Subgroups — C₅₉×#26442 #28438551

Order 15104.

710 conjugacy classes of subgroups.

The subgroup lattice has 412 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅₉×#2551	C₂	1	1	yes	maximal, characteristic
2	C₅₉×#2369	C₂	1	1	yes	maximal, characteristic
3	C₅₉×#2088	C₂	1	2	yes	maximal
4	C₅₉×#2058	C₂	1	2	yes	maximal
5	C₅₉×#1990	C₂	1	1	yes	maximal, characteristic
6	C₅₉×#1988	C₂	1	2	yes	maximal
7	C₅₉×#1987	C₂	1	1	yes	maximal, characteristic
8	C₅₉×#1948	C₂	1	1	yes	maximal, characteristic
9	C₅₉×#1939	C₂	1	1	yes	maximal, characteristic
10	C₅₉×#1919	C₂	1	2	yes	maximal
11	C₄×#106×C₅₉	C₂	1	1	yes	maximal, characteristic
12	C₂×C₄⋊Q₈×C₅₉	—	2	1	no	—
13	C₂×C₄⋊Q₈×C₅₉	C₂²	1	2	yes	—
14	C₂×C₄⋊Q₈×C₅₉	C₂²	1	1	yes	characteristic
15	C₂×#106×C₅₉	C₂²	1	1	yes	characteristic
16	C₂×#106×C₅₉	C₂²	1	2	yes	—
17	C₂×#106×C₅₉	C₂²	1	1	yes	characteristic
18	C₂×C₄⋊C₈×C₅₉	C₂²	1	1	yes	characteristic
19	C₂×C₄⋊C₈×C₅₉	C₂²	1	2	yes	—
20	C₂×C₄×C₈×C₅₉	C₂²	1	1	yes	characteristic
21	C₅₉×#395	—	2	2	no	—
22	C₅₉×#391	—	2	2	no	—
23	C₅₉×#389	—	2	1	no	—
24	C₅₉×#389	—	2	1	no	—
25	C₅₉×#389	C₂²	1	2	yes	—
26	C₅₉×#389	C₂²	1	2	yes	—
27	C₅₉×#384	C₂²	1	1	yes	characteristic
28	C₄×C₄⋊C₄×C₅₉	—	2	1	no	—
29	C₄×C₄⋊C₄×C₅₉	C₂²	1	1	yes	characteristic
30	C₄×C₄⋊C₄×C₅₉	C₂²	1	2	yes	—
31	C₄×C₄⋊C₄×C₅₉	C₂²	1	1	yes	characteristic
32	C₄×C₄⋊C₄×C₅₉	C₂²	1	1	yes	characteristic
33	C₅₉×#340	C₂²	1	2	yes	—
34	C₅₉×#340	C₂²	1	2	yes	—
35	C₅₉×#340	C₂²	1	1	yes	characteristic
36	C₅₉×#340	C₂²	1	2	yes	—
37	C₅₉×#340	C₂²	1	2	yes	—
38	C₅₉×#340	C₂²	1	2	yes	—
39	C₅₉×#340	C₂²	1	1	yes	characteristic
40	C₅₉×#336	C₂²	1	2	yes	—
41	C₂²×Q₈×C₅₉	—	2	1	no	—
42	C₂²×Q₈×C₅₉	—	2	2	no	—
43	C₂²×C₈×C₅₉	C₂³	1	2	yes	—
44	C₂²×C₈×C₅₉	C₂³	1	1	yes	characteristic
45	C₂²×C₈×C₅₉	C₂³	1	1	yes	characteristic
46	C₄⋊Q₈×C₅₉	—	2	4	no	—
47	C₄⋊Q₈×C₅₉	—	2	2	no	—
48	C₄⋊Q₈×C₅₉	—	4	2	no	—
49	C₄⋊Q₈×C₅₉	—	4	4	no	—
50	C₄⋊Q₈×C₅₉	Q₈	1	4	yes	complemented
51	C₂×C₄⋊C₄×C₅₉	—	2	1	no	—
