Subgroups — C₅₉×#22130 #28434239

Order 15104.

648 conjugacy classes of subgroups.

The subgroup lattice has 490 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅₉×#3076	C₂	1	1	yes	maximal, characteristic
2	C₅₉×#2960	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅₉×#2922	C₂	1	1	yes	maximal, characteristic
4	C₅₉×#1986	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅₉×#1950	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅₉×#1945	C₂	1	2	yes	maximal, complemented
7	C₅₉×#1937	C₂	1	2	yes	maximal
8	C₅₉×#1929	C₂	1	2	yes	maximal
9	C₅₉×#1922	C₂	1	2	yes	maximal, complemented
10	C₅₉×#1806	C₂	1	1	yes	maximal, characteristic
11	C₈×C₄⋊C₄×C₅₉	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅₉×#533	C₂²	1	1	yes	characteristic
13	C₄×#41×C₅₉	C₂²	1	1	yes	characteristic
14	C₅₉×#479	C₄	1	2	yes	complemented
15	C₅₉×#478	C₄	1	2	yes	complemented
16	C₅₉×#477	C₄	1	1	yes	characteristic, complemented
17	C₅₉×#476	C₄	1	1	yes	characteristic, complemented
18	C₅₉×#475	C₄	1	1	yes	characteristic, complemented
19	C₅₉×#474	C₄	1	1	yes	characteristic, complemented
20	C₅₉×#446	—	2	1	no	—
21	C₅₉×#446	—	2	1	no	—
22	C₈×Q₈×C₅₉	—	2	1	no	—
23	C₈×Q₈×C₅₉	—	2	1	no	—
24	C₅₉×#433	—	2	1	no	—
25	C₅₉×#433	—	2	1	no	—
26	C₅₉×#431	—	2	1	no	—
27	C₅₉×#431	—	2	1	no	—
28	C₂×#108×C₅₉	C₂²	1	2	yes	—
29	C₅₉×#427	C₂²	1	2	yes	—
30	C₅₉×#424	C₂²	1	1	yes	characteristic
31	C₅₉×#424	C₂²	1	1	yes	characteristic
32	C₅₉×#424	C₂²	1	2	yes	—
33	C₅₉×#423	C₂²	1	1	yes	characteristic
34	C₂×C₄⋊C₈×C₅₉	C₂²	1	1	yes	characteristic
35	C₂×#104×C₅₉	C₂²	1	2	yes	—
36	C₅₉×#416	C₂²	1	2	yes	—
37	C₅₉×#408	C₂²	1	1	yes	characteristic
38	C₅₉×#408	C₂²	1	1	yes	characteristic
39	C₅₉×#405	C₂²	1	2	yes	—
40	C₄×M₁₆×C₅₉	C₂²	1	1	yes	characteristic
41	C₂×C₄×C₈×C₅₉	C₂²	1	2	yes	—
42	C₂×C₄×C₈×C₅₉	C₂²	1	1	yes	characteristic
43	C₄×C₄⋊C₄×C₅₉	C₂²	1	1	yes	characteristic
44	C₅₉×#341	C₂²	1	2	yes	—
45	C₅₉×#339	C₂²	1	2	yes	—
46	C₅₉×#339	C₂²	1	2	yes	—
47	C₅₉×#339	C₂²	1	2	yes	—
48	C₅₉×#336	C₂²	1	2	yes	—
49	C₂×#41×C₅₉	C₂³	1	1	yes	characteristic
50	C₂×M₁₆×C₅₉	C₂³	1	1	yes	characteristic
