Subgroups — #15860942

Order 3328.

1042 conjugacy classes of subgroups.

The subgroup lattice has 416 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	#13123252	C₂	1	2	yes	maximal
4	C₂×C₄×#6094	C₂	1	1	yes	maximal, characteristic
5	#13114723	C₂	1	1	yes	maximal, characteristic, complemented
6	#13114722	C₂	1	1	yes	maximal, characteristic, complemented
7	#13114721	C₂	1	2	yes	maximal, complemented
8	#13114715	C₂	1	1	yes	maximal, characteristic, complemented
9	#13114714	C₂	1	2	yes	maximal, complemented
10	D₁₃×#339	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×#6094	C₂²	1	1	yes	characteristic
15	D₁₃×#117	C₂²	1	2	yes	—
16	C₂×C₄²×D₁₃	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×#88055	C₂²	1	1	yes	characteristic
28	#11718659	C₂²	1	2	yes	—
29	#11718658	C₂²	1	2	yes	—
30	C₂×C₄×#1055	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	#11718368	—	2	2	no	—
36	#11718350	—	2	2	no	—
37	C₄×#6094	—	2	2	no	—
38	C₄×#6094	C₄	1	8	yes	complemented
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	—	2	1	no	—
44	C₂²×C₄×D₁₃	C₂³	1	1	yes	characteristic
45	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
46	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
47	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
48	C₁₃×#117	C₂³	1	2	yes	—
49	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
50	#88180	C₂³	1	2	yes	—
51	C₂×C₄×Dic₁₃	—	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×#6094	C₂×C₄	1	4	yes	—
64	C₂×#6094	D₄	1	2	yes	—
65	C₂×#6094	D₄	1	2	yes	—
66	C₂×#6094	Q₈	1	4	yes	—
67	C₂×C₈×D₁₃	—	2	2	no	—
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	C₄²×D₁₃	—	2	2	no	—
74	C₄²×D₁₃	—	2	2	no	—
75	C₄²×D₁₃	C₂×C₄	1	4	yes	—
76	C₁₃×#108	C₂×C₄	1	4	yes	complemented
77	C₁₃×#107	C₂×C₄	1	2	yes	complemented
78	C₁₃×#106	C₂×C₄	1	2	yes	complemented
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	complemented
85	#88057	C₂×C₄	1	2	yes	complemented
86	#88055	—	2	2	no	—
87	#88055	—	2	2	no	—
88	#88055	C₂×C₄	1	4	yes	complemented
89	#88055	C₂×C₄	1	4	yes	complemented
90	C₈×Dic₁₃	—	2	2	no	—
91	C₈×Dic₁₃	—	2	2	no	—
92	#88048	C₂×C₄	1	4	yes	complemented
93	#88047	C₂×C₄	1	4	yes	complemented
94	#88043	—	2	2	no	—
95	C₄×#1055	—	2	2	no	—
96	C₄×#1055	C₂×C₄	1	4	yes	complemented
97	#20445	—	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	—	2	4	no	—
105	C₂×C₄×D₁₃	—	4	4	no	—
106	C₂×C₄×D₁₃	C₂²×C₄	1	2	yes	—
107	C₂×C₄×D₁₃	C₂²×C₄	1	2	yes	—
