Subgroups — #15834689

Order 3328.

654 conjugacy classes of subgroups.

The subgroup lattice has 428 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13125395	C₂	1	1	yes	maximal, characteristic
2	#13123783	C₂	1	1	yes	maximal, characteristic, complemented
3	#13123582	C₂	1	1	yes	maximal, characteristic
4	#13113728	C₂	1	2	yes	maximal, complemented
5	#13113681	C₂	1	2	yes	maximal, complemented
6	#13113674	C₂	1	2	yes	maximal, complemented
7	C₈×#6095	C₂	1	2	yes	maximal, complemented
8	C₂×#11718049	C₂	1	1	yes	maximal, characteristic, complemented
9	#13113240	C₂	1	1	yes	maximal, characteristic, complemented
10	#13113236	C₂	1	1	yes	maximal, characteristic
11	C₈×C₁₃×M₁₆	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#88161	—	2	1	no	—
13	#11719182	C₂²	1	1	yes	characteristic
14	#11719175	C₂²	1	1	yes	characteristic
15	C₁₃×#431	C₂²	1	1	yes	characteristic
16	C₄×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
17	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
18	#11718790	—	2	1	no	—
19	#11718783	—	2	1	no	—
20	#11718780	—	2	1	no	—
21	#11718775	C₄	1	2	yes	—
22	#11718775	C₄	1	2	yes	—
23	C₂×C₄⋊#1055	C₂²	1	1	yes	characteristic
24	C₂×C₄⋊#1055	C₂²	1	1	yes	characteristic
25	#11718367	—	2	2	no	—
26	#11718362	—	2	2	no	—
27	#11718355	C₄	1	1	yes	characteristic
28	#11718354	C₄	1	1	yes	characteristic
29	C₄×#6095	C₂²	1	2	yes	—
30	C₄×#6095	C₂²	1	2	yes	—
31	#11718349	C₂²	1	2	yes	—
32	C₈×D₅₂	C₂²	1	2	yes	—
33	#11718342	C₄	1	1	yes	characteristic
34	#11718341	C₄	1	1	yes	characteristic
35	#11718340	C₂²	1	2	yes	—
36	C₈×Dic₂₆	C₂²	1	2	yes	—
37	C₁₃×#322	C₂²	1	2	yes	—
38	C₈²×C₁₃	C₂²	1	2	yes	—
39	#11718051	C₂²	1	2	yes	—
40	#11718051	C₂²	1	2	yes	—
41	#11718049	C₂²	1	1	yes	characteristic
42	#11718049	C₂²	1	1	yes	characteristic
43	#11718049	C₂²	1	1	yes	characteristic
44	#11718049	C₂²	1	1	yes	characteristic
45	#11718048	C₂²	1	2	yes	—
46	#11718048	C₂²	1	2	yes	—
47	C₂×#6127	—	2	1	no	—
48	C₂×C₁₃×M₁₆	D₄	1	1	yes	characteristic
49	C₂×C₁₃×M₁₆	D₄	1	1	yes	characteristic
50	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
51	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
52	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
53	#88184	—	2	1	no	—
54	#88184	C₂×C₄	1	2	yes	—
55	#88180	—	2	1	no	—
56	#88178	—	2	1	no	—
