Subgroups — C₁₃×#21675 #15708014

Order 3328.

674 conjugacy classes of subgroups.

The subgroup lattice has 412 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×C₁₃×#125	C₂	1	1	yes	maximal, characteristic
2	C₁₃×#1939	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#1939	C₂	1	1	yes	maximal, characteristic
4	C₁₃×#1917	C₂	1	2	yes	maximal
5	C₁₃×#1917	C₂	1	2	yes	maximal
6	C₁₃×#1831	C₂	1	1	yes	maximal, characteristic
7	C₁₃×#1771	C₂	1	2	yes	maximal
8	C₁₃×#1770	C₂	1	2	yes	maximal
9	C₁₃×#1770	C₂	1	1	yes	maximal, characteristic
10	C₈×C₁₃×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic
11	C₄×C₁₃×#97	C₂	1	1	yes	maximal, characteristic
12	C₂×C₁₃×#125	C₄	1	1	yes	characteristic
13	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
14	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
15	C₂×C₁₃×C₄⋊C₈	C₂²	1	2	yes	—
16	C₂×C₁₃×C₄⋊C₈	C₂²	1	2	yes	—
17	C₂×C₁₃×#97	C₂²	1	2	yes	—
18	C₂×C₁₃×#97	C₂²	1	1	yes	characteristic
19	C₂×C₁₃×#97	C₂²	1	1	yes	characteristic
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	2	yes	—
23	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
24	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
25	C₁₃×#389	C₄	1	1	yes	characteristic
26	C₁₃×#389	C₄	1	1	yes	characteristic
27	C₁₃×#387	C₄	1	2	yes	—
28	C₁₃×#387	C₄	1	2	yes	—
29	C₁₃×#382	C₄	1	1	yes	characteristic
30	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
31	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
32	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
33	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
34	C₄³×C₁₃	C₂²	1	1	yes	characteristic
35	C₁₃×#336	C₂²	1	2	yes	—
36	C₁₃×#336	C₂²	1	2	yes	—
37	C₁₃×#336	C₂²	1	2	yes	—
38	C₁₃×#336	C₂²	1	2	yes	—
39	C₁₃×#336	C₂²	1	2	yes	—
40	C₁₃×#336	C₂²	1	2	yes	—
41	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
42	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
43	C₂²×C₈×C₁₃	C₂³	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	1	yes	characteristic
47	C₁₃×#125	—	2	4	no	—
48	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
49	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
50	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	2	yes	—
51	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	2	yes	—
52	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
53	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	2	yes	—
54	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	2	yes	—
55	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
56	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
57	C₂×C₄²×C₁₃	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	C₂³	1	2	yes	—
61	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
62	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
63	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
64	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
