Subgroups — #16807085

Order 3328.

590 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	#13131203	C₂	1	2	yes	maximal, complemented
2	#13131202	C₂	1	2	yes	maximal, complemented
3	#13131200	C₂	1	1	yes	maximal, characteristic, complemented
4	#13131197	C₂	1	1	yes	maximal, characteristic, complemented
5	#13131196	C₂	1	1	yes	maximal, characteristic, complemented
6	#13131193	C₂	1	1	yes	maximal, characteristic, complemented
7	#13131169	C₂	1	1	yes	maximal, characteristic, complemented
8	D₁₃⋊(C₄⋊C₁₆)	C₂	1	1	yes	maximal, characteristic, complemented
9	#13131067	C₂	1	2	yes	maximal
10	#13131046	C₂	1	2	yes	maximal, complemented
11	C₄×#88161	C₂	1	1	yes	maximal, characteristic
12	C₂×#88161	C₄	1	1	yes	characteristic
13	C₂×#88161	C₂²	1	1	yes	characteristic
14	C₄×#6127	C₄	1	1	yes	characteristic
15	C₂×#88098	C₂²	1	2	yes	—
16	C₂×D₁₃⋊C₁₆	C₂²	1	2	yes	—
17	C₄×C₁₃×M₁₆	C₄	1	1	yes	characteristic
18	#11718783	C₄	1	1	yes	characteristic
19	#11718783	C₂²	1	1	yes	characteristic
20	C₂×C₄×#1055	C₂²	1	1	yes	characteristic
21	#11718369	C₄	1	1	yes	characteristic
22	#11718369	C₄	1	1	yes	characteristic
23	#11718369	C₂²	1	1	yes	characteristic
24	#11718369	C₂²	1	1	yes	characteristic
25	C₄×#6094	C₄	1	1	yes	characteristic
26	C₄×#6094	C₄	1	1	yes	characteristic
27	C₄×C₈×D₁₃	C₂²	1	1	yes	characteristic
28	C₄×C₈×D₁₃	C₂²	1	1	yes	characteristic
29	C₂²⋊#6092	C₂²	1	2	yes	—
30	C₂²⋊#6092	C₂²	1	2	yes	—
31	#11718260	C₂²	1	2	yes	—
32	#11718260	C₂²	1	2	yes	—
33	#11718259	C₂²	1	2	yes	—
34	#11718259	C₂²	1	2	yes	—
35	#11718258	C₂²	1	2	yes	—
36	#11718257	C₂²	1	2	yes	—
37	#11718231	C₂²	1	2	yes	—
38	C₄⋊#6092	C₂²	1	1	yes	characteristic
39	C₄⋊#6092	C₂²	1	1	yes	characteristic
40	C₄⋊#6092	C₂²	1	1	yes	characteristic
41	C₄⋊#6092	C₂²	1	1	yes	characteristic
42	C₄×#6092	C₂²	1	2	yes	—
43	C₂×#6127	C₂×C₄	1	1	yes	characteristic
44	C₂×C₁₃×M₁₆	C₂×C₄	1	1	yes	characteristic
45	C₂×C₁₃×M₁₆	C₂×C₄	1	1	yes	characteristic
46	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
47	C₄×C₂²⋊D₁₃	C₈	1	1	yes	characteristic
48	C₄×C₂²⋊D₁₃	C₈	1	1	yes	characteristic
49	C₄×C₂²⋊D₁₃	C₈	1	1	yes	characteristic
50	C₄×C₂²⋊D₁₃	C₈	1	1	yes	characteristic
51	#88180	C₂×C₄	1	1	yes	characteristic
52	C₂²×#1055	C₂×C₄	1	1	yes	characteristic
53	C₂²×#1055	C₂³	1	1	yes	characteristic
54	#88161	—	2	4	no	—
55	#88161	—	2	2	no	—
56	#88161	—	2	2	no	—
57	C₂×#6094	C₂×C₄	1	1	yes	characteristic
58	C₂×#6094	C₂×C₄	1	1	yes	characteristic