51	C₂×M₁₆×C₅₉	C₂³	1	1	yes	characteristic
52	C₂×M₁₆×C₅₉	C₂³	1	2	yes	—
53	C₂²×C₈×C₅₉	C₂³	1	2	yes	—
54	C₂²×C₈×C₅₉	C₂³	1	1	yes	characteristic
55	C₂²×C₈×C₅₉	C₂³	1	1	yes	characteristic
56	C₄⋊Q₈×C₅₉	C₂×C₄	1	1	yes	characteristic
57	C₄⋊Q₈×C₅₉	C₂×C₄	1	1	yes	characteristic
58	#125×C₅₉	C₂×C₄	1	2	yes	—
59	C₂²⋊Q₈×C₅₉	—	2	1	no	—
60	C₂²⋊Q₈×C₅₉	—	2	1	no	—
61	C₄×Q₈×C₅₉	—	2	1	no	—
62	C₄×Q₈×C₅₉	—	2	1	no	—
63	C₄×Q₈×C₅₉	C₂×C₄	1	1	yes	characteristic
64	C₄×Q₈×C₅₉	C₂×C₄	1	1	yes	characteristic
65	C₄×D₄×C₅₉	—	2	1	no	—
66	C₄×D₄×C₅₉	—	2	1	no	—
67	C₄×D₄×C₅₉	C₂×C₄	1	1	yes	characteristic
68	C₄×D₄×C₅₉	C₂×C₄	1	1	yes	characteristic
69	#117×C₅₉	—	2	1	no	—
70	#117×C₅₉	C₂³	1	2	yes	—
71	#117×C₅₉	C₂³	1	1	yes	characteristic
72	C₂×C₄⋊C₄×C₅₉	—	2	1	no	—
73	C₂×C₄²×C₅₉	—	2	1	no	—
74	C₂×C₄²×C₅₉	C₂³	1	2	yes	—
75	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
76	#108×C₅₉	—	4	2	no	—
77	#107×C₅₉	C₂×C₄	1	2	yes	—
78	#107×C₅₉	C₂×C₄	1	2	yes	—
79	#106×C₅₉	C₂×C₄	1	2	yes	—
80	#106×C₅₉	C₂×C₄	1	2	yes	—
81	C₄⋊C₈×C₅₉	—	2	1	no	—
82	C₄⋊C₈×C₅₉	—	2	1	no	—
83	C₄⋊C₈×C₅₉	—	2	1	no	—
84	C₄⋊C₈×C₅₉	—	2	1	no	—
85	C₄⋊C₈×C₅₉	—	2	2	no	—
86	C₄⋊C₈×C₅₉	—	2	2	no	—
87	C₄⋊C₈×C₅₉	—	2	1	no	—
88	C₄⋊C₈×C₅₉	—	2	1	no	—
89	C₄⋊C₈×C₅₉	C₂×C₄	1	1	yes	characteristic
90	C₄⋊C₈×C₅₉	C₂×C₄	1	1	yes	characteristic
91	C₄⋊C₈×C₅₉	C₂×C₄	1	2	yes	—
92	#104×C₅₉	—	4	2	no	—
93	#103×C₅₉	C₂×C₄	1	2	yes	—
94	#103×C₅₉	C₂×C₄	1	2	yes	—
95	#102×C₅₉	C₂×C₄	1	2	yes	—
96	#102×C₅₉	C₂×C₄	1	2	yes	—
97	C₂²⋊C₈×C₅₉	—	2	1	no	—
98	C₂²⋊C₈×C₅₉	—	2	1	no	—
99	C₂²⋊C₈×C₅₉	—	2	1	no	—
100	C₂²⋊C₈×C₅₉	—	2	1	no	—
101	#97×C₅₉	—	2	2	no	—
102	#97×C₅₉	—	2	1	no	—
103	C₄×C₈×C₅₉	—	2	2	no	—
104	C₄×C₈×C₅₉	—	2	1	no	—
105	C₄×C₈×C₅₉	—	4	2	no	—
106	C₄×C₈×C₅₉	D₄	1	1	yes	characteristic
107	C₄×C₈×C₅₉	D₄	1	1	yes	characteristic
108	C₄×C₈×C₅₉	D₄	1	1	yes	characteristic
109	C₄×C₈×C₅₉	D₄	1	1	yes	characteristic
110	#95×C₅₉	—	2	1	no	—
111	#41×C₅₉	—	2	1	no	—
112	#41×C₅₉	—	2	1	no	—
113	#41×C₅₉	—	2	1	no	—
114	#41×C₅₉	—	2	1	no	—
115	C₂×Q₈×C₅₉	—	2	1	no	—
116	C₂×Q₈×C₅₉	—	2	1	no	—
117	C₂×Q₈×C₅₉	C₂²×C₄	1	1	yes	characteristic
118	C₂×D₄×C₅₉	—	2	1	no	—
