Subgroups — #13123866

Order 1664.

464 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×D₄×D₁₃	C₂	1	1	yes	maximal, characteristic
2	C₁₃×#435	C₂	1	1	yes	maximal, characteristic, complemented
3	#11718789	C₂	1	1	yes	maximal, characteristic, complemented
4	#11718787	C₂	1	1	yes	maximal, characteristic, complemented
5	C₈×C₂²⋊D₁₃	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#88060	C₂	1	1	yes	maximal, characteristic, complemented
7	#11718672	C₂	1	1	yes	maximal, characteristic, complemented
8	#11718497	C₂	1	1	yes	maximal, characteristic, complemented
9	#11718494	C₂	1	1	yes	maximal, characteristic, complemented
10	#11718390	C₂	1	1	yes	maximal, characteristic, complemented
11	#11718387	C₂	1	1	yes	maximal, characteristic, complemented
12	#11718386	C₂	1	1	yes	maximal, characteristic, complemented
13	D₁₃×C₂²⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
14	#11718367	C₂	1	1	yes	maximal, characteristic, complemented
15	#11718366	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×D₄×D₁₃	C₄	1	1	yes	characteristic
17	C₂²×C₄×D₁₃	C₂²	1	1	yes	characteristic
18	C₂²×C₄×D₁₃	C₂²	1	1	yes	characteristic
19	C₂×C₁₃×M₁₆	C₂²	1	1	yes	characteristic, complemented
20	C₂²×C₈×C₁₃	C₂²	1	1	yes	characteristic, complemented
21	C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
22	D₄×Dic₁₃	C₄	1	1	yes	characteristic
23	C₄×C₂²⋊D₁₃	C₂²	1	1	yes	characteristic
24	C₄×C₂²⋊D₁₃	C₂²	1	1	yes	characteristic
25	C₂×#6099	C₂²	1	1	yes	characteristic, complemented
26	C₂²×#1055	C₂²	1	1	yes	characteristic, complemented
27	C₂×#6094	C₂²	1	1	yes	characteristic, complemented
28	C₂×#6094	C₂²	1	1	yes	characteristic, complemented
29	C₂×C₈×D₁₃	C₂²	1	1	yes	characteristic, complemented
30	C₂×C₈×D₁₃	C₂²	1	1	yes	characteristic, complemented
31	#88147	C₄	1	1	yes	characteristic
32	C₄⋊C₄×D₁₃	C₄	1	1	yes	characteristic
33	#88135	C₄	1	1	yes	characteristic
34	#88135	C₄	1	1	yes	characteristic
35	C₂²⋊C₄×D₁₃	C₄	1	1	yes	characteristic
36	C₂²⋊C₄×D₁₃	C₄	1	1	yes	characteristic
37	C₄×D₅₂	C₂²	1	1	yes	characteristic
38	C₄²×D₁₃	C₂²	1	1	yes	characteristic
39	C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
40	C₁₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic, complemented
41	C₁₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic, complemented
42	C₁₃×#97	C₂²	1	1	yes	characteristic, complemented
43	C₂²⋊#1055	C₂²	1	1	yes	characteristic, complemented
44	C₂²⋊#1055	C₂²	1	1	yes	characteristic, complemented
45	#88060	C₂²	1	1	yes	characteristic
46	#88060	C₂²	1	1	yes	characteristic
