Subgroups — C₁₃×#17982 #15704321

Order 3328.

606 conjugacy classes of subgroups.

The subgroup lattice has 370 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3168	C₂	1	1	yes	maximal, characteristic
2	C₁₃×#2966	C₂	1	2	yes	maximal, complemented
3	C₁₃×#1588	C₂	1	2	yes	maximal, complemented
4	C₁₃×#1587	C₂	1	2	yes	maximal, complemented
5	C₁₃×#1586	C₂	1	2	yes	maximal, complemented
6	C₁₃×#1585	C₂	1	2	yes	maximal, complemented
7	C₁₃×#1568	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#1494	C₂	1	2	yes	maximal, complemented
9	C₂×C₁₃×#322	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#529	C₂²	1	2	yes	—
11	C₁₃×#499	C₄	1	1	yes	characteristic
12	C₁₃×#495	C₄	1	1	yes	characteristic
13	C₁₃×#488	C₄	1	2	yes	—
14	C₁₃×#467	C₄	1	1	yes	characteristic
15	C₁₃×#466	C₄	1	1	yes	characteristic
16	C₁₃×#465	C₄	1	2	yes	—
17	C₁₃×#446	C₂²	1	2	yes	—
18	C₈×Q₈×C₁₃	C₂²	1	2	yes	—
19	C₄×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic
20	C₄×C₁₃×SD₁₆	C₂²	1	2	yes	—
21	C₄×C₁₃×D₈	C₂²	1	1	yes	characteristic
22	C₁₃×#436	C₂²	1	2	yes	—
23	C₁₃×#435	—	2	2	no	—
24	C₈×D₄×C₁₃	—	2	2	no	—
25	C₈×D₄×C₁₃	C₂²	1	2	yes	—
26	C₁₃×#433	—	2	2	no	—
27	C₁₃×#432	C₂²	1	2	yes	—
28	C₁₃×#405	—	2	2	no	—
29	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
30	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
31	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
32	C₁₃×#335	C₂²	1	1	yes	characteristic
33	C₁₃×#335	C₂²	1	1	yes	characteristic
34	C₁₃×#334	C₂²	1	2	yes	—
35	C₁₃×Q₈⋊C₈	C₂²	1	2	yes	—
36	C₁₃×Q₈⋊C₈	C₂²	1	2	yes	—
37	C₁₃×D₄⋊C₈	C₂²	1	2	yes	—
38	C₁₃×D₄⋊C₈	C₂²	1	2	yes	—
39	C₁₃×#322	C₂²	1	2	yes	—
40	C₁₃×#322	C₂²	1	2	yes	—
41	C₂×C₁₃×Q₁₆	C₂×C₄	1	1	yes	characteristic
42	C₂×C₁₃×SD₁₆	C₂×C₄	1	2	yes	—
43	C₂×C₁₃×D₈	C₂×C₄	1	1	yes	characteristic
44	C₂×C₁₃×M₁₆	—	2	2	no	—
45	C₂²×C₈×C₁₃	—	2	1	no	—
46	C₂²×C₈×C₁₃	—	2	2	no	—
47	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
48	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
49	C₂²×C₈×C₁₃	D₄	1	1	yes	characteristic
50	C₂²×C₈×C₁₃	D₄	1	1	yes	characteristic
51	C₁₃×#126	—	2	2	no	—
52	C₁₃×#125	C₂×C₄	1	2	yes	—
53	C₁₃×#124	C₂×C₄	1	2	yes	—
54	C₁₃×#123	—	2	2	no	—
55	C₁₃×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
56	C₁₃×#121	C₂×C₄	1	2	yes	—
57	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
58	C₄×D₄×C₁₃	—	2	2	no	—
59	C₄×D₄×C₁₃	C₂³	1	2	yes	—
60	C₁₃×#117	—	2	2	no	—
61	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
62	C₁₃×#107	C₂×C₄	1	1	yes	characteristic
63	C₁₃×#107	C₂×C₄	1	1	yes	characteristic
64	C₁₃×#106	C₂×C₄	1	2	yes	—
65	C₁₃×C₄⋊C₈	—	2	2	no	—
66	C₁₃×C₄⋊C₈	—	2	2	no	—
67	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
68	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
