Subgroups — #15834133

Order 3328.

598 conjugacy classes of subgroups.

The subgroup lattice has 430 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13124901	C₂	1	1	yes	maximal, characteristic
2	#13123965	C₂	1	1	yes	maximal, characteristic
3	#13113726	C₂	1	2	yes	maximal, complemented
4	#13113714	C₂	1	2	yes	maximal, complemented
5	#13113705	C₂	1	2	yes	maximal, complemented
6	C₈×#6107	C₂	1	2	yes	maximal, complemented
7	#13113624	C₂	1	1	yes	maximal, characteristic, complemented
8	#13113291	C₂	1	1	yes	maximal, characteristic, complemented
9	#13113216	C₂	1	1	yes	maximal, characteristic
10	#13113120	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#2986	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#533	C₂²	1	1	yes	characteristic
13	C₄×#6127	C₂²	1	1	yes	characteristic
14	C₁₃×#446	—	2	1	no	—
15	C₁₃×#446	C₂²	1	2	yes	—
16	C₈×Q₈×C₁₃	—	2	1	no	—
17	C₈×Q₈×C₁₃	C₂²	1	2	yes	—
18	C₁₃×#433	—	2	2	no	—
19	C₁₃×#431	C₂²	1	1	yes	characteristic
20	C₁₃×#431	C₂²	1	1	yes	characteristic
21	#11718755	C₄	1	1	yes	characteristic
22	#11718751	C₄	1	1	yes	characteristic
23	#11718748	C₄	1	1	yes	characteristic
24	#11718744	C₄	1	1	yes	characteristic
25	#11718708	C₄	1	2	yes	—
26	#11718706	C₄	1	2	yes	—
27	C₄×#6107	C₂²	1	2	yes	—
28	C₄×#6106	C₂²	1	2	yes	—
29	#11718586	C₂²	1	1	yes	characteristic
30	#11718585	C₂²	1	1	yes	characteristic
31	C₂×C₄×#1055	C₂²	1	1	yes	characteristic
32	#11718498	—	2	1	no	—
33	#11718494	—	2	1	no	—
34	#11718390	—	2	2	no	—
35	#11718349	C₂²	1	2	yes	—
36	C₈×Dic₂₆	C₂²	1	2	yes	—
37	Q₈⋊#1055	C₂²	1	2	yes	—
38	Q₈⋊#1055	C₂²	1	2	yes	—
39	#11718076	C₂²	1	1	yes	characteristic
40	#11718076	C₂²	1	1	yes	characteristic
41	#11718075	C₂²	1	1	yes	characteristic
42	#11718075	C₂²	1	1	yes	characteristic
43	#11718072	C₂²	1	2	yes	—
44	#11718071	C₂²	1	2	yes	—
45	#11718046	C₂²	1	2	yes	—
46	C₈×#1055	C₂²	1	2	yes	—
47	C₂×#6127	C₂×C₄	1	1	yes	characteristic
48	C₁₃×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
49	C₁₃×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
50	C₁₃×#125	—	2	1	no	—
51	C₁₃×C₂²⋊Q₈	—	2	1	no	—
52	C₁₃×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
53	C₄×Q₈×C₁₃	—	2	1	no	—
54	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
