Subgroups — #16797230

Order 3328.

986 conjugacy classes of subgroups.

The subgroup lattice has 466 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	C₄×#88237	C₂	1	1	yes	maximal, characteristic
3	#13130625	C₂	1	4	yes	maximal, complemented
4	#13130567	C₂	1	4	yes	maximal
5	#13130549	C₂	1	1	yes	maximal, characteristic, complemented
6	#13130549	C₂	1	1	yes	maximal, characteristic, complemented
7	C₄×#88100	C₂	1	1	yes	maximal, characteristic, complemented
8	C₄×C₈×#261	C₂	1	1	yes	maximal, characteristic, complemented
9	D₁₃×#431	C₂	1	1	yes	maximal, characteristic
10	C₂×#88237	C₂²	1	2	yes	—
11	C₂×C₄²×D₁₃	C₂²	1	1	yes	characteristic
12	C₄×C₂²⋊#261	C₄	1	2	yes	—
13	C₄×C₂²⋊#261	C₄	1	2	yes	—
14	#11719125	C₄	1	2	yes	complemented
15	D₁₃⋊(C₂²⋊C₈)	C₂²	1	2	yes	—
16	#11719119	C₄	1	2	yes	complemented
17	C₂×#88100	C₂²	1	4	yes	—
18	C₂×C₈×#261	C₂²	1	4	yes	—
19	C₄×C₄⋊#261	C₄	1	2	yes	—
20	C₄×C₄⋊#261	C₄	1	2	yes	—
21	#11719057	C₂²	1	2	yes	—
22	C₄²×#261	C₂²	1	1	yes	characteristic
23	C₄²×#261	C₂²	1	1	yes	characteristic
24	#11719051	C₄	1	2	yes	complemented
25	D₁₃⋊(C₄⋊C₈)	C₂²	1	2	yes	—
26	#11719049	C₄	1	2	yes	complemented
27	C₄×D₁₃⋊C₈	C₂²	1	1	yes	characteristic
28	C₄×D₁₃⋊C₈	C₂²	1	1	yes	characteristic
29	C₁₃×#431	C₄	1	1	yes	characteristic, complemented
30	#11718586	C₄	1	1	yes	characteristic, complemented
31	#11718494	C₄	1	2	yes	complemented
32	D₁₃×C₄⋊C₈	C₂²	1	2	yes	—
33	D₁₃×C₂²⋊C₈	C₂²	1	2	yes	—
34	#11718379	C₄	1	2	yes	complemented
35	#11718346	C₄	1	1	yes	characteristic, complemented
36	#11718346	C₄	1	1	yes	characteristic, complemented
37	C₄×C₈×D₁₃	C₂²	1	1	yes	characteristic
38	C₄×C₈×D₁₃	C₂²	1	1	yes	characteristic
39	(C₂×#261)⋊C₈	C₂²	1	4	yes	—
40	(C₂×#261)⋊C₈	C₂²	1	4	yes	—
41	C₂²×C₄×D₁₃	C₂×C₄	1	1	yes	characteristic
42	C₂²×C₄×D₁₃	C₂×C₄	1	1	yes	characteristic
43	C₂²×C₄×D₁₃	C₂³	1	1	yes	characteristic
44	C₂×C₂²⋊#261	C₂×C₄	1	4	yes	—
45	#88237	—	2	8	no	—
46	C₂×C₄⋊#261	C₂×C₄	1	4	yes	—
47	C₂×C₄×#261	C₂×C₄	1	2	yes	—
48	C₂×C₄×#261	C₂×C₄	1	2	yes	—
49	C₂×C₄×#261	C₂×C₄	1	2	yes	—
50	C₂×C₄×#261	C₂×C₄	1	2	yes	—
51	C₂×C₄×#261	C₂³	1	2	yes	—
52	C₂×C₄×#261	C₂³	1	2	yes	—
53	C₂×D₁₃⋊C₈	C₂³	1	2	yes	—
54	C₂×D₁₃⋊C₈	C₂³	1	2	yes	—
55	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
56	C₂×C₄×Dic₁₃	C₂×C₄	1	1	yes	characteristic
57	C₂×C₄×Dic₁₃	C₂×C₄	1	1	yes	characteristic
58	C₂×C₄×Dic₁₃	C₂×C₄	1	1	yes	characteristic
59	C₂×C₈×D₁₃	C₂³	1	2	yes	—
60	C₂×C₈×D₁₃	C₂³	1	2	yes	—
61	C₄²×D₁₃	C₂×C₄	1	1	yes	characteristic