69	C₁₃×#103	C₂×C₄	1	2	yes	—
70	C₁₃×#103	C₂×C₄	1	2	yes	—
71	C₁₃×#102	C₂×C₄	1	2	yes	—
72	C₁₃×#102	C₂×C₄	1	2	yes	—
73	C₁₃×C₂²⋊C₈	—	2	2	no	—
74	C₁₃×C₂²⋊C₈	—	2	2	no	—
75	C₁₃×C₂²⋊C₈	—	2	2	no	—
76	C₁₃×#97	—	2	2	no	—
77	C₁₃×#97	—	2	2	no	—
78	C₄×C₈×C₁₃	—	2	2	no	—
79	C₄×C₈×C₁₃	—	2	1	no	—
80	C₄×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
81	C₄×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
82	C₄×C₈×C₁₃	D₄	1	2	yes	—
83	C₄×C₈×C₁₃	C₂³	1	2	yes	—
84	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
85	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
86	C₄×C₈×C₁₃	C₂³	1	2	yes	—
87	#17982	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
88	C₂×Q₈×C₁₃	C₂²×C₄	1	2	yes	—
89	C₂×D₄×C₁₃	—	2	2	no	—
90	C₂×D₄×C₁₃	C₂²×C₄	1	2	yes	—
91	C₂²×C₄×C₁₃	—	2	2	no	—
92	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
93	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
94	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
95	C₁₃×Q₁₆	—	4	1	no	—
96	C₁₃×SD₁₆	—	4	2	no	—
97	C₁₃×D₈	—	4	1	no	—
98	C₁₃×M₁₆	—	4	4	no	—
99	C₂×C₈×C₁₃	—	2	4	no	—
100	C₂×C₈×C₁₃	—	2	2	no	—
101	C₂×C₈×C₁₃	—	2	2	no	—
102	C₂×C₈×C₁₃	—	2	2	no	—
103	C₂×C₈×C₁₃	—	4	1	no	—
104	C₂×C₈×C₁₃	—	4	1	no	—
105	C₂×C₈×C₁₃	—	4	1	no	—
106	C₂×C₈×C₁₃	—	4	1	no	—
107	C₂×C₈×C₁₃	—	4	4	no	—
108	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
109	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
110	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
111	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
112	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
113	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
114	C₁₃×C₄⋊C₄	—	2	2	no	—
115	C₁₃×C₄⋊C₄	—	2	2	no	—
116	C₁₃×C₄⋊C₄	—	2	2	no	—
117	C₁₃×C₄⋊C₄	—	2	2	no	—
118	C₁₃×C₄⋊C₄	C₂²×C₄	1	2	yes	—
119	C₁₃×C₄⋊C₄	C₂²×C₄	1	2	yes	—
120	C₁₃×C₂²⋊C₄	—	2	2	no	—
121	C₁₃×C₂²⋊C₄	—	2	2	no	—
122	C₁₃×C₂²⋊C₄	—	2	2	no	—
123	C₁₃×C₂²⋊C₄	—	2	2	no	—
124	C₁₃×C₂²⋊C₄	—	2	2	no	—
125	C₄²×C₁₃	—	2	2	no	—
126	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
127	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
128	C₄²×C₁₃	#41	1	1	yes	characteristic
129	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
130	#3168	C₂×C₁₃	1	1	yes	characteristic
131	#2966	C₂×C₁₃	1	2	yes	complemented
132	#1588	C₂×C₁₃	1	2	yes	complemented
133	#1587	C₂×C₁₃	1	2	yes	complemented
134	#1586	C₂×C₁₃	1	2	yes	complemented
135	#1585	C₂×C₁₃	1	2	yes	complemented
136	#1568	C₂×C₁₃	1	1	yes	characteristic, complemented
137	#1494	C₂×C₁₃	1	2	yes	complemented
138	C₂×#322	C₂×C₁₃	1	1	yes	characteristic, complemented
139	C₂³×C₁₃	—	2	2	no	—
140	C₂³×C₁₃	C₄×D₄	1	1	yes	characteristic
141	Q₈×C₁₃	—	2	2	no	—
142	Q₈×C₁₃	—	2	2	no	—
