Subgroups — C₁₃×#61011 #15747350

Order 3328.

1896 conjugacy classes of subgroups.

The subgroup lattice has 394 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3508	C₂	1	2	yes	maximal, complemented
2	C₁₃×#3259	C₂	1	4	yes	maximal, complemented
3	C₁₃×#3228	C₂	1	4	yes	maximal, complemented
4	C₁₃×#3205	C₂	1	4	yes	maximal, complemented
5	C₁₃×#3199	C₂	1	4	yes	maximal, complemented
6	C₁₃×#3184	C₂	1	2	yes	maximal, complemented
7	C₁₃×#3169	C₂	1	2	yes	maximal, complemented
8	C₁₃×#3122	C₂	1	8	yes	maximal, complemented
9	C₁₃×#2922	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#559	—	2	4	no	—
11	C₁₃×#550	—	2	4	no	—
12	C₁₃×#546	—	2	4	no	—
13	C₁₃×#546	—	2	4	no	—
14	C₁₃×#540	C₂²	1	4	yes	—
15	C₁₃×#540	C₂²	1	4	yes	complemented
16	C₁₃×#535	C₂²	1	4	yes	—
17	C₁₃×#533	C₂²	1	2	yes	complemented
18	C₁₃×#532	C₂²	1	4	yes	—
19	C₁₃×#532	C₂²	1	4	yes	complemented
20	C₂×C₁₃×#127	C₂²	1	2	yes	complemented
21	C₁₃×#518	C₂²	1	4	yes	complemented
22	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic
23	C₁₃×#500	C₂²	1	2	yes	complemented
24	C₁₃×#498	C₂²	1	2	yes	complemented
25	C₁₃×#493	C₂²	1	2	yes	—
26	C₁₃×#493	C₂²	1	2	yes	—
27	C₁₃×#486	C₂²	1	4	yes	complemented
28	C₁₃×#486	C₂²	1	4	yes	complemented
29	C₁₃×#482	C₂²	1	16	yes	complemented
30	C₁₃×#478	C₂²	1	16	yes	complemented
31	C₁₃×#469	C₂²	1	8	yes	complemented
32	C₁₃×#466	C₂²	1	8	yes	complemented
33	C₁₃×#459	C₂²	1	16	yes	complemented
34	C₁₃×#447	C₂²	1	16	yes	complemented
35	C₁₃×#442	C₂²	1	8	yes	complemented
36	C₄×C₁₃×D₈	C₂²	1	8	yes	complemented
37	C₁₃×#433	C₂²	1	4	yes	complemented
38	C₁₃×#431	C₂²	1	4	yes	complemented
39	C₁₃×#424	C₂²	1	2	yes	complemented
40	C₁₃×#408	C₂²	1	2	yes	—
41	C₄×C₁₃×M₁₆	C₂²	1	1	yes	characteristic, complemented
42	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic, complemented
43	C₂×C₁₃×#41	—	2	4	no	—
44	C₂×C₁₃×#41	—	2	4	no	—
45	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
46	C₂²×D₄×C₁₃	—	2	4	no	—
47	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
48	C₂×C₁₃×D₈	C₂³	1	8	yes	—
49	C₂×C₁₃×D₈	C₂³	1	8	yes	—
50	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
51	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
52	C₁₃×C₄⋊Q₈	C₂³	1	4	yes	—
53	C₁₃×#127	—	2	4	no	—
54	C₁₃×#127	—	2	4	no	—
55	C₁₃×#127	C₂³	1	4	yes	—
56	C₁₃×#127	C₂³	1	4	yes	—
57	C₁₃×#125	C₂³	1	4	yes	—
58	C₁₃×#124	—	2	4	no	—
59	C₁₃×#124	—	2	4	no	—
60	C₁₃×#124	—	2	4	no	—
61	C₁₃×#123	—	2	8	no	—
62	C₁₃×#123	—	2	8	no	—
63	C₁₃×C₂²⋊Q₈	—	2	4	no	—
64	C₁₃×#121	—	2	4	no	—
65	C₁₃×#121	—	2	4	no	—
66	C₁₃×#121	—	2	8	no	—