62	C₄²×D₁₃	C₂×C₄	1	1	yes	characteristic
63	C₄²×D₁₃	C₂×C₄	1	1	yes	characteristic
64	C₄²×D₁₃	C₂×C₄	1	1	yes	characteristic
65	C₄²×D₁₃	C₂×C₄	1	1	yes	characteristic
66	C₄²×D₁₃	C₂×C₄	1	1	yes	characteristic
67	C₄²×D₁₃	C₂³	1	1	yes	characteristic
68	C₄²×D₁₃	C₂³	1	1	yes	characteristic
69	C₂²⋊#1057	C₂×C₄	1	4	yes	—
70	(C₂×#261)⋊C₄	C₂×C₄	1	4	yes	—
71	(C₂×#261)⋊C₄	C₂×C₄	1	4	yes	—
72	#88112	C₂×C₄	1	4	yes	—
73	#88111	C₂×C₄	1	4	yes	—
74	C₄⋊#1057	C₂×C₄	1	4	yes	—
75	C₄×#1057	C₂×C₄	1	2	yes	—
76	C₄×#1057	C₂×C₄	1	2	yes	—
77	C₄×#1057	C₂×C₄	1	2	yes	—
78	C₄×#1057	C₂×C₄	1	2	yes	—
79	#88100	—	2	8	no	—
80	C₈×#261	—	2	8	no	—
81	C₁₃×C₄⋊C₈	C₂×C₄	1	2	yes	—
82	C₁₃×C₂²⋊C₈	C₂×C₄	1	2	yes	—
83	C₄×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
84	C₄×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
85	C₂²⋊#1055	C₂×C₄	1	2	yes	—
86	#88060	C₂×C₄	1	2	yes	—
87	#88060	C₂×C₄	1	2	yes	—
88	#88054	C₂×C₄	1	2	yes	—
89	#88054	C₂×C₄	1	2	yes	—
90	C₈×Dic₁₃	C₂×C₄	1	2	yes	—
91	C₈×Dic₁₃	C₂×C₄	1	2	yes	—
92	C₄⋊#1055	C₂×C₄	1	2	yes	—
93	C₄×#1055	C₂×C₄	1	1	yes	characteristic
94	C₄×#1055	C₂×C₄	1	1	yes	characteristic
95	#20462	—	13	1	no	maximal, Sylow
96	C₂³×D₁₃	C₂²×C₄	1	1	yes	characteristic
97	C₂²×#261	C₂²×C₄	1	4	yes	—
98	C₂²×#261	C₂²×C₄	1	4	yes	—
99	C₂²×C₄×C₁₃	C₄²	1	1	yes	characteristic
100	C₂²×C₄×C₁₃	C₄²	1	1	yes	characteristic
101	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
102	C₂²×Dic₁₃	C₄²	1	1	yes	characteristic
103	C₂²×Dic₁₃	C₄²	1	1	yes	characteristic
104	C₂²×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
105	C₂×C₄×D₁₃	—	2	4	no	—
106	C₂×C₄×D₁₃	—	2	4	no	—
107	C₂×C₄×D₁₃	—	2	4	no	—
108	C₂×C₄×D₁₃	C₄²	1	1	yes	characteristic
109	C₂×C₄×D₁₃	C₄²	1	1	yes	characteristic
110	C₂×C₄×D₁₃	C₄²	1	1	yes	characteristic
111	C₂×C₄×D₁₃	C₄²	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	C₂²×C₄	1	1	yes	characteristic
116	C₂×C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
117	C₂×C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
118	C₂×C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
119	C₂×C₄×D₁₃	C₂⁴	1	1	yes	characteristic
120	C₂²⋊#261	—	2	8	no	—
121	C₂×#1057	C₂²×C₄	1	4	yes	—
122	C₂×#1057	C₂²×C₄	1	4	yes	—
123	C₄⋊#261	—	2	8	no	—
124	C₄×#261	—	2	4	no	—
125	C₄×#261	—	2	4	no	—
126	C₄×#261	—	2	4	no	—
127	C₄×#261	—	2	4	no	—
128	C₄×#261	—	2	4	no	—
129	C₄×#261	#41	1	8	yes	—
130	D₁₃⋊C₈	—	2	4	no	—
131	D₁₃⋊C₈	—	2	4	no	—
132	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