55	C₁₃×#117	—	2	1	no	—
56	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
57	C₂×#6107	C₂×C₄	1	2	yes	—
58	C₂×#6106	C₂×C₄	1	2	yes	—
59	C₄×C₂²⋊D₁₃	—	2	1	no	—
60	C₄×C₂²⋊D₁₃	—	2	1	no	—
61	#88180	C₂×C₄	1	1	yes	characteristic
62	C₂×#6099	—	2	1	no	—
63	C₂²×#1055	—	2	1	no	—
64	C₂×#6094	—	2	2	no	—
65	C₄×D₅₂	C₂×C₄	1	1	yes	characteristic
66	C₄×D₅₂	C₂³	1	1	yes	characteristic
67	#88126	—	2	1	no	—
68	C₄²×D₁₃	—	2	1	no	—
69	C₄×Dic₂₆	C₂×C₄	1	1	yes	characteristic
70	C₄×Dic₂₆	C₂³	1	1	yes	characteristic
71	C₁₃×C₄⋊C₈	—	2	2	no	—
72	C₁₃×C₄⋊C₈	—	2	2	no	—
73	C₁₃×C₄⋊C₈	D₄	1	1	yes	characteristic
74	C₁₃×C₄⋊C₈	D₄	1	1	yes	characteristic
75	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
76	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
77	C₁₃×C₂²⋊C₈	—	2	1	no	—
78	C₁₃×C₂²⋊C₈	D₄	1	2	yes	—
79	C₁₃×#97	—	2	2	no	—
80	C₄×C₈×C₁₃	—	2	2	no	—
81	C₄×C₈×C₁₃	—	2	1	no	—
82	C₄×C₈×C₁₃	C₂³	1	2	yes	—
83	#88075	C₂×C₄	1	2	yes	—
84	#88075	C₂×C₄	1	2	yes	—
85	C₂²⋊#1055	C₂×C₄	1	2	yes	—
86	#88060	—	2	2	no	—
87	#88054	—	2	2	no	—
88	C₈×Dic₁₃	—	2	2	no	—
89	#88050	C₂×C₄	1	2	yes	—
90	#88049	C₂×C₄	1	2	yes	—
91	#88048	C₂×C₄	1	2	yes	—
92	#88047	C₂×C₄	1	2	yes	—
93	C₄⋊#1055	—	2	1	no	—
94	C₄⋊#1055	C₂×C₄	1	1	yes	characteristic
95	C₄⋊#1055	C₂×C₄	1	1	yes	characteristic
96	C₄⋊#1055	C₂³	1	2	yes	—
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	2	yes	—
101	#18019	—	13	1	no	maximal, Sylow
102	C₂×Q₈×C₁₃	—	2	1	no	—
103	C₂×Q₈×C₁₃	C₂²×C₄	1	2	yes	—
104	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
105	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
106	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
107	C₂×C₂²⋊D₁₃	—	2	1	no	—
108	#6127	—	2	2	no	—
109	#6127	—	4	1	no	—
110	C₂×D₅₂	C₂²×C₄	1	1	yes	characteristic
111	C₂×C₄×D₁₃	—	2	1	no	—
112	C₂×C₄×D₁₃	—	2	1	no	—
113	C₂×C₄×D₁₃	—	2	1	no	—
114	C₂×Dic₂₆	C₂²×C₄	1	1	yes	characteristic
115	C₂×C₈×C₁₃	—	2	1	no	—
116	C₂×C₈×C₁₃	—	2	1	no	—
117	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
118	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
119	C₁₃×C₄⋊C₄	—	2	1	no	—
120	C₁₃×C₄⋊C₄	—	2	1	no	—
121	C₁₃×C₄⋊C₄	—	2	1	no	—
122	C₁₃×C₄⋊C₄	—	2	2	no	—
123	C₁₃×C₄⋊C₄	—	2	2	no	—
124	C₁₃×C₄⋊C₄	C₂²×C₄	1	2	yes	—
125	C₁₃×C₂²⋊C₄	—	2	2	no	—
