Subgroups — C₁₃×#60868 #15747207

Order 3328.

1754 conjugacy classes of subgroups.

The subgroup lattice has 386 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3458	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₃×#540	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#3241	C₂	1	16	yes	maximal, complemented
4	C₁₃×#3166	C₂	1	2	yes	maximal, complemented
5	C₁₃×#3138	C₂	1	2	yes	maximal, complemented
6	C₁₃×#3094	C₂	1	4	yes	maximal, complemented
7	C₁₃×#3077	C₂	1	4	yes	maximal, complemented
8	C₁₃×#2921	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#544	—	2	2	no	—
10	C₁₃×#544	C₂²	1	8	yes	complemented
11	C₁₃×#543	—	2	2	no	—
12	C₁₃×#540	—	2	4	no	—
13	C₁₃×#540	C₂²	1	8	yes	—
14	C₁₃×#533	—	2	4	no	—
15	C₁₃×#533	C₂²	1	2	yes	—
16	C₁₃×#533	C₂²	1	2	yes	—
17	C₂×C₁₃×#127	C₂²	1	1	yes	characteristic
18	C₂×C₁₃×#125	C₂²	1	1	yes	characteristic
19	C₂×C₁₃×#123	—	2	2	no	—
20	C₂×C₁₃×#121	—	2	2	no	—
21	C₂×C₁₃×#121	C₂²	1	2	yes	—
22	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
23	C₂×C₁₃×#117	C₂²	1	2	yes	—
24	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
25	C₁₃×#501	C₂²	1	8	yes	complemented
26	C₁₃×#499	C₂²	1	8	yes	complemented
27	C₁₃×#490	C₂²	1	8	yes	complemented
28	C₁₃×#486	C₂²	1	8	yes	complemented
29	C₁₃×#482	C₂²	1	16	yes	complemented
30	C₁₃×#481	C₂²	1	8	yes	complemented
31	C₁₃×#480	C₂²	1	8	yes	complemented
32	C₁₃×#478	C₂²	1	16	yes	complemented
33	C₁₃×#476	C₂²	1	8	yes	complemented
34	C₁₃×#474	C₂²	1	8	yes	complemented
35	C₁₃×#433	C₂²	1	8	yes	complemented
36	C₁₃×#428	C₂²	1	8	yes	—
37	C₁₃×#423	C₂²	1	2	yes	—
38	C₁₃×#418	C₂²	1	8	yes	—
39	C₁₃×#407	C₂²	1	2	yes	—
40	C₄×C₁₃×M₁₆	C₂²	1	2	yes	—
41	C₂²×D₄×C₁₃	—	2	2	no	—
42	C₂²×D₄×C₁₃	—	2	2	no	—
43	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
44	C₂³×C₄×C₁₃	—	2	2	no	—
45	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
46	C₂×C₁₃×M₁₆	C₂³	1	4	yes	—
47	C₁₃×C₄⋊Q₈	—	2	8	no	—
48	C₁₃×C₄⋊Q₈	C₂³	1	4	yes	—
49	C₁₃×C₄⋊Q₈	C₂³	1	4	yes	—
50	C₁₃×#127	—	2	2	no	—
51	C₁₃×#127	C₂³	1	4	yes	—
52	C₁₃×#125	—	2	8	no	—
53	C₁₃×#125	—	2	2	no	—
54	C₁₃×#125	C₂³	1	4	yes	—
55	C₁₃×#125	C₂³	1	4	yes	—
56	C₁₃×#125	C₂³	1	4	yes	—
57	C₁₃×#123	—	2	16	no	—
58	C₁₃×C₂²⋊Q₈	—	2	4	no	—
59	C₁₃×C₂²⋊Q₈	—	2	4	no	—
60	C₁₃×C₂²⋊Q₈	—	2	8	no	—
61	C₁₃×C₂²⋊Q₈	—	2	8	no	—
62	C₁₃×#121	—	2	4	no	—
63	C₁₃×#121	—	2	16	no	—