133	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
134	C₄²×C₁₃	C₄²	1	1	yes	characteristic
135	C₄²×C₁₃	C₄²	1	1	yes	characteristic
136	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
137	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
138	C₄×Dic₁₃	C₄²	1	1	yes	characteristic
139	C₄×Dic₁₃	C₄²	1	1	yes	characteristic
140	C₄×Dic₁₃	C₄²	1	1	yes	characteristic
141	C₄×Dic₁₃	C₄²	1	1	yes	characteristic
142	C₄×Dic₁₃	C₄²	1	1	yes	characteristic
143	C₄×Dic₁₃	C₄²	1	1	yes	characteristic
144	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
145	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
146	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
147	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
148	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
149	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
150	C₂×#1055	C₂²×C₄	1	2	yes	—
151	C₂×#1055	C₂²×C₄	1	2	yes	—
152	C₈×D₁₃	—	2	4	no	—
153	C₈×D₁₃	—	2	4	no	—
154	C₂×#431	—	13	1	no	—
155	C₂×#431	—	13	1	no	—
156	C₄×#117	—	13	1	no	—
157	#1768	—	13	4	no	—
158	#1750	—	13	4	no	—
159	#1744	—	13	1	no	—
160	#1744	—	13	1	no	—
161	C₄×#97	—	13	1	no	—
162	C₄²×C₈	—	13	1	no	—
163	C₂³×C₁₃	C₂×C₄²	1	1	yes	characteristic
164	C₂²×D₁₃	—	2	2	no	—
165	C₂²×D₁₃	—	2	2	no	—
166	C₂²×D₁₃	—	2	2	no	—
167	C₂²×D₁₃	C₂×C₄²	1	1	yes	characteristic
168	C₂²×D₁₃	C₂³×C₄	1	1	yes	characteristic
169	C₂×#261	—	2	4	no	—
170	C₂×#261	—	2	4	no	—
171	C₂×#261	—	2	4	no	—
172	C₂×#261	—	2	4	no	—
173	C₂×#261	—	2	4	no	—
174	C₂×#261	#117	1	8	yes	—
175	C₂×C₄×C₁₃	—	2	2	no	—
176	C₂×C₄×C₁₃	—	2	2	no	—
177	C₂×C₄×C₁₃	—	2	2	no	—
178	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
179	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
180	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
181	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
182	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
183	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
184	C₂×Dic₁₃	—	2	2	no	—
185	C₂×Dic₁₃	—	2	2	no	—
186	C₂×Dic₁₃	—	2	2	no	—
187	C₂×Dic₁₃	C₂×C₄²	1	1	yes	characteristic
188	C₂×Dic₁₃	C₂×C₄²	1	1	yes	characteristic
189	C₂×Dic₁₃	C₂×C₄²	1	1	yes	characteristic
190	C₂×Dic₁₃	C₂×C₄²	1	1	yes	characteristic
191	C₂×Dic₁₃	C₂×C₄²	1	1	yes	characteristic
192	C₂×Dic₁₃	C₂³×C₄	1	1	yes	characteristic
193	C₄×D₁₃	—	2	2	no	—
194	C₄×D₁₃	—	2	2	no	—
195	C₄×D₁₃	—	2	2	no	—
196	C₄×D₁₃	—	2	2	no	—
197	C₄×D₁₃	—	2	2	no	—
198	C₄×D₁₃	—	2	2	no	—
