Subgroups — C₂×C₈×Q₈×D₁₃ #16727268

Order 3328.

2478 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×C₄×Q₈×D₁₃	C₂	1	1	yes	maximal, characteristic
2	C₂×Q₈×#1055	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₈×Dic₂₆	C₂	1	3	yes	maximal, complemented
4	C₂×#11718491	C₂	1	3	yes	maximal, complemented
5	C₈×Q₈×D₁₃	C₂	1	16	yes	maximal, direct product factor
6	C₂×D₁₃×C₄⋊C₈	C₂	1	3	yes	maximal
7	C₂×C₄×C₈×D₁₃	C₂	1	3	yes	maximal
8	C₂×C₈×Q₈×C₁₃	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂²×Q₈×D₁₃	C₄	1	1	yes	characteristic
10	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
11	C₂×Q₈×Dic₁₃	C₄	1	1	yes	characteristic
12	C₂²×C₈×D₁₃	C₂²	1	3	yes	—
13	C₂²×C₈×D₁₃	C₂²	1	1	yes	characteristic
14	C₄×Q₈×D₁₃	C₄	1	8	yes	—
15	C₄×Q₈×D₁₃	C₂²	1	8	yes	—
16	C₂×C₄⋊C₄×D₁₃	C₄	1	3	yes	—
17	C₂×#88141	C₄	1	3	yes	—
18	C₂×C₄²×D₁₃	C₂²	1	3	yes	—
19	C₂×C₄×Dic₂₆	C₂²	1	3	yes	—
20	C₈×Q₈×C₁₃	C₂²	1	8	yes	complemented
21	C₂×C₁₃×C₄⋊C₈	C₂²	1	3	yes	—
22	C₂×C₄×C₈×C₁₃	C₂²	1	3	yes	—
23	C₂×#88054	C₂²	1	6	yes	—
24	C₂×C₈×Dic₁₃	C₂²	1	3	yes	—
25	C₂×C₈×Dic₁₃	C₂²	1	3	yes	—
26	Q₈×#1055	C₂²	1	8	yes	complemented
27	C₂×C₄⋊#1055	C₂²	1	3	yes	—
28	C₂×C₄×#1055	C₂²	1	3	yes	—
29	D₁₃×C₄⋊C₈	C₂²	1	24	yes	—
30	#11718491	C₂²	1	24	yes	complemented
31	C₄×C₈×D₁₃	C₂²	1	24	yes	—
32	C₈×Dic₂₆	C₂²	1	24	yes	complemented
33	C₂²×Q₈×C₁₃	C₂×C₄	1	1	yes	characteristic
34	C₂×Q₈×D₁₃	C₈	1	16	yes	direct product factor
35	C₂×Q₈×D₁₃	C₂×C₄	1	8	yes	—
36	C₂²×C₄×D₁₃	C₂×C₄	1	3	yes	—
37	C₂²×C₄×D₁₃	C₂×C₄	1	3	yes	—
38	C₂²×C₄×D₁₃	C₂³	1	1	yes	characteristic
39	C₂²×Dic₂₆	C₂×C₄	1	3	yes	—
40	C₂²×C₈×C₁₃	C₂³	1	3	yes	—
41	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
42	C₄×Q₈×C₁₃	C₂×C₄	1	4	yes	—
43	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
44	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	3	yes	—
45	C₂×C₄²×C₁₃	C₂³	1	3	yes	—
46	Q₈×Dic₁₃	C₂×C₄	1	8	yes	—
47	C₂×C₄⋊Dic₁₃	C₂×C₄	1	3	yes	—
48	C₂×#6101	C₂×C₄	1	6	yes	—
49	C₂×C₄×Dic₁₃	C₂×C₄	1	3	yes	—
