Subgroups — C₁₃×#33737 #15720076

Order 3328.

554 conjugacy classes of subgroups.

The subgroup lattice has 398 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3169	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃×#3168	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#2255	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#2250	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#2244	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#2243	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#2220	C₂	1	2	yes	maximal, complemented
8	C₁₃×#2218	C₂	1	2	yes	maximal, complemented
9	C₄×C₁₃×SD₃₂	C₂	1	2	yes	maximal, complemented
10	C₄×C₁₃×D₁₆	C₂	1	2	yes	maximal, complemented
11	C₄×C₁₃×M₃₂	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#532	—	2	1	no	—
13	C₁₃×#529	—	2	1	no	—
14	C₂×C₁₃×SD₃₂	C₂²	1	2	yes	—
15	C₂×C₁₃×D₁₆	C₂²	1	2	yes	—
16	C₂×C₁₃×M₃₂	C₂²	1	2	yes	—
17	C₁₃×#500	C₂²	1	1	yes	characteristic
18	C₁₃×#499	C₂²	1	1	yes	characteristic
19	C₁₃×#495	C₂²	1	1	yes	characteristic
20	C₁₃×#493	C₂²	1	1	yes	characteristic
21	C₁₃×#488	—	2	1	no	—
22	C₁₃×#486	—	2	1	no	—
23	C₁₃×#467	C₂²	1	1	yes	characteristic
24	C₁₃×#466	—	2	1	no	—
25	C₁₃×#466	C₂²	1	1	yes	characteristic
26	C₁₃×#466	C₂²	1	2	yes	—
27	C₁₃×#465	—	2	1	no	—
28	C₄×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic
29	C₄×C₁₃×SD₁₆	—	2	1	no	—
30	C₄×C₁₃×D₈	—	2	1	no	—
31	C₄×C₁₃×D₈	C₂²	1	1	yes	characteristic
32	C₄×C₁₃×D₈	C₂²	1	2	yes	—
33	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
34	C₁₃×#367	C₂²	1	2	yes	—
35	C₁₃×#366	C₂²	1	2	yes	—
36	C₁₃×#358	C₂²	1	2	yes	—
37	C₁₃×#357	C₂²	1	2	yes	—
38	C₁₃×#357	C₂²	1	2	yes	—
39	C₁₃×#357	C₂²	1	2	yes	—
40	C₁₃×#346	C₂²	1	1	yes	characteristic
41	C₁₃×#346	C₂²	1	1	yes	characteristic
42	C₄×C₁₃×C₁₆	C₂²	1	2	yes	—
43	C₂×C₁₃×#41	—	4	1	no	—
44	C₂×C₁₃×Q₁₆	C₂³	1	1	yes	characteristic
45	C₂×C₁₃×SD₁₆	—	2	1	no	—
46	C₂×C₁₃×D₈	—	2	1	no	—
47	C₂×C₁₃×D₈	C₂³	1	2	yes	—
48	C₂×C₁₃×D₈	C₂³	1	1	yes	characteristic
49	C₂²×C₈×C₁₃	D₄	1	1	yes	characteristic
50	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
51	C₁₃×C₄⋊Q₈	—	2	1	no	—
52	C₁₃×#127	—	2	1	no	—
53	C₁₃×#126	—	4	1	no	—
54	C₁₃×#125	—	2	1	no	—
55	C₁₃×#124	—	2	1	no	—
56	C₁₃×#124	—	4	1	no	—
57	C₁₃×#123	—	4	1	no	—
58	C₁₃×C₂²⋊Q₈	—	2	1	no	—
59	C₁₃×#121	—	2	1	no	—
60	C₁₃×#121	—	2	2	no	—
61	C₁₃×#121	—	4	1	no	—
62	C₄×Q₈×C₁₃	—	2	1	no	—
63	C₄×D₄×C₁₃	—	2	2	no	—
64	C₄×D₄×C₁₃	—	2	1	no	—
65	C₄×D₄×C₁₃	—	4	1	no	—
66	C₄×D₄×C₁₃	—	4	1	no	—
67	C₁₃×#117	—	4	1	no	—
68	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
69	C₁₃×SD₃₂	—	2	4	no	—
70	C₁₃×D₁₆	—	2	4	no	—