57	#88178	C₂×C₄	1	2	yes	—
58	C₂²×#1055	—	2	1	no	—
59	C₂²×#1055	—	2	1	no	—
60	#88161	—	4	4	no	—
61	C₂×#6095	C₂×C₄	1	2	yes	—
62	C₂×#6095	C₂×C₄	1	2	yes	—
63	C₂×#6094	—	2	2	no	—
64	C₂×C₈×D₁₃	—	2	2	no	—
65	#88129	—	2	1	no	—
66	#88128	C₂×C₄	1	1	yes	characteristic
67	C₄×D₅₂	—	2	1	no	—
68	C₄×D₅₂	C₂³	1	2	yes	—
69	#88124	—	2	1	no	—
70	#88123	C₂×C₄	1	1	yes	characteristic
71	#88123	C₂×C₄	1	1	yes	characteristic
72	#88123	C₂×C₄	1	1	yes	characteristic
73	C₄×Dic₂₆	—	2	1	no	—
74	C₄×Dic₂₆	C₂³	1	2	yes	—
75	C₁₃×C₄⋊C₈	—	2	1	no	—
76	C₁₃×C₂²⋊C₈	—	2	1	no	—
77	C₁₃×#97	D₄	1	2	yes	—
78	C₄×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
79	C₄×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
80	C₄×C₈×C₁₃	C₂³	1	2	yes	—
81	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
82	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
83	C₄×C₈×C₁₃	C₂³	1	2	yes	—
84	#88061	C₂×C₄	1	2	yes	—
85	#88061	C₂×C₄	1	2	yes	—
86	#88060	—	2	2	no	—
87	#88060	—	2	2	no	—
88	#88057	C₂×C₄	1	2	yes	—
89	#88057	C₂×C₄	1	2	yes	—
90	#88056	C₂×C₄	1	2	yes	—
91	#88056	C₂×C₄	1	2	yes	—
92	#88055	—	2	2	no	—
93	#88054	—	2	2	no	—
94	#88054	—	2	2	no	—
95	C₈×Dic₁₃	—	2	2	no	—
96	C₄⋊#1055	—	2	1	no	—
97	C₄⋊#1055	—	2	1	no	—
98	C₄⋊#1055	C₂³	1	1	yes	characteristic
99	C₄⋊#1055	C₂³	1	1	yes	characteristic
100	C₄⋊#1055	C₂³	1	1	yes	characteristic
101	C₄⋊#1055	C₂³	1	1	yes	characteristic
102	#18067	—	13	1	no	maximal, Sylow
103	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
104	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
105	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
106	C₂×C₂²⋊D₁₃	—	2	2	no	—
107	#6127	—	4	2	no	—
108	#6127	—	4	2	no	—
109	C₂×D₅₂	—	2	1	no	—
110	C₂×D₅₂	—	2	1	no	—
111	C₂×D₅₂	C₂²×C₄	1	2	yes	—
112	C₂×C₄×D₁₃	—	2	2	no	—
113	C₂×Dic₂₆	—	2	1	no	—
114	C₂×Dic₂₆	—	2	1	no	—
115	C₂×Dic₂₆	C₂²×C₄	1	2	yes	—
116	C₁₃×M₁₆	—	2	2	no	—
117	C₁₃×M₁₆	SD₁₆	1	4	yes	complemented
118	C₂×C₈×C₁₃	—	2	2	no	—
119	C₂×C₈×C₁₃	—	2	2	no	—
120	C₂×C₈×C₁₃	—	4	1	no	—
121	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
122	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
123	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
124	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
125	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
126	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