119	C₂×D₄×C₅₉	C₂²×C₄	1	1	yes	characteristic
120	C₂²×C₄×C₅₉	—	2	2	no	—
121	C₂²×C₄×C₅₉	—	2	1	no	—
122	C₂²×C₄×C₅₉	—	2	1	no	—
123	C₂²×C₄×C₅₉	—	2	1	no	—
124	C₂²×C₄×C₅₉	#41	1	1	yes	characteristic
125	C₂²×C₄×C₅₉	#41	1	1	yes	characteristic
126	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
127	M₁₆×C₅₉	—	2	2	no	—
128	M₁₆×C₅₉	—	2	1	no	—
129	M₁₆×C₅₉	—	2	1	no	—
130	M₁₆×C₅₉	—	2	1	no	—
131	M₁₆×C₅₉	—	2	1	no	—
132	M₁₆×C₅₉	—	2	2	no	—
133	C₂×C₈×C₅₉	—	2	1	no	—
134	C₂×C₈×C₅₉	—	2	2	no	—
135	C₂×C₈×C₅₉	—	2	2	no	—
136	C₂×C₈×C₅₉	—	2	1	no	—
137	C₂×C₈×C₅₉	—	2	1	no	—
138	C₂×C₈×C₅₉	—	2	1	no	—
139	C₂×C₈×C₅₉	—	2	1	no	—
140	C₂×C₈×C₅₉	—	2	1	no	—
141	C₂×C₈×C₅₉	—	2	2	no	—
142	C₂×C₈×C₅₉	C₂²×C₄	1	2	yes	—
143	C₂×C₈×C₅₉	C₂²×C₄	1	2	yes	—
144	C₂×C₈×C₅₉	C₂×D₄	1	1	yes	characteristic
145	C₂×C₈×C₅₉	C₂×D₄	1	1	yes	characteristic
146	C₂×C₈×C₅₉	C₂×D₄	1	1	yes	characteristic
147	C₂×C₈×C₅₉	C₂×D₄	1	1	yes	characteristic
148	C₄⋊C₄×C₅₉	—	2	4	no	—
149	C₄⋊C₄×C₅₉	—	2	1	no	—
150	C₄⋊C₄×C₅₉	—	2	1	no	—
151	C₄⋊C₄×C₅₉	—	2	2	no	—
152	C₄⋊C₄×C₅₉	—	2	2	no	—
153	C₄⋊C₄×C₅₉	—	2	1	no	—
154	C₄⋊C₄×C₅₉	—	2	1	no	—
155	C₄⋊C₄×C₅₉	C₂²×C₄	1	2	yes	—
156	C₄⋊C₄×C₅₉	C₂²×C₄	1	2	yes	—
157	C₄⋊C₄×C₅₉	C₂²×C₄	1	1	yes	characteristic
158	C₄⋊C₄×C₅₉	C₂²×C₄	1	1	yes	characteristic
159	C₂²⋊C₄×C₅₉	—	2	1	no	—
160	C₂²⋊C₄×C₅₉	—	2	2	no	—
161	C₂²⋊C₄×C₅₉	—	2	1	no	—
162	C₂²⋊C₄×C₅₉	—	2	1	no	—
163	C₄²×C₅₉	—	2	1	no	—
164	C₄²×C₅₉	—	2	1	no	—
165	C₄²×C₅₉	—	2	2	no	—
166	C₄²×C₅₉	—	2	1	no	—
167	C₄²×C₅₉	—	2	2	no	—
168	C₄²×C₅₉	—	2	2	no	—
169	C₄²×C₅₉	C₂²×C₄	1	1	yes	characteristic
170	C₄²×C₅₉	C₂²×C₄	1	1	yes	characteristic
171	C₄²×C₅₉	C₂×D₄	1	1	yes	characteristic
172	C₄²×C₅₉	C₂×D₄	1	1	yes	characteristic
173	C₂³×C₅₉	—	2	1	no	—
174	C₂³×C₅₉	C₂×#41	1	1	yes	characteristic
175	Q₈×C₅₉	—	2	1	no	—
176	Q₈×C₅₉	—	2	1	no	—
177	Q₈×C₅₉	—	4	2	no	—
178	Q₈×C₅₉	—	4	2	no	—
179	D₄×C₅₉	—	2	1	no	—
180	D₄×C₅₉	—	2	1	no	—
181	D₄×C₅₉	—	4	1	no	—
182	D₄×C₅₉	—	4	1	no	—
183	C₂×C₄×C₅₉	—	2	2	no	—
184	C₂×C₄×C₅₉	—	2	4	no	—
185	C₂×C₄×C₅₉	—	2	1	no	—
186	C₂×C₄×C₅₉	—	2	1	no	—
187	C₂×C₄×C₅₉	—	2	1	no	—
188	C₂×C₄×C₅₉	—	2	2	no	—
