Subgroups — #15860935

Order 3328.

1018 conjugacy classes of subgroups.

The subgroup lattice has 412 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11718554	C₂	1	1	yes	maximal, characteristic
2	#13123424	C₂	1	1	yes	maximal, characteristic
3	C₂×#11718350	C₂	1	1	yes	maximal, characteristic
4	D₁₃×#405	C₂	1	2	yes	maximal
5	#13114723	C₂	1	1	yes	maximal, characteristic, complemented
6	#13114722	C₂	1	1	yes	maximal, characteristic, complemented
7	#13114719	C₂	1	2	yes	maximal, complemented
8	#13114716	C₂	1	2	yes	maximal, complemented
9	#13114715	C₂	1	1	yes	maximal, characteristic, complemented
10	#13114544	C₂	1	2	yes	maximal
11	C₁₃×#1772	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×M₁₆×D₁₃	C₂²	1	2	yes	—
13	C₂²×#6094	C₂²	1	1	yes	characteristic
14	C₂²×C₈×D₁₃	C₂²	1	1	yes	characteristic
15	D₁₃×#117	C₂²	1	2	yes	—
16	C₂×#88126	C₂²	1	1	yes	characteristic
17	C₂×C₁₃×#108	C₂²	1	1	yes	characteristic
18	C₁₃×#427	C₂²	1	1	yes	characteristic
19	C₁₃×#405	C₂²	1	2	yes	—
20	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
21	C₂×#88062	C₂²	1	2	yes	—
22	#11718783	C₂²	1	2	yes	—
23	C₂×#88059	C₂²	1	1	yes	characteristic
24	#11718767	C₂²	1	1	yes	characteristic
25	#11718762	C₂²	1	2	yes	—
26	C₂×#88055	C₂²	1	1	yes	characteristic
27	C₂×C₈×Dic₁₃	C₂²	1	1	yes	characteristic
28	#11718659	C₂²	1	2	yes	—
29	#11718658	C₂²	1	2	yes	—
30	C₂×#88043	C₂²	1	1	yes	characteristic
31	#11718554	C₄	1	8	yes	complemented
32	#11718542	C₄	1	4	yes	complemented
33	#11718522	C₄	1	4	yes	complemented
34	#11718369	—	2	2	no	—
35	D₁₃×#97	—	2	2	no	—
36	#11718350	—	2	2	no	—
37	#11718350	C₄	1	8	yes	complemented
38	C₄×C₈×D₁₃	—	2	2	no	—
39	C₁₃×#339	C₂²	1	2	yes	—
40	#11718147	C₂²	1	2	yes	—
41	#11718124	C₂²	1	2	yes	—
42	#11718115	C₂²	1	2	yes	—
43	C₂²×C₄×D₁₃	C₂³	1	1	yes	characteristic
44	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
45	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
46	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
47	C₁₃×#117	C₂³	1	2	yes	—
48	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
49	C₂×#6103	—	2	1	no	—
50	#88180	C₂³	1	2	yes	—
51	C₂×#6101	—	2	1	no	—
52	C₂×C₄×Dic₁₃	C₂³	1	1	yes	characteristic
53	C₂×#6099	C₂³	1	2	yes	—
54	C₂²×#1055	C₂³	1	1	yes	characteristic
