Subgroups — C₅₉×#21250 #28433359

Order 15104.

1434 conjugacy classes of subgroups.

The subgroup lattice has 584 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#137×C₅₉	C₂	1	1	yes	maximal, characteristic
2	C₂×C₅₉×#430	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅₉×#2896	C₂	1	1	yes	maximal, characteristic
4	C₂×C₅₉×#419	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₅₉×#413	C₂	1	1	yes	maximal, characteristic
6	C₂²×#101×C₅₉	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅₉×#2873	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅₉×#1979	C₂	1	4	yes	maximal, complemented
9	C₅₉×#1977	C₂	1	4	yes	maximal, complemented
10	C₂²×#41×C₅₉	C₂²	1	1	yes	characteristic
11	C₂³×Q₈×C₅₉	C₂²	1	1	yes	characteristic
12	C₂×#137×C₅₉	—	2	2	no	—
13	C₂×#137×C₅₉	—	2	2	no	—
14	C₂×#137×C₅₉	—	2	4	no	—
15	C₂×#137×C₅₉	C₄	1	8	yes	complemented
16	C₂²×Q₁₆×C₅₉	C₂²	1	2	yes	—
17	C₂²×SD₁₆×C₅₉	C₂²	1	2	yes	—
18	C₂²×M₁₆×C₅₉	C₂²	1	1	yes	characteristic
19	C₂²×M₁₆×C₅₉	C₂²	1	1	yes	characteristic
20	C₂²×M₁₆×C₅₉	C₂²	1	1	yes	characteristic
21	C₂²×M₁₆×C₅₉	C₂²	1	1	yes	characteristic
22	C₂×#117×C₅₉	C₂²	1	1	yes	characteristic
23	C₅₉×#430	—	2	4	no	—
24	C₂×#108×C₅₉	C₂²	1	4	yes	—
25	C₅₉×#419	—	2	2	no	—
26	C₅₉×#419	C₂²	1	4	yes	—
27	C₅₉×#419	C₂²	1	2	yes	—
28	C₅₉×#418	C₂²	1	2	yes	—
29	C₅₉×#417	—	2	2	no	—
30	C₅₉×#416	—	2	2	no	—
31	C₂×#103×C₅₉	—	2	2	no	—
32	C₅₉×#413	—	2	4	no	—
33	C₂×#101×C₅₉	—	2	4	no	—
34	C₂×#101×C₅₉	C₂²	1	4	yes	—
35	C₂×#101×C₅₉	C₂²	1	2	yes	—
36	C₂×#100×C₅₉	C₂²	1	2	yes	—
37	C₅₉×#405	—	2	2	no	—
38	C₅₉×#405	C₂²	1	4	yes	—
39	C₄×M₁₆×C₅₉	—	2	2	no	—
40	C₂×#41×C₅₉	—	2	2	no	—
41	C₂×#41×C₅₉	—	2	1	no	—
42	C₂×#41×C₅₉	—	2	1	no	—
43	C₂×#41×C₅₉	—	2	1	no	—
44	C₂×#41×C₅₉	—	2	1	no	—
45	C₂×#41×C₅₉	—	2	2	no	—
46	C₂×#41×C₅₉	—	2	2	no	—
47	C₂×#41×C₅₉	C₂×C₄	1	4	yes	—
48	C₂²×Q₈×C₅₉	—	2	2	no	—
49	C₂²×Q₈×C₅₉	—	2	1	no	—
50	C₂²×Q₈×C₅₉	—	2	1	no	—
51	C₂²×Q₈×C₅₉	—	2	1	no	—
52	C₂²×Q₈×C₅₉	—	2	1	no	—
53	C₂²×Q₈×C₅₉	—	2	1	no	—
54	C₂²×Q₈×C₅₉	—	2	2	no	—
55	C₂²×Q₈×C₅₉	—	2	2	no	—
