Subgroups — #15869376

Order 3328.

910 conjugacy classes of subgroups.

The subgroup lattice has 562 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13124293	C₂	1	1	yes	maximal, characteristic
2	C₂×#11718378	C₂	1	2	yes	maximal, complemented
3	#13123549	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄×#88155	C₂	1	1	yes	maximal, characteristic, complemented
5	#13115754	C₂	1	1	yes	maximal, characteristic, complemented
6	#13115612	C₂	1	1	yes	maximal, characteristic, complemented
7	#13115485	C₂	1	2	yes	maximal, complemented
8	#13115162	C₂	1	2	yes	maximal, complemented
9	#13114857	C₂	1	1	yes	maximal, characteristic, complemented
10	#13114680	C₂	1	2	yes	maximal, complemented
11	C₁₃×#1770	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#88158	C₂²	1	2	yes	—
13	C₂×#88155	C₂²	1	1	yes	characteristic
14	C₂×#88155	C₂²	1	2	yes	—
15	C₂×#88155	C₂²	1	1	yes	characteristic
16	#11719182	C₂²	1	1	yes	characteristic
17	C₄×#6127	C₂²	1	1	yes	characteristic
18	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
19	C₂×C₁₃×#97	C₂²	1	2	yes	—
20	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
21	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
22	#11718774	C₂²	1	2	yes	—
23	#11718771	C₂²	1	2	yes	—
24	C₂×#88059	C₂²	1	2	yes	—
25	#11718762	C₂²	1	1	yes	characteristic
26	#11718762	C₂²	1	1	yes	characteristic
27	C₂×#88045	C₂²	1	2	yes	—
28	C₂×#88045	C₂²	1	2	yes	—
29	C₂×#88045	C₂²	1	2	yes	—
30	#11718585	C₂²	1	1	yes	characteristic
31	C₄×#6099	C₂²	1	1	yes	characteristic
32	#11718510	C₄	1	1	yes	characteristic, complemented
33	#11718509	C₄	1	1	yes	characteristic, complemented
34	#11718506	C₄	1	2	yes	complemented
35	#11718505	C₄	1	2	yes	complemented
36	#11718504	C₄	1	1	yes	characteristic, complemented
37	#11718502	C₄	1	1	yes	characteristic, complemented
38	#11718378	—	2	8	no	—
39	#11718350	—	2	1	no	—
40	#11718350	—	2	1	no	—
41	#11718349	—	2	1	no	—
42	#11718349	—	2	1	no	—
43	C₄×#6094	—	2	1	no	—
44	C₈×D₅₂	—	2	1	no	—
45	C₈×D₅₂	—	2	1	no	—
46	C₄×C₈×D₁₃	—	2	1	no	—
47	C₁₃×#336	C₂²	1	2	yes	—
48	#11718144	C₂²	1	2	yes	—
49	#11718115	C₂²	1	2	yes	—
50	C₂×#6127	C₂³	1	2	yes	—
51	C₂×#6127	C₂³	1	1	yes	characteristic
52	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
53	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
54	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
55	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
56	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
