Subgroups — C₅₉×#35624 #28447733

Order 15104.

2402 conjugacy classes of subgroups.

The subgroup lattice has 458 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅₉×#541	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₅₉×#518	C₂	1	1	yes	maximal, characteristic
3	C₅₉×#2566	C₂	1	2	yes	maximal, complemented
4	C₅₉×#2547	C₂	1	2	yes	maximal, complemented
5	C₅₉×#2499	C₂	1	2	yes	maximal, complemented
6	C₅₉×#2480	C₂	1	8	yes	maximal, complemented
7	C₅₉×#2460	C₂	1	8	yes	maximal, complemented
8	C₅₉×#2435	C₂	1	2	yes	maximal
9	C₅₉×#2326	C₂	1	2	yes	maximal, complemented
10	C₄×#124×C₅₉	C₂	1	2	yes	maximal, complemented
11	C₅₉×#2298	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂³×D₄×C₅₉	C₂²	1	1	yes	characteristic
13	C₅₉×#541	—	2	8	no	—
14	C₂×C₄⋊Q₈×C₅₉	C₂²	1	1	yes	characteristic, complemented
15	C₂×#126×C₅₉	C₂²	1	4	yes	—
16	C₂×#125×C₅₉	C₂²	1	1	yes	characteristic, complemented
17	C₂×#125×C₅₉	C₂²	1	4	yes	complemented
18	C₂×#124×C₅₉	C₂²	1	2	yes	—
19	C₂×#124×C₅₉	C₂²	1	2	yes	—
20	C₂×C₂²⋊Q₈×C₅₉	C₂²	1	2	yes	—
21	C₅₉×#518	—	2	8	no	—
22	C₂×C₄×Q₈×C₅₉	C₂²	1	2	yes	complemented
23	C₂×C₄×D₄×C₅₉	C₂²	1	2	yes	—
24	C₂×C₄×D₄×C₅₉	C₂²	1	2	yes	—
25	C₂×C₄×D₄×C₅₉	C₂²	1	4	yes	—
26	C₂×#117×C₅₉	C₂²	1	1	yes	characteristic
27	C₂×#117×C₅₉	C₂²	1	1	yes	characteristic
28	C₂²×C₂²⋊C₄×C₅₉	C₂²	1	4	yes	—
29	C₅₉×#397	C₂²	1	8	yes	—
30	C₅₉×#397	C₂²	1	8	yes	complemented
31	C₅₉×#396	C₂²	1	8	yes	complemented
32	C₅₉×#394	C₂²	1	8	yes	—
33	C₅₉×#391	C₂²	1	2	yes	complemented
34	C₅₉×#391	C₂²	1	2	yes	complemented
35	C₅₉×#390	C₂²	1	2	yes	—
36	C₅₉×#390	C₂²	1	2	yes	—
37	C₅₉×#388	C₂²	1	4	yes	—
38	C₅₉×#388	C₂²	1	8	yes	complemented
39	C₅₉×#388	C₂²	1	8	yes	complemented
40	C₅₉×#387	C₂²	1	8	yes	complemented
41	C₅₉×#387	C₂²	1	4	yes	complemented
42	C₅₉×#385	C₂²	1	8	yes	complemented
43	C₅₉×#385	C₂²	1	8	yes	complemented
44	C₅₉×#384	C₂²	1	2	yes	complemented
45	C₅₉×#382	C₂²	1	2	yes	complemented
46	C₅₉×#380	C₂²	1	8	yes	complemented
47	C₅₉×#379	C₂²	1	8	yes	—
48	C₄×C₄⋊C₄×C₅₉	C₂²	1	2	yes	complemented
49	C₄×C₂²⋊C₄×C₅₉	C₂²	1	2	yes	—
