Subgroups — C₅₉×#35617 #28447726

Order 15104.

3146 conjugacy classes of subgroups.

The subgroup lattice has 538 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅₉×#536	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₅₉×#535	C₂	1	1	yes	maximal, characteristic
3	C₂²×#124×C₅₉	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₅₉×#518	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅₉×#2547	C₂	1	4	yes	maximal, complemented
6	C₅₉×#2544	C₂	1	4	yes	maximal, complemented
7	C₅₉×#2427	C₂	1	8	yes	maximal, complemented
8	C₅₉×#2412	C₂	1	8	yes	maximal, complemented
9	C₅₉×#2310	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅₉×#2297	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅₉×#2296	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×#41×C₅₉	C₂²	1	1	yes	characteristic
13	C₂³×Q₈×C₅₉	C₂²	1	1	yes	characteristic
14	C₂³×D₄×C₅₉	C₂²	1	1	yes	characteristic
15	C₅₉×#536	—	2	8	no	—
16	C₅₉×#535	—	2	8	no	—
17	C₂×C₄⋊Q₈×C₅₉	C₂²	1	2	yes	complemented
18	C₂×#127×C₅₉	C₂²	1	2	yes	—
19	C₂×#124×C₅₉	—	2	8	no	—
20	C₂×#124×C₅₉	C₂²	1	4	yes	—
21	C₂×#124×C₅₉	C₂²	1	2	yes	—
22	C₂×#124×C₅₉	C₂²	1	4	yes	—
23	C₂×#124×C₅₉	C₂²	1	2	yes	complemented
24	C₂×#123×C₅₉	C₂²	1	4	yes	—
25	C₂×C₂²⋊Q₈×C₅₉	C₂²	1	4	yes	complemented
26	C₂×#121×C₅₉	C₂²	1	4	yes	—
27	C₂×#120×C₅₉	C₂²	1	4	yes	—
28	C₅₉×#518	—	2	8	no	—
29	C₂×C₄×D₄×C₅₉	C₂²	1	4	yes	—
30	C₂×C₄×D₄×C₅₉	C₂²	1	4	yes	—
31	C₂×#117×C₅₉	C₂²	1	1	yes	characteristic
32	C₂×#117×C₅₉	C₂²	1	1	yes	characteristic
33	C₂×#117×C₅₉	C₂²	1	1	yes	characteristic
34	C₂²×C₂²⋊C₄×C₅₉	C₂²	1	4	yes	—
35	C₂²×C₂²⋊C₄×C₅₉	C₂²	1	4	yes	—
36	C₂²×C₄²×C₅₉	C₂²	1	1	yes	characteristic
37	C₅₉×#397	C₂²	1	16	yes	complemented
38	C₅₉×#394	C₂²	1	16	yes	complemented
39	C₅₉×#391	C₂²	1	4	yes	complemented
40	C₅₉×#391	C₂²	1	2	yes	complemented
41	C₅₉×#391	C₂²	1	4	yes	complemented
42	C₅₉×#390	C₂²	1	2	yes	complemented
43	C₅₉×#389	C₂²	1	4	yes	complemented
44	C₅₉×#386	C₂²	1	4	yes	—
45	C₅₉×#386	C₂²	1	16	yes	complemented
46	C₅₉×#385	C₂²	1	4	yes	—
47	C₅₉×#381	C₂²	1	4	yes	—
48	C₅₉×#380	C₂²	1	16	yes	complemented
49	C₄×C₄⋊C₄×C₅₉	C₂²	1	4	yes	complemented
50	C₄×C₂²⋊C₄×C₅₉	C₂²	1	4	yes	complemented
51	C₂⁵×C₅₉	C₂³	1	2	yes	—
52	C₂×#41×C₅₉	—	2	4	no	—
53	C₂×#41×C₅₉	—	2	4	no	—
54	C₂×#41×C₅₉	—	2	4	no	—
55	C₂²×Q₈×C₅₉	—	2	4	no	—