126	C₄²×C₁₃	—	2	2	no	—
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	1	no	—
132	#6107	—	2	4	no	—
133	#6106	—	4	2	no	—
134	#6103	—	2	1	no	—
135	#6103	—	2	1	no	—
136	C₄⋊Dic₁₃	C₂²×C₄	1	1	yes	characteristic
137	C₄⋊Dic₁₃	C₂²×C₄	1	1	yes	characteristic
138	#6101	—	2	1	no	—
139	#6101	—	2	1	no	—
140	C₄×Dic₁₃	—	2	1	no	—
141	C₄×Dic₁₃	—	2	1	no	—
142	C₄×Dic₁₃	—	2	1	no	—
143	#6099	—	8	1	no	—
144	C₂×#1055	—	2	4	no	—
145	C₂×#1055	—	2	1	no	—
146	C₂×#1055	—	2	1	no	—
147	C₂×#1055	—	2	2	no	—
148	C₂×#1055	C₂²×C₄	1	2	yes	—
149	C₂×#1055	C₂²×C₄	1	2	yes	—
150	#6094	—	8	2	no	—
151	#3107	—	13	1	no	—
152	#2991	—	13	1	no	—
153	#2986	D₁₃	1	1	yes	characteristic, complemented
154	#1590	—	13	2	no	—
155	#1588	—	13	2	no	—
156	#1587	—	13	2	no	—
157	C₈×Q₁₆	—	13	2	no	—
158	#1574	—	13	1	no	—
159	#1493	—	13	1	no	—
160	#1476	—	13	1	no	—
161	#1450	—	13	1	no	—
162	C₂³×C₁₃	C₄×D₄	1	1	yes	characteristic
163	C₂²×D₁₃	—	2	1	no	—
164	Q₈×C₁₃	—	2	2	no	—
165	Q₈×C₁₃	—	2	2	no	—
166	Q₈×C₁₃	—	4	2	no	—
167	C₂×C₄×C₁₃	—	2	1	no	—
168	C₂×C₄×C₁₃	—	2	1	no	—
169	C₂×C₄×C₁₃	—	2	1	no	—
170	C₂×C₄×C₁₃	—	2	1	no	—
171	C₂×C₄×C₁₃	—	2	2	no	—
172	C₂×C₄×C₁₃	—	2	2	no	—
173	C₂×C₄×C₁₃	—	2	2	no	—
174	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
175	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
176	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
177	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
178	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
179	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
180	C₂²⋊D₁₃	—	4	2	no	—
181	C₂×Dic₁₃	—	2	1	no	—
182	C₂×Dic₁₃	—	2	1	no	—
183	C₂×Dic₁₃	—	2	1	no	—
184	D₅₂	—	2	1	no	—
185	D₅₂	—	2	1	no	—
186	C₄×D₁₃	—	4	2	no	—
187	C₄×D₁₃	—	4	1	no	—
188	C₄×D₁₃	—	4	1	no	—
189	C₄×D₁₃	—	4	2	no	—
190	Dic₂₆	—	2	1	no	—
191	Dic₂₆	#131	1	2	yes	—
192	C₈×C₁₃	—	2	2	no	—
193	C₈×C₁₃	—	2	2	no	—
194	C₈×C₁₃	—	4	1	no	—
195	C₈×C₁₃	—	4	1	no	—
196	#1055	—	2	2	no	—
197	#1055	—	2	2	no	—
198	#1055	—	2	2	no	—
199	#1055	—	2	2	no	—
200	#1055	—	4	2	no	—
201	#533	C₂×D₁₃	1	1	yes	characteristic
202	C₄×#41	—	13	1	no	—
203	#485	—	13	2	no	—
204	#475	—	13	1	no	—
205	#474	—	13	1	no	—
206	#462	—	13	1	no	—
207	#461	—	13	1	no	—
208	#452	—	13	2	no	—
209	#446	—	2	1	no	—
