Subgroups — #15845665

Order 3328.

642 conjugacy classes of subgroups.

The subgroup lattice has 442 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13125415	C₂	1	1	yes	maximal, characteristic, complemented
2	#13124896	C₂	1	2	yes	maximal, complemented
3	#13114376	C₂	1	2	yes	maximal, complemented
4	#13114369	C₂	1	2	yes	maximal, complemented
5	#13114364	C₂	1	1	yes	maximal, characteristic, complemented
6	#13114359	C₂	1	1	yes	maximal, characteristic, complemented
7	#13114320	C₂	1	1	yes	maximal, characteristic, complemented
8	#13114315	C₂	1	1	yes	maximal, characteristic, complemented
9	#13113584	C₂	1	1	yes	maximal, characteristic, complemented
10	#13113496	C₂	1	2	yes	maximal, complemented
11	C₁₃×#2965	C₂	1	1	yes	maximal, characteristic, complemented
12	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic
13	#11719182	C₂²	1	2	yes	—
14	C₁₃×#446	C₂²	1	1	yes	characteristic
15	C₁₃×#446	C₂²	1	1	yes	characteristic
16	C₁₃×#436	C₂²	1	1	yes	characteristic
17	C₁₃×#436	C₂²	1	1	yes	characteristic
18	C₁₃×#435	—	2	1	no	—
19	C₁₃×#435	—	2	1	no	—
20	C₁₃×#431	—	2	1	no	—
21	C₁₃×#431	C₂²	1	1	yes	characteristic
22	C₄×C₁₃×M₁₆	—	2	1	no	—
23	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
24	#11718899	—	2	2	no	—
25	#11718776	—	2	1	no	—
26	#11718776	—	2	1	no	—
27	#11718688	C₂²	1	2	yes	—
28	C₄×#6106	—	2	2	no	—
29	#11718682	C₂²	1	2	yes	—
30	#11718676	C₂²	1	2	yes	—
31	C₄×#6104	—	2	2	no	—
32	#11718669	C₂²	1	2	yes	—
33	#11718664	—	2	2	no	—
34	#11718586	C₂²	1	2	yes	—
35	#11718356	C₂²	1	1	yes	characteristic
36	#11718355	C₂²	1	2	yes	—
37	C₄×D₁₀₄	—	2	1	no	—
38	C₄×D₁₀₄	—	2	1	no	—
39	#11718343	C₂²	1	1	yes	characteristic
40	#11718077	C₂²	1	2	yes	—
41	#11718077	C₂²	1	2	yes	—
42	#11718073	C₂²	1	2	yes	—
43	#11718073	C₂²	1	2	yes	—
44	#11718050	C₂²	1	2	yes	—
45	#11718049	C₂²	1	1	yes	characteristic
46	#11718049	C₂²	1	1	yes	characteristic
47	C₂×C₁₃×#41	D₄	1	1	yes	characteristic
48	C₂×#6127	—	2	2	no	—
49	C₂×C₁₃×M₁₆	—	2	1	no	—
50	C₂×C₁₃×M₁₆	—	2	1	no	—
51	C₂²×C₈×C₁₃	D₄	1	1	yes	characteristic
52	C₂²×C₈×C₁₃	D₄	1	1	yes	characteristic
53	C₄×Q₈×C₁₃	D₄	1	1	yes	characteristic
54	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
55	C₄×D₄×C₁₃	—	2	1	no	—
56	C₄×D₄×C₁₃	—	2	1	no	—
57	C₄×D₄×C₁₃	D₄	1	1	yes	characteristic
58	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
59	C₁₃×#117	—	2	1	no	—