56	C₂²×Q₈×C₅₉	—	2	4	no	—
57	C₂²×Q₈×C₅₉	—	2	4	no	—
58	C₂²×Q₈×C₅₉	C₂³	1	2	yes	—
59	C₂²×Q₈×C₅₉	C₂³	1	2	yes	—
60	C₂²×Q₈×C₅₉	C₂³	1	1	yes	characteristic
61	C₂²×D₄×C₅₉	—	2	4	no	—
62	C₂²×D₄×C₅₉	—	2	4	no	—
63	C₂²×D₄×C₅₉	D₄	1	8	yes	—
64	C₂²×D₄×C₅₉	C₂³	1	2	yes	—
65	C₂²×D₄×C₅₉	C₂³	1	1	yes	characteristic
66	C₂²×D₄×C₅₉	C₂³	1	2	yes	—
67	C₂²×D₄×C₅₉	C₂³	1	2	yes	—
68	C₂²×D₄×C₅₉	C₂³	1	8	yes	—
69	C₂³×C₄×C₅₉	C₂³	1	2	yes	—
70	C₂³×C₄×C₅₉	C₂³	1	2	yes	—
71	C₂³×C₄×C₅₉	C₂³	1	8	yes	—
72	C₂³×C₄×C₅₉	C₂³	1	2	yes	—
73	C₂³×C₄×C₅₉	C₂³	1	1	yes	characteristic
74	C₄⋊Q₈×C₅₉	—	2	8	no	—
75	#127×C₅₉	—	2	8	no	—
76	#124×C₅₉	—	2	16	no	—
77	#124×C₅₉	—	2	16	no	—
78	#124×C₅₉	—	2	8	no	—
79	#124×C₅₉	—	2	8	no	—
80	#123×C₅₉	—	2	16	no	—
81	C₂²⋊Q₈×C₅₉	—	2	16	no	—
82	#121×C₅₉	—	2	16	no	—
83	#120×C₅₉	—	2	16	no	—
84	C₄×D₄×C₅₉	—	2	16	no	—
85	C₄×D₄×C₅₉	—	2	16	no	—
86	#117×C₅₉	—	2	4	no	—
87	#117×C₅₉	—	2	4	no	—
88	#117×C₅₉	D₄	1	8	yes	complemented
89	C₂×C₄⋊C₄×C₅₉	C₂³	1	8	yes	—
90	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
91	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
92	C₂×C₄⋊C₄×C₅₉	C₂³	1	8	yes	—
93	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
94	C₂×C₂²⋊C₄×C₅₉	—	2	16	no	—
95	C₂×C₂²⋊C₄×C₅₉	—	2	16	no	—
96	C₂×C₂²⋊C₄×C₅₉	C₂³	1	8	yes	—
97	C₂×C₂²⋊C₄×C₅₉	C₂³	1	16	yes	—
98	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
99	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
100	C₂×C₂²⋊C₄×C₅₉	C₂³	1	8	yes	—
101	C₂×C₂²⋊C₄×C₅₉	C₂³	1	8	yes	—
102	C₂×C₂²⋊C₄×C₅₉	C₂³	1	8	yes	—
103	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
104	C₂×C₄²×C₅₉	—	2	4	no	—
105	C₂×C₄²×C₅₉	C₂³	1	2	yes	—
106	C₂×C₄²×C₅₉	C₂³	1	2	yes	—
107	C₂×C₄²×C₅₉	C₂³	1	2	yes	—
108	C₂×C₄²×C₅₉	C₂³	1	2	yes	—
109	C₂×C₄²×C₅₉	C₂³	1	2	yes	—
110	#95×C₅₉	C₂³	1	8	yes	—
111	#95×C₅₉	C₂³	1	8	yes	—
112	#95×C₅₉	C₂³	1	16	yes	—
113	C₂⁴×C₅₉	—	2	4	no	—
114	C₂⁴×C₅₉	—	2	4	no	—
115	C₂⁴×C₅₉	—	4	8	no	—
116	C₂⁴×C₅₉	C₂×D₄	1	8	yes	—
117	C₂⁴×C₅₉	C₂⁴	1	2	yes	—
118	C₂⁴×C₅₉	C₂⁴	1	4	yes	—
119	C₂⁴×C₅₉	C₂⁴	1	1	yes	characteristic
120	#41×C₅₉	—	4	16	no	—
121	C₂×Q₈×C₅₉	—	2	4	no	—
122	C₂×Q₈×C₅₉	—	2	4	no	—
123	C₂×Q₈×C₅₉	—	2	4	no	—
124	C₂×Q₈×C₅₉	—	2	2	no	—
125	C₂×Q₈×C₅₉	—	2	4	no	—
126	C₂×Q₈×C₅₉	—	2	2	no	—
127	C₂×Q₈×C₅₉	—	2	4	no	—
128	C₂×Q₈×C₅₉	—	2	4	no	—
129	C₂×Q₈×C₅₉	—	2	2	no	—
