Subgroups — #15870762

Order 3328.

738 conjugacy classes of subgroups.

The subgroup lattice has 506 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13124626	C₂	1	1	yes	maximal, characteristic
2	#13123770	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄×#88155	C₂	1	1	yes	maximal, characteristic
4	#13115779	C₂	1	1	yes	maximal, characteristic, complemented
5	#13115612	C₂	1	1	yes	maximal, characteristic, complemented
6	#13115436	C₂	1	2	yes	maximal, complemented
7	#13115114	C₂	1	2	yes	maximal
8	#13114857	C₂	1	1	yes	maximal, characteristic
9	#13114720	C₂	1	2	yes	maximal, complemented
10	#13114680	C₂	1	2	yes	maximal
11	C₁₃×#1770	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#88155	C₂²	1	1	yes	characteristic
13	C₂×#88155	C₂²	1	1	yes	characteristic
14	C₄×#6127	C₂²	1	1	yes	characteristic
15	#11719175	C₂²	1	1	yes	characteristic
16	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
17	C₂×C₁₃×#97	C₂²	1	2	yes	—
18	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
19	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
20	#11718774	C₂²	1	2	yes	—
21	C₂×#88059	C₂²	1	2	yes	—
22	#11718767	C₂²	1	2	yes	—
23	#11718763	C₂²	1	2	yes	—
24	#11718762	C₂²	1	1	yes	characteristic
25	#11718762	C₂²	1	2	yes	—
26	#11718762	C₂²	1	1	yes	characteristic
27	C₂×#88045	C₂²	1	2	yes	—
28	#11718585	C₂²	1	1	yes	characteristic
29	C₄×#6099	C₂²	1	1	yes	characteristic
30	#11718512	C₄	1	1	yes	characteristic, complemented
31	#11718511	C₄	1	1	yes	characteristic, complemented
32	#11718508	C₄	1	2	yes	complemented
33	#11718507	C₄	1	1	yes	characteristic, complemented
34	#11718503	C₄	1	1	yes	characteristic, complemented
35	#11718490	C₄	1	2	yes	complemented
36	#11718350	—	2	1	no	—
37	#11718350	—	2	1	no	—
38	C₄×#6094	—	2	1	no	—
39	C₄×C₈×D₁₃	—	2	1	no	—
40	#11718340	—	2	1	no	—
41	#11718340	—	2	1	no	—
42	C₈×Dic₂₆	—	2	1	no	—
43	C₈×Dic₂₆	—	2	1	no	—
44	C₁₃×#336	C₂²	1	2	yes	—
45	#11718144	C₂²	1	2	yes	—
46	#11718115	C₂²	1	2	yes	—
47	#11718115	C₂²	1	2	yes	—
48	#11718115	C₂²	1	2	yes	—
49	C₂×#6127	C₂³	1	1	yes	characteristic
50	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
51	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
52	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
53	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
