Subgroups — #16792674

Order 3328.

836 conjugacy classes of subgroups.

The subgroup lattice has 424 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₁₃⋊#431	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×#6118	C₂	1	1	yes	maximal, characteristic
3	#13130054	C₂	1	4	yes	maximal, complemented
4	#13130048	C₂	1	2	yes	maximal, complemented
5	#13130043	C₂	1	2	yes	maximal, complemented
6	#13130038	C₂	1	2	yes	maximal, complemented
7	M₁₆×#1057	C₂	1	2	yes	maximal, complemented
8	#13123468	C₂	1	1	yes	maximal, characteristic
9	C₂²×#6118	C₄	1	2	yes	—
10	C₂×C₄²×D₁₃	C₂²	1	1	yes	characteristic
11	#11719125	C₄	1	2	yes	—
12	D₁₃⋊(C₂²⋊C₈)	C₄	1	2	yes	—
13	C₂×#88110	C₄	1	2	yes	—
14	#11719119	C₂²	1	1	yes	characteristic
15	#11719119	C₂²	1	1	yes	characteristic
16	C₂×C₄×#1057	C₂²	1	2	yes	—
17	#11719051	C₄	1	2	yes	—
18	D₁₃⋊(C₄⋊C₈)	C₄	1	2	yes	—
19	#11719049	C₂²	1	2	yes	—
20	C₄×#6118	C₄	1	2	yes	—
21	C₄×#6118	C₄	1	2	yes	—
22	C₄×#6118	C₂²	1	1	yes	characteristic
23	C₄×#6118	C₂²	1	1	yes	characteristic
24	C₄×#6118	C₂²	1	2	yes	—
25	C₄×D₁₃⋊C₈	C₂²	1	2	yes	—
26	C₁₃×#423	C₄	1	1	yes	characteristic
27	#11718787	C₄	1	2	yes	—
28	M₁₆×Dic₁₃	C₂²	1	2	yes	—
29	#11718585	C₄	1	1	yes	characteristic
30	#11718496	C₄	1	2	yes	—
31	#11718496	C₄	1	2	yes	—
32	#11718494	C₂²	1	2	yes	—
33	#11718494	C₂²	1	2	yes	—
34	#1057⋊C₈	C₂²	1	4	yes	complemented
35	#1057⋊C₈	C₂²	1	4	yes	complemented
36	#11718251	C₂²	1	4	yes	complemented
37	C₈×#1057	C₂²	1	4	yes	complemented
38	C₂²×C₄×D₁₃	C₂×C₄	1	1	yes	characteristic
39	C₂²×C₄×D₁₃	C₂×C₄	1	1	yes	characteristic
40	C₂²×C₄×D₁₃	C₂×C₄	1	1	yes	characteristic
41	C₂²×#1057	C₂×C₄	1	4	yes	—
42	C₂×#6118	—	2	8	no	—
43	C₂×#6118	C₂×C₄	1	2	yes	—
44	C₂×#6118	C₂×C₄	1	4	yes	—
45	C₂×#6118	C₂×C₄	1	2	yes	—
46	C₂×D₁₃⋊C₈	C₂×C₄	1	4	yes	—
47	C₂×C₁₃×M₁₆	C₂×C₄	1	2	yes	—
48	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
49	C₂×C₄×Dic₁₃	C₂×C₄	1	1	yes	characteristic
50	C₂×C₄×Dic₁₃	C₂×C₄	1	1	yes	characteristic
51	C₂×C₄×Dic₁₃	C₂³	1	1	yes	characteristic
52	C₂×#6099	C₂×C₄	1	2	yes	—
53	C₄²×D₁₃	C₂×C₄	1	1	yes	characteristic
54	C₄²×D₁₃	C₂×C₄	1	1	yes	characteristic
55	C₄²×D₁₃	C₂×C₄	1	1	yes	characteristic
56	C₄²×D₁₃	C₂×C₄	1	1	yes	characteristic
57	C₄²×D₁₃	C₂×C₄	1	1	yes	characteristic
58	C₄²×D₁₃	C₂×C₄	1	1	yes	characteristic
