Subgroups — #28596091

Order 15104.

768 conjugacy classes of subgroups.

The subgroup lattice has 698 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#21434005	C₂	1	1	yes	maximal, characteristic
2	#21432800	C₂	1	1	yes	maximal, characteristic
3	#21432514	C₂	1	1	yes	maximal, characteristic, complemented
4	#21424747	C₂	1	1	yes	maximal, characteristic, complemented
5	#21424747	C₂	1	1	yes	maximal, characteristic, complemented
6	#21424698	C₂	1	1	yes	maximal, characteristic, complemented
7	#21424698	C₂	1	1	yes	maximal, characteristic, complemented
8	#21424301	C₂	1	1	yes	maximal, characteristic, complemented
9	#21424196	C₂	1	1	yes	maximal, characteristic, complemented
10	#21423979	C₂	1	1	yes	maximal, characteristic, complemented
11	#21423974	C₂	1	1	yes	maximal, characteristic, complemented
12	#21423941	C₂	1	1	yes	maximal, characteristic, complemented
13	#21423934	C₂	1	1	yes	maximal, characteristic, complemented
14	#21423880	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅₉×#1871	C₂	1	1	yes	maximal, characteristic
16	C₂×#14273734	C₂²	1	1	yes	characteristic
17	C₂²×#11745664	C₂²	1	1	yes	characteristic
18	C₂×#14273686	C₂²	1	1	yes	characteristic
19	#16837740	C₄	1	1	yes	characteristic, complemented
20	#16837740	C₄	1	1	yes	characteristic, complemented
21	#16837735	C₄	1	1	yes	characteristic, complemented
22	#16837730	C₄	1	1	yes	characteristic, complemented
23	#16837723	C₄	1	1	yes	characteristic, complemented
24	#16837723	C₄	1	1	yes	characteristic, complemented
25	#16837718	C₄	1	1	yes	characteristic, complemented
26	#16837713	C₄	1	1	yes	characteristic, complemented
27	#16837480	—	2	1	no	—
28	#16837480	—	2	1	no	—
29	#16837474	—	2	1	no	—
30	#16837474	—	2	1	no	—
31	C₂×#14273662	C₂²	1	1	yes	characteristic
32	C₂×#14273662	C₂²	1	1	yes	characteristic
33	#16837438	C₂²	1	1	yes	characteristic
34	#16837438	C₂²	1	1	yes	characteristic
35	#16837429	C₂²	1	1	yes	characteristic
36	#16837398	C₂²	1	1	yes	characteristic
37	#16837398	C₂²	1	1	yes	characteristic
38	#16837369	C₂²	1	1	yes	characteristic
39	#16837366	C₂²	1	1	yes	characteristic
40	C₂×C₂²⋊(C₅₉⋊C₈)	C₂²	1	1	yes	characteristic
41	#16837360	C₂²	1	1	yes	characteristic
42	#16837360	C₂²	1	1	yes	characteristic
43	#16837360	C₂²	1	1	yes	characteristic
44	#16837360	C₂²	1	1	yes	characteristic
45	#16837358	C₂²	1	1	yes	characteristic
46	#16837357	—	2	1	no	—
47	#16837357	—	2	1	no	—
48	M₁₆×Dic₅₉	—	2	1	no	—
49	M₁₆×Dic₅₉	—	2	1	no	—
50	C₂×#14273638	C₂²	1	1	yes	characteristic
51	C₂×C₄×C₅₉⋊C₈	C₂²	1	1	yes	characteristic
52	#16837166	C₂²	1	1	yes	characteristic
53	#16837166	C₂²	1	1	yes	characteristic
54	#16837162	C₂²	1	1	yes	characteristic
55	#16837162	C₂²	1	1	yes	characteristic
56	#16837162	C₂²	1	1	yes	characteristic