54	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
55	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
56	C₄×C₂²⋊D₁₃	—	2	1	no	—
57	C₄×C₂²⋊D₁₃	—	2	1	no	—
58	#88180	C₂³	1	2	yes	—
59	#88180	C₂³	1	1	yes	characteristic
60	#88178	—	2	1	no	—
61	#88178	—	2	1	no	—
62	C₂×#6099	C₂³	1	2	yes	—
63	C₂×#6099	C₂³	1	1	yes	characteristic
64	C₂×#6099	C₂³	1	1	yes	characteristic
65	#88155	—	2	2	no	—
66	#88155	—	2	2	no	—
67	#88155	—	2	2	no	—
68	#88155	Q₈	1	4	yes	complemented
69	C₂×#6094	—	2	1	no	—
70	C₂×#6094	—	2	1	no	—
71	C₂×C₈×D₁₃	—	2	1	no	—
72	C₂×C₈×D₁₃	—	2	1	no	—
73	C₄×D₅₂	C₂×C₄	1	1	yes	characteristic
74	C₄×D₅₂	C₂×C₄	1	1	yes	characteristic
75	#88126	—	2	1	no	—
76	C₄²×D₁₃	—	2	1	no	—
77	#88124	C₂×C₄	1	2	yes	—
78	#88123	C₂×C₄	1	1	yes	characteristic
79	#88123	C₂×C₄	1	1	yes	characteristic
80	C₄×Dic₂₆	—	2	1	no	—
81	C₄×Dic₂₆	—	2	1	no	—
82	C₄×Dic₂₆	C₂×C₄	1	1	yes	characteristic
83	C₄×Dic₂₆	C₂×C₄	1	1	yes	characteristic
84	C₁₃×C₄⋊C₈	C₂×C₄	1	2	yes	—
85	C₁₃×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
86	C₁₃×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
87	C₁₃×#97	—	2	4	no	—
88	C₄×C₈×C₁₃	D₄	1	1	yes	characteristic
89	C₄×C₈×C₁₃	D₄	1	1	yes	characteristic
90	C₄×C₈×C₁₃	D₄	1	1	yes	characteristic
91	C₄×C₈×C₁₃	D₄	1	1	yes	characteristic
92	C₁₃×#95	—	2	1	no	—
93	#88061	C₂×C₄	1	2	yes	—
94	#88061	C₂×C₄	1	2	yes	—
95	#88059	—	2	4	no	—
96	#88058	C₂×C₄	1	2	yes	—
97	#88058	C₂×C₄	1	2	yes	—
98	#88057	C₂×C₄	1	2	yes	—
99	#88057	C₂×C₄	1	2	yes	—
100	#88056	C₂×C₄	1	2	yes	—
101	#88056	C₂×C₄	1	2	yes	—
102	#88055	—	2	2	no	—
103	#88055	—	2	1	no	—
104	#88055	—	2	1	no	—
105	#88054	—	2	2	no	—
106	#88054	—	2	2	no	—
107	C₈×Dic₁₃	—	2	2	no	—
108	C₈×Dic₁₃	—	2	1	no	—
109	C₈×Dic₁₃	—	2	1	no	—
110	#88045	—	2	4	no	—
111	C₄⋊#1055	—	2	1	no	—
112	C₄⋊#1055	—	2	1	no	—
113	#88043	—	2	1	no	—
114	C₄×#1055	—	2	1	no	—
115	#21628	—	13	1	no	maximal, Sylow
116	C₂²×C₄×C₁₃	—	2	2	no	—
117	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
118	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
119	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
120	C₂×C₂²⋊D₁₃	—	2	1	no	—
121	#6127	—	2	1	no	—
122	#6127	—	2	1	no	—
123	#6127	C₂×Q₈	1	2	yes	—
124	#6127	#41	1	2	yes	—
125	C₂×D₅₂	C₂²×C₄	1	1	yes	characteristic
126	C₂×C₄×D₁₃	—	2	1	no	—
127	C₂×C₄×D₁₃	—	2	1	no	—
