Subgroups — C₂×C₁₃×#3292 #15747442

Order 3328.

2766 conjugacy classes of subgroups.

The subgroup lattice has 322 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#576	C₂	1	4	yes	maximal, complemented
2	C₁₃×#3292	C₂	1	16	yes	maximal, direct product factor
3	C₂×C₁₃×#493	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₁₃×#472	C₂	1	4	yes	maximal, complemented
5	C₂×C₁₃×#453	C₂	1	4	yes	maximal, complemented
6	C₂×C₁₃×#443	C₂	1	2	yes	maximal, complemented
7	C₂×C₁₃×H(5,𝔽₂)	C₂²	1	4	yes	complemented
8	C₁₃×#576	—	2	16	no	—
9	C₁₃×#576	C₂²	1	32	yes	complemented
10	C₂×C₁₃×AGL(1,ℤ/8)	—	2	8	no	—
11	C₂×C₁₃×AGL(1,ℤ/8)	C₂²	1	8	yes	complemented
12	C₂×C₁₃×#135	—	2	4	no	—
13	C₂×C₁₃×#135	C₂²	1	2	yes	—
14	C₂²×C₁₃×D₈	—	2	4	no	—
15	C₂²×C₁₃×D₈	C₂²	1	4	yes	complemented
16	C₂×C₁₃×#131	C₂²	1	4	yes	complemented
17	C₂×C₁₃×#127	C₂²	1	2	yes	complemented
18	C₁₃×#493	C₂²	1	8	yes	complemented
19	C₁₃×#472	C₂²	1	32	yes	complemented
20	C₁₃×#453	C₂²	1	32	yes	complemented
21	C₁₃×#443	C₂²	1	16	yes	complemented
22	C₂×C₁₃×#108	C₂²	1	2	yes	complemented
23	C₂×C₁₃×#104	C₂²	1	4	yes	complemented
24	C₂×C₁₃×#100	C₂²	1	4	yes	complemented
25	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic, complemented
26	C₁₃×H(5,𝔽₂)	—	2	16	no	—
27	C₁₃×H(5,𝔽₂)	—	4	4	no	—
28	C₁₃×H(5,𝔽₂)	C₂³	1	16	yes	complemented
29	C₂×C₁₃×#41	—	2	8	no	—
30	C₂×C₁₃×#41	C₂³	1	4	yes	—
31	C₂²×D₄×C₁₃	—	2	8	no	—
32	C₂²×D₄×C₁₃	—	4	2	no	—
33	C₂²×D₄×C₁₃	—	4	4	no	—
34	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
35	C₁₃×AGL(1,ℤ/8)	—	2	16	no	—
36	C₁₃×AGL(1,ℤ/8)	—	2	64	no	—
37	C₁₃×AGL(1,ℤ/8)	C₂³	1	32	yes	complemented
38	C₁₃×#135	—	2	32	no	—
39	C₁₃×#135	D₄	1	8	yes	complemented
40	C₁₃×#135	C₂³	1	8	yes	—
41	C₂×C₁₃×Q₁₆	D₄	1	2	yes	complemented
42	C₂×C₁₃×SD₁₆	—	2	8	no	—
43	C₂×C₁₃×SD₁₆	D₄	1	4	yes	complemented
44	C₂×C₁₃×D₈	—	2	8	no	—
45	C₂×C₁₃×D₈	—	2	32	no	—
46	C₂×C₁₃×D₈	—	2	4	no	—
47	C₂×C₁₃×D₈	—	2	4	no	—
48	C₂×C₁₃×D₈	—	2	8	no	—
49	C₂×C₁₃×D₈	D₄	1	2	yes	complemented
50	C₂×C₁₃×D₈	C₂³	1	16	yes	complemented
51	C₁₃×#131	—	2	8	no	—
52	C₁₃×#131	C₂³	1	16	yes	complemented
53	C₂×C₁₃×M₁₆	—	2	4	no	—
54	C₂×C₁₃×M₁₆	C₂³	1	4	yes	—
55	C₂²×C₈×C₁₃	—	2	4	no	—