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×C₄×D₁₃	#41	1	2	yes	—
112	C₁₃×M₁₆	—	2	2	no	—
113	C₁₃×M₁₆	C₂²×C₄	1	4	yes	—
114	C₂×C₈×C₁₃	—	2	2	no	—
115	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
116	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
117	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
118	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
119	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
120	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
121	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
122	C₂×C₈×C₁₃	C₂×Q₈	1	2	yes	—
123	C₁₃×C₄⋊C₄	C₂²×C₄	1	4	yes	—
124	C₁₃×C₂²⋊C₄	—	2	2	no	—
125	C₄²×C₁₃	—	2	2	no	—
126	C₄²×C₁₃	—	2	1	no	—
127	C₄²×C₁₃	C₂²×C₄	1	2	yes	—
128	C₂²⋊Dic₁₃	—	2	2	no	—
129	#6103	—	2	4	no	—
130	C₄⋊Dic₁₃	C₂²×C₄	1	4	yes	—
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	—	2	4	no	—
136	C₄×Dic₁₃	C₂²×C₄	1	2	yes	—
137	#6099	—	2	2	no	—
138	#6099	C₂²×C₄	1	4	yes	—
139	C₂×#1055	—	2	2	no	—
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	C₂²×C₄	1	2	yes	—
144	C₂×#1055	C₂×D₄	1	2	yes	—
145	C₂×#1055	C₂×Q₈	1	2	yes	—
146	#6094	—	2	8	no	—
147	#6094	C₄²	1	8	yes	—
148	#6094	C₄²	1	8	yes	—
149	#6094	C₄⋊C₄	1	8	yes	—
150	#6094	C₄⋊C₄	1	8	yes	—
151	C₈×D₁₃	—	2	8	no	—
152	C₂×#430	—	13	1	no	—
153	#2911	—	13	1	no	—
154	#2873	—	13	2	no	—
155	C₂×C₄×M₁₆	—	13	1	no	—
156	#1773	—	13	1	no	—
157	#1773	—	13	1	no	—
158	#1773	—	13	2	no	—
159	#1772	—	13	1	no	—
160	#1772	—	13	2	no	—
161	#1772	D₁₃	1	1	yes	characteristic, complemented
162	C₂×#339	—	13	2	no	—
163	C₂³×C₁₃	C₂×#41	1	1	yes	characteristic
164	C₂²×D₁₃	—	4	2	no	—
165	C₂²×D₁₃	#117	1	2	yes	—
166	C₂²×D₁₃	C₄×D₄	1	2	yes	—
167	C₂²×D₁₃	C₄×Q₈	1	2	yes	—
168	C₂×C₄×C₁₃	—	2	4	no	—
169	C₂×C₄×C₁₃	—	2	2	no	—
170	C₂×C₄×C₁₃	—	2	4	no	—
171	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
172	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
173	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
174	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
175	C₂×C₄×C₁₃	C₂²×Q₈	1	1	yes	characteristic
176	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
177	C₂×Dic₁₃	—	2	2	no	—
178	C₂×Dic₁₃	—	2	4	no	—
179	C₂×Dic₁₃	—	4	2	no	—
180	C₂×Dic₁₃	#117	1	2	yes	—
181	C₂×Dic₁₃	C₄×D₄	1	2	yes	—
182	C₂×Dic₁₃	C₄×Q₈	1	2	yes	—
183	C₄×D₁₃	—	4	8	no	—
184	C₄×D₁₃	—	8	4	no	—
185	C₄×D₁₃	C₂×C₄²	1	4	yes	—
186	C₄×D₁₃	C₂×C₄⋊C₄	1	4	yes	—
