Subgroups — C₁₃×#63092 #15749431

Order 3328.

10796 conjugacy classes of subgroups.

The subgroup lattice has 288 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×2₋¹⁺⁶	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃×H(7,𝔽₂)	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3586	C₂	1	15	yes	maximal, complemented
4	C₁₃×#3585	C₂	1	15	yes	maximal, complemented
5	C₁₃×#3584	C₂	1	15	yes	maximal, complemented
6	C₂×C₁₃×#577	C₂	1	15	yes	maximal, complemented
7	C₁₃×#3573	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#585	—	2	6	no	—
9	C₁₃×#585	—	2	10	no	—
10	C₁₃×#585	C₂²	1	1	yes	characteristic
11	C₁₃×#585	C₂²	1	15	yes	complemented
12	C₁₃×#585	C₂²	1	15	yes	complemented
13	C₂×C₁₃×2₋¹⁺⁴	—	2	6	no	—
14	C₂×C₁₃×2₋¹⁺⁴	C₂²	1	15	yes	complemented
15	C₂×C₁₃×H(5,𝔽₂)	—	2	10	no	—
16	C₂×C₁₃×H(5,𝔽₂)	C₂²	1	15	yes	complemented
17	C₁₃×#578	C₂²	1	60	yes	complemented
18	C₁₃×#577	C₂²	1	60	yes	complemented
19	C₁₃×#577	C₂²	1	120	yes	complemented
20	C₁₃×#577	C₂²	1	20	yes	complemented
21	C₁₃×#576	C₂²	1	60	yes	complemented
22	C₁₃×#575	C₂²	1	90	yes	complemented
23	C₂×C₁₃×#137	C₂²	1	45	yes	complemented
24	C₂×C₁₃×AGL(1,ℤ/8)	C₂²	1	45	yes	complemented
25	C₂×C₁₃×#135	C₂²	1	45	yes	complemented
26	C₂²×C₁₃×SD₁₆	C₂²	1	15	yes	complemented
27	C₁₃×#568	C₂²	1	15	yes	complemented
28	C₂×C₁₃×#131	C₂²	1	15	yes	complemented
29	C₁₃×2₋¹⁺⁴	—	2	60	no	—
30	C₁₃×2₋¹⁺⁴	—	2	15	no	—
31	C₁₃×2₋¹⁺⁴	—	2	15	no	—
32	C₁₃×2₋¹⁺⁴	D₄	1	6	yes	—
33	C₁₃×2₋¹⁺⁴	C₂³	1	20	yes	—
34	C₁₃×2₋¹⁺⁴	C₂³	1	60	yes	complemented
35	C₁₃×H(5,𝔽₂)	—	2	60	no	—
36	C₁₃×H(5,𝔽₂)	—	2	45	no	—
37	C₁₃×H(5,𝔽₂)	—	2	45	no	—
38	C₁₃×H(5,𝔽₂)	D₄	1	10	yes	—
39	C₁₃×H(5,𝔽₂)	C₂³	1	60	yes	—
40	C₁₃×H(5,𝔽₂)	C₂³	1	20	yes	complemented
41	C₂×C₁₃×#41	—	2	60	no	—
42	C₂×C₁₃×#41	—	2	60	no	—
43	C₂×C₁₃×#41	—	2	15	no	—
44	C₂×C₁₃×#41	—	2	45	no	—
45	C₂×C₁₃×#41	C₂³	1	45	yes	—
46	C₂×C₁₃×#41	C₂³	1	15	yes	—
47	C₂×C₁₃×#41	C₂³	1	45	yes	complemented
48	C₂²×Q₈×C₁₃	—	2	15	no	—
49	C₂²×Q₈×C₁₃	C₂³	1	15	yes	complemented
50	C₂²×D₄×C₁₃	—	2	45	no	—
51	C₂²×D₄×C₁₃	C₂³	1	15	yes	—