127	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
128	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
129	C₄²×C₁₃	#41	1	1	yes	characteristic
130	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
131	C₂²⋊Dic₁₃	—	2	2	no	—
132	#6103	—	2	2	no	—
133	#6103	—	2	2	no	—
134	C₄⋊Dic₁₃	—	2	1	no	—
135	C₄⋊Dic₁₃	—	2	1	no	—
136	C₄⋊Dic₁₃	—	2	1	no	—
137	C₄⋊Dic₁₃	—	2	1	no	—
138	C₄⋊Dic₁₃	C₂²×C₄	1	2	yes	—
139	C₄⋊Dic₁₃	C₂²×C₄	1	2	yes	—
140	#6101	—	2	2	no	—
141	#6101	—	2	2	no	—
142	C₄×Dic₁₃	—	2	2	no	—
143	C₂×#1055	—	2	1	no	—
144	C₂×#1055	—	2	1	no	—
145	C₂×#1055	—	2	1	no	—
146	C₂×#1055	—	2	1	no	—
147	C₂×#1055	—	4	2	no	—
148	C₂×#1055	—	4	2	no	—
149	#6095	—	2	4	no	—
150	#6095	—	4	2	no	—
151	#6094	—	4	4	no	—
152	C₈×D₁₃	—	4	4	no	—
153	#3167	—	13	1	no	—
154	#2962	—	13	1	no	—
155	#2935	—	13	1	no	—
156	#1590	—	13	2	no	—
157	#1583	—	13	2	no	—
158	#1582	—	13	2	no	—
159	C₈×SD₁₆	—	13	2	no	—
160	C₂×#334	—	13	1	no	—
161	#1481	—	13	1	no	—
162	#1480	—	13	1	no	—
163	C₈×M₁₆	D₁₃	1	1	yes	characteristic, complemented
164	C₂³×C₁₃	C₄×D₄	1	1	yes	characteristic
165	C₂²×D₁₃	—	2	2	no	—
166	C₂×C₄×C₁₃	—	2	1	no	—
167	C₂×C₄×C₁₃	—	2	1	no	—
168	C₂×C₄×C₁₃	—	4	1	no	—
169	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
170	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
171	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
172	C₂×C₄×C₁₃	C₂×SD₁₆	1	2	yes	—
173	C₂×C₄×C₁₃	#135	1	2	yes	—
174	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
175	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
176	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
177	C₂²⋊D₁₃	—	4	4	no	—
178	C₂×Dic₁₃	—	2	2	no	—
179	C₂×Dic₁₃	—	2	2	no	—
180	C₂×Dic₁₃	—	2	2	no	—
181	D₅₂	—	2	2	no	—
182	D₅₂	—	2	2	no	—
183	D₅₂	—	4	2	no	—
184	D₅₂	—	8	1	no	—
185	C₄×D₁₃	—	4	2	no	—
186	C₄×D₁₃	—	4	2	no	—
187	Dic₂₆	—	2	2	no	—
188	Dic₂₆	—	2	2	no	—
189	Dic₂₆	—	4	2	no	—
190	Dic₂₆	—	8	1	no	—
191	C₈×C₁₃	—	2	1	no	—
192	C₈×C₁₃	—	2	1	no	—
193	C₈×C₁₃	—	2	1	no	—
194	C₈×C₁₃	—	2	2	no	—
195	C₈×C₁₃	—	4	2	no	—
196	C₈×C₁₃	#131	1	2	yes	complemented
197	C₈×C₁₃	C₂×SD₁₆	1	4	yes	—
198	#1055	—	4	1	no	—
199	#1055	—	4	1	no	—
200	#1055	—	4	1	no	—
201	#1055	—	4	1	no	—
202	C₂×#131	—	26	1	no	—
203	#533	—	13	1	no	—
204	#532	—	13	1	no	—
205	#498	—	13	1	no	—
206	#492	—	13	1	no	—
