Subgroups — C₁₃×#33766 #15720105

Order 3328.

584 conjugacy classes of subgroups.

The subgroup lattice has 406 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3059	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃×#3058	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#2237	C₂	1	2	yes	maximal, complemented
4	C₁₃×#2234	C₂	1	2	yes	maximal, complemented
5	C₁₃×#2220	C₂	1	2	yes	maximal, complemented
6	C₁₃×#2217	C₂	1	2	yes	maximal, complemented
7	C₁₃×#2187	C₂	1	2	yes	maximal, complemented
8	C₁₃×#2185	C₂	1	2	yes	maximal, complemented
9	C₁₃×#2113	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂²×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic, complemented
11	C₂²×C₁₃×D₈	C₂²	1	1	yes	characteristic
12	C₂×C₁₃×#131	C₂²	1	1	yes	characteristic
13	C₁₃×#536	—	2	1	no	—
14	C₁₃×#535	—	2	1	no	—
15	C₂×C₁₃×SD₃₂	C₂²	1	2	yes	—
16	C₂×C₁₃×SD₃₂	C₂²	1	2	yes	—
17	C₂×C₁₃×M₃₂	C₂²	1	1	yes	characteristic, complemented
18	C₂²×C₁₃×C₁₆	C₂²	1	1	yes	characteristic, complemented
19	C₁₃×#470	—	2	1	no	—
20	C₁₃×#470	—	2	1	no	—
21	C₁₃×#469	—	2	1	no	—
22	C₁₃×#469	—	2	1	no	—
23	C₁₃×#467	C₂²	1	2	yes	—
24	C₁₃×#467	C₂²	1	2	yes	complemented
25	C₁₃×#466	C₂²	1	2	yes	—
26	C₁₃×#466	C₂²	1	2	yes	—
27	C₁₃×#427	C₂²	1	1	yes	characteristic
28	C₁₃×#427	C₂²	1	1	yes	characteristic, complemented
29	C₁₃×#419	—	2	1	no	—
30	C₁₃×#418	—	2	1	no	—
31	C₁₃×#367	C₂²	1	2	yes	complemented
32	C₁₃×#366	C₂²	1	2	yes	complemented
33	C₁₃×#358	C₂²	1	2	yes	complemented
34	C₁₃×#358	C₂²	1	2	yes	complemented
35	C₁₃×#357	C₂²	1	2	yes	—
36	C₁₃×#357	C₂²	1	2	yes	—
37	C₁₃×C₂²⋊C₁₆	C₂²	1	2	yes	—
38	C₁₃×C₂²⋊C₁₆	C₂²	1	2	yes	complemented
39	C₂×C₁₃×#41	D₄	1	1	yes	characteristic
40	C₂²×Q₈×C₁₃	—	2	1	no	—
41	C₂²×D₄×C₁₃	—	2	1	no	—
42	C₂×C₁₃×Q₁₆	—	2	1	no	—
43	C₂×C₁₃×Q₁₆	—	4	1	no	—
44	C₂×C₁₃×Q₁₆	—	4	1	no	—
45	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
46	C₂×C₁₃×D₈	—	2	1	no	—
47	C₂×C₁₃×D₈	—	4	1	no	—
48	C₂×C₁₃×D₈	—	4	1	no	—
49	C₂×C₁₃×D₈	C₂³	1	2	yes	—
50	C₁₃×#131	—	4	1	no	—
51	C₁₃×#131	—	4	1	no	—
52	C₂×C₁₃×M₁₆	D₄	1	1	yes	characteristic
53	C₂×C₁₃×M₁₆	D₄	1	1	yes	characteristic
54	C₂×C₁₃×M₁₆	D₄	1	1	yes	characteristic
55	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
56	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
57	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