64	C₁₃×#121	C₂³	1	8	yes	—
65	C₄×Q₈×C₁₃	—	2	4	no	—
66	C₄×Q₈×C₁₃	—	2	4	no	—
67	C₄×D₄×C₁₃	—	2	4	no	—
68	C₄×D₄×C₁₃	C₂³	1	8	yes	—
69	C₁₃×#117	—	2	2	no	—
70	C₁₃×#117	—	2	2	no	—
71	C₁₃×#117	D₄	1	4	yes	—
72	C₁₃×#117	C₂³	1	4	yes	—
73	C₁₃×#117	C₂³	1	4	yes	—
74	C₁₃×#117	C₂³	1	4	yes	—
75	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
76	C₂×C₁₃×C₄⋊C₄	D₄	1	2	yes	—
77	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
78	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
79	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
80	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
81	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
82	C₂×C₁₃×C₂²⋊C₄	D₄	1	2	yes	—
83	C₂×C₄²×C₁₃	—	2	2	no	—
84	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
85	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
86	C₁₃×#107	C₂³	1	16	yes	—
87	C₁₃×#106	C₂³	1	16	yes	—
88	C₁₃×C₄⋊C₈	C₂³	1	8	yes	—
89	C₁₃×#102	C₂³	1	16	yes	—
90	C₁₃×#102	C₂³	1	16	yes	—
91	C₁₃×C₂²⋊C₈	C₂³	1	8	yes	—
92	C₁₃×#97	C₂³	1	4	yes	—
93	C₄×C₈×C₁₃	C₂³	1	4	yes	—
94	#60868	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
95	C₂⁴×C₁₃	—	2	2	no	—
96	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
97	C₂×Q₈×C₁₃	—	2	4	no	—
98	C₂×Q₈×C₁₃	—	2	4	no	—
99	C₂×D₄×C₁₃	—	2	8	no	—
100	C₂×D₄×C₁₃	—	2	2	no	—
101	C₂×D₄×C₁₃	—	2	8	no	—
102	C₂×D₄×C₁₃	—	2	8	no	—
103	C₂×D₄×C₁₃	—	8	4	no	—
104	C₂×D₄×C₁₃	—	8	4	no	—
105	C₂×D₄×C₁₃	C₂⁴	1	4	yes	—
106	C₂²×C₄×C₁₃	—	2	4	no	—
107	C₂²×C₄×C₁₃	—	2	2	no	—
108	C₂²×C₄×C₁₃	—	2	4	no	—
109	C₂²×C₄×C₁₃	—	2	8	no	—
110	C₂²×C₄×C₁₃	—	8	4	no	—
111	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
112	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
113	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
114	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
115	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
116	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
117	C₁₃×M₁₆	—	2	8	no	—
118	C₂×C₈×C₁₃	C₂⁴	1	8	yes	—
119	C₁₃×C₄⋊C₄	—	2	8	no	—
120	C₁₃×C₄⋊C₄	—	2	4	no	—
121	C₁₃×C₄⋊C₄	—	2	2	no	—
122	C₁₃×C₄⋊C₄	—	2	4	no	—
123	C₁₃×C₄⋊C₄	—	2	4	no	—
124	C₁₃×C₄⋊C₄	—	2	8	no	—
125	C₁₃×C₄⋊C₄	—	2	8	no	—
126	C₁₃×C₄⋊C₄	C₂×D₄	1	8	yes	—
127	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
128	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
129	C₁₃×C₂²⋊C₄	—	2	4	no	—
