Subgroups — C₂×C₅₉×#2063 #28435708

Order 15104.

1134 conjugacy classes of subgroups.

The subgroup lattice has 516 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#108×C₅₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₅₉×#428	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₅₉×#424	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₅₉×#418	C₂	1	1	yes	maximal, characteristic
5	C₂²×#102×C₅₉	C₂	1	1	yes	maximal, characteristic
6	C₂²×#100×C₅₉	C₂	1	1	yes	maximal, characteristic
7	C₅₉×#2063	C₂	1	8	yes	maximal, direct product factor
8	C₂×C₅₉×#343	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂³×D₄×C₅₉	C₂²	1	1	yes	characteristic
10	C₂²×M₁₆×C₅₉	C₂²	1	1	yes	characteristic
11	C₂²×M₁₆×C₅₉	C₂²	1	1	yes	characteristic
12	C₂²×M₁₆×C₅₉	C₂²	1	1	yes	characteristic
13	C₂³×C₈×C₅₉	C₂²	1	1	yes	characteristic
14	C₂×#117×C₅₉	C₂²	1	1	yes	characteristic
15	C₂²×C₄⋊C₄×C₅₉	C₂²	1	1	yes	characteristic
16	C₂×#108×C₅₉	—	2	4	no	—
17	C₂×#108×C₅₉	C₂²	1	4	yes	complemented
18	C₅₉×#428	—	2	2	no	—
19	C₅₉×#428	C₂²	1	4	yes	complemented
20	C₂×#107×C₅₉	—	2	1	no	—
21	C₂×#106×C₅₉	—	2	1	no	—
22	C₅₉×#424	—	2	2	no	—
23	C₅₉×#424	C₂²	1	4	yes	complemented
24	C₂×C₄⋊C₈×C₅₉	—	2	2	no	—
25	C₅₉×#418	—	2	2	no	—
26	C₅₉×#418	C₂²	1	4	yes	—
27	C₂×#102×C₅₉	—	2	2	no	—
28	C₂×#102×C₅₉	—	2	2	no	—
29	C₂×#102×C₅₉	—	2	1	no	—
30	C₂×#102×C₅₉	—	2	1	no	—
31	C₂×#102×C₅₉	C₂²	1	4	yes	—
32	C₂×#100×C₅₉	—	2	4	no	—
33	C₂×#100×C₅₉	C₂²	1	4	yes	—
34	C₅₉×#343	C₂²	1	4	yes	complemented
35	C₂⁵×C₅₉	—	2	1	no	—
36	C₂²×D₄×C₅₉	—	2	1	no	—
37	C₂²×D₄×C₅₉	—	2	1	no	—
38	C₂²×D₄×C₅₉	—	2	1	no	—
39	C₂²×D₄×C₅₉	—	2	1	no	—
40	C₂²×D₄×C₅₉	—	2	2	no	—
41	C₂²×D₄×C₅₉	—	2	2	no	—
42	C₂²×D₄×C₅₉	—	2	2	no	—
43	C₂²×D₄×C₅₉	—	2	1	no	—
44	C₂²×D₄×C₅₉	Q₈	1	4	yes	—
45	C₂²×D₄×C₅₉	C₂³	1	2	yes	—
46	C₂³×C₄×C₅₉	—	2	1	no	—
47	C₂³×C₄×C₅₉	C₂³	1	1	yes	characteristic
48	C₂×M₁₆×C₅₉	—	2	1	no	—
49	C₂×M₁₆×C₅₉	—	2	2	no	—
50	C₂×M₁₆×C₅₉	—	2	1	no	—
51	C₂×M₁₆×C₅₉	—	2	1	no	—
52	C₂×M₁₆×C₅₉	—	2	2	no	—
53	C₂×M₁₆×C₅₉	—	2	2	no	—
54	C₂×M₁₆×C₅₉	—	2	2	no	—
