Subgroups — C₁₃×#33668 #15720007

Order 3328.

552 conjugacy classes of subgroups.

The subgroup lattice has 390 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3168	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×C₁₃×Q₁₆	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#2235	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#2232	C₂	1	1	yes	maximal, characteristic
5	C₁₃×#2229	C₂	1	2	yes	maximal, complemented
6	C₁₃×#2211	C₂	1	2	yes	maximal, complemented
7	C₁₃×#2188	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#2185	C₂	1	1	yes	maximal, characteristic
9	C₄×C₁₃×Q₃₂	C₂	1	2	yes	maximal, complemented
10	C₄×C₁₃×SD₃₂	C₂	1	2	yes	maximal, complemented
11	C₁₃×#2162	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic
13	C₁₃×#529	—	2	1	no	—
14	C₂×C₄×Q₈×C₁₃	—	2	1	no	—
15	C₂×C₁₃×Q₃₂	C₂²	1	2	yes	—
16	C₂×C₁₃×SD₃₂	C₂²	1	2	yes	—
17	C₁₃×#499	C₂²	1	1	yes	characteristic
18	C₁₃×#495	C₂²	1	1	yes	characteristic
19	C₁₃×#488	—	2	1	no	—
20	C₁₃×#467	C₂²	1	1	yes	characteristic
21	C₁₃×#466	C₂²	1	1	yes	characteristic
22	C₁₃×#465	—	2	1	no	—
23	C₄×C₁₃×Q₁₆	—	2	1	no	—
24	C₄×C₁₃×Q₁₆	—	2	1	no	—
25	C₄×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic
26	C₄×C₁₃×Q₁₆	C₂²	1	2	yes	—
27	C₄×C₁₃×Q₁₆	C₂²	1	2	yes	—
28	C₄×C₁₃×SD₁₆	—	2	1	no	—
29	C₄×C₁₃×D₈	C₂²	1	1	yes	characteristic
30	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
31	C₂×C₁₃×#103	—	2	1	no	—
32	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
33	C₁₃×#367	C₂²	1	2	yes	—
34	C₁₃×#366	C₂²	1	2	yes	—
35	C₁₃×C₄⋊C₁₆	C₂²	1	2	yes	—
36	C₁₃×#358	C₂²	1	2	yes	—
37	C₁₃×#358	C₂²	1	2	yes	—
38	C₁₃×#358	C₂²	1	2	yes	—
39	C₁₃×#357	C₂²	1	2	yes	—
40	C₁₃×C₂²⋊C₁₆	C₂²	1	1	yes	characteristic
41	C₁₃×C₂²⋊C₁₆	C₂²	1	1	yes	characteristic
42	C₄×C₁₃×C₁₆	C₂²	1	2	yes	—
43	C₂²×Q₈×C₁₃	—	2	1	no	—
44	C₂×C₁₃×Q₁₆	—	2	4	no	—
45	C₂×C₁₃×Q₁₆	—	2	1	no	—
46	C₂×C₁₃×Q₁₆	C₂³	1	1	yes	characteristic
47	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
48	C₂×C₁₃×SD₁₆	—	2	1	no	—
49	C₂×C₁₃×D₈	C₂³	1	1	yes	characteristic
50	C₂²×C₈×C₁₃	D₄	1	1	yes	characteristic
51	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
52	C₁₃×#126	—	4	1	no	—
53	C₁₃×#125	—	2	1	no	—
54	C₁₃×#124	—	2	1	no	—
55	C₁₃×#123	—	4	1	no	—
56	C₁₃×C₂²⋊Q₈	—	2	1	no	—
