Subgroups — #15832955

Order 3328.

624 conjugacy classes of subgroups.

The subgroup lattice has 454 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13124908	C₂	1	1	yes	maximal, characteristic
2	#13123792	C₂	1	1	yes	maximal, characteristic
3	#13123766	C₂	1	1	yes	maximal, characteristic, complemented
4	#13113685	C₂	1	2	yes	maximal, complemented
5	#13113671	C₂	1	2	yes	maximal, complemented
6	#13113654	C₂	1	2	yes	maximal, complemented
7	#13113647	C₂	1	2	yes	maximal, complemented
8	#13113273	C₂	1	1	yes	maximal, characteristic
9	#13113256	C₂	1	1	yes	maximal, characteristic, complemented
10	#13113126	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#1574	C₂	1	1	yes	maximal, characteristic, complemented
12	C₄×#6127	C₂²	1	1	yes	characteristic
13	#11719175	C₂²	1	1	yes	characteristic
14	C₁₃×#431	C₂²	1	1	yes	characteristic
15	C₁₃×#431	C₂²	1	1	yes	characteristic
16	C₁₃×#423	C₂²	1	1	yes	characteristic
17	#11718783	—	2	1	no	—
18	#11718780	—	2	1	no	—
19	C₄×#6099	C₂²	1	1	yes	characteristic
20	C₂×C₄×#1055	C₂²	1	1	yes	characteristic
21	#11718512	C₄	1	1	yes	characteristic
22	#11718510	C₄	1	1	yes	characteristic
23	#11718507	C₄	1	1	yes	characteristic
24	#11718502	C₄	1	1	yes	characteristic
25	#11718495	C₂²	1	1	yes	characteristic
26	#11718495	C₂²	1	1	yes	characteristic
27	#11718492	—	2	1	no	—
28	#11718492	C₂²	1	2	yes	—
29	#11718491	—	2	1	no	—
30	#11718491	C₂²	1	2	yes	—
31	#11718491	C₂²	1	1	yes	characteristic
32	#11718491	C₂²	1	1	yes	characteristic
33	#11718394	C₄	1	2	yes	—
34	#11718386	—	2	1	no	—
35	#11718386	—	2	1	no	—
36	#11718384	C₄	1	2	yes	—
37	C₄×Dic₅₂	C₂²	1	2	yes	—
38	C₄×#6095	C₂²	1	2	yes	—
39	#11718346	—	2	1	no	—
40	C₄×C₈×D₁₃	—	2	1	no	—
41	C₁₃×#335	C₂²	1	2	yes	—
42	C₁₃×#334	C₂²	1	2	yes	—
43	#11718076	C₂²	1	2	yes	—
44	#11718076	C₂²	1	2	yes	—
45	#11718076	C₂²	1	2	yes	—
46	#11718075	C₂²	1	2	yes	—
47	#11718047	C₂²	1	2	yes	—
48	#11718046	C₂²	1	2	yes	—
49	C₂×#6127	C₂×C₄	1	1	yes	characteristic
50	C₂×C₁₃×M₁₆	—	2	1	no	—
51	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
52	C₄×C₂²⋊D₁₃	—	2	1	no	—
53	C₄×C₂²⋊D₁₃	—	2	1	no	—
54	#88180	—	2	1	no	—
55	#88180	C₂×C₄	1	1	yes	characteristic
56	#88178	—	2	1	no	—
57	#88178	C₂×C₄	1	2	yes	—
58	C₂×#6099	—	2	1	no	—
59	C₂²×#1055	D₄	1	1	yes	characteristic
60	C₂²×#1055	D₄	1	1	yes	characteristic
61	C₂×Dic₅₂	C₂×C₄	1	2	yes	—
