Subgroups — C₁₃×#33786 #15720125

Order 3328.

618 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3176	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃×#3155	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#2250	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#2246	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#2244	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#2242	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#2210	C₂	1	2	yes	maximal, complemented
8	C₁₃×#2206	C₂	1	2	yes	maximal, complemented
9	C₁₃×#2186	C₂	1	2	yes	maximal, complemented
10	C₁₃×#2184	C₂	1	2	yes	maximal, complemented
11	C₁₃×#2164	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₁₃×AGL(1,ℤ/8)	—	2	1	no	—
13	C₂×C₁₃×#135	C₂²	1	1	yes	characteristic
14	C₂²×C₁₃×D₈	C₂²	1	1	yes	characteristic
15	C₁₃×#540	—	2	1	no	—
16	C₁₃×#535	—	2	1	no	—
17	C₂×C₁₃×SD₃₂	C₂²	1	2	yes	complemented
18	C₂×C₁₃×D₁₆	C₂²	1	2	yes	—
19	C₂×C₁₃×D₁₆	C₂²	1	2	yes	—
20	C₂×C₁₃×D₁₆	C₂²	1	2	yes	complemented
21	C₁₃×#499	C₂²	1	1	yes	characteristic, complemented
22	C₁₃×#496	—	2	1	no	—
23	C₁₃×#496	—	2	1	no	—
24	C₁₃×#495	C₂²	1	1	yes	characteristic
25	C₁₃×#495	C₂²	1	1	yes	characteristic
26	C₁₃×#493	C₂²	1	1	yes	characteristic
27	C₁₃×#493	C₂²	1	1	yes	characteristic
28	C₁₃×#493	C₂²	1	1	yes	characteristic, complemented
29	C₁₃×#490	—	2	1	no	—
30	C₁₃×#469	—	2	1	no	—
31	C₁₃×#466	C₂²	1	2	yes	—
32	C₁₃×#442	—	2	1	no	—
33	C₄×C₁₃×D₈	C₂²	1	2	yes	complemented
34	C₁₃×#405	C₂²	1	1	yes	characteristic
35	C₁₃×C₄⋊C₁₆	C₂²	1	2	yes	complemented
36	C₁₃×#358	C₂²	1	2	yes	complemented
37	C₁₃×#357	C₂²	1	2	yes	—
38	C₁₃×#357	C₂²	1	2	yes	—
39	C₁₃×#357	C₂²	1	2	yes	complemented
40	C₁₃×C₂²⋊C₁₆	C₂²	1	2	yes	—
41	C₁₃×#346	C₂²	1	1	yes	characteristic, complemented
42	C₄×C₁₃×C₁₆	C₂²	1	1	yes	characteristic, complemented
43	C₂×C₁₃×#41	—	2	1	no	—
44	C₂²×D₄×C₁₃	—	2	1	no	—
45	C₁₃×AGL(1,ℤ/8)	—	4	4	no	—
46	C₁₃×#135	—	4	2	no	—
47	C₂×C₁₃×Q₁₆	C₂³	1	1	yes	characteristic
48	C₂×C₁₃×SD₁₆	—	2	1	no	—
49	C₂×C₁₃×SD₁₆	—	2	1	no	—
50	C₂×C₁₃×SD₁₆	—	2	1	no	—
51	C₂×C₁₃×D₈	—	2	1	no	—
52	C₂×C₁₃×D₈	—	2	1	no	—
53	C₂×C₁₃×D₈	—	2	1	no	—
54	C₂×C₁₃×D₈	—	2	1	no	—
55	C₂×C₁₃×D₈	—	4	2	no	—
56	C₂×C₁₃×D₈	C₂³	1	1	yes	characteristic
57	C₂×C₁₃×D₈	C₂³	1	1	yes	characteristic
58	C₂×C₁₃×D₈	C₂³	1	1	yes	characteristic
59	C₂×C₁₃×D₈	C₂³	1	2	yes	—
