Subgroups — C₁₃×#33653 #15719992

Order 3328.

568 conjugacy classes of subgroups.

The subgroup lattice has 378 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3061	C₂	1	1	yes	maximal, characteristic
2	C₁₃×#2913	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#2237	C₂	1	2	yes	maximal, complemented
4	C₁₃×#2235	C₂	1	2	yes	maximal, complemented
5	C₁₃×#2234	C₂	1	2	yes	maximal, complemented
6	C₁₃×#2233	C₂	1	2	yes	maximal, complemented
7	C₁₃×#2159	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₁₃×#367	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#2139	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#2138	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#2113	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₁₃×#135	C₂²	1	1	yes	characteristic
13	C₂×C₁₃×#131	C₂²	1	1	yes	characteristic
14	C₁₃×#537	—	2	1	no	—
15	C₁₃×#520	—	2	1	no	—
16	C₂×C₁₃×M₃₂	C₂²	1	1	yes	characteristic
17	C₂²×C₁₃×C₁₆	C₂²	1	1	yes	characteristic
18	C₁₃×#468	—	2	2	no	—
19	C₁₃×#467	C₂²	1	2	yes	—
20	C₁₃×#466	C₂²	1	2	yes	—
21	C₁₃×#428	—	2	1	no	—
22	C₁₃×#428	—	2	2	no	—
23	C₁₃×#427	C₂²	1	1	yes	characteristic
24	C₁₃×#427	C₂²	1	2	yes	—
25	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
26	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
27	C₂×C₁₃×#107	C₂²	1	2	yes	—
28	C₁₃×#417	—	2	1	no	—
29	C₁₃×#367	C₂²	1	2	yes	—
30	C₁₃×#367	C₂²	1	2	yes	—
31	C₁₃×#367	C₂²	1	2	yes	—
32	C₁₃×#366	C₂²	1	2	yes	—
33	C₁₃×#358	C₂²	1	1	yes	characteristic
34	C₁₃×#358	C₂²	1	1	yes	characteristic
35	C₁₃×#358	C₂²	1	2	yes	—
36	C₁₃×#357	C₂²	1	1	yes	characteristic
37	C₁₃×#357	C₂²	1	1	yes	characteristic
38	C₁₃×#357	C₂²	1	2	yes	—
39	C₁₃×C₂²⋊C₁₆	C₂²	1	2	yes	—
40	C₁₃×C₂²⋊C₁₆	C₂²	1	2	yes	—
41	C₂×C₁₃×#41	—	2	1	no	—
42	C₂×C₁₃×#41	D₄	1	1	yes	characteristic
43	C₁₃×#135	—	2	2	no	—
44	C₁₃×#135	—	2	2	no	—
45	C₂×C₁₃×Q₁₆	C₂³	1	1	yes	characteristic
46	C₂×C₁₃×SD₁₆	—	2	1	no	—
47	C₂×C₁₃×D₈	C₂³	1	1	yes	characteristic
48	C₁₃×#131	—	2	2	no	—
49	C₁₃×#131	—	2	2	no	—
50	C₂×C₁₃×M₁₆	D₄	1	1	yes	characteristic
51	C₂×C₁₃×M₁₆	D₄	1	2	yes	—
52	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