60	C₁₃×#117	D₄	1	1	yes	characteristic
61	C₂×C₄²×C₁₃	—	2	1	no	—
62	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
63	C₂×#6106	—	2	2	no	—
64	C₂×#6104	—	2	2	no	—
65	#88184	—	2	2	no	—
66	#88184	—	2	2	no	—
67	C₂×D₁₀₄	—	2	1	no	—
68	C₂×D₁₀₄	—	2	1	no	—
69	#88129	—	2	2	no	—
70	#88128	C₂³	1	2	yes	—
71	C₄×D₅₂	—	2	2	no	—
72	C₄×D₅₂	—	2	2	no	—
73	#88123	C₂³	1	2	yes	—
74	C₁₃×C₄⋊C₈	—	2	1	no	—
75	C₁₃×C₄⋊C₈	—	2	1	no	—
76	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
77	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
78	C₁₃×C₂²⋊C₈	—	2	1	no	—
79	C₁₃×C₂²⋊C₈	—	2	1	no	—
80	C₁₃×C₂²⋊C₈	—	2	1	no	—
81	C₁₃×#97	—	2	1	no	—
82	C₁₃×#97	—	2	1	no	—
83	C₄×C₈×C₁₃	—	2	1	no	—
84	C₄×C₈×C₁₃	D₄	1	1	yes	characteristic
85	C₄×C₈×C₁₃	D₄	1	1	yes	characteristic
86	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
87	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
88	#88075	—	2	2	no	—
89	#88072	—	2	2	no	—
90	C₂²⋊#1055	—	2	2	no	—
91	#88061	—	2	2	no	—
92	#88061	—	2	2	no	—
93	#88058	—	2	1	no	—
94	#88058	—	2	1	no	—
95	#88049	—	2	2	no	—
96	#88049	—	2	2	no	—
97	#88048	—	2	2	no	—
98	#88047	—	2	2	no	—
99	C₄⋊#1055	C₂³	1	2	yes	—
100	C₄⋊#1055	C₂³	1	2	yes	—
101	C₄×#1055	—	2	2	no	—
102	#19160	—	13	1	no	maximal, Sylow
103	C₁₃×#41	—	4	2	no	—
104	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
105	C₂×D₄×C₁₃	—	2	1	no	—
106	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
107	C₂²×C₄×C₁₃	—	2	1	no	—
108	C₂²×C₄×C₁₃	—	2	1	no	—
109	C₂²×C₄×C₁₃	—	2	1	no	—
110	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
111	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
112	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
113	C₂×C₂²⋊D₁₃	—	4	2	no	—
114	#6127	—	8	4	no	—
115	C₂×D₅₂	—	2	2	no	—
116	C₂×D₅₂	—	2	2	no	—
117	C₂×D₅₂	—	2	2	no	—
118	C₂×C₄×D₁₃	—	4	2	no	—
119	C₂×Dic₂₆	—	2	2	no	—
120	C₁₃×M₁₆	—	4	2	no	—
121	C₁₃×M₁₆	—	4	2	no	—
122	C₂×C₈×C₁₃	—	2	2	no	—
123	C₂×C₈×C₁₃	—	2	1	no	—
124	C₂×C₈×C₁₃	—	2	1	no	—
125	C₂×C₈×C₁₃	—	4	1	no	—
126	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
127	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
128	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
129	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
130	C₁₃×C₄⋊C₄	—	2	1	no	—
131	C₁₃×C₄⋊C₄	—	2	1	no	—
132	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