67	C₁₃×#121	—	2	8	no	—
68	C₁₃×#121	C₂³	1	8	yes	—
69	C₁₃×#121	C₂³	1	8	yes	—
70	C₁₃×#120	—	2	4	no	—
71	C₁₃×#120	—	2	4	no	—
72	C₄×Q₈×C₁₃	—	2	4	no	—
73	C₄×Q₈×C₁₃	D₄	1	2	yes	—
74	C₄×D₄×C₁₃	—	2	8	no	—
75	C₄×D₄×C₁₃	—	2	4	no	—
76	C₄×D₄×C₁₃	—	2	4	no	—
77	C₄×D₄×C₁₃	D₄	1	2	yes	—
78	C₄×D₄×C₁₃	D₄	1	4	yes	—
79	C₄×D₄×C₁₃	C₂³	1	8	yes	—
80	C₄×D₄×C₁₃	C₂³	1	8	yes	—
81	C₁₃×#117	C₂³	1	4	yes	—
82	C₁₃×#117	C₂³	1	1	yes	characteristic
83	C₁₃×#117	C₂³	1	2	yes	—
84	C₂×C₁₃×C₂²⋊C₄	—	2	8	no	—
85	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
86	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
87	C₁₃×#107	C₂³	1	8	yes	—
88	C₁₃×#106	C₂³	1	8	yes	—
89	C₁₃×C₄⋊C₈	C₂³	1	8	yes	—
90	C₁₃×#102	C₂³	1	16	yes	—
91	C₁₃×#102	C₂³	1	16	yes	—
92	C₁₃×C₂²⋊C₈	C₂³	1	8	yes	—
93	C₁₃×#97	C₂³	1	2	yes	—
94	C₄×C₈×C₁₃	C₂³	1	2	yes	—
95	C₄×C₈×C₁₃	C₂³	1	2	yes	—
96	C₄×C₈×C₁₃	C₂³	1	2	yes	—
97	#61011	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
98	C₂⁴×C₁₃	—	2	4	no	—
99	C₁₃×#41	—	4	2	no	—
100	C₁₃×#41	—	8	8	no	—
101	C₁₃×#41	—	8	8	no	—
102	C₂×Q₈×C₁₃	—	2	4	no	—
103	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
104	C₂×D₄×C₁₃	—	2	8	no	—
105	C₂×D₄×C₁₃	—	2	8	no	—
106	C₂×D₄×C₁₃	—	2	4	no	—
107	C₂×D₄×C₁₃	—	2	4	no	—
108	C₂×D₄×C₁₃	—	2	4	no	—
109	C₂×D₄×C₁₃	—	2	8	no	—
110	C₂×D₄×C₁₃	—	4	8	no	—
111	C₂×D₄×C₁₃	—	8	8	no	—
112	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
113	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
114	C₂×D₄×C₁₃	C₂⁴	1	8	yes	—
115	C₂²×C₄×C₁₃	—	2	8	no	—
116	C₂²×C₄×C₁₃	—	2	8	no	—
117	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
118	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
119	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
120	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
121	C₁₃×D₈	—	4	8	no	—
122	C₁₃×D₈	—	4	8	no	—
123	C₁₃×M₁₆	—	4	2	no	—
124	C₂×C₈×C₁₃	—	4	2	no	—
125	C₂×C₈×C₁₃	C₂⁴	1	4	yes	—
126	C₂×C₈×C₁₃	C₂⁴	1	4	yes	—
127	C₁₃×C₄⋊C₄	—	2	4	no	—
128	C₁₃×C₄⋊C₄	—	2	8	no	—
129	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
130	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
131	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
132	C₁₃×C₂²⋊C₄	—	2	4	no	—
133	C₁₃×C₂²⋊C₄	—	2	8	no	—
134	C₁₃×C₂²⋊C₄	—	2	8	no	—
135	C₁₃×C₂²⋊C₄	—	2	8	no	—
136	C₁₃×C₂²⋊C₄	—	2	8	no	—
137	C₁₃×C₂²⋊C₄	C₂×D₄	1	4	yes	—
138	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
139	C₄²×C₁₃	—	2	4	no	—
140	C₄²×C₁₃	C₂×D₄	1	2	yes	—
141	C₄²×C₁₃	C₂×D₄	1	4	yes	—
142	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
