Subgroups — C₅₉×#26482 #28438591

Order 15104.

846 conjugacy classes of subgroups.

The subgroup lattice has 456 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅₉×#499	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₄×D₈×C₅₉	C₂	1	1	yes	maximal, characteristic
3	C₅₉×#2454	C₂	1	2	yes	maximal, complemented
4	C₅₉×#2065	C₂	1	2	yes	maximal, complemented
5	C₅₉×#2025	C₂	1	2	yes	maximal, complemented
6	C₅₉×#1970	C₂	1	1	yes	maximal, characteristic
7	C₅₉×#1970	C₂	1	1	yes	maximal, characteristic
8	C₅₉×#1942	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅₉×#1942	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅₉×#1864	C₂	1	2	yes	maximal, complemented
11	C₈×C₄⋊C₄×C₅₉	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×D₈×C₅₉	C₂²	1	1	yes	characteristic
13	C₂×#125×C₅₉	C₂²	1	2	yes	—
14	C₂×C₄×D₄×C₅₉	C₂²	1	2	yes	—
15	C₅₉×#499	—	2	4	no	—
16	C₄×D₈×C₅₉	—	2	4	no	—
17	C₂×#107×C₅₉	C₂²	1	1	yes	characteristic
18	C₂×#107×C₅₉	C₂²	1	1	yes	characteristic
19	C₂×#107×C₅₉	C₂²	1	1	yes	characteristic
20	C₂×#106×C₅₉	C₂²	1	2	yes	—
21	C₂×C₄⋊C₈×C₅₉	C₂²	1	1	yes	characteristic
22	C₂×#102×C₅₉	C₂²	1	2	yes	—
23	C₂×#102×C₅₉	C₂²	1	2	yes	—
24	C₂×#102×C₅₉	C₂²	1	2	yes	—
25	C₂×C₄×C₈×C₅₉	C₂²	1	1	yes	characteristic
26	C₂×C₄×C₈×C₅₉	C₂²	1	1	yes	characteristic
27	C₂×C₄×C₈×C₅₉	C₂²	1	1	yes	characteristic
28	C₅₉×#399	—	2	2	no	—
29	C₅₉×#396	—	2	2	no	—
30	C₅₉×#390	C₂²	1	2	yes	—
31	C₅₉×#390	C₂²	1	2	yes	—
32	C₅₉×#389	C₂²	1	2	yes	—
33	C₅₉×#389	C₂²	1	2	yes	—
34	C₅₉×#385	—	2	2	no	—
35	C₅₉×#380	—	2	2	no	—
36	C₄×C₄⋊C₄×C₅₉	C₂²	1	1	yes	characteristic
37	C₅₉×#340	C₂²	1	2	yes	—
38	C₅₉×#340	C₂²	1	2	yes	—
39	C₅₉×#336	C₂²	1	1	yes	characteristic
40	C₅₉×#336	C₂²	1	1	yes	characteristic
41	C₂²×D₄×C₅₉	C₂³	1	2	yes	—
42	C₂³×C₄×C₅₉	—	2	2	no	—
43	C₂×D₈×C₅₉	—	2	2	no	—
44	C₂×D₈×C₅₉	—	2	2	no	—
45	C₂×D₈×C₅₉	Q₈	1	4	yes	—
46	C₂²×C₈×C₅₉	C₂³	1	1	yes	characteristic
47	C₂²×C₈×C₅₉	C₂³	1	1	yes	characteristic
48	C₂²×C₈×C₅₉	C₂³	1	1	yes	characteristic
49	C₂²×C₈×C₅₉	C₂³	1	1	yes	characteristic
50	#125×C₅₉	—	2	4	no	—
51	#125×C₅₉	—	4	2	no	—
52	C₄×D₄×C₅₉	—	2	4	no	—
53	C₄×D₄×C₅₉	—	4	2	no	—
54	C₂×C₄⋊C₄×C₅₉	—	2	2	no	—
55	C₂×C₄⋊C₄×C₅₉	—	2	2	no	—
