Subgroups — #15860840

Order 3328.

1146 conjugacy classes of subgroups.

The subgroup lattice has 366 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11718585	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₄⋊#1055	C₂	1	1	yes	maximal, characteristic
3	C₂×#11718658	C₂	1	2	yes	maximal
4	#13114693	C₂	1	4	yes	maximal, complemented
5	#13114689	C₂	1	2	yes	maximal, complemented
6	C₄×C₄⋊#1055	C₂	1	2	yes	maximal, complemented
7	#13114533	C₂	1	2	yes	maximal
8	C₄×C₁₃×#117	C₂	1	1	yes	maximal, characteristic
9	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
10	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
11	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
12	C₂²×#6099	C₂²	1	2	yes	—
13	C₂³×#1055	C₂²	1	2	yes	—
14	C₄×C₁₃×C₄⋊C₄	C₄	1	2	yes	—
15	C₄×C₁₃×C₄⋊C₄	C₄	1	2	yes	—
16	C₄×C₁₃×C₂²⋊C₄	C₄	1	2	yes	—
17	C₄×C₁₃×C₂²⋊C₄	C₄	1	2	yes	—
18	C₁₃×#376	C₂²	1	2	yes	—
19	C₄³×C₁₃	C₂²	1	2	yes	—
20	#11718658	—	2	8	no	—
21	#11718585	C₄	1	8	yes	complemented
22	C₂×C₄⋊#1055	C₄	1	8	yes	complemented
23	C₂×C₄⋊#1055	C₂²	1	1	yes	characteristic
24	C₂×C₄⋊#1055	C₂²	1	1	yes	characteristic
25	C₂×C₄⋊#1055	C₂²	1	2	yes	—
26	C₂×C₄⋊#1055	C₂²	1	2	yes	—
27	C₂×C₄⋊#1055	C₂²	1	2	yes	—
28	C₂×#88043	C₂²	1	4	yes	—
29	C₂×C₄×#1055	C₂²	1	4	yes	—
30	#11718116	C₂²	1	4	yes	—
31	#11718116	C₂²	1	4	yes	—
32	C₂³×C₄×C₁₃	C₂×C₄	1	1	yes	characteristic
33	C₂³×C₄×C₁₃	C₂×C₄	1	1	yes	characteristic
34	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
35	C₁₃×#117	—	2	2	no	—
36	C₁₃×#117	—	2	2	no	—
37	C₁₃×#117	D₄	1	4	yes	—
38	C₁₃×#117	Q₈	1	4	yes	—
39	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	2	yes	—
40	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	2	yes	—
41	C₂×C₁₃×C₂²⋊C₄	C₂×C₄	1	2	yes	—
42	C₂×C₁₃×C₂²⋊C₄	C₂×C₄	1	2	yes	—
43	C₂×C₄²×C₁₃	C₂×C₄	1	4	yes	—
44	C₂×C₄²×C₁₃	C₂×C₄	1	4	yes	—
45	C₂×C₄²×C₁₃	C₂×C₄	1	4	yes	—
46	C₂×C₄²×C₁₃	C₂×C₄	1	4	yes	—
47	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
48	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
49	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
50	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