130	C₂×Q₈×C₅₉	—	4	16	no	—
131	C₂×D₄×C₅₉	—	2	4	no	—
132	C₂×D₄×C₅₉	—	2	4	no	—
133	C₂×D₄×C₅₉	—	2	4	no	—
134	C₂×D₄×C₅₉	—	2	16	no	—
135	C₂×D₄×C₅₉	—	2	32	no	—
136	C₂×D₄×C₅₉	—	2	4	no	—
137	C₂×D₄×C₅₉	—	2	4	no	—
138	C₂×D₄×C₅₉	—	2	2	no	—
139	C₂×D₄×C₅₉	—	2	2	no	—
140	C₂×D₄×C₅₉	—	2	4	no	—
141	C₂×D₄×C₅₉	—	2	4	no	—
142	C₂×D₄×C₅₉	—	2	2	no	—
143	C₂×D₄×C₅₉	—	4	16	no	—
144	C₂×D₄×C₅₉	C₂×D₄	1	8	yes	—
145	C₂×D₄×C₅₉	C₂×D₄	1	8	yes	—
146	C₂²×C₄×C₅₉	—	2	4	no	—
147	C₂²×C₄×C₅₉	—	2	4	no	—
148	C₂²×C₄×C₅₉	—	2	4	no	—
149	C₂²×C₄×C₅₉	—	2	4	no	—
150	C₂²×C₄×C₅₉	—	2	4	no	—
151	C₂²×C₄×C₅₉	—	2	4	no	—
152	C₂²×C₄×C₅₉	—	2	4	no	—
153	C₂²×C₄×C₅₉	—	2	16	no	—
154	C₂²×C₄×C₅₉	—	4	4	no	—
155	C₂²×C₄×C₅₉	—	4	16	no	—
156	C₂²×C₄×C₅₉	C₂×D₄	1	4	yes	—
157	C₂²×C₄×C₅₉	C₂×D₄	1	4	yes	—
158	C₂²×C₄×C₅₉	#41	1	4	yes	—
159	C₂²×C₄×C₅₉	C₂⁴	1	4	yes	—
160	C₂²×C₄×C₅₉	C₂⁴	1	4	yes	—
161	C₂²×C₄×C₅₉	C₂⁴	1	4	yes	—
162	C₂²×C₄×C₅₉	C₂⁴	1	4	yes	—
163	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
164	C₂²×C₄×C₅₉	C₂⁴	1	4	yes	—
165	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
166	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
167	C₄⋊C₄×C₅₉	—	2	4	no	—
168	C₄⋊C₄×C₅₉	—	2	4	no	—
169	C₄⋊C₄×C₅₉	—	2	16	no	—
170	C₄⋊C₄×C₅₉	—	4	8	no	—
171	C₄⋊C₄×C₅₉	C₂×D₄	1	8	yes	—
172	C₂²⋊C₄×C₅₉	—	2	4	no	—
173	C₂²⋊C₄×C₅₉	—	2	32	no	—
174	C₂²⋊C₄×C₅₉	—	2	4	no	—
175	C₂²⋊C₄×C₅₉	—	2	16	no	—
176	C₂²⋊C₄×C₅₉	—	2	16	no	—
177	C₂²⋊C₄×C₅₉	—	2	16	no	—
178	C₂²⋊C₄×C₅₉	—	4	8	no	—
179	C₂²⋊C₄×C₅₉	C₂×D₄	1	8	yes	—
180	C₄²×C₅₉	—	2	4	no	—
181	C₄²×C₅₉	—	2	4	no	—
182	C₄²×C₅₉	—	2	4	no	—
183	C₄²×C₅₉	—	2	4	no	—
184	C₄²×C₅₉	C₂×D₄	1	8	yes	—
185	C₂³×C₅₉	—	2	4	no	—
186	C₂³×C₅₉	—	2	4	no	—
187	C₂³×C₅₉	—	2	4	no	—
188	C₂³×C₅₉	—	2	16	no	—
189	C₂³×C₅₉	—	2	16	no	—
190	C₂³×C₅₉	—	2	2	no	—
191	C₂³×C₅₉	—	2	2	no	—
192	C₂³×C₅₉	—	2	2	no	—
193	C₂³×C₅₉	—	2	8	no	—
194	C₂³×C₅₉	—	4	16	no	—
195	C₂³×C₅₉	—	8	8	no	—
196	C₂³×C₅₉	—	8	8	no	—
197	C₂³×C₅₉	C₂²×D₄	1	8	yes	—
198	C₂³×C₅₉	C₂²×D₄	1	2	yes	—
199	C₂³×C₅₉	C₂²×D₄	1	2	yes	—
200	C₂³×C₅₉	C₂×#41	1	2	yes	—
201	C₂³×C₅₉	C₂⁵	1	1	yes	characteristic
202	Q₈×C₅₉	—	4	8	no	—
203	Q₈×C₅₉	—	4	8	no	—
204	Q₈×C₅₉	—	4	4	no	—
205	D₄×C₅₉	—	2	16	no	—
206	D₄×C₅₉	—	2	16	no	—
207	D₄×C₅₉	—	4	8	no	—
208	D₄×C₅₉	—	4	4	no	—
209	D₄×C₅₉	—	8	16	no	—
210	C₂×C₄×C₅₉	—	2	8	no	—
211	C₂×C₄×C₅₉	—	2	4	no	—