62	C₂×#6095	C₂×C₄	1	2	yes	—
63	C₂×C₈×D₁₃	—	2	1	no	—
64	C₂×C₈×D₁₃	—	2	1	no	—
65	C₄×D₅₂	C₂×C₄	1	1	yes	characteristic
66	C₄×D₅₂	C₂³	1	1	yes	characteristic
67	#88126	—	2	1	no	—
68	C₄²×D₁₃	—	2	1	no	—
69	#88124	—	2	1	no	—
70	#88123	C₂×C₄	1	1	yes	characteristic
71	#88123	C₂×C₄	1	1	yes	characteristic
72	C₄×Dic₂₆	—	2	1	no	—
73	C₄×Dic₂₆	C₂×C₄	1	1	yes	characteristic
74	C₄×Dic₂₆	C₂³	1	2	yes	—
75	C₄×Dic₂₆	C₂³	1	1	yes	characteristic
76	C₁₃×C₄⋊C₈	—	2	1	no	—
77	C₁₃×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
78	C₁₃×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
79	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
80	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
81	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
82	C₁₃×C₂²⋊C₈	—	2	1	no	—
83	C₁₃×C₂²⋊C₈	C₂×C₄	1	2	yes	—
84	C₄×C₈×C₁₃	—	2	1	no	—
85	C₄×C₈×C₁₃	C₂³	1	2	yes	—
86	#88061	C₂×C₄	1	2	yes	—
87	#88060	—	2	1	no	—
88	#88060	—	2	1	no	—
89	#88058	C₂×C₄	1	2	yes	—
90	#88057	C₂×C₄	1	2	yes	—
91	#88056	C₂×C₄	1	2	yes	—
92	#88056	C₂×C₄	1	2	yes	—
93	#88056	C₂×C₄	1	2	yes	—
94	#88055	—	2	2	no	—
95	#88054	—	2	2	no	—
96	#88054	—	2	2	no	—
97	#88054	—	2	1	no	—
98	#88054	—	2	1	no	—
99	C₈×Dic₁₃	—	2	2	no	—
100	C₈×Dic₁₃	—	2	1	no	—
101	C₈×Dic₁₃	—	2	1	no	—
102	#88043	—	2	1	no	—
103	C₄×#1055	D₄	1	1	yes	characteristic
104	C₄×#1055	D₄	1	1	yes	characteristic
105	C₄×#1055	C₂³	1	2	yes	—
106	C₄×#1055	C₂³	1	1	yes	characteristic
107	C₄×#1055	C₂³	1	1	yes	characteristic
108	#17916	—	13	1	no	maximal, Sylow
109	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
110	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
111	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
112	C₂×C₂²⋊D₁₃	—	2	1	no	—
113	#6127	—	2	2	no	—
114	#6127	—	2	2	no	—
115	C₂×D₅₂	C₂²×C₄	1	1	yes	characteristic
116	C₂×C₄×D₁₃	—	2	1	no	—
117	C₂×C₄×D₁₃	—	2	1	no	—
118	C₂×C₄×D₁₃	—	2	1	no	—
119	C₂×Dic₂₆	—	2	1	no	—
120	C₂×Dic₂₆	C₂²×C₄	1	2	yes	—
121	C₂×Dic₂₆	C₂²×C₄	1	1	yes	characteristic
122	C₁₃×M₁₆	—	4	2	no	—
123	C₂×C₈×C₁₃	—	2	1	no	—
124	C₂×C₈×C₁₃	—	2	1	no	—
125	C₂×C₈×C₁₃	—	2	2	no	—
126	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
127	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
128	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
129	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
130	C₄²×C₁₃	#41	1	1	yes	characteristic
