Subgroups — #16797334

Order 3328.

950 conjugacy classes of subgroups.

The subgroup lattice has 458 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×D₁₃⋊M₁₆	C₂	1	1	yes	maximal, characteristic
2	#13131283	C₂	1	1	yes	maximal, characteristic
3	#13130633	C₂	1	2	yes	maximal, complemented
4	#13130629	C₂	1	2	yes	maximal, complemented
5	#13130579	C₂	1	4	yes	maximal
6	#13130554	C₂	1	2	yes	maximal, complemented
7	#13130492	C₂	1	2	yes	maximal, complemented
8	D₁₃×#431	C₂	1	1	yes	maximal, characteristic
9	C₂×D₁₃⋊M₁₆	C₂²	1	2	yes	—
10	C₂×C₄²×D₁₃	C₂²	1	1	yes	characteristic
11	#11719136	C₄	1	2	yes	—
12	#11719135	C₄	1	2	yes	—
13	C₄×C₂²⋊#261	C₂²	1	2	yes	—
14	C₄×#6122	C₄	1	2	yes	complemented
15	C₄×#6122	C₄	1	2	yes	complemented
16	C₂×#88100	C₂²	1	4	yes	—
17	C₂×C₈×#261	C₂²	1	4	yes	—
18	#11719061	C₄	1	2	yes	—
19	#11719060	C₄	1	2	yes	—
20	C₄×C₄⋊#261	C₂²	1	2	yes	—
21	#11719057	C₂²	1	2	yes	—
22	C₄×#6118	C₄	1	2	yes	complemented
23	C₄×#6118	C₄	1	2	yes	complemented
24	#11719047	C₂²	1	1	yes	characteristic
25	#11719047	C₂²	1	1	yes	characteristic
26	C₄×D₁₃⋊C₈	C₂²	1	2	yes	—
27	C₁₃×#431	C₄	1	1	yes	characteristic, complemented
28	#11718586	C₄	1	1	yes	characteristic, complemented
29	#11718494	C₄	1	1	yes	characteristic, complemented
30	#11718494	C₄	1	1	yes	characteristic, complemented
31	D₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
32	D₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
33	D₁₃×C₂²⋊C₈	C₂²	1	2	yes	—
34	#11718379	C₄	1	2	yes	complemented
35	#11718346	C₄	1	2	yes	complemented
36	C₄×C₈×D₁₃	C₂²	1	2	yes	—
37	(C₂×#261)⋊C₈	C₂²	1	4	yes	—
38	(C₂×#261)⋊C₈	C₂²	1	4	yes	—
39	C₂²×C₄×D₁₃	C₂×C₄	1	1	yes	characteristic
40	C₂²×C₄×D₁₃	C₂×C₄	1	1	yes	characteristic
41	C₂²×C₄×D₁₃	C₂³	1	1	yes	characteristic
42	C₂×C₂²⋊#261	C₂×C₄	1	4	yes	—
43	C₂×#6122	C₂×C₄	1	4	yes	—
44	C₂×C₄⋊#261	C₂×C₄	1	4	yes	—
45	C₂×C₄×#261	C₂³	1	4	yes	—
46	D₁₃⋊M₁₆	—	2	4	no	—
47	D₁₃⋊M₁₆	—	2	4	no	—
48	C₂×#6118	C₂×C₄	1	4	yes	—
49	C₂×D₁₃⋊C₈	C₂³	1	2	yes	—
50	C₂×D₁₃⋊C₈	C₂³	1	2	yes	—
51	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
52	C₂×C₄×Dic₁₃	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×C₈×D₁₃	C₂³	1	2	yes	—
56	C₂×C₈×D₁₃	C₂³	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	(C₂×#261)⋊C₄	C₂×C₄	1	4	yes	—
66	(C₂×#261)⋊C₄	C₂×C₄	1	4	yes	—
67	(C₂×#261)⋊C₄	C₂×C₄	1	4	yes	—
