Subgroups — #16792636

Order 3328.

874 conjugacy classes of subgroups.

The subgroup lattice has 442 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13131513	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×D₁₃⋊C₈	C₂	1	1	yes	maximal, characteristic
3	#13130052	C₂	1	2	yes	maximal, complemented
4	#13130048	C₂	1	2	yes	maximal, complemented
5	#13130043	C₂	1	2	yes	maximal, complemented
6	#13130042	C₂	1	2	yes	maximal, complemented
7	#13130038	C₂	1	2	yes	maximal, complemented
8	M₁₆×#1057	C₂	1	2	yes	maximal, complemented
9	#13123468	C₂	1	1	yes	maximal, characteristic
10	C₂²×D₁₃⋊C₈	C₄	1	2	yes	—
11	C₂×C₄²×D₁₃	C₂²	1	1	yes	characteristic
12	#11719130	C₄	1	2	yes	—
13	#11719127	C₄	1	2	yes	—
14	#11719119	C₂²	1	2	yes	—
15	C₂×C₄×#1057	C₄	1	2	yes	—
16	C₂×C₄×#1057	C₂²	1	1	yes	characteristic
17	C₂×C₄×#1057	C₂²	1	1	yes	characteristic
18	#11719054	C₄	1	2	yes	—
19	#11719052	C₄	1	2	yes	—
20	#11719051	C₂²	1	2	yes	—
21	C₄×#6118	C₂²	1	2	yes	—
22	C₄×D₁₃⋊C₈	C₄	1	2	yes	—
23	C₄×D₁₃⋊C₈	C₄	1	2	yes	—
24	C₄×D₁₃⋊C₈	C₂²	1	1	yes	characteristic
25	C₄×D₁₃⋊C₈	C₂²	1	1	yes	characteristic
26	C₄×D₁₃⋊C₈	C₂²	1	1	yes	characteristic
27	C₄×D₁₃⋊C₈	C₂²	1	1	yes	characteristic
28	C₁₃×#423	C₄	1	1	yes	characteristic
29	#11718787	C₄	1	2	yes	—
30	M₁₆×Dic₁₃	C₂²	1	2	yes	—
31	#11718585	C₄	1	1	yes	characteristic
32	#11718496	C₄	1	2	yes	—
33	#11718496	C₄	1	2	yes	—
34	#11718494	C₂²	1	2	yes	—
35	#11718494	C₂²	1	2	yes	—
36	#1057⋊C₈	C₂²	1	4	yes	complemented
37	#1057⋊C₈	C₂²	1	4	yes	complemented
38	#11718251	C₂²	1	4	yes	complemented
39	C₈×#1057	C₂²	1	4	yes	complemented
40	C₂²×C₄×D₁₃	C₂×C₄	1	1	yes	characteristic
41	C₂²×C₄×D₁₃	C₂×C₄	1	1	yes	characteristic
42	C₂²×C₄×D₁₃	C₂×C₄	1	1	yes	characteristic
43	C₂²×#1057	C₂×C₄	1	2	yes	—
44	C₂²×#1057	C₂×C₄	1	2	yes	—
45	C₂×#6118	C₂×C₄	1	4	yes	—
46	C₂×D₁₃⋊C₈	—	2	8	no	—
47	C₂×D₁₃⋊C₈	C₂×C₄	1	2	yes	—
48	C₂×D₁₃⋊C₈	C₂×C₄	1	2	yes	—
49	C₂×D₁₃⋊C₈	C₂×C₄	1	2	yes	—
50	C₂×D₁₃⋊C₈	C₂×C₄	1	2	yes	—
51	C₂×C₁₃×M₁₆	C₂×C₄	1	2	yes	—
52	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
53	C₂×C₄×Dic₁₃	C₂×C₄	1	1	yes	characteristic
54	C₂×C₄×Dic₁₃	C₂×C₄	1	1	yes	characteristic
55	C₂×C₄×Dic₁₃	C₂³	1	1	yes	characteristic
56	C₂×#6099	C₂×C₄	1	2	yes	—
57	C₄²×D₁₃	C₂×C₄	1	1	yes	characteristic
58	C₄²×D₁₃	C₂×C₄	1	1	yes	characteristic
59	C₄²×D₁₃	C₂×C₄	1	1	yes	characteristic
60	C₄²×D₁₃	C₂×C₄	1	1	yes	characteristic
