Subgroups — #15863500

Order 3328.

810 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13117445	C₂	1	2	yes	maximal
2	#13115004	C₂	1	2	yes	maximal, complemented
3	#13114967	C₂	1	1	yes	maximal, characteristic, complemented
4	#13114964	C₂	1	1	yes	maximal, characteristic, complemented
5	#13114869	C₂	1	2	yes	maximal
6	#13114865	C₂	1	1	yes	maximal, characteristic
7	#13114861	C₂	1	1	yes	maximal, characteristic
8	#13114733	C₂	1	2	yes	maximal, complemented
9	C₄×#88058	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄×#88057	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₁₃×#405	C₂	1	1	yes	maximal, characteristic
12	C₂²×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
13	C₂³×C₈×C₁₃	C₂²	1	1	yes	characteristic
14	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
15	C₁₃×#405	C₄	1	8	yes	complemented
16	C₂×C₁₃×#97	C₂²	1	1	yes	characteristic
17	C₂×C₁₃×#97	C₂²	1	1	yes	characteristic
18	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
19	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
20	#11718873	C₂²	1	2	yes	—
21	#11718873	C₂²	1	2	yes	—
22	C₂×#88058	C₂²	1	2	yes	—
23	C₂×#88058	C₂²	1	2	yes	—
24	C₂×#88057	C₂²	1	2	yes	—
25	C₂×#88057	C₂²	1	2	yes	—
26	#11718642	—	2	2	no	—
27	#11718642	—	2	2	no	—
28	#11718612	—	2	2	no	—
29	#11718612	—	2	2	no	—
30	#11718597	C₂²	1	2	yes	—
31	#11718596	C₂²	1	2	yes	—
32	C₄×C₄⋊Dic₁₃	C₂²	1	2	yes	—
33	C₄×C₄⋊Dic₁₃	C₂²	1	2	yes	—
34	#11718143	C₂²	1	1	yes	characteristic
35	#11718143	C₂²	1	1	yes	characteristic
36	#11718143	C₂²	1	2	yes	—
37	#11718143	C₂²	1	1	yes	characteristic
38	#11718143	C₂²	1	1	yes	characteristic
39	#11718143	C₂²	1	2	yes	—
40	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
41	C₂×C₁₃×M₁₆	—	2	4	no	—
42	C₂×C₁₃×M₁₆	C₂×C₄	1	4	yes	—
43	C₂²×C₈×C₁₃	—	2	4	no	—
44	C₂²×C₈×C₁₃	C₂×C₄	1	4	yes	—
45	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
46	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
47	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
48	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
49	C₁₃×#117	C₂×C₄	1	4	yes	—
50	C₁₃×#117	Q₈	1	4	yes	—
51	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
52	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