65	C₁₃×C₄⋊C₈	—	2	4	no	—
66	C₁₃×C₄⋊C₈	—	2	4	no	—
67	C₁₃×C₄⋊C₈	—	2	2	no	—
68	C₁₃×C₄⋊C₈	—	2	2	no	—
69	C₁₃×#97	—	2	2	no	—
70	C₁₃×#97	—	2	2	no	—
71	C₁₃×#97	—	2	2	no	—
72	C₁₃×#97	—	2	2	no	—
73	C₁₃×#97	—	2	4	no	—
74	C₄×C₈×C₁₃	—	2	4	no	—
75	C₄×C₈×C₁₃	—	2	2	no	—
76	C₄×C₈×C₁₃	Q₈	1	4	yes	—
77	C₁₃×#95	C₂×C₄	1	2	yes	—
78	C₁₃×#95	C₂×C₄	1	2	yes	—
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	#21675	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
84	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
85	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
86	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
87	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
88	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
89	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
90	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
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	1	yes	characteristic
94	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
95	C₂×C₈×C₁₃	—	2	1	no	—
96	C₂×C₈×C₁₃	—	2	1	no	—
97	C₂×C₈×C₁₃	—	2	1	no	—
98	C₂×C₈×C₁₃	—	2	1	no	—
99	C₂×C₈×C₁₃	—	2	1	no	—
100	C₂×C₈×C₁₃	—	2	1	no	—
101	C₂×C₈×C₁₃	—	2	2	no	—
102	C₂×C₈×C₁₃	—	2	2	no	—
103	C₂×C₈×C₁₃	—	2	2	no	—
104	C₂×C₈×C₁₃	—	2	2	no	—
105	C₂×C₈×C₁₃	—	2	2	no	—
106	C₂×C₈×C₁₃	—	2	2	no	—
107	C₂×C₈×C₁₃	C₂×Q₈	1	2	yes	—
108	C₂×C₈×C₁₃	C₂×Q₈	1	2	yes	—
109	C₂×C₈×C₁₃	#41	1	2	yes	—
110	C₂×C₈×C₁₃	#41	1	2	yes	—
111	C₂×C₈×C₁₃	#41	1	2	yes	—
112	C₂×C₈×C₁₃	#41	1	2	yes	—
113	C₁₃×C₄⋊C₄	—	2	4	no	—
114	C₁₃×C₄⋊C₄	—	2	4	no	—
115	C₁₃×C₄⋊C₄	—	2	2	no	—
116	C₁₃×C₄⋊C₄	—	2	2	no	—
117	C₁₃×C₄⋊C₄	—	2	2	no	—
118	C₁₃×C₄⋊C₄	—	4	2	no	—
119	C₁₃×C₄⋊C₄	—	4	2	no	—
120	C₁₃×C₄⋊C₄	M₁₆	1	4	yes	—
121	C₄²×C₁₃	—	2	2	no	—
122	C₄²×C₁₃	—	2	2	no	—
123	C₄²×C₁₃	—	2	2	no	—
124	C₄²×C₁₃	—	2	2	no	—
125	C₄²×C₁₃	—	2	1	no	—
126	C₄²×C₁₃	—	2	1	no	—
127	C₄²×C₁₃	—	2	1	no	—
128	C₄²×C₁₃	—	2	1	no	—
129	C₄²×C₁₃	—	2	2	no	—
130	C₄²×C₁₃	—	2	2	no	—
131	C₄²×C₁₃	—	4	1	no	—
132	C₄²×C₁₃	—	4	1	no	—
133	C₄²×C₁₃	C₂×Q₈	1	2	yes	—
134	C₄²×C₁₃	#41	1	2	yes	—
135	C₄×#125	C₂×C₁₃	1	1	yes	characteristic
136	#1939	C₂×C₁₃	1	1	yes	characteristic
137	#1939	C₂×C₁₃	1	1	yes	characteristic
138	#1917	C₂×C₁₃	1	2	yes	—
139	#1917	C₂×C₁₃	1	2	yes	—
140	#1831	C₂×C₁₃	1	1	yes	characteristic
141	#1771	C₂×C₁₃	1	2	yes	—
142	#1770	C₂×C₁₃	1	2	yes	—
143	#1770	C₂×C₁₃	1	1	yes	characteristic
144	C₈×C₄⋊C₄	C₂×C₁₃	1	1	yes	characteristic
145	C₄×#97	C₂×C₁₃	1	1	yes	characteristic
146	C₂³×C₁₃	C₂³×C₄	1	1	yes	characteristic
147	C₂×C₄×C₁₃	—	2	2	no	—
148	C₂×C₄×C₁₃	—	2	1	no	—
149	C₂×C₄×C₁₃	—	2	1	no	—
150	C₂×C₄×C₁₃	—	2	2	no	—
151	C₂×C₄×C₁₃	—	2	2	no	—
152	C₂×C₄×C₁₃	—	2	1	no	—
153	C₂×C₄×C₁₃	—	2	1	no	—
154	C₂×C₄×C₁₃	—	2	2	no	—
155	C₂×C₄×C₁₃	—	2	1	no	—
156	C₂×C₄×C₁₃	—	2	1	no	—
157	C₂×C₄×C₁₃	—	2	2	no	—
158	C₂×C₄×C₁₃	—	2	1	no	—
159	C₂×C₄×C₁₃	—	2	1	no	—
160	C₂×C₄×C₁₃	—	2	2	no	—
161	C₂×C₄×C₁₃	—	2	1	no	—
162	C₂×C₄×C₁₃	—	2	1	no	—