60	C₂×C₁₃×M₁₆	D₄	1	1	yes	characteristic
61	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
62	C₁₃×#127	—	2	1	no	—
63	C₁₃×#127	—	2	1	no	—
64	C₁₃×#127	—	2	1	no	—
65	C₁₃×#125	—	2	1	no	—
66	C₁₃×#124	—	2	1	no	—
67	C₁₃×#124	—	2	1	no	—
68	C₁₃×#123	—	4	2	no	—
69	C₁₃×#121	—	2	2	no	—
70	C₁₃×#121	—	4	2	no	—
71	C₁₃×#121	—	4	2	no	—
72	C₁₃×#120	—	4	2	no	—
73	C₄×D₄×C₁₃	—	2	2	no	—
74	C₁₃×#117	D₄	1	1	yes	characteristic
75	C₁₃×SD₃₂	—	4	2	no	—
76	C₁₃×D₁₆	—	4	2	no	—
77	C₁₃×D₁₆	—	4	2	no	—
78	C₁₃×D₁₆	—	4	2	no	—
79	C₂×C₁₃×C₁₆	C₂³	1	2	yes	—
80	C₂×C₁₃×C₁₆	C₂³	1	2	yes	—
81	C₁₃×#107	C₂³	1	2	yes	—
82	C₁₃×#106	—	2	1	no	—
83	C₁₃×#102	—	2	2	no	—
84	C₁₃×#102	—	2	2	no	—
85	C₁₃×#97	D₄	1	1	yes	characteristic
86	C₁₃×#97	D₄	1	1	yes	characteristic
87	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
88	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
89	#33786	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
90	C₂⁴×C₁₃	—	4	1	no	—
91	C₁₃×#41	—	4	2	no	—
92	C₁₃×#41	—	4	2	no	—
93	C₂×Q₈×C₁₃	—	2	1	no	—
94	C₂×D₄×C₁₃	—	2	2	no	—
95	C₂×D₄×C₁₃	—	2	1	no	—
96	C₂×D₄×C₁₃	—	2	1	no	—
97	C₂×D₄×C₁₃	—	2	1	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	—	4	2	no	—
102	C₂×D₄×C₁₃	—	4	1	no	—
103	C₂×D₄×C₁₃	—	4	2	no	—
104	C₂×D₄×C₁₃	—	4	2	no	—
105	C₂×D₄×C₁₃	—	4	2	no	—
106	C₂²×C₄×C₁₃	—	4	1	no	—
107	C₂²×C₄×C₁₃	—	4	2	no	—
108	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
109	C₁₃×Q₁₆	—	2	2	no	—
110	C₁₃×SD₁₆	—	4	2	no	—
111	C₁₃×SD₁₆	—	4	2	no	—
112	C₁₃×SD₁₆	—	4	2	no	—
113	C₁₃×D₈	—	2	2	no	—
114	C₁₃×D₈	—	2	2	no	—
115	C₁₃×D₈	—	2	2	no	—
116	C₁₃×D₈	—	2	2	no	—
117	C₁₃×D₈	—	2	2	no	—
118	C₁₃×D₈	—	4	2	no	—
119	C₁₃×D₈	—	4	2	no	—
120	C₁₃×D₈	—	4	2	no	—
121	C₁₃×D₈	—	4	2	no	—
122	C₁₃×M₁₆	—	2	2	no	—
123	C₂×C₈×C₁₃	—	2	2	no	—
124	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
125	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
126	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
127	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
128	C₁₃×C₄⋊C₄	—	2	2	no	—
129	C₁₃×C₄⋊C₄	—	4	2	no	—
130	C₁₃×C₄⋊C₄	D₈	1	2	yes	—
131	C₁₃×C₂²⋊C₄	—	4	2	no	—
132	C₁₃×C₂²⋊C₄	—	4	2	no	—
133	C₁₃×C₂²⋊C₄	—	4	2	no	—
134	C₁₃×C₂²⋊C₄	—	4	2	no	—
135	C₁₃×C₂²⋊C₄	D₈	1	2	yes	—
136	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
137	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
138	C₁₃×C₁₆	—	2	2	no	—