56	C₂×C₄⋊C₄×C₅₉	—	2	2	no	—
57	C₂×C₄⋊C₄×C₅₉	—	2	2	no	—
58	C₂×C₄⋊C₄×C₅₉	D₄	1	1	yes	characteristic
59	C₂×C₄⋊C₄×C₅₉	D₄	1	1	yes	characteristic
60	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
61	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
62	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
63	C₂×C₂²⋊C₄×C₅₉	—	2	2	no	—
64	C₂×C₂²⋊C₄×C₅₉	—	2	2	no	—
65	C₂×C₂²⋊C₄×C₅₉	—	2	2	no	—
66	C₂×C₂²⋊C₄×C₅₉	—	2	2	no	—
67	C₂×C₂²⋊C₄×C₅₉	—	2	2	no	—
68	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
69	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
70	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
71	#107×C₅₉	—	2	2	no	—
72	#107×C₅₉	—	2	2	no	—
73	#107×C₅₉	D₄	1	4	yes	—
74	#106×C₅₉	—	2	4	no	—
75	C₄⋊C₈×C₅₉	—	2	2	no	—
76	#102×C₅₉	—	2	4	no	—
77	#102×C₅₉	—	2	4	no	—
78	#102×C₅₉	—	4	2	no	—
79	C₄×C₈×C₅₉	—	2	2	no	—
80	C₄×C₈×C₅₉	—	2	2	no	—
81	C₄×C₈×C₅₉	—	2	2	no	—
82	#95×C₅₉	—	2	2	no	—
83	#95×C₅₉	—	2	2	no	—
84	#95×C₅₉	D₄	1	1	yes	characteristic
85	#95×C₅₉	D₄	1	1	yes	characteristic
86	C₂⁴×C₅₉	—	2	2	no	—
87	C₂×D₄×C₅₉	—	2	2	no	—
88	C₂×D₄×C₅₉	—	2	2	no	—
89	C₂×D₄×C₅₉	—	2	2	no	—
90	C₂×D₄×C₅₉	—	2	2	no	—
91	C₂×D₄×C₅₉	—	2	2	no	—
92	C₂×D₄×C₅₉	C₂×Q₈	1	4	yes	—
93	C₂²×C₄×C₅₉	—	2	2	no	—
94	C₂²×C₄×C₅₉	—	2	2	no	—
95	C₂²×C₄×C₅₉	—	2	2	no	—
96	C₂²×C₄×C₅₉	—	4	4	no	—
97	C₂²×C₄×C₅₉	—	4	4	no	—
98	C₂²×C₄×C₅₉	—	8	2	no	—
99	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
100	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
101	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
102	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
103	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
104	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
105	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
106	D₈×C₅₉	—	2	8	no	—
107	C₂×C₈×C₅₉	—	2	1	no	—
108	C₂×C₈×C₅₉	—	2	1	no	—
109	C₂×C₈×C₅₉	—	2	1	no	—
110	C₂×C₈×C₅₉	—	2	1	no	—
111	C₂×C₈×C₅₉	—	2	1	no	—
112	C₂×C₈×C₅₉	—	2	1	no	—
113	C₂×C₈×C₅₉	—	2	1	no	—
114	C₂×C₈×C₅₉	—	2	1	no	—
115	C₂×C₈×C₅₉	C₂×D₄	1	2	yes	—
116	C₂×C₈×C₅₉	C₂×Q₈	1	2	yes	—
117	C₂×C₈×C₅₉	#41	1	2	yes	—
118	C₂×C₈×C₅₉	#41	1	2	yes	—
119	C₄⋊C₄×C₅₉	—	2	2	no	—
120	C₄⋊C₄×C₅₉	—	2	2	no	—