61	C₄²×D₁₃	C₂×C₄	1	1	yes	characteristic
62	C₄²×D₁₃	C₂×C₄	1	1	yes	characteristic
63	C₄²×D₁₃	C₂³	1	1	yes	characteristic
64	C₄²×D₁₃	C₂³	1	1	yes	characteristic
65	C₂²⋊#1057	C₂×C₄	1	4	yes	—
66	#88111	C₂×C₄	1	4	yes	—
67	#88110	C₂×C₄	1	4	yes	—
68	C₄⋊#1057	C₂×C₄	1	4	yes	—
69	C₄⋊#1057	C₂×C₄	1	4	yes	—
70	C₄×#1057	C₂×C₄	1	2	yes	—
71	C₄×#1057	C₂×C₄	1	2	yes	—
72	C₄×#1057	C₂×C₄	1	2	yes	—
73	C₄×#1057	C₂×C₄	1	2	yes	—
74	C₄×#1057	C₂×C₄	1	2	yes	—
75	C₄×#1057	C₂×C₄	1	2	yes	—
76	C₄×#1057	C₂³	1	1	yes	characteristic
77	C₄×#1057	C₂³	1	4	yes	—
78	C₄×#1057	C₂³	1	1	yes	characteristic
79	C₄×#1057	C₂³	1	1	yes	characteristic
80	C₄×#1057	C₂³	1	1	yes	characteristic
81	C₁₃×C₄⋊C₈	C₂×C₄	1	2	yes	—
82	C₁₃×C₄⋊C₈	C₂×C₄	1	2	yes	—
83	#88060	C₂×C₄	1	4	yes	—
84	#88060	C₂×C₄	1	4	yes	—
85	#88055	C₂×C₄	1	4	yes	—
86	C₈×Dic₁₃	C₂³	1	4	yes	—
87	C₄⋊#1055	C₂×C₄	1	2	yes	—
88	C₄⋊#1055	C₂×C₄	1	2	yes	—
89	#17323	—	13	1	no	maximal, Sylow
90	C₂³×D₁₃	C₄²	1	1	yes	characteristic
91	C₂²×C₄×C₁₃	C₄²	1	1	yes	characteristic
92	C₂²×C₄×C₁₃	C₄²	1	1	yes	characteristic
93	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
94	C₂²×Dic₁₃	C₄²	1	1	yes	characteristic
95	C₂²×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
96	C₂²×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
97	C₂×C₄×D₁₃	—	2	2	no	—
98	C₂×C₄×D₁₃	—	2	2	no	—
99	C₂×C₄×D₁₃	—	2	4	no	—
100	C₂×C₄×D₁₃	—	2	4	no	—
101	C₂×C₄×D₁₃	C₄²	1	1	yes	characteristic
102	C₂×C₄×D₁₃	C₄²	1	1	yes	characteristic
103	C₂×C₄×D₁₃	C₄²	1	1	yes	characteristic
104	C₂×C₄×D₁₃	C₄²	1	1	yes	characteristic
105	C₂×C₄×D₁₃	C₄²	1	1	yes	characteristic
106	C₂×C₄×D₁₃	C₄²	1	1	yes	characteristic
107	C₂×C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
108	C₂×C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
109	C₂×C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
110	C₂×C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
111	C₂×C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
112	C₂×C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
113	C₂×#1057	—	2	4	no	—
114	C₂×#1057	—	2	4	no	—
115	C₂×#1057	C₂²×C₄	1	2	yes	—
116	C₂×#1057	C₂²×C₄	1	2	yes	—
117	C₂×#1057	C₂²×C₄	1	8	yes	—
118	C₂×#1057	C₂²×C₄	1	2	yes	—
119	C₂×#1057	C₂²×C₄	1	2	yes	—
120	#6118	—	2	8	no	—
121	D₁₃⋊C₈	—	2	4	no	—
122	D₁₃⋊C₈	—	2	4	no	—
123	D₁₃⋊C₈	—	2	4	no	—
124	D₁₃⋊C₈	M₁₆	1	8	yes	complemented
