Subgroups — C₁₃×#34941 #15721280

Order 3328.

1900 conjugacy classes of subgroups.

The subgroup lattice has 682 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#2574	C₂	1	4	yes	maximal, complemented
2	C₁₃×#2567	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#2563	C₂	1	1	yes	maximal, characteristic
4	C₁₃×#2552	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#2538	C₂	1	1	yes	maximal, characteristic
6	C₁₃×#2508	C₂	1	2	yes	maximal, complemented
7	C₁₃×#2497	C₂	1	2	yes	maximal, complemented
8	C₁₃×#2454	C₂	1	2	yes	maximal
9	C₁₃×#2423	C₂	1	2	yes	maximal, complemented
10	C₁₃×#2396	C₂	1	4	yes	maximal, complemented
11	C₄×C₁₃×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
12	C₄×C₁₃×#125	C₂	1	2	yes	maximal, complemented
13	C₄×C₁₃×C₂²⋊Q₈	C₂	1	2	yes	maximal, complemented
14	C₁₃×#2293	C₂	1	2	yes	maximal
15	C₁₃×#2285	C₂	1	2	yes	maximal, complemented
16	C₄²×Q₈×C₁₃	C₂	1	1	yes	maximal, characteristic, complemented
17	C₄²×D₄×C₁₃	C₂	1	1	yes	maximal, characteristic
18	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
19	C₂×C₁₃×#125	C₂²	1	2	yes	—
20	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	—
21	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
22	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
23	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
24	C₂×C₄×Q₈×C₁₃	C₂²	1	2	yes	—
25	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
26	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
27	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
28	C₂×C₁₃×#117	C₂²	1	4	yes	—
29	C₂²×C₄²×C₁₃	C₂²	1	2	yes	—
30	C₁₃×#400	C₂²	1	4	yes	—
31	C₁₃×#399	C₂²	1	4	yes	—
32	C₁₃×#398	C₂²	1	4	yes	—
33	C₁₃×#398	C₂²	1	4	yes	—
34	C₁₃×#396	C₂²	1	4	yes	—
35	C₁₃×#396	C₂²	1	4	yes	—
36	C₁₃×#395	C₂²	1	4	yes	—
37	C₁₃×#393	C₂²	1	4	yes	—
38	C₁₃×#391	C₂²	1	2	yes	—
39	C₁₃×#391	C₂²	1	2	yes	—
40	C₁₃×#390	C₂²	1	2	yes	—
41	C₁₃×#390	C₂²	1	2	yes	—
42	C₁₃×#389	C₂²	1	2	yes	—
43	C₁₃×#389	C₂²	1	2	yes	—
44	C₁₃×#389	C₂²	1	2	yes	—
45	C₁₃×#389	C₂²	1	2	yes	—
46	C₁₃×#389	C₂²	1	2	yes	—
47	C₁₃×#389	C₂²	1	2	yes	—
48	C₁₃×#389	C₂²	1	2	yes	—
49	C₁₃×#388	C₂²	1	4	yes	—
50	C₁₃×#388	C₂²	1	4	yes	—
51	C₁₃×#387	C₂²	1	4	yes	—
52	C₁₃×#387	C₂²	1	4	yes	—
53	C₁₃×#387	C₂²	1	4	yes	—
54	C₁₃×#385	C₂²	1	4	yes	—
55	C₁₃×#384	C₂²	1	2	yes	—
56	C₁₃×#384	C₂²	1	1	yes	characteristic
57	C₁₃×#384	C₂²	1	2	yes	—
58	C₁₃×#382	C₂²	1	4	yes	—
59	C₁₃×#382	C₂²	1	2	yes	—
60	C₁₃×#380	C₂²	1	2	yes	—
61	C₁₃×#380	C₂²	1	2	yes	—
62	C₁₃×#380	C₂²	1	2	yes	—
63	C₁₃×#380	C₂²	1	4	yes	—
64	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
65	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
66	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
67	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
68	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
69	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
70	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
71	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
72	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
73	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
74	C₄×C₁₃×C₄⋊C₄	C₂²	1	4	yes	—
75	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
76	C₄×C₁₃×C₄⋊C₄	C₂²	1	4	yes	—
77	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
78	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
