Subgroups — C₁₃×#33433 #15719772

Order 3328.

682 conjugacy classes of subgroups.

The subgroup lattice has 324 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#504	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₁₃×M₃₂	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#2929	C₂	1	1	yes	maximal, characteristic
4	C₁₃×#2169	C₂	1	4	yes	maximal, complemented
5	C₁₃×#2168	C₂	1	4	yes	maximal, complemented
6	C₁₃×#2151	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#2113	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#2112	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#2108	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₁₃×#131	C₂²	1	1	yes	characteristic
11	C₂³×C₈×C₁₃	C₂²	1	1	yes	characteristic
12	C₁₃×#525	C₄	1	1	yes	characteristic
13	C₁₃×#504	—	2	4	no	—
14	C₂×C₁₃×M₃₂	—	2	4	no	—
15	C₂×C₁₃×M₃₂	C₂²	1	1	yes	characteristic
16	C₂×C₁₃×M₃₂	C₂²	1	1	yes	characteristic
17	C₂×C₁₃×M₃₂	C₂²	1	2	yes	—
18	C₂×C₁₃×M₃₂	C₂²	1	2	yes	—
19	C₂×C₁₃×M₃₂	C₂²	1	2	yes	complemented
20	C₂²×C₁₃×C₁₆	C₂²	1	1	yes	characteristic
21	C₂²×C₁₃×C₁₆	C₂²	1	1	yes	characteristic
22	C₂²×C₁₃×C₁₆	C₂²	1	2	yes	complemented
23	C₁₃×#435	C₄	1	4	yes	—
24	C₈×D₄×C₁₃	C₂²	1	4	yes	—
25	C₁₃×#424	C₄	1	1	yes	characteristic
26	C₁₃×#408	C₄	1	1	yes	characteristic
27	C₁₃×#407	C₄	1	1	yes	characteristic
28	C₁₃×#405	C₂²	1	1	yes	characteristic
29	C₁₃×C₄⋊C₁₆	C₂²	1	4	yes	complemented
30	C₁₃×C₂²⋊C₁₆	C₂²	1	4	yes	—
31	C₁₃×C₂²⋊C₁₆	C₂²	1	4	yes	complemented
32	C₁₃×#346	C₂²	1	2	yes	complemented
33	C₄×C₁₃×C₁₆	C₂²	1	2	yes	complemented
34	C₂×C₁₃×#41	C₂×C₄	1	1	yes	characteristic
35	C₂³×C₄×C₁₃	C₂×C₄	1	1	yes	characteristic
36	C₁₃×#131	—	2	2	no	—
37	C₁₃×#131	—	2	2	no	—
38	C₂×C₁₃×M₁₆	C₂×C₄	1	1	yes	characteristic
39	C₂×C₁₃×M₁₆	C₂×C₄	1	1	yes	characteristic
40	C₂×C₁₃×M₁₆	C₂×C₄	1	2	yes	—
41	C₂²×C₈×C₁₃	—	2	2	no	—
42	C₂²×C₈×C₁₃	—	2	2	no	—
43	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
44	C₂²×C₈×C₁₃	C₂×C₄	1	2	yes	—
45	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
46	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
