Subgroups — #15832540

Order 3328.

662 conjugacy classes of subgroups.

The subgroup lattice has 466 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13123792	C₂	1	1	yes	maximal, characteristic
2	C₂×#11718685	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄×#88196	C₂	1	1	yes	maximal, characteristic
4	#13113710	C₂	1	2	yes	maximal, complemented
5	#13113696	C₂	1	2	yes	maximal, complemented
6	#13113689	C₂	1	2	yes	maximal, complemented
7	#13113675	C₂	1	2	yes	maximal, complemented
8	#13113589	C₂	1	1	yes	maximal, characteristic, complemented
9	#13113224	C₂	1	1	yes	maximal, characteristic
10	#13113126	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#1479	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
13	C₂×#88196	C₄	1	1	yes	characteristic
14	C₄×#6127	C₂²	1	1	yes	characteristic
15	C₁₃×#431	C₂²	1	1	yes	characteristic
16	C₁₃×#431	C₂²	1	1	yes	characteristic
17	#11718886	C₄	1	1	yes	characteristic
18	#11718691	C₄	1	2	yes	—
19	C₄×#6107	C₂²	1	2	yes	—
20	#11718687	C₄	1	2	yes	—
21	C₄×#6106	C₂²	1	2	yes	—
22	#11718685	—	2	1	no	—
23	#11718685	—	2	1	no	—
24	#11718685	C₂²	1	2	yes	—
25	#11718685	C₂²	1	2	yes	—
26	#11718627	C₄	1	1	yes	characteristic
27	#11718625	C₄	1	1	yes	characteristic
28	C₂×C₄⋊#1055	—	2	1	no	—
29	C₂×C₄⋊#1055	C₂²	1	1	yes	characteristic
30	C₄×#6099	C₂²	1	1	yes	characteristic
31	C₂×#88043	—	2	1	no	—
32	C₂×C₄×#1055	C₂²	1	1	yes	characteristic
33	#11718495	C₂²	1	1	yes	characteristic
34	#11718495	C₂²	1	1	yes	characteristic
35	#11718491	C₂²	1	1	yes	characteristic
36	#11718491	C₂²	1	1	yes	characteristic
37	#11718386	—	2	1	no	—
38	#11718386	—	2	1	no	—
39	#11718346	—	2	1	no	—
40	C₄×C₈×D₁₃	—	2	1	no	—
41	C₁₃×Q₈⋊C₈	C₂²	1	2	yes	—
42	C₁₃×Q₈⋊C₈	C₂²	1	2	yes	—
43	#11718072	C₂²	1	2	yes	—
44	#11718071	C₂²	1	2	yes	—
45	#11718051	C₂²	1	2	yes	—
46	#11718048	C₂²	1	2	yes	—
47	#11718047	C₂²	1	2	yes	—
48	#11718046	C₂²	1	2	yes	—
49	C₂²×Q₈×C₁₃	C₂×C₄	1	1	yes	characteristic
50	C₂×#6127	C₂×C₄	1	1	yes	characteristic
51	C₄×Q₈×C₁₃	—	2	1	no	—
52	C₄×Q₈×C₁₃	—	2	1	no	—
53	C₄×Q₈×C₁₃	C₂×C₄	1	2	yes	—
54	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
55	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
56	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
57	C₂×C₄²×C₁₃	—	2	1	no	—
58	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
59	C₂×#6107	C₂×C₄	1	2	yes	—
60	#88196	—	2	4	no	—