52	C₁₃×#137	C₂³	1	180	yes	complemented
53	C₁₃×#137	C₂³	1	60	yes	complemented
54	C₁₃×AGL(1,ℤ/8)	C₂³	1	180	yes	complemented
55	C₁₃×AGL(1,ℤ/8)	C₂³	1	60	yes	complemented
56	C₁₃×#135	C₂³	1	60	yes	complemented
57	C₁₃×#135	C₂³	1	180	yes	complemented
58	C₂×C₁₃×Q₁₆	C₂³	1	45	yes	complemented
59	C₂×C₁₃×SD₁₆	C₂³	1	45	yes	complemented
60	C₂×C₁₃×SD₁₆	C₂³	1	90	yes	complemented
61	C₂×C₁₃×SD₁₆	C₂³	1	15	yes	complemented
62	C₂×C₁₃×D₈	C₂³	1	45	yes	complemented
63	C₁₃×#131	C₂³	1	20	yes	complemented
64	C₁₃×#131	C₂³	1	60	yes	complemented
65	C₂×C₁₃×M₁₆	C₂³	1	45	yes	complemented
66	C₂²×C₈×C₁₃	C₂³	1	15	yes	complemented
67	#63092	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
68	C₂⁴×C₁₃	—	2	15	no	—
69	C₁₃×#41	—	2	60	no	—
70	C₁₃×#41	—	2	20	no	—
71	C₁₃×#41	—	2	60	no	—
72	C₁₃×#41	—	2	180	no	—
73	C₁₃×#41	—	2	90	no	—
74	C₁₃×#41	—	2	90	no	—
75	C₁₃×#41	C₂×D₄	1	60	yes	—
76	C₁₃×#41	C₂⁴	1	60	yes	—
77	C₁₃×#41	C₂⁴	1	60	yes	—
78	C₁₃×#41	C₂⁴	1	20	yes	—
79	C₂×Q₈×C₁₃	—	2	60	no	—
80	C₂×Q₈×C₁₃	—	2	20	no	—
81	C₂×Q₈×C₁₃	—	2	45	no	—
82	C₂×Q₈×C₁₃	C₂×D₄	1	15	yes	—
83	C₂×Q₈×C₁₃	C₂⁴	1	45	yes	—
84	C₂×Q₈×C₁₃	C₂⁴	1	15	yes	—
85	C₂×D₄×C₁₃	—	2	45	no	—
86	C₂×D₄×C₁₃	—	2	45	no	—
87	C₂×D₄×C₁₃	—	2	180	no	—
88	C₂×D₄×C₁₃	—	2	60	no	—
89	C₂×D₄×C₁₃	—	2	45	no	—
90	C₂×D₄×C₁₃	C₂×D₄	1	45	yes	—
91	C₂×D₄×C₁₃	C₂⁴	1	15	yes	—
92	C₂×D₄×C₁₃	C₂⁴	1	45	yes	—
93	C₂²×C₄×C₁₃	—	2	15	no	—
94	C₂²×C₄×C₁₃	—	2	45	no	—
95	C₂²×C₄×C₁₃	—	2	45	no	—
96	C₂²×C₄×C₁₃	C₂⁴	1	15	yes	—
97	C₁₃×Q₁₆	C₂⁴	1	60	yes	—
98	C₁₃×SD₁₆	C₂⁴	1	10	yes	—
99	C₁₃×SD₁₆	C₂⁴	1	6	yes	—
100	C₁₃×SD₁₆	C₂⁴	1	90	yes	—
101	C₁₃×SD₁₆	C₂⁴	1	30	yes	—
102	C₁₃×D₈	C₂⁴	1	60	yes	—
103	C₁₃×M₁₆	C₂⁴	1	60	yes	—
104	C₂×C₈×C₁₃	C₂⁴	1	15	yes	—
105	C₂×C₈×C₁₃	C₂⁴	1	45	yes	—
106	2₋¹⁺⁶	C₂×C₁₃	1	1	yes	characteristic, complemented
107	H(7,𝔽₂)	C₂×C₁₃	1	1	yes	characteristic, complemented
108	#3586	C₂×C₁₃	1	15	yes	complemented
109	#3585	C₂×C₁₃	1	15	yes	complemented
110	#3584	C₂×C₁₃	1	15	yes	complemented
111	C₂×#577	C₂×C₁₃	1	15	yes	complemented
112	#3573	C₂×C₁₃	1	1	yes	characteristic, complemented
113	C₂³×C₁₃	—	2	15	no	—