47	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
48	C₁₃×#123	C₈	1	2	yes	—
49	C₁₃×C₂²⋊Q₈	C₈	1	2	yes	—
50	C₁₃×#121	C₈	1	2	yes	—
51	C₁₃×#120	C₈	1	2	yes	—
52	C₄×D₄×C₁₃	C₂×C₄	1	4	yes	—
53	C₁₃×#117	C₂×C₄	1	1	yes	characteristic
54	C₁₃×M₃₂	—	2	2	no	—
55	C₁₃×M₃₂	—	2	2	no	—
56	C₁₃×M₃₂	—	2	4	no	—
57	C₁₃×M₃₂	—	2	4	no	—
58	C₁₃×M₃₂	—	2	4	no	—
59	C₂×C₁₃×C₁₆	—	2	2	no	—
60	C₂×C₁₃×C₁₆	—	2	4	no	—
61	C₂×C₁₃×C₁₆	D₄	1	4	yes	complemented
62	C₂×C₁₃×C₁₆	C₂³	1	2	yes	—
63	C₂×C₁₃×C₁₆	C₂³	1	2	yes	—
64	C₂×C₁₃×C₁₆	C₂³	1	2	yes	—
65	C₂×C₁₃×C₁₆	C₂³	1	1	yes	characteristic
66	C₂×C₁₃×C₁₆	C₂³	1	1	yes	characteristic
67	C₁₃×C₄⋊C₈	C₂×C₄	1	4	yes	—
68	C₁₃×C₂²⋊C₈	C₂×C₄	1	4	yes	—
69	C₁₃×C₂²⋊C₈	C₂×C₄	1	4	yes	—
70	C₁₃×#97	C₂×C₄	1	2	yes	—
71	C₄×C₈×C₁₃	C₂³	1	2	yes	—
72	#33433	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
73	C₂⁴×C₁₃	C₂×C₈	1	1	yes	characteristic
74	C₁₃×#41	—	2	2	no	—
75	C₁₃×#41	—	2	2	no	—
76	C₂×Q₈×C₁₃	C₂×C₈	1	1	yes	characteristic
77	C₂×D₄×C₁₃	C₂×C₈	1	2	yes	—
78	C₂×D₄×C₁₃	C₂×C₈	1	1	yes	characteristic
79	C₂×D₄×C₁₃	C₂×C₈	1	4	yes	—
80	C₂²×C₄×C₁₃	—	2	2	no	—
81	C₂²×C₄×C₁₃	—	2	2	no	—
82	C₂²×C₄×C₁₃	C₂×C₈	1	2	yes	—
83	C₂²×C₄×C₁₃	C₂×C₈	1	1	yes	characteristic
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	C₁₃×M₁₆	—	2	2	no	—
88	C₁₃×M₁₆	—	2	2	no	—
89	C₁₃×M₁₆	—	2	4	no	—
90	C₂×C₈×C₁₃	—	2	2	no	—
91	C₂×C₈×C₁₃	—	2	4	no	—
92	C₂×C₈×C₁₃	—	2	2	no	—
93	C₂×C₈×C₁₃	—	2	2	no	—
94	C₂×C₈×C₁₃	—	2	2	no	—
95	C₂×C₈×C₁₃	—	2	2	no	—
96	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
97	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
98	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
99	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
100	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
101	C₂×C₈×C₁₃	#41	1	2	yes	—
102	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
103	C₁₃×C₄⋊C₄	C₂×C₈	1	2	yes	—
104	C₁₃×C₄⋊C₄	C₂×C₈	1	4	yes	—
105	C₁₃×C₂²⋊C₄	C₂×C₈	1	2	yes	—
106	C₁₃×C₂²⋊C₄	C₂×C₈	1	4	yes	—
107	C₁₃×C₂²⋊C₄	C₂×C₈	1	4	yes	—
108	C₄²×C₁₃	C₂²×C₄	1	2	yes	—
109	C₁₃×C₁₆	—	2	2	no	—
