Subgroups — #15845977

Order 3328.

778 conjugacy classes of subgroups.

The subgroup lattice has 440 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13125957	C₂	1	1	yes	maximal, characteristic, complemented
2	#13125754	C₂	1	1	yes	maximal, characteristic
3	#13123549	C₂	1	1	yes	maximal, characteristic, complemented
4	#13114298	C₂	1	4	yes	maximal, complemented
5	#13114174	C₂	1	4	yes	maximal, complemented
6	#13113584	C₂	1	1	yes	maximal, characteristic, complemented
7	#13113508	C₂	1	1	yes	maximal, characteristic, complemented
8	#13113504	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₁₃×#492	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂²×C₁₃×SD₁₆	—	2	1	no	—
11	C₂²×C₁₃×SD₁₆	—	2	1	no	—
12	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
13	C₂×C₁₃×#127	C₂²	1	1	yes	characteristic
14	C₂×#88155	—	2	1	no	—
15	#11719182	C₂²	1	1	yes	characteristic
16	C₁₃×#492	—	2	1	no	—
17	C₁₃×#492	—	2	1	no	—
18	C₁₃×#492	C₂²	1	2	yes	—
19	C₁₃×#492	C₂²	1	2	yes	—
20	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
21	#11718878	—	2	2	no	—
22	#11718771	—	2	1	no	—
23	#11718749	—	2	1	no	—
24	#11718748	C₂²	1	4	yes	complemented
25	#11718739	—	2	1	no	—
26	#11718734	—	2	1	no	—
27	#11718733	C₂²	1	4	yes	—
28	#11718731	—	2	1	no	—
29	#11718628	—	2	2	no	—
30	#11718586	C₂²	1	1	yes	characteristic
31	#11718586	C₂²	1	1	yes	characteristic
32	#11718585	C₂²	1	1	yes	characteristic
33	#11718349	—	2	1	no	—
34	#11718349	C₂²	1	2	yes	complemented
35	C₈×D₅₂	—	2	1	no	—
36	C₈×D₅₂	C₂²	1	2	yes	complemented
37	#11718139	C₂²	1	4	yes	complemented
38	#11718136	C₂²	1	4	yes	—
39	#11718050	C₂²	1	2	yes	complemented
40	#11718049	C₂²	1	2	yes	complemented
41	C₂²×Q₈×C₁₃	—	2	1	no	—
42	C₂²×D₄×C₁₃	—	2	1	no	—
43	C₂²×D₄×C₁₃	—	2	1	no	—
44	C₂²×D₄×C₁₃	—	2	1	no	—
45	C₂×#6127	—	2	1	no	—
46	C₂×C₁₃×SD₁₆	—	2	2	no	—
47	C₂×C₁₃×SD₁₆	—	2	2	no	—
48	C₂×C₁₃×SD₁₆	—	2	2	no	—
49	C₂×C₁₃×SD₁₆	—	2	2	no	—
50	C₂×C₁₃×SD₁₆	—	4	4	no	—
51	C₂×C₁₃×SD₁₆	—	4	4	no	—
52	C₂²×C₈×C₁₃	D₄	1	1	yes	characteristic
53	C₂²×C₈×C₁₃	D₄	1	1	yes	characteristic
54	C₁₃×C₄⋊Q₈	—	2	1	no	—
55	C₁₃×C₄⋊Q₈	—	2	1	no	—
56	C₁₃×C₄⋊Q₈	—	2	1	no	—
57	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
58	C₁₃×#127	—	2	1	no	—
59	C₁₃×#127	—	2	1	no	—
60	C₁₃×#127	—	2	1	no	—
61	C₁₃×#127	C₂³	1	2	yes	—
