Subgroups — C₅₉×#35325 #28447434

Order 15104.

2370 conjugacy classes of subgroups.

The subgroup lattice has 574 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅₉×#533	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×#117×C₅₉	C₂	1	1	yes	maximal, characteristic
3	C₅₉×#2855	C₂	1	2	yes	maximal, complemented
4	C₅₉×#2848	C₂	1	2	yes	maximal
5	C₅₉×#2628	C₂	1	2	yes	maximal, complemented
6	C₅₉×#2621	C₂	1	2	yes	maximal, complemented
7	C₅₉×#2611	C₂	1	4	yes	maximal, complemented
8	C₅₉×#2599	C₂	1	4	yes	maximal, complemented
9	C₅₉×#2583	C₂	1	2	yes	maximal, complemented
10	C₅₉×#2561	C₂	1	2	yes	maximal
11	C₅₉×#2484	C₂	1	2	yes	maximal, complemented
12	C₅₉×#2482	C₂	1	2	yes	maximal
13	C₅₉×#2323	C₂	1	4	yes	maximal, complemented
14	C₅₉×#2283	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂⁴×C₄×C₅₉	C₂²	1	1	yes	characteristic
16	C₅₉×#533	—	2	8	no	—
17	C₂×C₄⋊Q₈×C₅₉	C₂²	1	1	yes	characteristic, complemented
18	C₂×C₄⋊Q₈×C₅₉	C₂²	1	1	yes	characteristic, complemented
19	C₂×#125×C₅₉	C₂²	1	2	yes	complemented
20	C₂×C₂²⋊Q₈×C₅₉	C₂²	1	2	yes	—
21	C₂×C₂²⋊Q₈×C₅₉	C₂²	1	4	yes	—
22	C₂×C₂²⋊Q₈×C₅₉	C₂²	1	2	yes	—
23	C₂×C₄×Q₈×C₅₉	C₂²	1	2	yes	complemented
24	C₂×C₄×Q₈×C₅₉	C₂²	1	2	yes	complemented
25	C₂×#117×C₅₉	—	2	8	no	—
26	C₂×#117×C₅₉	C₂²	1	2	yes	—
27	C₂×#117×C₅₉	C₂²	1	2	yes	—
28	C₂×#117×C₅₉	C₂²	1	2	yes	—
29	C₂×#117×C₅₉	C₂²	1	2	yes	—
30	C₂×#117×C₅₉	C₂²	1	2	yes	—
31	C₂²×C₄⋊C₄×C₅₉	C₂²	1	1	yes	characteristic
32	C₂²×C₄⋊C₄×C₅₉	C₂²	1	1	yes	characteristic
33	C₂²×C₂²⋊C₄×C₅₉	C₂²	1	1	yes	characteristic
34	C₂²×C₂²⋊C₄×C₅₉	C₂²	1	1	yes	characteristic
35	C₂²×C₄²×C₅₉	C₂²	1	1	yes	characteristic
36	C₂²×C₄²×C₅₉	C₂²	1	1	yes	characteristic
37	C₅₉×#400	C₂²	1	4	yes	complemented
38	C₅₉×#399	C₂²	1	4	yes	—
39	C₅₉×#398	C₂²	1	4	yes	complemented
40	C₅₉×#398	C₂²	1	4	yes	complemented
41	C₅₉×#397	C₂²	1	4	yes	—
42	C₅₉×#397	C₂²	1	4	yes	—
43	C₅₉×#395	C₂²	1	4	yes	complemented
44	C₅₉×#393	C₂²	1	4	yes	—
45	C₅₉×#391	C₂²	1	4	yes	complemented
46	C₅₉×#389	C₂²	1	8	yes	complemented
47	C₅₉×#389	C₂²	1	4	yes	complemented
48	C₅₉×#388	C₂²	1	8	yes	—
49	C₅₉×#388	C₂²	1	8	yes	—
50	C₅₉×#387	C₂²	1	8	yes	complemented
51	C₅₉×#387	C₂²	1	8	yes	complemented
52	C₅₉×#385	C₂²	1	4	yes	—
53	C₅₉×#385	C₂²	1	4	yes	—
54	C₅₉×#385	C₂²	1	8	yes	—
55	C₅₉×#383	C₂²	1	2	yes	complemented
56	C₅₉×#382	C₂²	1	2	yes	complemented
57	C₅₉×#381	C₂²	1	2	yes	—
58	C₅₉×#381	C₂²	1	4	yes	—
59	C₅₉×#380	C₂²	1	2	yes	—
60	C₅₉×#380	C₂²	1	4	yes	—
61	C₅₉×#379	C₂²	1	4	yes	—
62	C₄×C₄⋊C₄×C₅₉	C₂²	1	2	yes	complemented
63	C₄×C₂²⋊C₄×C₅₉	C₂²	1	2	yes	—
64	C₅₉×#376	C₂²	1	2	yes	complemented