53	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
54	C₁₃×C₂²⋊Q₈	—	2	2	no	—
55	C₁₃×C₂²⋊Q₈	—	4	1	no	—
56	C₁₃×#121	—	2	2	no	—
57	C₁₃×#121	—	4	1	no	—
58	C₁₃×#121	—	4	2	no	—
59	C₄×Q₈×C₁₃	—	4	1	no	—
60	C₄×D₄×C₁₃	—	4	2	no	—
61	C₄×D₄×C₁₃	—	4	1	no	—
62	C₁₃×#117	—	2	2	no	—
63	C₁₃×#117	—	2	1	no	—
64	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
65	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
66	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
67	C₁₃×M₃₂	—	2	2	no	—
68	C₂×C₁₃×C₁₆	—	2	2	no	—
69	C₂×C₁₃×C₁₆	C₂³	1	2	yes	—
70	C₂×C₁₃×C₁₆	C₂³	1	1	yes	characteristic
71	C₂×C₁₃×C₁₆	C₂³	1	1	yes	characteristic
72	C₁₃×#107	—	2	2	no	—
73	C₁₃×#107	—	2	1	no	—
74	C₁₃×#107	—	2	1	no	—
75	C₁₃×#107	C₂³	1	2	yes	—
76	C₁₃×#107	C₂³	1	1	yes	characteristic
77	C₁₃×#107	C₂³	1	2	yes	—
78	C₁₃×#107	C₂³	1	1	yes	characteristic
79	C₁₃×#106	—	2	2	no	—
80	C₁₃×#106	—	2	1	no	—
81	C₁₃×#103	—	2	2	no	—
82	C₁₃×#102	—	2	2	no	—
83	#33653	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
84	C₁₃×#41	—	2	2	no	—
85	C₁₃×#41	—	2	2	no	—
86	C₁₃×#41	—	4	2	no	—
87	C₁₃×#41	—	4	2	no	—
88	C₂×Q₈×C₁₃	—	2	1	no	—
89	C₂×Q₈×C₁₃	D₈	1	1	yes	characteristic
90	C₂×D₄×C₁₃	—	2	1	no	—
91	C₂×D₄×C₁₃	—	4	1	no	—
92	C₂×D₄×C₁₃	—	4	2	no	—
93	C₂×D₄×C₁₃	D₈	1	2	yes	—
94	C₂×D₄×C₁₃	D₈	1	1	yes	characteristic
95	C₂²×C₄×C₁₃	—	4	2	no	—
96	C₂²×C₄×C₁₃	—	4	1	no	—
97	C₂²×C₄×C₁₃	—	4	1	no	—
98	C₂²×C₄×C₁₃	—	4	1	no	—
99	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
100	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
101	C₁₃×Q₁₆	—	2	1	no	—
102	C₁₃×Q₁₆	—	2	1	no	—
103	C₁₃×SD₁₆	—	4	2	no	—
104	C₁₃×D₈	—	2	1	no	—
105	C₁₃×D₈	—	2	1	no	—
106	C₁₃×M₁₆	—	2	2	no	—
107	C₁₃×M₁₆	—	2	4	no	—
108	C₂×C₈×C₁₃	—	2	2	no	—
109	C₂×C₈×C₁₃	—	2	2	no	—
110	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
111	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
112	C₂×C₈×C₁₃	#41	1	2	yes	—
113	C₂×C₈×C₁₃	#41	1	2	yes	—
114	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
115	C₁₃×C₄⋊C₄	—	2	2	no	—
116	C₁₃×C₄⋊C₄	—	2	1	no	—
117	C₁₃×C₄⋊C₄	—	2	2	no	—
118	C₁₃×C₄⋊C₄	—	2	1	no	—
119	C₁₃×C₄⋊C₄	—	4	2	no	—
120	C₁₃×C₄⋊C₄	—	4	1	no	—
121	C₁₃×C₄⋊C₄	—	4	1	no	—