55	C₂²×#1055	C₂³	1	1	yes	characteristic
56	M₁₆×D₁₃	—	2	4	no	—
57	M₁₆×D₁₃	C₂×C₄	1	8	yes	—
58	C₂×#6094	—	2	2	no	—
59	C₂×#6094	C₂×C₄	1	2	yes	—
60	C₂×#6094	C₂×C₄	1	2	yes	—
61	C₂×#6094	C₂×C₄	1	4	yes	—
62	C₂×#6094	C₂×C₄	1	4	yes	—
63	C₂×C₈×D₁₃	—	2	2	no	—
64	C₂×C₈×D₁₃	C₂×C₄	1	4	yes	—
65	C₂×C₈×D₁₃	D₄	1	2	yes	—
66	C₂×C₈×D₁₃	D₄	1	2	yes	—
67	C₂×C₈×D₁₃	Q₈	1	4	yes	—
68	#88146	C₂×C₄	1	4	yes	—
69	C₄⋊C₄×D₁₃	C₂×C₄	1	4	yes	—
70	C₂²⋊C₄×D₁₃	—	2	2	no	—
71	#88131	—	2	2	no	—
72	#88126	—	2	2	no	—
73	#88126	—	2	2	no	—
74	#88126	C₂×C₄	1	4	yes	—
75	C₄²×D₁₃	—	2	2	no	—
76	C₁₃×#108	C₂×C₄	1	4	yes	complemented
77	C₁₃×#107	C₂×C₄	1	2	yes	—
78	C₁₃×#106	C₂×C₄	1	2	yes	—
79	C₁₃×#97	—	2	2	no	—
80	C₄×C₈×C₁₃	—	2	2	no	—
81	C₄×C₈×C₁₃	C₂×C₄	1	4	yes	complemented
82	#88062	C₂×C₄	1	8	yes	complemented
83	#88059	C₂×C₄	1	4	yes	complemented
84	#88058	C₂×C₄	1	2	yes	—
85	#88057	C₂×C₄	1	2	yes	—
86	#88055	—	2	2	no	—
87	#88055	—	2	2	no	—
88	#88055	C₂×C₄	1	4	yes	complemented
89	C₈×Dic₁₃	—	2	2	no	—
90	C₈×Dic₁₃	—	2	2	no	—
91	C₈×Dic₁₃	C₂×C₄	1	4	yes	complemented
92	#88048	C₂×C₄	1	4	yes	—
93	#88047	C₂×C₄	1	4	yes	—
94	#88043	—	2	2	no	—
95	#88043	C₂×C₄	1	4	yes	complemented
96	C₄×#1055	—	2	2	no	—
97	#20444	—	13	1	no	maximal, Sylow
98	C₂³×D₁₃	#41	1	1	yes	characteristic
99	C₂²×C₄×C₁₃	—	2	1	no	—
100	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
101	C₂²×Dic₁₃	—	2	1	no	—
102	C₂²×Dic₁₃	#41	1	1	yes	characteristic
103	C₂×C₄×D₁₃	—	2	4	no	—
104	C₂×C₄×D₁₃	C₂²×C₄	1	2	yes	—
105	C₂×C₄×D₁₃	C₂²×C₄	1	2	yes	—
106	C₂×C₄×D₁₃	C₂²×C₄	1	2	yes	—
107	C₂×C₄×D₁₃	C₂×D₄	1	2	yes	—
108	C₂×C₄×D₁₃	C₂×Q₈	1	2	yes	—
109	C₂×C₄×D₁₃	#41	1	2	yes	—
110	C₁₃×M₁₆	—	2	2	no	—
111	C₁₃×M₁₆	C₂²×C₄	1	4	yes	—
112	C₂×C₈×C₁₃	—	2	2	no	—
113	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
114	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
115	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
116	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
117	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
118	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
119	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
120	C₂×C₈×C₁₃	C₂×Q₈	1	2	yes	—
121	C₁₃×C₄⋊C₄	C₂²×C₄	1	4	yes	—
122	C₁₃×C₂²⋊C₄	—	2	2	no	—
123	C₄²×C₁₃	—	2	2	no	—
124	C₄²×C₁₃	—	2	1	no	—
125	C₄²×C₁₃	C₂²×C₄	1	2	yes	—
