Subgroups — C₅₉×#26492 #28438601

Order 15104.

834 conjugacy classes of subgroups.

The subgroup lattice has 418 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×C₅₉×#442	C₂	1	1	yes	maximal, characteristic
3	C₅₉×#2454	C₂	1	2	yes	maximal, complemented
4	C₅₉×#2067	C₂	1	2	yes	maximal, complemented
5	C₅₉×#2025	C₂	1	2	yes	maximal, complemented
6	C₅₉×#1972	C₂	1	1	yes	maximal, characteristic
7	C₅₉×#1970	C₂	1	1	yes	maximal, characteristic
8	C₅₉×#1944	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅₉×#1943	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅₉×#1862	C₂	1	2	yes	maximal, complemented
11	C₅₉×#1771	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	C₅₉×#442	—	2	4	no	—
17	C₂×#107×C₅₉	C₂²	1	1	yes	characteristic
18	C₂×#107×C₅₉	C₂²	1	2	yes	—
19	C₂×#106×C₅₉	C₂²	1	1	yes	characteristic
20	C₂×#106×C₅₉	C₂²	1	1	yes	characteristic
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×#97×C₅₉	C₂²	1	1	yes	characteristic
26	C₂×#97×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	2	yes	—
59	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
60	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
61	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
62	C₂×C₂²⋊C₄×C₅₉	—	2	2	no	—
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×C₄²×C₅₉	C₂³	1	1	yes	characteristic
68	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
69	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
70	#107×C₅₉	—	2	2	no	—
71	#107×C₅₉	—	2	4	no	—
72	#106×C₅₉	—	2	2	no	—
73	#106×C₅₉	D₄	1	4	yes	—
74	C₄⋊C₈×C₅₉	—	2	2	no	—
75	#102×C₅₉	—	2	4	no	—
76	#102×C₅₉	—	2	4	no	—
77	#102×C₅₉	—	4	2	no	—
78	#97×C₅₉	—	2	2	no	—
79	#97×C₅₉	—	2	2	no	—
80	C₄×C₈×C₅₉	—	2	2	no	—
81	#95×C₅₉	—	2	2	no	—
82	#95×C₅₉	—	2	2	no	—
83	#95×C₅₉	D₄	1	2	yes	—
84	C₂⁴×C₅₉	—	2	2	no	—
85	C₂×D₄×C₅₉	—	2	2	no	—
86	C₂×D₄×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	C₂×Q₈	1	4	yes	—
91	C₂²×C₄×C₅₉	—	2	2	no	—
92	C₂²×C₄×C₅₉	—	2	2	no	—
93	C₂²×C₄×C₅₉	—	2	2	no	—
94	C₂²×C₄×C₅₉	—	4	4	no	—
95	C₂²×C₄×C₅₉	—	4	4	no	—
96	C₂²×C₄×C₅₉	—	8	2	no	—
97	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
98	C₂²×C₄×C₅₉	C₂×D₄	1	2	yes	—
99	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
100	C₂²×C₄×C₅₉	C₂×D₄	1	2	yes	—
101	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
102	D₈×C₅₉	—	2	8	no	—
103	C₂×C₈×C₅₉	—	2	1	no	—
104	C₂×C₈×C₅₉	—	2	1	no	—
105	C₂×C₈×C₅₉	—	2	1	no	—