52	C₂×C₄⋊C₄×C₅₉	—	2	1	no	—
53	C₂×C₄⋊C₄×C₅₉	—	2	2	no	—
54	C₂×C₄⋊C₄×C₅₉	—	2	2	no	—
55	C₂×C₄⋊C₄×C₅₉	—	2	1	no	—
56	C₂×C₄⋊C₄×C₅₉	—	2	2	no	—
57	C₂×C₄⋊C₄×C₅₉	D₄	1	1	yes	characteristic
58	C₂×C₄⋊C₄×C₅₉	D₄	1	1	yes	characteristic
59	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
60	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
61	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
62	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
63	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
64	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
65	C₂×C₄²×C₅₉	—	2	1	no	—
66	C₂×C₄²×C₅₉	—	2	1	no	—
67	C₂×C₄²×C₅₉	—	2	2	no	—
68	C₂×C₄²×C₅₉	C₂³	1	2	yes	—
69	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
70	#106×C₅₉	—	2	2	no	—
71	#106×C₅₉	—	4	2	no	—
72	#106×C₅₉	Q₈	1	4	yes	complemented
73	C₄⋊C₈×C₅₉	—	2	2	no	—
74	C₄⋊C₈×C₅₉	—	4	2	no	—
75	C₄×C₈×C₅₉	—	2	2	no	—
76	#95×C₅₉	—	2	2	no	—
77	#95×C₅₉	—	2	2	no	—
78	#95×C₅₉	—	2	1	no	—
79	#95×C₅₉	—	2	1	no	—
80	#95×C₅₉	—	2	2	no	—
81	#95×C₅₉	D₄	1	2	yes	—
82	C₂×Q₈×C₅₉	—	2	4	no	—
83	C₂×Q₈×C₅₉	—	4	4	no	—
84	C₂×Q₈×C₅₉	—	4	4	no	—
85	C₂×Q₈×C₅₉	—	8	2	no	—
86	C₂×Q₈×C₅₉	—	8	1	no	—
87	C₂×Q₈×C₅₉	—	8	1	no	—
88	C₂²×C₄×C₅₉	—	2	1	no	—
89	C₂²×C₄×C₅₉	—	2	1	no	—
90	C₂²×C₄×C₅₉	—	2	2	no	—
91	C₂²×C₄×C₅₉	—	2	1	no	—
92	C₂²×C₄×C₅₉	—	2	1	no	—
93	C₂²×C₄×C₅₉	—	2	2	no	—
94	C₂²×C₄×C₅₉	C₂×D₄	1	2	yes	—
95	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
96	C₂²×C₄×C₅₉	C₂×D₄	1	2	yes	—
97	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
98	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
99	C₂×C₈×C₅₉	—	2	1	no	—
100	C₂×C₈×C₅₉	—	2	1	no	—
101	C₂×C₈×C₅₉	—	2	1	no	—
102	C₂×C₈×C₅₉	—	2	2	no	—
103	C₂×C₈×C₅₉	—	2	1	no	—
104	C₂×C₈×C₅₉	—	2	2	no	—
105	C₂×C₈×C₅₉	—	2	2	no	—
106	C₂×C₈×C₅₉	—	2	1	no	—
107	C₂×C₈×C₅₉	C₂×Q₈	1	2	yes	—
108	C₄⋊C₄×C₅₉	—	2	4	no	—
109	C₄⋊C₄×C₅₉	—	2	2	no	—
110	C₄⋊C₄×C₅₉	—	2	2	no	—
111	C₄⋊C₄×C₅₉	—	2	1	no	—
112	C₄⋊C₄×C₅₉	—	2	1	no	—