187	C₄×D₁₃	C₄×D₄	1	4	yes	—
188	C₄×D₁₃	C₄×Q₈	1	4	yes	—
189	C₈×C₁₃	—	2	4	no	—
190	C₈×C₁₃	C₂×C₄²	1	2	yes	—
191	C₈×C₁₃	C₂×C₄²	1	2	yes	—
192	C₈×C₁₃	C₂×C₄⋊C₄	1	2	yes	—
193	C₈×C₁₃	C₂×C₄⋊C₄	1	2	yes	—
194	#1055	—	2	4	no	—
195	#1055	C₂×C₄²	1	4	yes	—
196	#1055	C₂×C₄⋊C₄	1	4	yes	—
197	C₂²×M₁₆	—	13	1	no	—
198	C₂²×M₁₆	—	13	1	no	—
199	C₂²×M₁₆	—	13	2	no	—
200	C₂×#117	—	13	2	no	—
201	C₂²×C₄²	—	13	1	no	—
202	#430	—	13	8	no	—
203	C₂×#108	—	13	2	no	—
204	C₂×#108	—	13	1	no	—
205	C₂×#108	C₂×D₁₃	1	1	yes	characteristic
206	#428	—	13	4	no	—
207	#428	—	13	4	no	—
208	#427	—	13	1	no	—
209	#427	—	13	2	no	—
210	#427	C₂×D₁₃	1	1	yes	characteristic
211	#405	—	13	2	no	—
212	#405	—	13	2	no	—
213	#405	—	13	2	no	—
214	#405	—	26	2	no	—
215	#405	—	26	2	no	—
216	#405	C₂×D₁₃	1	2	yes	—
217	C₄×M₁₆	—	13	8	no	—
218	C₄×M₁₆	—	26	2	no	—
219	C₄×M₁₆	—	26	2	no	—
220	C₂×#97	—	13	1	no	—
221	C₂×#97	—	13	1	no	—
222	C₂×C₄×C₈	—	13	1	no	—
223	C₂×C₄×C₈	C₂×D₁₃	1	1	yes	characteristic
224	#339	—	13	2	no	—
225	#339	—	13	2	no	—
226	#339	—	13	2	no	—
227	#339	C₂×D₁₃	1	2	yes	—
228	C₂²×C₁₃	—	2	2	no	—
229	C₂²×C₁₃	C₂×#117	1	1	yes	characteristic
230	C₂²×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
231	C₂²×C₁₃	C₂×C₄×Q₈	1	1	yes	characteristic
232	C₂×D₁₃	—	2	4	no	—
233	C₂×D₁₃	—	4	2	no	—
234	C₂×D₁₃	—	4	2	no	—
235	C₂×D₁₃	C₄×C₄⋊C₄	1	4	yes	—
236	C₄×C₁₃	—	2	4	no	—
237	C₄×C₁₃	—	4	4	no	—
238	C₄×C₁₃	C₂²×C₄²	1	1	yes	characteristic
239	C₄×C₁₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
240	C₄×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
241	C₄×C₁₃	C₂×C₄×Q₈	1	1	yes	characteristic
242	Dic₁₃	—	4	2	no	—
243	Dic₁₃	—	4	4	no	—
244	Dic₁₃	C₄×C₄⋊C₄	1	4	yes	—
245	C₂³×C₄	—	13	1	no	—
246	C₂³×C₄	—	26	1	no	—
247	C₂×M₁₆	—	13	4	no	—
248	C₂×M₁₆	—	13	4	no	—
249	C₂×M₁₆	—	13	2	no	—
250	C₂×M₁₆	—	13	2	no	—
251	C₂×M₁₆	—	13	4	no	—
252	C₂×M₁₆	—	13	2	no	—
253	C₂×M₁₆	—	13	2	no	—
254	C₂×M₁₆	—	13	4	no	—
255	C₂×M₁₆	—	13	2	no	—
256	C₂×M₁₆	—	13	8	no	—
257	C₂×M₁₆	—	26	2	no	—
258	C₂×M₁₆	—	26	4	no	—
259	C₂×M₁₆	C₂²×D₁₃	1	2	yes	—
260	C₂²×C₈	—	13	1	no	—
261	C₂²×C₈	—	13	1	no	—
262	C₂²×C₈	—	26	2	no	—
263	C₂²×C₈	C₂²×D₁₃	1	1	yes	characteristic
264	C₂²×C₈	C₂²×D₁₃	1	1	yes	characteristic
265	#117	—	13	2	no	—
266	#117	—	13	4	no	—
267	#117	—	26	2	no	—
268	#117	—	26	2	no	—
269	#117	C₂²×D₁₃	1	2	yes	—
270	C₂×C₄⋊C₄	—	13	4	no	—
271	C₂×C₂²⋊C₄	—	26	2	no	—
272	C₂×C₄²	—	13	1	no	—
273	C₂×C₄²	—	13	4	no	—
274	C₂×C₄²	—	26	2	no	—