131	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
132	C₂²⋊Dic₁₃	—	2	2	no	—
133	C₂²⋊Dic₁₃	—	2	1	no	—
134	#6103	—	2	1	no	—
135	#6103	—	2	1	no	—
136	C₄⋊Dic₁₃	—	2	1	no	—
137	C₄⋊Dic₁₃	—	2	1	no	—
138	C₄⋊Dic₁₃	—	2	1	no	—
139	C₄⋊Dic₁₃	C₂²×C₄	1	1	yes	characteristic
140	C₄⋊Dic₁₃	C₂²×C₄	1	2	yes	—
141	C₄⋊Dic₁₃	C₂²×C₄	1	1	yes	characteristic
142	#6101	—	2	2	no	—
143	#6101	—	2	1	no	—
144	#6101	—	2	2	no	—
145	#6101	—	2	1	no	—
146	C₄×Dic₁₃	—	2	1	no	—
147	C₄×Dic₁₃	—	2	1	no	—
148	C₄×Dic₁₃	—	2	2	no	—
149	C₄×Dic₁₃	—	2	1	no	—
150	#6099	—	4	2	no	—
151	C₂×#1055	—	2	2	no	—
152	C₂×#1055	—	2	2	no	—
153	C₂×#1055	—	4	1	no	—
154	C₂×#1055	C₂×D₄	1	1	yes	characteristic
155	C₂×#1055	C₂×D₄	1	1	yes	characteristic
156	C₂×#1055	C₂×D₄	1	1	yes	characteristic
157	C₂×#1055	C₂×D₄	1	1	yes	characteristic
158	Dic₅₂	—	2	4	no	—
159	#6095	—	2	4	no	—
160	C₈×D₁₃	—	4	2	no	—
161	C₈×D₁₃	—	4	2	no	—
162	#3107	—	13	1	no	—
163	C₈×#41	—	13	1	no	—
164	#2960	—	13	1	no	—
165	#1584	—	13	2	no	—
166	#1582	—	13	2	no	—
167	#1579	—	13	2	no	—
168	SD₁₆⋊C₈	—	13	2	no	—
169	#1574	D₁₃	1	1	yes	characteristic, complemented
170	#1489	—	13	1	no	—
171	#1485	—	13	1	no	—
172	#1451	—	13	1	no	—
173	C₂³×C₁₃	C₄×D₄	1	1	yes	characteristic
174	C₂²×D₁₃	—	2	1	no	—
175	C₂×C₄×C₁₃	—	2	1	no	—
176	C₂×C₄×C₁₃	—	2	1	no	—
177	C₂×C₄×C₁₃	—	2	1	no	—
178	C₂×C₄×C₁₃	—	2	1	no	—
179	C₂×C₄×C₁₃	—	2	2	no	—
180	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
181	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
182	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
183	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
184	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
185	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
186	C₂²⋊D₁₃	—	2	4	no	—
187	C₂×Dic₁₃	—	2	1	no	—
188	C₂×Dic₁₃	—	2	1	no	—
189	C₂×Dic₁₃	—	2	1	no	—
190	C₂×Dic₁₃	—	2	2	no	—
191	C₂×Dic₁₃	—	2	2	no	—
192	D₅₂	—	2	1	no	—
193	D₅₂	#131	1	2	yes	—
194	C₄×D₁₃	—	2	4	no	—
195	C₄×D₁₃	—	4	1	no	—
196	C₄×D₁₃	—	4	1	no	—
197	C₄×D₁₃	—	4	2	no	—
198	Dic₂₆	—	2	1	no	—
199	Dic₂₆	—	2	2	no	—
200	Dic₂₆	—	2	2	no	—
201	Dic₂₆	—	4	2	no	—
202	Dic₂₆	#131	1	2	yes	—
203	C₈×C₁₃	—	2	2	no	—
204	C₈×C₁₃	—	2	2	no	—
205	C₈×C₁₃	—	4	1	no	—
206	C₈×C₁₃	—	4	1	no	—
207	C₈×C₁₃	—	4	2	no	—
208	#1055	—	2	1	no	—
209	#1055	—	2	1	no	—
210	#1055	—	2	1	no	—
211	#1055	—	4	2	no	—
212	#1055	#137	1	2	yes	—
