Subgroups — C₂×C₁₃×#3176 #15747019

Order 3328.

2098 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	C₂×C₁₃×#540	C₂	1	2	yes	maximal, complemented
2	C₁₃×#3176	C₂	1	16	yes	maximal, direct product factor
3	C₂×C₁₃×#499	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₁₃×#493	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₁₃×#490	C₂	1	2	yes	maximal, complemented
6	C₂×C₁₃×#469	C₂	1	2	yes	maximal, complemented
7	C₂×C₁₃×#466	C₂	1	2	yes	maximal, complemented
8	C₂×C₁₃×#442	C₂	1	2	yes	maximal, complemented
9	C₂×C₄×C₁₃×D₈	C₂	1	2	yes	maximal, complemented
10	C₂×C₁₃×#405	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂²×C₁₃×D₈	C₂²	1	2	yes	—
12	C₂²×C₁₃×D₈	C₂²	1	2	yes	—
13	C₂²×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
14	C₂³×C₈×C₁₃	C₂²	1	1	yes	characteristic
15	C₁₃×#540	—	2	8	no	—
16	C₁₃×#540	C₂²	1	16	yes	complemented
17	C₂×C₁₃×#127	C₂²	1	2	yes	—
18	C₂×C₁₃×#125	C₂²	1	2	yes	—
19	C₂×C₁₃×#123	—	2	4	no	—
20	C₂×C₁₃×#121	—	2	4	no	—
21	C₂×C₁₃×#121	C₂²	1	4	yes	—
22	C₂×C₄×D₄×C₁₃	C₂²	1	4	yes	—
23	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
24	C₁₃×#499	C₂²	1	8	yes	complemented
25	C₁₃×#493	C₂²	1	8	yes	complemented
26	C₁₃×#490	C₂²	1	16	yes	complemented
27	C₁₃×#469	C₂²	1	16	yes	complemented
28	C₁₃×#466	C₂²	1	16	yes	complemented
29	C₁₃×#442	C₂²	1	16	yes	complemented
30	C₄×C₁₃×D₈	C₂²	1	16	yes	complemented
31	C₂×C₁₃×#107	C₂²	1	2	yes	—
32	C₂×C₁₃×#106	C₂²	1	2	yes	—
33	C₂×C₁₃×#102	C₂²	1	4	yes	—
34	C₂×C₁₃×#102	C₂²	1	4	yes	—
35	C₁₃×#405	C₂²	1	8	yes	complemented
36	C₂×C₁₃×#97	C₂²	1	1	yes	characteristic
37	C₂×C₁₃×#97	C₂²	1	1	yes	characteristic
38	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
39	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
40	C₂²×D₄×C₁₃	—	2	4	no	—
41	C₂²×D₄×C₁₃	—	2	4	no	—
42	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
43	C₂³×C₄×C₁₃	—	2	4	no	—
44	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
45	C₂×C₁₃×D₈	—	2	8	no	—
46	C₂×C₁₃×D₈	—	2	8	no	—
47	C₂×C₁₃×D₈	C₂³	1	8	yes	—
48	C₂×C₁₃×D₈	C₂³	1	8	yes	—
49	C₂×C₁₃×M₁₆	—	2	4	no	—
50	C₂×C₁₃×M₁₆	C₂³	1	4	yes	—
51	C₂²×C₈×C₁₃	—	2	4	no	—
52	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
53	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
54	C₂²×C₈×C₁₃	C₂³	1	4	yes	—
55	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
56	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
57	C₁₃×#127	—	2	4	no	—
58	C₁₃×#127	C₂³	1	8	yes	—
59	C₁₃×#125	—	2	4	no	—
60	C₁₃×#125	C₂³	1	8	yes	—
61	C₁₃×#123	—	2	32	no	—
62	C₁₃×#121	—	2	8	no	—
63	C₁₃×#121	—	2	32	no	—
64	C₁₃×#121	C₂³	1	16	yes	—
65	C₄×D₄×C₁₃	—	2	8	no	—
66	C₄×D₄×C₁₃	C₂³	1	16	yes	—
67	C₁₃×#117	D₄	1	4	yes	—
68	C₁₃×#117	C₂³	1	4	yes	—
69	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
70	C₂×C₁₃×C₄⋊C₄	D₄	1	2	yes	—
71	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
72	C₂×C₁₃×C₂²⋊C₄	—	2	4	no	—
73	C₂×C₁₃×C₂²⋊C₄	—	2	4	no	—
74	C₂×C₁₃×C₂²⋊C₄	D₄	1	2	yes	—