113	C₄⋊C₄×C₅₉	—	2	1	no	—
114	C₄⋊C₄×C₅₉	—	2	1	no	—
115	C₄⋊C₄×C₅₉	—	2	2	no	—
116	C₄⋊C₄×C₅₉	—	2	1	no	—
117	C₄⋊C₄×C₅₉	—	2	2	no	—
118	C₄⋊C₄×C₅₉	—	4	4	no	—
119	C₄⋊C₄×C₅₉	—	4	4	no	—
120	C₄⋊C₄×C₅₉	—	4	2	no	—
121	C₄⋊C₄×C₅₉	—	8	1	no	—
122	C₄⋊C₄×C₅₉	—	8	2	no	—
123	C₄⋊C₄×C₅₉	SD₁₆	1	4	yes	—
124	C₄⋊C₄×C₅₉	C₂×Q₈	1	2	yes	—
125	C₄⋊C₄×C₅₉	C₂×Q₈	1	2	yes	—
126	C₄⋊C₄×C₅₉	C₂×Q₈	1	4	yes	—
127	C₄⋊C₄×C₅₉	#41	1	2	yes	—
128	C₄²×C₅₉	—	2	2	no	—
129	C₄²×C₅₉	—	2	2	no	—
130	C₄²×C₅₉	—	4	2	no	—
131	C₄²×C₅₉	—	4	2	no	—
132	C₄²×C₅₉	—	8	2	no	—
133	C₄²×C₅₉	C₂×Q₈	1	2	yes	—
134	C₄²×C₅₉	#41	1	2	yes	—
135	C₂³×C₅₉	C₂²×D₄	1	1	yes	characteristic
136	Q₈×C₅₉	—	8	4	no	—
137	Q₈×C₅₉	—	8	8	no	—
138	C₂×C₄×C₅₉	—	2	2	no	—
139	C₂×C₄×C₅₉	—	2	2	no	—
140	C₂×C₄×C₅₉	—	2	1	no	—
141	C₂×C₄×C₅₉	—	2	1	no	—
142	C₂×C₄×C₅₉	—	2	4	no	—
143	C₂×C₄×C₅₉	—	2	2	no	—
144	C₂×C₄×C₅₉	—	2	2	no	—
145	C₂×C₄×C₅₉	—	2	2	no	—
146	C₂×C₄×C₅₉	—	2	2	no	—
147	C₂×C₄×C₅₉	—	2	2	no	—
148	C₂×C₄×C₅₉	—	2	2	no	—
149	C₂×C₄×C₅₉	—	4	1	no	—
150	C₂×C₄×C₅₉	—	4	1	no	—
151	C₂×C₄×C₅₉	—	4	1	no	—
152	C₂×C₄×C₅₉	—	4	1	no	—
153	C₂×C₄×C₅₉	—	4	2	no	—
154	C₂×C₄×C₅₉	—	4	1	no	—
155	C₂×C₄×C₅₉	—	4	2	no	—
156	C₂×C₄×C₅₉	—	4	1	no	—
157	C₂×C₄×C₅₉	—	4	2	no	—
158	C₂×C₄×C₅₉	—	4	1	no	—
159	C₂×C₄×C₅₉	—	4	2	no	—
160	C₂×C₄×C₅₉	—	4	1	no	—
161	C₂×C₄×C₅₉	—	4	2	no	—
162	C₂×C₄×C₅₉	—	4	1	no	—
163	C₂×C₄×C₅₉	C₂²⋊Q₈	1	2	yes	—
164	C₂×C₄×C₅₉	C₂²⋊Q₈	1	2	yes	—
165	C₂×C₄×C₅₉	C₂×SD₁₆	1	4	yes	—
166	C₂×C₄×C₅₉	C₂×SD₁₆	1	2	yes	—
167	C₂×C₄×C₅₉	#137	1	2	yes	—
168	C₂×C₄×C₅₉	C₂²×Q₈	1	1	yes	characteristic
169	C₂×C₄×C₅₉	C₂²×Q₈	1	1	yes	characteristic
170	C₂×C₄×C₅₉	C₂×#41	1	1	yes	characteristic
171	C₂×C₄×C₅₉	C₂×#41	1	1	yes	characteristic
172	C₂×C₄×C₅₉	H(5,𝔽₂)	1	1	yes	characteristic
173	C₂×C₄×C₅₉	2₋¹⁺⁴	1	1	yes	characteristic
174	C₈×C₅₉	—	2	2	no	—
175	C₈×C₅₉	—	4	1	no	—
176	C₈×C₅₉	—	4	2	no	—
177	#26442	C₅₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
178	C₂²×C₅₉	C₂×C₂²⋊Q₈	1	1	yes	characteristic