58	C₁₃×C₄⋊Q₈	—	4	1	no	—
59	C₁₃×#127	—	4	1	no	—
60	C₁₃×#124	—	4	1	no	—
61	C₁₃×#124	—	4	1	no	—
62	C₁₃×#123	—	4	1	no	—
63	C₁₃×#123	—	4	1	no	—
64	C₁₃×C₂²⋊Q₈	—	2	2	no	—
65	C₁₃×C₂²⋊Q₈	—	2	2	no	—
66	C₁₃×#121	—	2	2	no	—
67	C₁₃×#121	—	2	2	no	—
68	C₁₃×#120	—	4	1	no	—
69	C₁₃×#120	—	4	1	no	—
70	C₁₃×#117	—	2	1	no	—
71	C₁₃×#117	—	2	1	no	—
72	C₁₃×SD₃₂	—	4	2	no	—
73	C₁₃×SD₃₂	—	4	2	no	—
74	C₁₃×M₃₂	—	4	1	no	—
75	C₂×C₁₃×C₁₆	—	4	1	no	—
76	C₂×C₁₃×C₁₆	C₂³	1	2	yes	—
77	C₂×C₁₃×C₁₆	C₂³	1	2	yes	—
78	C₁₃×#107	C₂³	1	2	yes	—
79	C₁₃×#107	C₂³	1	2	yes	—
80	C₁₃×#106	—	2	1	no	—
81	C₁₃×#106	—	2	1	no	—
82	C₁₃×#103	—	2	2	no	—
83	C₁₃×#103	—	2	2	no	—
84	C₁₃×#102	—	2	2	no	—
85	C₁₃×#102	—	2	2	no	—
86	#33766	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
87	C₂⁴×C₁₃	—	4	1	no	—
88	C₁₃×#41	—	4	1	no	—
89	C₁₃×#41	—	4	1	no	—
90	C₂×Q₈×C₁₃	—	2	2	no	—
91	C₂×Q₈×C₁₃	—	4	2	no	—
92	C₂×Q₈×C₁₃	—	4	2	no	—
93	C₂×Q₈×C₁₃	—	4	1	no	—
94	C₂×Q₈×C₁₃	D₈	1	1	yes	characteristic
95	C₂×D₄×C₁₃	—	2	2	no	—
96	C₂×D₄×C₁₃	—	4	2	no	—
97	C₂×D₄×C₁₃	—	4	2	no	—
98	C₂×D₄×C₁₃	—	4	2	no	—
99	C₂×D₄×C₁₃	—	4	2	no	—
100	C₂×D₄×C₁₃	—	4	1	no	—
101	C₂×D₄×C₁₃	D₈	1	1	yes	characteristic
102	C₂×D₄×C₁₃	D₈	1	1	yes	characteristic
103	C₂×D₄×C₁₃	D₈	1	1	yes	characteristic
104	C₂²×C₄×C₁₃	—	4	1	no	—
105	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
106	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
107	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
108	C₁₃×Q₁₆	—	2	2	no	—
109	C₁₃×Q₁₆	—	2	2	no	—
110	C₁₃×Q₁₆	—	4	2	no	—
111	C₁₃×D₈	—	2	2	no	—
112	C₁₃×D₈	—	2	2	no	—
113	C₁₃×D₈	—	4	2	no	—
114	C₁₃×M₁₆	—	4	1	no	—
115	C₁₃×M₁₆	—	4	1	no	—
116	C₁₃×M₁₆	—	4	1	no	—
117	C₂×C₈×C₁₃	—	2	1	no	—
118	C₂×C₈×C₁₃	—	2	1	no	—
119	C₂×C₈×C₁₃	—	2	1	no	—
120	C₂×C₈×C₁₃	—	2	1	no	—
121	C₂×C₈×C₁₃	—	2	1	no	—
122	C₂×C₈×C₁₃	—	2	1	no	—
123	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
124	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
125	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
126	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
127	C₁₃×C₄⋊C₄	—	2	2	no	—
128	C₁₃×C₄⋊C₄	—	2	2	no	—
129	C₁₃×C₄⋊C₄	—	4	2	no	—
130	C₁₃×C₄⋊C₄	—	4	2	no	—
131	C₁₃×C₂²⋊C₄	—	4	1	no	—
132	C₁₃×C₂²⋊C₄	—	4	1	no	—
133	C₁₃×C₂²⋊C₄	—	4	2	no	—
134	C₁₃×C₂²⋊C₄	—	4	2	no	—
135	C₁₃×C₂²⋊C₄	—	4	2	no	—
136	C₁₃×C₂²⋊C₄	—	4	2	no	—
137	C₄²×C₁₃	—	4	1	no	—
138	C₄²×C₁₃	—	4	1	no	—
