Subgroups — #16797273

Order 3328.

1050 conjugacy classes of subgroups.

The subgroup lattice has 476 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	#13130634	C₂	1	4	yes	maximal, complemented
4	#13130576	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	C₄×M₁₆×D₁₃	C₂	1	1	yes	maximal, characteristic
10	C₂×#88237	C₄	1	2	yes	—
11	C₂×M₁₆×D₁₃	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	#11719125	C₄	1	2	yes	complemented
16	D₁₃⋊(C₂²⋊C₈)	C₂²	1	2	yes	—
17	#11719119	C₄	1	2	yes	complemented
18	C₂×#88100	C₂²	1	4	yes	—
19	C₂×C₈×#261	C₂²	1	4	yes	—
20	C₄×C₄⋊#261	C₄	1	2	yes	—
21	C₄×C₄⋊#261	C₂²	1	2	yes	—
22	#11719057	C₄	1	2	yes	—
23	C₄²×#261	C₂²	1	1	yes	characteristic
24	C₄²×#261	C₂²	1	1	yes	characteristic
25	#11719051	C₄	1	2	yes	complemented
26	D₁₃⋊(C₄⋊C₈)	C₂²	1	2	yes	—
27	#11719049	C₄	1	2	yes	complemented
28	C₄×D₁₃⋊C₈	C₂²	1	1	yes	characteristic
29	C₄×D₁₃⋊C₈	C₂²	1	1	yes	characteristic
30	C₄×C₁₃×M₁₆	C₄	1	1	yes	characteristic, complemented
31	M₁₆×Dic₁₃	C₄	1	2	yes	complemented
32	C₄×#6099	C₄	1	1	yes	characteristic, complemented
33	#11718368	C₄	1	2	yes	complemented
34	D₁₃×#97	C₂²	1	2	yes	—
35	C₄×#6094	C₄	1	1	yes	characteristic, complemented
36	C₄×#6094	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×C₁₃×M₁₆	C₂×C₄	1	2	yes	—
56	C₂×C₄²×C₁₃	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×C₄×Dic₁₃	C₂×C₄	1	1	yes	characteristic
60	C₂×#6099	C₂×C₄	1	2	yes	—
61	M₁₆×D₁₃	—	2	8	no	—
62	C₂×#6094	C₂×C₄	1	2	yes	—
63	C₂×#6094	C₂×C₄	1	2	yes	—
64	C₂×C₈×D₁₃	C₂³	1	2	yes	—
65	C₂×C₈×D₁₃	C₂³	1	2	yes	—
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	C₂×C₄	1	1	yes	characteristic
71	C₄²×D₁₃	C₂×C₄	1	1	yes	characteristic
72	C₄²×D₁₃	C₂³	1	1	yes	characteristic
73	C₄²×D₁₃	C₂³	1	1	yes	characteristic
74	C₂²⋊#1057	C₂×C₄	1	4	yes	—
75	(C₂×#261)⋊C₄	C₂×C₄	1	4	yes	—
76	(C₂×#261)⋊C₄	C₂×C₄	1	4	yes	—
77	#88112	C₂×C₄	1	4	yes	—
78	#88111	C₂×C₄	1	4	yes	—
79	C₄⋊#1057	C₂×C₄	1	4	yes	—
80	C₄×#1057	C₂×C₄	1	2	yes	—
81	C₄×#1057	C₂×C₄	1	2	yes	—
82	C₄×#1057	C₂×C₄	1	2	yes	—
83	C₄×#1057	C₂×C₄	1	2	yes	—
84	#88100	—	2	8	no	—
85	C₈×#261	—	2	8	no	—
86	C₁₃×#97	C₂×C₄	1	2	yes	—
87	C₄×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
88	C₄×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
89	#88055	C₂×C₄	1	2	yes	—
90	#88055	C₂×C₄	1	2	yes	—
91	C₈×Dic₁₃	C₂×C₄	1	2	yes	—
