³	C₂²×C₁₃	1	1	yes	characteristic
177	C₄³	C₂²×C₁₃	1	2	yes	—
178	#336	C₂²×C₁₃	1	1	yes	characteristic
179	#336	C₂²×C₁₃	1	2	yes	—
180	#336	C₂²×C₁₃	1	4	yes	—
181	#336	C₂²×C₁₃	1	2	yes	—
182	#336	C₂²×C₁₃	1	1	yes	characteristic
183	C₂²×C₁₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
184	C₂²×C₁₃	C₄×#41	1	1	yes	characteristic
185	C₂²×C₁₃	#519	1	1	yes	characteristic
186	C₂²×C₁₃	C₂²×M₁₆	1	1	yes	characteristic
187	C₂²×C₁₃	C₂²×M₁₆	1	1	yes	characteristic
188	C₂²×C₁₃	C₂×#131	1	1	yes	characteristic
189	C₂²×C₁₃	#568	1	1	yes	characteristic
190	C₄×C₁₃	—	2	4	no	—
191	C₄×C₁₃	—	2	2	no	—
192	C₄×C₁₃	—	2	4	no	—
193	C₄×C₁₃	—	2	2	no	—
194	C₄×C₁₃	—	2	4	no	—
195	C₄×C₁₃	—	2	2	no	—
196	C₄×C₁₃	—	2	2	no	—
197	C₄×C₁₃	—	4	2	no	—
198	C₄×C₁₃	—	4	1	no	—
199	C₄×C₁₃	#423	1	4	yes	—
200	C₄×C₁₃	#548	1	2	yes	—
201	C₄×C₁₃	#557	1	2	yes	—
202	C₂²×Q₈	C₂×C₄×C₁₃	1	1	yes	characteristic
203	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
204	C₂²×C₈	C₂³×C₁₃	1	4	yes	—
205	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
206	C₄×Q₈	—	2	4	no	—
207	C₄×Q₈	—	2	4	no	—
208	C₄×Q₈	D₄×C₁₃	1	4	yes	—
209	C₄×Q₈	Q₈×C₁₃	1	4	yes	—
210	C₂×C₄⋊C₄	C₂×C₄×C₁₃	1	1	yes	characteristic
211	C₂×C₄⋊C₄	C₂×C₄×C₁₃	1	2	yes	—
212	C₂×C₄⋊C₄	C₂×C₄×C₁₃	1	2	yes	—
213	C₂×C₄⋊C₄	C₂×C₄×C₁₃	1	2	yes	—
214	C₂×C₄⋊C₄	C₂×C₄×C₁₃	1	1	yes	characteristic
215	C₂×C₄⋊C₄	C₂×C₄×C₁₃	1	1	yes	characteristic
216	C₂×C₄²	C₂×C₄×C₁₃	1	2	yes	—
217	C₂×C₄²	C₂×C₄×C₁₃	1	1	yes	characteristic
218	C₂×C₄²	C₂×C₄×C₁₃	1	2	yes	—
219	C₂×C₄²	C₂×C₄×C₁₃	1	2	yes	—
220	C₂×C₄²	C₂×C₄×C₁₃	1	1	yes	characteristic
221	C₂×C₄²	C₂×C₄×C₁₃	1	1	yes	characteristic
222	C₂×C₄²	C₂×C₄×C₁₃	1	2	yes	—
223	C₂×C₄²	C₂×C₄×C₁₃	1	1	yes	characteristic
224	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
225	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
226	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
227	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
228	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
229	C₄⋊C₈	—	2	8	no	—
230	C₄⋊C₈	—	2	4	no	—
231	C₄⋊C₈	—	2	4	no	—
232	C₄⋊C₈	—	2	8	no	—
233	#97	—	2	8	no	—
234	C₄×C₈	—	2	4	no	—
235	#95	C₂×C₄×C₁₃	1	2	yes	—
236	#95	C₂×C₄×C₁₃	1	2	yes	—
237	#95	C₂×C₄×C₁₃	1	2	yes	—
238	C₂×C₁₃	#2351	1	1	yes	characteristic
239	C₂×C₁₃	C₂×#423	1	1	yes	characteristic
240	C₂×C₁₃	#2906	1	1	yes	characteristic
241	C₂×C₁₃	#2965	1	1	yes	characteristic
242	C₂×C₁₃	#2970	1	1	yes	characteristic
243	C₂×C₁₃	#2983	1	1	yes	characteristic
244	C₂×C₁₃	#2984	1	1	yes	characteristic
245	C₂×Q₈	—	2	2	no	—
246	C₂×Q₈	—	2	2	no	—
247	C₂×Q₈	C₁₃×C₄⋊C₄	1	4	yes	—
248	C₂²×C₄	C₂²×C₄×C₁₃	1	2	yes	—
249	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
250	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
251	C₂²×C₄	C₂²×C₄×C₁₃	1	2	yes	—
252	C₂²×C₄	C₂²×C₄×C₁₃	1	2	yes	—
253	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
254	C₂²×C₄	C₂²×C₄×C₁₃	1	2	yes	—
255	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
256	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
257	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