189	C₂×C₄×C₅₉	—	2	2	no	—
190	C₂×C₄×C₅₉	—	4	1	no	—
191	C₂×C₄×C₅₉	—	4	2	no	—
192	C₂×C₄×C₅₉	—	4	2	no	—
193	C₂×C₄×C₅₉	—	4	2	no	—
194	C₂×C₄×C₅₉	—	4	1	no	—
195	C₂×C₄×C₅₉	—	4	1	no	—
196	C₂×C₄×C₅₉	—	4	2	no	—
197	C₂×C₄×C₅₉	C₄×D₄	1	1	yes	characteristic
198	C₂×C₄×C₅₉	C₄×D₄	1	1	yes	characteristic
199	C₂×C₄×C₅₉	C₄×D₄	1	1	yes	characteristic
200	C₂×C₄×C₅₉	C₄×D₄	1	1	yes	characteristic
201	C₂×C₄×C₅₉	C₂³×C₄	1	1	yes	characteristic
202	C₂×C₄×C₅₉	C₂²×D₄	1	1	yes	characteristic
203	C₂×C₄×C₅₉	H(5,𝔽₂)	1	1	yes	characteristic
204	C₂×C₄×C₅₉	2₋¹⁺⁴	1	1	yes	characteristic
205	C₂×C₄×C₅₉	2₋¹⁺⁴	1	1	yes	characteristic
206	C₂×C₄×C₅₉	2₋¹⁺⁴	1	1	yes	characteristic
207	C₈×C₅₉	—	2	2	no	—
208	C₈×C₅₉	—	2	2	no	—
209	C₈×C₅₉	—	2	1	no	—
210	C₈×C₅₉	—	2	1	no	—
211	C₈×C₅₉	—	2	1	no	—
212	C₈×C₅₉	—	2	1	no	—
213	C₈×C₅₉	—	4	1	no	—
214	C₈×C₅₉	—	4	1	no	—
215	C₈×C₅₉	—	4	2	no	—
216	#22130	C₅₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
217	C₂²×C₅₉	—	2	1	no	—
218	C₂²×C₅₉	—	2	1	no	—
219	C₂²×C₅₉	—	4	1	no	—
220	C₂²×C₅₉	—	4	1	no	—
221	C₂²×C₅₉	—	4	1	no	—
222	C₂²×C₅₉	C₂×C₄×D₄	1	1	yes	characteristic
223	C₂²×C₅₉	#541	1	1	yes	characteristic
224	C₂²×C₅₉	#542	1	1	yes	characteristic
225	C₄×C₅₉	—	2	1	no	—
226	C₄×C₅₉	—	2	1	no	—
227	C₄×C₅₉	—	2	1	no	—
228	C₄×C₅₉	—	4	4	no	—
229	C₄×C₅₉	—	4	1	no	—
230	C₄×C₅₉	—	4	1	no	—
231	C₄×C₅₉	—	4	2	no	—
232	C₄×C₅₉	—	4	1	no	—
233	C₄×C₅₉	—	4	2	no	—
234	C₄×C₅₉	#443	1	2	yes	—
235	C₄×C₅₉	#519	1	1	yes	characteristic
236	C₄×C₅₉	#520	1	1	yes	characteristic
237	C₄×C₅₉	#536	1	1	yes	characteristic
238	C₄×C₅₉	#537	1	1	yes	characteristic
239	#3076	C₂×C₅₉	1	1	yes	characteristic
240	#2960	C₂×C₅₉	1	1	yes	characteristic, complemented
241	#2922	C₂×C₅₉	1	1	yes	characteristic
242	#1986	C₂×C₅₉	1	1	yes	characteristic, complemented
243	#1950	C₂×C₅₉	1	1	yes	characteristic, complemented
244	#1945	C₂×C₅₉	1	2	yes	complemented
245	#1937	C₂×C₅₉	1	2	yes	—
246	#1929	C₂×C₅₉	1	2	yes	—
247	#1922	C₂×C₅₉	1	2	yes	complemented
248	#1806	C₂×C₅₉	1	1	yes	characteristic
249	C₈×C₄⋊C₄	C₂×C₅₉	1	1	yes	characteristic, complemented
250	C₂×C₅₉	—	2	1	no	—
251	C₂×C₅₉	—	2	1	no	—