199	C₄×D₁₃	—	2	2	no	—
200	C₄×D₁₃	—	2	2	no	—
201	C₄×D₁₃	—	2	2	no	—
202	C₄×D₁₃	#131	1	4	yes	—
203	C₄×D₁₃	#131	1	4	yes	—
204	C₄×D₁₃	C₂×#41	1	4	yes	—
205	#1057	—	2	4	no	—
206	#1057	—	2	4	no	—
207	C₈×C₁₃	—	2	2	no	—
208	C₈×C₁₃	—	2	2	no	—
209	#1055	—	2	2	no	—
210	#1055	—	2	2	no	—
211	C₂×#117	—	13	2	no	—
212	C₂²×C₄²	—	13	1	no	—
213	#431	—	13	2	no	—
214	#431	—	13	2	no	—
215	#431	—	13	2	no	—
216	#431	—	13	2	no	—
217	#431	—	13	1	no	—
218	#431	—	13	2	no	—
219	#431	—	13	2	no	—
220	#431	—	13	1	no	—
221	#431	—	13	1	no	—
222	#431	#261	1	1	yes	characteristic, complemented
223	C₂×C₄⋊C₈	—	13	2	no	—
224	C₂×C₄⋊C₈	—	13	2	no	—
225	C₂×C₂²⋊C₈	—	13	2	no	—
226	C₂×C₂²⋊C₈	—	13	2	no	—
227	C₂×#97	—	13	4	no	—
228	C₂×C₄×C₈	—	13	1	no	—
229	C₂×C₄×C₈	—	13	1	no	—
230	C₂×C₄×C₈	—	13	1	no	—
231	C₂×C₄×C₈	—	13	1	no	—
232	C₂×C₄×C₈	—	13	4	no	—
233	C₄×C₄⋊C₄	—	13	2	no	—
234	C₄×C₄⋊C₄	—	13	2	no	—
235	C₄×C₂²⋊C₄	—	13	2	no	—
236	C₄×C₂²⋊C₄	—	13	2	no	—
237	#376	—	13	2	no	—
238	C₄³	—	13	1	no	—
239	C₄³	—	13	1	no	—
240	#336	—	13	4	no	—
241	#336	—	13	4	no	—
242	C₂²×C₁₃	—	2	1	no	—
243	C₂²×C₁₃	—	2	1	no	—
244	C₂²×C₁₃	—	2	1	no	—
245	C₂²×C₁₃	C₂²×C₄²	1	1	yes	characteristic
246	C₂×D₁₃	—	2	1	no	—
247	C₂×D₁₃	—	2	1	no	—
248	C₂×D₁₃	—	2	1	no	—
249	C₂×D₁₃	—	4	4	no	—
250	C₂×D₁₃	C₂×#117	1	2	yes	—
251	C₂×D₁₃	C₂×#131	1	2	yes	—
252	C₂×D₁₃	C₂×#131	1	2	yes	—
253	#261	—	2	8	no	—
254	#261	—	4	4	no	—
255	C₄×C₁₃	—	2	1	no	—
256	C₄×C₁₃	—	2	1	no	—
257	C₄×C₁₃	—	2	1	no	—
258	C₄×C₁₃	#405	1	2	yes	—
259	C₄×C₁₃	#405	1	2	yes	—
260	C₄×C₁₃	C₄×#41	1	2	yes	—
261	Dic₁₃	—	2	1	no	—
262	Dic₁₃	—	2	1	no	—
263	Dic₁₃	—	2	1	no	—
264	Dic₁₃	#405	1	2	yes	—
265	Dic₁₃	#405	1	2	yes	—
266	Dic₁₃	C₄×#41	1	2	yes	—
267	C₂³×C₄	—	13	1	no	—
268	C₂³×C₄	—	13	1	no	—
269	C₂³×C₄	—	13	1	no	—
270	C₂²×C₈	—	13	2	no	—
271	C₂²×C₈	—	13	2	no	—
272	C₂²×C₈	—	13	2	no	—
273	C₂²×C₈	—	13	2	no	—
274	#117	—	26	8	no	—
275	C₂×C₄⋊C₄	—	13	4	no	—
276	C₂×C₂²⋊C₄	—	13	4	no	—
277	C₂×C₄²	—	13	2	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	1	no	—
286	C₂×C₄²	—	13	1	no	—
287	C₂×C₄²	—	13	1	no	—
288	C₂×C₄²	—	13	1	no	—
289	C₂×C₄²	—	13	2	no	—
290	C₂×C₄²	—	13	2	no	—
291	C₂×C₄²	—	13	2	no	—
292	C₂×C₄²	—	13	2	no	—
293	C₂×C₄²	—	13	2	no	—
294	C₂×C₄²	C₂×#261	1	1	yes	characteristic
295	C₄⋊C₈	—	13	4	no	—
296	C₄⋊C₈	—	13	4	no	—
297	C₄⋊C₈	—	13	2	no	—
298	C₄⋊C₈	—	13	2	no	—
299	C₄⋊C₈	—	13	2	no	—
300	C₄⋊C₈	C₂×#261	1	2	yes	—
301	C₂²⋊C₈	—	13	4	no	—
302	C₂²⋊C₈	—	13	4	no	—
303	C₂²⋊C₈	—	13	2	no	—