106	C₂×C₈×C₅₉	—	2	1	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	C₂×D₄	1	2	yes	—
112	C₂×C₈×C₅₉	C₂×Q₈	1	2	yes	—
113	C₂×C₈×C₅₉	#41	1	2	yes	—
114	C₂×C₈×C₅₉	#41	1	2	yes	—
115	C₄⋊C₄×C₅₉	—	2	2	no	—
116	C₄⋊C₄×C₅₉	—	2	2	no	—
117	C₄⋊C₄×C₅₉	—	2	2	no	—
118	C₄⋊C₄×C₅₉	—	2	2	no	—
119	C₄⋊C₄×C₅₉	—	2	2	no	—
120	C₄⋊C₄×C₅₉	—	4	2	no	—
121	C₄⋊C₄×C₅₉	—	4	4	no	—
122	C₄⋊C₄×C₅₉	—	4	4	no	—
123	C₄⋊C₄×C₅₉	—	8	2	no	—
124	C₄⋊C₄×C₅₉	—	8	2	no	—
125	C₄⋊C₄×C₅₉	C₂×D₄	1	4	yes	—
126	C₂²⋊C₄×C₅₉	—	4	4	no	—
127	C₂²⋊C₄×C₅₉	—	4	4	no	—
128	C₂²⋊C₄×C₅₉	—	8	2	no	—
129	C₂²⋊C₄×C₅₉	—	8	2	no	—
130	C₂²⋊C₄×C₅₉	—	8	2	no	—
131	C₄²×C₅₉	—	2	1	no	—
132	C₄²×C₅₉	—	2	1	no	—
133	C₄²×C₅₉	—	2	1	no	—
134	C₄²×C₅₉	—	2	1	no	—
135	C₄²×C₅₉	—	2	1	no	—
136	C₄²×C₅₉	—	2	1	no	—
137	C₂³×C₅₉	—	2	4	no	—
138	C₂³×C₅₉	—	4	2	no	—
139	C₂³×C₅₉	—	4	2	no	—
140	C₂³×C₅₉	—	4	2	no	—
141	C₂³×C₅₉	—	4	2	no	—
142	C₂³×C₅₉	—	4	2	no	—
143	C₂³×C₅₉	—	4	2	no	—
144	C₂³×C₅₉	C₂²×D₄	1	1	yes	characteristic
145	D₄×C₅₉	—	2	4	no	—
146	D₄×C₅₉	—	2	4	no	—
147	D₄×C₅₉	—	4	2	no	—
148	D₄×C₅₉	—	4	2	no	—
149	C₂×C₄×C₅₉	—	2	1	no	—
150	C₂×C₄×C₅₉	—	2	1	no	—
151	C₂×C₄×C₅₉	—	2	2	no	—
152	C₂×C₄×C₅₉	—	2	2	no	—
153	C₂×C₄×C₅₉	—	2	4	no	—
154	C₂×C₄×C₅₉	—	2	2	no	—
155	C₂×C₄×C₅₉	—	2	2	no	—
156	C₂×C₄×C₅₉	—	2	2	no	—
157	C₂×C₄×C₅₉	—	2	2	no	—
158	C₂×C₄×C₅₉	—	2	2	no	—
159	C₂×C₄×C₅₉	—	2	2	no	—
160	C₂×C₄×C₅₉	—	4	2	no	—
161	C₂×C₄×C₅₉	—	4	2	no	—
162	C₂×C₄×C₅₉	—	4	2	no	—
163	C₂×C₄×C₅₉	—	4	2	no	—
164	C₂×C₄×C₅₉	—	4	2	no	—
165	C₂×C₄×C₅₉	—	4	2	no	—
166	C₂×C₄×C₅₉	—	4	2	no	—
167	C₂×C₄×C₅₉	—	4	2	no	—
168	C₂×C₄×C₅₉	—	8	8	no	—
169	C₂×C₄×C₅₉	C₂²×D₄	1	1	yes	characteristic
170	C₂×C₄×C₅₉	C₂²×Q₈	1	1	yes	characteristic
171	C₂×C₄×C₅₉	C₂×#41	1	1	yes	characteristic
172	C₂×C₄×C₅₉	C₂×#41	1	1	yes	characteristic
173	C₂×C₄×C₅₉	H(5,𝔽₂)	1	1	yes	characteristic
174	C₂×C₄×C₅₉	2₋¹⁺⁴	1	1	yes	characteristic
175	C₈×C₅₉	—	2	2	no	—
176	C₈×C₅₉	—	4	1	no	—
177	C₈×C₅₉	—	4	1	no	—
178	C₈×C₅₉	C₂²⋊Q₈	1	4	yes	—
179	#26492	C₅₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
180	C₂²×C₅₉	—	4	4	no	—
181	C₂²×C₅₉	—	4	4	no	—
182	C₂²×C₅₉	—	4	4	no	—
183	C₂²×C₅₉	—	8	2	no	—
184	C₂²×C₅₉	—	8	2	no	—
185	C₂²×C₅₉	—	8	2	no	—
186	C₂²×C₅₉	—	8	2	no	—
187	C₂²×C₅₉	#532	1	1	yes	characteristic
188	C₂²×C₅₉	D₄²	1	1	yes	characteristic
189	C₂²×C₅₉	D₄×Q₈	1	1	yes	characteristic
190	C₂²×C₅₉	#575	1	2	yes	—
191	C₂²×C₅₉	#576	1	2	yes	—
192	C₄×C₅₉	—	4	1	no	—
193	C₄×C₅₉	—	4	1	no	—
194	C₄×C₅₉	—	4	2	no	—