51	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
52	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
53	C₂×#6099	—	2	4	no	—
54	C₂×#6099	—	2	4	no	—
55	C₂×#6099	C₂×C₄	1	8	yes	—
56	C₂²×#1055	—	2	4	no	—
57	C₂²×#1055	—	2	4	no	—
58	C₂²×#1055	C₂×C₄	1	8	yes	—
59	C₂²×#1055	C₂³	1	2	yes	—
60	C₂²×#1055	C₂³	1	2	yes	—
61	C₂²×#1055	C₂³	1	4	yes	—
62	C₁₃×#95	C₂×C₄	1	4	yes	—
63	C₁₃×#95	C₂×C₄	1	4	yes	—
64	C₄⋊#1055	C₂×C₄	1	4	yes	—
65	C₄⋊#1055	C₂×C₄	1	4	yes	—
66	C₄⋊#1055	C₂×C₄	1	8	yes	—
67	C₄⋊#1055	C₂×C₄	1	8	yes	—
68	C₄⋊#1055	C₂×C₄	1	8	yes	—
69	#88043	—	2	8	no	—
70	C₄×#1055	—	2	8	no	—
71	#20431	—	13	1	no	maximal, Sylow
72	C₂⁴×C₁₃	C₂²×C₄	1	1	yes	characteristic
73	C₂²×C₄×C₁₃	—	2	4	no	—
74	C₂²×C₄×C₁₃	—	4	2	no	—
75	C₂²×C₄×C₁₃	C₄²	1	4	yes	—
76	C₂²×C₄×C₁₃	C₄²	1	4	yes	—
77	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
78	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
79	C₂²×C₄×C₁₃	C₂²×C₄	1	4	yes	—
80	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
81	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
82	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
83	C₂²×C₄×C₁₃	C₂²×C₄	1	4	yes	—
84	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
85	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
86	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
87	C₂²×C₄×C₁₃	C₂×Q₈	1	2	yes	—
88	C₂²×C₄×C₁₃	#41	1	2	yes	—
89	C₂²×C₄×C₁₃	#41	1	2	yes	—
90	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
91	C₁₃×C₄⋊C₄	—	2	4	no	—
92	C₁₃×C₄⋊C₄	C₄⋊C₄	1	8	yes	—
93	C₁₃×C₂²⋊C₄	—	2	4	no	—
94	C₁₃×C₂²⋊C₄	C₄⋊C₄	1	8	yes	—
95	C₄²×C₁₃	—	2	8	no	—
96	C₄²×C₁₃	—	2	2	no	—
97	C₄²×C₁₃	—	2	2	no	—
98	C₄²×C₁₃	—	4	4	no	—
99	C₄²×C₁₃	C₄²	1	4	yes	—
100	C₄²×C₁₃	C₄²	1	4	yes	—
101	C₄²×C₁₃	C₂²×C₄	1	2	yes	—
102	C₄²×C₁₃	C₂²×C₄	1	2	yes	—
103	C₄²×C₁₃	C₂²×C₄	1	2	yes	—
104	C₄²×C₁₃	C₂²×C₄	1	2	yes	—
105	C₄²×C₁₃	C₂×D₄	1	4	yes	—
106	C₄²×C₁₃	C₂×Q₈	1	4	yes	—
107	#6099	—	2	16	no	—
108	C₂×#1055	—	2	16	no	—
109	C₂×#1055	—	2	2	no	—
110	C₂×#1055	—	2	2	no	—
111	C₂×#1055	—	2	4	no	—
112	C₂×#1055	—	2	2	no	—
113	C₂×#1055	—	2	2	no	—
114	C₂×#1055	—	2	4	no	—
115	C₂×#1055	C₂²×C₄	1	4	yes	—
116	C₂×#1055	C₂²×C₄	1	4	yes	—