55	C₂×M₁₆×C₅₉	—	2	2	no	—
56	C₂×M₁₆×C₅₉	D₄	1	4	yes	—
57	C₂×M₁₆×C₅₉	C₂³	1	2	yes	—
58	C₂×M₁₆×C₅₉	C₂³	1	2	yes	—
59	C₂×M₁₆×C₅₉	C₂³	1	2	yes	—
60	C₂²×C₈×C₅₉	—	2	1	no	—
61	C₂²×C₈×C₅₉	—	2	2	no	—
62	C₂²×C₈×C₅₉	—	2	2	no	—
63	C₂²×C₈×C₅₉	—	2	1	no	—
64	C₂²×C₈×C₅₉	—	2	1	no	—
65	C₂²×C₈×C₅₉	D₄	1	2	yes	—
66	C₂²×C₈×C₅₉	D₄	1	2	yes	—
67	C₂²×C₈×C₅₉	C₂³	1	2	yes	—
68	#117×C₅₉	—	2	1	no	—
69	#117×C₅₉	—	2	1	no	—
70	#117×C₅₉	D₄	1	2	yes	—
71	#117×C₅₉	C₂³	1	2	yes	—
72	C₂×C₄⋊C₄×C₅₉	—	2	1	no	—
73	C₂×C₄⋊C₄×C₅₉	—	2	1	no	—
74	C₂×C₄⋊C₄×C₅₉	—	2	1	no	—
75	C₂×C₄⋊C₄×C₅₉	—	2	1	no	—
76	C₂×C₄⋊C₄×C₅₉	—	2	1	no	—
77	C₂×C₄⋊C₄×C₅₉	D₄	1	1	yes	characteristic
78	C₂×C₄⋊C₄×C₅₉	D₄	1	1	yes	characteristic
79	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
80	C₂×C₂²⋊C₄×C₅₉	—	2	1	no	—
81	C₂×C₄²×C₅₉	—	2	1	no	—
82	#108×C₅₉	—	2	8	no	—
83	#107×C₅₉	—	2	4	no	—
84	#106×C₅₉	—	2	4	no	—
85	C₄⋊C₈×C₅₉	—	2	8	no	—
86	#102×C₅₉	—	2	8	no	—
87	#102×C₅₉	—	2	4	no	—
88	#102×C₅₉	—	2	4	no	—
89	#100×C₅₉	—	2	8	no	—
90	C₂⁴×C₅₉	—	2	4	no	—
91	C₂⁴×C₅₉	—	2	2	no	—
92	C₂⁴×C₅₉	—	4	1	no	—
93	C₂⁴×C₅₉	—	4	1	no	—
94	C₂⁴×C₅₉	—	4	2	no	—
95	C₂⁴×C₅₉	—	8	2	no	—
96	C₂⁴×C₅₉	—	8	2	no	—
97	C₂⁴×C₅₉	#41	1	1	yes	characteristic
98	C₂×D₄×C₅₉	—	2	4	no	—
99	C₂×D₄×C₅₉	—	2	4	no	—
100	C₂×D₄×C₅₉	—	2	4	no	—
101	C₂×D₄×C₅₉	—	2	4	no	—
102	C₂×D₄×C₅₉	—	2	4	no	—
103	C₂×D₄×C₅₉	—	2	2	no	—
104	C₂×D₄×C₅₉	—	2	2	no	—
105	C₂×D₄×C₅₉	—	2	2	no	—
106	C₂×D₄×C₅₉	—	2	2	no	—
107	C₂×D₄×C₅₉	—	2	2	no	—
108	C₂×D₄×C₅₉	—	4	2	no	—
109	C₂×D₄×C₅₉	—	4	2	no	—
110	C₂×D₄×C₅₉	—	4	2	no	—
111	C₂×D₄×C₅₉	—	4	2	no	—
112	C₂×D₄×C₅₉	—	4	1	no	—
113	C₂×D₄×C₅₉	—	4	1	no	—
114	C₂×D₄×C₅₉	—	4	2	no	—
115	C₂×D₄×C₅₉	C₂×Q₈	1	4	yes	—
116	C₂²×C₄×C₅₉	—	2	1	no	—
117	C₂²×C₄×C₅₉	—	2	1	no	—
118	C₂²×C₄×C₅₉	—	2	2	no	—
119	C₂²×C₄×C₅₉	—	4	1	no	—
120	C₂²×C₄×C₅₉	—	4	1	no	—
121	C₂²×C₄×C₅₉	—	8	2	no	—
122	C₂²×C₄×C₅₉	C₂×D₄	1	2	yes	—
123	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
124	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
125	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
