Subgroups — C₁₃×#3510 #13112568

Order 1664.

1040 conjugacy classes of subgroups.

The subgroup lattice has 304 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#559	C₂	1	4	yes	maximal, complemented
2	C₁₃×#556	C₂	1	4	yes	maximal, complemented
3	C₁₃×#551	C₂	1	8	yes	maximal, complemented
4	C₁₃×#542	C₂	1	4	yes	maximal, complemented
5	C₁₃×#536	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#535	C₂	1	1	yes	maximal, characteristic
7	C₁₃×#533	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#529	C₂	1	4	yes	maximal, complemented
9	C₂×C₁₃×#124	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#519	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#518	C₂	1	1	yes	maximal, characteristic, complemented
12	C₄×C₁₃×#41	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×C₁₃×#41	C₂²	1	1	yes	characteristic
14	C₂²×Q₈×C₁₃	C₂²	1	1	yes	characteristic
15	C₂²×D₄×C₁₃	C₂²	1	1	yes	characteristic
16	C₁₃×C₄⋊Q₈	C₂²	1	2	yes	complemented
17	C₁₃×C₄⋊Q₈	C₂²	1	2	yes	complemented
18	C₁₃×#127	C₂²	1	2	yes	—
19	C₁₃×#126	C₂²	1	8	yes	complemented
20	C₁₃×#126	C₂²	1	8	yes	complemented
21	C₁₃×#125	C₂²	1	2	yes	complemented
22	C₁₃×#124	C₂²	1	2	yes	—
23	C₁₃×#124	C₂²	1	2	yes	—
24	C₁₃×#124	C₂²	1	4	yes	—
25	C₁₃×#124	C₂²	1	2	yes	—
26	C₁₃×#124	C₂²	1	2	yes	complemented
27	C₁₃×#124	C₂²	1	8	yes	complemented
28	C₁₃×#123	C₂²	1	4	yes	—
29	C₁₃×#123	C₂²	1	8	yes	complemented
30	C₁₃×#123	C₂²	1	8	yes	complemented
31	C₁₃×C₂²⋊Q₈	C₂²	1	4	yes	—
32	C₁₃×C₂²⋊Q₈	C₂²	1	4	yes	complemented
33	C₁₃×C₂²⋊Q₈	C₂²	1	8	yes	complemented
34	C₁₃×#121	C₂²	1	4	yes	—
35	C₁₃×#120	C₂²	1	4	yes	—
36	C₄×Q₈×C₁₃	C₂²	1	2	yes	complemented
37	C₄×Q₈×C₁₃	C₂²	1	4	yes	complemented
38	C₄×Q₈×C₁₃	C₂²	1	4	yes	complemented
39	C₄×Q₈×C₁₃	C₂²	1	4	yes	complemented
40	C₄×D₄×C₁₃	C₂²	1	4	yes	—
41	C₄×D₄×C₁₃	C₂²	1	4	yes	—
42	C₄×D₄×C₁₃	C₂²	1	4	yes	—
43	C₄×D₄×C₁₃	C₂²	1	2	yes	complemented
44	C₄×D₄×C₁₃	C₂²	1	8	yes	complemented
45	C₁₃×#117	C₂²	1	1	yes	characteristic
46	C₁₃×#117	C₂²	1	1	yes	characteristic
47	C₁₃×#117	C₂²	1	1	yes	characteristic
48	C₁₃×#117	C₂²	1	4	yes	—
49	C₁₃×#117	C₂²	1	2	yes	complemented
50	C₁₃×#117	C₂²	1	8	yes	complemented
51	C₂×C₁₃×C₂²⋊C₄	C₂²	1	4	yes	—
52	C₂×C₁₃×C₂²⋊C₄	C₂²	1	4	yes	—
53	C₂×C₄²×C₁₃	C₂²	1	1	yes	characteristic
54	C₂×C₄²×C₁₃	C₂²	1	2	yes	complemented
55	C₂⁴×C₁₃	C₂³	1	2	yes	—
56	C₁₃×#41	—	2	4	no	—
57	C₂×Q₈×C₁₃	—	2	4	no	—
58	C₂×Q₈×C₁₃	C₂³	1	2	yes	—
59	C₂×Q₈×C₁₃	C₂³	1	2	yes	—
60	C₂×Q₈×C₁₃	C₂³	1	1	yes	characteristic
61	C₂×Q₈×C₁₃	C₂³	1	4	yes	—
62	C₂×D₄×C₁₃	—	2	4	no	—
63	C₂×D₄×C₁₃	C₂³	1	2	yes	—
64	C₂×D₄×C₁₃	C₂³	1	2	yes	—
65	C₂×D₄×C₁₃	C₂³	1	2	yes	—
66	C₂×D₄×C₁₃	C₂³	1	1	yes	characteristic