59	C₄²×D₁₃	C₂³	1	1	yes	characteristic
60	C₄²×D₁₃	C₂³	1	1	yes	characteristic
61	C₂²⋊#1057	C₂×C₄	1	2	yes	—
62	C₂²⋊#1057	C₂×C₄	1	2	yes	—
63	#88112	C₂×C₄	1	4	yes	—
64	#88111	C₂×C₄	1	4	yes	—
65	#88110	C₂×C₄	1	2	yes	—
66	#88110	C₂×C₄	1	4	yes	—
67	#88110	C₂×C₄	1	2	yes	—
68	C₄⋊#1057	C₂×C₄	1	2	yes	—
69	C₄⋊#1057	C₂×C₄	1	2	yes	—
70	C₄×#1057	C₂×C₄	1	4	yes	—
71	C₄×#1057	C₂×C₄	1	4	yes	—
72	C₄×#1057	C₂³	1	2	yes	—
73	C₄×#1057	C₂³	1	2	yes	—
74	C₄×#1057	C₂³	1	2	yes	—
75	C₄×#1057	C₂³	1	2	yes	—
76	C₁₃×C₄⋊C₈	C₂×C₄	1	2	yes	—
77	C₁₃×C₄⋊C₈	C₂×C₄	1	2	yes	—
78	#88060	C₂×C₄	1	4	yes	—
79	#88060	C₂×C₄	1	4	yes	—
80	#88055	C₂×C₄	1	4	yes	—
81	C₈×Dic₁₃	C₂³	1	4	yes	—
82	C₄⋊#1055	C₂×C₄	1	2	yes	—
83	C₄⋊#1055	C₂×C₄	1	2	yes	—
84	#17327	—	13	1	no	maximal, Sylow
85	C₂³×D₁₃	C₄²	1	1	yes	characteristic
86	C₂²×C₄×C₁₃	C₄²	1	1	yes	characteristic
87	C₂²×C₄×C₁₃	C₄²	1	1	yes	characteristic
88	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
89	C₂²×Dic₁₃	C₄²	1	1	yes	characteristic
90	C₂²×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
91	C₂²×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
92	C₂×C₄×D₁₃	—	2	2	no	—
93	C₂×C₄×D₁₃	—	2	2	no	—
94	C₂×C₄×D₁₃	—	2	4	no	—
95	C₂×C₄×D₁₃	—	4	2	no	—
96	C₂×C₄×D₁₃	C₄²	1	1	yes	characteristic
97	C₂×C₄×D₁₃	C₄²	1	1	yes	characteristic
98	C₂×C₄×D₁₃	C₄²	1	1	yes	characteristic
99	C₂×C₄×D₁₃	C₄²	1	1	yes	characteristic
100	C₂×C₄×D₁₃	C₄²	1	1	yes	characteristic
101	C₂×C₄×D₁₃	C₄²	1	1	yes	characteristic
102	C₂×C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
103	C₂×C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
104	C₂×C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
105	C₂×C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
106	C₂×C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
107	C₂×C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
108	C₂×#1057	—	2	8	no	—
109	C₂×#1057	C₂²×C₄	1	4	yes	—
110	C₂×#1057	C₂²×C₄	1	4	yes	—
111	C₂×#1057	C₂²×C₄	1	4	yes	—
112	C₂×#1057	C₂²×C₄	1	4	yes	—
113	#6118	—	2	4	no	—
114	#6118	—	2	8	no	—
115	#6118	M₁₆	1	8	yes	complemented
116	D₁₃⋊C₈	—	4	4	no	—
117	C₁₃×M₁₆	—	2	4	no	—
118	C₂×C₈×C₁₃	C₂²×C₄	1	4	yes	—
119	C₄²×C₁₃	C₄²	1	1	yes	characteristic
120	C₄²×C₁₃	C₄²	1	1	yes	characteristic
121	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
