Subgroups — #16797278

Order 3328.

1050 conjugacy classes of subgroups.

The subgroup lattice has 472 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	C₄×#88237	C₂	1	1	yes	maximal, characteristic
3	#13130637	C₂	1	4	yes	maximal, complemented
4	#13130579	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	C₄	1	2	yes	—
11	C₂×D₁₃⋊M₁₆	C₂²	1	2	yes	—
12	C₂×C₄²×D₁₃	C₂²	1	1	yes	characteristic
13	C₄×C₂²⋊#261	C₄	1	2	yes	—
14	C₄×C₂²⋊#261	C₂²	1	2	yes	—
15	C₄×#6122	C₄	1	2	yes	complemented
16	C₄×#6122	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	C₂²	1	2	yes	—
21	#11719057	C₄	1	2	yes	—
22	C₄²×#261	C₂²	1	1	yes	characteristic
23	C₄²×#261	C₂²	1	1	yes	characteristic
24	C₄×#6118	C₄	1	2	yes	complemented
25	C₄×#6118	C₄	1	2	yes	complemented
26	#11719047	C₂²	1	2	yes	—
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	C₂×#6122	C₂×C₄	1	4	yes	—
46	#88237	—	2	8	no	—
47	C₂×C₄⋊#261	C₂×C₄	1	4	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	C₂×C₄	1	2	yes	—
52	C₂×C₄×#261	C₂³	1	2	yes	—
53	C₂×C₄×#261	C₂³	1	2	yes	—
54	D₁₃⋊M₁₆	—	2	8	no	—
55	C₂×#6118	C₂×C₄	1	4	yes	—
56	C₂×D₁₃⋊C₈	C₂³	1	2	yes	—
57	C₂×D₁₃⋊C₈	C₂³	1	2	yes	—
58	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
59	C₂×C₄×Dic₁₃	C₂×C₄	1	1	yes	characteristic
60	C₂×C₄×Dic₁₃	C₂×C₄	1	1	yes	characteristic
61	C₂×C₄×Dic₁₃	C₂×C₄	1	1	yes	characteristic
62	C₂×C₈×D₁₃	C₂³	1	2	yes	—
63	C₂×C₈×D₁₃	C₂³	1	2	yes	—
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	C₂×C₄	1	1	yes	characteristic
68	C₄²×D₁₃	C₂×C₄	1	1	yes	characteristic
69	C₄²×D₁₃	C₂×C₄	1	1	yes	characteristic
70	C₄²×D₁₃	C₂³	1	1	yes	characteristic
71	C₄²×D₁₃	C₂³	1	1	yes	characteristic
72	(C₂×#261)⋊C₄	C₂×C₄	1	4	yes	—
73	(C₂×#261)⋊C₄	C₂×C₄	1	4	yes	—
74	#88110	C₂×C₄	1	4	yes	—
75	#88110	C₂×C₄	1	4	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	C₄×#1057	C₂×C₄	1	2	yes	—
80	#88100	—	2	8	no	—
81	C₈×#261	—	2	8	no	—
82	C₁₃×C₄⋊C₈	C₂×C₄	1	2	yes	—
83	C₁₃×C₂²⋊C₈	C₂×C₄	1	2	yes	—
84	C₄×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
85	C₄×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
86	C₂²⋊#1055	C₂×C₄	1	2	yes	—
87	#88060	C₂×C₄	1	2	yes	—
88	#88060	C₂×C₄	1	2	yes	—
89	#88054	C₂×C₄	1	2	yes	—
90	#88054	C₂×C₄	1	2	yes	—
91	C₈×Dic₁₃	C₂×C₄	1	2	yes	—
92	C₈×Dic₁₃	C₂×C₄	1	2	yes	—
93	C₄⋊#1055	C₂×C₄	1	2	yes	—
94	C₄×#1055	C₂×C₄	1	1	yes	characteristic
95	C₄×#1055	C₂×C₄	1	1	yes	characteristic
96	#20472	—	13	1	no	maximal, Sylow
97	C₂³×D₁₃	C₂²×C₄	1	1	yes	characteristic
98	C₂²×#261	C₂²×C₄	1	4	yes	—