68	(C₂×#261)⋊C₄	C₂×C₄	1	4	yes	—
69	#88110	C₂×C₄	1	2	yes	—
70	#88110	C₂×C₄	1	2	yes	—
71	#88110	C₂×C₄	1	2	yes	—
72	#88110	C₂×C₄	1	2	yes	—
73	C₄×#1057	C₂×C₄	1	4	yes	—
74	C₄×#1057	C₂×C₄	1	4	yes	—
75	#88100	—	2	8	no	—
76	C₈×#261	—	2	8	no	—
77	C₁₃×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
78	C₁₃×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
79	C₁₃×C₂²⋊C₈	C₂×C₄	1	2	yes	—
80	C₄×C₈×C₁₃	C₂×C₄	1	2	yes	—
81	C₂²⋊#1055	C₂×C₄	1	2	yes	—
82	#88060	C₂×C₄	1	2	yes	—
83	#88060	C₂×C₄	1	2	yes	—
84	#88054	C₂×C₄	1	2	yes	—
85	#88054	C₂×C₄	1	2	yes	—
86	C₈×Dic₁₃	C₂×C₄	1	2	yes	—
87	C₈×Dic₁₃	C₂×C₄	1	2	yes	—
88	C₄⋊#1055	C₂×C₄	1	1	yes	characteristic
89	C₄⋊#1055	C₂×C₄	1	1	yes	characteristic
90	C₄×#1055	C₂×C₄	1	2	yes	—
91	#20482	—	13	1	no	maximal, Sylow
92	C₂³×D₁₃	C₂²×C₄	1	1	yes	characteristic
93	C₂²×#261	C₂²×C₄	1	8	yes	—
94	C₂²×C₄×C₁₃	C₄²	1	1	yes	characteristic
95	C₂²×C₄×C₁₃	C₄²	1	1	yes	characteristic
96	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
97	C₂²×Dic₁₃	C₄²	1	1	yes	characteristic
98	C₂²×Dic₁₃	C₄²	1	1	yes	characteristic
99	C₂²×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
100	C₂×C₄×D₁₃	—	2	4	no	—
101	C₂×C₄×D₁₃	—	2	2	no	—
102	C₂×C₄×D₁₃	—	2	2	no	—
103	C₂×C₄×D₁₃	—	4	2	no	—
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	C₄²	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×C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
114	C₂×C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
115	C₂×C₄×D₁₃	C₂⁴	1	1	yes	characteristic
116	C₂²⋊#261	—	4	4	no	—
117	#6122	—	2	8	no	—
118	C₂×#1057	C₂²×C₄	1	4	yes	—
119	C₂×#1057	C₂²×C₄	1	4	yes	—
120	C₄⋊#261	—	2	8	no	—
121	C₄×#261	—	2	4	no	—
122	C₄×#261	—	2	4	no	—
123	#6118	—	2	8	no	—
124	D₁₃⋊C₈	—	2	2	no	—
125	D₁₃⋊C₈	—	2	2	no	—
126	D₁₃⋊C₈	#41	1	4	yes	—
127	D₁₃⋊C₈	#41	1	4	yes	—
128	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
129	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
130	C₄²×C₁₃	C₄²	1	1	yes	characteristic
131	C₄²×C₁₃	C₄²	1	1	yes	characteristic
132	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
133	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
134	C₄×Dic₁₃	C₄²	1	1	yes	characteristic
135	C₄×Dic₁₃	C₄²	1	1	yes	characteristic
136	C₄×Dic₁₃	C₄²	1	1	yes	characteristic
137	C₄×Dic₁₃	C₄²	1	1	yes	characteristic