126	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
127	C₂²×C₄×C₅₉	C₂×Q₈	1	2	yes	—
128	C₂²×C₄×C₅₉	#41	1	1	yes	characteristic
129	C₂²×C₄×C₅₉	#41	1	2	yes	—
130	C₂²×C₄×C₅₉	#41	1	2	yes	—
131	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
132	M₁₆×C₅₉	—	2	4	no	—
133	M₁₆×C₅₉	—	2	2	no	—
134	M₁₆×C₅₉	—	2	2	no	—
135	M₁₆×C₅₉	—	2	2	no	—
136	M₁₆×C₅₉	—	2	2	no	—
137	M₁₆×C₅₉	—	2	2	no	—
138	M₁₆×C₅₉	—	4	2	no	—
139	M₁₆×C₅₉	—	4	2	no	—
140	M₁₆×C₅₉	C₂×D₄	1	4	yes	—
141	C₂×C₈×C₅₉	—	2	4	no	—
142	C₂×C₈×C₅₉	—	2	4	no	—
143	C₂×C₈×C₅₉	—	2	4	no	—
144	C₂×C₈×C₅₉	—	2	2	no	—
145	C₂×C₈×C₅₉	—	2	2	no	—
146	C₂×C₈×C₅₉	—	2	2	no	—
147	C₂×C₈×C₅₉	—	2	2	no	—
148	C₂×C₈×C₅₉	—	2	2	no	—
149	C₂×C₈×C₅₉	—	4	2	no	—
150	C₂×C₈×C₅₉	—	4	2	no	—
151	C₂×C₈×C₅₉	C₂×D₄	1	4	yes	—
152	C₄⋊C₄×C₅₉	—	2	1	no	—
153	C₄⋊C₄×C₅₉	—	2	1	no	—
154	C₄⋊C₄×C₅₉	—	2	2	no	—
155	C₄⋊C₄×C₅₉	—	2	2	no	—
156	C₄⋊C₄×C₅₉	—	4	1	no	—
157	C₄⋊C₄×C₅₉	—	4	1	no	—
158	C₄⋊C₄×C₅₉	C₂×D₄	1	2	yes	—
159	C₄⋊C₄×C₅₉	C₂×D₄	1	2	yes	—
160	C₂²⋊C₄×C₅₉	—	2	2	no	—
161	C₂²⋊C₄×C₅₉	—	2	2	no	—
162	C₄²×C₅₉	—	2	2	no	—
163	C₄²×C₅₉	—	2	2	no	—
164	C₂³×C₅₉	—	2	2	no	—
165	C₂³×C₅₉	—	2	2	no	—
166	C₂³×C₅₉	—	2	4	no	—
167	C₂³×C₅₉	—	4	2	no	—
168	C₂³×C₅₉	—	4	2	no	—
169	C₂³×C₅₉	—	4	4	no	—
170	C₂³×C₅₉	—	4	4	no	—
171	C₂³×C₅₉	—	8	8	no	—
172	C₂³×C₅₉	—	8	2	no	—
173	C₂³×C₅₉	—	8	2	no	—
174	C₂³×C₅₉	—	8	8	no	—
175	C₂³×C₅₉	—	8	2	no	—
176	C₂³×C₅₉	—	8	2	no	—
177	C₂³×C₅₉	—	8	2	no	—
178	C₂³×C₅₉	—	8	2	no	—
179	C₂³×C₅₉	#121	1	1	yes	characteristic
180	C₂³×C₅₉	#121	1	1	yes	characteristic
181	C₂³×C₅₉	C₂²⋊Q₈	1	2	yes	—
182	C₂³×C₅₉	#126	1	2	yes	—
183	C₂³×C₅₉	C₂×#41	1	1	yes	characteristic
184	D₄×C₅₉	—	2	4	no	—
185	D₄×C₅₉	—	2	4	no	—
186	D₄×C₅₉	—	4	2	no	—
187	D₄×C₅₉	—	4	2	no	—
188	D₄×C₅₉	—	4	4	no	—
189	D₄×C₅₉	—	4	4	no	—
190	C₂×C₄×C₅₉	—	2	2	no	—
191	C₂×C₄×C₅₉	—	2	2	no	—
192	C₂×C₄×C₅₉	—	4	2	no	—
193	C₂×C₄×C₅₉	—	4	2	no	—
194	C₂×C₄×C₅₉	—	4	2	no	—
195	C₂×C₄×C₅₉	—	8	2	no	—
196	C₂×C₄×C₅₉	—	8	2	no	—
197	C₂×C₄×C₅₉	—	8	2	no	—
198	C₂×C₄×C₅₉	#121	1	2	yes	—
199	C₂×C₄×C₅₉	#121	1	2	yes	—
200	C₂×C₄×C₅₉	#121	1	2	yes	—