57	C₁₃×#121	—	2	1	no	—
58	C₄×Q₈×C₁₃	—	2	1	no	—
59	C₄×Q₈×C₁₃	—	2	2	no	—
60	C₄×Q₈×C₁₃	—	2	2	no	—
61	C₄×Q₈×C₁₃	—	4	1	no	—
62	C₄×Q₈×C₁₃	—	4	1	no	—
63	C₄×D₄×C₁₃	—	2	1	no	—
64	C₄×D₄×C₁₃	—	4	1	no	—
65	C₁₃×#117	—	4	1	no	—
66	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
67	C₂×C₁₃×C₄⋊C₄	—	4	1	no	—
68	C₂×C₄²×C₁₃	—	4	1	no	—
69	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
70	C₁₃×Q₃₂	—	2	4	no	—
71	C₁₃×SD₃₂	—	2	4	no	—
72	C₂×C₁₃×C₁₆	C₂³	1	2	yes	—
73	C₂×C₁₃×C₁₆	C₂³	1	2	yes	—
74	C₁₃×#107	—	2	1	no	—
75	C₁₃×#107	C₂³	1	2	yes	—
76	C₁₃×#107	C₂³	1	1	yes	characteristic
77	C₁₃×#107	C₂³	1	1	yes	characteristic
78	C₁₃×#106	—	2	1	no	—
79	C₁₃×#103	—	2	2	no	—
80	C₁₃×#103	—	2	2	no	—
81	C₁₃×#103	—	2	1	no	—
82	C₁₃×#103	—	2	1	no	—
83	C₁₃×#102	—	2	1	no	—
84	C₁₃×#102	—	2	1	no	—
85	C₄×C₈×C₁₃	D₄	1	1	yes	characteristic
86	C₄×C₈×C₁₃	D₄	1	1	yes	characteristic
87	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
88	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
89	#33668	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
90	C₂×Q₈×C₁₃	—	2	4	no	—
91	C₂×Q₈×C₁₃	—	2	2	no	—
92	C₂×Q₈×C₁₃	—	2	1	no	—
93	C₂×Q₈×C₁₃	—	4	2	no	—
94	C₂×Q₈×C₁₃	—	4	1	no	—
95	C₂×D₄×C₁₃	—	2	1	no	—
96	C₂×D₄×C₁₃	—	4	1	no	—
97	C₂²×C₄×C₁₃	—	4	1	no	—
98	C₂²×C₄×C₁₃	—	4	1	no	—
99	C₂²×C₄×C₁₃	—	4	1	no	—
100	C₂²×C₄×C₁₃	D₈	1	1	yes	characteristic
101	C₂²×C₄×C₁₃	D₈	1	1	yes	characteristic
102	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
103	C₁₃×Q₁₆	—	2	4	no	—
104	C₁₃×Q₁₆	—	2	2	no	—
105	C₁₃×Q₁₆	—	2	2	no	—
106	C₁₃×Q₁₆	#41	1	4	yes	—
107	C₁₃×SD₁₆	—	4	2	no	—
108	C₁₃×D₈	—	2	2	no	—
109	C₂×C₈×C₁₃	—	2	2	no	—
110	C₂×C₈×C₁₃	—	4	1	no	—
111	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
112	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
113	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
114	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
115	C₁₃×C₄⋊C₄	—	2	1	no	—
116	C₁₃×C₄⋊C₄	—	2	1	no	—
117	C₁₃×C₄⋊C₄	—	2	2	no	—
118	C₁₃×C₄⋊C₄	—	4	1	no	—
119	C₁₃×C₄⋊C₄	—	4	2	no	—
120	C₁₃×C₄⋊C₄	—	4	2	no	—
121	C₁₃×C₄⋊C₄	—	4	1	no	—
122	C₁₃×C₄⋊C₄	—	4	1	no	—
123	C₁₃×C₄⋊C₄	—	4	1	no	—
124	C₁₃×C₄⋊C₄	—	4	1	no	—
125	C₁₃×C₂²⋊C₄	—	4	1	no	—
126	C₁₃×C₂²⋊C₄	—	4	1	no	—
127	C₁₃×C₂²⋊C₄	—	4	1	no	—
128	C₁₃×C₂²⋊C₄	—	4	1	no	—