179	C₂²×C₅₉	#546	1	1	yes	characteristic
180	C₂²×C₅₉	D₄×Q₈	1	1	yes	characteristic
181	C₂²×C₅₉	C₂²×SD₁₆	1	1	yes	characteristic
182	C₂²×C₅₉	C₂×#137	1	1	yes	characteristic
183	C₂²×C₅₉	#576	1	1	yes	characteristic
184	C₂²×C₅₉	#577	1	1	yes	characteristic
185	C₄×C₅₉	—	2	2	no	—
186	C₄×C₅₉	—	2	4	no	—
187	C₄×C₅₉	—	4	2	no	—
188	C₄×C₅₉	—	4	4	no	—
189	C₄×C₅₉	—	4	2	no	—
190	C₄×C₅₉	—	4	2	no	—
191	C₄×C₅₉	—	4	2	no	—
192	C₄×C₅₉	—	8	1	no	—
193	C₄×C₅₉	—	8	2	no	—
194	C₄×C₅₉	#475	1	4	yes	—
195	C₄×C₅₉	#533	1	1	yes	characteristic
196	C₄×C₅₉	#542	1	1	yes	characteristic
197	C₄×C₅₉	#557	1	1	yes	characteristic
198	C₄×C₅₉	Q₈²	1	1	yes	characteristic
199	#2551	C₂×C₅₉	1	1	yes	characteristic
200	#2369	C₂×C₅₉	1	1	yes	characteristic
201	#2088	C₂×C₅₉	1	2	yes	—
202	#2058	C₂×C₅₉	1	2	yes	—
203	#1990	C₂×C₅₉	1	1	yes	characteristic
204	#1988	C₂×C₅₉	1	2	yes	—
205	#1987	C₂×C₅₉	1	1	yes	characteristic
206	#1948	C₂×C₅₉	1	1	yes	characteristic
207	#1939	C₂×C₅₉	1	1	yes	characteristic
208	#1919	C₂×C₅₉	1	2	yes	—
209	C₄×#106	C₂×C₅₉	1	1	yes	characteristic
210	C₂×C₅₉	#2451	1	1	yes	characteristic
211	C₂×C₅₉	C₂×#475	1	1	yes	characteristic
212	C₂×C₅₉	#3081	1	1	yes	characteristic
213	C₂×C₅₉	#3295	1	1	yes	characteristic
214	C₂×C₅₉	#3329	1	1	yes	characteristic
215	C₂×C₅₉	Q₈×SD₁₆	1	1	yes	characteristic
216	C₂×C₅₉	#3385	1	1	yes	characteristic
217	C₂×C₄⋊Q₈	—	2	1	no	—
218	C₂×C₄⋊Q₈	C₂²×C₅₉	1	2	yes	—
219	C₂×C₄⋊Q₈	C₂²×C₅₉	1	1	yes	characteristic
220	C₂×#106	C₂²×C₅₉	1	1	yes	characteristic
221	C₂×#106	C₂²×C₅₉	1	2	yes	—
222	C₂×#106	C₂²×C₅₉	1	1	yes	characteristic
223	C₂×C₄⋊C₈	C₂²×C₅₉	1	1	yes	characteristic
224	C₂×C₄⋊C₈	C₂²×C₅₉	1	2	yes	—
225	C₂×C₄×C₈	C₂²×C₅₉	1	1	yes	characteristic
226	#395	—	2	2	no	—
227	#391	—	2	2	no	—
228	#389	—	2	1	no	—
229	#389	—	2	1	no	—
230	#389	C₂²×C₅₉	1	2	yes	—
231	#389	C₂²×C₅₉	1	2	yes	—
232	#384	C₂²×C₅₉	1	1	yes	characteristic
233	C₄×C₄⋊C₄	—	2	1	no	—
234	C₄×C₄⋊C₄	C₂²×C₅₉	1	2	yes	—