65	C₂⁵×C₅₉	C₂³	1	1	yes	characteristic
66	C₂²×Q₈×C₅₉	C₂³	1	2	yes	—
67	C₂²×Q₈×C₅₉	C₂³	1	2	yes	—
68	C₂³×C₄×C₅₉	—	2	4	no	—
69	C₂³×C₄×C₅₉	—	2	8	no	—
70	C₂³×C₄×C₅₉	C₂³	1	1	yes	characteristic
71	C₂³×C₄×C₅₉	C₂³	1	1	yes	characteristic
72	C₂³×C₄×C₅₉	C₂³	1	2	yes	—
73	C₂³×C₄×C₅₉	C₂³	1	1	yes	characteristic
74	C₂³×C₄×C₅₉	C₂³	1	1	yes	characteristic
75	C₂³×C₄×C₅₉	C₂³	1	2	yes	—
76	C₂³×C₄×C₅₉	C₂³	1	1	yes	characteristic
77	C₂³×C₄×C₅₉	C₂³	1	1	yes	characteristic
78	C₄⋊Q₈×C₅₉	—	2	4	no	—
79	C₄⋊Q₈×C₅₉	—	2	4	no	—
80	#125×C₅₉	—	2	8	no	—
81	C₂²⋊Q₈×C₅₉	—	2	8	no	—
82	C₂²⋊Q₈×C₅₉	—	2	8	no	—
83	C₂²⋊Q₈×C₅₉	—	2	16	no	—
84	C₄×Q₈×C₅₉	—	2	8	no	—
85	C₄×Q₈×C₅₉	—	2	8	no	—
86	#117×C₅₉	—	2	8	no	—
87	#117×C₅₉	—	2	8	no	—
88	#117×C₅₉	—	2	8	no	—
89	#117×C₅₉	—	2	8	no	—
90	#117×C₅₉	—	2	8	no	—
91	C₂×C₄⋊C₄×C₅₉	—	2	4	no	—
92	C₂×C₄⋊C₄×C₅₉	—	2	4	no	—
93	C₂×C₄⋊C₄×C₅₉	C₂³	1	4	yes	—
94	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
95	C₂×C₄⋊C₄×C₅₉	C₂³	1	4	yes	—
96	C₂×C₄⋊C₄×C₅₉	C₂³	1	8	yes	—
97	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
98	C₂×C₄⋊C₄×C₅₉	C₂³	1	4	yes	—
99	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
100	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
101	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
102	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
103	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
104	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
105	C₂×C₄⋊C₄×C₅₉	C₂³	1	8	yes	—
106	C₂×C₂²⋊C₄×C₅₉	—	2	4	no	—
107	C₂×C₂²⋊C₄×C₅₉	—	2	4	no	—
108	C₂×C₂²⋊C₄×C₅₉	C₂³	1	4	yes	—
109	C₂×C₂²⋊C₄×C₅₉	C₂³	1	4	yes	—
110	C₂×C₂²⋊C₄×C₅₉	C₂³	1	8	yes	—
111	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
112	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
113	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
114	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
115	C₂×C₂²⋊C₄×C₅₉	C₂³	1	8	yes	—
116	C₂×C₄²×C₅₉	—	2	4	no	—
117	C₂×C₄²×C₅₉	D₄	1	8	yes	—
118	C₂×C₄²×C₅₉	C₂³	1	2	yes	—
119	C₂×C₄²×C₅₉	C₂³	1	4	yes	—
120	C₂×C₄²×C₅₉	C₂³	1	2	yes	—
121	C₂×C₄²×C₅₉	C₂³	1	4	yes	—
122	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
123	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
124	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
125	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
126	#95×C₅₉	C₂³	1	4	yes	—
127	#95×C₅₉	C₂³	1	4	yes	—
128	#95×C₅₉	C₂³	1	4	yes	—
129	#95×C₅₉	C₂³	1	4	yes	—
130	#95×C₅₉	C₂³	1	8	yes	—
131	#95×C₅₉	C₂³	1	8	yes	—
132	#95×C₅₉	C₂³	1	8	yes	—
133	#95×C₅₉	C₂³	1	8	yes	—
134	C₂⁴×C₅₉	—	2	2	no	—