79	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
80	C₄×C₁₃×C₂²⋊C₄	C₂²	1	4	yes	—
81	C₄³×C₁₃	C₂²	1	1	yes	characteristic
82	C₄³×C₁₃	C₂²	1	2	yes	—
83	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
84	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
85	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
86	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
87	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
88	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
89	C₁₃×C₄⋊Q₈	—	2	4	no	—
90	C₁₃×#125	—	2	8	no	—
91	C₁₃×C₂²⋊Q₈	—	2	8	no	—
92	C₄×Q₈×C₁₃	—	2	4	no	—
93	C₄×Q₈×C₁₃	—	2	4	no	—
94	C₄×Q₈×C₁₃	—	2	4	no	—
95	C₄×Q₈×C₁₃	—	4	4	no	—
96	C₄×D₄×C₁₃	—	2	4	no	—
97	C₄×D₄×C₁₃	—	2	4	no	—
98	C₄×D₄×C₁₃	Q₈	1	8	yes	complemented
99	C₁₃×#117	—	4	8	no	—
100	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
101	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
102	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
103	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
104	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
105	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
106	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
107	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
108	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
109	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
110	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
111	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
112	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
113	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
114	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
115	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
116	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
117	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
118	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
119	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
120	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
121	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
122	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
123	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
124	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
125	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
126	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
127	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
128	C₂×C₄²×C₁₃	—	2	8	no	—
129	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
130	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
131	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
132	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
133	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
134	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
135	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
136	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
137	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
138	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
139	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
140	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
141	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
142	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
