Subgroups — C₂×C₁₃×#3392 #15747727

Order 3328.

2238 conjugacy classes of subgroups.

The subgroup lattice has 340 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#557	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₃×#550	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#3392	C₂	1	16	yes	maximal, direct product factor
4	C₂×C₁₃×#492	C₂	1	3	yes	maximal, complemented
5	C₂×C₁₃×#460	C₂	1	3	yes	maximal, complemented
6	C₂×C₁₃×#461	C₂	1	3	yes	maximal, complemented
7	C₂×C₈×Q₈×C₁₃	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₄×C₁₃×SD₁₆	C₂	1	3	yes	maximal, complemented
9	C₂²×C₁₃×#41	—	2	1	no	—
10	C₂²×C₁₃×SD₁₆	C₂²	1	3	yes	—
11	C₂²×C₁₃×SD₁₆	C₂²	1	6	yes	—
12	C₁₃×#557	—	2	4	no	—
13	C₁₃×#557	C₂²	1	8	yes	complemented
14	C₁₃×#550	—	2	4	no	—
15	C₁₃×#550	C₂²	1	8	yes	—
16	C₂×C₁₃×C₄⋊Q₈	C₂²	1	3	yes	—
17	C₂×C₁₃×#127	C₂²	1	3	yes	—
18	C₂×C₁₃×#125	—	2	3	no	—
19	C₂×C₁₃×#121	—	2	3	no	—
20	C₂×C₄×Q₈×C₁₃	—	2	1	no	—
21	C₂×C₄×Q₈×C₁₃	C₂²	1	3	yes	—
22	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
23	C₂×C₄×D₄×C₁₃	C₂²	1	3	yes	—
24	C₁₃×#492	C₂²	1	24	yes	complemented
25	C₁₃×#461	C₂²	1	24	yes	complemented
26	C₁₃×#460	C₂²	1	24	yes	complemented
27	C₈×Q₈×C₁₃	C₂²	1	8	yes	complemented
28	C₄×C₁₃×SD₁₆	C₂²	1	24	yes	complemented
29	C₂×C₁₃×#106	C₂²	1	1	yes	characteristic
30	C₂×C₁₃×C₄⋊C₈	C₂²	1	3	yes	—
31	C₂×C₁₃×#103	C₂²	1	3	yes	—
32	C₂×C₁₃×#102	C₂²	1	3	yes	—
33	C₂×C₄×C₈×C₁₃	C₂²	1	3	yes	—
34	C₂×C₁₃×#41	—	2	8	no	—
35	C₂×C₁₃×#41	—	4	8	no	—
36	C₂²×Q₈×C₁₃	D₄	1	1	yes	characteristic
37	C₂²×Q₈×C₁₃	C₂³	1	3	yes	—
38	C₂²×D₄×C₁₃	—	2	3	no	—
39	C₂²×D₄×C₁₃	—	2	3	no	—
40	C₂²×D₄×C₁₃	C₂³	1	3	yes	—
41	C₂³×C₄×C₁₃	—	2	3	no	—
42	C₂×C₁₃×SD₁₆	—	2	12	no	—
43	C₂×C₁₃×SD₁₆	—	4	12	no	—
44	C₂×C₁₃×SD₁₆	C₂³	1	12	yes	—
45	C₂×C₁₃×SD₁₆	C₂³	1	24	yes	—
46	C₂²×C₈×C₁₃	C₂³	1	3	yes	—
47	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
48	C₁₃×C₄⋊Q₈	—	2	6	no	—
49	C₁₃×C₄⋊Q₈	C₂³	1	12	yes	—
50	C₁₃×#127	—	2	6	no	—
51	C₁₃×#127	C₂³	1	12	yes	—
52	C₁₃×#125	—	2	24	no	—
53	C₁₃×#121	—	2	24	no	—
54	C₄×Q₈×C₁₃	—	2	8	no	—
55	C₄×Q₈×C₁₃	—	2	6	no	—
56	C₄×Q₈×C₁₃	D₄	1	4	yes	—
