Subgroups — C₁₃×#33507 #15719846

Order 3328.

492 conjugacy classes of subgroups.

The subgroup lattice has 340 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#2966	C₂	1	1	yes	maximal, characteristic
2	C₁₃×#2183	C₂	1	1	yes	maximal, characteristic, complemented
3	Q₈×C₁₃×C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#2169	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#2169	C₂	1	2	yes	maximal, complemented
6	C₁₃×#2168	C₂	1	2	yes	maximal, complemented
7	D₄×C₁₃×C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#2164	C₂	1	2	yes	maximal, complemented
9	C₁₃×#2162	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#2151	C₂	1	2	yes	maximal, complemented
11	C₁₃×#2150	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#529	C₄	1	1	yes	characteristic
13	C₂×C₁₃×M₃₂	C₂²	1	2	yes	—
14	C₂×C₁₃×M₃₂	C₂²	1	2	yes	—
15	C₂²×C₁₃×C₁₆	C₂²	1	2	yes	—
16	C₁₃×#446	C₄	1	1	yes	characteristic
17	C₈×Q₈×C₁₃	C₂²	1	1	yes	characteristic
18	C₁₃×#436	C₄	1	1	yes	characteristic
19	C₁₃×#435	C₄	1	2	yes	—
20	C₈×D₄×C₁₃	C₂²	1	1	yes	characteristic
21	C₈×D₄×C₁₃	C₂²	1	2	yes	—
22	C₁₃×#433	C₄	1	2	yes	—
23	C₁₃×#432	C₄	1	1	yes	characteristic
24	C₁₃×#405	C₂²	1	2	yes	—
25	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
26	C₁₃×C₄⋊C₁₆	C₂²	1	2	yes	—
27	C₁₃×C₄⋊C₁₆	C₂²	1	1	yes	characteristic
28	C₁₃×C₄⋊C₁₆	C₂²	1	1	yes	characteristic
29	C₁₃×C₄⋊C₁₆	C₂²	1	1	yes	characteristic
30	C₁₃×C₄⋊C₁₆	C₂²	1	2	yes	—
31	C₁₃×C₄⋊C₁₆	C₂²	1	2	yes	—
32	C₁₃×C₄⋊C₁₆	C₂²	1	1	yes	characteristic
33	C₁₃×C₂²⋊C₁₆	C₂²	1	1	yes	characteristic
34	C₁₃×C₂²⋊C₁₆	C₂²	1	1	yes	characteristic
35	C₁₃×C₂²⋊C₁₆	C₂²	1	2	yes	—
36	C₁₃×C₂²⋊C₁₆	C₂²	1	2	yes	—
37	C₁₃×#346	C₂²	1	2	yes	—
38	C₄×C₁₃×C₁₆	C₂²	1	1	yes	characteristic
39	C₄×C₁₃×C₁₆	C₂²	1	1	yes	characteristic
40	C₄×C₁₃×C₁₆	C₂²	1	2	yes	—
41	C₂×C₁₃×M₁₆	C₂×C₄	1	2	yes	—
42	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
43	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
44	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
45	C₁₃×#126	C₈	1	2	yes	—
46	C₁₃×#125	C₈	1	1	yes	characteristic
47	C₁₃×#124	C₈	1	1	yes	characteristic
48	C₁₃×#123	C₈	1	2	yes	—
49	C₁₃×C₂²⋊Q₈	C₈	1	1	yes	characteristic
50	C₁₃×#121	C₈	1	1	yes	characteristic
51	C₄×Q₈×C₁₃	C₂×C₄	1	1	yes	characteristic