143	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
144	C₄²×C₁₃	C₂⁴	1	2	yes	—
145	#3508	C₂×C₁₃	1	2	yes	complemented
146	#3259	C₂×C₁₃	1	4	yes	complemented
147	#3228	C₂×C₁₃	1	4	yes	complemented
148	#3205	C₂×C₁₃	1	4	yes	complemented
149	#3199	C₂×C₁₃	1	4	yes	complemented
150	#3184	C₂×C₁₃	1	2	yes	complemented
151	#3169	C₂×C₁₃	1	2	yes	complemented
152	#3122	C₂×C₁₃	1	8	yes	complemented
153	#2922	C₂×C₁₃	1	1	yes	characteristic, complemented
154	C₂³×C₁₃	—	2	8	no	—
155	C₂³×C₁₃	—	4	8	no	—
156	C₂³×C₁₃	—	8	8	no	—
157	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
158	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
159	Q₈×C₁₃	—	4	1	no	—
160	Q₈×C₁₃	—	4	8	no	—
161	D₄×C₁₃	—	2	16	no	—
162	D₄×C₁₃	—	4	2	no	—
163	D₄×C₁₃	—	4	1	no	—
164	D₄×C₁₃	—	4	8	no	—
165	D₄×C₁₃	—	4	8	no	—
166	D₄×C₁₃	—	4	8	no	—
167	D₄×C₁₃	—	8	8	no	—
168	D₄×C₁₃	—	8	8	no	—
169	D₄×C₁₃	—	8	8	no	—
170	C₂×C₄×C₁₃	—	2	8	no	—
171	C₂×C₄×C₁₃	—	2	4	no	—
172	C₂×C₄×C₁₃	—	2	2	no	—
173	C₂×C₄×C₁₃	—	2	4	no	—
174	C₂×C₄×C₁₃	—	2	8	no	—
175	C₂×C₄×C₁₃	—	8	8	no	—
176	C₂×C₄×C₁₃	—	8	8	no	—
177	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
178	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
179	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
180	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
181	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
182	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
183	C₈×C₁₃	—	2	4	no	—
184	C₈×C₁₃	—	2	4	no	—
185	#559	—	2	4	no	—
186	#550	—	2	4	no	—
187	#546	—	2	4	no	—
188	#546	—	2	4	no	—
189	#540	C₂²×C₁₃	1	4	yes	—
190	#540	C₂²×C₁₃	1	4	yes	complemented
191	#535	C₂²×C₁₃	1	4	yes	—
192	#533	C₂²×C₁₃	1	2	yes	complemented
193	#532	C₂²×C₁₃	1	4	yes	—
194	#532	C₂²×C₁₃	1	4	yes	complemented
195	C₂×#127	C₂²×C₁₃	1	2	yes	complemented
196	#518	C₂²×C₁₃	1	4	yes	complemented
197	C₄×#41	C₂²×C₁₃	1	1	yes	characteristic
198	#500	C₂²×C₁₃	1	2	yes	complemented
199	#498	C₂²×C₁₃	1	2	yes	complemented
200	#493	C₂²×C₁₃	1	2	yes	—
201	#493	C₂²×C₁₃	1	2	yes	—
202	#486	C₂²×C₁₃	1	4	yes	complemented
203	#486	C₂²×C₁₃	1	4	yes	complemented
204	#482	C₂²×C₁₃	1	16	yes	complemented
205	#478	C₂²×C₁₃	1	16	yes	complemented
206	#469	C₂²×C₁₃	1	8	yes	complemented
207	#466	C₂²×C₁₃	1	8	yes	complemented
208	#459	C₂²×C₁₃	1	16	yes	complemented
209	#447	C₂²×C₁₃	1	16	yes	complemented
210	#442	C₂²×C₁₃	1	8	yes	complemented
211	C₄×D₈	C₂²×C₁₃	1	8	yes	complemented
212	#433	C₂²×C₁₃	1	4	yes	complemented
213	#431	C₂²×C₁₃	1	4	yes	complemented
214	#424	C₂²×C₁₃	1	2	yes	complemented
215	#408	C₂²×C₁₃	1	2	yes	—