57	#16837162	C₂²	1	1	yes	characteristic
58	#16837157	C₂²	1	1	yes	characteristic
59	#16837157	C₂²	1	1	yes	characteristic
60	C₂²×M₁₆×C₅₉	C₂²	1	1	yes	characteristic
61	C₅₉×#525	C₂²	1	1	yes	characteristic
62	C₂×#104×C₅₉	C₂²	1	1	yes	characteristic
63	C₂×#104×C₅₉	C₂²	1	1	yes	characteristic
64	C₄×C₂²⋊C₄×C₅₉	C₂²	1	1	yes	characteristic
65	C₅₉×#339	C₂²	1	1	yes	characteristic
66	C₅₉×#339	C₂²	1	1	yes	characteristic
67	#14273734	—	2	2	no	—
68	#14273734	—	2	2	no	—
69	C₂×#11745664	—	2	1	no	—
70	C₂×#11745664	—	2	2	no	—
71	C₂×#11745664	—	2	2	no	—
72	C₂×#11745664	D₄	1	1	yes	characteristic
73	C₂×#11745664	D₄	1	1	yes	characteristic
74	C₂×#11745664	D₄	1	1	yes	characteristic
75	C₂×#11745664	D₄	1	1	yes	characteristic
76	C₂×#11745664	C₂³	1	1	yes	characteristic
77	C₂×#11745664	C₂³	1	1	yes	characteristic
78	C₂²×C₅₉⋊C₈	—	2	1	no	—
79	C₂²×C₅₉⋊C₈	C₂³	1	1	yes	characteristic
80	C₂²×C₅₉⋊C₈	C₂³	1	1	yes	characteristic
81	C₂²×C₅₉⋊C₈	C₂³	1	1	yes	characteristic
82	C₂²×C₅₉⋊C₈	C₂³	1	1	yes	characteristic
83	#14273686	—	2	1	no	—
84	#14273686	—	2	1	no	—
85	#14273686	C₂×C₄	1	1	yes	characteristic
86	#14273686	C₂×C₄	1	1	yes	characteristic
87	#14273686	C₂³	1	1	yes	characteristic
88	#14273686	C₂³	1	1	yes	characteristic
89	C₂×C₄⋊Dic₅₉	C₂×C₄	1	1	yes	characteristic
90	C₂×C₄⋊Dic₅₉	C₂×C₄	1	1	yes	characteristic
91	C₂×C₂²⋊Dic₅₉	—	2	1	no	—
92	C₂×C₄×Dic₅₉	—	2	1	no	—
93	#14273662	—	2	2	no	—
94	#14273662	—	2	2	no	—
95	#14273660	C₂×C₄	1	1	yes	characteristic
96	#14273660	C₂×C₄	1	1	yes	characteristic
97	#14273660	C₂×C₄	1	1	yes	characteristic
98	#14273660	C₂×C₄	1	1	yes	characteristic
99	#14273658	C₂×C₄	1	1	yes	characteristic
100	#14273658	C₂×C₄	1	1	yes	characteristic
101	#14273658	C₂×C₄	1	1	yes	characteristic
102	#14273658	C₂×C₄	1	1	yes	characteristic
103	C₄⋊(C₅₉⋊C₈)	—	2	1	no	—
104	C₄⋊(C₅₉⋊C₈)	—	2	1	no	—
105	#14273651	C₂×C₄	1	1	yes	characteristic
106	#14273651	C₂×C₄	1	1	yes	characteristic
107	#14273651	C₂×C₄	1	1	yes	characteristic
108	#14273651	C₂×C₄	1	1	yes	characteristic
109	#14273648	C₂×C₄	1	1	yes	characteristic
110	#14273648	C₂×C₄	1	1	yes	characteristic
111	#14273648	C₂×C₄	1	1	yes	characteristic
112	#14273648	C₂×C₄	1	1	yes	characteristic
113	C₂²⋊(C₅₉⋊C₈)	—	2	1	no	—
114	C₂²⋊(C₅₉⋊C₈)	—	2	1	no	—
115	C₂²⋊(C₅₉⋊C₈)	—	2	1	no	—
116	C₂²⋊(C₅₉⋊C₈)	—	2	1	no	—
117	C₂²⋊(C₅₉⋊C₈)	C₂×C₄	1	1	yes	characteristic
118	C₂²⋊(C₅₉⋊C₈)	C₂×C₄	1	1	yes	characteristic
119	C₂²⋊(C₅₉⋊C₈)	C₂×C₄	1	1	yes	characteristic
120	C₂²⋊(C₅₉⋊C₈)	C₂×C₄	1	1	yes	characteristic
121	#14273638	—	2	1	no	—
122	#14273638	—	2	2	no	—
123	#14273637	—	2	1	no	—
124	#14273637	—	2	1	no	—
125	#14273637	—	2	1	no	—
126	#14273637	—	2	1	no	—
127	C₄×C₅₉⋊C₈	—	2	1	no	—
128	C₄×C₅₉⋊C₈	—	2	2	no	—
129	C₈×Dic₅₉	—	2	1	no	—
130	C₈×Dic₅₉	—	2	1	no	—
131	C₈×Dic₅₉	—	2	1	no	—