126	C₂²⋊Dic₁₃	—	2	2	no	—
127	#6103	—	2	4	no	—
128	#6103	—	2	4	no	—
129	C₄⋊Dic₁₃	C₂²×C₄	1	4	yes	—
130	#6101	—	2	4	no	—
131	#6101	—	2	4	no	—
132	C₄×Dic₁₃	—	2	2	no	—
133	C₄×Dic₁₃	—	2	1	no	—
134	C₄×Dic₁₃	—	2	4	no	—
135	C₄×Dic₁₃	C₂²×C₄	1	2	yes	—
136	#6099	—	2	2	no	—
137	#6099	C₂²×C₄	1	4	yes	—
138	C₂×#1055	—	2	2	no	—
139	C₂×#1055	C₂²×C₄	1	2	yes	—
140	C₂×#1055	C₂²×C₄	1	2	yes	—
141	C₂×#1055	C₂²×C₄	1	2	yes	—
142	C₂×#1055	C₂²×C₄	1	2	yes	—
143	C₂×#1055	C₂×D₄	1	2	yes	—
144	C₂×#1055	C₂×Q₈	1	2	yes	—
145	#6094	—	2	8	no	—
146	#6094	C₄²	1	8	yes	—
147	#6094	C₄²	1	8	yes	—
148	C₈×D₁₃	—	2	8	no	—
149	C₈×D₁₃	C₄⋊C₄	1	8	yes	—
150	C₈×D₁₃	C₄⋊C₄	1	8	yes	—
151	C₂×#430	—	13	1	no	—
152	#2911	—	13	1	no	—
153	C₂×#405	—	13	1	no	—
154	C₂×#405	—	13	2	no	—
155	#1773	—	13	1	no	—
156	#1773	—	13	1	no	—
157	#1773	—	13	2	no	—
158	#1772	—	13	2	no	—
159	#1772	—	13	1	no	—
160	#1772	D₁₃	1	1	yes	characteristic, complemented
161	#1733	—	13	2	no	—
162	C₂³×C₁₃	C₂×#41	1	1	yes	characteristic
163	C₂²×D₁₃	—	4	2	no	—
164	C₂²×D₁₃	#117	1	2	yes	—
165	C₂²×D₁₃	C₄×D₄	1	2	yes	—
166	C₂²×D₁₃	C₄×Q₈	1	2	yes	—
167	C₂×C₄×C₁₃	—	2	2	no	—
168	C₂×C₄×C₁₃	—	2	4	no	—
169	C₂×C₄×C₁₃	—	4	2	no	—
170	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
171	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
172	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
173	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
174	C₂×C₄×C₁₃	C₂²×Q₈	1	1	yes	characteristic
175	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
176	C₂×Dic₁₃	—	2	2	no	—
177	C₂×Dic₁₃	—	2	4	no	—
178	C₂×Dic₁₃	—	4	2	no	—
179	C₂×Dic₁₃	#117	1	2	yes	—
180	C₂×Dic₁₃	C₄×D₄	1	2	yes	—
181	C₂×Dic₁₃	C₄×Q₈	1	2	yes	—
182	C₄×D₁₃	—	4	8	no	—
183	C₄×D₁₃	C₂×C₄²	1	4	yes	—
184	C₄×D₁₃	C₂×C₄⋊C₄	1	4	yes	—
185	C₄×D₁₃	C₄×D₄	1	4	yes	—
186	C₄×D₁₃	C₄×Q₈	1	4	yes	—
187	C₈×C₁₃	—	2	4	no	—
188	C₈×C₁₃	C₂×C₄²	1	2	yes	—
189	C₈×C₁₃	C₂×C₄²	1	2	yes	—
190	C₈×C₁₃	C₂×C₄⋊C₄	1	2	yes	—
191	C₈×C₁₃	C₂×C₄⋊C₄	1	2	yes	—
192	#1055	—	2	4	no	—
193	#1055	C₂×C₄²	1	4	yes	—
194	#1055	C₂×C₄⋊C₄	1	4	yes	—
195	C₂²×M₁₆	—	13	1	no	—
196	C₂²×M₁₆	—	13	2	no	—
197	C₂³×C₈	—	13	1	no	—
198	C₂×#117	—	13	1	no	—
199	C₂×#117	—	13	2	no	—
200	#430	—	13	8	no	—
201	C₂×#108	—	13	2	no	—
202	C₂×#108	—	13	1	no	—
203	C₂×#108	C₂×D₁₃	1	1	yes	characteristic