47	#88060	C₂²	1	1	yes	characteristic
48	#88060	C₂²	1	1	yes	characteristic
49	#88060	C₂²	1	1	yes	characteristic, complemented
50	#88060	C₂²	1	1	yes	characteristic, complemented
51	#88060	C₂²	1	1	yes	characteristic, complemented
52	#88060	C₂²	1	1	yes	characteristic, complemented
53	#88054	C₂²	1	1	yes	characteristic, complemented
54	#88054	C₂²	1	1	yes	characteristic, complemented
55	C₈×Dic₁₃	C₂²	1	1	yes	characteristic, complemented
56	C₈×Dic₁₃	C₂²	1	1	yes	characteristic, complemented
57	C₄⋊#1055	C₂²	1	1	yes	characteristic, complemented
58	#88043	C₂²	1	1	yes	characteristic, complemented
59	C₂³×D₁₃	C₂×C₄	1	1	yes	characteristic
60	C₂³×D₁₃	C₂×C₄	1	1	yes	characteristic
61	C₂×D₄×C₁₃	C₂×C₄	1	1	yes	characteristic
62	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
63	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
64	C₂×C₂²⋊D₁₃	C₂×C₄	1	1	yes	characteristic
65	C₂×C₂²⋊D₁₃	C₂×C₄	1	1	yes	characteristic
66	C₂²×Dic₁₃	C₂×C₄	1	1	yes	characteristic
67	C₂²×Dic₁₃	C₂×C₄	1	1	yes	characteristic
68	D₄×D₁₃	—	2	4	no	—
69	C₂×D₅₂	C₂×C₄	1	1	yes	characteristic
70	C₂×C₄×D₁₃	—	4	1	no	—
71	C₂×C₄×D₁₃	—	4	1	no	—
72	C₂×C₄×D₁₃	—	4	1	no	—
73	C₂×C₄×D₁₃	—	4	1	no	—
74	C₂×C₄×D₁₃	C₂×C₄	1	1	yes	characteristic
75	C₂×C₄×D₁₃	C₂×C₄	1	1	yes	characteristic
76	C₂×C₄×D₁₃	C₂×C₄	1	1	yes	characteristic
77	C₂×C₄×D₁₃	C₂×C₄	1	1	yes	characteristic
78	C₂×C₄×D₁₃	C₂×C₄	1	1	yes	characteristic
79	C₂×C₄×D₁₃	C₂×C₄	1	1	yes	characteristic
80	C₂×C₄×D₁₃	C₂³	1	1	yes	characteristic
81	C₂×C₄×D₁₃	C₂³	1	1	yes	characteristic
82	C₂×C₄×D₁₃	C₂³	1	1	yes	characteristic
83	C₁₃×M₁₆	—	4	1	no	—
84	C₂×C₈×C₁₃	—	4	1	no	—
85	C₂×C₈×C₁₃	C₂³	1	1	yes	characteristic
86	C₂×C₈×C₁₃	C₂³	1	1	yes	characteristic
87	C₂×C₈×C₁₃	C₂³	1	1	yes	characteristic
88	C₂×C₈×C₁₃	C₂³	1	1	yes	characteristic
89	C₁₃×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
90	C₁₃×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
91	C₁₃×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
92	C₄²×C₁₃	C₂³	1	1	yes	characteristic
93	C₂²⋊Dic₁₃	C₂×C₄	1	1	yes	characteristic
94	C₂²⋊Dic₁₃	C₂×C₄	1	1	yes	characteristic
95	#6103	C₂×C₄	1	1	yes	characteristic
96	#6103	C₂×C₄	1	1	yes	characteristic
97	#6103	C₂×C₄	1	1	yes	characteristic
98	#6103	C₂×C₄	1	1	yes	characteristic
99	C₄⋊Dic₁₃	C₂×C₄	1	1	yes	characteristic
100	#6101	C₂×C₄	1	1	yes	characteristic
101	#6101	C₂×C₄	1	1	yes	characteristic
102	C₄×Dic₁₃	C₂×C₄	1	1	yes	characteristic
103	C₄×Dic₁₃	C₂×C₄	1	1	yes	characteristic
104	C₄×Dic₁₃	C₂³	1	1	yes	characteristic
105	#6099	—	4	1	no	—
106	C₂×#1055	—	4	1	no	—
107	C₂×#1055	C₂³	1	1	yes	characteristic
