Subgroups — C₁₃×#20571 #15706910

Order 3328.

826 conjugacy classes of subgroups.

The subgroup lattice has 344 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#446	C₂	1	1	yes	maximal, characteristic
2	C₂×C₈×Q₈×C₁₃	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#2295	C₂	1	1	yes	maximal, characteristic
4	C₁₃×#1771	C₂	1	2	yes	maximal
5	C₁₃×#1770	C₂	1	1	yes	maximal, characteristic
6	C₈×C₁₃×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic
7	C₈×C₁₃×C₄⋊C₄	C₂	1	2	yes	maximal
8	C₁₃×#1768	C₂	1	2	yes	maximal
9	C₄×C₁₃×C₄⋊C₈	C₂	1	1	yes	maximal, characteristic
10	C₁₃×#1746	C₂	1	2	yes	maximal
11	C₁₃×#1744	C₂	1	1	yes	maximal, characteristic
12	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
13	C₁₃×#446	C₄	1	8	yes	complemented
14	C₈×Q₈×C₁₃	C₄	1	8	yes	complemented
15	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
16	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
17	C₂×C₁₃×C₄⋊C₈	C₂²	1	2	yes	—
18	C₂×C₁₃×C₄⋊C₈	C₂²	1	2	yes	—
19	C₂×C₁₃×#97	C₂²	1	2	yes	—
20	C₂×C₁₃×#97	C₂²	1	2	yes	—
21	C₂×C₄×C₈×C₁₃	C₂²	1	2	yes	—
22	C₂×C₄×C₈×C₁₃	C₂²	1	2	yes	—
23	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
24	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
25	C₂×C₄×C₈×C₁₃	C₂²	1	2	yes	—
26	C₁₃×#391	C₄	1	2	yes	—
27	C₁₃×#389	C₄	1	2	yes	—
28	C₁₃×#387	C₄	1	4	yes	—
29	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
30	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
31	C₁₃×#376	C₂²	1	2	yes	—
32	C₄³×C₁₃	C₂²	1	1	yes	characteristic
33	C₁₃×#336	C₂²	1	1	yes	characteristic
34	C₁₃×#336	C₂²	1	1	yes	characteristic
35	C₁₃×#336	C₂²	1	1	yes	characteristic
36	C₁₃×#336	C₂²	1	1	yes	characteristic
37	C₁₃×#336	C₂²	1	2	yes	—
38	C₁₃×#336	C₂²	1	2	yes	—
39	C₁₃×#336	C₂²	1	2	yes	—
40	C₂²×Q₈×C₁₃	C₂×C₄	1	1	yes	characteristic
41	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
42	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
43	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
44	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
45	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
46	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
47	C₄×Q₈×C₁₃	C₂×C₄	1	4	yes	—
48	C₄×Q₈×C₁₃	C₂×C₄	1	4	yes	—
49	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	4	yes	—
50	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	2	yes	—
51	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	2	yes	—
52	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
53	C₂×C₄²×C₁₃	C₂×C₄	1	2	yes	—
54	C₂×C₄²×C₁₃	C₂×C₄	1	2	yes	—
55	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