57	C₄×Q₈×C₁₃	C₂³	1	12	yes	—
58	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
59	C₄×D₄×C₁₃	—	2	6	no	—
60	C₄×D₄×C₁₃	C₂³	1	12	yes	—
61	C₂×C₁₃×C₄⋊C₄	—	2	3	no	—
62	C₂×C₁₃×C₄⋊C₄	—	2	3	no	—
63	C₂×C₁₃×C₄⋊C₄	—	2	3	no	—
64	C₂×C₁₃×C₄⋊C₄	D₄	1	3	yes	—
65	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
66	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
67	C₂×C₁₃×C₂²⋊C₄	—	2	3	no	—
68	C₂×C₄²×C₁₃	—	2	3	no	—
69	C₂×C₄²×C₁₃	C₂³	1	3	yes	—
70	C₁₃×#106	C₂³	1	4	yes	—
71	C₁₃×C₄⋊C₈	C₂³	1	12	yes	—
72	C₁₃×#103	C₂³	1	12	yes	—
73	C₁₃×#102	C₂³	1	12	yes	—
74	C₄×C₈×C₁₃	C₂³	1	12	yes	—
75	C₂×#3392	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
76	C₂⁴×C₁₃	—	2	3	no	—
77	C₁₃×#41	—	4	32	no	—
78	C₂×Q₈×C₁₃	—	2	3	no	—
79	C₂×Q₈×C₁₃	—	2	6	no	—
80	C₂×Q₈×C₁₃	—	2	6	no	—
81	C₂×Q₈×C₁₃	SD₁₆	1	8	yes	complemented
82	C₂×Q₈×C₁₃	C₂×D₄	1	4	yes	—
83	C₂×Q₈×C₁₃	C₂⁴	1	6	yes	—
84	C₂×D₄×C₁₃	—	2	3	no	—
85	C₂×D₄×C₁₃	—	2	12	no	—
86	C₂×D₄×C₁₃	—	2	12	no	—
87	C₂×D₄×C₁₃	—	2	6	no	—
88	C₂×D₄×C₁₃	—	2	6	no	—
89	C₂×D₄×C₁₃	—	4	12	no	—
90	C₂×D₄×C₁₃	—	8	6	no	—
91	C₂×D₄×C₁₃	C₂⁴	1	6	yes	—
92	C₂²×C₄×C₁₃	—	2	1	no	—
93	C₂²×C₄×C₁₃	—	2	3	no	—
94	C₂²×C₄×C₁₃	—	2	1	no	—
95	C₂²×C₄×C₁₃	—	2	12	no	—
96	C₂²×C₄×C₁₃	—	4	12	no	—
97	C₂²×C₄×C₁₃	C₂×D₄	1	3	yes	—
98	C₂²×C₄×C₁₃	C₂×D₄	1	3	yes	—
99	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
100	C₁₃×SD₁₆	—	2	24	no	—
101	C₁₃×SD₁₆	—	4	24	no	—
102	C₂×C₈×C₁₃	—	2	6	no	—
103	C₂×C₈×C₁₃	#41	1	4	yes	complemented
104	C₂×C₈×C₁₃	C₂⁴	1	6	yes	—
105	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
106	C₁₃×C₄⋊C₄	—	2	12	no	—
107	C₁₃×C₄⋊C₄	—	2	12	no	—
108	C₁₃×C₄⋊C₄	—	2	12	no	—
109	C₁₃×C₄⋊C₄	—	2	1	no	—
110	C₁₃×C₄⋊C₄	—	2	1	no	—
111	C₁₃×C₄⋊C₄	C₂×D₄	1	12	yes	—
112	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
113	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
114	C₁₃×C₂²⋊C₄	—	2	12	no	—
115	C₄²×C₁₃	—	2	12	no	—
116	C₄²×C₁₃	C₂×D₄	1	6	yes	—
117	C₄²×C₁₃	C₂⁴	1	6	yes	—
118	C₂×#557	C₂×C₁₃	1	1	yes	characteristic, complemented
119	C₂×#550	C₂×C₁₃	1	1	yes	characteristic
120	#3392	C₂×C₁₃	1	16	yes	direct product factor
121	C₂×#492	C₂×C₁₃	1	3	yes	complemented