122	C₁₃×C₄⋊C₄	—	4	2	no	—
123	C₁₃×C₂²⋊C₄	—	4	2	no	—
124	C₁₃×C₂²⋊C₄	—	4	1	no	—
125	C₁₃×C₂²⋊C₄	—	4	2	no	—
126	C₁₃×C₂²⋊C₄	—	4	2	no	—
127	C₄²×C₁₃	—	4	2	no	—
128	C₄²×C₁₃	—	4	1	no	—
129	C₁₃×C₁₆	—	2	1	no	—
130	C₁₃×C₁₆	—	2	1	no	—
131	C₁₃×C₁₆	—	2	2	no	—
132	#3061	C₂×C₁₃	1	1	yes	characteristic
133	#2913	C₂×C₁₃	1	1	yes	characteristic, complemented
134	#2237	C₂×C₁₃	1	2	yes	complemented
135	#2235	C₂×C₁₃	1	2	yes	complemented
136	#2234	C₂×C₁₃	1	2	yes	complemented
137	#2233	C₂×C₁₃	1	2	yes	complemented
138	#2159	C₂×C₁₃	1	1	yes	characteristic, complemented
139	C₂×#367	C₂×C₁₃	1	1	yes	characteristic, complemented
140	#2139	C₂×C₁₃	1	1	yes	characteristic, complemented
141	#2138	C₂×C₁₃	1	1	yes	characteristic, complemented
142	#2113	C₂×C₁₃	1	1	yes	characteristic, complemented
143	C₂³×C₁₃	—	4	1	no	—
144	C₂³×C₁₃	C₂×D₈	1	2	yes	—
145	C₂³×C₁₃	C₂×D₈	1	1	yes	characteristic
146	Q₈×C₁₃	—	2	2	no	—
147	Q₈×C₁₃	—	4	1	no	—
148	Q₈×C₁₃	—	4	1	no	—
149	D₄×C₁₃	—	2	4	no	—
150	D₄×C₁₃	—	2	2	no	—
151	D₄×C₁₃	—	4	1	no	—
152	D₄×C₁₃	—	4	1	no	—
153	D₄×C₁₃	—	8	2	no	—
154	D₄×C₁₃	—	16	2	no	—
155	C₂×C₄×C₁₃	—	2	2	no	—
156	C₂×C₄×C₁₃	—	2	2	no	—
157	C₂×C₄×C₁₃	—	4	1	no	—
158	C₂×C₄×C₁₃	—	4	2	no	—
159	C₂×C₄×C₁₃	—	4	1	no	—
160	C₂×C₄×C₁₃	—	4	2	no	—
161	C₂×C₄×C₁₃	—	4	1	no	—
162	C₂×C₄×C₁₃	—	8	2	no	—
163	C₂×C₄×C₁₃	—	16	1	no	—
164	C₂×C₄×C₁₃	—	16	2	no	—
165	C₂×C₄×C₁₃	—	16	1	no	—
166	C₂×C₄×C₁₃	#123	1	2	yes	—
167	C₂×C₄×C₁₃	C₂×D₈	1	2	yes	—
168	C₂×C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
169	C₂×C₄×C₁₃	#137	1	2	yes	—
170	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
171	C₈×C₁₃	—	2	2	no	—
172	C₈×C₁₃	#123	1	2	yes	—
173	C₈×C₁₃	C₂×#41	1	1	yes	characteristic
174	C₈×C₁₃	C₂×#41	1	1	yes	characteristic
175	C₂×#135	C₂²×C₁₃	1	1	yes	characteristic
176	C₂×#131	C₂²×C₁₃	1	1	yes	characteristic
177	#537	—	2	1	no	—
178	#520	—	2	1	no	—
179	C₂×M₃₂	C₂²×C₁₃	1	1	yes	characteristic
180	C₂²×C₁₆	C₂²×C₁₃	1	1	yes	characteristic
181	#468	—	2	2	no	—
182	#467	C₂²×C₁₃	1	2	yes	—
183	#466	C₂²×C₁₃	1	2	yes	—
184	#428	—	2	1	no	—
185	#428	—	2	2	no	—
186	#427	C₂²×C₁₃	1	1	yes	characteristic
187	#427	C₂²×C₁₃	1	2	yes	—
