Subgroups — #15832142

Order 3328.

702 conjugacy classes of subgroups.

The subgroup lattice has 418 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13123792	C₂	1	1	yes	maximal, characteristic
2	#13123405	C₂	1	1	yes	maximal, characteristic
3	#13123401	C₂	1	1	yes	maximal, characteristic
4	#13113607	C₂	1	1	yes	maximal, characteristic, complemented
5	#13113605	C₂	1	2	yes	maximal, complemented
6	#13113605	C₂	1	2	yes	maximal, complemented
7	#13113591	C₂	1	1	yes	maximal, characteristic, complemented
8	#13113590	C₂	1	2	yes	maximal, complemented
9	C₂×#11718072	C₂	1	1	yes	maximal, characteristic, complemented
10	D₁₃×#334	C₂	1	2	yes	maximal, complemented
11	C₁₃×#1570	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#88161	—	2	1	no	—
13	C₂×#88155	—	2	1	no	—
14	C₄×#6127	C₂²	1	1	yes	characteristic
15	C₁₃×#431	C₂²	1	1	yes	characteristic
16	C₁₃×#423	C₂²	1	1	yes	characteristic
17	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
18	#11718780	—	2	1	no	—
19	#11718763	—	2	1	no	—
20	#11718585	C₂²	1	1	yes	characteristic
21	C₂×C₄⋊#1055	C₂²	1	1	yes	characteristic
22	C₂×C₄×#1055	C₂²	1	1	yes	characteristic
23	#11718500	—	2	2	no	—
24	#11718500	—	2	2	no	—
25	#11718498	C₂²	1	2	yes	—
26	#11718498	C₂²	1	2	yes	—
27	#11718495	C₄	1	1	yes	characteristic
28	#11718495	C₄	1	1	yes	characteristic
29	D₁₃×C₄⋊C₈	C₂²	1	2	yes	—
30	D₁₃×C₄⋊C₈	C₂²	1	2	yes	—
31	#11718491	C₄	1	1	yes	characteristic
32	#11718491	C₄	1	1	yes	characteristic
33	#11718386	C₄	1	2	yes	—
34	#11718386	C₄	1	2	yes	—
35	#11718346	C₂²	1	2	yes	—
36	C₄×C₈×D₁₃	C₂²	1	2	yes	—
37	C₁₃×#334	C₂²	1	2	yes	—
38	C₁₃×#334	C₂²	1	2	yes	—
39	#11718072	C₂²	1	1	yes	characteristic
40	#11718072	C₂²	1	1	yes	characteristic
41	#11718072	C₂²	1	2	yes	—
42	#11718072	C₂²	1	1	yes	characteristic
43	#11718072	C₂²	1	2	yes	—
44	#11718072	C₂²	1	1	yes	characteristic
45	#11718049	C₂²	1	2	yes	—
46	#11718049	C₂²	1	2	yes	—
47	C₂×#6127	D₄	1	1	yes	characteristic
48	C₂×C₁₃×M₁₆	—	2	1	no	—
49	C₂²×C₈×C₁₃	—	2	1	no	—
50	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
51	C₄×C₂²⋊D₁₃	C₂×C₄	1	2	yes	—
52	C₄×C₂²⋊D₁₃	Q₈	1	2	yes	—
53	#88180	D₄	1	1	yes	characteristic
54	C₂×#6099	—	2	1	no	—
55	C₂²×#1055	—	2	1	no	—
56	C₂²×#1055	C₂×C₄	1	1	yes	characteristic
57	C₂²×#1055	C₂×C₄	1	1	yes	characteristic