92	C₈×Dic₁₃	C₂×C₄	1	2	yes	—
93	#88043	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	C₂×#1057	C₂²×C₄	1	4	yes	—
123	C₂×#1057	C₂²×C₄	1	4	yes	—
124	C₄⋊#261	—	2	8	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	—	2	4	no	—
130	C₄×#261	M₁₆	1	8	yes	complemented
131	D₁₃⋊C₈	—	2	4	no	—
132	D₁₃⋊C₈	—	2	4	no	—
133	C₁₃×M₁₆	—	2	4	no	—
134	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
135	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
136	C₄²×C₁₃	C₄²	1	1	yes	characteristic
137	C₄²×C₁₃	C₄²	1	1	yes	characteristic
138	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
139	C₄²×C₁₃	C₂²×C₄	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	C₄²	1	1	yes	characteristic
145	C₄×Dic₁₃	C₄²	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	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
151	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
152	#6099	—	2	4	no	—
153	C₂×#1055	C₂²×C₄	1	2	yes	—
154	C₂×#1055	C₂²×C₄	1	2	yes	—
155	#6094	—	2	4	no	—
156	#6094	—	2	4	no	—
157	C₈×D₁₃	—	2	4	no	—
158	C₈×D₁₃	#41	1	8	yes	—
159	C₂×#431	—	13	1	no	—
160	C₂×C₄×M₁₆	—	13	1	no	—
161	C₄×#117	—	13	1	no	—
162	#1771	—	13	4	no	—
163	#1753	—	13	4	no	—
164	#1744	—	13	1	no	—
165	#1744	—	13	1	no	—
166	C₄×#97	—	13	1	no	—
167	C₄²×C₈	—	13	1	no	—
168	C₂³×C₁₃	C₂×C₄²	1	1	yes	characteristic
169	C₂²×D₁₃	—	2	2	no	—
170	C₂²×D₁₃	—	2	2	no	—
171	C₂²×D₁₃	—	2	2	no	—
172	C₂²×D₁₃	C₂×C₄²	1	1	yes	characteristic
173	C₂²×D₁₃	C₂³×C₄	1	1	yes	characteristic
174	C₂×#261	—	2	4	no	—
175	C₂×#261	—	2	4	no	—
176	C₂×#261	—	2	4	no	—
177	C₂×#261	—	2	4	no	—
178	C₂×#261	—	2	4	no	—
179	C₂×#261	C₂×M₁₆	1	8	yes	—
180	C₂×C₄×C₁₃	—	2	2	no	—
181	C₂×C₄×C₁₃	—	2	2	no	—
182	C₂×C₄×C₁₃	—	2	2	no	—
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	C₂×C₄²	1	1	yes	characteristic
187	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
188	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
189	C₂×Dic₁₃	—	2	2	no	—
190	C₂×Dic₁₃	—	2	2	no	—
191	C₂×Dic₁₃	—	2	2	no	—
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	C₂×C₄²	1	1	yes	characteristic
196	C₂×Dic₁₃	C₂×C₄²	1	1	yes	characteristic
197	C₂×Dic₁₃	C₂³×C₄	1	1	yes	characteristic
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	—	2	2	no	—
206	C₄×D₁₃	—	2	2	no	—
207	C₄×D₁₃	C₂×M₁₆	1	4	yes	—
208	C₄×D₁₃	#131	1	4	yes	—
209	C₄×D₁₃	C₂×#41	1	4	yes	—