53	C₂×C₁₃×C₂²⋊C₄	D₄	1	1	yes	characteristic
54	C₂×C₁₃×C₂²⋊C₄	D₄	1	1	yes	characteristic
55	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
56	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
57	C₂×C₂²⋊Dic₁₃	—	2	2	no	—
58	C₂×C₂²⋊Dic₁₃	—	2	2	no	—
59	C₂×C₄⋊Dic₁₃	—	2	2	no	—
60	C₂×C₄⋊Dic₁₃	—	2	2	no	—
61	C₂×C₄⋊Dic₁₃	C₂³	1	2	yes	—
62	C₂×C₄⋊Dic₁₃	C₂³	1	2	yes	—
63	C₂×C₄⋊Dic₁₃	C₂³	1	2	yes	—
64	C₂×C₄⋊Dic₁₃	C₂³	1	2	yes	—
65	C₂×C₄×Dic₁₃	—	2	2	no	—
66	C₂×C₄×Dic₁₃	—	2	2	no	—
67	C₁₃×#97	C₂×C₄	1	4	yes	—
68	C₁₃×#97	C₂×C₄	1	4	yes	—
69	C₄×C₈×C₁₃	C₂×C₄	1	4	yes	—
70	C₄×C₈×C₁₃	C₂×C₄	1	4	yes	—
71	#88071	—	2	2	no	—
72	#88071	—	2	2	no	—
73	#88071	—	2	2	no	—
74	#88071	—	2	2	no	—
75	#88071	—	2	2	no	—
76	#88071	—	2	2	no	—
77	#88058	—	2	4	no	—
78	#88058	—	2	4	no	—
79	#88057	—	2	4	no	—
80	#88057	—	2	4	no	—
81	#20822	—	13	1	no	maximal, Sylow
82	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
83	C₂²×C₄×C₁₃	—	2	2	no	—
84	C₂²×C₄×C₁₃	—	2	2	no	—
85	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
86	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
87	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
88	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
89	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
90	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
91	C₂²×C₄×C₁₃	C₂×Q₈	1	2	yes	—
92	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
93	C₂²×Dic₁₃	—	2	2	no	—
94	C₂²×Dic₁₃	—	2	2	no	—
95	C₂²×Dic₁₃	—	2	2	no	—
96	C₂²×Dic₁₃	—	2	2	no	—
97	C₁₃×M₁₆	—	2	8	no	—
98	C₂×C₈×C₁₃	—	2	2	no	—
99	C₂×C₈×C₁₃	—	2	2	no	—
100	C₂×C₈×C₁₃	—	2	8	no	—
101	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
102	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
103	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
104	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
105	C₂×C₈×C₁₃	#41	1	4	yes	—
106	C₂×C₈×C₁₃	#41	1	4	yes	—
107	C₁₃×C₄⋊C₄	C₄⋊C₄	1	4	yes	—
108	C₁₃×C₄⋊C₄	C₄⋊C₄	1	4	yes	—
109	C₁₃×C₂²⋊C₄	C₄⋊C₄	1	4	yes	—
110	C₁₃×C₂²⋊C₄	C₄⋊C₄	1	4	yes	—
111	C₄²×C₁₃	C₂²×C₄	1	2	yes	—
112	C₄²×C₁₃	C₂²×C₄	1	2	yes	—
113	C₄²×C₁₃	C₂×Q₈	1	2	yes	—
114	C₄²×C₁₃	C₂×Q₈	1	2	yes	—
115	C₂²⋊Dic₁₃	—	8	2	no	—
116	C₂²⋊Dic₁₃	—	8	2	no	—
117	C₄⋊Dic₁₃	—	2	2	no	—