138	C₄×Dic₁₃	C₄²	1	1	yes	characteristic
139	C₄×Dic₁₃	C₄²	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	C₂²×C₄	1	1	yes	characteristic
143	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
144	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
145	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
146	C₂×#1055	C₂²×C₄	1	2	yes	—
147	C₂×#1055	C₂²×C₄	1	2	yes	—
148	C₈×D₁₃	—	2	4	no	—
149	C₈×D₁₃	—	2	4	no	—
150	C₂×#431	—	13	1	no	—
151	C₂×C₄×M₁₆	—	13	1	no	—
152	#2283	—	13	1	no	—
153	#1770	—	13	2	no	—
154	C₈×C₄⋊C₄	—	13	2	no	—
155	#1753	—	13	4	no	—
156	#1746	—	13	2	no	—
157	#1726	—	13	2	no	—
158	C₂³×C₁₃	C₂×C₄²	1	1	yes	characteristic
159	C₂²×D₁₃	—	2	2	no	—
160	C₂²×D₁₃	—	2	2	no	—
161	C₂²×D₁₃	—	2	2	no	—
162	C₂²×D₁₃	C₂×C₄²	1	1	yes	characteristic
163	C₂²×D₁₃	C₂³×C₄	1	1	yes	characteristic
164	C₂×#261	—	2	8	no	—
165	C₂×#261	—	2	8	no	—
166	C₂×#261	—	2	8	no	—
167	C₂×C₄×C₁₃	—	2	1	no	—
168	C₂×C₄×C₁₃	—	2	1	no	—
169	C₂×C₄×C₁₃	—	2	2	no	—
170	C₂×C₄×C₁₃	—	4	1	no	—
171	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
172	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
173	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
174	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
175	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
176	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
177	C₂×Dic₁₃	—	2	2	no	—
178	C₂×Dic₁₃	—	2	2	no	—
179	C₂×Dic₁₃	—	4	1	no	—
180	C₂×Dic₁₃	C₂×C₄²	1	1	yes	characteristic
181	C₂×Dic₁₃	C₂×C₄²	1	1	yes	characteristic
182	C₂×Dic₁₃	C₂×C₄²	1	1	yes	characteristic
183	C₂×Dic₁₃	C₂×C₄²	1	1	yes	characteristic
184	C₂×Dic₁₃	C₂×C₄²	1	1	yes	characteristic
185	C₂×Dic₁₃	C₂³×C₄	1	1	yes	characteristic
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	1	no	—
191	C₄×D₁₃	—	2	1	no	—
192	C₄×D₁₃	—	2	2	no	—
193	C₄×D₁₃	—	2	2	no	—
194	C₄×D₁₃	—	2	2	no	—
195	C₄×D₁₃	—	4	1	no	—
196	C₄×D₁₃	—	4	1	no	—
197	C₄×D₁₃	#131	1	4	yes	—
198	C₄×D₁₃	C₂×#41	1	2	yes	—
199	C₄×D₁₃	C₂×#41	1	2	yes	—
200	#1057	—	2	4	no	—
201	#1057	#117	1	8	yes	—
202	C₈×C₁₃	—	2	2	no	—
203	C₈×C₁₃	—	2	2	no	—
204	#1055	—	2	2	no	—
205	#1055	—	2	2	no	—
206	C₂²×M₁₆	—	13	2	no	—
207	C₂²×C₄²	—	13	1	no	—
208	#431	—	13	1	no	—
209	#431	—	13	1	no	—
210	#431	—	13	1	no	—
211	#431	—	13	2	no	—
212	#431	—	13	2	no	—
213	#431	#261	1	1	yes	characteristic, complemented