212	C₂×C₄×C₅₉	—	2	4	no	—
213	C₂×C₄×C₅₉	—	2	4	no	—
214	C₂×C₄×C₅₉	—	2	2	no	—
215	C₂×C₄×C₅₉	—	2	4	no	—
216	C₂×C₄×C₅₉	—	2	4	no	—
217	C₂×C₄×C₅₉	—	2	2	no	—
218	C₂×C₄×C₅₉	—	2	2	no	—
219	C₂×C₄×C₅₉	—	2	4	no	—
220	C₂×C₄×C₅₉	—	2	4	no	—
221	C₂×C₄×C₅₉	—	2	8	no	—
222	C₂×C₄×C₅₉	—	2	4	no	—
223	C₂×C₄×C₅₉	—	2	8	no	—
224	C₂×C₄×C₅₉	—	4	8	no	—
225	C₂×C₄×C₅₉	—	4	8	no	—
226	C₂×C₄×C₅₉	—	4	8	no	—
227	C₂×C₄×C₅₉	—	8	16	no	—
228	C₂×C₄×C₅₉	#121	1	16	yes	—
229	C₂×C₄×C₅₉	C₂²×D₄	1	8	yes	—
230	C₂×C₄×C₅₉	C₂²×D₄	1	2	yes	—
231	C₂×C₄×C₅₉	C₂²×D₄	1	2	yes	—
232	C₂×C₄×C₅₉	C₂²×D₄	1	2	yes	—
233	C₂×C₄×C₅₉	C₂²×D₄	1	2	yes	—
234	C₂×C₄×C₅₉	C₂×#41	1	2	yes	—
235	C₂×C₄×C₅₉	C₂×#41	1	2	yes	—
236	#35617	C₅₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
237	C₂²×C₅₉	—	2	4	no	—
238	C₂²×C₅₉	—	2	4	no	—
239	C₂²×C₅₉	—	2	4	no	—
240	C₂²×C₅₉	—	2	8	no	—
241	C₂²×C₅₉	—	2	16	no	—
242	C₂²×C₅₉	—	4	8	no	—
243	C₂²×C₅₉	—	4	8	no	—
244	C₂²×C₅₉	—	4	2	no	—
245	C₂²×C₅₉	—	4	4	no	—
246	C₂²×C₅₉	—	4	4	no	—
247	C₂²×C₅₉	—	4	4	no	—
248	C₂²×C₅₉	—	8	16	no	—
249	C₂²×C₅₉	C₂×#121	1	4	yes	—
250	C₂²×C₅₉	C₂³×D₄	1	1	yes	characteristic
251	C₂²×C₅₉	C₂³×D₄	1	1	yes	characteristic
252	C₂²×C₅₉	C₂²×#41	1	1	yes	characteristic
253	C₂²×C₅₉	#585	1	4	yes	—
254	C₄×C₅₉	—	2	8	no	—
255	C₄×C₅₉	—	4	2	no	—
256	C₄×C₅₉	—	4	4	no	—
257	C₄×C₅₉	—	4	4	no	—
258	C₄×C₅₉	—	4	4	no	—
259	C₄×C₅₉	—	4	4	no	—
260	C₄×C₅₉	C₂×#121	1	4	yes	—
261	C₄×C₅₉	C₂×#121	1	4	yes	—
262	C₂×#536	C₂×C₅₉	1	1	yes	characteristic, complemented
263	C₂×#535	C₂×C₅₉	1	1	yes	characteristic
264	C₂²×#124	C₂×C₅₉	1	1	yes	characteristic, complemented
265	C₂×#518	C₂×C₅₉	1	1	yes	characteristic, complemented
266	#2547	C₂×C₅₉	1	4	yes	complemented
267	#2544	C₂×C₅₉	1	4	yes	complemented
268	#2427	C₂×C₅₉	1	8	yes	complemented
269	#2412	C₂×C₅₉	1	8	yes	complemented
270	#2310	C₂×C₅₉	1	1	yes	characteristic, complemented
271	#2297	C₂×C₅₉	1	1	yes	characteristic, complemented
272	#2296	C₂×C₅₉	1	1	yes	characteristic, complemented
273	C₂×C₅₉	—	2	4	no	—
274	C₂×C₅₉	—	4	8	no	—
275	C₂×C₅₉	—	8	2	no	—
276	C₂×C₅₉	C₂²×#121	1	1	yes	characteristic
277	C₂×C₅₉	#3485	1	2	yes	—
278	C₂×C₅₉	#3500	1	2	yes	—
279	C₂×C₅₉	#3510	1	2	yes	—
280	C₂²×#41	C₂²×C₅₉	1	1	yes	characteristic
281	C₂³×Q₈	C₂²×C₅₉	1	1	yes	characteristic
282	C₂³×D₄	C₂²×C₅₉	1	1	yes	characteristic
