Subgroups — #16797289

Order 3328.

906 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⋊#433	C₂	1	1	yes	maximal, characteristic
2	#13131298	C₂	1	1	yes	maximal, characteristic
3	#13130634	C₂	1	2	yes	maximal, complemented
4	#13130630	C₂	1	2	yes	maximal, complemented
5	#13130576	C₂	1	2	yes	maximal
6	#13130572	C₂	1	2	yes	maximal
7	#13130556	C₂	1	1	yes	maximal, characteristic, complemented
8	#13130552	C₂	1	1	yes	maximal, characteristic, complemented
9	#13130492	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄×#88100	C₂	1	1	yes	maximal, characteristic, complemented
11	D₁₃×#405	C₂	1	1	yes	maximal, characteristic
12	C₂×M₁₆×D₁₃	C₂²	1	1	yes	characteristic
13	C₂²×C₈×D₁₃	C₂²	1	1	yes	characteristic
14	D₁₃×#117	C₂²	1	1	yes	characteristic
15	C₄×C₂²⋊#261	C₂²	1	2	yes	—
16	D₁₃⋊(C₂²⋊C₈)	C₂²	1	2	yes	—
17	C₂×#88100	C₂²	1	2	yes	—
18	C₂×#88100	C₂²	1	2	yes	—
19	C₂×#88100	C₂²	1	2	yes	—
20	C₂×C₈×#261	C₂²	1	2	yes	—
21	#11719082	C₄	1	4	yes	—
22	#11719077	C₄	1	4	yes	complemented
23	#11719071	C₄	1	4	yes	—
24	#11719068	C₄	1	4	yes	complemented
25	C₄×C₄⋊#261	C₂²	1	2	yes	—
26	#11719057	C₂²	1	1	yes	characteristic
27	C₄²×#261	C₂²	1	1	yes	characteristic
28	D₁₃⋊(C₄⋊C₈)	C₂²	1	2	yes	—
29	#11719047	C₂²	1	1	yes	characteristic
30	C₄×D₁₃⋊C₈	C₂²	1	1	yes	characteristic
31	C₁₃×#405	C₄	1	1	yes	characteristic, complemented
32	#11718783	C₄	1	1	yes	characteristic, complemented
33	#11718762	C₄	1	1	yes	characteristic, complemented
34	#11718658	C₄	1	1	yes	characteristic, complemented
35	#11718369	C₄	1	1	yes	characteristic, complemented
36	#11718369	C₄	1	1	yes	characteristic, complemented
37	D₁₃×#97	C₂²	1	1	yes	characteristic
38	D₁₃×#97	C₂²	1	1	yes	characteristic
39	#11718350	C₄	1	1	yes	characteristic, complemented
40	#11718350	C₄	1	1	yes	characteristic, complemented
41	C₄×C₈×D₁₃	C₂²	1	1	yes	characteristic
42	C₄×C₈×D₁₃	C₂²	1	1	yes	characteristic
43	(C₂×#261)⋊C₈	C₂²	1	2	yes	—
44	(C₂×#261)⋊C₈	C₂²	1	2	yes	—
45	(C₂×#261)⋊C₈	C₂²	1	2	yes	—
46	(C₂×#261)⋊C₈	C₂²	1	2	yes	—
47	C₂²×C₄×D₁₃	C₂³	1	1	yes	characteristic
48	C₂×C₂²⋊#261	C₂×C₄	1	4	yes	—
49	C₂×C₄⋊#261	C₂×C₄	1	4	yes	—