139	C₁₃×C₁₆	—	2	2	no	—
140	#3176	C₂×C₁₃	1	1	yes	characteristic, complemented
141	#3155	C₂×C₁₃	1	1	yes	characteristic, complemented
142	#2250	C₂×C₁₃	1	1	yes	characteristic, complemented
143	#2246	C₂×C₁₃	1	1	yes	characteristic, complemented
144	#2244	C₂×C₁₃	1	1	yes	characteristic, complemented
145	#2242	C₂×C₁₃	1	1	yes	characteristic, complemented
146	#2210	C₂×C₁₃	1	2	yes	complemented
147	#2206	C₂×C₁₃	1	2	yes	complemented
148	#2186	C₂×C₁₃	1	2	yes	complemented
149	#2184	C₂×C₁₃	1	2	yes	complemented
150	#2164	C₂×C₁₃	1	1	yes	characteristic, complemented
151	C₂³×C₁₃	—	4	2	no	—
152	C₂³×C₁₃	—	4	1	no	—
153	C₂³×C₁₃	—	4	1	no	—
154	C₂³×C₁₃	—	4	1	no	—
155	C₂³×C₁₃	—	8	2	no	—
156	C₂³×C₁₃	—	16	2	no	—
157	C₂³×C₁₃	C₂×D₈	1	1	yes	characteristic
158	Q₈×C₁₃	—	4	1	no	—
159	Q₈×C₁₃	—	4	1	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	1	no	—
165	D₄×C₁₃	—	4	1	no	—
166	D₄×C₁₃	—	4	1	no	—
167	D₄×C₁₃	—	4	2	no	—
168	D₄×C₁₃	—	8	2	no	—
169	D₄×C₁₃	—	8	2	no	—
170	D₄×C₁₃	—	16	2	no	—
171	D₄×C₁₃	—	16	2	no	—
172	D₄×C₁₃	—	16	2	no	—
173	D₄×C₁₃	—	16	2	no	—
174	C₂×C₄×C₁₃	—	2	1	no	—
175	C₂×C₄×C₁₃	—	2	1	no	—
176	C₂×C₄×C₁₃	—	4	1	no	—
177	C₂×C₄×C₁₃	—	4	2	no	—
178	C₂×C₄×C₁₃	—	8	2	no	—
179	C₂×C₄×C₁₃	—	16	2	no	—
180	C₂×C₄×C₁₃	C₂×D₈	1	2	yes	—
181	C₂×C₄×C₁₃	C₂×D₈	1	2	yes	—
182	C₂×C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
183	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
184	C₈×C₁₃	—	2	1	no	—
185	C₈×C₁₃	—	2	1	no	—
186	C₈×C₁₃	AGL(1,ℤ/8)	1	2	yes	—
187	C₈×C₁₃	H(5,𝔽₂)	1	2	yes	—
188	C₂×AGL(1,ℤ/8)	—	2	1	no	—
189	C₂×#135	C₂²×C₁₃	1	1	yes	characteristic
190	C₂²×D₈	C₂²×C₁₃	1	1	yes	characteristic
191	#540	—	2	1	no	—
192	#535	—	2	1	no	—
193	C₂×SD₃₂	C₂²×C₁₃	1	2	yes	complemented
194	C₂×D₁₆	C₂²×C₁₃	1	2	yes	—
195	C₂×D₁₆	C₂²×C₁₃	1	2	yes	—
196	C₂×D₁₆	C₂²×C₁₃	1	2	yes	complemented
197	#499	C₂²×C₁₃	1	1	yes	characteristic, complemented
198	#496	—	2	1	no	—
199	#496	—	2	1	no	—
200	#495	C₂²×C₁₃	1	1	yes	characteristic
201	#495	C₂²×C₁₃	1	1	yes	characteristic
202	#493	C₂²×C₁₃	1	1	yes	characteristic
203	#493	C₂²×C₁₃	1	1	yes	characteristic
204	#493	C₂²×C₁₃	1	1	yes	characteristic, complemented
205	#490	—	2	1	no	—
206	#469	—	2	1	no	—
207	#466	C₂²×C₁₃	1	2	yes	—
208	#442	—	2	1	no	—
209	C₄×D₈	C₂²×C₁₃	1	2	yes	complemented
210	#405	C₂²×C₁₃	1	1	yes	characteristic
211	C₄⋊C₁₆	C₂²×C₁₃	1	2	yes	complemented