283	#536	—	2	8	no	—
284	#535	—	2	8	no	—
285	C₂×C₄⋊Q₈	C₂²×C₅₉	1	2	yes	complemented
286	C₂×#127	C₂²×C₅₉	1	2	yes	—
287	C₂×#124	—	2	8	no	—
288	C₂×#124	C₂²×C₅₉	1	4	yes	—
289	C₂×#124	C₂²×C₅₉	1	4	yes	—
290	C₂×#124	C₂²×C₅₉	1	2	yes	—
291	C₂×#124	C₂²×C₅₉	1	2	yes	complemented
292	C₂×#123	C₂²×C₅₉	1	4	yes	—
293	C₂×C₂²⋊Q₈	C₂²×C₅₉	1	4	yes	complemented
294	C₂×#121	C₂²×C₅₉	1	4	yes	—
295	C₂×#120	C₂²×C₅₉	1	4	yes	—
296	#518	—	2	8	no	—
297	C₂×C₄×D₄	C₂²×C₅₉	1	4	yes	—
298	C₂×C₄×D₄	C₂²×C₅₉	1	4	yes	—
299	C₂×#117	C₂²×C₅₉	1	1	yes	characteristic
300	C₂×#117	C₂²×C₅₉	1	1	yes	characteristic
301	C₂×#117	C₂²×C₅₉	1	1	yes	characteristic
302	C₂²×C₂²⋊C₄	C₂²×C₅₉	1	4	yes	—
303	C₂²×C₂²⋊C₄	C₂²×C₅₉	1	4	yes	—
304	C₂²×C₄²	C₂²×C₅₉	1	1	yes	characteristic
305	#397	C₂²×C₅₉	1	16	yes	complemented
306	#394	C₂²×C₅₉	1	16	yes	complemented
307	#391	C₂²×C₅₉	1	4	yes	complemented
308	#391	C₂²×C₅₉	1	4	yes	complemented
309	#391	C₂²×C₅₉	1	2	yes	complemented
310	#390	C₂²×C₅₉	1	2	yes	complemented
311	#389	C₂²×C₅₉	1	4	yes	complemented
312	#386	C₂²×C₅₉	1	4	yes	—
313	#386	C₂²×C₅₉	1	16	yes	complemented
314	#385	C₂²×C₅₉	1	4	yes	—
315	#381	C₂²×C₅₉	1	4	yes	—
316	#380	C₂²×C₅₉	1	16	yes	complemented
317	C₄×C₄⋊C₄	C₂²×C₅₉	1	4	yes	complemented
318	C₄×C₂²⋊C₄	C₂²×C₅₉	1	4	yes	complemented
319	C₅₉	#35617	1	1	yes	characteristic, direct product factor, Sylow
320	C₂⁵	C₂³×C₅₉	1	2	yes	—
321	C₂×#41	—	2	4	no	—
322	C₂×#41	—	2	4	no	—
323	C₂×#41	—	2	4	no	—
324	C₂²×Q₈	—	2	4	no	—
325	C₂²×Q₈	—	2	4	no	—
326	C₂²×Q₈	—	2	4	no	—
327	C₂²×Q₈	C₂³×C₅₉	1	2	yes	—
328	C₂²×Q₈	C₂³×C₅₉	1	2	yes	—
329	C₂²×Q₈	C₂³×C₅₉	1	1	yes	characteristic
330	C₂²×D₄	—	2	4	no	—
331	C₂²×D₄	—	2	4	no	—
332	C₂²×D₄	D₄×C₅₉	1	8	yes	—
333	C₂²×D₄	C₂³×C₅₉	1	2	yes	—
334	C₂²×D₄	C₂³×C₅₉	1	1	yes	characteristic
335	C₂²×D₄	C₂³×C₅₉	1	2	yes	—
336	C₂²×D₄	C₂³×C₅₉	1	2	yes	—
337	C₂²×D₄	C₂³×C₅₉	1	8	yes	—
338	C₂³×C₄	C₂³×C₅₉	1	2	yes	—
339	C₂³×C₄	C₂³×C₅₉	1	2	yes	—
340	C₂³×C₄	C₂³×C₅₉	1	2	yes	—
341	C₂³×C₄	C₂³×C₅₉	1	8	yes	—
342	C₂³×C₄	C₂³×C₅₉	1	1	yes	characteristic
343	C₄⋊Q₈	—	2	8	no	—
344	#127	—	2	8	no	—
345	#124	—	2	16	no	—
346	#124	—	2	16	no	—
347	#124	—	2	8	no	—
348	#124	—	2	8	no	—
349	#123	—	2	16	no	—
350	C₂²⋊Q₈	—	2	16	no	—
351	#121	—	2	16	no	—
352	#120	—	2	16	no	—
353	C₄×D₄	—	2	16	no	—
354	C₄×D₄	—	2	16	no	—