52	C₄×D₄×C₁₃	C₂×C₄	1	2	yes	—
53	C₄×D₄×C₁₃	C₂×C₄	1	1	yes	characteristic
54	C₁₃×#117	C₂×C₄	1	2	yes	—
55	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
56	C₁₃×M₃₂	—	4	2	no	—
57	C₁₃×M₃₂	—	4	2	no	—
58	C₂×C₁₃×C₁₆	—	4	2	no	—
59	C₂×C₁₃×C₁₆	C₂³	1	1	yes	characteristic
60	C₂×C₁₃×C₁₆	C₂³	1	1	yes	characteristic
61	C₂×C₁₃×C₁₆	C₂³	1	1	yes	characteristic
62	C₂×C₁₃×C₁₆	C₂³	1	1	yes	characteristic
63	C₂×C₁₃×C₁₆	C₂³	1	2	yes	—
64	C₂×C₁₃×C₁₆	C₂³	1	2	yes	—
65	C₁₃×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
66	C₁₃×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
67	C₁₃×C₄⋊C₈	C₂×C₄	1	2	yes	—
68	C₁₃×C₄⋊C₈	C₂×C₄	1	2	yes	—
69	C₁₃×C₂²⋊C₈	C₂×C₄	1	2	yes	—
70	C₁₃×C₂²⋊C₈	C₂×C₄	1	2	yes	—
71	C₁₃×C₂²⋊C₈	C₂×C₄	1	2	yes	—
72	C₁₃×#97	C₂×C₄	1	2	yes	—
73	C₁₃×#97	C₂×C₄	1	2	yes	—
74	C₄×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
75	C₄×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
76	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
77	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
78	C₄×C₈×C₁₃	C₂³	1	2	yes	—
79	#33507	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
80	C₂×Q₈×C₁₃	C₂×C₈	1	1	yes	characteristic
81	C₂×D₄×C₁₃	C₂×C₈	1	1	yes	characteristic
82	C₂×D₄×C₁₃	C₂×C₈	1	2	yes	—
83	C₂²×C₄×C₁₃	C₂×C₈	1	1	yes	characteristic
84	C₂²×C₄×C₁₃	C₂×C₈	1	1	yes	characteristic
85	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
86	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
87	C₁₃×M₁₆	—	4	2	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	2	no	—
92	C₂×C₈×C₁₃	—	4	1	no	—
93	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
94	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
95	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
96	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
97	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
98	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
99	C₁₃×C₄⋊C₄	C₂×C₈	1	2	yes	—
100	C₁₃×C₄⋊C₄	C₂×C₈	1	2	yes	—
101	C₁₃×C₄⋊C₄	C₂×C₈	1	1	yes	characteristic
102	C₁₃×C₄⋊C₄	C₂×C₈	1	2	yes	—
103	C₁₃×C₄⋊C₄	C₂×C₈	1	1	yes	characteristic
104	C₁₃×C₄⋊C₄	C₂×C₈	1	2	yes	—
105	C₁₃×C₂²⋊C₄	C₂×C₈	1	2	yes	—
106	C₁₃×C₂²⋊C₄	C₂×C₈	1	2	yes	—
107	C₁₃×C₂²⋊C₄	C₂×C₈	1	2	yes	—
108	C₁₃×C₂²⋊C₄	C₂×C₈	1	2	yes	—