122	C₂×#460	C₂×C₁₃	1	3	yes	complemented
123	C₂×#461	C₂×C₁₃	1	3	yes	complemented
124	C₂×C₈×Q₈	C₂×C₁₃	1	1	yes	characteristic, complemented
125	C₂×C₄×SD₁₆	C₂×C₁₃	1	3	yes	complemented
126	C₂³×C₁₃	—	2	6	no	—
127	C₂³×C₁₃	—	4	6	no	—
128	C₂³×C₁₃	—	4	6	no	—
129	C₂³×C₁₃	—	4	6	no	—
130	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
131	Q₈×C₁₃	—	2	6	no	—
132	Q₈×C₁₃	—	2	6	no	—
133	Q₈×C₁₃	—	4	6	no	—
134	Q₈×C₁₃	C₂×SD₁₆	1	16	yes	complemented
135	D₄×C₁₃	—	2	6	no	—
136	D₄×C₁₃	—	2	6	no	—
137	D₄×C₁₃	—	4	6	no	—
138	D₄×C₁₃	—	4	24	no	—
139	D₄×C₁₃	—	8	12	no	—
140	C₂×C₄×C₁₃	—	2	6	no	—
141	C₂×C₄×C₁₃	—	2	2	no	—
142	C₂×C₄×C₁₃	—	2	6	no	—
143	C₂×C₄×C₁₃	—	2	2	no	—
144	C₂×C₄×C₁₃	—	4	6	no	—
145	C₂×C₄×C₁₃	—	4	2	no	—
146	C₂×C₄×C₁₃	—	4	2	no	—
147	C₂×C₄×C₁₃	—	4	24	no	—
148	C₂×C₄×C₁₃	C₂×SD₁₆	1	12	yes	—
149	C₂×C₄×C₁₃	C₂²×D₄	1	6	yes	—
150	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
151	C₂×C₄×C₁₃	C₂²×D₄	1	6	yes	—
152	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
153	C₂×C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
154	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
155	C₈×C₁₃	—	2	6	no	—
156	C₈×C₁₃	C₂×#41	1	4	yes	complemented
157	C₂²×#41	—	2	1	no	—
158	C₂²×SD₁₆	C₂²×C₁₃	1	3	yes	—
159	C₂²×SD₁₆	C₂²×C₁₃	1	6	yes	—
160	#557	—	2	4	no	—
161	#557	C₂²×C₁₃	1	8	yes	complemented
162	#550	—	2	4	no	—
163	#550	C₂²×C₁₃	1	8	yes	—
164	C₂×C₄⋊Q₈	C₂²×C₁₃	1	3	yes	—
165	C₂×#127	C₂²×C₁₃	1	3	yes	—
166	C₂×#125	—	2	3	no	—
167	C₂×#121	—	2	3	no	—
168	C₂×C₄×Q₈	—	2	1	no	—
169	C₂×C₄×Q₈	C₂²×C₁₃	1	3	yes	—
170	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
171	C₂×C₄×D₄	C₂²×C₁₃	1	3	yes	—
172	#492	C₂²×C₁₃	1	24	yes	complemented
173	#461	C₂²×C₁₃	1	24	yes	complemented
174	#460	C₂²×C₁₃	1	24	yes	complemented
175	C₈×Q₈	C₂²×C₁₃	1	8	yes	complemented
176	C₄×SD₁₆	C₂²×C₁₃	1	24	yes	complemented
177	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic
178	C₂×C₄⋊C₈	C₂²×C₁₃	1	3	yes	—
179	C₂×#103	C₂²×C₁₃	1	3	yes	—
180	C₂×#102	C₂²×C₁₃	1	3	yes	—
181	C₂×C₄×C₈	C₂²×C₁₃	1	3	yes	—
182	C₂²×C₁₃	—	4	6	no	—
183	C₂²×C₁₃	—	4	6	no	—
184	C₂²×C₁₃	—	4	6	no	—