50	C₄×C₂²⋊C₄×C₅₉	C₂²	1	8	yes	complemented
51	C₅₉×#376	C₂²	1	1	yes	characteristic, complemented
52	C₄³×C₅₉	C₂²	1	1	yes	characteristic, complemented
53	C₂⁵×C₅₉	C₂³	1	2	yes	—
54	C₂²×Q₈×C₅₉	C₂³	1	2	yes	—
55	C₂²×D₄×C₅₉	—	2	8	no	—
56	C₂²×D₄×C₅₉	—	2	4	no	—
57	C₂²×D₄×C₅₉	C₂³	1	2	yes	—
58	C₂²×D₄×C₅₉	C₂³	1	2	yes	—
59	C₂³×C₄×C₅₉	C₂³	1	1	yes	characteristic
60	C₂³×C₄×C₅₉	C₂³	1	4	yes	—
61	C₂³×C₄×C₅₉	C₂³	1	4	yes	—
62	C₄⋊Q₈×C₅₉	—	2	4	no	—
63	#126×C₅₉	—	2	16	no	—
64	#125×C₅₉	—	2	16	no	—
65	#125×C₅₉	—	2	4	no	—
66	#124×C₅₉	—	2	8	no	—
67	#124×C₅₉	—	2	8	no	—
68	C₂²⋊Q₈×C₅₉	—	2	8	no	—
69	C₄×Q₈×C₅₉	—	2	8	no	—
70	C₄×D₄×C₅₉	—	2	16	no	—
71	C₄×D₄×C₅₉	—	2	8	no	—
72	C₄×D₄×C₅₉	—	2	8	no	—
73	#117×C₅₉	—	2	4	no	—
74	#117×C₅₉	D₄	1	8	yes	—
75	C₂×C₄⋊C₄×C₅₉	C₂³	1	4	yes	—
76	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
77	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
78	C₂×C₄⋊C₄×C₅₉	C₂³	1	4	yes	—
79	C₂×C₄⋊C₄×C₅₉	C₂³	1	4	yes	—
80	C₂×C₄⋊C₄×C₅₉	C₂³	1	4	yes	—
81	C₂×C₄⋊C₄×C₅₉	C₂³	1	4	yes	—
82	C₂×C₄⋊C₄×C₅₉	C₂³	1	8	yes	—
83	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
84	C₂×C₂²⋊C₄×C₅₉	—	2	16	no	—
85	C₂×C₂²⋊C₄×C₅₉	C₂³	1	8	yes	—
86	C₂×C₂²⋊C₄×C₅₉	C₂³	1	4	yes	—
87	C₂×C₂²⋊C₄×C₅₉	C₂³	1	8	yes	—
88	C₂×C₂²⋊C₄×C₅₉	C₂³	1	4	yes	—
89	C₂×C₂²⋊C₄×C₅₉	C₂³	1	4	yes	—
90	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
91	C₂×C₂²⋊C₄×C₅₉	C₂³	1	4	yes	—
92	C₂×C₂²⋊C₄×C₅₉	C₂³	1	8	yes	—
93	C₂×C₂²⋊C₄×C₅₉	C₂³	1	8	yes	—
94	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
95	C₂×C₄²×C₅₉	C₂³	1	2	yes	—
96	C₂×C₄²×C₅₉	C₂³	1	2	yes	—
97	C₂×C₄²×C₅₉	C₂³	1	4	yes	—
98	C₂×C₄²×C₅₉	C₂³	1	2	yes	—
99	C₂×C₄²×C₅₉	C₂³	1	4	yes	—
100	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
101	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
102	#95×C₅₉	C₂³	1	4	yes	—
103	#95×C₅₉	C₂³	1	4	yes	—
104	#95×C₅₉	C₂³	1	8	yes	—
105	#95×C₅₉	C₂³	1	8	yes	—
106	#95×C₅₉	C₂³	1	4	yes	—
107	#95×C₅₉	C₂³	1	8	yes	—
108	C₂⁴×C₅₉	—	2	4	no	—
109	C₂⁴×C₅₉	—	2	8	no	—
110	C₂⁴×C₅₉	—	4	8	no	—
111	C₂⁴×C₅₉	C₂⁴	1	1	yes	characteristic
112	C₂⁴×C₅₉	C₂⁴	1	4	yes	—
113	C₂×Q₈×C₅₉	—	2	4	no	—