67	C₂×D₄×C₁₃	C₂³	1	8	yes	—
68	C₂²×C₄×C₁₃	C₂³	1	2	yes	—
69	C₂²×C₄×C₁₃	C₂³	1	2	yes	—
70	C₂²×C₄×C₁₃	C₂³	1	2	yes	—
71	C₂²×C₄×C₁₃	C₂³	1	4	yes	—
72	C₂²×C₄×C₁₃	C₂³	1	8	yes	—
73	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
74	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
75	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
76	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
77	C₁₃×C₄⋊C₄	C₂³	1	8	yes	—
78	C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
79	C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
80	C₁₃×C₄⋊C₄	C₂³	1	8	yes	—
81	C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
82	C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
83	C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
84	C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
85	C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
86	C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
87	C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
88	C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
89	C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
90	C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
91	C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
92	C₄²×C₁₃	C₂³	1	1	yes	characteristic
93	C₄²×C₁₃	C₂³	1	1	yes	characteristic
94	C₄²×C₁₃	C₂³	1	2	yes	—
95	C₄²×C₁₃	C₂³	1	2	yes	—
96	C₄²×C₁₃	C₂³	1	4	yes	—
97	C₄²×C₁₃	C₂³	1	8	yes	—
98	C₄²×C₁₃	C₂³	1	2	yes	—
99	C₄²×C₁₃	C₂³	1	2	yes	—
100	#3510	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
101	C₂³×C₁₃	—	2	4	no	—
102	C₂³×C₁₃	—	4	4	no	—
103	C₂³×C₁₃	C₂⁴	1	4	yes	—
104	C₂³×C₁₃	C₂⁴	1	2	yes	—
105	C₂³×C₁₃	C₂⁴	1	1	yes	characteristic
106	Q₈×C₁₃	—	2	4	no	—
107	Q₈×C₁₃	—	2	4	no	—
108	Q₈×C₁₃	—	2	2	no	—
109	Q₈×C₁₃	—	4	4	no	—
110	D₄×C₁₃	—	2	4	no	—
111	D₄×C₁₃	—	2	4	no	—
112	D₄×C₁₃	—	2	4	no	—
113	D₄×C₁₃	—	2	2	no	—
114	D₄×C₁₃	—	4	8	no	—
115	C₂×C₄×C₁₃	—	2	4	no	—
116	C₂×C₄×C₁₃	—	2	4	no	—
117	C₂×C₄×C₁₃	—	4	4	no	—
118	C₂×C₄×C₁₃	—	4	8	no	—
119	C₂×C₄×C₁₃	—	4	2	no	—
120	C₂×C₄×C₁₃	#41	1	4	yes	—
121	C₂×C₄×C₁₃	C₂⁴	1	2	yes	—
122	C₂×C₄×C₁₃	C₂⁴	1	4	yes	—
123	C₂×C₄×C₁₃	C₂⁴	1	4	yes	—
124	C₂×C₄×C₁₃	C₂⁴	1	4	yes	—
125	C₂×C₄×C₁₃	C₂⁴	1	2	yes	—
126	C₂×C₄×C₁₃	C₂⁴	1	2	yes	—
127	C₂×C₄×C₁₃	C₂⁴	1	4	yes	—
128	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
129	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
130	#559	C₂×C₁₃	1	4	yes	complemented
131	#556	C₂×C₁₃	1	4	yes	complemented
132	#551	C₂×C₁₃	1	8	yes	complemented
133	#542	C₂×C₁₃	1	4	yes	complemented
134	#536	C₂×C₁₃	1	1	yes	characteristic, complemented
135	#535	C₂×C₁₃	1	1	yes	characteristic