135	C₂⁴×C₅₉	—	2	4	no	—
136	C₂⁴×C₅₉	—	2	4	no	—
137	C₂⁴×C₅₉	—	4	2	no	—
138	C₂⁴×C₅₉	C₂⁴	1	2	yes	—
139	C₂⁴×C₅₉	C₂⁴	1	1	yes	characteristic
140	C₂×Q₈×C₅₉	—	2	4	no	—
141	C₂×Q₈×C₅₉	—	2	4	no	—
142	C₂×Q₈×C₅₉	—	2	8	no	—
143	C₂×Q₈×C₅₉	—	4	4	no	—
144	C₂²×C₄×C₅₉	—	2	32	no	—
145	C₂²×C₄×C₅₉	—	2	2	no	—
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	4	no	—
154	C₂²×C₄×C₅₉	—	2	2	no	—
155	C₂²×C₄×C₅₉	—	2	2	no	—
156	C₂²×C₄×C₅₉	—	2	4	no	—
157	C₂²×C₄×C₅₉	—	4	2	no	—
158	C₂²×C₄×C₅₉	—	4	2	no	—
159	C₂²×C₄×C₅₉	C₂×D₄	1	4	yes	—
160	C₂²×C₄×C₅₉	C₂×D₄	1	4	yes	—
161	C₂²×C₄×C₅₉	C₂×D₄	1	4	yes	—
162	C₂²×C₄×C₅₉	#41	1	8	yes	—
163	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
164	C₂²×C₄×C₅₉	C₂⁴	1	8	yes	—
165	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
166	C₂²×C₄×C₅₉	C₂⁴	1	4	yes	—
167	C₂²×C₄×C₅₉	C₂⁴	1	4	yes	—
168	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
169	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
170	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
171	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
172	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
173	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
174	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
175	C₄⋊C₄×C₅₉	—	2	4	no	—
176	C₄⋊C₄×C₅₉	—	2	4	no	—
177	C₄⋊C₄×C₅₉	—	2	4	no	—
178	C₄⋊C₄×C₅₉	—	2	4	no	—
179	C₄⋊C₄×C₅₉	—	2	4	no	—
180	C₄⋊C₄×C₅₉	—	2	4	no	—
181	C₄⋊C₄×C₅₉	—	2	8	no	—
182	C₄⋊C₄×C₅₉	—	2	8	no	—
183	C₄⋊C₄×C₅₉	—	2	4	no	—
184	C₄⋊C₄×C₅₉	—	2	4	no	—
185	C₄⋊C₄×C₅₉	—	2	8	no	—
186	C₄⋊C₄×C₅₉	—	2	16	no	—
187	C₄⋊C₄×C₅₉	—	4	8	no	—
188	C₂²⋊C₄×C₅₉	—	2	8	no	—
189	C₂²⋊C₄×C₅₉	—	2	16	no	—
190	C₂²⋊C₄×C₅₉	—	2	8	no	—
191	C₂²⋊C₄×C₅₉	—	2	4	no	—
192	C₂²⋊C₄×C₅₉	—	2	4	no	—
193	C₂²⋊C₄×C₅₉	—	2	4	no	—
194	C₂²⋊C₄×C₅₉	—	2	4	no	—
195	C₂²⋊C₄×C₅₉	—	4	8	no	—
196	C₄²×C₅₉	—	2	4	no	—
197	C₄²×C₅₉	—	2	4	no	—
198	C₄²×C₅₉	—	2	8	no	—
199	C₄²×C₅₉	—	4	4	no	—
200	C₄²×C₅₉	C₂×D₄	1	4	yes	—
201	C₄²×C₅₉	C₂×D₄	1	4	yes	—
202	C₄²×C₅₉	C₂×D₄	1	4	yes	—
203	C₄²×C₅₉	C₂×D₄	1	4	yes	—
204	C₂³×C₅₉	—	2	2	no	—
205	C₂³×C₅₉	—	2	2	no	—
206	C₂³×C₅₉	—	2	8	no	—
207	C₂³×C₅₉	—	2	2	no	—
208	C₂³×C₅₉	—	2	2	no	—
209	C₂³×C₅₉	—	2	4	no	—
210	C₂³×C₅₉	—	2	4	no	—
211	C₂³×C₅₉	—	4	16	no	—
212	C₂³×C₅₉	—	4	4	no	—
213	C₂³×C₅₉	—	4	4	no	—
214	C₂³×C₅₉	C₂²×D₄	1	2	yes	—
215	C₂³×C₅₉	C₂×#41	1	4	yes	—
216	C₂³×C₅₉	2₋¹⁺⁴	1	4	yes	—
217	C₂³×C₅₉	C₂⁵	1	1	yes	characteristic
218	Q₈×C₅₉	—	4	8	no	—
219	Q₈×C₅₉	—	4	8	no	—
220	C₂×C₄×C₅₉	—	2	16	no	—
221	C₂×C₄×C₅₉	—	2	8	no	—
222	C₂×C₄×C₅₉	—	2	8	no	—
223	C₂×C₄×C₅₉	—	2	2	no	—
224	C₂×C₄×C₅₉	—	2	2	no	—