130	C₁₃×C₂²⋊C₄	—	2	4	no	—
131	C₁₃×C₂²⋊C₄	—	2	8	no	—
132	C₁₃×C₂²⋊C₄	—	2	8	no	—
133	C₁₃×C₂²⋊C₄	C₂×D₄	1	8	yes	—
134	C₄²×C₁₃	—	2	4	no	—
135	C₄²×C₁₃	—	2	4	no	—
136	C₄²×C₁₃	C₂×D₄	1	2	yes	—
137	C₄²×C₁₃	C₂×D₄	1	2	yes	—
138	C₄²×C₁₃	C₂⁴	1	2	yes	—
139	C₄²×C₁₃	C₂⁴	1	2	yes	—
140	#3458	C₂×C₁₃	1	1	yes	characteristic, complemented
141	C₂×#540	C₂×C₁₃	1	1	yes	characteristic
142	#3241	C₂×C₁₃	1	16	yes	complemented
143	#3166	C₂×C₁₃	1	2	yes	complemented
144	#3138	C₂×C₁₃	1	2	yes	complemented
145	#3094	C₂×C₁₃	1	4	yes	complemented
146	#3077	C₂×C₁₃	1	4	yes	complemented
147	#2921	C₂×C₁₃	1	1	yes	characteristic, complemented
148	C₂³×C₁₃	—	2	2	no	—
149	C₂³×C₁₃	—	2	4	no	—
150	C₂³×C₁₃	—	4	2	no	—
151	C₂³×C₁₃	—	4	4	no	—
152	C₂³×C₁₃	—	4	4	no	—
153	C₂³×C₁₃	—	4	4	no	—
154	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
155	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
156	Q₈×C₁₃	—	8	4	no	—
157	Q₈×C₁₃	—	8	4	no	—
158	D₄×C₁₃	—	2	8	no	—
159	D₄×C₁₃	—	4	4	no	—
160	D₄×C₁₃	—	8	8	no	—
161	D₄×C₁₃	—	8	8	no	—
162	C₂×C₄×C₁₃	—	2	2	no	—
163	C₂×C₄×C₁₃	—	2	4	no	—
164	C₂×C₄×C₁₃	—	2	4	no	—
165	C₂×C₄×C₁₃	—	2	8	no	—
166	C₂×C₄×C₁₃	—	2	4	no	—
167	C₂×C₄×C₁₃	—	4	2	no	—
168	C₂×C₄×C₁₃	—	4	2	no	—
169	C₂×C₄×C₁₃	—	4	4	no	—
170	C₂×C₄×C₁₃	—	8	8	no	—
171	C₂×C₄×C₁₃	—	8	4	no	—
172	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
173	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
174	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
175	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
176	C₂×C₄×C₁₃	2₋¹⁺⁴	1	4	yes	—
177	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
178	C₈×C₁₃	—	2	8	no	—
179	#544	—	2	2	no	—
180	#544	C₂²×C₁₃	1	8	yes	complemented
181	#543	—	2	2	no	—
182	#540	—	2	4	no	—
183	#540	C₂²×C₁₃	1	8	yes	—
184	#533	—	2	4	no	—
185	#533	C₂²×C₁₃	1	2	yes	—
186	#533	C₂²×C₁₃	1	2	yes	—
187	C₂×#127	C₂²×C₁₃	1	1	yes	characteristic
188	C₂×#125	C₂²×C₁₃	1	1	yes	characteristic
189	C₂×#123	—	2	2	no	—
190	C₂×#121	—	2	2	no	—
191	C₂×#121	C₂²×C₁₃	1	2	yes	—
192	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
193	C₂×#117	C₂²×C₁₃	1	2	yes	—
194	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
195	#501	C₂²×C₁₃	1	8	yes	complemented
196	#499	C₂²×C₁₃	1	8	yes	complemented
197	#490	C₂²×C₁₃	1	8	yes	complemented
198	#486	C₂²×C₁₃	1	8	yes	complemented
199	#482	C₂²×C₁₃	1	16	yes	complemented
