Subgroups — #28596082

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	#21432514	C₂	1	1	yes	maximal, characteristic, complemented
3	#21424741	C₂	1	1	yes	maximal, characteristic, complemented
4	#21424741	C₂	1	1	yes	maximal, characteristic, complemented
5	#21424692	C₂	1	1	yes	maximal, characteristic, complemented
6	#21424692	C₂	1	1	yes	maximal, characteristic, complemented
7	#21424399	C₂	1	1	yes	maximal, characteristic
8	#21424300	C₂	1	1	yes	maximal, characteristic, complemented
9	#21424193	C₂	1	1	yes	maximal, characteristic, complemented
10	#21423981	C₂	1	1	yes	maximal, characteristic, complemented
11	#21423976	C₂	1	1	yes	maximal, characteristic, complemented
12	#21423938	C₂	1	1	yes	maximal, characteristic, complemented
13	#21423931	C₂	1	1	yes	maximal, characteristic, complemented
14	#21423877	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅₉×#2930	C₂	1	1	yes	maximal, characteristic
16	C₂²×#11745664	C₂²	1	1	yes	characteristic
17	C₂×#14273686	C₂²	1	1	yes	characteristic
18	#16837740	C₄	1	1	yes	characteristic, complemented
19	#16837740	C₄	1	1	yes	characteristic, complemented
20	#16837735	C₄	1	1	yes	characteristic, complemented
21	#16837730	C₄	1	1	yes	characteristic, complemented
22	#16837723	C₄	1	1	yes	characteristic, complemented
23	#16837723	C₄	1	1	yes	characteristic, complemented
24	#16837718	C₄	1	1	yes	characteristic, complemented
25	#16837713	C₄	1	1	yes	characteristic, complemented
26	C₂×#14273662	C₂²	1	1	yes	characteristic
27	C₂×#14273662	C₂²	1	1	yes	characteristic
28	#16837438	C₂²	1	1	yes	characteristic
29	#16837438	C₂²	1	1	yes	characteristic
30	C₂×#14273654	C₂²	1	1	yes	characteristic
31	C₂×#14273654	C₂²	1	1	yes	characteristic
32	#16837398	C₂²	1	1	yes	characteristic
33	#16837398	C₂²	1	1	yes	characteristic
34	C₂×C₂²⋊(C₅₉⋊C₈)	C₂²	1	1	yes	characteristic
35	#16837360	—	2	1	no	—
36	#16837360	—	2	1	no	—
37	#16837357	C₂²	1	1	yes	characteristic
38	#16837357	C₂²	1	1	yes	characteristic
39	#16837357	C₂²	1	1	yes	characteristic
40	#16837357	C₂²	1	1	yes	characteristic
41	M₁₆×Dic₅₉	—	2	1	no	—
42	M₁₆×Dic₅₉	—	2	1	no	—
43	C₂×#14273637	C₂²	1	1	yes	characteristic
44	C₂×C₈×Dic₅₉	C₂²	1	1	yes	characteristic
45	C₄×C₂²⋊Dic₅₉	C₂²	1	1	yes	characteristic
46	#16837166	C₂²	1	1	yes	characteristic
47	#16837166	C₂²	1	1	yes	characteristic
48	#16837163	C₂²	1	1	yes	characteristic