143	D₄×C₁₃	—	2	2	no	—
144	D₄×C₁₃	—	2	2	no	—
145	D₄×C₁₃	—	4	4	no	—
146	C₂×C₄×C₁₃	—	2	2	no	—
147	C₂×C₄×C₁₃	—	2	1	no	—
148	C₂×C₄×C₁₃	—	2	1	no	—
149	C₂×C₄×C₁₃	—	2	1	no	—
150	C₂×C₄×C₁₃	—	2	1	no	—
151	C₂×C₄×C₁₃	—	2	2	no	—
152	C₂×C₄×C₁₃	—	2	2	no	—
153	C₂×C₄×C₁₃	—	2	2	no	—
154	C₂×C₄×C₁₃	—	4	2	no	—
155	C₂×C₄×C₁₃	—	4	2	no	—
156	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
157	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
158	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
159	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
160	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
161	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
162	C₈×C₁₃	—	2	4	no	—
163	C₈×C₁₃	—	2	1	no	—
164	C₈×C₁₃	—	2	1	no	—
165	C₈×C₁₃	—	2	1	no	—
166	C₈×C₁₃	—	2	1	no	—
167	C₈×C₁₃	—	2	2	no	—
168	C₈×C₁₃	—	2	2	no	—
169	C₈×C₁₃	—	4	2	no	—
170	C₈×C₁₃	—	4	2	no	—
171	#529	C₂²×C₁₃	1	2	yes	—
172	#499	C₄×C₁₃	1	1	yes	characteristic
173	#495	C₄×C₁₃	1	1	yes	characteristic
174	#488	C₄×C₁₃	1	2	yes	—
175	#467	C₄×C₁₃	1	1	yes	characteristic
176	#466	C₄×C₁₃	1	1	yes	characteristic
177	#465	C₄×C₁₃	1	2	yes	—
178	#446	C₂²×C₁₃	1	2	yes	—
179	C₈×Q₈	C₂²×C₁₃	1	2	yes	—
180	C₄×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic
181	C₄×SD₁₆	C₂²×C₁₃	1	2	yes	—
182	C₄×D₈	C₂²×C₁₃	1	1	yes	characteristic
183	#436	C₂²×C₁₃	1	2	yes	—
184	#435	—	2	2	no	—
185	C₈×D₄	—	2	2	no	—
186	C₈×D₄	C₂²×C₁₃	1	2	yes	—
187	#433	—	2	2	no	—
188	#432	C₂²×C₁₃	1	2	yes	—
189	#405	—	2	2	no	—
190	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
191	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
192	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
193	#335	C₂²×C₁₃	1	1	yes	characteristic
194	#335	C₂²×C₁₃	1	1	yes	characteristic
195	#334	C₂²×C₁₃	1	2	yes	—
196	Q₈⋊C₈	C₂²×C₁₃	1	2	yes	—
197	Q₈⋊C₈	C₂²×C₁₃	1	2	yes	—
198	D₄⋊C₈	C₂²×C₁₃	1	2	yes	—
199	D₄⋊C₈	C₂²×C₁₃	1	2	yes	—
200	#322	C₂²×C₁₃	1	2	yes	—
201	#322	C₂²×C₁₃	1	2	yes	—
202	C₂²×C₁₃	—	2	1	no	—
203	C₂²×C₁₃	—	2	1	no	—
204	C₂²×C₁₃	—	4	2	no	—
205	C₂²×C₁₃	—	4	2	no	—
206	C₂²×C₁₃	—	4	2	no	—
207	C₂²×C₁₃	#443	1	2	yes	—
208	C₂²×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
209	C₄×C₁₃	—	2	1	no	—
210	C₄×C₁₃	—	2	1	no	—
211	C₄×C₁₃	—	2	1	no	—
212	C₄×C₁₃	—	2	1	no	—
213	C₄×C₁₃	—	4	2	no	—
214	C₄×C₁₃	—	4	2	no	—
215	C₄×C₁₃	—	4	2	no	—
216	C₄×C₁₃	#568	1	1	yes	characteristic
217	C₄×C₁₃	#568	1	1	yes	characteristic
218	C₄×C₁₃	#575	1	1	yes	characteristic
219	C₄×C₁₃	#575	1	1	yes	characteristic
220	C₂×Q₁₆	C₂×C₄×C₁₃	1	1	yes	characteristic
221	C₂×SD₁₆	C₂×C₄×C₁₃	1	2	yes	—
222	C₂×D₈	C₂×C₄×C₁₃	1	1	yes	characteristic
223	C₂×M₁₆	—	2	2	no	—
224	C₂²×C₈	—	2	1	no	—
225	C₂²×C₈	—	2	2	no	—
226	C₂²×C₈	C₂×C₄×C₁₃	1	1	yes	characteristic