200	#481	C₂²×C₁₃	1	8	yes	complemented
201	#480	C₂²×C₁₃	1	8	yes	complemented
202	#478	C₂²×C₁₃	1	16	yes	complemented
203	#476	C₂²×C₁₃	1	8	yes	complemented
204	#474	C₂²×C₁₃	1	8	yes	complemented
205	#433	C₂²×C₁₃	1	8	yes	complemented
206	#428	C₂²×C₁₃	1	8	yes	—
207	#423	C₂²×C₁₃	1	2	yes	—
208	#418	C₂²×C₁₃	1	8	yes	—
209	#407	C₂²×C₁₃	1	2	yes	—
210	C₄×M₁₆	C₂²×C₁₃	1	2	yes	—
211	C₂²×C₁₃	—	2	2	no	—
212	C₂²×C₁₃	—	2	4	no	—
213	C₂²×C₁₃	—	2	2	no	—
214	C₂²×C₁₃	—	4	4	no	—
215	C₂²×C₁₃	—	4	4	no	—
216	C₂²×C₁₃	—	4	4	no	—
217	C₂²×C₁₃	—	8	2	no	—
218	C₂²×C₁₃	—	8	8	no	—
219	C₂²×C₁₃	#536	1	2	yes	—
220	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
221	C₄×C₁₃	—	2	4	no	—
222	C₄×C₁₃	—	2	4	no	—
223	C₄×C₁₃	—	2	2	no	—
224	C₄×C₁₃	—	4	4	no	—
225	C₄×C₁₃	—	4	8	no	—
226	C₄×C₁₃	#536	1	2	yes	—
227	C₄×C₁₃	C₂×2₋¹⁺⁴	1	2	yes	—
228	C₂²×D₄	—	2	2	no	—
229	C₂²×D₄	—	2	2	no	—
230	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
231	C₂³×C₄	—	2	2	no	—
232	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
233	C₂×M₁₆	C₂³×C₁₃	1	4	yes	—
234	C₄⋊Q₈	—	2	8	no	—
235	C₄⋊Q₈	C₂³×C₁₃	1	4	yes	—
236	C₄⋊Q₈	C₂³×C₁₃	1	4	yes	—
237	#127	—	2	2	no	—
238	#127	C₂³×C₁₃	1	4	yes	—
239	#125	—	2	8	no	—
240	#125	—	2	2	no	—
241	#125	C₂³×C₁₃	1	4	yes	—
242	#125	C₂³×C₁₃	1	4	yes	—
243	#125	C₂³×C₁₃	1	4	yes	—
244	#123	—	2	16	no	—
245	C₂²⋊Q₈	—	2	4	no	—
246	C₂²⋊Q₈	—	2	4	no	—
247	C₂²⋊Q₈	—	2	8	no	—
248	C₂²⋊Q₈	—	2	8	no	—
249	#121	—	2	4	no	—
250	#121	—	2	16	no	—
251	#121	C₂³×C₁₃	1	8	yes	—
252	C₄×Q₈	—	2	4	no	—
253	C₄×Q₈	—	2	4	no	—
254	C₄×D₄	—	2	4	no	—
255	C₄×D₄	C₂³×C₁₃	1	8	yes	—
256	#117	—	2	2	no	—
257	#117	—	2	2	no	—
258	#117	D₄×C₁₃	1	4	yes	—
259	#117	C₂³×C₁₃	1	4	yes	—
260	#117	C₂³×C₁₃	1	4	yes	—
261	#117	C₂³×C₁₃	1	4	yes	—
262	C₂×C₄⋊C₄	—	2	2	no	—
263	C₂×C₄⋊C₄	D₄×C₁₃	1	2	yes	—
264	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
265	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
266	C₂×C₂²⋊C₄	—	2	2	no	—
267	C₂×C₂²⋊C₄	—	2	2	no	—
268	C₂×C₂²⋊C₄	—	2	2	no	—
269	C₂×C₂²⋊C₄	D₄×C₁₃	1	2	yes	—
270	C₂×C₄²	—	2	2	no	—
271	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
272	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
273	#107	C₂³×C₁₃	1	16	yes	—
274	#106	C₂³×C₁₃	1	16	yes	—
275	C₄⋊C₈	C₂³×C₁₃	1	8	yes	—
276	#102	C₂³×C₁₃	1	16	yes	—
277	#102	C₂³×C₁₃	1	16	yes	—
278	C₂²⋊C₈	C₂³×C₁₃	1	8	yes	—