49	#16837163	C₂²	1	1	yes	characteristic
50	#16837163	C₂²	1	1	yes	characteristic
51	#16837163	C₂²	1	1	yes	characteristic
52	#16837161	C₂²	1	1	yes	characteristic
53	#16837161	C₂²	1	1	yes	characteristic
54	#16837156	C₂²	1	1	yes	characteristic
55	#16837156	C₂²	1	1	yes	characteristic
56	C₂×#131×C₅₉	C₂²	1	1	yes	characteristic
57	C₂²×M₁₆×C₅₉	C₂²	1	1	yes	characteristic
58	C₅₉×#525	C₂²	1	1	yes	characteristic
59	C₅₉×#436	—	2	1	no	—
60	C₅₉×#436	—	2	1	no	—
61	C₅₉×#435	—	2	1	no	—
62	C₅₉×#435	—	2	1	no	—
63	C₅₉×#424	C₂²	1	1	yes	characteristic
64	C₅₉×#408	C₂²	1	1	yes	characteristic
65	C₅₉×#407	C₂²	1	1	yes	characteristic
66	C₅₉×#405	C₂²	1	1	yes	characteristic
67	C₂×#11745664	—	2	1	no	—
68	C₂×#11745664	—	2	2	no	—
69	C₂×#11745664	—	2	2	no	—
70	C₂×#11745664	C₂³	1	1	yes	characteristic
71	C₂×#11745664	C₂³	1	1	yes	characteristic
72	C₂²×C₅₉⋊C₈	—	2	1	no	—
73	C₂²×C₅₉⋊C₈	C₂³	1	1	yes	characteristic
74	C₂²×C₅₉⋊C₈	C₂³	1	1	yes	characteristic
75	#14273686	—	2	1	no	—
76	#14273686	—	2	1	no	—
77	#14273686	C₂×C₄	1	1	yes	characteristic
78	#14273686	C₂×C₄	1	1	yes	characteristic
79	#14273686	C₂³	1	1	yes	characteristic
80	#14273686	C₂³	1	1	yes	characteristic
81	C₂×C₄⋊Dic₅₉	C₂×C₄	1	1	yes	characteristic
82	C₂×C₄⋊Dic₅₉	C₂×C₄	1	1	yes	characteristic
83	C₂×C₂²⋊Dic₅₉	—	2	1	no	—
84	C₂×C₂²⋊Dic₅₉	—	2	1	no	—
85	C₂×C₄×Dic₅₉	—	2	1	no	—
86	C₂×C₄×Dic₅₉	C₂³	1	1	yes	characteristic
87	C₂×C₄×Dic₅₉	C₂³	1	1	yes	characteristic
88	#14273662	—	2	2	no	—
89	#14273662	—	2	2	no	—
90	#14273660	C₂×C₄	1	1	yes	characteristic
91	#14273660	C₂×C₄	1	1	yes	characteristic
92	#14273660	C₂×C₄	1	1	yes	characteristic
93	#14273660	C₂×C₄	1	1	yes	characteristic
94	#14273658	C₂×C₄	1	1	yes	characteristic
95	#14273658	C₂×C₄	1	1	yes	characteristic
96	#14273658	C₂×C₄	1	1	yes	characteristic
97	#14273658	C₂×C₄	1	1	yes	characteristic
98	#14273654	—	2	2	no	—
99	#14273654	—	2	2	no	—
100	#14273651	C₂×C₄	1	1	yes	characteristic
101	#14273651	C₂×C₄	1	1	yes	characteristic
102	#14273651	C₂×C₄	1	1	yes	characteristic
103	#14273651	C₂×C₄	1	1	yes	characteristic
104	#14273648	C₂×C₄	1	1	yes	characteristic
105	#14273648	C₂×C₄	1	1	yes	characteristic
106	#14273648	C₂×C₄	1	1	yes	characteristic
107	#14273648	C₂×C₄	1	1	yes	characteristic
108	C₂²⋊(C₅₉⋊C₈)	C₂×C₄	1	1	yes	characteristic
109	C₂²⋊(C₅₉⋊C₈)	C₂×C₄	1	1	yes	characteristic
110	C₂²⋊(C₅₉⋊C₈)	C₂×C₄	1	1	yes	characteristic