56	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
57	C₁₃×#127	—	4	2	no	—
58	C₁₃×#127	C₂³	1	8	yes	complemented
59	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
60	C₁₃×#108	C₂³	1	8	yes	complemented
61	C₁₃×#104	C₂³	1	16	yes	complemented
62	C₁₃×#100	C₂³	1	16	yes	complemented
63	C₄×C₈×C₁₃	C₂³	1	4	yes	complemented
64	C₂×#3292	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
65	C₂⁴×C₁₃	—	2	4	no	—
66	C₂⁴×C₁₃	—	4	4	no	—
67	C₁₃×#41	—	2	4	no	—
68	C₁₃×#41	—	2	4	no	—
69	C₁₃×#41	—	2	32	no	—
70	C₁₃×#41	—	4	16	no	—
71	C₁₃×#41	C₂×D₄	1	8	yes	—
72	C₁₃×#41	C₂⁴	1	8	yes	—
73	C₂×Q₈×C₁₃	C₂×D₄	1	4	yes	—
74	C₂×D₄×C₁₃	—	2	4	no	—
75	C₂×D₄×C₁₃	—	2	32	no	—
76	C₂×D₄×C₁₃	—	2	8	no	—
77	C₂×D₄×C₁₃	—	2	8	no	—
78	C₂×D₄×C₁₃	—	2	4	no	—
79	C₂×D₄×C₁₃	—	4	16	no	—
80	C₂×D₄×C₁₃	—	4	8	no	—
81	C₂×D₄×C₁₃	—	4	8	no	—
82	C₂×D₄×C₁₃	—	4	16	no	—
83	C₂×D₄×C₁₃	—	4	16	no	—
84	C₂×D₄×C₁₃	—	8	8	no	—
85	C₂×D₄×C₁₃	C₂×D₄	1	4	yes	—
86	C₂×D₄×C₁₃	C₂⁴	1	8	yes	—
87	C₂²×C₄×C₁₃	—	2	1	no	—
88	C₂²×C₄×C₁₃	—	2	4	no	—
89	C₂²×C₄×C₁₃	—	4	4	no	—
90	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
91	C₁₃×Q₁₆	C₂×D₄	1	8	yes	complemented
92	C₁₃×SD₁₆	—	2	32	no	—
93	C₁₃×SD₁₆	C₂×D₄	1	16	yes	complemented
94	C₁₃×D₈	—	2	32	no	—
95	C₁₃×D₈	—	2	16	no	—
96	C₁₃×D₈	—	2	16	no	—
97	C₁₃×D₈	C₂×D₄	1	8	yes	complemented
98	C₁₃×M₁₆	—	2	4	no	—
99	C₁₃×M₁₆	—	2	16	no	—
100	C₁₃×M₁₆	C₂⁴	1	8	yes	—
101	C₂×C₈×C₁₃	—	2	4	no	—
102	C₂×C₈×C₁₃	—	2	16	no	—
103	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
104	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
105	C₂×C₈×C₁₃	C₂×D₄	1	4	yes	—
106	C₂×C₈×C₁₃	C₂⁴	1	4	yes	—
107	C₄²×C₁₃	—	2	1	no	—
108	C₄²×C₁₃	C₂⁴	1	2	yes	—
109	C₂×#576	C₂×C₁₃	1	4	yes	complemented
110	#3292	C₂×C₁₃	1	16	yes	direct product factor
111	C₂×#493	C₂×C₁₃	1	1	yes	characteristic, complemented
112	C₂×#472	C₂×C₁₃	1	4	yes	complemented
113	C₂×#453	C₂×C₁₃	1	4	yes	complemented
114	C₂×#443	C₂×C₁₃	1	2	yes	complemented
115	C₂³×C₁₃	—	2	4	no	—
116	C₂³×C₁₃	—	2	8	no	—
117	C₂³×C₁₃	—	4	16	no	—
118	C₂³×C₁₃	—	4	4	no	—
119	C₂³×C₁₃	—	4	4	no	—
120	C₂³×C₁₃	—	8	8	no	—
121	C₂³×C₁₃	—	16	8	no	—
122	C₂³×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
123	Q₈×C₁₃	—	2	4	no	—
124	Q₈×C₁₃	C₂²×D₄	1	8	yes	—