355	#117	—	2	4	no	—
356	#117	—	2	4	no	—
357	#117	D₄×C₅₉	1	8	yes	complemented
358	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
359	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
360	C₂×C₄⋊C₄	C₂³×C₅₉	1	8	yes	—
361	C₂×C₄⋊C₄	C₂³×C₅₉	1	8	yes	—
362	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
363	C₂×C₂²⋊C₄	—	2	16	no	—
364	C₂×C₂²⋊C₄	—	2	16	no	—
365	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
366	C₂×C₂²⋊C₄	C₂³×C₅₉	1	8	yes	—
367	C₂×C₂²⋊C₄	C₂³×C₅₉	1	16	yes	—
368	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
369	C₂×C₂²⋊C₄	C₂³×C₅₉	1	8	yes	—
370	C₂×C₂²⋊C₄	C₂³×C₅₉	1	8	yes	—
371	C₂×C₂²⋊C₄	C₂³×C₅₉	1	8	yes	—
372	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
373	C₂×C₄²	—	2	4	no	—
374	C₂×C₄²	C₂³×C₅₉	1	2	yes	—
375	C₂×C₄²	C₂³×C₅₉	1	2	yes	—
376	C₂×C₄²	C₂³×C₅₉	1	2	yes	—
377	C₂×C₄²	C₂³×C₅₉	1	2	yes	—
378	C₂×C₄²	C₂³×C₅₉	1	2	yes	—
379	#95	C₂³×C₅₉	1	8	yes	—
380	#95	C₂³×C₅₉	1	8	yes	—
381	#95	C₂³×C₅₉	1	16	yes	—
382	C₂⁴	—	2	4	no	—
383	C₂⁴	—	2	4	no	—
384	C₂⁴	—	4	8	no	—
385	C₂⁴	C₂×D₄×C₅₉	1	8	yes	—
386	C₂⁴	C₂⁴×C₅₉	1	2	yes	—
387	C₂⁴	C₂⁴×C₅₉	1	4	yes	—
388	C₂⁴	C₂⁴×C₅₉	1	1	yes	characteristic
389	#41	—	4	16	no	—
390	C₂×Q₈	—	2	4	no	—
391	C₂×Q₈	—	2	4	no	—
392	C₂×Q₈	—	2	4	no	—
393	C₂×Q₈	—	2	2	no	—
394	C₂×Q₈	—	2	4	no	—
395	C₂×Q₈	—	2	2	no	—
396	C₂×Q₈	—	2	4	no	—
397	C₂×Q₈	—	2	4	no	—
398	C₂×Q₈	—	2	2	no	—
399	C₂×Q₈	—	4	16	no	—
400	C₂×D₄	—	2	4	no	—
401	C₂×D₄	—	2	4	no	—
402	C₂×D₄	—	2	4	no	—
403	C₂×D₄	—	2	16	no	—
404	C₂×D₄	—	2	32	no	—
405	C₂×D₄	—	2	4	no	—
406	C₂×D₄	—	2	4	no	—
407	C₂×D₄	—	2	2	no	—
408	C₂×D₄	—	2	2	no	—
409	C₂×D₄	—	2	4	no	—
410	C₂×D₄	—	2	4	no	—
411	C₂×D₄	—	2	2	no	—
412	C₂×D₄	—	4	16	no	—
413	C₂×D₄	C₂×D₄×C₅₉	1	8	yes	—
414	C₂×D₄	C₂×D₄×C₅₉	1	8	yes	—
415	C₂²×C₄	—	2	4	no	—
416	C₂²×C₄	—	2	4	no	—
417	C₂²×C₄	—	2	4	no	—
418	C₂²×C₄	—	2	4	no	—
419	C₂²×C₄	—	2	4	no	—
420	C₂²×C₄	—	2	4	no	—
421	C₂²×C₄	—	2	4	no	—
422	C₂²×C₄	—	2	16	no	—
423	C₂²×C₄	—	4	4	no	—
424	C₂²×C₄	—	4	16	no	—
425	C₂²×C₄	C₂×D₄×C₅₉	1	4	yes	—
426	C₂²×C₄	C₂×D₄×C₅₉	1	4	yes	—
427	C₂²×C₄	#41×C₅₉	1	4	yes	—
428	C₂²×C₄	C₂⁴×C₅₉	1	4	yes	—
429	C₂²×C₄	C₂⁴×C₅₉	1	4	yes	—
430	C₂²×C₄	C₂⁴×C₅₉	1	4	yes	—
431	C₂²×C₄	C₂⁴×C₅₉	1	4	yes	—
432	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
433	C₂²×C₄	C₂⁴×C₅₉	1	4	yes	—