121	C₄⋊C₄×C₅₉	—	2	2	no	—
122	C₄⋊C₄×C₅₉	—	2	2	no	—
123	C₄⋊C₄×C₅₉	—	2	2	no	—
124	C₄⋊C₄×C₅₉	—	2	2	no	—
125	C₄⋊C₄×C₅₉	—	2	2	no	—
126	C₄⋊C₄×C₅₉	—	4	4	no	—
127	C₄⋊C₄×C₅₉	—	4	4	no	—
128	C₄⋊C₄×C₅₉	—	8	2	no	—
129	C₄⋊C₄×C₅₉	—	8	2	no	—
130	C₄⋊C₄×C₅₉	C₂×D₄	1	4	yes	—
131	C₂²⋊C₄×C₅₉	—	4	4	no	—
132	C₂²⋊C₄×C₅₉	—	4	4	no	—
133	C₂²⋊C₄×C₅₉	—	8	2	no	—
134	C₂²⋊C₄×C₅₉	—	8	2	no	—
135	C₂²⋊C₄×C₅₉	—	8	2	no	—
136	C₄²×C₅₉	—	2	1	no	—
137	C₄²×C₅₉	—	2	1	no	—
138	C₄²×C₅₉	—	2	1	no	—
139	C₄²×C₅₉	—	2	1	no	—
140	C₄²×C₅₉	—	2	1	no	—
141	C₄²×C₅₉	—	2	1	no	—
142	C₂³×C₅₉	—	2	4	no	—
143	C₂³×C₅₉	—	4	2	no	—
144	C₂³×C₅₉	—	4	2	no	—
145	C₂³×C₅₉	—	4	2	no	—
146	C₂³×C₅₉	—	4	2	no	—
147	C₂³×C₅₉	—	4	2	no	—
148	C₂³×C₅₉	—	4	2	no	—
149	C₂³×C₅₉	C₂²×D₄	1	1	yes	characteristic
150	D₄×C₅₉	—	2	4	no	—
151	D₄×C₅₉	—	2	4	no	—
152	D₄×C₅₉	—	4	2	no	—
153	D₄×C₅₉	—	4	2	no	—
154	C₂×C₄×C₅₉	—	2	1	no	—
155	C₂×C₄×C₅₉	—	2	1	no	—
156	C₂×C₄×C₅₉	—	2	1	no	—
157	C₂×C₄×C₅₉	—	2	1	no	—
158	C₂×C₄×C₅₉	—	2	1	no	—
159	C₂×C₄×C₅₉	—	2	1	no	—
160	C₂×C₄×C₅₉	—	2	1	no	—
161	C₂×C₄×C₅₉	—	2	1	no	—
162	C₂×C₄×C₅₉	—	2	4	no	—
163	C₂×C₄×C₅₉	—	2	1	no	—
164	C₂×C₄×C₅₉	—	2	1	no	—
165	C₂×C₄×C₅₉	—	2	1	no	—
166	C₂×C₄×C₅₉	—	2	1	no	—
167	C₂×C₄×C₅₉	—	2	1	no	—
168	C₂×C₄×C₅₉	—	2	1	no	—
169	C₂×C₄×C₅₉	—	2	1	no	—
170	C₂×C₄×C₅₉	—	2	1	no	—
171	C₂×C₄×C₅₉	—	4	2	no	—
172	C₂×C₄×C₅₉	—	4	2	no	—
173	C₂×C₄×C₅₉	—	4	2	no	—
174	C₂×C₄×C₅₉	—	4	2	no	—
175	C₂×C₄×C₅₉	—	4	2	no	—
176	C₂×C₄×C₅₉	—	4	2	no	—
177	C₂×C₄×C₅₉	—	4	2	no	—
178	C₂×C₄×C₅₉	—	4	2	no	—
179	C₂×C₄×C₅₉	—	8	8	no	—
180	C₂×C₄×C₅₉	#135	1	2	yes	—
181	C₂×C₄×C₅₉	#135	1	2	yes	—
182	C₂×C₄×C₅₉	C₂²×D₄	1	1	yes	characteristic
183	C₂×C₄×C₅₉	C₂²×Q₈	1	1	yes	characteristic
184	C₂×C₄×C₅₉	C₂×#41	1	1	yes	characteristic
185	C₂×C₄×C₅₉	C₂×#41	1	1	yes	characteristic
186	C₂×C₄×C₅₉	H(5,𝔽₂)	1	1	yes	characteristic
187	C₂×C₄×C₅₉	2₋¹⁺⁴	1	1	yes	characteristic
188	C₈×C₅₉	—	2	2	no	—
189	C₈×C₅₉	—	4	1	no	—
190	C₈×C₅₉	—	4	1	no	—
191	C₈×C₅₉	C₂²⋊Q₈	1	4	yes	—
192	#26482	C₅₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
193	C₂²×C₅₉	—	4	4	no	—
194	C₂²×C₅₉	—	4	4	no	—
195	C₂²×C₅₉	—	4	4	no	—
196	C₂²×C₅₉	—	8	2	no	—
197	C₂²×C₅₉	—	8	2	no	—
198	C₂²×C₅₉	—	8	2	no	—
199	C₂²×C₅₉	—	8	2	no	—