213	#533	—	13	1	no	—
214	C₄×#41	—	13	1	no	—
215	#485	—	13	2	no	—
216	#475	—	13	1	no	—
217	#474	—	13	1	no	—
218	#462	—	13	1	no	—
219	#461	—	13	1	no	—
220	#452	—	13	2	no	—
221	#446	—	13	2	no	—
222	#446	—	26	1	no	—
223	C₈×Q₈	—	13	2	no	—
224	C₈×Q₈	—	13	1	no	—
225	C₈×Q₈	—	13	1	no	—
226	C₈×Q₈	—	26	1	no	—
227	C₄×Q₁₆	—	13	2	no	—
228	C₄×SD₁₆	—	13	2	no	—
229	C₈×D₄	—	13	1	no	—
230	C₈×D₄	—	13	1	no	—
231	C₈×D₄	—	26	1	no	—
232	C₈×D₄	—	26	1	no	—
233	#431	—	26	1	no	—
234	#431	C₂×D₁₃	1	1	yes	characteristic
235	#431	C₂×D₁₃	1	1	yes	characteristic
236	#424	—	26	1	no	—
237	#423	C₂×D₁₃	1	1	yes	characteristic
238	#405	—	26	1	no	—
239	C₄×M₁₆	—	13	1	no	—
240	C₂×C₄×C₈	—	13	1	no	—
241	C₂×C₄×C₈	—	26	1	no	—
242	#335	C₂×D₁₃	1	2	yes	—
243	#334	C₂×D₁₃	1	2	yes	—
244	Q₈⋊C₈	—	13	2	no	—
245	Q₈⋊C₈	—	13	2	no	—
246	Q₈⋊C₈	—	13	2	no	—
247	D₄⋊C₈	—	13	2	no	—
248	#322	—	13	2	no	—
249	#322	—	13	2	no	—
250	C₂²×C₁₃	—	2	1	no	—
251	C₂²×C₁₃	—	2	1	no	—
252	C₂²×C₁₃	—	2	1	no	—
253	C₂²×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
254	C₂×D₁₃	—	2	2	no	—
255	C₂×D₁₃	—	4	1	no	—
256	C₂×D₁₃	—	4	1	no	—
257	C₄×C₁₃	—	2	1	no	—
258	C₄×C₁₃	—	2	1	no	—
259	C₄×C₁₃	—	2	1	no	—
260	C₄×C₁₃	#444	1	2	yes	—
261	C₄×C₁₃	C₂×#131	1	1	yes	characteristic
262	C₄×C₁₃	C₂×#131	1	1	yes	characteristic
263	C₄×C₁₃	C₂×#137	1	1	yes	characteristic
264	C₄×C₁₃	#575	1	1	yes	characteristic
265	Dic₁₃	—	2	2	no	—
266	Dic₁₃	—	4	2	no	—
267	Dic₁₃	—	4	1	no	—
268	Dic₁₃	—	4	2	no	—
269	Dic₁₃	—	4	1	no	—
270	C₂×#41	—	13	1	no	—
271	C₂×Q₁₆	—	13	2	no	—
272	C₂×SD₁₆	—	13	2	no	—
273	C₂×M₁₆	—	2	1	no	—
274	C₂×M₁₆	—	26	1	no	—
275	C₂²×C₈	—	13	1	no	—
276	C₂²×C₈	—	13	1	no	—
277	C₂²×C₈	—	26	1	no	—
278	C₂²×C₈	—	26	1	no	—
279	C₄⋊Q₈	—	13	1	no	—
280	C₄⋊Q₈	—	13	1	no	—
281	#125	—	26	1	no	—
282	C₂²⋊Q₈	—	13	2	no	—
283	C₂²⋊Q₈	—	26	1	no	—
284	C₄×Q₈	—	13	1	no	—
285	C₄×Q₈	—	13	1	no	—
286	C₄×Q₈	—	13	2	no	—
287	C₄×Q₈	—	26	1	no	—
288	C₄×D₄	—	13	1	no	—
289	C₄×D₄	—	13	1	no	—
290	C₄×D₄	—	26	1	no	—
291	C₄×D₄	—	26	1	no	—
292	#117	—	13	1	no	—
293	#117	—	26	1	no	—
294	#117	—	26	1	no	—
295	C₂×C₄²	—	26	1	no	—
296	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
297	#107	—	13	2	no	—
298	#106	—	13	2	no	—
299	C₄⋊C₈	—	2	1	no	—
300	C₄⋊C₈	—	26	2	no	—
301	C₄⋊C₈	—	26	2	no	—
302	C₄⋊C₈	—	26	1	no	—
303	C₄⋊C₈	—	26	1	no	—
304	C₄⋊C₈	C₄×D₁₃	1	1	yes	characteristic
305	C₄⋊C₈	C₄×D₁₃	1	1	yes	characteristic