57	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
58	#88184	—	2	1	no	—
59	#88184	—	2	1	no	—
60	C₄×C₂²⋊D₁₃	—	2	1	no	—
61	C₄×C₂²⋊D₁₃	—	2	1	no	—
62	#88180	C₂³	1	1	yes	characteristic
63	C₂×#6099	C₂³	1	2	yes	—
64	C₂×#6099	C₂³	1	1	yes	characteristic
65	C₂×#6099	C₂³	1	1	yes	characteristic
66	C₂×Dic₅₂	C₂×C₄	1	2	yes	—
67	#88158	—	2	4	no	—
68	#88158	—	2	4	no	—
69	C₂×D₁₀₄	C₂×C₄	1	2	yes	—
70	C₂×#6095	C₂×C₄	1	2	yes	—
71	C₂×#6095	C₂×C₄	1	2	yes	—
72	#88155	—	2	2	no	—
73	#88155	—	2	2	no	—
74	#88155	—	2	2	no	—
75	#88155	—	2	4	no	—
76	#88155	—	2	4	no	—
77	#88155	D₄	1	4	yes	complemented
78	C₂×#6094	—	2	1	no	—
79	C₂×#6094	—	2	1	no	—
80	C₂×#6094	—	2	2	no	—
81	C₂×C₈×D₁₃	—	2	1	no	—
82	C₂×C₈×D₁₃	—	2	1	no	—
83	C₂×C₈×D₁₃	—	2	2	no	—
84	#88129	C₂×C₄	1	2	yes	—
85	#88128	C₂×C₄	1	1	yes	characteristic
86	C₄×D₅₂	—	2	1	no	—
87	C₄×D₅₂	—	2	1	no	—
88	C₄×D₅₂	C₂×C₄	1	1	yes	characteristic
89	C₄×D₅₂	C₂×C₄	1	1	yes	characteristic
90	#88126	—	2	1	no	—
91	C₄²×D₁₃	—	2	1	no	—
92	#88123	C₂×C₄	1	1	yes	characteristic
93	C₄×Dic₂₆	C₂×C₄	1	1	yes	characteristic
94	C₄×Dic₂₆	C₂×C₄	1	1	yes	characteristic
95	C₁₃×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
96	C₁₃×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
97	C₁₃×C₄⋊C₈	C₂×C₄	1	2	yes	—
98	C₁₃×#97	—	2	4	no	—
99	C₄×C₈×C₁₃	D₄	1	1	yes	characteristic
100	C₄×C₈×C₁₃	D₄	1	1	yes	characteristic
101	C₄×C₈×C₁₃	D₄	1	1	yes	characteristic
102	C₄×C₈×C₁₃	D₄	1	1	yes	characteristic
103	C₁₃×#95	—	2	1	no	—
104	#88061	C₂×C₄	1	2	yes	—
105	#88061	C₂×C₄	1	2	yes	—
106	#88060	—	2	2	no	—
107	#88060	—	2	2	no	—
108	#88059	—	2	4	no	—
109	#88056	C₂×C₄	1	2	yes	—
110	#88056	C₂×C₄	1	2	yes	—
111	#88055	—	2	1	no	—
112	#88055	—	2	1	no	—
113	C₈×Dic₁₃	—	2	1	no	—
114	C₈×Dic₁₃	—	2	1	no	—
115	#88045	—	2	4	no	—
116	#88045	—	2	4	no	—
117	#88045	—	2	4	no	—
118	C₄⋊#1055	—	2	1	no	—
119	C₄⋊#1055	—	2	1	no	—
120	#88043	—	2	1	no	—
121	C₄×#1055	—	2	1	no	—
122	#21518	—	13	1	no	maximal, Sylow
123	C₂²×C₄×C₁₃	—	2	2	no	—
124	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
125	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
126	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
127	C₂×C₂²⋊D₁₃	—	2	1	no	—
128	C₂×C₂²⋊D₁₃	—	2	2	no	—
129	#6127	—	2	1	no	—
130	#6127	—	2	1	no	—
131	#6127	—	2	2	no	—
132	#6127	—	2	2	no	—
133	#6127	—	2	2	no	—
134	#6127	—	2	2	no	—
135	#6127	C₂×D₄	1	2	yes	—
136	#6127	#41	1	2	yes	—
137	C₂×D₅₂	—	2	1	no	—
138	C₂×D₅₂	—	2	1	no	—
139	C₂×D₅₂	C₂²×C₄	1	2	yes	—
140	C₂×D₅₂	C₂²×C₄	1	1	yes	characteristic
