Subgroups — C₂×C₁₃×#1791 #15706950

Order 3328.

3662 conjugacy classes of subgroups.

The subgroup lattice has 372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#585	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₃×#413	C₂	1	3	yes	maximal, complemented
3	C₂×C₁₃×#408	C₂	1	3	yes	maximal, complemented
4	C₁₃×#1791	C₂	1	8	yes	maximal, direct product factor
5	C₁₃×#585	—	2	6	no	—
6	C₁₃×#585	—	2	6	no	—
7	C₁₃×#585	C₄	1	4	yes	—
8	C₁₃×#585	C₂²	1	4	yes	—
9	C₂×C₁₃×2₋¹⁺⁴	—	2	3	no	—
10	C₂×C₁₃×H(5,𝔽₂)	—	2	3	no	—
11	C₂×C₁₃×H(5,𝔽₂)	C₄	1	4	yes	—
12	C₂²×C₁₃×#41	—	2	6	no	—
13	C₂²×C₁₃×#41	C₂²	1	3	yes	—
14	C₂²×C₁₃×M₁₆	C₂²	1	3	yes	complemented
15	C₂³×C₈×C₁₃	C₂²	1	1	yes	characteristic, complemented
16	C₁₃×#413	—	2	6	no	—
17	C₁₃×#413	C₂²	1	12	yes	complemented
18	C₂×C₁₃×#101	—	2	3	no	—
19	C₂×C₁₃×#100	—	2	3	no	—
20	C₁₃×#408	—	2	6	no	—
21	C₁₃×#408	C₂²	1	12	yes	complemented
22	C₂×C₁₃×C₂²⋊C₈	—	2	6	no	—
23	C₁₃×2₋¹⁺⁴	—	2	24	no	—
24	C₁₃×2₋¹⁺⁴	—	2	12	no	—
25	C₁₃×2₋¹⁺⁴	—	2	12	no	—
26	C₁₃×H(5,𝔽₂)	—	2	24	no	—
27	C₁₃×H(5,𝔽₂)	—	2	12	no	—
28	C₁₃×H(5,𝔽₂)	—	2	24	no	—
29	C₁₃×H(5,𝔽₂)	—	2	12	no	—
30	C₁₃×H(5,𝔽₂)	C₂×C₄	1	16	yes	—
31	C₂×C₁₃×#41	—	2	4	no	—
32	C₂×C₁₃×#41	—	2	12	no	—
33	C₂×C₁₃×#41	—	2	24	no	—
34	C₂×C₁₃×#41	—	2	24	no	—
35	C₂×C₁₃×#41	—	2	12	no	—
36	C₂×C₁₃×#41	—	2	24	no	—
37	C₂×C₁₃×#41	—	2	6	no	—
38	C₂×C₁₃×#41	—	2	24	no	—
39	C₂×C₁₃×#41	—	2	6	no	—
40	C₂×C₁₃×#41	—	2	6	no	—
41	C₂×C₁₃×#41	—	2	6	no	—
42	C₂×C₁₃×#41	C₂×C₄	1	6	yes	—
43	C₂×C₁₃×#41	D₄	1	6	yes	—
44	C₂×C₁₃×#41	D₄	1	6	yes	—
45	C₂×C₁₃×#41	C₂³	1	6	yes	—
46	C₂²×Q₈×C₁₃	—	2	6	no	—
47	C₂²×Q₈×C₁₃	D₄	1	3	yes	—
48	C₂²×D₄×C₁₃	—	2	6	no	—
49	C₂²×D₄×C₁₃	—	2	12	no	—
50	C₂²×D₄×C₁₃	C₂×C₄	1	6	yes	—
51	C₂²×D₄×C₁₃	D₄	1	3	yes	—
52	C₂³×C₄×C₁₃	—	2	4	no	—
53	C₂³×C₄×C₁₃	D₄	1	6	yes	—
54	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
55	C₂×C₁₃×M₁₆	—	2	3	no	—
56	C₂×C₁₃×M₁₆	—	2	6	no	—
57	C₂×C₁₃×M₁₆	—	2	6	no	—
58	C₂×C₁₃×M₁₆	C₂³	1	6	yes	complemented
59	C₂²×C₈×C₁₃	—	2	3	no	—
60	C₂²×C₈×C₁₃	—	2	3	no	—