56	C₂²×Q₈×C₅₉	C₂×C₄	1	4	yes	—
57	C₂²×Q₈×C₅₉	C₂³	1	2	yes	—
58	C₂²×Q₈×C₅₉	C₂³	1	1	yes	characteristic
59	C₂²×D₄×C₅₉	—	2	1	no	—
60	C₂²×D₄×C₅₉	C₂³	1	1	yes	characteristic
61	C₂³×C₄×C₅₉	—	2	1	no	—
62	C₂³×C₄×C₅₉	—	2	1	no	—
63	C₂³×C₄×C₅₉	C₂³	1	1	yes	characteristic
64	#137×C₅₉	—	2	16	no	—
65	#137×C₅₉	—	2	16	no	—
66	C₂×Q₁₆×C₅₉	—	2	4	no	—
67	C₂×Q₁₆×C₅₉	—	2	4	no	—
68	C₂×Q₁₆×C₅₉	C₂×C₄	1	8	yes	complemented
69	C₂×SD₁₆×C₅₉	—	2	4	no	—
70	C₂×SD₁₆×C₅₉	—	2	4	no	—
71	C₂×SD₁₆×C₅₉	C₂×C₄	1	8	yes	complemented
72	C₂×M₁₆×C₅₉	—	2	1	no	—
73	C₂×M₁₆×C₅₉	—	2	2	no	—
74	C₂×M₁₆×C₅₉	—	2	1	no	—
75	C₂×M₁₆×C₅₉	—	2	1	no	—
76	C₂×M₁₆×C₅₉	—	2	2	no	—
77	C₂×M₁₆×C₅₉	—	2	2	no	—
78	C₂×M₁₆×C₅₉	—	2	2	no	—
79	C₂×M₁₆×C₅₉	—	2	2	no	—
80	C₂×M₁₆×C₅₉	C₂×C₄	1	4	yes	—
81	C₂×M₁₆×C₅₉	D₄	1	4	yes	—
82	C₂×M₁₆×C₅₉	D₄	1	2	yes	—
83	C₂×M₁₆×C₅₉	D₄	1	2	yes	—
84	C₂×M₁₆×C₅₉	D₄	1	4	yes	—
85	C₂×M₁₆×C₅₉	C₂³	1	2	yes	—
86	C₂×M₁₆×C₅₉	C₂³	1	2	yes	—
87	C₂×M₁₆×C₅₉	C₂³	1	2	yes	—
88	C₂²×C₈×C₅₉	—	2	1	no	—
89	C₂²×C₈×C₅₉	—	2	1	no	—
90	C₂²×C₈×C₅₉	—	2	1	no	—
91	C₂²×C₈×C₅₉	C₂³	1	2	yes	—
92	#117×C₅₉	—	2	1	no	—
93	#117×C₅₉	—	2	1	no	—
94	#117×C₅₉	D₄	1	2	yes	—
95	#117×C₅₉	C₂³	1	2	yes	—
96	C₂×C₄⋊C₄×C₅₉	D₄	1	2	yes	—
97	C₂×C₂²⋊C₄×C₅₉	—	2	1	no	—
98	C₂×C₄²×C₅₉	—	2	1	no	—
99	#108×C₅₉	—	2	8	no	—
100	#103×C₅₉	—	2	8	no	—
101	#103×C₅₉	—	2	4	no	—
102	#102×C₅₉	—	2	4	no	—
103	#101×C₅₉	—	2	8	no	—
104	#101×C₅₉	—	2	4	no	—
105	#100×C₅₉	—	2	4	no	—
106	#97×C₅₉	—	2	4	no	—
107	C₄×C₈×C₅₉	—	2	4	no	—
108	C₂⁴×C₅₉	—	2	1	no	—
109	C₂⁴×C₅₉	#41	1	1	yes	characteristic
110	#41×C₅₉	—	2	4	no	—
111	#41×C₅₉	—	2	4	no	—
112	#41×C₅₉	—	2	4	no	—
113	#41×C₅₉	—	2	4	no	—
114	#41×C₅₉	—	4	2	no	—
115	#41×C₅₉	—	4	2	no	—
116	#41×C₅₉	—	4	2	no	—
117	#41×C₅₉	—	4	2	no	—
118	C₂×Q₈×C₅₉	—	2	4	no	—
119	C₂×Q₈×C₅₉	—	2	2	no	—
120	C₂×Q₈×C₅₉	—	2	1	no	—
121	C₂×Q₈×C₅₉	—	2	4	no	—
122	C₂×Q₈×C₅₉	—	2	4	no	—
123	C₂×Q₈×C₅₉	—	2	4	no	—
124	C₂×Q₈×C₅₉	—	2	4	no	—
125	C₂×Q₈×C₅₉	—	2	2	no	—
126	C₂×Q₈×C₅₉	—	2	1	no	—
127	C₂×Q₈×C₅₉	—	2	2	no	—
128	C₂×Q₈×C₅₉	—	2	2	no	—