108	C₂×#1055	C₂³	1	1	yes	characteristic
109	C₂×#1055	C₂³	1	1	yes	characteristic
110	C₂×#1055	C₂³	1	1	yes	characteristic
111	#6094	—	4	1	no	—
112	#6094	—	4	1	no	—
113	C₈×D₁₃	—	4	1	no	—
114	C₈×D₁₃	—	4	1	no	—
115	#2974	—	13	1	no	maximal, Sylow
116	C₂³×C₁₃	C₂²×C₄	1	1	yes	characteristic
117	C₂³×C₁₃	C₂²×C₄	1	1	yes	characteristic
118	C₂²×D₁₃	—	2	2	no	—
119	C₂²×D₁₃	—	2	2	no	—
120	C₂²×D₁₃	—	2	2	no	—
121	C₂²×D₁₃	—	2	2	no	—
122	C₂²×D₁₃	—	4	1	no	—
123	C₂²×D₁₃	—	4	1	no	—
124	C₂²×D₁₃	C₂²×C₄	1	1	yes	characteristic
125	C₂²×D₁₃	C₂²×C₄	1	1	yes	characteristic
126	C₂²×D₁₃	C₂²×C₄	1	1	yes	characteristic
127	D₄×C₁₃	—	2	2	no	—
128	C₂×C₄×C₁₃	—	2	1	no	—
129	C₂×C₄×C₁₃	—	2	1	no	—
130	C₂×C₄×C₁₃	—	2	1	no	—
131	C₂×C₄×C₁₃	—	2	1	no	—
132	C₂×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
133	C₂×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
134	C₂×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
135	C₂×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
136	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
137	C₂²⋊D₁₃	—	2	2	no	—
138	C₂²⋊D₁₃	M₁₆	1	4	yes	complemented
139	C₂×Dic₁₃	—	4	1	no	—
140	C₂×Dic₁₃	—	4	1	no	—
141	C₂×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
142	C₂×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
143	C₂×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
144	C₂×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
145	C₂×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
146	D₅₂	—	2	2	no	—
147	C₄×D₁₃	—	2	2	no	—
148	C₄×D₁₃	—	2	1	no	—
149	C₄×D₁₃	—	2	1	no	—
150	C₄×D₁₃	—	2	1	no	—
151	C₄×D₁₃	—	2	1	no	—
152	C₄×D₁₃	—	2	1	no	—
153	C₄×D₁₃	—	2	1	no	—
154	C₄×D₁₃	—	2	2	no	—
155	C₄×D₁₃	—	4	1	no	—
156	C₄×D₁₃	—	4	1	no	—
157	C₄×D₁₃	—	4	1	no	—
158	C₄×D₁₃	—	4	1	no	—
159	C₈×C₁₃	—	2	1	no	—
160	C₈×C₁₃	—	2	1	no	—
161	C₈×C₁₃	—	2	1	no	—
162	C₈×C₁₃	—	2	1	no	—
163	#1055	—	2	1	no	—
164	#1055	—	2	1	no	—
165	#1055	—	2	1	no	—
166	#1055	—	2	1	no	—
167	C₂×C₄×D₄	—	13	1	no	—
168	#436	—	13	1	no	—
169	#436	—	13	1	no	—
170	#435	—	13	1	no	—
171	#435	—	13	1	no	—
172	#435	—	13	1	no	—
173	#435	D₁₃	1	1	yes	characteristic, complemented
174	C₈×D₄	—	13	1	no	—
175	C₈×D₄	—	13	1	no	—
176	#432	—	13	1	no	—
177	#431	—	13	1	no	—
178	#407	—	13	1	no	—
179	#407	—	13	1	no	—
180	C₂×C₂²⋊C₈	—	13	1	no	—
181	C₂×C₂²⋊C₈	—	13	1	no	—
182	C₂²×C₁₃	—	2	1	no	—
183	C₂²×C₁₃	—	2	1	no	—
184	C₂²×C₁₃	—	2	1	no	—
185	C₂²×C₁₃	—	2	1	no	—
186	C₂²×C₁₃	—	2	1	no	—
187	C₂²×C₁₃	C₂×M₁₆	1	2	yes	—
188	C₂²×C₁₃	C₂³×C₄	1	1	yes	characteristic
189	C₂×D₁₃	—	2	1	no	—
190	C₂×D₁₃	—	2	1	no	—
191	C₂×D₁₃	—	2	1	no	—