225	C₂×C₄×C₅₉	—	2	2	no	—
226	C₂×C₄×C₅₉	—	2	2	no	—
227	C₂×C₄×C₅₉	—	2	2	no	—
228	C₂×C₄×C₅₉	—	2	2	no	—
229	C₂×C₄×C₅₉	—	2	2	no	—
230	C₂×C₄×C₅₉	—	2	8	no	—
231	C₂×C₄×C₅₉	—	2	16	no	—
232	C₂×C₄×C₅₉	—	2	2	no	—
233	C₂×C₄×C₅₉	—	2	2	no	—
234	C₂×C₄×C₅₉	—	2	4	no	—
235	C₂×C₄×C₅₉	—	2	4	no	—
236	C₂×C₄×C₅₉	—	2	8	no	—
237	C₂×C₄×C₅₉	—	2	8	no	—
238	C₂×C₄×C₅₉	—	2	8	no	—
239	C₂×C₄×C₅₉	—	2	4	no	—
240	C₂×C₄×C₅₉	—	2	8	no	—
241	C₂×C₄×C₅₉	—	2	8	no	—
242	C₂×C₄×C₅₉	—	2	4	no	—
243	C₂×C₄×C₅₉	—	4	4	no	—
244	C₂×C₄×C₅₉	—	4	4	no	—
245	C₂×C₄×C₅₉	—	4	4	no	—
246	C₂×C₄×C₅₉	C₂²×D₄	1	2	yes	—
247	C₂×C₄×C₅₉	C₂²×D₄	1	2	yes	—
248	C₂×C₄×C₅₉	C₂²×D₄	1	2	yes	—
249	C₂×C₄×C₅₉	C₂²×D₄	1	2	yes	—
250	C₂×C₄×C₅₉	C₂²×D₄	1	2	yes	—
251	C₂×C₄×C₅₉	C₂²×D₄	1	2	yes	—
252	C₂×C₄×C₅₉	C₂×#41	1	4	yes	—
253	C₂×C₄×C₅₉	C₂×#41	1	4	yes	—
254	#35325	C₅₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
255	C₂²×C₅₉	—	2	2	no	—
256	C₂²×C₅₉	—	2	2	no	—
257	C₂²×C₅₉	—	2	8	no	—
258	C₂²×C₅₉	—	2	4	no	—
259	C₂²×C₅₉	—	2	8	no	—
260	C₂²×C₅₉	—	4	16	no	—
261	C₂²×C₅₉	—	4	2	no	—
262	C₂²×C₅₉	—	4	2	no	—
263	C₂²×C₅₉	—	4	4	no	—
264	C₂²×C₅₉	#536	1	4	yes	—
265	C₂²×C₅₉	C₂³×D₄	1	1	yes	characteristic
266	C₂²×C₅₉	C₂²×#41	1	2	yes	—
267	C₂²×C₅₉	C₂×2₋¹⁺⁴	1	2	yes	—
268	C₂²×C₅₉	#585	1	2	yes	—
269	C₄×C₅₉	—	2	2	no	—
270	C₄×C₅₉	—	2	4	no	—
271	C₄×C₅₉	—	2	2	no	—
272	C₄×C₅₉	—	2	2	no	—
273	C₄×C₅₉	—	2	2	no	—
274	C₄×C₅₉	—	2	2	no	—
275	C₄×C₅₉	—	4	4	no	—
276	C₄×C₅₉	—	4	2	no	—
277	C₄×C₅₉	—	4	2	no	—
278	C₄×C₅₉	—	4	4	no	—
279	C₄×C₅₉	—	4	8	no	—
280	C₄×C₅₉	#525	1	4	yes	—
281	C₂×#533	C₂×C₅₉	1	1	yes	characteristic, complemented
282	C₂²×#117	C₂×C₅₉	1	1	yes	characteristic
283	#2855	C₂×C₅₉	1	2	yes	complemented
284	#2848	C₂×C₅₉	1	2	yes	—
285	#2628	C₂×C₅₉	1	2	yes	complemented
286	#2621	C₂×C₅₉	1	2	yes	complemented
287	#2611	C₂×C₅₉	1	4	yes	complemented
288	#2599	C₂×C₅₉	1	4	yes	complemented
289	#2583	C₂×C₅₉	1	2	yes	complemented
290	#2561	C₂×C₅₉	1	2	yes	—
291	#2484	C₂×C₅₉	1	2	yes	complemented
292	#2482	C₂×C₅₉	1	2	yes	—
293	#2323	C₂×C₅₉	1	4	yes	complemented
294	#2283	C₂×C₅₉	1	1	yes	characteristic, complemented
295	C₂×C₅₉	—	2	4	no	—
296	C₂×C₅₉	—	4	4	no	—
297	C₂×C₅₉	C₂×#525	1	1	yes	characteristic
298	C₂×C₅₉	C₂×#536	1	1	yes	characteristic
299	C₂×C₅₉	#3449	1	1	yes	characteristic
300	C₂×C₅₉	#3495	1	4	yes	—
301	C₂⁴×C₄	C₂²×C₅₉	1	1	yes	characteristic
302	#533	—	2	8	no	—
303	C₂×C₄⋊Q₈	C₂²×C₅₉	1	1	yes	characteristic, complemented
304	C₂×C₄⋊Q₈	C₂²×C₅₉	1	1	yes	characteristic, complemented
305	C₂×#125	C₂²×C₅₉	1	2	yes	complemented
306	C₂×C₂²⋊Q₈	C₂²×C₅₉	1	2	yes	—
307	C₂×C₂²⋊Q₈	C₂²×C₅₉	1	4	yes	—