125	C₁₃×M₁₆	—	2	4	no	—
126	C₂×C₈×C₁₃	C₂²×C₄	1	4	yes	—
127	C₄²×C₁₃	C₄²	1	1	yes	characteristic
128	C₄²×C₁₃	C₄²	1	1	yes	characteristic
129	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
130	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
131	C₄×Dic₁₃	C₄²	1	1	yes	characteristic
132	C₄×Dic₁₃	C₄²	1	1	yes	characteristic
133	C₄×Dic₁₃	C₄²	1	1	yes	characteristic
134	C₄×Dic₁₃	C₄²	1	1	yes	characteristic
135	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
136	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
137	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
138	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
139	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
140	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
141	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
142	C₄×Dic₁₃	C₂⁴	1	1	yes	characteristic
143	#6099	—	2	4	no	—
144	C₂×#1055	C₂²×C₄	1	4	yes	—
145	#2920	—	13	1	no	—
146	#2920	—	13	1	no	—
147	C₂²×C₄×C₈	—	13	1	no	—
148	#1452	—	13	2	no	—
149	#1451	—	13	2	no	—
150	#1451	—	13	2	no	—
151	#1450	—	13	2	no	—
152	C₈×M₁₆	—	13	2	no	—
153	C₈×M₁₆	—	13	2	no	—
154	C₂³×C₁₃	C₂×C₄²	1	1	yes	characteristic
155	C₂²×D₁₃	—	2	2	no	—
156	C₂²×D₁₃	—	2	2	no	—
157	C₂²×D₁₃	—	2	2	no	—
158	C₂²×D₁₃	C₂×C₄²	1	1	yes	characteristic
159	C₂²×D₁₃	C₂×C₄²	1	1	yes	characteristic
160	C₂×C₄×C₁₃	—	2	2	no	—
161	C₂×C₄×C₁₃	—	2	2	no	—
162	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
163	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
164	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
165	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
166	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
167	C₂×C₄×C₁₃	#131	1	2	yes	—
168	C₂×C₄×C₁₃	#131	1	2	yes	—
169	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
170	C₂×Dic₁₃	—	2	2	no	—
171	C₂×Dic₁₃	—	2	2	no	—
172	C₂×Dic₁₃	—	2	2	no	—
173	C₂×Dic₁₃	C₂×C₄²	1	1	yes	characteristic
174	C₂×Dic₁₃	C₂×C₄²	1	1	yes	characteristic
175	C₂×Dic₁₃	C₂×C₄²	1	1	yes	characteristic
176	C₂×Dic₁₃	C₂×C₄²	1	1	yes	characteristic
177	C₂×Dic₁₃	C₂³×C₄	1	1	yes	characteristic
178	C₂×Dic₁₃	C₂³×C₄	1	1	yes	characteristic
179	C₄×D₁₃	—	2	2	no	—
180	C₄×D₁₃	—	2	2	no	—
181	C₄×D₁₃	—	2	1	no	—
182	C₄×D₁₃	—	2	1	no	—
183	C₄×D₁₃	—	2	1	no	—
184	C₄×D₁₃	—	2	1	no	—
185	C₄×D₁₃	—	2	2	no	—
186	C₄×D₁₃	—	2	2	no	—