163	C₂×C₄×C₁₃	—	2	2	no	—
164	C₂×C₄×C₁₃	—	2	2	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	C₄×Q₈	1	2	yes	—
173	C₂×C₄×C₁₃	C₄×Q₈	1	2	yes	—
174	C₂×C₄×C₁₃	C₂×M₁₆	1	4	yes	—
175	C₂×C₄×C₁₃	C₂×M₁₆	1	2	yes	—
176	C₂×C₄×C₁₃	#131	1	2	yes	—
177	C₂×C₄×C₁₃	C₂²×Q₈	1	1	yes	characteristic
178	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
179	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
180	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
181	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
182	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
183	C₈×C₁₃	—	2	2	no	—
184	C₈×C₁₃	—	2	2	no	—
185	C₈×C₁₃	—	2	2	no	—
186	C₈×C₁₃	—	4	2	no	—
187	C₈×C₁₃	—	4	2	no	—
188	C₈×C₁₃	#125	1	4	yes	complemented
189	C₂×#125	C₄×C₁₃	1	1	yes	characteristic
190	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
191	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
192	C₂×C₄⋊C₈	C₂²×C₁₃	1	2	yes	—
193	C₂×C₄⋊C₈	C₂²×C₁₃	1	2	yes	—
194	C₂×#97	C₂²×C₁₃	1	1	yes	characteristic
195	C₂×#97	C₂²×C₁₃	1	1	yes	characteristic
196	C₂×#97	C₂²×C₁₃	1	1	yes	characteristic
197	C₂×#97	C₂²×C₁₃	1	1	yes	characteristic
198	C₂×#97	C₂²×C₁₃	1	2	yes	—
199	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
200	C₂×C₄×C₈	C₂²×C₁₃	1	2	yes	—
201	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
202	#389	C₄×C₁₃	1	1	yes	characteristic
203	#389	C₄×C₁₃	1	1	yes	characteristic
204	#387	C₄×C₁₃	1	2	yes	—
205	#387	C₄×C₁₃	1	2	yes	—
206	#382	C₄×C₁₃	1	1	yes	characteristic
207	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
208	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
209	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
210	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
211	C₄³	C₂²×C₁₃	1	1	yes	characteristic
212	#336	C₂²×C₁₃	1	2	yes	—
213	#336	C₂²×C₁₃	1	2	yes	—
214	#336	C₂²×C₁₃	1	2	yes	—
215	#336	C₂²×C₁₃	1	2	yes	—
216	#336	C₂²×C₁₃	1	2	yes	—
217	#336	C₂²×C₁₃	1	2	yes	—
218	C₂²×C₁₃	C₂×C₄×Q₈	1	1	yes	characteristic
219	C₂²×C₁₃	C₄×#41	1	1	yes	characteristic
220	C₂²×C₁₃	C₄×#41	1	1	yes	characteristic
221	C₂²×C₁₃	C₂²×M₁₆	1	1	yes	characteristic
222	C₂²×C₁₃	C₂×#131	1	1	yes	characteristic
223	C₂²×C₁₃	#568	1	1	yes	characteristic
224	C₂²×C₁₃	#568	1	1	yes	characteristic
225	C₄×C₁₃	—	2	2	no	—
226	C₄×C₁₃	—	2	4	no	—
227	C₄×C₁₃	—	4	1	no	—
228	C₄×C₁₃	—	4	1	no	—
229	C₄×C₁₃	—	4	2	no	—
230	C₄×C₁₃	—	4	2	no	—
231	C₄×C₁₃	—	4	1	no	—
232	C₄×C₁₃	—	4	1	no	—
233	C₄×C₁₃	—	4	2	no	—
234	C₄×C₁₃	#446	1	4	yes	—
235	C₄×C₁₃	C₂×#125	1	1	yes	characteristic
236	C₄×C₁₃	#529	1	1	yes	characteristic
237	C₄×C₁₃	#529	1	1	yes	characteristic
238	C₄×C₁₃	#533	1	1	yes	characteristic
239	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
240	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
241	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
242	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