99	C₂²×#261	C₂²×C₄	1	4	yes	—
100	C₂²×C₄×C₁₃	C₄²	1	1	yes	characteristic
101	C₂²×C₄×C₁₃	C₄²	1	1	yes	characteristic
102	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
103	C₂²×Dic₁₃	C₄²	1	1	yes	characteristic
104	C₂²×Dic₁₃	C₄²	1	1	yes	characteristic
105	C₂²×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
106	C₂×C₄×D₁₃	—	2	4	no	—
107	C₂×C₄×D₁₃	—	2	4	no	—
108	C₂×C₄×D₁₃	—	2	4	no	—
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	C₄²	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	C₂²×C₄	1	1	yes	characteristic
120	C₂×C₄×D₁₃	C₂⁴	1	1	yes	characteristic
121	C₂²⋊#261	—	2	8	no	—
122	#6122	—	2	8	no	—
123	C₂×#1057	C₂²×C₄	1	4	yes	—
124	C₂×#1057	C₂²×C₄	1	4	yes	—
125	C₄⋊#261	—	2	8	no	—
126	C₄×#261	—	2	4	no	—
127	C₄×#261	—	2	4	no	—
128	C₄×#261	—	2	4	no	—
129	C₄×#261	—	2	4	no	—
130	C₄×#261	—	2	4	no	—
131	C₄×#261	M₁₆	1	8	yes	complemented
132	#6118	—	2	8	no	—
133	D₁₃⋊C₈	—	2	4	no	—
134	D₁₃⋊C₈	#41	1	8	yes	—
135	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
136	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
137	C₄²×C₁₃	C₄²	1	1	yes	characteristic
138	C₄²×C₁₃	C₄²	1	1	yes	characteristic
139	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
140	C₄²×C₁₃	C₂²×C₄	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	C₄²	1	1	yes	characteristic
145	C₄×Dic₁₃	C₄²	1	1	yes	characteristic
146	C₄×Dic₁₃	C₄²	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	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
151	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
152	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
153	C₂×#1055	C₂²×C₄	1	2	yes	—
154	C₂×#1055	C₂²×C₄	1	2	yes	—
155	C₈×D₁₃	—	2	4	no	—
156	C₈×D₁₃	—	2	4	no	—
157	C₂×#431	—	13	1	no	—
158	C₂×C₄×M₁₆	—	13	1	no	—
159	C₄×#117	—	13	1	no	—
160	#1771	—	13	4	no	—
161	#1753	—	13	4	no	—
162	#1744	—	13	1	no	—
163	#1744	—	13	1	no	—
164	C₄×#97	—	13	1	no	—
165	C₄²×C₈	—	13	1	no	—
166	C₂³×C₁₃	C₂×C₄²	1	1	yes	characteristic
167	C₂²×D₁₃	—	2	2	no	—
168	C₂²×D₁₃	—	2	2	no	—
169	C₂²×D₁₃	—	2	2	no	—
170	C₂²×D₁₃	C₂×C₄²	1	1	yes	characteristic
171	C₂²×D₁₃	C₂³×C₄	1	1	yes	characteristic
172	C₂×#261	—	2	4	no	—
173	C₂×#261	—	2	4	no	—
174	C₂×#261	—	2	4	no	—
175	C₂×#261	—	2	4	no	—
176	C₂×#261	—	2	4	no	—
177	C₂×#261	C₂×M₁₆	1	8	yes	—
178	C₂×C₄×C₁₃	—	2	2	no	—
179	C₂×C₄×C₁₃	—	2	2	no	—
180	C₂×C₄×C₁₃	—	2	2	no	—
181	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
182	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
