Subgroups — C₅₉×#32672 #28444781

Order 15104.

764 conjugacy classes of subgroups.

The subgroup lattice has 428 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅₉×#2592	C₂	1	2	yes	maximal, complemented
2	C₅₉×#2055	C₂	1	2	yes	maximal, complemented
3	C₅₉×#2015	C₂	1	2	yes	maximal, complemented
4	C₅₉×#2012	C₂	1	2	yes	maximal
5	C₅₉×#1984	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅₉×#1970	C₂	1	1	yes	maximal, characteristic
7	C₅₉×#1969	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅₉×#1928	C₂	1	2	yes	maximal, complemented
9	C₅₉×#1925	C₂	1	2	yes	maximal, complemented
10	C₂²×Q₁₆×C₅₉	C₂²	1	1	yes	characteristic
11	C₂²×SD₁₆×C₅₉	C₂²	1	2	yes	—
12	C₂²×D₈×C₅₉	C₂²	1	1	yes	characteristic
13	C₂×#124×C₅₉	C₂²	1	2	yes	—
14	C₂×C₄×Q₈×C₅₉	C₂²	1	1	yes	characteristic
15	C₂×#107×C₅₉	C₂²	1	1	yes	characteristic
16	C₂×#107×C₅₉	C₂²	1	1	yes	characteristic
17	C₂×C₄⋊C₈×C₅₉	C₂²	1	1	yes	characteristic
18	C₂×#103×C₅₉	C₂²	1	2	yes	—
19	C₂×#103×C₅₉	C₂²	1	2	yes	—
20	C₂×#102×C₅₉	C₂²	1	2	yes	—
21	C₂×#102×C₅₉	C₂²	1	2	yes	—
22	C₂×C₄×C₈×C₅₉	C₂²	1	1	yes	characteristic
23	C₅₉×#397	—	2	2	no	—
24	C₅₉×#393	—	2	2	no	—
25	C₅₉×#391	C₂²	1	2	yes	—
26	C₅₉×#391	C₂²	1	2	yes	—
27	C₅₉×#390	C₂²	1	2	yes	—
28	C₅₉×#390	C₂²	1	2	yes	—
29	C₅₉×#388	—	2	2	no	—
30	C₅₉×#388	—	2	2	no	—
31	C₄×C₄⋊C₄×C₅₉	C₂²	1	2	yes	—
32	C₅₉×#340	C₂²	1	2	yes	—
33	C₅₉×#336	C₂²	1	2	yes	—
34	C₅₉×#336	C₂²	1	2	yes	—
35	C₂²×Q₈×C₅₉	D₄	1	1	yes	characteristic
36	C₂²×Q₈×C₅₉	C₂³	1	2	yes	—
37	C₂²×D₄×C₅₉	C₂³	1	2	yes	—
38	C₂×Q₁₆×C₅₉	—	2	2	no	—
39	C₂×Q₁₆×C₅₉	—	4	1	no	—
40	C₂×Q₁₆×C₅₉	—	4	1	no	—
41	C₂×SD₁₆×C₅₉	—	4	2	no	—
42	C₂×SD₁₆×C₅₉	—	4	2	no	—
43	C₂×SD₁₆×C₅₉	—	4	2	no	—
44	C₂×D₈×C₅₉	—	2	2	no	—
45	C₂×D₈×C₅₉	—	4	1	no	—
46	C₂×D₈×C₅₉	—	4	1	no	—
47	C₂²×C₈×C₅₉	C₂³	1	2	yes	—
48	C₂²×C₈×C₅₉	C₂³	1	1	yes	characteristic
49	C₂²×C₈×C₅₉	C₂³	1	1	yes	characteristic
50	#124×C₅₉	—	4	2	no	—
51	#124×C₅₉	—	4	2	no	—
52	C₄×Q₈×C₅₉	—	4	1	no	—
53	C₄×Q₈×C₅₉	—	4	1	no	—
54	C₂×C₄⋊C₄×C₅₉	D₄	1	1	yes	characteristic
55	C₂×C₄⋊C₄×C₅₉	D₄	1	2	yes	—
56	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
57	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