204	#428	—	13	4	no	—
205	#428	—	13	4	no	—
206	#427	—	13	1	no	—
207	#427	—	13	2	no	—
208	#427	C₂×D₁₃	1	1	yes	characteristic
209	#405	—	13	8	no	—
210	#405	—	13	2	no	—
211	#405	—	13	2	no	—
212	#405	—	13	2	no	—
213	#405	—	26	2	no	—
214	#405	—	26	2	no	—
215	#405	C₂×D₁₃	1	2	yes	—
216	C₂×#97	—	13	1	no	—
217	C₂×#97	—	13	1	no	—
218	C₂×#97	—	26	2	no	—
219	C₂×C₄×C₈	—	13	1	no	—
220	C₂×C₄×C₈	—	26	2	no	—
221	C₂×C₄×C₈	C₂×D₁₃	1	1	yes	characteristic
222	#339	—	13	2	no	—
223	#339	—	13	2	no	—
224	#339	—	13	2	no	—
225	#339	C₂×D₁₃	1	2	yes	—
226	C₂²×C₁₃	—	2	2	no	—
227	C₂²×C₁₃	C₂×#117	1	1	yes	characteristic
228	C₂²×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
229	C₂²×C₁₃	C₂×C₄×Q₈	1	1	yes	characteristic
230	C₂×D₁₃	—	2	4	no	—
231	C₂×D₁₃	—	4	2	no	—
232	C₂×D₁₃	—	4	2	no	—
233	C₂×D₁₃	C₄×C₄⋊C₄	1	4	yes	—
234	C₄×C₁₃	—	4	2	no	—
235	C₄×C₁₃	—	4	4	no	—
236	C₄×C₁₃	C₂²×C₄²	1	1	yes	characteristic
237	C₄×C₁₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
238	C₄×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
239	C₄×C₁₃	C₂×C₄×Q₈	1	1	yes	characteristic
240	Dic₁₃	—	4	2	no	—
241	Dic₁₃	—	4	4	no	—
242	Dic₁₃	C₄×C₄⋊C₄	1	4	yes	—
243	C₂³×C₄	—	13	1	no	—
244	C₂×M₁₆	—	13	4	no	—
245	C₂×M₁₆	—	13	2	no	—
246	C₂×M₁₆	—	13	2	no	—
247	C₂×M₁₆	—	13	4	no	—
248	C₂×M₁₆	—	13	2	no	—
249	C₂×M₁₆	—	13	8	no	—
250	C₂×M₁₆	—	26	2	no	—
251	C₂×M₁₆	—	26	4	no	—
252	C₂×M₁₆	C₂²×D₁₃	1	2	yes	—
253	C₂²×C₈	—	13	1	no	—
254	C₂²×C₈	—	13	1	no	—
255	C₂²×C₈	—	13	4	no	—
256	C₂²×C₈	—	13	2	no	—
257	C₂²×C₈	—	13	2	no	—
258	C₂²×C₈	—	13	4	no	—
259	C₂²×C₈	—	26	2	no	—
260	C₂²×C₈	C₂²×D₁₃	1	1	yes	characteristic
261	C₂²×C₈	C₂²×D₁₃	1	1	yes	characteristic
262	#117	—	13	4	no	—
263	#117	—	13	2	no	—
264	#117	—	13	4	no	—
265	#117	—	26	2	no	—
266	#117	—	26	2	no	—
267	#117	—	26	2	no	—
268	#117	C₂²×D₁₃	1	2	yes	—
269	C₂×C₄⋊C₄	—	13	4	no	—
270	C₂×C₄⋊C₄	—	26	1	no	—
271	C₂×C₂²⋊C₄	—	26	2	no	—
272	C₂×C₂²⋊C₄	—	26	1	no	—
273	C₂×C₄²	—	13	1	no	—
274	C₂×C₄²	—	26	2	no	—
275	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
276	#108	—	13	8	no	—
277	#108	—	13	4	no	—
278	#108	C₄×D₁₃	1	4	yes	complemented
279	#107	—	13	2	no	—
280	#107	—	13	4	no	—
281	#107	C₄×D₁₃	1	2	yes	—
282	#106	—	13	2	no	—
283	#106	—	13	4	no	—
284	#106	C₄×D₁₃	1	2	yes	—
285	#97	—	2	2	no	—