308	C₂×C₂²⋊Q₈	C₂²×C₅₉	1	2	yes	—
309	C₂×C₄×Q₈	C₂²×C₅₉	1	2	yes	complemented
310	C₂×C₄×Q₈	C₂²×C₅₉	1	2	yes	complemented
311	C₂×#117	—	2	8	no	—
312	C₂×#117	C₂²×C₅₉	1	2	yes	—
313	C₂×#117	C₂²×C₅₉	1	2	yes	—
314	C₂×#117	C₂²×C₅₉	1	2	yes	—
315	C₂×#117	C₂²×C₅₉	1	2	yes	—
316	C₂×#117	C₂²×C₅₉	1	2	yes	—
317	C₂²×C₄⋊C₄	C₂²×C₅₉	1	1	yes	characteristic
318	C₂²×C₄⋊C₄	C₂²×C₅₉	1	1	yes	characteristic
319	C₂²×C₂²⋊C₄	C₂²×C₅₉	1	1	yes	characteristic
320	C₂²×C₂²⋊C₄	C₂²×C₅₉	1	1	yes	characteristic
321	C₂²×C₄²	C₂²×C₅₉	1	1	yes	characteristic
322	C₂²×C₄²	C₂²×C₅₉	1	1	yes	characteristic
323	#400	C₂²×C₅₉	1	4	yes	complemented
324	#399	C₂²×C₅₉	1	4	yes	—
325	#398	C₂²×C₅₉	1	4	yes	complemented
326	#398	C₂²×C₅₉	1	4	yes	complemented
327	#397	C₂²×C₅₉	1	4	yes	—
328	#397	C₂²×C₅₉	1	4	yes	—
329	#395	C₂²×C₅₉	1	4	yes	complemented
330	#393	C₂²×C₅₉	1	4	yes	—
331	#391	C₂²×C₅₉	1	4	yes	complemented
332	#389	C₂²×C₅₉	1	8	yes	complemented
333	#389	C₂²×C₅₉	1	4	yes	complemented
334	#388	C₂²×C₅₉	1	8	yes	—
335	#388	C₂²×C₅₉	1	8	yes	—
336	#387	C₂²×C₅₉	1	8	yes	complemented
337	#387	C₂²×C₅₉	1	8	yes	complemented
338	#385	C₂²×C₅₉	1	4	yes	—
339	#385	C₂²×C₅₉	1	4	yes	—
340	#385	C₂²×C₅₉	1	8	yes	—
341	#383	C₂²×C₅₉	1	2	yes	complemented
342	#382	C₂²×C₅₉	1	2	yes	complemented
343	#381	C₂²×C₅₉	1	4	yes	—
344	#381	C₂²×C₅₉	1	2	yes	—
345	#380	C₂²×C₅₉	1	4	yes	—
346	#380	C₂²×C₅₉	1	2	yes	—
347	#379	C₂²×C₅₉	1	4	yes	—
348	C₄×C₄⋊C₄	C₂²×C₅₉	1	2	yes	complemented
349	C₄×C₂²⋊C₄	C₂²×C₅₉	1	2	yes	—
350	#376	C₂²×C₅₉	1	2	yes	complemented
351	C₅₉	#35325	1	1	yes	characteristic, direct product factor, Sylow
352	C₂⁵	C₂³×C₅₉	1	1	yes	characteristic
353	C₂²×Q₈	C₂³×C₅₉	1	2	yes	—
354	C₂²×Q₈	C₂³×C₅₉	1	2	yes	—
355	C₂³×C₄	—	2	4	no	—
356	C₂³×C₄	—	2	8	no	—
357	C₂³×C₄	C₂³×C₅₉	1	1	yes	characteristic
358	C₂³×C₄	C₂³×C₅₉	1	1	yes	characteristic
359	C₂³×C₄	C₂³×C₅₉	1	2	yes	—
360	C₂³×C₄	C₂³×C₅₉	1	1	yes	characteristic
361	C₂³×C₄	C₂³×C₅₉	1	1	yes	characteristic
362	C₂³×C₄	C₂³×C₅₉	1	2	yes	—
363	C₂³×C₄	C₂³×C₅₉	1	1	yes	characteristic
364	C₂³×C₄	C₂³×C₅₉	1	1	yes	characteristic
365	C₄⋊Q₈	—	2	4	no	—
366	C₄⋊Q₈	—	2	4	no	—
367	#125	—	2	8	no	—
368	C₂²⋊Q₈	—	2	8	no	—
369	C₂²⋊Q₈	—	2	8	no	—
370	C₂²⋊Q₈	—	2	16	no	—
371	C₄×Q₈	—	2	8	no	—
372	C₄×Q₈	—	2	8	no	—
373	#117	—	2	8	no	—
374	#117	—	2	8	no	—
375	#117	—	2	8	no	—
376	#117	—	2	8	no	—
377	#117	—	2	8	no	—
378	C₂×C₄⋊C₄	—	2	4	no	—
379	C₂×C₄⋊C₄	—	2	4	no	—
380	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
381	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
382	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