61	C₂²×C₈×C₁₃	—	2	3	no	—
62	C₂²×C₈×C₁₃	C₂³	1	2	yes	complemented
63	C₁₃×#101	—	2	12	no	—
64	C₁₃×#100	—	2	12	no	—
65	C₁₃×C₂²⋊C₈	—	2	24	no	—
66	C₂×#1791	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
67	C₂⁴×C₁₃	—	2	4	no	—
68	C₂⁴×C₁₃	C₂²⋊C₄	1	6	yes	—
69	C₂⁴×C₁₃	C₂²×C₄	1	1	yes	characteristic
70	C₁₃×#41	—	2	16	no	—
71	C₁₃×#41	—	2	16	no	—
72	C₁₃×#41	—	2	48	no	—
73	C₁₃×#41	—	2	48	no	—
74	C₁₃×#41	—	2	48	no	—
75	C₁₃×#41	—	2	12	no	—
76	C₁₃×#41	—	2	48	no	—
77	C₁₃×#41	—	2	12	no	—
78	C₁₃×#41	—	2	12	no	—
79	C₁₃×#41	—	2	12	no	—
80	C₁₃×#41	—	2	12	no	—
81	C₁₃×#41	—	2	12	no	—
82	C₁₃×#41	—	2	12	no	—
83	C₁₃×#41	—	2	12	no	—
84	C₂×Q₈×C₁₃	—	2	4	no	—
85	C₂×Q₈×C₁₃	—	2	24	no	—
86	C₂×Q₈×C₁₃	—	2	24	no	—
87	C₂×Q₈×C₁₃	—	2	6	no	—
88	C₂×Q₈×C₁₃	—	2	6	no	—
89	C₂×Q₈×C₁₃	C₂²⋊C₄	1	6	yes	—
90	C₂×Q₈×C₁₃	C₂×D₄	1	6	yes	—
91	C₂×D₄×C₁₃	—	2	12	no	—
92	C₂×D₄×C₁₃	—	2	48	no	—
93	C₂×D₄×C₁₃	—	2	24	no	—
94	C₂×D₄×C₁₃	—	2	24	no	—
95	C₂×D₄×C₁₃	—	2	12	no	—
96	C₂×D₄×C₁₃	—	2	48	no	—
97	C₂×D₄×C₁₃	—	2	12	no	—
98	C₂×D₄×C₁₃	—	2	6	no	—
99	C₂×D₄×C₁₃	—	2	6	no	—
100	C₂×D₄×C₁₃	C₂²⋊C₄	1	12	yes	—
101	C₂×D₄×C₁₃	C₂²⋊C₄	1	6	yes	—
102	C₂×D₄×C₁₃	C₂²×C₄	1	12	yes	—
103	C₂×D₄×C₁₃	C₂×D₄	1	6	yes	—
104	C₂²×C₄×C₁₃	—	2	12	no	—
105	C₂²×C₄×C₁₃	—	2	16	no	—
106	C₂²×C₄×C₁₃	—	2	16	no	—
107	C₂²×C₄×C₁₃	—	2	6	no	—
108	C₂²×C₄×C₁₃	—	2	6	no	—
109	C₂²×C₄×C₁₃	—	2	6	no	—
110	C₂²×C₄×C₁₃	—	2	6	no	—
111	C₂²×C₄×C₁₃	C₂²⋊C₄	1	6	yes	—
112	C₂²×C₄×C₁₃	C₂²⋊C₄	1	12	yes	—
113	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
114	C₂²×C₄×C₁₃	C₂×D₄	1	12	yes	—
115	C₂²×C₄×C₁₃	C₂×D₄	1	3	yes	—
116	C₂²×C₄×C₁₃	C₂×D₄	1	3	yes	—
117	C₂²×C₄×C₁₃	C₂×D₄	1	3	yes	—
118	C₂²×C₄×C₁₃	C₂×D₄	1	3	yes	—
119	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
120	C₁₃×M₁₆	—	2	12	no	—
121	C₁₃×M₁₆	—	4	6	no	—
122	C₂×C₈×C₁₃	—	2	6	no	—
123	C₂×C₈×C₁₃	—	2	6	no	—
124	C₂×C₈×C₁₃	—	4	3	no	—
125	C₂×C₈×C₁₃	—	4	3	no	—
126	C₂×C₈×C₁₃	—	4	3	no	—
127	C₂×C₈×C₁₃	—	4	1	no	—
128	C₂×#585	C₂×C₁₃	1	1	yes	characteristic
129	C₂×#413	C₂×C₁₃	1	3	yes	complemented
