Subgroups — C₁₃×#20492 #15706831

Order 3328.

1122 conjugacy classes of subgroups.

The subgroup lattice has 358 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#435	C₂	1	2	yes	maximal
2	C₂×C₁₃×#405	C₂	1	2	yes	maximal, complemented
3	C₁₃×#2293	C₂	1	1	yes	maximal, characteristic
4	C₁₃×#1771	C₂	1	2	yes	maximal, complemented
5	C₄×C₁₃×C₄⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#1753	C₂	1	2	yes	maximal, complemented
7	C₈×C₁₃×C₂²⋊C₄	C₂	1	2	yes	maximal, complemented
8	C₁₃×#1750	C₂	1	2	yes	maximal, complemented
9	C₄×C₁₃×#97	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂²×C₁₃×M₁₆	C₂²	1	2	yes	—
11	C₂³×C₈×C₁₃	C₂²	1	2	yes	—
12	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
13	C₂×C₁₃×#117	C₂²	1	2	yes	—
14	C₁₃×#435	C₄	1	16	yes	complemented
15	C₂×C₁₃×C₄⋊C₈	C₂²	1	2	yes	—
16	C₂×C₁₃×C₂²⋊C₈	C₂²	1	2	yes	—
17	C₂×C₁₃×C₂²⋊C₈	C₂²	1	2	yes	—
18	C₁₃×#405	—	2	8	no	—
19	C₂×C₁₃×#97	C₂²	1	1	yes	characteristic
20	C₂×C₁₃×#97	C₂²	1	2	yes	—
21	C₂×C₁₃×#97	C₂²	1	2	yes	—
22	C₂×C₁₃×#97	C₂²	1	1	yes	characteristic
23	C₂×C₄×C₈×C₁₃	C₂²	1	2	yes	—
24	C₂×C₄×C₈×C₁₃	C₂²	1	2	yes	—
25	C₂×C₄×C₈×C₁₃	C₂²	1	2	yes	—
26	C₁₃×#390	C₄	1	2	yes	—
27	C₁₃×#389	C₄	1	2	yes	—
28	C₁₃×#388	C₄	1	4	yes	—
29	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
30	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
31	C₄³×C₁₃	C₂²	1	1	yes	characteristic
32	C₁₃×#336	C₂²	1	2	yes	—
33	C₁₃×#336	C₂²	1	2	yes	—
34	C₁₃×#336	C₂²	1	1	yes	characteristic
35	C₁₃×#336	C₂²	1	1	yes	characteristic
36	C₂²×D₄×C₁₃	C₂×C₄	1	1	yes	characteristic
37	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
38	C₂×C₁₃×M₁₆	—	2	4	no	—
39	C₂×C₁₃×M₁₆	—	2	4	no	—
40	C₂×C₁₃×M₁₆	C₂×C₄	1	8	yes	—
41	C₂²×C₈×C₁₃	—	2	4	no	—
42	C₂²×C₈×C₁₃	—	2	4	no	—
43	C₂²×C₈×C₁₃	C₂×C₄	1	8	yes	—
44	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
45	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
46	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
47	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
48	C₄×D₄×C₁₃	C₂×C₄	1	8	yes	—
49	C₁₃×#117	—	2	4	no	—
50	C₁₃×#117	—	2	4	no	—
51	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	4	yes	—