187	C₄×D₁₃	—	2	2	no	—
188	C₄×D₁₃	—	2	2	no	—
189	C₄×D₁₃	—	2	2	no	—
190	C₄×D₁₃	—	2	2	no	—
191	C₄×D₁₃	C₂×M₁₆	1	4	yes	—
192	C₄×D₁₃	#131	1	4	yes	—
193	#1057	—	2	2	no	—
194	#1057	—	2	2	no	—
195	#1057	—	2	8	no	—
196	#1057	C₂×M₁₆	1	4	yes	—
197	#1057	C₂×M₁₆	1	4	yes	—
198	C₈×C₁₃	—	2	4	no	—
199	#1055	—	2	4	no	—
200	C₂³×C₈	—	13	2	no	—
201	C₂²×C₄²	—	13	1	no	—
202	#432	—	13	2	no	—
203	#432	—	13	2	no	—
204	#432	—	13	2	no	—
205	#432	—	13	2	no	—
206	#431	—	13	2	no	—
207	#431	—	13	2	no	—
208	#431	—	13	2	no	—
209	#431	—	13	2	no	—
210	#423	—	13	2	no	—
211	#423	—	13	1	no	—
212	#423	#261	1	1	yes	characteristic
213	#407	—	13	2	no	—
214	#407	—	13	2	no	—
215	C₄×M₁₆	—	13	2	no	—
216	C₄×M₁₆	—	13	2	no	—
217	C₂×C₄×C₈	—	13	2	no	—
218	C₂×C₄×C₈	—	13	2	no	—
219	C₂×C₄×C₈	—	13	1	no	—
220	C₂×C₄×C₈	—	13	1	no	—
221	C₂×C₄×C₈	—	13	1	no	—
222	C₂×C₄×C₈	—	13	1	no	—
223	C₂×C₄×C₈	—	13	1	no	—
224	C₂×C₄×C₈	—	13	1	no	—
225	C₂×C₄×C₈	—	13	2	no	—
226	#322	—	13	4	no	—
227	#322	—	13	4	no	—
228	#322	—	13	4	no	—
229	C₈²	—	13	4	no	—
230	C₂²×C₁₃	—	2	1	no	—
231	C₂²×C₁₃	—	2	1	no	—
232	C₂²×C₁₃	#405	1	2	yes	—
233	C₂²×C₁₃	C₂²×C₄²	1	1	yes	characteristic
234	C₂×D₁₃	—	2	8	no	—
235	C₂×D₁₃	—	2	1	no	—
236	C₂×D₁₃	—	2	1	no	—
237	C₂×D₁₃	—	2	1	no	—
238	C₂×D₁₃	—	2	1	no	—
239	C₂×D₁₃	C₄×M₁₆	1	2	yes	—
240	C₂×D₁₃	#405	1	2	yes	—
241	C₄×C₁₃	—	2	1	no	—
242	C₄×C₁₃	—	2	1	no	—
243	C₄×C₁₃	C₄×M₁₆	1	2	yes	—
244	C₄×C₁₃	#405	1	2	yes	—
245	C₄×C₁₃	#405	1	2	yes	—
246	C₄×C₁₃	C₂×#131	1	1	yes	characteristic
247	C₄×C₁₃	C₂×#131	1	1	yes	characteristic
248	Dic₁₃	—	2	1	no	—
249	Dic₁₃	—	2	1	no	—
250	Dic₁₃	—	2	1	no	—
251	Dic₁₃	—	2	1	no	—
252	Dic₁₃	C₂²×M₁₆	1	2	yes	—
253	Dic₁₃	C₂×#131	1	2	yes	—
254	C₂³×C₄	—	13	1	no	—
255	C₂³×C₄	—	13	1	no	—
256	C₂³×C₄	—	13	1	no	—
257	C₂×M₁₆	—	13	4	no	—
258	C₂×M₁₆	—	13	2	no	—
259	C₂×M₁₆	C₂×#261	1	2	yes	—
260	C₂²×C₈	—	13	2	no	—
261	C₂²×C₈	—	13	2	no	—
262	C₂²×C₈	—	13	2	no	—
263	C₂²×C₈	—	13	2	no	—
264	C₂²×C₈	—	13	2	no	—
265	C₂²×C₈	—	13	2	no	—
266	C₂²×C₈	—	26	8	no	—
267	C₂×C₄²	—	13	1	no	—
268	C₂×C₄²	—	13	1	no	—
269	C₂×C₄²	—	13	1	no	—
270	C₂×C₄²	—	13	1	no	—
271	C₂×C₄²	—	13	1	no	—
272	C₂×C₄²	—	13	1	no	—
273	C₂×C₄²	—	13	1	no	—
274	C₂×C₄²	—	13	1	no	—
275	C₂×C₄²	—	13	1	no	—
276	C₂×C₄²	—	13	1	no	—
277	C₂×C₄²	—	13	1	no	—
278	C₂×C₄²	C₂×#261	1	1	yes	characteristic
279	C₄⋊C₈	—	13	4	no	—
280	C₄⋊C₈	—	13	4	no	—
281	C₄⋊C₈	—	13	2	no	—