56	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
57	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
58	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
59	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
60	C₁₃×C₄⋊C₈	C₂×C₄	1	4	yes	—
61	C₁₃×C₄⋊C₈	C₂×C₄	1	8	yes	—
62	C₁₃×C₄⋊C₈	C₂×C₄	1	4	yes	—
63	C₁₃×C₄⋊C₈	C₂×C₄	1	8	yes	—
64	C₁₃×#97	—	4	2	no	—
65	C₁₃×#97	C₂×C₄	1	8	yes	—
66	C₄×C₈×C₁₃	—	4	2	no	—
67	C₄×C₈×C₁₃	—	4	2	no	—
68	C₄×C₈×C₁₃	C₂×C₄	1	4	yes	—
69	C₄×C₈×C₁₃	C₂×C₄	1	8	yes	—
70	C₄×C₈×C₁₃	C₂×C₄	1	4	yes	—
71	C₁₃×#95	C₂×C₄	1	2	yes	—
72	C₁₃×#95	C₂×C₄	1	4	yes	—
73	C₁₃×#95	C₂×C₄	1	4	yes	—
74	C₁₃×#95	C₂×C₄	1	4	yes	—
75	#20571	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
76	C₂×Q₈×C₁₃	—	2	4	no	—
77	C₂×Q₈×C₁₃	C₄²	1	4	yes	—
78	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
79	C₂²×C₄×C₁₃	C₂²×C₄	1	4	yes	—
80	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
81	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
82	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
83	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
84	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
85	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
86	C₂×C₈×C₁₃	—	2	2	no	—
87	C₂×C₈×C₁₃	—	2	1	no	—
88	C₂×C₈×C₁₃	—	2	2	no	—
89	C₂×C₈×C₁₃	—	2	1	no	—
90	C₂×C₈×C₁₃	—	2	1	no	—
91	C₂×C₈×C₁₃	—	2	1	no	—
92	C₂×C₈×C₁₃	—	2	1	no	—
93	C₂×C₈×C₁₃	—	2	1	no	—
94	C₂×C₈×C₁₃	—	2	2	no	—
95	C₂×C₈×C₁₃	—	2	1	no	—
96	C₂×C₈×C₁₃	—	2	2	no	—
97	C₂×C₈×C₁₃	—	2	1	no	—
98	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
99	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
100	C₂×C₈×C₁₃	C₂²×C₄	1	4	yes	—
101	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
102	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
103	C₂×C₈×C₁₃	C₂²×C₄	1	4	yes	—
104	C₁₃×C₄⋊C₄	—	2	8	no	—
105	C₁₃×C₄⋊C₄	—	2	4	no	—
106	C₁₃×C₄⋊C₄	C₄²	1	8	yes	—
107	C₁₃×C₄⋊C₄	C₄²	1	4	yes	—
108	C₄²×C₁₃	—	2	4	no	—
109	C₄²×C₁₃	—	2	4	no	—
110	C₄²×C₁₃	—	2	1	no	—
111	C₄²×C₁₃	—	2	2	no	—
112	C₄²×C₁₃	—	2	1	no	—
113	C₄²×C₁₃	—	2	1	no	—
114	C₄²×C₁₃	—	2	1	no	—
115	C₄²×C₁₃	—	2	2	no	—
116	C₄²×C₁₃	C₂²×C₄	1	4	yes	—
117	C₄²×C₁₃	C₂²×C₄	1	2	yes	—
118	C₄²×C₁₃	C₂²×C₄	1	2	yes	—
119	C₄²×C₁₃	C₂²×C₄	1	4	yes	—
120	C₂×#446	C₂×C₁₃	1	1	yes	characteristic
121	C₂×C₈×Q₈	C₂×C₁₃	1	1	yes	characteristic
122	#2295	C₂×C₁₃	1	1	yes	characteristic
123	#1771	C₂×C₁₃	1	2	yes	—
124	#1770	C₂×C₁₃	1	1	yes	characteristic
125	C₈×C₄⋊C₄	C₂×C₁₃	1	2	yes	—
126	C₈×C₄⋊C₄	C₂×C₁₃	1	1	yes	characteristic
127	#1768	C₂×C₁₃	1	2	yes	—
128	C₄×C₄⋊C₈	C₂×C₁₃	1	1	yes	characteristic
129	#1746	C₂×C₁₃	1	2	yes	—