117	C₂×#1055	C₂²×C₄	1	8	yes	—
118	C₂×#423	—	13	1	no	—
119	C₂²×C₄⋊C₈	—	13	1	no	—
120	C₂×#405	—	13	2	no	—
121	C₄×#117	D₁₃	1	1	yes	characteristic
122	#1768	—	13	4	no	—
123	#1767	—	13	2	no	—
124	C₄×C₄⋊C₈	—	13	2	no	—
125	#1729	—	13	2	no	—
126	C₂³×C₁₃	—	2	2	no	—
127	C₂³×C₁₃	—	2	2	no	—
128	C₂³×C₁₃	C₂×C₄²	1	2	yes	—
129	C₂³×C₁₃	C₂×C₄⋊C₄	1	2	yes	—
130	C₂³×C₁₃	#117	1	2	yes	—
131	C₂³×C₁₃	C₂³×C₄	1	1	yes	characteristic
132	C₂×C₄×C₁₃	—	2	4	no	—
133	C₂×C₄×C₁₃	—	2	2	no	—
134	C₂×C₄×C₁₃	—	2	2	no	—
135	C₂×C₄×C₁₃	—	2	4	no	—
136	C₂×C₄×C₁₃	—	2	2	no	—
137	C₂×C₄×C₁₃	—	2	8	no	—
138	C₂×C₄×C₁₃	—	2	4	no	—
139	C₂×C₄×C₁₃	—	2	4	no	—
140	C₂×C₄×C₁₃	—	2	4	no	—
141	C₂×C₄×C₁₃	—	4	4	no	—
142	C₂×C₄×C₁₃	C₂×C₄²	1	2	yes	—
143	C₂×C₄×C₁₃	C₂×C₄²	1	2	yes	—
144	C₂×C₄×C₁₃	C₂×C₄²	1	2	yes	—
145	C₂×C₄×C₁₃	C₂×C₄²	1	2	yes	—
146	C₂×C₄×C₁₃	C₂×C₄²	1	2	yes	—
147	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	8	yes	—
148	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	2	yes	—
149	C₂×C₄×C₁₃	#117	1	2	yes	—
150	C₂×C₄×C₁₃	C₄×D₄	1	4	yes	—
151	C₂×C₄×C₁₃	C₄×D₄	1	4	yes	—
152	C₂×C₄×C₁₃	C₄×Q₈	1	4	yes	—
153	C₂×C₄×C₁₃	C₄×Q₈	1	4	yes	—
154	C₂×C₄×C₁₃	#131	1	4	yes	—
155	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
156	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
157	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
158	C₂×C₄×C₁₃	C₂²×Q₈	1	1	yes	characteristic
159	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
160	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
161	#1055	—	2	4	no	—
162	#1055	—	2	4	no	—
163	#1055	—	2	8	no	—
164	C₂²×M₁₆	—	13	2	no	—
165	C₂³×C₈	—	13	2	no	—
166	C₂×#117	C₂×D₁₃	1	1	yes	characteristic
167	C₂×#117	C₂×D₁₃	1	1	yes	characteristic
168	C₂²×C₄²	C₂×D₁₃	1	1	yes	characteristic
169	#423	—	13	8	no	—
170	C₂×C₄⋊C₈	—	13	8	no	—
171	C₂×C₄⋊C₈	—	13	1	no	—
172	C₂×C₄⋊C₈	—	13	1	no	—
173	C₂×C₄⋊C₈	—	13	2	no	—
174	C₂×C₄⋊C₈	—	13	2	no	—
175	C₂×C₄⋊C₈	—	13	2	no	—
176	#405	—	26	8	no	—
177	C₂×#97	—	13	4	no	—
178	C₂×C₄×C₈	—	13	4	no	—
179	C₄×C₄⋊C₄	Dic₁₃	1	2	yes	—
180	C₄×C₄⋊C₄	Dic₁₃	1	2	yes	—
181	C₄×C₂²⋊C₄	Dic₁₃	1	2	yes	—
182	C₄×C₂²⋊C₄	Dic₁₃	1	2	yes	—
183	#376	C₂×D₁₃	1	2	yes	—