59	C₂×#6094	C₂×C₄	1	1	yes	characteristic
60	C₂×#6094	C₂×C₄	1	1	yes	characteristic
61	C₂×C₈×D₁₃	C₂×C₄	1	1	yes	characteristic
62	C₂×C₈×D₁₃	C₂×C₄	1	1	yes	characteristic
63	C₂×C₈×D₁₃	C₂³	1	1	yes	characteristic
64	C₂×C₈×D₁₃	C₂³	1	1	yes	characteristic
65	C₄×D₅₂	C₈	1	1	yes	characteristic
66	C₄×D₅₂	C₈	1	1	yes	characteristic
67	#88126	C₂×C₄	1	1	yes	characteristic
68	#88126	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	C₄×Dic₂₆	C₈	1	1	yes	characteristic
72	C₄×Dic₂₆	C₈	1	1	yes	characteristic
73	C₂×#6092	C₂³	1	2	yes	—
74	C₂×#6092	C₂³	1	2	yes	—
75	C₂×#6092	C₂³	1	2	yes	—
76	C₂×#6092	C₂³	1	2	yes	—
77	#88098	—	2	4	no	—
78	D₁₃⋊C₁₆	—	2	4	no	—
79	C₁₃×#97	C₂×C₄	1	1	yes	characteristic
80	C₁₃×#97	C₂×C₄	1	1	yes	characteristic
81	C₄×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
82	C₄×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
83	#88055	C₂×C₄	1	1	yes	characteristic
84	#88055	C₂×C₄	1	1	yes	characteristic
85	#88055	C₂×C₄	1	1	yes	characteristic
86	#88055	C₂×C₄	1	1	yes	characteristic
87	C₈×Dic₁₃	C₂×C₄	1	1	yes	characteristic
88	C₈×Dic₁₃	C₂×C₄	1	1	yes	characteristic
89	C₈×Dic₁₃	C₂³	1	1	yes	characteristic
90	C₈×Dic₁₃	C₂³	1	1	yes	characteristic
91	C₄×#1055	C₂×C₄	1	1	yes	characteristic
92	C₄×#1055	C₂×C₄	1	1	yes	characteristic
93	C₄×#1055	C₂³	1	1	yes	characteristic
94	C₄×#1055	C₂³	1	1	yes	characteristic
95	#33423	—	13	1	no	maximal, Sylow
96	C₂²×C₄×C₁₃	C₂×C₈	1	1	yes	characteristic
97	C₂²×C₄×C₁₃	C₂×C₈	1	1	yes	characteristic
98	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
99	C₂×C₂²⋊D₁₃	C₂×C₈	1	1	yes	characteristic
100	C₂×C₂²⋊D₁₃	C₂×C₈	1	1	yes	characteristic
101	#6127	—	2	2	no	—
102	#6127	—	2	2	no	—
103	C₂×D₅₂	C₂×C₈	1	1	yes	characteristic
104	C₂×C₄×D₁₃	C₂×C₈	1	1	yes	characteristic
105	C₂×C₄×D₁₃	C₂×C₈	1	1	yes	characteristic
106	C₂×C₄×D₁₃	C₂×C₈	1	1	yes	characteristic
107	C₂×C₄×D₁₃	C₂×C₈	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×Dic₂₆	C₂×C₈	1	1	yes	characteristic
111	C₁₃×M₁₆	—	2	2	no	—
112	C₁₃×M₁₆	—	2	2	no	—
113	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
114	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
115	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
116	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
117	C₄²×C₁₃	C₂×C₈	1	1	yes	characteristic
118	C₄²×C₁₃	C₂×C₈	1	1	yes	characteristic
119	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
120	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