58	C₂×C₂²⋊C₄×C₅₉	—	2	2	no	—
59	C₂×C₂²⋊C₄×C₅₉	—	2	2	no	—
60	C₂×C₂²⋊C₄×C₅₉	—	2	2	no	—
61	C₂×C₂²⋊C₄×C₅₉	—	2	2	no	—
62	C₂×C₂²⋊C₄×C₅₉	—	2	2	no	—
63	C₂×C₂²⋊C₄×C₅₉	—	2	2	no	—
64	C₂×C₄²×C₅₉	—	2	2	no	—
65	C₂×C₄²×C₅₉	C₂³	1	2	yes	—
66	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
67	#107×C₅₉	—	4	1	no	—
68	#107×C₅₉	—	4	1	no	—
69	C₄⋊C₈×C₅₉	—	4	1	no	—
70	#103×C₅₉	—	2	4	no	—
71	#103×C₅₉	—	4	2	no	—
72	#102×C₅₉	—	2	4	no	—
73	#102×C₅₉	—	4	2	no	—
74	C₄×C₈×C₅₉	—	4	1	no	—
75	#95×C₅₉	—	2	2	no	—
76	#95×C₅₉	—	2	2	no	—
77	#95×C₅₉	—	2	2	no	—
78	#95×C₅₉	—	2	2	no	—
79	#95×C₅₉	—	2	2	no	—
80	C₂⁴×C₅₉	—	2	2	no	—
81	C₂×Q₈×C₅₉	—	2	2	no	—
82	C₂×Q₈×C₅₉	—	2	2	no	—
83	C₂×Q₈×C₅₉	—	2	2	no	—
84	C₂×Q₈×C₅₉	—	2	2	no	—
85	C₂×Q₈×C₅₉	—	2	2	no	—
86	C₂×Q₈×C₅₉	—	2	2	no	—
87	C₂×Q₈×C₅₉	—	2	2	no	—
88	C₂×Q₈×C₅₉	—	4	1	no	—
89	C₂×Q₈×C₅₉	—	4	1	no	—
90	C₂×D₄×C₅₉	—	2	2	no	—
91	C₂×D₄×C₅₉	—	2	2	no	—
92	C₂×D₄×C₅₉	—	2	2	no	—
93	C₂×D₄×C₅₉	—	2	2	no	—
94	C₂×D₄×C₅₉	—	2	2	no	—
95	C₂×D₄×C₅₉	—	2	2	no	—
96	C₂²×C₄×C₅₉	—	2	2	no	—
97	C₂²×C₄×C₅₉	—	2	2	no	—
98	C₂²×C₄×C₅₉	—	2	2	no	—
99	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
100	C₂²×C₄×C₅₉	C₂×D₄	1	2	yes	—
101	C₂²×C₄×C₅₉	C₂×D₄	1	2	yes	—
102	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
103	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
104	Q₁₆×C₅₉	—	4	4	no	—
105	SD₁₆×C₅₉	—	4	8	no	—
106	D₈×C₅₉	—	4	4	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	2	no	—
112	C₂×C₈×C₅₉	—	2	2	no	—
113	C₂×C₈×C₅₉	—	2	2	no	—
114	C₂×C₈×C₅₉	#41	1	2	yes	—
115	C₂×C₈×C₅₉	#41	1	2	yes	—
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	1	no	—
121	C₄⋊C₄×C₅₉	—	4	2	no	—
122	C₂²⋊C₄×C₅₉	—	4	4	no	—
123	C₂²⋊C₄×C₅₉	—	4	4	no	—
124	C₂²⋊C₄×C₅₉	—	4	4	no	—
125	C₂²⋊C₄×C₅₉	—	4	4	no	—
126	C₂²⋊C₄×C₅₉	—	8	2	no	—
127	C₂²⋊C₄×C₅₉	—	8	2	no	—
128	C₄²×C₅₉	—	2	1	no	—
129	C₄²×C₅₉	—	2	1	no	—
130	C₄²×C₅₉	—	2	2	no	—
131	C₄²×C₅₉	—	2	2	no	—
132	C₄²×C₅₉	—	8	2	no	—
133	C₂³×C₅₉	—	4	2	no	—
134	C₂³×C₅₉	—	4	2	no	—
135	C₂³×C₅₉	—	4	2	no	—
136	C₂³×C₅₉	—	4	2	no	—
137	C₂³×C₅₉	—	4	2	no	—
138	C₂³×C₅₉	—	4	2	no	—
139	C₂³×C₅₉	—	4	2	no	—
140	C₂³×C₅₉	C₂²×D₄	1	1	yes	characteristic
141	Q₈×C₅₉	—	4	4	no	—