111	C₂²⋊(C₅₉⋊C₈)	C₂×C₄	1	1	yes	characteristic
112	#14273637	—	2	1	no	—
113	#14273637	—	2	1	no	—
114	#14273637	—	2	1	no	—
115	#14273637	—	2	1	no	—
116	#14273637	—	2	2	no	—
117	C₈×Dic₅₉	—	2	1	no	—
118	C₈×Dic₅₉	—	2	1	no	—
119	C₈×Dic₅₉	—	2	1	no	—
120	C₈×Dic₅₉	—	2	1	no	—
121	C₈×Dic₅₉	—	2	2	no	—
122	C₅₉⋊#95	—	2	1	no	—
123	C₂×#41×C₅₉	C₂³	1	1	yes	characteristic
124	C₂³×C₄×C₅₉	C₂³	1	1	yes	characteristic
125	#131×C₅₉	—	2	2	no	—
126	#131×C₅₉	—	2	2	no	—
127	C₂×M₁₆×C₅₉	—	2	1	no	—
128	C₂×M₁₆×C₅₉	—	2	2	no	—
129	C₂×M₁₆×C₅₉	—	2	2	no	—
130	C₂×M₁₆×C₅₉	D₄	1	1	yes	characteristic
131	C₂×M₁₆×C₅₉	D₄	1	1	yes	characteristic
132	C₂×M₁₆×C₅₉	D₄	1	1	yes	characteristic
133	C₂×M₁₆×C₅₉	D₄	1	1	yes	characteristic
134	C₂×M₁₆×C₅₉	C₂³	1	1	yes	characteristic
135	C₂×M₁₆×C₅₉	C₂³	1	1	yes	characteristic
136	C₂²×C₈×C₅₉	—	2	1	no	—
137	C₂²×C₈×C₅₉	C₂³	1	1	yes	characteristic
138	C₂²×C₈×C₅₉	C₂³	1	1	yes	characteristic
139	#123×C₅₉	—	2	1	no	—
140	C₂²⋊Q₈×C₅₉	C₂×C₄	1	1	yes	characteristic
141	C₂²⋊Q₈×C₅₉	C₂×C₄	1	1	yes	characteristic
142	#121×C₅₉	C₂×C₄	1	1	yes	characteristic
143	#121×C₅₉	C₂×C₄	1	1	yes	characteristic
144	#120×C₅₉	—	2	1	no	—
145	C₄×D₄×C₅₉	—	2	1	no	—
146	C₄×D₄×C₅₉	—	2	1	no	—
147	#117×C₅₉	C₂³	1	1	yes	characteristic
148	C₄⋊C₈×C₅₉	—	2	1	no	—
149	C₄⋊C₈×C₅₉	—	2	1	no	—
150	C₂²⋊C₈×C₅₉	—	2	1	no	—
151	C₂²⋊C₈×C₅₉	—	2	1	no	—
152	C₂²⋊C₈×C₅₉	—	2	1	no	—
153	C₂²⋊C₈×C₅₉	—	2	1	no	—
154	#97×C₅₉	—	2	1	no	—
155	C₄×C₈×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	C₂²×C₄	1	1	yes	characteristic
172	C₂²×C₄×C₅₉	C₂²×C₄	1	1	yes	characteristic
173	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
174	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
175	C₂²×C₄×C₅₉	#41	1	1	yes	characteristic
176	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
177	C₂²×Dic₅₉	—	2	1	no	—
178	C₂²×Dic₅₉	—	2	1	no	—
179	C₂²×Dic₅₉	—	2	1	no	—
180	C₂²×Dic₅₉	—	2	1	no	—
181	M₁₆×C₅₉	—	2	2	no	—
182	M₁₆×C₅₉	—	2	2	no	—
183	M₁₆×C₅₉	—	2	2	no	—
184	M₁₆×C₅₉	—	2	2	no	—
185	M₁₆×C₅₉	—	2	1	no	—
186	M₁₆×C₅₉	—	2	1	no	—
187	M₁₆×C₅₉	—	2	1	no	—
188	M₁₆×C₅₉	—	2	1	no	—
189	M₁₆×C₅₉	—	4	2	no	—
190	C₂×C₈×C₅₉	—	2	1	no	—
191	C₂×C₈×C₅₉	—	2	1	no	—
192	C₂×C₈×C₅₉	—	2	1	no	—
193	C₂×C₈×C₅₉	—	2	1	no	—
194	C₂×C₈×C₅₉	—	4	2	no	—
195	C₂×C₈×C₅₉	C₂×D₄	1	1	yes	characteristic
196	C₂×C₈×C₅₉	C₂×D₄	1	1	yes	characteristic
197	C₂×C₈×C₅₉	C₂×D₄	1	1	yes	characteristic
198	C₂×C₈×C₅₉	C₂×D₄	1	1	yes	characteristic