306	C₄⋊C₈	C₂²×D₁₃	1	2	yes	—
307	C₄⋊C₈	C₂²×D₁₃	1	1	yes	characteristic
308	C₄⋊C₈	C₂²×D₁₃	1	1	yes	characteristic
309	#103	—	13	2	no	—
310	#103	—	13	2	no	—
311	#103	—	13	2	no	—
312	#102	—	13	2	no	—
313	C₂²⋊C₈	—	2	1	no	—
314	C₂²⋊C₈	—	26	1	no	—
315	C₂²⋊C₈	—	26	1	no	—
316	C₂²⋊C₈	C₄×D₁₃	1	2	yes	—
317	#97	—	26	2	no	—
318	#97	—	26	1	no	—
319	C₄×C₈	—	2	1	no	—
320	C₄×C₈	—	13	1	no	—
321	C₄×C₈	—	13	1	no	—
322	C₄×C₈	—	13	1	no	—
323	C₄×C₈	—	13	1	no	—
324	C₄×C₈	—	13	2	no	—
325	C₄×C₈	—	26	1	no	—
326	C₄×C₈	—	26	1	no	—
327	C₄×C₈	—	26	2	no	—
328	C₄×C₈	C₂²×D₁₃	1	2	yes	—
329	C₂×C₁₃	—	4	1	no	—
330	C₂×C₁₃	#2929	1	1	yes	characteristic
331	C₂×C₁₃	C₄×#137	1	1	yes	characteristic
332	C₂×C₁₃	C₂×#444	1	1	yes	characteristic
333	D₁₃	—	4	2	no	—
334	#41	—	26	2	no	—
335	#41	—	26	2	no	—
336	C₂×Q₈	—	13	1	no	—
337	C₂×Q₈	—	13	2	no	—
338	C₂×Q₈	—	26	1	no	—
339	C₂×D₄	—	13	1	no	—
340	C₂×D₄	—	26	1	no	—
341	C₂²×C₄	—	26	1	no	—
342	C₂²×C₄	—	26	1	no	—
343	C₂²×C₄	—	26	1	no	—
344	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
345	C₂²×C₄	D₄×D₁₃	1	1	yes	characteristic
346	C₂²×C₄	#6131	1	1	yes	characteristic
347	Q₁₆	—	26	4	no	—
348	SD₁₆	—	26	4	no	—
349	M₁₆	—	4	2	no	—
350	M₁₆	—	52	2	no	—
351	C₂×C₈	—	2	1	no	—
352	C₂×C₈	—	2	1	no	—
353	C₂×C₈	—	2	2	no	—
354	C₂×C₈	—	13	1	no	—
355	C₂×C₈	—	13	1	no	—
356	C₂×C₈	—	13	1	no	—
357	C₂×C₈	—	13	1	no	—
358	C₂×C₈	—	26	2	no	—
359	C₂×C₈	—	26	2	no	—
360	C₂×C₈	—	52	2	no	—
361	C₂×C₈	—	52	2	no	—
362	C₂×C₈	—	52	1	no	—
363	C₂×C₈	C₂×C₄×D₁₃	1	2	yes	—
364	C₂×C₈	C₂×C₄×D₁₃	1	2	yes	—
365	C₄⋊C₄	—	13	2	no	—
366	C₄⋊C₄	—	13	1	no	—
367	C₄⋊C₄	—	13	1	no	—
368	C₄⋊C₄	—	26	1	no	—
369	C₄⋊C₄	—	26	1	no	—
370	C₄⋊C₄	—	26	1	no	—
371	C₄⋊C₄	—	26	2	no	—
372	C₄⋊C₄	—	26	1	no	—
373	C₄⋊C₄	—	26	1	no	—
374	C₄⋊C₄	—	26	2	no	—
375	C₂²⋊C₄	—	26	1	no	—
376	C₂²⋊C₄	—	26	2	no	—
377	C₂²⋊C₄	—	26	1	no	—
378	C₂²⋊C₄	—	26	1	no	—
379	C₄²	—	26	1	no	—
380	C₄²	—	26	1	no	—
381	C₄²	—	26	1	no	—
382	C₄²	—	26	2	no	—
383	C₄²	C₂×C₄×D₁₃	1	1	yes	characteristic
384	C₄²	D₄×D₁₃	1	1	yes	characteristic
385	C₄²	#6131	1	1	yes	characteristic
386	C₄²	C₂³×D₁₃	1	1	yes	characteristic
387	C₁₃	#17916	1	1	yes	characteristic, complemented, Sylow
388	C₂³	—	26	1	no	—
389	C₂³	#88147	1	1	yes	characteristic
390	Q₈	—	13	2	no	—
391	Q₈	—	26	1	no	—
392	Q₈	—	26	2	no	—
393	Q₈	—	26	2	no	—
394	Q₈	—	52	2	no	—
395	D₄	—	13	2	no	—
396	D₄	—	26	4	no	—