141	C₂×C₄×D₁₃	—	2	1	no	—
142	C₂×C₄×D₁₃	—	2	1	no	—
143	C₂×C₄×D₁₃	—	2	1	no	—
144	C₂×C₄×D₁₃	—	2	2	no	—
145	C₂×Dic₂₆	C₂²×C₄	1	2	yes	—
146	C₂×Dic₂₆	C₂²×C₄	1	1	yes	characteristic
147	C₂×C₈×C₁₃	—	2	2	no	—
148	C₂×C₈×C₁₃	—	2	1	no	—
149	C₂×C₈×C₁₃	—	2	1	no	—
150	C₂×C₈×C₁₃	—	2	2	no	—
151	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
152	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
153	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
154	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
155	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
156	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
157	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
158	C₂×C₈×C₁₃	#41	1	2	yes	—
159	C₁₃×C₄⋊C₄	—	4	2	no	—
160	C₄²×C₁₃	—	2	2	no	—
161	C₄²×C₁₃	—	2	2	no	—
162	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
163	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
164	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
165	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
166	C₂²⋊Dic₁₃	—	2	1	no	—
167	#6103	—	2	1	no	—
168	#6103	—	2	1	no	—
169	#6103	—	2	2	no	—
170	#6103	—	2	2	no	—
171	C₄⋊Dic₁₃	—	2	1	no	—
172	C₄⋊Dic₁₃	—	2	1	no	—
173	C₄⋊Dic₁₃	C₂²×C₄	1	1	yes	characteristic
174	C₄⋊Dic₁₃	C₂²×C₄	1	1	yes	characteristic
175	#6101	—	2	1	no	—
176	#6101	—	2	1	no	—
177	C₄×Dic₁₃	—	2	1	no	—
178	C₄×Dic₁₃	—	2	1	no	—
179	C₄×Dic₁₃	—	2	1	no	—
180	#6099	—	2	1	no	—
181	#6099	—	2	1	no	—
182	#6099	—	2	2	no	—
183	#6099	—	2	2	no	—
184	#6099	C₂×D₄	1	2	yes	—
185	#6099	#41	1	2	yes	—
186	C₂×#1055	—	2	1	no	—
187	C₂×#1055	—	2	1	no	—
188	C₂×#1055	—	2	2	no	—
189	Dic₅₂	—	2	4	no	—
190	D₁₀₄	—	2	4	no	—
191	#6095	—	2	4	no	—
192	#6095	—	2	4	no	—
193	#6094	—	2	4	no	—
194	#6094	—	2	4	no	—
195	#6094	—	4	4	no	—
196	C₈×D₁₃	—	2	4	no	—
197	C₈×D₁₃	—	2	4	no	—
198	C₈×D₁₃	—	4	4	no	—
199	#3035	—	13	1	no	—
200	C₂×#444	—	13	2	no	—
201	#2931	—	13	1	no	—
202	C₄×#131	—	13	1	no	—
203	#1980	—	13	1	no	—
204	#1950	—	13	1	no	—
205	#1929	—	13	2	no	—
206	#1876	—	13	2	no	—
207	#1806	—	13	1	no	—
208	#1770	D₁₃	1	1	yes	characteristic, complemented
209	#1765	—	13	2	no	—
210	C₂³×C₁₃	C₂×#41	1	1	yes	characteristic
211	C₂²×D₁₃	—	2	1	no	—
212	C₂²×D₁₃	—	2	2	no	—
213	C₂×C₄×C₁₃	—	2	2	no	—
214	C₂×C₄×C₁₃	—	4	1	no	—
215	C₂×C₄×C₁₃	—	4	2	no	—
216	C₂×C₄×C₁₃	—	4	2	no	—
217	C₂×C₄×C₁₃	—	4	2	no	—
218	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
219	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
220	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