61	C₂×#6106	C₂×C₄	1	2	yes	—
62	C₄×C₂²⋊D₁₃	—	2	1	no	—
63	C₄×C₂²⋊D₁₃	—	2	1	no	—
64	#88180	C₂×C₄	1	1	yes	characteristic
65	C₂×#6099	C₂×C₄	1	1	yes	characteristic
66	C₂×#6099	C₂×C₄	1	1	yes	characteristic
67	C₂²×#1055	—	2	1	no	—
68	C₂²×#1055	D₄	1	1	yes	characteristic
69	C₂²×#1055	D₄	1	1	yes	characteristic
70	C₂×C₈×D₁₃	—	2	1	no	—
71	C₂×C₈×D₁₃	—	2	1	no	—
72	C₄×D₅₂	C₂×C₄	1	1	yes	characteristic
73	C₄×D₅₂	C₂³	1	1	yes	characteristic
74	#88126	—	2	1	no	—
75	C₄²×D₁₃	—	2	1	no	—
76	C₄×Dic₂₆	C₂×C₄	1	1	yes	characteristic
77	C₄×Dic₂₆	C₂³	1	1	yes	characteristic
78	C₁₃×C₄⋊C₈	—	2	1	no	—
79	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
80	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
81	C₁₃×C₂²⋊C₈	—	2	1	no	—
82	C₁₃×C₂²⋊C₈	—	2	1	no	—
83	C₄×C₈×C₁₃	—	2	1	no	—
84	C₄×C₈×C₁₃	C₂³	1	2	yes	—
85	#88075	C₂×C₄	1	2	yes	—
86	#88075	C₂×C₄	1	2	yes	—
87	#88060	—	2	1	no	—
88	#88060	—	2	1	no	—
89	#88054	—	2	1	no	—
90	#88054	—	2	1	no	—
91	C₈×Dic₁₃	—	2	1	no	—
92	C₈×Dic₁₃	—	2	1	no	—
93	#88050	C₂×C₄	1	2	yes	—
94	#88049	C₂×C₄	1	2	yes	—
95	#88048	C₂×C₄	1	2	yes	—
96	#88047	C₂×C₄	1	2	yes	—
97	C₄⋊#1055	—	2	1	no	—
98	C₄⋊#1055	—	2	2	no	—
99	C₄⋊#1055	—	2	2	no	—
100	C₄⋊#1055	C₂³	1	2	yes	—
101	#88043	—	2	2	no	—
102	#88043	—	2	2	no	—
103	#88043	C₂×C₄	1	2	yes	—
104	C₄×#1055	D₄	1	1	yes	characteristic
105	C₄×#1055	D₄	1	1	yes	characteristic
106	C₄×#1055	C₂³	1	2	yes	—
107	C₄×#1055	C₂³	1	1	yes	characteristic
108	C₄×#1055	C₂³	1	1	yes	characteristic
109	#17872	—	13	1	no	maximal, Sylow
110	C₂×Q₈×C₁₃	—	2	1	no	—
111	C₂×Q₈×C₁₃	—	2	2	no	—
112	C₂×Q₈×C₁₃	—	2	2	no	—
113	C₂×Q₈×C₁₃	C₂²×C₄	1	2	yes	—
114	C₂²×C₄×C₁₃	—	2	1	no	—
115	C₂²×C₄×C₁₃	—	2	1	no	—
116	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
117	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
118	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
119	C₂×C₂²⋊D₁₃	—	2	1	no	—
120	#6127	—	2	2	no	—
121	#6127	M₁₆	1	4	yes	—
122	C₂×D₅₂	C₂²×C₄	1	1	yes	characteristic
123	C₂×C₄×D₁₃	—	2	1	no	—
124	C₂×C₄×D₁₃	—	2	1	no	—
125	C₂×C₄×D₁₃	—	2	1	no	—
126	C₂×Dic₂₆	C₂²×C₄	1	1	yes	characteristic
127	C₂×C₈×C₁₃	—	2	1	no	—
128	C₂×C₈×C₁₃	—	2	1	no	—
129	C₂×C₈×C₁₃	—	2	2	no	—
130	C₁₃×C₄⋊C₄	—	2	2	no	—
131	C₁₃×C₄⋊C₄	—	2	1	no	—
132	C₁₃×C₄⋊C₄	—	2	2	no	—
133	C₁₃×C₄⋊C₄	C₂²×C₄	1	2	yes	—
134	C₄²×C₁₃	—	2	2	no	—
135	C₄²×C₁₃	—	2	2	no	—
136	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