207	#487	—	13	1	no	—
208	#486	—	13	1	no	—
209	#465	—	13	2	no	—
210	#465	—	13	2	no	—
211	#446	—	13	2	no	—
212	#446	—	26	2	no	—
213	C₈×Q₈	—	13	2	no	—
214	C₄×SD₁₆	—	13	2	no	—
215	C₄×SD₁₆	—	13	2	no	—
216	#436	—	13	2	no	—
217	#435	—	26	2	no	—
218	C₈×D₄	—	13	2	no	—
219	#431	C₂×D₁₃	1	1	yes	characteristic
220	#424	—	26	1	no	—
221	C₂×C₄⋊C₈	—	13	1	no	—
222	C₂×C₄⋊C₈	—	13	1	no	—
223	#408	—	26	1	no	—
224	#405	—	26	1	no	—
225	C₄×M₁₆	C₂×D₁₃	1	1	yes	characteristic
226	C₂×C₄×C₈	C₂×D₁₃	1	1	yes	characteristic
227	#334	—	13	1	no	—
228	#334	—	13	1	no	—
229	#334	—	13	1	no	—
230	#334	—	13	1	no	—
231	Q₈⋊C₈	—	13	2	no	—
232	Q₈⋊C₈	—	13	2	no	—
233	D₄⋊C₈	—	13	2	no	—
234	D₄⋊C₈	—	13	2	no	—
235	#322	C₂×D₁₃	1	2	yes	—
236	C₈²	C₂×D₁₃	1	2	yes	—
237	C₂²×C₁₃	—	2	1	no	—
238	C₂²×C₁₃	—	2	1	no	—
239	C₂²×C₁₃	C₄×SD₁₆	1	2	yes	—
240	C₂²×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
241	C₂×D₁₃	—	4	2	no	—
242	C₂×D₁₃	—	4	2	no	—
243	C₂×D₁₃	—	4	2	no	—
244	C₄×C₁₃	—	2	1	no	—
245	C₄×C₁₃	—	2	1	no	—
246	C₄×C₁₃	—	2	1	no	—
247	C₄×C₁₃	C₄×SD₁₆	1	2	yes	—
248	C₄×C₁₃	C₂×#131	1	1	yes	characteristic
249	C₄×C₁₃	#568	1	1	yes	characteristic
250	C₄×C₁₃	C₂²×SD₁₆	1	1	yes	characteristic
251	C₄×C₁₃	C₂×#135	1	1	yes	characteristic
252	Dic₁₃	—	4	2	no	—
253	Dic₁₃	—	4	2	no	—
254	Dic₁₃	—	4	2	no	—
255	C₂×#41	—	26	1	no	—
256	C₂×SD₁₆	—	13	2	no	—
257	C₂×SD₁₆	—	13	2	no	—
258	#131	—	52	4	no	—
259	C₂×M₁₆	—	26	2	no	—
260	C₂×M₁₆	D₅₂	1	1	yes	characteristic
261	C₂×M₁₆	D₅₂	1	1	yes	characteristic
262	C₂²×C₈	—	26	1	no	—
263	C₂²×C₈	—	26	1	no	—
264	C₂²×C₈	—	26	2	no	—
265	C₂²×C₈	C₄×D₁₃	1	1	yes	characteristic
266	C₂²×C₈	C₄×D₁₃	1	1	yes	characteristic
267	C₄⋊Q₈	—	13	1	no	—
268	C₄⋊Q₈	—	13	1	no	—
269	C₄⋊Q₈	—	13	1	no	—
270	#127	—	13	1	no	—
271	#125	—	26	1	no	—
272	#124	—	26	1	no	—
273	C₂²⋊Q₈	—	13	2	no	—
274	C₂²⋊Q₈	—	26	1	no	—
275	#121	—	13	2	no	—
276	#121	—	26	1	no	—
277	C₄×Q₈	—	13	2	no	—
278	C₄×Q₈	—	26	1	no	—
279	C₄×D₄	—	13	2	no	—
280	C₄×D₄	—	26	1	no	—
281	#117	—	26	1	no	—
282	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
283	#106	—	13	2	no	—
284	#106	—	13	2	no	—
285	C₄⋊C₈	—	2	1	no	—
286	C₄⋊C₈	—	13	1	no	—
287	C₄⋊C₈	—	13	1	no	—
288	C₄⋊C₈	—	13	1	no	—
289	C₄⋊C₈	—	13	1	no	—
290	C₄⋊C₈	—	26	2	no	—
291	C₄⋊C₈	—	26	2	no	—
292	C₄⋊C₈	—	26	1	no	—
293	C₄⋊C₈	—	26	1	no	—
294	#103	—	13	2	no	—