130	C₂×#408	C₂×C₁₃	1	3	yes	complemented
131	#1791	C₂×C₁₃	1	8	yes	direct product factor
132	C₂³×C₁₃	—	2	16	no	—
133	C₂³×C₁₃	—	2	6	no	—
134	C₂³×C₁₃	—	2	6	no	—
135	C₂³×C₁₃	—	4	2	no	—
136	C₂³×C₁₃	—	4	12	no	—
137	C₂³×C₁₃	—	8	8	no	—
138	C₂³×C₁₃	C₂×C₂²⋊C₄	1	3	yes	—
139	C₂³×C₁₃	C₂×C₂²⋊C₄	1	12	yes	—
140	C₂³×C₁₃	C₂×C₂²⋊C₄	1	3	yes	—
141	C₂³×C₁₃	C₂³×C₄	1	1	yes	characteristic
142	Q₈×C₁₃	—	2	16	no	—
143	Q₈×C₁₃	—	2	12	no	—
144	Q₈×C₁₃	—	2	12	no	—
145	D₄×C₁₃	—	2	48	no	—
146	D₄×C₁₃	—	2	24	no	—
147	D₄×C₁₃	—	2	24	no	—
148	D₄×C₁₃	—	2	12	no	—
149	D₄×C₁₃	—	2	12	no	—
150	C₂×C₄×C₁₃	—	2	48	no	—
151	C₂×C₄×C₁₃	—	2	6	no	—
152	C₂×C₄×C₁₃	—	2	6	no	—
153	C₂×C₄×C₁₃	—	2	12	no	—
154	C₂×C₄×C₁₃	—	2	12	no	—
155	C₂×C₄×C₁₃	—	2	12	no	—
156	C₂×C₄×C₁₃	—	2	12	no	—
157	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	12	yes	—
158	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	3	yes	—
159	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	3	yes	—
160	C₂×C₄×C₁₃	#120	1	3	yes	—
161	C₂×C₄×C₁₃	#120	1	3	yes	—
162	C₂×C₄×C₁₃	#120	1	3	yes	—
163	C₂×C₄×C₁₃	#120	1	6	yes	—
164	C₂×C₄×C₁₃	#120	1	1	yes	characteristic
165	C₂×C₄×C₁₃	C₂²×D₄	1	3	yes	—
166	C₂×C₄×C₁₃	C₂²×D₄	1	3	yes	—
167	C₈×C₁₃	—	4	2	no	—
168	C₈×C₁₃	—	4	6	no	—
169	#585	—	2	6	no	—
170	#585	—	2	6	no	—
171	#585	C₄×C₁₃	1	4	yes	—
172	#585	C₂²×C₁₃	1	4	yes	—
173	C₂×2₋¹⁺⁴	—	2	3	no	—
174	C₂×H(5,𝔽₂)	—	2	3	no	—
175	C₂×H(5,𝔽₂)	C₄×C₁₃	1	4	yes	—
176	C₂²×#41	—	2	6	no	—
177	C₂²×#41	C₂²×C₁₃	1	3	yes	—
178	C₂²×M₁₆	C₂²×C₁₃	1	3	yes	complemented
179	C₂³×C₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
180	#413	—	2	6	no	—
181	#413	C₂²×C₁₃	1	12	yes	complemented
182	C₂×#101	—	2	3	no	—
183	C₂×#100	—	2	3	no	—
184	#408	—	2	6	no	—
185	#408	C₂²×C₁₃	1	12	yes	complemented
186	C₂×C₂²⋊C₈	—	2	6	no	—
187	C₂²×C₁₃	—	2	6	no	—
188	C₂²×C₁₃	—	2	12	no	—
189	C₂²×C₁₃	—	4	3	no	—
190	C₂²×C₁₃	—	4	1	no	—
191	C₂²×C₁₃	—	4	12	no	—
192	C₂²×C₁₃	—	4	12	no	—
193	C₂²×C₁₃	—	8	6	no	—
194	C₂²×C₁₃	—	8	16	no	—
195	C₂²×C₁₃	#379	1	3	yes	—