201	C₂×C₄×C₅₉	#121	1	2	yes	—
202	C₂×C₄×C₅₉	#121	1	1	yes	characteristic
203	C₂×C₄×C₅₉	#121	1	1	yes	characteristic
204	C₂×C₄×C₅₉	C₂²⋊Q₈	1	2	yes	—
205	C₂×C₄×C₅₉	C₂²⋊Q₈	1	2	yes	—
206	C₂×C₄×C₅₉	C₂²⋊Q₈	1	2	yes	—
207	C₂×C₄×C₅₉	C₂²⋊Q₈	1	2	yes	—
208	C₂×C₄×C₅₉	C₂²⋊Q₈	1	2	yes	—
209	C₂×C₄×C₅₉	#126	1	2	yes	—
210	C₂×C₄×C₅₉	C₂²×D₄	1	1	yes	characteristic
211	C₂×C₄×C₅₉	C₂²×D₄	1	1	yes	characteristic
212	C₂×C₄×C₅₉	C₂²×D₄	1	1	yes	characteristic
213	C₂×C₄×C₅₉	C₂²×Q₈	1	1	yes	characteristic
214	C₂×C₄×C₅₉	C₂×#41	1	1	yes	characteristic
215	C₂×C₄×C₅₉	C₂×#41	1	1	yes	characteristic
216	C₈×C₅₉	—	2	4	no	—
217	C₈×C₅₉	—	2	4	no	—
218	C₈×C₅₉	—	4	2	no	—
219	C₈×C₅₉	—	4	2	no	—
220	C₂×#2063	C₅₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
221	C₂²×C₅₉	—	2	4	no	—
222	C₂²×C₅₉	—	2	4	no	—
223	C₂²×C₅₉	—	2	1	no	—
224	C₂²×C₅₉	—	2	1	no	—
225	C₂²×C₅₉	—	2	1	no	—
226	C₂²×C₅₉	—	2	1	no	—
227	C₂²×C₅₉	—	4	4	no	—
228	C₂²×C₅₉	—	8	4	no	—
229	C₂²×C₅₉	—	8	4	no	—
230	C₂²×C₅₉	—	8	8	no	—
231	C₂²×C₅₉	—	8	8	no	—
232	C₂²×C₅₉	—	8	2	no	—
233	C₂²×C₅₉	—	8	2	no	—
234	C₂²×C₅₉	#396	1	2	yes	—
235	C₂²×C₅₉	#396	1	2	yes	—
236	C₂²×C₅₉	#471	1	2	yes	—
237	C₂²×C₅₉	#472	1	2	yes	—
238	C₂²×C₅₉	C₂×#121	1	1	yes	characteristic
239	C₂²×C₅₉	C₂×C₂²⋊Q₈	1	1	yes	characteristic
240	C₂²×C₅₉	C₂×#126	1	1	yes	characteristic
241	C₄×C₅₉	—	4	2	no	—
242	C₄×C₅₉	—	4	2	no	—
243	C₄×C₅₉	—	8	2	no	—
244	C₄×C₅₉	#396	1	2	yes	—
245	C₄×C₅₉	#396	1	2	yes	—
246	C₄×C₅₉	C₂×#121	1	1	yes	characteristic
247	C₄×C₅₉	C₂×#121	1	1	yes	characteristic
248	C₄×C₅₉	C₂×C₂²⋊Q₈	1	1	yes	characteristic
249	C₄×C₅₉	C₂×C₂²⋊Q₈	1	1	yes	characteristic
250	C₂²×#108	C₂×C₅₉	1	1	yes	characteristic, complemented
251	C₂×#428	C₂×C₅₉	1	1	yes	characteristic, complemented
252	C₂×#424	C₂×C₅₉	1	1	yes	characteristic, complemented
253	C₂×#418	C₂×C₅₉	1	1	yes	characteristic
254	C₂²×#102	C₂×C₅₉	1	1	yes	characteristic
255	C₂²×#100	C₂×C₅₉	1	1	yes	characteristic
256	#2063	C₂×C₅₉	1	8	yes	direct product factor
257	C₂×#343	C₂×C₅₉	1	1	yes	characteristic, complemented
258	C₂×C₅₉	—	2	1	no	—
259	C₂×C₅₉	—	2	1	no	—