295	#103	—	13	2	no	—
296	#102	—	13	2	no	—
297	#102	—	13	2	no	—
298	C₂²⋊C₈	—	2	1	no	—
299	C₂²⋊C₈	—	26	2	no	—
300	C₂²⋊C₈	—	26	2	no	—
301	#97	—	26	2	no	—
302	#97	D₅₂	1	2	yes	—
303	C₄×C₈	—	26	2	no	—
304	C₄×C₈	C₄×D₁₃	1	1	yes	characteristic
305	C₄×C₈	C₄×D₁₃	1	1	yes	characteristic
306	C₄×C₈	C₂²×D₁₃	1	2	yes	—
307	C₄×C₈	C₂²×D₁₃	1	1	yes	characteristic
308	C₄×C₈	C₂²×D₁₃	1	1	yes	characteristic
309	C₄×C₈	C₂²×D₁₃	1	2	yes	—
310	C₂×C₁₃	—	2	2	no	—
311	C₂×C₁₃	#2935	1	1	yes	characteristic
312	C₂×C₁₃	C₂×C₄×SD₁₆	1	1	yes	characteristic
313	C₂×C₁₃	#2957	1	1	yes	characteristic
314	D₁₃	—	8	2	no	—
315	#41	—	52	2	no	—
316	#41	—	52	2	no	—
317	C₂×Q₈	—	13	2	no	—
318	C₂×Q₈	—	26	1	no	—
319	C₂×Q₈	—	26	1	no	—
320	C₂×D₄	—	13	2	no	—
321	C₂×D₄	—	26	2	no	—
322	C₂×D₄	—	26	1	no	—
323	C₂×D₄	—	26	1	no	—
324	C₂²×C₄	—	26	2	no	—
325	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
326	C₂²×C₄	C₂×D₅₂	1	1	yes	characteristic
327	C₂²×C₄	#6127	1	1	yes	characteristic
328	SD₁₆	—	26	4	no	—
329	SD₁₆	—	52	2	no	—
330	M₁₆	—	2	2	no	—
331	M₁₆	—	52	4	no	—
332	M₁₆	#6095	1	4	yes	complemented
333	C₂×C₈	—	2	2	no	—
334	C₂×C₈	—	2	2	no	—
335	C₂×C₈	—	4	1	no	—
336	C₂×C₈	—	26	1	no	—
337	C₂×C₈	—	26	1	no	—
338	C₂×C₈	—	26	1	no	—
339	C₂×C₈	—	26	1	no	—
340	C₂×C₈	—	52	2	no	—
341	C₂×C₈	—	52	2	no	—
342	C₂×C₈	—	52	4	no	—
343	C₂×C₈	C₂×C₄×D₁₃	1	1	yes	characteristic
344	C₂×C₈	C₂×C₄×D₁₃	1	1	yes	characteristic
345	C₂×C₈	C₂×C₄×D₁₃	1	1	yes	characteristic
346	C₂×C₈	C₂×C₄×D₁₃	1	1	yes	characteristic
347	C₂×C₈	C₂×D₅₂	1	2	yes	—
348	C₂×C₈	C₂×D₅₂	1	2	yes	—
349	C₄⋊C₄	—	13	2	no	—
350	C₄⋊C₄	—	13	2	no	—
351	C₄⋊C₄	—	26	1	no	—
352	C₄⋊C₄	—	26	1	no	—
353	C₄⋊C₄	—	26	1	no	—
354	C₄⋊C₄	—	26	2	no	—
355	C₄⋊C₄	—	26	1	no	—
356	C₄⋊C₄	—	26	2	no	—
357	C₂²⋊C₄	—	26	2	no	—
358	C₂²⋊C₄	—	26	2	no	—
359	C₂²⋊C₄	—	26	2	no	—
360	C₄²	—	26	2	no	—
361	C₄²	C₂×C₄×D₁₃	1	1	yes	characteristic
362	C₄²	C₂×D₅₂	1	1	yes	characteristic
363	C₄²	#6127	1	1	yes	characteristic
364	C₄²	C₂³×D₁₃	1	1	yes	characteristic
365	C₁₃	#18067	1	1	yes	characteristic, complemented, Sylow
366	C₂³	—	26	2	no	—
367	C₂³	C₄×D₅₂	1	1	yes	characteristic
368	Q₈	—	26	2	no	—
369	Q₈	—	26	2	no	—
370	Q₈	—	52	2	no	—
371	Q₈	—	104	1	no	—
372	D₄	—	26	2	no	—
373	D₄	—	26	2	no	—
374	D₄	—	52	4	no	—
375	D₄	—	52	2	no	—
376	D₄	—	104	1	no	—
377	C₂×C₄	—	2	1	no	—
378	C₂×C₄	—	2	1	no	—