185	C₂²×C₁₃	—	8	12	no	—
186	C₂²×C₁₃	#550	1	2	yes	—
187	C₂²×C₁₃	C₂²×SD₁₆	1	2	yes	—
188	C₂²×C₁₃	#577	1	2	yes	—
189	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
190	C₄×C₁₃	—	2	6	no	—
191	C₄×C₁₃	—	4	6	no	—
192	C₄×C₁₃	—	4	2	no	—
193	C₄×C₁₃	—	4	2	no	—
194	C₄×C₁₃	#550	1	2	yes	—
195	C₄×C₁₃	C₂²×SD₁₆	1	12	yes	—
196	C₄×C₁₃	C₂²×#41	1	1	yes	characteristic
197	C₄×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
198	C₂×#41	—	2	8	no	—
199	C₂×#41	—	4	8	no	—
200	C₂²×Q₈	D₄×C₁₃	1	1	yes	characteristic
201	C₂²×Q₈	C₂³×C₁₃	1	3	yes	—
202	C₂²×D₄	—	2	3	no	—
203	C₂²×D₄	—	2	3	no	—
204	C₂²×D₄	C₂³×C₁₃	1	3	yes	—
205	C₂³×C₄	—	2	3	no	—
206	C₂×SD₁₆	—	2	12	no	—
207	C₂×SD₁₆	—	4	12	no	—
208	C₂×SD₁₆	C₂³×C₁₃	1	12	yes	—
209	C₂×SD₁₆	C₂³×C₁₃	1	24	yes	—
210	C₂²×C₈	C₂³×C₁₃	1	3	yes	—
211	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
212	C₄⋊Q₈	—	2	6	no	—
213	C₄⋊Q₈	C₂³×C₁₃	1	12	yes	—
214	#127	—	2	6	no	—
215	#127	C₂³×C₁₃	1	12	yes	—
216	#125	—	2	24	no	—
217	#121	—	2	24	no	—
218	C₄×Q₈	—	2	8	no	—
219	C₄×Q₈	—	2	6	no	—
220	C₄×Q₈	D₄×C₁₃	1	4	yes	—
221	C₄×Q₈	C₂³×C₁₃	1	12	yes	—
222	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
223	C₄×D₄	—	2	6	no	—
224	C₄×D₄	C₂³×C₁₃	1	12	yes	—
225	C₂×C₄⋊C₄	—	2	3	no	—
226	C₂×C₄⋊C₄	—	2	3	no	—
227	C₂×C₄⋊C₄	—	2	3	no	—
228	C₂×C₄⋊C₄	D₄×C₁₃	1	3	yes	—
229	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
230	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
231	C₂×C₂²⋊C₄	—	2	3	no	—
232	C₂×C₄²	—	2	3	no	—
233	C₂×C₄²	C₂³×C₁₃	1	3	yes	—
234	#106	C₂³×C₁₃	1	4	yes	—
235	C₄⋊C₈	C₂³×C₁₃	1	12	yes	—
236	#103	C₂³×C₁₃	1	12	yes	—
237	#102	C₂³×C₁₃	1	12	yes	—
238	C₄×C₈	C₂³×C₁₃	1	12	yes	—
239	C₂×C₁₃	—	8	6	no	—
240	C₂×C₁₃	#3392	1	4	yes	direct product factor
241	C₂×C₁₃	C₂×#550	1	1	yes	characteristic
242	C₂×C₁₃	C₂³×SD₁₆	1	1	yes	characteristic
243	C₂×C₁₃	C₂×#577	1	1	yes	characteristic
244	C₂⁴	—	2	3	no	—
245	#41	—	4	32	no	—
246	C₂×Q₈	—	2	3	no	—
247	C₂×Q₈	—	2	6	no	—
248	C₂×Q₈	—	2	6	no	—
249	C₂×Q₈	C₁₃×SD₁₆	1	8	yes	complemented
250	C₂×Q₈	C₂×D₄×C₁₃	1	4	yes	—
251	C₂×Q₈	C₂⁴×C₁₃	1	6	yes	—
252	C₂×D₄	—	2	3	no	—
253	C₂×D₄	—	2	12	no	—