383	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
384	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
385	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
386	C₂×C₄⋊C₄	C₂³×C₅₉	1	4	yes	—
387	C₂×C₄⋊C₄	C₂³×C₅₉	1	4	yes	—
388	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
389	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
390	C₂×C₄⋊C₄	C₂³×C₅₉	1	4	yes	—
391	C₂×C₄⋊C₄	C₂³×C₅₉	1	8	yes	—
392	C₂×C₄⋊C₄	C₂³×C₅₉	1	8	yes	—
393	C₂×C₂²⋊C₄	—	2	4	no	—
394	C₂×C₂²⋊C₄	—	2	4	no	—
395	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
396	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
397	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
398	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
399	C₂×C₂²⋊C₄	C₂³×C₅₉	1	4	yes	—
400	C₂×C₂²⋊C₄	C₂³×C₅₉	1	8	yes	—
401	C₂×C₂²⋊C₄	C₂³×C₅₉	1	4	yes	—
402	C₂×C₂²⋊C₄	C₂³×C₅₉	1	8	yes	—
403	C₂×C₄²	—	2	4	no	—
404	C₂×C₄²	D₄×C₅₉	1	8	yes	—
405	C₂×C₄²	C₂³×C₅₉	1	2	yes	—
406	C₂×C₄²	C₂³×C₅₉	1	2	yes	—
407	C₂×C₄²	C₂³×C₅₉	1	4	yes	—
408	C₂×C₄²	C₂³×C₅₉	1	4	yes	—
409	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
410	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
411	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
412	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
413	#95	C₂³×C₅₉	1	4	yes	—
414	#95	C₂³×C₅₉	1	4	yes	—
415	#95	C₂³×C₅₉	1	4	yes	—
416	#95	C₂³×C₅₉	1	4	yes	—
417	#95	C₂³×C₅₉	1	8	yes	—
418	#95	C₂³×C₅₉	1	8	yes	—
419	#95	C₂³×C₅₉	1	8	yes	—
420	#95	C₂³×C₅₉	1	8	yes	—
421	C₂⁴	—	2	2	no	—
422	C₂⁴	—	2	4	no	—
423	C₂⁴	—	2	4	no	—
424	C₂⁴	—	4	2	no	—
425	C₂⁴	C₂⁴×C₅₉	1	2	yes	—
426	C₂⁴	C₂⁴×C₅₉	1	1	yes	characteristic
427	C₂×Q₈	—	2	4	no	—
428	C₂×Q₈	—	2	4	no	—
429	C₂×Q₈	—	2	8	no	—
430	C₂×Q₈	—	4	4	no	—
431	C₂²×C₄	—	2	32	no	—
432	C₂²×C₄	—	2	2	no	—
433	C₂²×C₄	—	2	4	no	—
434	C₂²×C₄	—	2	4	no	—
435	C₂²×C₄	—	2	4	no	—
436	C₂²×C₄	—	2	4	no	—
437	C₂²×C₄	—	2	4	no	—
438	C₂²×C₄	—	2	4	no	—
439	C₂²×C₄	—	2	4	no	—
440	C₂²×C₄	—	2	4	no	—
441	C₂²×C₄	—	2	2	no	—
442	C₂²×C₄	—	2	2	no	—
443	C₂²×C₄	—	2	4	no	—
444	C₂²×C₄	—	4	2	no	—
445	C₂²×C₄	—	4	2	no	—
446	C₂²×C₄	C₂×D₄×C₅₉	1	4	yes	—
447	C₂²×C₄	C₂×D₄×C₅₉	1	4	yes	—
448	C₂²×C₄	C₂×D₄×C₅₉	1	4	yes	—
449	C₂²×C₄	#41×C₅₉	1	8	yes	—
450	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
451	C₂²×C₄	C₂⁴×C₅₉	1	8	yes	—
452	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
453	C₂²×C₄	C₂⁴×C₅₉	1	4	yes	—
454	C₂²×C₄	C₂⁴×C₅₉	1	4	yes	—
455	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
456	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
457	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