212	#358	C₂²×C₁₃	1	2	yes	complemented
213	#357	C₂²×C₁₃	1	2	yes	—
214	#357	C₂²×C₁₃	1	2	yes	—
215	#357	C₂²×C₁₃	1	2	yes	complemented
216	C₂²⋊C₁₆	C₂²×C₁₃	1	2	yes	—
217	#346	C₂²×C₁₃	1	1	yes	characteristic, complemented
218	C₄×C₁₆	C₂²×C₁₃	1	1	yes	characteristic, complemented
219	C₂²×C₁₃	—	2	2	no	—
220	C₂²×C₁₃	—	2	1	no	—
221	C₂²×C₁₃	—	8	2	no	—
222	C₂²×C₁₃	—	8	2	no	—
223	C₂²×C₁₃	—	8	2	no	—
224	C₂²×C₁₃	—	8	2	no	—
225	C₂²×C₁₃	—	8	2	no	—
226	C₂²×C₁₃	—	8	1	no	—
227	C₂²×C₁₃	—	8	1	no	—
228	C₂²×C₁₃	—	8	1	no	—
229	C₂²×C₁₃	—	8	2	no	—
230	C₂²×C₁₃	—	16	4	no	—
231	C₂²×C₁₃	C₂²×D₈	1	1	yes	characteristic
232	C₄×C₁₃	—	2	2	no	—
233	C₄×C₁₃	—	2	2	no	—
234	C₄×C₁₃	—	2	1	no	—
235	C₄×C₁₃	—	8	2	no	—
236	C₄×C₁₃	—	8	1	no	—
237	C₄×C₁₃	#535	1	1	yes	characteristic
238	C₄×C₁₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
239	C₂×#41	—	2	1	no	—
240	C₂²×D₄	—	2	1	no	—
241	AGL(1,ℤ/8)	—	4	4	no	—
242	#135	—	4	2	no	—
243	C₂×Q₁₆	C₂³×C₁₃	1	1	yes	characteristic
244	C₂×SD₁₆	—	2	1	no	—
245	C₂×SD₁₆	—	2	1	no	—
246	C₂×SD₁₆	—	2	1	no	—
247	C₂×D₈	—	2	1	no	—
248	C₂×D₈	—	2	1	no	—
249	C₂×D₈	—	2	1	no	—
250	C₂×D₈	—	2	1	no	—
251	C₂×D₈	—	4	2	no	—
252	C₂×D₈	C₂³×C₁₃	1	1	yes	characteristic
253	C₂×D₈	C₂³×C₁₃	1	1	yes	characteristic
254	C₂×D₈	C₂³×C₁₃	1	1	yes	characteristic
255	C₂×D₈	C₂³×C₁₃	1	2	yes	—
256	C₂×M₁₆	D₄×C₁₃	1	1	yes	characteristic
257	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
258	#127	—	2	1	no	—
259	#127	—	2	1	no	—
260	#127	—	2	1	no	—
261	#125	—	2	1	no	—
262	#124	—	2	1	no	—
263	#124	—	2	1	no	—
264	#123	—	4	2	no	—
265	#121	—	2	2	no	—
266	#121	—	4	2	no	—
267	#121	—	4	2	no	—
268	#120	—	4	2	no	—
269	C₄×D₄	—	2	2	no	—
270	#117	D₄×C₁₃	1	1	yes	characteristic
271	SD₃₂	—	4	2	no	—
272	D₁₆	—	4	2	no	—
273	D₁₆	—	4	2	no	—
274	D₁₆	—	4	2	no	—
275	C₂×C₁₆	C₂³×C₁₃	1	2	yes	—
276	C₂×C₁₆	C₂³×C₁₃	1	2	yes	—
277	#107	C₂³×C₁₃	1	2	yes	—
278	#106	—	2	1	no	—
279	#102	—	2	2	no	—
280	#102	—	2	2	no	—
281	#97	D₄×C₁₃	1	1	yes	characteristic
282	#97	D₄×C₁₃	1	1	yes	characteristic
283	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
284	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
285	C₂×C₁₃	—	4	1	no	—
286	C₂×C₁₃	—	16	2	no	—
287	C₂×C₁₃	—	16	1	no	—
288	C₂×C₁₃	—	16	1	no	—
289	C₂×C₁₃	—	16	1	no	—
290	C₂×C₁₃	#3205	1	1	yes	characteristic
291	C₂×C₁₃	#3415	1	2	yes	—
292	C₂⁴	—	4	1	no	—
293	#41	—	4	2	no	—