235	C₄×C₄⋊C₄	C₂²×C₅₉	1	1	yes	characteristic
236	C₄×C₄⋊C₄	C₂²×C₅₉	1	1	yes	characteristic
237	C₄×C₄⋊C₄	C₂²×C₅₉	1	1	yes	characteristic
238	#340	C₂²×C₅₉	1	2	yes	—
239	#340	C₂²×C₅₉	1	2	yes	—
240	#340	C₂²×C₅₉	1	1	yes	characteristic
241	#340	C₂²×C₅₉	1	2	yes	—
242	#340	C₂²×C₅₉	1	2	yes	—
243	#340	C₂²×C₅₉	1	2	yes	—
244	#340	C₂²×C₅₉	1	1	yes	characteristic
245	#336	C₂²×C₅₉	1	2	yes	—
246	C₅₉	#26442	1	1	yes	characteristic, direct product factor, Sylow
247	C₂²×Q₈	—	2	1	no	—
248	C₂²×Q₈	—	2	2	no	—
249	C₂²×C₈	C₂³×C₅₉	1	2	yes	—
250	C₂²×C₈	C₂³×C₅₉	1	1	yes	characteristic
251	C₂²×C₈	C₂³×C₅₉	1	1	yes	characteristic
252	C₄⋊Q₈	—	2	4	no	—
253	C₄⋊Q₈	—	2	2	no	—
254	C₄⋊Q₈	—	4	2	no	—
255	C₄⋊Q₈	—	4	4	no	—
256	C₄⋊Q₈	Q₈×C₅₉	1	4	yes	complemented
257	C₂×C₄⋊C₄	—	2	1	no	—
258	C₂×C₄⋊C₄	—	2	1	no	—
259	C₂×C₄⋊C₄	—	2	2	no	—
260	C₂×C₄⋊C₄	—	2	2	no	—
261	C₂×C₄⋊C₄	—	2	1	no	—
262	C₂×C₄⋊C₄	—	2	2	no	—
263	C₂×C₄⋊C₄	D₄×C₅₉	1	1	yes	characteristic
264	C₂×C₄⋊C₄	D₄×C₅₉	1	1	yes	characteristic
265	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
266	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
267	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
268	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
269	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
270	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
271	C₂×C₄²	—	2	1	no	—
272	C₂×C₄²	—	2	1	no	—
273	C₂×C₄²	—	2	2	no	—
274	C₂×C₄²	C₂³×C₅₉	1	2	yes	—
275	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
276	#106	—	2	2	no	—
277	#106	—	4	2	no	—
278	#106	Q₈×C₅₉	1	4	yes	complemented
279	C₄⋊C₈	—	2	2	no	—
280	C₄⋊C₈	—	4	2	no	—
281	C₄×C₈	—	2	2	no	—
282	#95	—	2	2	no	—
283	#95	—	2	2	no	—
284	#95	—	2	1	no	—
285	#95	—	2	1	no	—
286	#95	—	2	2	no	—
287	#95	D₄×C₅₉	1	2	yes	—
288	C₂×Q₈	—	2	4	no	—
289	C₂×Q₈	—	4	4	no	—
290	C₂×Q₈	—	4	4	no	—
291	C₂×Q₈	—	8	2	no	—
292	C₂×Q₈	—	8	1	no	—
293	C₂×Q₈	—	8	1	no	—
294	C₂²×C₄	—	2	1	no	—
295	C₂²×C₄	—	2	1	no	—
296	C₂²×C₄	—	2	2	no	—
