Subgroups — #15833529

Order 3328.

662 conjugacy classes of subgroups.

The subgroup lattice has 464 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13125431	C₂	1	1	yes	maximal, characteristic
2	#13123811	C₂	1	1	yes	maximal, characteristic, complemented
3	#13123549	C₂	1	1	yes	maximal, characteristic, complemented
4	#13113728	C₂	1	2	yes	maximal, complemented
5	#13113722	C₂	1	2	yes	maximal, complemented
6	#13113661	C₂	1	2	yes	maximal, complemented
7	#13113650	C₂	1	2	yes	maximal, complemented
8	#13113603	C₂	1	1	yes	maximal, characteristic, complemented
9	#13113306	C₂	1	1	yes	maximal, characteristic, complemented
10	#13113302	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈×C₁₃×M₁₆	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#88155	—	2	1	no	—
13	#11719184	C₂²	1	1	yes	characteristic
14	#11719182	C₂²	1	1	yes	characteristic
15	C₁₃×#431	C₂²	1	1	yes	characteristic
16	C₄×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
17	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
18	#11718796	C₄	1	2	yes	—
19	#11718795	C₄	1	2	yes	—
20	#11718772	—	2	1	no	—
21	#11718771	—	2	1	no	—
22	C₈×C₂²⋊D₁₃	—	2	1	no	—
23	#11718587	C₂²	1	1	yes	characteristic
24	#11718585	C₂²	1	1	yes	characteristic
25	#11718375	C₄	1	1	yes	characteristic
26	#11718374	C₄	1	1	yes	characteristic
27	#11718373	C₄	1	1	yes	characteristic
28	#11718363	C₄	1	1	yes	characteristic
29	C₄×D₁₀₄	C₂²	1	2	yes	—
30	C₄×#6095	C₂²	1	2	yes	—
31	#11718351	—	2	1	no	—
32	#11718350	—	2	1	no	—
33	#11718349	—	2	1	no	—
34	#11718349	C₂²	1	1	yes	characteristic
35	#11718349	C₂²	1	2	yes	—
36	C₈×D₅₂	—	2	1	no	—
37	C₈×D₅₂	C₂²	1	2	yes	—
38	C₈×D₅₂	C₂²	1	1	yes	characteristic
39	#11718340	C₂²	1	1	yes	characteristic
40	C₈×Dic₂₆	C₂²	1	1	yes	characteristic
41	C₁₃×#322	C₂²	1	2	yes	—
42	C₈²×C₁₃	C₂²	1	2	yes	—
43	#11718051	C₂²	1	2	yes	—
44	#11718051	C₂²	1	2	yes	—
45	#11718051	C₂²	1	2	yes	—
46	#11718050	C₂²	1	2	yes	—
47	#11718049	C₂²	1	2	yes	—
48	#11718048	C₂²	1	2	yes	—
49	C₂×#6127	—	2	1	no	—
50	C₂×C₁₃×M₁₆	C₂×C₄	1	2	yes	—
51	C₂²×C₈×C₁₃	D₄	1	1	yes	characteristic
52	C₂²×C₈×C₁₃	D₄	1	1	yes	characteristic
53	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
54	#88184	—	2	1	no	—
55	#88184	C₂×C₄	1	2	yes	—
56	#88184	C₂×C₄	1	1	yes	characteristic
57	#88183	—	2	1	no	—
58	C₄×C₂²⋊D₁₃	—	2	1	no	—
59	#88178	C₂×C₄	1	1	yes	characteristic
60	C₂×#6099	—	2	1	no	—
61	C₂×D₁₀₄	C₂×C₄	1	2	yes	—
62	C₂×#6095	C₂×C₄	1	2	yes	—