121	C₂²⋊Dic₁₃	C₂×C₈	1	1	yes	characteristic
122	C₂²⋊Dic₁₃	C₂×C₈	1	1	yes	characteristic
123	#6103	C₂×C₈	1	1	yes	characteristic
124	#6103	C₂×C₈	1	1	yes	characteristic
125	#6103	C₂×C₈	1	1	yes	characteristic
126	#6103	C₂×C₈	1	1	yes	characteristic
127	C₄⋊Dic₁₃	C₂×C₈	1	1	yes	characteristic
128	C₄⋊Dic₁₃	C₂×C₈	1	1	yes	characteristic
129	#6101	C₂×C₈	1	1	yes	characteristic
130	#6101	C₂×C₈	1	1	yes	characteristic
131	#6101	C₂×C₈	1	1	yes	characteristic
132	#6101	C₂×C₈	1	1	yes	characteristic
133	C₄×Dic₁₃	C₂×C₈	1	1	yes	characteristic
134	C₄×Dic₁₃	C₂×C₈	1	1	yes	characteristic
135	C₄×Dic₁₃	C₂×C₈	1	1	yes	characteristic
136	C₄×Dic₁₃	C₂×C₈	1	1	yes	characteristic
137	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
138	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
139	C₂×#1055	—	2	2	no	—
140	C₂×#1055	—	2	1	no	—
141	C₂×#1055	—	2	1	no	—
142	C₂×#1055	C₂²×C₄	1	1	yes	characteristic
143	C₂×#1055	C₂²×C₄	1	1	yes	characteristic
144	C₂×#1055	C₂²×C₄	1	1	yes	characteristic
145	C₂×#1055	C₂⁴	1	1	yes	characteristic
146	#6094	—	2	2	no	—
147	#6094	—	2	2	no	—
148	#6094	—	2	2	no	—
149	#6094	M₁₆	1	4	yes	—
150	C₈×D₁₃	—	2	2	no	—
151	C₈×D₁₃	—	2	2	no	—
152	C₈×D₁₃	—	2	1	no	—
153	C₈×D₁₃	—	2	1	no	—
154	C₈×D₁₃	#41	1	2	yes	—
155	C₈×D₁₃	#41	1	2	yes	—
156	#6092	—	2	2	no	—
157	#6092	—	2	2	no	—
158	#6092	—	2	2	no	—
159	#6092	—	2	2	no	—
160	C₄×#131	—	13	1	no	—
161	#2164	—	13	2	no	—
162	#2164	—	13	2	no	—
163	#2163	—	13	1	no	—
164	#2163	—	13	1	no	—
165	#2162	—	13	1	no	—
166	#2162	—	13	1	no	—
167	#2150	—	13	1	no	—
168	C₂×C₄⋊C₁₆	—	13	1	no	—
169	#2113	—	13	2	no	—
170	#2108	—	13	2	no	—
171	C₂³×C₁₃	C₂²×C₈	1	1	yes	characteristic
172	C₂²×D₁₃	C₂²×C₈	1	1	yes	characteristic
173	C₂²×D₁₃	C₂²×C₈	1	1	yes	characteristic
174	C₂×C₄×C₁₃	—	2	1	no	—
175	C₂×C₄×C₁₃	—	2	1	no	—
176	C₂×C₄×C₁₃	—	2	2	no	—
177	C₂×C₄×C₁₃	—	4	1	no	—
178	C₂×C₄×C₁₃	C₂²×C₈	1	1	yes	characteristic
179	C₂×C₄×C₁₃	C₂²×C₈	1	1	yes	characteristic
180	C₂×C₄×C₁₃	C₂²×C₈	1	1	yes	characteristic
181	C₂×C₄×C₁₃	C₂²×C₈	1	1	yes	characteristic
182	C₂×C₄×C₁₃	C₂²×C₈	1	1	yes	characteristic
183	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
184	C₂²⋊D₁₃	—	2	2	no	—
185	C₂²⋊D₁₃	—	2	2	no	—
186	C₂×Dic₁₃	C₂²×C₈	1	1	yes	characteristic
187	C₂×Dic₁₃	C₂²×C₈	1	1	yes	characteristic
188	C₂×Dic₁₃	C₂²×C₈	1	1	yes	characteristic
189	C₂×Dic₁₃	C₂²×C₈	1	1	yes	characteristic
190	C₂×Dic₁₃	C₂²×C₈	1	1	yes	characteristic
191	C₂×Dic₁₃	C₂²×C₈	1	1	yes	characteristic