216	C₄×M₁₆	C₂²×C₁₃	1	1	yes	characteristic, complemented
217	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
218	C₂²×C₁₃	—	2	2	no	—
219	C₂²×C₁₃	—	2	1	no	—
220	C₂²×C₁₃	—	2	2	no	—
221	C₂²×C₁₃	—	2	4	no	—
222	C₂²×C₁₃	—	4	8	no	—
223	C₂²×C₁₃	—	4	8	no	—
224	C₂²×C₁₃	—	4	8	no	—
225	C₂²×C₁₃	—	16	8	no	—
226	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
227	C₄×C₁₃	—	2	2	no	—
228	C₄×C₁₃	—	2	1	no	—
229	C₄×C₁₃	—	2	2	no	—
230	C₄×C₁₃	—	2	4	no	—
231	C₄×C₁₃	—	4	8	no	—
232	C₄×C₁₃	#576	1	4	yes	—
233	C₄×C₁₃	#585	1	2	yes	—
234	C₂×#41	—	2	4	no	—
235	C₂×#41	—	2	4	no	—
236	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
237	C₂²×D₄	—	2	4	no	—
238	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
239	C₂×D₈	C₂³×C₁₃	1	8	yes	—
240	C₂×D₈	C₂³×C₁₃	1	8	yes	—
241	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
242	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
243	C₄⋊Q₈	C₂³×C₁₃	1	4	yes	—
244	#127	—	2	4	no	—
245	#127	—	2	4	no	—
246	#127	C₂³×C₁₃	1	4	yes	—
247	#127	C₂³×C₁₃	1	4	yes	—
248	#125	C₂³×C₁₃	1	4	yes	—
249	#124	—	2	4	no	—
250	#124	—	2	4	no	—
251	#124	—	2	4	no	—
252	#123	—	2	8	no	—
253	#123	—	2	8	no	—
254	C₂²⋊Q₈	—	2	4	no	—
255	#121	—	2	4	no	—
256	#121	—	2	4	no	—
257	#121	—	2	8	no	—
258	#121	—	2	8	no	—
259	#121	C₂³×C₁₃	1	8	yes	—
260	#121	C₂³×C₁₃	1	8	yes	—
261	#120	—	2	4	no	—
262	#120	—	2	4	no	—
263	C₄×Q₈	—	2	4	no	—
264	C₄×Q₈	D₄×C₁₃	1	2	yes	—
265	C₄×D₄	—	2	8	no	—
266	C₄×D₄	—	2	4	no	—
267	C₄×D₄	—	2	4	no	—
268	C₄×D₄	D₄×C₁₃	1	2	yes	—
269	C₄×D₄	D₄×C₁₃	1	4	yes	—
270	C₄×D₄	C₂³×C₁₃	1	8	yes	—
271	C₄×D₄	C₂³×C₁₃	1	8	yes	—
272	#117	C₂³×C₁₃	1	4	yes	—
273	#117	C₂³×C₁₃	1	2	yes	—
274	#117	C₂³×C₁₃	1	1	yes	characteristic
275	C₂×C₂²⋊C₄	—	2	8	no	—
276	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
277	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
278	#107	C₂³×C₁₃	1	8	yes	—
279	#106	C₂³×C₁₃	1	8	yes	—
280	C₄⋊C₈	C₂³×C₁₃	1	8	yes	—
281	#102	C₂³×C₁₃	1	16	yes	—
282	#102	C₂³×C₁₃	1	16	yes	—
283	C₂²⋊C₈	C₂³×C₁₃	1	8	yes	—
284	#97	C₂³×C₁₃	1	2	yes	—
285	C₄×C₈	C₂³×C₁₃	1	2	yes	—
286	C₄×C₈	C₂³×C₁₃	1	2	yes	—
287	C₄×C₈	C₂³×C₁₃	1	2	yes	—
288	C₂×C₁₃	—	4	1	no	—
289	C₂×C₁₃	—	4	2	no	—
290	C₂×C₁₃	—	8	8	no	—
291	C₂×C₁₃	#3449	1	1	yes	characteristic
292	C₂×C₁₃	C₂×#576	1	2	yes	—
293	C₂⁴	—	2	4	no	—
294	#41	—	4	2	no	—
295	#41	—	8	8	no	—
296	#41	—	8	8	no	—
297	C₂×Q₈	—	2	4	no	—
298	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
299	C₂×D₄	—	2	8	no	—
300	C₂×D₄	—	2	8	no	—
301	C₂×D₄	—	2	4	no	—
302	C₂×D₄	—	2	4	no	—
303	C₂×D₄	—	2	4	no	—
304	C₂×D₄	—	2	8	no	—