139	C₁₃×C₁₆	—	2	2	no	—
140	C₁₃×C₁₆	—	2	2	no	—
141	#3059	C₂×C₁₃	1	1	yes	characteristic, complemented
142	#3058	C₂×C₁₃	1	1	yes	characteristic
143	#2237	C₂×C₁₃	1	2	yes	complemented
144	#2234	C₂×C₁₃	1	2	yes	complemented
145	#2220	C₂×C₁₃	1	2	yes	complemented
146	#2217	C₂×C₁₃	1	2	yes	complemented
147	#2187	C₂×C₁₃	1	2	yes	complemented
148	#2185	C₂×C₁₃	1	2	yes	complemented
149	#2113	C₂×C₁₃	1	1	yes	characteristic, complemented
150	C₂³×C₁₃	—	4	2	no	—
151	C₂³×C₁₃	—	8	2	no	—
152	C₂³×C₁₃	—	16	2	no	—
153	C₂³×C₁₃	C₂×D₈	1	1	yes	characteristic
154	C₂³×C₁₃	C₂×D₈	1	1	yes	characteristic
155	C₂³×C₁₃	C₂×D₈	1	1	yes	characteristic
156	Q₈×C₁₃	—	4	1	no	—
157	Q₈×C₁₃	—	4	2	no	—
158	Q₈×C₁₃	—	4	2	no	—
159	Q₈×C₁₃	—	8	2	no	—
160	D₄×C₁₃	—	4	1	no	—
161	D₄×C₁₃	—	4	1	no	—
162	D₄×C₁₃	—	4	1	no	—
163	D₄×C₁₃	—	4	2	no	—
164	D₄×C₁₃	—	4	2	no	—
165	D₄×C₁₃	—	8	2	no	—
166	D₄×C₁₃	—	16	2	no	—
167	D₄×C₁₃	—	16	2	no	—
168	C₂×C₄×C₁₃	—	2	1	no	—
169	C₂×C₄×C₁₃	—	2	1	no	—
170	C₂×C₄×C₁₃	—	2	1	no	—
171	C₂×C₄×C₁₃	—	2	1	no	—
172	C₂×C₄×C₁₃	—	2	1	no	—
173	C₂×C₄×C₁₃	—	2	1	no	—
174	C₂×C₄×C₁₃	—	4	2	no	—
175	C₂×C₄×C₁₃	—	4	2	no	—
176	C₂×C₄×C₁₃	—	4	2	no	—
177	C₂×C₄×C₁₃	—	8	2	no	—
178	C₂×C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
179	C₂×C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
180	C₂×C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
181	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
182	C₈×C₁₃	—	2	1	no	—
183	C₈×C₁₃	—	2	1	no	—
184	C₈×C₁₃	—	2	1	no	—
185	C₈×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
186	C₈×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
187	C₂²×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic, complemented
188	C₂²×D₈	C₂²×C₁₃	1	1	yes	characteristic
189	C₂×#131	C₂²×C₁₃	1	1	yes	characteristic
190	#536	—	2	1	no	—
191	#535	—	2	1	no	—
192	C₂×SD₃₂	C₂²×C₁₃	1	2	yes	—
193	C₂×SD₃₂	C₂²×C₁₃	1	2	yes	—
194	C₂×M₃₂	C₂²×C₁₃	1	1	yes	characteristic, complemented
195	C₂²×C₁₆	C₂²×C₁₃	1	1	yes	characteristic, complemented
196	#470	—	2	1	no	—
197	#470	—	2	1	no	—
198	#469	—	2	1	no	—
199	#469	—	2	1	no	—
200	#467	C₂²×C₁₃	1	2	yes	—
201	#467	C₂²×C₁₃	1	2	yes	complemented
202	#466	C₂²×C₁₃	1	2	yes	—
203	#466	C₂²×C₁₃	1	2	yes	—
204	#427	C₂²×C₁₃	1	1	yes	characteristic
205	#427	C₂²×C₁₃	1	1	yes	characteristic, complemented
206	#419	—	2	1	no	—
207	#418	—	2	1	no	—