129	C₂×Q₈×C₅₉	—	2	1	no	—
130	C₂×Q₈×C₅₉	—	2	1	no	—
131	C₂×Q₈×C₅₉	—	2	2	no	—
132	C₂×Q₈×C₅₉	—	2	1	no	—
133	C₂×Q₈×C₅₉	—	4	1	no	—
134	C₂×Q₈×C₅₉	—	4	1	no	—
135	C₂×Q₈×C₅₉	—	4	2	no	—
136	C₂×Q₈×C₅₉	—	4	2	no	—
137	C₂×Q₈×C₅₉	—	4	2	no	—
138	C₂×Q₈×C₅₉	—	4	2	no	—
139	C₂×Q₈×C₅₉	—	4	2	no	—
140	C₂×Q₈×C₅₉	C₂²×C₄	1	4	yes	—
141	C₂×Q₈×C₅₉	C₂²×C₄	1	2	yes	—
142	C₂×D₄×C₅₉	—	2	4	no	—
143	C₂×D₄×C₅₉	—	2	1	no	—
144	C₂×D₄×C₅₉	—	2	1	no	—
145	C₂×D₄×C₅₉	—	2	1	no	—
146	C₂×D₄×C₅₉	—	2	1	no	—
147	C₂×D₄×C₅₉	—	2	1	no	—
148	C₂×D₄×C₅₉	—	4	1	no	—
149	C₂×D₄×C₅₉	—	4	1	no	—
150	C₂×D₄×C₅₉	—	4	2	no	—
151	C₂×D₄×C₅₉	C₂²×C₄	1	2	yes	—
152	C₂²×C₄×C₅₉	—	2	4	no	—
153	C₂²×C₄×C₅₉	—	2	1	no	—
154	C₂²×C₄×C₅₉	—	2	2	no	—
155	C₂²×C₄×C₅₉	—	2	2	no	—
156	C₂²×C₄×C₅₉	—	2	4	no	—
157	C₂²×C₄×C₅₉	—	4	1	no	—
158	C₂²×C₄×C₅₉	—	4	1	no	—
159	C₂²×C₄×C₅₉	—	4	2	no	—
160	C₂²×C₄×C₅₉	—	4	1	no	—
161	C₂²×C₄×C₅₉	—	4	1	no	—
162	C₂²×C₄×C₅₉	—	4	2	no	—
163	C₂²×C₄×C₅₉	C₂²×C₄	1	2	yes	—
164	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
165	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
166	C₂²×C₄×C₅₉	C₂×D₄	1	2	yes	—
167	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
168	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
169	C₂²×C₄×C₅₉	C₂×D₄	1	2	yes	—
170	C₂²×C₄×C₅₉	#41	1	1	yes	characteristic
171	C₂²×C₄×C₅₉	#41	1	2	yes	—
172	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
173	Q₁₆×C₅₉	—	2	16	no	—
174	SD₁₆×C₅₉	—	2	16	no	—
175	M₁₆×C₅₉	—	2	4	no	—
176	M₁₆×C₅₉	—	2	2	no	—
177	M₁₆×C₅₉	—	2	2	no	—
178	M₁₆×C₅₉	—	2	2	no	—
179	M₁₆×C₅₉	—	2	2	no	—
180	M₁₆×C₅₉	—	2	2	no	—
181	M₁₆×C₅₉	—	4	2	no	—
182	M₁₆×C₅₉	—	4	2	no	—
183	M₁₆×C₅₉	C₂²⋊C₄	1	8	yes	—
184	M₁₆×C₅₉	C₂²⋊C₄	1	8	yes	—
185	M₁₆×C₅₉	C₂×D₄	1	4	yes	—
186	C₂×C₈×C₅₉	—	2	4	no	—
187	C₂×C₈×C₅₉	—	2	2	no	—
188	C₂×C₈×C₅₉	—	2	2	no	—
189	C₂×C₈×C₅₉	—	2	2	no	—
190	C₂×C₈×C₅₉	—	4	2	no	—
191	C₂×C₈×C₅₉	—	4	2	no	—
192	C₂×C₈×C₅₉	C₂²×C₄	1	4	yes	—
193	C₂×C₈×C₅₉	C₂×D₄	1	4	yes	—
194	C₂×C₈×C₅₉	C₂×D₄	1	4	yes	—
195	C₄⋊C₄×C₅₉	—	2	2	no	—
196	C₄⋊C₄×C₅₉	C₂×D₄	1	4	yes	—