50	C₂×C₄×Dic₁₃	C₂×C₄	1	3	yes	—
51	C₂×C₄×Dic₁₃	C₂³	1	3	yes	—
52	C₂²×#1055	C₂³	1	3	yes	—
53	C₂²×#1055	C₂³	1	1	yes	characteristic
54	C₂×C₈×D₁₃	—	2	12	no	—
55	C₂×C₈×D₁₃	Q₈	1	8	yes	direct product factor
56	C₂×C₈×D₁₃	C₂³	1	12	yes	—
57	C₂×C₈×D₁₃	C₂³	1	4	yes	—
58	C₄⋊C₄×D₁₃	C₂×C₄	1	24	yes	—
59	#88141	C₂×C₄	1	24	yes	—
60	C₄²×D₁₃	C₂×C₄	1	12	yes	—
61	C₄²×D₁₃	C₂³	1	12	yes	—
62	C₄×Dic₂₆	C₂×C₄	1	12	yes	—
63	C₄×Dic₂₆	C₂³	1	12	yes	—
64	C₁₃×C₄⋊C₈	C₂³	1	12	yes	—
65	C₄×C₈×C₁₃	C₂³	1	12	yes	—
66	#88054	C₂³	1	24	yes	—
67	C₈×Dic₁₃	C₂³	1	12	yes	—
68	C₈×Dic₁₃	C₂³	1	12	yes	—
69	C₄⋊#1055	C₂³	1	12	yes	—
70	C₄×#1055	C₂³	1	12	yes	—
71	C₂²×C₈×Q₈	—	13	1	no	maximal, Sylow
72	C₂³×D₁₃	C₂²×C₄	1	1	yes	characteristic
73	C₂×Q₈×C₁₃	C₂×C₈	1	8	yes	complemented
74	C₂×Q₈×C₁₃	C₂²×C₄	1	4	yes	—
75	C₂²×C₄×C₁₃	C₂²×C₄	1	3	yes	—
76	C₂²×C₄×C₁₃	C₂²×C₄	1	3	yes	—
77	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
78	C₂²×Dic₁₃	C₂²×C₄	1	3	yes	—
79	C₂²×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
80	C₂²×Dic₁₃	C₂²×C₄	1	3	yes	—
81	Q₈×D₁₃	C₂×C₈	1	64	yes	direct product factor
82	C₂×C₄×D₁₃	—	2	12	no	—
83	C₂×C₄×D₁₃	C₂×C₈	1	24	yes	—
84	C₂×C₄×D₁₃	C₂²×C₄	1	12	yes	—
85	C₂×C₄×D₁₃	C₂²×C₄	1	2	yes	—
86	C₂×C₄×D₁₃	C₂²×C₄	1	12	yes	—
87	C₂×C₄×D₁₃	C₂×Q₈	1	4	yes	—
88	C₂×C₄×D₁₃	#41	1	4	yes	—
89	C₂×C₄×D₁₃	C₂⁴	1	2	yes	—
90	C₂×Dic₂₆	C₂×C₈	1	24	yes	complemented
91	C₂×Dic₂₆	C₂²×C₄	1	12	yes	—
92	C₂×C₈×C₁₃	—	2	6	no	—
93	C₂×C₈×C₁₃	C₂×Q₈	1	4	yes	complemented
94	C₂×C₈×C₁₃	C₂⁴	1	6	yes	—
95	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
96	C₁₃×C₄⋊C₄	C₂²×C₄	1	12	yes	—
97	C₄²×C₁₃	C₂²×C₄	1	6	yes	—
98	C₄²×C₁₃	C₂⁴	1	6	yes	—
99	C₄⋊Dic₁₃	C₂²×C₄	1	12	yes	—
100	#6101	C₂²×C₄	1	24	yes	—
101	C₄×Dic₁₃	C₂²×C₄	1	6	yes	—
102	C₄×Dic₁₃	C₂²×C₄	1	12	yes	—
103	C₄×Dic₁₃	C₂²×C₄	1	12	yes	—
104	C₄×Dic₁₃	C₂⁴	1	6	yes	—
105	C₂×#1055	—	2	6	no	—
106	C₂×#1055	C₂×Q₈	1	4	yes	complemented
107	C₂×#1055	C₂⁴	1	6	yes	—
108	C₂×#1055	C₂⁴	1	2	yes	—
109	C₈×D₁₃	—	2	24	no	—
110	C₈×D₁₃	C₂×Q₈	1	16	yes	direct product factor