132	C₈×Dic₅₉	—	2	1	no	—
133	C₂×#41×C₅₉	C₂³	1	1	yes	characteristic
134	C₂³×C₄×C₅₉	C₂³	1	1	yes	characteristic
135	C₂×M₁₆×C₅₉	—	2	1	no	—
136	C₂×M₁₆×C₅₉	—	2	2	no	—
137	C₂×M₁₆×C₅₉	—	2	2	no	—
138	C₂×M₁₆×C₅₉	C₂³	1	1	yes	characteristic
139	C₂×M₁₆×C₅₉	C₂³	1	1	yes	characteristic
140	C₂²×C₈×C₅₉	—	2	1	no	—
141	#123×C₅₉	—	2	1	no	—
142	C₂²⋊Q₈×C₅₉	C₂×C₄	1	1	yes	characteristic
143	C₂²⋊Q₈×C₅₉	C₂×C₄	1	1	yes	characteristic
144	#121×C₅₉	C₂×C₄	1	1	yes	characteristic
145	#121×C₅₉	C₂×C₄	1	1	yes	characteristic
146	#120×C₅₉	—	2	1	no	—
147	C₄×D₄×C₅₉	—	2	1	no	—
148	C₄×D₄×C₅₉	—	2	1	no	—
149	#117×C₅₉	C₂³	1	1	yes	characteristic
150	C₂×C₂²⋊C₄×C₅₉	—	2	1	no	—
151	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
152	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
153	#104×C₅₉	—	2	2	no	—
154	#104×C₅₉	—	2	2	no	—
155	#95×C₅₉	—	2	1	no	—
156	C₂⁴×C₅₉	#41	1	1	yes	characteristic
157	#41×C₅₉	—	2	1	no	—
158	#41×C₅₉	—	2	1	no	—
159	#41×C₅₉	—	2	1	no	—
160	#41×C₅₉	—	2	1	no	—
161	C₂×Q₈×C₅₉	C₂²×C₄	1	1	yes	characteristic
162	C₂×D₄×C₅₉	—	2	1	no	—
163	C₂×D₄×C₅₉	—	2	1	no	—
164	C₂×D₄×C₅₉	—	2	1	no	—
165	C₂×D₄×C₅₉	C₂²×C₄	1	1	yes	characteristic
166	C₂²×C₄×C₅₉	—	2	1	no	—
167	C₂²×C₄×C₅₉	—	2	1	no	—
168	C₂²×C₄×C₅₉	—	2	1	no	—
169	C₂²×C₄×C₅₉	—	2	1	no	—
170	C₂²×C₄×C₅₉	—	2	1	no	—
171	C₂²×C₄×C₅₉	—	2	1	no	—
172	C₂²×C₄×C₅₉	—	2	1	no	—
173	C₂²×C₄×C₅₉	C₂²×C₄	1	1	yes	characteristic
174	C₂²×C₄×C₅₉	C₂²×C₄	1	1	yes	characteristic
175	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
176	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
177	C₂²×C₄×C₅₉	#41	1	1	yes	characteristic
178	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
179	C₂²×Dic₅₉	—	2	1	no	—
180	C₂²×Dic₅₉	—	2	1	no	—
181	M₁₆×C₅₉	—	2	4	no	—
182	M₁₆×C₅₉	—	2	1	no	—
183	M₁₆×C₅₉	—	2	1	no	—
184	M₁₆×C₅₉	#41	1	2	yes	—
185	M₁₆×C₅₉	#41	1	2	yes	—
186	C₂×C₈×C₅₉	—	2	4	no	—
187	C₂×C₈×C₅₉	—	2	1	no	—
188	C₂×C₈×C₅₉	—	2	1	no	—
189	C₄⋊C₄×C₅₉	—	2	1	no	—
190	C₄⋊C₄×C₅₉	—	2	1	no	—
191	C₄⋊C₄×C₅₉	C₂²×C₄	1	1	yes	characteristic
192	C₄⋊C₄×C₅₉	C₂²×C₄	1	1	yes	characteristic
193	C₂²⋊C₄×C₅₉	—	2	1	no	—
194	C₂²⋊C₄×C₅₉	—	2	1	no	—
195	C₂²⋊C₄×C₅₉	—	2	1	no	—
196	C₂²⋊C₄×C₅₉	—	2	1	no	—
197	C₂²⋊C₄×C₅₉	—	2	1	no	—
198	C₂²⋊C₄×C₅₉	—	4	2	no	—
199	C₄²×C₅₉	—	2	1	no	—
200	C₄²×C₅₉	—	2	1	no	—
201	C₄²×C₅₉	—	2	1	no	—
202	C₄²×C₅₉	—	2	1	no	—
203	C₄²×C₅₉	—	2	1	no	—
204	C₂²⋊Dic₅₉	—	2	1	no	—
205	C₂²⋊Dic₅₉	—	2	1	no	—
206	C₂²⋊Dic₅₉	—	2	1	no	—
207	C₂²⋊Dic₅₉	—	2	1	no	—
208	C₄⋊Dic₅₉	—	2	1	no	—
209	C₄⋊Dic₅₉	—	2	1	no	—
210	C₄⋊Dic₅₉	C₂²×C₄	1	1	yes	characteristic
211	C₄⋊Dic₅₉	C₂²×C₄	1	1	yes	characteristic
212	C₄⋊Dic₅₉	C₂²×C₄	1	1	yes	characteristic
213	C₄⋊Dic₅₉	C₂²×C₄	1	1	yes	characteristic
214	C₄×Dic₅₉	—	2	1	no	—
215	C₄×Dic₅₉	—	2	1	no	—
216	C₄×Dic₅₉	—	2	1	no	—
217	C₄×Dic₅₉	—	2	1	no	—
218	#11745664	—	2	2	no	—