75	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
76	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
77	C₁₃×#107	C₂³	1	8	yes	—
78	C₁₃×#106	C₂³	1	8	yes	—
79	C₁₃×#102	C₂³	1	16	yes	—
80	C₁₃×#102	C₂³	1	16	yes	—
81	C₁₃×#97	C₂³	1	4	yes	—
82	C₁₃×#97	C₂³	1	4	yes	—
83	C₄×C₈×C₁₃	C₂³	1	4	yes	—
84	C₄×C₈×C₁₃	C₂³	1	4	yes	—
85	C₂×#3176	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
86	C₂⁴×C₁₃	—	2	4	no	—
87	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
88	C₂×D₄×C₁₃	—	2	16	no	—
89	C₂×D₄×C₁₃	—	2	4	no	—
90	C₂×D₄×C₁₃	—	2	16	no	—
91	C₂×D₄×C₁₃	—	2	8	no	—
92	C₂×D₄×C₁₃	—	2	8	no	—
93	C₂×D₄×C₁₃	—	8	8	no	—
94	C₂×D₄×C₁₃	—	8	8	no	—
95	C₂×D₄×C₁₃	C₂⁴	1	8	yes	—
96	C₂²×C₄×C₁₃	—	2	2	no	—
97	C₂²×C₄×C₁₃	—	2	2	no	—
98	C₂²×C₄×C₁₃	—	2	4	no	—
99	C₂²×C₄×C₁₃	—	2	16	no	—
100	C₂²×C₄×C₁₃	—	8	8	no	—
101	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
102	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
103	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
104	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
105	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
106	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
107	C₁₃×D₈	—	2	16	no	—
108	C₁₃×D₈	—	2	16	no	—
109	C₁₃×M₁₆	—	2	8	no	—
110	C₂×C₈×C₁₃	—	2	2	no	—
111	C₂×C₈×C₁₃	—	2	2	no	—
112	C₂×C₈×C₁₃	—	2	8	no	—
113	C₂×C₈×C₁₃	#41	1	4	yes	—
114	C₂×C₈×C₁₃	#41	1	4	yes	—
115	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
116	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
117	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
118	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
119	C₁₃×C₄⋊C₄	—	2	16	no	—
120	C₁₃×C₄⋊C₄	—	2	4	no	—
121	C₁₃×C₄⋊C₄	C₂×D₄	1	8	yes	—
122	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
123	C₁₃×C₂²⋊C₄	—	2	16	no	—
124	C₁₃×C₂²⋊C₄	—	2	16	no	—
125	C₁₃×C₂²⋊C₄	C₂×D₄	1	8	yes	—
126	C₄²×C₁₃	C₂×D₄	1	2	yes	—
127	C₄²×C₁₃	C₂×D₄	1	2	yes	—
128	C₄²×C₁₃	C₂⁴	1	2	yes	—
129	C₄²×C₁₃	C₂⁴	1	2	yes	—
130	C₂×#540	C₂×C₁₃	1	2	yes	complemented
131	#3176	C₂×C₁₃	1	16	yes	direct product factor
132	C₂×#499	C₂×C₁₃	1	1	yes	characteristic, complemented
133	C₂×#493	C₂×C₁₃	1	1	yes	characteristic, complemented
134	C₂×#490	C₂×C₁₃	1	2	yes	complemented
135	C₂×#469	C₂×C₁₃	1	2	yes	complemented
136	C₂×#466	C₂×C₁₃	1	2	yes	complemented
137	C₂×#442	C₂×C₁₃	1	2	yes	complemented
138	C₂×C₄×D₈	C₂×C₁₃	1	2	yes	complemented
139	C₂×#405	C₂×C₁₃	1	1	yes	characteristic, complemented
140	C₂³×C₁₃	—	2	2	no	—
141	C₂³×C₁₃	—	2	4	no	—
142	C₂³×C₁₃	—	2	8	no	—
143	C₂³×C₁₃	—	4	8	no	—
144	C₂³×C₁₃	—	4	8	no	—
145	C₂³×C₁₃	—	4	8	no	—
146	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
147	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
148	D₄×C₁₃	—	2	8	no	—
149	D₄×C₁₃	—	2	8	no	—
150	D₄×C₁₃	—	4	8	no	—
151	D₄×C₁₃	—	8	16	no	—
152	D₄×C₁₃	—	8	16	no	—
153	C₂×C₄×C₁₃	—	2	2	no	—
154	C₂×C₄×C₁₃	—	2	4	no	—
155	C₂×C₄×C₁₃	—	2	4	no	—
156	C₂×C₄×C₁₃	—	2	4	no	—