114	C₂×Q₈×C₅₉	—	2	4	no	—
115	C₂×Q₈×C₅₉	—	2	4	no	—
116	C₂×D₄×C₅₉	—	2	32	no	—
117	C₂×D₄×C₅₉	—	2	8	no	—
118	C₂×D₄×C₅₉	—	2	4	no	—
119	C₂×D₄×C₅₉	—	2	4	no	—
120	C₂×D₄×C₅₉	—	2	4	no	—
121	C₂×D₄×C₅₉	#41	1	8	yes	—
122	C₂²×C₄×C₅₉	—	2	4	no	—
123	C₂²×C₄×C₅₉	—	2	8	no	—
124	C₂²×C₄×C₅₉	—	2	8	no	—
125	C₂²×C₄×C₅₉	—	4	8	no	—
126	C₂²×C₄×C₅₉	—	4	8	no	—
127	C₂²×C₄×C₅₉	C₂×D₄	1	4	yes	—
128	C₂²×C₄×C₅₉	C₂⁴	1	4	yes	—
129	C₂²×C₄×C₅₉	C₂⁴	1	4	yes	—
130	C₂²×C₄×C₅₉	C₂⁴	1	4	yes	—
131	C₂²×C₄×C₅₉	C₂⁴	1	4	yes	—
132	C₂²×C₄×C₅₉	C₂⁴	1	4	yes	—
133	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
134	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
135	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
136	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
137	C₄⋊C₄×C₅₉	—	2	4	no	—
138	C₄⋊C₄×C₅₉	—	2	4	no	—
139	C₄⋊C₄×C₅₉	—	2	8	no	—
140	C₄⋊C₄×C₅₉	—	2	8	no	—
141	C₄⋊C₄×C₅₉	—	2	8	no	—
142	C₄⋊C₄×C₅₉	—	2	8	no	—
143	C₄⋊C₄×C₅₉	—	4	4	no	—
144	C₄⋊C₄×C₅₉	—	4	8	no	—
145	C₄⋊C₄×C₅₉	C₂×D₄	1	8	yes	—
146	C₂²⋊C₄×C₅₉	—	2	4	no	—
147	C₂²⋊C₄×C₅₉	—	2	8	no	—
148	C₂²⋊C₄×C₅₉	—	2	16	no	—
149	C₂²⋊C₄×C₅₉	—	2	16	no	—
150	C₂²⋊C₄×C₅₉	—	2	8	no	—
151	C₂²⋊C₄×C₅₉	—	2	8	no	—
152	C₂²⋊C₄×C₅₉	—	4	8	no	—
153	C₂²⋊C₄×C₅₉	—	4	4	no	—
154	C₂²⋊C₄×C₅₉	—	4	8	no	—
155	C₂²⋊C₄×C₅₉	C₂×D₄	1	8	yes	—
156	C₄²×C₅₉	—	2	4	no	—
157	C₄²×C₅₉	—	2	8	no	—
158	C₄²×C₅₉	—	2	4	no	—
159	C₄²×C₅₉	—	2	4	no	—
160	C₄²×C₅₉	—	4	4	no	—
161	C₄²×C₅₉	C₂×D₄	1	4	yes	—
162	C₄²×C₅₉	C₂×D₄	1	4	yes	—
163	C₂³×C₅₉	—	2	16	no	—
164	C₂³×C₅₉	—	2	4	no	—
165	C₂³×C₅₉	—	2	2	no	—
166	C₂³×C₅₉	—	2	4	no	—
167	C₂³×C₅₉	—	2	8	no	—
168	C₂³×C₅₉	—	2	8	no	—
169	C₂³×C₅₉	—	2	4	no	—
170	C₂³×C₅₉	—	8	8	no	—
171	C₂³×C₅₉	—	8	16	no	—
172	C₂³×C₅₉	C₂²×D₄	1	2	yes	—
173	C₂³×C₅₉	C₂×#41	1	8	yes	—
174	C₂³×C₅₉	C₂⁵	1	1	yes	characteristic
175	Q₈×C₅₉	—	4	8	no	—
176	D₄×C₅₉	—	2	16	no	—
177	D₄×C₅₉	—	2	16	no	—
178	C₂×C₄×C₅₉	—	2	2	no	—
179	C₂×C₄×C₅₉	—	2	4	no	—
180	C₂×C₄×C₅₉	—	2	4	no	—
181	C₂×C₄×C₅₉	—	2	8	no	—
182	C₂×C₄×C₅₉	—	2	4	no	—
183	C₂×C₄×C₅₉	—	2	4	no	—
184	C₂×C₄×C₅₉	—	2	4	no	—
185	C₂×C₄×C₅₉	—	2	4	no	—
186	C₂×C₄×C₅₉	—	2	4	no	—