214	C₂×C₄⋊C₈	—	13	1	no	—
215	C₂×C₄⋊C₈	—	13	1	no	—
216	C₂×C₂²⋊C₈	—	13	2	no	—
217	C₄×M₁₆	—	13	2	no	—
218	C₄×M₁₆	—	13	2	no	—
219	C₄×M₁₆	—	13	2	no	—
220	C₄×M₁₆	—	13	2	no	—
221	C₂×#97	—	13	1	no	—
222	C₂×#97	—	13	1	no	—
223	C₂×#97	—	13	4	no	—
224	C₂×C₄×C₈	—	13	2	no	—
225	C₂×C₄×C₈	—	13	2	no	—
226	C₂×C₄×C₈	—	13	4	no	—
227	#383	—	13	2	no	—
228	#382	—	13	2	no	—
229	#381	—	13	2	no	—
230	#380	—	13	2	no	—
231	C₄×C₄⋊C₄	—	13	2	no	—
232	C₄×C₂²⋊C₄	—	13	2	no	—
233	#376	—	13	2	no	—
234	#336	—	13	4	no	—
235	#336	—	13	4	no	—
236	C₂²×C₁₃	—	2	1	no	—
237	C₂²×C₁₃	—	2	1	no	—
238	C₂²×C₁₃	—	2	1	no	—
239	C₂²×C₁₃	C₂²×C₄²	1	1	yes	characteristic
240	C₂×D₁₃	—	2	1	no	—
241	C₂×D₁₃	—	2	1	no	—
242	C₂×D₁₃	—	2	1	no	—
243	C₂×D₁₃	—	4	4	no	—
244	C₂×D₁₃	C₄×#41	1	2	yes	—
245	C₂×D₁₃	C₂×#131	1	2	yes	—
246	C₂×D₁₃	#568	1	2	yes	—
247	#261	—	4	8	no	—
248	C₄×C₁₃	—	2	1	no	—
249	C₄×C₁₃	—	2	1	no	—
250	C₄×C₁₃	—	2	1	no	—
251	C₄×C₁₃	—	2	1	no	—
252	C₄×C₁₃	#405	1	2	yes	—
253	C₄×C₁₃	C₄×#41	1	1	yes	characteristic
254	C₄×C₁₃	C₄×#41	1	1	yes	characteristic
255	Dic₁₃	—	2	1	no	—
256	Dic₁₃	—	2	1	no	—
257	Dic₁₃	—	2	1	no	—
258	Dic₁₃	—	2	1	no	—
259	Dic₁₃	#405	1	2	yes	—
260	Dic₁₃	C₂×#117	1	2	yes	—
261	C₂³×C₄	—	13	1	no	—
262	C₂³×C₄	—	13	1	no	—
263	C₂³×C₄	—	13	1	no	—
264	C₂×M₁₆	—	13	4	no	—
265	C₂×M₁₆	—	13	4	no	—
266	C₂×M₁₆	—	26	4	no	—
267	C₂×M₁₆	—	26	4	no	—
268	C₂²×C₈	—	13	2	no	—
269	C₂²×C₈	—	13	2	no	—
270	C₂²×C₈	—	13	2	no	—
271	C₂²×C₈	—	13	2	no	—
272	C₂×C₄⋊C₄	—	13	4	no	—
273	C₂×C₂²⋊C₄	—	13	4	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	—	13	1	no	—
279	C₂×C₄²	—	13	1	no	—
280	C₂×C₄²	—	13	1	no	—
281	C₂×C₄²	—	13	1	no	—
282	C₂×C₄²	—	13	1	no	—
283	C₂×C₄²	—	13	1	no	—
284	C₂×C₄²	—	13	1	no	—
285	C₂×C₄²	—	13	4	no	—
286	C₂×C₄²	C₂×#261	1	1	yes	characteristic
287	C₄⋊C₈	—	13	2	no	—
288	C₄⋊C₈	—	13	2	no	—
289	C₄⋊C₈	—	13	1	no	—
290	C₄⋊C₈	—	13	1	no	—
291	C₄⋊C₈	C₂×#261	1	1	yes	characteristic
292	C₄⋊C₈	C₂×#261	1	1	yes	characteristic
293	C₂²⋊C₈	—	13	2	no	—
294	C₂²⋊C₈	—	13	2	no	—
295	C₂²⋊C₈	—	13	2	no	—
296	C₂²⋊C₈	C₂×#261	1	2	yes	—
297	#97	—	13	2	no	—
298	#97	—	13	2	no	—
299	#97	—	13	2	no	—
300	#97	—	13	2	no	—
301	#97	—	26	8	no	—
302	C₄×C₈	—	13	4	no	—
303	C₄×C₈	—	13	4	no	—
304	C₄×C₈	—	13	2	no	—
305	C₄×C₈	—	13	2	no	—
306	C₄×C₈	—	13	2	no	—
307	C₄×C₈	—	26	8	no	—
308	C₄×C₈	C₂×#261	1	2	yes	—
309	#95	—	13	4	no	—