114	C₂³×C₁₃	—	2	45	no	—
115	C₂³×C₁₃	—	16	15	no	—
116	C₂³×C₁₃	C₂²×D₄	1	15	yes	—
117	Q₈×C₁₃	—	2	45	no	—
118	Q₈×C₁₃	—	2	15	no	—
119	Q₈×C₁₃	C₂²×D₄	1	20	yes	—
120	Q₈×C₁₃	C₂⁵	1	10	yes	—
121	Q₈×C₁₃	C₂⁵	1	6	yes	—
122	D₄×C₁₃	—	2	60	no	—
123	D₄×C₁₃	—	2	60	no	—
124	D₄×C₁₃	—	2	45	no	—
125	D₄×C₁₃	—	2	15	no	—
126	D₄×C₁₃	C₂²×D₄	1	60	yes	—
127	D₄×C₁₃	C₂⁵	1	6	yes	—
128	D₄×C₁₃	C₂⁵	1	10	yes	—
129	C₂×C₄×C₁₃	—	2	15	no	—
130	C₂×C₄×C₁₃	—	2	45	no	—
131	C₂×C₄×C₁₃	—	2	60	no	—
132	C₂×C₄×C₁₃	—	2	60	no	—
133	C₂×C₄×C₁₃	C₂²×D₄	1	45	yes	—
134	C₂×C₄×C₁₃	C₂⁵	1	15	yes	—
135	C₈×C₁₃	C₂⁵	1	1	yes	characteristic
136	C₈×C₁₃	C₂⁵	1	15	yes	—
137	#585	—	2	6	no	—
138	#585	—	2	10	no	—
139	#585	C₂²×C₁₃	1	1	yes	characteristic
140	#585	C₂²×C₁₃	1	15	yes	complemented
141	#585	C₂²×C₁₃	1	15	yes	complemented
142	C₂×2₋¹⁺⁴	—	2	6	no	—
143	C₂×2₋¹⁺⁴	C₂²×C₁₃	1	15	yes	complemented
144	C₂×H(5,𝔽₂)	—	2	10	no	—
145	C₂×H(5,𝔽₂)	C₂²×C₁₃	1	15	yes	complemented
146	#578	C₂²×C₁₃	1	60	yes	complemented
147	#577	C₂²×C₁₃	1	60	yes	complemented
148	#577	C₂²×C₁₃	1	120	yes	complemented
149	#577	C₂²×C₁₃	1	20	yes	complemented
150	#576	C₂²×C₁₃	1	60	yes	complemented
151	#575	C₂²×C₁₃	1	90	yes	complemented
152	C₂×#137	C₂²×C₁₃	1	45	yes	complemented
153	C₂×AGL(1,ℤ/8)	C₂²×C₁₃	1	45	yes	complemented
154	C₂×#135	C₂²×C₁₃	1	45	yes	complemented
155	C₂²×SD₁₆	C₂²×C₁₃	1	15	yes	complemented
156	#568	C₂²×C₁₃	1	15	yes	complemented
157	C₂×#131	C₂²×C₁₃	1	15	yes	complemented
158	C₂²×C₁₃	—	2	6	no	—
159	C₂²×C₁₃	—	2	10	no	—
160	C₂²×C₁₃	—	4	15	no	—
161	C₂²×C₁₃	—	8	15	no	—
162	C₂²×C₁₃	—	8	45	no	—
163	C₂²×C₁₃	C₂³×D₄	1	15	yes	—
164	C₄×C₁₃	—	2	6	no	—
165	C₄×C₁₃	—	2	10	no	—
166	C₄×C₁₃	C₂³×D₄	1	15	yes	—
167	C₄×C₁₃	C₂⁶	1	1	yes	characteristic
168	2₋¹⁺⁴	—	2	60	no	—
169	2₋¹⁺⁴	—	2	15	no	—
170	2₋¹⁺⁴	—	2	15	no	—
171	2₋¹⁺⁴	D₄×C₁₃	1	6	yes	—
172	2₋¹⁺⁴	C₂³×C₁₃	1	20	yes	—
173	2₋¹⁺⁴	C₂³×C₁₃	1	60	yes	complemented
174	H(5,𝔽₂)	—	2	60	no	—
175	H(5,𝔽₂)	—	2	45	no	—
176	H(5,𝔽₂)	—	2	45	no	—
177	H(5,𝔽₂)	D₄×C₁₃	1	10	yes	—
178	H(5,𝔽₂)	C₂³×C₁₃	1	60	yes	—
179	H(5,𝔽₂)	C₂³×C₁₃	1	20	yes	complemented