136	#533	C₂×C₁₃	1	1	yes	characteristic, complemented
137	#529	C₂×C₁₃	1	4	yes	complemented
138	C₂×#124	C₂×C₁₃	1	1	yes	characteristic, complemented
139	#519	C₂×C₁₃	1	1	yes	characteristic, complemented
140	#518	C₂×C₁₃	1	1	yes	characteristic, complemented
141	C₄×#41	C₂×C₁₃	1	1	yes	characteristic, complemented
142	C₂²×C₁₃	—	2	2	no	—
143	C₂²×C₁₃	—	2	2	no	—
144	C₂²×C₁₃	—	2	4	no	—
145	C₂²×C₁₃	—	2	4	no	—
146	C₂²×C₁₃	—	2	8	no	—
147	C₂²×C₁₃	—	8	4	no	—
148	C₂²×C₁₃	C₂×#41	1	2	yes	—
149	C₂²×C₁₃	C₂⁵	1	1	yes	characteristic
150	C₄×C₁₃	—	2	2	no	—
151	C₄×C₁₃	—	2	4	no	—
152	C₄×C₁₃	—	2	2	no	—
153	C₄×C₁₃	—	2	4	no	—
154	C₄×C₁₃	—	2	4	no	—
155	C₄×C₁₃	—	2	2	no	—
156	C₄×C₁₃	—	2	4	no	—
157	C₄×C₁₃	C₂×#41	1	2	yes	—
158	C₄×C₁₃	C₂×#41	1	2	yes	—
159	C₂×#41	C₂²×C₁₃	1	1	yes	characteristic
160	C₂²×Q₈	C₂²×C₁₃	1	1	yes	characteristic
161	C₂²×D₄	C₂²×C₁₃	1	1	yes	characteristic
162	C₄⋊Q₈	C₂²×C₁₃	1	2	yes	complemented
163	C₄⋊Q₈	C₂²×C₁₃	1	2	yes	complemented
164	#127	C₂²×C₁₃	1	2	yes	—
165	#126	C₂²×C₁₃	1	8	yes	complemented
166	#126	C₂²×C₁₃	1	8	yes	complemented
167	#125	C₂²×C₁₃	1	2	yes	complemented
168	#124	C₂²×C₁₃	1	2	yes	—
169	#124	C₂²×C₁₃	1	2	yes	—
170	#124	C₂²×C₁₃	1	4	yes	—
171	#124	C₂²×C₁₃	1	2	yes	—
172	#124	C₂²×C₁₃	1	2	yes	complemented
173	#124	C₂²×C₁₃	1	8	yes	complemented
174	#123	C₂²×C₁₃	1	4	yes	—
175	#123	C₂²×C₁₃	1	8	yes	complemented
176	#123	C₂²×C₁₃	1	8	yes	complemented
177	C₂²⋊Q₈	C₂²×C₁₃	1	4	yes	—
178	C₂²⋊Q₈	C₂²×C₁₃	1	4	yes	complemented
179	C₂²⋊Q₈	C₂²×C₁₃	1	8	yes	complemented
180	#121	C₂²×C₁₃	1	4	yes	—
181	#120	C₂²×C₁₃	1	4	yes	—
182	C₄×Q₈	C₂²×C₁₃	1	2	yes	complemented
183	C₄×Q₈	C₂²×C₁₃	1	4	yes	complemented
184	C₄×Q₈	C₂²×C₁₃	1	4	yes	complemented
185	C₄×Q₈	C₂²×C₁₃	1	4	yes	complemented
186	C₄×D₄	C₂²×C₁₃	1	4	yes	—
187	C₄×D₄	C₂²×C₁₃	1	4	yes	—
188	C₄×D₄	C₂²×C₁₃	1	4	yes	—
189	C₄×D₄	C₂²×C₁₃	1	2	yes	complemented
190	C₄×D₄	C₂²×C₁₃	1	8	yes	complemented
191	#117	C₂²×C₁₃	1	1	yes	characteristic
192	#117	C₂²×C₁₃	1	1	yes	characteristic
193	#117	C₂²×C₁₃	1	1	yes	characteristic
194	#117	C₂²×C₁₃	1	4	yes	—
195	#117	C₂²×C₁₃	1	2	yes	complemented
196	#117	C₂²×C₁₃	1	8	yes	complemented
197	C₂×C₂²⋊C₄	C₂²×C₁₃	1	4	yes	—
198	C₂×C₂²⋊C₄	C₂²×C₁₃	1	4	yes	—
199	C₂×C₄²	C₂²×C₁₃	1	1	yes	characteristic
200	C₂×C₄²	C₂²×C₁₃	1	2	yes	complemented
201	C₂×C₁₃	—	2	2	no	—
202	C₂×C₁₃	—	4	2	no	—
203	C₂×C₁₃	—	4	4	no	—
204	C₂×C₁₃	C₂²×#41	1	1	yes	characteristic
205	C₂×C₁₃	#585	1	2	yes	—
206	C₂⁴	C₂³×C₁₃	1	2	yes	—
207	#41	—	2	4	no	—
208	C₂×Q₈	—	2	4	no	—
209	C₂×Q₈	C₂³×C₁₃	1	2	yes	—
210	C₂×Q₈	C₂³×C₁₃	1	2	yes	—
211	C₂×Q₈	C₂³×C₁₃	1	1	yes	characteristic
212	C₂×Q₈	C₂³×C₁₃	1	4	yes	—
213	C₂×D₄	—	2	4	no	—
214	C₂×D₄	C₂³×C₁₃	1	2	yes	—