187	C₂×C₄×C₅₉	—	2	4	no	—
188	C₂×C₄×C₅₉	—	2	4	no	—
189	C₂×C₄×C₅₉	—	2	4	no	—
190	C₂×C₄×C₅₉	—	2	4	no	—
191	C₂×C₄×C₅₉	—	2	8	no	—
192	C₂×C₄×C₅₉	—	2	4	no	—
193	C₂×C₄×C₅₉	—	2	4	no	—
194	C₂×C₄×C₅₉	—	2	8	no	—
195	C₂×C₄×C₅₉	—	8	8	no	—
196	C₂×C₄×C₅₉	—	8	8	no	—
197	C₂×C₄×C₅₉	C₂²×D₄	1	4	yes	—
198	C₂×C₄×C₅₉	C₂²×D₄	1	2	yes	—
199	C₂×C₄×C₅₉	C₂²×D₄	1	4	yes	—
200	C₂×C₄×C₅₉	C₂²×D₄	1	2	yes	—
201	C₂×C₄×C₅₉	C₂×#41	1	4	yes	—
202	#35624	C₅₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
203	C₂²×C₅₉	—	2	2	no	—
204	C₂²×C₅₉	—	2	8	no	—
205	C₂²×C₅₉	—	2	4	no	—
206	C₂²×C₅₉	—	2	16	no	—
207	C₂²×C₅₉	—	4	4	no	—
208	C₂²×C₅₉	—	4	4	no	—
209	C₂²×C₅₉	—	4	8	no	—
210	C₂²×C₅₉	—	4	4	no	—
211	C₂²×C₅₉	—	8	16	no	—
212	C₂²×C₅₉	C₂³×D₄	1	1	yes	characteristic
213	C₂²×C₅₉	C₂²×#41	1	2	yes	—
214	C₂²×C₅₉	#585	1	4	yes	—
215	C₄×C₅₉	—	2	2	no	—
216	C₄×C₅₉	—	2	4	no	—
217	C₄×C₅₉	—	2	4	no	—
218	C₄×C₅₉	—	4	4	no	—
219	C₄×C₅₉	—	4	4	no	—
220	C₄×C₅₉	—	4	4	no	—
221	C₄×C₅₉	—	4	4	no	—
222	C₄×C₅₉	—	4	4	no	—
223	C₄×C₅₉	#525	1	4	yes	—
224	C₂×#541	C₂×C₅₉	1	1	yes	characteristic, complemented
225	C₂×#518	C₂×C₅₉	1	1	yes	characteristic
226	#2566	C₂×C₅₉	1	2	yes	complemented
227	#2547	C₂×C₅₉	1	2	yes	complemented
228	#2499	C₂×C₅₉	1	2	yes	complemented
229	#2480	C₂×C₅₉	1	8	yes	complemented
230	#2460	C₂×C₅₉	1	8	yes	complemented
231	#2435	C₂×C₅₉	1	2	yes	—
232	#2326	C₂×C₅₉	1	2	yes	complemented
233	C₄×#124	C₂×C₅₉	1	2	yes	complemented
234	#2298	C₂×C₅₉	1	1	yes	characteristic, complemented
235	C₂×C₅₉	—	4	8	no	—
236	C₂×C₅₉	—	4	2	no	—
237	C₂×C₅₉	C₂×#525	1	1	yes	characteristic
238	C₂×C₅₉	#3500	1	2	yes	—
239	C₂×C₅₉	#3521	1	4	yes	—
240	C₂³×D₄	C₂²×C₅₉	1	1	yes	characteristic
241	#541	—	2	8	no	—
242	C₂×C₄⋊Q₈	C₂²×C₅₉	1	1	yes	characteristic, complemented
243	C₂×#126	C₂²×C₅₉	1	4	yes	—
244	C₂×#125	C₂²×C₅₉	1	1	yes	characteristic, complemented
245	C₂×#125	C₂²×C₅₉	1	4	yes	complemented
246	C₂×#124	C₂²×C₅₉	1	2	yes	—
247	C₂×#124	C₂²×C₅₉	1	2	yes	—
248	C₂×C₂²⋊Q₈	C₂²×C₅₉	1	2	yes	—
249	#518	—	2	8	no	—
250	C₂×C₄×Q₈	C₂²×C₅₉	1	2	yes	complemented
251	C₂×C₄×D₄	C₂²×C₅₉	1	2	yes	—