129	C₁₃×C₂²⋊C₄	—	4	1	no	—
130	C₄²×C₁₃	—	4	2	no	—
131	C₄²×C₁₃	—	4	2	no	—
132	C₄²×C₁₃	—	4	1	no	—
133	C₄²×C₁₃	D₈	1	1	yes	characteristic
134	C₄²×C₁₃	D₈	1	1	yes	characteristic
135	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
136	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
137	C₁₃×C₁₆	—	2	2	no	—
138	C₁₃×C₁₆	—	2	2	no	—
139	#3168	C₂×C₁₃	1	1	yes	characteristic
140	C₂×C₄×Q₁₆	C₂×C₁₃	1	1	yes	characteristic, complemented
141	#2235	C₂×C₁₃	1	1	yes	characteristic, complemented
142	#2232	C₂×C₁₃	1	1	yes	characteristic
143	#2229	C₂×C₁₃	1	2	yes	complemented
144	#2211	C₂×C₁₃	1	2	yes	complemented
145	#2188	C₂×C₁₃	1	1	yes	characteristic, complemented
146	#2185	C₂×C₁₃	1	1	yes	characteristic
147	C₄×Q₃₂	C₂×C₁₃	1	2	yes	complemented
148	C₄×SD₃₂	C₂×C₁₃	1	2	yes	complemented
149	#2162	C₂×C₁₃	1	1	yes	characteristic, complemented
150	C₂³×C₁₃	—	4	1	no	—
151	C₂³×C₁₃	C₂×D₈	1	1	yes	characteristic
152	Q₈×C₁₃	—	2	4	no	—
153	Q₈×C₁₃	—	4	4	no	—
154	Q₈×C₁₃	—	4	2	no	—
155	Q₈×C₁₃	—	4	1	no	—
156	Q₈×C₁₃	—	4	1	no	—
157	D₄×C₁₃	—	4	1	no	—
158	D₄×C₁₃	—	4	1	no	—
159	D₄×C₁₃	—	8	2	no	—
160	C₂×C₄×C₁₃	—	2	2	no	—
161	C₂×C₄×C₁₃	—	2	1	no	—
162	C₂×C₄×C₁₃	—	2	1	no	—
163	C₂×C₄×C₁₃	—	2	2	no	—
164	C₂×C₄×C₁₃	—	4	4	no	—
165	C₂×C₄×C₁₃	—	4	2	no	—
166	C₂×C₄×C₁₃	—	4	2	no	—
167	C₂×C₄×C₁₃	—	4	1	no	—
168	C₂×C₄×C₁₃	—	4	1	no	—
169	C₂×C₄×C₁₃	—	4	1	no	—
170	C₂×C₄×C₁₃	—	8	2	no	—
171	C₂×C₄×C₁₃	—	8	2	no	—
172	C₂×C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
173	C₂×C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
174	C₂×C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
175	C₂×C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
176	C₂×C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
177	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
178	C₈×C₁₃	—	2	1	no	—
179	C₈×C₁₃	—	2	1	no	—
180	C₈×C₁₃	—	2	1	no	—
181	C₈×C₁₃	C₂×#41	1	2	yes	—
182	C₂²×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic
183	#529	—	2	1	no	—
184	C₂×C₄×Q₈	—	2	1	no	—
185	C₂×Q₃₂	C₂²×C₁₃	1	2	yes	—
186	C₂×SD₃₂	C₂²×C₁₃	1	2	yes	—
187	#499	C₂²×C₁₃	1	1	yes	characteristic
188	#495	C₂²×C₁₃	1	1	yes	characteristic
189	#488	—	2	1	no	—
190	#467	C₂²×C₁₃	1	1	yes	characteristic
191	#466	C₂²×C₁₃	1	1	yes	characteristic