133	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
134	C₁₃×C₂²⋊C₄	—	2	1	no	—
135	C₁₃×C₂²⋊C₄	—	2	1	no	—
136	C₁₃×C₂²⋊C₄	—	2	1	no	—
137	C₄²×C₁₃	—	2	1	no	—
138	C₄²×C₁₃	—	2	1	no	—
139	C₄²×C₁₃	—	2	1	no	—
140	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
141	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
142	C₄²×C₁₃	#41	1	1	yes	characteristic
143	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
144	#6106	—	4	4	no	—
145	#6104	—	4	4	no	—
146	#6103	—	4	2	no	—
147	#6103	—	4	2	no	—
148	C₄⋊Dic₁₃	—	2	2	no	—
149	C₄⋊Dic₁₃	—	2	2	no	—
150	C₂×#1055	—	2	2	no	—
151	C₂×#1055	—	2	2	no	—
152	D₁₀₄	—	4	2	no	—
153	D₁₀₄	—	4	2	no	—
154	#3169	—	13	1	no	—
155	#3106	—	13	2	no	—
156	#2965	D₁₃	1	1	yes	characteristic, complemented
157	#1698	—	13	2	no	—
158	#1697	—	13	2	no	—
159	#1696	—	13	1	no	—
160	#1695	—	13	1	no	—
161	#1688	—	13	1	no	—
162	#1687	—	13	1	no	—
163	#1564	—	13	1	no	—
164	#1543	—	13	2	no	—
165	C₂³×C₁₃	—	2	1	no	—
166	C₂³×C₁₃	#121	1	1	yes	characteristic
167	C₂²×D₁₃	—	4	2	no	—
168	Q₈×C₁₃	—	2	2	no	—
169	D₄×C₁₃	—	2	2	no	—
170	D₄×C₁₃	—	4	2	no	—
171	C₂×C₄×C₁₃	—	2	1	no	—
172	C₂×C₄×C₁₃	—	2	1	no	—
173	C₂×C₄×C₁₃	—	2	2	no	—
174	C₂×C₄×C₁₃	—	2	2	no	—
175	C₂×C₄×C₁₃	—	2	1	no	—
176	C₂×C₄×C₁₃	—	2	1	no	—
177	C₂×C₄×C₁₃	—	2	1	no	—
178	C₂×C₄×C₁₃	—	4	2	no	—
179	C₂×C₄×C₁₃	—	4	1	no	—
180	C₂×C₄×C₁₃	—	4	1	no	—
181	C₂×C₄×C₁₃	—	4	2	no	—
182	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
183	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
184	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
185	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
186	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
187	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
188	C₂²⋊D₁₃	—	8	4	no	—
189	C₂×Dic₁₃	—	4	2	no	—
190	D₅₂	—	4	2	no	—
191	D₅₂	—	4	2	no	—
192	D₅₂	—	4	2	no	—
193	D₅₂	—	4	2	no	—
194	D₅₂	—	8	2	no	—
195	C₄×D₁₃	—	8	4	no	—
196	Dic₂₆	—	8	2	no	—
197	C₈×C₁₃	—	2	1	no	—
198	C₈×C₁₃	—	2	1	no	—
199	C₈×C₁₃	—	2	1	no	—
200	C₈×C₁₃	—	4	1	no	—
201	C₈×C₁₃	—	4	1	no	—
202	C₈×C₁₃	#135	1	2	yes	—
203	#1055	—	4	2	no	—
204	#1055	—	4	2	no	—
205	#532	—	13	2	no	—
206	C₄×#41	C₂×D₁₃	1	1	yes	characteristic
207	#500	—	13	1	no	—
208	#493	—	13	1	no	—
209	#486	—	13	2	no	—
210	#482	—	26	2	no	—
211	#477	—	13	2	no	—
212	#476	—	13	2	no	—
213	#466	—	26	1	no	—
214	#466	—	26	1	no	—
215	#460	—	13	2	no	—
216	#459	—	13	2	no	—