52	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	2	yes	—
53	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
54	C₂×C₁₃×C₂²⋊C₄	C₂×C₄	1	4	yes	—
55	C₂×C₁₃×C₂²⋊C₄	C₂×C₄	1	4	yes	—
56	C₂×C₁₃×C₂²⋊C₄	C₂×C₄	1	2	yes	—
57	C₂×C₄²×C₁₃	C₂×C₄	1	2	yes	—
58	C₂×C₄²×C₁₃	C₂×C₄	1	2	yes	—
59	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
60	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
61	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
62	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
63	C₁₃×C₄⋊C₈	C₂×C₄	1	8	yes	—
64	C₁₃×C₂²⋊C₈	C₂×C₄	1	8	yes	—
65	C₁₃×C₂²⋊C₈	C₂×C₄	1	8	yes	—
66	C₁₃×#97	—	2	4	no	—
67	C₁₃×#97	—	2	2	no	—
68	C₁₃×#97	C₂×C₄	1	8	yes	—
69	C₁₃×#97	D₄	1	4	yes	complemented
70	C₄×C₈×C₁₃	—	2	4	no	—
71	C₄×C₈×C₁₃	—	2	4	no	—
72	C₄×C₈×C₁₃	—	2	4	no	—
73	C₁₃×#95	C₂×C₄	1	4	yes	—
74	C₁₃×#95	C₂×C₄	1	2	yes	—
75	#20492	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
76	C₂⁴×C₁₃	C₂²×C₄	1	2	yes	—
77	C₂×D₄×C₁₃	—	4	2	no	—
78	C₂×D₄×C₁₃	C₄²	1	4	yes	—
79	C₂²×C₄×C₁₃	—	2	2	no	—
80	C₂²×C₄×C₁₃	—	2	2	no	—
81	C₂²×C₄×C₁₃	—	2	2	no	—
82	C₂²×C₄×C₁₃	—	2	2	no	—
83	C₂²×C₄×C₁₃	C₂²×C₄	1	4	yes	—
84	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
85	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
86	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
87	C₂²×C₄×C₁₃	C₂²×C₄	1	4	yes	—
88	C₂²×C₄×C₁₃	C₂²×C₄	1	4	yes	—
89	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
90	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
91	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
92	C₁₃×M₁₆	—	2	16	no	—
93	C₂×C₈×C₁₃	—	2	2	no	—
94	C₂×C₈×C₁₃	—	2	2	no	—
95	C₂×C₈×C₁₃	—	2	2	no	—
96	C₂×C₈×C₁₃	—	2	2	no	—
97	C₂×C₈×C₁₃	—	2	2	no	—
98	C₂×C₈×C₁₃	—	2	2	no	—
99	C₂×C₈×C₁₃	—	2	16	no	—
100	C₂×C₈×C₁₃	C₂²×C₄	1	4	yes	—
101	C₂×C₈×C₁₃	C₂²×C₄	1	4	yes	—
102	C₂×C₈×C₁₃	C₂²×C₄	1	4	yes	—
103	C₂×C₈×C₁₃	C₂²×C₄	1	4	yes	—
104	C₂×C₈×C₁₃	C₂×D₄	1	4	yes	—
105	C₂×C₈×C₁₃	#41	1	4	yes	—
106	C₁₃×C₄⋊C₄	—	2	8	no	—
107	C₁₃×C₄⋊C₄	—	4	2	no	—
108	C₁₃×C₄⋊C₄	C₄²	1	4	yes	—
109	C₁₃×C₂²⋊C₄	—	2	8	no	—
110	C₁₃×C₂²⋊C₄	—	2	8	no	—
111	C₁₃×C₂²⋊C₄	C₄²	1	8	yes	—
112	C₄²×C₁₃	—	2	4	no	—
113	C₄²×C₁₃	—	2	2	no	—
114	C₄²×C₁₃	—	2	2	no	—