71	C₁₃×M₃₂	—	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	1	yes	characteristic
76	C₁₃×#107	C₂³	1	1	yes	characteristic
77	C₁₃×#107	C₂³	1	2	yes	—
78	C₁₃×#106	—	2	1	no	—
79	C₁₃×#103	—	2	1	no	—
80	C₁₃×#103	—	2	1	no	—
81	C₁₃×#102	—	2	2	no	—
82	C₁₃×#102	—	2	1	no	—
83	C₁₃×#102	—	2	2	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	#33737	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
90	C₁₃×#41	—	8	4	no	—
91	C₂×Q₈×C₁₃	—	2	1	no	—
92	C₂×Q₈×C₁₃	—	4	1	no	—
93	C₂×D₄×C₁₃	—	2	1	no	—
94	C₂×D₄×C₁₃	—	2	2	no	—
95	C₂×D₄×C₁₃	—	4	1	no	—
96	C₂×D₄×C₁₃	—	4	2	no	—
97	C₂×D₄×C₁₃	—	4	1	no	—
98	C₂×D₄×C₁₃	—	4	1	no	—
99	C₂²×C₄×C₁₃	—	4	1	no	—
100	C₂²×C₄×C₁₃	—	4	2	no	—
101	C₂²×C₄×C₁₃	D₈	1	1	yes	characteristic
102	C₂²×C₄×C₁₃	D₈	1	1	yes	characteristic
103	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
104	C₁₃×Q₁₆	—	2	2	no	—
105	C₁₃×SD₁₆	—	4	2	no	—
106	C₁₃×D₈	—	2	2	no	—
107	C₁₃×D₈	—	2	2	no	—
108	C₁₃×D₈	—	2	2	no	—
109	C₁₃×D₈	—	4	2	no	—
110	C₂×C₈×C₁₃	—	2	2	no	—
111	C₂×C₈×C₁₃	—	2	2	no	—
112	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
113	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
114	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
115	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
116	C₁₃×C₄⋊C₄	—	2	2	no	—
117	C₁₃×C₄⋊C₄	—	2	1	no	—
118	C₁₃×C₄⋊C₄	—	2	1	no	—
119	C₁₃×C₄⋊C₄	—	4	1	no	—
120	C₁₃×C₄⋊C₄	—	4	1	no	—
121	C₁₃×C₄⋊C₄	—	4	1	no	—
122	C₁₃×C₄⋊C₄	—	4	1	no	—
123	C₁₃×C₄⋊C₄	—	4	1	no	—
124	C₁₃×C₂²⋊C₄	—	4	1	no	—
125	C₁₃×C₂²⋊C₄	—	4	1	no	—
126	C₁₃×C₂²⋊C₄	—	4	1	no	—
127	C₁₃×C₂²⋊C₄	—	4	2	no	—
128	C₁₃×C₂²⋊C₄	—	4	1	no	—
129	C₁₃×C₂²⋊C₄	—	4	2	no	—
130	C₁₃×C₂²⋊C₄	—	4	1	no	—
131	C₄²×C₁₃	—	4	1	no	—
132	C₄²×C₁₃	D₈	1	1	yes	characteristic
133	C₄²×C₁₃	D₈	1	1	yes	characteristic
134	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
135	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
136	C₁₃×C₁₆	—	2	2	no	—
137	C₁₃×C₁₆	#41	1	4	yes	complemented
138	#3169	C₂×C₁₃	1	1	yes	characteristic, complemented
139	#3168	C₂×C₁₃	1	1	yes	characteristic, complemented
140	#2255	C₂×C₁₃	1	1	yes	characteristic, complemented
141	#2250	C₂×C₁₃	1	1	yes	characteristic, complemented
142	#2244	C₂×C₁₃	1	1	yes	characteristic, complemented
143	#2243	C₂×C₁₃	1	1	yes	characteristic, complemented
144	#2220	C₂×C₁₃	1	2	yes	complemented
145	#2218	C₂×C₁₃	1	2	yes	complemented
146	C₄×SD₃₂	C₂×C₁₃	1	2	yes	complemented
147	C₄×D₁₆	C₂×C₁₃	1	2	yes	complemented
148	C₄×M₃₂	C₂×C₁₃	1	1	yes	characteristic, complemented
149	C₂³×C₁₃	—	4	1	no	—
150	C₂³×C₁₃	—	4	2	no	—
151	C₂³×C₁₃	C₂×D₈	1	1	yes	characteristic
152	Q₈×C₁₃	—	4	1	no	—
153	Q₈×C₁₃	—	4	1	no	—
154	Q₈×C₁₃	—	8	2	no	—