110	C₁₃×C₁₆	—	2	2	no	—
111	C₁₃×C₁₆	—	2	2	no	—
112	C₁₃×C₁₆	C₂×D₄	1	2	yes	—
113	C₁₃×C₁₆	C₂×D₄	1	2	yes	—
114	C₂×#504	C₂×C₁₃	1	1	yes	characteristic, complemented
115	C₂²×M₃₂	C₂×C₁₃	1	1	yes	characteristic, complemented
116	#2929	C₂×C₁₃	1	1	yes	characteristic
117	#2169	C₂×C₁₃	1	4	yes	complemented
118	#2168	C₂×C₁₃	1	4	yes	complemented
119	#2151	C₂×C₁₃	1	1	yes	characteristic, complemented
120	#2113	C₂×C₁₃	1	1	yes	characteristic, complemented
121	#2112	C₂×C₁₃	1	1	yes	characteristic, complemented
122	#2108	C₂×C₁₃	1	1	yes	characteristic, complemented
123	C₂³×C₁₃	—	2	2	no	—
124	C₂³×C₁₃	—	4	2	no	—
125	C₂³×C₁₃	C₂²×C₈	1	2	yes	—
126	C₂³×C₁₃	C₂²×C₈	1	2	yes	—
127	C₂³×C₁₃	C₂²×C₈	1	1	yes	characteristic
128	Q₈×C₁₃	—	2	2	no	—
129	D₄×C₁₃	—	2	4	no	—
130	D₄×C₁₃	—	2	2	no	—
131	D₄×C₁₃	—	4	4	no	—
132	C₂×C₄×C₁₃	—	2	2	no	—
133	C₂×C₄×C₁₃	—	2	2	no	—
134	C₂×C₄×C₁₃	—	2	2	no	—
135	C₂×C₄×C₁₃	—	2	2	no	—
136	C₂×C₄×C₁₃	—	2	2	no	—
137	C₂×C₄×C₁₃	—	2	4	no	—
138	C₂×C₄×C₁₃	C₄×D₄	1	2	yes	—
139	C₂×C₄×C₁₃	C₂²×C₈	1	4	yes	—
140	C₂×C₄×C₁₃	C₂²×C₈	1	2	yes	—
141	C₂×C₄×C₁₃	C₂²×C₈	1	2	yes	—
142	C₂×C₄×C₁₃	C₂²×C₈	1	1	yes	characteristic
143	C₂×C₄×C₁₃	#131	1	2	yes	—
144	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
145	C₈×C₁₃	—	2	2	no	—
146	C₈×C₁₃	—	2	2	no	—
147	C₈×C₁₃	—	2	2	no	—
148	C₈×C₁₃	C₄×D₄	1	2	yes	—
149	C₈×C₁₃	C₂²×D₄	1	1	yes	characteristic
150	C₈×C₁₃	C₂×#41	1	1	yes	characteristic
151	C₂×#131	C₂²×C₁₃	1	1	yes	characteristic
152	C₂³×C₈	C₂²×C₁₃	1	1	yes	characteristic
153	#525	C₄×C₁₃	1	1	yes	characteristic
154	#504	—	2	4	no	—
155	C₂×M₃₂	—	2	4	no	—
156	C₂×M₃₂	C₂²×C₁₃	1	1	yes	characteristic
157	C₂×M₃₂	C₂²×C₁₃	1	1	yes	characteristic
158	C₂×M₃₂	C₂²×C₁₃	1	2	yes	—
159	C₂×M₃₂	C₂²×C₁₃	1	2	yes	—
160	C₂×M₃₂	C₂²×C₁₃	1	2	yes	complemented
161	C₂²×C₁₆	C₂²×C₁₃	1	1	yes	characteristic
162	C₂²×C₁₆	C₂²×C₁₃	1	1	yes	characteristic
163	C₂²×C₁₆	C₂²×C₁₃	1	2	yes	complemented
164	#435	C₄×C₁₃	1	4	yes	—
165	C₈×D₄	C₂²×C₁₃	1	4	yes	—
166	#424	C₄×C₁₃	1	1	yes	characteristic
167	#408	C₄×C₁₃	1	1	yes	characteristic
168	#407	C₄×C₁₃	1	1	yes	characteristic