305	C₂×D₄	—	4	8	no	—
306	C₂×D₄	—	8	8	no	—
307	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
308	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
309	C₂×D₄	C₂⁴×C₁₃	1	8	yes	—
310	C₂²×C₄	—	2	8	no	—
311	C₂²×C₄	—	2	8	no	—
312	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
313	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
314	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
315	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
316	D₈	—	4	8	no	—
317	D₈	—	4	8	no	—
318	M₁₆	—	4	2	no	—
319	C₂×C₈	—	4	2	no	—
320	C₂×C₈	C₂⁴×C₁₃	1	4	yes	—
321	C₂×C₈	C₂⁴×C₁₃	1	4	yes	—
322	C₄⋊C₄	—	2	4	no	—
323	C₄⋊C₄	—	2	8	no	—
324	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
325	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
326	C₄⋊C₄	C₂⁴×C₁₃	1	8	yes	—
327	C₂²⋊C₄	—	2	4	no	—
328	C₂²⋊C₄	—	2	8	no	—
329	C₂²⋊C₄	—	2	8	no	—
330	C₂²⋊C₄	—	2	8	no	—
331	C₂²⋊C₄	—	2	8	no	—
332	C₂²⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
333	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
334	C₄²	—	2	4	no	—
335	C₄²	C₂×D₄×C₁₃	1	2	yes	—
336	C₄²	C₂×D₄×C₁₃	1	4	yes	—
337	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
338	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
339	C₄²	C₂⁴×C₁₃	1	2	yes	—
340	C₁₃	#61011	1	1	yes	characteristic, direct product factor, Sylow
341	C₂³	—	2	8	no	—
342	C₂³	—	4	8	no	—
343	C₂³	—	8	8	no	—
344	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
345	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
346	Q₈	—	4	1	no	—
347	Q₈	—	4	8	no	—
348	D₄	—	2	16	no	—
349	D₄	—	4	2	no	—
350	D₄	—	4	1	no	—
351	D₄	—	4	8	no	—
352	D₄	—	4	8	no	—
353	D₄	—	4	8	no	—
354	D₄	—	8	8	no	—
355	D₄	—	8	8	no	—
356	D₄	—	8	8	no	—
357	C₂×C₄	—	2	8	no	—
358	C₂×C₄	—	2	4	no	—
359	C₂×C₄	—	2	2	no	—
360	C₂×C₄	—	2	4	no	—
361	C₂×C₄	—	2	8	no	—
362	C₂×C₄	—	8	8	no	—
363	C₂×C₄	—	8	8	no	—
364	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
365	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
366	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
367	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
368	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
369	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
370	C₈	—	2	4	no	—
371	C₈	—	2	4	no	—
372	C₂²	—	2	2	no	—
373	C₂²	—	2	4	no	—
374	C₂²	—	2	2	no	—
375	C₂²	—	2	1	no	—
376	C₂²	—	4	8	no	—
377	C₂²	—	4	8	no	—
378	C₂²	—	4	8	no	—
379	C₂²	—	16	8	no	—
380	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
381	C₄	—	2	2	no	—
382	C₄	—	2	4	no	—
383	C₄	—	2	2	no	—