192	C₂×D₁₃	—	2	1	no	—
193	C₂×D₁₃	—	2	1	no	—
194	C₂×D₁₃	—	2	1	no	—
195	C₂×D₁₃	—	2	1	no	—
196	C₂×D₁₃	—	4	4	no	—
197	C₂×D₁₃	—	4	4	no	—
198	C₂×D₁₃	C₂×M₁₆	1	2	yes	—
199	C₂×D₁₃	#131	1	2	yes	—
200	C₄×C₁₃	—	2	1	no	—
201	C₄×C₁₃	—	2	1	no	—
202	C₄×C₁₃	—	2	1	no	—
203	C₄×C₁₃	—	2	1	no	—
204	C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
205	C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
206	Dic₁₃	—	2	1	no	—
207	Dic₁₃	—	2	1	no	—
208	Dic₁₃	—	2	1	no	—
209	Dic₁₃	—	2	1	no	—
210	Dic₁₃	C₂×M₁₆	1	2	yes	—
211	C₂²×D₄	—	13	1	no	—
212	C₂³×C₄	—	13	1	no	—
213	C₂³×C₄	—	13	1	no	—
214	C₂×M₁₆	—	13	1	no	—
215	C₂×M₁₆	—	13	1	no	—
216	C₂×M₁₆	—	13	1	no	—
217	C₂×M₁₆	C₂×D₁₃	1	1	yes	characteristic, complemented
218	C₂²×C₈	—	13	1	no	—
219	C₂²×C₈	—	13	1	no	—
220	C₂²×C₈	—	13	1	no	—
221	C₂²×C₈	C₂×D₁₃	1	1	yes	characteristic, complemented
222	C₄×D₄	—	13	1	no	—
223	C₄×D₄	—	13	1	no	—
224	C₄×D₄	—	13	1	no	—
225	C₄×D₄	—	13	1	no	—
226	C₄×D₄	—	13	1	no	—
227	C₄×D₄	—	13	1	no	—
228	C₄×D₄	—	13	1	no	—
229	C₄×D₄	C₂×D₁₃	1	1	yes	characteristic
230	C₂×C₄⋊C₄	—	13	1	no	—
231	C₂×C₂²⋊C₄	—	13	1	no	—
232	C₂×C₂²⋊C₄	—	13	1	no	—
233	C₂×C₄²	—	13	1	no	—
234	C₄⋊C₈	—	13	1	no	—
235	C₄⋊C₈	—	13	1	no	—
236	C₄⋊C₈	—	13	1	no	—
237	C₄⋊C₈	C₂×D₁₃	1	1	yes	characteristic, complemented
238	C₂²⋊C₈	—	13	1	no	—
239	C₂²⋊C₈	—	13	1	no	—
240	C₂²⋊C₈	—	13	1	no	—
241	C₂²⋊C₈	—	13	1	no	—
242	C₂²⋊C₈	—	13	1	no	—
243	C₂²⋊C₈	—	13	1	no	—
244	C₂²⋊C₈	—	13	1	no	—
245	C₂²⋊C₈	—	13	1	no	—
246	C₂²⋊C₈	—	13	1	no	—
247	C₂²⋊C₈	—	13	1	no	—
248	C₂²⋊C₈	C₂×D₁₃	1	1	yes	characteristic, complemented
249	C₂²⋊C₈	C₂×D₁₃	1	1	yes	characteristic, complemented
250	#97	—	13	1	no	—
251	#97	C₂×D₁₃	1	1	yes	characteristic, complemented
252	C₄×C₈	—	13	1	no	—
253	C₄×C₈	—	13	1	no	—
254	C₂×C₁₃	—	2	2	no	—
255	C₂×C₁₃	—	4	1	no	—
256	C₂×C₁₃	#518	1	1	yes	characteristic
257	C₂×C₁₃	C₂²×M₁₆	1	1	yes	characteristic
258	C₂×C₁₃	C₂×#131	1	1	yes	characteristic
259	D₁₃	—	2	2	no	—
260	D₁₃	—	2	2	no	—
261	D₁₃	—	4	1	no	—
262	C₂⁴	—	13	1	no	—
263	C₂⁴	—	13	1	no	—
264	C₂×D₄	—	13	1	no	—
265	C₂×D₄	—	13	1	no	—
266	C₂×D₄	—	13	1	no	—
267	C₂×D₄	—	26	4	no	—
268	C₂×D₄	C₄×D₁₃	1	1	yes	characteristic
269	C₂²×C₄	—	13	1	no	—
270	C₂²×C₄	—	13	1	no	—
271	C₂²×C₄	—	13	1	no	—
272	C₂²×C₄	—	13	1	no	—
273	C₂²×C₄	—	13	1	no	—
274	C₂²×C₄	—	13	1	no	—
275	C₂²×C₄	—	13	1	no	—
276	C₂²×C₄	—	13	1	no	—
277	C₂²×C₄	—	13	1	no	—
278	C₂²×C₄	—	13	1	no	—
279	C₂²×C₄	—	13	1	no	—
280	C₂²×C₄	—	52	1	no	—
281	C₂²×C₄	—	52	1	no	—
282	C₂²×C₄	—	52	1	no	—
283	C₂²×C₄	—	52	1	no	—
284	C₂²×C₄	C₂²×D₁₃	1	1	yes	characteristic