379	C₂×C₄	—	4	1	no	—
380	C₂×C₄	—	26	2	no	—
381	C₂×C₄	—	26	2	no	—
382	C₂×C₄	—	26	2	no	—
383	C₂×C₄	—	52	2	no	—
384	C₂×C₄	—	52	2	no	—
385	C₂×C₄	C₄×D₅₂	1	1	yes	characteristic
386	C₂×C₄	C₄×D₅₂	1	1	yes	characteristic
387	C₂×C₄	C₄×D₅₂	1	1	yes	characteristic
388	C₂×C₄	C₂×#6095	1	2	yes	—
389	C₂×C₄	#88158	1	2	yes	—
390	C₂×C₄	C₂²×C₄×D₁₃	1	1	yes	characteristic
391	C₂×C₄	C₂²×D₅₂	1	1	yes	characteristic
392	C₂×C₄	C₂×#6127	1	1	yes	characteristic
393	C₈	—	2	2	no	—
394	C₈	—	2	1	no	—
395	C₈	—	2	1	no	—
396	C₈	—	2	1	no	—
397	C₈	—	4	2	no	—
398	C₈	—	52	1	no	—
399	C₈	—	52	1	no	—
400	C₈	—	52	1	no	—
401	C₈	—	52	1	no	—
402	C₈	C₂×#6095	1	4	yes	—
403	C₈	#88161	1	2	yes	complemented
404	C₂²	—	2	1	no	—
405	C₂²	—	2	1	no	—
406	C₂²	—	52	2	no	—
407	C₂²	—	52	2	no	—
408	C₂²	—	52	2	no	—
409	C₂²	C₄×#6095	1	2	yes	—
410	C₂²	C₂×C₄×D₅₂	1	1	yes	characteristic
411	C₄	—	2	1	no	—
412	C₄	—	2	1	no	—
413	C₄	—	2	1	no	—
414	C₄	—	52	2	no	—
415	C₄	—	52	2	no	—
416	C₄	—	52	2	no	—
417	C₄	C₄×#6095	1	2	yes	—
418	C₄	C₂²×#6095	1	1	yes	characteristic
419	C₄	C₂×#88158	1	1	yes	characteristic
420	C₄	C₂×#88161	1	1	yes	characteristic
421	C₄	#11719450	1	1	yes	characteristic
422	C₂	—	2	2	no	—
423	C₂	—	104	2	no	—
424	C₂	#13123582	1	1	yes	characteristic
425	C₂	C₂×C₄×#6095	1	1	yes	characteristic
426	C₂	#13123754	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²×D₅₂
commutator	C₂×C₄×C₁₃	C₂³×C₄
Frattini	C₄²	C₂³×D₁₃
Fitting	C₈×C₁₃×M₁₆	C₂
socle	C₂²×C₁₃	C₂×C₄×D₄
prime radical	#11719182	C₂²
cosocle	C₄²×C₁₃	C₂⁴
hypercenter	C₈×M₁₆	D₁₃
hypocenter	C₁₃	#18067
LCS	G ▷ C₂×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₄ ◁ C₄×M₁₆ ◁ C₈×M₁₆

Complements

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

N	H ≅ G/N	type
2. #13123783	C₂	semidirect
4. #13113728	C₂	semidirect
5. #13113681	C₂	semidirect
6. #13113674	C₂	semidirect
7. C₈×#6095	C₂	semidirect
8. C₂×#11718049	C₂	semidirect
9. #13113240	C₂	semidirect
11. C₈×C₁₃×M₁₆	C₂	semidirect
117. C₁₃×M₁₆	SD₁₆	semidirect
163. C₈×M₁₆	D₁₃	semidirect
196. C₈×C₁₃	#131	semidirect
332. M₁₆	#6095	semidirect
365. C₁₃	#18067	semidirect
403. C₈	#88161	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
#13125395	2
#13123783	2
#13123582	2
#13113728	2
#13113681	2
#13113674	2
C₈×#6095	2
C₂×#11718049	2
#13113240	2
#13113236	2
C₈×C₁₃×M₁₆	2
#18067	13