384	C₄	—	2	1	no	—
385	C₄	—	4	8	no	—
386	C₄	C₁₃×#576	1	4	yes	—
387	C₄	C₁₃×#585	1	2	yes	—
388	C₂	—	4	2	no	—
389	C₂	—	4	1	no	—
390	C₂	—	8	8	no	—
391	C₂	C₁₃×#3449	1	1	yes	characteristic
392	C₂	C₂×C₁₃×#576	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₃
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₄×C₁₃×#41 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₃×#3508	C₂	semidirect
2. C₁₃×#3259	C₂	semidirect
3. C₁₃×#3228	C₂	semidirect
4. C₁₃×#3205	C₂	semidirect
5. C₁₃×#3199	C₂	semidirect
6. C₁₃×#3184	C₂	semidirect
7. C₁₃×#3169	C₂	semidirect
8. C₁₃×#3122	C₂	semidirect
9. C₁₃×#2922	C₂	semidirect
15. C₁₃×#540	C₂²	semidirect
17. C₁₃×#533	C₂²	semidirect
19. C₁₃×#532	C₂²	semidirect
20. C₂×C₁₃×#127	C₂²	semidirect
21. C₁₃×#518	C₂²	semidirect
23. C₁₃×#500	C₂²	semidirect
24. C₁₃×#498	C₂²	semidirect
27. C₁₃×#486	C₂²	semidirect
28. C₁₃×#486	C₂²	semidirect
29. C₁₃×#482	C₂²	semidirect
30. C₁₃×#478	C₂²	semidirect
31. C₁₃×#469	C₂²	semidirect
32. C₁₃×#466	C₂²	semidirect
33. C₁₃×#459	C₂²	semidirect
34. C₁₃×#447	C₂²	semidirect
35. C₁₃×#442	C₂²	semidirect
36. C₄×C₁₃×D₈	C₂²	semidirect
37. C₁₃×#433	C₂²	semidirect
38. C₁₃×#431	C₂²	semidirect
39. C₁₃×#424	C₂²	semidirect
41. C₄×C₁₃×M₁₆	C₂²	semidirect
42. C₂×C₄×C₈×C₁₃	C₂²	semidirect
97. #61011	C₁₃	direct (N × H)
145. #3508	C₂×C₁₃	semidirect
146. #3259	C₂×C₁₃	semidirect
147. #3228	C₂×C₁₃	semidirect
148. #3205	C₂×C₁₃	semidirect
149. #3199	C₂×C₁₃	semidirect
150. #3184	C₂×C₁₃	semidirect
151. #3169	C₂×C₁₃	semidirect
152. #3122	C₂×C₁₃	semidirect
153. #2922	C₂×C₁₃	semidirect
190. #540	C₂²×C₁₃	semidirect
192. #533	C₂²×C₁₃	semidirect
194. #532	C₂²×C₁₃	semidirect
195. C₂×#127	C₂²×C₁₃	semidirect
196. #518	C₂²×C₁₃	semidirect
198. #500	C₂²×C₁₃	semidirect
199. #498	C₂²×C₁₃	semidirect
202. #486	C₂²×C₁₃	semidirect
203. #486	C₂²×C₁₃	semidirect
204. #482	C₂²×C₁₃	semidirect
205. #478	C₂²×C₁₃	semidirect
206. #469	C₂²×C₁₃	semidirect
207. #466	C₂²×C₁₃	semidirect
208. #459	C₂²×C₁₃	semidirect
209. #447	C₂²×C₁₃	semidirect
210. #442	C₂²×C₁₃	semidirect
211. C₄×D₈	C₂²×C₁₃	semidirect
212. #433	C₂²×C₁₃	semidirect
213. #431	C₂²×C₁₃	semidirect
214. #424	C₂²×C₁₃	semidirect
216. C₄×M₁₆	C₂²×C₁₃	semidirect
217. C₂×C₄×C₈	C₂²×C₁₃	semidirect
340. C₁₃	#61011	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×#3508	2
C₁₃×#3259	2
C₁₃×#3228	2
C₁₃×#3205	2
C₁₃×#3199	2
C₁₃×#3184	2
C₁₃×#3169	2
C₁₃×#3122	2
C₁₃×#2922	2
#61011	13

Subgroups — C13×#61011 #15747350

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#61011 #15747350