128	C₂×C₄×D₁₃	—	2	1	no	—
129	C₂×Dic₂₆	—	2	1	no	—
130	C₂×Dic₂₆	—	2	1	no	—
131	C₂×Dic₂₆	C₂²×C₄	1	1	yes	characteristic
132	C₂×C₈×C₁₃	—	2	2	no	—
133	C₂×C₈×C₁₃	—	2	1	no	—
134	C₂×C₈×C₁₃	—	2	1	no	—
135	C₂×C₈×C₁₃	—	2	2	no	—
136	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
137	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
138	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
139	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
140	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
141	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
142	C₂×C₈×C₁₃	C₂×Q₈	1	2	yes	—
143	C₂×C₈×C₁₃	#41	1	2	yes	—
144	C₁₃×C₄⋊C₄	—	4	2	no	—
145	C₄²×C₁₃	—	2	2	no	—
146	C₄²×C₁₃	—	2	2	no	—
147	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
148	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
149	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
150	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
151	C₂²⋊Dic₁₃	—	2	2	no	—
152	C₂²⋊Dic₁₃	—	2	1	no	—
153	#6103	—	2	1	no	—
154	#6103	—	2	1	no	—
155	C₄⋊Dic₁₃	—	2	1	no	—
156	C₄⋊Dic₁₃	—	2	1	no	—
157	C₄⋊Dic₁₃	C₂²×C₄	1	1	yes	characteristic
158	C₄⋊Dic₁₃	C₂²×C₄	1	1	yes	characteristic
159	C₄⋊Dic₁₃	C₂²×C₄	1	2	yes	—
160	C₄⋊Dic₁₃	C₂²×C₄	1	2	yes	—
161	#6101	—	2	2	no	—
162	#6101	—	2	2	no	—
163	#6101	—	2	1	no	—
164	#6101	—	2	1	no	—
165	C₄×Dic₁₃	—	2	1	no	—
166	C₄×Dic₁₃	—	2	1	no	—
167	C₄×Dic₁₃	—	2	2	no	—
168	C₄×Dic₁₃	—	2	1	no	—
169	#6099	—	2	1	no	—
170	#6099	—	2	1	no	—
171	#6099	—	2	2	no	—
172	#6099	—	2	2	no	—
173	#6099	C₂×Q₈	1	2	yes	—
174	#6099	#41	1	2	yes	—
175	C₂×#1055	—	2	1	no	—
176	C₂×#1055	—	2	1	no	—
177	C₂×#1055	—	2	2	no	—
178	#6094	—	2	4	no	—
179	#6094	—	2	4	no	—
180	C₈×D₁₃	—	2	4	no	—
181	C₈×D₁₃	—	2	4	no	—
182	#3076	—	13	1	no	—
183	#2960	—	13	1	no	—
184	C₄×#131	—	13	1	no	—
185	#1986	—	13	1	no	—
186	#1950	—	13	1	no	—
187	#1922	—	13	2	no	—
188	#1866	—	13	2	no	—
189	#1806	—	13	1	no	—
190	#1773	—	13	2	no	—
191	#1770	D₁₃	1	1	yes	characteristic, complemented
192	#1765	—	13	2	no	—
193	C₂³×C₁₃	C₂×#41	1	1	yes	characteristic
194	C₂²×D₁₃	—	2	1	no	—
195	C₂×C₄×C₁₃	—	2	2	no	—
196	C₂×C₄×C₁₃	—	4	1	no	—
197	C₂×C₄×C₁₃	—	4	2	no	—
198	C₂×C₄×C₁₃	—	4	2	no	—
199	C₂×C₄×C₁₃	—	4	2	no	—
200	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
201	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