254	C₂×D₄	—	2	12	no	—
255	C₂×D₄	—	2	6	no	—
256	C₂×D₄	—	2	6	no	—
257	C₂×D₄	—	4	12	no	—
258	C₂×D₄	—	8	6	no	—
259	C₂×D₄	C₂⁴×C₁₃	1	6	yes	—
260	C₂²×C₄	—	2	1	no	—
261	C₂²×C₄	—	2	3	no	—
262	C₂²×C₄	—	2	1	no	—
263	C₂²×C₄	—	2	12	no	—
264	C₂²×C₄	—	4	12	no	—
265	C₂²×C₄	C₂×D₄×C₁₃	1	3	yes	—
266	C₂²×C₄	C₂×D₄×C₁₃	1	3	yes	—
267	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
268	SD₁₆	—	2	24	no	—
269	SD₁₆	—	4	24	no	—
270	C₂×C₈	—	2	6	no	—
271	C₂×C₈	C₁₃×#41	1	4	yes	complemented
272	C₂×C₈	C₂⁴×C₁₃	1	6	yes	—
273	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
274	C₄⋊C₄	—	2	12	no	—
275	C₄⋊C₄	—	2	12	no	—
276	C₄⋊C₄	—	2	12	no	—
277	C₄⋊C₄	—	2	1	no	—
278	C₄⋊C₄	—	2	1	no	—
279	C₄⋊C₄	C₂×D₄×C₁₃	1	12	yes	—
280	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
281	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
282	C₂²⋊C₄	—	2	12	no	—
283	C₄²	—	2	12	no	—
284	C₄²	C₂×D₄×C₁₃	1	6	yes	—
285	C₄²	C₂⁴×C₁₃	1	6	yes	—
286	C₁₃	C₂×#3392	1	1	yes	characteristic, direct product factor, Sylow
287	C₂³	—	2	6	no	—
288	C₂³	—	4	6	no	—
289	C₂³	—	4	6	no	—
290	C₂³	—	4	6	no	—
291	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
292	Q₈	—	2	6	no	—
293	Q₈	—	2	6	no	—
294	Q₈	—	4	6	no	—
295	Q₈	C₂×C₁₃×SD₁₆	1	16	yes	complemented
296	D₄	—	2	6	no	—
297	D₄	—	2	6	no	—
298	D₄	—	4	6	no	—
299	D₄	—	4	24	no	—
300	D₄	—	8	12	no	—
301	C₂×C₄	—	2	6	no	—
302	C₂×C₄	—	2	2	no	—
303	C₂×C₄	—	2	6	no	—
304	C₂×C₄	—	2	2	no	—
305	C₂×C₄	—	4	6	no	—
306	C₂×C₄	—	4	2	no	—
307	C₂×C₄	—	4	2	no	—
308	C₂×C₄	—	4	24	no	—
309	C₂×C₄	C₂×C₁₃×SD₁₆	1	12	yes	—
310	C₂×C₄	C₂²×D₄×C₁₃	1	6	yes	—
311	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
312	C₂×C₄	C₂²×D₄×C₁₃	1	6	yes	—
313	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
314	C₂×C₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
315	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
316	C₈	—	2	6	no	—
317	C₈	C₂×C₁₃×#41	1	4	yes	complemented
318	C₂²	—	4	6	no	—
319	C₂²	—	4	6	no	—
320	C₂²	—	4	6	no	—
321	C₂²	—	8	12	no	—
322	C₂²	C₁₃×#550	1	2	yes	—
323	C₂²	C₂²×C₁₃×SD₁₆	1	2	yes	—
324	C₂²	C₁₃×#577	1	2	yes	—