221	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
222	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
223	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
224	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
225	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
226	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
227	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
228	C₂²⋊D₁₃	—	2	2	no	—
229	C₂²⋊D₁₃	—	2	2	no	—
230	C₂²⋊D₁₃	—	4	2	no	—
231	C₂²⋊D₁₃	—	4	2	no	—
232	C₂×Dic₁₃	—	2	1	no	—
233	C₂×Dic₁₃	—	2	1	no	—
234	C₂×Dic₁₃	—	2	1	no	—
235	C₂×Dic₁₃	—	2	2	no	—
236	D₅₂	—	2	2	no	—
237	D₅₂	—	2	1	no	—
238	D₅₂	—	2	2	no	—
239	D₅₂	—	4	2	no	—
240	D₅₂	—	4	2	no	—
241	D₅₂	C₄×D₄	1	2	yes	—
242	C₄×D₁₃	—	2	2	no	—
243	C₄×D₁₃	—	2	2	no	—
244	C₄×D₁₃	—	4	2	no	—
245	C₄×D₁₃	—	4	2	no	—
246	C₄×D₁₃	—	4	2	no	—
247	C₄×D₁₃	—	4	2	no	—
248	Dic₂₆	—	2	1	no	—
249	Dic₂₆	—	2	2	no	—
250	Dic₂₆	—	2	2	no	—
251	Dic₂₆	C₄×D₄	1	2	yes	—
252	C₈×C₁₃	—	2	2	no	—
253	C₈×C₁₃	—	2	2	no	—
254	C₈×C₁₃	—	2	1	no	—
255	C₈×C₁₃	—	2	1	no	—
256	C₈×C₁₃	#121	1	2	yes	—
257	C₈×C₁₃	#121	1	2	yes	—
258	#1055	—	2	2	no	—
259	#1055	—	2	2	no	—
260	#1055	—	4	2	no	—
261	C₂×#135	—	13	2	no	—
262	C₂×#131	—	13	1	no	—
263	C₂×#131	—	13	1	no	—
264	C₂×#131	—	13	2	no	—
265	#532	—	13	1	no	—
266	C₄×#41	—	13	1	no	—
267	#464	—	13	2	no	—
268	#463	—	13	2	no	—
269	#462	—	13	1	no	—
270	#461	—	13	1	no	—
271	#460	—	13	1	no	—
272	#459	—	13	1	no	—
273	#444	—	26	8	no	—
274	#436	—	26	1	no	—
275	#436	—	26	1	no	—
276	C₈×D₄	—	26	1	no	—
277	C₈×D₄	—	26	1	no	—
278	C₂×#108	—	13	2	no	—
279	#423	—	13	1	no	—
280	C₂×C₄⋊C₈	C₂×D₁₃	1	1	yes	characteristic
281	C₂×#104	—	13	2	no	—
282	C₂×#104	—	13	2	no	—
283	C₂×#104	—	13	2	no	—
284	#416	—	13	2	no	—
285	#408	—	13	2	no	—
286	#405	—	13	1	no	—
287	#405	—	13	1	no	—
288	#405	—	26	1	no	—
289	#405	—	26	1	no	—
290	C₄×M₁₆	—	13	1	no	—
291	C₄×M₁₆	—	26	1	no	—
292	C₂×#97	C₂×D₁₃	1	2	yes	—
293	C₂×C₄×C₈	—	26	1	no	—
294	C₂×C₄×C₈	C₂×D₁₃	1	1	yes	characteristic
295	C₄×C₄⋊C₄	C₂×D₁₃	1	1	yes	characteristic
296	#341	—	13	2	no	—
297	#339	—	13	2	no	—
298	#336	C₂×D₁₃	1	2	yes	—
299	C₂²×C₁₃	—	2	1	no	—
300	C₂²×C₁₃	—	2	1	no	—
301	C₂²×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
302	C₂²×C₁₃	#529	1	1	yes	characteristic
303	C₂²×C₁₃	#532	1	1	yes	characteristic
304	C₂×D₁₃	—	2	2	no	—
305	C₂×D₁₃	—	4	1	no	—
306	C₂×D₁₃	—	4	1	no	—
307	C₂×D₁₃	—	4	2	no	—
308	C₂×D₁₃	—	4	2	no	—
309	C₂×D₁₃	—	4	2	no	—
310	C₄×C₁₃	—	2	1	no	—
311	C₄×C₁₃	—	2	1	no	—