199	C₂×C₈×C₅₉	#41	1	2	yes	—
200	C₂×C₈×C₅₉	#41	1	2	yes	—
201	C₄⋊C₄×C₅₉	—	2	1	no	—
202	C₄⋊C₄×C₅₉	—	2	1	no	—
203	C₄⋊C₄×C₅₉	C₂²×C₄	1	1	yes	characteristic
204	C₄⋊C₄×C₅₉	C₂²×C₄	1	1	yes	characteristic
205	C₂²⋊C₄×C₅₉	—	2	1	no	—
206	C₂²⋊C₄×C₅₉	—	2	1	no	—
207	C₂²⋊C₄×C₅₉	—	2	1	no	—
208	C₂²⋊C₄×C₅₉	—	2	1	no	—
209	C₂²⋊C₄×C₅₉	—	2	1	no	—
210	C₄²×C₅₉	—	2	1	no	—
211	C₂²⋊Dic₅₉	—	2	1	no	—
212	C₂²⋊Dic₅₉	—	2	1	no	—
213	C₂²⋊Dic₅₉	—	2	1	no	—
214	C₂²⋊Dic₅₉	—	2	1	no	—
215	C₂²⋊Dic₅₉	—	4	2	no	—
216	C₄⋊Dic₅₉	—	2	1	no	—
217	C₄⋊Dic₅₉	—	2	1	no	—
218	C₄⋊Dic₅₉	C₂²×C₄	1	1	yes	characteristic
219	C₄⋊Dic₅₉	C₂²×C₄	1	1	yes	characteristic
220	C₄⋊Dic₅₉	C₂²×C₄	1	1	yes	characteristic
221	C₄⋊Dic₅₉	C₂²×C₄	1	1	yes	characteristic
222	C₄×Dic₅₉	—	2	1	no	—
223	C₄×Dic₅₉	—	2	1	no	—
224	C₄×Dic₅₉	—	2	1	no	—
225	C₄×Dic₅₉	—	2	1	no	—
226	C₄×Dic₅₉	—	2	1	no	—
227	C₄×Dic₅₉	—	2	1	no	—
228	C₄×Dic₅₉	—	2	1	no	—
229	C₄×Dic₅₉	—	2	1	no	—
230	#11745664	—	2	4	no	—
231	#11745664	—	2	1	no	—
232	#11745664	—	2	1	no	—
233	#11745664	#41	1	2	yes	—
234	#11745664	#41	1	2	yes	—
235	C₂×C₅₉⋊C₈	—	2	4	no	—
236	C₂×C₅₉⋊C₈	—	2	1	no	—
237	C₂×C₅₉⋊C₈	—	2	1	no	—
238	C₂×C₅₉⋊C₈	—	2	1	no	—
239	C₂×C₅₉⋊C₈	—	2	1	no	—
240	C₂×C₅₉⋊C₈	—	2	1	no	—
241	C₂×C₅₉⋊C₈	—	2	1	no	—
242	C₂×C₅₉⋊C₈	C₂²×C₄	1	1	yes	characteristic
243	C₂×C₅₉⋊C₈	C₂²×C₄	1	1	yes	characteristic
244	C₂×C₅₉⋊C₈	C₂²×C₄	1	1	yes	characteristic
245	C₂×C₅₉⋊C₈	C₂²×C₄	1	1	yes	characteristic
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	1	no	—
273	C₂×C₄×C₅₉	—	2	1	no	—
274	C₂×C₄×C₅₉	—	2	1	no	—
275	C₂×C₄×C₅₉	—	4	1	no	—
276	C₂×C₄×C₅₉	—	4	1	no	—
277	C₂×C₄×C₅₉	C₄×D₄	1	1	yes	characteristic
278	C₂×C₄×C₅₉	C₄×D₄	1	1	yes	characteristic
279	C₂×C₄×C₅₉	C₂³×C₄	1	1	yes	characteristic
280	C₂×C₄×C₅₉	C₂²×D₄	1	1	yes	characteristic
281	C₂×C₄×C₅₉	C₂×#41	1	1	yes	characteristic
282	C₂×C₄×C₅₉	C₂×#41	1	1	yes	characteristic
283	C₂×C₄×C₅₉	C₂×#41	1	1	yes	characteristic
284	C₂×C₄×C₅₉	C₂×#41	1	1	yes	characteristic
285	C₂×Dic₅₉	—	2	2	no	—
286	C₂×Dic₅₉	—	2	1	no	—
287	C₂×Dic₅₉	—	2	1	no	—
288	C₂×Dic₅₉	—	2	1	no	—
289	C₂×Dic₅₉	—	2	1	no	—
290	C₂×Dic₅₉	—	4	1	no	—
291	C₂×Dic₅₉	—	4	1	no	—
292	C₂×Dic₅₉	—	4	1	no	—
293	C₂×Dic₅₉	—	4	1	no	—
294	C₂×Dic₅₉	—	4	1	no	—
295	C₂×Dic₅₉	—	8	1	no	—
296	C₂×Dic₅₉	—	8	1	no	—
297	C₈×C₅₉	—	2	1	no	—
298	C₈×C₅₉	—	2	1	no	—
299	C₈×C₅₉	—	4	1	no	—
300	C₈×C₅₉	—	4	1	no	—
301	C₈×C₅₉	#123	1	2	yes	—
302	C₈×C₅₉	#123	1	2	yes	—