137	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
138	C₄²×C₁₃	#41	1	1	yes	characteristic
139	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
140	C₂²⋊Dic₁₃	—	2	1	no	—
141	#6107	—	2	4	no	—
142	#6106	—	2	4	no	—
143	#6103	—	2	1	no	—
144	#6103	—	2	1	no	—
145	C₄⋊Dic₁₃	C₂²×C₄	1	1	yes	characteristic
146	C₄⋊Dic₁₃	C₂²×C₄	1	1	yes	characteristic
147	#6101	—	2	1	no	—
148	#6101	—	2	1	no	—
149	C₄×Dic₁₃	—	2	1	no	—
150	C₄×Dic₁₃	—	2	1	no	—
151	C₄×Dic₁₃	—	2	1	no	—
152	#6099	—	2	2	no	—
153	#6099	—	2	2	no	—
154	C₂×#1055	—	2	2	no	—
155	C₂×#1055	—	2	2	no	—
156	C₂×#1055	—	4	1	no	—
157	C₂×#1055	—	4	2	no	—
158	C₂×#1055	C₂²×C₄	1	2	yes	—
159	C₂×#1055	C₂²×C₄	1	2	yes	—
160	C₂×#1055	C₂×D₄	1	1	yes	characteristic
161	C₂×#1055	C₂×D₄	1	1	yes	characteristic
162	C₂×#1055	C₂×D₄	1	1	yes	characteristic
163	C₂×#1055	C₂×D₄	1	1	yes	characteristic
164	C₈×D₁₃	—	4	2	no	—
165	C₈×D₁₃	—	4	2	no	—
166	C₈×#41	—	13	1	no	—
167	C₂×#446	—	13	1	no	—
168	C₄×#137	—	13	1	no	—
169	#1587	—	13	2	no	—
170	#1585	—	13	2	no	—
171	#1584	—	13	2	no	—
172	#1582	—	13	2	no	—
173	#1565	—	13	1	no	—
174	#1479	D₁₃	1	1	yes	characteristic, complemented
175	#1477	—	13	1	no	—
176	#1451	—	13	1	no	—
177	C₂³×C₁₃	C₄×D₄	1	1	yes	characteristic
178	C₂²×D₁₃	—	2	1	no	—
179	Q₈×C₁₃	—	2	2	no	—
180	Q₈×C₁₃	—	2	2	no	—
181	Q₈×C₁₃	—	4	2	no	—
182	C₂×C₄×C₁₃	—	2	1	no	—
183	C₂×C₄×C₁₃	—	2	1	no	—
184	C₂×C₄×C₁₃	—	2	2	no	—
185	C₂×C₄×C₁₃	—	2	2	no	—
186	C₂×C₄×C₁₃	—	4	1	no	—
187	C₂×C₄×C₁₃	—	4	2	no	—
188	C₂×C₄×C₁₃	—	4	2	no	—
189	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
190	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
191	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
192	C₂×C₄×C₁₃	C₂×M₁₆	1	2	yes	—
193	C₂×C₄×C₁₃	#131	1	2	yes	—
194	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
195	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
196	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
197	C₂²⋊D₁₃	—	2	4	no	—
198	C₂×Dic₁₃	—	2	1	no	—
199	C₂×Dic₁₃	—	2	1	no	—
200	C₂×Dic₁₃	—	2	1	no	—
201	D₅₂	—	2	1	no	—
202	D₅₂	C₂×M₁₆	1	2	yes	—
203	C₄×D₁₃	—	2	4	no	—
204	C₄×D₁₃	—	4	2	no	—
205	C₄×D₁₃	—	4	1	no	—
206	C₄×D₁₃	—	4	1	no	—
207	Dic₂₆	—	2	1	no	—
208	Dic₂₆	C₂×M₁₆	1	2	yes	—
209	C₈×C₁₃	—	4	2	no	—
210	C₈×C₁₃	—	4	1	no	—
211	C₈×C₁₃	—	4	1	no	—
212	#1055	—	2	2	no	—
213	#1055	—	2	2	no	—
214	#1055	—	2	1	no	—
215	#1055	—	2	1	no	—
216	#1055	—	2	1	no	—
217	#1055	—	4	2	no	—