210	#1057	—	2	4	no	—
211	#1057	—	2	4	no	—
212	C₈×C₁₃	—	2	2	no	—
213	C₈×C₁₃	#117	1	4	yes	complemented
214	#1055	—	2	2	no	—
215	#1055	#117	1	4	yes	complemented
216	C₂²×M₁₆	—	13	2	no	—
217	C₂×#117	—	13	2	no	—
218	C₂²×C₄²	—	13	1	no	—
219	#431	—	13	2	no	—
220	#431	—	13	2	no	—
221	#431	—	13	2	no	—
222	#431	—	13	2	no	—
223	C₂×C₄⋊C₈	—	13	2	no	—
224	C₂×C₂²⋊C₈	—	13	2	no	—
225	C₄×M₁₆	—	13	2	no	—
226	C₄×M₁₆	—	13	1	no	—
227	C₄×M₁₆	—	13	2	no	—
228	C₄×M₁₆	—	13	1	no	—
229	C₄×M₁₆	—	13	1	no	—
230	C₄×M₁₆	#261	1	1	yes	characteristic, complemented
231	C₂×#97	—	13	2	no	—
232	C₂×#97	—	13	4	no	—
233	C₂×C₄×C₈	—	13	1	no	—
234	C₂×C₄×C₈	—	13	1	no	—
235	C₂×C₄×C₈	—	13	1	no	—
236	C₂×C₄×C₈	—	13	1	no	—
237	C₂×C₄×C₈	—	13	4	no	—
238	C₄×C₄⋊C₄	—	13	2	no	—
239	C₄×C₄⋊C₄	—	13	2	no	—
240	C₄×C₂²⋊C₄	—	13	2	no	—
241	C₄×C₂²⋊C₄	—	13	2	no	—
242	#376	—	13	2	no	—
243	C₄³	—	13	1	no	—
244	C₄³	—	13	1	no	—
245	#336	—	13	4	no	—
246	#336	—	13	4	no	—
247	C₂²×C₁₃	—	2	1	no	—
248	C₂²×C₁₃	—	2	1	no	—
249	C₂²×C₁₃	—	2	1	no	—
250	C₂²×C₁₃	C₂²×C₄²	1	1	yes	characteristic
251	C₂×D₁₃	—	2	1	no	—
252	C₂×D₁₃	—	2	1	no	—
253	C₂×D₁₃	—	2	1	no	—
254	C₂×D₁₃	—	4	4	no	—
255	C₂×D₁₃	C₄×#41	1	2	yes	—
256	C₂×D₁₃	C₂²×M₁₆	1	2	yes	—
257	C₂×D₁₃	C₂×#131	1	2	yes	—
258	#261	—	2	8	no	—
259	#261	—	4	4	no	—
260	C₄×C₁₃	—	2	1	no	—
261	C₄×C₁₃	—	2	1	no	—
262	C₄×C₁₃	—	2	1	no	—
263	C₄×C₁₃	C₄×M₁₆	1	2	yes	—
264	C₄×C₁₃	#405	1	2	yes	—
265	C₄×C₁₃	C₂×#117	1	2	yes	—
266	Dic₁₃	—	2	1	no	—
267	Dic₁₃	—	2	1	no	—
268	Dic₁₃	—	2	1	no	—
269	Dic₁₃	C₄×M₁₆	1	2	yes	—
270	Dic₁₃	#405	1	2	yes	—
271	Dic₁₃	C₄×#41	1	2	yes	—
272	C₂³×C₄	—	13	1	no	—
273	C₂³×C₄	—	13	1	no	—
274	C₂³×C₄	—	13	1	no	—
275	C₂×M₁₆	—	13	2	no	—
276	C₂×M₁₆	—	13	2	no	—
277	C₂×M₁₆	—	13	2	no	—
278	C₂×M₁₆	—	26	8	no	—
279	C₂×M₁₆	C₂×#261	1	2	yes	—
280	C₂²×C₈	—	13	2	no	—
281	C₂²×C₈	—	13	2	no	—
282	C₂²×C₈	—	13	2	no	—
283	C₂²×C₈	—	13	2	no	—
284	#117	—	26	8	no	—
285	C₂×C₄⋊C₄	—	13	4	no	—
286	C₂×C₂²⋊C₄	—	13	4	no	—
287	C₂×C₄²	—	13	2	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	1	no	—
296	C₂×C₄²	—	13	1	no	—
297	C₂×C₄²	—	13	1	no	—
298	C₂×C₄²	—	13	1	no	—
299	C₂×C₄²	—	13	2	no	—
300	C₂×C₄²	—	13	2	no	—
301	C₂×C₄²	—	13	2	no	—
302	C₂×C₄²	—	13	2	no	—
303	C₂×C₄²	—	13	2	no	—
304	C₂×C₄²	C₂×#261	1	1	yes	characteristic
305	C₄⋊C₈	—	13	4	no	—
306	C₄⋊C₈	—	13	4	no	—
307	C₂²⋊C₈	—	13	4	no	—
308	C₂²⋊C₈	—	13	4	no	—