217	#449	—	26	2	no	—
218	#446	C₂×D₁₃	1	1	yes	characteristic
219	#446	C₂×D₁₃	1	1	yes	characteristic
220	C₄×SD₁₆	—	26	2	no	—
221	C₄×D₈	—	26	2	no	—
222	C₄×D₈	—	26	1	no	—
223	C₄×D₈	—	26	1	no	—
224	#436	C₂×D₁₃	1	1	yes	characteristic
225	#436	C₂×D₁₃	1	1	yes	characteristic
226	#435	—	2	1	no	—
227	#435	—	2	1	no	—
228	#431	—	2	1	no	—
229	#431	—	13	2	no	—
230	#431	C₂×D₁₃	1	1	yes	characteristic
231	C₄×M₁₆	—	2	1	no	—
232	C₂×C₄×C₈	C₂×D₁₃	1	1	yes	characteristic
233	#335	—	13	2	no	—
234	#334	—	13	1	no	—
235	#334	—	13	1	no	—
236	#333	—	13	2	no	—
237	#333	—	13	2	no	—
238	#331	—	13	2	no	—
239	#331	—	13	2	no	—
240	C₂²×C₁₃	—	2	1	no	—
241	C₂²×C₁₃	—	2	1	no	—
242	C₂²×C₁₃	—	2	1	no	—
243	C₂²×C₁₃	—	4	1	no	—
244	C₂²×C₁₃	—	4	1	no	—
245	C₂²×C₁₃	—	4	1	no	—
246	C₂²×C₁₃	C₂×#121	1	1	yes	characteristic
247	C₂×D₁₃	—	8	2	no	—
248	C₂×D₁₃	—	8	2	no	—
249	C₂×D₁₃	—	8	2	no	—
250	C₄×C₁₃	—	2	1	no	—
251	C₄×C₁₃	—	2	1	no	—
252	C₄×C₁₃	—	2	1	no	—
253	C₄×C₁₃	—	4	1	no	—
254	C₄×C₁₃	—	4	1	no	—
255	C₄×C₁₃	—	4	1	no	—
256	C₄×C₁₃	#472	1	2	yes	—
257	C₄×C₁₃	C₂×#135	1	1	yes	characteristic
258	C₄×C₁₃	#575	1	2	yes	—
259	C₄×C₁₃	#575	1	1	yes	characteristic
260	Dic₁₃	—	8	2	no	—
261	C₂×#41	—	26	2	no	—
262	C₂×#41	D₅₂	1	1	yes	characteristic
263	C₂×SD₁₆	—	26	2	no	—
264	C₂×D₈	—	26	2	no	—
265	C₂×D₈	—	26	1	no	—
266	C₂×D₈	—	26	1	no	—
267	C₂×M₁₆	—	2	1	no	—
268	C₂×M₁₆	—	2	1	no	—
269	C₂²×C₈	C₂²⋊D₁₃	1	1	yes	characteristic
270	C₂²×C₈	C₂²⋊D₁₃	1	1	yes	characteristic
271	C₄⋊Q₈	—	13	2	no	—
272	#127	—	13	2	no	—
273	#124	—	26	2	no	—
274	#121	—	26	2	no	—
275	#121	—	26	2	no	—
276	C₄×Q₈	D₅₂	1	1	yes	characteristic
277	C₄×Q₈	C₂²×D₁₃	1	1	yes	characteristic
278	C₄×D₄	—	2	1	no	—
279	C₄×D₄	—	2	1	no	—
280	C₄×D₄	—	26	2	no	—
281	C₄×D₄	—	26	2	no	—
282	C₄×D₄	D₅₂	1	1	yes	characteristic
283	C₄×D₄	C₂²×D₁₃	1	1	yes	characteristic
284	#117	—	2	1	no	—
285	#117	D₅₂	1	1	yes	characteristic
286	C₂×C₄²	—	2	1	no	—
287	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
288	#107	—	26	1	no	—
289	#107	—	26	1	no	—
290	#107	—	26	2	no	—
291	#106	—	26	2	no	—
292	C₄⋊C₈	—	2	1	no	—
293	C₄⋊C₈	—	2	1	no	—
294	C₄⋊C₈	—	13	2	no	—
295	C₄⋊C₈	—	13	2	no	—
296	C₄⋊C₈	C₂²×D₁₃	1	1	yes	characteristic
297	C₄⋊C₈	C₂²×D₁₃	1	1	yes	characteristic
298	#103	—	26	2	no	—
299	#102	—	26	2	no	—
300	#102	—	26	2	no	—
301	#102	—	26	2	no	—
302	#102	—	26	2	no	—
303	#102	—	26	2	no	—
304	C₂²⋊C₈	—	2	1	no	—