111	C₂²×C₄×Q₈	—	13	1	no	—
112	C₂×C₈×Q₈	—	13	16	no	—
113	C₂×C₈×Q₈	—	13	3	no	—
114	C₂×C₈×Q₈	—	13	3	no	—
115	C₂×C₈×Q₈	—	13	1	no	—
116	C₂×C₈×Q₈	D₁₃	1	1	yes	characteristic, direct product factor
117	C₂²×C₄⋊C₈	—	13	3	no	—
118	C₂²×C₄×C₈	—	13	3	no	—
119	C₂³×C₁₃	C₂³×C₄	1	1	yes	characteristic
120	C₂²×D₁₃	C₄×Q₈	1	4	yes	—
121	C₂²×D₁₃	C₂²×C₈	1	4	yes	—
122	C₂²×D₁₃	#131	1	4	yes	—
123	C₂²×D₁₃	C₂³×C₄	1	2	yes	—
124	Q₈×C₁₃	C₂²×C₈	1	16	yes	complemented
125	C₂×C₄×C₁₃	—	2	6	no	—
126	C₂×C₄×C₁₃	C₂²×C₈	1	12	yes	—
127	C₂×C₄×C₁₃	C₂³×C₄	1	6	yes	—
128	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
129	C₂×C₄×C₁₃	C₂³×C₄	1	6	yes	—
130	C₂×C₄×C₁₃	C₂²×Q₈	1	2	yes	—
131	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
132	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
133	C₂×Dic₁₃	—	2	6	no	—
134	C₂×Dic₁₃	C₄×Q₈	1	4	yes	—
135	C₂×Dic₁₃	C₂²×C₈	1	12	yes	—
136	C₂×Dic₁₃	C₂³×C₄	1	6	yes	—
137	C₂×Dic₁₃	C₂³×C₄	1	2	yes	—
138	C₂×Dic₁₃	C₂³×C₄	1	6	yes	—
139	C₄×D₁₃	—	2	24	no	—
140	C₄×D₁₃	C₄×Q₈	1	8	yes	—
141	C₄×D₁₃	C₂²×C₈	1	48	yes	—
142	C₄×D₁₃	C₂²×Q₈	1	4	yes	—
143	C₄×D₁₃	C₂×#41	1	4	yes	—
144	Dic₂₆	C₂²×C₈	1	48	yes	complemented
145	C₈×C₁₃	—	2	6	no	—
146	C₈×C₁₃	C₂²×Q₈	1	4	yes	complemented
147	#1055	—	2	6	no	—
148	#1055	C₂²×Q₈	1	4	yes	complemented
149	C₂³×Q₈	—	13	1	no	—
150	C₂³×C₈	—	13	1	no	—
151	C₂³×C₈	—	13	3	no	—
152	C₂×C₄×Q₈	—	13	1	no	—
153	C₂×C₄×Q₈	—	13	8	no	—
154	C₂×C₄×Q₈	—	13	8	no	—
155	C₂×C₄×Q₈	—	13	3	no	—
156	C₂×C₄×Q₈	—	13	3	no	—
157	C₂×C₄×Q₈	C₂×D₁₃	1	1	yes	characteristic
158	C₂²×C₄⋊C₄	—	13	3	no	—
159	C₂²×C₄²	—	13	3	no	—
160	C₈×Q₈	—	13	8	no	—
161	C₈×Q₈	—	13	24	no	—
162	C₈×Q₈	—	13	24	no	—
163	C₈×Q₈	C₂×D₁₃	1	8	yes	direct product factor
164	C₂×C₄⋊C₈	—	13	6	no	—
165	C₂×C₄⋊C₈	—	13	3	no	—
166	C₂×C₄⋊C₈	—	13	24	no	—
167	C₂×C₄⋊C₈	C₂×D₁₃	1	3	yes	—
168	C₂×C₄×C₈	—	13	3	no	—
169	C₂×C₄×C₈	—	13	3	no	—
170	C₂×C₄×C₈	—	13	3	no	—
171	C₂×C₄×C₈	—	13	24	no	—
172	C₂×C₄×C₈	C₂×D₁₃	1	3	yes	—
173	C₂²×C₁₃	C₂×C₄×Q₈	1	2	yes	—
174	C₂²×C₁₃	C₂³×C₈	1	2	yes	—