243	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
244	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
245	#125	—	2	4	no	—
246	C₂×C₄⋊C₄	C₂×C₄×C₁₃	1	2	yes	—
247	C₂×C₄⋊C₄	C₂×C₄×C₁₃	1	2	yes	—
248	C₂×C₄⋊C₄	C₂×C₄×C₁₃	1	1	yes	characteristic
249	C₂×C₄⋊C₄	C₂×C₄×C₁₃	1	1	yes	characteristic
250	C₂×C₄⋊C₄	C₂×C₄×C₁₃	1	1	yes	characteristic
251	C₂×C₄⋊C₄	C₂×C₄×C₁₃	1	2	yes	—
252	C₂×C₄⋊C₄	C₂×C₄×C₁₃	1	2	yes	—
253	C₂×C₄⋊C₄	C₂×C₄×C₁₃	1	1	yes	characteristic
254	C₂×C₄²	C₂×C₄×C₁₃	1	1	yes	characteristic
255	C₂×C₄²	C₂×C₄×C₁₃	1	1	yes	characteristic
256	C₂×C₄²	C₂×C₄×C₁₃	1	1	yes	characteristic
257	C₂×C₄²	C₂×C₄×C₁₃	1	1	yes	characteristic
258	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
259	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
260	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
261	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
262	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
263	C₄⋊C₈	—	2	4	no	—
264	C₄⋊C₈	—	2	4	no	—
265	C₄⋊C₈	—	2	2	no	—
266	C₄⋊C₈	—	2	2	no	—
267	#97	—	2	2	no	—
268	#97	—	2	2	no	—
269	#97	—	2	2	no	—
270	#97	—	2	2	no	—
271	#97	—	2	4	no	—
272	C₄×C₈	—	2	4	no	—
273	C₄×C₈	—	2	2	no	—
274	C₄×C₈	Q₈×C₁₃	1	4	yes	—
275	#95	C₂×C₄×C₁₃	1	2	yes	—
276	#95	C₂×C₄×C₁₃	1	2	yes	—
277	#95	C₂×C₄×C₁₃	1	2	yes	—
278	#95	C₂×C₄×C₁₃	1	2	yes	—
279	#95	C₂×C₄×C₁₃	1	2	yes	—
280	#95	C₂×C₄×C₁₃	1	2	yes	—
281	C₂×C₁₃	C₄×#125	1	1	yes	characteristic
282	C₂×C₁₃	C₂×#446	1	1	yes	characteristic
283	C₂×C₁₃	#2961	1	1	yes	characteristic
284	C₂×C₁₃	#2969	1	1	yes	characteristic
285	C₂×C₁₃	#2969	1	1	yes	characteristic
286	C₂×C₁₃	#2970	1	1	yes	characteristic
287	C₂×C₁₃	#2971	1	1	yes	characteristic
288	C₂²×C₄	C₂²×C₄×C₁₃	1	2	yes	—
289	C₂²×C₄	C₂²×C₄×C₁₃	1	2	yes	—
290	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
291	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
292	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
293	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
294	C₂²×C₄	C₂²×C₄×C₁₃	1	2	yes	—
295	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
296	C₂²×C₄	C₂²×C₄×C₁₃	1	2	yes	—
297	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
298	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
299	C₂×C₈	—	2	1	no	—
300	C₂×C₈	—	2	1	no	—
301	C₂×C₈	—	2	1	no	—
302	C₂×C₈	—	2	1	no	—
303	C₂×C₈	—	2	1	no	—
304	C₂×C₈	—	2	1	no	—
305	C₂×C₈	—	2	2	no	—
306	C₂×C₈	—	2	2	no	—
307	C₂×C₈	—	2	2	no	—
308	C₂×C₈	—	2	2	no	—
309	C₂×C₈	—	2	2	no	—
310	C₂×C₈	—	2	2	no	—
311	C₂×C₈	C₂×Q₈×C₁₃	1	2	yes	—
312	C₂×C₈	C₂×Q₈×C₁₃	1	2	yes	—
313	C₂×C₈	C₁₃×#41	1	2	yes	—
314	C₂×C₈	C₁₃×#41	1	2	yes	—
315	C₂×C₈	C₁₃×#41	1	2	yes	—
316	C₂×C₈	C₁₃×#41	1	2	yes	—
317	C₄⋊C₄	—	2	4	no	—
318	C₄⋊C₄	—	2	4	no	—
319	C₄⋊C₄	—	2	2	no	—
320	C₄⋊C₄	—	2	2	no	—
321	C₄⋊C₄	—	2	2	no	—
322	C₄⋊C₄	—	4	2	no	—
323	C₄⋊C₄	—	4	2	no	—
324	C₄⋊C₄	C₁₃×M₁₆	1	4	yes	—
325	C₄²	—	2	2	no	—
326	C₄²	—	2	2	no	—
327	C₄²	—	2	2	no	—
328	C₄²	—	2	1	no	—
329	C₄²	—	2	1	no	—