258	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
259	C₂×C₈	—	2	2	no	—
260	C₂×C₈	—	2	2	no	—
261	C₂×C₈	—	2	2	no	—
262	C₂×C₈	—	2	4	no	—
263	C₂×C₈	—	2	2	no	—
264	C₂×C₈	—	2	4	no	—
265	C₂×C₈	—	2	2	no	—
266	C₂×C₈	—	2	4	no	—
267	C₂×C₈	C₁₃×#41	1	4	yes	—
268	C₄⋊C₄	—	2	4	no	—
269	C₄⋊C₄	—	2	4	no	—
270	C₄⋊C₄	—	2	2	no	—
271	C₄⋊C₄	C₁₃×C₄⋊C₄	1	8	yes	—
272	C₄⋊C₄	C₁₃×C₄⋊C₄	1	4	yes	—
273	C₄⋊C₄	C₁₃×M₁₆	1	4	yes	—
274	C₄²	—	2	4	no	—
275	C₄²	—	2	2	no	—
276	C₄²	—	2	4	no	—
277	C₄²	—	2	2	no	—
278	C₄²	—	2	4	no	—
279	C₄²	—	2	2	no	—
280	C₄²	—	2	4	no	—
281	C₄²	—	2	2	no	—
282	C₄²	—	4	2	no	—
283	C₄²	—	4	1	no	—
284	C₄²	C₁₃×M₁₆	1	4	yes	—
285	C₄²	C₂×D₄×C₁₃	1	2	yes	—
286	C₄²	C₂×D₄×C₁₃	1	4	yes	—
287	C₄²	C₂×Q₈×C₁₃	1	4	yes	—
288	C₄²	C₂×Q₈×C₁₃	1	2	yes	—
289	C₁₃	#22736	1	1	yes	characteristic, direct product factor, Sylow
290	C₂³	C₂³×C₄×C₁₃	1	1	yes	characteristic
291	Q₈	—	2	8	no	—
292	C₂×C₄	—	2	1	no	—
293	C₂×C₄	—	2	2	no	—
294	C₂×C₄	—	2	1	no	—
295	C₂×C₄	—	2	1	no	—
296	C₂×C₄	—	2	1	no	—
297	C₂×C₄	—	2	2	no	—
298	C₂×C₄	—	2	2	no	—
299	C₂×C₄	—	2	1	no	—
300	C₂×C₄	—	2	2	no	—
301	C₂×C₄	—	2	1	no	—
302	C₂×C₄	—	2	1	no	—
303	C₂×C₄	—	2	2	no	—
304	C₂×C₄	—	2	1	no	—
305	C₂×C₄	—	2	2	no	—
306	C₂×C₄	—	2	2	no	—
307	C₂×C₄	—	2	1	no	—
308	C₂×C₄	—	2	2	no	—
309	C₂×C₄	—	2	1	no	—
310	C₂×C₄	—	2	2	no	—
311	C₂×C₄	—	2	1	no	—
312	C₂×C₄	C₂×C₁₃×C₄⋊C₄	1	2	yes	—
313	C₂×C₄	C₂×C₁₃×C₄⋊C₄	1	4	yes	—
314	C₂×C₄	C₂×C₁₃×C₄⋊C₄	1	4	yes	—
315	C₂×C₄	C₂×C₁₃×C₄⋊C₄	1	2	yes	—
316	C₂×C₄	C₂×C₁₃×M₁₆	1	2	yes	—
317	C₂×C₄	C₂×C₁₃×M₁₆	1	4	yes	—
318	C₂×C₄	C₂×C₁₃×M₁₆	1	2	yes	—
319	C₂×C₄	C₂×C₁₃×M₁₆	1	2	yes	—
320	C₂×C₄	C₂×C₁₃×M₁₆	1	2	yes	—
321	C₂×C₄	C₁₃×#131	1	2	yes	—
322	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
323	C₂×C₄	C₂²×Q₈×C₁₃	1	1	yes	characteristic
324	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
325	C₂×C₄	C₁₃×2₋¹⁺⁴	1	2	yes	—
326	C₈	—	2	4	no	—
327	C₈	—	4	2	no	—
328	C₈	—	4	4	no	—
329	C₂²	C₂²×C₁₃×C₄⋊C₄	1	1	yes	characteristic
330	C₂²	C₄×C₁₃×#41	1	1	yes	characteristic
331	C₂²	C₁₃×#519	1	1	yes	characteristic
332	C₂²	C₂²×C₁₃×M₁₆	1	1	yes	characteristic
333	C₂²	C₂²×C₁₃×M₁₆	1	1	yes	characteristic
334	C₂²	C₂×C₁₃×#131	1	1	yes	characteristic
335	C₂²	C₁₃×#568	1	1	yes	characteristic
336	C₄	—	2	4	no	—
337	C₄	—	2	2	no	—
338	C₄	—	2	4	no	—
339	C₄	—	2	2	no	—
340	C₄	—	2	4	no	—
341	C₄	—	2	2	no	—
342	C₄	—	2	2	no	—
343	C₄	—	4	2	no	—
344	C₄	—	4	1	no	—
345	C₄	C₁₃×#423	1	4	yes	—
346	C₄	C₁₃×#548	1	2	yes	—
347	C₄	C₁₃×#557	1	2	yes	—
348	C₂	C₁₃×#2351	1	1	yes	characteristic
349	C₂	C₂×C₁₃×#423	1	1	yes	characteristic
350	C₂	C₁₃×#2906	1	1	yes	characteristic
351	C₂	C₁₃×#2965	1	1	yes	characteristic
352	C₂	C₁₃×#2970	1	1	yes	characteristic
353	C₂	C₁₃×#2983	1	1	yes	characteristic
354	C₂	C₁₃×#2984	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
68. #22736	C₁₃	direct (N × H)
289. C₁₃	#22736	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
C₄²×Q₈×C₁₃	2
C₁₃×#1940	2
C₁₃×#1939	2
C₁₃×#1831	2
C₁₃×#1767	2
C₄×C₁₃×C₄⋊C₈	2
#22736	13

Subgroups — C13×#22736 #15709075

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#22736 #15709075