143	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
144	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
145	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
146	C₁₃×#95	C₂³	1	2	yes	—
147	C₁₃×#95	C₂³	1	2	yes	—
148	C₁₃×#95	C₂³	1	2	yes	—
149	C₁₃×#95	C₂³	1	4	yes	—
150	C₁₃×#95	C₂³	1	4	yes	—
151	C₁₃×#95	C₂³	1	2	yes	—
152	C₁₃×#95	C₂³	1	2	yes	—
153	C₁₃×#95	C₂³	1	2	yes	—
154	C₁₃×#95	C₂³	1	4	yes	—
155	C₁₃×#95	C₂³	1	4	yes	—
156	C₁₃×#95	C₂³	1	4	yes	—
157	C₁₃×#95	C₂³	1	4	yes	—
158	C₁₃×#95	C₂³	1	4	yes	—
159	C₁₃×#95	C₂³	1	4	yes	—
160	#34941	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
161	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
162	C₂×Q₈×C₁₃	—	2	2	no	—
163	C₂×Q₈×C₁₃	—	2	2	no	—
164	C₂×Q₈×C₁₃	—	2	4	no	—
165	C₂×Q₈×C₁₃	—	4	2	no	—
166	C₂×Q₈×C₁₃	—	4	2	no	—
167	C₂×Q₈×C₁₃	#41	1	4	yes	—
168	C₂×D₄×C₁₃	—	2	2	no	—
169	C₂×D₄×C₁₃	—	2	2	no	—
170	C₂×D₄×C₁₃	C₂×Q₈	1	4	yes	—
171	C₂²×C₄×C₁₃	—	2	4	no	—
172	C₂²×C₄×C₁₃	—	2	4	no	—
173	C₂²×C₄×C₁₃	—	2	4	no	—
174	C₂²×C₄×C₁₃	—	2	4	no	—
175	C₂²×C₄×C₁₃	—	2	4	no	—
176	C₂²×C₄×C₁₃	—	2	4	no	—
177	C₂²×C₄×C₁₃	—	2	4	no	—
178	C₂²×C₄×C₁₃	—	4	2	no	—
179	C₂²×C₄×C₁₃	C₂×Q₈	1	8	yes	—
180	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
181	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
182	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
183	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
184	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
185	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
186	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
187	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
188	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
189	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
190	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
191	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
192	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
193	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
194	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
195	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
196	C₁₃×C₄⋊C₄	—	2	2	no	—
197	C₁₃×C₄⋊C₄	—	2	4	no	—
198	C₁₃×C₄⋊C₄	—	2	4	no	—
199	C₁₃×C₄⋊C₄	—	2	4	no	—
200	C₁₃×C₄⋊C₄	—	2	2	no	—
201	C₁₃×C₄⋊C₄	—	2	2	no	—
202	C₁₃×C₄⋊C₄	—	2	2	no	—
203	C₁₃×C₄⋊C₄	—	2	4	no	—
204	C₁₃×C₄⋊C₄	—	2	8	no	—
205	C₁₃×C₄⋊C₄	—	2	8	no	—
206	C₁₃×C₄⋊C₄	—	2	8	no	—
207	C₁₃×C₄⋊C₄	—	2	4	no	—
208	C₁₃×C₄⋊C₄	—	2	4	no	—
209	C₁₃×C₄⋊C₄	—	2	4	no	—
210	C₁₃×C₄⋊C₄	—	4	4	no	—
211	C₁₃×C₄⋊C₄	—	4	4	no	—
212	C₁₃×C₄⋊C₄	—	4	4	no	—
213	C₁₃×C₄⋊C₄	—	4	2	no	—
214	C₁₃×C₄⋊C₄	—	4	4	no	—
215	C₁₃×C₄⋊C₄	C₂×Q₈	1	4	yes	—
216	C₁₃×C₄⋊C₄	#41	1	4	yes	—
217	C₁₃×C₂²⋊C₄	—	2	4	no	—
218	C₁₃×C₂²⋊C₄	—	2	4	no	—
219	C₁₃×C₂²⋊C₄	—	2	8	no	—
220	C₁₃×C₂²⋊C₄	—	4	4	no	—
221	C₁₃×C₂²⋊C₄	—	4	4	no	—
222	C₁₃×C₂²⋊C₄	—	4	4	no	—
223	C₁₃×C₂²⋊C₄	C₂×Q₈	1	8	yes	—
224	C₄²×C₁₃	—	2	4	no	—
225	C₄²×C₁₃	—	2	4	no	—
226	C₄²×C₁₃	—	2	4	no	—
227	C₄²×C₁₃	—	2	2	no	—
228	C₄²×C₁₃	—	2	4	no	—
229	C₄²×C₁₃	—	2	2	no	—
230	C₄²×C₁₃	—	2	4	no	—
231	C₄²×C₁₃	—	2	4	no	—
232	C₄²×C₁₃	—	2	4	no	—
233	C₄²×C₁₃	—	2	4	no	—
234	C₄²×C₁₃	—	2	8	no	—
235	C₄²×C₁₃	—	2	2	no	—
236	C₄²×C₁₃	—	4	1	no	—
237	C₄²×C₁₃	—	4	2	no	—
238	C₄²×C₁₃	C₂×Q₈	1	4	yes	—
239	C₄²×C₁₃	#41	1	4	yes	—
240	C₄²×C₁₃	#41	1	4	yes	—
241	#2574	C₂×C₁₃	1	4	yes	complemented
242	#2567	C₂×C₁₃	1	1	yes	characteristic, complemented