115	C₄²×C₁₃	—	2	2	no	—
116	C₄²×C₁₃	—	4	2	no	—
117	C₄²×C₁₃	C₂²×C₄	1	4	yes	—
118	C₄²×C₁₃	C₂×D₄	1	2	yes	—
119	C₄²×C₁₃	#41	1	2	yes	—
120	C₂×#435	C₂×C₁₃	1	2	yes	—
121	C₂×#405	C₂×C₁₃	1	2	yes	complemented
122	#2293	C₂×C₁₃	1	1	yes	characteristic
123	#1771	C₂×C₁₃	1	2	yes	complemented
124	C₄×C₄⋊C₈	C₂×C₁₃	1	1	yes	characteristic, complemented
125	#1753	C₂×C₁₃	1	2	yes	complemented
126	C₈×C₂²⋊C₄	C₂×C₁₃	1	2	yes	complemented
127	#1750	C₂×C₁₃	1	2	yes	complemented
128	C₄×#97	C₂×C₁₃	1	1	yes	characteristic, complemented
129	C₂³×C₁₃	—	2	2	no	—
130	C₂³×C₁₃	—	2	2	no	—
131	C₂³×C₁₃	—	2	4	no	—
132	C₂³×C₁₃	—	2	4	no	—
133	C₂³×C₁₃	C₂×C₄²	1	4	yes	—
134	C₂³×C₁₃	C₂³×C₄	1	1	yes	characteristic
135	D₄×C₁₃	—	4	4	no	—
136	C₂×C₄×C₁₃	—	2	2	no	—
137	C₂×C₄×C₁₃	—	2	2	no	—
138	C₂×C₄×C₁₃	—	2	2	no	—
139	C₂×C₄×C₁₃	—	2	2	no	—
140	C₂×C₄×C₁₃	—	2	2	no	—
141	C₂×C₄×C₁₃	—	2	2	no	—
142	C₂×C₄×C₁₃	—	2	2	no	—
143	C₂×C₄×C₁₃	—	2	2	no	—
144	C₂×C₄×C₁₃	—	2	4	no	—
145	C₂×C₄×C₁₃	—	2	4	no	—
146	C₂×C₄×C₁₃	—	2	4	no	—
147	C₂×C₄×C₁₃	—	2	4	no	—
148	C₂×C₄×C₁₃	—	2	4	no	—
149	C₂×C₄×C₁₃	—	2	4	no	—
150	C₂×C₄×C₁₃	—	2	4	no	—
151	C₂×C₄×C₁₃	C₂×C₄²	1	2	yes	—
152	C₂×C₄×C₁₃	C₂×C₄²	1	2	yes	—
153	C₂×C₄×C₁₃	C₂×C₄²	1	4	yes	—
154	C₂×C₄×C₁₃	C₄×D₄	1	4	yes	—
155	C₂×C₄×C₁₃	#131	1	4	yes	—
156	C₂×C₄×C₁₃	C₂³×C₄	1	2	yes	—
157	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
158	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
159	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
160	C₈×C₁₃	—	2	4	no	—
161	C₈×C₁₃	—	2	4	no	—
162	C₈×C₁₃	—	2	4	no	—
163	C₈×C₁₃	C₄×D₄	1	8	yes	—
164	C₂²×M₁₆	C₂²×C₁₃	1	2	yes	—
165	C₂³×C₈	C₂²×C₁₃	1	2	yes	—
166	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
167	C₂×#117	C₂²×C₁₃	1	2	yes	—
168	#435	C₄×C₁₃	1	16	yes	complemented
169	C₂×C₄⋊C₈	C₂²×C₁₃	1	2	yes	—
170	C₂×C₂²⋊C₈	C₂²×C₁₃	1	2	yes	—
171	C₂×C₂²⋊C₈	C₂²×C₁₃	1	2	yes	—
172	#405	—	2	8	no	—
173	C₂×#97	C₂²×C₁₃	1	2	yes	—
174	C₂×#97	C₂²×C₁₃	1	1	yes	characteristic
175	C₂×#97	C₂²×C₁₃	1	2	yes	—
176	C₂×#97	C₂²×C₁₃	1	1	yes	characteristic
177	C₂×C₄×C₈	C₂²×C₁₃	1	2	yes	—
178	C₂×C₄×C₈	C₂²×C₁₃	1	2	yes	—
179	C₂×C₄×C₈	C₂²×C₁₃	1	2	yes	—
180	#390	C₄×C₁₃	1	2	yes	—
181	#389	C₄×C₁₃	1	2	yes	—