58	#88161	—	4	4	no	—
59	#88155	—	4	4	no	—
60	C₂×#6094	—	2	2	no	—
61	C₂×#6094	—	2	2	no	—
62	C₂×C₈×D₁₃	—	2	2	no	—
63	C₂×C₈×D₁₃	—	2	2	no	—
64	C₂×C₈×D₁₃	C₂×C₄	1	2	yes	—
65	C₂×C₈×D₁₃	C₂×C₄	1	2	yes	—
66	C₄×D₅₂	C₂×C₄	1	1	yes	characteristic
67	C₄×D₅₂	Q₈	1	1	yes	characteristic
68	#88126	D₄	1	2	yes	—
69	C₄²×D₁₃	C₂³	1	2	yes	—
70	C₄×Dic₂₆	C₂×C₄	1	1	yes	characteristic
71	C₄×Dic₂₆	Q₈	1	1	yes	characteristic
72	C₁₃×C₄⋊C₈	—	2	1	no	—
73	C₁₃×C₄⋊C₈	—	2	1	no	—
74	C₁₃×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
75	C₁₃×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
76	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
77	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
78	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
79	C₁₃×C₂²⋊C₈	C₂×C₄	1	2	yes	—
80	C₄×C₈×C₁₃	C₂³	1	2	yes	—
81	#88060	C₂×C₄	1	2	yes	—
82	#88060	C₂×C₄	1	2	yes	—
83	#88054	—	2	2	no	—
84	#88054	—	2	2	no	—
85	#88054	—	2	2	no	—
86	#88054	—	2	2	no	—
87	#88054	C₂×C₄	1	2	yes	—
88	#88054	C₂×C₄	1	2	yes	—
89	C₈×Dic₁₃	C₂×C₄	1	2	yes	—
90	C₈×Dic₁₃	C₂×C₄	1	2	yes	—
91	C₄⋊#1055	—	2	1	no	—
92	C₄⋊#1055	—	2	1	no	—
93	C₄⋊#1055	C₂³	1	1	yes	characteristic
94	C₄⋊#1055	C₂³	1	2	yes	—
95	C₄⋊#1055	C₂³	1	1	yes	characteristic
96	C₄×#1055	C₂×C₄	1	1	yes	characteristic
97	C₄×#1055	C₂×C₄	1	1	yes	characteristic
98	C₄×#1055	C₂³	1	1	yes	characteristic
99	C₄×#1055	C₂³	1	1	yes	characteristic
100	#17826	—	13	1	no	maximal, Sylow
101	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
102	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
103	C₂²×C₄×C₁₃	C₂×Q₈	1	1	yes	characteristic
104	C₂×C₂²⋊D₁₃	C₄⋊C₄	1	2	yes	—
105	#6127	SD₁₆	1	4	yes	—
106	#6127	SD₁₆	1	4	yes	—
107	C₂×D₅₂	C₄⋊C₄	1	1	yes	characteristic
108	C₂×C₄×D₁₃	C₂²×C₄	1	2	yes	—
109	C₂×C₄×D₁₃	C₂×D₄	1	2	yes	—
110	C₂×C₄×D₁₃	C₂×Q₈	1	2	yes	—
111	C₂×Dic₂₆	C₄⋊C₄	1	1	yes	characteristic
112	C₁₃×M₁₆	—	4	2	no	—
113	C₂×C₈×C₁₃	—	2	1	no	—
114	C₂×C₈×C₁₃	—	2	2	no	—
115	C₂×C₈×C₁₃	—	2	1	no	—
116	C₂×C₈×C₁₃	—	4	2	no	—
117	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
118	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
119	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
120	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
121	C₄²×C₁₃	C₂×Q₈	1	1	yes	characteristic