202	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
203	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
204	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
205	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
206	C₂×C₄×C₁₃	C₂²×Q₈	1	1	yes	characteristic
207	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
208	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
209	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
210	C₂²⋊D₁₃	—	2	2	no	—
211	C₂²⋊D₁₃	—	2	2	no	—
212	C₂×Dic₁₃	—	2	1	no	—
213	C₂×Dic₁₃	—	2	1	no	—
214	C₂×Dic₁₃	—	2	1	no	—
215	C₂×Dic₁₃	—	2	2	no	—
216	C₂×Dic₁₃	—	2	2	no	—
217	D₅₂	—	2	1	no	—
218	D₅₂	C₄×Q₈	1	2	yes	—
219	C₄×D₁₃	—	2	2	no	—
220	C₄×D₁₃	—	2	2	no	—
221	C₄×D₁₃	—	4	2	no	—
222	C₄×D₁₃	—	4	2	no	—
223	Dic₂₆	—	2	1	no	—
224	Dic₂₆	—	4	2	no	—
225	Dic₂₆	—	4	2	no	—
226	Dic₂₆	C₄×Q₈	1	2	yes	—
227	C₈×C₁₃	—	2	2	no	—
228	C₈×C₁₃	—	2	2	no	—
229	C₈×C₁₃	—	2	1	no	—
230	C₈×C₁₃	—	2	1	no	—
231	C₈×C₁₃	C₂²⋊Q₈	1	2	yes	—
232	C₈×C₁₃	C₂²⋊Q₈	1	2	yes	—
233	#1055	—	2	2	no	—
234	#1055	—	2	2	no	—
235	#1055	—	4	2	no	—
236	C₂×#131	—	13	1	no	—
237	C₂×#131	—	13	1	no	—
238	#533	—	13	1	no	—
239	C₄×#41	—	13	1	no	—
240	#479	—	13	2	no	—
241	#478	—	13	2	no	—
242	#477	—	13	1	no	—
243	#476	—	13	1	no	—
244	#475	—	13	1	no	—
245	#474	—	13	1	no	—
246	#446	—	26	1	no	—
247	#446	—	26	1	no	—
248	C₈×Q₈	—	26	1	no	—
249	C₈×Q₈	—	26	1	no	—
250	C₂×#108	—	13	2	no	—
251	#427	—	13	2	no	—
252	#424	—	13	2	no	—
253	#423	—	13	1	no	—
254	C₂×C₄⋊C₈	C₂×D₁₃	1	1	yes	characteristic
255	C₂×#104	—	13	2	no	—
256	#416	—	13	2	no	—
257	#405	—	13	1	no	—
258	#405	—	13	1	no	—
259	#405	—	13	2	no	—
260	#405	—	26	1	no	—
261	#405	—	26	1	no	—
262	C₄×M₁₆	—	13	1	no	—
263	C₄×M₁₆	—	26	1	no	—
264	C₂×#97	C₂×D₁₃	1	2	yes	—
265	C₂×C₄×C₈	—	26	1	no	—
266	C₂×C₄×C₈	C₂×D₁₃	1	1	yes	characteristic
267	C₄×C₄⋊C₄	C₂×D₁₃	1	1	yes	characteristic
268	#341	—	13	2	no	—
269	#339	—	13	2	no	—
270	#339	—	13	2	no	—
271	#339	—	13	2	no	—
272	#336	C₂×D₁₃	1	2	yes	—
273	C₂²×C₁₃	—	2	1	no	—
274	C₂²×C₁₃	—	2	1	no	—
275	C₂²×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
276	C₂²×C₁₃	#529	1	1	yes	characteristic
277	C₂²×C₁₃	#533	1	1	yes	characteristic
278	C₂×D₁₃	—	2	2	no	—
279	C₂×D₁₃	—	4	1	no	—
280	C₂×D₁₃	—	4	1	no	—
281	C₄×C₁₃	—	2	1	no	—
282	C₄×C₁₃	—	2	1	no	—
283	C₄×C₁₃	—	2	1	no	—