397	D₄	—	26	1	no	—
398	C₂×C₄	—	2	1	no	—
399	C₂×C₄	—	2	1	no	—
400	C₂×C₄	—	2	1	no	—
401	C₂×C₄	—	2	1	no	—
402	C₂×C₄	—	2	2	no	—
403	C₂×C₄	—	26	4	no	—
404	C₂×C₄	—	26	1	no	—
405	C₂×C₄	—	26	1	no	—
406	C₂×C₄	—	26	1	no	—
407	C₂×C₄	—	26	2	no	—
408	C₂×C₄	—	26	2	no	—
409	C₂×C₄	—	52	1	no	—
410	C₂×C₄	—	52	1	no	—
411	C₂×C₄	—	52	2	no	—
412	C₂×C₄	#88147	1	1	yes	characteristic
413	C₂×C₄	#88147	1	1	yes	characteristic
414	C₂×C₄	#88147	1	1	yes	characteristic
415	C₂×C₄	C₂²×C₄×D₁₃	1	1	yes	characteristic
416	C₂×C₄	C₂×D₄×D₁₃	1	1	yes	characteristic
417	C₂×C₄	C₂×#6131	1	1	yes	characteristic
418	C₈	—	2	2	no	—
419	C₈	—	2	2	no	—
420	C₈	—	4	1	no	—
421	C₈	—	4	2	no	—
422	C₈	—	4	1	no	—
423	C₈	—	13	2	no	—
424	C₈	—	26	1	no	—
425	C₈	—	26	1	no	—
426	C₈	—	26	1	no	—
427	C₈	—	52	2	no	—
428	C₂²	—	2	1	no	—
429	C₂²	—	2	1	no	—
430	C₂²	—	2	1	no	—
431	C₂²	—	26	2	no	—
432	C₂²	—	52	1	no	—
433	C₂²	—	52	1	no	—
434	C₂²	C₂×#88147	1	1	yes	characteristic
435	C₄	—	2	1	no	—
436	C₄	—	2	1	no	—
437	C₄	—	2	1	no	—
438	C₄	—	26	2	no	—
439	C₄	—	52	1	no	—
440	C₄	—	52	1	no	—
441	C₄	—	52	2	no	—
442	C₄	—	52	2	no	—
443	C₄	#11718555	1	2	yes	—
444	C₄	D₁₃×#131	1	1	yes	characteristic
445	C₄	D₁₃×#131	1	1	yes	characteristic
446	C₄	#11719478	1	1	yes	characteristic
447	C₄	D₁₃×#137	1	1	yes	characteristic
448	C₂	—	4	1	no	—
449	C₂	—	52	2	no	—
450	C₂	#13123529	1	1	yes	characteristic
451	C₂	#13123654	1	1	yes	characteristic
452	C₂	C₂×#11718555	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₁₃
commutator	C₂×C₄×C₁₃	C₂³×C₄
Frattini	C₄²	C₂³×D₁₃
Fitting	C₁₃×#1574	C₂
socle	C₂²×C₁₃	C₂×C₄×D₄
prime radical	C₂×#6127	C₂×C₄
cosocle	C₄²×C₁₃	C₂⁴
hypercenter	#1574	D₁₃
hypocenter	C₁₃	#17916
LCS	G ▷ C₂×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1574

Complements

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

N	H ≅ G/N	type
3. #13123766	C₂	semidirect
4. #13113685	C₂	semidirect
5. #13113671	C₂	semidirect
6. #13113654	C₂	semidirect
7. #13113647	C₂	semidirect
9. #13113256	C₂	semidirect
10. #13113126	C₂	semidirect
11. C₁₃×#1574	C₂	semidirect
169. #1574	D₁₃	semidirect
387. C₁₃	#17916	semidirect

Maximal subgroups

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

subgroup	index
#13124908	2
#13123792	2
#13123766	2
#13113685	2
#13113671	2
#13113654	2
#13113647	2
#13113273	2
#13113256	2
#13113126	2
C₁₃×#1574	2
#17916	13