180	C₂×#41	—	2	60	no	—
181	C₂×#41	—	2	60	no	—
182	C₂×#41	—	2	15	no	—
183	C₂×#41	—	2	45	no	—
184	C₂×#41	C₂³×C₁₃	1	45	yes	—
185	C₂×#41	C₂³×C₁₃	1	15	yes	—
186	C₂×#41	C₂³×C₁₃	1	45	yes	complemented
187	C₂²×Q₈	—	2	15	no	—
188	C₂²×Q₈	C₂³×C₁₃	1	15	yes	complemented
189	C₂²×D₄	—	2	45	no	—
190	C₂²×D₄	C₂³×C₁₃	1	15	yes	—
191	#137	C₂³×C₁₃	1	180	yes	complemented
192	#137	C₂³×C₁₃	1	60	yes	complemented
193	AGL(1,ℤ/8)	C₂³×C₁₃	1	180	yes	complemented
194	AGL(1,ℤ/8)	C₂³×C₁₃	1	60	yes	complemented
195	#135	C₂³×C₁₃	1	60	yes	complemented
196	#135	C₂³×C₁₃	1	180	yes	complemented
197	C₂×Q₁₆	C₂³×C₁₃	1	45	yes	complemented
198	C₂×SD₁₆	C₂³×C₁₃	1	45	yes	complemented
199	C₂×SD₁₆	C₂³×C₁₃	1	90	yes	complemented
200	C₂×SD₁₆	C₂³×C₁₃	1	15	yes	complemented
201	C₂×D₈	C₂³×C₁₃	1	45	yes	complemented
202	#131	C₂³×C₁₃	1	20	yes	complemented
203	#131	C₂³×C₁₃	1	60	yes	complemented
204	C₂×M₁₆	C₂³×C₁₃	1	45	yes	complemented
205	C₂²×C₈	C₂³×C₁₃	1	15	yes	complemented
206	C₂×C₁₃	—	2	15	no	—
207	C₂×C₁₃	—	4	6	no	—
208	C₂×C₁₃	—	4	10	no	—
209	C₂×C₁₃	C₂⁴×D₄	1	1	yes	characteristic
210	C₂⁴	—	2	15	no	—
211	#41	—	2	60	no	—
212	#41	—	2	20	no	—
213	#41	—	2	60	no	—
214	#41	—	2	180	no	—
215	#41	—	2	90	no	—
216	#41	—	2	90	no	—
217	#41	C₂×D₄×C₁₃	1	60	yes	—
218	#41	C₂⁴×C₁₃	1	60	yes	—
219	#41	C₂⁴×C₁₃	1	60	yes	—
220	#41	C₂⁴×C₁₃	1	20	yes	—
221	C₂×Q₈	—	2	60	no	—
222	C₂×Q₈	—	2	20	no	—
223	C₂×Q₈	—	2	45	no	—
224	C₂×Q₈	C₂×D₄×C₁₃	1	15	yes	—
225	C₂×Q₈	C₂⁴×C₁₃	1	45	yes	—
226	C₂×Q₈	C₂⁴×C₁₃	1	15	yes	—
227	C₂×D₄	—	2	45	no	—
228	C₂×D₄	—	2	45	no	—
229	C₂×D₄	—	2	180	no	—
230	C₂×D₄	—	2	60	no	—
231	C₂×D₄	—	2	45	no	—
232	C₂×D₄	C₂×D₄×C₁₃	1	45	yes	—
233	C₂×D₄	C₂⁴×C₁₃	1	15	yes	—
234	C₂×D₄	C₂⁴×C₁₃	1	45	yes	—
235	C₂²×C₄	—	2	15	no	—
236	C₂²×C₄	—	2	45	no	—
237	C₂²×C₄	—	2	45	no	—
238	C₂²×C₄	C₂⁴×C₁₃	1	15	yes	—
239	Q₁₆	C₂⁴×C₁₃	1	60	yes	—
240	SD₁₆	C₂⁴×C₁₃	1	10	yes	—
241	SD₁₆	C₂⁴×C₁₃	1	6	yes	—
242	SD₁₆	C₂⁴×C₁₃	1	90	yes	—
243	SD₁₆	C₂⁴×C₁₃	1	30	yes	—
244	D₈	C₂⁴×C₁₃	1	60	yes	—
245	M₁₆	C₂⁴×C₁₃	1	60	yes	—
246	C₂×C₈	C₂⁴×C₁₃	1	15	yes	—
247	C₂×C₈	C₂⁴×C₁₃	1	45	yes	—