192	#465	—	2	1	no	—
193	C₄×Q₁₆	—	2	1	no	—
194	C₄×Q₁₆	—	2	1	no	—
195	C₄×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic
196	C₄×Q₁₆	C₂²×C₁₃	1	2	yes	—
197	C₄×Q₁₆	C₂²×C₁₃	1	2	yes	—
198	C₄×SD₁₆	—	2	1	no	—
199	C₄×D₈	C₂²×C₁₃	1	1	yes	characteristic
200	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
201	C₂×#103	—	2	1	no	—
202	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
203	#367	C₂²×C₁₃	1	2	yes	—
204	#366	C₂²×C₁₃	1	2	yes	—
205	C₄⋊C₁₆	C₂²×C₁₃	1	2	yes	—
206	#358	C₂²×C₁₃	1	2	yes	—
207	#358	C₂²×C₁₃	1	2	yes	—
208	#358	C₂²×C₁₃	1	2	yes	—
209	#357	C₂²×C₁₃	1	2	yes	—
210	C₂²⋊C₁₆	C₂²×C₁₃	1	1	yes	characteristic
211	C₂²⋊C₁₆	C₂²×C₁₃	1	1	yes	characteristic
212	C₄×C₁₆	C₂²×C₁₃	1	2	yes	—
213	C₂²×C₁₃	—	2	1	no	—
214	C₂²×C₁₃	—	2	1	no	—
215	C₂²×C₁₃	—	8	1	no	—
216	C₂²×C₁₃	—	8	1	no	—
217	C₂²×C₁₃	—	8	1	no	—
218	C₂²×C₁₃	#508	1	2	yes	—
219	C₂²×C₁₃	C₂²×D₈	1	1	yes	characteristic
220	C₄×C₁₃	—	2	1	no	—
221	C₄×C₁₃	—	2	1	no	—
222	C₄×C₁₃	—	2	1	no	—
223	C₄×C₁₃	—	2	1	no	—
224	C₄×C₁₃	—	4	4	no	—
225	C₄×C₁₃	—	8	1	no	—
226	C₄×C₁₃	—	8	2	no	—
227	C₄×C₁₃	—	8	1	no	—
228	C₄×C₁₃	—	8	1	no	—
229	C₄×C₁₃	#510	1	2	yes	—
230	C₄×C₁₃	#525	1	1	yes	characteristic
231	C₄×C₁₃	#575	1	1	yes	characteristic
232	C₂²×Q₈	—	2	1	no	—
233	C₂×Q₁₆	—	2	4	no	—
234	C₂×Q₁₆	—	2	1	no	—
235	C₂×Q₁₆	C₂³×C₁₃	1	1	yes	characteristic
236	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
237	C₂×SD₁₆	—	2	1	no	—
238	C₂×D₈	C₂³×C₁₃	1	1	yes	characteristic
239	C₂²×C₈	D₄×C₁₃	1	1	yes	characteristic
240	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
241	#126	—	4	1	no	—
242	#125	—	2	1	no	—
243	#124	—	2	1	no	—
244	#123	—	4	1	no	—
245	C₂²⋊Q₈	—	2	1	no	—
246	#121	—	2	1	no	—
247	C₄×Q₈	—	2	2	no	—
248	C₄×Q₈	—	2	2	no	—
249	C₄×Q₈	—	2	1	no	—
250	C₄×Q₈	—	4	1	no	—
251	C₄×Q₈	—	4	1	no	—
252	C₄×D₄	—	2	1	no	—
253	C₄×D₄	—	4	1	no	—
254	#117	—	4	1	no	—
255	C₂×C₄⋊C₄	—	2	1	no	—
256	C₂×C₄⋊C₄	—	4	1	no	—
257	C₂×C₄²	—	4	1	no	—
258	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
259	Q₃₂	—	2	4	no	—
260	SD₃₂	—	2	4	no	—
261	C₂×C₁₆	C₂³×C₁₃	1	2	yes	—
262	C₂×C₁₆	C₂³×C₁₃	1	2	yes	—
263	#107	—	2	1	no	—
264	#107	C₂³×C₁₃	1	2	yes	—
265	#107	C₂³×C₁₃	1	1	yes	characteristic
266	#107	C₂³×C₁₃	1	1	yes	characteristic
267	#106	—	2	1	no	—
268	#103	—	2	2	no	—