118	C₄⋊Dic₁₃	—	2	2	no	—
119	C₄⋊Dic₁₃	—	2	2	no	—
120	C₄⋊Dic₁₃	—	2	2	no	—
121	C₄⋊Dic₁₃	—	2	2	no	—
122	C₄⋊Dic₁₃	—	2	2	no	—
123	C₄⋊Dic₁₃	—	2	2	no	—
124	C₄⋊Dic₁₃	—	2	2	no	—
125	C₄⋊Dic₁₃	—	8	2	no	—
126	C₄⋊Dic₁₃	—	8	2	no	—
127	C₄×Dic₁₃	—	8	2	no	—
128	C₄×Dic₁₃	—	8	2	no	—
129	C₂×#405	D₁₃	1	1	yes	characteristic
130	#2314	—	13	2	no	—
131	#1847	—	13	2	no	—
132	#1835	—	13	1	no	—
133	#1834	—	13	1	no	—
134	#1809	—	13	2	no	—
135	#1808	—	13	1	no	—
136	#1807	—	13	1	no	—
137	#1776	—	13	2	no	—
138	C₄×#107	—	13	1	no	—
139	C₄×#106	—	13	1	no	—
140	C₂³×C₁₃	—	2	2	no	—
141	C₂³×C₁₃	—	2	1	no	—
142	C₂³×C₁₃	—	2	2	no	—
143	C₂³×C₁₃	—	2	1	no	—
144	C₂³×C₁₃	C₂×C₄⋊C₄	1	2	yes	—
145	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
146	C₂×C₄×C₁₃	—	2	2	no	—
147	C₂×C₄×C₁₃	—	2	1	no	—
148	C₂×C₄×C₁₃	—	2	1	no	—
149	C₂×C₄×C₁₃	—	2	2	no	—
150	C₂×C₄×C₁₃	—	2	2	no	—
151	C₂×C₄×C₁₃	—	2	1	no	—
152	C₂×C₄×C₁₃	—	2	1	no	—
153	C₂×C₄×C₁₃	—	2	2	no	—
154	C₂×C₄×C₁₃	—	2	2	no	—
155	C₂×C₄×C₁₃	—	2	4	no	—
156	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	2	yes	—
157	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	2	yes	—
158	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	2	yes	—
159	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	2	yes	—
160	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	2	yes	—
161	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
162	C₂×C₄×C₁₃	C₂²×Q₈	1	1	yes	characteristic
163	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
164	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
165	C₂×Dic₁₃	—	4	2	no	—
166	C₂×Dic₁₃	—	4	2	no	—
167	C₂×Dic₁₃	—	4	2	no	—
168	C₂×Dic₁₃	—	4	2	no	—
169	C₂×Dic₁₃	—	4	2	no	—
170	C₂×Dic₁₃	—	4	2	no	—
171	C₂×Dic₁₃	—	4	2	no	—
172	C₂×Dic₁₃	—	4	2	no	—
173	C₂×Dic₁₃	—	4	2	no	—
174	C₂×Dic₁₃	—	4	2	no	—
175	C₂×Dic₁₃	—	4	2	no	—
176	C₂×Dic₁₃	—	4	2	no	—
177	C₈×C₁₃	—	2	2	no	—
178	C₈×C₁₃	—	2	2	no	—
179	C₈×C₁₃	#117	1	4	yes	—
180	C₈×C₁₃	#117	1	4	yes	—
181	C₂²×M₁₆	C₂×D₁₃	1	1	yes	characteristic
182	C₂³×C₈	C₂×D₁₃	1	1	yes	characteristic
183	C₂×#117	C₂×D₁₃	1	1	yes	characteristic
184	C₂×#107	—	13	2	no	—
185	C₂×#107	—	13	2	no	—
186	C₂×#106	—	13	2	no	—
187	C₂×#106	—	13	2	no	—
188	#405	Dic₁₃	1	8	yes	complemented
189	C₂×#97	C₂×D₁₃	1	1	yes	characteristic