188	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
189	C₂×#107	C₂²×C₁₃	1	2	yes	—
190	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
191	#417	—	2	1	no	—
192	#367	C₂²×C₁₃	1	2	yes	—
193	#367	C₂²×C₁₃	1	2	yes	—
194	#367	C₂²×C₁₃	1	2	yes	—
195	#366	C₂²×C₁₃	1	2	yes	—
196	#358	C₂²×C₁₃	1	1	yes	characteristic
197	#358	C₂²×C₁₃	1	1	yes	characteristic
198	#358	C₂²×C₁₃	1	2	yes	—
199	#357	C₂²×C₁₃	1	1	yes	characteristic
200	#357	C₂²×C₁₃	1	1	yes	characteristic
201	#357	C₂²×C₁₃	1	2	yes	—
202	C₂²⋊C₁₆	C₂²×C₁₃	1	2	yes	—
203	C₂²⋊C₁₆	C₂²×C₁₃	1	2	yes	—
204	C₂²×C₁₃	—	2	1	no	—
205	C₂²×C₁₃	—	2	1	no	—
206	C₂²×C₁₃	—	2	2	no	—
207	C₂²×C₁₃	—	2	2	no	—
208	C₂²×C₁₃	—	2	2	no	—
209	C₂²×C₁₃	—	8	1	no	—
210	C₂²×C₁₃	—	8	1	no	—
211	C₂²×C₁₃	—	8	1	no	—
212	C₂²×C₁₃	#480	1	2	yes	—
213	C₂²×C₁₃	C₂²×D₈	1	1	yes	characteristic
214	C₄×C₁₃	—	2	2	no	—
215	C₄×C₁₃	—	8	1	no	—
216	C₄×C₁₃	—	8	1	no	—
217	C₄×C₁₃	—	8	2	no	—
218	C₄×C₁₃	—	8	1	no	—
219	C₄×C₁₃	—	8	2	no	—
220	C₄×C₁₃	#480	1	2	yes	—
221	C₄×C₁₃	C₂×#123	1	1	yes	characteristic
222	C₄×C₁₃	C₂×#137	1	1	yes	characteristic
223	C₂×#41	—	2	1	no	—
224	C₂×#41	D₄×C₁₃	1	1	yes	characteristic
225	#135	—	2	2	no	—
226	#135	—	2	2	no	—
227	C₂×Q₁₆	C₂³×C₁₃	1	1	yes	characteristic
228	C₂×SD₁₆	—	2	1	no	—
229	C₂×D₈	C₂³×C₁₃	1	1	yes	characteristic
230	#131	—	2	2	no	—
231	#131	—	2	2	no	—
232	C₂×M₁₆	D₄×C₁₃	1	1	yes	characteristic
233	C₂×M₁₆	D₄×C₁₃	1	2	yes	—
234	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
235	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
236	C₂²⋊Q₈	—	2	2	no	—
237	C₂²⋊Q₈	—	4	1	no	—
238	#121	—	2	2	no	—
239	#121	—	4	1	no	—
240	#121	—	4	2	no	—
241	C₄×Q₈	—	4	1	no	—
242	C₄×D₄	—	4	2	no	—
243	C₄×D₄	—	4	1	no	—
244	#117	—	2	2	no	—
245	#117	—	2	1	no	—
246	C₂×C₄⋊C₄	—	2	2	no	—
247	C₂×C₄⋊C₄	—	2	1	no	—
248	C₂×C₄⋊C₄	—	2	1	no	—
249	M₃₂	—	2	2	no	—
250	C₂×C₁₆	—	2	2	no	—
251	C₂×C₁₆	C₂³×C₁₃	1	2	yes	—
252	C₂×C₁₆	C₂³×C₁₃	1	1	yes	characteristic
253	C₂×C₁₆	C₂³×C₁₃	1	1	yes	characteristic
254	#107	—	2	2	no	—
255	#107	—	2	1	no	—
256	#107	—	2	1	no	—
257	#107	C₂³×C₁₃	1	1	yes	characteristic
258	#107	C₂³×C₁₃	1	1	yes	characteristic
259	#107	C₂³×C₁₃	1	2	yes	—