62	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
63	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
64	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
65	C₂×#6104	—	2	4	no	—
66	#88184	—	2	1	no	—
67	#88184	D₄	1	2	yes	—
68	C₂×#6099	—	2	1	no	—
69	#88155	—	4	4	no	—
70	C₂×#6094	—	2	2	no	—
71	C₂×C₈×D₁₃	—	2	2	no	—
72	#88129	—	2	1	no	—
73	#88128	D₄	1	1	yes	characteristic
74	C₄×D₅₂	—	2	1	no	—
75	C₄×D₅₂	C₂³	1	2	yes	—
76	#88123	D₄	1	1	yes	characteristic
77	C₄×C₈×C₁₃	D₄	1	1	yes	characteristic
78	C₄×C₈×C₁₃	D₄	1	1	yes	characteristic
79	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
80	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
81	#88072	—	2	4	no	—
82	C₂²⋊#1055	—	2	1	no	—
83	C₂²⋊#1055	—	2	1	no	—
84	#88060	—	2	2	no	—
85	#88060	—	2	2	no	—
86	#88049	—	2	4	no	—
87	#88047	—	2	4	no	—
88	C₄⋊#1055	—	2	1	no	—
89	C₄⋊#1055	C₂³	1	2	yes	—
90	C₄⋊#1055	C₂³	1	2	yes	—
91	C₄⋊#1055	C₂³	1	2	yes	—
92	C₄×#1055	—	2	1	no	—
93	C₄×#1055	—	2	1	no	—
94	#19186	—	13	1	no	maximal, Sylow
95	C₂⁴×C₁₃	—	4	1	no	—
96	C₂×Q₈×C₁₃	—	2	2	no	—
97	C₂×Q₈×C₁₃	—	4	1	no	—
98	C₂×Q₈×C₁₃	—	4	2	no	—
99	C₂×Q₈×C₁₃	—	4	2	no	—
100	C₂×D₄×C₁₃	—	2	2	no	—
101	C₂×D₄×C₁₃	—	2	2	no	—
102	C₂×D₄×C₁₃	—	2	2	no	—
103	C₂×D₄×C₁₃	—	4	1	no	—
104	C₂×D₄×C₁₃	—	4	1	no	—
105	C₂×D₄×C₁₃	—	4	1	no	—
106	C₂×D₄×C₁₃	—	4	2	no	—
107	C₂×D₄×C₁₃	—	4	2	no	—
108	C₂×D₄×C₁₃	—	8	2	no	—
109	C₂×D₄×C₁₃	—	8	2	no	—
110	C₂²×C₄×C₁₃	—	4	1	no	—
111	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
112	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
113	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
114	C₂×C₂²⋊D₁₃	—	2	2	no	—
115	#6127	—	4	2	no	—
116	#6127	—	4	2	no	—
117	C₂×D₅₂	—	2	1	no	—
118	C₂×D₅₂	—	2	1	no	—
119	C₂×D₅₂	C₂×D₄	1	2	yes	—
120	C₂×C₄×D₁₃	—	2	2	no	—
121	C₂×Dic₂₆	—	2	1	no	—
122	C₁₃×SD₁₆	—	4	4	no	—
123	C₁₃×SD₁₆	—	4	4	no	—
124	C₁₃×SD₁₆	—	4	4	no	—
125	C₁₃×SD₁₆	—	4	4	no	—
126	C₂×C₈×C₁₃	—	2	2	no	—
127	C₂×C₈×C₁₃	D₈	1	4	yes	complemented
128	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
129	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
130	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
131	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
132	C₁₃×C₄⋊C₄	—	2	2	no	—
133	C₁₃×C₄⋊C₄	—	2	2	no	—
134	C₁₃×C₄⋊C₄	—	4	1	no	—
135	C₁₃×C₄⋊C₄	—	4	1	no	—