50	C₂×C₄×#261	C₂×C₄	1	4	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×C₁₃×M₁₆	C₂×C₄	1	1	yes	characteristic
56	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
57	C₁₃×#117	C₂×C₄	1	1	yes	characteristic
58	#88180	C₂×C₄	1	1	yes	characteristic
59	C₂×#6099	C₂×C₄	1	1	yes	characteristic
60	C₂²×#1055	C₂×C₄	1	1	yes	characteristic
61	M₁₆×D₁₃	—	2	4	no	—
62	C₂×#6094	C₂×C₄	1	1	yes	characteristic
63	C₂×#6094	C₂×C₄	1	1	yes	characteristic
64	C₂×C₈×D₁₃	—	2	4	no	—
65	C₂×C₈×D₁₃	C₂×C₄	1	1	yes	characteristic
66	C₂×C₈×D₁₃	C₂×C₄	1	1	yes	characteristic
67	C₂×C₈×D₁₃	C₂³	1	1	yes	characteristic
68	C₂×C₈×D₁₃	C₂³	1	1	yes	characteristic
69	C₂×C₈×D₁₃	C₂³	1	1	yes	characteristic
70	C₂×C₈×D₁₃	C₂³	1	1	yes	characteristic
71	#88146	C₂×C₄	1	2	yes	—
72	C₄⋊C₄×D₁₃	C₂×C₄	1	2	yes	—
73	C₂²⋊C₄×D₁₃	C₂×C₄	1	2	yes	—
74	#88131	C₂×C₄	1	2	yes	—
75	#88126	C₂×C₄	1	1	yes	characteristic
76	#88126	C₂×C₄	1	1	yes	characteristic
77	C₄²×D₁₃	C₂³	1	1	yes	characteristic
78	C₄²×D₁₃	C₂³	1	1	yes	characteristic
79	C₂²⋊#1057	C₂×C₄	1	4	yes	—
80	(C₂×#261)⋊C₄	C₂×C₄	1	4	yes	—
81	(C₂×#261)⋊C₄	C₂×C₄	1	4	yes	—
82	(C₂×#261)⋊C₄	C₂×C₄	1	4	yes	—
83	#88112	C₂×C₄	1	4	yes	—
84	#88111	C₂×C₄	1	4	yes	—
85	#88110	C₂×C₄	1	4	yes	—
86	C₄⋊#1057	C₂×C₄	1	4	yes	—
87	C₄×#1057	C₂×C₄	1	4	yes	—
88	#88100	—	2	4	no	—
89	#88100	—	2	4	no	—
90	#88100	—	2	4	no	—
91	C₈×#261	—	2	4	no	—
92	C₁₃×#97	C₂×C₄	1	1	yes	characteristic
93	C₁₃×#97	C₂×C₄	1	1	yes	characteristic
94	C₄×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
95	C₄×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
96	#88055	C₂×C₄	1	1	yes	characteristic
97	#88055	C₂×C₄	1	1	yes	characteristic
98	#88055	C₂×C₄	1	1	yes	characteristic
99	#88055	C₂×C₄	1	1	yes	characteristic
100	C₈×Dic₁₃	C₂×C₄	1	1	yes	characteristic
101	C₈×Dic₁₃	C₂×C₄	1	1	yes	characteristic
102	C₈×Dic₁₃	C₂×C₄	1	1	yes	characteristic
103	C₈×Dic₁₃	C₂×C₄	1	1	yes	characteristic
104	#88043	C₂×C₄	1	1	yes	characteristic
105	#88043	C₂×C₄	1	1	yes	characteristic
106	C₄×#1055	C₂×C₄	1	1	yes	characteristic
107	C₄×#1055	C₂×C₄	1	1	yes	characteristic
108	#20475	—	13	1	no	maximal, Sylow
109	C₂³×D₁₃	C₂²×C₄	1	1	yes	characteristic