208	#367	C₂²×C₁₃	1	2	yes	complemented
209	#366	C₂²×C₁₃	1	2	yes	complemented
210	#358	C₂²×C₁₃	1	2	yes	complemented
211	#358	C₂²×C₁₃	1	2	yes	complemented
212	#357	C₂²×C₁₃	1	2	yes	—
213	#357	C₂²×C₁₃	1	2	yes	—
214	C₂²⋊C₁₆	C₂²×C₁₃	1	2	yes	—
215	C₂²⋊C₁₆	C₂²×C₁₃	1	2	yes	complemented
216	C₂²×C₁₃	—	2	2	no	—
217	C₂²×C₁₃	—	2	2	no	—
218	C₂²×C₁₃	—	2	2	no	—
219	C₂²×C₁₃	—	2	1	no	—
220	C₂²×C₁₃	—	2	1	no	—
221	C₂²×C₁₃	—	2	1	no	—
222	C₂²×C₁₃	—	8	2	no	—
223	C₂²×C₁₃	—	8	2	no	—
224	C₂²×C₁₃	—	8	2	no	—
225	C₂²×C₁₃	—	16	4	no	—
226	C₂²×C₁₃	C₂²×D₈	1	1	yes	characteristic
227	C₄×C₁₃	—	2	1	no	—
228	C₄×C₁₃	—	2	1	no	—
229	C₄×C₁₃	—	2	1	no	—
230	C₄×C₁₃	—	8	2	no	—
231	C₄×C₁₃	—	8	2	no	—
232	C₄×C₁₃	—	8	2	no	—
233	C₄×C₁₃	#534	1	1	yes	characteristic
234	C₄×C₁₃	#575	1	1	yes	characteristic
235	C₂×#41	D₄×C₁₃	1	1	yes	characteristic
236	C₂²×Q₈	—	2	1	no	—
237	C₂²×D₄	—	2	1	no	—
238	C₂×Q₁₆	—	2	1	no	—
239	C₂×Q₁₆	—	4	1	no	—
240	C₂×Q₁₆	—	4	1	no	—
241	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
242	C₂×D₈	—	2	1	no	—
243	C₂×D₈	—	4	1	no	—
244	C₂×D₈	—	4	1	no	—
245	C₂×D₈	C₂³×C₁₃	1	2	yes	—
246	#131	—	4	1	no	—
247	#131	—	4	1	no	—
248	C₂×M₁₆	D₄×C₁₃	1	1	yes	characteristic
249	C₂×M₁₆	D₄×C₁₃	1	1	yes	characteristic
250	C₂×M₁₆	D₄×C₁₃	1	1	yes	characteristic
251	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
252	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
253	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
254	C₄⋊Q₈	—	4	1	no	—
255	#127	—	4	1	no	—
256	#124	—	4	1	no	—
257	#124	—	4	1	no	—
258	#123	—	4	1	no	—
259	#123	—	4	1	no	—
260	C₂²⋊Q₈	—	2	2	no	—
261	C₂²⋊Q₈	—	2	2	no	—
262	#121	—	2	2	no	—
263	#121	—	2	2	no	—
264	#120	—	4	1	no	—
265	#120	—	4	1	no	—
266	#117	—	2	1	no	—
267	#117	—	2	1	no	—
268	SD₃₂	—	4	2	no	—
269	SD₃₂	—	4	2	no	—
270	M₃₂	—	4	1	no	—
271	C₂×C₁₆	—	4	1	no	—
272	C₂×C₁₆	C₂³×C₁₃	1	2	yes	—
273	C₂×C₁₆	C₂³×C₁₃	1	2	yes	—
274	#107	C₂³×C₁₃	1	2	yes	—
275	#107	C₂³×C₁₃	1	2	yes	—
276	#106	—	2	1	no	—
277	#106	—	2	1	no	—
278	#103	—	2	2	no	—
279	#103	—	2	2	no	—
280	#102	—	2	2	no	—
281	#102	—	2	2	no	—
282	C₂×C₁₃	—	4	1	no	—
283	C₂×C₁₃	—	4	1	no	—
284	C₂×C₁₃	—	4	1	no	—
285	C₂×C₁₃	—	16	2	no	—
286	C₂×C₁₃	#3186	1	1	yes	characteristic
287	C₂×C₁₃	#3416	1	2	yes	—
288	C₂⁴	—	4	1	no	—
289	#41	—	4	1	no	—
290	#41	—	4	1	no	—
291	C₂×Q₈	—	2	2	no	—
292	C₂×Q₈	—	4	2	no	—