169	#405	C₂²×C₁₃	1	1	yes	characteristic
170	C₄⋊C₁₆	C₂²×C₁₃	1	4	yes	complemented
171	C₂²⋊C₁₆	C₂²×C₁₃	1	4	yes	—
172	C₂²⋊C₁₆	C₂²×C₁₃	1	4	yes	complemented
173	#346	C₂²×C₁₃	1	2	yes	complemented
174	C₄×C₁₆	C₂²×C₁₃	1	2	yes	complemented
175	C₂²×C₁₃	—	2	2	no	—
176	C₂²×C₁₃	—	2	2	no	—
177	C₂²×C₁₃	—	2	4	no	—
178	C₂²×C₁₃	—	2	2	no	—
179	C₂²×C₁₃	—	2	2	no	—
180	C₂²×C₁₃	—	2	2	no	—
181	C₂²×C₁₃	—	4	4	no	—
182	C₂²×C₁₃	C₈×D₄	1	2	yes	—
183	C₂²×C₁₃	C₂³×C₈	1	1	yes	characteristic
184	C₄×C₁₃	—	2	4	no	—
185	C₄×C₁₃	—	2	2	no	—
186	C₄×C₁₃	—	2	2	no	—
187	C₄×C₁₃	C₈×D₄	1	2	yes	—
188	C₄×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
189	C₄×C₁₃	C₂×#131	1	1	yes	characteristic
190	C₂×#41	C₂×C₄×C₁₃	1	1	yes	characteristic
191	C₂³×C₄	C₂×C₄×C₁₃	1	1	yes	characteristic
192	#131	—	2	2	no	—
193	#131	—	2	2	no	—
194	C₂×M₁₆	C₂×C₄×C₁₃	1	1	yes	characteristic
195	C₂×M₁₆	C₂×C₄×C₁₃	1	2	yes	—
196	C₂×M₁₆	C₂×C₄×C₁₃	1	1	yes	characteristic
197	C₂²×C₈	—	2	2	no	—
198	C₂²×C₈	—	2	2	no	—
199	C₂²×C₈	C₂×C₄×C₁₃	1	1	yes	characteristic
200	C₂²×C₈	C₂×C₄×C₁₃	1	2	yes	—
201	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
202	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
203	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
204	#123	C₈×C₁₃	1	2	yes	—
205	C₂²⋊Q₈	C₈×C₁₃	1	2	yes	—
206	#121	C₈×C₁₃	1	2	yes	—
207	#120	C₈×C₁₃	1	2	yes	—
208	C₄×D₄	C₂×C₄×C₁₃	1	4	yes	—
209	#117	C₂×C₄×C₁₃	1	1	yes	characteristic
210	M₃₂	—	2	2	no	—
211	M₃₂	—	2	2	no	—
212	M₃₂	—	2	4	no	—
213	M₃₂	—	2	4	no	—
214	M₃₂	—	2	4	no	—
215	C₂×C₁₆	—	2	2	no	—
216	C₂×C₁₆	—	2	4	no	—
217	C₂×C₁₆	D₄×C₁₃	1	4	yes	complemented
218	C₂×C₁₆	C₂³×C₁₃	1	2	yes	—
219	C₂×C₁₆	C₂³×C₁₃	1	2	yes	—
220	C₂×C₁₆	C₂³×C₁₃	1	2	yes	—
221	C₂×C₁₆	C₂³×C₁₃	1	1	yes	characteristic
222	C₂×C₁₆	C₂³×C₁₃	1	1	yes	characteristic
223	C₄⋊C₈	C₂×C₄×C₁₃	1	4	yes	—
224	C₂²⋊C₈	C₂×C₄×C₁₃	1	4	yes	—
225	C₂²⋊C₈	C₂×C₄×C₁₃	1	4	yes	—
226	#97	C₂×C₄×C₁₃	1	2	yes	—
227	C₄×C₈	C₂³×C₁₃	1	2	yes	—
228	C₂×C₁₃	—	2	2	no	—
229	C₂×C₁₃	—	4	2	no	—
230	C₂×C₁₃	—	4	2	no	—
231	C₂×C₁₃	C₂×C₈×D₄	1	1	yes	characteristic