303	C₅₉⋊C₈	—	2	1	no	—
304	C₅₉⋊C₈	—	2	1	no	—
305	C₅₉⋊C₈	—	2	1	no	—
306	C₅₉⋊C₈	—	2	1	no	—
307	C₅₉⋊C₈	—	2	2	no	—
308	C₅₉⋊C₈	—	2	2	no	—
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	1	no	—
329	C₄×C₅₉	—	4	1	no	—
330	C₄×C₅₉	—	4	1	no	—
331	C₄×C₅₉	C₄×#41	1	1	yes	characteristic
332	C₄×C₅₉	C₄×#41	1	1	yes	characteristic
333	C₄×C₅₉	C₂×#123	1	1	yes	characteristic
334	C₄×C₅₉	#525	1	1	yes	characteristic
335	Dic₅₉	—	4	2	no	—
336	Dic₅₉	—	4	1	no	—
337	Dic₅₉	—	4	1	no	—
338	Dic₅₉	—	4	1	no	—
339	Dic₅₉	—	4	1	no	—
340	Dic₅₉	—	8	1	no	—
341	#3091	—	59	1	no	—
342	#2930	D₅₉	1	1	yes	characteristic
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	—	59	1	no	—
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	C₂×D₅₉	1	1	yes	characteristic
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	—	2	1	no	—
378	#436	—	2	1	no	—
379	#435	—	2	1	no	—
380	#435	—	2	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	C₂×D₅₉	1	1	yes	characteristic
386	C₂×#104	—	59	1	no	—
387	C₂×#104	—	59	1	no	—
388	#416	—	59	1	no	—
389	#416	—	59	1	no	—
390	#408	C₂×D₅₉	1	1	yes	characteristic
391	#407	C₂×D₅₉	1	1	yes	characteristic
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	—	118	1	no	—
398	#405	—	118	1	no	—
399	#405	C₂×D₅₉	1	1	yes	characteristic
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	—	59	1	no	—
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	—	59	1	no	—
412	#339	—	59	1	no	—
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	—	2	2	no	—
419	#131	—	2	2	no	—
420	C₂×M₁₆	—	2	2	no	—
421	C₂×M₁₆	—	2	2	no	—
422	C₂×M₁₆	—	2	1	no	—
423	C₂×M₁₆	—	59	1	no	—
424	C₂×M₁₆	—	59	1	no	—
425	C₂×M₁₆	—	118	2	no	—
426	C₂×M₁₆	—	118	2	no	—
427	C₂×M₁₆	—	118	1	no	—
428	C₂×M₁₆	C₂²⋊D₅₉	1	1	yes	characteristic
429	C₂×M₁₆	C₂²⋊D₅₉	1	1	yes	characteristic
430	C₂×M₁₆	C₂²⋊D₅₉	1	1	yes	characteristic
431	C₂×M₁₆	C₂²⋊D₅₉	1	1	yes	characteristic
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	—	118	1	no	—
438	C₂²×C₈	C₂²×D₅₉	1	1	yes	characteristic
439	C₂²×C₈	C₂²×D₅₉	1	1	yes	characteristic
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	—	118	1	no	—
458	C₂×C₂²⋊C₄	—	118	1	no	—
459	C₂×C₄²	—	59	1	no	—
460	C₂×C₄²	—	59	1	no	—
461	C₂×C₄²	—	118	1	no	—
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	—	2	1	no	—
473	C₄⋊C₈	—	2	1	no	—
474	#104	—	118	2	no	—
475	#104	—	118	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	—	2	1	no	—