285	C₂²×C₄	C₂²×D₁₃	1	1	yes	characteristic
286	M₁₆	—	4	1	no	—
287	M₁₆	—	52	1	no	—
288	M₁₆	—	52	1	no	—
289	M₁₆	—	52	1	no	—
290	C₂×C₈	—	4	1	no	—
291	C₂×C₈	—	13	1	no	—
292	C₂×C₈	—	13	1	no	—
293	C₂×C₈	—	13	1	no	—
294	C₂×C₈	—	13	1	no	—
295	C₂×C₈	—	52	1	no	—
296	C₂×C₈	—	52	1	no	—
297	C₂×C₈	—	52	1	no	—
298	C₂×C₈	C₂²×D₁₃	1	1	yes	characteristic
299	C₂×C₈	C₂²×D₁₃	1	1	yes	characteristic
300	C₂×C₈	C₂²×D₁₃	1	1	yes	characteristic
301	C₂×C₈	C₂²×D₁₃	1	1	yes	characteristic
302	C₄⋊C₄	—	13	1	no	—
303	C₄⋊C₄	—	13	1	no	—
304	C₄⋊C₄	—	13	1	no	—
305	C₄⋊C₄	C₄×D₁₃	1	1	yes	characteristic
306	C₂²⋊C₄	—	13	1	no	—
307	C₂²⋊C₄	—	13	1	no	—
308	C₂²⋊C₄	—	13	1	no	—
309	C₂²⋊C₄	—	13	1	no	—
310	C₂²⋊C₄	—	13	1	no	—
311	C₂²⋊C₄	—	13	1	no	—
312	C₂²⋊C₄	C₄×D₁₃	1	1	yes	characteristic
313	C₂²⋊C₄	C₄×D₁₃	1	1	yes	characteristic
314	C₄²	—	13	1	no	—
315	C₄²	—	13	1	no	—
316	C₄²	—	13	1	no	—
317	C₄²	C₂²×D₁₃	1	1	yes	characteristic
318	C₁₃	#2974	1	1	yes	characteristic, complemented, Sylow
319	C₂³	—	13	1	no	—
320	C₂³	—	13	1	no	—
321	C₂³	—	13	1	no	—
322	C₂³	—	26	2	no	—
323	C₂³	—	26	2	no	—
324	C₂³	—	26	2	no	—
325	C₂³	—	26	2	no	—
326	C₂³	—	52	1	no	—
327	C₂³	—	52	1	no	—
328	C₂³	C₂×C₄×D₁₃	1	1	yes	characteristic
329	C₂³	C₂×C₄×D₁₃	1	1	yes	characteristic
330	D₄	—	2	2	no	—
331	D₄	—	13	4	no	—
332	D₄	—	26	2	no	—
333	D₄	—	26	2	no	—
334	C₂×C₄	—	2	1	no	—
335	C₂×C₄	—	2	1	no	—
336	C₂×C₄	—	2	1	no	—
337	C₂×C₄	—	2	1	no	—
338	C₂×C₄	—	13	1	no	—
339	C₂×C₄	—	13	1	no	—
340	C₂×C₄	—	13	1	no	—
341	C₂×C₄	—	13	1	no	—
342	C₂×C₄	—	13	1	no	—
343	C₂×C₄	—	26	2	no	—
344	C₂×C₄	—	26	2	no	—
345	C₂×C₄	—	26	1	no	—
346	C₂×C₄	—	26	1	no	—
347	C₂×C₄	—	26	1	no	—
348	C₂×C₄	—	26	1	no	—
349	C₂×C₄	—	26	1	no	—
350	C₂×C₄	—	26	1	no	—
351	C₂×C₄	—	52	1	no	—
352	C₂×C₄	—	52	1	no	—
353	C₂×C₄	—	52	1	no	—
354	C₂×C₄	—	52	1	no	—
355	C₂×C₄	—	52	1	no	—
356	C₂×C₄	—	52	1	no	—
357	C₂×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
358	C₂×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
359	C₂×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
360	C₂×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
361	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
362	C₈	—	2	1	no	—
363	C₈	—	2	1	no	—
364	C₈	—	2	1	no	—
365	C₈	—	2	1	no	—
366	C₈	—	26	1	no	—
367	C₈	—	26	1	no	—
368	C₈	—	26	1	no	—
369	C₈	—	26	1	no	—
370	C₂²	—	2	1	no	—
371	C₂²	—	2	1	no	—
372	C₂²	—	2	1	no	—
373	C₂²	—	2	1	no	—
374	C₂²	—	2	1	no	—
375	C₂²	—	13	2	no	—
376	C₂²	—	13	2	no	—
377	C₂²	—	26	1	no	—
378	C₂²	—	26	1	no	—
379	C₂²	—	26	1	no	—
380	C₂²	—	26	1	no	—
381	C₂²	—	26	1	no	—
382	C₂²	—	26	1	no	—
383	C₂²	—	26	1	no	—