310	#95	—	13	4	no	—
311	#95	—	13	4	no	—
312	#95	—	13	4	no	—
313	C₂×C₁₃	—	4	1	no	—
314	C₂×C₁₃	C₄×#117	1	1	yes	characteristic
315	C₂×C₁₃	C₂×#405	1	1	yes	characteristic
316	C₂×C₁₃	#2873	1	1	yes	characteristic
317	D₁₃	—	4	1	no	—
318	D₁₃	#2969	1	4	yes	—
319	C₂⁴	—	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	—	13	1	no	—
326	C₂²×C₄	—	13	1	no	—
327	C₂²×C₄	—	13	1	no	—
328	C₂²×C₄	—	13	1	no	—
329	C₂²×C₄	—	13	1	no	—
330	C₂²×C₄	—	13	1	no	—
331	C₂²×C₄	—	13	1	no	—
332	C₂²×C₄	—	13	1	no	—
333	C₂²×C₄	—	13	1	no	—
334	C₂²×C₄	—	13	1	no	—
335	C₂²×C₄	—	13	8	no	—
336	C₂²×C₄	—	26	2	no	—
337	C₂²×C₄	—	26	2	no	—
338	C₂²×C₄	—	26	4	no	—
339	C₂²×C₄	—	52	2	no	—
340	C₂²×C₄	C₄×#261	1	1	yes	characteristic
341	C₂²×C₄	C₄×#261	1	1	yes	characteristic
342	C₂²×C₄	C₂²×#261	1	1	yes	characteristic
343	M₁₆	—	26	8	no	—
344	M₁₆	—	26	8	no	—
345	C₂×C₈	—	13	4	no	—
346	C₂×C₈	—	13	4	no	—
347	C₂×C₈	—	13	4	no	—
348	C₂×C₈	—	13	4	no	—
349	C₂×C₈	—	13	2	no	—
350	C₂×C₈	—	13	2	no	—
351	C₂×C₈	—	26	4	no	—
352	C₂×C₈	—	26	4	no	—
353	C₂×C₈	—	26	2	no	—
354	C₂×C₈	—	26	2	no	—
355	C₂×C₈	C₂²×#261	1	2	yes	—
356	C₂×C₈	C₂²×#261	1	2	yes	—
357	C₄⋊C₄	—	26	8	no	—
358	C₂²⋊C₄	—	52	4	no	—
359	C₄²	—	13	1	no	—
360	C₄²	—	13	1	no	—
361	C₄²	—	13	1	no	—
362	C₄²	—	13	1	no	—
363	C₄²	—	13	1	no	—
364	C₄²	—	13	1	no	—
365	C₄²	—	13	1	no	—
366	C₄²	—	13	1	no	—
367	C₄²	—	13	1	no	—
368	C₄²	—	13	1	no	—
369	C₄²	—	13	1	no	—
370	C₄²	—	13	1	no	—
371	C₄²	—	26	4	no	—
372	C₄²	—	26	4	no	—
373	C₄²	C₄×#261	1	1	yes	characteristic
374	C₄²	C₄×#261	1	1	yes	characteristic
375	C₄²	C₂²×#261	1	1	yes	characteristic
376	C₄²	C₂²×#261	1	1	yes	characteristic
377	C₁₃	#20482	1	1	yes	characteristic, complemented, Sylow
378	C₂³	—	13	1	no	—
379	C₂³	—	13	1	no	—
380	C₂³	—	26	2	no	—
381	C₂³	—	26	2	no	—
382	C₂³	—	26	2	no	—
383	C₂³	C₂×C₄×#261	1	1	yes	characteristic
384	C₂×C₄	—	2	2	no	—
385	C₂×C₄	—	2	1	no	—
386	C₂×C₄	—	2	1	no	—
387	C₂×C₄	—	4	1	no	—
388	C₂×C₄	—	13	1	no	—
389	C₂×C₄	—	13	1	no	—
390	C₂×C₄	—	13	4	no	—
391	C₂×C₄	—	13	2	no	—
392	C₂×C₄	—	13	2	no	—
393	C₂×C₄	—	13	1	no	—
394	C₂×C₄	—	13	1	no	—
395	C₂×C₄	—	13	1	no	—
396	C₂×C₄	—	13	1	no	—
397	C₂×C₄	—	26	2	no	—
398	C₂×C₄	—	26	2	no	—
399	C₂×C₄	—	26	2	no	—
400	C₂×C₄	—	26	2	no	—
401	C₂×C₄	—	26	2	no	—
402	C₂×C₄	—	26	2	no	—
403	C₂×C₄	—	26	2	no	—
404	C₂×C₄	—	26	2	no	—
405	C₂×C₄	—	26	2	no	—