269	#103	—	2	2	no	—
270	#103	—	2	1	no	—
271	#103	—	2	1	no	—
272	#102	—	2	1	no	—
273	#102	—	2	1	no	—
274	C₄×C₈	D₄×C₁₃	1	1	yes	characteristic
275	C₄×C₈	D₄×C₁₃	1	1	yes	characteristic
276	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
277	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
278	C₂×C₁₃	—	2	2	no	—
279	C₂×C₁₃	—	16	1	no	—
280	C₂×C₁₃	#3100	1	1	yes	characteristic
281	C₂×C₁₃	C₂×#508	1	1	yes	characteristic
282	C₂×C₁₃	C₂×#510	1	1	yes	characteristic
283	C₂×Q₈	—	2	4	no	—
284	C₂×Q₈	—	2	2	no	—
285	C₂×Q₈	—	2	1	no	—
286	C₂×Q₈	—	4	2	no	—
287	C₂×Q₈	—	4	1	no	—
288	C₂×D₄	—	2	1	no	—
289	C₂×D₄	—	4	1	no	—
290	C₂²×C₄	—	4	1	no	—
291	C₂²×C₄	—	4	1	no	—
292	C₂²×C₄	—	4	1	no	—
293	C₂²×C₄	C₁₃×D₈	1	1	yes	characteristic
294	C₂²×C₄	C₁₃×D₈	1	1	yes	characteristic
295	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
296	Q₁₆	—	2	4	no	—
297	Q₁₆	—	2	2	no	—
298	Q₁₆	—	2	2	no	—
299	Q₁₆	C₁₃×#41	1	4	yes	—
300	SD₁₆	—	4	2	no	—
301	D₈	—	2	2	no	—
302	C₂×C₈	—	2	2	no	—
303	C₂×C₈	—	4	1	no	—
304	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
305	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
306	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
307	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
308	C₄⋊C₄	—	2	1	no	—
309	C₄⋊C₄	—	2	1	no	—
310	C₄⋊C₄	—	2	2	no	—
311	C₄⋊C₄	—	4	1	no	—
312	C₄⋊C₄	—	4	2	no	—
313	C₄⋊C₄	—	4	2	no	—
314	C₄⋊C₄	—	4	1	no	—
315	C₄⋊C₄	—	4	1	no	—
316	C₄⋊C₄	—	4	1	no	—
317	C₄⋊C₄	—	4	1	no	—
318	C₂²⋊C₄	—	4	1	no	—
319	C₂²⋊C₄	—	4	1	no	—
320	C₂²⋊C₄	—	4	1	no	—
321	C₂²⋊C₄	—	4	1	no	—
322	C₂²⋊C₄	—	4	1	no	—
323	C₄²	—	4	2	no	—
324	C₄²	—	4	2	no	—
325	C₄²	—	4	1	no	—
326	C₄²	C₁₃×D₈	1	1	yes	characteristic
327	C₄²	C₁₃×D₈	1	1	yes	characteristic
328	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
329	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
330	C₁₆	—	2	2	no	—
331	C₁₆	—	2	2	no	—
332	C₁₃	#33668	1	1	yes	characteristic, direct product factor, Sylow
333	C₂³	—	4	1	no	—
334	C₂³	C₂×C₁₃×D₈	1	1	yes	characteristic
335	Q₈	—	2	4	no	—
336	Q₈	—	4	4	no	—
337	Q₈	—	4	2	no	—
338	Q₈	—	4	1	no	—
339	Q₈	—	4	1	no	—
340	D₄	—	4	1	no	—
341	D₄	—	4	1	no	—
342	D₄	—	8	2	no	—
343	C₂×C₄	—	2	2	no	—
344	C₂×C₄	—	2	2	no	—
345	C₂×C₄	—	2	1	no	—
346	C₂×C₄	—	2	1	no	—