293	C₂×Q₈	—	4	2	no	—
294	C₂×Q₈	—	4	1	no	—
295	C₂×Q₈	C₁₃×D₈	1	1	yes	characteristic
296	C₂×D₄	—	2	2	no	—
297	C₂×D₄	—	4	2	no	—
298	C₂×D₄	—	4	2	no	—
299	C₂×D₄	—	4	2	no	—
300	C₂×D₄	—	4	2	no	—
301	C₂×D₄	—	4	1	no	—
302	C₂×D₄	C₁₃×D₈	1	1	yes	characteristic
303	C₂×D₄	C₁₃×D₈	1	1	yes	characteristic
304	C₂×D₄	C₁₃×D₈	1	1	yes	characteristic
305	C₂²×C₄	—	4	1	no	—
306	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
307	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
308	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
309	Q₁₆	—	2	2	no	—
310	Q₁₆	—	2	2	no	—
311	Q₁₆	—	4	2	no	—
312	D₈	—	2	2	no	—
313	D₈	—	2	2	no	—
314	D₈	—	4	2	no	—
315	M₁₆	—	4	1	no	—
316	M₁₆	—	4	1	no	—
317	M₁₆	—	4	1	no	—
318	C₂×C₈	—	2	1	no	—
319	C₂×C₈	—	2	1	no	—
320	C₂×C₈	—	2	1	no	—
321	C₂×C₈	—	2	1	no	—
322	C₂×C₈	—	2	1	no	—
323	C₂×C₈	—	2	1	no	—
324	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
325	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
326	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
327	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
328	C₄⋊C₄	—	2	2	no	—
329	C₄⋊C₄	—	2	2	no	—
330	C₄⋊C₄	—	4	2	no	—
331	C₄⋊C₄	—	4	2	no	—
332	C₂²⋊C₄	—	4	1	no	—
333	C₂²⋊C₄	—	4	1	no	—
334	C₂²⋊C₄	—	4	2	no	—
335	C₂²⋊C₄	—	4	2	no	—
336	C₂²⋊C₄	—	4	2	no	—
337	C₂²⋊C₄	—	4	2	no	—
338	C₄²	—	4	1	no	—
339	C₄²	—	4	1	no	—
340	C₁₆	—	2	2	no	—
341	C₁₆	—	2	2	no	—
342	C₁₃	#33766	1	1	yes	characteristic, direct product factor, Sylow
343	C₂³	—	4	2	no	—
344	C₂³	—	8	2	no	—
345	C₂³	—	16	2	no	—
346	C₂³	C₂×C₁₃×D₈	1	1	yes	characteristic
347	C₂³	C₂×C₁₃×D₈	1	1	yes	characteristic
348	C₂³	C₂×C₁₃×D₈	1	1	yes	characteristic
349	Q₈	—	4	1	no	—
350	Q₈	—	4	2	no	—
351	Q₈	—	4	2	no	—
352	Q₈	—	8	2	no	—
353	D₄	—	4	1	no	—
354	D₄	—	4	1	no	—
355	D₄	—	4	1	no	—
356	D₄	—	4	2	no	—
357	D₄	—	4	2	no	—
358	D₄	—	8	2	no	—
359	D₄	—	16	2	no	—
360	D₄	—	16	2	no	—
361	C₂×C₄	—	2	1	no	—
362	C₂×C₄	—	2	1	no	—
363	C₂×C₄	—	2	1	no	—
364	C₂×C₄	—	2	1	no	—
365	C₂×C₄	—	2	1	no	—
366	C₂×C₄	—	2	1	no	—
367	C₂×C₄	—	4	2	no	—
368	C₂×C₄	—	4	2	no	—
369	C₂×C₄	—	4	2	no	—
370	C₂×C₄	—	8	2	no	—
371	C₂×C₄	C₂×C₁₃×D₈	1	1	yes	characteristic
372	C₂×C₄	C₂×C₁₃×D₈	1	1	yes	characteristic
373	C₂×C₄	C₂×C₁₃×D₈	1	1	yes	characteristic
374	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
375	C₈	—	2	1	no	—
376	C₈	—	2	1	no	—
377	C₈	—	2	1	no	—