110	C₂²×#261	C₂²×C₄	1	4	yes	—
111	C₂²×#261	C₂²×C₄	1	4	yes	—
112	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
113	C₂²×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
114	C₂×C₄×D₁₃	—	2	2	no	—
115	C₂×C₄×D₁₃	—	2	2	no	—
116	C₂×C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
117	C₂×C₄×D₁₃	C₂²×C₄	1	2	yes	—
118	C₂×C₄×D₁₃	C₂²×C₄	1	2	yes	—
119	C₂×C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
120	C₂×C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
121	C₂×C₄×D₁₃	C₂⁴	1	1	yes	characteristic
122	C₂²⋊#261	—	4	4	no	—
123	C₂×#1057	C₂²×C₄	1	4	yes	—
124	C₂×#1057	C₂²×C₄	1	4	yes	—
125	C₄⋊#261	—	4	4	no	—
126	C₄×#261	—	2	2	no	—
127	C₄×#261	—	2	2	no	—
128	C₄×#261	—	2	2	no	—
129	C₄×#261	—	2	2	no	—
130	C₄×#261	—	4	4	no	—
131	D₁₃⋊C₈	—	2	2	no	—
132	D₁₃⋊C₈	—	2	2	no	—
133	D₁₃⋊C₈	—	2	2	no	—
134	D₁₃⋊C₈	—	2	2	no	—
135	C₁₃×M₁₆	—	2	2	no	—
136	C₂×C₈×C₁₃	—	2	2	no	—
137	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
138	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
139	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
140	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
141	C₁₃×C₄⋊C₄	C₄²	1	2	yes	—
142	C₁₃×C₂²⋊C₄	C₄²	1	2	yes	—
143	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
144	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
145	C₂²⋊Dic₁₃	C₄²	1	2	yes	—
146	#6103	C₄²	1	2	yes	—
147	#6103	C₄²	1	2	yes	—
148	C₄⋊Dic₁₃	C₄²	1	2	yes	—
149	#6101	C₄²	1	2	yes	—
150	#6101	C₄²	1	2	yes	—
151	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
152	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
153	C₄×Dic₁₃	C₂²×C₄	1	2	yes	—
154	C₄×Dic₁₃	C₂²×C₄	1	2	yes	—
155	#6099	—	2	2	no	—
156	C₂×#1055	—	2	2	no	—
157	C₂×#1055	C₂²×C₄	1	1	yes	characteristic
158	C₂×#1055	C₂²×C₄	1	1	yes	characteristic
159	C₂×#1055	C₂²×C₄	1	1	yes	characteristic
160	C₂×#1055	C₂²×C₄	1	1	yes	characteristic
161	#6094	—	2	2	no	—
162	#6094	—	2	2	no	—
163	C₈×D₁₃	—	2	2	no	—
164	C₈×D₁₃	—	2	2	no	—
165	C₈×D₁₃	—	2	2	no	—
166	C₈×D₁₃	—	2	2	no	—
167	C₈×D₁₃	#41	1	4	yes	—
168	C₈×D₁₃	#41	1	4	yes	—
169	C₂×#433	—	13	1	no	—
170	C₂×#405	—	13	1	no	—