122	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
123	C₂²⋊Dic₁₃	C₄⋊C₄	1	2	yes	—
124	#6103	C₄⋊C₄	1	2	yes	—
125	#6103	C₄⋊C₄	1	2	yes	—
126	C₄⋊Dic₁₃	C₄⋊C₄	1	1	yes	characteristic
127	C₄⋊Dic₁₃	C₄⋊C₄	1	1	yes	characteristic
128	#6101	C₄⋊C₄	1	2	yes	—
129	#6101	C₄⋊C₄	1	2	yes	—
130	C₄×Dic₁₃	C₂²×C₄	1	2	yes	—
131	C₄×Dic₁₃	C₂×D₄	1	2	yes	—
132	C₄×Dic₁₃	C₂×Q₈	1	2	yes	—
133	#6099	—	4	2	no	—
134	C₂×#1055	—	2	2	no	—
135	C₂×#1055	—	2	1	no	—
136	C₂×#1055	—	2	2	no	—
137	C₂×#1055	—	2	1	no	—
138	C₂×#1055	—	4	1	no	—
139	C₂×#1055	—	4	2	no	—
140	C₂×#1055	C₂²×C₄	1	1	yes	characteristic
141	C₂×#1055	C₂²×C₄	1	1	yes	characteristic
142	C₂×#1055	C₂²×C₄	1	1	yes	characteristic
143	C₂×#1055	C₂²×C₄	1	1	yes	characteristic
144	#6094	—	4	4	no	—
145	#6094	—	4	4	no	—
146	C₈×D₁₃	—	2	4	no	—
147	C₈×D₁₃	—	4	2	no	—
148	C₈×D₁₃	—	4	4	no	—
149	C₈×D₁₃	—	4	4	no	—
150	C₈×#41	—	13	1	no	—
151	#2906	—	13	1	no	—
152	#2906	—	13	1	no	—
153	#1570	—	13	1	no	—
154	#1570	—	13	2	no	—
155	#1570	—	13	2	no	—
156	#1570	D₁₃	1	1	yes	characteristic, complemented
157	#1566	—	13	1	no	—
158	#1566	—	13	2	no	—
159	C₂×#334	—	13	1	no	—
160	C₂×#334	—	13	2	no	—
161	C₂³×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
162	C₂²×D₁₃	C₂×C₄⋊C₄	1	2	yes	—
163	C₂×C₄×C₁₃	—	2	1	no	—
164	C₂×C₄×C₁₃	—	2	1	no	—
165	C₂×C₄×C₁₃	—	4	1	no	—
166	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
167	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
168	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
169	C₂×C₄×C₁₃	C₂×SD₁₆	1	2	yes	—
170	C₂×C₄×C₁₃	C₂×SD₁₆	1	2	yes	—
171	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
172	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
173	C₂×C₄×C₁₃	C₂²×Q₈	1	1	yes	characteristic
174	C₂²⋊D₁₃	#106	1	8	yes	—
175	C₂×Dic₁₃	C₂×C₄⋊C₄	1	2	yes	—
176	C₂×Dic₁₃	C₂×C₄⋊C₄	1	2	yes	—
177	C₂×Dic₁₃	C₂×C₄⋊C₄	1	2	yes	—
178	D₅₂	#106	1	4	yes	—
179	C₄×D₁₃	—	2	2	no	—
180	C₄×D₁₃	—	2	2	no	—
181	C₄×D₁₃	—	4	2	no	—
182	C₄×D₁₃	C₂×SD₁₆	1	4	yes	—
183	C₄×D₁₃	C₂×SD₁₆	1	4	yes	—
184	Dic₂₆	#106	1	4	yes	—
185	C₈×C₁₃	—	2	2	no	—
186	C₈×C₁₃	—	2	2	no	—
187	C₈×C₁₃	—	4	1	no	—
188	C₈×C₁₃	—	4	2	no	—
189	C₈×C₁₃	—	4	1	no	—
190	#1055	—	2	1	no	—
191	#1055	—	2	1	no	—
192	#1055	—	2	1	no	—
193	#1055	—	4	1	no	—
194	#1055	—	4	2	no	—