195	C₄×C₅₉	—	4	2	no	—
196	C₄×C₅₉	—	4	4	no	—
197	C₄×C₅₉	—	8	2	no	—
198	C₄×C₅₉	—	8	2	no	—
199	C₄×C₅₉	C₂×C₂²⋊Q₈	1	1	yes	characteristic
200	C₄×C₅₉	#542	1	1	yes	characteristic
201	C₄×C₅₉	#548	1	1	yes	characteristic
202	C₄×C₅₉	#554	1	1	yes	characteristic
203	C₂×#499	C₂×C₅₉	1	1	yes	characteristic, complemented
204	C₂×#442	C₂×C₅₉	1	1	yes	characteristic
205	#2454	C₂×C₅₉	1	2	yes	complemented
206	#2067	C₂×C₅₉	1	2	yes	complemented
207	#2025	C₂×C₅₉	1	2	yes	complemented
208	#1972	C₂×C₅₉	1	1	yes	characteristic
209	#1970	C₂×C₅₉	1	1	yes	characteristic
210	#1944	C₂×C₅₉	1	1	yes	characteristic, complemented
211	#1943	C₂×C₅₉	1	1	yes	characteristic, complemented
212	#1862	C₂×C₅₉	1	2	yes	complemented
213	#1771	C₂×C₅₉	1	1	yes	characteristic, complemented
214	C₂×C₅₉	—	8	4	no	—
215	C₂×C₅₉	#2452	1	1	yes	characteristic
216	C₂×C₅₉	#3176	1	1	yes	characteristic
217	C₂×C₅₉	#3183	1	1	yes	characteristic
218	C₂×C₅₉	#3268	1	2	yes	—
219	C₂×C₅₉	#3389	1	2	yes	—
220	C₂²×D₈	C₂²×C₅₉	1	1	yes	characteristic
221	C₂×#125	C₂²×C₅₉	1	2	yes	—
222	C₂×C₄×D₄	C₂²×C₅₉	1	2	yes	—
223	#499	—	2	4	no	—
224	#442	—	2	4	no	—
225	C₂×#107	C₂²×C₅₉	1	2	yes	—
226	C₂×#107	C₂²×C₅₉	1	1	yes	characteristic
227	C₂×#106	C₂²×C₅₉	1	1	yes	characteristic
228	C₂×#106	C₂²×C₅₉	1	1	yes	characteristic
229	C₂×C₄⋊C₈	C₂²×C₅₉	1	1	yes	characteristic
230	C₂×#102	C₂²×C₅₉	1	2	yes	—
231	C₂×#102	C₂²×C₅₉	1	2	yes	—
232	C₂×#102	C₂²×C₅₉	1	2	yes	—
233	C₂×#97	C₂²×C₅₉	1	1	yes	characteristic
234	C₂×#97	C₂²×C₅₉	1	1	yes	characteristic
235	C₂×C₄×C₈	C₂²×C₅₉	1	1	yes	characteristic
236	#399	—	2	2	no	—
237	#396	—	2	2	no	—
238	#390	C₂²×C₅₉	1	2	yes	—
239	#390	C₂²×C₅₉	1	2	yes	—
240	#389	C₂²×C₅₉	1	2	yes	—
241	#389	C₂²×C₅₉	1	2	yes	—
242	#385	—	2	2	no	—
243	#380	—	2	2	no	—
244	C₄×C₄⋊C₄	C₂²×C₅₉	1	1	yes	characteristic
245	#340	C₂²×C₅₉	1	2	yes	—
246	#340	C₂²×C₅₉	1	2	yes	—
247	#336	C₂²×C₅₉	1	1	yes	characteristic
248	#336	C₂²×C₅₉	1	1	yes	characteristic
249	C₅₉	#26492	1	1	yes	characteristic, direct product factor, Sylow
250	C₂²×D₄	C₂³×C₅₉	1	2	yes	—
251	C₂³×C₄	—	2	2	no	—
252	C₂×D₈	—	2	2	no	—
253	C₂×D₈	—	2	2	no	—
254	C₂×D₈	Q₈×C₅₉	1	4	yes	—
255	C₂²×C₈	C₂³×C₅₉	1	1	yes	characteristic
256	C₂²×C₈	C₂³×C₅₉	1	1	yes	characteristic
257	C₂²×C₈	C₂³×C₅₉	1	1	yes	characteristic
258	C₂²×C₈	C₂³×C₅₉	1	1	yes	characteristic
259	#125	—	2	4	no	—
260	#125	—	4	2	no	—
261	C₄×D₄	—	2	4	no	—
262	C₄×D₄	—	4	2	no	—
263	C₂×C₄⋊C₄	—	2	2	no	—
264	C₂×C₄⋊C₄	—	2	2	no	—