157	C₂×C₄×C₁₃	—	2	2	no	—
158	C₂×C₄×C₁₃	—	2	2	no	—
159	C₂×C₄×C₁₃	—	2	8	no	—
160	C₂×C₄×C₁₃	—	4	8	no	—
161	C₂×C₄×C₁₃	—	8	16	no	—
162	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
163	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
164	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
165	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
166	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
167	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
168	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
169	C₈×C₁₃	—	2	2	no	—
170	C₈×C₁₃	—	2	2	no	—
171	C₈×C₁₃	C₂×#41	1	4	yes	—
172	C₈×C₁₃	C₂×#41	1	4	yes	—
173	C₂²×D₈	C₂²×C₁₃	1	2	yes	—
174	C₂²×D₈	C₂²×C₁₃	1	2	yes	—
175	C₂²×M₁₆	C₂²×C₁₃	1	1	yes	characteristic
176	C₂³×C₈	C₂²×C₁₃	1	1	yes	characteristic
177	#540	—	2	8	no	—
178	#540	C₂²×C₁₃	1	16	yes	complemented
179	C₂×#127	C₂²×C₁₃	1	2	yes	—
180	C₂×#125	C₂²×C₁₃	1	2	yes	—
181	C₂×#123	—	2	4	no	—
182	C₂×#121	—	2	4	no	—
183	C₂×#121	C₂²×C₁₃	1	4	yes	—
184	C₂×C₄×D₄	C₂²×C₁₃	1	4	yes	—
185	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
186	#499	C₂²×C₁₃	1	8	yes	complemented
187	#493	C₂²×C₁₃	1	8	yes	complemented
188	#490	C₂²×C₁₃	1	16	yes	complemented
189	#469	C₂²×C₁₃	1	16	yes	complemented
190	#466	C₂²×C₁₃	1	16	yes	complemented
191	#442	C₂²×C₁₃	1	16	yes	complemented
192	C₄×D₈	C₂²×C₁₃	1	16	yes	complemented
193	C₂×#107	C₂²×C₁₃	1	2	yes	—
194	C₂×#106	C₂²×C₁₃	1	2	yes	—
195	C₂×#102	C₂²×C₁₃	1	4	yes	—
196	C₂×#102	C₂²×C₁₃	1	4	yes	—
197	#405	C₂²×C₁₃	1	8	yes	complemented
198	C₂×#97	C₂²×C₁₃	1	1	yes	characteristic
199	C₂×#97	C₂²×C₁₃	1	1	yes	characteristic
200	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
201	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
202	C₂²×C₁₃	—	2	2	no	—
203	C₂²×C₁₃	—	2	4	no	—
204	C₂²×C₁₃	—	4	4	no	—
205	C₂²×C₁₃	—	4	8	no	—
206	C₂²×C₁₃	—	4	8	no	—
207	C₂²×C₁₃	—	4	8	no	—
208	C₂²×C₁₃	—	8	16	no	—
209	C₂²×C₁₃	#532	1	2	yes	—
210	C₂²×C₁₃	#576	1	4	yes	—
211	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
212	C₄×C₁₃	—	2	2	no	—
213	C₄×C₁₃	—	2	4	no	—
214	C₄×C₁₃	—	2	4	no	—
215	C₄×C₁₃	—	4	8	no	—
216	C₄×C₁₃	#532	1	2	yes	—
217	C₄×C₁₃	C₂²×#41	1	1	yes	characteristic
218	C₄×C₁₃	C₂²×#41	1	1	yes	characteristic
219	C₂²×D₄	—	2	4	no	—
220	C₂²×D₄	—	2	4	no	—
221	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
222	C₂³×C₄	—	2	4	no	—
223	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
224	C₂×D₈	—	2	8	no	—
225	C₂×D₈	—	2	8	no	—
226	C₂×D₈	C₂³×C₁₃	1	8	yes	—
227	C₂×D₈	C₂³×C₁₃	1	8	yes	—
228	C₂×M₁₆	—	2	4	no	—
229	C₂×M₁₆	C₂³×C₁₃	1	4	yes	—
230	C₂²×C₈	—	2	4	no	—
231	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
232	C₂²×C₈	C₂³×C₁₃	1	4	yes	—
233	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
234	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
235	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
236	#127	—	2	4	no	—
237	#127	C₂³×C₁₃	1	8	yes	—
238	#125	—	2	4	no	—