219	#11745664	—	2	2	no	—
220	#11745664	—	2	2	no	—
221	#11745664	—	2	2	no	—
222	#11745664	—	2	1	no	—
223	#11745664	—	2	1	no	—
224	#11745664	—	2	1	no	—
225	#11745664	—	2	1	no	—
226	#11745664	—	4	2	no	—
227	C₂×C₅₉⋊C₈	—	2	1	no	—
228	C₂×C₅₉⋊C₈	—	2	1	no	—
229	C₂×C₅₉⋊C₈	—	2	1	no	—
230	C₂×C₅₉⋊C₈	—	2	1	no	—
231	C₂×C₅₉⋊C₈	—	2	1	no	—
232	C₂×C₅₉⋊C₈	—	2	1	no	—
233	C₂×C₅₉⋊C₈	—	2	1	no	—
234	C₂×C₅₉⋊C₈	—	2	1	no	—
235	C₂×C₅₉⋊C₈	—	4	2	no	—
236	C₂×C₅₉⋊C₈	C₂²×C₄	1	1	yes	characteristic
237	C₂×C₅₉⋊C₈	C₂²×C₄	1	1	yes	characteristic
238	C₂×C₅₉⋊C₈	C₂²×C₄	1	1	yes	characteristic
239	C₂×C₅₉⋊C₈	C₂²×C₄	1	1	yes	characteristic
240	C₂×C₅₉⋊C₈	C₂×D₄	1	1	yes	characteristic
241	C₂×C₅₉⋊C₈	C₂×D₄	1	1	yes	characteristic
242	C₂×C₅₉⋊C₈	C₂×D₄	1	1	yes	characteristic
243	C₂×C₅₉⋊C₈	C₂×D₄	1	1	yes	characteristic
244	C₂×C₅₉⋊C₈	#41	1	2	yes	—
245	C₂×C₅₉⋊C₈	#41	1	2	yes	—
246	C₂³×C₅₉	—	2	1	no	—
247	C₂³×C₅₉	—	2	1	no	—
248	C₂³×C₅₉	—	2	1	no	—
249	C₂³×C₅₉	—	4	1	no	—
250	C₂³×C₅₉	—	4	1	no	—
251	C₂³×C₅₉	C₄×D₄	1	1	yes	characteristic
252	C₂³×C₅₉	C₄×D₄	1	1	yes	characteristic
253	C₂³×C₅₉	C₂×#41	1	1	yes	characteristic
254	Q₈×C₅₉	—	2	1	no	—
255	Q₈×C₅₉	—	2	1	no	—
256	D₄×C₅₉	—	2	1	no	—
257	D₄×C₅₉	—	2	1	no	—
258	D₄×C₅₉	—	4	1	no	—
259	D₄×C₅₉	—	4	1	no	—
260	D₄×C₅₉	—	8	1	no	—
261	D₄×C₅₉	—	8	1	no	—
262	C₂×C₄×C₅₉	—	2	1	no	—
263	C₂×C₄×C₅₉	—	2	1	no	—
264	C₂×C₄×C₅₉	—	2	1	no	—
265	C₂×C₄×C₅₉	—	2	1	no	—
266	C₂×C₄×C₅₉	—	2	1	no	—
267	C₂×C₄×C₅₉	—	2	1	no	—
268	C₂×C₄×C₅₉	—	2	1	no	—
269	C₂×C₄×C₅₉	—	2	1	no	—
270	C₂×C₄×C₅₉	—	2	1	no	—
271	C₂×C₄×C₅₉	—	2	1	no	—
272	C₂×C₄×C₅₉	—	2	2	no	—
273	C₂×C₄×C₅₉	—	2	1	no	—
274	C₂×C₄×C₅₉	—	2	1	no	—
275	C₂×C₄×C₅₉	—	2	1	no	—
276	C₂×C₄×C₅₉	—	4	1	no	—
277	C₂×C₄×C₅₉	—	4	1	no	—
278	C₂×C₄×C₅₉	—	4	1	no	—
279	C₂×C₄×C₅₉	—	4	1	no	—
280	C₂×C₄×C₅₉	—	4	1	no	—
281	C₂×C₄×C₅₉	—	4	1	no	—
282	C₂×C₄×C₅₉	—	4	1	no	—
283	C₂×C₄×C₅₉	C₄×D₄	1	1	yes	characteristic
284	C₂×C₄×C₅₉	C₄×D₄	1	1	yes	characteristic
285	C₂×C₄×C₅₉	C₂³×C₄	1	1	yes	characteristic
286	C₂×C₄×C₅₉	C₂²×D₄	1	1	yes	characteristic
287	C₂×C₄×C₅₉	C₂×#41	1	1	yes	characteristic
288	C₂×C₄×C₅₉	C₂×#41	1	1	yes	characteristic
289	C₂×C₄×C₅₉	C₂×#41	1	1	yes	characteristic
290	C₂×C₄×C₅₉	C₂×#41	1	1	yes	characteristic
291	C₂×Dic₅₉	—	2	1	no	—
292	C₂×Dic₅₉	—	2	1	no	—
293	C₂×Dic₅₉	—	2	1	no	—
294	C₂×Dic₅₉	—	2	1	no	—
295	C₂×Dic₅₉	—	8	1	no	—
296	C₂×Dic₅₉	—	8	1	no	—
297	C₈×C₅₉	—	2	2	no	—
298	C₈×C₅₉	—	2	2	no	—
299	C₅₉⋊C₈	—	2	1	no	—
300	C₅₉⋊C₈	—	2	1	no	—
301	C₅₉⋊C₈	—	2	1	no	—
302	C₅₉⋊C₈	—	2	1	no	—
303	C₅₉⋊C₈	—	2	1	no	—
304	C₅₉⋊C₈	—	2	1	no	—
305	C₅₉⋊C₈	—	4	1	no	—
306	C₅₉⋊C₈	—	4	1	no	—
307	C₅₉⋊C₈	#123	1	2	yes	—
308	C₅₉⋊C₈	#123	1	2	yes	—
309	#21594	—	59	1	no	maximal, Sylow
310	C₂²×C₅₉	—	2	1	no	—
311	C₂²×C₅₉	—	2	1	no	—
312	C₂²×C₅₉	—	2	1	no	—
313	C₂²×C₅₉	—	2	1	no	—