155	D₄×C₁₃	—	4	1	no	—
156	D₄×C₁₃	—	4	2	no	—
157	D₄×C₁₃	—	4	2	no	—
158	D₄×C₁₃	—	4	1	no	—
159	D₄×C₁₃	—	8	2	no	—
160	D₄×C₁₃	—	8	2	no	—
161	D₄×C₁₃	—	8	2	no	—
162	D₄×C₁₃	—	8	4	no	—
163	C₂×C₄×C₁₃	—	2	1	no	—
164	C₂×C₄×C₁₃	—	2	1	no	—
165	C₂×C₄×C₁₃	—	2	2	no	—
166	C₂×C₄×C₁₃	—	4	1	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	—	4	2	no	—
171	C₂×C₄×C₁₃	—	8	2	no	—
172	C₂×C₄×C₁₃	—	8	4	no	—
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	C₂×D₈	1	1	yes	characteristic
178	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
179	C₈×C₁₃	—	2	1	no	—
180	C₈×C₁₃	—	2	1	no	—
181	C₈×C₁₃	#135	1	2	yes	—
182	C₈×C₁₃	C₂×#41	1	2	yes	—
183	#532	—	2	1	no	—
184	#529	—	2	1	no	—
185	C₂×SD₃₂	C₂²×C₁₃	1	2	yes	—
186	C₂×D₁₆	C₂²×C₁₃	1	2	yes	—
187	C₂×M₃₂	C₂²×C₁₃	1	2	yes	—
188	#500	C₂²×C₁₃	1	1	yes	characteristic
189	#499	C₂²×C₁₃	1	1	yes	characteristic
190	#495	C₂²×C₁₃	1	1	yes	characteristic
191	#493	C₂²×C₁₃	1	1	yes	characteristic
192	#488	—	2	1	no	—
193	#486	—	2	1	no	—
194	#467	C₂²×C₁₃	1	1	yes	characteristic
195	#466	—	2	1	no	—
196	#466	C₂²×C₁₃	1	1	yes	characteristic
197	#466	C₂²×C₁₃	1	2	yes	—
198	#465	—	2	1	no	—
199	C₄×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic
200	C₄×SD₁₆	—	2	1	no	—
201	C₄×D₈	—	2	1	no	—
202	C₄×D₈	C₂²×C₁₃	1	1	yes	characteristic
203	C₄×D₈	C₂²×C₁₃	1	2	yes	—
204	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
205	#367	C₂²×C₁₃	1	2	yes	—
206	#366	C₂²×C₁₃	1	2	yes	—
207	#358	C₂²×C₁₃	1	2	yes	—
208	#357	C₂²×C₁₃	1	2	yes	—
209	#357	C₂²×C₁₃	1	2	yes	—
210	#357	C₂²×C₁₃	1	2	yes	—
211	#346	C₂²×C₁₃	1	1	yes	characteristic
212	#346	C₂²×C₁₃	1	1	yes	characteristic
213	C₄×C₁₆	C₂²×C₁₃	1	2	yes	—
214	C₂²×C₁₃	—	2	1	no	—
215	C₂²×C₁₃	—	2	1	no	—
216	C₂²×C₁₃	—	2	1	no	—
217	C₂²×C₁₃	—	8	2	no	—
218	C₂²×C₁₃	—	8	1	no	—
219	C₂²×C₁₃	—	8	2	no	—
220	C₂²×C₁₃	—	8	1	no	—
221	C₂²×C₁₃	—	8	2	no	—
222	C₂²×C₁₃	—	8	1	no	—
223	C₂²×C₁₃	C₂²×D₈	1	1	yes	characteristic
224	C₄×C₁₃	—	2	1	no	—
225	C₄×C₁₃	—	2	1	no	—
226	C₄×C₁₃	—	2	1	no	—
227	C₄×C₁₃	—	2	1	no	—
228	C₄×C₁₃	—	8	1	no	—
229	C₄×C₁₃	—	8	2	no	—
230	C₄×C₁₃	—	8	1	no	—
231	C₄×C₁₃	—	8	1	no	—
232	C₄×C₁₃	#509	1	2	yes	—
233	C₄×C₁₃	#532	1	1	yes	characteristic
234	C₄×C₁₃	C₂×#135	1	1	yes	characteristic
235	C₂×#41	—	4	1	no	—
236	C₂×Q₁₆	C₂³×C₁₃	1	1	yes	characteristic
237	C₂×SD₁₆	—	2	1	no	—
238	C₂×D₈	—	2	1	no	—
239	C₂×D₈	C₂³×C₁₃	1	2	yes	—
240	C₂×D₈	C₂³×C₁₃	1	1	yes	characteristic
241	C₂²×C₈	D₄×C₁₃	1	1	yes	characteristic
242	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
243	C₄⋊Q₈	—	2	1	no	—
244	#127	—	2	1	no	—
245	#126	—	4	1	no	—
246	#125	—	2	1	no	—
247	#124	—	2	1	no	—
248	#124	—	4	1	no	—