260	C₂×C₅₉	—	2	2	no	—
261	C₂×C₅₉	—	8	4	no	—
262	C₂×C₅₉	#2063	1	4	yes	direct product factor
263	C₂×C₅₉	C₂×#396	1	1	yes	characteristic
264	C₂×C₅₉	C₂×#471	1	1	yes	characteristic
265	C₂×C₅₉	C₂×#472	1	1	yes	characteristic
266	C₂³×D₄	C₂²×C₅₉	1	1	yes	characteristic
267	C₂²×M₁₆	C₂²×C₅₉	1	1	yes	characteristic
268	C₂²×M₁₆	C₂²×C₅₉	1	1	yes	characteristic
269	C₂²×M₁₆	C₂²×C₅₉	1	1	yes	characteristic
270	C₂³×C₈	C₂²×C₅₉	1	1	yes	characteristic
271	C₂×#117	C₂²×C₅₉	1	1	yes	characteristic
272	C₂²×C₄⋊C₄	C₂²×C₅₉	1	1	yes	characteristic
273	C₂×#108	—	2	4	no	—
274	C₂×#108	C₂²×C₅₉	1	4	yes	complemented
275	#428	—	2	2	no	—
276	#428	C₂²×C₅₉	1	4	yes	complemented
277	C₂×#107	—	2	1	no	—
278	C₂×#106	—	2	1	no	—
279	#424	—	2	2	no	—
280	#424	C₂²×C₅₉	1	4	yes	complemented
281	C₂×C₄⋊C₈	—	2	2	no	—
282	#418	—	2	2	no	—
283	#418	C₂²×C₅₉	1	4	yes	—
284	C₂×#102	—	2	2	no	—
285	C₂×#102	—	2	2	no	—
286	C₂×#102	—	2	1	no	—
287	C₂×#102	—	2	1	no	—
288	C₂×#102	C₂²×C₅₉	1	4	yes	—
289	C₂×#100	—	2	4	no	—
290	C₂×#100	C₂²×C₅₉	1	4	yes	—
291	#343	C₂²×C₅₉	1	4	yes	complemented
292	C₅₉	C₂×#2063	1	1	yes	characteristic, direct product factor, Sylow
293	C₂⁵	—	2	1	no	—
294	C₂²×D₄	—	2	1	no	—
295	C₂²×D₄	—	2	1	no	—
296	C₂²×D₄	—	2	1	no	—
297	C₂²×D₄	—	2	1	no	—
298	C₂²×D₄	—	2	2	no	—
299	C₂²×D₄	—	2	2	no	—
300	C₂²×D₄	—	2	2	no	—
301	C₂²×D₄	—	2	1	no	—
302	C₂²×D₄	Q₈×C₅₉	1	4	yes	—
303	C₂²×D₄	C₂³×C₅₉	1	2	yes	—
304	C₂³×C₄	—	2	1	no	—
305	C₂³×C₄	C₂³×C₅₉	1	1	yes	characteristic
306	C₂×M₁₆	—	2	1	no	—
307	C₂×M₁₆	—	2	2	no	—
308	C₂×M₁₆	—	2	1	no	—
309	C₂×M₁₆	—	2	1	no	—
310	C₂×M₁₆	—	2	2	no	—
311	C₂×M₁₆	—	2	2	no	—
312	C₂×M₁₆	—	2	2	no	—
313	C₂×M₁₆	—	2	2	no	—
314	C₂×M₁₆	D₄×C₅₉	1	4	yes	—
315	C₂×M₁₆	C₂³×C₅₉	1	2	yes	—
316	C₂×M₁₆	C₂³×C₅₉	1	2	yes	—
317	C₂×M₁₆	C₂³×C₅₉	1	2	yes	—
318	C₂²×C₈	—	2	2	no	—
319	C₂²×C₈	—	2	1	no	—
320	C₂²×C₈	—	2	2	no	—
321	C₂²×C₈	—	2	1	no	—
322	C₂²×C₈	—	2	1	no	—
323	C₂²×C₈	D₄×C₅₉	1	2	yes	—
324	C₂²×C₈	D₄×C₅₉	1	2	yes	—
325	C₂²×C₈	C₂³×C₅₉	1	2	yes	—
326	#117	—	2	1	no	—
327	#117	—	2	1	no	—
328	#117	D₄×C₅₉	1	2	yes	—