142	Q₈×C₅₉	—	4	2	no	—
143	Q₈×C₅₉	—	4	2	no	—
144	Q₈×C₅₉	—	4	2	no	—
145	Q₈×C₅₉	—	4	2	no	—
146	D₄×C₅₉	—	4	2	no	—
147	D₄×C₅₉	—	4	2	no	—
148	D₄×C₅₉	—	4	2	no	—
149	D₄×C₅₉	—	4	2	no	—
150	C₂×C₄×C₅₉	—	2	1	no	—
151	C₂×C₄×C₅₉	—	2	1	no	—
152	C₂×C₄×C₅₉	—	2	2	no	—
153	C₂×C₄×C₅₉	—	2	2	no	—
154	C₂×C₄×C₅₉	—	2	1	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	1	no	—
159	C₂×C₄×C₅₉	—	2	1	no	—
160	C₂×C₄×C₅₉	—	2	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	—	4	2	no	—
169	C₂×C₄×C₅₉	—	4	2	no	—
170	C₂×C₄×C₅₉	#135	1	2	yes	—
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	H(5,𝔽₂)	1	1	yes	characteristic
175	C₂×C₄×C₅₉	H(5,𝔽₂)	1	1	yes	characteristic
176	C₂×C₄×C₅₉	H(5,𝔽₂)	1	1	yes	characteristic
177	C₈×C₅₉	—	2	2	no	—
178	C₈×C₅₉	—	2	2	no	—
179	C₈×C₅₉	—	4	2	no	—
180	#32672	C₅₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
181	C₂²×C₅₉	—	8	2	no	—
182	C₂²×C₅₉	—	8	2	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	—	8	2	no	—
188	C₂²×C₅₉	#534	1	1	yes	characteristic
189	C₂²×C₅₉	#550	1	1	yes	characteristic
190	C₂²×C₅₉	#550	1	1	yes	characteristic
191	C₂²×C₅₉	C₂×#135	1	1	yes	characteristic
192	C₂²×C₅₉	#575	1	1	yes	characteristic
193	C₂²×C₅₉	#576	1	1	yes	characteristic
194	C₂²×C₅₉	#578	1	1	yes	characteristic
195	C₄×C₅₉	—	2	2	no	—
196	C₄×C₅₉	—	4	2	no	—
197	C₄×C₅₉	—	4	2	no	—
198	C₄×C₅₉	—	4	1	no	—
199	C₄×C₅₉	—	8	2	no	—
200	C₄×C₅₉	—	8	2	no	—
201	C₄×C₅₉	—	8	2	no	—
202	C₄×C₅₉	#538	1	1	yes	characteristic
203	C₄×C₅₉	#538	1	1	yes	characteristic
204	C₄×C₅₉	#555	1	1	yes	characteristic
205	C₄×C₅₉	H(3,𝔽₄)	1	1	yes	characteristic
206	#2592	C₂×C₅₉	1	2	yes	complemented
207	#2055	C₂×C₅₉	1	2	yes	complemented
208	#2015	C₂×C₅₉	1	2	yes	complemented
209	#2012	C₂×C₅₉	1	2	yes	—
210	#1984	C₂×C₅₉	1	1	yes	characteristic, complemented
211	#1970	C₂×C₅₉	1	1	yes	characteristic
212	#1969	C₂×C₅₉	1	1	yes	characteristic, complemented
213	#1928	C₂×C₅₉	1	2	yes	complemented
214	#1925	C₂×C₅₉	1	2	yes	complemented
215	C₂×C₅₉	—	16	2	no	—
216	C₂×C₅₉	#2733	1	1	yes	characteristic
217	C₂×C₅₉	#3191	1	1	yes	characteristic
218	C₂×C₅₉	#3203	1	1	yes	characteristic
219	C₂×C₅₉	#3393	1	1	yes	characteristic