130	#1744	C₂×C₁₃	1	1	yes	characteristic
131	C₂³×C₁₃	C₂³×C₄	1	1	yes	characteristic
132	Q₈×C₁₃	—	2	8	no	—
133	C₂×C₄×C₁₃	—	2	2	no	—
134	C₂×C₄×C₁₃	—	2	2	no	—
135	C₂×C₄×C₁₃	—	2	2	no	—
136	C₂×C₄×C₁₃	—	2	4	no	—
137	C₂×C₄×C₁₃	—	2	4	no	—
138	C₂×C₄×C₁₃	—	2	2	no	—
139	C₂×C₄×C₁₃	—	2	4	no	—
140	C₂×C₄×C₁₃	—	2	2	no	—
141	C₂×C₄×C₁₃	—	2	2	no	—
142	C₂×C₄×C₁₃	—	2	4	no	—
143	C₂×C₄×C₁₃	—	2	4	no	—
144	C₂×C₄×C₁₃	C₂×C₄²	1	2	yes	—
145	C₂×C₄×C₁₃	C₂×C₄²	1	4	yes	—
146	C₂×C₄×C₁₃	C₂×C₄²	1	4	yes	—
147	C₂×C₄×C₁₃	C₂×C₄²	1	2	yes	—
148	C₂×C₄×C₁₃	#131	1	4	yes	—
149	C₂×C₄×C₁₃	#131	1	4	yes	—
150	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
151	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
152	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
153	C₂×C₄×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
154	C₂×C₄×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
155	C₂×C₄×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
156	C₈×C₁₃	—	2	2	no	—
157	C₈×C₁₃	—	2	2	no	—
158	C₈×C₁₃	—	2	4	no	—
159	C₈×C₁₃	—	2	2	no	—
160	C₈×C₁₃	—	2	4	no	—
161	C₈×C₁₃	—	2	2	no	—
162	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
163	#446	C₄×C₁₃	1	8	yes	complemented
164	C₈×Q₈	C₄×C₁₃	1	8	yes	complemented
165	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
166	C₂×C₄⋊C₈	C₂²×C₁₃	1	2	yes	—
167	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
168	C₂×C₄⋊C₈	C₂²×C₁₃	1	2	yes	—
169	C₂×#97	C₂²×C₁₃	1	2	yes	—
170	C₂×#97	C₂²×C₁₃	1	2	yes	—
171	C₂×C₄×C₈	C₂²×C₁₃	1	2	yes	—
172	C₂×C₄×C₈	C₂²×C₁₃	1	2	yes	—
173	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
174	C₂×C₄×C₈	C₂²×C₁₃	1	2	yes	—
175	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
176	#391	C₄×C₁₃	1	2	yes	—
177	#389	C₄×C₁₃	1	2	yes	—
178	#387	C₄×C₁₃	1	4	yes	—
179	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
180	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
181	#376	C₂²×C₁₃	1	2	yes	—
182	C₄³	C₂²×C₁₃	1	1	yes	characteristic
183	#336	C₂²×C₁₃	1	1	yes	characteristic
184	#336	C₂²×C₁₃	1	1	yes	characteristic
185	#336	C₂²×C₁₃	1	1	yes	characteristic
186	#336	C₂²×C₁₃	1	1	yes	characteristic
187	#336	C₂²×C₁₃	1	2	yes	—
188	#336	C₂²×C₁₃	1	2	yes	—
189	#336	C₂²×C₁₃	1	2	yes	—
190	C₂²×C₁₃	C₂²×C₄²	1	1	yes	characteristic
191	C₂²×C₁₃	#519	1	1	yes	characteristic
192	C₂²×C₁₃	#520	1	1	yes	characteristic
193	C₂²×C₁₃	C₂×#131	1	2	yes	—
194	C₂²×C₁₃	C₂×#131	1	2	yes	—
195	C₄×C₁₃	—	2	4	no	—
196	C₄×C₁₃	—	2	2	no	—
197	C₄×C₁₃	—	2	4	no	—
198	C₄×C₁₃	—	2	4	no	—
199	C₄×C₁₃	—	4	2	no	—
200	C₄×C₁₃	—	4	4	no	—
201	C₄×C₁₃	#405	1	4	yes	—
202	C₄×C₁₃	#519	1	1	yes	characteristic