252	C₂×C₄×D₄	C₂²×C₅₉	1	2	yes	—
253	C₂×C₄×D₄	C₂²×C₅₉	1	4	yes	—
254	C₂×#117	C₂²×C₅₉	1	1	yes	characteristic
255	C₂×#117	C₂²×C₅₉	1	1	yes	characteristic
256	C₂²×C₂²⋊C₄	C₂²×C₅₉	1	4	yes	—
257	#397	C₂²×C₅₉	1	8	yes	—
258	#397	C₂²×C₅₉	1	8	yes	complemented
259	#396	C₂²×C₅₉	1	8	yes	complemented
260	#394	C₂²×C₅₉	1	8	yes	—
261	#391	C₂²×C₅₉	1	2	yes	complemented
262	#391	C₂²×C₅₉	1	2	yes	complemented
263	#390	C₂²×C₅₉	1	2	yes	—
264	#390	C₂²×C₅₉	1	2	yes	—
265	#388	C₂²×C₅₉	1	4	yes	—
266	#388	C₂²×C₅₉	1	8	yes	complemented
267	#388	C₂²×C₅₉	1	8	yes	complemented
268	#387	C₂²×C₅₉	1	8	yes	complemented
269	#387	C₂²×C₅₉	1	4	yes	complemented
270	#385	C₂²×C₅₉	1	8	yes	complemented
271	#385	C₂²×C₅₉	1	8	yes	complemented
272	#384	C₂²×C₅₉	1	2	yes	complemented
273	#382	C₂²×C₅₉	1	2	yes	complemented
274	#380	C₂²×C₅₉	1	8	yes	complemented
275	#379	C₂²×C₅₉	1	8	yes	—
276	C₄×C₄⋊C₄	C₂²×C₅₉	1	2	yes	complemented
277	C₄×C₂²⋊C₄	C₂²×C₅₉	1	2	yes	—
278	C₄×C₂²⋊C₄	C₂²×C₅₉	1	8	yes	complemented
279	#376	C₂²×C₅₉	1	1	yes	characteristic, complemented
280	C₄³	C₂²×C₅₉	1	1	yes	characteristic, complemented
281	C₅₉	#35624	1	1	yes	characteristic, direct product factor, Sylow
282	C₂⁵	C₂³×C₅₉	1	2	yes	—
283	C₂²×Q₈	C₂³×C₅₉	1	2	yes	—
284	C₂²×D₄	—	2	8	no	—
285	C₂²×D₄	—	2	4	no	—
286	C₂²×D₄	C₂³×C₅₉	1	2	yes	—
287	C₂²×D₄	C₂³×C₅₉	1	2	yes	—
288	C₂³×C₄	C₂³×C₅₉	1	1	yes	characteristic
289	C₂³×C₄	C₂³×C₅₉	1	4	yes	—
290	C₂³×C₄	C₂³×C₅₉	1	4	yes	—
291	C₄⋊Q₈	—	2	4	no	—
292	#126	—	2	16	no	—
293	#125	—	2	16	no	—
294	#125	—	2	4	no	—
295	#124	—	2	8	no	—
296	#124	—	2	8	no	—
297	C₂²⋊Q₈	—	2	8	no	—
298	C₄×Q₈	—	2	8	no	—
299	C₄×D₄	—	2	16	no	—
300	C₄×D₄	—	2	8	no	—
301	C₄×D₄	—	2	8	no	—
302	#117	—	2	4	no	—
303	#117	D₄×C₅₉	1	8	yes	—
304	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
305	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
306	C₂×C₄⋊C₄	C₂³×C₅₉	1	4	yes	—
307	C₂×C₄⋊C₄	C₂³×C₅₉	1	4	yes	—
308	C₂×C₄⋊C₄	C₂³×C₅₉	1	4	yes	—
309	C₂×C₄⋊C₄	C₂³×C₅₉	1	4	yes	—
310	C₂×C₄⋊C₄	C₂³×C₅₉	1	4	yes	—
311	C₂×C₄⋊C₄	C₂³×C₅₉	1	8	yes	—
312	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