458	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
459	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
460	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
461	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
462	C₄⋊C₄	—	2	4	no	—
463	C₄⋊C₄	—	2	4	no	—
464	C₄⋊C₄	—	2	4	no	—
465	C₄⋊C₄	—	2	4	no	—
466	C₄⋊C₄	—	2	4	no	—
467	C₄⋊C₄	—	2	4	no	—
468	C₄⋊C₄	—	2	8	no	—
469	C₄⋊C₄	—	2	8	no	—
470	C₄⋊C₄	—	2	4	no	—
471	C₄⋊C₄	—	2	4	no	—
472	C₄⋊C₄	—	2	8	no	—
473	C₄⋊C₄	—	2	16	no	—
474	C₄⋊C₄	—	4	8	no	—
475	C₂²⋊C₄	—	2	8	no	—
476	C₂²⋊C₄	—	2	16	no	—
477	C₂²⋊C₄	—	2	8	no	—
478	C₂²⋊C₄	—	2	4	no	—
479	C₂²⋊C₄	—	2	4	no	—
480	C₂²⋊C₄	—	2	4	no	—
481	C₂²⋊C₄	—	2	4	no	—
482	C₂²⋊C₄	—	4	8	no	—
483	C₄²	—	2	4	no	—
484	C₄²	—	2	4	no	—
485	C₄²	—	2	8	no	—
486	C₄²	—	4	4	no	—
487	C₄²	C₂×D₄×C₅₉	1	4	yes	—
488	C₄²	C₂×D₄×C₅₉	1	4	yes	—
489	C₄²	C₂×D₄×C₅₉	1	4	yes	—
490	C₄²	C₂×D₄×C₅₉	1	4	yes	—
491	C₂³	—	2	2	no	—
492	C₂³	—	2	2	no	—
493	C₂³	—	2	8	no	—
494	C₂³	—	2	2	no	—
495	C₂³	—	2	2	no	—
496	C₂³	—	2	4	no	—
497	C₂³	—	2	4	no	—
498	C₂³	—	4	16	no	—
499	C₂³	—	4	4	no	—
500	C₂³	—	4	4	no	—
501	C₂³	C₂²×D₄×C₅₉	1	2	yes	—
502	C₂³	C₂×#41×C₅₉	1	4	yes	—
503	C₂³	2₋¹⁺⁴×C₅₉	1	4	yes	—
504	C₂³	C₂⁵×C₅₉	1	1	yes	characteristic
505	Q₈	—	4	8	no	—
506	Q₈	—	4	8	no	—
507	C₂×C₄	—	2	16	no	—
508	C₂×C₄	—	2	8	no	—
509	C₂×C₄	—	2	8	no	—
510	C₂×C₄	—	2	2	no	—
511	C₂×C₄	—	2	2	no	—
512	C₂×C₄	—	2	2	no	—
513	C₂×C₄	—	2	2	no	—
514	C₂×C₄	—	2	2	no	—
515	C₂×C₄	—	2	2	no	—
516	C₂×C₄	—	2	2	no	—
517	C₂×C₄	—	2	8	no	—
518	C₂×C₄	—	2	16	no	—
519	C₂×C₄	—	2	2	no	—
520	C₂×C₄	—	2	2	no	—
521	C₂×C₄	—	2	4	no	—
522	C₂×C₄	—	2	4	no	—
523	C₂×C₄	—	2	8	no	—
524	C₂×C₄	—	2	8	no	—
525	C₂×C₄	—	2	8	no	—
526	C₂×C₄	—	2	4	no	—
527	C₂×C₄	—	2	8	no	—
528	C₂×C₄	—	2	8	no	—
529	C₂×C₄	—	2	4	no	—
530	C₂×C₄	—	4	4	no	—
531	C₂×C₄	—	4	4	no	—
532	C₂×C₄	—	4	4	no	—
533	C₂×C₄	C₂²×D₄×C₅₉	1	2	yes	—
534	C₂×C₄	C₂²×D₄×C₅₉	1	2	yes	—
535	C₂×C₄	C₂²×D₄×C₅₉	1	2	yes	—
536	C₂×C₄	C₂²×D₄×C₅₉	1	2	yes	—
537	C₂×C₄	C₂²×D₄×C₅₉	1	2	yes	—
538	C₂×C₄	C₂²×D₄×C₅₉	1	2	yes	—
539	C₂×C₄	C₂×#41×C₅₉	1	4	yes	—
540	C₂×C₄	C₂×#41×C₅₉	1	4	yes	—
541	C₂²	—	2	2	no	—
542	C₂²	—	2	2	no	—
543	C₂²	—	2	8	no	—
544	C₂²	—	2	4	no	—
545	C₂²	—	2	8	no	—
546	C₂²	—	4	16	no	—
547	C₂²	—	4	2	no	—
548	C₂²	—	4	2	no	—
549	C₂²	—	4	4	no	—
550	C₂²	C₅₉×#536	1	4	yes	—
551	C₂²	C₂³×D₄×C₅₉	1	1	yes	characteristic
552	C₂²	C₂²×#41×C₅₉	1	2	yes	—
553	C₂²	C₂×2₋¹⁺⁴×C₅₉	1	2	yes	—
554	C₂²	C₅₉×#585	1	2	yes	—
555	C₄	—	2	2	no	—
556	C₄	—	2	4	no	—
557	C₄	—	2	2	no	—
558	C₄	—	2	2	no	—
559	C₄	—	2	2	no	—
560	C₄	—	2	2	no	—