125	D₄×C₁₃	—	2	8	no	—
126	D₄×C₁₃	—	2	8	no	—
127	D₄×C₁₃	—	2	4	no	—
128	D₄×C₁₃	—	2	16	no	—
129	D₄×C₁₃	—	4	32	no	—
130	D₄×C₁₃	—	4	8	no	—
131	D₄×C₁₃	—	8	16	no	—
132	D₄×C₁₃	C₂²×D₄	1	8	yes	—
133	C₂×C₄×C₁₃	—	2	4	no	—
134	C₂×C₄×C₁₃	—	2	4	no	—
135	C₂×C₄×C₁₃	—	2	2	no	—
136	C₂×C₄×C₁₃	—	2	8	no	—
137	C₂×C₄×C₁₃	—	2	8	no	—
138	C₂×C₄×C₁₃	—	4	16	no	—
139	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
140	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
141	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
142	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
143	C₈×C₁₃	—	2	8	no	—
144	C₈×C₁₃	C₂²×D₄	1	4	yes	—
145	C₈×C₁₃	C₂²×D₄	1	4	yes	—
146	C₂×H(5,𝔽₂)	C₂²×C₁₃	1	4	yes	complemented
147	#576	—	2	16	no	—
148	#576	C₂²×C₁₃	1	32	yes	complemented
149	C₂×AGL(1,ℤ/8)	—	2	8	no	—
150	C₂×AGL(1,ℤ/8)	C₂²×C₁₃	1	8	yes	complemented
151	C₂×#135	—	2	4	no	—
152	C₂×#135	C₂²×C₁₃	1	2	yes	—
153	C₂²×D₈	—	2	4	no	—
154	C₂²×D₈	C₂²×C₁₃	1	4	yes	complemented
155	C₂×#131	C₂²×C₁₃	1	4	yes	complemented
156	C₂×#127	C₂²×C₁₃	1	2	yes	complemented
157	#493	C₂²×C₁₃	1	8	yes	complemented
158	#472	C₂²×C₁₃	1	32	yes	complemented
159	#453	C₂²×C₁₃	1	32	yes	complemented
160	#443	C₂²×C₁₃	1	16	yes	complemented
161	C₂×#108	C₂²×C₁₃	1	2	yes	complemented
162	C₂×#104	C₂²×C₁₃	1	4	yes	complemented
163	C₂×#100	C₂²×C₁₃	1	4	yes	complemented
164	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
165	C₂²×C₁₃	—	2	2	no	—
166	C₂²×C₁₃	—	2	8	no	—
167	C₂²×C₁₃	—	4	8	no	—
168	C₂²×C₁₃	—	4	8	no	—
169	C₂²×C₁₃	—	8	8	no	—
170	C₂²×C₁₃	—	8	8	no	—
171	C₂²×C₁₃	—	16	4	no	—
172	C₂²×C₁₃	—	16	16	no	—
173	C₂²×C₁₃	D₄²	1	1	yes	characteristic
174	C₂²×C₁₃	D₄²	1	1	yes	characteristic
175	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
176	C₄×C₁₃	—	2	4	no	—
177	C₄×C₁₃	—	2	8	no	—
178	C₄×C₁₃	D₄²	1	2	yes	—
179	C₄×C₁₃	C₂³×D₄	1	2	yes	—
180	H(5,𝔽₂)	—	2	16	no	—
181	H(5,𝔽₂)	—	4	4	no	—
182	H(5,𝔽₂)	C₂³×C₁₃	1	16	yes	complemented
183	C₂×#41	—	2	8	no	—
184	C₂×#41	C₂³×C₁₃	1	4	yes	—
185	C₂²×D₄	—	2	8	no	—
186	C₂²×D₄	—	4	2	no	—
187	C₂²×D₄	—	4	4	no	—
188	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
189	AGL(1,ℤ/8)	—	2	16	no	—
190	AGL(1,ℤ/8)	—	2	64	no	—