182	#388	C₄×C₁₃	1	4	yes	—
183	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
184	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
185	C₄³	C₂²×C₁₃	1	1	yes	characteristic
186	#336	C₂²×C₁₃	1	2	yes	—
187	#336	C₂²×C₁₃	1	2	yes	—
188	#336	C₂²×C₁₃	1	1	yes	characteristic
189	#336	C₂²×C₁₃	1	1	yes	characteristic
190	C₂²×C₁₃	—	2	4	no	—
191	C₂²×C₁₃	—	2	4	no	—
192	C₂²×C₁₃	—	2	4	no	—
193	C₂²×C₁₃	—	4	4	no	—
194	C₂²×C₁₃	—	4	4	no	—
195	C₂²×C₁₃	C₂²×C₄²	1	1	yes	characteristic
196	C₂²×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
197	C₂²×C₁₃	C₄×#41	1	1	yes	characteristic
198	C₂²×C₁₃	C₂×#131	1	2	yes	—
199	C₂²×C₁₃	#568	1	2	yes	—
200	C₄×C₁₃	—	2	2	no	—
201	C₄×C₁₃	—	2	2	no	—
202	C₄×C₁₃	—	2	4	no	—
203	C₄×C₁₃	—	2	4	no	—
204	C₄×C₁₃	—	2	4	no	—
205	C₄×C₁₃	—	4	4	no	—
206	C₄×C₁₃	C₂×C₄×D₄	1	2	yes	—
207	C₄×C₁₃	C₄×#41	1	2	yes	—
208	C₂²×D₄	C₂×C₄×C₁₃	1	1	yes	characteristic
209	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
210	C₂×M₁₆	—	2	4	no	—
211	C₂×M₁₆	—	2	4	no	—
212	C₂×M₁₆	C₂×C₄×C₁₃	1	8	yes	—
213	C₂²×C₈	—	2	4	no	—
214	C₂²×C₈	—	2	4	no	—
215	C₂²×C₈	C₂×C₄×C₁₃	1	8	yes	—
216	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
217	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
218	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
219	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
220	C₄×D₄	C₂×C₄×C₁₃	1	8	yes	—
221	#117	—	2	4	no	—
222	#117	—	2	4	no	—
223	C₂×C₄⋊C₄	C₂×C₄×C₁₃	1	4	yes	—
224	C₂×C₄⋊C₄	C₂×C₄×C₁₃	1	2	yes	—
225	C₂×C₄⋊C₄	C₂×C₄×C₁₃	1	1	yes	characteristic
226	C₂×C₂²⋊C₄	C₂×C₄×C₁₃	1	4	yes	—
227	C₂×C₂²⋊C₄	C₂×C₄×C₁₃	1	4	yes	—
228	C₂×C₂²⋊C₄	C₂×C₄×C₁₃	1	2	yes	—
229	C₂×C₄²	C₂×C₄×C₁₃	1	2	yes	—
230	C₂×C₄²	C₂×C₄×C₁₃	1	2	yes	—
231	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
232	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
233	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
234	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
235	C₄⋊C₈	C₂×C₄×C₁₃	1	8	yes	—
236	C₂²⋊C₈	C₂×C₄×C₁₃	1	8	yes	—
237	C₂²⋊C₈	C₂×C₄×C₁₃	1	8	yes	—
238	#97	—	2	4	no	—
239	#97	—	2	2	no	—
240	#97	C₂×C₄×C₁₃	1	8	yes	—
241	#97	D₄×C₁₃	1	4	yes	complemented
242	C₄×C₈	—	2	4	no	—