210	#446	C₂×D₁₃	1	2	yes	—
211	C₈×Q₈	—	2	1	no	—
212	C₈×Q₈	—	13	2	no	—
213	C₈×Q₈	C₂×D₁₃	1	2	yes	—
214	C₄×Q₁₆	—	13	2	no	—
215	C₄×SD₁₆	—	13	2	no	—
216	#436	—	13	2	no	—
217	#436	—	26	2	no	—
218	#433	—	2	2	no	—
219	#431	—	13	1	no	—
220	#431	—	26	1	no	—
221	#431	C₂×D₁₃	1	1	yes	characteristic
222	#431	C₂×D₁₃	1	1	yes	characteristic
223	#423	—	13	1	no	—
224	#423	—	26	1	no	—
225	C₂×C₄×C₈	—	13	1	no	—
226	#335	—	13	2	no	—
227	#334	—	13	2	no	—
228	Q₈⋊C₈	—	13	2	no	—
229	Q₈⋊C₈	—	13	2	no	—
230	Q₈⋊C₈	—	13	1	no	—
231	Q₈⋊C₈	—	13	1	no	—
232	D₄⋊C₈	—	13	1	no	—
233	D₄⋊C₈	—	13	1	no	—
234	#322	—	13	2	no	—
235	C₈²	—	13	2	no	—
236	C₂²×C₁₃	—	2	1	no	—
237	C₂²×C₁₃	—	2	1	no	—
238	C₂²×C₁₃	—	2	1	no	—
239	C₂²×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
240	C₂×D₁₃	—	4	1	no	—
241	C₂×D₁₃	—	4	1	no	—
242	C₂×D₁₃	—	4	1	no	—
243	C₄×C₁₃	—	2	1	no	—
244	C₄×C₁₃	—	2	1	no	—
245	C₄×C₁₃	—	2	1	no	—
246	C₄×C₁₃	—	4	2	no	—
247	C₄×C₁₃	—	4	2	no	—
248	C₄×C₁₃	#443	1	2	yes	—
249	C₄×C₁₃	C₂×#131	1	1	yes	characteristic
250	C₄×C₁₃	#568	1	1	yes	characteristic
251	C₄×C₁₃	#577	1	1	yes	characteristic
252	C₄×C₁₃	#578	1	1	yes	characteristic
253	Dic₁₃	—	2	2	no	—
254	Dic₁₃	—	4	1	no	—
255	Dic₁₃	—	4	1	no	—
256	C₂×#41	—	13	1	no	—
257	C₂×Q₁₆	—	13	2	no	—
258	C₂×SD₁₆	—	13	2	no	—
259	C₂×M₁₆	—	26	1	no	—
260	C₂×M₁₆	—	26	2	no	—
261	C₂²×C₈	—	26	1	no	—
262	C₄⋊Q₈	C₄×D₁₃	1	1	yes	characteristic
263	C₄⋊Q₈	C₄×D₁₃	1	1	yes	characteristic
264	#125	—	2	1	no	—
265	C₂²⋊Q₈	—	2	1	no	—
266	C₂²⋊Q₈	C₄×D₁₃	1	2	yes	—
267	C₄×Q₈	—	2	1	no	—
268	C₄×Q₈	—	13	1	no	—
269	C₄×Q₈	—	13	1	no	—
270	C₄×Q₈	C₂²×D₁₃	1	2	yes	—
271	C₄×D₄	—	13	1	no	—
272	C₄×D₄	—	13	1	no	—
273	C₄×D₄	—	26	1	no	—
274	C₄×D₄	—	26	1	no	—
275	#117	—	2	1	no	—
276	#117	—	13	1	no	—
277	#117	—	26	1	no	—
278	C₂×C₄²	—	26	1	no	—
279	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
280	#107	—	13	2	no	—
281	#106	—	13	2	no	—
282	C₄⋊C₈	—	2	2	no	—
283	C₄⋊C₈	—	2	2	no	—
284	C₄⋊C₈	—	13	1	no	—
285	C₄⋊C₈	—	13	1	no	—
286	C₄⋊C₈	—	13	2	no	—
287	C₄⋊C₈	—	26	2	no	—
288	C₄⋊C₈	—	26	1	no	—
289	C₄⋊C₈	C₂²⋊D₁₃	1	1	yes	characteristic
290	C₄⋊C₈	C₂²⋊D₁₃	1	1	yes	characteristic
291	C₄⋊C₈	C₂²×D₁₃	1	1	yes	characteristic
292	C₄⋊C₈	C₂²×D₁₃	1	1	yes	characteristic
293	#103	—	13	2	no	—
294	#103	—	13	2	no	—