203	C₄×C₁₃	#519	1	1	yes	characteristic
204	C₄×C₁₃	#520	1	1	yes	characteristic
205	C₄×C₁₃	#520	1	1	yes	characteristic
206	C₂²×Q₈	C₂×C₄×C₁₃	1	1	yes	characteristic
207	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
208	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
209	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
210	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
211	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
212	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
213	C₄×Q₈	C₂×C₄×C₁₃	1	4	yes	—
214	C₄×Q₈	C₂×C₄×C₁₃	1	4	yes	—
215	C₂×C₄⋊C₄	C₂×C₄×C₁₃	1	4	yes	—
216	C₂×C₄⋊C₄	C₂×C₄×C₁₃	1	2	yes	—
217	C₂×C₄⋊C₄	C₂×C₄×C₁₃	1	2	yes	—
218	C₂×C₄⋊C₄	C₂×C₄×C₁₃	1	1	yes	characteristic
219	C₂×C₄²	C₂×C₄×C₁₃	1	2	yes	—
220	C₂×C₄²	C₂×C₄×C₁₃	1	2	yes	—
221	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
222	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
223	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
224	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
225	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
226	C₄⋊C₈	C₂×C₄×C₁₃	1	4	yes	—
227	C₄⋊C₈	C₂×C₄×C₁₃	1	8	yes	—
228	C₄⋊C₈	C₂×C₄×C₁₃	1	4	yes	—
229	C₄⋊C₈	C₂×C₄×C₁₃	1	8	yes	—
230	#97	—	4	2	no	—
231	#97	C₂×C₄×C₁₃	1	8	yes	—
232	C₄×C₈	—	4	2	no	—
233	C₄×C₈	—	4	2	no	—
234	C₄×C₈	C₂×C₄×C₁₃	1	4	yes	—
235	C₄×C₈	C₂×C₄×C₁₃	1	8	yes	—
236	C₄×C₈	C₂×C₄×C₁₃	1	4	yes	—
237	#95	C₂×C₄×C₁₃	1	4	yes	—
238	#95	C₂×C₄×C₁₃	1	4	yes	—
239	#95	C₂×C₄×C₁₃	1	2	yes	—
240	#95	C₂×C₄×C₁₃	1	4	yes	—
241	C₂×C₁₃	#2276	1	1	yes	characteristic
242	C₂×C₁₃	C₂×#405	1	1	yes	characteristic
243	C₂×C₁₃	C₄×#131	1	1	yes	characteristic
244	C₂×C₁₃	#2986	1	2	yes	—
245	C₂×C₁₃	#2994	1	2	yes	—
246	C₂×Q₈	—	2	4	no	—
247	C₂×Q₈	C₄²×C₁₃	1	4	yes	—
248	C₂²×C₄	C₂²×C₄×C₁₃	1	2	yes	—
249	C₂²×C₄	C₂²×C₄×C₁₃	1	4	yes	—
250	C₂²×C₄	C₂²×C₄×C₁₃	1	2	yes	—
251	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
252	C₂²×C₄	C₂²×C₄×C₁₃	1	2	yes	—
253	C₂²×C₄	C₂²×C₄×C₁₃	1	2	yes	—
254	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
255	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
256	C₂×C₈	—	2	2	no	—
257	C₂×C₈	—	2	1	no	—
258	C₂×C₈	—	2	2	no	—
259	C₂×C₈	—	2	1	no	—
260	C₂×C₈	—	2	1	no	—
261	C₂×C₈	—	2	1	no	—
262	C₂×C₈	—	2	1	no	—
263	C₂×C₈	—	2	1	no	—
264	C₂×C₈	—	2	1	no	—
265	C₂×C₈	—	2	2	no	—
266	C₂×C₈	—	2	2	no	—
267	C₂×C₈	—	2	1	no	—
268	C₂×C₈	C₂²×C₄×C₁₃	1	2	yes	—
269	C₂×C₈	C₂²×C₄×C₁₃	1	2	yes	—
270	C₂×C₈	C₂²×C₄×C₁₃	1	4	yes	—
271	C₂×C₈	C₂²×C₄×C₁₃	1	2	yes	—
272	C₂×C₈	C₂²×C₄×C₁₃	1	2	yes	—
273	C₂×C₈	C₂²×C₄×C₁₃	1	4	yes	—
274	C₄⋊C₄	—	2	8	no	—
275	C₄⋊C₄	—	2	4	no	—
276	C₄⋊C₄	C₄²×C₁₃	1	8	yes	—