313	C₂×C₂²⋊C₄	—	2	16	no	—
314	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
315	C₂×C₂²⋊C₄	C₂³×C₅₉	1	4	yes	—
316	C₂×C₂²⋊C₄	C₂³×C₅₉	1	4	yes	—
317	C₂×C₂²⋊C₄	C₂³×C₅₉	1	4	yes	—
318	C₂×C₂²⋊C₄	C₂³×C₅₉	1	8	yes	—
319	C₂×C₂²⋊C₄	C₂³×C₅₉	1	8	yes	—
320	C₂×C₂²⋊C₄	C₂³×C₅₉	1	4	yes	—
321	C₂×C₂²⋊C₄	C₂³×C₅₉	1	8	yes	—
322	C₂×C₂²⋊C₄	C₂³×C₅₉	1	8	yes	—
323	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
324	C₂×C₄²	C₂³×C₅₉	1	2	yes	—
325	C₂×C₄²	C₂³×C₅₉	1	4	yes	—
326	C₂×C₄²	C₂³×C₅₉	1	2	yes	—
327	C₂×C₄²	C₂³×C₅₉	1	2	yes	—
328	C₂×C₄²	C₂³×C₅₉	1	4	yes	—
329	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
330	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
331	#95	C₂³×C₅₉	1	4	yes	—
332	#95	C₂³×C₅₉	1	4	yes	—
333	#95	C₂³×C₅₉	1	8	yes	—
334	#95	C₂³×C₅₉	1	8	yes	—
335	#95	C₂³×C₅₉	1	4	yes	—
336	#95	C₂³×C₅₉	1	8	yes	—
337	C₂⁴	—	2	4	no	—
338	C₂⁴	—	2	8	no	—
339	C₂⁴	—	4	8	no	—
340	C₂⁴	C₂⁴×C₅₉	1	1	yes	characteristic
341	C₂⁴	C₂⁴×C₅₉	1	4	yes	—
342	C₂×Q₈	—	2	4	no	—
343	C₂×Q₈	—	2	4	no	—
344	C₂×Q₈	—	2	4	no	—
345	C₂×D₄	—	2	32	no	—
346	C₂×D₄	—	2	8	no	—
347	C₂×D₄	—	2	4	no	—
348	C₂×D₄	—	2	4	no	—
349	C₂×D₄	—	2	4	no	—
350	C₂×D₄	#41×C₅₉	1	8	yes	—
351	C₂²×C₄	—	2	4	no	—
352	C₂²×C₄	—	2	8	no	—
353	C₂²×C₄	—	2	8	no	—
354	C₂²×C₄	—	4	8	no	—
355	C₂²×C₄	—	4	8	no	—
356	C₂²×C₄	C₂×D₄×C₅₉	1	4	yes	—
357	C₂²×C₄	C₂⁴×C₅₉	1	4	yes	—
358	C₂²×C₄	C₂⁴×C₅₉	1	4	yes	—
359	C₂²×C₄	C₂⁴×C₅₉	1	4	yes	—
360	C₂²×C₄	C₂⁴×C₅₉	1	4	yes	—
361	C₂²×C₄	C₂⁴×C₅₉	1	4	yes	—
362	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
363	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
364	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
365	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
366	C₄⋊C₄	—	2	4	no	—
367	C₄⋊C₄	—	2	4	no	—
368	C₄⋊C₄	—	2	8	no	—
369	C₄⋊C₄	—	2	8	no	—
370	C₄⋊C₄	—	2	8	no	—
371	C₄⋊C₄	—	2	8	no	—
372	C₄⋊C₄	—	4	4	no	—
373	C₄⋊C₄	—	4	8	no	—
374	C₄⋊C₄	C₂×D₄×C₅₉	1	8	yes	—
375	C₂²⋊C₄	—	2	4	no	—
376	C₂²⋊C₄	—	2	8	no	—
377	C₂²⋊C₄	—	2	16	no	—
378	C₂²⋊C₄	—	2	16	no	—
379	C₂²⋊C₄	—	2	8	no	—
380	C₂²⋊C₄	—	2	8	no	—
381	C₂²⋊C₄	—	4	8	no	—