171	#2298	—	13	1	no	—
172	#1771	—	13	2	no	—
173	#1770	—	13	2	no	—
174	#1753	—	13	2	no	—
175	#1752	—	13	2	no	—
176	#1746	—	13	1	no	—
177	#1745	—	13	1	no	—
178	#1726	—	13	1	no	—
179	C₄×#97	—	13	1	no	—
180	C₂³×C₁₃	C₂×C₄²	1	1	yes	characteristic
181	C₂²×D₁₃	—	2	2	no	—
182	C₂²×D₁₃	—	2	4	no	—
183	C₂²×D₁₃	C₂×C₄²	1	1	yes	characteristic
184	C₂²×D₁₃	C₂³×C₄	1	1	yes	characteristic
185	C₂×#261	—	2	4	no	—
186	C₂×#261	—	2	4	no	—
187	C₂×#261	—	2	4	no	—
188	C₂×#261	—	2	4	no	—
189	C₂×#261	—	2	4	no	—
190	C₂×#261	—	2	4	no	—
191	C₂×C₄×C₁₃	—	2	1	no	—
192	C₂×C₄×C₁₃	—	2	1	no	—
193	C₂×C₄×C₁₃	C₂×C₄²	1	2	yes	—
194	C₂×C₄×C₁₃	C₂×C₄²	1	2	yes	—
195	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
196	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
197	C₂×Dic₁₃	—	2	2	no	—
198	C₂×Dic₁₃	C₂×C₄²	1	2	yes	—
199	C₂×Dic₁₃	C₂×C₄²	1	2	yes	—
200	C₂×Dic₁₃	C₂×C₄²	1	1	yes	characteristic
201	C₂×Dic₁₃	C₂³×C₄	1	1	yes	characteristic
202	C₄×D₁₃	—	2	2	no	—
203	C₄×D₁₃	—	2	4	no	—
204	C₄×D₁₃	—	2	4	no	—
205	C₄×D₁₃	—	2	1	no	—
206	C₄×D₁₃	—	2	1	no	—
207	C₄×D₁₃	—	2	2	no	—
208	C₄×D₁₃	C₂×#41	1	2	yes	—
209	C₄×D₁₃	C₂×#41	1	2	yes	—
210	#1057	—	2	4	no	—
211	#1057	—	2	4	no	—
212	C₈×C₁₃	—	2	1	no	—
213	C₈×C₁₃	—	2	1	no	—
214	C₈×C₁₃	#117	1	2	yes	—
215	C₈×C₁₃	#117	1	2	yes	—
216	#1055	—	2	1	no	—
217	#1055	—	2	1	no	—
218	#1055	#117	1	2	yes	—
219	#1055	#117	1	2	yes	—
220	C₂²×M₁₆	—	13	1	no	—
221	C₂³×C₈	—	13	1	no	—
222	C₂×#117	—	13	1	no	—
223	#433	—	13	4	no	—
224	#433	—	13	4	no	—
225	C₂×C₄⋊C₈	—	13	2	no	—
226	C₂×C₂²⋊C₈	—	13	2	no	—
227	#405	—	13	1	no	—
228	#405	—	13	1	no	—
229	#405	—	13	1	no	—
230	#405	—	13	1	no	—
231	#405	—	13	1	no	—
232	#405	—	13	1	no	—
233	#405	—	13	1	no	—
234	#405	#261	1	1	yes	characteristic, complemented
235	C₂×#97	—	13	1	no	—
236	C₂×#97	—	13	1	no	—
237	C₂×#97	—	13	1	no	—
238	C₂×#97	—	13	2	no	—
239	C₂×#97	—	13	2	no	—
240	C₂×#97	—	13	2	no	—
241	C₂×C₄×C₈	—	13	1	no	—
242	C₂×C₄×C₈	—	13	1	no	—
243	C₂×C₄×C₈	—	13	1	no	—
244	C₂×C₄×C₈	—	13	2	no	—
245	#388	—	13	4	no	—
246	#387	—	13	4	no	—
247	C₄×C₄⋊C₄	—	13	2	no	—
248	C₄×C₂²⋊C₄	—	13	2	no	—
249	#376	—	13	1	no	—
250	C₄³	—	13	1	no	—
251	#336	—	13	2	no	—