265	C₂×C₄⋊C₄	—	2	2	no	—
266	C₂×C₄⋊C₄	—	2	2	no	—
267	C₂×C₄⋊C₄	D₄×C₅₉	1	2	yes	—
268	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
269	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
270	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
271	C₂×C₂²⋊C₄	—	2	2	no	—
272	C₂×C₂²⋊C₄	—	2	2	no	—
273	C₂×C₂²⋊C₄	—	2	2	no	—
274	C₂×C₂²⋊C₄	—	2	2	no	—
275	C₂×C₂²⋊C₄	—	2	2	no	—
276	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
277	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
278	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
279	#107	—	2	2	no	—
280	#107	—	2	4	no	—
281	#106	—	2	2	no	—
282	#106	D₄×C₅₉	1	4	yes	—
283	C₄⋊C₈	—	2	2	no	—
284	#102	—	2	4	no	—
285	#102	—	2	4	no	—
286	#102	—	4	2	no	—
287	#97	—	2	2	no	—
288	#97	—	2	2	no	—
289	C₄×C₈	—	2	2	no	—
290	#95	—	2	2	no	—
291	#95	—	2	2	no	—
292	#95	D₄×C₅₉	1	2	yes	—
293	C₂⁴	—	2	2	no	—
294	C₂×D₄	—	2	2	no	—
295	C₂×D₄	—	2	2	no	—
296	C₂×D₄	—	2	2	no	—
297	C₂×D₄	—	2	2	no	—
298	C₂×D₄	—	2	2	no	—
299	C₂×D₄	C₂×Q₈×C₅₉	1	4	yes	—
300	C₂²×C₄	—	2	2	no	—
301	C₂²×C₄	—	2	2	no	—
302	C₂²×C₄	—	2	2	no	—
303	C₂²×C₄	—	4	4	no	—
304	C₂²×C₄	—	4	4	no	—
305	C₂²×C₄	—	8	2	no	—
306	C₂²×C₄	C₂×D₄×C₅₉	1	1	yes	characteristic
307	C₂²×C₄	C₂×D₄×C₅₉	1	2	yes	—
308	C₂²×C₄	C₂×D₄×C₅₉	1	1	yes	characteristic
309	C₂²×C₄	C₂×D₄×C₅₉	1	2	yes	—
310	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
311	D₈	—	2	8	no	—
312	C₂×C₈	—	2	1	no	—
313	C₂×C₈	—	2	1	no	—
314	C₂×C₈	—	2	1	no	—
315	C₂×C₈	—	2	1	no	—
316	C₂×C₈	—	2	1	no	—
317	C₂×C₈	—	2	1	no	—
318	C₂×C₈	—	2	1	no	—
319	C₂×C₈	—	2	1	no	—
320	C₂×C₈	C₂×D₄×C₅₉	1	2	yes	—
321	C₂×C₈	C₂×Q₈×C₅₉	1	2	yes	—
322	C₂×C₈	#41×C₅₉	1	2	yes	—
323	C₂×C₈	#41×C₅₉	1	2	yes	—
324	C₄⋊C₄	—	2	2	no	—
325	C₄⋊C₄	—	2	2	no	—
326	C₄⋊C₄	—	2	2	no	—
327	C₄⋊C₄	—	2	2	no	—
328	C₄⋊C₄	—	2	2	no	—
329	C₄⋊C₄	—	4	2	no	—
330	C₄⋊C₄	—	4	4	no	—
331	C₄⋊C₄	—	4	4	no	—
332	C₄⋊C₄	—	8	2	no	—
333	C₄⋊C₄	—	8	2	no	—
334	C₄⋊C₄	C₂×D₄×C₅₉	1	4	yes	—
335	C₂²⋊C₄	—	4	4	no	—
336	C₂²⋊C₄	—	4	4	no	—
337	C₂²⋊C₄	—	8	2	no	—
338	C₂²⋊C₄	—	8	2	no	—
339	C₂²⋊C₄	—	8	2	no	—
340	C₄²	—	2	1	no	—
341	C₄²	—	2	1	no	—
342	C₄²	—	2	1	no	—
343	C₄²	—	2	1	no	—
344	C₄²	—	2	1	no	—
345	C₄²	—	2	1	no	—
346	C₂³	—	2	4	no	—
347	C₂³	—	4	2	no	—
348	C₂³	—	4	2	no	—
349	C₂³	—	4	2	no	—
350	C₂³	—	4	2	no	—
351	C₂³	—	4	2	no	—
352	C₂³	—	4	2	no	—
353	C₂³	C₂²×D₄×C₅₉	1	1	yes	characteristic
354	D₄	—	2	4	no	—
355	D₄	—	2	4	no	—
356	D₄	—	4	2	no	—