309	#97	—	13	2	no	—
310	#97	—	13	2	no	—
311	#97	—	13	2	no	—
312	#97	—	26	8	no	—
313	#97	C₂×#261	1	2	yes	—
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	2	no	—
319	C₄×C₈	—	13	2	no	—
320	C₄×C₈	—	13	1	no	—
321	C₄×C₈	—	13	1	no	—
322	C₄×C₈	—	26	8	no	—
323	C₄×C₈	C₂×#261	1	1	yes	characteristic
324	C₄×C₈	C₂×#261	1	1	yes	characteristic
325	#95	—	13	4	no	—
326	#95	—	13	4	no	—
327	C₂×C₁₃	—	4	1	no	—
328	C₂×C₁₃	C₄×#117	1	1	yes	characteristic
329	C₂×C₁₃	C₂×C₄×M₁₆	1	1	yes	characteristic
330	C₂×C₁₃	C₂×#405	1	1	yes	characteristic
331	D₁₃	—	4	1	no	—
332	D₁₃	#2965	1	4	yes	—
333	C₂⁴	—	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	4	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	1	no	—
349	C₂²×C₄	—	13	1	no	—
350	C₂²×C₄	—	13	4	no	—
351	C₂²×C₄	—	26	4	no	—
352	C₂²×C₄	—	26	4	no	—
353	C₂²×C₄	—	26	4	no	—
354	C₂²×C₄	C₄×#261	1	1	yes	characteristic
355	C₂²×C₄	C₄×#261	1	1	yes	characteristic
356	C₂²×C₄	C₂²×#261	1	1	yes	characteristic
357	M₁₆	—	2	4	no	—
358	M₁₆	—	26	4	no	—
359	M₁₆	—	26	4	no	—
360	M₁₆	—	26	4	no	—
361	C₂×C₈	—	13	2	no	—
362	C₂×C₈	—	13	8	no	—
363	C₂×C₈	—	13	4	no	—
364	C₂×C₈	—	13	4	no	—
365	C₂×C₈	—	13	2	no	—
366	C₂×C₈	—	26	4	no	—
367	C₂×C₈	—	26	4	no	—
368	C₂×C₈	—	26	4	no	—
369	C₂×C₈	C₂²×#261	1	2	yes	—
370	C₂×C₈	C₂²×#261	1	2	yes	—
371	C₄⋊C₄	—	26	8	no	—
372	C₂²⋊C₄	—	26	8	no	—
373	C₄²	—	13	8	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	—	13	1	no	—
383	C₄²	—	13	1	no	—
384	C₄²	—	13	1	no	—
385	C₄²	—	13	1	no	—
386	C₄²	—	26	4	no	—
387	C₄²	—	26	4	no	—
388	C₄²	—	26	4	no	—
389	C₄²	—	26	4	no	—
390	C₄²	—	26	4	no	—
391	C₄²	C₄×#261	1	1	yes	characteristic
392	C₄²	C₄×#261	1	1	yes	characteristic
393	C₄²	C₂²×#261	1	1	yes	characteristic
394	C₄²	C₂²×#261	1	1	yes	characteristic
395	C₁₃	#20472	1	1	yes	characteristic, complemented, Sylow
396	C₂³	—	13	1	no	—
397	C₂³	—	13	1	no	—
398	C₂³	—	26	2	no	—
399	C₂³	—	26	2	no	—
400	C₂³	—	26	2	no	—
401	C₂³	C₂×C₄×#261	1	1	yes	characteristic
402	C₂×C₄	—	2	2	no	—
403	C₂×C₄	—	2	2	no	—
404	C₂×C₄	—	2	2	no	—
405	C₂×C₄	—	13	1	no	—
406	C₂×C₄	—	13	1	no	—
407	C₂×C₄	—	13	1	no	—
408	C₂×C₄	—	13	4	no	—
409	C₂×C₄	—	13	4	no	—
410	C₂×C₄	—	13	4	no	—
411	C₂×C₄	—	13	8	no	—
412	C₂×C₄	—	13	1	no	—
413	C₂×C₄	—	13	1	no	—
414	C₂×C₄	—	13	1	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	2	no	—
421	C₂×C₄	—	26	2	no	—
422	C₂×C₄	—	26	2	no	—