243	#2563	C₂×C₁₃	1	1	yes	characteristic
244	#2552	C₂×C₁₃	1	1	yes	characteristic, complemented
245	#2538	C₂×C₁₃	1	1	yes	characteristic
246	#2508	C₂×C₁₃	1	2	yes	complemented
247	#2497	C₂×C₁₃	1	2	yes	complemented
248	#2454	C₂×C₁₃	1	2	yes	—
249	#2423	C₂×C₁₃	1	2	yes	complemented
250	#2396	C₂×C₁₃	1	4	yes	complemented
251	C₄×C₄⋊Q₈	C₂×C₁₃	1	1	yes	characteristic, complemented
252	C₄×#125	C₂×C₁₃	1	2	yes	complemented
253	C₄×C₂²⋊Q₈	C₂×C₁₃	1	2	yes	complemented
254	#2293	C₂×C₁₃	1	2	yes	—
255	#2285	C₂×C₁₃	1	2	yes	complemented
256	C₄²×Q₈	C₂×C₁₃	1	1	yes	characteristic, complemented
257	C₄²×D₄	C₂×C₁₃	1	1	yes	characteristic
258	C₂³×C₁₃	—	2	2	no	—
259	C₂³×C₁₃	—	2	2	no	—
260	C₂³×C₁₃	—	2	2	no	—
261	C₂³×C₁₃	—	2	2	no	—
262	C₂³×C₁₃	—	2	2	no	—
263	C₂³×C₁₃	—	2	2	no	—
264	C₂³×C₁₃	C₂²×Q₈	1	4	yes	—
265	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
266	Q₈×C₁₃	—	2	8	no	—
267	Q₈×C₁₃	—	4	8	no	—
268	D₄×C₁₃	—	2	8	no	—
269	C₂×C₄×C₁₃	—	2	1	no	—
270	C₂×C₄×C₁₃	—	2	2	no	—
271	C₂×C₄×C₁₃	—	2	2	no	—
272	C₂×C₄×C₁₃	—	2	2	no	—
273	C₂×C₄×C₁₃	—	2	2	no	—
274	C₂×C₄×C₁₃	—	2	1	no	—
275	C₂×C₄×C₁₃	—	2	1	no	—
276	C₂×C₄×C₁₃	—	2	2	no	—
277	C₂×C₄×C₁₃	—	2	1	no	—
278	C₂×C₄×C₁₃	—	2	1	no	—
279	C₂×C₄×C₁₃	—	2	1	no	—
280	C₂×C₄×C₁₃	—	2	2	no	—
281	C₂×C₄×C₁₃	—	2	16	no	—
282	C₂×C₄×C₁₃	—	2	2	no	—
283	C₂×C₄×C₁₃	—	2	1	no	—
284	C₂×C₄×C₁₃	—	2	2	no	—
285	C₂×C₄×C₁₃	—	2	2	no	—
286	C₂×C₄×C₁₃	—	2	2	no	—
287	C₂×C₄×C₁₃	—	2	1	no	—
288	C₂×C₄×C₁₃	—	2	2	no	—
289	C₂×C₄×C₁₃	—	2	2	no	—
290	C₂×C₄×C₁₃	—	2	4	no	—
291	C₂×C₄×C₁₃	—	2	2	no	—
292	C₂×C₄×C₁₃	—	2	4	no	—
293	C₂×C₄×C₁₃	—	2	2	no	—
294	C₂×C₄×C₁₃	—	2	4	no	—
295	C₂×C₄×C₁₃	—	2	2	no	—
296	C₂×C₄×C₁₃	—	2	2	no	—
297	C₂×C₄×C₁₃	—	2	4	no	—
298	C₂×C₄×C₁₃	—	2	4	no	—
299	C₂×C₄×C₁₃	—	2	1	no	—
300	C₂×C₄×C₁₃	—	2	2	no	—
301	C₂×C₄×C₁₃	—	2	2	no	—
302	C₂×C₄×C₁₃	—	2	4	no	—
303	C₂×C₄×C₁₃	—	4	8	no	—
304	C₂×C₄×C₁₃	—	4	8	no	—
305	C₂×C₄×C₁₃	C₂²×Q₈	1	2	yes	—
306	C₂×C₄×C₁₃	C₂²×Q₈	1	4	yes	—
307	C₂×C₄×C₁₃	C₂²×Q₈	1	2	yes	—
308	C₂×C₄×C₁₃	C₂²×Q₈	1	2	yes	—
309	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
310	C₂×C₄×C₁₃	C₂×#41	1	4	yes	—
311	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
312	C₂×C₄×C₁₃	C₂×#41	1	4	yes	—
313	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
314	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
315	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
316	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
317	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
318	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
319	C₂×C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
320	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
321	C₂×#125	C₂²×C₁₃	1	2	yes	—
322	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	—
323	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
324	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
325	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
326	C₂×C₄×Q₈	C₂²×C₁₃	1	2	yes	—
327	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
328	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
329	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
330	C₂×#117	C₂²×C₁₃	1	4	yes	—
331	C₂²×C₄²	C₂²×C₁₃	1	2	yes	—
332	#400	C₂²×C₁₃	1	4	yes	—
333	#399	C₂²×C₁₃	1	4	yes	—
334	#398	C₂²×C₁₃	1	4	yes	—
335	#398	C₂²×C₁₃	1	4	yes	—
336	#396	C₂²×C₁₃	1	4	yes	—
337	#396	C₂²×C₁₃	1	4	yes	—