175	C₂²×C₁₃	C₂×#131	1	2	yes	—
176	C₂²×C₁₃	C₂⁴×C₄	1	1	yes	characteristic
177	C₂×D₁₃	C₈×Q₈	1	16	yes	direct product factor
178	C₂×D₁₃	C₂×C₄×Q₈	1	4	yes	—
179	C₂×D₁₃	C₂³×C₈	1	4	yes	—
180	C₂×D₁₃	C₂×#131	1	4	yes	—
181	C₄×C₁₃	—	2	6	no	—
182	C₄×C₁₃	C₂×C₄×Q₈	1	2	yes	—
183	C₄×C₁₃	C₂³×C₈	1	12	yes	—
184	C₄×C₁₃	C₂³×Q₈	1	1	yes	characteristic
185	C₄×C₁₃	C₂²×#41	1	1	yes	characteristic
186	Dic₁₃	—	2	6	no	—
187	Dic₁₃	C₂×C₄×Q₈	1	4	yes	—
188	Dic₁₃	C₂³×C₈	1	12	yes	—
189	C₂²×Q₈	—	13	16	no	—
190	C₂²×Q₈	—	13	8	no	—
191	C₂²×Q₈	—	13	3	no	—
192	C₂²×Q₈	C₄×D₁₃	1	1	yes	characteristic
193	C₂³×C₄	—	13	3	no	—
194	C₂³×C₄	—	13	1	no	—
195	C₂³×C₄	—	13	3	no	—
196	C₂²×C₈	—	13	1	no	—
197	C₂²×C₈	—	13	8	no	—
198	C₂²×C₈	—	13	4	no	—
199	C₂²×C₈	—	13	3	no	—
200	C₂²×C₈	—	13	12	no	—
201	C₂²×C₈	—	26	12	no	—
202	C₂²×C₈	C₂²×D₁₃	1	3	yes	—
203	C₂²×C₈	C₂²×D₁₃	1	1	yes	characteristic
204	C₄×Q₈	—	13	8	no	—
205	C₄×Q₈	—	13	24	no	—
206	C₄×Q₈	—	13	12	no	—
207	C₄×Q₈	—	13	12	no	—
208	C₄×Q₈	C₄×D₁₃	1	4	yes	—
209	C₄×Q₈	C₂²×D₁₃	1	4	yes	—
210	C₂×C₄⋊C₄	—	13	6	no	—
211	C₂×C₄⋊C₄	—	13	3	no	—
212	C₂×C₄⋊C₄	—	13	24	no	—
213	C₂×C₄⋊C₄	C₄×D₁₃	1	3	yes	—
214	C₂×C₄²	—	13	3	no	—
215	C₂×C₄²	—	13	3	no	—
216	C₂×C₄²	—	13	3	no	—
217	C₂×C₄²	—	13	12	no	—
218	C₂×C₄²	—	13	12	no	—
219	C₂×C₄²	C₂²×D₁₃	1	3	yes	—
220	C₄⋊C₈	—	13	24	no	—
221	C₄⋊C₈	—	13	12	no	—
222	C₄⋊C₈	C₂²×D₁₃	1	12	yes	—
223	C₄×C₈	—	13	12	no	—
224	C₄×C₈	—	13	12	no	—
225	C₄×C₈	—	13	12	no	—
226	C₄×C₈	C₂²×D₁₃	1	12	yes	—
227	C₂×C₁₃	C₂×C₈×Q₈	1	4	yes	complemented
228	C₂×C₁₃	C₂²×C₄×Q₈	1	1	yes	characteristic
229	C₂×C₁₃	C₂⁴×C₈	1	1	yes	characteristic
230	C₂×C₁₃	C₂²×#131	1	1	yes	characteristic
231	D₁₃	C₂×C₈×Q₈	1	8	yes	direct product factor
232	C₂⁴	—	13	1	no	—
233	C₂×Q₈	—	13	64	no	—
234	C₂×Q₈	—	13	24	no	—
235	C₂×Q₈	—	13	12	no	—
236	C₂×Q₈	C₈×D₁₃	1	8	yes	direct product factor
237	C₂×Q₈	C₂×C₄×D₁₃	1	4	yes	—
238	C₂²×C₄	—	13	1	no	—
239	C₂²×C₄	—	13	3	no	—
240	C₂²×C₄	—	13	24	no	—
241	C₂²×C₄	—	13	2	no	—
242	C₂²×C₄	—	13	12	no	—