184	C₄³	C₂×D₁₃	1	2	yes	—
185	#336	—	13	4	no	—
186	#336	—	13	4	no	—
187	C₂²×C₁₃	—	2	2	no	—
188	C₂²×C₁₃	—	2	2	no	—
189	C₂²×C₁₃	—	2	4	no	—
190	C₂²×C₁₃	—	2	4	no	—
191	C₂²×C₁₃	C₄×C₄⋊C₄	1	4	yes	—
192	C₂²×C₁₃	C₂²×C₄²	1	1	yes	characteristic
193	C₂²×C₁₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
194	C₂²×C₁₃	C₂×#117	1	1	yes	characteristic
195	C₂²×C₁₃	C₂×#131	1	2	yes	—
196	C₂²×C₁₃	#568	1	2	yes	—
197	C₄×C₁₃	—	2	2	no	—
198	C₄×C₁₃	—	2	2	no	—
199	C₄×C₁₃	—	2	2	no	—
200	C₄×C₁₃	—	2	8	no	—
201	C₄×C₁₃	—	4	4	no	—
202	C₄×C₁₃	C₄×C₄⋊C₄	1	4	yes	—
203	C₄×C₁₃	#405	1	4	yes	complemented
204	C₄×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
205	C₄×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
206	C₄×C₁₃	C₂×C₄×Q₈	1	1	yes	characteristic
207	C₄×C₁₃	C₂×C₄×Q₈	1	1	yes	characteristic
208	C₂³×C₄	C₂×Dic₁₃	1	1	yes	characteristic
209	C₂³×C₄	C₂×Dic₁₃	1	1	yes	characteristic
210	C₂³×C₄	C₂²×D₁₃	1	1	yes	characteristic
211	C₂×M₁₆	—	13	8	no	—
212	C₂×M₁₆	—	26	4	no	—
213	C₂×M₁₆	—	26	4	no	—
214	C₂²×C₈	—	13	8	no	—
215	C₂²×C₈	—	13	2	no	—
216	C₂²×C₈	—	13	2	no	—
217	C₂²×C₈	—	13	4	no	—
218	C₂²×C₈	—	26	4	no	—
219	C₂²×C₈	—	26	4	no	—
220	#117	—	2	2	no	—
221	#117	—	2	2	no	—
222	#117	Dic₂₆	1	4	yes	—
223	#117	D₅₂	1	4	yes	—
224	C₂×C₄⋊C₄	C₂×Dic₁₃	1	2	yes	—
225	C₂×C₄⋊C₄	C₂×Dic₁₃	1	2	yes	—
226	C₂×C₂²⋊C₄	C₂×Dic₁₃	1	2	yes	—
227	C₂×C₂²⋊C₄	C₂×Dic₁₃	1	2	yes	—
228	C₂×C₄²	C₄×D₁₃	1	4	yes	—
229	C₂×C₄²	C₄×D₁₃	1	4	yes	—
230	C₂×C₄²	C₂×Dic₁₃	1	4	yes	—
231	C₂×C₄²	C₂×Dic₁₃	1	4	yes	—
232	C₂×C₄²	C₂×Dic₁₃	1	1	yes	characteristic
233	C₂×C₄²	C₂×Dic₁₃	1	1	yes	characteristic
234	C₂×C₄²	C₂²×D₁₃	1	2	yes	—
235	C₂×C₄²	C₂²×D₁₃	1	2	yes	—
236	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
237	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
238	C₄⋊C₈	—	13	4	no	—
239	C₄⋊C₈	—	13	4	no	—
240	C₄⋊C₈	—	13	8	no	—
241	C₄⋊C₈	—	13	8	no	—
242	C₄⋊C₈	—	13	8	no	—
243	#97	—	26	8	no	—
244	C₄×C₈	—	26	8	no	—
245	#95	C₂×Dic₁₃	1	4	yes	—
246	#95	C₂×Dic₁₃	1	4	yes	—
247	C₂×C₁₃	—	2	4	no	—
248	C₂×C₁₃	C₂×C₄×C₄⋊C₄	1	1	yes	characteristic
249	C₂×C₁₃	C₂×#405	1	1	yes	characteristic
250	C₂×C₁₃	#2873	1	1	yes	characteristic