314	C₂²×C₅₉	—	2	1	no	—
315	C₂²×C₅₉	—	2	1	no	—
316	C₂²×C₅₉	—	2	1	no	—
317	C₂²×C₅₉	—	2	1	no	—
318	C₂²×C₅₉	—	4	1	no	—
319	C₂²×C₅₉	—	4	1	no	—
320	C₂²×C₅₉	—	4	1	no	—
321	C₂²×C₅₉	—	8	1	no	—
322	C₂²×C₅₉	—	8	1	no	—
323	C₂²×C₅₉	C₂×C₄×D₄	1	1	yes	characteristic
324	C₂²×C₅₉	#529	1	1	yes	characteristic
325	C₂²×C₅₉	#529	1	1	yes	characteristic
326	C₄×C₅₉	—	2	1	no	—
327	C₄×C₅₉	—	2	1	no	—
328	C₄×C₅₉	—	4	2	no	—
329	C₄×C₅₉	—	4	1	no	—
330	C₄×C₅₉	—	4	1	no	—
331	C₄×C₅₉	—	4	1	no	—
332	C₄×C₅₉	—	8	1	no	—
333	C₄×C₅₉	C₄×#41	1	1	yes	characteristic
334	C₄×C₅₉	C₄×#41	1	1	yes	characteristic
335	C₄×C₅₉	C₂×#123	1	1	yes	characteristic
336	C₄×C₅₉	#525	1	1	yes	characteristic
337	Dic₅₉	—	4	1	no	—
338	Dic₅₉	—	4	1	no	—
339	Dic₅₉	—	4	1	no	—
340	Dic₅₉	—	4	1	no	—
341	#3091	—	59	1	no	—
342	#2930	—	59	1	no	—
343	#2873	—	59	1	no	—
344	#1929	—	59	1	no	—
345	#1929	—	59	1	no	—
346	#1922	—	59	1	no	—
347	#1922	—	59	1	no	—
348	#1871	D₅₉	1	1	yes	characteristic
349	#1855	—	59	1	no	—
350	#1826	—	59	1	no	—
351	#1773	—	59	1	no	—
352	#1772	—	59	1	no	—
353	#1765	—	59	1	no	—
354	#1764	—	59	1	no	—
355	#1753	—	59	1	no	—
356	C₂×C₅₉	—	2	1	no	—
357	C₂×C₅₉	—	2	1	no	—
358	C₂×C₅₉	—	4	1	no	—
359	C₂×C₅₉	—	4	1	no	—
360	C₂×C₅₉	—	8	1	no	—
361	C₂×C₅₉	C₄×#123	1	1	yes	characteristic
362	C₂×C₅₉	#2956	1	1	yes	characteristic
363	C₂×C₅₉	#2957	1	1	yes	characteristic
364	C₂×#131	—	59	1	no	—
365	C₂²×M₁₆	—	59	1	no	—
366	C₂²×M₁₆	C₂×D₅₉	1	1	yes	characteristic
367	#525	C₂×D₅₉	1	1	yes	characteristic
368	C₂×#117	—	59	1	no	—
369	#485	—	59	1	no	—
370	#485	—	59	1	no	—
371	#484	—	59	1	no	—
372	#483	—	59	1	no	—
373	#482	—	59	1	no	—
374	#482	—	59	1	no	—
375	#481	—	59	1	no	—
376	#480	—	59	1	no	—
377	#436	—	118	1	no	—
378	#436	—	118	1	no	—
379	#435	—	118	1	no	—
380	#435	—	118	1	no	—
381	C₂×#108	—	59	1	no	—
382	C₂×#108	—	59	1	no	—
383	#427	—	59	1	no	—
384	#427	—	59	1	no	—
385	#424	—	59	1	no	—
386	C₂×#104	C₂×D₅₉	1	1	yes	characteristic
387	C₂×#104	C₂×D₅₉	1	1	yes	characteristic
388	#416	—	59	1	no	—
389	#416	—	59	1	no	—
390	#408	—	59	1	no	—
391	#407	—	59	1	no	—
392	C₂×C₂²⋊C₈	—	59	1	no	—
393	#405	—	59	1	no	—
394	#405	—	59	1	no	—
395	#405	—	59	1	no	—
396	#405	—	59	1	no	—
397	#405	—	59	1	no	—
398	#405	—	118	1	no	—
399	#405	—	118	1	no	—
400	C₄×M₁₆	—	118	1	no	—
401	C₄×M₁₆	—	118	1	no	—
402	C₂×#97	—	59	1	no	—
403	C₂×C₄×C₈	—	59	1	no	—
404	C₄×C₂²⋊C₄	C₂×D₅₉	1	1	yes	characteristic
405	#341	—	59	1	no	—
406	#341	—	59	1	no	—
407	#339	—	59	1	no	—
408	#339	—	59	1	no	—
409	#339	—	59	1	no	—
410	#339	—	59	1	no	—
411	#339	C₂×D₅₉	1	1	yes	characteristic
412	#339	C₂×D₅₉	1	1	yes	characteristic
413	#336	—	59	1	no	—
414	#336	—	59	1	no	—
415	C₅₉	#21594	1	1	yes	characteristic, complemented, Sylow
416	C₂×#41	C₂²×D₅₉	1	1	yes	characteristic
417	C₂³×C₄	C₂²×D₅₉	1	1	yes	characteristic