382	C₂²⋊C₄	—	4	4	no	—
383	C₂²⋊C₄	—	4	8	no	—
384	C₂²⋊C₄	C₂×D₄×C₅₉	1	8	yes	—
385	C₄²	—	2	4	no	—
386	C₄²	—	2	8	no	—
387	C₄²	—	2	4	no	—
388	C₄²	—	2	4	no	—
389	C₄²	—	4	4	no	—
390	C₄²	C₂×D₄×C₅₉	1	4	yes	—
391	C₄²	C₂×D₄×C₅₉	1	4	yes	—
392	C₂³	—	2	16	no	—
393	C₂³	—	2	4	no	—
394	C₂³	—	2	2	no	—
395	C₂³	—	2	4	no	—
396	C₂³	—	2	8	no	—
397	C₂³	—	2	8	no	—
398	C₂³	—	2	4	no	—
399	C₂³	—	8	16	no	—
400	C₂³	—	8	8	no	—
401	C₂³	C₂²×D₄×C₅₉	1	2	yes	—
402	C₂³	C₂×#41×C₅₉	1	8	yes	—
403	C₂³	C₂⁵×C₅₉	1	1	yes	characteristic
404	Q₈	—	4	8	no	—
405	D₄	—	2	16	no	—
406	D₄	—	2	16	no	—
407	C₂×C₄	—	2	2	no	—
408	C₂×C₄	—	2	4	no	—
409	C₂×C₄	—	2	4	no	—
410	C₂×C₄	—	2	8	no	—
411	C₂×C₄	—	2	4	no	—
412	C₂×C₄	—	2	4	no	—
413	C₂×C₄	—	2	4	no	—
414	C₂×C₄	—	2	4	no	—
415	C₂×C₄	—	2	4	no	—
416	C₂×C₄	—	2	4	no	—
417	C₂×C₄	—	2	4	no	—
418	C₂×C₄	—	2	4	no	—
419	C₂×C₄	—	2	4	no	—
420	C₂×C₄	—	2	4	no	—
421	C₂×C₄	—	2	8	no	—
422	C₂×C₄	—	2	4	no	—
423	C₂×C₄	—	2	8	no	—
424	C₂×C₄	—	8	8	no	—
425	C₂×C₄	—	8	8	no	—
426	C₂×C₄	C₂²×D₄×C₅₉	1	4	yes	—
427	C₂×C₄	C₂²×D₄×C₅₉	1	2	yes	—
428	C₂×C₄	C₂²×D₄×C₅₉	1	4	yes	—
429	C₂×C₄	C₂²×D₄×C₅₉	1	2	yes	—
430	C₂×C₄	C₂×#41×C₅₉	1	4	yes	—
431	C₂²	—	2	16	no	—
432	C₂²	—	2	2	no	—
433	C₂²	—	2	8	no	—
434	C₂²	—	2	4	no	—
435	C₂²	—	4	4	no	—
436	C₂²	—	4	8	no	—
437	C₂²	—	4	4	no	—
438	C₂²	—	4	4	no	—
439	C₂²	—	8	16	no	—
440	C₂²	C₂³×D₄×C₅₉	1	1	yes	characteristic
441	C₂²	C₂²×#41×C₅₉	1	2	yes	—
442	C₂²	C₅₉×#585	1	4	yes	—
443	C₄	—	2	2	no	—
444	C₄	—	2	4	no	—
445	C₄	—	2	4	no	—
446	C₄	—	4	4	no	—
447	C₄	—	4	4	no	—
448	C₄	—	4	4	no	—
449	C₄	—	4	4	no	—
450	C₄	—	4	4	no	—
451	C₄	C₅₉×#525	1	4	yes	—
452	C₂	—	4	2	no	—
453	C₂	—	4	8	no	—
454	C₂	C₂×C₅₉×#525	1	1	yes	characteristic
455	C₂	C₅₉×#3500	1	2	yes	—
456	C₂	C₅₉×#3521	1	4	yes	—

	subgroup	G/H
center, socle	C₂³×C₅₉	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₅₉
prime radical	C₂³×D₄×C₅₉	C₂²
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₅₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₅₉×#541	C₂	semidirect
3. C₅₉×#2566	C₂	semidirect
4. C₅₉×#2547	C₂	semidirect