305	C₂²⋊C₈	—	2	1	no	—
306	C₂²⋊C₈	—	2	1	no	—
307	C₂²⋊C₈	—	26	2	no	—
308	#97	—	2	1	no	—
309	#97	—	2	1	no	—
310	C₄×C₈	—	2	1	no	—
311	C₄×C₈	—	26	2	no	—
312	C₄×C₈	C₂²⋊D₁₃	1	1	yes	characteristic
313	C₄×C₈	C₂²⋊D₁₃	1	1	yes	characteristic
314	C₄×C₈	C₂²×D₁₃	1	1	yes	characteristic
315	C₄×C₈	C₂²×D₁₃	1	1	yes	characteristic
316	C₂×C₁₃	—	4	1	no	—
317	C₂×C₁₃	—	8	1	no	—
318	C₂×C₁₃	#3035	1	1	yes	characteristic
319	C₂×C₁₃	#3054	1	1	yes	characteristic
320	C₂×C₁₃	C₂×#472	1	1	yes	characteristic
321	D₁₃	—	16	2	no	—
322	#41	—	4	2	no	—
323	#41	—	104	4	no	—
324	C₂×Q₈	—	26	2	no	—
325	C₂×Q₈	C₂×D₅₂	1	1	yes	characteristic
326	C₂×D₄	—	2	1	no	—
327	C₂×D₄	—	26	2	no	—
328	C₂×D₄	—	26	2	no	—
329	C₂×D₄	—	26	2	no	—
330	C₂×D₄	—	52	2	no	—
331	C₂×D₄	C₂×D₅₂	1	1	yes	characteristic
332	C₂²×C₄	—	2	1	no	—
333	C₂²×C₄	—	2	1	no	—
334	C₂²×C₄	—	2	1	no	—
335	C₂²×C₄	—	52	2	no	—
336	C₂²×C₄	C₂×D₅₂	1	1	yes	characteristic
337	C₂²×C₄	#6127	1	1	yes	characteristic
338	C₂²×C₄	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
339	SD₁₆	—	52	4	no	—
340	D₈	—	52	2	no	—
341	D₈	—	52	4	no	—
342	D₈	—	52	2	no	—
343	M₁₆	—	4	2	no	—
344	M₁₆	—	4	2	no	—
345	C₂×C₈	—	2	2	no	—
346	C₂×C₈	—	2	1	no	—
347	C₂×C₈	—	2	1	no	—
348	C₂×C₈	—	4	1	no	—
349	C₂×C₈	—	26	2	no	—
350	C₂×C₈	—	26	2	no	—
351	C₂×C₈	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
352	C₂×C₈	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
353	C₂×C₈	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
354	C₂×C₈	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
355	C₄⋊C₄	—	2	1	no	—
356	C₄⋊C₄	—	2	1	no	—
357	C₄⋊C₄	—	26	2	no	—
358	C₄⋊C₄	—	26	2	no	—
359	C₄⋊C₄	C₂×D₅₂	1	1	yes	characteristic
360	C₄⋊C₄	C₂×D₅₂	1	1	yes	characteristic
361	C₂²⋊C₄	—	2	1	no	—
362	C₂²⋊C₄	—	2	1	no	—
363	C₂²⋊C₄	—	2	1	no	—
364	C₂²⋊C₄	—	52	2	no	—
365	C₂²⋊C₄	—	52	2	no	—
366	C₄²	—	2	1	no	—
367	C₄²	—	2	1	no	—
368	C₄²	—	2	1	no	—
369	C₄²	C₂×D₅₂	1	1	yes	characteristic
370	C₄²	#6127	1	1	yes	characteristic
371	C₄²	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
372	C₄²	C₂³×D₁₃	1	1	yes	characteristic
373	C₁₃	#19160	1	1	yes	characteristic, complemented, Sylow
374	C₂³	—	2	1	no	—
375	C₂³	—	52	2	no	—
376	C₂³	#88184	1	1	yes	characteristic
377	Q₈	—	2	2	no	—
378	Q₈	—	104	2	no	—
379	D₄	—	2	2	no	—
380	D₄	—	4	2	no	—
381	D₄	—	52	2	no	—
382	D₄	—	52	2	no	—
383	D₄	—	52	2	no	—
384	D₄	—	52	2	no	—