304	C₂²⋊C₈	—	13	2	no	—
305	C₂²⋊C₈	—	13	2	no	—
306	C₂²⋊C₈	C₂×#261	1	2	yes	—
307	#97	—	26	8	no	—
308	C₄×C₈	—	13	2	no	—
309	C₄×C₈	—	13	2	no	—
310	C₄×C₈	—	13	2	no	—
311	C₄×C₈	—	13	2	no	—
312	C₄×C₈	—	13	2	no	—
313	C₄×C₈	—	13	2	no	—
314	C₄×C₈	—	13	1	no	—
315	C₄×C₈	—	13	1	no	—
316	C₄×C₈	—	26	8	no	—
317	C₄×C₈	C₂×#261	1	1	yes	characteristic
318	C₄×C₈	C₂×#261	1	1	yes	characteristic
319	#95	—	13	4	no	—
320	#95	—	13	4	no	—
321	C₂×C₁₃	—	4	1	no	—
322	C₂×C₁₃	C₄×#117	1	1	yes	characteristic
323	C₂×C₁₃	C₂×#405	1	1	yes	characteristic
324	C₂×C₁₃	C₂×#405	1	1	yes	characteristic
325	D₁₃	—	4	1	no	—
326	D₁₃	#2922	1	4	yes	—
327	C₂⁴	—	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	4	no	—
332	C₂²×C₄	—	13	1	no	—
333	C₂²×C₄	—	13	1	no	—
334	C₂²×C₄	—	13	1	no	—
335	C₂²×C₄	—	13	1	no	—
336	C₂²×C₄	—	13	1	no	—
337	C₂²×C₄	—	13	1	no	—
338	C₂²×C₄	—	13	1	no	—
339	C₂²×C₄	—	13	1	no	—
340	C₂²×C₄	—	13	1	no	—
341	C₂²×C₄	—	13	1	no	—
342	C₂²×C₄	—	13	1	no	—
343	C₂²×C₄	—	13	1	no	—
344	C₂²×C₄	—	13	4	no	—
345	C₂²×C₄	—	26	4	no	—
346	C₂²×C₄	—	26	4	no	—
347	C₂²×C₄	—	26	4	no	—
348	C₂²×C₄	C₄×#261	1	1	yes	characteristic
349	C₂²×C₄	C₄×#261	1	1	yes	characteristic
350	C₂²×C₄	C₂²×#261	1	1	yes	characteristic
351	C₂×C₈	—	13	4	no	—
352	C₂×C₈	—	13	4	no	—
353	C₂×C₈	—	13	2	no	—
354	C₂×C₈	—	13	2	no	—
355	C₂×C₈	—	26	4	no	—
356	C₂×C₈	—	26	4	no	—
357	C₂×C₈	—	26	4	no	—
358	C₂×C₈	—	26	4	no	—
359	C₂×C₈	C₂²×#261	1	2	yes	—
360	C₂×C₈	C₂²×#261	1	2	yes	—
361	C₄⋊C₄	—	26	8	no	—
362	C₂²⋊C₄	—	26	8	no	—
363	C₄²	—	13	8	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	—	13	1	no	—
372	C₄²	—	13	1	no	—
373	C₄²	—	13	1	no	—
374	C₄²	—	13	1	no	—
375	C₄²	—	13	1	no	—
376	C₄²	—	26	4	no	—
377	C₄²	—	26	4	no	—
378	C₄²	—	26	4	no	—
379	C₄²	—	26	4	no	—
380	C₄²	—	26	4	no	—
381	C₄²	C₄×#261	1	1	yes	characteristic
382	C₄²	C₄×#261	1	1	yes	characteristic
383	C₄²	C₂²×#261	1	1	yes	characteristic
384	C₄²	C₂²×#261	1	1	yes	characteristic
385	C₁₃	#20462	1	1	yes	characteristic, complemented, Sylow
386	C₂³	—	13	1	no	—
387	C₂³	—	13	1	no	—
388	C₂³	—	26	2	no	—
389	C₂³	—	26	2	no	—
390	C₂³	—	26	2	no	—
391	C₂³	C₂×C₄×#261	1	1	yes	characteristic
392	C₂×C₄	—	2	2	no	—
393	C₂×C₄	—	2	2	no	—
394	C₂×C₄	—	2	2	no	—
395	C₂×C₄	—	13	1	no	—
396	C₂×C₄	—	13	1	no	—
397	C₂×C₄	—	13	1	no	—
398	C₂×C₄	—	13	4	no	—
399	C₂×C₄	—	13	4	no	—
400	C₂×C₄	—	13	4	no	—
401	C₂×C₄	—	13	8	no	—
402	C₂×C₄	—	13	1	no	—
403	C₂×C₄	—	13	1	no	—
404	C₂×C₄	—	13	1	no	—
405	C₂×C₄	—	26	2	no	—
406	C₂×C₄	—	26	2	no	—