190	C₂×#97	C₂×D₁₃	1	1	yes	characteristic
191	C₂×C₄×C₈	C₂×D₁₃	1	1	yes	characteristic
192	C₂×C₄×C₈	C₂×D₁₃	1	1	yes	characteristic
193	#388	—	26	2	no	—
194	#388	—	26	2	no	—
195	#387	—	26	2	no	—
196	#387	—	26	2	no	—
197	#384	—	13	2	no	—
198	#382	—	13	2	no	—
199	#380	—	13	2	no	—
200	#380	—	13	2	no	—
201	C₄×C₄⋊C₄	—	13	2	no	—
202	C₄×C₄⋊C₄	—	13	2	no	—
203	#340	—	13	1	no	—
204	#340	—	13	1	no	—
205	#340	—	13	1	no	—
206	#340	—	13	1	no	—
207	#340	—	13	2	no	—
208	#340	—	13	2	no	—
209	C₂²×C₁₃	—	2	2	no	—
210	C₂²×C₁₃	—	2	2	no	—
211	C₂²×C₁₃	—	2	2	no	—
212	C₂²×C₁₃	—	4	2	no	—
213	C₂²×C₁₃	—	4	2	no	—
214	C₂²×C₁₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
215	C₂²×C₁₃	#532	1	2	yes	—
216	C₂²×C₁₃	#576	1	1	yes	characteristic
217	C₂²×C₁₃	#577	1	2	yes	—
218	C₂²×C₁₃	#578	1	1	yes	characteristic
219	C₄×C₁₃	—	2	2	no	—
220	C₄×C₁₃	—	2	2	no	—
221	C₄×C₁₃	—	2	2	no	—
222	C₄×C₁₃	—	2	2	no	—
223	C₄×C₁₃	—	2	2	no	—
224	C₄×C₁₃	C₂×#117	1	1	yes	characteristic
225	C₄×C₁₃	C₂×#117	1	1	yes	characteristic
226	C₄×C₁₃	#533	1	2	yes	—
227	Dic₁₃	—	8	2	no	—
228	Dic₁₃	—	8	2	no	—
229	Dic₁₃	—	8	2	no	—
230	Dic₁₃	—	8	2	no	—
231	C₂³×C₄	C₂²×D₁₃	1	1	yes	characteristic
232	C₂×M₁₆	—	2	4	no	—
233	C₂×M₁₆	C₂×Dic₁₃	1	4	yes	—
234	C₂²×C₈	—	2	4	no	—
235	C₂²×C₈	C₂×Dic₁₃	1	4	yes	—
236	C₂²×C₈	C₂²×D₁₃	1	1	yes	characteristic
237	C₂²×C₈	C₂²×D₁₃	1	1	yes	characteristic
238	C₂²×C₈	C₂²×D₁₃	1	1	yes	characteristic
239	C₂²×C₈	C₂²×D₁₃	1	1	yes	characteristic
240	#117	Dic₂₆	1	4	yes	—
241	#117	C₂×Dic₁₃	1	4	yes	—
242	C₂×C₄⋊C₄	—	13	2	no	—
243	C₂×C₄⋊C₄	—	13	2	no	—
244	C₂×C₄⋊C₄	—	13	2	no	—
245	C₂×C₄⋊C₄	—	13	2	no	—
246	C₂×C₄⋊C₄	—	26	2	no	—
247	C₂×C₄⋊C₄	—	26	2	no	—
248	C₂×C₄⋊C₄	D₅₂	1	1	yes	characteristic
249	C₂×C₄⋊C₄	D₅₂	1	1	yes	characteristic
250	C₂×C₂²⋊C₄	—	26	2	no	—
251	C₂×C₂²⋊C₄	—	26	2	no	—
252	C₂×C₂²⋊C₄	D₅₂	1	1	yes	characteristic
253	C₂×C₂²⋊C₄	D₅₂	1	1	yes	characteristic
254	C₂×C₄²	—	26	2	no	—
255	C₂×C₄²	—	26	2	no	—
256	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
257	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
258	#107	—	26	4	no	—
259	#107	—	26	4	no	—
260	#106	—	26	4	no	—
261	#106	—	26	4	no	—
262	#97	C₂×Dic₁₃	1	4	yes	—
263	#97	C₂×Dic₁₃	1	4	yes	—
264	C₄×C₈	C₂×Dic₁₃	1	4	yes	—