200	C₂²×C₅₉	#532	1	1	yes	characteristic
201	C₂²×C₅₉	D₄²	1	1	yes	characteristic
202	C₂²×C₅₉	D₄×Q₈	1	1	yes	characteristic
203	C₂²×C₅₉	C₂×#135	1	1	yes	characteristic
204	C₂²×C₅₉	C₂×#135	1	1	yes	characteristic
205	C₂²×C₅₉	#576	1	1	yes	characteristic
206	C₂²×C₅₉	#576	1	1	yes	characteristic
207	C₄×C₅₉	—	2	2	no	—
208	C₄×C₅₉	—	2	2	no	—
209	C₄×C₅₉	—	4	1	no	—
210	C₄×C₅₉	—	4	1	no	—
211	C₄×C₅₉	—	4	4	no	—
212	C₄×C₅₉	—	4	1	no	—
213	C₄×C₅₉	—	4	1	no	—
214	C₄×C₅₉	—	8	2	no	—
215	C₄×C₅₉	—	8	2	no	—
216	C₄×C₅₉	C₂×C₂²⋊Q₈	1	1	yes	characteristic
217	C₄×C₅₉	#542	1	1	yes	characteristic
218	C₄×C₅₉	#548	1	1	yes	characteristic
219	C₄×C₅₉	#554	1	1	yes	characteristic
220	C₂×#499	C₂×C₅₉	1	1	yes	characteristic, complemented
221	C₂×C₄×D₈	C₂×C₅₉	1	1	yes	characteristic
222	#2454	C₂×C₅₉	1	2	yes	complemented
223	#2065	C₂×C₅₉	1	2	yes	complemented
224	#2025	C₂×C₅₉	1	2	yes	complemented
225	#1970	C₂×C₅₉	1	1	yes	characteristic
226	#1970	C₂×C₅₉	1	1	yes	characteristic
227	#1942	C₂×C₅₉	1	1	yes	characteristic, complemented
228	#1942	C₂×C₅₉	1	1	yes	characteristic, complemented
229	#1864	C₂×C₅₉	1	2	yes	complemented
230	C₈×C₄⋊C₄	C₂×C₅₉	1	1	yes	characteristic, complemented
231	C₂×C₅₉	—	8	4	no	—
232	C₂×C₅₉	#2452	1	1	yes	characteristic
233	C₂×C₅₉	#3168	1	1	yes	characteristic
234	C₂×C₅₉	#3176	1	1	yes	characteristic
235	C₂×C₅₉	#3280	1	1	yes	characteristic
236	C₂×C₅₉	#3287	1	1	yes	characteristic
237	C₂×C₅₉	#3380	1	1	yes	characteristic
238	C₂×C₅₉	#3380	1	1	yes	characteristic
239	C₂²×D₈	C₂²×C₅₉	1	1	yes	characteristic
240	C₂×#125	C₂²×C₅₉	1	2	yes	—
241	C₂×C₄×D₄	C₂²×C₅₉	1	2	yes	—
242	#499	—	2	4	no	—
243	C₄×D₈	—	2	4	no	—
244	C₂×#107	C₂²×C₅₉	1	1	yes	characteristic
245	C₂×#107	C₂²×C₅₉	1	1	yes	characteristic
246	C₂×#107	C₂²×C₅₉	1	1	yes	characteristic
247	C₂×#106	C₂²×C₅₉	1	2	yes	—
248	C₂×C₄⋊C₈	C₂²×C₅₉	1	1	yes	characteristic
249	C₂×#102	C₂²×C₅₉	1	2	yes	—
250	C₂×#102	C₂²×C₅₉	1	2	yes	—
251	C₂×#102	C₂²×C₅₉	1	2	yes	—
252	C₂×C₄×C₈	C₂²×C₅₉	1	1	yes	characteristic
253	C₂×C₄×C₈	C₂²×C₅₉	1	1	yes	characteristic
254	C₂×C₄×C₈	C₂²×C₅₉	1	1	yes	characteristic
255	#399	—	2	2	no	—
256	#396	—	2	2	no	—
257	#390	C₂²×C₅₉	1	2	yes	—
258	#390	C₂²×C₅₉	1	2	yes	—
259	#389	C₂²×C₅₉	1	2	yes	—