329	#117	C₂³×C₅₉	1	2	yes	—
330	C₂×C₄⋊C₄	—	2	1	no	—
331	C₂×C₄⋊C₄	—	2	1	no	—
332	C₂×C₄⋊C₄	—	2	1	no	—
333	C₂×C₄⋊C₄	—	2	1	no	—
334	C₂×C₄⋊C₄	—	2	1	no	—
335	C₂×C₄⋊C₄	D₄×C₅₉	1	1	yes	characteristic
336	C₂×C₄⋊C₄	D₄×C₅₉	1	1	yes	characteristic
337	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
338	C₂×C₂²⋊C₄	—	2	1	no	—
339	C₂×C₄²	—	2	1	no	—
340	#108	—	2	8	no	—
341	#107	—	2	4	no	—
342	#106	—	2	4	no	—
343	C₄⋊C₈	—	2	8	no	—
344	#102	—	2	8	no	—
345	#102	—	2	4	no	—
346	#102	—	2	4	no	—
347	#100	—	2	8	no	—
348	C₂⁴	—	2	4	no	—
349	C₂⁴	—	2	2	no	—
350	C₂⁴	—	4	1	no	—
351	C₂⁴	—	4	1	no	—
352	C₂⁴	—	4	2	no	—
353	C₂⁴	—	8	2	no	—
354	C₂⁴	—	8	2	no	—
355	C₂⁴	#41×C₅₉	1	1	yes	characteristic
356	C₂×D₄	—	2	4	no	—
357	C₂×D₄	—	2	4	no	—
358	C₂×D₄	—	2	4	no	—
359	C₂×D₄	—	2	4	no	—
360	C₂×D₄	—	2	4	no	—
361	C₂×D₄	—	2	2	no	—
362	C₂×D₄	—	2	2	no	—
363	C₂×D₄	—	2	2	no	—
364	C₂×D₄	—	2	2	no	—
365	C₂×D₄	—	2	2	no	—
366	C₂×D₄	—	4	1	no	—
367	C₂×D₄	—	4	1	no	—
368	C₂×D₄	—	4	2	no	—
369	C₂×D₄	—	4	2	no	—
370	C₂×D₄	—	4	2	no	—
371	C₂×D₄	—	4	2	no	—
372	C₂×D₄	—	4	2	no	—
373	C₂×D₄	C₂×Q₈×C₅₉	1	4	yes	—
374	C₂²×C₄	—	2	1	no	—
375	C₂²×C₄	—	2	1	no	—
376	C₂²×C₄	—	2	2	no	—
377	C₂²×C₄	—	4	1	no	—
378	C₂²×C₄	—	4	1	no	—
379	C₂²×C₄	—	8	2	no	—
380	C₂²×C₄	C₂×D₄×C₅₉	1	2	yes	—
381	C₂²×C₄	C₂×D₄×C₅₉	1	1	yes	characteristic
382	C₂²×C₄	C₂×D₄×C₅₉	1	1	yes	characteristic
383	C₂²×C₄	C₂×D₄×C₅₉	1	1	yes	characteristic
384	C₂²×C₄	C₂×D₄×C₅₉	1	1	yes	characteristic
385	C₂²×C₄	C₂×Q₈×C₅₉	1	2	yes	—
386	C₂²×C₄	#41×C₅₉	1	1	yes	characteristic
387	C₂²×C₄	#41×C₅₉	1	2	yes	—
388	C₂²×C₄	#41×C₅₉	1	2	yes	—
389	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
390	M₁₆	—	2	4	no	—
391	M₁₆	—	2	2	no	—
392	M₁₆	—	2	2	no	—
393	M₁₆	—	2	2	no	—
394	M₁₆	—	2	2	no	—
395	M₁₆	—	2	2	no	—
396	M₁₆	—	4	2	no	—
397	M₁₆	—	4	2	no	—
398	M₁₆	C₂×D₄×C₅₉	1	4	yes	—
399	C₂×C₈	—	2	4	no	—
400	C₂×C₈	—	2	4	no	—
401	C₂×C₈	—	2	4	no	—
402	C₂×C₈	—	2	2	no	—
403	C₂×C₈	—	2	2	no	—
404	C₂×C₈	—	2	2	no	—
405	C₂×C₈	—	2	2	no	—
406	C₂×C₈	—	2	2	no	—
407	C₂×C₈	—	4	2	no	—
408	C₂×C₈	—	4	2	no	—