195	#1055	—	4	1	no	—
196	#1055	#131	1	2	yes	complemented
197	C₂×#131	—	26	1	no	—
198	C₂×#131	—	26	1	no	—
199	C₄×#41	—	13	1	no	—
200	C₈×Q₈	—	13	1	no	—
201	C₈×Q₈	—	13	1	no	—
202	C₈×D₄	—	13	1	no	—
203	C₈×D₄	—	13	1	no	—
204	C₈×D₄	—	13	2	no	—
205	C₈×D₄	—	13	2	no	—
206	#431	—	13	2	no	—
207	#431	C₂×D₁₃	1	1	yes	characteristic
208	#424	—	26	2	no	—
209	#424	—	26	2	no	—
210	#424	—	26	1	no	—
211	#424	—	26	1	no	—
212	#423	—	13	1	no	—
213	#423	—	13	2	no	—
214	#423	—	13	2	no	—
215	#423	C₂×D₁₃	1	1	yes	characteristic
216	C₂×C₄⋊C₈	—	13	1	no	—
217	C₂×C₄⋊C₈	—	13	2	no	—
218	C₂×C₄⋊C₈	—	13	2	no	—
219	C₂×C₄⋊C₈	C₂×D₁₃	1	1	yes	characteristic
220	C₂×C₄×C₈	—	13	1	no	—
221	C₂×C₄×C₈	—	13	2	no	—
222	#334	—	13	1	no	—
223	#334	—	13	2	no	—
224	#334	—	13	1	no	—
225	#334	—	13	1	no	—
226	#334	—	13	1	no	—
227	#334	—	13	2	no	—
228	#334	—	13	2	no	—
229	#334	—	13	2	no	—
230	#334	C₂×D₁₃	1	2	yes	—
231	#334	C₂×D₁₃	1	2	yes	—
232	C₂²×C₁₃	—	2	1	no	—
233	C₂²×C₁₃	—	2	1	no	—
234	C₂²×C₁₃	C₂×#106	1	2	yes	—
235	C₂²×C₁₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
236	C₂×D₁₃	—	2	2	no	—
237	C₂×D₁₃	—	2	2	no	—
238	C₂×D₁₃	C₂×#106	1	4	yes	—
239	C₄×C₁₃	—	2	1	no	—
240	C₄×C₁₃	—	2	1	no	—
241	C₄×C₁₃	—	2	1	no	—
242	C₄×C₁₃	C₂×#106	1	2	yes	—
243	C₄×C₁₃	C₂×#131	1	1	yes	characteristic
244	C₄×C₁₃	#568	1	1	yes	characteristic
245	C₄×C₁₃	C₂²×SD₁₆	1	1	yes	characteristic
246	C₄×C₁₃	C₂²×SD₁₆	1	1	yes	characteristic
247	Dic₁₃	—	2	2	no	—
248	Dic₁₃	—	2	2	no	—
249	Dic₁₃	C₂×#106	1	4	yes	—
250	C₂×#41	—	13	1	no	—
251	#131	—	52	4	no	—
252	#131	—	52	4	no	—
253	C₂×M₁₆	—	2	1	no	—
254	C₂×M₁₆	—	26	2	no	—
255	C₂×M₁₆	—	26	2	no	—
256	C₂×M₁₆	—	26	1	no	—
257	C₂²×C₈	—	2	1	no	—
258	C₂²×C₈	—	13	1	no	—
259	C₂²×C₈	—	13	1	no	—
260	C₂²×C₈	—	13	2	no	—
261	C₂²×C₈	—	13	2	no	—
262	C₂²×C₈	—	26	2	no	—
263	C₂²×C₈	—	26	2	no	—
264	C₂²×C₈	—	26	1	no	—
265	C₄×Q₈	—	13	1	no	—
266	C₄×Q₈	—	13	1	no	—
267	C₄×D₄	—	13	2	no	—
268	C₄×D₄	—	13	2	no	—
269	C₄×D₄	—	13	1	no	—
270	C₄×D₄	—	13	1	no	—
271	#117	—	13	1	no	—
272	#117	—	13	2	no	—
273	C₂×C₄²	—	13	2	no	—
274	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
275	C₄⋊C₈	—	2	1	no	—
276	C₄⋊C₈	—	2	1	no	—
277	C₄⋊C₈	—	13	2	no	—
278	C₄⋊C₈	—	13	2	no	—
279	C₄⋊C₈	—	13	1	no	—
280	C₄⋊C₈	—	13	1	no	—
281	C₄⋊C₈	—	13	2	no	—
282	C₄⋊C₈	—	26	2	no	—