275	C₂×C₄²	—	26	2	no	—
276	C₂×C₄²	—	26	1	no	—
277	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
278	#108	—	13	8	no	—
279	#108	—	13	4	no	—
280	#108	C₄×D₁₃	1	4	yes	complemented
281	#107	—	13	2	no	—
282	#107	—	13	4	no	—
283	#107	C₄×D₁₃	1	2	yes	complemented
284	#106	—	13	2	no	—
285	#106	—	13	4	no	—
286	#106	C₄×D₁₃	1	2	yes	complemented
287	#97	—	2	2	no	—
288	#97	—	13	4	no	—
289	#97	—	13	4	no	—
290	#97	—	26	2	no	—
291	#97	—	26	2	no	—
292	#97	—	26	2	no	—
293	C₄×C₈	—	2	2	no	—
294	C₄×C₈	—	13	4	no	—
295	C₄×C₈	—	26	2	no	—
296	C₄×C₈	—	26	2	no	—
297	C₄×C₈	—	26	2	no	—
298	C₄×C₈	C₄×D₁₃	1	4	yes	complemented
299	C₂×C₁₃	—	2	1	no	—
300	C₂×C₁₃	—	2	1	no	—
301	C₂×C₁₃	C₂×C₄×C₄⋊C₄	1	1	yes	characteristic
302	C₂×C₁₃	#2956	1	2	yes	—
303	D₁₃	—	2	4	no	—
304	C₂⁴	—	13	1	no	—
305	C₂²×C₄	—	2	1	no	—
306	C₂²×C₄	—	13	1	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	—	13	2	no	—
312	C₂²×C₄	—	13	2	no	—
313	C₂²×C₄	—	26	4	no	—
314	C₂²×C₄	—	26	4	no	—
315	C₂²×C₄	—	26	1	no	—
316	C₂²×C₄	—	52	4	no	—
317	C₂²×C₄	C₂³×D₁₃	1	1	yes	characteristic
318	M₁₆	—	2	2	no	—
319	M₁₆	—	13	8	no	—
320	M₁₆	—	13	8	no	—
321	M₁₆	—	13	8	no	—
322	M₁₆	—	13	8	no	—
323	M₁₆	—	13	4	no	—
324	M₁₆	—	26	8	no	—
325	M₁₆	—	26	2	no	—
326	M₁₆	C₂×C₄×D₁₃	1	4	yes	—
327	C₂×C₈	—	2	2	no	—
328	C₂×C₈	—	13	2	no	—
329	C₂×C₈	—	13	2	no	—
330	C₂×C₈	—	13	2	no	—
331	C₂×C₈	—	13	2	no	—
332	C₂×C₈	—	13	2	no	—
333	C₂×C₈	—	13	2	no	—
334	C₂×C₈	—	26	8	no	—
335	C₂×C₈	—	26	2	no	—
336	C₂×C₈	C₂×C₄×D₁₃	1	2	yes	—
337	C₂×C₈	C₂×C₄×D₁₃	1	1	yes	characteristic
338	C₂×C₈	C₂×C₄×D₁₃	1	1	yes	characteristic
339	C₂×C₈	C₂×C₄×D₁₃	1	2	yes	—
340	C₂×C₈	C₂×C₄×D₁₃	1	2	yes	—
341	C₂×C₈	D₄×D₁₃	1	1	yes	characteristic
342	C₂×C₈	D₄×D₁₃	1	1	yes	characteristic
343	C₂×C₈	Q₈×D₁₃	1	2	yes	—
344	C₄⋊C₄	—	13	4	no	—
345	C₄⋊C₄	—	26	4	no	—
346	C₄⋊C₄	C₂×C₄×D₁₃	1	4	yes	—
347	C₂²⋊C₄	—	2	2	no	—
348	C₂²⋊C₄	—	26	4	no	—
349	C₂²⋊C₄	—	26	2	no	—
350	C₄²	—	2	2	no	—
351	C₄²	—	2	1	no	—
352	C₄²	—	13	2	no	—
353	C₄²	—	26	4	no	—
354	C₄²	—	26	4	no	—
355	C₄²	—	26	2	no	—
356	C₄²	—	26	1	no	—
357	C₄²	C₂×C₄×D₁₃	1	2	yes	—
358	C₁₃	#20445	1	1	yes	characteristic, complemented, Sylow
359	C₂³	—	13	2	no	—
360	C₂³	—	13	2	no	—
361	C₂³	—	13	2	no	—
362	C₂³	—	52	2	no	—
363	C₂³	#41×D₁₃	1	1	yes	characteristic
364	C₂×C₄	—	2	4	no	—
365	C₂×C₄	—	2	2	no	—
366	C₂×C₄	—	2	4	no	—
367	C₂×C₄	—	13	2	no	—
368	C₂×C₄	—	13	2	no	—
369	C₂×C₄	—	13	2	no	—
370	C₂×C₄	—	13	4	no	—
371	C₂×C₄	—	13	4	no	—