282	C₄⋊C₈	—	13	2	no	—
283	C₄⋊C₈	C₂×#261	1	2	yes	—
284	C₄⋊C₈	C₂×#261	1	2	yes	—
285	C₂²⋊C₈	—	13	4	no	—
286	C₂²⋊C₈	—	13	4	no	—
287	C₂²⋊C₈	—	13	4	no	—
288	C₂²⋊C₈	—	13	4	no	—
289	#97	—	13	4	no	—
290	#97	—	13	4	no	—
291	C₄×C₈	—	13	2	no	—
292	C₄×C₈	—	13	2	no	—
293	C₄×C₈	—	13	2	no	—
294	C₄×C₈	—	13	2	no	—
295	C₄×C₈	—	13	2	no	—
296	C₄×C₈	—	13	2	no	—
297	C₄×C₈	—	13	1	no	—
298	C₄×C₈	—	13	4	no	—
299	C₄×C₈	—	13	1	no	—
300	C₄×C₈	—	13	1	no	—
301	C₄×C₈	—	13	1	no	—
302	C₄×C₈	—	13	4	no	—
303	C₂×C₁₃	—	2	2	no	—
304	C₂×C₁₃	C₂×C₄×M₁₆	1	1	yes	characteristic
305	C₂×C₁₃	C₂×#405	1	1	yes	characteristic
306	C₂×C₁₃	C₂×#405	1	1	yes	characteristic
307	D₁₃	—	2	2	no	—
308	D₁₃	—	2	2	no	—
309	C₂⁴	—	13	1	no	—
310	C₂²×C₄	—	13	1	no	—
311	C₂²×C₄	—	13	1	no	—
312	C₂²×C₄	—	13	1	no	—
313	C₂²×C₄	—	13	1	no	—
314	C₂²×C₄	—	13	1	no	—
315	C₂²×C₄	—	13	1	no	—
316	C₂²×C₄	—	13	1	no	—
317	C₂²×C₄	—	13	1	no	—
318	C₂²×C₄	—	13	1	no	—
319	C₂²×C₄	—	13	1	no	—
320	C₂²×C₄	—	13	1	no	—
321	C₂²×C₄	—	13	1	no	—
322	C₂²×C₄	—	13	1	no	—
323	C₂²×C₄	—	13	1	no	—
324	C₂²×C₄	—	13	1	no	—
325	C₂²×C₄	—	26	4	no	—
326	C₂²×C₄	—	26	4	no	—
327	C₂²×C₄	—	26	2	no	—
328	C₂²×C₄	—	26	2	no	—
329	C₂²×C₄	C₄×#261	1	1	yes	characteristic
330	C₂²×C₄	C₄×#261	1	1	yes	characteristic
331	C₂²×C₄	C₂²×#261	1	1	yes	characteristic
332	M₁₆	—	2	4	no	—
333	M₁₆	—	26	8	no	—
334	M₁₆	—	26	4	no	—
335	C₂×C₈	—	13	2	no	—
336	C₂×C₈	—	13	2	no	—
337	C₂×C₈	—	13	8	no	—
338	C₂×C₈	—	13	2	no	—
339	C₂×C₈	—	13	2	no	—
340	C₂×C₈	—	13	8	no	—
341	C₂×C₈	—	13	4	no	—
342	C₂×C₈	—	26	4	no	—
343	C₂×C₈	—	26	4	no	—
344	C₂×C₈	—	26	4	no	—
345	C₂×C₈	—	26	4	no	—
346	C₂×C₈	—	26	4	no	—
347	C₂×C₈	C₂²×#261	1	4	yes	—
348	C₄²	—	13	1	no	—
349	C₄²	—	13	1	no	—
350	C₄²	—	13	1	no	—
351	C₄²	—	13	1	no	—
352	C₄²	—	13	1	no	—
353	C₄²	—	13	1	no	—
354	C₄²	—	13	1	no	—
355	C₄²	—	13	1	no	—
356	C₄²	—	13	1	no	—
357	C₄²	—	13	1	no	—
358	C₄²	—	13	1	no	—
359	C₄²	—	13	1	no	—
360	C₄²	C₄×#261	1	1	yes	characteristic
361	C₄²	C₄×#261	1	1	yes	characteristic
362	C₄²	C₂²×#261	1	1	yes	characteristic
363	C₄²	C₂²×#261	1	1	yes	characteristic
364	C₁₃	#17323	1	1	yes	characteristic, complemented, Sylow
365	C₂³	—	13	1	no	—
366	C₂³	—	13	1	no	—
367	C₂³	—	26	2	no	—
368	C₂³	—	26	2	no	—
369	C₂³	—	26	2	no	—
370	C₂³	C₂×C₄×#261	1	1	yes	characteristic
371	C₂×C₄	—	2	2	no	—
372	C₂×C₄	—	2	2	no	—
373	C₂×C₄	—	13	1	no	—
374	C₂×C₄	—	13	1	no	—