191	AGL(1,ℤ/8)	C₂³×C₁₃	1	32	yes	complemented
192	#135	—	2	32	no	—
193	#135	D₄×C₁₃	1	8	yes	complemented
194	#135	C₂³×C₁₃	1	8	yes	—
195	C₂×Q₁₆	D₄×C₁₃	1	2	yes	complemented
196	C₂×SD₁₆	—	2	8	no	—
197	C₂×SD₁₆	D₄×C₁₃	1	4	yes	complemented
198	C₂×D₈	—	2	8	no	—
199	C₂×D₈	—	2	32	no	—
200	C₂×D₈	—	2	4	no	—
201	C₂×D₈	—	2	4	no	—
202	C₂×D₈	—	2	8	no	—
203	C₂×D₈	D₄×C₁₃	1	2	yes	complemented
204	C₂×D₈	C₂³×C₁₃	1	16	yes	complemented
205	#131	—	2	8	no	—
206	#131	C₂³×C₁₃	1	16	yes	complemented
207	C₂×M₁₆	—	2	4	no	—
208	C₂×M₁₆	C₂³×C₁₃	1	4	yes	—
209	C₂²×C₈	—	2	4	no	—
210	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
211	#127	—	4	2	no	—
212	#127	C₂³×C₁₃	1	8	yes	complemented
213	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
214	#108	C₂³×C₁₃	1	8	yes	complemented
215	#104	C₂³×C₁₃	1	16	yes	complemented
216	#100	C₂³×C₁₃	1	16	yes	complemented
217	C₄×C₈	C₂³×C₁₃	1	4	yes	complemented
218	C₂×C₁₃	—	2	1	no	—
219	C₂×C₁₃	—	2	1	no	—
220	C₂×C₁₃	—	4	8	no	—
221	C₂×C₁₃	—	8	8	no	—
222	C₂×C₁₃	#3292	1	2	yes	direct product factor
223	C₂×C₁₃	C₂×D₄²	1	1	yes	characteristic
224	C₂⁴	—	2	4	no	—
225	C₂⁴	—	4	4	no	—
226	#41	—	2	4	no	—
227	#41	—	2	4	no	—
228	#41	—	2	32	no	—
229	#41	—	4	16	no	—
230	#41	C₂×D₄×C₁₃	1	8	yes	—
231	#41	C₂⁴×C₁₃	1	8	yes	—
232	C₂×Q₈	C₂×D₄×C₁₃	1	4	yes	—
233	C₂×D₄	—	2	4	no	—
234	C₂×D₄	—	2	32	no	—
235	C₂×D₄	—	2	8	no	—
236	C₂×D₄	—	2	8	no	—
237	C₂×D₄	—	2	4	no	—
238	C₂×D₄	—	4	16	no	—
239	C₂×D₄	—	4	8	no	—
240	C₂×D₄	—	4	8	no	—
241	C₂×D₄	—	4	16	no	—
242	C₂×D₄	—	4	16	no	—
243	C₂×D₄	—	8	8	no	—
244	C₂×D₄	C₂×D₄×C₁₃	1	4	yes	—
245	C₂×D₄	C₂⁴×C₁₃	1	8	yes	—
246	C₂²×C₄	—	2	1	no	—
247	C₂²×C₄	—	2	4	no	—
248	C₂²×C₄	—	4	4	no	—
249	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
250	Q₁₆	C₂×D₄×C₁₃	1	8	yes	complemented
251	SD₁₆	—	2	32	no	—
252	SD₁₆	C₂×D₄×C₁₃	1	16	yes	complemented
253	D₈	—	2	32	no	—
254	D₈	—	2	16	no	—
255	D₈	—	2	16	no	—
256	D₈	C₂×D₄×C₁₃	1	8	yes	complemented
257	M₁₆	—	2	4	no	—
258	M₁₆	—	2	16	no	—
259	M₁₆	C₂⁴×C₁₃	1	8	yes	—
260	C₂×C₈	—	2	4	no	—
261	C₂×C₈	—	2	16	no	—
262	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
263	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
264	C₂×C₈	C₂×D₄×C₁₃	1	4	yes	—
265	C₂×C₈	C₂⁴×C₁₃	1	4	yes	—