109	C₁₃×C₂²⋊C₄	C₂×C₈	1	2	yes	—
110	C₄²×C₁₃	C₂×C₈	1	1	yes	characteristic
111	C₄²×C₁₃	C₂×C₈	1	1	yes	characteristic
112	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
113	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
114	C₄²×C₁₃	C₂²×C₄	1	2	yes	—
115	C₁₃×C₁₆	—	2	1	no	—
116	C₁₃×C₁₆	—	2	2	no	—
117	C₁₃×C₁₆	—	2	1	no	—
118	C₁₃×C₁₆	—	2	2	no	—
119	C₁₃×C₁₆	—	2	1	no	—
120	C₁₃×C₁₆	—	2	1	no	—
121	#2966	C₂×C₁₃	1	1	yes	characteristic
122	#2183	C₂×C₁₃	1	1	yes	characteristic, complemented
123	Q₈×C₁₆	C₂×C₁₃	1	1	yes	characteristic, complemented
124	#2169	C₂×C₁₃	1	1	yes	characteristic, complemented
125	#2169	C₂×C₁₃	1	2	yes	complemented
126	#2168	C₂×C₁₃	1	2	yes	complemented
127	D₄×C₁₆	C₂×C₁₃	1	1	yes	characteristic, complemented
128	#2164	C₂×C₁₃	1	2	yes	complemented
129	#2162	C₂×C₁₃	1	1	yes	characteristic, complemented
130	#2151	C₂×C₁₃	1	2	yes	complemented
131	#2150	C₂×C₁₃	1	1	yes	characteristic, complemented
132	C₂³×C₁₃	C₂²×C₈	1	2	yes	—
133	C₂³×C₁₃	C₂²×C₈	1	1	yes	characteristic
134	Q₈×C₁₃	—	2	2	no	—
135	D₄×C₁₃	—	2	2	no	—
136	D₄×C₁₃	—	4	2	no	—
137	C₂×C₄×C₁₃	—	2	2	no	—
138	C₂×C₄×C₁₃	—	2	1	no	—
139	C₂×C₄×C₁₃	—	2	1	no	—
140	C₂×C₄×C₁₃	—	2	2	no	—
141	C₂×C₄×C₁₃	—	2	2	no	—
142	C₂×C₄×C₁₃	—	4	1	no	—
143	C₂×C₄×C₁₃	C₂²×C₈	1	1	yes	characteristic
144	C₂×C₄×C₁₃	C₂²×C₈	1	1	yes	characteristic
145	C₂×C₄×C₁₃	C₂²×C₈	1	1	yes	characteristic
146	C₂×C₄×C₁₃	C₂²×C₈	1	1	yes	characteristic
147	C₂×C₄×C₁₃	C₂²×C₈	1	2	yes	—
148	C₂×C₄×C₁₃	C₂²×C₈	1	2	yes	—
149	C₂×C₄×C₁₃	C₂²×C₈	1	2	yes	—
150	C₂×C₄×C₁₃	C₂²×C₈	1	1	yes	characteristic
151	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
152	C₈×C₁₃	—	2	2	no	—
153	C₈×C₁₃	—	2	1	no	—
154	C₈×C₁₃	—	2	1	no	—
155	C₈×C₁₃	—	2	1	no	—
156	C₈×C₁₃	—	2	2	no	—
157	C₈×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
158	C₈×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
159	#529	C₄×C₁₃	1	1	yes	characteristic
160	C₂×M₃₂	C₂²×C₁₃	1	2	yes	—
161	C₂×M₃₂	C₂²×C₁₃	1	2	yes	—
162	C₂²×C₁₆	C₂²×C₁₃	1	2	yes	—
163	#446	C₄×C₁₃	1	1	yes	characteristic
164	C₈×Q₈	C₂²×C₁₃	1	1	yes	characteristic
165	#436	C₄×C₁₃	1	1	yes	characteristic
166	#435	C₄×C₁₃	1	2	yes	—
167	C₈×D₄	C₂²×C₁₃	1	1	yes	characteristic
168	C₈×D₄	C₂²×C₁₃	1	2	yes	—
169	#433	C₄×C₁₃	1	2	yes	—
170	#432	C₄×C₁₃	1	1	yes	characteristic