63	#88155	—	4	4	no	—
64	C₂×#6094	—	2	2	no	—
65	C₂×#6094	—	2	1	no	—
66	C₂×C₈×D₁₃	—	2	2	no	—
67	C₂×C₈×D₁₃	—	2	1	no	—
68	#88130	—	2	1	no	—
69	#88129	—	2	1	no	—
70	#88129	C₂×C₄	1	1	yes	characteristic
71	#88128	C₂×C₄	1	1	yes	characteristic
72	C₄×D₅₂	—	2	1	no	—
73	C₄×D₅₂	C₂³	1	2	yes	—
74	C₄×D₅₂	C₂³	1	1	yes	characteristic
75	#88126	—	2	1	no	—
76	#88124	C₂×C₄	1	1	yes	characteristic
77	#88123	C₂×C₄	1	1	yes	characteristic
78	C₄×Dic₂₆	C₂³	1	1	yes	characteristic
79	C₁₃×C₄⋊C₈	—	2	1	no	—
80	C₁₃×C₂²⋊C₈	—	2	1	no	—
81	C₁₃×#97	C₂×C₄	1	1	yes	characteristic
82	C₁₃×#97	C₂×C₄	1	1	yes	characteristic
83	C₄×C₈×C₁₃	D₄	1	1	yes	characteristic
84	C₄×C₈×C₁₃	D₄	1	1	yes	characteristic
85	C₄×C₈×C₁₃	C₂³	1	2	yes	—
86	C₄×C₈×C₁₃	C₂³	1	2	yes	—
87	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
88	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
89	C₂²⋊#1055	—	2	1	no	—
90	#88061	C₂×C₄	1	2	yes	—
91	#88061	C₂×C₄	1	2	yes	—
92	#88061	C₂×C₄	1	2	yes	—
93	#88060	—	2	1	no	—
94	#88060	—	2	2	no	—
95	#88060	—	2	2	no	—
96	#88060	—	2	1	no	—
97	#88058	C₂×C₄	1	2	yes	—
98	#88057	C₂×C₄	1	2	yes	—
99	#88056	C₂×C₄	1	2	yes	—
100	#88055	—	2	1	no	—
101	#88054	—	2	1	no	—
102	#88054	—	2	1	no	—
103	C₈×Dic₁₃	—	2	1	no	—
104	C₄⋊#1055	—	2	1	no	—
105	C₄⋊#1055	C₂³	1	2	yes	—
106	C₄⋊#1055	C₂³	1	1	yes	characteristic
107	C₄⋊#1055	C₂³	1	1	yes	characteristic
108	#88043	—	2	1	no	—
109	#17966	—	13	1	no	maximal, Sylow
110	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
111	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
112	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
113	C₂×C₂²⋊D₁₃	—	2	1	no	—
114	C₂×C₂²⋊D₁₃	—	2	2	no	—
115	#6127	—	4	2	no	—
116	#6127	—	4	2	no	—
117	C₂×D₅₂	—	2	1	no	—
118	C₂×D₅₂	—	2	1	no	—
119	C₂×D₅₂	C₂²×C₄	1	2	yes	—
120	C₂×D₅₂	C₂²×C₄	1	1	yes	characteristic
121	C₂×C₄×D₁₃	—	2	1	no	—
122	C₂×C₄×D₁₃	—	2	2	no	—
123	C₂×Dic₂₆	—	2	1	no	—
124	C₂×Dic₂₆	C₂²×C₄	1	1	yes	characteristic
125	C₁₃×M₁₆	—	2	4	no	—
126	C₂×C₈×C₁₃	—	2	2	no	—
127	C₂×C₈×C₁₃	—	2	2	no	—
128	C₂×C₈×C₁₃	—	4	1	no	—
129	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
130	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
131	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
132	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
133	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
134	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