260	#389	C₂²×C₅₉	1	2	yes	—
261	#385	—	2	2	no	—
262	#380	—	2	2	no	—
263	C₄×C₄⋊C₄	C₂²×C₅₉	1	1	yes	characteristic
264	#340	C₂²×C₅₉	1	2	yes	—
265	#340	C₂²×C₅₉	1	2	yes	—
266	#336	C₂²×C₅₉	1	1	yes	characteristic
267	#336	C₂²×C₅₉	1	1	yes	characteristic
268	C₅₉	#26482	1	1	yes	characteristic, direct product factor, Sylow
269	C₂²×D₄	C₂³×C₅₉	1	2	yes	—
270	C₂³×C₄	—	2	2	no	—
271	C₂×D₈	—	2	2	no	—
272	C₂×D₈	—	2	2	no	—
273	C₂×D₈	Q₈×C₅₉	1	4	yes	—
274	C₂²×C₈	C₂³×C₅₉	1	1	yes	characteristic
275	C₂²×C₈	C₂³×C₅₉	1	1	yes	characteristic
276	C₂²×C₈	C₂³×C₅₉	1	1	yes	characteristic
277	C₂²×C₈	C₂³×C₅₉	1	1	yes	characteristic
278	#125	—	2	4	no	—
279	#125	—	4	2	no	—
280	C₄×D₄	—	2	4	no	—
281	C₄×D₄	—	4	2	no	—
282	C₂×C₄⋊C₄	—	2	2	no	—
283	C₂×C₄⋊C₄	—	2	2	no	—
284	C₂×C₄⋊C₄	—	2	2	no	—
285	C₂×C₄⋊C₄	—	2	2	no	—
286	C₂×C₄⋊C₄	D₄×C₅₉	1	1	yes	characteristic
287	C₂×C₄⋊C₄	D₄×C₅₉	1	1	yes	characteristic
288	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
289	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
290	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
291	C₂×C₂²⋊C₄	—	2	2	no	—
292	C₂×C₂²⋊C₄	—	2	2	no	—
293	C₂×C₂²⋊C₄	—	2	2	no	—
294	C₂×C₂²⋊C₄	—	2	2	no	—
295	C₂×C₂²⋊C₄	—	2	2	no	—
296	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
297	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
298	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
299	#107	—	2	2	no	—
300	#107	—	2	2	no	—
301	#107	D₄×C₅₉	1	4	yes	—
302	#106	—	2	4	no	—
303	C₄⋊C₈	—	2	2	no	—
304	#102	—	2	4	no	—
305	#102	—	2	4	no	—
306	#102	—	4	2	no	—
307	C₄×C₈	—	2	2	no	—
308	C₄×C₈	—	2	2	no	—
309	C₄×C₈	—	2	2	no	—
310	#95	—	2	2	no	—
311	#95	—	2	2	no	—
312	#95	D₄×C₅₉	1	1	yes	characteristic
313	#95	D₄×C₅₉	1	1	yes	characteristic
314	C₂⁴	—	2	2	no	—
315	C₂×D₄	—	2	2	no	—
316	C₂×D₄	—	2	2	no	—
317	C₂×D₄	—	2	2	no	—
318	C₂×D₄	—	2	2	no	—
319	C₂×D₄	—	2	2	no	—
320	C₂×D₄	C₂×Q₈×C₅₉	1	4	yes	—
321	C₂²×C₄	—	2	2	no	—
322	C₂²×C₄	—	2	2	no	—
323	C₂²×C₄	—	2	2	no	—
324	C₂²×C₄	—	4	4	no	—
325	C₂²×C₄	—	4	4	no	—
326	C₂²×C₄	—	8	2	no	—
327	C₂²×C₄	C₂×D₄×C₅₉	1	1	yes	characteristic
328	C₂²×C₄	C₂×D₄×C₅₉	1	1	yes	characteristic
329	C₂²×C₄	C₂×D₄×C₅₉	1	1	yes	characteristic