171	#405	C₂²×C₁₃	1	2	yes	—
172	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
173	C₄⋊C₁₆	C₂²×C₁₃	1	2	yes	—
174	C₄⋊C₁₆	C₂²×C₁₃	1	1	yes	characteristic
175	C₄⋊C₁₆	C₂²×C₁₃	1	1	yes	characteristic
176	C₄⋊C₁₆	C₂²×C₁₃	1	1	yes	characteristic
177	C₄⋊C₁₆	C₂²×C₁₃	1	2	yes	—
178	C₄⋊C₁₆	C₂²×C₁₃	1	2	yes	—
179	C₄⋊C₁₆	C₂²×C₁₃	1	1	yes	characteristic
180	C₂²⋊C₁₆	C₂²×C₁₃	1	1	yes	characteristic
181	C₂²⋊C₁₆	C₂²×C₁₃	1	1	yes	characteristic
182	C₂²⋊C₁₆	C₂²×C₁₃	1	2	yes	—
183	C₂²⋊C₁₆	C₂²×C₁₃	1	2	yes	—
184	#346	C₂²×C₁₃	1	2	yes	—
185	C₄×C₁₆	C₂²×C₁₃	1	1	yes	characteristic
186	C₄×C₁₆	C₂²×C₁₃	1	1	yes	characteristic
187	C₄×C₁₆	C₂²×C₁₃	1	2	yes	—
188	C₂²×C₁₃	—	2	1	no	—
189	C₂²×C₁₃	—	2	2	no	—
190	C₂²×C₁₃	—	2	1	no	—
191	C₂²×C₁₃	—	2	2	no	—
192	C₂²×C₁₃	—	2	1	no	—
193	C₂²×C₁₃	—	2	2	no	—
194	C₂²×C₁₃	C₂³×C₈	1	1	yes	characteristic
195	C₄×C₁₃	—	2	1	no	—
196	C₄×C₁₃	—	2	2	no	—
197	C₄×C₁₃	—	2	1	no	—
198	C₄×C₁₃	—	2	1	no	—
199	C₄×C₁₃	—	2	2	no	—
200	C₄×C₁₃	—	2	1	no	—
201	C₄×C₁₃	—	2	2	no	—
202	C₄×C₁₃	#504	1	2	yes	—
203	C₄×C₁₃	#520	1	1	yes	characteristic
204	C₄×C₁₃	#568	1	1	yes	characteristic
205	C₂×M₁₆	C₂×C₄×C₁₃	1	2	yes	—
206	C₂²×C₈	C₂×C₄×C₁₃	1	1	yes	characteristic
207	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
208	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
209	#126	C₈×C₁₃	1	2	yes	—
210	#125	C₈×C₁₃	1	1	yes	characteristic
211	#124	C₈×C₁₃	1	1	yes	characteristic
212	#123	C₈×C₁₃	1	2	yes	—
213	C₂²⋊Q₈	C₈×C₁₃	1	1	yes	characteristic
214	#121	C₈×C₁₃	1	1	yes	characteristic
215	C₄×Q₈	C₂×C₄×C₁₃	1	1	yes	characteristic
216	C₄×D₄	C₂×C₄×C₁₃	1	2	yes	—
217	C₄×D₄	C₂×C₄×C₁₃	1	1	yes	characteristic
218	#117	C₂×C₄×C₁₃	1	2	yes	—
219	C₂×C₄²	C₂×C₄×C₁₃	1	1	yes	characteristic
220	M₃₂	—	4	2	no	—
221	M₃₂	—	4	2	no	—
222	C₂×C₁₆	—	4	2	no	—
223	C₂×C₁₆	C₂³×C₁₃	1	1	yes	characteristic
224	C₂×C₁₆	C₂³×C₁₃	1	1	yes	characteristic
225	C₂×C₁₆	C₂³×C₁₃	1	1	yes	characteristic
226	C₂×C₁₆	C₂³×C₁₃	1	1	yes	characteristic
227	C₂×C₁₆	C₂³×C₁₃	1	2	yes	—
228	C₂×C₁₆	C₂³×C₁₃	1	2	yes	—
229	C₄⋊C₈	C₂×C₄×C₁₃	1	1	yes	characteristic
230	C₄⋊C₈	C₂×C₄×C₁₃	1	1	yes	characteristic
231	C₄⋊C₈	C₂×C₄×C₁₃	1	2	yes	—
232	C₄⋊C₈	C₂×C₄×C₁₃	1	2	yes	—
233	C₂²⋊C₈	C₂×C₄×C₁₃	1	2	yes	—
234	C₂²⋊C₈	C₂×C₄×C₁₃	1	2	yes	—
235	C₂²⋊C₈	C₂×C₄×C₁₃	1	2	yes	—