406	C₂×C₄	—	26	1	no	—
407	C₂×C₄	—	26	1	no	—
408	C₂×C₄	—	26	8	no	—
409	C₂×C₄	—	26	8	no	—
410	C₂×C₄	—	26	8	no	—
411	C₂×C₄	—	52	1	no	—
412	C₂×C₄	—	52	1	no	—
413	C₂×C₄	—	52	1	no	—
414	C₂×C₄	C₂×C₄×#261	1	1	yes	characteristic
415	C₂×C₄	C₂×C₄×#261	1	1	yes	characteristic
416	C₂×C₄	C₂×C₄×#261	1	1	yes	characteristic
417	C₂×C₄	C₂×C₄×#261	1	1	yes	characteristic
418	C₂×C₄	C₂×C₄×#261	1	1	yes	characteristic
419	C₂×C₄	C₂³×#261	1	1	yes	characteristic
420	C₈	—	2	2	no	—
421	C₈	—	2	2	no	—
422	C₈	—	13	8	no	—
423	C₈	—	26	4	no	—
424	C₈	—	26	2	no	—
425	C₈	—	26	2	no	—
426	C₂²	—	2	1	no	—
427	C₂²	—	2	1	no	—
428	C₂²	—	2	1	no	—
429	C₂²	—	13	2	no	—
430	C₂²	—	13	2	no	—
431	C₂²	—	13	2	no	—
432	C₂²	—	26	1	no	—
433	C₂²	—	26	1	no	—
434	C₂²	—	26	1	no	—
435	C₂²	—	52	4	no	—
436	C₂²	C₂²×C₄×#261	1	1	yes	characteristic
437	C₄	—	2	1	no	—
438	C₄	—	2	1	no	—
439	C₄	—	2	1	no	—
440	C₄	—	2	1	no	—
441	C₄	—	13	2	no	—
442	C₄	—	13	2	no	—
443	C₄	—	26	1	no	—
444	C₄	—	26	1	no	—
445	C₄	—	26	1	no	—
446	C₄	—	26	1	no	—
447	C₄	—	52	8	no	—
448	C₄	#11719089	1	2	yes	—
449	C₄	#41×#261	1	1	yes	characteristic
450	C₄	#41×#261	1	1	yes	characteristic
451	C₂	—	4	1	no	—
452	C₂	—	13	4	no	—
453	C₂	—	52	1	no	—
454	C₂	#117×#261	1	1	yes	characteristic
455	C₂	C₂×#11719089	1	1	yes	characteristic
456	C₂	#13131399	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂³×#261
commutator, socle	C₂²×C₁₃	C₂²×C₄²
Fitting	C₁₃×#431	C₄
prime radical	C₂³×D₁₃	C₂²×C₄
cosocle	C₂×C₄×D₁₃	C₂⁴
hypercenter	#431	#261
hypocenter	C₁₃	#20482
LCS	G ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₄ ◁ #431

Complements

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

N	H ≅ G/N	type
3. #13130633	C₂	semidirect
4. #13130629	C₂	semidirect
6. #13130554	C₂	semidirect
7. #13130492	C₂	semidirect
14. C₄×#6122	C₄	semidirect
15. C₄×#6122	C₄	semidirect
22. C₄×#6118	C₄	semidirect
23. C₄×#6118	C₄	semidirect
27. C₁₃×#431	C₄	semidirect
28. #11718586	C₄	semidirect
29. #11718494	C₄	semidirect
30. #11718494	C₄	semidirect
34. #11718379	C₄	semidirect
35. #11718346	C₄	semidirect
213. #431	#261	semidirect
377. C₁₃	#20482	semidirect

Maximal subgroups

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

subgroup	index
C₄×D₁₃⋊M₁₆	2
#13131283	2
#13130633	2
#13130629	2
#13130579	2
#13130554	2
#13130492	2
D₁₃×#431	2
#20482	13