325	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
326	C₄	—	2	6	no	—
327	C₄	—	4	2	no	—
328	C₄	—	4	2	no	—
329	C₄	—	4	6	no	—
330	C₄	C₁₃×#550	1	2	yes	—
331	C₄	C₂²×C₁₃×SD₁₆	1	12	yes	—
332	C₄	C₂²×C₁₃×#41	1	1	yes	characteristic
333	C₄	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
334	C₂	—	8	6	no	—
335	C₂	C₁₃×#3392	1	4	yes	direct product factor
336	C₂	C₂×C₁₃×#550	1	1	yes	characteristic
337	C₂	C₂³×C₁₃×SD₁₆	1	1	yes	characteristic
338	C₂	C₂×C₁₃×#577	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₃
prime radical	C₂×C₁₃×#550	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ C₂×C₄×Q₈×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₃×#557	C₂	semidirect
3. C₁₃×#3392	C₂	direct (N × H)
4. C₂×C₁₃×#492	C₂	semidirect
5. C₂×C₁₃×#460	C₂	semidirect
6. C₂×C₁₃×#461	C₂	semidirect
7. C₂×C₈×Q₈×C₁₃	C₂	semidirect
8. C₂×C₄×C₁₃×SD₁₆	C₂	semidirect
13. C₁₃×#557	C₂²	semidirect
24. C₁₃×#492	C₂²	semidirect
25. C₁₃×#461	C₂²	semidirect
26. C₁₃×#460	C₂²	semidirect
27. C₈×Q₈×C₁₃	C₂²	semidirect
28. C₄×C₁₃×SD₁₆	C₂²	semidirect
75. C₂×#3392	C₁₃	direct (N × H)
81. C₂×Q₈×C₁₃	SD₁₆	semidirect
103. C₂×C₈×C₁₃	#41	semidirect
118. C₂×#557	C₂×C₁₃	semidirect
120. #3392	C₂×C₁₃	direct (N × H)
121. C₂×#492	C₂×C₁₃	semidirect
122. C₂×#460	C₂×C₁₃	semidirect
123. C₂×#461	C₂×C₁₃	semidirect
124. C₂×C₈×Q₈	C₂×C₁₃	semidirect
125. C₂×C₄×SD₁₆	C₂×C₁₃	semidirect
134. Q₈×C₁₃	C₂×SD₁₆	semidirect
156. C₈×C₁₃	C₂×#41	semidirect
161. #557	C₂²×C₁₃	semidirect
172. #492	C₂²×C₁₃	semidirect
173. #461	C₂²×C₁₃	semidirect
174. #460	C₂²×C₁₃	semidirect
175. C₈×Q₈	C₂²×C₁₃	semidirect
176. C₄×SD₁₆	C₂²×C₁₃	semidirect
240. C₂×C₁₃	#3392	direct (N × H)
249. C₂×Q₈	C₁₃×SD₁₆	semidirect
271. C₂×C₈	C₁₃×#41	semidirect
286. C₁₃	C₂×#3392	direct (N × H)
295. Q₈	C₂×C₁₃×SD₁₆	semidirect
317. C₈	C₂×C₁₃×#41	semidirect
335. C₂	C₁₃×#3392	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×#557	2
C₂×C₁₃×#550	2
C₁₃×#3392	2
C₂×C₁₃×#492	2
C₂×C₁₃×#460	2
C₂×C₁₃×#461	2
C₂×C₈×Q₈×C₁₃	2
C₂×C₄×C₁₃×SD₁₆	2
C₂×#3392	13

Subgroups — C2×C13×#3392 #15747727

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₃×#3392 #15747727