423	C₂×C₄	—	26	2	no	—
424	C₂×C₄	—	26	4	no	—
425	C₂×C₄	—	26	4	no	—
426	C₂×C₄	—	26	2	no	—
427	C₂×C₄	—	26	2	no	—
428	C₂×C₄	—	26	2	no	—
429	C₂×C₄	—	26	4	no	—
430	C₂×C₄	—	26	4	no	—
431	C₂×C₄	—	26	4	no	—
432	C₂×C₄	C₂×C₄×#261	1	1	yes	characteristic
433	C₂×C₄	C₂×C₄×#261	1	1	yes	characteristic
434	C₂×C₄	C₂×C₄×#261	1	1	yes	characteristic
435	C₂×C₄	C₂×C₄×#261	1	1	yes	characteristic
436	C₂×C₄	C₂×C₄×#261	1	1	yes	characteristic
437	C₂×C₄	C₂³×#261	1	1	yes	characteristic
438	C₈	—	2	2	no	—
439	C₈	—	13	4	no	—
440	C₈	—	26	4	no	—
441	C₈	—	26	4	no	—
442	C₈	—	26	2	no	—
443	C₈	#88237	1	4	yes	complemented
444	C₂²	—	2	1	no	—
445	C₂²	—	2	1	no	—
446	C₂²	—	2	1	no	—
447	C₂²	—	13	2	no	—
448	C₂²	—	13	2	no	—
449	C₂²	—	13	2	no	—
450	C₂²	—	26	1	no	—
451	C₂²	—	26	1	no	—
452	C₂²	—	26	1	no	—
453	C₂²	—	52	4	no	—
454	C₂²	C₂²×C₄×#261	1	1	yes	characteristic
455	C₄	—	2	1	no	—
456	C₄	—	2	1	no	—
457	C₄	—	2	1	no	—
458	C₄	—	13	2	no	—
459	C₄	—	13	2	no	—
460	C₄	—	13	2	no	—
461	C₄	—	26	8	no	—
462	C₄	—	26	1	no	—
463	C₄	—	26	1	no	—
464	C₄	—	26	1	no	—
465	C₄	—	52	4	no	—
466	C₄	M₁₆×#261	1	2	yes	—
467	C₄	#11719099	1	2	yes	—
468	C₄	C₂×#88237	1	2	yes	—
469	C₂	—	4	1	no	—
470	C₂	—	13	4	no	—
471	C₂	—	52	1	no	—
472	C₂	C₄×#88237	1	1	yes	characteristic
473	C₂	C₂×M₁₆×#261	1	1	yes	characteristic
474	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	C₄×C₁₃×M₁₆	C₄
prime radical	C₂³×D₁₃	C₂²×C₄
cosocle	C₂×C₄×D₁₃	C₂⁴
hypercenter	C₄×M₁₆	#261
hypocenter	C₁₃	#20472
LCS	G ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₄² ◁ C₄×M₁₆

Complements

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

N	H ≅ G/N	type
3. #13130634	C₂	semidirect
5. #13130549	C₂	semidirect
6. #13130549	C₂	semidirect
7. C₄×#88100	C₂	semidirect
8. C₄×C₈×#261	C₂	semidirect
15. #11719125	C₄	semidirect
17. #11719119	C₄	semidirect
25. #11719051	C₄	semidirect
27. #11719049	C₄	semidirect
30. C₄×C₁₃×M₁₆	C₄	semidirect
31. M₁₆×Dic₁₃	C₄	semidirect
32. C₄×#6099	C₄	semidirect
33. #11718368	C₄	semidirect
35. C₄×#6094	C₄	semidirect
36. C₄×#6094	C₄	semidirect
130. C₄×#261	M₁₆	semidirect
213. C₈×C₁₃	#117	semidirect
215. #1055	#117	semidirect
230. C₄×M₁₆	#261	semidirect
395. C₁₃	#20472	semidirect
443. C₈	#88237	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
#13130634	2
#13130576	2
#13130549	2
C₄×#88100	2
C₄×C₈×#261	2
C₄×M₁₆×D₁₃	2
#20472	13