277	C₄⋊C₄	C₄²×C₁₃	1	4	yes	—
278	C₄²	—	2	4	no	—
279	C₄²	—	2	4	no	—
280	C₄²	—	2	1	no	—
281	C₄²	—	2	2	no	—
282	C₄²	—	2	1	no	—
283	C₄²	—	2	1	no	—
284	C₄²	—	2	1	no	—
285	C₄²	—	2	2	no	—
286	C₄²	C₂²×C₄×C₁₃	1	4	yes	—
287	C₄²	C₂²×C₄×C₁₃	1	2	yes	—
288	C₄²	C₂²×C₄×C₁₃	1	2	yes	—
289	C₄²	C₂²×C₄×C₁₃	1	4	yes	—
290	C₁₃	#20571	1	1	yes	characteristic, direct product factor, Sylow
291	C₂³	C₂³×C₄×C₁₃	1	1	yes	characteristic
292	Q₈	—	2	8	no	—
293	C₂×C₄	—	2	2	no	—
294	C₂×C₄	—	2	2	no	—
295	C₂×C₄	—	2	2	no	—
296	C₂×C₄	—	2	4	no	—
297	C₂×C₄	—	2	4	no	—
298	C₂×C₄	—	2	2	no	—
299	C₂×C₄	—	2	4	no	—
300	C₂×C₄	—	2	2	no	—
301	C₂×C₄	—	2	2	no	—
302	C₂×C₄	—	2	4	no	—
303	C₂×C₄	—	2	4	no	—
304	C₂×C₄	C₂×C₄²×C₁₃	1	2	yes	—
305	C₂×C₄	C₂×C₄²×C₁₃	1	4	yes	—
306	C₂×C₄	C₂×C₄²×C₁₃	1	4	yes	—
307	C₂×C₄	C₂×C₄²×C₁₃	1	2	yes	—
308	C₂×C₄	C₁₃×#131	1	4	yes	—
309	C₂×C₄	C₁₃×#131	1	4	yes	—
310	C₂×C₄	C₂³×C₄×C₁₃	1	1	yes	characteristic
311	C₂×C₄	C₂³×C₄×C₁₃	1	1	yes	characteristic
312	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
313	C₂×C₄	C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
314	C₂×C₄	C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
315	C₂×C₄	C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
316	C₈	—	2	2	no	—
317	C₈	—	2	2	no	—
318	C₈	—	2	4	no	—
319	C₈	—	2	2	no	—
320	C₈	—	2	4	no	—
321	C₈	—	2	2	no	—
322	C₂²	C₂²×C₄²×C₁₃	1	1	yes	characteristic
323	C₂²	C₁₃×#519	1	1	yes	characteristic
324	C₂²	C₁₃×#520	1	1	yes	characteristic
325	C₂²	C₂×C₁₃×#131	1	2	yes	—
326	C₂²	C₂×C₁₃×#131	1	2	yes	—
327	C₄	—	2	4	no	—
328	C₄	—	2	2	no	—
329	C₄	—	2	4	no	—
330	C₄	—	2	4	no	—
331	C₄	—	4	2	no	—
332	C₄	—	4	4	no	—
333	C₄	C₁₃×#405	1	4	yes	—
334	C₄	C₁₃×#519	1	1	yes	characteristic
335	C₄	C₁₃×#519	1	1	yes	characteristic
336	C₄	C₁₃×#520	1	1	yes	characteristic
337	C₄	C₁₃×#520	1	1	yes	characteristic
338	C₂	C₁₃×#2276	1	1	yes	characteristic
339	C₂	C₂×C₁₃×#405	1	1	yes	characteristic
340	C₂	C₄×C₁₃×#131	1	1	yes	characteristic
341	C₂	C₁₃×#2986	1	2	yes	—
342	C₂	C₁₃×#2994	1	2	yes	—

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

Complements

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

N	H ≅ G/N	type
13. C₁₃×#446	C₄	semidirect
14. C₈×Q₈×C₁₃	C₄	semidirect
75. #20571	C₁₃	direct (N × H)
163. #446	C₄×C₁₃	semidirect
164. C₈×Q₈	C₄×C₁₃	semidirect
290. C₁₃	#20571	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×#446	2
C₂×C₈×Q₈×C₁₃	2
C₁₃×#2295	2
C₁₃×#1771	2
C₁₃×#1770	2
C₈×C₁₃×C₄⋊C₄	2
C₁₃×#1768	2
C₄×C₁₃×C₄⋊C₈	2
C₁₃×#1746	2
C₁₃×#1744	2
#20571	13

Subgroups — C13×#20571 #15706910

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#20571 #15706910