347	C₂×C₄	—	4	4	no	—
348	C₂×C₄	—	4	2	no	—
349	C₂×C₄	—	4	2	no	—
350	C₂×C₄	—	4	1	no	—
351	C₂×C₄	—	4	1	no	—
352	C₂×C₄	—	4	1	no	—
353	C₂×C₄	—	8	2	no	—
354	C₂×C₄	—	8	2	no	—
355	C₂×C₄	C₂×C₁₃×D₈	1	1	yes	characteristic
356	C₂×C₄	C₂×C₁₃×D₈	1	1	yes	characteristic
357	C₂×C₄	C₂×C₁₃×D₈	1	1	yes	characteristic
358	C₂×C₄	C₂×C₁₃×D₈	1	1	yes	characteristic
359	C₂×C₄	C₂×C₁₃×D₈	1	1	yes	characteristic
360	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
361	C₈	—	2	1	no	—
362	C₈	—	2	1	no	—
363	C₈	—	2	1	no	—
364	C₈	C₂×C₁₃×#41	1	2	yes	—
365	C₂²	—	2	1	no	—
366	C₂²	—	2	1	no	—
367	C₂²	—	8	1	no	—
368	C₂²	—	8	1	no	—
369	C₂²	—	8	1	no	—
370	C₂²	C₁₃×#508	1	2	yes	—
371	C₂²	C₂²×C₁₃×D₈	1	1	yes	characteristic
372	C₄	—	2	1	no	—
373	C₄	—	2	1	no	—
374	C₄	—	2	1	no	—
375	C₄	—	2	1	no	—
376	C₄	—	4	4	no	—
377	C₄	—	8	1	no	—
378	C₄	—	8	2	no	—
379	C₄	—	8	1	no	—
380	C₄	—	8	1	no	—
381	C₄	C₁₃×#510	1	2	yes	—
382	C₄	C₁₃×#525	1	1	yes	characteristic
383	C₄	C₁₃×#575	1	1	yes	characteristic
384	C₂	—	2	2	no	—
385	C₂	—	16	1	no	—
386	C₂	C₁₃×#3100	1	1	yes	characteristic
387	C₂	C₂×C₁₃×#508	1	1	yes	characteristic
388	C₂	C₂×C₁₃×#510	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₁₃	C₂×D₈
commutator, Frattini, cosocle	C₂×C₈	C₂⁴×C₁₃
socle	C₂²×C₁₃	C₂²×D₈
prime radical	C₁₃×#466	C₂²
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₃ ◁ C₂×C₄²×C₁₃ ◁ C₂×C₄×C₈×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₄×C₁₃×Q₁₆	C₂	semidirect
3. C₁₃×#2235	C₂	semidirect
5. C₁₃×#2229	C₂	semidirect
6. C₁₃×#2211	C₂	semidirect
7. C₁₃×#2188	C₂	semidirect
9. C₄×C₁₃×Q₃₂	C₂	semidirect
10. C₄×C₁₃×SD₃₂	C₂	semidirect
11. C₁₃×#2162	C₂	semidirect
89. #33668	C₁₃	direct (N × H)
140. C₂×C₄×Q₁₆	C₂×C₁₃	semidirect
141. #2235	C₂×C₁₃	semidirect
143. #2229	C₂×C₁₃	semidirect
144. #2211	C₂×C₁₃	semidirect
145. #2188	C₂×C₁₃	semidirect
147. C₄×Q₃₂	C₂×C₁₃	semidirect
148. C₄×SD₃₂	C₂×C₁₃	semidirect
149. #2162	C₂×C₁₃	semidirect
332. C₁₃	#33668	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×#3168	2
C₂×C₄×C₁₃×Q₁₆	2
C₁₃×#2235	2
C₁₃×#2232	2
C₁₃×#2229	2
C₁₃×#2211	2
C₁₃×#2188	2
C₁₃×#2185	2
C₄×C₁₃×Q₃₂	2
C₄×C₁₃×SD₃₂	2
C₁₃×#2162	2
#33668	13

Subgroups — C13×#33668 #15720007

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#33668 #15720007