286	#97	—	13	4	no	—
287	#97	—	13	4	no	—
288	#97	—	26	2	no	—
289	#97	—	26	2	no	—
290	#97	—	26	2	no	—
291	C₄×C₈	—	2	2	no	—
292	C₄×C₈	—	13	4	no	—
293	C₄×C₈	—	26	2	no	—
294	C₄×C₈	—	26	2	no	—
295	C₄×C₈	—	26	2	no	—
296	C₄×C₈	C₄×D₁₃	1	4	yes	complemented
297	C₂×C₁₃	—	2	1	no	—
298	C₂×C₁₃	—	2	1	no	—
299	C₂×C₁₃	C₂×C₄×C₄⋊C₄	1	1	yes	characteristic
300	C₂×C₁₃	#2955	1	2	yes	—
301	D₁₃	—	2	4	no	—
302	C₂⁴	—	13	1	no	—
303	C₂²×C₄	—	2	1	no	—
304	C₂²×C₄	—	13	1	no	—
305	C₂²×C₄	—	13	2	no	—
306	C₂²×C₄	—	13	2	no	—
307	C₂²×C₄	—	13	2	no	—
308	C₂²×C₄	—	13	2	no	—
309	C₂²×C₄	—	13	2	no	—
310	C₂²×C₄	—	13	2	no	—
311	C₂²×C₄	—	26	4	no	—
312	C₂²×C₄	—	26	1	no	—
313	C₂²×C₄	C₂³×D₁₃	1	1	yes	characteristic
314	M₁₆	—	2	2	no	—
315	M₁₆	—	13	8	no	—
316	M₁₆	—	13	8	no	—
317	M₁₆	—	13	4	no	—
318	M₁₆	—	26	8	no	—
319	M₁₆	—	26	2	no	—
320	M₁₆	C₂×C₄×D₁₃	1	4	yes	—
321	C₂×C₈	—	2	2	no	—
322	C₂×C₈	—	13	2	no	—
323	C₂×C₈	—	13	2	no	—
324	C₂×C₈	—	13	2	no	—
325	C₂×C₈	—	13	2	no	—
326	C₂×C₈	—	13	2	no	—
327	C₂×C₈	—	13	2	no	—
328	C₂×C₈	—	13	8	no	—
329	C₂×C₈	—	13	8	no	—
330	C₂×C₈	—	26	8	no	—
331	C₂×C₈	—	26	2	no	—
332	C₂×C₈	C₂×C₄×D₁₃	1	2	yes	—
333	C₂×C₈	C₂×C₄×D₁₃	1	1	yes	characteristic
334	C₂×C₈	C₂×C₄×D₁₃	1	1	yes	characteristic
335	C₂×C₈	C₂×C₄×D₁₃	1	2	yes	—
336	C₂×C₈	C₂×C₄×D₁₃	1	2	yes	—
337	C₂×C₈	D₄×D₁₃	1	1	yes	characteristic
338	C₂×C₈	D₄×D₁₃	1	1	yes	characteristic
339	C₂×C₈	Q₈×D₁₃	1	2	yes	—
340	C₄⋊C₄	—	13	4	no	—
341	C₄⋊C₄	—	26	4	no	—
342	C₄⋊C₄	—	26	4	no	—
343	C₄⋊C₄	C₂×C₄×D₁₃	1	4	yes	—
344	C₂²⋊C₄	—	2	2	no	—
345	C₂²⋊C₄	—	26	4	no	—
346	C₂²⋊C₄	—	26	4	no	—
347	C₂²⋊C₄	—	26	2	no	—
348	C₄²	—	2	2	no	—
349	C₄²	—	2	1	no	—
350	C₄²	—	13	2	no	—
351	C₄²	—	26	4	no	—
352	C₄²	—	26	2	no	—
353	C₄²	—	26	1	no	—
354	C₄²	C₂×C₄×D₁₃	1	2	yes	—
355	C₁₃	#20444	1	1	yes	characteristic, complemented, Sylow
356	C₂³	—	13	2	no	—
357	C₂³	—	13	2	no	—
358	C₂³	—	13	2	no	—
359	C₂³	—	52	2	no	—
360	C₂³	#41×D₁₃	1	1	yes	characteristic
361	C₂×C₄	—	2	2	no	—
362	C₂×C₄	—	2	4	no	—
363	C₂×C₄	—	4	2	no	—
364	C₂×C₄	—	13	2	no	—
365	C₂×C₄	—	13	2	no	—
366	C₂×C₄	—	13	2	no	—
367	C₂×C₄	—	13	4	no	—
368	C₂×C₄	—	13	4	no	—
369	C₂×C₄	—	13	4	no	—
370	C₂×C₄	—	13	4	no	—
371	C₂×C₄	—	26	2	no	—
372	C₂×C₄	—	26	4	no	—
373	C₂×C₄	—	52	8	no	—
374	C₂×C₄	—	52	2	no	—
375	C₂×C₄	C₂²×C₄×D₁₃	1	1	yes	characteristic