418	#131	—	118	2	no	—
419	#131	—	118	2	no	—
420	C₂×M₁₆	—	2	1	no	—
421	C₂×M₁₆	—	2	2	no	—
422	C₂×M₁₆	—	2	2	no	—
423	C₂×M₁₆	—	59	1	no	—
424	C₂×M₁₆	—	59	1	no	—
425	C₂×M₁₆	—	59	1	no	—
426	C₂×M₁₆	—	59	1	no	—
427	C₂×M₁₆	—	59	1	no	—
428	C₂×M₁₆	—	59	1	no	—
429	C₂×M₁₆	—	118	2	no	—
430	C₂×M₁₆	—	118	2	no	—
431	C₂×M₁₆	—	118	1	no	—
432	C₂×M₁₆	C₂²×D₅₉	1	1	yes	characteristic
433	C₂×M₁₆	C₂²×D₅₉	1	1	yes	characteristic
434	C₂²×C₈	—	2	1	no	—
435	C₂²×C₈	—	59	1	no	—
436	C₂²×C₈	—	59	1	no	—
437	C₂²×C₈	—	59	1	no	—
438	C₂²×C₈	—	59	1	no	—
439	C₂²×C₈	—	118	1	no	—
440	#123	—	2	1	no	—
441	C₂²⋊Q₈	C₄×D₅₉	1	1	yes	characteristic
442	C₂²⋊Q₈	C₄×D₅₉	1	1	yes	characteristic
443	#121	C₄×D₅₉	1	1	yes	characteristic
444	#121	C₄×D₅₉	1	1	yes	characteristic
445	#120	—	2	1	no	—
446	C₄×D₄	—	2	1	no	—
447	C₄×D₄	—	2	1	no	—
448	#117	—	59	1	no	—
449	#117	—	59	1	no	—
450	#117	—	59	1	no	—
451	#117	—	59	1	no	—
452	#117	—	118	1	no	—
453	#117	—	118	1	no	—
454	#117	C₂²×D₅₉	1	1	yes	characteristic
455	C₂×C₄⋊C₄	—	59	1	no	—
456	C₂×C₄⋊C₄	—	59	1	no	—
457	C₂×C₂²⋊C₄	—	2	1	no	—
458	C₂×C₂²⋊C₄	—	118	1	no	—
459	C₂×C₄²	—	118	1	no	—
460	C₂×C₄²	C₂²×D₅₉	1	1	yes	characteristic
461	C₂×C₄²	C₂²×D₅₉	1	1	yes	characteristic
462	#108	—	118	2	no	—
463	#108	—	118	2	no	—
464	#107	—	59	1	no	—
465	#107	—	59	1	no	—
466	#107	—	59	1	no	—
467	#107	—	59	1	no	—
468	#106	—	59	1	no	—
469	#106	—	59	1	no	—
470	#106	—	59	1	no	—
471	#106	—	59	1	no	—
472	C₄⋊C₈	—	118	1	no	—
473	C₄⋊C₈	—	118	1	no	—
474	#104	—	2	2	no	—
475	#104	—	2	2	no	—
476	#103	—	59	1	no	—
477	#103	—	59	1	no	—
478	#103	—	59	1	no	—
479	#103	—	59	1	no	—
480	#102	—	59	1	no	—
481	#102	—	59	1	no	—
482	#102	—	59	1	no	—
483	#102	—	59	1	no	—
484	C₂²⋊C₈	—	59	1	no	—
485	C₂²⋊C₈	—	59	1	no	—
486	C₂²⋊C₈	—	59	1	no	—
487	C₂²⋊C₈	—	59	1	no	—
488	C₂²⋊C₈	—	118	1	no	—
489	C₂²⋊C₈	—	118	1	no	—
490	C₂²⋊C₈	—	118	1	no	—
491	C₂²⋊C₈	—	118	1	no	—
492	#97	—	118	2	no	—
493	#97	—	118	1	no	—
494	#97	—	118	1	no	—
495	#97	—	118	1	no	—
496	#97	—	118	1	no	—
497	#97	—	118	1	no	—
498	C₄×C₈	—	118	2	no	—
499	C₄×C₈	—	118	1	no	—
500	C₄×C₈	—	118	1	no	—
501	C₄×C₈	—	118	1	no	—
502	C₄×C₈	—	118	1	no	—
503	C₄×C₈	—	118	1	no	—
504	#95	—	2	1	no	—
505	C₂⁴	#11745687	1	1	yes	characteristic
506	#41	—	2	1	no	—
507	#41	—	2	1	no	—
508	#41	—	2	1	no	—
509	#41	—	2	1	no	—
510	C₂×Q₈	C₂×C₄×D₅₉	1	1	yes	characteristic
511	C₂×D₄	—	2	1	no	—
512	C₂×D₄	—	2	1	no	—
513	C₂×D₄	—	2	1	no	—
514	C₂×D₄	C₂×C₄×D₅₉	1	1	yes	characteristic
515	C₂²×C₄	—	2	1	no	—
516	C₂²×C₄	—	2	1	no	—
517	C₂²×C₄	—	2	1	no	—
518	C₂²×C₄	—	2	1	no	—
519	C₂²×C₄	—	2	1	no	—
520	C₂²×C₄	—	2	1	no	—
521	C₂²×C₄	—	2	1	no	—
522	C₂²×C₄	—	118	1	no	—
523	C₂²×C₄	—	118	1	no	—
524	C₂²×C₄	C₂×C₄×D₅₉	1	1	yes	characteristic
525	C₂²×C₄	C₂×C₄×D₅₉	1	1	yes	characteristic
526	C₂²×C₄	D₄×D₅₉	1	1	yes	characteristic