434	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
435	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
436	C₄⋊C₄	—	2	4	no	—
437	C₄⋊C₄	—	2	4	no	—
438	C₄⋊C₄	—	2	16	no	—
439	C₄⋊C₄	—	4	8	no	—
440	C₄⋊C₄	C₂×D₄×C₅₉	1	8	yes	—
441	C₂²⋊C₄	—	2	4	no	—
442	C₂²⋊C₄	—	2	32	no	—
443	C₂²⋊C₄	—	2	4	no	—
444	C₂²⋊C₄	—	2	16	no	—
445	C₂²⋊C₄	—	2	16	no	—
446	C₂²⋊C₄	—	2	16	no	—
447	C₂²⋊C₄	—	4	8	no	—
448	C₂²⋊C₄	C₂×D₄×C₅₉	1	8	yes	—
449	C₄²	—	2	4	no	—
450	C₄²	—	2	4	no	—
451	C₄²	—	2	4	no	—
452	C₄²	—	2	4	no	—
453	C₄²	C₂×D₄×C₅₉	1	8	yes	—
454	C₂³	—	2	4	no	—
455	C₂³	—	2	4	no	—
456	C₂³	—	2	4	no	—
457	C₂³	—	2	16	no	—
458	C₂³	—	2	16	no	—
459	C₂³	—	2	2	no	—
460	C₂³	—	2	2	no	—
461	C₂³	—	2	2	no	—
462	C₂³	—	2	8	no	—
463	C₂³	—	4	16	no	—
464	C₂³	—	8	8	no	—
465	C₂³	—	8	8	no	—
466	C₂³	C₂²×D₄×C₅₉	1	8	yes	—
467	C₂³	C₂²×D₄×C₅₉	1	2	yes	—
468	C₂³	C₂²×D₄×C₅₉	1	2	yes	—
469	C₂³	C₂×#41×C₅₉	1	2	yes	—
470	C₂³	C₂⁵×C₅₉	1	1	yes	characteristic
471	Q₈	—	4	8	no	—
472	Q₈	—	4	8	no	—
473	Q₈	—	4	4	no	—
474	D₄	—	2	16	no	—
475	D₄	—	2	16	no	—
476	D₄	—	4	8	no	—
477	D₄	—	4	4	no	—
478	D₄	—	8	16	no	—
479	C₂×C₄	—	2	8	no	—
480	C₂×C₄	—	2	4	no	—
481	C₂×C₄	—	2	4	no	—
482	C₂×C₄	—	2	4	no	—
483	C₂×C₄	—	2	2	no	—
484	C₂×C₄	—	2	4	no	—
485	C₂×C₄	—	2	4	no	—
486	C₂×C₄	—	2	2	no	—
487	C₂×C₄	—	2	2	no	—
488	C₂×C₄	—	2	4	no	—
489	C₂×C₄	—	2	4	no	—
490	C₂×C₄	—	2	8	no	—
491	C₂×C₄	—	2	4	no	—
492	C₂×C₄	—	2	8	no	—
493	C₂×C₄	—	4	8	no	—
494	C₂×C₄	—	4	8	no	—
495	C₂×C₄	—	4	8	no	—
496	C₂×C₄	—	8	16	no	—
497	C₂×C₄	#121×C₅₉	1	16	yes	—
498	C₂×C₄	C₂²×D₄×C₅₉	1	8	yes	—
499	C₂×C₄	C₂²×D₄×C₅₉	1	2	yes	—
500	C₂×C₄	C₂²×D₄×C₅₉	1	2	yes	—
501	C₂×C₄	C₂²×D₄×C₅₉	1	2	yes	—
502	C₂×C₄	C₂²×D₄×C₅₉	1	2	yes	—
503	C₂×C₄	C₂×#41×C₅₉	1	2	yes	—
504	C₂×C₄	C₂×#41×C₅₉	1	2	yes	—
505	C₂²	—	2	4	no	—
506	C₂²	—	2	4	no	—
507	C₂²	—	2	4	no	—
508	C₂²	—	2	8	no	—
509	C₂²	—	2	16	no	—
510	C₂²	—	4	8	no	—
511	C₂²	—	4	8	no	—
512	C₂²	—	4	4	no	—
513	C₂²	—	4	2	no	—
514	C₂²	—	4	4	no	—
515	C₂²	—	4	4	no	—
516	C₂²	—	8	16	no	—
517	C₂²	C₂×#121×C₅₉	1	4	yes	—
518	C₂²	C₂³×D₄×C₅₉	1	1	yes	characteristic
519	C₂²	C₂³×D₄×C₅₉	1	1	yes	characteristic
520	C₂²	C₂²×#41×C₅₉	1	1	yes	characteristic
521	C₂²	C₅₉×#585	1	4	yes	—
522	C₄	—	2	8	no	—
523	C₄	—	4	2	no	—
524	C₄	—	4	4	no	—
525	C₄	—	4	4	no	—
526	C₄	—	4	4	no	—
527	C₄	—	4	4	no	—
528	C₄	C₂×#121×C₅₉	1	4	yes	—