136	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
137	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
138	C₄²×C₁₃	#41	1	1	yes	characteristic
139	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
140	#6104	—	8	4	no	—
141	#6103	—	2	2	no	—
142	#6103	—	2	2	no	—
143	C₄⋊Dic₁₃	—	2	1	no	—
144	C₄⋊Dic₁₃	C₂×D₄	1	2	yes	—
145	#6099	—	4	2	no	—
146	C₂×#1055	—	2	2	no	—
147	C₂×#1055	—	2	2	no	—
148	C₂×#1055	—	2	2	no	—
149	#6094	—	4	4	no	—
150	C₈×D₁₃	—	4	4	no	—
151	#3226	—	13	1	no	—
152	#3205	—	13	1	no	—
153	C₂×#492	D₁₃	1	1	yes	characteristic, complemented
154	#2931	—	13	1	no	—
155	#1685	—	13	4	no	—
156	#1665	—	13	4	no	—
157	#1564	—	13	1	no	—
158	#1546	—	13	1	no	—
159	#1545	—	13	1	no	—
160	C₂³×C₁₃	—	4	2	no	—
161	C₂³×C₁₃	—	8	2	no	—
162	C₂³×C₁₃	—	8	2	no	—
163	C₂³×C₁₃	—	8	2	no	—
164	C₂³×C₁₃	#121	1	1	yes	characteristic
165	C₂²×D₁₃	—	2	2	no	—
166	Q₈×C₁₃	—	4	2	no	—
167	Q₈×C₁₃	—	4	2	no	—
168	Q₈×C₁₃	—	8	2	no	—
169	D₄×C₁₃	—	4	2	no	—
170	D₄×C₁₃	—	4	2	no	—
171	D₄×C₁₃	—	4	4	no	—
172	D₄×C₁₃	—	8	2	no	—
173	D₄×C₁₃	—	8	2	no	—
174	D₄×C₁₃	—	8	2	no	—
175	D₄×C₁₃	—	8	2	no	—
176	C₂×C₄×C₁₃	—	2	2	no	—
177	C₂×C₄×C₁₃	—	2	2	no	—
178	C₂×C₄×C₁₃	—	4	2	no	—
179	C₂×C₄×C₁₃	—	8	2	no	—
180	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
181	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
182	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
183	C₂×C₄×C₁₃	C₂×D₈	1	2	yes	—
184	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	2	yes	—
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	—	4	4	no	—
189	C₂×Dic₁₃	—	2	2	no	—
190	D₅₂	—	2	4	no	—
191	D₅₂	—	4	2	no	—
192	D₅₂	—	4	2	no	—
193	C₄×D₁₃	—	4	2	no	—
194	C₄×D₁₃	—	4	2	no	—
195	Dic₂₆	—	4	2	no	—
196	C₈×C₁₃	—	2	1	no	—
197	C₈×C₁₃	—	2	1	no	—
198	C₈×C₁₃	C₂×D₈	1	2	yes	—
199	C₈×C₁₃	C₂×D₈	1	2	yes	—
200	#1055	—	4	2	no	—
201	#1055	—	4	2	no	—
202	#1055	—	4	2	no	—
203	C₂²×SD₁₆	—	2	1	no	—
204	C₂²×SD₁₆	—	2	1	no	—
205	C₂×#131	—	26	1	no	—
206	#532	—	13	1	no	—
207	C₂×C₄⋊Q₈	C₂×D₁₃	1	1	yes	characteristic
208	C₂×#127	C₂×D₁₃	1	1	yes	characteristic
209	#500	—	26	1	no	—
210	#493	—	26	1	no	—
211	#492	—	2	1	no	—
212	#492	—	2	1	no	—
213	#492	C₂×D₁₃	1	2	yes	—
214	#492	C₂×D₁₃	1	2	yes	—
215	#486	—	26	1	no	—
216	#486	—	26	1	no	—
217	#480	—	26	2	no	—
218	#474	—	13	4	no	—
219	#459	—	13	4	no	—