243	C₄×C₈	—	2	4	no	—
244	C₄×C₈	—	2	4	no	—
245	#95	C₂×C₄×C₁₃	1	4	yes	—
246	#95	C₂×C₄×C₁₃	1	2	yes	—
247	C₂×C₁₃	—	4	4	no	—
248	C₂×C₁₃	C₄²×D₄	1	1	yes	characteristic
249	C₂×C₁₃	#2873	1	1	yes	characteristic
250	C₂×C₁₃	C₄×#131	1	1	yes	characteristic
251	C₂×C₁₃	#2935	1	2	yes	—
252	C₂×C₁₃	#2968	1	2	yes	—
253	C₂⁴	C₂²×C₄×C₁₃	1	2	yes	—
254	C₂×D₄	—	4	2	no	—
255	C₂×D₄	C₄²×C₁₃	1	4	yes	—
256	C₂²×C₄	—	2	2	no	—
257	C₂²×C₄	—	2	2	no	—
258	C₂²×C₄	—	2	2	no	—
259	C₂²×C₄	—	2	2	no	—
260	C₂²×C₄	C₂²×C₄×C₁₃	1	4	yes	—
261	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
262	C₂²×C₄	C₂²×C₄×C₁₃	1	2	yes	—
263	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
264	C₂²×C₄	C₂²×C₄×C₁₃	1	4	yes	—
265	C₂²×C₄	C₂²×C₄×C₁₃	1	4	yes	—
266	C₂²×C₄	C₂²×C₄×C₁₃	1	2	yes	—
267	C₂²×C₄	C₂²×C₄×C₁₃	1	2	yes	—
268	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
269	M₁₆	—	2	16	no	—
270	C₂×C₈	—	2	2	no	—
271	C₂×C₈	—	2	2	no	—
272	C₂×C₈	—	2	2	no	—
273	C₂×C₈	—	2	2	no	—
274	C₂×C₈	—	2	2	no	—
275	C₂×C₈	—	2	2	no	—
276	C₂×C₈	—	2	16	no	—
277	C₂×C₈	C₂²×C₄×C₁₃	1	4	yes	—
278	C₂×C₈	C₂²×C₄×C₁₃	1	4	yes	—
279	C₂×C₈	C₂²×C₄×C₁₃	1	4	yes	—
280	C₂×C₈	C₂²×C₄×C₁₃	1	4	yes	—
281	C₂×C₈	C₂×D₄×C₁₃	1	4	yes	—
282	C₂×C₈	C₁₃×#41	1	4	yes	—
283	C₄⋊C₄	—	2	8	no	—
284	C₄⋊C₄	—	4	2	no	—
285	C₄⋊C₄	C₄²×C₁₃	1	4	yes	—
286	C₂²⋊C₄	—	2	8	no	—
287	C₂²⋊C₄	—	2	8	no	—
288	C₂²⋊C₄	C₄²×C₁₃	1	8	yes	—
289	C₄²	—	2	4	no	—
290	C₄²	—	2	2	no	—
291	C₄²	—	2	2	no	—
292	C₄²	—	2	2	no	—
293	C₄²	—	4	2	no	—
294	C₄²	C₂²×C₄×C₁₃	1	4	yes	—
295	C₄²	C₂×D₄×C₁₃	1	2	yes	—
296	C₄²	C₁₃×#41	1	2	yes	—
297	C₁₃	#20492	1	1	yes	characteristic, direct product factor, Sylow
298	C₂³	—	2	2	no	—
299	C₂³	—	2	2	no	—
300	C₂³	—	2	4	no	—
301	C₂³	—	2	4	no	—
302	C₂³	C₂×C₄²×C₁₃	1	4	yes	—
303	C₂³	C₂³×C₄×C₁₃	1	1	yes	characteristic
304	D₄	—	4	4	no	—
305	C₂×C₄	—	2	2	no	—
306	C₂×C₄	—	2	2	no	—
307	C₂×C₄	—	2	2	no	—
308	C₂×C₄	—	2	2	no	—
309	C₂×C₄	—	2	2	no	—
310	C₂×C₄	—	2	2	no	—
311	C₂×C₄	—	2	2	no	—
312	C₂×C₄	—	2	2	no	—
313	C₂×C₄	—	2	4	no	—
314	C₂×C₄	—	2	4	no	—
315	C₂×C₄	—	2	4	no	—
316	C₂×C₄	—	2	4	no	—
317	C₂×C₄	—	2	4	no	—
318	C₂×C₄	—	2	4	no	—
319	C₂×C₄	—	2	4	no	—
320	C₂×C₄	C₂×C₄²×C₁₃	1	2	yes	—
321	C₂×C₄	C₂×C₄²×C₁₃	1	2	yes	—