297	C₂²×C₄	—	2	1	no	—
298	C₂²×C₄	—	2	1	no	—
299	C₂²×C₄	—	2	2	no	—
300	C₂²×C₄	C₂×D₄×C₅₉	1	2	yes	—
301	C₂²×C₄	C₂×D₄×C₅₉	1	1	yes	characteristic
302	C₂²×C₄	C₂×D₄×C₅₉	1	2	yes	—
303	C₂²×C₄	C₂×D₄×C₅₉	1	1	yes	characteristic
304	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
305	C₂×C₈	—	2	1	no	—
306	C₂×C₈	—	2	1	no	—
307	C₂×C₈	—	2	1	no	—
308	C₂×C₈	—	2	2	no	—
309	C₂×C₈	—	2	1	no	—
310	C₂×C₈	—	2	2	no	—
311	C₂×C₈	—	2	2	no	—
312	C₂×C₈	—	2	1	no	—
313	C₂×C₈	C₂×Q₈×C₅₉	1	2	yes	—
314	C₄⋊C₄	—	2	4	no	—
315	C₄⋊C₄	—	2	2	no	—
316	C₄⋊C₄	—	2	2	no	—
317	C₄⋊C₄	—	2	1	no	—
318	C₄⋊C₄	—	2	1	no	—
319	C₄⋊C₄	—	2	1	no	—
320	C₄⋊C₄	—	2	1	no	—
321	C₄⋊C₄	—	2	2	no	—
322	C₄⋊C₄	—	2	1	no	—
323	C₄⋊C₄	—	2	2	no	—
324	C₄⋊C₄	—	4	4	no	—
325	C₄⋊C₄	—	4	4	no	—
326	C₄⋊C₄	—	4	2	no	—
327	C₄⋊C₄	—	8	1	no	—
328	C₄⋊C₄	—	8	2	no	—
329	C₄⋊C₄	SD₁₆×C₅₉	1	4	yes	—
330	C₄⋊C₄	C₂×Q₈×C₅₉	1	2	yes	—
331	C₄⋊C₄	C₂×Q₈×C₅₉	1	2	yes	—
332	C₄⋊C₄	C₂×Q₈×C₅₉	1	4	yes	—
333	C₄⋊C₄	#41×C₅₉	1	2	yes	—
334	C₄²	—	2	2	no	—
335	C₄²	—	2	2	no	—
336	C₄²	—	4	2	no	—
337	C₄²	—	4	2	no	—
338	C₄²	—	8	2	no	—
339	C₄²	C₂×Q₈×C₅₉	1	2	yes	—
340	C₄²	#41×C₅₉	1	2	yes	—
341	C₂³	C₂²×D₄×C₅₉	1	1	yes	characteristic
342	Q₈	—	8	4	no	—
343	Q₈	—	8	8	no	—
344	C₂×C₄	—	2	2	no	—
345	C₂×C₄	—	2	2	no	—
346	C₂×C₄	—	2	1	no	—
347	C₂×C₄	—	2	1	no	—
348	C₂×C₄	—	2	4	no	—
349	C₂×C₄	—	2	2	no	—
350	C₂×C₄	—	2	2	no	—
351	C₂×C₄	—	2	2	no	—
352	C₂×C₄	—	2	2	no	—
353	C₂×C₄	—	2	2	no	—
354	C₂×C₄	—	2	2	no	—
355	C₂×C₄	—	4	1	no	—
356	C₂×C₄	—	4	1	no	—
357	C₂×C₄	—	4	1	no	—
358	C₂×C₄	—	4	1	no	—
359	C₂×C₄	—	4	2	no	—
360	C₂×C₄	—	4	1	no	—
361	C₂×C₄	—	4	2	no	—
362	C₂×C₄	—	4	1	no	—
363	C₂×C₄	—	4	2	no	—
364	C₂×C₄	—	4	1	no	—
365	C₂×C₄	—	4	2	no	—
366	C₂×C₄	—	4	1	no	—
367	C₂×C₄	—	4	2	no	—
368	C₂×C₄	—	4	1	no	—
369	C₂×C₄	C₂²⋊Q₈×C₅₉	1	2	yes	—
370	C₂×C₄	C₂²⋊Q₈×C₅₉	1	2	yes	—
371	C₂×C₄	C₂×SD₁₆×C₅₉	1	4	yes	—
372	C₂×C₄	C₂×SD₁₆×C₅₉	1	2	yes	—
373	C₂×C₄	#137×C₅₉	1	2	yes	—
374	C₂×C₄	C₂²×Q₈×C₅₉	1	1	yes	characteristic