135	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
136	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
137	C₄²×C₁₃	#41	1	1	yes	characteristic
138	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
139	C₂²⋊Dic₁₃	—	2	1	no	—
140	#6103	—	2	1	no	—
141	#6103	—	2	1	no	—
142	#6103	—	2	2	no	—
143	#6103	—	2	1	no	—
144	#6103	—	2	2	no	—
145	#6103	—	2	1	no	—
146	C₄⋊Dic₁₃	—	2	1	no	—
147	C₄⋊Dic₁₃	C₂²×C₄	1	1	yes	characteristic
148	C₄⋊Dic₁₃	C₂²×C₄	1	2	yes	—
149	C₄⋊Dic₁₃	C₂²×C₄	1	1	yes	characteristic
150	#6101	—	2	1	no	—
151	#6101	—	2	1	no	—
152	#6101	—	2	1	no	—
153	#6101	—	2	1	no	—
154	C₄×Dic₁₃	—	2	1	no	—
155	#6099	—	4	2	no	—
156	C₂×#1055	—	2	1	no	—
157	C₂×#1055	—	2	1	no	—
158	C₂×#1055	—	2	2	no	—
159	D₁₀₄	—	2	4	no	—
160	#6095	—	2	4	no	—
161	#6094	—	4	2	no	—
162	#6094	—	4	4	no	—
163	C₈×D₁₃	—	4	2	no	—
164	C₈×D₁₃	—	4	4	no	—
165	#3171	—	13	1	no	—
166	#2966	—	13	1	no	—
167	#2931	—	13	1	no	—
168	#1590	—	13	2	no	—
169	#1589	—	13	2	no	—
170	#1580	—	13	2	no	—
171	SD₁₆⋊C₈	—	13	2	no	—
172	#1569	—	13	1	no	—
173	#1496	—	13	1	no	—
174	#1495	—	13	1	no	—
175	C₈×M₁₆	D₁₃	1	1	yes	characteristic, complemented
176	C₂³×C₁₃	C₄×D₄	1	1	yes	characteristic
177	C₂²×D₁₃	—	2	1	no	—
178	C₂²×D₁₃	—	2	2	no	—
179	C₂×C₄×C₁₃	—	2	2	no	—
180	C₂×C₄×C₁₃	—	2	1	no	—
181	C₂×C₄×C₁₃	—	2	1	no	—
182	C₂×C₄×C₁₃	—	4	1	no	—
183	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
184	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
185	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
186	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
187	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
188	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
189	C₂²⋊D₁₃	—	4	4	no	—
190	C₂²⋊D₁₃	—	4	2	no	—
191	C₂×Dic₁₃	—	2	1	no	—
192	C₂×Dic₁₃	—	2	1	no	—
193	C₂×Dic₁₃	—	2	1	no	—
194	C₂×Dic₁₃	—	2	2	no	—
195	D₅₂	—	2	2	no	—
196	D₅₂	—	2	2	no	—
197	D₅₂	—	2	2	no	—
198	D₅₂	—	4	2	no	—
199	D₅₂	—	4	2	no	—
200	C₄×D₁₃	—	4	2	no	—
201	C₄×D₁₃	—	4	1	no	—
202	C₄×D₁₃	—	4	1	no	—
203	C₄×D₁₃	—	4	2	no	—
204	Dic₂₆	—	2	2	no	—
205	Dic₂₆	—	4	2	no	—
206	C₈×C₁₃	—	2	2	no	—
207	C₈×C₁₃	—	2	1	no	—
208	C₈×C₁₃	—	2	1	no	—
209	C₈×C₁₃	—	2	1	no	—
210	C₈×C₁₃	—	4	2	no	—
211	C₈×C₁₃	#131	1	4	yes	complemented
212	C₈×C₁₃	AGL(1,ℤ/8)	1	2	yes	—
213	#1055	—	4	2	no	—
214	#1055	—	4	1	no	—
215	#1055	—	4	1	no	—
216	C₂×#131	—	26	1	no	—
217	#532	—	13	1	no	—
218	#529	—	13	1	no	—
219	#501	—	13	1	no	—
220	#496	—	13	1	no	—
221	#490	—	13	1	no	—