279	#97	C₂³×C₁₃	1	4	yes	—
280	C₄×C₈	C₂³×C₁₃	1	4	yes	—
281	C₂×C₁₃	—	2	2	no	—
282	C₂×C₁₃	—	4	2	no	—
283	C₂×C₁₃	—	8	4	no	—
284	C₂×C₁₃	C₂×#536	1	1	yes	characteristic
285	C₂×C₁₃	#3585	1	2	yes	—
286	C₂⁴	—	2	2	no	—
287	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
288	C₂×Q₈	—	2	4	no	—
289	C₂×Q₈	—	2	4	no	—
290	C₂×D₄	—	2	8	no	—
291	C₂×D₄	—	2	2	no	—
292	C₂×D₄	—	2	8	no	—
293	C₂×D₄	—	2	8	no	—
294	C₂×D₄	—	8	4	no	—
295	C₂×D₄	—	8	4	no	—
296	C₂×D₄	C₂⁴×C₁₃	1	4	yes	—
297	C₂²×C₄	—	2	4	no	—
298	C₂²×C₄	—	2	2	no	—
299	C₂²×C₄	—	2	4	no	—
300	C₂²×C₄	—	2	8	no	—
301	C₂²×C₄	—	8	4	no	—
302	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
303	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
304	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
305	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
306	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
307	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
308	M₁₆	—	2	8	no	—
309	C₂×C₈	C₂⁴×C₁₃	1	8	yes	—
310	C₄⋊C₄	—	2	8	no	—
311	C₄⋊C₄	—	2	4	no	—
312	C₄⋊C₄	—	2	2	no	—
313	C₄⋊C₄	—	2	4	no	—
314	C₄⋊C₄	—	2	4	no	—
315	C₄⋊C₄	—	2	8	no	—
316	C₄⋊C₄	—	2	8	no	—
317	C₄⋊C₄	C₂×D₄×C₁₃	1	8	yes	—
318	C₄⋊C₄	C₂⁴×C₁₃	1	8	yes	—
319	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
320	C₂²⋊C₄	—	2	4	no	—
321	C₂²⋊C₄	—	2	4	no	—
322	C₂²⋊C₄	—	2	8	no	—
323	C₂²⋊C₄	—	2	8	no	—
324	C₂²⋊C₄	C₂×D₄×C₁₃	1	8	yes	—
325	C₄²	—	2	4	no	—
326	C₄²	—	2	4	no	—
327	C₄²	C₂×D₄×C₁₃	1	2	yes	—
328	C₄²	C₂×D₄×C₁₃	1	2	yes	—
329	C₄²	C₂⁴×C₁₃	1	2	yes	—
330	C₄²	C₂⁴×C₁₃	1	2	yes	—
331	C₁₃	#60868	1	1	yes	characteristic, direct product factor, Sylow
332	C₂³	—	2	2	no	—
333	C₂³	—	2	4	no	—
334	C₂³	—	4	2	no	—
335	C₂³	—	4	4	no	—
336	C₂³	—	4	4	no	—
337	C₂³	—	4	4	no	—
338	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
339	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
340	Q₈	—	8	4	no	—
341	Q₈	—	8	4	no	—
342	D₄	—	2	8	no	—
343	D₄	—	4	4	no	—
344	D₄	—	8	8	no	—
345	D₄	—	8	8	no	—
346	C₂×C₄	—	2	2	no	—
347	C₂×C₄	—	2	4	no	—
348	C₂×C₄	—	2	4	no	—
349	C₂×C₄	—	2	8	no	—
350	C₂×C₄	—	2	4	no	—
351	C₂×C₄	—	4	2	no	—
352	C₂×C₄	—	4	2	no	—
353	C₂×C₄	—	4	4	no	—
354	C₂×C₄	—	8	8	no	—
355	C₂×C₄	—	8	4	no	—
356	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
357	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
358	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