196	C₂²×C₁₃	#379	1	1	yes	characteristic
197	C₂²×C₁₃	C₂²×C₂²⋊C₄	1	3	yes	—
198	C₄×C₁₃	—	2	12	no	—
199	C₄×C₁₃	#379	1	1	yes	characteristic
200	C₄×C₁₃	#379	1	3	yes	—
201	C₄×C₁₃	C₂×#120	1	1	yes	characteristic
202	C₄×C₁₃	C₂×#120	1	3	yes	—
203	2₋¹⁺⁴	—	2	24	no	—
204	2₋¹⁺⁴	—	2	12	no	—
205	2₋¹⁺⁴	—	2	12	no	—
206	H(5,𝔽₂)	—	2	24	no	—
207	H(5,𝔽₂)	—	2	12	no	—
208	H(5,𝔽₂)	—	2	24	no	—
209	H(5,𝔽₂)	—	2	12	no	—
210	H(5,𝔽₂)	C₂×C₄×C₁₃	1	16	yes	—
211	C₂×#41	—	2	4	no	—
212	C₂×#41	—	2	12	no	—
213	C₂×#41	—	2	24	no	—
214	C₂×#41	—	2	24	no	—
215	C₂×#41	—	2	12	no	—
216	C₂×#41	—	2	24	no	—
217	C₂×#41	—	2	6	no	—
218	C₂×#41	—	2	24	no	—
219	C₂×#41	—	2	6	no	—
220	C₂×#41	—	2	6	no	—
221	C₂×#41	—	2	6	no	—
222	C₂×#41	C₂×C₄×C₁₃	1	6	yes	—
223	C₂×#41	D₄×C₁₃	1	6	yes	—
224	C₂×#41	D₄×C₁₃	1	6	yes	—
225	C₂×#41	C₂³×C₁₃	1	6	yes	—
226	C₂²×Q₈	—	2	6	no	—
227	C₂²×Q₈	D₄×C₁₃	1	3	yes	—
228	C₂²×D₄	—	2	6	no	—
229	C₂²×D₄	—	2	12	no	—
230	C₂²×D₄	C₂×C₄×C₁₃	1	6	yes	—
231	C₂²×D₄	D₄×C₁₃	1	3	yes	—
232	C₂³×C₄	—	2	4	no	—
233	C₂³×C₄	D₄×C₁₃	1	6	yes	—
234	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
235	C₂×M₁₆	—	2	3	no	—
236	C₂×M₁₆	—	2	6	no	—
237	C₂×M₁₆	—	2	6	no	—
238	C₂×M₁₆	C₂³×C₁₃	1	6	yes	complemented
239	C₂²×C₈	—	2	3	no	—
240	C₂²×C₈	—	2	3	no	—
241	C₂²×C₈	—	2	3	no	—
242	C₂²×C₈	C₂³×C₁₃	1	2	yes	complemented
243	#101	—	2	12	no	—
244	#100	—	2	12	no	—
245	C₂²⋊C₈	—	2	24	no	—
246	C₂×C₁₃	—	2	3	no	—
247	C₂×C₁₃	—	2	3	no	—
248	C₂×C₁₃	—	4	12	no	—
249	C₂×C₁₃	#1791	1	2	yes	direct product factor
250	C₂×C₁₃	C₂×#379	1	1	yes	characteristic
251	C₂⁴	—	2	4	no	—
252	C₂⁴	C₁₃×C₂²⋊C₄	1	6	yes	—
253	C₂⁴	C₂²×C₄×C₁₃	1	1	yes	characteristic
254	#41	—	2	16	no	—
255	#41	—	2	16	no	—
256	#41	—	2	48	no	—
257	#41	—	2	48	no	—
258	#41	—	2	48	no	—
259	#41	—	2	12	no	—
260	#41	—	2	48	no	—
261	#41	—	2	12	no	—
262	#41	—	2	12	no	—
263	#41	—	2	12	no	—
264	#41	—	2	12	no	—
265	#41	—	2	12	no	—
266	#41	—	2	12	no	—
267	#41	—	2	12	no	—
268	C₂×Q₈	—	2	4	no	—
269	C₂×Q₈	—	2	24	no	—
270	C₂×Q₈	—	2	24	no	—
271	C₂×Q₈	—	2	6	no	—