192	D₅₂	—	2	2	no	—
193	C₄×D₁₃	—	2	1	no	—
194	C₄×D₁₃	—	2	1	no	—
195	C₄×D₁₃	—	2	2	no	—
196	C₄×D₁₃	—	2	2	no	—
197	C₄×D₁₃	—	4	1	no	—
198	C₄×D₁₃	—	4	1	no	—
199	C₄×D₁₃	#117	1	2	yes	—
200	C₄×D₁₃	C₂×M₁₆	1	2	yes	—
201	Dic₂₆	—	2	2	no	—
202	C₈×C₁₃	—	2	1	no	—
203	C₈×C₁₃	—	2	1	no	—
204	C₈×C₁₃	#117	1	2	yes	—
205	C₈×C₁₃	C₂×M₁₆	1	2	yes	—
206	#1055	—	2	1	no	—
207	#1055	—	2	1	no	—
208	#1055	C₂×M₁₆	1	2	yes	—
209	#1055	C₂×#41	1	1	yes	characteristic
210	#1055	C₂×#41	1	1	yes	characteristic
211	C₂×#131	—	13	1	no	—
212	C₂×#131	—	13	1	no	—
213	C₄×#41	—	13	1	no	—
214	C₂×M₃₂	—	13	2	no	—
215	C₂²×C₁₆	—	13	2	no	—
216	#405	—	13	1	no	—
217	#405	—	13	1	no	—
218	#405	—	13	1	no	—
219	#405	—	13	1	no	—
220	#405	—	13	1	no	—
221	#405	—	13	1	no	—
222	C₄×M₁₆	—	13	1	no	—
223	C₄×M₁₆	—	13	1	no	—
224	C₄×M₁₆	#261	1	1	yes	characteristic
225	C₂×C₄×C₈	—	13	1	no	—
226	C₂×C₄×C₈	—	13	1	no	—
227	C₂×C₄×C₈	—	13	1	no	—
228	C₄⋊C₁₆	—	13	1	no	—
229	C₄⋊C₁₆	—	13	1	no	—
230	C₄⋊C₁₆	—	13	1	no	—
231	C₄⋊C₁₆	—	13	1	no	—
232	C₄⋊C₁₆	—	13	2	no	—
233	C₄⋊C₁₆	—	13	2	no	—
234	C₂²⋊C₁₆	—	13	2	no	—
235	C₂²⋊C₁₆	—	13	2	no	—
236	C₂²⋊C₁₆	—	13	2	no	—
237	C₂²⋊C₁₆	—	13	2	no	—
238	#346	—	13	2	no	—
239	#346	—	13	2	no	—
240	C₄×C₁₆	—	13	2	no	—
241	C₄×C₁₆	—	13	2	no	—
242	C₂²×C₁₃	—	2	1	no	—
243	C₂²×C₁₃	—	2	1	no	—
244	C₂²×C₁₃	—	2	1	no	—
245	C₂²×C₁₃	C₂³×C₈	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	—	2	1	no	—
250	C₂×D₁₃	—	2	1	no	—
251	C₂×D₁₃	#431	1	2	yes	—
252	C₄×C₁₃	—	2	1	no	—
253	C₄×C₁₃	—	2	1	no	—
254	C₄×C₁₃	—	2	1	no	—
255	C₄×C₁₃	—	2	1	no	—
256	C₄×C₁₃	#504	1	2	yes	—
257	C₄×C₁₃	C₂×#117	1	1	yes	characteristic
258	C₄×C₁₃	C₂²×M₁₆	1	1	yes	characteristic
259	Dic₁₃	—	2	1	no	—
260	Dic₁₃	—	2	1	no	—
261	Dic₁₃	—	2	1	no	—
262	Dic₁₃	—	2	1	no	—
263	Dic₁₃	—	2	1	no	—
264	Dic₁₃	#431	1	2	yes	—
265	C₂×#41	—	13	1	no	—
266	#131	—	26	2	no	—
267	#131	—	26	2	no	—
268	#131	—	26	4	no	—
269	C₂×M₁₆	—	13	1	no	—
270	C₂×M₁₆	—	13	1	no	—
271	C₂×M₁₆	—	13	1	no	—
272	C₂×M₁₆	—	13	1	no	—
273	C₂×M₁₆	C₂×#261	1	1	yes	characteristic
274	C₂×M₁₆	C₂×#261	1	1	yes	characteristic
275	C₂²×C₈	—	13	1	no	—
276	C₂²×C₈	—	13	1	no	—
277	C₂²×C₈	—	13	1	no	—
278	C₂²×C₈	—	13	1	no	—
279	C₂²×C₈	—	13	1	no	—
280	C₂²×C₈	—	13	1	no	—
281	C₄×Q₈	—	13	1	no	—
282	C₄×Q₈	—	13	1	no	—
283	C₄×D₄	—	13	1	no	—
284	C₄×D₄	—	13	1	no	—
285	C₄×D₄	—	13	1	no	—
286	C₄×D₄	—	13	1	no	—
287	C₄×D₄	—	13	1	no	—
288	C₄×D₄	—	13	1	no	—
289	#117	—	13	1	no	—
290	#117	—	13	1	no	—
291	#117	—	13	1	no	—
292	C₂×C₄²	—	13	1	no	—