249	#123	—	4	1	no	—
250	C₂²⋊Q₈	—	2	1	no	—
251	#121	—	2	1	no	—
252	#121	—	2	2	no	—
253	#121	—	4	1	no	—
254	C₄×Q₈	—	2	1	no	—
255	C₄×D₄	—	2	1	no	—
256	C₄×D₄	—	2	2	no	—
257	C₄×D₄	—	4	1	no	—
258	C₄×D₄	—	4	1	no	—
259	#117	—	4	1	no	—
260	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
261	SD₃₂	—	2	4	no	—
262	D₁₆	—	2	4	no	—
263	M₃₂	—	2	4	no	—
264	C₂×C₁₆	C₂³×C₁₃	1	2	yes	—
265	C₂×C₁₆	C₂³×C₁₃	1	2	yes	—
266	#107	—	2	1	no	—
267	#107	C₂³×C₁₃	1	1	yes	characteristic
268	#107	C₂³×C₁₃	1	1	yes	characteristic
269	#107	C₂³×C₁₃	1	2	yes	—
270	#106	—	2	1	no	—
271	#103	—	2	1	no	—
272	#103	—	2	1	no	—
273	#102	—	2	2	no	—
274	#102	—	2	1	no	—
275	#102	—	2	2	no	—
276	#102	—	2	1	no	—
277	C₄×C₈	D₄×C₁₃	1	1	yes	characteristic
278	C₄×C₈	D₄×C₁₃	1	1	yes	characteristic
279	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
280	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
281	C₂×C₁₃	—	4	1	no	—
282	C₂×C₁₃	—	16	2	no	—
283	C₂×C₁₃	—	16	1	no	—
284	C₂×C₁₃	#3169	1	1	yes	characteristic
285	C₂×C₁₃	C₂×#509	1	1	yes	characteristic
286	C₂×C₁₃	#3414	1	1	yes	characteristic
287	#41	—	8	4	no	—
288	C₂×Q₈	—	2	1	no	—
289	C₂×Q₈	—	4	1	no	—
290	C₂×D₄	—	2	1	no	—
291	C₂×D₄	—	2	2	no	—
292	C₂×D₄	—	4	1	no	—
293	C₂×D₄	—	4	2	no	—
294	C₂×D₄	—	4	1	no	—
295	C₂×D₄	—	4	1	no	—
296	C₂²×C₄	—	4	1	no	—
297	C₂²×C₄	—	4	2	no	—
298	C₂²×C₄	C₁₃×D₈	1	1	yes	characteristic
299	C₂²×C₄	C₁₃×D₈	1	1	yes	characteristic
300	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
301	Q₁₆	—	2	2	no	—
302	SD₁₆	—	4	2	no	—
303	D₈	—	2	2	no	—
304	D₈	—	2	2	no	—
305	D₈	—	2	2	no	—
306	D₈	—	4	2	no	—
307	C₂×C₈	—	2	2	no	—
308	C₂×C₈	—	2	2	no	—
309	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
310	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
311	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
312	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
313	C₄⋊C₄	—	2	2	no	—
314	C₄⋊C₄	—	2	1	no	—
315	C₄⋊C₄	—	2	1	no	—
316	C₄⋊C₄	—	4	1	no	—
317	C₄⋊C₄	—	4	1	no	—
318	C₄⋊C₄	—	4	1	no	—
319	C₄⋊C₄	—	4	1	no	—
320	C₄⋊C₄	—	4	1	no	—
321	C₂²⋊C₄	—	4	1	no	—
322	C₂²⋊C₄	—	4	1	no	—
323	C₂²⋊C₄	—	4	1	no	—
324	C₂²⋊C₄	—	4	2	no	—
325	C₂²⋊C₄	—	4	1	no	—
326	C₂²⋊C₄	—	4	2	no	—
327	C₂²⋊C₄	—	4	1	no	—
328	C₄²	—	4	1	no	—
329	C₄²	C₁₃×D₈	1	1	yes	characteristic
330	C₄²	C₁₃×D₈	1	1	yes	characteristic
331	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
332	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
333	C₁₆	—	2	2	no	—
334	C₁₆	C₁₃×#41	1	4	yes	complemented
335	C₁₃	#33737	1	1	yes	characteristic, direct product factor, Sylow
336	C₂³	—	4	1	no	—
337	C₂³	—	4	2	no	—
338	C₂³	C₂×C₁₃×D₈	1	1	yes	characteristic