218	#1055	#137	1	2	yes	complemented
219	C₂×#137	—	13	1	no	—
220	C₄×#41	—	13	1	no	—
221	C₂×C₄×Q₈	C₂×D₁₃	1	1	yes	characteristic
222	#446	—	13	2	no	—
223	#446	—	13	2	no	—
224	#446	—	26	1	no	—
225	#446	—	26	1	no	—
226	C₈×Q₈	—	13	1	no	—
227	C₈×Q₈	—	13	1	no	—
228	#441	—	13	2	no	—
229	#440	—	13	2	no	—
230	C₄×Q₁₆	—	13	2	no	—
231	C₄×SD₁₆	—	13	2	no	—
232	C₈×D₄	—	13	1	no	—
233	C₈×D₄	—	13	1	no	—
234	C₈×D₄	—	26	1	no	—
235	C₈×D₄	—	26	1	no	—
236	#431	—	26	1	no	—
237	#431	C₂×D₁₃	1	1	yes	characteristic
238	#431	C₂×D₁₃	1	1	yes	characteristic
239	#428	—	13	1	no	—
240	C₂×C₄⋊C₈	—	13	1	no	—
241	C₂×C₄⋊C₈	—	26	1	no	—
242	#419	—	13	1	no	—
243	#417	—	13	1	no	—
244	C₄×M₁₆	—	13	1	no	—
245	C₂×#97	—	26	1	no	—
246	C₂×C₄×C₈	—	13	1	no	—
247	C₂×C₄×C₈	—	26	1	no	—
248	#335	—	13	2	no	—
249	#334	—	13	2	no	—
250	Q₈⋊C₈	—	13	2	no	—
251	Q₈⋊C₈	C₂×D₁₃	1	2	yes	—
252	Q₈⋊C₈	C₂×D₁₃	1	2	yes	—
253	D₄⋊C₈	—	13	2	no	—
254	#322	—	13	2	no	—
255	#322	—	13	2	no	—
256	C₂²×C₁₃	—	2	1	no	—
257	C₂²×C₁₃	—	2	1	no	—
258	C₂²×C₁₃	#435	1	2	yes	—
259	C₂²×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
260	C₂×D₁₃	—	2	2	no	—
261	C₂×D₁₃	—	4	1	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	—	4	2	no	—
267	C₄×C₁₃	—	4	2	no	—
268	C₄×C₁₃	#435	1	2	yes	—
269	C₄×C₁₃	C₂²×M₁₆	1	1	yes	characteristic
270	C₄×C₁₃	C₂×#131	1	1	yes	characteristic
271	C₄×C₁₃	C₂×#137	1	1	yes	characteristic
272	C₄×C₁₃	#575	1	1	yes	characteristic
273	Dic₁₃	—	2	2	no	—
274	Dic₁₃	—	4	1	no	—
275	Dic₁₃	—	4	1	no	—
276	C₂×#41	—	13	1	no	—
277	C₂²×Q₈	C₄×D₁₃	1	1	yes	characteristic
278	#137	—	26	4	no	—
279	C₂×Q₁₆	—	13	2	no	—
280	C₂×SD₁₆	—	13	2	no	—
281	C₂×M₁₆	—	13	1	no	—
282	C₂×M₁₆	—	13	1	no	—
283	C₂²×C₈	—	13	1	no	—
284	C₂²×C₈	—	13	1	no	—
285	C₂²×C₈	—	26	1	no	—
286	C₂²×C₈	—	26	1	no	—
287	C₂²×C₈	—	26	1	no	—
288	C₄×Q₈	—	2	1	no	—
289	C₄×Q₈	—	2	1	no	—
290	C₄×Q₈	—	13	1	no	—
291	C₄×Q₈	—	13	1	no	—
292	C₄×Q₈	C₄×D₁₃	1	2	yes	—
293	C₄×Q₈	C₂²×D₁₃	1	2	yes	—
294	C₄×D₄	—	13	1	no	—
295	C₄×D₄	—	13	1	no	—
296	C₄×D₄	—	26	1	no	—
297	C₄×D₄	—	26	1	no	—
298	#117	—	13	1	no	—
299	#117	—	26	1	no	—
300	C₂×C₄⋊C₄	—	2	1	no	—
301	C₂×C₄⋊C₄	C₄×D₁₃	1	1	yes	characteristic
302	C₂×C₄²	—	2	1	no	—
303	C₂×C₄²	—	26	1	no	—
304	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
305	#107	—	13	2	no	—
306	#106	—	13	2	no	—
307	C₄⋊C₈	—	2	1	no	—
308	C₄⋊C₈	—	13	2	no	—
309	C₄⋊C₈	—	26	2	no	—
310	C₄⋊C₈	—	26	2	no	—
311	C₄⋊C₈	—	26	1	no	—
312	C₄⋊C₈	—	26	1	no	—