266	C₄²	—	2	1	no	—
267	C₄²	C₂⁴×C₁₃	1	2	yes	—
268	C₁₃	C₂×#3292	1	1	yes	characteristic, direct product factor, Sylow
269	C₂³	—	2	4	no	—
270	C₂³	—	2	8	no	—
271	C₂³	—	4	16	no	—
272	C₂³	—	4	4	no	—
273	C₂³	—	4	4	no	—
274	C₂³	—	8	8	no	—
275	C₂³	—	16	8	no	—
276	C₂³	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
277	Q₈	—	2	4	no	—
278	Q₈	C₂²×D₄×C₁₃	1	8	yes	—
279	D₄	—	2	8	no	—
280	D₄	—	2	8	no	—
281	D₄	—	2	4	no	—
282	D₄	—	2	16	no	—
283	D₄	—	4	32	no	—
284	D₄	—	4	8	no	—
285	D₄	—	8	16	no	—
286	D₄	C₂²×D₄×C₁₃	1	8	yes	—
287	C₂×C₄	—	2	4	no	—
288	C₂×C₄	—	2	4	no	—
289	C₂×C₄	—	2	2	no	—
290	C₂×C₄	—	2	8	no	—
291	C₂×C₄	—	2	8	no	—
292	C₂×C₄	—	4	16	no	—
293	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
294	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
295	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
296	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
297	C₈	—	2	8	no	—
298	C₈	C₂²×D₄×C₁₃	1	4	yes	—
299	C₈	C₂²×D₄×C₁₃	1	4	yes	—
300	C₂²	—	2	2	no	—
301	C₂²	—	2	8	no	—
302	C₂²	—	4	8	no	—
303	C₂²	—	4	8	no	—
304	C₂²	—	8	8	no	—
305	C₂²	—	8	8	no	—
306	C₂²	—	16	4	no	—
307	C₂²	—	16	16	no	—
308	C₂²	D₄²×C₁₃	1	1	yes	characteristic
309	C₂²	D₄²×C₁₃	1	1	yes	characteristic
310	C₂²	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
311	C₄	—	2	4	no	—
312	C₄	—	2	8	no	—
313	C₄	D₄²×C₁₃	1	2	yes	—
314	C₄	C₂³×D₄×C₁₃	1	2	yes	—
315	C₂	—	2	1	no	—
316	C₂	—	2	1	no	—
317	C₂	—	4	8	no	—
318	C₂	—	8	8	no	—
319	C₂	C₁₃×#3292	1	2	yes	direct product factor
320	C₂	C₂×D₄²×C₁₃	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	D₄²
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₃
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₂²×C₄×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₃×#576	C₂	semidirect
2. C₁₃×#3292	C₂	direct (N × H)
3. C₂×C₁₃×#493	C₂	semidirect
4. C₂×C₁₃×#472	C₂	semidirect
5. C₂×C₁₃×#453	C₂	semidirect
6. C₂×C₁₃×#443	C₂	semidirect
7. C₂×C₁₃×H(5,𝔽₂)	C₂²	semidirect
9. C₁₃×#576	C₂²	semidirect
11. C₂×C₁₃×AGL(1,ℤ/8)	C₂²	semidirect
15. C₂²×C₁₃×D₈	C₂²	semidirect
16. C₂×C₁₃×#131	C₂²	semidirect
17. C₂×C₁₃×#127	C₂²	semidirect
18. C₁₃×#493	C₂²	semidirect
19. C₁₃×#472	C₂²	semidirect