312	C₄×C₁₃	—	2	1	no	—
313	C₄×C₁₃	—	8	2	no	—
314	C₄×C₁₃	#444	1	2	yes	complemented
315	C₄×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
316	C₄×C₁₃	C₄×#41	1	1	yes	characteristic
317	C₄×C₁₃	C₂×#121	1	1	yes	characteristic
318	C₄×C₁₃	#525	1	1	yes	characteristic
319	Dic₁₃	—	2	2	no	—
320	Dic₁₃	—	4	1	no	—
321	Dic₁₃	—	4	1	no	—
322	Dic₁₃	—	4	2	no	—
323	C₂×#41	—	13	1	no	—
324	C₂×#41	—	13	2	no	—
325	#135	—	26	4	no	—
326	#135	—	26	4	no	—
327	C₂×Q₁₆	—	13	2	no	—
328	C₂×SD₁₆	—	13	2	no	—
329	C₂×SD₁₆	—	13	2	no	—
330	C₂×D₈	—	13	2	no	—
331	#131	—	13	4	no	—
332	#131	—	26	2	no	—
333	#131	—	26	2	no	—
334	#131	—	26	2	no	—
335	#131	—	26	4	no	—
336	#131	—	26	4	no	—
337	C₂×M₁₆	—	13	1	no	—
338	C₂×M₁₆	—	13	1	no	—
339	C₂×M₁₆	—	13	2	no	—
340	C₂×M₁₆	—	26	1	no	—
341	C₂×M₁₆	—	26	1	no	—
342	C₂×M₁₆	—	26	2	no	—
343	C₂²×C₈	—	26	1	no	—
344	C₂²×C₈	—	26	1	no	—
345	C₂²×C₈	—	26	2	no	—
346	C₂²×C₈	C₂²×D₁₃	1	2	yes	—
347	C₂²×C₈	C₂²×D₁₃	1	1	yes	characteristic
348	C₂²×C₈	C₂²×D₁₃	1	1	yes	characteristic
349	C₄⋊Q₈	—	13	1	no	—
350	#127	—	13	1	no	—
351	#124	—	13	2	no	—
352	#121	—	26	1	no	—
353	#121	—	26	1	no	—
354	C₄×Q₈	—	13	1	no	—
355	C₄×Q₈	—	13	1	no	—
356	C₄×D₄	—	13	1	no	—
357	C₄×D₄	—	13	1	no	—
358	C₄×D₄	—	26	1	no	—
359	C₄×D₄	—	26	1	no	—
360	C₄×D₄	—	26	1	no	—
361	C₄×D₄	—	26	1	no	—
362	#117	—	13	1	no	—
363	#117	—	26	1	no	—
364	C₂×C₄⋊C₄	—	2	1	no	—
365	C₂×C₄²	—	26	1	no	—
366	C₂×C₄²	C₂²×D₁₃	1	2	yes	—
367	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
368	#108	—	26	4	no	—
369	C₄⋊C₈	—	26	1	no	—
370	C₄⋊C₈	—	26	1	no	—
371	C₄⋊C₈	C₄×D₁₃	1	1	yes	characteristic
372	C₄⋊C₈	C₄×D₁₃	1	1	yes	characteristic
373	C₄⋊C₈	C₄×D₁₃	1	2	yes	—
374	#104	—	26	4	no	—
375	#104	—	26	4	no	—
376	#104	—	26	4	no	—
377	#103	—	13	2	no	—
378	#103	—	13	2	no	—
379	#102	—	13	2	no	—
380	#102	—	13	2	no	—
381	C₂²⋊C₈	—	26	2	no	—
382	C₂²⋊C₈	—	26	2	no	—
383	#97	—	2	4	no	—
384	#97	—	26	1	no	—
385	#97	—	26	1	no	—
386	#97	—	26	1	no	—
387	C₄×C₈	—	26	1	no	—
388	C₄×C₈	—	26	1	no	—
389	C₄×C₈	—	26	1	no	—
390	C₄×C₈	D₅₂	1	1	yes	characteristic
391	C₄×C₈	D₅₂	1	1	yes	characteristic
392	C₄×C₈	D₅₂	1	1	yes	characteristic
393	C₄×C₈	D₅₂	1	1	yes	characteristic
394	#95	—	2	1	no	—
395	C₂×C₁₃	—	2	1	no	—
396	C₂×C₁₃	—	2	1	no	—
397	C₂×C₁₃	C₄×#121	1	1	yes	characteristic
398	C₂×C₁₃	C₂×#444	1	1	yes	characteristic
399	C₂×C₁₃	#2955	1	1	yes	characteristic
400	D₁₃	—	4	2	no	—
401	D₁₃	—	8	2	no	—
402	#41	—	13	2	no	—
403	#41	—	13	2	no	—
404	#41	—	26	1	no	—
405	#41	—	26	1	no	—
406	#41	—	26	2	no	—