122	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
123	C₄×Dic₁₃	C₄²	1	1	yes	characteristic
124	C₄×Dic₁₃	C₄²	1	1	yes	characteristic
125	C₄×Dic₁₃	C₄²	1	1	yes	characteristic
126	C₄×Dic₁₃	C₄²	1	1	yes	characteristic
127	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
128	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
129	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
130	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
131	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
132	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
133	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
134	C₄×Dic₁₃	C₂⁴	1	1	yes	characteristic
135	#6099	—	2	4	no	—
136	C₂×#1055	C₂²×C₄	1	4	yes	—
137	#2920	—	13	1	no	—
138	C₂×#431	—	13	1	no	—
139	C₂×C₄×M₁₆	—	13	1	no	—
140	#1453	—	13	4	no	—
141	#1451	—	13	2	no	—
142	#1451	—	13	2	no	—
143	C₈×M₁₆	—	13	2	no	—
144	C₈×M₁₆	—	13	2	no	—
145	C₂³×C₁₃	C₂×C₄²	1	1	yes	characteristic
146	C₂²×D₁₃	—	2	2	no	—
147	C₂²×D₁₃	—	2	2	no	—
148	C₂²×D₁₃	—	4	1	no	—
149	C₂²×D₁₃	C₂×C₄²	1	1	yes	characteristic
150	C₂²×D₁₃	C₂×C₄²	1	1	yes	characteristic
151	C₂×C₄×C₁₃	—	2	2	no	—
152	C₂×C₄×C₁₃	—	4	1	no	—
153	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
154	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
155	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
156	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
157	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
158	C₂×C₄×C₁₃	#131	1	2	yes	—
159	C₂×C₄×C₁₃	#131	1	2	yes	—
160	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
161	C₂×Dic₁₃	—	2	2	no	—
162	C₂×Dic₁₃	—	2	2	no	—
163	C₂×Dic₁₃	—	2	2	no	—
164	C₂×Dic₁₃	C₂×C₄²	1	1	yes	characteristic
165	C₂×Dic₁₃	C₂×C₄²	1	1	yes	characteristic
166	C₂×Dic₁₃	C₂×C₄²	1	1	yes	characteristic
167	C₂×Dic₁₃	C₂×C₄²	1	1	yes	characteristic
168	C₂×Dic₁₃	C₂³×C₄	1	1	yes	characteristic
169	C₂×Dic₁₃	C₂³×C₄	1	1	yes	characteristic
170	C₄×D₁₃	—	2	2	no	—
171	C₄×D₁₃	—	2	1	no	—
172	C₄×D₁₃	—	2	1	no	—
173	C₄×D₁₃	—	2	1	no	—
174	C₄×D₁₃	—	2	1	no	—
175	C₄×D₁₃	—	2	2	no	—
176	C₄×D₁₃	—	2	2	no	—
177	C₄×D₁₃	—	2	2	no	—
178	C₄×D₁₃	—	2	2	no	—
179	C₄×D₁₃	—	2	2	no	—
180	C₄×D₁₃	—	2	2	no	—
181	C₄×D₁₃	—	4	1	no	—
182	C₄×D₁₃	—	4	1	no	—
183	C₄×D₁₃	C₂×M₁₆	1	4	yes	—