251	C₂×C₁₃	#2906	1	2	yes	—
252	C₂×C₁₃	#2925	1	2	yes	—
253	C₂⁴	C₂²×Dic₁₃	1	1	yes	characteristic
254	C₂²×C₄	—	2	4	no	—
255	C₂²×C₄	—	4	2	no	—
256	C₂²×C₄	C₄×Dic₁₃	1	4	yes	—
257	C₂²×C₄	C₄×Dic₁₃	1	4	yes	—
258	C₂²×C₄	C₂×Dic₂₆	1	2	yes	—
259	C₂²×C₄	C₂×C₄×D₁₃	1	2	yes	—
260	C₂²×C₄	C₂×C₄×D₁₃	1	2	yes	—
261	C₂²×C₄	C₂×D₅₂	1	2	yes	—
262	C₂²×C₄	#6127	1	2	yes	—
263	C₂²×C₄	#6127	1	2	yes	—
264	C₂²×C₄	C₂²×Dic₁₃	1	4	yes	—
265	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
266	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
267	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
268	C₂²×C₄	C₂²×Dic₁₃	1	4	yes	—
269	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
270	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
271	C₂²×C₄	C₂³×D₁₃	1	1	yes	characteristic
272	M₁₆	—	26	16	no	—
273	C₂×C₈	—	13	4	no	—
274	C₂×C₈	—	13	4	no	—
275	C₂×C₈	—	13	8	no	—
276	C₂×C₈	—	26	16	no	—
277	C₂×C₈	—	26	2	no	—
278	C₂×C₈	—	26	4	no	—
279	C₂×C₈	—	26	2	no	—
280	C₂×C₈	—	26	2	no	—
281	C₂×C₈	—	26	2	no	—
282	C₂×C₈	—	26	4	no	—
283	C₄⋊C₄	—	2	4	no	—
284	C₄⋊C₄	C₄⋊Dic₁₃	1	8	yes	—
285	C₂²⋊C₄	—	2	4	no	—
286	C₂²⋊C₄	C₄⋊Dic₁₃	1	8	yes	—
287	C₄²	—	2	8	no	—
288	C₄²	—	2	2	no	—
289	C₄²	—	2	2	no	—
290	C₄²	—	4	4	no	—
291	C₄²	C₄×Dic₁₃	1	4	yes	—
292	C₄²	C₄×Dic₁₃	1	4	yes	—
293	C₄²	C₂×Dic₂₆	1	4	yes	—
294	C₄²	C₂×C₄×D₁₃	1	2	yes	—
295	C₄²	C₂×C₄×D₁₃	1	2	yes	—
296	C₄²	C₂×C₄×D₁₃	1	2	yes	—
297	C₄²	C₂×C₄×D₁₃	1	2	yes	—
298	C₄²	C₂×D₅₂	1	4	yes	—
299	C₁₃	#20431	1	1	yes	characteristic, complemented, Sylow
300	C₂³	—	2	2	no	—
301	C₂³	—	2	2	no	—
302	C₂³	C₂×C₄×Dic₁₃	1	2	yes	—
303	C₂³	C₂×C₄⋊Dic₁₃	1	2	yes	—
304	C₂³	#88180	1	2	yes	—
305	C₂³	C₂³×Dic₁₃	1	1	yes	characteristic
306	C₂×C₄	—	2	4	no	—
307	C₂×C₄	—	2	2	no	—
308	C₂×C₄	—	2	2	no	—
309	C₂×C₄	—	2	4	no	—
310	C₂×C₄	—	2	2	no	—
311	C₂×C₄	—	2	8	no	—
312	C₂×C₄	—	2	4	no	—
313	C₂×C₄	—	2	4	no	—
314	C₂×C₄	—	2	4	no	—
315	C₂×C₄	—	4	4	no	—
316	C₂×C₄	C₄×Dic₂₆	1	4	yes	—
317	C₂×C₄	C₄×Dic₂₆	1	4	yes	—
318	C₂×C₄	C₄×D₅₂	1	4	yes	—
319	C₂×C₄	C₄×D₅₂	1	4	yes	—
320	C₂×C₄	C₂×C₄×Dic₁₃	1	2	yes	—
321	C₂×C₄	C₂×C₄×Dic₁₃	1	2	yes	—
322	C₂×C₄	C₂×C₄×Dic₁₃	1	2	yes	—
323	C₂×C₄	C₂×C₄×Dic₁₃	1	2	yes	—