220	#447	—	26	2	no	—
221	#436	—	13	2	no	—
222	#436	—	26	1	no	—
223	C₈×D₄	—	13	2	no	—
224	C₈×D₄	—	26	1	no	—
225	#431	—	13	1	no	—
226	#431	—	13	1	no	—
227	#423	—	13	1	no	—
228	#408	—	26	1	no	—
229	C₂×C₄×C₈	C₂×D₁₃	1	1	yes	characteristic
230	#335	—	13	2	no	—
231	#334	—	13	2	no	—
232	#332	—	13	4	no	—
233	#331	—	13	4	no	—
234	C₂²×C₁₃	—	2	1	no	—
235	C₂²×C₁₃	—	2	1	no	—
236	C₂²×C₁₃	—	8	2	no	—
237	C₂²×C₁₃	—	8	2	no	—
238	C₂²×C₁₃	—	8	2	no	—
239	C₂²×C₁₃	—	16	4	no	—
240	C₂²×C₁₃	#459	1	2	yes	—
241	C₂²×C₁₃	C₂×#121	1	1	yes	characteristic
242	C₂×D₁₃	—	4	2	no	—
243	C₂×D₁₃	—	4	2	no	—
244	C₂×D₁₃	—	4	2	no	—
245	C₄×C₁₃	—	2	1	no	—
246	C₄×C₁₃	—	2	1	no	—
247	C₄×C₁₃	—	8	2	no	—
248	C₄×C₁₃	#459	1	2	yes	—
249	C₄×C₁₃	#471	1	2	yes	—
250	C₄×C₁₃	C₂²×D₈	1	1	yes	characteristic
251	C₄×C₁₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
252	C₄×C₁₃	#577	1	2	yes	—
253	Dic₁₃	—	4	2	no	—
254	C₂×#41	—	26	1	no	—
255	C₂²×Q₈	—	2	1	no	—
256	C₂²×D₄	—	2	1	no	—
257	C₂²×D₄	—	2	1	no	—
258	C₂²×D₄	—	2	1	no	—
259	C₂×SD₁₆	—	2	2	no	—
260	C₂×SD₁₆	—	2	2	no	—
261	C₂×SD₁₆	—	2	2	no	—
262	C₂×SD₁₆	—	2	2	no	—
263	C₂×SD₁₆	—	4	4	no	—
264	C₂×SD₁₆	—	4	4	no	—
265	C₂×D₈	—	26	4	no	—
266	#131	—	52	4	no	—
267	C₂×M₁₆	—	26	1	no	—
268	C₂×M₁₆	—	26	2	no	—
269	C₂²×C₈	—	26	2	no	—
270	C₂²×C₈	C₂²⋊D₁₃	1	1	yes	characteristic
271	C₂²×C₈	C₂²⋊D₁₃	1	1	yes	characteristic
272	C₄⋊Q₈	—	2	1	no	—
273	C₄⋊Q₈	—	2	1	no	—
274	C₄⋊Q₈	—	2	1	no	—
275	C₄⋊Q₈	—	13	1	no	—
276	C₄⋊Q₈	C₂²×D₁₃	1	2	yes	—
277	#127	—	2	1	no	—
278	#127	—	2	1	no	—
279	#127	—	2	1	no	—
280	#127	—	13	1	no	—
281	#127	C₂²×D₁₃	1	2	yes	—
282	#124	—	26	1	no	—
283	#121	—	13	2	no	—
284	#121	—	26	1	no	—
285	C₄×D₄	—	13	2	no	—
286	C₄×D₄	—	26	1	no	—
287	C₂×C₄⋊C₄	—	2	1	no	—
288	C₂×C₄⋊C₄	—	2	1	no	—
289	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
290	#107	—	26	4	no	—
291	C₄⋊C₈	—	13	2	no	—
292	C₄⋊C₈	—	13	2	no	—
293	C₄⋊C₈	—	13	2	no	—
294	C₄⋊C₈	—	26	1	no	—
295	#102	—	26	4	no	—
296	#102	—	26	4	no	—
297	C₂²⋊C₈	—	26	1	no	—
298	C₂²⋊C₈	—	26	1	no	—
299	C₂²⋊C₈	—	26	2	no	—
300	C₂²⋊C₈	—	26	2	no	—
301	C₄×C₈	—	26	1	no	—
302	C₄×C₈	—	26	1	no	—
303	C₄×C₈	C₂²⋊D₁₃	1	1	yes	characteristic
304	C₄×C₈	C₂²⋊D₁₃	1	1	yes	characteristic
305	C₄×C₈	C₂²×D₁₃	1	1	yes	characteristic
306	C₄×C₈	C₂²×D₁₃	1	1	yes	characteristic
307	C₂×C₁₃	—	2	2	no	—