407	#41	—	26	2	no	—
408	#41	—	26	2	no	—
409	#41	—	26	2	no	—
410	C₂×Q₈	—	13	1	no	—
411	C₂×Q₈	—	13	2	no	—
412	C₂×D₄	—	13	1	no	—
413	C₂×D₄	—	13	2	no	—
414	C₂×D₄	—	26	1	no	—
415	C₂×D₄	—	26	2	no	—
416	C₂×D₄	—	26	1	no	—
417	C₂×D₄	—	26	1	no	—
418	C₂²×C₄	—	2	2	no	—
419	C₂²×C₄	—	26	1	no	—
420	C₂²×C₄	—	26	1	no	—
421	C₂²×C₄	—	26	1	no	—
422	C₂²×C₄	—	26	2	no	—
423	C₂²×C₄	#6127	1	1	yes	characteristic
424	C₂²×C₄	#6127	1	1	yes	characteristic
425	C₂²×C₄	C₂³×D₁₃	1	1	yes	characteristic
426	Q₁₆	—	26	4	no	—
427	SD₁₆	—	26	4	no	—
428	SD₁₆	—	26	4	no	—
429	D₈	—	26	4	no	—
430	M₁₆	—	13	2	no	—
431	M₁₆	—	13	2	no	—
432	M₁₆	—	26	4	no	—
433	M₁₆	—	26	1	no	—
434	M₁₆	—	26	1	no	—
435	M₁₆	—	26	4	no	—
436	M₁₆	—	26	2	no	—
437	M₁₆	—	26	2	no	—
438	M₁₆	—	52	4	no	—
439	C₂×C₈	—	2	2	no	—
440	C₂×C₈	—	2	1	no	—
441	C₂×C₈	—	2	1	no	—
442	C₂×C₈	—	2	2	no	—
443	C₂×C₈	—	26	4	no	—
444	C₂×C₈	—	26	1	no	—
445	C₂×C₈	—	26	1	no	—
446	C₂×C₈	—	26	4	no	—
447	C₂×C₈	—	26	2	no	—
448	C₂×C₈	—	52	4	no	—
449	C₂×C₈	C₂×C₄×D₁₃	1	2	yes	—
450	C₂×C₈	C₂×C₄×D₁₃	1	2	yes	—
451	C₂×C₈	C₂×D₅₂	1	1	yes	characteristic
452	C₂×C₈	C₂×D₅₂	1	1	yes	characteristic
453	C₂×C₈	C₂×D₅₂	1	1	yes	characteristic
454	C₂×C₈	C₂×D₅₂	1	1	yes	characteristic
455	C₂×C₈	D₄×D₁₃	1	2	yes	—
456	C₂×C₈	#6131	1	2	yes	—
457	C₄⋊C₄	—	4	2	no	—
458	C₄⋊C₄	—	13	1	no	—
459	C₄⋊C₄	—	13	1	no	—
460	C₄⋊C₄	—	26	1	no	—
461	C₄⋊C₄	—	26	1	no	—
462	C₄⋊C₄	—	26	1	no	—
463	C₄⋊C₄	—	26	1	no	—
464	C₂²⋊C₄	—	26	1	no	—
465	C₂²⋊C₄	—	26	1	no	—
466	C₂²⋊C₄	—	26	1	no	—
467	C₂²⋊C₄	—	26	2	no	—
468	C₂²⋊C₄	—	26	2	no	—
469	C₄²	—	2	2	no	—
470	C₄²	—	2	2	no	—
471	C₄²	—	26	1	no	—
472	C₄²	—	26	1	no	—
473	C₄²	—	26	1	no	—
474	C₄²	C₂×C₄×D₁₃	1	1	yes	characteristic
475	C₄²	C₂×C₄×D₁₃	1	1	yes	characteristic
476	C₄²	C₂×D₅₂	1	1	yes	characteristic
477	C₄²	C₂×D₅₂	1	1	yes	characteristic
478	C₁₃	#21518	1	1	yes	characteristic, complemented, Sylow
479	C₂³	—	26	1	no	—
480	C₂³	—	26	2	no	—
481	C₂³	C₂×#6127	1	1	yes	characteristic
482	Q₈	—	13	2	no	—
483	Q₈	—	26	1	no	—
484	Q₈	—	26	2	no	—
485	Q₈	—	26	2	no	—
486	D₄	—	13	2	no	—
487	D₄	—	26	2	no	—
488	D₄	—	26	2	no	—
489	D₄	—	26	2	no	—
490	D₄	—	26	1	no	—
491	D₄	—	26	2	no	—
492	D₄	—	52	2	no	—
493	D₄	—	52	2	no	—
494	D₄	—	52	2	no	—
495	D₄	—	52	2	no	—
496	C₂×C₄	—	2	2	no	—
497	C₂×C₄	—	4	1	no	—
498	C₂×C₄	—	4	2	no	—
499	C₂×C₄	—	4	2	no	—
500	C₂×C₄	—	4	2	no	—
501	C₂×C₄	—	26	1	no	—
502	C₂×C₄	—	26	2	no	—
503	C₂×C₄	—	26	2	no	—
504	C₂×C₄	—	26	1	no	—
505	C₂×C₄	—	26	1	no	—
506	C₂×C₄	—	26	2	no	—
507	C₂×C₄	—	52	2	no	—
508	C₂×C₄	—	52	2	no	—