239	#125	C₂³×C₁₃	1	8	yes	—
240	#123	—	2	32	no	—
241	#121	—	2	8	no	—
242	#121	—	2	32	no	—
243	#121	C₂³×C₁₃	1	16	yes	—
244	C₄×D₄	—	2	8	no	—
245	C₄×D₄	C₂³×C₁₃	1	16	yes	—
246	#117	D₄×C₁₃	1	4	yes	—
247	#117	C₂³×C₁₃	1	4	yes	—
248	C₂×C₄⋊C₄	—	2	4	no	—
249	C₂×C₄⋊C₄	D₄×C₁₃	1	2	yes	—
250	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
251	C₂×C₂²⋊C₄	—	2	4	no	—
252	C₂×C₂²⋊C₄	—	2	4	no	—
253	C₂×C₂²⋊C₄	D₄×C₁₃	1	2	yes	—
254	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
255	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
256	#107	C₂³×C₁₃	1	8	yes	—
257	#106	C₂³×C₁₃	1	8	yes	—
258	#102	C₂³×C₁₃	1	16	yes	—
259	#102	C₂³×C₁₃	1	16	yes	—
260	#97	C₂³×C₁₃	1	4	yes	—
261	#97	C₂³×C₁₃	1	4	yes	—
262	C₄×C₈	C₂³×C₁₃	1	4	yes	—
263	C₄×C₈	C₂³×C₁₃	1	4	yes	—
264	C₂×C₁₃	—	4	2	no	—
265	C₂×C₁₃	—	8	8	no	—
266	C₂×C₁₃	#3176	1	4	yes	direct product factor
267	C₂×C₁₃	C₂×#532	1	1	yes	characteristic
268	C₂×C₁₃	C₂×#576	1	2	yes	—
269	C₂⁴	—	2	4	no	—
270	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
271	C₂×D₄	—	2	16	no	—
272	C₂×D₄	—	2	4	no	—
273	C₂×D₄	—	2	16	no	—
274	C₂×D₄	—	2	8	no	—
275	C₂×D₄	—	2	8	no	—
276	C₂×D₄	—	8	8	no	—
277	C₂×D₄	—	8	8	no	—
278	C₂×D₄	C₂⁴×C₁₃	1	8	yes	—
279	C₂²×C₄	—	2	2	no	—
280	C₂²×C₄	—	2	2	no	—
281	C₂²×C₄	—	2	4	no	—
282	C₂²×C₄	—	2	16	no	—
283	C₂²×C₄	—	8	8	no	—
284	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
285	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
286	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
287	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
288	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
289	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
290	D₈	—	2	16	no	—
291	D₈	—	2	16	no	—
292	M₁₆	—	2	8	no	—
293	C₂×C₈	—	2	2	no	—
294	C₂×C₈	—	2	2	no	—
295	C₂×C₈	—	2	8	no	—
296	C₂×C₈	C₁₃×#41	1	4	yes	—
297	C₂×C₈	C₁₃×#41	1	4	yes	—
298	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
299	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
300	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
301	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
302	C₄⋊C₄	—	2	16	no	—
303	C₄⋊C₄	—	2	4	no	—
304	C₄⋊C₄	C₂×D₄×C₁₃	1	8	yes	—
305	C₄⋊C₄	C₂⁴×C₁₃	1	8	yes	—
306	C₂²⋊C₄	—	2	16	no	—
307	C₂²⋊C₄	—	2	16	no	—
308	C₂²⋊C₄	C₂×D₄×C₁₃	1	8	yes	—
309	C₄²	C₂×D₄×C₁₃	1	2	yes	—
310	C₄²	C₂×D₄×C₁₃	1	2	yes	—
311	C₄²	C₂⁴×C₁₃	1	2	yes	—
312	C₄²	C₂⁴×C₁₃	1	2	yes	—
313	C₁₃	C₂×#3176	1	1	yes	characteristic, direct product factor, Sylow
314	C₂³	—	2	2	no	—
315	C₂³	—	2	4	no	—
316	C₂³	—	2	8	no	—
317	C₂³	—	4	8	no	—
318	C₂³	—	4	8	no	—
319	C₂³	—	4	8	no	—
320	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
321	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
322	D₄	—	2	8	no	—
323	D₄	—	2	8	no	—
324	D₄	—	4	8	no	—
325	D₄	—	8	16	no	—
326	D₄	—	8	16	no	—
327	C₂×C₄	—	2	2	no	—
328	C₂×C₄	—	2	4	no	—
329	C₂×C₄	—	2	4	no	—
330	C₂×C₄	—	2	4	no	—
331	C₂×C₄	—	2	2	no	—
332	C₂×C₄	—	2	2	no	—