184	#1057	—	2	4	no	—
185	#1057	—	2	4	no	—
186	#1057	—	2	4	no	—
187	#1057	C₂×M₁₆	1	8	yes	—
188	C₈×C₁₃	—	2	4	no	—
189	#1055	—	2	4	no	—
190	C₂²×M₁₆	—	13	2	no	—
191	C₂²×C₄²	—	13	1	no	—
192	#432	—	13	2	no	—
193	#432	—	13	2	no	—
194	#431	—	13	2	no	—
195	#431	—	13	2	no	—
196	#431	—	13	1	no	—
197	#431	—	13	1	no	—
198	#431	—	13	2	no	—
199	#431	—	13	2	no	—
200	#431	—	13	2	no	—
201	#423	—	13	1	no	—
202	#423	#261	1	1	yes	characteristic
203	C₂×C₄⋊C₈	—	13	2	no	—
204	#407	—	13	2	no	—
205	C₂×C₂²⋊C₈	—	13	2	no	—
206	C₄×M₁₆	—	13	2	no	—
207	C₄×M₁₆	—	13	2	no	—
208	C₄×M₁₆	—	13	1	no	—
209	C₄×M₁₆	—	13	1	no	—
210	C₄×M₁₆	—	13	2	no	—
211	C₄×M₁₆	—	13	2	no	—
212	C₂×#97	—	13	2	no	—
213	C₂×C₄×C₈	—	13	2	no	—
214	C₂×C₄×C₈	—	13	2	no	—
215	#322	—	13	4	no	—
216	#322	—	13	4	no	—
217	#322	—	13	4	no	—
218	C₈²	—	13	4	no	—
219	C₂²×C₁₃	—	2	1	no	—
220	C₂²×C₁₃	—	2	1	no	—
221	C₂²×C₁₃	#405	1	2	yes	—
222	C₂²×C₁₃	C₂²×C₄²	1	1	yes	characteristic
223	C₂×D₁₃	—	2	1	no	—
224	C₂×D₁₃	—	2	1	no	—
225	C₂×D₁₃	—	2	1	no	—
226	C₂×D₁₃	—	2	1	no	—
227	C₂×D₁₃	—	2	1	no	—
228	C₂×D₁₃	—	4	4	no	—
229	C₂×D₁₃	C₄×M₁₆	1	2	yes	—
230	C₄×C₁₃	—	2	1	no	—
231	C₄×C₁₃	—	2	1	no	—
232	C₄×C₁₃	—	2	1	no	—
233	C₄×C₁₃	C₄×M₁₆	1	2	yes	—
234	C₄×C₁₃	#405	1	2	yes	—
235	C₄×C₁₃	C₂×#131	1	1	yes	characteristic
236	C₄×C₁₃	C₂×#131	1	1	yes	characteristic
237	Dic₁₃	—	2	1	no	—
238	Dic₁₃	—	2	1	no	—
239	Dic₁₃	—	2	1	no	—
240	Dic₁₃	—	2	1	no	—
241	Dic₁₃	C₂²×M₁₆	1	2	yes	—
242	Dic₁₃	#568	1	2	yes	—
243	C₂³×C₄	—	13	1	no	—
244	C₂³×C₄	—	13	1	no	—
245	C₂³×C₄	—	13	1	no	—
246	C₂×M₁₆	—	13	2	no	—
247	C₂×M₁₆	—	13	4	no	—
248	C₂×M₁₆	—	13	2	no	—
249	C₂×M₁₆	—	13	2	no	—
250	C₂×M₁₆	—	26	8	no	—
251	C₂×M₁₆	C₂×#261	1	2	yes	—
252	C₂²×C₈	—	13	4	no	—
253	C₂²×C₈	—	13	4	no	—
254	C₂×C₄²	—	13	1	no	—
255	C₂×C₄²	—	13	1	no	—
256	C₂×C₄²	—	13	1	no	—
257	C₂×C₄²	—	13	1	no	—
258	C₂×C₄²	—	13	1	no	—
259	C₂×C₄²	—	13	1	no	—
260	C₂×C₄²	—	13	1	no	—
261	C₂×C₄²	—	13	1	no	—
262	C₂×C₄²	—	13	1	no	—
263	C₂×C₄²	—	13	1	no	—
264	C₂×C₄²	—	13	1	no	—
265	C₂×C₄²	C₂×#261	1	1	yes	characteristic
266	C₄⋊C₈	—	13	2	no	—
267	C₄⋊C₈	—	13	2	no	—
268	C₄⋊C₈	—	13	4	no	—
269	C₄⋊C₈	—	13	2	no	—
270	C₄⋊C₈	—	13	2	no	—
271	C₄⋊C₈	C₂×#261	1	2	yes	—
272	C₄⋊C₈	C₂×#261	1	2	yes	—
273	C₂²⋊C₈	—	13	4	no	—
274	C₂²⋊C₈	—	13	2	no	—
275	C₂²⋊C₈	—	13	2	no	—