409	C₂×C₈	C₂×D₄×C₅₉	1	4	yes	—
410	C₄⋊C₄	—	2	1	no	—
411	C₄⋊C₄	—	2	1	no	—
412	C₄⋊C₄	—	2	2	no	—
413	C₄⋊C₄	—	2	2	no	—
414	C₄⋊C₄	—	4	1	no	—
415	C₄⋊C₄	—	4	1	no	—
416	C₄⋊C₄	C₂×D₄×C₅₉	1	2	yes	—
417	C₄⋊C₄	C₂×D₄×C₅₉	1	2	yes	—
418	C₂²⋊C₄	—	2	2	no	—
419	C₂²⋊C₄	—	2	2	no	—
420	C₄²	—	2	2	no	—
421	C₄²	—	2	2	no	—
422	C₂³	—	2	2	no	—
423	C₂³	—	2	2	no	—
424	C₂³	—	2	4	no	—
425	C₂³	—	4	4	no	—
426	C₂³	—	4	4	no	—
427	C₂³	—	4	2	no	—
428	C₂³	—	4	2	no	—
429	C₂³	—	8	2	no	—
430	C₂³	—	8	2	no	—
431	C₂³	—	8	8	no	—
432	C₂³	—	8	2	no	—
433	C₂³	—	8	2	no	—
434	C₂³	—	8	8	no	—
435	C₂³	—	8	2	no	—
436	C₂³	—	8	2	no	—
437	C₂³	#121×C₅₉	1	1	yes	characteristic
438	C₂³	#121×C₅₉	1	1	yes	characteristic
439	C₂³	C₂²⋊Q₈×C₅₉	1	2	yes	—
440	C₂³	#126×C₅₉	1	2	yes	—
441	C₂³	C₂×#41×C₅₉	1	1	yes	characteristic
442	D₄	—	2	4	no	—
443	D₄	—	2	4	no	—
444	D₄	—	4	4	no	—
445	D₄	—	4	4	no	—
446	D₄	—	4	2	no	—
447	D₄	—	4	2	no	—
448	C₂×C₄	—	2	2	no	—
449	C₂×C₄	—	2	2	no	—
450	C₂×C₄	—	4	2	no	—
451	C₂×C₄	—	4	2	no	—
452	C₂×C₄	—	4	2	no	—
453	C₂×C₄	—	8	2	no	—
454	C₂×C₄	—	8	2	no	—
455	C₂×C₄	—	8	2	no	—
456	C₂×C₄	#121×C₅₉	1	1	yes	characteristic
457	C₂×C₄	#121×C₅₉	1	1	yes	characteristic
458	C₂×C₄	#121×C₅₉	1	2	yes	—
459	C₂×C₄	#121×C₅₉	1	2	yes	—
460	C₂×C₄	#121×C₅₉	1	2	yes	—
461	C₂×C₄	#121×C₅₉	1	2	yes	—
462	C₂×C₄	C₂²⋊Q₈×C₅₉	1	2	yes	—
463	C₂×C₄	C₂²⋊Q₈×C₅₉	1	2	yes	—
464	C₂×C₄	C₂²⋊Q₈×C₅₉	1	2	yes	—
465	C₂×C₄	C₂²⋊Q₈×C₅₉	1	2	yes	—
466	C₂×C₄	C₂²⋊Q₈×C₅₉	1	2	yes	—
467	C₂×C₄	#126×C₅₉	1	2	yes	—
468	C₂×C₄	C₂²×D₄×C₅₉	1	1	yes	characteristic
469	C₂×C₄	C₂²×D₄×C₅₉	1	1	yes	characteristic
470	C₂×C₄	C₂²×D₄×C₅₉	1	1	yes	characteristic
471	C₂×C₄	C₂²×Q₈×C₅₉	1	1	yes	characteristic
472	C₂×C₄	C₂×#41×C₅₉	1	1	yes	characteristic
473	C₂×C₄	C₂×#41×C₅₉	1	1	yes	characteristic
474	C₈	—	2	4	no	—
475	C₈	—	2	4	no	—
476	C₈	—	4	2	no	—
477	C₈	—	4	2	no	—
478	C₂²	—	2	1	no	—
479	C₂²	—	2	1	no	—
480	C₂²	—	2	1	no	—
481	C₂²	—	2	1	no	—
482	C₂²	—	2	4	no	—
483	C₂²	—	2	4	no	—
484	C₂²	—	4	4	no	—
485	C₂²	—	8	4	no	—
486	C₂²	—	8	8	no	—
487	C₂²	—	8	4	no	—
488	C₂²	—	8	2	no	—