232	C₂×C₁₃	#3407	1	2	yes	—
233	C₂⁴	C₂×C₈×C₁₃	1	1	yes	characteristic
234	#41	—	2	2	no	—
235	#41	—	2	2	no	—
236	C₂×Q₈	C₂×C₈×C₁₃	1	1	yes	characteristic
237	C₂×D₄	C₂×C₈×C₁₃	1	2	yes	—
238	C₂×D₄	C₂×C₈×C₁₃	1	1	yes	characteristic
239	C₂×D₄	C₂×C₈×C₁₃	1	4	yes	—
240	C₂²×C₄	—	2	2	no	—
241	C₂²×C₄	—	2	2	no	—
242	C₂²×C₄	C₂×C₈×C₁₃	1	2	yes	—
243	C₂²×C₄	C₂×C₈×C₁₃	1	1	yes	characteristic
244	C₂²×C₄	C₂²×C₄×C₁₃	1	2	yes	—
245	C₂²×C₄	C₂²×C₄×C₁₃	1	2	yes	—
246	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
247	M₁₆	—	2	2	no	—
248	M₁₆	—	2	2	no	—
249	M₁₆	—	2	4	no	—
250	C₂×C₈	—	2	2	no	—
251	C₂×C₈	—	2	4	no	—
252	C₂×C₈	—	2	2	no	—
253	C₂×C₈	—	2	2	no	—
254	C₂×C₈	—	2	2	no	—
255	C₂×C₈	—	2	2	no	—
256	C₂×C₈	C₂²×C₄×C₁₃	1	2	yes	—
257	C₂×C₈	C₂²×C₄×C₁₃	1	2	yes	—
258	C₂×C₈	C₂²×C₄×C₁₃	1	2	yes	—
259	C₂×C₈	C₂²×C₄×C₁₃	1	1	yes	characteristic
260	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
261	C₂×C₈	C₁₃×#41	1	2	yes	—
262	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
263	C₄⋊C₄	C₂×C₈×C₁₃	1	2	yes	—
264	C₄⋊C₄	C₂×C₈×C₁₃	1	4	yes	—
265	C₂²⋊C₄	C₂×C₈×C₁₃	1	2	yes	—
266	C₂²⋊C₄	C₂×C₈×C₁₃	1	4	yes	—
267	C₂²⋊C₄	C₂×C₈×C₁₃	1	4	yes	—
268	C₄²	C₂²×C₄×C₁₃	1	2	yes	—
269	C₁₆	—	2	2	no	—
270	C₁₆	—	2	2	no	—
271	C₁₆	—	2	2	no	—
272	C₁₆	C₂×D₄×C₁₃	1	2	yes	—
273	C₁₆	C₂×D₄×C₁₃	1	2	yes	—
274	C₁₃	#33433	1	1	yes	characteristic, direct product factor, Sylow
275	C₂³	—	2	2	no	—
276	C₂³	—	4	2	no	—
277	C₂³	C₂²×C₈×C₁₃	1	2	yes	—
278	C₂³	C₂²×C₈×C₁₃	1	2	yes	—
279	C₂³	C₂²×C₈×C₁₃	1	1	yes	characteristic
280	Q₈	—	2	2	no	—
281	D₄	—	2	4	no	—
282	D₄	—	2	2	no	—
283	D₄	—	4	4	no	—
284	C₂×C₄	—	2	2	no	—
285	C₂×C₄	—	2	4	no	—
286	C₂×C₄	—	2	2	no	—
287	C₂×C₄	—	2	2	no	—
288	C₂×C₄	—	2	2	no	—
289	C₂×C₄	—	2	2	no	—
290	C₂×C₄	C₄×D₄×C₁₃	1	2	yes	—
291	C₂×C₄	C₂²×C₈×C₁₃	1	4	yes	—
292	C₂×C₄	C₂²×C₈×C₁₃	1	2	yes	—
293	C₂×C₄	C₂²×C₈×C₁₃	1	2	yes	—
294	C₂×C₄	C₂²×C₈×C₁₃	1	1	yes	characteristic
295	C₂×C₄	C₁₃×#131	1	2	yes	—
296	C₂×C₄	C₂³×C₄×C₁₃	1	1	yes	characteristic
297	C₈	—	2	2	no	—
298	C₈	—	2	2	no	—
299	C₈	—	2	2	no	—
300	C₈	C₄×D₄×C₁₃	1	2	yes	—