284	C₄×C₁₃	—	8	2	no	—
285	C₄×C₁₃	#444	1	2	yes	—
286	C₄×C₁₃	C₂×C₄×Q₈	1	1	yes	characteristic
287	C₄×C₁₃	C₄×#41	1	1	yes	characteristic
288	C₄×C₁₃	C₂×C₂²⋊Q₈	1	1	yes	characteristic
289	C₄×C₁₃	#525	1	1	yes	characteristic
290	Dic₁₃	—	2	2	no	—
291	Dic₁₃	—	4	2	no	—
292	Dic₁₃	—	4	1	no	—
293	Dic₁₃	—	4	2	no	—
294	Dic₁₃	—	4	1	no	—
295	C₂×#41	—	13	1	no	—
296	#131	—	13	4	no	—
297	#131	—	26	2	no	—
298	#131	—	26	2	no	—
299	#131	—	26	2	no	—
300	C₂×M₁₆	—	13	1	no	—
301	C₂×M₁₆	—	13	1	no	—
302	C₂×M₁₆	—	13	2	no	—
303	C₂×M₁₆	—	26	1	no	—
304	C₂×M₁₆	—	26	1	no	—
305	C₂²×C₈	—	26	1	no	—
306	C₂²×C₈	—	26	1	no	—
307	C₂²×C₈	C₂²×D₁₃	1	2	yes	—
308	C₂²×C₈	C₂²×D₁₃	1	1	yes	characteristic
309	C₂²×C₈	C₂²×D₁₃	1	1	yes	characteristic
310	C₄⋊Q₈	—	13	1	no	—
311	C₄⋊Q₈	—	13	1	no	—
312	#125	—	13	2	no	—
313	C₂²⋊Q₈	—	26	1	no	—
314	C₂²⋊Q₈	—	26	1	no	—
315	C₄×Q₈	—	13	1	no	—
316	C₄×Q₈	—	13	1	no	—
317	C₄×Q₈	—	26	1	no	—
318	C₄×Q₈	—	26	1	no	—
319	C₄×D₄	—	13	1	no	—
320	C₄×D₄	—	13	1	no	—
321	C₄×D₄	—	26	1	no	—
322	C₄×D₄	—	26	1	no	—
323	#117	—	13	1	no	—
324	#117	—	13	2	no	—
325	#117	—	26	1	no	—
326	C₂×C₄⋊C₄	—	2	1	no	—
327	C₂×C₄²	—	26	1	no	—
328	C₂×C₄²	C₂²×D₁₃	1	2	yes	—
329	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
330	#108	—	26	4	no	—
331	#107	—	13	2	no	—
332	#107	—	13	2	no	—
333	#106	—	13	2	no	—
334	#106	—	13	2	no	—
335	C₄⋊C₈	—	26	2	no	—
336	C₄⋊C₈	—	26	2	no	—
337	C₄⋊C₈	—	26	1	no	—
338	C₄⋊C₈	—	26	1	no	—
339	C₄⋊C₈	C₄×D₁₃	1	1	yes	characteristic
340	C₄⋊C₈	C₄×D₁₃	1	1	yes	characteristic
341	C₄⋊C₈	C₄×D₁₃	1	2	yes	—
342	#104	—	26	4	no	—
343	#103	—	13	2	no	—
344	#103	—	13	2	no	—
345	#102	—	13	2	no	—
346	#102	—	13	2	no	—
347	#97	—	2	4	no	—
348	#97	—	26	1	no	—
349	#97	—	26	1	no	—
350	#97	—	26	2	no	—
351	#97	—	26	1	no	—
352	C₄×C₈	—	26	1	no	—
353	C₄×C₈	—	26	1	no	—
354	C₄×C₈	—	26	2	no	—
355	C₄×C₈	—	26	1	no	—
356	C₄×C₈	D₅₂	1	1	yes	characteristic
357	C₄×C₈	D₅₂	1	1	yes	characteristic
358	C₄×C₈	D₅₂	1	1	yes	characteristic
359	C₄×C₈	D₅₂	1	1	yes	characteristic
360	#95	—	2	1	no	—
361	C₂×C₁₃	—	2	1	no	—
362	C₂×C₁₃	—	2	1	no	—
363	C₂×C₁₃	C₄×C₂²⋊Q₈	1	1	yes	characteristic
364	C₂×C₁₃	C₂×#444	1	1	yes	characteristic
365	C₂×C₁₃	#2955	1	1	yes	characteristic
366	D₁₃	—	4	2	no	—
367	#41	—	13	2	no	—
368	#41	—	13	2	no	—
369	#41	—	26	1	no	—
370	#41	—	26	1	no	—
371	C₂×Q₈	—	13	1	no	—