222	#489	—	13	1	no	—
223	#469	—	13	2	no	—
224	#468	—	13	2	no	—
225	#446	—	13	1	no	—
226	C₈×Q₈	—	13	1	no	—
227	C₄×SD₁₆	—	13	2	no	—
228	C₄×D₈	—	13	2	no	—
229	#436	—	13	1	no	—
230	#436	—	13	2	no	—
231	#436	—	26	1	no	—
232	#435	—	26	1	no	—
233	C₈×D₄	—	13	2	no	—
234	C₈×D₄	—	13	1	no	—
235	C₈×D₄	—	26	1	no	—
236	C₈×D₄	—	26	1	no	—
237	#433	—	26	1	no	—
238	#432	—	13	1	no	—
239	#431	C₂×D₁₃	1	1	yes	characteristic
240	#423	—	13	1	no	—
241	#408	—	26	1	no	—
242	#405	—	26	1	no	—
243	C₄×M₁₆	C₂×D₁₃	1	1	yes	characteristic
244	C₂×C₄×C₈	C₂×D₁₃	1	1	yes	characteristic
245	#335	—	13	2	no	—
246	#334	—	13	2	no	—
247	Q₈⋊C₈	—	13	2	no	—
248	D₄⋊C₈	—	13	2	no	—
249	D₄⋊C₈	—	13	2	no	—
250	D₄⋊C₈	—	13	2	no	—
251	#322	C₂×D₁₃	1	2	yes	—
252	C₈²	C₂×D₁₃	1	2	yes	—
253	C₂²×C₁₃	—	2	1	no	—
254	C₂²×C₁₃	—	2	1	no	—
255	C₂²×C₁₃	—	2	1	no	—
256	C₂²×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
257	C₂×D₁₃	—	4	2	no	—
258	C₂×D₁₃	—	4	1	no	—
259	C₂×D₁₃	—	4	2	no	—
260	C₂×D₁₃	—	4	1	no	—
261	C₂×D₁₃	—	4	2	no	—
262	C₂×D₁₃	—	4	1	no	—
263	C₄×C₁₃	—	2	1	no	—
264	C₄×C₁₃	—	2	1	no	—
265	C₄×C₁₃	—	2	1	no	—
266	C₄×C₁₃	—	2	1	no	—
267	C₄×C₁₃	C₂×#131	1	2	yes	—
268	C₄×C₁₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
269	C₄×C₁₃	#575	1	1	yes	characteristic
270	Dic₁₃	—	4	1	no	—
271	Dic₁₃	—	4	2	no	—
272	Dic₁₃	—	4	1	no	—
273	Dic₁₃	—	4	1	no	—
274	C₂×#41	—	26	1	no	—
275	C₂×SD₁₆	—	13	2	no	—
276	C₂×D₈	—	13	2	no	—
277	#131	—	52	4	no	—
278	C₂×M₁₆	—	26	1	no	—
279	C₂×M₁₆	—	26	2	no	—
280	C₂×M₁₆	—	26	1	no	—
281	C₂×M₁₆	C₄×D₁₃	1	2	yes	—
282	C₂²×C₈	—	26	2	no	—
283	C₂²×C₈	—	26	1	no	—
284	C₂²×C₈	D₅₂	1	1	yes	characteristic
285	C₂²×C₈	D₅₂	1	1	yes	characteristic
286	C₄⋊Q₈	—	13	1	no	—
287	#127	—	13	1	no	—
288	#126	—	26	1	no	—
289	#125	—	13	1	no	—
290	#124	—	13	1	no	—
291	#124	—	26	1	no	—
292	#123	—	26	1	no	—
293	C₂²⋊Q₈	—	13	1	no	—
294	#121	—	13	1	no	—
295	#121	—	13	2	no	—
296	#121	—	26	1	no	—
297	C₄×Q₈	—	13	1	no	—
298	C₄×D₄	—	13	1	no	—
299	C₄×D₄	—	13	2	no	—
300	C₄×D₄	—	26	1	no	—
301	C₄×D₄	—	26	1	no	—
302	#117	—	26	1	no	—
303	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
304	#107	—	13	2	no	—
305	#106	—	13	2	no	—
306	C₄⋊C₈	—	2	1	no	—
307	C₄⋊C₈	—	13	1	no	—
308	C₄⋊C₈	—	13	1	no	—
309	C₄⋊C₈	—	13	2	no	—
310	C₄⋊C₈	—	26	1	no	—
311	C₄⋊C₈	—	26	1	no	—
312	C₄⋊C₈	—	26	1	no	—
313	#103	—	13	2	no	—
314	#102	—	13	2	no	—
315	#102	—	13	2	no	—
316	#102	—	13	2	no	—
317	C₂²⋊C₈	—	2	1	no	—
318	C₂²⋊C₈	—	26	1	no	—