378	C₈	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
379	C₈	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
380	C₂²	—	2	2	no	—
381	C₂²	—	2	2	no	—
382	C₂²	—	2	2	no	—
383	C₂²	—	2	1	no	—
384	C₂²	—	2	1	no	—
385	C₂²	—	2	1	no	—
386	C₂²	—	8	2	no	—
387	C₂²	—	8	2	no	—
388	C₂²	—	8	2	no	—
389	C₂²	—	16	4	no	—
390	C₂²	C₂²×C₁₃×D₈	1	1	yes	characteristic
391	C₄	—	2	1	no	—
392	C₄	—	2	1	no	—
393	C₄	—	2	1	no	—
394	C₄	—	8	2	no	—
395	C₄	—	8	2	no	—
396	C₄	—	8	2	no	—
397	C₄	C₁₃×#534	1	1	yes	characteristic
398	C₄	C₁₃×#575	1	1	yes	characteristic
399	C₂	—	4	1	no	—
400	C₂	—	4	1	no	—
401	C₂	—	4	1	no	—
402	C₂	—	16	2	no	—
403	C₂	C₁₃×#3186	1	1	yes	characteristic
404	C₂	C₁₃×#3416	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂²×D₈
commutator, Frattini, cosocle	C₂×C₈	C₂⁴×C₁₃
prime radical	C₁₃×#3058	C₂
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₂×C₁₃×#41 ◁ C₂×C₁₃×#131 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₃×#3059	C₂	semidirect
3. C₁₃×#2237	C₂	semidirect
4. C₁₃×#2234	C₂	semidirect
5. C₁₃×#2220	C₂	semidirect
6. C₁₃×#2217	C₂	semidirect
7. C₁₃×#2187	C₂	semidirect
8. C₁₃×#2185	C₂	semidirect
9. C₁₃×#2113	C₂	semidirect
10. C₂²×C₁₃×Q₁₆	C₂²	semidirect
17. C₂×C₁₃×M₃₂	C₂²	semidirect
18. C₂²×C₁₃×C₁₆	C₂²	semidirect
24. C₁₃×#467	C₂²	semidirect
28. C₁₃×#427	C₂²	semidirect
31. C₁₃×#367	C₂²	semidirect
32. C₁₃×#366	C₂²	semidirect
33. C₁₃×#358	C₂²	semidirect
34. C₁₃×#358	C₂²	semidirect
38. C₁₃×C₂²⋊C₁₆	C₂²	semidirect
86. #33766	C₁₃	direct (N × H)
141. #3059	C₂×C₁₃	semidirect
143. #2237	C₂×C₁₃	semidirect
144. #2234	C₂×C₁₃	semidirect
145. #2220	C₂×C₁₃	semidirect
146. #2217	C₂×C₁₃	semidirect
147. #2187	C₂×C₁₃	semidirect
148. #2185	C₂×C₁₃	semidirect
149. #2113	C₂×C₁₃	semidirect
187. C₂²×Q₁₆	C₂²×C₁₃	semidirect
194. C₂×M₃₂	C₂²×C₁₃	semidirect
195. C₂²×C₁₆	C₂²×C₁₃	semidirect
201. #467	C₂²×C₁₃	semidirect
205. #427	C₂²×C₁₃	semidirect
208. #367	C₂²×C₁₃	semidirect
209. #366	C₂²×C₁₃	semidirect
210. #358	C₂²×C₁₃	semidirect
211. #358	C₂²×C₁₃	semidirect
215. C₂²⋊C₁₆	C₂²×C₁₃	semidirect
342. C₁₃	#33766	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×#3059	2
C₁₃×#3058	2
C₁₃×#2237	2
C₁₃×#2234	2
C₁₃×#2220	2
C₁₃×#2217	2
C₁₃×#2187	2
C₁₃×#2185	2
C₁₃×#2113	2
#33766	13

Subgroups — C13×#33766 #15720105

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#33766 #15720105