357	D₄	—	4	2	no	—
358	C₂×C₄	—	2	1	no	—
359	C₂×C₄	—	2	1	no	—
360	C₂×C₄	—	2	2	no	—
361	C₂×C₄	—	2	2	no	—
362	C₂×C₄	—	2	4	no	—
363	C₂×C₄	—	2	2	no	—
364	C₂×C₄	—	2	2	no	—
365	C₂×C₄	—	2	2	no	—
366	C₂×C₄	—	2	2	no	—
367	C₂×C₄	—	2	2	no	—
368	C₂×C₄	—	2	2	no	—
369	C₂×C₄	—	4	2	no	—
370	C₂×C₄	—	4	2	no	—
371	C₂×C₄	—	4	2	no	—
372	C₂×C₄	—	4	2	no	—
373	C₂×C₄	—	4	2	no	—
374	C₂×C₄	—	4	2	no	—
375	C₂×C₄	—	4	2	no	—
376	C₂×C₄	—	4	2	no	—
377	C₂×C₄	—	8	8	no	—
378	C₂×C₄	C₂²×D₄×C₅₉	1	1	yes	characteristic
379	C₂×C₄	C₂²×Q₈×C₅₉	1	1	yes	characteristic
380	C₂×C₄	C₂×#41×C₅₉	1	1	yes	characteristic
381	C₂×C₄	C₂×#41×C₅₉	1	1	yes	characteristic
382	C₂×C₄	H(5,𝔽₂)×C₅₉	1	1	yes	characteristic
383	C₂×C₄	2₋¹⁺⁴×C₅₉	1	1	yes	characteristic
384	C₈	—	2	2	no	—
385	C₈	—	4	1	no	—
386	C₈	—	4	1	no	—
387	C₈	C₂²⋊Q₈×C₅₉	1	4	yes	—
388	C₂²	—	4	4	no	—
389	C₂²	—	4	4	no	—
390	C₂²	—	4	4	no	—
391	C₂²	—	8	2	no	—
392	C₂²	—	8	2	no	—
393	C₂²	—	8	2	no	—
394	C₂²	—	8	2	no	—
395	C₂²	C₅₉×#532	1	1	yes	characteristic
396	C₂²	D₄²×C₅₉	1	1	yes	characteristic
397	C₂²	D₄×Q₈×C₅₉	1	1	yes	characteristic
398	C₂²	C₅₉×#575	1	2	yes	—
399	C₂²	C₅₉×#576	1	2	yes	—
400	C₄	—	4	2	no	—
401	C₄	—	4	2	no	—
402	C₄	—	4	4	no	—
403	C₄	—	4	1	no	—
404	C₄	—	4	1	no	—
405	C₄	—	8	2	no	—
406	C₄	—	8	2	no	—
407	C₄	C₂×C₂²⋊Q₈×C₅₉	1	1	yes	characteristic
408	C₄	C₅₉×#542	1	1	yes	characteristic
409	C₄	C₅₉×#548	1	1	yes	characteristic
410	C₄	C₅₉×#554	1	1	yes	characteristic
411	C₂	—	8	4	no	—
412	C₂	C₅₉×#2452	1	1	yes	characteristic
413	C₂	C₅₉×#3176	1	1	yes	characteristic
414	C₂	C₅₉×#3183	1	1	yes	characteristic
415	C₂	C₅₉×#3268	1	2	yes	—
416	C₂	C₅₉×#3389	1	2	yes	—

	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×#2067	C₂	semidirect
5. C₅₉×#2025	C₂	semidirect
8. C₅₉×#1944	C₂	semidirect
9. C₅₉×#1943	C₂	semidirect
10. C₅₉×#1862	C₂	semidirect
11. C₅₉×#1771	C₂	semidirect
179. #26492	C₅₉	direct (N × H)
203. C₂×#499	C₂×C₅₉	semidirect
205. #2454	C₂×C₅₉	semidirect
206. #2067	C₂×C₅₉	semidirect
207. #2025	C₂×C₅₉	semidirect
210. #1944	C₂×C₅₉	semidirect
211. #1943	C₂×C₅₉	semidirect
212. #1862	C₂×C₅₉	semidirect
213. #1771	C₂×C₅₉	semidirect
249. C₅₉	#26492	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×C₅₉×#442	2
C₅₉×#2454	2
C₅₉×#2067	2
C₅₉×#2025	2
C₅₉×#1972	2
C₅₉×#1970	2
C₅₉×#1944	2
C₅₉×#1943	2
C₅₉×#1862	2
C₅₉×#1771	2
#26492	59

Subgroups — C59×#26492 #28438601

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₉×#26492 #28438601