248	C₁₃	#63092	1	1	yes	characteristic, direct product factor, Sylow
249	C₂³	—	2	15	no	—
250	C₂³	—	2	45	no	—
251	C₂³	—	16	15	no	—
252	C₂³	C₂²×D₄×C₁₃	1	15	yes	—
253	Q₈	—	2	45	no	—
254	Q₈	—	2	15	no	—
255	Q₈	C₂²×D₄×C₁₃	1	20	yes	—
256	Q₈	C₂⁵×C₁₃	1	10	yes	—
257	Q₈	C₂⁵×C₁₃	1	6	yes	—
258	D₄	—	2	60	no	—
259	D₄	—	2	60	no	—
260	D₄	—	2	45	no	—
261	D₄	—	2	15	no	—
262	D₄	C₂²×D₄×C₁₃	1	60	yes	—
263	D₄	C₂⁵×C₁₃	1	6	yes	—
264	D₄	C₂⁵×C₁₃	1	10	yes	—
265	C₂×C₄	—	2	15	no	—
266	C₂×C₄	—	2	45	no	—
267	C₂×C₄	—	2	60	no	—
268	C₂×C₄	—	2	60	no	—
269	C₂×C₄	C₂²×D₄×C₁₃	1	45	yes	—
270	C₂×C₄	C₂⁵×C₁₃	1	15	yes	—
271	C₈	C₂⁵×C₁₃	1	1	yes	characteristic
272	C₈	C₂⁵×C₁₃	1	15	yes	—
273	C₂²	—	2	6	no	—
274	C₂²	—	2	10	no	—
275	C₂²	—	4	15	no	—
276	C₂²	—	8	15	no	—
277	C₂²	—	8	45	no	—
278	C₂²	C₂³×D₄×C₁₃	1	15	yes	—
279	C₄	—	2	6	no	—
280	C₄	—	2	10	no	—
281	C₄	C₂³×D₄×C₁₃	1	15	yes	—
282	C₄	C₂⁶×C₁₃	1	1	yes	characteristic
283	C₂	—	2	15	no	—
284	C₂	—	4	10	no	—
285	C₂	—	4	6	no	—
286	C₂	C₂⁴×D₄×C₁₃	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂×C₁₃	C₂⁴×D₄
commutator, Frattini, cosocle	C₄	C₂⁶×C₁₃
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₃ ◁ C₁₃×#585 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₃×2₋¹⁺⁶	C₂	semidirect
2. C₁₃×H(7,𝔽₂)	C₂	semidirect
3. C₁₃×#3586	C₂	semidirect
4. C₁₃×#3585	C₂	semidirect
5. C₁₃×#3584	C₂	semidirect
6. C₂×C₁₃×#577	C₂	semidirect
7. C₁₃×#3573	C₂	semidirect
11. C₁₃×#585	C₂²	semidirect
12. C₁₃×#585	C₂²	semidirect
14. C₂×C₁₃×2₋¹⁺⁴	C₂²	semidirect
16. C₂×C₁₃×H(5,𝔽₂)	C₂²	semidirect
17. C₁₃×#578	C₂²	semidirect
18. C₁₃×#577	C₂²	semidirect
19. C₁₃×#577	C₂²	semidirect
20. C₁₃×#577	C₂²	semidirect
21. C₁₃×#576	C₂²	semidirect
22. C₁₃×#575	C₂²	semidirect
23. C₂×C₁₃×#137	C₂²	semidirect
24. C₂×C₁₃×AGL(1,ℤ/8)	C₂²	semidirect
25. C₂×C₁₃×#135	C₂²	semidirect
26. C₂²×C₁₃×SD₁₆	C₂²	semidirect
27. C₁₃×#568	C₂²	semidirect
28. C₂×C₁₃×#131	C₂²	semidirect
34. C₁₃×2₋¹⁺⁴	C₂³	semidirect
40. C₁₃×H(5,𝔽₂)	C₂³	semidirect
47. C₂×C₁₃×#41	C₂³	semidirect
49. C₂²×Q₈×C₁₃	C₂³	semidirect
52. C₁₃×#137	C₂³	semidirect
53. C₁₃×#137	C₂³	semidirect