294	#41	—	4	2	no	—
295	C₂×Q₈	—	2	1	no	—
296	C₂×D₄	—	2	2	no	—
297	C₂×D₄	—	2	1	no	—
298	C₂×D₄	—	2	1	no	—
299	C₂×D₄	—	2	1	no	—
300	C₂×D₄	—	4	2	no	—
301	C₂×D₄	—	4	2	no	—
302	C₂×D₄	—	4	1	no	—
303	C₂×D₄	—	4	2	no	—
304	C₂×D₄	—	4	1	no	—
305	C₂×D₄	—	4	2	no	—
306	C₂×D₄	—	4	2	no	—
307	C₂×D₄	—	4	2	no	—
308	C₂²×C₄	—	4	1	no	—
309	C₂²×C₄	—	4	2	no	—
310	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
311	Q₁₆	—	2	2	no	—
312	SD₁₆	—	4	2	no	—
313	SD₁₆	—	4	2	no	—
314	SD₁₆	—	4	2	no	—
315	D₈	—	2	2	no	—
316	D₈	—	2	2	no	—
317	D₈	—	2	2	no	—
318	D₈	—	2	2	no	—
319	D₈	—	2	2	no	—
320	D₈	—	4	2	no	—
321	D₈	—	4	2	no	—
322	D₈	—	4	2	no	—
323	D₈	—	4	2	no	—
324	M₁₆	—	2	2	no	—
325	C₂×C₈	—	2	2	no	—
326	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
327	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
328	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
329	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
330	C₄⋊C₄	—	2	2	no	—
331	C₄⋊C₄	—	4	2	no	—
332	C₄⋊C₄	C₁₃×D₈	1	2	yes	—
333	C₂²⋊C₄	—	4	2	no	—
334	C₂²⋊C₄	—	4	2	no	—
335	C₂²⋊C₄	—	4	2	no	—
336	C₂²⋊C₄	—	4	2	no	—
337	C₂²⋊C₄	C₁₃×D₈	1	2	yes	—
338	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
339	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
340	C₁₆	—	2	2	no	—
341	C₁₆	—	2	2	no	—
342	C₁₃	#33786	1	1	yes	characteristic, direct product factor, Sylow
343	C₂³	—	4	2	no	—
344	C₂³	—	4	1	no	—
345	C₂³	—	4	1	no	—
346	C₂³	—	4	1	no	—
347	C₂³	—	8	2	no	—
348	C₂³	—	16	2	no	—
349	C₂³	C₂×C₁₃×D₈	1	1	yes	characteristic
350	Q₈	—	4	1	no	—
351	Q₈	—	4	1	no	—
352	D₄	—	4	1	no	—
353	D₄	—	4	1	no	—
354	D₄	—	4	1	no	—
355	D₄	—	4	2	no	—
356	D₄	—	4	1	no	—
357	D₄	—	4	1	no	—
358	D₄	—	4	1	no	—
359	D₄	—	4	2	no	—
360	D₄	—	8	2	no	—
361	D₄	—	8	2	no	—
362	D₄	—	16	2	no	—
363	D₄	—	16	2	no	—
364	D₄	—	16	2	no	—
365	D₄	—	16	2	no	—
366	C₂×C₄	—	2	1	no	—
367	C₂×C₄	—	2	1	no	—
368	C₂×C₄	—	4	1	no	—
369	C₂×C₄	—	4	2	no	—
370	C₂×C₄	—	8	2	no	—
371	C₂×C₄	—	16	2	no	—
372	C₂×C₄	C₂×C₁₃×D₈	1	2	yes	—
373	C₂×C₄	C₂×C₁₃×D₈	1	2	yes	—
374	C₂×C₄	C₂×C₁₃×D₈	1	1	yes	characteristic
375	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
376	C₈	—	2	1	no	—
377	C₈	—	2	1	no	—
378	C₈	C₁₃×AGL(1,ℤ/8)	1	2	yes	—
379	C₈	C₁₃×H(5,𝔽₂)	1	2	yes	—
380	C₂²	—	2	2	no	—
381	C₂²	—	2	1	no	—
382	C₂²	—	8	2	no	—
383	C₂²	—	8	2	no	—
384	C₂²	—	8	2	no	—
385	C₂²	—	8	2	no	—