529	C₄	C₂×#121×C₅₉	1	4	yes	—
530	C₂	—	2	4	no	—
531	C₂	—	4	8	no	—
532	C₂	—	8	2	no	—
533	C₂	C₂²×#121×C₅₉	1	1	yes	characteristic
534	C₂	C₅₉×#3485	1	2	yes	—
535	C₂	C₅₉×#3500	1	2	yes	—
536	C₂	C₅₉×#3510	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₅₉	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₅₉
prime radical	C₂×C₅₉×#535	C₂
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×#536	C₂	semidirect
3. C₂²×#124×C₅₉	C₂	semidirect
4. C₂×C₅₉×#518	C₂	semidirect
5. C₅₉×#2547	C₂	semidirect
6. C₅₉×#2544	C₂	semidirect
7. C₅₉×#2427	C₂	semidirect
8. C₅₉×#2412	C₂	semidirect
9. C₅₉×#2310	C₂	semidirect
10. C₅₉×#2297	C₂	semidirect
11. C₅₉×#2296	C₂	semidirect
17. C₂×C₄⋊Q₈×C₅₉	C₂²	semidirect
23. C₂×#124×C₅₉	C₂²	semidirect
25. C₂×C₂²⋊Q₈×C₅₉	C₂²	semidirect
37. C₅₉×#397	C₂²	semidirect
38. C₅₉×#394	C₂²	semidirect
39. C₅₉×#391	C₂²	semidirect
40. C₅₉×#391	C₂²	semidirect
41. C₅₉×#391	C₂²	semidirect
42. C₅₉×#390	C₂²	semidirect
43. C₅₉×#389	C₂²	semidirect
45. C₅₉×#386	C₂²	semidirect
48. C₅₉×#380	C₂²	semidirect
49. C₄×C₄⋊C₄×C₅₉	C₂²	semidirect
50. C₄×C₂²⋊C₄×C₅₉	C₂²	semidirect
88. #117×C₅₉	D₄	semidirect
236. #35617	C₅₉	direct (N × H)
262. C₂×#536	C₂×C₅₉	semidirect
264. C₂²×#124	C₂×C₅₉	semidirect
265. C₂×#518	C₂×C₅₉	semidirect
266. #2547	C₂×C₅₉	semidirect
267. #2544	C₂×C₅₉	semidirect
268. #2427	C₂×C₅₉	semidirect
269. #2412	C₂×C₅₉	semidirect
270. #2310	C₂×C₅₉	semidirect
271. #2297	C₂×C₅₉	semidirect
272. #2296	C₂×C₅₉	semidirect
285. C₂×C₄⋊Q₈	C₂²×C₅₉	semidirect
291. C₂×#124	C₂²×C₅₉	semidirect
293. C₂×C₂²⋊Q₈	C₂²×C₅₉	semidirect
305. #397	C₂²×C₅₉	semidirect
306. #394	C₂²×C₅₉	semidirect
307. #391	C₂²×C₅₉	semidirect
308. #391	C₂²×C₅₉	semidirect
309. #391	C₂²×C₅₉	semidirect
310. #390	C₂²×C₅₉	semidirect
311. #389	C₂²×C₅₉	semidirect
313. #386	C₂²×C₅₉	semidirect
316. #380	C₂²×C₅₉	semidirect
317. C₄×C₄⋊C₄	C₂²×C₅₉	semidirect
318. C₄×C₂²⋊C₄	C₂²×C₅₉	semidirect
319. C₅₉	#35617	direct (N × H)
357. #117	D₄×C₅₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₅₉×#536	2
C₂×C₅₉×#535	2
C₂²×#124×C₅₉	2
C₂×C₅₉×#518	2
C₅₉×#2547	2
C₅₉×#2544	2
C₅₉×#2427	2
C₅₉×#2412	2
C₅₉×#2310	2
C₅₉×#2297	2
C₅₉×#2296	2
#35617	59

Subgroups — C59×#35617 #28447726

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₉×#35617 #28447726