295	#103	—	13	2	no	—
296	#102	—	13	2	no	—
297	C₂²⋊C₈	—	2	1	no	—
298	C₂²⋊C₈	—	13	2	no	—
299	C₂²⋊C₈	—	26	2	no	—
300	C₂²⋊C₈	C₂²⋊D₁₃	1	2	yes	—
301	#97	—	2	2	no	—
302	C₄×C₈	—	2	2	no	—
303	C₄×C₈	—	2	1	no	—
304	C₄×C₈	—	13	2	no	—
305	C₄×C₈	—	13	1	no	—
306	C₄×C₈	—	13	1	no	—
307	C₄×C₈	—	26	2	no	—
308	C₄×C₈	—	26	1	no	—
309	C₄×C₈	C₂²×D₁₃	1	2	yes	—
310	C₂×C₁₃	—	4	1	no	—
311	C₂×C₁₃	#2933	1	1	yes	characteristic
312	C₂×C₁₃	#2947	1	1	yes	characteristic
313	C₂×C₁₃	C₂×#443	1	1	yes	characteristic
314	D₁₃	—	8	1	no	—
315	#41	—	26	2	no	—
316	#41	—	52	1	no	—
317	C₂×Q₈	—	2	1	no	—
318	C₂×Q₈	—	13	1	no	—
319	C₂×Q₈	C₂×C₄×D₁₃	1	2	yes	—
320	C₂×D₄	—	13	1	no	—
321	C₂×D₄	—	26	1	no	—
322	C₂²×C₄	—	26	1	no	—
323	C₂²×C₄	—	26	1	no	—
324	C₂²×C₄	—	26	1	no	—
325	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
326	C₂²×C₄	#6127	1	1	yes	characteristic
327	C₂²×C₄	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
328	Q₁₆	—	26	4	no	—
329	SD₁₆	—	52	2	no	—
330	M₁₆	—	104	2	no	—
331	M₁₆	—	104	1	no	—
332	C₂×C₈	—	2	1	no	—
333	C₂×C₈	—	2	1	no	—
334	C₂×C₈	—	13	2	no	—
335	C₂×C₈	—	13	2	no	—
336	C₂×C₈	—	26	4	no	—
337	C₂×C₈	—	26	1	no	—
338	C₂×C₈	—	26	1	no	—
339	C₂×C₈	—	26	2	no	—
340	C₂×C₈	C₂×C₂²⋊D₁₃	1	2	yes	—
341	C₂×C₈	C₂×C₂²⋊D₁₃	1	2	yes	—
342	C₄⋊C₄	—	2	1	no	—
343	C₄⋊C₄	—	2	1	no	—
344	C₄⋊C₄	—	2	1	no	—
345	C₄⋊C₄	—	2	2	no	—
346	C₄⋊C₄	—	2	2	no	—
347	C₄⋊C₄	—	13	1	no	—
348	C₄⋊C₄	—	13	1	no	—
349	C₄⋊C₄	—	26	1	no	—
350	C₄⋊C₄	—	26	1	no	—
351	C₄⋊C₄	C₂×C₄×D₁₃	1	2	yes	—
352	C₂²⋊C₄	—	2	2	no	—
353	C₂²⋊C₄	—	26	1	no	—
354	C₂²⋊C₄	—	26	1	no	—
355	C₂²⋊C₄	—	26	1	no	—
356	C₄²	—	2	2	no	—
357	C₄²	—	26	1	no	—
358	C₄²	—	26	1	no	—
359	C₄²	—	26	1	no	—
360	C₄²	C₂×C₄×D₁₃	1	1	yes	characteristic
361	C₄²	#6127	1	1	yes	characteristic
362	C₄²	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
363	C₄²	C₂³×D₁₃	1	1	yes	characteristic
364	C₁₃	#18019	1	1	yes	characteristic, complemented, Sylow
365	C₂³	—	26	1	no	—
366	C₂³	C₄×C₂²⋊D₁₃	1	1	yes	characteristic
367	Q₈	—	2	2	no	—
368	Q₈	—	2	2	no	—
369	Q₈	—	4	2	no	—
370	Q₈	—	13	2	no	—
371	Q₈	—	26	1	no	—
372	D₄	—	26	1	no	—
373	D₄	—	26	1	no	—
374	D₄	—	52	2	no	—
375	C₂×C₄	—	2	1	no	—
376	C₂×C₄	—	2	1	no	—
377	C₂×C₄	—	2	1	no	—
378	C₂×C₄	—	2	1	no	—
379	C₂×C₄	—	2	2	no	—