338	#395	C₂²×C₁₃	1	4	yes	—
339	#393	C₂²×C₁₃	1	4	yes	—
340	#391	C₂²×C₁₃	1	2	yes	—
341	#391	C₂²×C₁₃	1	2	yes	—
342	#390	C₂²×C₁₃	1	2	yes	—
343	#390	C₂²×C₁₃	1	2	yes	—
344	#389	C₂²×C₁₃	1	2	yes	—
345	#389	C₂²×C₁₃	1	2	yes	—
346	#389	C₂²×C₁₃	1	2	yes	—
347	#389	C₂²×C₁₃	1	2	yes	—
348	#389	C₂²×C₁₃	1	2	yes	—
349	#389	C₂²×C₁₃	1	2	yes	—
350	#389	C₂²×C₁₃	1	2	yes	—
351	#388	C₂²×C₁₃	1	4	yes	—
352	#388	C₂²×C₁₃	1	4	yes	—
353	#387	C₂²×C₁₃	1	4	yes	—
354	#387	C₂²×C₁₃	1	4	yes	—
355	#387	C₂²×C₁₃	1	4	yes	—
356	#385	C₂²×C₁₃	1	4	yes	—
357	#384	C₂²×C₁₃	1	1	yes	characteristic
358	#384	C₂²×C₁₃	1	2	yes	—
359	#384	C₂²×C₁₃	1	2	yes	—
360	#382	C₂²×C₁₃	1	2	yes	—
361	#382	C₂²×C₁₃	1	4	yes	—
362	#380	C₂²×C₁₃	1	2	yes	—
363	#380	C₂²×C₁₃	1	2	yes	—
364	#380	C₂²×C₁₃	1	4	yes	—
365	#380	C₂²×C₁₃	1	2	yes	—
366	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
367	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
368	C₄×C₄⋊C₄	C₂²×C₁₃	1	4	yes	—
369	C₄×C₄⋊C₄	C₂²×C₁₃	1	4	yes	—
370	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
371	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
372	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
373	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
374	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
375	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
376	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
377	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
378	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
379	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
380	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
381	C₄×C₂²⋊C₄	C₂²×C₁₃	1	4	yes	—
382	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
383	C₄³	C₂²×C₁₃	1	2	yes	—
384	C₄³	C₂²×C₁₃	1	1	yes	characteristic
385	C₂²×C₁₃	—	2	4	no	—
386	C₂²×C₁₃	—	2	4	no	—
387	C₂²×C₁₃	—	2	4	no	—
388	C₂²×C₁₃	—	4	2	no	—
389	C₂²×C₁₃	—	4	2	no	—
390	C₂²×C₁₃	—	4	2	no	—
391	C₂²×C₁₃	—	4	2	no	—
392	C₂²×C₁₃	C₂³×Q₈	1	1	yes	characteristic
393	C₂²×C₁₃	C₂²×#41	1	1	yes	characteristic
394	C₂²×C₁₃	C₂²×#41	1	1	yes	characteristic
395	C₂²×C₁₃	C₂²×#41	1	1	yes	characteristic
396	C₂²×C₁₃	C₂²×#41	1	1	yes	characteristic
397	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
398	C₂²×C₁₃	#585	1	1	yes	characteristic
399	C₄×C₁₃	—	2	4	no	—
400	C₄×C₁₃	—	2	2	no	—
401	C₄×C₁₃	—	2	4	no	—
402	C₄×C₁₃	—	2	2	no	—
403	C₄×C₁₃	—	2	4	no	—
404	C₄×C₁₃	—	2	2	no	—
405	C₄×C₁₃	—	4	2	no	—
406	C₄×C₁₃	—	4	2	no	—
407	C₄×C₁₃	—	4	4	no	—
408	C₄×C₁₃	—	4	2	no	—
409	C₄×C₁₃	—	4	1	no	—
410	C₄×C₁₃	—	4	2	no	—
411	C₄×C₁₃	—	4	4	no	—
412	C₄×C₁₃	#529	1	4	yes	—
413	C₄×C₁₃	#533	1	4	yes	—
414	C₄×C₁₃	#554	1	4	yes	—
415	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
416	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
417	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
418	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
419	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
420	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
421	C₄⋊Q₈	—	2	4	no	—
422	#125	—	2	8	no	—
423	C₂²⋊Q₈	—	2	8	no	—
424	C₄×Q₈	—	2	4	no	—
425	C₄×Q₈	—	2	4	no	—
426	C₄×Q₈	—	2	4	no	—
427	C₄×Q₈	—	4	4	no	—
428	C₄×D₄	—	2	4	no	—
429	C₄×D₄	—	2	4	no	—
430	C₄×D₄	Q₈×C₁₃	1	8	yes	complemented
431	#117	—	4	8	no	—
432	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