330	C₂²×C₄	C₂×D₄×C₅₉	1	1	yes	characteristic
331	C₂²×C₄	C₂×D₄×C₅₉	1	1	yes	characteristic
332	C₂²×C₄	C₂×D₄×C₅₉	1	1	yes	characteristic
333	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
334	D₈	—	2	8	no	—
335	C₂×C₈	—	2	1	no	—
336	C₂×C₈	—	2	1	no	—
337	C₂×C₈	—	2	1	no	—
338	C₂×C₈	—	2	1	no	—
339	C₂×C₈	—	2	1	no	—
340	C₂×C₈	—	2	1	no	—
341	C₂×C₈	—	2	1	no	—
342	C₂×C₈	—	2	1	no	—
343	C₂×C₈	C₂×D₄×C₅₉	1	2	yes	—
344	C₂×C₈	C₂×Q₈×C₅₉	1	2	yes	—
345	C₂×C₈	#41×C₅₉	1	2	yes	—
346	C₂×C₈	#41×C₅₉	1	2	yes	—
347	C₄⋊C₄	—	2	2	no	—
348	C₄⋊C₄	—	2	2	no	—
349	C₄⋊C₄	—	2	2	no	—
350	C₄⋊C₄	—	2	2	no	—
351	C₄⋊C₄	—	2	2	no	—
352	C₄⋊C₄	—	2	2	no	—
353	C₄⋊C₄	—	2	2	no	—
354	C₄⋊C₄	—	4	4	no	—
355	C₄⋊C₄	—	4	4	no	—
356	C₄⋊C₄	—	8	2	no	—
357	C₄⋊C₄	—	8	2	no	—
358	C₄⋊C₄	C₂×D₄×C₅₉	1	4	yes	—
359	C₂²⋊C₄	—	4	4	no	—
360	C₂²⋊C₄	—	4	4	no	—
361	C₂²⋊C₄	—	8	2	no	—
362	C₂²⋊C₄	—	8	2	no	—
363	C₂²⋊C₄	—	8	2	no	—
364	C₄²	—	2	1	no	—
365	C₄²	—	2	1	no	—
366	C₄²	—	2	1	no	—
367	C₄²	—	2	1	no	—
368	C₄²	—	2	1	no	—
369	C₄²	—	2	1	no	—
370	C₂³	—	2	4	no	—
371	C₂³	—	4	2	no	—
372	C₂³	—	4	2	no	—
373	C₂³	—	4	2	no	—
374	C₂³	—	4	2	no	—
375	C₂³	—	4	2	no	—
376	C₂³	—	4	2	no	—
377	C₂³	C₂²×D₄×C₅₉	1	1	yes	characteristic
378	D₄	—	2	4	no	—
379	D₄	—	2	4	no	—
380	D₄	—	4	2	no	—
381	D₄	—	4	2	no	—
382	C₂×C₄	—	2	1	no	—
383	C₂×C₄	—	2	1	no	—
384	C₂×C₄	—	2	1	no	—
385	C₂×C₄	—	2	1	no	—
386	C₂×C₄	—	2	1	no	—
387	C₂×C₄	—	2	1	no	—
388	C₂×C₄	—	2	1	no	—
389	C₂×C₄	—	2	1	no	—
390	C₂×C₄	—	2	4	no	—
391	C₂×C₄	—	2	1	no	—
392	C₂×C₄	—	2	1	no	—
393	C₂×C₄	—	2	1	no	—
394	C₂×C₄	—	2	1	no	—
395	C₂×C₄	—	2	1	no	—
396	C₂×C₄	—	2	1	no	—
397	C₂×C₄	—	2	1	no	—
398	C₂×C₄	—	2	1	no	—
399	C₂×C₄	—	4	2	no	—
400	C₂×C₄	—	4	2	no	—
401	C₂×C₄	—	4	2	no	—
402	C₂×C₄	—	4	2	no	—
403	C₂×C₄	—	4	2	no	—
404	C₂×C₄	—	4	2	no	—
405	C₂×C₄	—	4	2	no	—
406	C₂×C₄	—	4	2	no	—
407	C₂×C₄	—	8	8	no	—
408	C₂×C₄	#135×C₅₉	1	2	yes	—
409	C₂×C₄	#135×C₅₉	1	2	yes	—
410	C₂×C₄	C₂²×D₄×C₅₉	1	1	yes	characteristic
411	C₂×C₄	C₂²×Q₈×C₅₉	1	1	yes	characteristic
412	C₂×C₄	C₂×#41×C₅₉	1	1	yes	characteristic
413	C₂×C₄	C₂×#41×C₅₉	1	1	yes	characteristic
414	C₂×C₄	H(5,𝔽₂)×C₅₉	1	1	yes	characteristic
415	C₂×C₄	2₋¹⁺⁴×C₅₉	1	1	yes	characteristic
416	C₈	—	2	2	no	—