183	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
184	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
185	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
186	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
187	C₂×Dic₁₃	—	2	2	no	—
188	C₂×Dic₁₃	—	2	2	no	—
189	C₂×Dic₁₃	—	2	2	no	—
190	C₂×Dic₁₃	C₂×C₄²	1	1	yes	characteristic
191	C₂×Dic₁₃	C₂×C₄²	1	1	yes	characteristic
192	C₂×Dic₁₃	C₂×C₄²	1	1	yes	characteristic
193	C₂×Dic₁₃	C₂×C₄²	1	1	yes	characteristic
194	C₂×Dic₁₃	C₂×C₄²	1	1	yes	characteristic
195	C₂×Dic₁₃	C₂³×C₄	1	1	yes	characteristic
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	—	2	2	no	—
203	C₄×D₁₃	—	2	2	no	—
204	C₄×D₁₃	—	2	2	no	—
205	C₄×D₁₃	C₂×M₁₆	1	4	yes	—
206	C₄×D₁₃	#131	1	4	yes	—
207	C₄×D₁₃	C₂×#41	1	4	yes	—
208	#1057	—	2	4	no	—
209	#1057	#117	1	8	yes	complemented
210	C₈×C₁₃	—	2	2	no	—
211	C₈×C₁₃	—	2	2	no	—
212	#1055	—	2	2	no	—
213	#1055	—	2	2	no	—
214	C₂²×M₁₆	—	13	2	no	—
215	C₂×#117	—	13	2	no	—
216	C₂²×C₄²	—	13	1	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×C₂²⋊C₈	—	13	2	no	—
225	C₄×M₁₆	—	13	2	no	—
226	C₄×M₁₆	—	13	2	no	—
227	C₄×M₁₆	—	13	2	no	—
228	C₄×M₁₆	—	13	2	no	—
229	C₂×#97	—	13	2	no	—
230	C₂×#97	—	13	4	no	—
231	C₂×C₄×C₈	—	13	1	no	—
232	C₂×C₄×C₈	—	13	1	no	—
233	C₂×C₄×C₈	—	13	1	no	—
234	C₂×C₄×C₈	—	13	1	no	—
235	C₂×C₄×C₈	—	13	4	no	—
236	C₄×C₄⋊C₄	—	13	2	no	—
237	C₄×C₄⋊C₄	—	13	2	no	—
238	C₄×C₂²⋊C₄	—	13	2	no	—
239	C₄×C₂²⋊C₄	—	13	2	no	—
240	#376	—	13	2	no	—
241	C₄³	—	13	1	no	—
242	C₄³	—	13	1	no	—
243	#336	—	13	4	no	—
244	#336	—	13	4	no	—
245	C₂²×C₁₃	—	2	1	no	—
246	C₂²×C₁₃	—	2	1	no	—
247	C₂²×C₁₃	—	2	1	no	—
248	C₂²×C₁₃	C₂²×C₄²	1	1	yes	characteristic
249	C₂×D₁₃	—	2	1	no	—
250	C₂×D₁₃	—	2	1	no	—
251	C₂×D₁₃	—	2	1	no	—
252	C₂×D₁₃	—	4	4	no	—
253	C₂×D₁₃	C₄×#41	1	2	yes	—
254	C₂×D₁₃	C₂²×M₁₆	1	2	yes	—
255	C₂×D₁₃	C₂×#131	1	2	yes	—
256	#261	—	2	8	no	—
257	#261	—	4	4	no	—
258	C₄×C₁₃	—	2	1	no	—
259	C₄×C₁₃	—	2	1	no	—
260	C₄×C₁₃	—	2	1	no	—
261	C₄×C₁₃	C₄×M₁₆	1	2	yes	—
262	C₄×C₁₃	#405	1	2	yes	—
263	C₄×C₁₃	C₄×#41	1	2	yes	—
264	Dic₁₃	—	2	1	no	—
265	Dic₁₃	—	2	1	no	—
266	Dic₁₃	—	2	1	no	—
267	Dic₁₃	C₄×M₁₆	1	2	yes	—
268	Dic₁₃	#405	1	2	yes	—
269	Dic₁₃	C₂×#117	1	2	yes	—
270	C₂³×C₄	—	13	1	no	—
271	C₂³×C₄	—	13	1	no	—
272	C₂³×C₄	—	13	1	no	—
273	C₂×M₁₆	—	13	4	no	—
274	C₂×M₁₆	—	13	4	no	—
275	C₂×M₁₆	—	26	8	no	—
276	C₂²×C₈	—	13	2	no	—
277	C₂²×C₈	—	13	2	no	—
278	C₂²×C₈	—	13	2	no	—
279	C₂²×C₈	—	13	2	no	—
280	#117	—	26	8	no	—
281	C₂×C₄⋊C₄	—	13	4	no	—
282	C₂×C₂²⋊C₄	—	13	4	no	—