433	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
434	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
435	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
436	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
437	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
438	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
439	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
440	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
441	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
442	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
443	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
444	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
445	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
446	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
447	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
448	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
449	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
450	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
451	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
452	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
453	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
454	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
455	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
456	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
457	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
458	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
459	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
460	C₂×C₄²	—	2	8	no	—
461	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
462	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
463	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
464	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
465	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
466	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
467	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
468	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
469	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
470	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
471	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
472	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
473	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
474	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
475	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
476	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
477	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
478	#95	C₂³×C₁₃	1	2	yes	—
479	#95	C₂³×C₁₃	1	2	yes	—
480	#95	C₂³×C₁₃	1	2	yes	—
481	#95	C₂³×C₁₃	1	4	yes	—
482	#95	C₂³×C₁₃	1	4	yes	—
483	#95	C₂³×C₁₃	1	2	yes	—
484	#95	C₂³×C₁₃	1	2	yes	—
485	#95	C₂³×C₁₃	1	2	yes	—
486	#95	C₂³×C₁₃	1	4	yes	—
487	#95	C₂³×C₁₃	1	4	yes	—
488	#95	C₂³×C₁₃	1	4	yes	—
489	#95	C₂³×C₁₃	1	4	yes	—
490	#95	C₂³×C₁₃	1	4	yes	—
491	#95	C₂³×C₁₃	1	4	yes	—
492	C₂×C₁₃	—	4	4	no	—
493	C₂×C₁₃	C₂×#529	1	1	yes	characteristic
494	C₂×C₁₃	C₂×#533	1	1	yes	characteristic
495	C₂×C₁₃	#3460	1	1	yes	characteristic
496	C₂×C₁₃	C₂×#554	1	1	yes	characteristic
497	C₂×C₁₃	#3475	1	1	yes	characteristic
498	C₂×C₁₃	Q₈×#41	1	1	yes	characteristic
499	C₂×C₁₃	#3483	1	1	yes	characteristic
500	C₂⁴	C₂⁴×C₁₃	1	2	yes	—