372	C₂×C₄	—	13	4	no	—
373	C₂×C₄	—	13	4	no	—
374	C₂×C₄	—	26	2	no	—
375	C₂×C₄	—	26	4	no	—
376	C₂×C₄	—	52	8	no	—
377	C₂×C₄	—	52	2	no	—
378	C₂×C₄	—	104	4	no	—
379	C₂×C₄	C₂²×C₄×D₁₃	1	1	yes	characteristic
380	C₂×C₄	C₂²×C₄×D₁₃	1	1	yes	characteristic
381	C₂×C₄	C₂²×C₄×D₁₃	1	1	yes	characteristic
382	C₂×C₄	C₂×D₄×D₁₃	1	1	yes	characteristic
383	C₂×C₄	C₂×Q₈×D₁₃	1	1	yes	characteristic
384	C₂×C₄	#41×D₁₃	1	1	yes	characteristic
385	C₈	—	2	4	no	—
386	C₈	—	13	4	no	—
387	C₈	—	13	4	no	—
388	C₈	—	26	4	no	—
389	C₈	C₄²×D₁₃	1	2	yes	—
390	C₈	C₄²×D₁₃	1	2	yes	—
391	C₈	C₄⋊C₄×D₁₃	1	2	yes	—
392	C₈	C₄⋊C₄×D₁₃	1	2	yes	—
393	C₂²	—	2	2	no	—
394	C₂²	—	13	4	no	—
395	C₂²	—	26	4	no	—
396	C₂²	—	52	2	no	—
397	C₂²	—	52	2	no	—
398	C₂²	D₁₃×#117	1	1	yes	characteristic
399	C₂²	C₄×D₄×D₁₃	1	1	yes	characteristic
400	C₂²	C₄×Q₈×D₁₃	1	1	yes	characteristic
401	C₄	—	2	4	no	—
402	C₄	—	4	4	no	—
403	C₄	—	13	4	no	—
404	C₄	—	52	2	no	—
405	C₄	—	52	4	no	—
406	C₄	C₂×C₄²×D₁₃	1	1	yes	characteristic
407	C₄	C₂×C₄⋊C₄×D₁₃	1	1	yes	characteristic
408	C₄	C₄×D₄×D₁₃	1	1	yes	characteristic
409	C₄	C₄×Q₈×D₁₃	1	1	yes	characteristic
410	C₂	—	2	1	no	—
411	C₂	—	2	1	no	—
412	C₂	—	26	4	no	—
413	C₂	C₄×C₄⋊C₄×D₁₃	1	1	yes	characteristic
414	C₂	#13123741	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	C₂×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	#20445
LCS	G ▷ C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₄ ◁ 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. #13114721	C₂	semidirect
8. #13114715	C₂	semidirect
9. #13114714	C₂	semidirect
11. C₁₃×#1772	C₂	semidirect
31. #11718554	C₄	semidirect
32. #11718542	C₄	semidirect
33. #11718522	C₄	semidirect
38. C₄×#6094	C₄	semidirect
76. C₁₃×#108	C₂×C₄	semidirect
77. C₁₃×#107	C₂×C₄	semidirect
78. C₁₃×#106	C₂×C₄	semidirect
81. C₄×C₈×C₁₃	C₂×C₄	semidirect
82. #88062	C₂×C₄	semidirect
83. #88059	C₂×C₄	semidirect
84. #88058	C₂×C₄	semidirect
85. #88057	C₂×C₄	semidirect
88. #88055	C₂×C₄	semidirect
89. #88055	C₂×C₄	semidirect
92. #88048	C₂×C₄	semidirect
93. #88047	C₂×C₄	semidirect
96. C₄×#1055	C₂×C₄	semidirect
161. #1772	D₁₃	semidirect
280. #108	C₄×D₁₃	semidirect
283. #107	C₄×D₁₃	semidirect
286. #106	C₄×D₁₃	semidirect
298. C₄×C₈	C₄×D₁₃	semidirect
358. C₁₃	#20445	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
#13123252	2
C₂×C₄×#6094	2
#13114723	2
#13114722	2
#13114721	2
#13114715	2
#13114714	2
D₁₃×#339	2
C₁₃×#1772	2
#20445	13