324	C₂×C₄	C₂×C₄×Dic₁₃	1	2	yes	—
325	C₂×C₄	C₂×C₄⋊Dic₁₃	1	8	yes	—
326	C₂×C₄	C₂×C₄⋊Dic₁₃	1	2	yes	—
327	C₂×C₄	#88180	1	2	yes	—
328	C₂×C₄	#88202	1	4	yes	—
329	C₂×C₄	C₂²×Dic₂₆	1	1	yes	characteristic
330	C₂×C₄	C₂²×C₄×D₁₃	1	1	yes	characteristic
331	C₂×C₄	C₂²×C₄×D₁₃	1	1	yes	characteristic
332	C₂×C₄	C₂²×D₅₂	1	1	yes	characteristic
333	C₂×C₄	C₂×#6127	1	1	yes	characteristic
334	C₂×C₄	C₂×#6127	1	1	yes	characteristic
335	C₈	—	26	4	no	—
336	C₈	—	26	4	no	—
337	C₈	—	26	8	no	—
338	C₂²	—	2	4	no	—
339	C₂²	—	2	4	no	—
340	C₂²	—	2	2	no	—
341	C₂²	—	2	2	no	—
342	C₂²	C₄×C₄⋊Dic₁₃	1	4	yes	—
343	C₂²	C₂²×C₄×Dic₁₃	1	1	yes	characteristic
344	C₂²	C₂²×C₄⋊Dic₁₃	1	1	yes	characteristic
345	C₂²	C₂×#88180	1	1	yes	characteristic
346	C₂²	C₂×#88202	1	2	yes	—
347	C₂²	#11719524	1	2	yes	—
348	C₄	—	2	8	no	—
349	C₄	—	2	2	no	—
350	C₄	—	2	2	no	—
351	C₄	—	2	2	no	—
352	C₄	—	4	4	no	—
353	C₄	C₄×C₄⋊Dic₁₃	1	4	yes	—
354	C₄	#11718658	1	4	yes	complemented
355	C₄	C₂×C₄×Dic₂₆	1	1	yes	characteristic
356	C₄	C₂×C₄×Dic₂₆	1	1	yes	characteristic
357	C₄	C₂×C₄×D₅₂	1	1	yes	characteristic
358	C₄	C₂×C₄×D₅₂	1	1	yes	characteristic
359	C₂	—	2	4	no	—
360	C₂	C₂×C₄×C₄⋊Dic₁₃	1	1	yes	characteristic
361	C₂	C₂×#11718658	1	1	yes	characteristic
362	C₂	#13123255	1	1	yes	characteristic
363	C₂	#13123404	1	2	yes	—
364	C₂	#13123502	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂³×D₁₃
commutator	C₂²×C₁₃	C₂²×C₄²
Fitting	C₄×C₁₃×#117	C₂
socle	C₂³×C₁₃	C₂³×C₄
prime radical	C₂⁴×C₁₃	C₂²×C₄
cosocle	C₂²×C₄×C₁₃	C₂⁴
hypercenter	C₄×#117	D₁₃
hypocenter	C₁₃	#20431
LCS	G ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂²×C₄ ◁ C₄×#117

Complements

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

N	H ≅ G/N	type
4. #13114693	C₂	semidirect
5. #13114689	C₂	semidirect
6. C₄×C₄⋊#1055	C₂	semidirect
21. #11718585	C₄	semidirect
22. C₂×C₄⋊#1055	C₄	semidirect
203. C₄×C₁₃	#405	semidirect
299. C₁₃	#20431	semidirect
354. C₄	#11718658	semidirect

Maximal subgroups

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

subgroup	index
C₂×#11718585	2
C₂²×C₄⋊#1055	2
C₂×#11718658	2
#13114693	2
#13114689	2
C₄×C₄⋊#1055	2
#13114533	2
C₄×C₁₃×#117	2
#20431	13