220	C₂×C₅₉	#3396	1	1	yes	characteristic
221	C₂×C₅₉	#3402	1	1	yes	characteristic
222	C₂×C₅₉	#3403	1	1	yes	characteristic
223	C₂²×Q₁₆	C₂²×C₅₉	1	1	yes	characteristic
224	C₂²×SD₁₆	C₂²×C₅₉	1	2	yes	—
225	C₂²×D₈	C₂²×C₅₉	1	1	yes	characteristic
226	C₂×#124	C₂²×C₅₉	1	2	yes	—
227	C₂×C₄×Q₈	C₂²×C₅₉	1	1	yes	characteristic
228	C₂×#107	C₂²×C₅₉	1	1	yes	characteristic
229	C₂×#107	C₂²×C₅₉	1	1	yes	characteristic
230	C₂×C₄⋊C₈	C₂²×C₅₉	1	1	yes	characteristic
231	C₂×#103	C₂²×C₅₉	1	2	yes	—
232	C₂×#103	C₂²×C₅₉	1	2	yes	—
233	C₂×#102	C₂²×C₅₉	1	2	yes	—
234	C₂×#102	C₂²×C₅₉	1	2	yes	—
235	C₂×C₄×C₈	C₂²×C₅₉	1	1	yes	characteristic
236	#397	—	2	2	no	—
237	#393	—	2	2	no	—
238	#391	C₂²×C₅₉	1	2	yes	—
239	#391	C₂²×C₅₉	1	2	yes	—
240	#390	C₂²×C₅₉	1	2	yes	—
241	#390	C₂²×C₅₉	1	2	yes	—
242	#388	—	2	2	no	—
243	#388	—	2	2	no	—
244	C₄×C₄⋊C₄	C₂²×C₅₉	1	2	yes	—
245	#340	C₂²×C₅₉	1	2	yes	—
246	#336	C₂²×C₅₉	1	2	yes	—
247	#336	C₂²×C₅₉	1	2	yes	—
248	C₅₉	#32672	1	1	yes	characteristic, direct product factor, Sylow
249	C₂²×Q₈	D₄×C₅₉	1	1	yes	characteristic
250	C₂²×Q₈	C₂³×C₅₉	1	2	yes	—
251	C₂²×D₄	C₂³×C₅₉	1	2	yes	—
252	C₂×Q₁₆	—	2	2	no	—
253	C₂×Q₁₆	—	4	1	no	—
254	C₂×Q₁₆	—	4	1	no	—
255	C₂×SD₁₆	—	4	2	no	—
256	C₂×SD₁₆	—	4	2	no	—
257	C₂×SD₁₆	—	4	2	no	—
258	C₂×D₈	—	2	2	no	—
259	C₂×D₈	—	4	1	no	—
260	C₂×D₈	—	4	1	no	—
261	C₂²×C₈	C₂³×C₅₉	1	2	yes	—
262	C₂²×C₈	C₂³×C₅₉	1	1	yes	characteristic
263	C₂²×C₈	C₂³×C₅₉	1	1	yes	characteristic
264	#124	—	4	2	no	—
265	#124	—	4	2	no	—
266	C₄×Q₈	—	4	1	no	—
267	C₄×Q₈	—	4	1	no	—
268	C₂×C₄⋊C₄	D₄×C₅₉	1	1	yes	characteristic
269	C₂×C₄⋊C₄	D₄×C₅₉	1	2	yes	—
270	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
271	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
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×C₂²⋊C₄	—	2	2	no	—
277	C₂×C₂²⋊C₄	—	2	2	no	—
278	C₂×C₄²	—	2	2	no	—
279	C₂×C₄²	C₂³×C₅₉	1	2	yes	—
280	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
281	#107	—	4	1	no	—
282	#107	—	4	1	no	—
283	C₄⋊C₈	—	4	1	no	—
284	#103	—	2	4	no	—
285	#103	—	4	2	no	—
286	#102	—	2	4	no	—
287	#102	—	4	2	no	—
288	C₄×C₈	—	4	1	no	—
289	#95	—	2	2	no	—
290	#95	—	2	2	no	—
291	#95	—	2	2	no	—