407	C₂×C₄	—	26	2	no	—
408	C₂×C₄	—	26	2	no	—
409	C₂×C₄	—	26	2	no	—
410	C₂×C₄	—	26	2	no	—
411	C₂×C₄	—	26	2	no	—
412	C₂×C₄	—	26	2	no	—
413	C₂×C₄	—	26	2	no	—
414	C₂×C₄	—	26	4	no	—
415	C₂×C₄	—	26	4	no	—
416	C₂×C₄	—	26	2	no	—
417	C₂×C₄	—	26	2	no	—
418	C₂×C₄	—	26	2	no	—
419	C₂×C₄	—	26	4	no	—
420	C₂×C₄	—	26	4	no	—
421	C₂×C₄	—	26	4	no	—
422	C₂×C₄	C₂×C₄×#261	1	1	yes	characteristic
423	C₂×C₄	C₂×C₄×#261	1	1	yes	characteristic
424	C₂×C₄	C₂×C₄×#261	1	1	yes	characteristic
425	C₂×C₄	C₂×C₄×#261	1	1	yes	characteristic
426	C₂×C₄	C₂×C₄×#261	1	1	yes	characteristic
427	C₂×C₄	C₂³×#261	1	1	yes	characteristic
428	C₈	—	2	2	no	—
429	C₈	—	2	2	no	—
430	C₈	—	26	4	no	—
431	C₈	—	26	4	no	—
432	C₈	—	26	2	no	—
433	C₈	—	26	2	no	—
434	C₂²	—	2	1	no	—
435	C₂²	—	2	1	no	—
436	C₂²	—	2	1	no	—
437	C₂²	—	13	2	no	—
438	C₂²	—	13	2	no	—
439	C₂²	—	13	2	no	—
440	C₂²	—	26	1	no	—
441	C₂²	—	26	1	no	—
442	C₂²	—	26	1	no	—
443	C₂²	—	52	4	no	—
444	C₂²	C₂²×C₄×#261	1	1	yes	characteristic
445	C₄	—	2	1	no	—
446	C₄	—	2	1	no	—
447	C₄	—	2	1	no	—
448	C₄	—	13	2	no	—
449	C₄	—	13	2	no	—
450	C₄	—	13	2	no	—
451	C₄	—	26	8	no	—
452	C₄	—	26	1	no	—
453	C₄	—	26	1	no	—
454	C₄	—	26	1	no	—
455	C₄	—	52	4	no	—
456	C₄	#11719089	1	2	yes	—
457	C₄	#11719099	1	2	yes	—
458	C₄	#41×#261	1	2	yes	—
459	C₂	—	4	1	no	—
460	C₂	—	13	4	no	—
461	C₂	—	52	1	no	—
462	C₂	#117×#261	1	1	yes	characteristic
463	C₂	C₂×#11719089	1	1	yes	characteristic
464	C₂	C₂×#11719099	1	1	yes	characteristic

	subgroup	G/H
center	C₄²	C₂²×#261
commutator, socle	C₂²×C₁₃	C₂²×C₄²
Frattini	C₂×C₄	C₂³×#261
Fitting	C₁₃×#431	C₄
prime radical	C₂³×D₁₃	C₂²×C₄
cosocle	C₂×C₄×D₁₃	C₂⁴
hypercenter	#431	#261
hypocenter	C₁₃	#20462
LCS	G ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₄² ◁ #431

Complements

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

N	H ≅ G/N	type
3. #13130625	C₂	semidirect
5. #13130549	C₂	semidirect
6. #13130549	C₂	semidirect
7. C₄×#88100	C₂	semidirect
8. C₄×C₈×#261	C₂	semidirect
14. #11719125	C₄	semidirect
16. #11719119	C₄	semidirect
24. #11719051	C₄	semidirect
26. #11719049	C₄	semidirect
29. C₁₃×#431	C₄	semidirect
30. #11718586	C₄	semidirect
31. #11718494	C₄	semidirect
34. #11718379	C₄	semidirect
35. #11718346	C₄	semidirect
36. #11718346	C₄	semidirect
222. #431	#261	semidirect
385. C₁₃	#20462	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
C₄×#88237	2
#13130625	2
#13130567	2
#13130549	2
C₄×#88100	2
C₄×C₈×#261	2
D₁₃×#431	2
#20462	13