380	C₂×C₄	—	2	2	no	—
381	C₂×C₄	—	2	2	no	—
382	C₂×C₄	—	26	1	no	—
383	C₂×C₄	—	26	1	no	—
384	C₂×C₄	—	26	1	no	—
385	C₂×C₄	—	52	2	no	—
386	C₂×C₄	—	52	1	no	—
387	C₂×C₄	—	52	1	no	—
388	C₂×C₄	—	52	2	no	—
389	C₂×C₄	C₄×C₂²⋊D₁₃	1	1	yes	characteristic
390	C₂×C₄	C₄×C₂²⋊D₁₃	1	1	yes	characteristic
391	C₂×C₄	C₄×C₂²⋊D₁₃	1	1	yes	characteristic
392	C₂×C₄	C₂²×C₄×D₁₃	1	1	yes	characteristic
393	C₂×C₄	C₂×#6127	1	1	yes	characteristic
394	C₂×C₄	C₂²×C₂²⋊D₁₃	1	1	yes	characteristic
395	C₈	—	2	2	no	—
396	C₈	—	2	2	no	—
397	C₈	—	4	1	no	—
398	C₈	—	4	1	no	—
399	C₈	—	26	2	no	—
400	C₈	—	26	2	no	—
401	C₈	—	26	2	no	—
402	C₈	—	26	2	no	—
403	C₈	—	52	2	no	—
404	C₂²	—	2	1	no	—
405	C₂²	—	2	1	no	—
406	C₂²	—	2	1	no	—
407	C₂²	—	52	1	no	—
408	C₂²	—	52	1	no	—
409	C₂²	—	52	1	no	—
410	C₂²	C₂×C₄×C₂²⋊D₁₃	1	1	yes	characteristic
411	C₄	—	2	1	no	—
412	C₄	—	2	1	no	—
413	C₄	—	2	1	no	—
414	C₄	—	4	2	no	—
415	C₄	—	4	2	no	—
416	C₄	—	26	2	no	—
417	C₄	—	52	1	no	—
418	C₄	—	52	1	no	—
419	C₄	#11718805	1	2	yes	—
420	C₄	D₁₃×#131	1	1	yes	characteristic
421	C₄	#11719455	1	1	yes	characteristic
422	C₄	#11719542	1	1	yes	characteristic
423	C₄	#11719543	1	1	yes	characteristic
424	C₂	—	4	1	no	—
425	C₂	—	104	1	no	—
426	C₂	#13123558	1	1	yes	characteristic
427	C₂	#13123679	1	1	yes	characteristic
428	C₂	C₂×#11718805	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²×C₂²⋊D₁₃
commutator	C₂×C₄×C₁₃	C₂³×C₄
Frattini	C₄²	C₂³×D₁₃
Fitting	C₁₃×#2986	C₂
socle	C₂²×C₁₃	C₂×C₄×D₄
prime radical	C₂×#6127	C₂×C₄
cosocle	C₄²×C₁₃	C₂⁴
hypercenter	#2986	D₁₃
hypocenter	C₁₃	#18019
LCS	G ▷ C₂×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₄ ◁ #431 ◁ #2986

Complements

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

N	H ≅ G/N	type
3. #13113726	C₂	semidirect
4. #13113714	C₂	semidirect
5. #13113705	C₂	semidirect
6. C₈×#6107	C₂	semidirect
7. #13113624	C₂	semidirect
8. #13113291	C₂	semidirect
10. #13113120	C₂	semidirect
11. C₁₃×#2986	C₂	semidirect
153. #2986	D₁₃	semidirect
364. C₁₃	#18019	semidirect

Maximal subgroups

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

subgroup	index
#13124901	2
#13123965	2
#13113726	2
#13113714	2
#13113705	2
C₈×#6107	2
#13113624	2
#13113291	2
#13113216	2
#13113120	2
C₁₃×#2986	2
#18019	13