292	#95	—	2	2	no	—
293	#95	—	2	2	no	—
294	C₂⁴	—	2	2	no	—
295	C₂×Q₈	—	2	2	no	—
296	C₂×Q₈	—	2	2	no	—
297	C₂×Q₈	—	2	2	no	—
298	C₂×Q₈	—	2	2	no	—
299	C₂×Q₈	—	2	2	no	—
300	C₂×Q₈	—	2	2	no	—
301	C₂×Q₈	—	2	2	no	—
302	C₂×Q₈	—	4	1	no	—
303	C₂×Q₈	—	4	1	no	—
304	C₂×D₄	—	2	2	no	—
305	C₂×D₄	—	2	2	no	—
306	C₂×D₄	—	2	2	no	—
307	C₂×D₄	—	2	2	no	—
308	C₂×D₄	—	2	2	no	—
309	C₂×D₄	—	2	2	no	—
310	C₂²×C₄	—	2	2	no	—
311	C₂²×C₄	—	2	2	no	—
312	C₂²×C₄	—	2	2	no	—
313	C₂²×C₄	C₂×D₄×C₅₉	1	1	yes	characteristic
314	C₂²×C₄	C₂×D₄×C₅₉	1	2	yes	—
315	C₂²×C₄	C₂×D₄×C₅₉	1	2	yes	—
316	C₂²×C₄	C₂×D₄×C₅₉	1	1	yes	characteristic
317	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
318	Q₁₆	—	4	4	no	—
319	SD₁₆	—	4	8	no	—
320	D₈	—	4	4	no	—
321	C₂×C₈	—	2	1	no	—
322	C₂×C₈	—	2	1	no	—
323	C₂×C₈	—	2	1	no	—
324	C₂×C₈	—	2	1	no	—
325	C₂×C₈	—	2	2	no	—
326	C₂×C₈	—	2	2	no	—
327	C₂×C₈	—	2	2	no	—
328	C₂×C₈	#41×C₅₉	1	2	yes	—
329	C₂×C₈	#41×C₅₉	1	2	yes	—
330	C₄⋊C₄	—	2	2	no	—
331	C₄⋊C₄	—	2	2	no	—
332	C₄⋊C₄	—	2	2	no	—
333	C₄⋊C₄	—	2	2	no	—
334	C₄⋊C₄	—	4	1	no	—
335	C₄⋊C₄	—	4	2	no	—
336	C₂²⋊C₄	—	4	4	no	—
337	C₂²⋊C₄	—	4	4	no	—
338	C₂²⋊C₄	—	4	4	no	—
339	C₂²⋊C₄	—	4	4	no	—
340	C₂²⋊C₄	—	8	2	no	—
341	C₂²⋊C₄	—	8	2	no	—
342	C₄²	—	2	1	no	—
343	C₄²	—	2	1	no	—
344	C₄²	—	2	2	no	—
345	C₄²	—	2	2	no	—
346	C₄²	—	8	2	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	—	4	2	no	—
354	C₂³	C₂²×D₄×C₅₉	1	1	yes	characteristic
355	Q₈	—	4	4	no	—
356	Q₈	—	4	2	no	—
357	Q₈	—	4	2	no	—
358	Q₈	—	4	2	no	—
359	Q₈	—	4	2	no	—
360	D₄	—	4	2	no	—
361	D₄	—	4	2	no	—
362	D₄	—	4	2	no	—
363	D₄	—	4	2	no	—
364	C₂×C₄	—	2	1	no	—
365	C₂×C₄	—	2	1	no	—
366	C₂×C₄	—	2	2	no	—
367	C₂×C₄	—	2	2	no	—
368	C₂×C₄	—	2	1	no	—
369	C₂×C₄	—	2	2	no	—
370	C₂×C₄	—	2	2	no	—
371	C₂×C₄	—	2	2	no	—
372	C₂×C₄	—	2	1	no	—
373	C₂×C₄	—	2	1	no	—
374	C₂×C₄	—	2	2	no	—
375	C₂×C₄	—	4	2	no	—
376	C₂×C₄	—	4	2	no	—
377	C₂×C₄	—	4	2	no	—
378	C₂×C₄	—	4	2	no	—
379	C₂×C₄	—	4	2	no	—
380	C₂×C₄	—	4	2	no	—
381	C₂×C₄	—	4	2	no	—
382	C₂×C₄	—	4	2	no	—
383	C₂×C₄	—	4	2	no	—
384	C₂×C₄	#135×C₅₉	1	2	yes	—
385	C₂×C₄	C₂×#41×C₅₉	1	1	yes	characteristic
386	C₂×C₄	C₂×#41×C₅₉	1	1	yes	characteristic