265	C₄×C₈	C₂×Dic₁₃	1	4	yes	—
266	#95	—	26	2	no	—
267	#95	—	26	2	no	—
268	#95	—	26	2	no	—
269	#95	—	26	2	no	—
270	#95	—	26	2	no	—
271	#95	—	26	2	no	—
272	C₂×C₁₃	—	4	2	no	—
273	C₂×C₁₃	#2285	1	1	yes	characteristic
274	C₂×C₁₃	#2912	1	1	yes	characteristic
275	C₂×C₁₃	#2913	1	1	yes	characteristic
276	C₂×C₁₃	#3178	1	2	yes	—
277	C₂×C₁₃	#3179	1	2	yes	—
278	C₂⁴	C₂×D₅₂	1	1	yes	characteristic
279	C₂²×C₄	—	2	2	no	—
280	C₂²×C₄	—	2	2	no	—
281	C₂²×C₄	—	26	2	no	—
282	C₂²×C₄	—	26	2	no	—
283	C₂²×C₄	—	26	2	no	—
284	C₂²×C₄	—	26	2	no	—
285	C₂²×C₄	C₂×Dic₂₆	1	2	yes	—
286	C₂²×C₄	C₂×D₅₂	1	1	yes	characteristic
287	C₂²×C₄	C₂×D₅₂	1	1	yes	characteristic
288	C₂²×C₄	C₂×D₅₂	1	1	yes	characteristic
289	C₂²×C₄	C₂×D₅₂	1	1	yes	characteristic
290	C₂²×C₄	C₂×D₅₂	1	1	yes	characteristic
291	C₂²×C₄	C₂²×Dic₁₃	1	2	yes	—
292	C₂²×C₄	C₂³×D₁₃	1	1	yes	characteristic
293	M₁₆	—	2	8	no	—
294	C₂×C₈	—	2	2	no	—
295	C₂×C₈	—	2	2	no	—
296	C₂×C₈	—	2	8	no	—
297	C₂×C₈	#6127	1	4	yes	—
298	C₂×C₈	#6127	1	4	yes	—
299	C₂×C₈	C₂²×Dic₁₃	1	2	yes	—
300	C₂×C₈	C₂²×Dic₁₃	1	2	yes	—
301	C₂×C₈	C₂²×Dic₁₃	1	2	yes	—
302	C₂×C₈	C₂²×Dic₁₃	1	2	yes	—
303	C₄⋊C₄	—	26	2	no	—
304	C₄⋊C₄	—	26	2	no	—
305	C₄⋊C₄	—	26	2	no	—
306	C₄⋊C₄	—	26	2	no	—
307	C₄⋊C₄	—	26	2	no	—
308	C₄⋊C₄	—	26	2	no	—
309	C₄⋊C₄	—	26	2	no	—
310	C₄⋊C₄	—	26	2	no	—
311	C₄⋊C₄	—	104	2	no	—
312	C₄⋊C₄	—	104	2	no	—
313	C₄⋊C₄	C₄⋊Dic₁₃	1	4	yes	—
314	C₄⋊C₄	C₄⋊Dic₁₃	1	4	yes	—
315	C₂²⋊C₄	—	104	2	no	—
316	C₂²⋊C₄	—	104	2	no	—
317	C₂²⋊C₄	C₄⋊Dic₁₃	1	4	yes	—
318	C₂²⋊C₄	C₄⋊Dic₁₃	1	4	yes	—
319	C₄²	—	104	2	no	—
320	C₄²	—	104	2	no	—
321	C₄²	C₂×Dic₂₆	1	2	yes	—
322	C₄²	C₂×Dic₂₆	1	2	yes	—
323	C₄²	C₂²×Dic₁₃	1	2	yes	—
324	C₄²	C₂²×Dic₁₃	1	2	yes	—
325	C₁₃	#20822	1	1	yes	characteristic, complemented, Sylow
326	C₂³	—	2	2	no	—
327	C₂³	—	2	2	no	—
328	C₂³	—	2	1	no	—
329	C₂³	—	2	1	no	—
330	C₂³	C₂×C₄⋊Dic₁₃	1	2	yes	—
331	C₂³	C₂²×D₅₂	1	1	yes	characteristic
332	C₂×C₄	—	2	2	no	—
333	C₂×C₄	—	2	2	no	—
334	C₂×C₄	—	2	2	no	—
335	C₂×C₄	—	2	1	no	—
336	C₂×C₄	—	2	1	no	—
337	C₂×C₄	—	2	1	no	—
338	C₂×C₄	—	2	1	no	—
339	C₂×C₄	—	2	4	no	—
340	C₂×C₄	—	2	2	no	—
341	C₂×C₄	—	2	2	no	—
342	C₂×C₄	—	52	2	no	—
343	C₂×C₄	—	52	2	no	—
344	C₂×C₄	—	52	2	no	—
345	C₂×C₄	—	52	2	no	—
346	C₂×C₄	—	52	2	no	—
347	C₂×C₄	—	52	2	no	—