319	C₂²⋊C₈	—	26	2	no	—
320	C₂²⋊C₈	—	26	2	no	—
321	C₂²⋊C₈	—	26	1	no	—
322	C₂²⋊C₈	—	26	1	no	—
323	#97	—	26	1	no	—
324	#97	—	26	1	no	—
325	#97	C₄×D₁₃	1	1	yes	characteristic
326	#97	C₄×D₁₃	1	1	yes	characteristic
327	C₄×C₈	—	26	1	no	—
328	C₄×C₈	D₅₂	1	1	yes	characteristic
329	C₄×C₈	D₅₂	1	1	yes	characteristic
330	C₄×C₈	C₂²×D₁₃	1	2	yes	—
331	C₄×C₈	C₂²×D₁₃	1	2	yes	—
332	C₄×C₈	C₂²×D₁₃	1	1	yes	characteristic
333	C₄×C₈	C₂²×D₁₃	1	1	yes	characteristic
334	C₂×C₁₃	—	4	1	no	—
335	C₂×C₁₃	#2931	1	1	yes	characteristic
336	C₂×C₁₃	C₄×AGL(1,ℤ/8)	1	1	yes	characteristic
337	C₂×C₁₃	#2955	1	1	yes	characteristic
338	D₁₃	—	8	2	no	—
339	D₁₃	—	8	1	no	—
340	#41	—	52	2	no	—
341	#41	—	52	2	no	—
342	C₂×Q₈	—	13	1	no	—
343	C₂×Q₈	—	26	1	no	—
344	C₂×D₄	—	13	1	no	—
345	C₂×D₄	—	13	2	no	—
346	C₂×D₄	—	26	1	no	—
347	C₂×D₄	—	26	2	no	—
348	C₂×D₄	—	26	1	no	—
349	C₂×D₄	—	26	1	no	—
350	C₂²×C₄	—	26	1	no	—
351	C₂²×C₄	—	26	2	no	—
352	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
353	C₂²×C₄	C₂×D₅₂	1	1	yes	characteristic
354	C₂²×C₄	#6127	1	1	yes	characteristic
355	SD₁₆	—	26	4	no	—
356	D₈	—	26	4	no	—
357	M₁₆	—	2	4	no	—
358	M₁₆	—	52	2	no	—
359	M₁₆	—	52	4	no	—
360	M₁₆	—	52	2	no	—
361	C₂×C₈	—	2	2	no	—
362	C₂×C₈	—	2	2	no	—
363	C₂×C₈	—	4	1	no	—
364	C₂×C₈	—	26	1	no	—
365	C₂×C₈	—	26	1	no	—
366	C₂×C₈	—	26	2	no	—
367	C₂×C₈	—	52	4	no	—
368	C₂×C₈	—	52	2	no	—
369	C₂×C₈	C₂×C₄×D₁₃	1	2	yes	—
370	C₂×C₈	C₂×C₄×D₁₃	1	2	yes	—
371	C₂×C₈	C₂×D₅₂	1	1	yes	characteristic
372	C₂×C₈	C₂×D₅₂	1	1	yes	characteristic
373	C₂×C₈	C₂×D₅₂	1	1	yes	characteristic
374	C₂×C₈	C₂×D₅₂	1	1	yes	characteristic
375	C₄⋊C₄	—	13	1	no	—
376	C₄⋊C₄	—	13	1	no	—
377	C₄⋊C₄	—	13	2	no	—
378	C₄⋊C₄	—	26	1	no	—
379	C₄⋊C₄	—	26	1	no	—
380	C₄⋊C₄	—	26	1	no	—
381	C₄⋊C₄	—	26	1	no	—
382	C₄⋊C₄	—	26	1	no	—
383	C₂²⋊C₄	—	26	1	no	—
384	C₂²⋊C₄	—	26	1	no	—
385	C₂²⋊C₄	—	26	1	no	—
386	C₂²⋊C₄	—	26	2	no	—
387	C₂²⋊C₄	—	26	1	no	—
388	C₂²⋊C₄	—	26	2	no	—
389	C₂²⋊C₄	—	26	1	no	—
390	C₄²	—	26	1	no	—
391	C₄²	C₂×C₄×D₁₃	1	1	yes	characteristic
392	C₄²	C₂×D₅₂	1	1	yes	characteristic
393	C₄²	#6127	1	1	yes	characteristic
394	C₄²	C₂³×D₁₃	1	1	yes	characteristic
395	C₁₃	#17966	1	1	yes	characteristic, complemented, Sylow
396	C₂³	—	26	1	no	—
397	C₂³	—	26	2	no	—
398	C₂³	C₄×D₅₂	1	1	yes	characteristic
399	Q₈	—	26	2	no	—
400	Q₈	—	52	2	no	—
401	D₄	—	26	2	no	—
402	D₄	—	26	2	no	—
403	D₄	—	26	2	no	—
404	D₄	—	52	2	no	—
405	D₄	—	52	2	no	—
406	D₄	—	52	2	no	—
407	D₄	—	52	4	no	—