308	C₂×C₁₃	—	16	2	no	—
309	C₂×C₁₃	C₂×#459	1	1	yes	characteristic
310	C₂×C₁₃	#3057	1	1	yes	characteristic
311	C₂×C₁₃	C₂×#471	1	1	yes	characteristic
312	D₁₃	—	8	2	no	—
313	C₂⁴	—	4	1	no	—
314	#41	—	52	2	no	—
315	#41	—	52	2	no	—
316	C₂×Q₈	—	2	2	no	—
317	C₂×Q₈	—	4	1	no	—
318	C₂×Q₈	—	4	2	no	—
319	C₂×Q₈	—	4	2	no	—
320	C₂×Q₈	—	26	1	no	—
321	C₂×D₄	—	2	2	no	—
322	C₂×D₄	—	2	2	no	—
323	C₂×D₄	—	2	2	no	—
324	C₂×D₄	—	4	2	no	—
325	C₂×D₄	—	4	2	no	—
326	C₂×D₄	—	4	1	no	—
327	C₂×D₄	—	4	1	no	—
328	C₂×D₄	—	4	1	no	—
329	C₂×D₄	—	8	2	no	—
330	C₂×D₄	—	8	2	no	—
331	C₂×D₄	—	13	2	no	—
332	C₂×D₄	—	26	2	no	—
333	C₂×D₄	—	26	1	no	—
334	C₂×D₄	—	26	1	no	—
335	C₂²×C₄	—	4	1	no	—
336	C₂²×C₄	—	26	2	no	—
337	C₂²×C₄	D₄×D₁₃	1	1	yes	characteristic
338	C₂²×C₄	#6129	1	1	yes	characteristic
339	C₂²×C₄	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
340	SD₁₆	—	4	4	no	—
341	SD₁₆	—	4	4	no	—
342	SD₁₆	—	4	4	no	—
343	SD₁₆	—	4	4	no	—
344	D₈	—	104	4	no	—
345	M₁₆	—	52	2	no	—
346	M₁₆	—	52	4	no	—
347	C₂×C₈	—	2	2	no	—
348	C₂×C₈	—	26	2	no	—
349	C₂×C₈	—	26	2	no	—
350	C₂×C₈	—	26	2	no	—
351	C₂×C₈	—	52	4	no	—
352	C₂×C₈	#6104	1	4	yes	complemented
353	C₂×C₈	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
354	C₂×C₈	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
355	C₂×C₈	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
356	C₂×C₈	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
357	C₄⋊C₄	—	2	2	no	—
358	C₄⋊C₄	—	2	2	no	—
359	C₄⋊C₄	—	4	1	no	—
360	C₄⋊C₄	—	4	1	no	—
361	C₄⋊C₄	—	13	2	no	—
362	C₄⋊C₄	—	26	1	no	—
363	C₂²⋊C₄	—	26	2	no	—
364	C₂²⋊C₄	—	26	2	no	—
365	C₄²	D₄×D₁₃	1	1	yes	characteristic
366	C₄²	#6129	1	1	yes	characteristic
367	C₄²	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
368	C₄²	C₂³×D₁₃	1	1	yes	characteristic
369	C₁₃	#19186	1	1	yes	characteristic, complemented, Sylow
370	C₂³	—	4	2	no	—
371	C₂³	—	8	2	no	—
372	C₂³	—	8	2	no	—
373	C₂³	—	8	2	no	—
374	C₂³	—	26	2	no	—
375	C₂³	#88192	1	1	yes	characteristic
376	Q₈	—	4	2	no	—
377	Q₈	—	4	2	no	—
378	Q₈	—	8	2	no	—
379	Q₈	—	52	2	no	—
380	D₄	—	4	4	no	—
381	D₄	—	4	2	no	—
382	D₄	—	4	2	no	—
383	D₄	—	8	2	no	—
384	D₄	—	8	2	no	—
385	D₄	—	8	2	no	—
386	D₄	—	8	2	no	—
387	D₄	—	26	4	no	—
388	D₄	—	52	4	no	—
389	D₄	—	52	2	no	—
390	D₄	—	52	2	no	—
391	C₂×C₄	—	2	2	no	—
392	C₂×C₄	—	2	2	no	—
393	C₂×C₄	—	4	2	no	—