501	C₂×Q₈	—	2	2	no	—
502	C₂×Q₈	—	2	2	no	—
503	C₂×Q₈	—	2	4	no	—
504	C₂×Q₈	—	4	2	no	—
505	C₂×Q₈	—	4	2	no	—
506	C₂×Q₈	C₁₃×#41	1	4	yes	—
507	C₂×D₄	—	2	2	no	—
508	C₂×D₄	—	2	2	no	—
509	C₂×D₄	C₂×Q₈×C₁₃	1	4	yes	—
510	C₂²×C₄	—	2	4	no	—
511	C₂²×C₄	—	2	4	no	—
512	C₂²×C₄	—	2	4	no	—
513	C₂²×C₄	—	2	4	no	—
514	C₂²×C₄	—	2	4	no	—
515	C₂²×C₄	—	2	4	no	—
516	C₂²×C₄	—	2	4	no	—
517	C₂²×C₄	—	4	2	no	—
518	C₂²×C₄	C₂×Q₈×C₁₃	1	8	yes	—
519	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
520	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
521	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
522	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
523	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
524	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
525	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
526	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
527	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
528	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
529	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
530	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
531	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
532	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
533	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
534	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
535	C₄⋊C₄	—	2	2	no	—
536	C₄⋊C₄	—	2	4	no	—
537	C₄⋊C₄	—	2	4	no	—
538	C₄⋊C₄	—	2	4	no	—
539	C₄⋊C₄	—	2	2	no	—
540	C₄⋊C₄	—	2	2	no	—
541	C₄⋊C₄	—	2	2	no	—
542	C₄⋊C₄	—	2	4	no	—
543	C₄⋊C₄	—	2	8	no	—
544	C₄⋊C₄	—	2	8	no	—
545	C₄⋊C₄	—	2	8	no	—
546	C₄⋊C₄	—	2	4	no	—
547	C₄⋊C₄	—	2	4	no	—
548	C₄⋊C₄	—	2	4	no	—
549	C₄⋊C₄	—	4	4	no	—
550	C₄⋊C₄	—	4	4	no	—
551	C₄⋊C₄	—	4	2	no	—
552	C₄⋊C₄	—	4	4	no	—
553	C₄⋊C₄	—	4	4	no	—
554	C₄⋊C₄	C₂×Q₈×C₁₃	1	4	yes	—
555	C₄⋊C₄	C₁₃×#41	1	4	yes	—
556	C₂²⋊C₄	—	2	4	no	—
557	C₂²⋊C₄	—	2	4	no	—
558	C₂²⋊C₄	—	2	8	no	—
559	C₂²⋊C₄	—	4	4	no	—
560	C₂²⋊C₄	—	4	4	no	—
561	C₂²⋊C₄	—	4	4	no	—
562	C₂²⋊C₄	C₂×Q₈×C₁₃	1	8	yes	—
563	C₄²	—	2	4	no	—
564	C₄²	—	2	4	no	—
565	C₄²	—	2	4	no	—
566	C₄²	—	2	2	no	—
567	C₄²	—	2	4	no	—
568	C₄²	—	2	2	no	—
569	C₄²	—	2	4	no	—
570	C₄²	—	2	4	no	—
571	C₄²	—	2	4	no	—
572	C₄²	—	2	4	no	—
573	C₄²	—	2	8	no	—
574	C₄²	—	2	2	no	—
575	C₄²	—	4	1	no	—
576	C₄²	—	4	2	no	—
577	C₄²	C₂×Q₈×C₁₃	1	4	yes	—
578	C₄²	C₁₃×#41	1	4	yes	—
579	C₄²	C₁₃×#41	1	4	yes	—
580	C₁₃	#34941	1	1	yes	characteristic, direct product factor, Sylow
581	C₂³	—	2	2	no	—
582	C₂³	—	2	2	no	—
583	C₂³	—	2	2	no	—
584	C₂³	—	2	2	no	—
585	C₂³	—	2	2	no	—
586	C₂³	—	2	2	no	—
587	C₂³	C₂²×Q₈×C₁₃	1	4	yes	—
588	C₂³	C₂⁵×C₁₃	1	1	yes	characteristic
589	Q₈	—	2	8	no	—
590	Q₈	—	4	8	no	—
591	D₄	—	2	8	no	—
592	C₂×C₄	—	2	1	no	—
593	C₂×C₄	—	2	2	no	—
594	C₂×C₄	—	2	2	no	—
595	C₂×C₄	—	2	2	no	—
596	C₂×C₄	—	2	2	no	—
597	C₂×C₄	—	2	1	no	—
598	C₂×C₄	—	2	1	no	—
599	C₂×C₄	—	2	2	no	—
600	C₂×C₄	—	2	1	no	—
601	C₂×C₄	—	2	1	no	—
602	C₂×C₄	—	2	1	no	—
603	C₂×C₄	—	2	2	no	—
604	C₂×C₄	—	2	16	no	—
605	C₂×C₄	—	2	2	no	—
606	C₂×C₄	—	2	1	no	—
607	C₂×C₄	—	2	2	no	—
608	C₂×C₄	—	2	2	no	—
609	C₂×C₄	—	2	2	no	—
610	C₂×C₄	—	2	1	no	—
611	C₂×C₄	—	2	2	no	—
612	C₂×C₄	—	2	2	no	—
613	C₂×C₄	—	2	4	no	—
614	C₂×C₄	—	2	2	no	—
615	C₂×C₄	—	2	4	no	—
616	C₂×C₄	—	2	2	no	—
617	C₂×C₄	—	2	4	no	—
618	C₂×C₄	—	2	2	no	—
619	C₂×C₄	—	2	2	no	—
620	C₂×C₄	—	2	4	no	—
621	C₂×C₄	—	2	4	no	—
622	C₂×C₄	—	2	1	no	—