227	C₂²×C₈	C₂×C₄×C₁₃	1	1	yes	characteristic
228	C₂²×C₈	D₄×C₁₃	1	1	yes	characteristic
229	C₂²×C₈	D₄×C₁₃	1	1	yes	characteristic
230	#126	—	2	2	no	—
231	#125	C₂×C₄×C₁₃	1	2	yes	—
232	#124	C₂×C₄×C₁₃	1	2	yes	—
233	#123	—	2	2	no	—
234	C₂²⋊Q₈	C₂×C₄×C₁₃	1	2	yes	—
235	#121	C₂×C₄×C₁₃	1	2	yes	—
236	C₄×Q₈	C₂³×C₁₃	1	2	yes	—
237	C₄×D₄	—	2	2	no	—
238	C₄×D₄	C₂³×C₁₃	1	2	yes	—
239	#117	—	2	2	no	—
240	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
241	#107	C₂×C₄×C₁₃	1	1	yes	characteristic
242	#107	C₂×C₄×C₁₃	1	1	yes	characteristic
243	#106	C₂×C₄×C₁₃	1	2	yes	—
244	C₄⋊C₈	—	2	2	no	—
245	C₄⋊C₈	—	2	2	no	—
246	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
247	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
248	#103	C₂×C₄×C₁₃	1	2	yes	—
249	#103	C₂×C₄×C₁₃	1	2	yes	—
250	#102	C₂×C₄×C₁₃	1	2	yes	—
251	#102	C₂×C₄×C₁₃	1	2	yes	—
252	C₂²⋊C₈	—	2	2	no	—
253	C₂²⋊C₈	—	2	2	no	—
254	C₂²⋊C₈	—	2	2	no	—
255	#97	—	2	2	no	—
256	#97	—	2	2	no	—
257	C₄×C₈	—	2	2	no	—
258	C₄×C₈	—	2	1	no	—
259	C₄×C₈	C₂×C₄×C₁₃	1	1	yes	characteristic
260	C₄×C₈	C₂×C₄×C₁₃	1	1	yes	characteristic
261	C₄×C₈	D₄×C₁₃	1	2	yes	—
262	C₄×C₈	C₂³×C₁₃	1	2	yes	—
263	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
264	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
265	C₄×C₈	C₂³×C₁₃	1	2	yes	—
266	C₂×C₁₃	—	2	2	no	—
267	C₂×C₁₃	—	8	2	no	—
268	C₂×C₁₃	#2932	1	1	yes	characteristic
269	C₂×C₁₃	#2943	1	1	yes	characteristic
270	C₂×C₁₃	C₂×#443	1	1	yes	characteristic
271	C₂×Q₈	C₂²×C₄×C₁₃	1	2	yes	—
272	C₂×D₄	—	2	2	no	—
273	C₂×D₄	C₂²×C₄×C₁₃	1	2	yes	—
274	C₂²×C₄	—	2	2	no	—
275	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
276	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
277	C₂²×C₄	C₁₃×#41	1	1	yes	characteristic
278	Q₁₆	—	4	1	no	—
279	SD₁₆	—	4	2	no	—
280	D₈	—	4	1	no	—
281	M₁₆	—	4	4	no	—
282	C₂×C₈	—	2	4	no	—
283	C₂×C₈	—	2	2	no	—
284	C₂×C₈	—	2	2	no	—
285	C₂×C₈	—	2	2	no	—
286	C₂×C₈	—	4	1	no	—
287	C₂×C₈	—	4	1	no	—
288	C₂×C₈	—	4	1	no	—
289	C₂×C₈	—	4	1	no	—
290	C₂×C₈	—	4	4	no	—
291	C₂×C₈	C₂²×C₄×C₁₃	1	1	yes	characteristic
292	C₂×C₈	C₂²×C₄×C₁₃	1	1	yes	characteristic
293	C₂×C₈	C₂²×C₄×C₁₃	1	1	yes	characteristic
294	C₂×C₈	C₂²×C₄×C₁₃	1	1	yes	characteristic
295	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
296	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
297	C₄⋊C₄	—	2	2	no	—
298	C₄⋊C₄	—	2	2	no	—
299	C₄⋊C₄	—	2	2	no	—
300	C₄⋊C₄	—	2	2	no	—
301	C₄⋊C₄	C₂²×C₄×C₁₃	1	2	yes	—
302	C₄⋊C₄	C₂²×C₄×C₁₃	1	2	yes	—
303	C₂²⋊C₄	—	2	2	no	—
304	C₂²⋊C₄	—	2	2	no	—
305	C₂²⋊C₄	—	2	2	no	—
306	C₂²⋊C₄	—	2	2	no	—
307	C₂²⋊C₄	—	2	2	no	—
308	C₄²	—	2	2	no	—
309	C₄²	C₂²×C₄×C₁₃	1	1	yes	characteristic
310	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