252	#336	—	13	2	no	—
253	#336	—	13	2	no	—
254	#336	—	13	2	no	—
255	C₂²×C₁₃	—	2	2	no	—
256	C₂²×C₁₃	—	2	1	no	—
257	C₂²×C₁₃	C₂²×C₄²	1	1	yes	characteristic
258	C₂×D₁₃	—	2	2	no	—
259	C₂×D₁₃	—	2	1	no	—
260	C₂×D₁₃	—	4	4	no	—
261	C₂×D₁₃	C₄×#41	1	2	yes	—
262	C₂×D₁₃	#568	1	4	yes	—
263	#261	—	4	4	no	—
264	#261	—	4	4	no	—
265	C₄×C₁₃	—	2	2	no	—
266	C₄×C₁₃	—	2	2	no	—
267	C₄×C₁₃	—	2	1	no	—
268	C₄×C₁₃	C₂×#117	1	1	yes	characteristic
269	C₄×C₁₃	C₂×#117	1	1	yes	characteristic
270	Dic₁₃	—	2	2	no	—
271	Dic₁₃	—	2	2	no	—
272	Dic₁₃	—	2	1	no	—
273	Dic₁₃	C₄×#41	1	2	yes	—
274	C₂³×C₄	—	13	1	no	—
275	C₂×M₁₆	—	13	1	no	—
276	C₂×M₁₆	—	13	1	no	—
277	C₂×M₁₆	—	13	1	no	—
278	C₂×M₁₆	—	26	4	no	—
279	C₂×M₁₆	C₂×#261	1	1	yes	characteristic
280	C₂²×C₈	—	13	1	no	—
281	C₂²×C₈	—	13	1	no	—
282	C₂²×C₈	—	13	2	no	—
283	C₂²×C₈	—	13	2	no	—
284	C₂²×C₈	—	13	1	no	—
285	C₂²×C₈	—	13	1	no	—
286	C₂²×C₈	—	13	1	no	—
287	C₂²×C₈	—	13	1	no	—
288	C₂²×C₈	—	13	1	no	—
289	C₂²×C₈	—	26	4	no	—
290	C₂²×C₈	C₂×#261	1	1	yes	characteristic
291	#117	—	13	1	no	—
292	#117	—	13	2	no	—
293	#117	—	13	2	no	—
294	#117	—	13	1	no	—
295	#117	—	13	1	no	—
296	#117	C₂×#261	1	1	yes	characteristic
297	C₂×C₄⋊C₄	—	13	2	no	—
298	C₂×C₄⋊C₄	—	13	4	no	—
299	C₂×C₂²⋊C₄	—	13	2	no	—
300	C₂×C₂²⋊C₄	—	13	4	no	—
301	C₂×C₄²	—	13	1	no	—
302	C₂×C₄²	—	13	1	no	—
303	C₂×C₄²	—	13	2	no	—
304	C₂×C₄²	—	13	2	no	—
305	C₂×C₄²	—	13	4	no	—
306	C₄⋊C₈	—	13	4	no	—
307	C₄⋊C₈	—	13	4	no	—
308	C₂²⋊C₈	—	13	4	no	—
309	C₂²⋊C₈	—	13	4	no	—
310	#97	—	13	4	no	—
311	#97	—	13	1	no	—
312	#97	—	13	1	no	—
313	#97	—	13	1	no	—
314	#97	—	13	1	no	—
315	#97	—	13	1	no	—
316	#97	—	13	1	no	—
317	#97	—	26	4	no	—
318	#97	—	26	4	no	—
319	#97	—	26	4	no	—
320	#97	C₂×#261	1	1	yes	characteristic
321	#97	C₂×#261	1	1	yes	characteristic
322	C₄×C₈	—	13	4	no	—
323	C₄×C₈	—	13	1	no	—
324	C₄×C₈	—	13	1	no	—
325	C₄×C₈	—	13	1	no	—
326	C₄×C₈	—	13	1	no	—
327	C₄×C₈	—	13	1	no	—
328	C₄×C₈	—	13	1	no	—
329	C₄×C₈	—	26	4	no	—
330	C₄×C₈	C₂×#261	1	1	yes	characteristic
331	C₄×C₈	C₂×#261	1	1	yes	characteristic
332	#95	—	13	4	no	—
333	#95	—	13	4	no	—
334	#95	—	13	4	no	—
335	C₂×C₁₃	—	4	1	no	—