623	C₂×C₄	—	2	2	no	—
624	C₂×C₄	—	2	2	no	—
625	C₂×C₄	—	2	4	no	—
626	C₂×C₄	—	4	8	no	—
627	C₂×C₄	—	4	8	no	—
628	C₂×C₄	C₂²×Q₈×C₁₃	1	2	yes	—
629	C₂×C₄	C₂²×Q₈×C₁₃	1	4	yes	—
630	C₂×C₄	C₂²×Q₈×C₁₃	1	2	yes	—
631	C₂×C₄	C₂²×Q₈×C₁₃	1	2	yes	—
632	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
633	C₂×C₄	C₂×C₁₃×#41	1	4	yes	—
634	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
635	C₂×C₄	C₂×C₁₃×#41	1	4	yes	—
636	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
637	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
638	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
639	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
640	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
641	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
642	C₂×C₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
643	C₂²	—	2	4	no	—
644	C₂²	—	2	4	no	—
645	C₂²	—	2	4	no	—
646	C₂²	—	4	2	no	—
647	C₂²	—	4	2	no	—
648	C₂²	—	4	2	no	—
649	C₂²	—	4	2	no	—
650	C₂²	C₂³×Q₈×C₁₃	1	1	yes	characteristic
651	C₂²	C₂²×C₁₃×#41	1	1	yes	characteristic
652	C₂²	C₂²×C₁₃×#41	1	1	yes	characteristic
653	C₂²	C₂²×C₁₃×#41	1	1	yes	characteristic
654	C₂²	C₂²×C₁₃×#41	1	1	yes	characteristic
655	C₂²	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
656	C₂²	C₁₃×#585	1	1	yes	characteristic
657	C₄	—	2	4	no	—
658	C₄	—	2	2	no	—
659	C₄	—	2	4	no	—
660	C₄	—	2	2	no	—
661	C₄	—	2	4	no	—
662	C₄	—	2	2	no	—
663	C₄	—	4	2	no	—
664	C₄	—	4	2	no	—
665	C₄	—	4	4	no	—
666	C₄	—	4	2	no	—
667	C₄	—	4	1	no	—
668	C₄	—	4	2	no	—
669	C₄	—	4	4	no	—
670	C₄	C₁₃×#529	1	4	yes	—
671	C₄	C₁₃×#533	1	4	yes	—
672	C₄	C₁₃×#554	1	4	yes	—
673	C₂	—	4	4	no	—
674	C₂	C₂×C₁₃×#529	1	1	yes	characteristic
675	C₂	C₂×C₁₃×#533	1	1	yes	characteristic
676	C₂	C₁₃×#3460	1	1	yes	characteristic
677	C₂	C₂×C₁₃×#554	1	1	yes	characteristic
678	C₂	C₁₃×#3475	1	1	yes	characteristic
679	C₂	Q₈×C₁₃×#41	1	1	yes	characteristic
680	C₂	C₁₃×#3483	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄×C₁₃	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁵×C₁₃
socle	C₂³×C₁₃	C₂⁵
prime radical	C₂²×D₄×C₁₃	C₂³
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
1. C₁₃×#2574	C₂	semidirect
2. C₁₃×#2567	C₂	semidirect
4. C₁₃×#2552	C₂	semidirect
6. C₁₃×#2508	C₂	semidirect
7. C₁₃×#2497	C₂	semidirect
9. C₁₃×#2423	C₂	semidirect
10. C₁₃×#2396	C₂	semidirect
11. C₄×C₁₃×C₄⋊Q₈	C₂	semidirect
12. C₄×C₁₃×#125	C₂	semidirect
13. C₄×C₁₃×C₂²⋊Q₈	C₂	semidirect
15. C₁₃×#2285	C₂	semidirect
16. C₄²×Q₈×C₁₃	C₂	semidirect
98. C₄×D₄×C₁₃	Q₈	semidirect
160. #34941	C₁₃	direct (N × H)
241. #2574	C₂×C₁₃	semidirect
242. #2567	C₂×C₁₃	semidirect
244. #2552	C₂×C₁₃	semidirect
246. #2508	C₂×C₁₃	semidirect
247. #2497	C₂×C₁₃	semidirect
249. #2423	C₂×C₁₃	semidirect
250. #2396	C₂×C₁₃	semidirect
251. C₄×C₄⋊Q₈	C₂×C₁₃	semidirect
252. C₄×#125	C₂×C₁₃	semidirect
253. C₄×C₂²⋊Q₈	C₂×C₁₃	semidirect
255. #2285	C₂×C₁₃	semidirect
256. C₄²×Q₈	C₂×C₁₃	semidirect
430. C₄×D₄	Q₈×C₁₃	semidirect
580. C₁₃	#34941	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×#2574	2
C₁₃×#2567	2
C₁₃×#2563	2
C₁₃×#2552	2
C₁₃×#2538	2
C₁₃×#2508	2
C₁₃×#2497	2
C₁₃×#2454	2
C₁₃×#2423	2
C₁₃×#2396	2
C₄×C₁₃×C₄⋊Q₈	2
C₄×C₁₃×#125	2
C₄×C₁₃×C₂²⋊Q₈	2
C₁₃×#2293	2
C₁₃×#2285	2
C₄²×Q₈×C₁₃	2
C₄²×D₄×C₁₃	2
#34941	13

Subgroups — C13×#34941 #15721280

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#34941 #15721280