485	C₂²⋊C₈	—	2	1	no	—
486	C₂²⋊C₈	—	2	1	no	—
487	C₂²⋊C₈	—	2	1	no	—
488	C₂²⋊C₈	—	59	1	no	—
489	C₂²⋊C₈	—	59	1	no	—
490	C₂²⋊C₈	—	59	1	no	—
491	C₂²⋊C₈	—	59	1	no	—
492	#97	—	2	1	no	—
493	#97	—	118	2	no	—
494	#97	—	118	1	no	—
495	#97	—	118	1	no	—
496	#97	—	118	1	no	—
497	#97	—	118	1	no	—
498	C₄×C₈	—	2	1	no	—
499	C₄×C₈	—	118	2	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	—	118	1	no	—
505	C₂⁴	#11745685	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	—	118	1	no	—
521	C₂²×C₄	—	118	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	#11745685	1	1	yes	characteristic
527	C₂²×C₄	C₂×C₂²⋊D₅₉	1	1	yes	characteristic
528	C₂²×C₄	C₂×C₂²⋊D₅₉	1	1	yes	characteristic
529	C₂²×C₄	C₂³×D₅₉	1	1	yes	characteristic
530	M₁₆	—	2	2	no	—
531	M₁₆	—	2	2	no	—
532	M₁₆	—	2	2	no	—
533	M₁₆	—	2	2	no	—
534	M₁₆	—	2	1	no	—
535	M₁₆	—	2	1	no	—
536	M₁₆	—	2	1	no	—
537	M₁₆	—	2	1	no	—
538	M₁₆	—	4	2	no	—
539	M₁₆	—	59	2	no	—
540	M₁₆	—	59	2	no	—
541	M₁₆	—	118	4	no	—
542	M₁₆	—	118	1	no	—
543	M₁₆	—	118	1	no	—
544	C₂×C₈	—	2	1	no	—
545	C₂×C₈	—	2	1	no	—
546	C₂×C₈	—	2	1	no	—
547	C₂×C₈	—	2	1	no	—
548	C₂×C₈	—	4	2	no	—
549	C₂×C₈	—	59	1	no	—
550	C₂×C₈	—	59	1	no	—
551	C₂×C₈	—	59	1	no	—
552	C₂×C₈	—	59	1	no	—
553	C₂×C₈	—	118	4	no	—
554	C₂×C₈	—	118	1	no	—
555	C₂×C₈	—	118	1	no	—
556	C₂×C₈	—	118	1	no	—
557	C₂×C₈	—	118	1	no	—
558	C₂×C₈	—	118	1	no	—
559	C₂×C₈	—	118	1	no	—
560	C₂×C₈	#11745687	1	2	yes	—
561	C₂×C₈	#11745687	1	2	yes	—
562	C₂×C₈	C₂×C₂²⋊D₅₉	1	1	yes	characteristic
563	C₂×C₈	C₂×C₂²⋊D₅₉	1	1	yes	characteristic
564	C₂×C₈	C₂×C₂²⋊D₅₉	1	1	yes	characteristic
565	C₂×C₈	C₂×C₂²⋊D₅₉	1	1	yes	characteristic
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	—	118	1	no	—
582	C₂²⋊C₄	—	118	1	no	—
583	C₂²⋊C₄	—	118	1	no	—
584	C₂²⋊C₄	—	118	1	no	—
585	C₂²⋊C₄	—	236	2	no	—
586	C₄²	—	2	1	no	—
587	C₄²	—	118	1	no	—
588	C₄²	—	118	1	no	—
589	C₄²	—	118	1	no	—
590	C₄²	—	118	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	C₄×C₂²⋊D₅₉	1	1	yes	characteristic
601	C₂³	C₄×C₂²⋊D₅₉	1	1	yes	characteristic
602	C₂³	C₂×#11745685	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	1	no	—
622	C₂×C₄	—	2	1	no	—
623	C₂×C₄	—	2	1	no	—
624	C₂×C₄	—	4	1	no	—
625	C₂×C₄	—	4	1	no	—
626	C₂×C₄	—	118	2	no	—
627	C₂×C₄	—	118	1	no	—
628	C₂×C₄	—	118	1	no	—
629	C₂×C₄	—	118	1	no	—
630	C₂×C₄	—	118	1	no	—
631	C₂×C₄	—	472	1	no	—
632	C₂×C₄	—	472	1	no	—