283	C₂×C₄²	—	13	2	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	1	no	—
290	C₂×C₄²	—	13	1	no	—
291	C₂×C₄²	—	13	1	no	—
292	C₂×C₄²	—	13	1	no	—
293	C₂×C₄²	—	13	1	no	—
294	C₂×C₄²	—	13	1	no	—
295	C₂×C₄²	—	13	2	no	—
296	C₂×C₄²	—	13	2	no	—
297	C₂×C₄²	—	13	2	no	—
298	C₂×C₄²	—	13	2	no	—
299	C₂×C₄²	—	13	2	no	—
300	C₂×C₄²	C₂×#261	1	1	yes	characteristic
301	C₄⋊C₈	—	13	2	no	—
302	C₄⋊C₈	—	13	2	no	—
303	C₄⋊C₈	—	13	2	no	—
304	C₄⋊C₈	C₂×#261	1	2	yes	—
305	C₂²⋊C₈	—	13	2	no	—
306	C₂²⋊C₈	—	13	2	no	—
307	C₂²⋊C₈	—	13	2	no	—
308	C₂²⋊C₈	C₂×#261	1	2	yes	—
309	#97	—	13	4	no	—
310	#97	—	13	4	no	—
311	#97	—	26	8	no	—
312	C₄×C₈	—	13	2	no	—
313	C₄×C₈	—	13	2	no	—
314	C₄×C₈	—	13	2	no	—
315	C₄×C₈	—	13	2	no	—
316	C₄×C₈	—	13	2	no	—
317	C₄×C₈	—	13	2	no	—
318	C₄×C₈	—	13	1	no	—
319	C₄×C₈	—	13	1	no	—
320	C₄×C₈	—	26	8	no	—
321	C₄×C₈	C₂×#261	1	1	yes	characteristic
322	C₄×C₈	C₂×#261	1	1	yes	characteristic
323	#95	—	13	4	no	—
324	#95	—	13	4	no	—
325	C₂×C₁₃	—	4	1	no	—
326	C₂×C₁₃	C₄×#117	1	1	yes	characteristic
327	C₂×C₁₃	C₂×C₄×M₁₆	1	1	yes	characteristic
328	C₂×C₁₃	C₂×#405	1	1	yes	characteristic
329	D₁₃	—	4	1	no	—
330	D₁₃	#2965	1	4	yes	—
331	C₂⁴	—	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	4	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	1	no	—
345	C₂²×C₄	—	13	1	no	—
346	C₂²×C₄	—	13	1	no	—
347	C₂²×C₄	—	13	1	no	—
348	C₂²×C₄	—	13	4	no	—
349	C₂²×C₄	—	26	4	no	—
350	C₂²×C₄	—	26	4	no	—
351	C₂²×C₄	—	26	4	no	—
352	C₂²×C₄	C₄×#261	1	1	yes	characteristic
353	C₂²×C₄	C₄×#261	1	1	yes	characteristic
354	C₂²×C₄	C₂²×#261	1	1	yes	characteristic
355	M₁₆	—	26	8	no	—
356	M₁₆	—	26	8	no	—
357	C₂×C₈	—	13	4	no	—
358	C₂×C₈	—	13	8	no	—
359	C₂×C₈	—	13	4	no	—
360	C₂×C₈	—	13	2	no	—
361	C₂×C₈	—	13	2	no	—
362	C₂×C₈	—	26	4	no	—
363	C₂×C₈	—	26	4	no	—
364	C₂×C₈	—	26	4	no	—
365	C₂×C₈	C₂²×#261	1	2	yes	—
366	C₂×C₈	C₂²×#261	1	2	yes	—
367	C₄⋊C₄	—	26	8	no	—
368	C₂²⋊C₄	—	26	8	no	—
369	C₄²	—	13	8	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	—	13	1	no	—
377	C₄²	—	13	1	no	—
378	C₄²	—	13	1	no	—
379	C₄²	—	13	1	no	—
380	C₄²	—	13	1	no	—
381	C₄²	—	13	1	no	—
382	C₄²	—	26	4	no	—
383	C₄²	—	26	4	no	—
384	C₄²	—	26	4	no	—
385	C₄²	—	26	4	no	—
386	C₄²	—	26	4	no	—
387	C₄²	C₄×#261	1	1	yes	characteristic
388	C₄²	C₄×#261	1	1	yes	characteristic
389	C₄²	C₂²×#261	1	1	yes	characteristic
390	C₄²	C₂²×#261	1	1	yes	characteristic
391	C₁₃	#20472	1	1	yes	characteristic, complemented, Sylow
392	C₂³	—	13	1	no	—
393	C₂³	—	13	1	no	—
394	C₂³	—	26	2	no	—
395	C₂³	—	26	2	no	—