215	C₂×D₄	C₂³×C₁₃	1	2	yes	—
216	C₂×D₄	C₂³×C₁₃	1	2	yes	—
217	C₂×D₄	C₂³×C₁₃	1	1	yes	characteristic
218	C₂×D₄	C₂³×C₁₃	1	8	yes	—
219	C₂²×C₄	C₂³×C₁₃	1	2	yes	—
220	C₂²×C₄	C₂³×C₁₃	1	2	yes	—
221	C₂²×C₄	C₂³×C₁₃	1	2	yes	—
222	C₂²×C₄	C₂³×C₁₃	1	4	yes	—
223	C₂²×C₄	C₂³×C₁₃	1	8	yes	—
224	C₂²×C₄	C₂³×C₁₃	1	1	yes	characteristic
225	C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
226	C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
227	C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
228	C₄⋊C₄	C₂³×C₁₃	1	8	yes	—
229	C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
230	C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
231	C₄⋊C₄	C₂³×C₁₃	1	8	yes	—
232	C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
233	C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
234	C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
235	C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
236	C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
237	C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
238	C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
239	C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
240	C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
241	C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
242	C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
243	C₄²	C₂³×C₁₃	1	1	yes	characteristic
244	C₄²	C₂³×C₁₃	1	1	yes	characteristic
245	C₄²	C₂³×C₁₃	1	2	yes	—
246	C₄²	C₂³×C₁₃	1	2	yes	—
247	C₄²	C₂³×C₁₃	1	4	yes	—
248	C₄²	C₂³×C₁₃	1	8	yes	—
249	C₄²	C₂³×C₁₃	1	2	yes	—
250	C₄²	C₂³×C₁₃	1	2	yes	—
251	C₁₃	#3510	1	1	yes	characteristic, direct product factor, Sylow
252	C₂³	—	2	4	no	—
253	C₂³	—	4	4	no	—
254	C₂³	C₂⁴×C₁₃	1	4	yes	—
255	C₂³	C₂⁴×C₁₃	1	2	yes	—
256	C₂³	C₂⁴×C₁₃	1	1	yes	characteristic
257	Q₈	—	2	4	no	—
258	Q₈	—	2	4	no	—
259	Q₈	—	2	2	no	—
260	Q₈	—	4	4	no	—
261	D₄	—	2	4	no	—
262	D₄	—	2	4	no	—
263	D₄	—	2	4	no	—
264	D₄	—	2	2	no	—
265	D₄	—	4	8	no	—
266	C₂×C₄	—	2	4	no	—
267	C₂×C₄	—	2	4	no	—
268	C₂×C₄	—	4	4	no	—
269	C₂×C₄	—	4	8	no	—
270	C₂×C₄	—	4	2	no	—
271	C₂×C₄	C₁₃×#41	1	4	yes	—
272	C₂×C₄	C₂⁴×C₁₃	1	2	yes	—
273	C₂×C₄	C₂⁴×C₁₃	1	4	yes	—
274	C₂×C₄	C₂⁴×C₁₃	1	4	yes	—
275	C₂×C₄	C₂⁴×C₁₃	1	4	yes	—
276	C₂×C₄	C₂⁴×C₁₃	1	2	yes	—
277	C₂×C₄	C₂⁴×C₁₃	1	2	yes	—
278	C₂×C₄	C₂⁴×C₁₃	1	4	yes	—
279	C₂×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
280	C₂×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
281	C₂²	—	2	2	no	—
282	C₂²	—	2	2	no	—
283	C₂²	—	2	4	no	—
284	C₂²	—	2	4	no	—
285	C₂²	—	2	8	no	—
286	C₂²	—	8	4	no	—
287	C₂²	C₂×C₁₃×#41	1	2	yes	—
288	C₂²	C₂⁵×C₁₃	1	1	yes	characteristic
289	C₄	—	2	2	no	—