633	C₂×C₄	—	236	1	no	—
634	C₂×C₄	—	236	1	no	—
635	C₂×C₄	—	236	1	no	—
636	C₂×C₄	—	236	1	no	—
637	C₂×C₄	—	236	1	no	—
638	C₂×C₄	C₄×C₂²⋊D₅₉	1	1	yes	characteristic
639	C₂×C₄	C₄×C₂²⋊D₅₉	1	1	yes	characteristic
640	C₂×C₄	C₂²×C₄×D₅₉	1	1	yes	characteristic
641	C₂×C₄	C₂²×C₂²⋊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	1	no	—
647	C₈	—	2	1	no	—
648	C₈	—	4	1	no	—
649	C₈	—	4	1	no	—
650	C₈	—	118	2	no	—
651	C₈	—	118	2	no	—
652	C₈	—	118	1	no	—
653	C₈	—	118	1	no	—
654	C₈	—	118	1	no	—
655	C₈	—	118	1	no	—
656	C₈	#14273708	1	2	yes	—
657	C₈	#14273708	1	2	yes	—
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×C₄×C₂²⋊D₅₉	1	1	yes	characteristic
672	C₂²	#16837932	1	1	yes	characteristic
673	C₂²	#16837932	1	1	yes	characteristic
674	C₄	—	2	1	no	—
675	C₄	—	2	1	no	—
676	C₄	—	4	1	no	—
677	C₄	—	4	1	no	—
678	C₄	—	4	1	no	—
679	C₄	—	472	1	no	—
680	C₄	—	236	2	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	C₂×#14273708	1	1	yes	characteristic
688	C₄	#16837909	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	C₄×#14273708	1	1	yes	characteristic
695	C₂	#21433003	1	1	yes	characteristic
696	C₂	#21433011	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²×C₂²⋊D₅₉
commutator	C₂×C₄×C₅₉	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₅₉
Fitting	C₅₉×#2930	C₂
socle	C₂²×C₅₉	C₂×C₄×D₄
prime radical	C₅₉×#525	C₂²
cosocle	C₂²×C₄×C₅₉	C₂⁴
hypercenter	#2930	D₅₉
hypocenter	C₅₉	#21594
LCS	G ▷ C₂×C₄×C₅₉ ▷ C₂×C₅₉ ▷ C₅₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×M₁₆ ◁ #2930

Complements

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

N	H ≅ G/N	type
2. #21432514	C₂	semidirect
3. #21424741	C₂	semidirect
4. #21424741	C₂	semidirect
5. #21424692	C₂	semidirect
6. #21424692	C₂	semidirect
8. #21424300	C₂	semidirect
9. #21424193	C₂	semidirect
10. #21423981	C₂	semidirect
11. #21423976	C₂	semidirect
12. #21423938	C₂	semidirect
13. #21423931	C₂	semidirect
14. #21423877	C₂	semidirect
18. #16837740	C₄	semidirect
19. #16837740	C₄	semidirect
20. #16837735	C₄	semidirect
21. #16837730	C₄	semidirect
22. #16837723	C₄	semidirect
23. #16837723	C₄	semidirect
24. #16837718	C₄	semidirect
25. #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
#21432514	2
#21424741	2
#21424692	2
#21424399	2
#21424300	2
#21424193	2
#21423981	2
#21423976	2
#21423938	2
#21423931	2
#21423877	2
C₅₉×#2930	2
#21594	59