276	C₂²⋊C₈	—	13	4	no	—
277	C₂²⋊C₈	—	13	4	no	—
278	#97	—	13	2	no	—
279	#97	—	13	4	no	—
280	#97	—	13	2	no	—
281	#97	—	13	4	no	—
282	C₄×C₈	—	13	4	no	—
283	C₄×C₈	—	13	4	no	—
284	C₄×C₈	—	13	2	no	—
285	C₄×C₈	—	13	2	no	—
286	C₄×C₈	—	13	2	no	—
287	C₄×C₈	—	13	2	no	—
288	C₄×C₈	—	13	4	no	—
289	C₂×C₁₃	—	2	2	no	—
290	C₂×C₁₃	C₂×C₄×M₁₆	1	1	yes	characteristic
291	C₂×C₁₃	C₂×#405	1	1	yes	characteristic
292	C₂×C₁₃	#2873	1	1	yes	characteristic
293	D₁₃	—	2	2	no	—
294	D₁₃	—	4	1	no	—
295	C₂⁴	—	13	1	no	—
296	C₂²×C₄	—	13	1	no	—
297	C₂²×C₄	—	13	1	no	—
298	C₂²×C₄	—	13	1	no	—
299	C₂²×C₄	—	13	1	no	—
300	C₂²×C₄	—	13	1	no	—
301	C₂²×C₄	—	13	1	no	—
302	C₂²×C₄	—	13	1	no	—
303	C₂²×C₄	—	13	1	no	—
304	C₂²×C₄	—	13	1	no	—
305	C₂²×C₄	—	13	1	no	—
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	—	26	4	no	—
312	C₂²×C₄	—	26	2	no	—
313	C₂²×C₄	—	26	2	no	—
314	C₂²×C₄	—	52	2	no	—
315	C₂²×C₄	C₄×#261	1	1	yes	characteristic
316	C₂²×C₄	C₄×#261	1	1	yes	characteristic
317	C₂²×C₄	C₂²×#261	1	1	yes	characteristic
318	M₁₆	—	2	4	no	—
319	M₁₆	—	13	8	no	—
320	M₁₆	—	26	8	no	—
321	M₁₆	—	26	4	no	—
322	M₁₆	—	26	4	no	—
323	C₂×C₈	—	13	4	no	—
324	C₂×C₈	—	13	4	no	—
325	C₂×C₈	—	13	4	no	—
326	C₂×C₈	—	13	4	no	—
327	C₂×C₈	—	13	4	no	—
328	C₂×C₈	—	26	8	no	—
329	C₂×C₈	—	52	4	no	—
330	C₂×C₈	C₂²×#261	1	4	yes	—
331	C₄²	—	13	1	no	—
332	C₄²	—	13	1	no	—
333	C₄²	—	13	1	no	—
334	C₄²	—	13	1	no	—
335	C₄²	—	13	1	no	—
336	C₄²	—	13	1	no	—
337	C₄²	—	13	1	no	—
338	C₄²	—	13	1	no	—
339	C₄²	—	13	1	no	—
340	C₄²	—	13	1	no	—
341	C₄²	—	13	1	no	—
342	C₄²	—	13	1	no	—
343	C₄²	C₄×#261	1	1	yes	characteristic
344	C₄²	C₄×#261	1	1	yes	characteristic
345	C₄²	C₂²×#261	1	1	yes	characteristic
346	C₄²	C₂²×#261	1	1	yes	characteristic
347	C₁₃	#17327	1	1	yes	characteristic, complemented, Sylow
348	C₂³	—	13	1	no	—
349	C₂³	—	13	1	no	—
350	C₂³	—	26	2	no	—
351	C₂³	—	26	2	no	—
352	C₂³	—	52	1	no	—
353	C₂³	C₂×C₄×#261	1	1	yes	characteristic
354	C₂×C₄	—	2	2	no	—
355	C₂×C₄	—	4	1	no	—
356	C₂×C₄	—	13	1	no	—
357	C₂×C₄	—	13	1	no	—
358	C₂×C₄	—	13	4	no	—
359	C₂×C₄	—	13	1	no	—
360	C₂×C₄	—	13	1	no	—
361	C₂×C₄	—	13	1	no	—
362	C₂×C₄	—	13	1	no	—
363	C₂×C₄	—	26	2	no	—
364	C₂×C₄	—	26	2	no	—
365	C₂×C₄	—	26	2	no	—
366	C₂×C₄	—	26	2	no	—
367	C₂×C₄	—	26	2	no	—
368	C₂×C₄	—	26	2	no	—