336	C₂×C₁₃	C₄×#117	1	1	yes	characteristic
337	C₂×C₁₃	#2875	1	2	yes	—
338	D₁₃	—	4	1	no	—
339	D₁₃	#2967	1	4	yes	—
340	C₂⁴	—	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	2	no	—
345	C₂²×C₄	—	13	2	no	—
346	C₂²×C₄	—	13	1	no	—
347	C₂²×C₄	—	13	1	no	—
348	C₂²×C₄	—	13	4	no	—
349	C₂²×C₄	—	13	4	no	—
350	C₂²×C₄	—	26	2	no	—
351	C₂²×C₄	—	26	2	no	—
352	C₂²×C₄	C₂²×#261	1	1	yes	characteristic
353	M₁₆	—	2	2	no	—
354	M₁₆	—	26	2	no	—
355	M₁₆	—	26	2	no	—
356	M₁₆	—	26	2	no	—
357	C₂×C₈	—	2	2	no	—
358	C₂×C₈	—	13	1	no	—
359	C₂×C₈	—	13	1	no	—
360	C₂×C₈	—	13	4	no	—
361	C₂×C₈	—	13	4	no	—
362	C₂×C₈	—	13	4	no	—
363	C₂×C₈	—	13	4	no	—
364	C₂×C₈	—	13	1	no	—
365	C₂×C₈	—	13	1	no	—
366	C₂×C₈	—	26	2	no	—
367	C₂×C₈	—	26	2	no	—
368	C₂×C₈	—	26	2	no	—
369	C₂×C₈	—	26	2	no	—
370	C₂×C₈	—	26	2	no	—
371	C₂×C₈	—	26	2	no	—
372	C₂×C₈	—	26	2	no	—
373	C₂×C₈	—	26	2	no	—
374	C₂×C₈	—	26	2	no	—
375	C₂×C₈	C₂²×#261	1	1	yes	characteristic
376	C₂×C₈	C₂²×#261	1	1	yes	characteristic
377	C₂×C₈	C₂²×#261	1	1	yes	characteristic
378	C₂×C₈	C₂²×#261	1	1	yes	characteristic
379	C₄⋊C₄	—	13	2	no	—
380	C₄⋊C₄	—	13	2	no	—
381	C₄⋊C₄	—	13	2	no	—
382	C₄⋊C₄	—	52	4	no	—
383	C₄⋊C₄	C₄×#261	1	2	yes	—
384	C₂²⋊C₄	—	13	2	no	—
385	C₂²⋊C₄	—	13	2	no	—
386	C₂²⋊C₄	—	13	2	no	—
387	C₂²⋊C₄	—	52	4	no	—
388	C₂²⋊C₄	C₄×#261	1	2	yes	—
389	C₄²	—	13	2	no	—
390	C₄²	—	13	2	no	—
391	C₄²	—	13	1	no	—
392	C₄²	—	13	1	no	—
393	C₄²	—	26	2	no	—
394	C₄²	—	26	2	no	—
395	C₄²	—	26	2	no	—
396	C₄²	—	26	2	no	—
397	C₄²	—	52	4	no	—
398	C₄²	C₂²×#261	1	1	yes	characteristic
399	C₄²	C₂²×#261	1	1	yes	characteristic
400	C₁₃	#20475	1	1	yes	characteristic, complemented, Sylow
401	C₂³	—	13	1	no	—
402	C₂³	—	13	1	no	—
403	C₂³	—	26	4	no	—
404	C₂³	—	26	2	no	—
405	C₂³	C₂×C₄×#261	1	1	yes	characteristic
406	C₂×C₄	—	2	1	no	—
407	C₂×C₄	—	2	1	no	—
408	C₂×C₄	—	13	1	no	—
409	C₂×C₄	—	13	2	no	—
410	C₂×C₄	—	13	2	no	—
411	C₂×C₄	—	13	2	no	—
412	C₂×C₄	—	13	2	no	—
413	C₂×C₄	—	13	1	no	—
414	C₂×C₄	—	26	2	no	—
415	C₂×C₄	—	26	4	no	—
416	C₂×C₄	—	26	4	no	—
417	C₂×C₄	—	26	2	no	—
418	C₂×C₄	—	26	2	no	—
419	C₂×C₄	—	26	1	no	—
420	C₂×C₄	—	26	1	no	—
421	C₂×C₄	—	26	4	no	—
422	C₂×C₄	—	26	4	no	—