313	C₄⋊C₈	—	26	1	no	—
314	C₄⋊C₈	C₂²×D₁₃	1	1	yes	characteristic
315	C₄⋊C₈	C₂²×D₁₃	1	1	yes	characteristic
316	#103	—	13	2	no	—
317	#103	—	13	2	no	—
318	#103	—	13	2	no	—
319	#102	—	13	2	no	—
320	C₂²⋊C₈	—	2	1	no	—
321	C₂²⋊C₈	—	2	1	no	—
322	C₂²⋊C₈	—	26	1	no	—
323	C₂²⋊C₈	—	26	1	no	—
324	#97	—	13	2	no	—
325	#97	—	26	2	no	—
326	#97	—	26	2	no	—
327	C₄×C₈	—	2	1	no	—
328	C₄×C₈	—	13	1	no	—
329	C₄×C₈	—	13	1	no	—
330	C₄×C₈	—	13	2	no	—
331	C₄×C₈	—	13	1	no	—
332	C₄×C₈	—	13	1	no	—
333	C₄×C₈	—	26	1	no	—
334	C₄×C₈	—	26	1	no	—
335	C₄×C₈	C₂²×D₁₃	1	2	yes	—
336	C₂×C₁₃	—	2	2	no	—
337	C₂×C₁₃	C₂×#435	1	1	yes	characteristic
338	C₂×C₁₃	C₄×#137	1	1	yes	characteristic
339	C₂×C₁₃	#2955	1	1	yes	characteristic
340	D₁₃	—	4	2	no	—
341	#41	—	13	4	no	—
342	#41	—	26	2	no	—
343	C₂×Q₈	—	2	1	no	—
344	C₂×Q₈	—	2	2	no	—
345	C₂×Q₈	—	2	2	no	—
346	C₂×Q₈	—	13	1	no	—
347	C₂×Q₈	C₂×C₄×D₁₃	1	2	yes	—
348	C₂×D₄	—	13	1	no	—
349	C₂×D₄	—	26	1	no	—
350	C₂²×C₄	—	2	1	no	—
351	C₂²×C₄	—	2	1	no	—
352	C₂²×C₄	—	26	1	no	—
353	C₂²×C₄	—	26	1	no	—
354	C₂²×C₄	—	26	1	no	—
355	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
356	C₂²×C₄	D₄×D₁₃	1	1	yes	characteristic
357	C₂²×C₄	#6129	1	1	yes	characteristic
358	Q₁₆	—	26	4	no	—
359	SD₁₆	—	26	4	no	—
360	M₁₆	—	26	2	no	—
361	M₁₆	—	26	2	no	—
362	C₂×C₈	—	2	1	no	—
363	C₂×C₈	—	2	1	no	—
364	C₂×C₈	—	2	2	no	—
365	C₂×C₈	—	13	1	no	—
366	C₂×C₈	—	13	2	no	—
367	C₂×C₈	—	13	2	no	—
368	C₂×C₈	—	13	1	no	—
369	C₂×C₈	—	13	1	no	—
370	C₂×C₈	—	13	1	no	—
371	C₂×C₈	—	26	2	no	—
372	C₂×C₈	—	26	2	no	—
373	C₂×C₈	—	52	2	no	—
374	C₂×C₈	—	52	2	no	—
375	C₂×C₈	—	52	1	no	—
376	C₂×C₈	—	52	2	no	—
377	C₄⋊C₄	—	2	2	no	—
378	C₄⋊C₄	—	2	1	no	—
379	C₄⋊C₄	—	2	2	no	—
380	C₄⋊C₄	—	13	1	no	—
381	C₄⋊C₄	—	13	1	no	—
382	C₄⋊C₄	—	26	1	no	—
383	C₄⋊C₄	—	26	1	no	—
384	C₄⋊C₄	C₂×C₄×D₁₃	1	2	yes	—
385	C₂²⋊C₄	—	26	1	no	—
386	C₂²⋊C₄	—	26	1	no	—
387	C₂²⋊C₄	—	26	1	no	—
388	C₄²	—	2	2	no	—
389	C₄²	—	2	2	no	—
390	C₄²	—	26	1	no	—
391	C₄²	—	26	1	no	—
392	C₄²	—	26	1	no	—
393	C₄²	C₂×C₄×D₁₃	1	1	yes	characteristic
394	C₄²	D₄×D₁₃	1	1	yes	characteristic
395	C₄²	#6129	1	1	yes	characteristic
396	C₄²	C₂³×D₁₃	1	1	yes	characteristic
397	C₁₃	#17872	1	1	yes	characteristic, complemented, Sylow
398	C₂³	—	26	1	no	—
399	C₂³	#88135	1	1	yes	characteristic
400	Q₈	—	2	2	no	—
401	Q₈	—	2	2	no	—
402	Q₈	—	4	2	no	—
403	Q₈	—	13	2	no	—
404	Q₈	—	26	1	no	—
405	D₄	—	13	2	no	—
406	D₄	—	26	4	no	—