283	C₄⋊C₈	—	26	2	no	—
284	C₄⋊C₈	—	26	2	no	—
285	C₄⋊C₈	—	26	2	no	—
286	C₄⋊C₈	—	26	1	no	—
287	C₄⋊C₈	—	26	1	no	—
288	C₄⋊C₈	C₄×D₁₃	1	1	yes	characteristic
289	C₄⋊C₈	C₄×D₁₃	1	1	yes	characteristic
290	C₄⋊C₈	C₂²×D₁₃	1	1	yes	characteristic
291	C₄⋊C₈	C₂²×D₁₃	1	2	yes	—
292	C₄⋊C₈	C₂²×D₁₃	1	1	yes	characteristic
293	C₂²⋊C₈	—	13	2	no	—
294	C₂²⋊C₈	—	13	2	no	—
295	C₂²⋊C₈	C₄×D₁₃	1	2	yes	—
296	C₄×C₈	—	13	2	no	—
297	C₄×C₈	—	13	2	no	—
298	C₄×C₈	—	13	1	no	—
299	C₄×C₈	—	13	1	no	—
300	C₄×C₈	—	13	1	no	—
301	C₄×C₈	—	13	1	no	—
302	C₄×C₈	C₂²×D₁₃	1	2	yes	—
303	C₂×C₁₃	—	2	2	no	—
304	C₂×C₁₃	#2906	1	1	yes	characteristic
305	C₂×C₁₃	C₂²×#106	1	1	yes	characteristic
306	C₂×C₁₃	#2916	1	1	yes	characteristic
307	D₁₃	—	2	4	no	—
308	#41	—	13	4	no	—
309	#41	—	13	4	no	—
310	C₂×Q₈	—	13	1	no	—
311	C₂×D₄	—	13	2	no	—
312	C₂×D₄	—	13	1	no	—
313	C₂²×C₄	—	13	2	no	—
314	C₂²×C₄	—	13	2	no	—
315	C₂²×C₄	—	13	2	no	—
316	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
317	C₂²×C₄	D₄×D₁₃	1	1	yes	characteristic
318	C₂²×C₄	Q₈×D₁₃	1	1	yes	characteristic
319	M₁₆	—	4	2	no	—
320	M₁₆	—	52	4	no	—
321	M₁₆	—	52	4	no	—
322	M₁₆	—	52	2	no	—
323	C₂×C₈	—	2	1	no	—
324	C₂×C₈	—	2	1	no	—
325	C₂×C₈	—	2	2	no	—
326	C₂×C₈	—	4	2	no	—
327	C₂×C₈	—	13	1	no	—
328	C₂×C₈	—	13	1	no	—
329	C₂×C₈	—	13	1	no	—
330	C₂×C₈	—	13	1	no	—
331	C₂×C₈	—	26	4	no	—
332	C₂×C₈	—	26	2	no	—
333	C₂×C₈	—	26	1	no	—
334	C₂×C₈	—	26	2	no	—
335	C₂×C₈	—	26	1	no	—
336	C₂×C₈	—	52	2	no	—
337	C₂×C₈	—	52	4	no	—
338	C₂×C₈	—	52	4	no	—
339	C₂×C₈	—	52	1	no	—
340	C₂×C₈	—	52	2	no	—
341	C₂×C₈	C₂×C₄×D₁₃	1	2	yes	—
342	C₂×C₈	C₂×C₄×D₁₃	1	2	yes	—
343	C₄⋊C₄	—	13	2	no	—
344	C₄⋊C₄	—	13	2	no	—
345	C₄⋊C₄	—	13	1	no	—
346	C₄⋊C₄	—	13	1	no	—
347	C₂²⋊C₄	—	13	2	no	—
348	C₂²⋊C₄	—	13	2	no	—
349	C₂²⋊C₄	—	13	2	no	—
350	C₄²	—	13	2	no	—
351	C₄²	—	13	2	no	—
352	C₄²	—	13	2	no	—
353	C₄²	C₂×C₄×D₁₃	1	1	yes	characteristic
354	C₄²	D₄×D₁₃	1	1	yes	characteristic
355	C₄²	Q₈×D₁₃	1	1	yes	characteristic
356	C₄²	C₂³×D₁₃	1	1	yes	characteristic
357	C₁₃	#17826	1	1	yes	characteristic, complemented, Sylow
358	C₂³	—	13	2	no	—
359	C₂³	C₄⋊C₄×D₁₃	1	1	yes	characteristic
360	Q₈	—	13	4	no	—
361	D₄	—	13	8	no	—
362	D₄	—	13	4	no	—
363	C₂×C₄	—	2	1	no	—
364	C₂×C₄	—	2	1	no	—
365	C₂×C₄	—	4	1	no	—
366	C₂×C₄	—	13	2	no	—
367	C₂×C₄	—	13	4	no	—