339	Q₈	—	4	1	no	—
340	Q₈	—	4	1	no	—
341	Q₈	—	8	2	no	—
342	D₄	—	4	1	no	—
343	D₄	—	4	2	no	—
344	D₄	—	4	2	no	—
345	D₄	—	4	1	no	—
346	D₄	—	8	2	no	—
347	D₄	—	8	2	no	—
348	D₄	—	8	2	no	—
349	D₄	—	8	4	no	—
350	C₂×C₄	—	2	2	no	—
351	C₂×C₄	—	2	1	no	—
352	C₂×C₄	—	2	1	no	—
353	C₂×C₄	—	4	1	no	—
354	C₂×C₄	—	4	1	no	—
355	C₂×C₄	—	4	1	no	—
356	C₂×C₄	—	4	1	no	—
357	C₂×C₄	—	4	2	no	—
358	C₂×C₄	—	8	2	no	—
359	C₂×C₄	—	8	4	no	—
360	C₂×C₄	C₂×C₁₃×D₈	1	1	yes	characteristic
361	C₂×C₄	C₂×C₁₃×D₈	1	1	yes	characteristic
362	C₂×C₄	C₂×C₁₃×D₈	1	1	yes	characteristic
363	C₂×C₄	C₂×C₁₃×D₈	1	1	yes	characteristic
364	C₂×C₄	C₂×C₁₃×D₈	1	1	yes	characteristic
365	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
366	C₈	—	2	1	no	—
367	C₈	—	2	1	no	—
368	C₈	C₁₃×#135	1	2	yes	—
369	C₈	C₂×C₁₃×#41	1	2	yes	—
370	C₂²	—	2	1	no	—
371	C₂²	—	2	1	no	—
372	C₂²	—	2	1	no	—
373	C₂²	—	8	2	no	—
374	C₂²	—	8	1	no	—
375	C₂²	—	8	2	no	—
376	C₂²	—	8	1	no	—
377	C₂²	—	8	2	no	—
378	C₂²	—	8	1	no	—
379	C₂²	C₂²×C₁₃×D₈	1	1	yes	characteristic
380	C₄	—	2	1	no	—
381	C₄	—	2	1	no	—
382	C₄	—	2	1	no	—
383	C₄	—	2	1	no	—
384	C₄	—	8	1	no	—
385	C₄	—	8	2	no	—
386	C₄	—	8	1	no	—
387	C₄	—	8	1	no	—
388	C₄	C₁₃×#509	1	2	yes	—
389	C₄	C₁₃×#532	1	1	yes	characteristic
390	C₄	C₂×C₁₃×#135	1	1	yes	characteristic
391	C₂	—	4	1	no	—
392	C₂	—	16	2	no	—
393	C₂	—	16	1	no	—
394	C₂	C₁₃×#3169	1	1	yes	characteristic
395	C₂	C₂×C₁₃×#509	1	1	yes	characteristic
396	C₂	C₁₃×#3414	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
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
1. C₁₃×#3169	C₂	semidirect
2. C₁₃×#3168	C₂	semidirect
3. C₁₃×#2255	C₂	semidirect
4. C₁₃×#2250	C₂	semidirect
5. C₁₃×#2244	C₂	semidirect
6. C₁₃×#2243	C₂	semidirect
7. C₁₃×#2220	C₂	semidirect
8. C₁₃×#2218	C₂	semidirect
9. C₄×C₁₃×SD₃₂	C₂	semidirect
10. C₄×C₁₃×D₁₆	C₂	semidirect
11. C₄×C₁₃×M₃₂	C₂	semidirect
89. #33737	C₁₃	direct (N × H)
137. C₁₃×C₁₆	#41	semidirect
138. #3169	C₂×C₁₃	semidirect
139. #3168	C₂×C₁₃	semidirect
140. #2255	C₂×C₁₃	semidirect
141. #2250	C₂×C₁₃	semidirect
142. #2244	C₂×C₁₃	semidirect
143. #2243	C₂×C₁₃	semidirect
144. #2220	C₂×C₁₃	semidirect
145. #2218	C₂×C₁₃	semidirect
146. C₄×SD₃₂	C₂×C₁₃	semidirect
147. C₄×D₁₆	C₂×C₁₃	semidirect
148. C₄×M₃₂	C₂×C₁₃	semidirect
334. C₁₆	C₁₃×#41	semidirect
335. C₁₃	#33737	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×#3169	2
C₁₃×#3168	2
C₁₃×#2255	2
C₁₃×#2250	2
C₁₃×#2244	2
C₁₃×#2243	2
C₁₃×#2220	2
C₁₃×#2218	2
C₄×C₁₃×SD₃₂	2
C₄×C₁₃×D₁₆	2
C₄×C₁₃×M₃₂	2
#33737	13

Subgroups — C13×#33737 #15720076

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#33737 #15720076