322	C₂×C₄	C₂×C₄²×C₁₃	1	4	yes	—
323	C₂×C₄	C₄×D₄×C₁₃	1	4	yes	—
324	C₂×C₄	C₁₃×#131	1	4	yes	—
325	C₂×C₄	C₂³×C₄×C₁₃	1	2	yes	—
326	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
327	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
328	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
329	C₈	—	2	4	no	—
330	C₈	—	2	4	no	—
331	C₈	—	2	4	no	—
332	C₈	C₄×D₄×C₁₃	1	8	yes	—
333	C₂²	—	2	4	no	—
334	C₂²	—	2	4	no	—
335	C₂²	—	2	4	no	—
336	C₂²	—	4	4	no	—
337	C₂²	—	4	4	no	—
338	C₂²	C₂²×C₄²×C₁₃	1	1	yes	characteristic
339	C₂²	C₂×C₄×D₄×C₁₃	1	1	yes	characteristic
340	C₂²	C₄×C₁₃×#41	1	1	yes	characteristic
341	C₂²	C₂×C₁₃×#131	1	2	yes	—
342	C₂²	C₁₃×#568	1	2	yes	—
343	C₄	—	2	4	no	—
344	C₄	—	2	2	no	—
345	C₄	—	2	2	no	—
346	C₄	—	2	4	no	—
347	C₄	—	2	4	no	—
348	C₄	—	4	4	no	—
349	C₄	C₂×C₄×D₄×C₁₃	1	2	yes	—
350	C₄	C₄×C₁₃×#41	1	2	yes	—
351	C₂	—	4	4	no	—
352	C₂	C₄²×D₄×C₁₃	1	1	yes	characteristic
353	C₂	C₁₃×#2873	1	1	yes	characteristic
354	C₂	C₄×C₁₃×#131	1	1	yes	characteristic
355	C₂	C₁₃×#2935	1	2	yes	—
356	C₂	C₁₃×#2968	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄×C₁₃	C₂⁴
commutator	C₂²	C₂²×C₄²×C₁₃
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
socle	C₂³×C₁₃	C₂³×C₄
prime radical	C₂²×D₄×C₁₃	C₂×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
2. C₂×C₁₃×#405	C₂	semidirect
4. C₁₃×#1771	C₂	semidirect
5. C₄×C₁₃×C₄⋊C₈	C₂	semidirect
6. C₁₃×#1753	C₂	semidirect
7. C₈×C₁₃×C₂²⋊C₄	C₂	semidirect
8. C₁₃×#1750	C₂	semidirect
9. C₄×C₁₃×#97	C₂	semidirect
14. C₁₃×#435	C₄	semidirect
69. C₁₃×#97	D₄	semidirect
75. #20492	C₁₃	direct (N × H)
121. C₂×#405	C₂×C₁₃	semidirect
123. #1771	C₂×C₁₃	semidirect
124. C₄×C₄⋊C₈	C₂×C₁₃	semidirect
125. #1753	C₂×C₁₃	semidirect
126. C₈×C₂²⋊C₄	C₂×C₁₃	semidirect
127. #1750	C₂×C₁₃	semidirect
128. C₄×#97	C₂×C₁₃	semidirect
168. #435	C₄×C₁₃	semidirect
241. #97	D₄×C₁₃	semidirect
297. C₁₃	#20492	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×#435	2
C₂×C₁₃×#405	2
C₁₃×#2293	2
C₁₃×#1771	2
C₄×C₁₃×C₄⋊C₈	2
C₁₃×#1753	2
C₈×C₁₃×C₂²⋊C₄	2
C₁₃×#1750	2
C₄×C₁₃×#97	2
#20492	13

Subgroups — C13×#20492 #15706831

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#20492 #15706831