527	C₂²×C₄	D₄×D₅₉	1	1	yes	characteristic
528	C₂²×C₄	#11745687	1	1	yes	characteristic
529	C₂²×C₄	C₂³×D₅₉	1	1	yes	characteristic
530	M₁₆	—	2	4	no	—
531	M₁₆	—	2	1	no	—
532	M₁₆	—	2	1	no	—
533	M₁₆	—	118	2	no	—
534	M₁₆	—	118	2	no	—
535	M₁₆	—	118	2	no	—
536	M₁₆	—	118	2	no	—
537	M₁₆	—	118	1	no	—
538	M₁₆	—	118	1	no	—
539	M₁₆	—	118	1	no	—
540	M₁₆	—	118	1	no	—
541	M₁₆	—	236	2	no	—
542	M₁₆	#11745687	1	2	yes	—
543	M₁₆	#11745687	1	2	yes	—
544	C₂×C₈	—	2	4	no	—
545	C₂×C₈	—	2	1	no	—
546	C₂×C₈	—	2	1	no	—
547	C₂×C₈	—	59	1	no	—
548	C₂×C₈	—	59	1	no	—
549	C₂×C₈	—	59	2	no	—
550	C₂×C₈	—	59	2	no	—
551	C₂×C₈	—	59	1	no	—
552	C₂×C₈	—	59	1	no	—
553	C₂×C₈	—	59	1	no	—
554	C₂×C₈	—	59	1	no	—
555	C₂×C₈	—	59	1	no	—
556	C₂×C₈	—	59	1	no	—
557	C₂×C₈	—	118	1	no	—
558	C₂×C₈	—	118	1	no	—
559	C₂×C₈	—	118	1	no	—
560	C₂×C₈	—	118	1	no	—
561	C₂×C₈	—	118	1	no	—
562	C₂×C₈	—	118	1	no	—
563	C₂×C₈	—	118	1	no	—
564	C₂×C₈	—	118	1	no	—
565	C₂×C₈	—	236	2	no	—
566	C₄⋊C₄	—	2	1	no	—
567	C₄⋊C₄	—	2	1	no	—
568	C₄⋊C₄	—	59	1	no	—
569	C₄⋊C₄	—	59	1	no	—
570	C₄⋊C₄	—	59	1	no	—
571	C₄⋊C₄	—	59	1	no	—
572	C₄⋊C₄	—	118	1	no	—
573	C₄⋊C₄	—	118	1	no	—
574	C₄⋊C₄	C₂×C₄×D₅₉	1	1	yes	characteristic
575	C₄⋊C₄	C₂×C₄×D₅₉	1	1	yes	characteristic
576	C₂²⋊C₄	—	2	1	no	—
577	C₂²⋊C₄	—	2	1	no	—
578	C₂²⋊C₄	—	2	1	no	—
579	C₂²⋊C₄	—	2	1	no	—
580	C₂²⋊C₄	—	2	1	no	—
581	C₂²⋊C₄	—	4	2	no	—
582	C₂²⋊C₄	—	118	1	no	—
583	C₂²⋊C₄	—	118	1	no	—
584	C₂²⋊C₄	—	118	1	no	—
585	C₂²⋊C₄	—	118	1	no	—
586	C₄²	—	2	1	no	—
587	C₄²	—	2	1	no	—
588	C₄²	—	2	1	no	—
589	C₄²	—	2	1	no	—
590	C₄²	—	2	1	no	—
591	C₄²	—	118	1	no	—
592	C₄²	—	118	1	no	—
593	C₄²	—	118	1	no	—
594	C₄²	—	118	1	no	—
595	C₂³	—	2	1	no	—
596	C₂³	—	2	1	no	—
597	C₂³	—	2	1	no	—
598	C₂³	—	4	1	no	—
599	C₂³	—	4	1	no	—
600	C₂³	(C₂²⋊D₅₉)⋊C₄	1	1	yes	characteristic
601	C₂³	(C₂²⋊D₅₉)⋊C₄	1	1	yes	characteristic
602	C₂³	C₂×#11745687	1	1	yes	characteristic
603	Q₈	—	2	1	no	—
604	Q₈	—	2	1	no	—
605	D₄	—	2	1	no	—
606	D₄	—	2	1	no	—
607	D₄	—	4	1	no	—
608	D₄	—	4	1	no	—
609	D₄	—	8	1	no	—
610	D₄	—	8	1	no	—
611	C₂×C₄	—	2	1	no	—
612	C₂×C₄	—	2	1	no	—
613	C₂×C₄	—	2	1	no	—
614	C₂×C₄	—	2	1	no	—
615	C₂×C₄	—	2	1	no	—
616	C₂×C₄	—	2	1	no	—
617	C₂×C₄	—	2	1	no	—
618	C₂×C₄	—	2	1	no	—
619	C₂×C₄	—	2	1	no	—
620	C₂×C₄	—	2	1	no	—
621	C₂×C₄	—	2	2	no	—
622	C₂×C₄	—	2	1	no	—
623	C₂×C₄	—	2	1	no	—
624	C₂×C₄	—	2	1	no	—
625	C₂×C₄	—	4	1	no	—
626	C₂×C₄	—	4	1	no	—
627	C₂×C₄	—	4	1	no	—
628	C₂×C₄	—	4	1	no	—
629	C₂×C₄	—	4	1	no	—
630	C₂×C₄	—	4	1	no	—
631	C₂×C₄	—	4	1	no	—
632	C₂×C₄	—	118	1	no	—
633	C₂×C₄	—	118	1	no	—
634	C₂×C₄	—	118	1	no	—
635	C₂×C₄	—	118	1	no	—
636	C₂×C₄	—	472	1	no	—
637	C₂×C₄	—	472	1	no	—
638	C₂×C₄	(C₂²⋊D₅₉)⋊C₄	1	1	yes	characteristic
639	C₂×C₄	(C₂²⋊D₅₉)⋊C₄	1	1	yes	characteristic
640	C₂×C₄	C₂²×C₄×D₅₉	1	1	yes	characteristic