375	C₂×C₄	—	13	4	no	—
376	C₂×C₄	—	13	4	no	—
377	C₂×C₄	—	13	1	no	—
378	C₂×C₄	—	13	1	no	—
379	C₂×C₄	—	13	1	no	—
380	C₂×C₄	—	13	1	no	—
381	C₂×C₄	—	26	2	no	—
382	C₂×C₄	—	26	2	no	—
383	C₂×C₄	—	26	2	no	—
384	C₂×C₄	—	26	2	no	—
385	C₂×C₄	—	26	2	no	—
386	C₂×C₄	—	26	2	no	—
387	C₂×C₄	—	26	2	no	—
388	C₂×C₄	—	26	2	no	—
389	C₂×C₄	—	26	2	no	—
390	C₂×C₄	—	26	2	no	—
391	C₂×C₄	—	26	2	no	—
392	C₂×C₄	—	26	1	no	—
393	C₂×C₄	—	26	1	no	—
394	C₂×C₄	—	26	1	no	—
395	C₂×C₄	—	26	1	no	—
396	C₂×C₄	C₂×C₄×#261	1	1	yes	characteristic
397	C₂×C₄	C₂×C₄×#261	1	1	yes	characteristic
398	C₂×C₄	C₂×C₄×#261	1	1	yes	characteristic
399	C₂×C₄	C₂×C₄×#261	1	1	yes	characteristic
400	C₂×C₄	C₂×C₄×#261	1	1	yes	characteristic
401	C₂×C₄	#88238	1	2	yes	—
402	C₂×C₄	#88240	1	2	yes	—
403	C₂×C₄	C₂³×#261	1	1	yes	characteristic
404	C₈	—	2	4	no	—
405	C₈	—	13	4	no	—
406	C₈	—	13	4	no	—
407	C₈	—	26	2	no	—
408	C₈	—	26	2	no	—
409	C₈	—	26	8	no	—
410	C₈	—	26	4	no	—
411	C₂²	—	2	1	no	—
412	C₂²	—	2	1	no	—
413	C₂²	—	13	2	no	—
414	C₂²	—	13	2	no	—
415	C₂²	—	26	8	no	—
416	C₂²	—	26	1	no	—
417	C₂²	—	26	1	no	—
418	C₂²	—	26	1	no	—
419	C₂²	—	26	1	no	—
420	C₂²	#11719072	1	2	yes	—
421	C₂²	C₂²×C₄×#261	1	1	yes	characteristic
422	C₄	—	2	1	no	—
423	C₄	—	2	1	no	—
424	C₄	—	13	2	no	—
425	C₄	—	13	2	no	—
426	C₄	—	26	1	no	—
427	C₄	—	26	1	no	—
428	C₄	—	26	1	no	—
429	C₄	—	26	1	no	—
430	C₄	#11719072	1	2	yes	—
431	C₄	M₁₆×#261	1	2	yes	—
432	C₄	#11719099	1	2	yes	—
433	C₄	C₂×#88238	1	1	yes	characteristic
434	C₄	C₂×#88240	1	1	yes	characteristic
435	C₂	—	2	2	no	—
436	C₂	—	26	2	no	—
437	C₂	—	26	2	no	—
438	C₂	C₂×M₁₆×#261	1	1	yes	characteristic
439	C₂	C₂×#11719072	1	1	yes	characteristic
440	C₂	C₂×#11719099	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	#17323
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. #13130052	C₂	semidirect
4. #13130048	C₂	semidirect
5. #13130043	C₂	semidirect
6. #13130042	C₂	semidirect
7. #13130038	C₂	semidirect
8. M₁₆×#1057	C₂	semidirect
36. #1057⋊C₈	C₂²	semidirect
37. #1057⋊C₈	C₂²	semidirect
38. #11718251	C₂²	semidirect
39. C₈×#1057	C₂²	semidirect
124. D₁₃⋊C₈	M₁₆	semidirect
364. C₁₃	#17323	semidirect

Maximal subgroups

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

subgroup	index
#13131513	2
C₂×C₄×D₁₃⋊C₈	2
#13130052	2
#13130048	2
#13130043	2
#13130042	2
#13130038	2
M₁₆×#1057	2
#13123468	2
#17323	13