5. C₅₉×#2499	C₂	semidirect
6. C₅₉×#2480	C₂	semidirect
7. C₅₉×#2460	C₂	semidirect
9. C₅₉×#2326	C₂	semidirect
10. C₄×#124×C₅₉	C₂	semidirect
11. C₅₉×#2298	C₂	semidirect
14. C₂×C₄⋊Q₈×C₅₉	C₂²	semidirect
16. C₂×#125×C₅₉	C₂²	semidirect
17. C₂×#125×C₅₉	C₂²	semidirect
22. C₂×C₄×Q₈×C₅₉	C₂²	semidirect
30. C₅₉×#397	C₂²	semidirect
31. C₅₉×#396	C₂²	semidirect
33. C₅₉×#391	C₂²	semidirect
34. C₅₉×#391	C₂²	semidirect
38. C₅₉×#388	C₂²	semidirect
39. C₅₉×#388	C₂²	semidirect
40. C₅₉×#387	C₂²	semidirect
41. C₅₉×#387	C₂²	semidirect
42. C₅₉×#385	C₂²	semidirect
43. C₅₉×#385	C₂²	semidirect
44. C₅₉×#384	C₂²	semidirect
45. C₅₉×#382	C₂²	semidirect
46. C₅₉×#380	C₂²	semidirect
48. C₄×C₄⋊C₄×C₅₉	C₂²	semidirect
50. C₄×C₂²⋊C₄×C₅₉	C₂²	semidirect
51. C₅₉×#376	C₂²	semidirect
52. C₄³×C₅₉	C₂²	semidirect
202. #35624	C₅₉	direct (N × H)
224. C₂×#541	C₂×C₅₉	semidirect
226. #2566	C₂×C₅₉	semidirect
227. #2547	C₂×C₅₉	semidirect
228. #2499	C₂×C₅₉	semidirect
229. #2480	C₂×C₅₉	semidirect
230. #2460	C₂×C₅₉	semidirect
232. #2326	C₂×C₅₉	semidirect
233. C₄×#124	C₂×C₅₉	semidirect
234. #2298	C₂×C₅₉	semidirect
242. C₂×C₄⋊Q₈	C₂²×C₅₉	semidirect
244. C₂×#125	C₂²×C₅₉	semidirect
245. C₂×#125	C₂²×C₅₉	semidirect
250. C₂×C₄×Q₈	C₂²×C₅₉	semidirect
258. #397	C₂²×C₅₉	semidirect
259. #396	C₂²×C₅₉	semidirect
261. #391	C₂²×C₅₉	semidirect
262. #391	C₂²×C₅₉	semidirect
266. #388	C₂²×C₅₉	semidirect
267. #388	C₂²×C₅₉	semidirect
268. #387	C₂²×C₅₉	semidirect
269. #387	C₂²×C₅₉	semidirect
270. #385	C₂²×C₅₉	semidirect
271. #385	C₂²×C₅₉	semidirect
272. #384	C₂²×C₅₉	semidirect
273. #382	C₂²×C₅₉	semidirect
274. #380	C₂²×C₅₉	semidirect
276. C₄×C₄⋊C₄	C₂²×C₅₉	semidirect
278. C₄×C₂²⋊C₄	C₂²×C₅₉	semidirect
279. #376	C₂²×C₅₉	semidirect
280. C₄³	C₂²×C₅₉	semidirect
281. C₅₉	#35624	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₅₉×#541	2
C₂×C₅₉×#518	2
C₅₉×#2566	2
C₅₉×#2547	2
C₅₉×#2499	2
C₅₉×#2480	2
C₅₉×#2460	2
C₅₉×#2435	2
C₅₉×#2326	2
C₄×#124×C₅₉	2
C₅₉×#2298	2
#35624	59

Subgroups — C59×#35624 #28447733

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₉×#35624 #28447733