236	#97	C₂×C₄×C₁₃	1	2	yes	—
237	#97	C₂×C₄×C₁₃	1	2	yes	—
238	C₄×C₈	C₂×C₄×C₁₃	1	1	yes	characteristic
239	C₄×C₈	C₂×C₄×C₁₃	1	1	yes	characteristic
240	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
241	C₄×C₈	C₂³×C₁₃	1	2	yes	—
242	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
243	C₂×C₁₃	—	4	1	no	—
244	C₂×C₁₃	—	4	2	no	—
245	C₂×C₁₃	#2988	1	1	yes	characteristic
246	C₂×C₁₃	C₂×#504	1	1	yes	characteristic
247	C₂×C₁₃	#3407	1	1	yes	characteristic
248	C₂×Q₈	C₂×C₈×C₁₃	1	1	yes	characteristic
249	C₂×D₄	C₂×C₈×C₁₃	1	1	yes	characteristic
250	C₂×D₄	C₂×C₈×C₁₃	1	2	yes	—
251	C₂²×C₄	C₂×C₈×C₁₃	1	1	yes	characteristic
252	C₂²×C₄	C₂×C₈×C₁₃	1	1	yes	characteristic
253	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
254	C₂²×C₄	C₂²×C₄×C₁₃	1	2	yes	—
255	M₁₆	—	4	2	no	—
256	C₂×C₈	—	2	2	no	—
257	C₂×C₈	—	2	1	no	—
258	C₂×C₈	—	2	1	no	—
259	C₂×C₈	—	2	2	no	—
260	C₂×C₈	—	4	1	no	—
261	C₂×C₈	C₂²×C₄×C₁₃	1	1	yes	characteristic
262	C₂×C₈	C₂²×C₄×C₁₃	1	1	yes	characteristic
263	C₂×C₈	C₂²×C₄×C₁₃	1	1	yes	characteristic
264	C₂×C₈	C₂²×C₄×C₁₃	1	2	yes	—
265	C₂×C₈	C₂²×C₄×C₁₃	1	2	yes	—
266	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
267	C₄⋊C₄	C₂×C₈×C₁₃	1	2	yes	—
268	C₄⋊C₄	C₂×C₈×C₁₃	1	2	yes	—
269	C₄⋊C₄	C₂×C₈×C₁₃	1	1	yes	characteristic
270	C₄⋊C₄	C₂×C₈×C₁₃	1	2	yes	—
271	C₄⋊C₄	C₂×C₈×C₁₃	1	1	yes	characteristic
272	C₄⋊C₄	C₂×C₈×C₁₃	1	2	yes	—
273	C₂²⋊C₄	C₂×C₈×C₁₃	1	2	yes	—
274	C₂²⋊C₄	C₂×C₈×C₁₃	1	2	yes	—
275	C₂²⋊C₄	C₂×C₈×C₁₃	1	2	yes	—
276	C₂²⋊C₄	C₂×C₈×C₁₃	1	2	yes	—
277	C₂²⋊C₄	C₂×C₈×C₁₃	1	2	yes	—
278	C₄²	C₂×C₈×C₁₃	1	1	yes	characteristic
279	C₄²	C₂×C₈×C₁₃	1	1	yes	characteristic
280	C₄²	C₂²×C₄×C₁₃	1	1	yes	characteristic
281	C₄²	C₂²×C₄×C₁₃	1	1	yes	characteristic
282	C₄²	C₂²×C₄×C₁₃	1	2	yes	—
283	C₁₆	—	2	1	no	—
284	C₁₆	—	2	2	no	—
285	C₁₆	—	2	1	no	—
286	C₁₆	—	2	2	no	—
287	C₁₆	—	2	1	no	—
288	C₁₆	—	2	1	no	—
289	C₁₃	#33507	1	1	yes	characteristic, direct product factor, Sylow
290	C₂³	C₂²×C₈×C₁₃	1	2	yes	—
291	C₂³	C₂²×C₈×C₁₃	1	1	yes	characteristic
292	Q₈	—	2	2	no	—
293	D₄	—	2	2	no	—
294	D₄	—	4	2	no	—
295	C₂×C₄	—	2	2	no	—
296	C₂×C₄	—	2	2	no	—
297	C₂×C₄	—	2	1	no	—
298	C₂×C₄	—	2	1	no	—
299	C₂×C₄	—	2	2	no	—
300	C₂×C₄	—	4	1	no	—
301	C₂×C₄	C₂²×C₈×C₁₃	1	1	yes	characteristic
302	C₂×C₄	C₂²×C₈×C₁₃	1	1	yes	characteristic