385	D₄	—	104	2	no	—
386	D₄	—	104	4	no	—
387	C₂×C₄	—	2	2	no	—
388	C₂×C₄	—	2	1	no	—
389	C₂×C₄	—	2	1	no	—
390	C₂×C₄	—	2	2	no	—
391	C₂×C₄	—	2	1	no	—
392	C₂×C₄	—	2	1	no	—
393	C₂×C₄	—	2	1	no	—
394	C₂×C₄	—	4	2	no	—
395	C₂×C₄	—	4	1	no	—
396	C₂×C₄	—	4	1	no	—
397	C₂×C₄	—	4	2	no	—
398	C₂×C₄	—	52	2	no	—
399	C₂×C₄	—	104	4	no	—
400	C₂×C₄	#88184	1	1	yes	characteristic
401	C₂×C₄	#88184	1	1	yes	characteristic
402	C₂×C₄	#88184	1	1	yes	characteristic
403	C₂×C₄	C₂²×D₅₂	1	1	yes	characteristic
404	C₂×C₄	C₂×#6127	1	1	yes	characteristic
405	C₂×C₄	C₂²×C₂²⋊D₁₃	1	1	yes	characteristic
406	C₈	—	2	1	no	—
407	C₈	—	2	1	no	—
408	C₈	—	2	1	no	—
409	C₈	—	4	1	no	—
410	C₈	—	4	1	no	—
411	C₈	—	52	2	no	—
412	C₈	—	52	2	no	—
413	C₈	#88204	1	2	yes	—
414	C₂²	—	2	1	no	—
415	C₂²	—	2	1	no	—
416	C₂²	—	2	1	no	—
417	C₂²	—	4	1	no	—
418	C₂²	—	4	1	no	—
419	C₂²	—	4	1	no	—
420	C₂²	—	104	2	no	—
421	C₂²	—	104	2	no	—
422	C₂²	—	104	2	no	—
423	C₂²	C₂×#88184	1	1	yes	characteristic
424	C₄	—	2	1	no	—
425	C₄	—	2	1	no	—
426	C₄	—	2	1	no	—
427	C₄	—	4	1	no	—
428	C₄	—	4	1	no	—
429	C₄	—	4	1	no	—
430	C₄	—	104	2	no	—
431	C₄	#11718803	1	2	yes	—
432	C₄	#11719453	1	2	yes	—
433	C₄	C₂×#88204	1	1	yes	characteristic
434	C₄	#11719527	1	1	yes	characteristic
435	C₂	—	4	1	no	—
436	C₂	—	8	1	no	—
437	C₂	—	208	2	no	—
438	C₂	#13124291	1	1	yes	characteristic
439	C₂	#13124445	1	1	yes	characteristic
440	C₂	C₂×#11718803	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	#88184
commutator, cosocle	C₄²×C₁₃	C₂⁴
Frattini	C₄²	C₂³×D₁₃
Fitting	C₁₃×#2965	C₂
socle	C₂²×C₁₃	C₂×#121
hypercenter	#2965	D₁₃
hypocenter	C₁₃	#19160
LCS	G ▷ C₄²×C₁₃ ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #2965

Complements

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

N	H ≅ G/N	type
1. #13125415	C₂	semidirect
2. #13124896	C₂	semidirect
3. #13114376	C₂	semidirect
4. #13114369	C₂	semidirect
5. #13114364	C₂	semidirect
6. #13114359	C₂	semidirect
7. #13114320	C₂	semidirect
8. #13114315	C₂	semidirect
9. #13113584	C₂	semidirect
10. #13113496	C₂	semidirect
11. C₁₃×#2965	C₂	semidirect
156. #2965	D₁₃	semidirect
373. C₁₃	#19160	semidirect

Maximal subgroups

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

subgroup	index
#13125415	2
#13124896	2
#13114376	2
#13114369	2
#13114364	2
#13114359	2
#13114320	2
#13114315	2
#13113584	2
#13113496	2
C₁₃×#2965	2
#19160	13