333	C₂×C₄	—	2	8	no	—
334	C₂×C₄	—	4	8	no	—
335	C₂×C₄	—	8	16	no	—
336	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
337	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
338	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
339	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
340	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
341	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
342	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
343	C₈	—	2	2	no	—
344	C₈	—	2	2	no	—
345	C₈	C₂×C₁₃×#41	1	4	yes	—
346	C₈	C₂×C₁₃×#41	1	4	yes	—
347	C₂²	—	2	4	no	—
348	C₂²	—	2	2	no	—
349	C₂²	—	4	4	no	—
350	C₂²	—	4	8	no	—
351	C₂²	—	4	8	no	—
352	C₂²	—	4	8	no	—
353	C₂²	—	8	16	no	—
354	C₂²	C₁₃×#532	1	2	yes	—
355	C₂²	C₁₃×#576	1	4	yes	—
356	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
357	C₄	—	2	4	no	—
358	C₄	—	2	4	no	—
359	C₄	—	2	2	no	—
360	C₄	—	4	8	no	—
361	C₄	C₁₃×#532	1	2	yes	—
362	C₄	C₂²×C₁₃×#41	1	1	yes	characteristic
363	C₄	C₂²×C₁₃×#41	1	1	yes	characteristic
364	C₂	—	4	2	no	—
365	C₂	—	8	8	no	—
366	C₂	C₁₃×#3176	1	4	yes	direct product factor
367	C₂	C₂×C₁₃×#532	1	1	yes	characteristic
368	C₂	C₂×C₁₃×#576	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₃
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ C₂×C₁₃×#117 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₃×#540	C₂	semidirect
2. C₁₃×#3176	C₂	direct (N × H)
3. C₂×C₁₃×#499	C₂	semidirect
4. C₂×C₁₃×#493	C₂	semidirect
5. C₂×C₁₃×#490	C₂	semidirect
6. C₂×C₁₃×#469	C₂	semidirect
7. C₂×C₁₃×#466	C₂	semidirect
8. C₂×C₁₃×#442	C₂	semidirect
9. C₂×C₄×C₁₃×D₈	C₂	semidirect
10. C₂×C₁₃×#405	C₂	semidirect
16. C₁₃×#540	C₂²	semidirect
24. C₁₃×#499	C₂²	semidirect
25. C₁₃×#493	C₂²	semidirect
26. C₁₃×#490	C₂²	semidirect
27. C₁₃×#469	C₂²	semidirect
28. C₁₃×#466	C₂²	semidirect
29. C₁₃×#442	C₂²	semidirect
30. C₄×C₁₃×D₈	C₂²	semidirect
35. C₁₃×#405	C₂²	semidirect
85. C₂×#3176	C₁₃	direct (N × H)
130. C₂×#540	C₂×C₁₃	semidirect
131. #3176	C₂×C₁₃	direct (N × H)
132. C₂×#499	C₂×C₁₃	semidirect
133. C₂×#493	C₂×C₁₃	semidirect
134. C₂×#490	C₂×C₁₃	semidirect
135. C₂×#469	C₂×C₁₃	semidirect
136. C₂×#466	C₂×C₁₃	semidirect
137. C₂×#442	C₂×C₁₃	semidirect
138. C₂×C₄×D₈	C₂×C₁₃	semidirect
139. C₂×#405	C₂×C₁₃	semidirect
178. #540	C₂²×C₁₃	semidirect
186. #499	C₂²×C₁₃	semidirect
187. #493	C₂²×C₁₃	semidirect
188. #490	C₂²×C₁₃	semidirect
189. #469	C₂²×C₁₃	semidirect
190. #466	C₂²×C₁₃	semidirect
191. #442	C₂²×C₁₃	semidirect
192. C₄×D₈	C₂²×C₁₃	semidirect
197. #405	C₂²×C₁₃	semidirect
266. C₂×C₁₃	#3176	direct (N × H)
313. C₁₃	C₂×#3176	direct (N × H)
366. C₂	C₁₃×#3176	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×#540	2
C₁₃×#3176	2
C₂×C₁₃×#499	2
C₂×C₁₃×#493	2
C₂×C₁₃×#490	2
C₂×C₁₃×#469	2
C₂×C₁₃×#466	2
C₂×C₁₃×#442	2
C₂×C₄×C₁₃×D₈	2
C₂×C₁₃×#405	2
C₂×#3176	13

Subgroups — C2×C13×#3176 #15747019

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₃×#3176 #15747019