252	C₂×C₅₉	—	8	1	no	—
253	C₂×C₅₉	#2323	1	1	yes	characteristic
254	C₂×C₅₉	C₂×#443	1	1	yes	characteristic
255	C₂×C₅₉	#2955	1	1	yes	characteristic
256	#533	C₂²×C₅₉	1	1	yes	characteristic
257	C₄×#41	C₂²×C₅₉	1	1	yes	characteristic
258	#479	C₄×C₅₉	1	2	yes	complemented
259	#478	C₄×C₅₉	1	2	yes	complemented
260	#477	C₄×C₅₉	1	1	yes	characteristic, complemented
261	#476	C₄×C₅₉	1	1	yes	characteristic, complemented
262	#475	C₄×C₅₉	1	1	yes	characteristic, complemented
263	#474	C₄×C₅₉	1	1	yes	characteristic, complemented
264	#446	—	2	1	no	—
265	#446	—	2	1	no	—
266	C₈×Q₈	—	2	1	no	—
267	C₈×Q₈	—	2	1	no	—
268	#433	—	2	1	no	—
269	#433	—	2	1	no	—
270	#431	—	2	1	no	—
271	#431	—	2	1	no	—
272	C₂×#108	C₂²×C₅₉	1	2	yes	—
273	#427	C₂²×C₅₉	1	2	yes	—
274	#424	C₂²×C₅₉	1	1	yes	characteristic
275	#424	C₂²×C₅₉	1	1	yes	characteristic
276	#424	C₂²×C₅₉	1	2	yes	—
277	#423	C₂²×C₅₉	1	1	yes	characteristic
278	C₂×C₄⋊C₈	C₂²×C₅₉	1	1	yes	characteristic
279	C₂×#104	C₂²×C₅₉	1	2	yes	—
280	#416	C₂²×C₅₉	1	2	yes	—
281	#408	C₂²×C₅₉	1	1	yes	characteristic
282	#408	C₂²×C₅₉	1	1	yes	characteristic
283	#405	C₂²×C₅₉	1	2	yes	—
284	C₄×M₁₆	C₂²×C₅₉	1	1	yes	characteristic
285	C₂×C₄×C₈	C₂²×C₅₉	1	2	yes	—
286	C₂×C₄×C₈	C₂²×C₅₉	1	1	yes	characteristic
287	C₄×C₄⋊C₄	C₂²×C₅₉	1	1	yes	characteristic
288	#341	C₂²×C₅₉	1	2	yes	—
289	#339	C₂²×C₅₉	1	2	yes	—
290	#339	C₂²×C₅₉	1	2	yes	—
291	#339	C₂²×C₅₉	1	2	yes	—
292	#336	C₂²×C₅₉	1	2	yes	—
293	C₅₉	#22130	1	1	yes	characteristic, direct product factor, Sylow
294	C₂×#41	C₂³×C₅₉	1	1	yes	characteristic
295	C₂×M₁₆	C₂³×C₅₉	1	1	yes	characteristic
296	C₂×M₁₆	C₂³×C₅₉	1	1	yes	characteristic
297	C₂×M₁₆	C₂³×C₅₉	1	2	yes	—
298	C₂²×C₈	C₂³×C₅₉	1	2	yes	—
299	C₂²×C₈	C₂³×C₅₉	1	1	yes	characteristic
300	C₂²×C₈	C₂³×C₅₉	1	1	yes	characteristic
301	C₄⋊Q₈	C₂×C₄×C₅₉	1	1	yes	characteristic
302	C₄⋊Q₈	C₂×C₄×C₅₉	1	1	yes	characteristic
303	#125	C₂×C₄×C₅₉	1	2	yes	—
304	C₂²⋊Q₈	—	2	1	no	—
305	C₂²⋊Q₈	—	2	1	no	—
306	C₄×Q₈	—	2	1	no	—
307	C₄×Q₈	—	2	1	no	—
308	C₄×Q₈	C₂×C₄×C₅₉	1	1	yes	characteristic
309	C₄×Q₈	C₂×C₄×C₅₉	1	1	yes	characteristic
310	C₄×D₄	—	2	1	no	—