303	C₂×C₄	C₂²×C₈×C₁₃	1	1	yes	characteristic
304	C₂×C₄	C₂²×C₈×C₁₃	1	1	yes	characteristic
305	C₂×C₄	C₂²×C₈×C₁₃	1	2	yes	—
306	C₂×C₄	C₂²×C₈×C₁₃	1	2	yes	—
307	C₂×C₄	C₂²×C₈×C₁₃	1	2	yes	—
308	C₂×C₄	C₂²×C₈×C₁₃	1	1	yes	characteristic
309	C₂×C₄	C₂³×C₄×C₁₃	1	1	yes	characteristic
310	C₈	—	2	2	no	—
311	C₈	—	2	1	no	—
312	C₈	—	2	1	no	—
313	C₈	—	2	1	no	—
314	C₈	—	2	2	no	—
315	C₈	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
316	C₈	C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
317	C₂²	—	2	1	no	—
318	C₂²	—	2	2	no	—
319	C₂²	—	2	1	no	—
320	C₂²	—	2	2	no	—
321	C₂²	—	2	1	no	—
322	C₂²	—	2	2	no	—
323	C₂²	C₂³×C₈×C₁₃	1	1	yes	characteristic
324	C₄	—	2	1	no	—
325	C₄	—	2	2	no	—
326	C₄	—	2	1	no	—
327	C₄	—	2	1	no	—
328	C₄	—	2	2	no	—
329	C₄	—	2	1	no	—
330	C₄	—	2	2	no	—
331	C₄	C₁₃×#504	1	2	yes	—
332	C₄	C₁₃×#520	1	1	yes	characteristic
333	C₄	C₁₃×#568	1	1	yes	characteristic
334	C₂	—	4	1	no	—
335	C₂	—	4	2	no	—
336	C₂	C₁₃×#2988	1	1	yes	characteristic
337	C₂	C₂×C₁₃×#504	1	1	yes	characteristic
338	C₂	C₁₃×#3407	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₈×C₁₃	C₂⁴
commutator	C₂²	C₂³×C₈×C₁₃
Frattini, cosocle	C₂×C₈	C₂⁴×C₁₃
socle	C₂²×C₁₃	C₂³×C₈
prime radical	C₁₃×#121	C₈
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₈×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₃×#2183	C₂	semidirect
3. Q₈×C₁₃×C₁₆	C₂	semidirect
4. C₁₃×#2169	C₂	semidirect
5. C₁₃×#2169	C₂	semidirect
6. C₁₃×#2168	C₂	semidirect
7. D₄×C₁₃×C₁₆	C₂	semidirect
8. C₁₃×#2164	C₂	semidirect
9. C₁₃×#2162	C₂	semidirect
10. C₁₃×#2151	C₂	semidirect
11. C₁₃×#2150	C₂	semidirect
79. #33507	C₁₃	direct (N × H)
122. #2183	C₂×C₁₃	semidirect
123. Q₈×C₁₆	C₂×C₁₃	semidirect
124. #2169	C₂×C₁₃	semidirect
125. #2169	C₂×C₁₃	semidirect
126. #2168	C₂×C₁₃	semidirect
127. D₄×C₁₆	C₂×C₁₃	semidirect
128. #2164	C₂×C₁₃	semidirect
129. #2162	C₂×C₁₃	semidirect
130. #2151	C₂×C₁₃	semidirect
131. #2150	C₂×C₁₃	semidirect
289. C₁₃	#33507	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×#2966	2
C₁₃×#2183	2
Q₈×C₁₃×C₁₆	2
C₁₃×#2169	2
C₁₃×#2168	2
D₄×C₁₃×C₁₆	2
C₁₃×#2164	2
C₁₃×#2162	2
C₁₃×#2151	2
C₁₃×#2150	2
#33507	13

Subgroups — C13×#33507 #15719846

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#33507 #15719846