197	C₂²⋊C₄×C₅₉	—	2	2	no	—
198	C₂²⋊C₄×C₅₉	—	2	2	no	—
199	C₄²×C₅₉	—	2	2	no	—
200	C₄²×C₅₉	—	2	2	no	—
201	C₂³×C₅₉	—	2	2	no	—
202	C₂³×C₅₉	—	4	2	no	—
203	C₂³×C₅₉	—	4	1	no	—
204	C₂³×C₅₉	—	4	1	no	—
205	C₂³×C₅₉	—	8	2	no	—
206	C₂³×C₅₉	C₄×D₄	1	2	yes	—
207	C₂³×C₅₉	#121	1	1	yes	characteristic
208	C₂³×C₅₉	#121	1	1	yes	characteristic
209	C₂³×C₅₉	#124	1	2	yes	—
210	C₂³×C₅₉	C₂×#41	1	1	yes	characteristic
211	Q₈×C₅₉	—	2	4	no	—
212	Q₈×C₅₉	—	2	2	no	—
213	Q₈×C₅₉	—	2	4	no	—
214	Q₈×C₅₉	—	2	2	no	—
215	Q₈×C₅₉	—	4	2	no	—
216	Q₈×C₅₉	—	4	1	no	—
217	Q₈×C₅₉	—	4	2	no	—
218	Q₈×C₅₉	—	4	1	no	—
219	Q₈×C₅₉	—	4	4	no	—
220	Q₈×C₅₉	—	4	4	no	—
221	D₄×C₅₉	—	2	2	no	—
222	D₄×C₅₉	—	2	2	no	—
223	D₄×C₅₉	—	4	4	no	—
224	D₄×C₅₉	—	4	4	no	—
225	D₄×C₅₉	—	4	1	no	—
226	D₄×C₅₉	—	4	1	no	—
227	C₂×C₄×C₅₉	—	2	2	no	—
228	C₂×C₄×C₅₉	—	2	4	no	—
229	C₂×C₄×C₅₉	—	2	4	no	—
230	C₂×C₄×C₅₉	—	4	1	no	—
231	C₂×C₄×C₅₉	—	4	2	no	—
232	C₂×C₄×C₅₉	—	4	1	no	—
233	C₂×C₄×C₅₉	—	4	2	no	—
234	C₂×C₄×C₅₉	—	4	4	no	—
235	C₂×C₄×C₅₉	—	4	4	no	—
236	C₂×C₄×C₅₉	—	4	4	no	—
237	C₂×C₄×C₅₉	—	4	4	no	—
238	C₂×C₄×C₅₉	—	8	2	no	—
239	C₂×C₄×C₅₉	C₂×C₂²⋊C₄	1	2	yes	—
240	C₂×C₄×C₅₉	C₂×C₂²⋊C₄	1	2	yes	—
241	C₂×C₄×C₅₉	C₄×D₄	1	2	yes	—
242	C₂×C₄×C₅₉	C₄×D₄	1	2	yes	—
243	C₂×C₄×C₅₉	C₄×D₄	1	2	yes	—
244	C₂×C₄×C₅₉	#121	1	2	yes	—
245	C₂×C₄×C₅₉	#121	1	2	yes	—
246	C₂×C₄×C₅₉	#121	1	1	yes	characteristic
247	C₂×C₄×C₅₉	#121	1	1	yes	characteristic
248	C₂×C₄×C₅₉	#124	1	2	yes	—
249	C₂×C₄×C₅₉	#127	1	2	yes	—
250	C₂×C₄×C₅₉	#127	1	2	yes	—
251	C₂×C₄×C₅₉	C₂³×C₄	1	1	yes	characteristic
252	C₂×C₄×C₅₉	C₂²×D₄	1	1	yes	characteristic
253	C₂×C₄×C₅₉	C₂²×D₄	1	1	yes	characteristic
254	C₂×C₄×C₅₉	C₂²×D₄	1	1	yes	characteristic
255	C₂×C₄×C₅₉	C₂²×D₄	1	1	yes	characteristic
256	C₂×C₄×C₅₉	C₂×#41	1	1	yes	characteristic
257	C₈×C₅₉	—	2	4	no	—
258	C₈×C₅₉	—	4	2	no	—
259	C₈×C₅₉	—	4	2	no	—
260	C₈×C₅₉	C₂×C₂²⋊C₄	1	8	yes	—
261	#21250	C₅₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
262	C₂²×C₅₉	—	2	2	no	—
263	C₂²×C₅₉	—	2	2	no	—
264	C₂²×C₅₉	—	2	2	no	—
265	C₂²×C₅₉	—	4	2	no	—