272	C₂×Q₈	—	2	6	no	—
273	C₂×Q₈	C₁₃×C₂²⋊C₄	1	6	yes	—
274	C₂×Q₈	C₂×D₄×C₁₃	1	6	yes	—
275	C₂×D₄	—	2	12	no	—
276	C₂×D₄	—	2	48	no	—
277	C₂×D₄	—	2	24	no	—
278	C₂×D₄	—	2	24	no	—
279	C₂×D₄	—	2	12	no	—
280	C₂×D₄	—	2	48	no	—
281	C₂×D₄	—	2	12	no	—
282	C₂×D₄	—	2	6	no	—
283	C₂×D₄	—	2	6	no	—
284	C₂×D₄	C₁₃×C₂²⋊C₄	1	12	yes	—
285	C₂×D₄	C₁₃×C₂²⋊C₄	1	6	yes	—
286	C₂×D₄	C₂²×C₄×C₁₃	1	12	yes	—
287	C₂×D₄	C₂×D₄×C₁₃	1	6	yes	—
288	C₂²×C₄	—	2	12	no	—
289	C₂²×C₄	—	2	16	no	—
290	C₂²×C₄	—	2	16	no	—
291	C₂²×C₄	—	2	6	no	—
292	C₂²×C₄	—	2	6	no	—
293	C₂²×C₄	—	2	6	no	—
294	C₂²×C₄	—	2	6	no	—
295	C₂²×C₄	C₁₃×C₂²⋊C₄	1	6	yes	—
296	C₂²×C₄	C₁₃×C₂²⋊C₄	1	12	yes	—
297	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
298	C₂²×C₄	C₂×D₄×C₁₃	1	12	yes	—
299	C₂²×C₄	C₂×D₄×C₁₃	1	3	yes	—
300	C₂²×C₄	C₂×D₄×C₁₃	1	3	yes	—
301	C₂²×C₄	C₂×D₄×C₁₃	1	3	yes	—
302	C₂²×C₄	C₂×D₄×C₁₃	1	3	yes	—
303	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
304	M₁₆	—	2	12	no	—
305	M₁₆	—	4	6	no	—
306	C₂×C₈	—	2	6	no	—
307	C₂×C₈	—	2	6	no	—
308	C₂×C₈	—	4	1	no	—
309	C₂×C₈	—	4	3	no	—
310	C₂×C₈	—	4	3	no	—
311	C₂×C₈	—	4	3	no	—
312	C₁₃	C₂×#1791	1	1	yes	characteristic, direct product factor, Sylow
313	C₂³	—	2	16	no	—
314	C₂³	—	2	6	no	—
315	C₂³	—	2	6	no	—
316	C₂³	—	4	2	no	—
317	C₂³	—	4	12	no	—
318	C₂³	—	8	8	no	—
319	C₂³	C₂×C₁₃×C₂²⋊C₄	1	3	yes	—
320	C₂³	C₂×C₁₃×C₂²⋊C₄	1	12	yes	—
321	C₂³	C₂×C₁₃×C₂²⋊C₄	1	3	yes	—
322	C₂³	C₂³×C₄×C₁₃	1	1	yes	characteristic
323	Q₈	—	2	16	no	—
324	Q₈	—	2	12	no	—
325	Q₈	—	2	12	no	—
326	D₄	—	2	48	no	—
327	D₄	—	2	24	no	—
328	D₄	—	2	24	no	—
329	D₄	—	2	12	no	—
330	D₄	—	2	12	no	—
331	C₂×C₄	—	2	48	no	—
332	C₂×C₄	—	2	6	no	—
333	C₂×C₄	—	2	6	no	—
334	C₂×C₄	—	2	12	no	—
335	C₂×C₄	—	2	12	no	—
336	C₂×C₄	—	2	12	no	—
337	C₂×C₄	—	2	12	no	—
338	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	12	yes	—
339	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	3	yes	—
340	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	3	yes	—
341	C₂×C₄	C₁₃×#120	1	1	yes	characteristic