301	C₈	C₂²×D₄×C₁₃	1	1	yes	characteristic
302	C₈	C₂×C₁₃×#41	1	1	yes	characteristic
303	C₂²	—	2	2	no	—
304	C₂²	—	2	2	no	—
305	C₂²	—	2	4	no	—
306	C₂²	—	2	2	no	—
307	C₂²	—	2	2	no	—
308	C₂²	—	2	2	no	—
309	C₂²	—	4	4	no	—
310	C₂²	C₈×D₄×C₁₃	1	2	yes	—
311	C₂²	C₂³×C₈×C₁₃	1	1	yes	characteristic
312	C₄	—	2	4	no	—
313	C₄	—	2	2	no	—
314	C₄	—	2	2	no	—
315	C₄	C₈×D₄×C₁₃	1	2	yes	—
316	C₄	C₂×C₄×D₄×C₁₃	1	1	yes	characteristic
317	C₄	C₂×C₁₃×#131	1	1	yes	characteristic
318	C₂	—	2	2	no	—
319	C₂	—	4	2	no	—
320	C₂	—	4	2	no	—
321	C₂	C₂×C₈×D₄×C₁₃	1	1	yes	characteristic
322	C₂	C₁₃×#3407	1	2	yes	—

	subgroup	G/H
center	C₂×C₈×C₁₃	C₂⁴
commutator	C₂²	C₂³×C₈×C₁₃
Frattini, cosocle	C₂×C₈	C₂⁴×C₁₃
socle	C₂²×C₁₃	C₂³×C₈
prime radical	C₁₃×#525	C₄
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₈×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₃×#504	C₂	semidirect
2. C₂²×C₁₃×M₃₂	C₂	semidirect
4. C₁₃×#2169	C₂	semidirect
5. C₁₃×#2168	C₂	semidirect
6. C₁₃×#2151	C₂	semidirect
7. C₁₃×#2113	C₂	semidirect
8. C₁₃×#2112	C₂	semidirect
9. C₁₃×#2108	C₂	semidirect
19. C₂×C₁₃×M₃₂	C₂²	semidirect
22. C₂²×C₁₃×C₁₆	C₂²	semidirect
29. C₁₃×C₄⋊C₁₆	C₂²	semidirect
31. C₁₃×C₂²⋊C₁₆	C₂²	semidirect
32. C₁₃×#346	C₂²	semidirect
33. C₄×C₁₃×C₁₆	C₂²	semidirect
61. C₂×C₁₃×C₁₆	D₄	semidirect
72. #33433	C₁₃	direct (N × H)
114. C₂×#504	C₂×C₁₃	semidirect
115. C₂²×M₃₂	C₂×C₁₃	semidirect
117. #2169	C₂×C₁₃	semidirect
118. #2168	C₂×C₁₃	semidirect
119. #2151	C₂×C₁₃	semidirect
120. #2113	C₂×C₁₃	semidirect
121. #2112	C₂×C₁₃	semidirect
122. #2108	C₂×C₁₃	semidirect
160. C₂×M₃₂	C₂²×C₁₃	semidirect
163. C₂²×C₁₆	C₂²×C₁₃	semidirect
170. C₄⋊C₁₆	C₂²×C₁₃	semidirect
172. C₂²⋊C₁₆	C₂²×C₁₃	semidirect
173. #346	C₂²×C₁₃	semidirect
174. C₄×C₁₆	C₂²×C₁₃	semidirect
217. C₂×C₁₆	D₄×C₁₃	semidirect
274. C₁₃	#33433	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×#504	2
C₂²×C₁₃×M₃₂	2
C₁₃×#2929	2
C₁₃×#2169	2
C₁₃×#2168	2
C₁₃×#2151	2
C₁₃×#2113	2
C₁₃×#2112	2
C₁₃×#2108	2
#33433	13

Subgroups — C13×#33433 #15719772

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#33433 #15719772