311	C₄²	C₁₃×#41	1	1	yes	characteristic
312	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
313	C₁₃	#17982	1	1	yes	characteristic, direct product factor, Sylow
314	C₂³	—	2	2	no	—
315	C₂³	C₄×D₄×C₁₃	1	1	yes	characteristic
316	Q₈	—	2	2	no	—
317	Q₈	—	2	2	no	—
318	D₄	—	2	2	no	—
319	D₄	—	2	2	no	—
320	D₄	—	4	4	no	—
321	C₂×C₄	—	2	2	no	—
322	C₂×C₄	—	2	1	no	—
323	C₂×C₄	—	2	1	no	—
324	C₂×C₄	—	2	1	no	—
325	C₂×C₄	—	2	1	no	—
326	C₂×C₄	—	2	2	no	—
327	C₂×C₄	—	2	2	no	—
328	C₂×C₄	—	2	2	no	—
329	C₂×C₄	—	4	2	no	—
330	C₂×C₄	—	4	2	no	—
331	C₂×C₄	C₄×D₄×C₁₃	1	1	yes	characteristic
332	C₂×C₄	C₄×D₄×C₁₃	1	1	yes	characteristic
333	C₂×C₄	C₄×D₄×C₁₃	1	1	yes	characteristic
334	C₂×C₄	C₂³×C₄×C₁₃	1	1	yes	characteristic
335	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
336	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
337	C₈	—	2	4	no	—
338	C₈	—	2	1	no	—
339	C₈	—	2	1	no	—
340	C₈	—	2	1	no	—
341	C₈	—	2	1	no	—
342	C₈	—	2	2	no	—
343	C₈	—	2	2	no	—
344	C₈	—	4	2	no	—
345	C₈	—	4	2	no	—
346	C₂²	—	2	1	no	—
347	C₂²	—	2	1	no	—
348	C₂²	—	4	2	no	—
349	C₂²	—	4	2	no	—
350	C₂²	—	4	2	no	—
351	C₂²	C₁₃×#443	1	2	yes	—
352	C₂²	C₂×C₄×D₄×C₁₃	1	1	yes	characteristic
353	C₄	—	2	1	no	—
354	C₄	—	2	1	no	—
355	C₄	—	2	1	no	—
356	C₄	—	2	1	no	—
357	C₄	—	4	2	no	—
358	C₄	—	4	2	no	—
359	C₄	—	4	2	no	—
360	C₄	C₁₃×#568	1	1	yes	characteristic
361	C₄	C₁₃×#568	1	1	yes	characteristic
362	C₄	C₁₃×#575	1	1	yes	characteristic
363	C₄	C₁₃×#575	1	1	yes	characteristic
364	C₂	—	2	2	no	—
365	C₂	—	8	2	no	—
366	C₂	C₁₃×#2932	1	1	yes	characteristic
367	C₂	C₁₃×#2943	1	1	yes	characteristic
368	C₂	C₂×C₁₃×#443	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₁₃	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₁₃
Frattini, cosocle	C₄²	C₂⁴×C₁₃
socle	C₂²×C₁₃	C₂×C₄×D₄
prime radical	C₁₃×#466	C₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₃ ◁ C₂×C₄×C₈×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₃×#2966	C₂	semidirect
3. C₁₃×#1588	C₂	semidirect
4. C₁₃×#1587	C₂	semidirect
5. C₁₃×#1586	C₂	semidirect
6. C₁₃×#1585	C₂	semidirect
7. C₁₃×#1568	C₂	semidirect
8. C₁₃×#1494	C₂	semidirect
9. C₂×C₁₃×#322	C₂	semidirect
87. #17982	C₁₃	direct (N × H)
131. #2966	C₂×C₁₃	semidirect
132. #1588	C₂×C₁₃	semidirect
133. #1587	C₂×C₁₃	semidirect
134. #1586	C₂×C₁₃	semidirect
135. #1585	C₂×C₁₃	semidirect
136. #1568	C₂×C₁₃	semidirect
137. #1494	C₂×C₁₃	semidirect
138. C₂×#322	C₂×C₁₃	semidirect
313. C₁₃	#17982	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×#3168	2
C₁₃×#2966	2
C₁₃×#1588	2
C₁₃×#1587	2
C₁₃×#1586	2
C₁₃×#1585	2
C₁₃×#1568	2
C₁₃×#1494	2
C₂×C₁₃×#322	2
#17982	13

Subgroups — C13×#17982 #15704321

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#17982 #15704321