311	C₄×D₄	—	2	1	no	—
312	C₄×D₄	C₂×C₄×C₅₉	1	1	yes	characteristic
313	C₄×D₄	C₂×C₄×C₅₉	1	1	yes	characteristic
314	#117	—	2	1	no	—
315	#117	C₂³×C₅₉	1	1	yes	characteristic
316	#117	C₂³×C₅₉	1	2	yes	—
317	C₂×C₄⋊C₄	—	2	1	no	—
318	C₂×C₄²	—	2	1	no	—
319	C₂×C₄²	C₂³×C₅₉	1	2	yes	—
320	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
321	#108	—	4	2	no	—
322	#107	C₂×C₄×C₅₉	1	2	yes	—
323	#107	C₂×C₄×C₅₉	1	2	yes	—
324	#106	C₂×C₄×C₅₉	1	2	yes	—
325	#106	C₂×C₄×C₅₉	1	2	yes	—
326	C₄⋊C₈	—	2	1	no	—
327	C₄⋊C₈	—	2	1	no	—
328	C₄⋊C₈	—	2	1	no	—
329	C₄⋊C₈	—	2	1	no	—
330	C₄⋊C₈	—	2	2	no	—
331	C₄⋊C₈	—	2	2	no	—
332	C₄⋊C₈	—	2	1	no	—
333	C₄⋊C₈	—	2	1	no	—
334	C₄⋊C₈	C₂×C₄×C₅₉	1	1	yes	characteristic
335	C₄⋊C₈	C₂×C₄×C₅₉	1	1	yes	characteristic
336	C₄⋊C₈	C₂×C₄×C₅₉	1	2	yes	—
337	#104	—	4	2	no	—
338	#103	C₂×C₄×C₅₉	1	2	yes	—
339	#103	C₂×C₄×C₅₉	1	2	yes	—
340	#102	C₂×C₄×C₅₉	1	2	yes	—
341	#102	C₂×C₄×C₅₉	1	2	yes	—
342	C₂²⋊C₈	—	2	1	no	—
343	C₂²⋊C₈	—	2	1	no	—
344	C₂²⋊C₈	—	2	1	no	—
345	C₂²⋊C₈	—	2	1	no	—
346	#97	—	2	2	no	—
347	#97	—	2	1	no	—
348	C₄×C₈	—	2	2	no	—
349	C₄×C₈	—	2	1	no	—
350	C₄×C₈	—	4	2	no	—
351	C₄×C₈	D₄×C₅₉	1	1	yes	characteristic
352	C₄×C₈	D₄×C₅₉	1	1	yes	characteristic
353	C₄×C₈	D₄×C₅₉	1	1	yes	characteristic
354	C₄×C₈	D₄×C₅₉	1	1	yes	characteristic
355	#95	—	2	1	no	—
356	#41	—	2	1	no	—
357	#41	—	2	1	no	—
358	#41	—	2	1	no	—
359	#41	—	2	1	no	—
360	C₂×Q₈	—	2	1	no	—
361	C₂×Q₈	—	2	1	no	—
362	C₂×Q₈	C₂²×C₄×C₅₉	1	1	yes	characteristic
363	C₂×D₄	—	2	1	no	—
364	C₂×D₄	C₂²×C₄×C₅₉	1	1	yes	characteristic
365	C₂²×C₄	—	2	2	no	—
366	C₂²×C₄	—	2	1	no	—
367	C₂²×C₄	—	2	1	no	—
368	C₂²×C₄	—	2	1	no	—
369	C₂²×C₄	#41×C₅₉	1	1	yes	characteristic
370	C₂²×C₄	#41×C₅₉	1	1	yes	characteristic
371	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
372	M₁₆	—	2	2	no	—
373	M₁₆	—	2	1	no	—
374	M₁₆	—	2	1	no	—
375	M₁₆	—	2	1	no	—
376	M₁₆	—	2	1	no	—
377	M₁₆	—	2	2	no	—
378	C₂×C₈	—	2	1	no	—
379	C₂×C₈	—	2	2	no	—
380	C₂×C₈	—	2	2	no	—
381	C₂×C₈	—	2	1	no	—
382	C₂×C₈	—	2	1	no	—
383	C₂×C₈	—	2	1	no	—
384	C₂×C₈	—	2	1	no	—
385	C₂×C₈	—	2	1	no	—
386	C₂×C₈	—	2	2	no	—