293	C₂×C₄²	—	13	1	no	—
294	C₂×C₄²	C₂×#261	1	1	yes	characteristic
295	M₃₂	—	26	4	no	—
296	C₂×C₁₆	—	13	2	no	—
297	C₂×C₁₆	—	13	2	no	—
298	C₂×C₁₆	—	13	2	no	—
299	C₂×C₁₆	—	13	2	no	—
300	C₂×C₁₆	—	26	4	no	—
301	#97	—	13	1	no	—
302	#97	—	13	1	no	—
303	#97	—	13	1	no	—
304	#97	—	13	1	no	—
305	#97	C₂×#261	1	1	yes	characteristic
306	#97	C₂×#261	1	1	yes	characteristic
307	C₄×C₈	—	13	1	no	—
308	C₄×C₈	—	13	1	no	—
309	C₄×C₈	—	13	1	no	—
310	C₄×C₈	—	13	1	no	—
311	C₄×C₈	—	13	1	no	—
312	C₄×C₈	—	13	1	no	—
313	C₄×C₈	—	13	1	no	—
314	C₄×C₈	—	13	1	no	—
315	C₄×C₈	C₂×#261	1	1	yes	characteristic
316	C₄×C₈	C₂×#261	1	1	yes	characteristic
317	C₂×C₁₃	—	4	1	no	—
318	C₂×C₁₃	C₂×#431	1	1	yes	characteristic
319	C₂×C₁₃	C₂×#504	1	1	yes	characteristic
320	C₂×C₁₃	#3407	1	1	yes	characteristic
321	D₁₃	—	2	2	no	—
322	D₁₃	—	4	1	no	—
323	#41	—	26	2	no	—
324	#41	—	26	2	no	—
325	C₂×Q₈	—	13	1	no	—
326	C₂×D₄	—	13	1	no	—
327	C₂×D₄	—	13	1	no	—
328	C₂×D₄	—	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	D₁₃⋊C₈	1	1	yes	characteristic
336	C₂²×C₄	D₁₃⋊C₈	1	1	yes	characteristic
337	C₂²×C₄	C₂²×#261	1	1	yes	characteristic
338	M₁₆	—	2	2	no	—
339	M₁₆	—	2	2	no	—
340	M₁₆	—	13	4	no	—
341	M₁₆	—	26	2	no	—
342	M₁₆	—	26	2	no	—
343	M₁₆	—	26	2	no	—
344	C₂×C₈	—	13	1	no	—
345	C₂×C₈	—	13	1	no	—
346	C₂×C₈	—	13	2	no	—
347	C₂×C₈	—	13	2	no	—
348	C₂×C₈	—	13	1	no	—
349	C₂×C₈	—	13	1	no	—
350	C₂×C₈	—	26	1	no	—
351	C₂×C₈	—	26	1	no	—
352	C₂×C₈	—	26	2	no	—
353	C₂×C₈	—	26	2	no	—
354	C₂×C₈	—	26	1	no	—
355	C₂×C₈	—	26	1	no	—
356	C₂×C₈	—	26	2	no	—
357	C₂×C₈	C₂²×#261	1	1	yes	characteristic
358	C₂×C₈	C₂²×#261	1	1	yes	characteristic
359	C₂×C₈	C₂²×#261	1	1	yes	characteristic
360	C₂×C₈	C₂²×#261	1	1	yes	characteristic
361	C₄⋊C₄	—	13	1	no	—
362	C₄⋊C₄	—	13	1	no	—
363	C₄⋊C₄	—	13	1	no	—
364	C₄⋊C₄	—	13	1	no	—
365	C₄⋊C₄	—	13	1	no	—
366	C₄⋊C₄	—	13	1	no	—
367	C₂²⋊C₄	—	13	1	no	—
368	C₂²⋊C₄	—	13	1	no	—
369	C₂²⋊C₄	—	13	1	no	—
370	C₂²⋊C₄	—	13	1	no	—
371	C₂²⋊C₄	—	13	1	no	—
372	C₂²⋊C₄	—	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	D₁₃⋊C₈	1	1	yes	characteristic
380	C₄²	D₁₃⋊C₈	1	1	yes	characteristic
381	C₄²	C₂²×#261	1	1	yes	characteristic
382	C₄²	C₂²×#261	1	1	yes	characteristic
383	C₁₆	—	26	2	no	—
384	C₁₆	—	26	2	no	—
385	C₁₆	—	26	2	no	—
386	C₁₆	—	26	2	no	—
387	C₁₃	#33423	1	1	yes	characteristic, complemented, Sylow
388	C₂³	—	13	1	no	—
389	C₂³	—	13	1	no	—
390	C₂³	C₂×D₁₃⋊C₈	1	1	yes	characteristic
391	Q₈	—	26	2	no	—