260	#107	C₂³×C₁₃	1	2	yes	—
261	#106	—	2	2	no	—
262	#106	—	2	1	no	—
263	#103	—	2	2	no	—
264	#102	—	2	2	no	—
265	C₂×C₁₃	—	2	2	no	—
266	C₂×C₁₃	—	4	2	no	—
267	C₂×C₁₃	—	16	1	no	—
268	C₂×C₁₃	C₂×#480	1	1	yes	characteristic
269	C₂×C₁₃	#3416	1	1	yes	characteristic
270	C₂×C₁₃	#3416	1	1	yes	characteristic
271	#41	—	2	2	no	—
272	#41	—	2	2	no	—
273	#41	—	4	2	no	—
274	#41	—	4	2	no	—
275	C₂×Q₈	—	2	1	no	—
276	C₂×Q₈	C₁₃×D₈	1	1	yes	characteristic
277	C₂×D₄	—	2	1	no	—
278	C₂×D₄	—	4	1	no	—
279	C₂×D₄	—	4	2	no	—
280	C₂×D₄	C₁₃×D₈	1	2	yes	—
281	C₂×D₄	C₁₃×D₈	1	1	yes	characteristic
282	C₂²×C₄	—	4	2	no	—
283	C₂²×C₄	—	4	1	no	—
284	C₂²×C₄	—	4	1	no	—
285	C₂²×C₄	—	4	1	no	—
286	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
287	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
288	Q₁₆	—	2	1	no	—
289	Q₁₆	—	2	1	no	—
290	SD₁₆	—	4	2	no	—
291	D₈	—	2	1	no	—
292	D₈	—	2	1	no	—
293	M₁₆	—	2	2	no	—
294	M₁₆	—	2	4	no	—
295	C₂×C₈	—	2	2	no	—
296	C₂×C₈	—	2	2	no	—
297	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
298	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
299	C₂×C₈	C₁₃×#41	1	2	yes	—
300	C₂×C₈	C₁₃×#41	1	2	yes	—
301	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
302	C₄⋊C₄	—	2	2	no	—
303	C₄⋊C₄	—	2	1	no	—
304	C₄⋊C₄	—	2	2	no	—
305	C₄⋊C₄	—	2	1	no	—
306	C₄⋊C₄	—	4	2	no	—
307	C₄⋊C₄	—	4	1	no	—
308	C₄⋊C₄	—	4	1	no	—
309	C₄⋊C₄	—	4	2	no	—
310	C₂²⋊C₄	—	4	2	no	—
311	C₂²⋊C₄	—	4	1	no	—
312	C₂²⋊C₄	—	4	2	no	—
313	C₂²⋊C₄	—	4	2	no	—
314	C₄²	—	4	2	no	—
315	C₄²	—	4	1	no	—
316	C₁₆	—	2	1	no	—
317	C₁₆	—	2	1	no	—
318	C₁₆	—	2	2	no	—
319	C₁₃	#33653	1	1	yes	characteristic, direct product factor, Sylow
320	C₂³	—	4	1	no	—
321	C₂³	C₂×C₁₃×D₈	1	2	yes	—
322	C₂³	C₂×C₁₃×D₈	1	1	yes	characteristic
323	Q₈	—	2	2	no	—
324	Q₈	—	4	1	no	—
325	Q₈	—	4	1	no	—
326	D₄	—	2	4	no	—
327	D₄	—	2	2	no	—
328	D₄	—	4	1	no	—
329	D₄	—	4	1	no	—
330	D₄	—	8	2	no	—
331	D₄	—	16	2	no	—
332	C₂×C₄	—	2	2	no	—
333	C₂×C₄	—	2	2	no	—
334	C₂×C₄	—	4	1	no	—
335	C₂×C₄	—	4	2	no	—
336	C₂×C₄	—	4	1	no	—
337	C₂×C₄	—	4	2	no	—
338	C₂×C₄	—	4	1	no	—
339	C₂×C₄	—	8	2	no	—
340	C₂×C₄	—	16	1	no	—
341	C₂×C₄	—	16	2	no	—
342	C₂×C₄	—	16	1	no	—