641	C₂×C₄	C₂×D₄×D₅₉	1	1	yes	characteristic
642	C₂×C₄	#41×D₅₉	1	1	yes	characteristic
643	C₂×C₄	#41×D₅₉	1	1	yes	characteristic
644	C₂×C₄	C₂×#11745687	1	1	yes	characteristic
645	C₂×C₄	C₂×#11745687	1	1	yes	characteristic
646	C₈	—	2	2	no	—
647	C₈	—	2	2	no	—
648	C₈	—	59	2	no	—
649	C₈	—	59	2	no	—
650	C₈	—	118	1	no	—
651	C₈	—	118	1	no	—
652	C₈	—	118	1	no	—
653	C₈	—	118	1	no	—
654	C₈	—	118	1	no	—
655	C₈	—	118	1	no	—
656	C₈	—	236	1	no	—
657	C₈	—	236	1	no	—
658	C₂²	—	2	1	no	—
659	C₂²	—	2	1	no	—
660	C₂²	—	2	1	no	—
661	C₂²	—	2	1	no	—
662	C₂²	—	2	1	no	—
663	C₂²	—	2	1	no	—
664	C₂²	—	2	1	no	—
665	C₂²	—	2	1	no	—
666	C₂²	—	4	1	no	—
667	C₂²	—	4	1	no	—
668	C₂²	—	4	1	no	—
669	C₂²	—	8	1	no	—
670	C₂²	—	8	1	no	—
671	C₂²	C₂×(C₂²⋊D₅₉)⋊C₄	1	1	yes	characteristic
672	C₂²	#16837933	1	1	yes	characteristic
673	C₂²	#16837933	1	1	yes	characteristic
674	C₄	—	2	1	no	—
675	C₄	—	2	1	no	—
676	C₄	—	4	2	no	—
677	C₄	—	4	1	no	—
678	C₄	—	4	1	no	—
679	C₄	—	4	1	no	—
680	C₄	—	8	1	no	—
681	C₄	—	236	1	no	—
682	C₄	—	236	1	no	—
683	C₄	—	236	1	no	—
684	C₄	—	236	1	no	—
685	C₄	C₄×#11745687	1	1	yes	characteristic
686	C₄	C₄×#11745687	1	1	yes	characteristic
687	C₄	#123×D₅₉	1	1	yes	characteristic
688	C₄	#16837908	1	1	yes	characteristic
689	C₂	—	2	1	no	—
690	C₂	—	2	1	no	—
691	C₂	—	4	1	no	—
692	C₂	—	4	1	no	—
693	C₂	—	8	1	no	—
694	C₂	#21426621	1	1	yes	characteristic
695	C₂	#21433002	1	1	yes	characteristic
696	C₂	#21433009	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₅₉
commutator	C₂×C₄×C₅₉	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₅₉
Fitting	C₅₉×#1871	C₂
socle	C₂²×C₅₉	C₂×C₄×D₄
prime radical	C₅₉×#525	C₂²
cosocle	C₂²×C₄×C₅₉	C₂⁴
hypercenter	#1871	D₅₉
hypocenter	C₅₉	#21594
LCS	G ▷ C₂×C₄×C₅₉ ▷ C₂×C₅₉ ▷ C₅₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂³×C₄ ◁ #1871

Complements

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

N	H ≅ G/N	type
3. #21432514	C₂	semidirect
4. #21424747	C₂	semidirect
5. #21424747	C₂	semidirect
6. #21424698	C₂	semidirect
7. #21424698	C₂	semidirect
8. #21424301	C₂	semidirect
9. #21424196	C₂	semidirect
10. #21423979	C₂	semidirect
11. #21423974	C₂	semidirect
12. #21423941	C₂	semidirect
13. #21423934	C₂	semidirect
14. #21423880	C₂	semidirect
19. #16837740	C₄	semidirect
20. #16837740	C₄	semidirect
21. #16837735	C₄	semidirect
22. #16837730	C₄	semidirect
23. #16837723	C₄	semidirect
24. #16837723	C₄	semidirect
25. #16837718	C₄	semidirect
26. #16837713	C₄	semidirect
415. C₅₉	#21594	semidirect

Maximal subgroups

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

subgroup	index
#21434005	2
#21432800	2
#21432514	2
#21424747	2
#21424698	2
#21424301	2
#21424196	2
#21423979	2
#21423974	2
#21423941	2
#21423934	2
#21423880	2
C₅₉×#1871	2
#21594	59