509	C₂×C₄	—	52	2	no	—
510	C₂×C₄	—	52	2	no	—
511	C₂×C₄	C₄×D₅₂	1	1	yes	characteristic
512	C₂×C₄	C₄×D₅₂	1	1	yes	characteristic
513	C₂×C₄	C₄×D₅₂	1	1	yes	characteristic
514	C₂×C₄	C₄×D₅₂	1	1	yes	characteristic
515	C₂×C₄	C₂²×C₄×D₁₃	1	1	yes	characteristic
516	C₂×C₄	C₂²×D₅₂	1	1	yes	characteristic
517	C₂×C₄	C₂×D₄×D₁₃	1	1	yes	characteristic
518	C₂×C₄	C₂×#6131	1	1	yes	characteristic
519	C₂×C₄	#41×D₁₃	1	1	yes	characteristic
520	C₂×C₄	#41×D₁₃	1	1	yes	characteristic
521	C₈	—	2	1	no	—
522	C₈	—	2	1	no	—
523	C₈	—	2	2	no	—
524	C₈	—	2	2	no	—
525	C₈	—	26	2	no	—
526	C₈	—	26	2	no	—
527	C₈	—	52	2	no	—
528	C₈	#88149	1	2	yes	—
529	C₈	#88149	1	2	yes	—
530	C₂²	—	2	1	no	—
531	C₂²	—	2	1	no	—
532	C₂²	—	26	2	no	—
533	C₂²	—	52	1	no	—
534	C₂²	—	52	1	no	—
535	C₂²	—	52	2	no	—
536	C₂²	—	52	2	no	—
537	C₂²	—	52	2	no	—
538	C₂²	C₂×C₄×D₅₂	1	1	yes	characteristic
539	C₂²	#11719253	1	1	yes	characteristic
540	C₂²	#11719285	1	1	yes	characteristic
541	C₄	—	2	1	no	—
542	C₄	—	2	1	no	—
543	C₄	—	2	1	no	—
544	C₄	—	8	2	no	—
545	C₄	—	26	2	no	—
546	C₄	—	52	1	no	—
547	C₄	—	52	1	no	—
548	C₄	—	52	2	no	—
549	C₄	#11718378	1	2	yes	complemented
550	C₄	C₂×#88149	1	1	yes	characteristic
551	C₄	#11719229	1	1	yes	characteristic
552	C₄	C₄×D₄×D₁₃	1	1	yes	characteristic
553	C₄	C₄×#6131	1	1	yes	characteristic
554	C₂	—	2	1	no	—
555	C₂	—	2	1	no	—
556	C₂	—	52	2	no	—
557	C₂	—	104	2	no	—
558	C₂	C₄×#88149	1	1	yes	characteristic
559	C₂	C₂×#11718378	1	1	yes	characteristic
560	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	#13124293	C₂
cosocle	C₂²×C₄×C₁₃	C₂⁴
hypercenter	#1770	D₁₃
hypocenter	C₁₃	#21518
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. C₂×#11718378	C₂	semidirect
3. #13123549	C₂	semidirect
4. C₄×#88155	C₂	semidirect
5. #13115754	C₂	semidirect
6. #13115612	C₂	semidirect
7. #13115485	C₂	semidirect
8. #13115162	C₂	semidirect
9. #13114857	C₂	semidirect
10. #13114680	C₂	semidirect
11. C₁₃×#1770	C₂	semidirect
32. #11718510	C₄	semidirect
33. #11718509	C₄	semidirect
34. #11718506	C₄	semidirect
35. #11718505	C₄	semidirect
36. #11718504	C₄	semidirect
37. #11718502	C₄	semidirect
77. #88155	D₄	semidirect
208. #1770	D₁₃	semidirect
314. C₄×C₁₃	#444	semidirect
478. C₁₃	#21518	semidirect
549. C₄	#11718378	semidirect

Maximal subgroups

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

subgroup	index
#13124293	2
C₂×#11718378	2
#13123549	2
C₄×#88155	2
#13115754	2
#13115612	2
#13115485	2
#13115162	2
#13114857	2
#13114680	2
C₁₃×#1770	2
#21518	13