243	C₂²×C₄	—	13	4	no	—
244	C₂²×C₄	—	13	4	no	—
245	C₂²×C₄	—	13	2	no	—
246	C₂²×C₄	—	13	3	no	—
247	C₂²×C₄	—	13	12	no	—
248	C₂²×C₄	—	26	12	no	—
249	C₂²×C₄	C₂×C₄×D₁₃	1	3	yes	—
250	C₂²×C₄	C₂×C₄×D₁₃	1	3	yes	—
251	C₂²×C₄	C₂³×D₁₃	1	1	yes	characteristic
252	C₂×C₈	—	2	6	no	—
253	C₂×C₈	—	13	4	no	—
254	C₂×C₈	—	13	2	no	—
255	C₂×C₈	—	13	16	no	—
256	C₂×C₈	—	13	6	no	—
257	C₂×C₈	—	26	24	no	—
258	C₂×C₈	—	26	6	no	—
259	C₂×C₈	Q₈×D₁₃	1	4	yes	direct product factor
260	C₂×C₈	C₂³×D₁₃	1	6	yes	—
261	C₂×C₈	C₂³×D₁₃	1	2	yes	—
262	C₄⋊C₄	—	13	24	no	—
263	C₄⋊C₄	—	13	12	no	—
264	C₄⋊C₄	C₂×C₄×D₁₃	1	12	yes	—
265	C₄²	—	13	12	no	—
266	C₄²	—	13	12	no	—
267	C₄²	—	13	6	no	—
268	C₄²	—	13	6	no	—
269	C₄²	C₂×C₄×D₁₃	1	6	yes	—
270	C₄²	C₂³×D₁₃	1	6	yes	—
271	C₁₃	C₂²×C₈×Q₈	1	1	yes	characteristic, complemented, Sylow
272	C₂³	—	13	4	no	—
273	C₂³	—	13	4	no	—
274	C₂³	—	13	4	no	—
275	C₂³	—	13	2	no	—
276	C₂³	C₂²×C₄×D₁₃	1	1	yes	characteristic
277	Q₈	—	13	48	no	—
278	Q₈	C₂×C₈×D₁₃	1	16	yes	direct product factor
279	C₂×C₄	—	2	6	no	—
280	C₂×C₄	—	13	12	no	—
281	C₂×C₄	—	13	4	no	—
282	C₂×C₄	—	13	2	no	—
283	C₂×C₄	—	13	6	no	—
284	C₂×C₄	—	13	48	no	—
285	C₂×C₄	—	13	8	no	—
286	C₂×C₄	—	13	4	no	—
287	C₂×C₄	—	13	4	no	—
288	C₂×C₄	—	13	6	no	—
289	C₂×C₄	—	26	24	no	—
290	C₂×C₄	—	26	6	no	—
291	C₂×C₄	C₂×C₈×D₁₃	1	12	yes	—
292	C₂×C₄	C₂²×C₄×D₁₃	1	6	yes	—
293	C₂×C₄	C₂²×C₄×D₁₃	1	6	yes	—
294	C₂×C₄	C₂²×C₄×D₁₃	1	1	yes	characteristic
295	C₂×C₄	C₂×Q₈×D₁₃	1	2	yes	—
296	C₂×C₄	#41×D₁₃	1	2	yes	—
297	C₂×C₄	C₂⁴×D₁₃	1	1	yes	characteristic
298	C₈	—	2	6	no	—
299	C₈	—	13	4	no	—
300	C₈	—	26	6	no	—
301	C₈	C₂×Q₈×D₁₃	1	4	yes	direct product factor
302	C₂²	—	13	4	no	—
303	C₂²	—	13	4	no	—
304	C₂²	—	13	4	no	—
305	C₂²	—	13	16	no	—
306	C₂²	C₄×Q₈×D₁₃	1	2	yes	—
307	C₂²	C₂²×C₈×D₁₃	1	2	yes	—
308	C₂²	D₁₃×#131	1	2	yes	—
309	C₂²	C₂³×C₄×D₁₃	1	1	yes	characteristic
310	C₄	—	2	6	no	—
311	C₄	—	13	12	no	—
312	C₄	—	13	4	no	—
313	C₄	—	26	6	no	—
314	C₄	C₄×Q₈×D₁₃	1	2	yes	—
315	C₄	C₂²×C₈×D₁₃	1	12	yes	—