372	C₂×Q₈	—	26	1	no	—
373	C₂×Q₈	—	26	1	no	—
374	C₂×D₄	—	13	1	no	—
375	C₂×D₄	—	26	1	no	—
376	C₂²×C₄	—	2	2	no	—
377	C₂²×C₄	—	26	1	no	—
378	C₂²×C₄	—	26	1	no	—
379	C₂²×C₄	—	26	1	no	—
380	C₂²×C₄	#6127	1	1	yes	characteristic
381	C₂²×C₄	#6127	1	1	yes	characteristic
382	C₂²×C₄	C₂³×D₁₃	1	1	yes	characteristic
383	M₁₆	—	13	2	no	—
384	M₁₆	—	13	2	no	—
385	M₁₆	—	26	4	no	—
386	M₁₆	—	26	1	no	—
387	M₁₆	—	26	1	no	—
388	M₁₆	—	26	4	no	—
389	M₁₆	—	26	2	no	—
390	M₁₆	—	26	2	no	—
391	C₂×C₈	—	2	2	no	—
392	C₂×C₈	—	2	2	no	—
393	C₂×C₈	—	2	1	no	—
394	C₂×C₈	—	2	1	no	—
395	C₂×C₈	—	26	4	no	—
396	C₂×C₈	—	26	1	no	—
397	C₂×C₈	—	26	1	no	—
398	C₂×C₈	—	26	4	no	—
399	C₂×C₈	—	26	2	no	—
400	C₂×C₈	C₂×C₄×D₁₃	1	2	yes	—
401	C₂×C₈	C₂×C₄×D₁₃	1	2	yes	—
402	C₂×C₈	C₂×D₅₂	1	1	yes	characteristic
403	C₂×C₈	C₂×D₅₂	1	1	yes	characteristic
404	C₂×C₈	C₂×D₅₂	1	1	yes	characteristic
405	C₂×C₈	C₂×D₅₂	1	1	yes	characteristic
406	C₂×C₈	#6129	1	2	yes	—
407	C₂×C₈	Q₈×D₁₃	1	2	yes	—
408	C₄⋊C₄	—	4	2	no	—
409	C₄⋊C₄	—	13	2	no	—
410	C₄⋊C₄	—	13	2	no	—
411	C₄⋊C₄	—	13	1	no	—
412	C₄⋊C₄	—	13	1	no	—
413	C₄⋊C₄	—	26	1	no	—
414	C₄⋊C₄	—	26	1	no	—
415	C₄⋊C₄	—	26	2	no	—
416	C₄⋊C₄	—	26	2	no	—
417	C₄⋊C₄	—	26	1	no	—
418	C₄⋊C₄	—	26	1	no	—
419	C₂²⋊C₄	—	26	1	no	—
420	C₂²⋊C₄	—	26	2	no	—
421	C₂²⋊C₄	—	26	1	no	—
422	C₂²⋊C₄	—	26	1	no	—
423	C₄²	—	2	2	no	—
424	C₄²	—	2	2	no	—
425	C₄²	—	26	1	no	—
426	C₄²	—	26	1	no	—
427	C₄²	—	26	1	no	—
428	C₄²	—	26	2	no	—
429	C₄²	C₂×C₄×D₁₃	1	1	yes	characteristic
430	C₄²	C₂×C₄×D₁₃	1	1	yes	characteristic
431	C₄²	C₂×D₅₂	1	1	yes	characteristic
432	C₄²	C₂×D₅₂	1	1	yes	characteristic
433	C₁₃	#21628	1	1	yes	characteristic, complemented, Sylow
434	C₂³	—	26	1	no	—
435	C₂³	C₂×#6127	1	1	yes	characteristic
436	Q₈	—	13	2	no	—
437	Q₈	—	26	1	no	—
438	Q₈	—	52	2	no	—
439	Q₈	—	52	2	no	—
440	D₄	—	13	2	no	—
441	D₄	—	26	2	no	—
442	D₄	—	26	2	no	—
443	D₄	—	26	1	no	—
444	C₂×C₄	—	2	2	no	—
445	C₂×C₄	—	4	1	no	—
446	C₂×C₄	—	4	2	no	—
447	C₂×C₄	—	4	2	no	—
448	C₂×C₄	—	4	2	no	—
449	C₂×C₄	—	26	1	no	—
450	C₂×C₄	—	26	2	no	—
451	C₂×C₄	—	26	2	no	—
452	C₂×C₄	—	26	1	no	—
453	C₂×C₄	—	26	1	no	—
454	C₂×C₄	—	26	2	no	—
455	C₂×C₄	—	26	2	no	—
456	C₂×C₄	—	52	2	no	—
457	C₂×C₄	—	52	2	no	—
458	C₂×C₄	C₄×D₅₂	1	1	yes	characteristic
459	C₂×C₄	C₄×D₅₂	1	1	yes	characteristic
460	C₂×C₄	C₄×D₅₂	1	1	yes	characteristic
461	C₂×C₄	C₄×D₅₂	1	1	yes	characteristic