376	C₂×C₄	C₂²×C₄×D₁₃	1	1	yes	characteristic
377	C₂×C₄	C₂²×C₄×D₁₃	1	1	yes	characteristic
378	C₂×C₄	C₂×D₄×D₁₃	1	1	yes	characteristic
379	C₂×C₄	C₂×Q₈×D₁₃	1	1	yes	characteristic
380	C₂×C₄	#41×D₁₃	1	1	yes	characteristic
381	C₈	—	2	4	no	—
382	C₈	—	13	4	no	—
383	C₈	—	13	4	no	—
384	C₈	—	26	4	no	—
385	C₈	C₄²×D₁₃	1	2	yes	—
386	C₈	C₄²×D₁₃	1	2	yes	—
387	C₈	C₄⋊C₄×D₁₃	1	2	yes	—
388	C₈	C₄⋊C₄×D₁₃	1	2	yes	—
389	C₂²	—	2	2	no	—
390	C₂²	—	13	4	no	—
391	C₂²	—	26	4	no	—
392	C₂²	—	52	2	no	—
393	C₂²	—	52	2	no	—
394	C₂²	D₁₃×#117	1	1	yes	characteristic
395	C₂²	C₄×D₄×D₁₃	1	1	yes	characteristic
396	C₂²	C₄×Q₈×D₁₃	1	1	yes	characteristic
397	C₄	—	4	2	no	—
398	C₄	—	4	4	no	—
399	C₄	—	13	4	no	—
400	C₄	—	52	2	no	—
401	C₄	—	52	4	no	—
402	C₄	C₂×C₄²×D₁₃	1	1	yes	characteristic
403	C₄	C₂×C₄⋊C₄×D₁₃	1	1	yes	characteristic
404	C₄	C₄×D₄×D₁₃	1	1	yes	characteristic
405	C₄	C₄×Q₈×D₁₃	1	1	yes	characteristic
406	C₂	—	2	1	no	—
407	C₂	—	2	1	no	—
408	C₂	—	26	4	no	—
409	C₂	C₄×C₄⋊C₄×D₁₃	1	1	yes	characteristic
410	C₂	#13123734	1	2	yes	—

	subgroup	G/H
center	C₂×C₈	D₄×D₁₃
commutator	C₄×C₁₃	C₂²×C₄²
Frattini	C₂²×C₄	C₂³×D₁₃
Fitting	C₁₃×#1772	C₂
socle	C₂²×C₁₃	C₂×C₄×D₄
prime radical	C₂³×D₁₃	#41
cosocle	C₂²×C₄×C₁₃	C₂⁴
hypercenter	#1772	D₁₃
hypocenter	C₁₃	#20444
LCS	G ▷ C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₈ ◁ C₂²×C₈ ◁ #1772

Complements

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

N	H ≅ G/N	type
5. #13114723	C₂	semidirect
6. #13114722	C₂	semidirect
7. #13114719	C₂	semidirect
8. #13114716	C₂	semidirect
9. #13114715	C₂	semidirect
11. C₁₃×#1772	C₂	semidirect
31. #11718554	C₄	semidirect
32. #11718542	C₄	semidirect
33. #11718522	C₄	semidirect
37. #11718350	C₄	semidirect
76. C₁₃×#108	C₂×C₄	semidirect
81. C₄×C₈×C₁₃	C₂×C₄	semidirect
82. #88062	C₂×C₄	semidirect
83. #88059	C₂×C₄	semidirect
88. #88055	C₂×C₄	semidirect
91. C₈×Dic₁₃	C₂×C₄	semidirect
95. #88043	C₂×C₄	semidirect
160. #1772	D₁₃	semidirect
278. #108	C₄×D₁₃	semidirect
296. C₄×C₈	C₄×D₁₃	semidirect
355. C₁₃	#20444	semidirect

Maximal subgroups

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

subgroup	index
C₂×#11718554	2
#13123424	2
C₂×#11718350	2
D₁₃×#405	2
#13114723	2
#13114722	2
#13114719	2
#13114716	2
#13114715	2
#13114544	2
C₁₃×#1772	2
#20444	13