386	C₂²	—	8	2	no	—
387	C₂²	—	8	1	no	—
388	C₂²	—	8	1	no	—
389	C₂²	—	8	1	no	—
390	C₂²	—	8	2	no	—
391	C₂²	—	16	4	no	—
392	C₂²	C₂²×C₁₃×D₈	1	1	yes	characteristic
393	C₄	—	2	2	no	—
394	C₄	—	2	2	no	—
395	C₄	—	2	1	no	—
396	C₄	—	8	2	no	—
397	C₄	—	8	1	no	—
398	C₄	C₁₃×#535	1	1	yes	characteristic
399	C₄	C₂×C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
400	C₂	—	4	1	no	—
401	C₂	—	16	1	no	—
402	C₂	—	16	1	no	—
403	C₂	—	16	2	no	—
404	C₂	—	16	1	no	—
405	C₂	C₁₃×#3205	1	1	yes	characteristic
406	C₂	C₁₃×#3415	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂²×D₈
commutator, Frattini, cosocle	C₂×C₈	C₂⁴×C₁₃
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₁₃×#117 ◁ C₁₃×#405 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₃×#3176	C₂	semidirect
2. C₁₃×#3155	C₂	semidirect
3. C₁₃×#2250	C₂	semidirect
4. C₁₃×#2246	C₂	semidirect
5. C₁₃×#2244	C₂	semidirect
6. C₁₃×#2242	C₂	semidirect
7. C₁₃×#2210	C₂	semidirect
8. C₁₃×#2206	C₂	semidirect
9. C₁₃×#2186	C₂	semidirect
10. C₁₃×#2184	C₂	semidirect
11. C₁₃×#2164	C₂	semidirect
17. C₂×C₁₃×SD₃₂	C₂²	semidirect
20. C₂×C₁₃×D₁₆	C₂²	semidirect
21. C₁₃×#499	C₂²	semidirect
28. C₁₃×#493	C₂²	semidirect
33. C₄×C₁₃×D₈	C₂²	semidirect
35. C₁₃×C₄⋊C₁₆	C₂²	semidirect
36. C₁₃×#358	C₂²	semidirect
39. C₁₃×#357	C₂²	semidirect
41. C₁₃×#346	C₂²	semidirect
42. C₄×C₁₃×C₁₆	C₂²	semidirect
89. #33786	C₁₃	direct (N × H)
140. #3176	C₂×C₁₃	semidirect
141. #3155	C₂×C₁₃	semidirect
142. #2250	C₂×C₁₃	semidirect
143. #2246	C₂×C₁₃	semidirect
144. #2244	C₂×C₁₃	semidirect
145. #2242	C₂×C₁₃	semidirect
146. #2210	C₂×C₁₃	semidirect
147. #2206	C₂×C₁₃	semidirect
148. #2186	C₂×C₁₃	semidirect
149. #2184	C₂×C₁₃	semidirect
150. #2164	C₂×C₁₃	semidirect
193. C₂×SD₃₂	C₂²×C₁₃	semidirect
196. C₂×D₁₆	C₂²×C₁₃	semidirect
197. #499	C₂²×C₁₃	semidirect
204. #493	C₂²×C₁₃	semidirect
209. C₄×D₈	C₂²×C₁₃	semidirect
211. C₄⋊C₁₆	C₂²×C₁₃	semidirect
212. #358	C₂²×C₁₃	semidirect
215. #357	C₂²×C₁₃	semidirect
217. #346	C₂²×C₁₃	semidirect
218. C₄×C₁₆	C₂²×C₁₃	semidirect
342. C₁₃	#33786	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×#3176	2
C₁₃×#3155	2
C₁₃×#2250	2
C₁₃×#2246	2
C₁₃×#2244	2
C₁₃×#2242	2
C₁₃×#2210	2
C₁₃×#2206	2
C₁₃×#2186	2
C₁₃×#2184	2
C₁₃×#2164	2
#33786	13

Subgroups — C13×#33786 #15720125

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#33786 #15720125