348	C₂×C₄	—	52	2	no	—
349	C₂×C₄	—	52	2	no	—
350	C₂×C₄	—	52	2	no	—
351	C₂×C₄	—	52	2	no	—
352	C₂×C₄	—	52	2	no	—
353	C₂×C₄	—	52	2	no	—
354	C₂×C₄	C₂×C₄⋊Dic₁₃	1	2	yes	—
355	C₂×C₄	C₂×C₄⋊Dic₁₃	1	2	yes	—
356	C₂×C₄	C₂×C₄⋊Dic₁₃	1	2	yes	—
357	C₂×C₄	C₂×C₄⋊Dic₁₃	1	2	yes	—
358	C₂×C₄	C₂×C₄⋊Dic₁₃	1	2	yes	—
359	C₂×C₄	C₂²×Dic₂₆	1	1	yes	characteristic
360	C₂×C₄	C₂×#6127	1	2	yes	—
361	C₂×C₄	C₂×#6127	1	2	yes	—
362	C₂×C₄	C₂³×Dic₁₃	1	1	yes	characteristic
363	C₈	—	2	2	no	—
364	C₈	—	2	2	no	—
365	C₈	#88180	1	4	yes	—
366	C₈	#88180	1	4	yes	—
367	C₂²	—	2	2	no	—
368	C₂²	—	2	2	no	—
369	C₂²	—	2	2	no	—
370	C₂²	—	4	2	no	—
371	C₂²	—	4	2	no	—
372	C₂²	#11719182	1	2	yes	—
373	C₂²	#11719456	1	2	yes	—
374	C₂²	#11719457	1	1	yes	characteristic
375	C₂²	#11719458	1	1	yes	characteristic
376	C₂²	C₂²×C₄⋊Dic₁₃	1	1	yes	characteristic
377	C₄	—	2	2	no	—
378	C₄	—	2	2	no	—
379	C₄	—	2	2	no	—
380	C₄	—	2	2	no	—
381	C₄	—	2	2	no	—
382	C₄	—	104	2	no	—
383	C₄	—	104	2	no	—
384	C₄	—	104	2	no	—
385	C₄	—	104	2	no	—
386	C₄	#11719175	1	2	yes	—
387	C₄	C₂×#88180	1	1	yes	characteristic
388	C₄	C₂×#88180	1	1	yes	characteristic
389	C₂	—	4	2	no	—
390	C₂	#13117243	1	1	yes	characteristic
391	C₂	#13123431	1	1	yes	characteristic
392	C₂	#13123436	1	1	yes	characteristic
393	C₂	#13125504	1	2	yes	—
394	C₂	#13125519	1	2	yes	—

	subgroup	G/H
center	C₂³	C₂²×D₅₂
commutator	C₂×C₄×C₁₃	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₁₃
Fitting	C₂×C₁₃×#405	C₂
socle	C₂³×C₁₃	C₂²×D₄
prime radical	C₂⁴×C₁₃	C₂×D₄
cosocle	C₂²×C₄×C₁₃	C₂⁴
hypercenter	C₂×#405	D₁₃
hypocenter	C₁₃	#20822
LCS	G ▷ C₂×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂³ ◁ C₂×#117 ◁ C₂×#405

Complements

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

N	H ≅ G/N	type
2. #13115004	C₂	semidirect
3. #13114967	C₂	semidirect
4. #13114964	C₂	semidirect
8. #13114733	C₂	semidirect
9. C₄×#88058	C₂	semidirect
10. C₄×#88057	C₂	semidirect
15. C₁₃×#405	C₄	semidirect
188. #405	Dic₁₃	semidirect
325. C₁₃	#20822	semidirect

Maximal subgroups

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

subgroup	index
#13117445	2
#13115004	2
#13114967	2
#13114964	2
#13114869	2
#13114865	2
#13114861	2
#13114733	2
C₄×#88058	2
C₄×#88057	2
C₂×C₁₃×#405	2
#20822	13