54. C₁₃×AGL(1,ℤ/8)	C₂³	semidirect
55. C₁₃×AGL(1,ℤ/8)	C₂³	semidirect
56. C₁₃×#135	C₂³	semidirect
57. C₁₃×#135	C₂³	semidirect
58. C₂×C₁₃×Q₁₆	C₂³	semidirect
59. C₂×C₁₃×SD₁₆	C₂³	semidirect
60. C₂×C₁₃×SD₁₆	C₂³	semidirect
61. C₂×C₁₃×SD₁₆	C₂³	semidirect
62. C₂×C₁₃×D₈	C₂³	semidirect
63. C₁₃×#131	C₂³	semidirect
64. C₁₃×#131	C₂³	semidirect
65. C₂×C₁₃×M₁₆	C₂³	semidirect
66. C₂²×C₈×C₁₃	C₂³	semidirect
67. #63092	C₁₃	direct (N × H)
106. 2₋¹⁺⁶	C₂×C₁₃	semidirect
107. H(7,𝔽₂)	C₂×C₁₃	semidirect
108. #3586	C₂×C₁₃	semidirect
109. #3585	C₂×C₁₃	semidirect
110. #3584	C₂×C₁₃	semidirect
111. C₂×#577	C₂×C₁₃	semidirect
112. #3573	C₂×C₁₃	semidirect
140. #585	C₂²×C₁₃	semidirect
141. #585	C₂²×C₁₃	semidirect
143. C₂×2₋¹⁺⁴	C₂²×C₁₃	semidirect
145. C₂×H(5,𝔽₂)	C₂²×C₁₃	semidirect
146. #578	C₂²×C₁₃	semidirect
147. #577	C₂²×C₁₃	semidirect
148. #577	C₂²×C₁₃	semidirect
149. #577	C₂²×C₁₃	semidirect
150. #576	C₂²×C₁₃	semidirect
151. #575	C₂²×C₁₃	semidirect
152. C₂×#137	C₂²×C₁₃	semidirect
153. C₂×AGL(1,ℤ/8)	C₂²×C₁₃	semidirect
154. C₂×#135	C₂²×C₁₃	semidirect
155. C₂²×SD₁₆	C₂²×C₁₃	semidirect
156. #568	C₂²×C₁₃	semidirect
157. C₂×#131	C₂²×C₁₃	semidirect
173. 2₋¹⁺⁴	C₂³×C₁₃	semidirect
179. H(5,𝔽₂)	C₂³×C₁₃	semidirect
186. C₂×#41	C₂³×C₁₃	semidirect
188. C₂²×Q₈	C₂³×C₁₃	semidirect
191. #137	C₂³×C₁₃	semidirect
192. #137	C₂³×C₁₃	semidirect
193. AGL(1,ℤ/8)	C₂³×C₁₃	semidirect
194. AGL(1,ℤ/8)	C₂³×C₁₃	semidirect
195. #135	C₂³×C₁₃	semidirect
196. #135	C₂³×C₁₃	semidirect
197. C₂×Q₁₆	C₂³×C₁₃	semidirect
198. C₂×SD₁₆	C₂³×C₁₃	semidirect
199. C₂×SD₁₆	C₂³×C₁₃	semidirect
200. C₂×SD₁₆	C₂³×C₁₃	semidirect
201. C₂×D₈	C₂³×C₁₃	semidirect
202. #131	C₂³×C₁₃	semidirect
203. #131	C₂³×C₁₃	semidirect
204. C₂×M₁₆	C₂³×C₁₃	semidirect
205. C₂²×C₈	C₂³×C₁₃	semidirect
248. C₁₃	#63092	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₁₃×2₋¹⁺⁶	2
C₁₃×H(7,𝔽₂)	2
C₁₃×#3586	2
C₁₃×#3585	2
C₁₃×#3584	2
C₂×C₁₃×#577	2
C₁₃×#3573	2
#63092	13

Subgroups — C13×#63092 #15749431

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#63092 #15749431