394	C₂×C₄	—	8	2	no	—
395	C₂×C₄	—	26	2	no	—
396	C₂×C₄	—	52	2	no	—
397	C₂×C₄	—	52	2	no	—
398	C₂×C₄	C₂×#6104	1	2	yes	—
399	C₂×C₄	#88186	1	2	yes	—
400	C₂×C₄	#88192	1	1	yes	characteristic
401	C₂×C₄	#88192	1	1	yes	characteristic
402	C₂×C₄	#88192	1	1	yes	characteristic
403	C₂×C₄	C₂×D₄×D₁₃	1	1	yes	characteristic
404	C₂×C₄	C₂×#6129	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	—	52	2	no	—
409	C₈	—	52	2	no	—
410	C₈	—	52	2	no	—
411	C₈	C₂×#6104	1	2	yes	—
412	C₈	C₂×#6104	1	2	yes	—
413	C₂²	—	2	1	no	—
414	C₂²	—	2	1	no	—
415	C₂²	—	8	2	no	—
416	C₂²	—	8	2	no	—
417	C₂²	—	8	2	no	—
418	C₂²	—	16	4	no	—
419	C₂²	—	52	2	no	—
420	C₂²	—	52	2	no	—
421	C₂²	—	52	2	no	—
422	C₂²	#11718733	1	2	yes	—
423	C₂²	C₂×#88192	1	1	yes	characteristic
424	C₄	—	2	1	no	—
425	C₄	—	2	1	no	—
426	C₄	—	8	2	no	—
427	C₄	—	52	2	no	—
428	C₄	#11718733	1	2	yes	—
429	C₄	#11718838	1	2	yes	—
430	C₄	#11719467	1	2	yes	—
431	C₄	C₂²×#6104	1	1	yes	characteristic
432	C₄	C₂×#88186	1	1	yes	characteristic
433	C₂	—	2	2	no	—
434	C₂	—	16	2	no	—
435	C₂	—	104	2	no	—
436	C₂	C₂×#11718733	1	1	yes	characteristic
437	C₂	#13124471	1	1	yes	characteristic
438	C₂	C₂×#11718838	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×#88192
commutator, cosocle	C₄²×C₁₃	C₂⁴
Frattini	C₄²	C₂³×D₁₃
Fitting	C₂×C₁₃×#492	C₂
socle	C₂²×C₁₃	C₂×#121
prime radical	#13125754	C₂
hypercenter	C₂×#492	D₁₃
hypocenter	C₁₃	#19186
LCS	G ▷ C₄²×C₁₃ ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ C₂×#492

Complements

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

N	H ≅ G/N	type
1. #13125957	C₂	semidirect
3. #13123549	C₂	semidirect
4. #13114298	C₂	semidirect
5. #13114174	C₂	semidirect
6. #13113584	C₂	semidirect
7. #13113508	C₂	semidirect
8. #13113504	C₂	semidirect
9. C₂×C₁₃×#492	C₂	semidirect
24. #11718748	C₂²	semidirect
34. #11718349	C₂²	semidirect
36. C₈×D₅₂	C₂²	semidirect
37. #11718139	C₂²	semidirect
39. #11718050	C₂²	semidirect
40. #11718049	C₂²	semidirect
127. C₂×C₈×C₁₃	D₈	semidirect
153. C₂×#492	D₁₃	semidirect
352. C₂×C₈	#6104	semidirect
369. C₁₃	#19186	semidirect

Maximal subgroups

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

subgroup	index
#13125957	2
#13125754	2
#13123549	2
#13114298	2
#13114174	2
#13113584	2
#13113508	2
#13113504	2
C₂×C₁₃×#492	2
#19186	13