387	C₂×C₈	C₂²×C₄×C₅₉	1	2	yes	—
388	C₂×C₈	C₂²×C₄×C₅₉	1	2	yes	—
389	C₂×C₈	C₂×D₄×C₅₉	1	1	yes	characteristic
390	C₂×C₈	C₂×D₄×C₅₉	1	1	yes	characteristic
391	C₂×C₈	C₂×D₄×C₅₉	1	1	yes	characteristic
392	C₂×C₈	C₂×D₄×C₅₉	1	1	yes	characteristic
393	C₄⋊C₄	—	2	4	no	—
394	C₄⋊C₄	—	2	1	no	—
395	C₄⋊C₄	—	2	1	no	—
396	C₄⋊C₄	—	2	2	no	—
397	C₄⋊C₄	—	2	2	no	—
398	C₄⋊C₄	—	2	1	no	—
399	C₄⋊C₄	—	2	1	no	—
400	C₄⋊C₄	C₂²×C₄×C₅₉	1	2	yes	—
401	C₄⋊C₄	C₂²×C₄×C₅₉	1	2	yes	—
402	C₄⋊C₄	C₂²×C₄×C₅₉	1	1	yes	characteristic
403	C₄⋊C₄	C₂²×C₄×C₅₉	1	1	yes	characteristic
404	C₂²⋊C₄	—	2	1	no	—
405	C₂²⋊C₄	—	2	2	no	—
406	C₂²⋊C₄	—	2	1	no	—
407	C₂²⋊C₄	—	2	1	no	—
408	C₄²	—	2	1	no	—
409	C₄²	—	2	1	no	—
410	C₄²	—	2	2	no	—
411	C₄²	—	2	1	no	—
412	C₄²	—	2	2	no	—
413	C₄²	—	2	2	no	—
414	C₄²	C₂²×C₄×C₅₉	1	1	yes	characteristic
415	C₄²	C₂²×C₄×C₅₉	1	1	yes	characteristic
416	C₄²	C₂×D₄×C₅₉	1	1	yes	characteristic
417	C₄²	C₂×D₄×C₅₉	1	1	yes	characteristic
418	C₂³	—	2	1	no	—
419	C₂³	C₂×#41×C₅₉	1	1	yes	characteristic
420	Q₈	—	2	1	no	—
421	Q₈	—	2	1	no	—
422	Q₈	—	4	2	no	—
423	Q₈	—	4	2	no	—
424	D₄	—	2	1	no	—
425	D₄	—	2	1	no	—
426	D₄	—	4	1	no	—
427	D₄	—	4	1	no	—
428	C₂×C₄	—	2	2	no	—
429	C₂×C₄	—	2	4	no	—
430	C₂×C₄	—	2	1	no	—
431	C₂×C₄	—	2	1	no	—
432	C₂×C₄	—	2	1	no	—
433	C₂×C₄	—	2	2	no	—
434	C₂×C₄	—	2	2	no	—
435	C₂×C₄	—	4	1	no	—
436	C₂×C₄	—	4	2	no	—
437	C₂×C₄	—	4	2	no	—
438	C₂×C₄	—	4	2	no	—
439	C₂×C₄	—	4	2	no	—
440	C₂×C₄	—	4	1	no	—
441	C₂×C₄	—	4	1	no	—
442	C₂×C₄	C₄×D₄×C₅₉	1	1	yes	characteristic
443	C₂×C₄	C₄×D₄×C₅₉	1	1	yes	characteristic
444	C₂×C₄	C₄×D₄×C₅₉	1	1	yes	characteristic
445	C₂×C₄	C₄×D₄×C₅₉	1	1	yes	characteristic
446	C₂×C₄	C₂³×C₄×C₅₉	1	1	yes	characteristic
447	C₂×C₄	C₂²×D₄×C₅₉	1	1	yes	characteristic
448	C₂×C₄	H(5,𝔽₂)×C₅₉	1	1	yes	characteristic
449	C₂×C₄	2₋¹⁺⁴×C₅₉	1	1	yes	characteristic
450	C₂×C₄	2₋¹⁺⁴×C₅₉	1	1	yes	characteristic
451	C₂×C₄	2₋¹⁺⁴×C₅₉	1	1	yes	characteristic
452	C₈	—	2	2	no	—
453	C₈	—	2	2	no	—
454	C₈	—	2	1	no	—
455	C₈	—	2	1	no	—
456	C₈	—	2	1	no	—
457	C₈	—	2	1	no	—
458	C₈	—	4	1	no	—
459	C₈	—	4	1	no	—
460	C₈	—	4	2	no	—
461	C₂²	—	2	1	no	—
462	C₂²	—	2	1	no	—