290	C₄	—	2	4	no	—
291	C₄	—	2	2	no	—
292	C₄	—	2	4	no	—
293	C₄	—	2	4	no	—
294	C₄	—	2	2	no	—
295	C₄	—	2	4	no	—
296	C₄	C₂×C₁₃×#41	1	2	yes	—
297	C₄	C₂×C₁₃×#41	1	2	yes	—
298	C₂	—	2	2	no	—
299	C₂	—	4	4	no	—
300	C₂	—	4	2	no	—
301	C₂	C₂²×C₁₃×#41	1	1	yes	characteristic
302	C₂	C₁₃×#585	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂⁵
commutator, Frattini, cosocle	C₂²	C₂⁵×C₁₃
prime radical	C₁₃×#535	C₂
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₃×#559	C₂	semidirect
2. C₁₃×#556	C₂	semidirect
3. C₁₃×#551	C₂	semidirect
4. C₁₃×#542	C₂	semidirect
5. C₁₃×#536	C₂	semidirect
7. C₁₃×#533	C₂	semidirect
8. C₁₃×#529	C₂	semidirect
9. C₂×C₁₃×#124	C₂	semidirect
10. C₁₃×#519	C₂	semidirect
11. C₁₃×#518	C₂	semidirect
12. C₄×C₁₃×#41	C₂	semidirect
16. C₁₃×C₄⋊Q₈	C₂²	semidirect
17. C₁₃×C₄⋊Q₈	C₂²	semidirect
19. C₁₃×#126	C₂²	semidirect
20. C₁₃×#126	C₂²	semidirect
21. C₁₃×#125	C₂²	semidirect
26. C₁₃×#124	C₂²	semidirect
27. C₁₃×#124	C₂²	semidirect
29. C₁₃×#123	C₂²	semidirect
30. C₁₃×#123	C₂²	semidirect
32. C₁₃×C₂²⋊Q₈	C₂²	semidirect
33. C₁₃×C₂²⋊Q₈	C₂²	semidirect
36. C₄×Q₈×C₁₃	C₂²	semidirect
37. C₄×Q₈×C₁₃	C₂²	semidirect
38. C₄×Q₈×C₁₃	C₂²	semidirect
39. C₄×Q₈×C₁₃	C₂²	semidirect
43. C₄×D₄×C₁₃	C₂²	semidirect
44. C₄×D₄×C₁₃	C₂²	semidirect
49. C₁₃×#117	C₂²	semidirect
50. C₁₃×#117	C₂²	semidirect
54. C₂×C₄²×C₁₃	C₂²	semidirect
100. #3510	C₁₃	direct (N × H)
130. #559	C₂×C₁₃	semidirect
131. #556	C₂×C₁₃	semidirect
132. #551	C₂×C₁₃	semidirect
133. #542	C₂×C₁₃	semidirect
134. #536	C₂×C₁₃	semidirect
136. #533	C₂×C₁₃	semidirect
137. #529	C₂×C₁₃	semidirect
138. C₂×#124	C₂×C₁₃	semidirect
139. #519	C₂×C₁₃	semidirect
140. #518	C₂×C₁₃	semidirect
141. C₄×#41	C₂×C₁₃	semidirect
162. C₄⋊Q₈	C₂²×C₁₃	semidirect
163. C₄⋊Q₈	C₂²×C₁₃	semidirect
165. #126	C₂²×C₁₃	semidirect
166. #126	C₂²×C₁₃	semidirect
167. #125	C₂²×C₁₃	semidirect
172. #124	C₂²×C₁₃	semidirect
173. #124	C₂²×C₁₃	semidirect
175. #123	C₂²×C₁₃	semidirect
176. #123	C₂²×C₁₃	semidirect
178. C₂²⋊Q₈	C₂²×C₁₃	semidirect
179. C₂²⋊Q₈	C₂²×C₁₃	semidirect
182. C₄×Q₈	C₂²×C₁₃	semidirect
183. C₄×Q₈	C₂²×C₁₃	semidirect
184. C₄×Q₈	C₂²×C₁₃	semidirect
185. C₄×Q₈	C₂²×C₁₃	semidirect
189. C₄×D₄	C₂²×C₁₃	semidirect
190. C₄×D₄	C₂²×C₁₃	semidirect
195. #117	C₂²×C₁₃	semidirect
196. #117	C₂²×C₁₃	semidirect
200. C₂×C₄²	C₂²×C₁₃	semidirect
251. C₁₃	#3510	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×#559	2
C₁₃×#556	2
C₁₃×#551	2
C₁₃×#542	2
C₁₃×#536	2
C₁₃×#535	2
C₁₃×#533	2
C₁₃×#529	2
C₂×C₁₃×#124	2
C₁₃×#519	2
C₁₃×#518	2
C₄×C₁₃×#41	2
#3510	13

Subgroups — C13×#3510 #13112568

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#3510 #13112568