316	C₄	C₂²×Q₈×D₁₃	1	1	yes	characteristic
317	C₄	C₂×#41×D₁₃	1	1	yes	characteristic
318	C₂	—	13	8	no	—
319	C₂	C₈×Q₈×D₁₃	1	4	yes	direct product factor
320	C₂	C₂×C₄×Q₈×D₁₃	1	1	yes	characteristic
321	C₂	C₂³×C₈×D₁₃	1	1	yes	characteristic
322	C₂	C₂×D₁₃×#131	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₈	C₂²×D₁₃
commutator	C₂×C₁₃	C₂⁴×C₈
Frattini	C₂×C₄	C₂⁴×D₁₃
Fitting	C₂×C₈×Q₈×C₁₃	C₂
socle	C₂³×C₁₃	C₂³×C₄
prime radical	C₂³×D₁₃	C₂²×C₄
cosocle	C₂×C₄×C₁₃	C₂⁵
hypercenter	C₂×C₈×Q₈	D₁₃
hypocenter	C₁₃	C₂²×C₈×Q₈
LCS	G ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂²×C₈ ◁ C₂×C₈×Q₈

Complements

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

N	H ≅ G/N	type
2. C₂×Q₈×#1055	C₂	semidirect
3. C₂×C₈×Dic₂₆	C₂	semidirect
4. C₂×#11718491	C₂	semidirect
5. C₈×Q₈×D₁₃	C₂	direct (N × H)
8. C₂×C₈×Q₈×C₁₃	C₂	semidirect
20. C₈×Q₈×C₁₃	C₂²	semidirect
26. Q₈×#1055	C₂²	semidirect
30. #11718491	C₂²	semidirect
32. C₈×Dic₂₆	C₂²	semidirect
34. C₂×Q₈×D₁₃	C₈	direct (N × H)
55. C₂×C₈×D₁₃	Q₈	direct (N × H)
73. C₂×Q₈×C₁₃	C₂×C₈	semidirect
81. Q₈×D₁₃	C₂×C₈	direct (N × H)
90. C₂×Dic₂₆	C₂×C₈	semidirect
93. C₂×C₈×C₁₃	C₂×Q₈	semidirect
106. C₂×#1055	C₂×Q₈	semidirect
110. C₈×D₁₃	C₂×Q₈	direct (N × H)
116. C₂×C₈×Q₈	D₁₃	direct (N × H)
124. Q₈×C₁₃	C₂²×C₈	semidirect
144. Dic₂₆	C₂²×C₈	semidirect
146. C₈×C₁₃	C₂²×Q₈	semidirect
148. #1055	C₂²×Q₈	semidirect
163. C₈×Q₈	C₂×D₁₃	direct (N × H)
177. C₂×D₁₃	C₈×Q₈	direct (N × H)
227. C₂×C₁₃	C₂×C₈×Q₈	semidirect
231. D₁₃	C₂×C₈×Q₈	direct (N × H)
236. C₂×Q₈	C₈×D₁₃	direct (N × H)
259. C₂×C₈	Q₈×D₁₃	direct (N × H)
271. C₁₃	C₂²×C₈×Q₈	semidirect
278. Q₈	C₂×C₈×D₁₃	direct (N × H)
301. C₈	C₂×Q₈×D₁₃	direct (N × H)
319. C₂	C₈×Q₈×D₁₃	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×C₄×Q₈×D₁₃	2
C₂×Q₈×#1055	2
C₂×C₈×Dic₂₆	2
C₂×#11718491	2
C₈×Q₈×D₁₃	2
C₂×D₁₃×C₄⋊C₈	2
C₂×C₄×C₈×D₁₃	2
C₂×C₈×Q₈×C₁₃	2
C₂²×C₈×Q₈	13

Subgroups — C2×C8×Q8×D13 #16727268

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₈×Q₈×D₁₃ #16727268