407	D₄	—	26	1	no	—
408	C₂×C₄	—	2	1	no	—
409	C₂×C₄	—	2	1	no	—
410	C₂×C₄	—	2	2	no	—
411	C₂×C₄	—	2	2	no	—
412	C₂×C₄	—	4	1	no	—
413	C₂×C₄	—	4	2	no	—
414	C₂×C₄	—	4	2	no	—
415	C₂×C₄	—	26	1	no	—
416	C₂×C₄	—	26	4	no	—
417	C₂×C₄	—	26	1	no	—
418	C₂×C₄	—	26	1	no	—
419	C₂×C₄	—	52	2	no	—
420	C₂×C₄	—	52	1	no	—
421	C₂×C₄	—	52	1	no	—
422	C₂×C₄	#88135	1	1	yes	characteristic
423	C₂×C₄	#88135	1	1	yes	characteristic
424	C₂×C₄	#88135	1	1	yes	characteristic
425	C₂×C₄	#88155	1	2	yes	—
426	C₂×C₄	M₁₆×D₁₃	1	2	yes	—
427	C₂×C₄	C₂²×C₄×D₁₃	1	1	yes	characteristic
428	C₂×C₄	C₂×D₄×D₁₃	1	1	yes	characteristic
429	C₂×C₄	C₂×#6129	1	1	yes	characteristic
430	C₈	—	4	2	no	—
431	C₈	—	4	1	no	—
432	C₈	—	4	1	no	—
433	C₈	—	13	2	no	—
434	C₈	—	26	2	no	—
435	C₈	—	26	2	no	—
436	C₈	—	26	1	no	—
437	C₈	—	26	1	no	—
438	C₈	—	26	1	no	—
439	C₈	—	52	2	no	—
440	C₂²	—	2	1	no	—
441	C₂²	—	2	1	no	—
442	C₂²	—	26	2	no	—
443	C₂²	—	52	1	no	—
444	C₂²	—	52	1	no	—
445	C₂²	#11718389	1	2	yes	—
446	C₂²	C₂×#88135	1	1	yes	characteristic
447	C₄	—	2	1	no	—
448	C₄	—	2	1	no	—
449	C₄	—	2	1	no	—
450	C₄	—	4	2	no	—
451	C₄	—	4	2	no	—
452	C₄	—	26	2	no	—
453	C₄	—	52	1	no	—
454	C₄	—	52	1	no	—
455	C₄	#11718389	1	2	yes	—
456	C₄	C₂×#88155	1	1	yes	characteristic
457	C₄	C₂×M₁₆×D₁₃	1	1	yes	characteristic
458	C₄	D₁₃×#137	1	1	yes	characteristic
459	C₄	#11719482	1	1	yes	characteristic
460	C₂	—	2	2	no	—
461	C₂	—	52	2	no	—
462	C₂	C₂×#11718389	1	1	yes	characteristic
463	C₂	#13123651	1	1	yes	characteristic
464	C₂	#13123735	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×#1479	C₂
socle	C₂²×C₁₃	C₂×C₄×D₄
prime radical	C₂×#6127	C₂×C₄
cosocle	C₄²×C₁₃	C₂⁴
hypercenter	#1479	D₁₃
hypocenter	C₁₃	#17872
LCS	G ▷ C₂×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1479

Complements

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

N	H ≅ G/N	type
2. C₂×#11718685	C₂	semidirect
4. #13113710	C₂	semidirect
5. #13113696	C₂	semidirect
6. #13113689	C₂	semidirect
7. #13113675	C₂	semidirect
8. #13113589	C₂	semidirect
10. #13113126	C₂	semidirect
11. C₁₃×#1479	C₂	semidirect
174. #1479	D₁₃	semidirect
218. #1055	#137	semidirect
397. C₁₃	#17872	semidirect

Maximal subgroups

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

subgroup	index
#13123792	2
C₂×#11718685	2
C₄×#88196	2
#13113710	2
#13113696	2
#13113689	2
#13113675	2
#13113589	2
#13113224	2
#13113126	2
C₁₃×#1479	2
#17872	13