423	C₂×C₄	—	26	4	no	—
424	C₂×C₄	—	26	4	no	—
425	C₂×C₄	—	26	4	no	—
426	C₂×C₄	—	26	4	no	—
427	C₂×C₄	C₂×C₄×#261	1	2	yes	—
428	C₂×C₄	C₂×C₄×#261	1	2	yes	—
429	C₂×C₄	C₂×C₄×#261	1	1	yes	characteristic
430	C₂×C₄	C₂³×#261	1	1	yes	characteristic
431	C₈	—	2	1	no	—
432	C₈	—	2	1	no	—
433	C₈	—	13	2	no	—
434	C₈	—	13	2	no	—
435	C₈	—	26	4	no	—
436	C₈	—	26	4	no	—
437	C₈	—	26	1	no	—
438	C₈	—	26	1	no	—
439	C₈	#88237	1	2	yes	—
440	C₈	#88237	1	2	yes	—
441	C₂²	—	2	1	no	—
442	C₂²	—	2	2	no	—
443	C₂²	—	13	2	no	—
444	C₂²	—	13	4	no	—
445	C₂²	—	26	1	no	—
446	C₂²	—	26	2	no	—
447	C₂²	—	52	4	no	—
448	C₂²	C₂²×C₄×#261	1	1	yes	characteristic
449	C₄	—	2	1	no	—
450	C₄	—	2	2	no	—
451	C₄	—	2	2	no	—
452	C₄	—	13	2	no	—
453	C₄	—	26	1	no	—
454	C₄	—	26	2	no	—
455	C₄	—	26	2	no	—
456	C₄	—	52	4	no	—
457	C₄	—	52	4	no	—
458	C₄	C₂×#88237	1	1	yes	characteristic
459	C₄	C₂×#88237	1	1	yes	characteristic
460	C₂	—	4	1	no	—
461	C₂	—	13	4	no	—
462	C₂	—	52	1	no	—
463	C₂	C₄×#88237	1	1	yes	characteristic
464	C₂	#13131406	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂×C₄	C₂³×#261
commutator, socle	C₂²×C₁₃	C₂²×C₄²
Fitting	C₁₃×#405	C₄
prime radical	C₂³×D₁₃	C₂²×C₄
cosocle	C₂×C₄×D₁₃	C₂⁴
hypercenter	#405	#261
hypocenter	C₁₃	#20475
LCS	G ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₄ ◁ #405

Complements

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

N	H ≅ G/N	type
3. #13130634	C₂	semidirect
4. #13130630	C₂	semidirect
7. #13130556	C₂	semidirect
8. #13130552	C₂	semidirect
9. #13130492	C₂	semidirect
10. C₄×#88100	C₂	semidirect
22. #11719077	C₄	semidirect
24. #11719068	C₄	semidirect
31. C₁₃×#405	C₄	semidirect
32. #11718783	C₄	semidirect
33. #11718762	C₄	semidirect
34. #11718658	C₄	semidirect
35. #11718369	C₄	semidirect
36. #11718369	C₄	semidirect
39. #11718350	C₄	semidirect
40. #11718350	C₄	semidirect
234. #405	#261	semidirect
400. C₁₃	#20475	semidirect

Maximal subgroups

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

subgroup	index
D₁₃⋊#433	2
#13131298	2
#13130634	2
#13130630	2
#13130576	2
#13130572	2
#13130556	2
#13130552	2
#13130492	2
C₄×#88100	2
D₁₃×#405	2
#20475	13