561	C₄	—	4	4	no	—
562	C₄	—	4	2	no	—
563	C₄	—	4	2	no	—
564	C₄	—	4	4	no	—
565	C₄	—	4	8	no	—
566	C₄	C₅₉×#525	1	4	yes	—
567	C₂	—	2	4	no	—
568	C₂	—	4	4	no	—
569	C₂	C₂×C₅₉×#525	1	1	yes	characteristic
570	C₂	C₂×C₅₉×#536	1	1	yes	characteristic
571	C₂	C₅₉×#3449	1	1	yes	characteristic
572	C₂	C₅₉×#3495	1	4	yes	—

	subgroup	G/H
center, socle	C₂³×C₅₉	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₅₉
prime radical	C₂⁵×C₅₉	C₂³
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×#533	C₂	semidirect
3. C₅₉×#2855	C₂	semidirect
5. C₅₉×#2628	C₂	semidirect
6. C₅₉×#2621	C₂	semidirect
7. C₅₉×#2611	C₂	semidirect
8. C₅₉×#2599	C₂	semidirect
9. C₅₉×#2583	C₂	semidirect
11. C₅₉×#2484	C₂	semidirect
13. C₅₉×#2323	C₂	semidirect
14. C₅₉×#2283	C₂	semidirect
17. C₂×C₄⋊Q₈×C₅₉	C₂²	semidirect
18. C₂×C₄⋊Q₈×C₅₉	C₂²	semidirect
19. C₂×#125×C₅₉	C₂²	semidirect
23. C₂×C₄×Q₈×C₅₉	C₂²	semidirect
24. C₂×C₄×Q₈×C₅₉	C₂²	semidirect
37. C₅₉×#400	C₂²	semidirect
39. C₅₉×#398	C₂²	semidirect
40. C₅₉×#398	C₂²	semidirect
43. C₅₉×#395	C₂²	semidirect
45. C₅₉×#391	C₂²	semidirect
46. C₅₉×#389	C₂²	semidirect
47. C₅₉×#389	C₂²	semidirect
50. C₅₉×#387	C₂²	semidirect
51. C₅₉×#387	C₂²	semidirect
55. C₅₉×#383	C₂²	semidirect
56. C₅₉×#382	C₂²	semidirect
62. C₄×C₄⋊C₄×C₅₉	C₂²	semidirect
64. C₅₉×#376	C₂²	semidirect
254. #35325	C₅₉	direct (N × H)
281. C₂×#533	C₂×C₅₉	semidirect
283. #2855	C₂×C₅₉	semidirect
285. #2628	C₂×C₅₉	semidirect
286. #2621	C₂×C₅₉	semidirect
287. #2611	C₂×C₅₉	semidirect
288. #2599	C₂×C₅₉	semidirect
289. #2583	C₂×C₅₉	semidirect
291. #2484	C₂×C₅₉	semidirect
293. #2323	C₂×C₅₉	semidirect
294. #2283	C₂×C₅₉	semidirect
303. C₂×C₄⋊Q₈	C₂²×C₅₉	semidirect
304. C₂×C₄⋊Q₈	C₂²×C₅₉	semidirect
305. C₂×#125	C₂²×C₅₉	semidirect
309. C₂×C₄×Q₈	C₂²×C₅₉	semidirect
310. C₂×C₄×Q₈	C₂²×C₅₉	semidirect
323. #400	C₂²×C₅₉	semidirect
325. #398	C₂²×C₅₉	semidirect
326. #398	C₂²×C₅₉	semidirect
329. #395	C₂²×C₅₉	semidirect
331. #391	C₂²×C₅₉	semidirect
332. #389	C₂²×C₅₉	semidirect
333. #389	C₂²×C₅₉	semidirect
336. #387	C₂²×C₅₉	semidirect
337. #387	C₂²×C₅₉	semidirect
341. #383	C₂²×C₅₉	semidirect
342. #382	C₂²×C₅₉	semidirect
348. C₄×C₄⋊C₄	C₂²×C₅₉	semidirect
350. #376	C₂²×C₅₉	semidirect
351. C₅₉	#35325	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×#533	2
C₂²×#117×C₅₉	2
C₅₉×#2855	2
C₅₉×#2848	2
C₅₉×#2628	2
C₅₉×#2621	2
C₅₉×#2611	2
C₅₉×#2599	2
C₅₉×#2583	2
C₅₉×#2561	2
C₅₉×#2484	2
C₅₉×#2482	2
C₅₉×#2323	2
C₅₉×#2283	2
#35325	59

Subgroups — C59×#35325 #28447434

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₉×#35325 #28447434