462	C₂×C₄	C₂²×C₄×D₁₃	1	1	yes	characteristic
463	C₂×C₄	C₂²×D₅₂	1	1	yes	characteristic
464	C₂×C₄	C₂×#6129	1	1	yes	characteristic
465	C₂×C₄	C₂×Q₈×D₁₃	1	1	yes	characteristic
466	C₂×C₄	#41×D₁₃	1	1	yes	characteristic
467	C₂×C₄	#41×D₁₃	1	1	yes	characteristic
468	C₈	—	2	1	no	—
469	C₈	—	2	1	no	—
470	C₈	—	2	2	no	—
471	C₈	—	2	2	no	—
472	C₈	—	26	2	no	—
473	C₈	—	26	2	no	—
474	C₈	—	52	2	no	—
475	C₈	#88151	1	2	yes	—
476	C₈	#88151	1	2	yes	—
477	C₂²	—	2	1	no	—
478	C₂²	—	2	1	no	—
479	C₂²	—	26	2	no	—
480	C₂²	—	52	1	no	—
481	C₂²	—	52	1	no	—
482	C₂²	C₂×C₄×D₅₂	1	1	yes	characteristic
483	C₂²	#11719262	1	1	yes	characteristic
484	C₂²	#11719283	1	1	yes	characteristic
485	C₄	—	2	1	no	—
486	C₄	—	2	1	no	—
487	C₄	—	2	1	no	—
488	C₄	—	8	2	no	—
489	C₄	—	26	2	no	—
490	C₄	—	52	1	no	—
491	C₄	—	52	2	no	—
492	C₄	—	52	1	no	—
493	C₄	—	52	2	no	—
494	C₄	#11718378	1	2	yes	—
495	C₄	C₂×#88151	1	1	yes	characteristic
496	C₄	#11719229	1	1	yes	characteristic
497	C₄	C₄×#6129	1	1	yes	characteristic
498	C₄	C₄×Q₈×D₁₃	1	1	yes	characteristic
499	C₂	—	2	1	no	—
500	C₂	—	2	1	no	—
501	C₂	—	52	2	no	—
502	C₂	C₄×#88151	1	1	yes	characteristic
503	C₂	C₂×#11718378	1	1	yes	characteristic
504	C₂	#13123740	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²×D₅₂
commutator	C₂×C₄×C₁₃	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₁₃
Fitting	C₁₃×#1770	C₂
socle	C₂²×C₁₃	C₂×C₄×D₄
prime radical	C₂×#6127	C₂³
cosocle	C₂²×C₄×C₁₃	C₂⁴
hypercenter	#1770	D₁₃
hypocenter	C₁₃	#21628
LCS	G ▷ C₂×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄×C₈ ◁ #1770

Complements

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

N	H ≅ G/N	type
2. #13123770	C₂	semidirect
4. #13115779	C₂	semidirect
5. #13115612	C₂	semidirect
6. #13115436	C₂	semidirect
9. #13114720	C₂	semidirect
11. C₁₃×#1770	C₂	semidirect
30. #11718512	C₄	semidirect
31. #11718511	C₄	semidirect
32. #11718508	C₄	semidirect
33. #11718507	C₄	semidirect
34. #11718503	C₄	semidirect
35. #11718490	C₄	semidirect
68. #88155	Q₈	semidirect
191. #1770	D₁₃	semidirect
433. C₁₃	#21628	semidirect

Maximal subgroups

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

subgroup	index
#13124626	2
#13123770	2
C₄×#88155	2
#13115779	2
#13115612	2
#13115436	2
#13115114	2
#13114857	2
#13114720	2
#13114680	2
C₁₃×#1770	2
#21628	13