392	D₄	—	26	2	no	—
393	D₄	—	26	2	no	—
394	D₄	—	26	2	no	—
395	C₂×C₄	—	2	2	no	—
396	C₂×C₄	—	2	1	no	—
397	C₂×C₄	—	2	1	no	—
398	C₂×C₄	—	4	1	no	—
399	C₂×C₄	—	13	1	no	—
400	C₂×C₄	—	13	2	no	—
401	C₂×C₄	—	13	2	no	—
402	C₂×C₄	—	13	1	no	—
403	C₂×C₄	—	13	1	no	—
404	C₂×C₄	—	13	1	no	—
405	C₂×C₄	—	13	1	no	—
406	C₂×C₄	—	13	1	no	—
407	C₂×C₄	—	26	2	no	—
408	C₂×C₄	—	26	2	no	—
409	C₂×C₄	—	26	1	no	—
410	C₂×C₄	—	26	1	no	—
411	C₂×C₄	—	52	1	no	—
412	C₂×C₄	—	52	1	no	—
413	C₂×C₄	C₂×D₁₃⋊C₈	1	1	yes	characteristic
414	C₂×C₄	C₂×D₁₃⋊C₈	1	1	yes	characteristic
415	C₂×C₄	C₂×D₁₃⋊C₈	1	1	yes	characteristic
416	C₂×C₄	C₂×D₁₃⋊C₈	1	1	yes	characteristic
417	C₂×C₄	C₂×D₁₃⋊C₈	1	1	yes	characteristic
418	C₂×C₄	C₂³×#261	1	1	yes	characteristic
419	C₈	—	2	1	no	—
420	C₈	—	2	1	no	—
421	C₈	—	13	2	no	—
422	C₈	—	13	1	no	—
423	C₈	—	13	1	no	—
424	C₈	—	26	1	no	—
425	C₈	—	26	1	no	—
426	C₈	D₁₃⋊M₁₆	1	2	yes	—
427	C₈	#88237	1	2	yes	—
428	C₂²	—	2	1	no	—
429	C₂²	—	2	1	no	—
430	C₂²	—	2	1	no	—
431	C₂²	—	13	2	no	—
432	C₂²	—	26	1	no	—
433	C₂²	—	26	1	no	—
434	C₂²	—	26	1	no	—
435	C₂²	—	26	1	no	—
436	C₂²	—	26	1	no	—
437	C₂²	C₂²×D₁₃⋊C₈	1	1	yes	characteristic
438	C₄	—	2	1	no	—
439	C₄	—	2	1	no	—
440	C₄	—	2	1	no	—
441	C₄	—	2	1	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	—	26	1	no	—
448	C₄	#11719096	1	2	yes	—
449	C₄	C₂×D₁₃⋊M₁₆	1	1	yes	characteristic
450	C₄	C₂×#88237	1	1	yes	characteristic
451	C₂	—	4	1	no	—
452	C₂	—	26	2	no	—
453	C₂	—	52	1	no	—
454	C₂	D₁₃⋊#431	1	1	yes	characteristic
455	C₂	C₂×#11719096	1	1	yes	characteristic
456	C₂	#13131805	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂³×#261
commutator, socle	C₂²×C₁₃	C₂³×C₈
Fitting	C₄×C₁₃×M₁₆	C₄
prime radical	C₂×#6127	C₂×C₄
cosocle	C₂×#1055	C₂⁴
hypercenter	C₄×M₁₆	#261
hypocenter	C₁₃	#33423
LCS	G ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₄ ◁ C₄×M₁₆

Complements

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

N	H ≅ G/N	type
1. #13131203	C₂	semidirect
2. #13131202	C₂	semidirect
3. #13131200	C₂	semidirect
4. #13131197	C₂	semidirect
5. #13131196	C₂	semidirect
6. #13131193	C₂	semidirect
7. #13131169	C₂	semidirect
8. D₁₃⋊(C₄⋊C₁₆)	C₂	semidirect
10. #13131046	C₂	semidirect
387. C₁₃	#33423	semidirect

Maximal subgroups

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

subgroup	index
#13131203	2
#13131202	2
#13131200	2
#13131197	2
#13131196	2
#13131193	2
#13131169	2
D₁₃⋊(C₄⋊C₁₆)	2
#13131067	2
#13131046	2
C₄×#88161	2
#33423	13