20. C₁₃×#453	C₂²	semidirect
21. C₁₃×#443	C₂²	semidirect
22. C₂×C₁₃×#108	C₂²	semidirect
23. C₂×C₁₃×#104	C₂²	semidirect
24. C₂×C₁₃×#100	C₂²	semidirect
25. C₂×C₄×C₈×C₁₃	C₂²	semidirect
28. C₁₃×H(5,𝔽₂)	C₂³	semidirect
37. C₁₃×AGL(1,ℤ/8)	C₂³	semidirect
39. C₁₃×#135	D₄	semidirect
41. C₂×C₁₃×Q₁₆	D₄	semidirect
43. C₂×C₁₃×SD₁₆	D₄	semidirect
49. C₂×C₁₃×D₈	D₄	semidirect
50. C₂×C₁₃×D₈	C₂³	semidirect
52. C₁₃×#131	C₂³	semidirect
58. C₁₃×#127	C₂³	semidirect
60. C₁₃×#108	C₂³	semidirect
61. C₁₃×#104	C₂³	semidirect
62. C₁₃×#100	C₂³	semidirect
63. C₄×C₈×C₁₃	C₂³	semidirect
64. C₂×#3292	C₁₃	direct (N × H)
91. C₁₃×Q₁₆	C₂×D₄	semidirect
93. C₁₃×SD₁₆	C₂×D₄	semidirect
97. C₁₃×D₈	C₂×D₄	semidirect
109. C₂×#576	C₂×C₁₃	semidirect
110. #3292	C₂×C₁₃	direct (N × H)
111. C₂×#493	C₂×C₁₃	semidirect
112. C₂×#472	C₂×C₁₃	semidirect
113. C₂×#453	C₂×C₁₃	semidirect
114. C₂×#443	C₂×C₁₃	semidirect
146. C₂×H(5,𝔽₂)	C₂²×C₁₃	semidirect
148. #576	C₂²×C₁₃	semidirect
150. C₂×AGL(1,ℤ/8)	C₂²×C₁₃	semidirect
154. C₂²×D₈	C₂²×C₁₃	semidirect
155. C₂×#131	C₂²×C₁₃	semidirect
156. C₂×#127	C₂²×C₁₃	semidirect
157. #493	C₂²×C₁₃	semidirect
158. #472	C₂²×C₁₃	semidirect
159. #453	C₂²×C₁₃	semidirect
160. #443	C₂²×C₁₃	semidirect
161. C₂×#108	C₂²×C₁₃	semidirect
162. C₂×#104	C₂²×C₁₃	semidirect
163. C₂×#100	C₂²×C₁₃	semidirect
164. C₂×C₄×C₈	C₂²×C₁₃	semidirect
182. H(5,𝔽₂)	C₂³×C₁₃	semidirect
191. AGL(1,ℤ/8)	C₂³×C₁₃	semidirect
193. #135	D₄×C₁₃	semidirect
195. C₂×Q₁₆	D₄×C₁₃	semidirect
197. C₂×SD₁₆	D₄×C₁₃	semidirect
203. C₂×D₈	D₄×C₁₃	semidirect
204. C₂×D₈	C₂³×C₁₃	semidirect
206. #131	C₂³×C₁₃	semidirect
212. #127	C₂³×C₁₃	semidirect
214. #108	C₂³×C₁₃	semidirect
215. #104	C₂³×C₁₃	semidirect
216. #100	C₂³×C₁₃	semidirect
217. C₄×C₈	C₂³×C₁₃	semidirect
222. C₂×C₁₃	#3292	direct (N × H)
250. Q₁₆	C₂×D₄×C₁₃	semidirect
252. SD₁₆	C₂×D₄×C₁₃	semidirect
256. D₈	C₂×D₄×C₁₃	semidirect
268. C₁₃	C₂×#3292	direct (N × H)
319. C₂	C₁₃×#3292	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×#576	2
C₁₃×#3292	2
C₂×C₁₃×#493	2
C₂×C₁₃×#472	2
C₂×C₁₃×#453	2
C₂×C₁₃×#443	2
C₂×#3292	13

Subgroups — C2×C13×#3292 #15747442

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₃×#3292 #15747442