330	C₄²	—	2	2	no	—
331	C₄²	—	2	1	no	—
332	C₄²	—	2	1	no	—
333	C₄²	—	2	2	no	—
334	C₄²	—	2	2	no	—
335	C₄²	—	4	1	no	—
336	C₄²	—	4	1	no	—
337	C₄²	C₂×Q₈×C₁₃	1	2	yes	—
338	C₄²	C₁₃×#41	1	2	yes	—
339	C₁₃	#21675	1	1	yes	characteristic, direct product factor, Sylow
340	C₂³	C₂³×C₄×C₁₃	1	1	yes	characteristic
341	C₂×C₄	—	2	2	no	—
342	C₂×C₄	—	2	1	no	—
343	C₂×C₄	—	2	1	no	—
344	C₂×C₄	—	2	2	no	—
345	C₂×C₄	—	2	2	no	—
346	C₂×C₄	—	2	1	no	—
347	C₂×C₄	—	2	1	no	—
348	C₂×C₄	—	2	2	no	—
349	C₂×C₄	—	2	1	no	—
350	C₂×C₄	—	2	1	no	—
351	C₂×C₄	—	2	2	no	—
352	C₂×C₄	—	2	1	no	—
353	C₂×C₄	—	2	1	no	—
354	C₂×C₄	—	2	2	no	—
355	C₂×C₄	—	2	1	no	—
356	C₂×C₄	—	2	1	no	—
357	C₂×C₄	—	2	2	no	—
358	C₂×C₄	—	2	2	no	—
359	C₂×C₄	—	2	1	no	—
360	C₂×C₄	—	2	1	no	—
361	C₂×C₄	—	2	1	no	—
362	C₂×C₄	—	2	1	no	—
363	C₂×C₄	—	2	2	no	—
364	C₂×C₄	—	2	2	no	—
365	C₂×C₄	—	2	2	no	—
366	C₂×C₄	C₄×Q₈×C₁₃	1	2	yes	—
367	C₂×C₄	C₄×Q₈×C₁₃	1	2	yes	—
368	C₂×C₄	C₂×C₁₃×M₁₆	1	4	yes	—
369	C₂×C₄	C₂×C₁₃×M₁₆	1	2	yes	—
370	C₂×C₄	C₁₃×#131	1	2	yes	—
371	C₂×C₄	C₂²×Q₈×C₁₃	1	1	yes	characteristic
372	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
373	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
374	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
375	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
376	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
377	C₈	—	2	2	no	—
378	C₈	—	2	2	no	—
379	C₈	—	2	2	no	—
380	C₈	—	4	2	no	—
381	C₈	—	4	2	no	—
382	C₈	C₁₃×#125	1	4	yes	complemented
383	C₂²	C₂×C₄×Q₈×C₁₃	1	1	yes	characteristic
384	C₂²	C₄×C₁₃×#41	1	1	yes	characteristic
385	C₂²	C₄×C₁₃×#41	1	1	yes	characteristic
386	C₂²	C₂²×C₁₃×M₁₆	1	1	yes	characteristic
387	C₂²	C₂×C₁₃×#131	1	1	yes	characteristic
388	C₂²	C₁₃×#568	1	1	yes	characteristic
389	C₂²	C₁₃×#568	1	1	yes	characteristic
390	C₄	—	2	2	no	—
391	C₄	—	2	4	no	—
392	C₄	—	4	1	no	—
393	C₄	—	4	1	no	—
394	C₄	—	4	2	no	—
395	C₄	—	4	2	no	—
396	C₄	—	4	1	no	—
397	C₄	—	4	1	no	—
398	C₄	—	4	2	no	—
399	C₄	C₁₃×#446	1	4	yes	—
400	C₄	C₂×C₁₃×#125	1	1	yes	characteristic
401	C₄	C₁₃×#529	1	1	yes	characteristic
402	C₄	C₁₃×#529	1	1	yes	characteristic
403	C₄	C₁₃×#533	1	1	yes	characteristic
404	C₂	C₄×C₁₃×#125	1	1	yes	characteristic
405	C₂	C₂×C₁₃×#446	1	1	yes	characteristic
406	C₂	C₁₃×#2961	1	1	yes	characteristic
407	C₂	C₁₃×#2969	1	1	yes	characteristic
408	C₂	C₁₃×#2969	1	1	yes	characteristic
409	C₂	C₁₃×#2970	1	1	yes	characteristic
410	C₂	C₁₃×#2971	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
83. #21675	C₁₃	direct (N × H)
188. C₈×C₁₃	#125	semidirect
339. C₁₃	#21675	direct (N × H)
382. C₈	C₁₃×#125	semidirect

Maximal subgroups

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

subgroup	index
C₄×C₁₃×#125	2
C₁₃×#1939	2
C₁₃×#1917	2
C₁₃×#1831	2
C₁₃×#1771	2
C₁₃×#1770	2
C₈×C₁₃×C₄⋊C₄	2
C₄×C₁₃×#97	2
#21675	13

Subgroups — C13×#21675 #15708014

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#21675 #15708014