343	C₂×C₄	C₁₃×#123	1	2	yes	—
344	C₂×C₄	C₂×C₁₃×D₈	1	2	yes	—
345	C₂×C₄	C₂×C₁₃×D₈	1	1	yes	characteristic
346	C₂×C₄	C₁₃×#137	1	2	yes	—
347	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
348	C₈	—	2	2	no	—
349	C₈	C₁₃×#123	1	2	yes	—
350	C₈	C₂×C₁₃×#41	1	1	yes	characteristic
351	C₈	C₂×C₁₃×#41	1	1	yes	characteristic
352	C₂²	—	2	1	no	—
353	C₂²	—	2	1	no	—
354	C₂²	—	2	2	no	—
355	C₂²	—	2	2	no	—
356	C₂²	—	2	2	no	—
357	C₂²	—	8	1	no	—
358	C₂²	—	8	1	no	—
359	C₂²	—	8	1	no	—
360	C₂²	C₁₃×#480	1	2	yes	—
361	C₂²	C₂²×C₁₃×D₈	1	1	yes	characteristic
362	C₄	—	2	2	no	—
363	C₄	—	8	1	no	—
364	C₄	—	8	1	no	—
365	C₄	—	8	2	no	—
366	C₄	—	8	1	no	—
367	C₄	—	8	2	no	—
368	C₄	C₁₃×#480	1	2	yes	—
369	C₄	C₂×C₁₃×#123	1	1	yes	characteristic
370	C₄	C₂×C₁₃×#137	1	1	yes	characteristic
371	C₂	—	2	2	no	—
372	C₂	—	4	2	no	—
373	C₂	—	16	1	no	—
374	C₂	C₂×C₁₃×#480	1	1	yes	characteristic
375	C₂	C₁₃×#3416	1	1	yes	characteristic
376	C₂	C₁₃×#3416	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂²×D₈
commutator, Frattini, cosocle	C₂×C₈	C₂⁴×C₁₃
prime radical	C₁₃×#3061	C₂
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₂×C₁₃×#41 ◁ C₂×C₁₃×#131 ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₃×#2913	C₂	semidirect
3. C₁₃×#2237	C₂	semidirect
4. C₁₃×#2235	C₂	semidirect
5. C₁₃×#2234	C₂	semidirect
6. C₁₃×#2233	C₂	semidirect
7. C₁₃×#2159	C₂	semidirect
8. C₂×C₁₃×#367	C₂	semidirect
9. C₁₃×#2139	C₂	semidirect
10. C₁₃×#2138	C₂	semidirect
11. C₁₃×#2113	C₂	semidirect
83. #33653	C₁₃	direct (N × H)
133. #2913	C₂×C₁₃	semidirect
134. #2237	C₂×C₁₃	semidirect
135. #2235	C₂×C₁₃	semidirect
136. #2234	C₂×C₁₃	semidirect
137. #2233	C₂×C₁₃	semidirect
138. #2159	C₂×C₁₃	semidirect
139. C₂×#367	C₂×C₁₃	semidirect
140. #2139	C₂×C₁₃	semidirect
141. #2138	C₂×C₁₃	semidirect
142. #2113	C₂×C₁₃	semidirect
319. C₁₃	#33653	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×#3061	2
C₁₃×#2913	2
C₁₃×#2237	2
C₁₃×#2235	2
C₁₃×#2234	2
C₁₃×#2233	2
C₁₃×#2159	2
C₂×C₁₃×#367	2
C₁₃×#2139	2
C₁₃×#2138	2
C₁₃×#2113	2
#33653	13

Subgroups — C13×#33653 #15719992

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#33653 #15719992