463	C₂²	—	4	1	no	—
464	C₂²	—	4	1	no	—
465	C₂²	—	4	1	no	—
466	C₂²	C₂×C₄×D₄×C₅₉	1	1	yes	characteristic
467	C₂²	C₅₉×#541	1	1	yes	characteristic
468	C₂²	C₅₉×#542	1	1	yes	characteristic
469	C₄	—	2	1	no	—
470	C₄	—	2	1	no	—
471	C₄	—	2	1	no	—
472	C₄	—	4	4	no	—
473	C₄	—	4	1	no	—
474	C₄	—	4	1	no	—
475	C₄	—	4	2	no	—
476	C₄	—	4	1	no	—
477	C₄	—	4	2	no	—
478	C₄	C₅₉×#443	1	2	yes	—
479	C₄	C₅₉×#519	1	1	yes	characteristic
480	C₄	C₅₉×#520	1	1	yes	characteristic
481	C₄	C₅₉×#536	1	1	yes	characteristic
482	C₄	C₅₉×#537	1	1	yes	characteristic
483	C₂	—	2	1	no	—
484	C₂	—	2	1	no	—
485	C₂	—	8	1	no	—
486	C₂	C₅₉×#2323	1	1	yes	characteristic
487	C₂	C₂×C₅₉×#443	1	1	yes	characteristic
488	C₂	C₅₉×#2955	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₅₉	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₅₉
Frattini, cosocle	C₂²×C₄	C₂⁴×C₅₉
socle	C₂²×C₅₉	C₂×C₄×D₄
prime radical	C₂×#41×C₅₉	C₂³
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₅₉ ◁ C₂×C₄×C₈×C₅₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₅₉×#2960	C₂	semidirect
4. C₅₉×#1986	C₂	semidirect
5. C₅₉×#1950	C₂	semidirect
6. C₅₉×#1945	C₂	semidirect
9. C₅₉×#1922	C₂	semidirect
11. C₈×C₄⋊C₄×C₅₉	C₂	semidirect
14. C₅₉×#479	C₄	semidirect
15. C₅₉×#478	C₄	semidirect
16. C₅₉×#477	C₄	semidirect
17. C₅₉×#476	C₄	semidirect
18. C₅₉×#475	C₄	semidirect
19. C₅₉×#474	C₄	semidirect
216. #22130	C₅₉	direct (N × H)
240. #2960	C₂×C₅₉	semidirect
242. #1986	C₂×C₅₉	semidirect
243. #1950	C₂×C₅₉	semidirect
244. #1945	C₂×C₅₉	semidirect
247. #1922	C₂×C₅₉	semidirect
249. C₈×C₄⋊C₄	C₂×C₅₉	semidirect
258. #479	C₄×C₅₉	semidirect
259. #478	C₄×C₅₉	semidirect
260. #477	C₄×C₅₉	semidirect
261. #476	C₄×C₅₉	semidirect
262. #475	C₄×C₅₉	semidirect
263. #474	C₄×C₅₉	semidirect
293. C₅₉	#22130	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×#3076	2
C₅₉×#2960	2
C₅₉×#2922	2
C₅₉×#1986	2
C₅₉×#1950	2
C₅₉×#1945	2
C₅₉×#1937	2
C₅₉×#1929	2
C₅₉×#1922	2
C₅₉×#1806	2
C₈×C₄⋊C₄×C₅₉	2
#22130	59

Subgroups — C59×#22130 #28434239

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₉×#22130 #28434239