417	C₈	—	4	1	no	—
418	C₈	—	4	1	no	—
419	C₈	C₂²⋊Q₈×C₅₉	1	4	yes	—
420	C₂²	—	4	4	no	—
421	C₂²	—	4	4	no	—
422	C₂²	—	4	4	no	—
423	C₂²	—	8	2	no	—
424	C₂²	—	8	2	no	—
425	C₂²	—	8	2	no	—
426	C₂²	—	8	2	no	—
427	C₂²	C₅₉×#532	1	1	yes	characteristic
428	C₂²	D₄²×C₅₉	1	1	yes	characteristic
429	C₂²	D₄×Q₈×C₅₉	1	1	yes	characteristic
430	C₂²	C₂×#135×C₅₉	1	1	yes	characteristic
431	C₂²	C₂×#135×C₅₉	1	1	yes	characteristic
432	C₂²	C₅₉×#576	1	1	yes	characteristic
433	C₂²	C₅₉×#576	1	1	yes	characteristic
434	C₄	—	2	2	no	—
435	C₄	—	2	2	no	—
436	C₄	—	4	1	no	—
437	C₄	—	4	4	no	—
438	C₄	—	4	1	no	—
439	C₄	—	4	1	no	—
440	C₄	—	4	1	no	—
441	C₄	—	8	2	no	—
442	C₄	—	8	2	no	—
443	C₄	C₂×C₂²⋊Q₈×C₅₉	1	1	yes	characteristic
444	C₄	C₅₉×#542	1	1	yes	characteristic
445	C₄	C₅₉×#548	1	1	yes	characteristic
446	C₄	C₅₉×#554	1	1	yes	characteristic
447	C₂	—	8	4	no	—
448	C₂	C₅₉×#2452	1	1	yes	characteristic
449	C₂	C₅₉×#3168	1	1	yes	characteristic
450	C₂	C₅₉×#3176	1	1	yes	characteristic
451	C₂	C₅₉×#3280	1	1	yes	characteristic
452	C₂	C₅₉×#3287	1	1	yes	characteristic
453	C₂	C₅₉×#3380	1	1	yes	characteristic
454	C₂	C₅₉×#3380	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₅₉	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₅₉
prime radical	C₂²×D₈×C₅₉	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₅₉ ◁ C₄×C₄⋊C₄×C₅₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₅₉×#499	C₂	semidirect
3. C₅₉×#2454	C₂	semidirect
4. C₅₉×#2065	C₂	semidirect
5. C₅₉×#2025	C₂	semidirect
8. C₅₉×#1942	C₂	semidirect
9. C₅₉×#1942	C₂	semidirect
10. C₅₉×#1864	C₂	semidirect
11. C₈×C₄⋊C₄×C₅₉	C₂	semidirect
192. #26482	C₅₉	direct (N × H)
220. C₂×#499	C₂×C₅₉	semidirect
222. #2454	C₂×C₅₉	semidirect
223. #2065	C₂×C₅₉	semidirect
224. #2025	C₂×C₅₉	semidirect
227. #1942	C₂×C₅₉	semidirect
228. #1942	C₂×C₅₉	semidirect
229. #1864	C₂×C₅₉	semidirect
230. C₈×C₄⋊C₄	C₂×C₅₉	semidirect
268. C₅₉	#26482	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×#499	2
C₂×C₄×D₈×C₅₉	2
C₅₉×#2454	2
C₅₉×#2065	2
C₅₉×#2025	2
C₅₉×#1970	2
C₅₉×#1942	2
C₅₉×#1864	2
C₈×C₄⋊C₄×C₅₉	2
#26482	59

Subgroups — C59×#26482 #28438591

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₉×#26482 #28438591