387	C₂×C₄	H(5,𝔽₂)×C₅₉	1	1	yes	characteristic
388	C₂×C₄	H(5,𝔽₂)×C₅₉	1	1	yes	characteristic
389	C₂×C₄	H(5,𝔽₂)×C₅₉	1	1	yes	characteristic
390	C₂×C₄	H(5,𝔽₂)×C₅₉	1	1	yes	characteristic
391	C₈	—	2	2	no	—
392	C₈	—	2	2	no	—
393	C₈	—	4	2	no	—
394	C₂²	—	8	2	no	—
395	C₂²	—	8	2	no	—
396	C₂²	—	8	2	no	—
397	C₂²	—	8	2	no	—
398	C₂²	—	8	2	no	—
399	C₂²	—	8	2	no	—
400	C₂²	—	8	2	no	—
401	C₂²	C₅₉×#534	1	1	yes	characteristic
402	C₂²	C₅₉×#550	1	1	yes	characteristic
403	C₂²	C₅₉×#550	1	1	yes	characteristic
404	C₂²	C₂×#135×C₅₉	1	1	yes	characteristic
405	C₂²	C₅₉×#575	1	1	yes	characteristic
406	C₂²	C₅₉×#576	1	1	yes	characteristic
407	C₂²	C₅₉×#578	1	1	yes	characteristic
408	C₄	—	2	2	no	—
409	C₄	—	4	2	no	—
410	C₄	—	4	2	no	—
411	C₄	—	4	1	no	—
412	C₄	—	8	2	no	—
413	C₄	—	8	2	no	—
414	C₄	—	8	2	no	—
415	C₄	C₅₉×#538	1	1	yes	characteristic
416	C₄	C₅₉×#538	1	1	yes	characteristic
417	C₄	C₅₉×#555	1	1	yes	characteristic
418	C₄	C₅₉×H(3,𝔽₄)	1	1	yes	characteristic
419	C₂	—	16	2	no	—
420	C₂	C₅₉×#2733	1	1	yes	characteristic
421	C₂	C₅₉×#3191	1	1	yes	characteristic
422	C₂	C₅₉×#3203	1	1	yes	characteristic
423	C₂	C₅₉×#3393	1	1	yes	characteristic
424	C₂	C₅₉×#3396	1	1	yes	characteristic
425	C₂	C₅₉×#3402	1	1	yes	characteristic
426	C₂	C₅₉×#3403	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 ◁ C₂×C₄×Q₈×C₅₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₅₉×#2592	C₂	semidirect
2. C₅₉×#2055	C₂	semidirect
3. C₅₉×#2015	C₂	semidirect
5. C₅₉×#1984	C₂	semidirect
7. C₅₉×#1969	C₂	semidirect
8. C₅₉×#1928	C₂	semidirect
9. C₅₉×#1925	C₂	semidirect
180. #32672	C₅₉	direct (N × H)
206. #2592	C₂×C₅₉	semidirect
207. #2055	C₂×C₅₉	semidirect
208. #2015	C₂×C₅₉	semidirect
210. #1984	C₂×C₅₉	semidirect
212. #1969	C₂×C₅₉	semidirect
213. #1928	C₂×C₅₉	semidirect
214. #1925	C₂×C₅₉	semidirect
248. C₅₉	#32672	direct (N × H)

Maximal subgroups

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

subgroup	index
C₅₉×#2592	2
C₅₉×#2055	2
C₅₉×#2015	2
C₅₉×#2012	2
C₅₉×#1984	2
C₅₉×#1970	2
C₅₉×#1969	2
C₅₉×#1928	2
C₅₉×#1925	2
#32672	59

Subgroups — C59×#32672 #28444781

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₉×#32672 #28444781