489	C₂²	—	8	2	no	—
490	C₂²	—	8	8	no	—
491	C₂²	C₅₉×#396	1	2	yes	—
492	C₂²	C₅₉×#396	1	2	yes	—
493	C₂²	C₅₉×#471	1	2	yes	—
494	C₂²	C₅₉×#472	1	2	yes	—
495	C₂²	C₂×#121×C₅₉	1	1	yes	characteristic
496	C₂²	C₂×C₂²⋊Q₈×C₅₉	1	1	yes	characteristic
497	C₂²	C₂×#126×C₅₉	1	1	yes	characteristic
498	C₄	—	4	2	no	—
499	C₄	—	4	2	no	—
500	C₄	—	8	2	no	—
501	C₄	C₅₉×#396	1	2	yes	—
502	C₄	C₅₉×#396	1	2	yes	—
503	C₄	C₂×#121×C₅₉	1	1	yes	characteristic
504	C₄	C₂×#121×C₅₉	1	1	yes	characteristic
505	C₄	C₂×C₂²⋊Q₈×C₅₉	1	1	yes	characteristic
506	C₄	C₂×C₂²⋊Q₈×C₅₉	1	1	yes	characteristic
507	C₂	—	2	2	no	—
508	C₂	—	2	1	no	—
509	C₂	—	2	1	no	—
510	C₂	—	8	4	no	—
511	C₂	C₅₉×#2063	1	4	yes	direct product factor
512	C₂	C₂×C₅₉×#396	1	1	yes	characteristic
513	C₂	C₂×C₅₉×#471	1	1	yes	characteristic
514	C₂	C₂×C₅₉×#472	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₅₉	#121
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₅₉
prime radical	C₂³×D₄×C₅₉	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₅₉ ◁ C₂³×C₄×C₅₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂²×#108×C₅₉	C₂	semidirect
2. C₂×C₅₉×#428	C₂	semidirect
3. C₂×C₅₉×#424	C₂	semidirect
7. C₅₉×#2063	C₂	direct (N × H)
8. C₂×C₅₉×#343	C₂	semidirect
17. C₂×#108×C₅₉	C₂²	semidirect
19. C₅₉×#428	C₂²	semidirect
23. C₅₉×#424	C₂²	semidirect
34. C₅₉×#343	C₂²	semidirect
220. C₂×#2063	C₅₉	direct (N × H)
250. C₂²×#108	C₂×C₅₉	semidirect
251. C₂×#428	C₂×C₅₉	semidirect
252. C₂×#424	C₂×C₅₉	semidirect
256. #2063	C₂×C₅₉	direct (N × H)
257. C₂×#343	C₂×C₅₉	semidirect
262. C₂×C₅₉	#2063	direct (N × H)
274. C₂×#108	C₂²×C₅₉	semidirect
276. #428	C₂²×C₅₉	semidirect
280. #424	C₂²×C₅₉	semidirect
291. #343	C₂²×C₅₉	semidirect
292. C₅₉	C₂×#2063	direct (N × H)
511. C₂	C₅₉×#2063	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×#108×C₅₉	2
C₂×C₅₉×#428	2
C₂×C₅₉×#424	2
C₂×C₅₉×#418	2
C₂²×#102×C₅₉	2
C₂²×#100×C₅₉	2
C₅₉×#2063	2
C₂×C₅₉×#343	2
C₂×#2063	59

Subgroups — C2×C59×#2063 #28435708

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅₉×#2063 #28435708