408	C₂×C₄	—	2	2	no	—
409	C₂×C₄	—	2	1	no	—
410	C₂×C₄	—	2	1	no	—
411	C₂×C₄	—	4	1	no	—
412	C₂×C₄	—	26	1	no	—
413	C₂×C₄	—	26	1	no	—
414	C₂×C₄	—	26	1	no	—
415	C₂×C₄	—	26	2	no	—
416	C₂×C₄	—	52	2	no	—
417	C₂×C₄	—	52	1	no	—
418	C₂×C₄	—	52	1	no	—
419	C₂×C₄	—	52	2	no	—
420	C₂×C₄	C₄×D₅₂	1	1	yes	characteristic
421	C₂×C₄	C₄×D₅₂	1	1	yes	characteristic
422	C₂×C₄	C₄×D₅₂	1	1	yes	characteristic
423	C₂×C₄	C₂²×C₄×D₁₃	1	1	yes	characteristic
424	C₂×C₄	C₂²×D₅₂	1	1	yes	characteristic
425	C₂×C₄	C₂×#6127	1	1	yes	characteristic
426	C₈	—	2	2	no	—
427	C₈	—	2	1	no	—
428	C₈	—	2	1	no	—
429	C₈	—	2	1	no	—
430	C₈	—	4	2	no	—
431	C₈	—	52	2	no	—
432	C₈	—	52	1	no	—
433	C₈	—	52	1	no	—
434	C₈	#88155	1	4	yes	complemented
435	C₈	#88162	1	2	yes	—
436	C₂²	—	2	1	no	—
437	C₂²	—	2	1	no	—
438	C₂²	—	2	1	no	—
439	C₂²	—	52	2	no	—
440	C₂²	—	52	1	no	—
441	C₂²	—	52	2	no	—
442	C₂²	—	52	1	no	—
443	C₂²	—	52	1	no	—
444	C₂²	—	52	2	no	—
445	C₂²	C₂×C₄×D₅₂	1	1	yes	characteristic
446	C₄	—	2	1	no	—
447	C₄	—	2	1	no	—
448	C₄	—	2	1	no	—
449	C₄	—	2	1	no	—
450	C₄	—	52	1	no	—
451	C₄	—	52	2	no	—
452	C₄	—	52	1	no	—
453	C₄	—	52	1	no	—
454	C₄	C₂×#88155	1	2	yes	—
455	C₄	C₂×#88162	1	1	yes	characteristic
456	C₄	#11719453	1	1	yes	characteristic
457	C₂	—	4	1	no	—
458	C₂	—	104	2	no	—
459	C₂	—	104	1	no	—
460	C₂	#13123549	1	1	yes	characteristic
461	C₂	C₄×#88162	1	1	yes	characteristic
462	C₂	#13123740	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²×D₅₂
commutator	C₂×C₄×C₁₃	C₂³×C₄
Frattini	C₄²	C₂³×D₁₃
Fitting	C₈×C₁₃×M₁₆	C₂
socle	C₂²×C₁₃	C₂×C₄×D₄
prime radical	#13125431	C₂
cosocle	C₄²×C₁₃	C₂⁴
hypercenter	C₈×M₁₆	D₁₃
hypocenter	C₁₃	#17966
LCS	G ▷ C₂×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄×C₈ ◁ C₈×M₁₆

Complements

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

N	H ≅ G/N	type
2. #13123811	C₂	semidirect
3. #13123549	C₂	semidirect
4. #13113728	C₂	semidirect
5. #13113722	C₂	semidirect
6. #13113661	C₂	semidirect
7. #13113650	C₂	semidirect
8. #13113603	C₂	semidirect
9. #13113306	C₂	semidirect
10. #13113302	C₂	semidirect
11. C₈×C₁₃×M₁₆	C₂	semidirect
175. C₈×M₁₆	D₁₃	semidirect
211. C₈×C₁₃	#131	semidirect
395. C₁₃	#17966	semidirect
434. C₈	#88155	semidirect

Maximal subgroups

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

subgroup	index
#13125431	2
#13123811	2
#13123549	2
#13113728	2
#13113722	2
#13113661	2
#13113650	2
#13113603	2
#13113306	2
#13113302	2
C₈×C₁₃×M₁₆	2
#17966	13