368	C₂×C₄	—	13	4	no	—
369	C₂×C₄	—	13	2	no	—
370	C₂×C₄	—	13	2	no	—
371	C₂×C₄	—	26	2	no	—
372	C₂×C₄	—	26	2	no	—
373	C₂×C₄	—	52	2	no	—
374	C₂×C₄	C₄⋊C₄×D₁₃	1	1	yes	characteristic
375	C₂×C₄	C₄⋊C₄×D₁₃	1	1	yes	characteristic
376	C₂×C₄	C₄⋊C₄×D₁₃	1	1	yes	characteristic
377	C₂×C₄	SD₁₆×D₁₃	1	2	yes	—
378	C₂×C₄	SD₁₆×D₁₃	1	2	yes	—
379	C₂×C₄	C₂²×C₄×D₁₃	1	1	yes	characteristic
380	C₂×C₄	C₂×D₄×D₁₃	1	1	yes	characteristic
381	C₂×C₄	C₂×Q₈×D₁₃	1	1	yes	characteristic
382	C₈	—	2	2	no	—
383	C₈	—	2	2	no	—
384	C₈	—	4	1	no	—
385	C₈	—	4	1	no	—
386	C₈	—	4	2	no	—
387	C₈	—	13	2	no	—
388	C₈	—	26	1	no	—
389	C₈	—	26	1	no	—
390	C₈	—	26	1	no	—
391	C₈	—	52	1	no	—
392	C₈	—	52	2	no	—
393	C₈	—	52	1	no	—
394	C₂²	—	2	1	no	—
395	C₂²	—	2	1	no	—
396	C₂²	—	13	4	no	—
397	C₂²	—	26	2	no	—
398	C₂²	—	26	2	no	—
399	C₂²	D₁₃×#106	1	2	yes	—
400	C₂²	C₂×C₄⋊C₄×D₁₃	1	1	yes	characteristic
401	C₄	—	2	1	no	—
402	C₄	—	2	1	no	—
403	C₄	—	2	1	no	—
404	C₄	—	13	4	no	—
405	C₄	—	26	2	no	—
406	C₄	—	26	2	no	—
407	C₄	D₁₃×#106	1	2	yes	—
408	C₄	D₁₃×#131	1	1	yes	characteristic
409	C₄	#11719455	1	1	yes	characteristic
410	C₄	C₂×SD₁₆×D₁₃	1	1	yes	characteristic
411	C₄	C₂×SD₁₆×D₁₃	1	1	yes	characteristic
412	C₂	—	2	2	no	—
413	C₂	—	26	4	no	—
414	C₂	#13123403	1	1	yes	characteristic
415	C₂	C₂×D₁₃×#106	1	1	yes	characteristic
416	C₂	#13123446	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₁₃
commutator	C₂×C₄×C₁₃	C₂³×C₄
Frattini	C₄²	C₂³×D₁₃
Fitting	C₁₃×#1570	C₂
socle	C₂²×C₁₃	C₂²×C₄⋊C₄
prime radical	C₂×#6127	D₄
cosocle	C₄²×C₁₃	C₂⁴
hypercenter	#1570	D₁₃
hypocenter	C₁₃	#17826
LCS	G ▷ C₂×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1570

Complements

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

N	H ≅ G/N	type
4. #13113607	C₂	semidirect
5. #13113605	C₂	semidirect
6. #13113605	C₂	semidirect
7. #13113591	C₂	semidirect
8. #13113590	C₂	semidirect
9. C₂×#11718072	C₂	semidirect
10. D₁₃×#334	C₂	semidirect
11. C₁₃×#1570	C₂	semidirect
156. #1570	D₁₃	semidirect
196. #1055	#131	semidirect
357. C₁₃	#17826	semidirect

Maximal subgroups

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

subgroup	index
#13123792	2
#13123405	2
#13123401	2
#13113607	2
#13113605	2
#13113591	2
#13113590	2
C₂×#11718072	2
D₁₃×#334	2
C₁₃×#1570	2
#17826	13