375	C₂×C₄	C₂²×Q₈×C₅₉	1	1	yes	characteristic
376	C₂×C₄	C₂×#41×C₅₉	1	1	yes	characteristic
377	C₂×C₄	C₂×#41×C₅₉	1	1	yes	characteristic
378	C₂×C₄	H(5,𝔽₂)×C₅₉	1	1	yes	characteristic
379	C₂×C₄	2₋¹⁺⁴×C₅₉	1	1	yes	characteristic
380	C₈	—	2	2	no	—
381	C₈	—	4	1	no	—
382	C₈	—	4	2	no	—
383	C₂²	C₂×C₂²⋊Q₈×C₅₉	1	1	yes	characteristic
384	C₂²	C₅₉×#546	1	1	yes	characteristic
385	C₂²	D₄×Q₈×C₅₉	1	1	yes	characteristic
386	C₂²	C₂²×SD₁₆×C₅₉	1	1	yes	characteristic
387	C₂²	C₂×#137×C₅₉	1	1	yes	characteristic
388	C₂²	C₅₉×#576	1	1	yes	characteristic
389	C₂²	C₅₉×#577	1	1	yes	characteristic
390	C₄	—	2	4	no	—
391	C₄	—	2	2	no	—
392	C₄	—	4	2	no	—
393	C₄	—	4	2	no	—
394	C₄	—	4	4	no	—
395	C₄	—	4	2	no	—
396	C₄	—	4	2	no	—
397	C₄	—	8	2	no	—
398	C₄	—	8	1	no	—
399	C₄	C₅₉×#475	1	4	yes	—
400	C₄	C₅₉×#533	1	1	yes	characteristic
401	C₄	C₅₉×#542	1	1	yes	characteristic
402	C₄	C₅₉×#557	1	1	yes	characteristic
403	C₄	Q₈²×C₅₉	1	1	yes	characteristic
404	C₂	C₅₉×#2451	1	1	yes	characteristic
405	C₂	C₂×C₅₉×#475	1	1	yes	characteristic
406	C₂	C₅₉×#3081	1	1	yes	characteristic
407	C₂	C₅₉×#3295	1	1	yes	characteristic
408	C₂	C₅₉×#3329	1	1	yes	characteristic
409	C₂	Q₈×SD₁₆×C₅₉	1	1	yes	characteristic
410	C₂	C₅₉×#3385	1	1	yes	characteristic

	subgroup	G/H
center, socle, prime radical	C₂³×C₅₉	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₅₉
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
50. C₄⋊Q₈×C₅₉	Q₈	semidirect
72. #106×C₅₉	Q₈	semidirect
177. #26442	C₅₉	direct (N × H)
246. C₅₉	#26442	direct (N × H)
256. C₄⋊Q₈	Q₈×C₅₉	semidirect
278. #106	Q₈×C₅₉	semidirect

Maximal subgroups

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

subgroup	index
C₅₉×#2551	2
C₅₉×#2369	2
C₅₉×#2088	2
C₅₉×#2058	2
C₅₉×#1990	2
C₅₉×#1988	2
C₅₉×#1987	2
C₅₉×#1948	2
C₅₉×#1939	2
C₅₉×#1919	2
C₄×#106×C₅₉	2
#26442	59

Subgroups — C59×#26442 #28438551

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₉×#26442 #28438551