396	C₂³	—	26	2	no	—
397	C₂³	C₂×C₄×#261	1	1	yes	characteristic
398	C₂×C₄	—	2	2	no	—
399	C₂×C₄	—	2	2	no	—
400	C₂×C₄	—	2	2	no	—
401	C₂×C₄	—	13	1	no	—
402	C₂×C₄	—	13	1	no	—
403	C₂×C₄	—	13	1	no	—
404	C₂×C₄	—	13	4	no	—
405	C₂×C₄	—	13	4	no	—
406	C₂×C₄	—	13	4	no	—
407	C₂×C₄	—	13	8	no	—
408	C₂×C₄	—	13	1	no	—
409	C₂×C₄	—	13	1	no	—
410	C₂×C₄	—	13	1	no	—
411	C₂×C₄	—	26	2	no	—
412	C₂×C₄	—	26	2	no	—
413	C₂×C₄	—	26	2	no	—
414	C₂×C₄	—	26	2	no	—
415	C₂×C₄	—	26	2	no	—
416	C₂×C₄	—	26	2	no	—
417	C₂×C₄	—	26	2	no	—
418	C₂×C₄	—	26	2	no	—
419	C₂×C₄	—	26	2	no	—
420	C₂×C₄	—	26	4	no	—
421	C₂×C₄	—	26	4	no	—
422	C₂×C₄	—	26	2	no	—
423	C₂×C₄	—	26	2	no	—
424	C₂×C₄	—	26	2	no	—
425	C₂×C₄	—	26	4	no	—
426	C₂×C₄	—	26	4	no	—
427	C₂×C₄	—	26	4	no	—
428	C₂×C₄	C₂×C₄×#261	1	1	yes	characteristic
429	C₂×C₄	C₂×C₄×#261	1	1	yes	characteristic
430	C₂×C₄	C₂×C₄×#261	1	1	yes	characteristic
431	C₂×C₄	C₂×C₄×#261	1	1	yes	characteristic
432	C₂×C₄	C₂×C₄×#261	1	1	yes	characteristic
433	C₂×C₄	C₂³×#261	1	1	yes	characteristic
434	C₈	—	2	2	no	—
435	C₈	—	2	2	no	—
436	C₈	—	13	8	no	—
437	C₈	—	26	4	no	—
438	C₈	—	26	2	no	—
439	C₈	—	26	2	no	—
440	C₂²	—	2	1	no	—
441	C₂²	—	2	1	no	—
442	C₂²	—	2	1	no	—
443	C₂²	—	13	2	no	—
444	C₂²	—	13	2	no	—
445	C₂²	—	13	2	no	—
446	C₂²	—	26	1	no	—
447	C₂²	—	26	1	no	—
448	C₂²	—	26	1	no	—
449	C₂²	—	52	4	no	—
450	C₂²	C₂²×C₄×#261	1	1	yes	characteristic
451	C₄	—	2	1	no	—
452	C₄	—	2	1	no	—
453	C₄	—	2	1	no	—
454	C₄	—	13	2	no	—
455	C₄	—	13	2	no	—
456	C₄	—	13	2	no	—
457	C₄	—	26	8	no	—
458	C₄	—	26	1	no	—
459	C₄	—	26	1	no	—
460	C₄	—	26	1	no	—
461	C₄	—	52	4	no	—
462	C₄	#11719089	1	2	yes	—
463	C₄	M₁₆×#261	1	2	yes	—
464	C₄	#41×#261	1	2	yes	—
465	C₂	—	4	1	no	—
466	C₂	—	13	4	no	—
467	C₂	—	52	1	no	—
468	C₂	#117×#261	1	1	yes	characteristic
469	C₂	C₂×M₁₆×#261	1	1	yes	characteristic
470	C₂	C₂×#11719089	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	#20472
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. #13130637	C₂	semidirect
5. #13130549	C₂	semidirect
6. #13130549	C₂	semidirect
7. C₄×#88100	C₂	semidirect
8. C₄×C₈×#261	C₂	semidirect
15. C₄×#6122	C₄	semidirect
16. C₄×#6122	C₄	semidirect
24. C₄×#6118	C₄	semidirect
25. C₄×#6118	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
131. C₄×#261	M₁₆	semidirect
209. #1057	#117	semidirect
222. #431	#261	semidirect
391. C₁₃	#20472	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
C₄×#88237	2
#13130637	2
#13130579	2
#13130549	2
C₄×#88100	2
C₄×C₈×#261	2
D₁₃×#431	2
#20472	13