384	C₂²	—	52	4	no	—
385	C₂²	—	52	4	no	—
386	C₂²	M₁₆×D₁₃	1	2	yes	—
387	C₂²	C₂²×C₄×D₁₃	1	1	yes	characteristic
388	C₄	—	2	1	no	—
389	C₄	—	2	1	no	—
390	C₄	—	2	1	no	—
391	C₄	—	2	1	no	—
392	C₄	—	13	2	no	—
393	C₄	—	26	1	no	—
394	C₄	—	26	1	no	—
395	C₄	—	26	1	no	—
396	C₄	—	26	1	no	—
397	C₄	#88251	1	1	yes	characteristic
398	C₄	#88256	1	1	yes	characteristic
399	C₂	—	2	2	no	—
400	C₂	—	4	1	no	—
401	C₂	—	26	2	no	—
402	C₂	—	26	2	no	—
403	C₂	—	52	1	no	—
404	C₂	#11719250	1	1	yes	characteristic
405	C₂	C₂×M₁₆×D₁₃	1	1	yes	characteristic
406	C₂	D₁₃×#131	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂³×D₁₃
commutator, socle	C₂²×C₁₃	C₂³×C₄
Fitting	C₁₃×#435	C₂
prime radical	C₂×D₄×D₁₃	C₄
cosocle	C₂×C₄×C₁₃	C₂⁴
hypercenter	#435	D₁₃
hypocenter	C₁₃	#2974
LCS	G ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₄ ◁ #435

Complements

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

N	H ≅ G/N	type
2. C₁₃×#435	C₂	semidirect
3. #11718789	C₂	semidirect
4. #11718787	C₂	semidirect
5. C₈×C₂²⋊D₁₃	C₂	semidirect
6. C₂×#88060	C₂	semidirect
7. #11718672	C₂	semidirect
8. #11718497	C₂	semidirect
9. #11718494	C₂	semidirect
10. #11718390	C₂	semidirect
11. #11718387	C₂	semidirect
12. #11718386	C₂	semidirect
13. D₁₃×C₂²⋊C₈	C₂	semidirect
14. #11718367	C₂	semidirect
15. #11718366	C₂	semidirect
19. C₂×C₁₃×M₁₆	C₂²	semidirect
20. C₂²×C₈×C₁₃	C₂²	semidirect
25. C₂×#6099	C₂²	semidirect
26. C₂²×#1055	C₂²	semidirect
27. C₂×#6094	C₂²	semidirect
28. C₂×#6094	C₂²	semidirect
29. C₂×C₈×D₁₃	C₂²	semidirect
30. C₂×C₈×D₁₃	C₂²	semidirect
39. C₁₃×C₄⋊C₈	C₂²	semidirect
40. C₁₃×C₂²⋊C₈	C₂²	semidirect
41. C₁₃×C₂²⋊C₈	C₂²	semidirect
42. C₁₃×#97	C₂²	semidirect
43. C₂²⋊#1055	C₂²	semidirect
44. C₂²⋊#1055	C₂²	semidirect
49. #88060	C₂²	semidirect
50. #88060	C₂²	semidirect
51. #88060	C₂²	semidirect
52. #88060	C₂²	semidirect
53. #88054	C₂²	semidirect
54. #88054	C₂²	semidirect
55. C₈×Dic₁₃	C₂²	semidirect
56. C₈×Dic₁₃	C₂²	semidirect
57. C₄⋊#1055	C₂²	semidirect
58. #88043	C₂²	semidirect
138. C₂²⋊D₁₃	M₁₆	semidirect
173. #435	D₁₃	semidirect
217. C₂×M₁₆	C₂×D₁₃	semidirect
221. C₂²×C₈	C₂×D₁₃	semidirect
237. C₄⋊C₈	C₂×D₁₃	semidirect
248. C₂²⋊C₈	C₂×D₁₃	semidirect
249. C₂²⋊C₈	C₂×D₁₃	semidirect
251. #97	C₂×D₁₃	semidirect
318. C₁₃	#2974	semidirect

Maximal subgroups

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

subgroup	index
C₄×D₄×D₁₃	2
C₁₃×#435	2
#11718789	2
#11718787	2
C₈×C₂²⋊D₁₃	2
C₂×#88060	2
#11718672	2
#11718497	2
#11718494	2
#11718390	2
#11718387	2
#11718386	2
D₁₃×C₂²⋊C₈	2
#11718367	2
#11718366	2
#2974	13