359	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
360	C₂×C₄	C₁₃×2₋¹⁺⁴	1	4	yes	—
361	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
362	C₈	—	2	8	no	—
363	C₂²	—	2	2	no	—
364	C₂²	—	2	4	no	—
365	C₂²	—	2	2	no	—
366	C₂²	—	4	4	no	—
367	C₂²	—	4	4	no	—
368	C₂²	—	4	4	no	—
369	C₂²	—	8	2	no	—
370	C₂²	—	8	8	no	—
371	C₂²	C₁₃×#536	1	2	yes	—
372	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
373	C₄	—	2	4	no	—
374	C₄	—	2	4	no	—
375	C₄	—	2	2	no	—
376	C₄	—	4	4	no	—
377	C₄	—	4	8	no	—
378	C₄	C₁₃×#536	1	2	yes	—
379	C₄	C₂×C₁₃×2₋¹⁺⁴	1	2	yes	—
380	C₂	—	2	2	no	—
381	C₂	—	4	2	no	—
382	C₂	—	8	4	no	—
383	C₂	C₂×C₁₃×#536	1	1	yes	characteristic
384	C₂	C₁₃×#3585	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₃
prime radical	C₂×C₁₃×#540	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₂×C₁₃×#117 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₃×#3458	C₂	semidirect
3. C₁₃×#3241	C₂	semidirect
4. C₁₃×#3166	C₂	semidirect
5. C₁₃×#3138	C₂	semidirect
6. C₁₃×#3094	C₂	semidirect
7. C₁₃×#3077	C₂	semidirect
8. C₁₃×#2921	C₂	semidirect
10. C₁₃×#544	C₂²	semidirect
25. C₁₃×#501	C₂²	semidirect
26. C₁₃×#499	C₂²	semidirect
27. C₁₃×#490	C₂²	semidirect
28. C₁₃×#486	C₂²	semidirect
29. C₁₃×#482	C₂²	semidirect
30. C₁₃×#481	C₂²	semidirect
31. C₁₃×#480	C₂²	semidirect
32. C₁₃×#478	C₂²	semidirect
33. C₁₃×#476	C₂²	semidirect
34. C₁₃×#474	C₂²	semidirect
35. C₁₃×#433	C₂²	semidirect
94. #60868	C₁₃	direct (N × H)
140. #3458	C₂×C₁₃	semidirect
142. #3241	C₂×C₁₃	semidirect
143. #3166	C₂×C₁₃	semidirect
144. #3138	C₂×C₁₃	semidirect
145. #3094	C₂×C₁₃	semidirect
146. #3077	C₂×C₁₃	semidirect
147. #2921	C₂×C₁₃	semidirect
180. #544	C₂²×C₁₃	semidirect
195. #501	C₂²×C₁₃	semidirect
196. #499	C₂²×C₁₃	semidirect
197. #490	C₂²×C₁₃	semidirect
198. #486	C₂²×C₁₃	semidirect
199. #482	C₂²×C₁₃	semidirect
200. #481	C₂²×C₁₃	semidirect
201. #480	C₂²×C₁₃	semidirect
202. #478	C₂²×C₁₃	semidirect
203. #476	C₂²×C₁₃	semidirect
204. #474	C₂²×C₁₃	semidirect
205. #433	C₂²×C₁₃	semidirect
331. C₁₃	#60868	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×#3458	2
C₂×C₁₃×#540	2
C₁₃×#3241	2
C₁₃×#3166	2
C₁₃×#3138	2
C₁₃×#3094	2
C₁₃×#3077	2
C₁₃×#2921	2
#60868	13

Subgroups — C13×#60868 #15747207

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#60868 #15747207