342	C₂×C₄	C₁₃×#120	1	3	yes	—
343	C₂×C₄	C₁₃×#120	1	3	yes	—
344	C₂×C₄	C₁₃×#120	1	3	yes	—
345	C₂×C₄	C₁₃×#120	1	6	yes	—
346	C₂×C₄	C₂²×D₄×C₁₃	1	3	yes	—
347	C₂×C₄	C₂²×D₄×C₁₃	1	3	yes	—
348	C₈	—	4	2	no	—
349	C₈	—	4	6	no	—
350	C₂²	—	2	6	no	—
351	C₂²	—	2	12	no	—
352	C₂²	—	4	3	no	—
353	C₂²	—	4	1	no	—
354	C₂²	—	4	12	no	—
355	C₂²	—	4	12	no	—
356	C₂²	—	8	6	no	—
357	C₂²	—	8	16	no	—
358	C₂²	C₁₃×#379	1	3	yes	—
359	C₂²	C₁₃×#379	1	1	yes	characteristic
360	C₂²	C₂²×C₁₃×C₂²⋊C₄	1	3	yes	—
361	C₄	—	2	12	no	—
362	C₄	C₁₃×#379	1	1	yes	characteristic
363	C₄	C₁₃×#379	1	3	yes	—
364	C₄	C₂×C₁₃×#120	1	1	yes	characteristic
365	C₄	C₂×C₁₃×#120	1	3	yes	—
366	C₂	—	2	3	no	—
367	C₂	—	2	3	no	—
368	C₂	—	4	12	no	—
369	C₂	C₁₃×#1791	1	2	yes	direct product factor
370	C₂	C₂×C₁₃×#379	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₁₃	#120
commutator	C₂³	C₂³×C₄×C₁₃
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
socle	C₂²×C₁₃	#379
prime radical	C₂×C₁₃×#585	C₂
LCS	G ▷ C₂³ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₃ ◁ C₂³×C₄×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₁₃×#413	C₂	semidirect
3. C₂×C₁₃×#408	C₂	semidirect
4. C₁₃×#1791	C₂	direct (N × H)
14. C₂²×C₁₃×M₁₆	C₂²	semidirect
15. C₂³×C₈×C₁₃	C₂²	semidirect
17. C₁₃×#413	C₂²	semidirect
21. C₁₃×#408	C₂²	semidirect
58. C₂×C₁₃×M₁₆	C₂³	semidirect
62. C₂²×C₈×C₁₃	C₂³	semidirect
66. C₂×#1791	C₁₃	direct (N × H)
129. C₂×#413	C₂×C₁₃	semidirect
130. C₂×#408	C₂×C₁₃	semidirect
131. #1791	C₂×C₁₃	direct (N × H)
178. C₂²×M₁₆	C₂²×C₁₃	semidirect
179. C₂³×C₈	C₂²×C₁₃	semidirect
181. #413	C₂²×C₁₃	semidirect
185. #408	C₂²×C₁₃	semidirect
238. C₂×M₁₆	C₂³×C₁₃	semidirect
242. C₂²×C₈	C₂³×C₁₃	semidirect
249. C₂×C₁₃	#1791	direct (N × H)
312. C₁₃	C₂×#1791	direct (N × H)
369. C₂	C₁₃×#1791	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×#585	2
C₂×C₁₃×#413	2
C₂×C₁₃×#408	2
C₁₃×#1791	2
C₂×#1791	13

Subgroups — C2×C13×#1791 #15706950

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₃×#1791 #15706950