369	C₂×C₄	—	26	2	no	—
370	C₂×C₄	—	26	2	no	—
371	C₂×C₄	—	26	2	no	—
372	C₂×C₄	—	26	2	no	—
373	C₂×C₄	—	26	1	no	—
374	C₂×C₄	—	26	1	no	—
375	C₂×C₄	—	26	1	no	—
376	C₂×C₄	—	26	1	no	—
377	C₂×C₄	—	52	1	no	—
378	C₂×C₄	—	52	1	no	—
379	C₂×C₄	C₂×C₄×#261	1	1	yes	characteristic
380	C₂×C₄	C₂×C₄×#261	1	1	yes	characteristic
381	C₂×C₄	C₂×C₄×#261	1	1	yes	characteristic
382	C₂×C₄	C₂×C₄×#261	1	1	yes	characteristic
383	C₂×C₄	C₂×C₄×#261	1	1	yes	characteristic
384	C₂×C₄	#88238	1	2	yes	—
385	C₂×C₄	#88240	1	2	yes	—
386	C₂×C₄	C₂³×#261	1	1	yes	characteristic
387	C₈	—	2	4	no	—
388	C₈	—	13	8	no	—
389	C₈	—	26	4	no	—
390	C₈	—	26	4	no	—
391	C₈	—	26	4	no	—
392	C₈	—	26	4	no	—
393	C₂²	—	2	1	no	—
394	C₂²	—	2	1	no	—
395	C₂²	—	13	2	no	—
396	C₂²	—	26	1	no	—
397	C₂²	—	26	1	no	—
398	C₂²	—	26	1	no	—
399	C₂²	—	26	1	no	—
400	C₂²	—	26	1	no	—
401	C₂²	—	52	4	no	—
402	C₂²	#11719072	1	2	yes	—
403	C₂²	C₂²×C₄×#261	1	1	yes	characteristic
404	C₄	—	2	1	no	—
405	C₄	—	2	1	no	—
406	C₄	—	2	1	no	—
407	C₄	—	13	2	no	—
408	C₄	—	13	2	no	—
409	C₄	—	26	1	no	—
410	C₄	—	26	1	no	—
411	C₄	—	26	1	no	—
412	C₄	—	26	1	no	—
413	C₄	#11719072	1	2	yes	—
414	C₄	M₁₆×#261	1	2	yes	—
415	C₄	C₂×#88238	1	1	yes	characteristic
416	C₄	C₂×#88240	1	1	yes	characteristic
417	C₂	—	2	2	no	—
418	C₂	—	26	2	no	—
419	C₂	—	52	1	no	—
420	C₂	C₂×M₁₆×#261	1	1	yes	characteristic
421	C₂	C₂×#11719072	1	1	yes	characteristic
422	C₂	#13131399	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂³×#261
commutator, socle	C₂²×C₁₃	C₂²×C₄²
Fitting	C₁₃×#423	C₄
prime radical	C₂³×D₁₃	C₄²
cosocle	C₄×Dic₁₃	C₂⁴
hypercenter	#423	#261
hypocenter	C₁₃	#17327
LCS	G ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₄ ◁ #423

Complements

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

N	H ≅ G/N	type
3. #13130054	C₂	semidirect
4. #13130048	C₂	semidirect
5. #13130043	C₂	semidirect
6. #13130038	C₂	semidirect
7. M₁₆×#1057	C₂	semidirect
34. #1057⋊C₈	C₂²	semidirect
35. #1057⋊C₈	C₂²	semidirect
36. #11718251	C₂²	semidirect
37. C₈×#1057	C₂²	semidirect
115. #6118	M₁₆	semidirect
347. C₁₃	#17327	semidirect

Maximal subgroups

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

subgroup	index
D₁₃⋊#431	2
C₂×C₄×#6118	2
#13130054	2
#13130048	2
#13130043	2
#13130038	2
M₁₆×#1057	2
#13123468	2
#17327	13