266	C₂²×C₅₉	—	4	2	no	—
267	C₂²×C₅₉	—	4	2	no	—
268	C₂²×C₅₉	—	8	2	no	—
269	C₂²×C₅₉	—	8	2	no	—
270	C₂²×C₅₉	—	8	2	no	—
271	C₂²×C₅₉	#390	1	2	yes	—
272	C₂²×C₅₉	#390	1	2	yes	—
273	C₂²×C₅₉	C₂×C₄×D₄	1	1	yes	characteristic
274	C₂²×C₅₉	C₂×#121	1	1	yes	characteristic
275	C₂²×C₅₉	C₂×#124	1	1	yes	characteristic
276	C₄×C₅₉	—	4	2	no	—
277	C₄×C₅₉	—	4	4	no	—
278	C₄×C₅₉	—	4	4	no	—
279	C₄×C₅₉	#390	1	2	yes	—
280	C₄×C₅₉	#390	1	2	yes	—
281	C₄×C₅₉	C₂²×C₂²⋊C₄	1	1	yes	characteristic
282	C₄×C₅₉	C₂×C₄×D₄	1	1	yes	characteristic
283	C₄×C₅₉	C₂×#121	1	1	yes	characteristic
284	C₄×C₅₉	C₂×#127	1	1	yes	characteristic
285	C₂²×#137	C₂×C₅₉	1	1	yes	characteristic
286	C₂×#430	C₂×C₅₉	1	1	yes	characteristic, complemented
287	#2896	C₂×C₅₉	1	1	yes	characteristic
288	C₂×#419	C₂×C₅₉	1	1	yes	characteristic, complemented
289	C₂×#413	C₂×C₅₉	1	1	yes	characteristic
290	C₂²×#101	C₂×C₅₉	1	1	yes	characteristic, complemented
291	#2873	C₂×C₅₉	1	1	yes	characteristic, complemented
292	#1979	C₂×C₅₉	1	4	yes	complemented
293	#1977	C₂×C₅₉	1	4	yes	complemented
294	C₂×C₅₉	—	2	1	no	—
295	C₂×C₅₉	—	2	1	no	—
296	C₂×C₅₉	—	2	2	no	—
297	C₂×C₅₉	—	2	2	no	—
298	C₂×C₅₉	—	8	2	no	—
299	C₂×C₅₉	C₂×#390	1	1	yes	characteristic
300	C₂×C₅₉	#3069	1	2	yes	—
301	C₂²×#41	C₂²×C₅₉	1	1	yes	characteristic
302	C₂³×Q₈	C₂²×C₅₉	1	1	yes	characteristic
303	C₂×#137	—	2	2	no	—
304	C₂×#137	—	2	2	no	—
305	C₂×#137	—	2	4	no	—
306	C₂×#137	C₄×C₅₉	1	8	yes	complemented
307	C₂²×Q₁₆	C₂²×C₅₉	1	2	yes	—
308	C₂²×SD₁₆	C₂²×C₅₉	1	2	yes	—
309	C₂²×M₁₆	C₂²×C₅₉	1	1	yes	characteristic
310	C₂²×M₁₆	C₂²×C₅₉	1	1	yes	characteristic
311	C₂²×M₁₆	C₂²×C₅₉	1	1	yes	characteristic
312	C₂²×M₁₆	C₂²×C₅₉	1	1	yes	characteristic
313	C₂×#117	C₂²×C₅₉	1	1	yes	characteristic
314	#430	—	2	4	no	—
315	C₂×#108	C₂²×C₅₉	1	4	yes	—
316	#419	—	2	2	no	—
317	#419	C₂²×C₅₉	1	4	yes	—
318	#419	C₂²×C₅₉	1	2	yes	—
319	#418	C₂²×C₅₉	1	2	yes	—
320	#417	—	2	2	no	—
321	#416	—	2	2	no	—
322	C₂×#103	—	2	2	no	—
323	#413	—	2	4	no	—
324	C₂×#101	—	2	4	no	—
325	C₂×#101	C₂²×C₅₉	1	4	yes	—
326	C₂×#101	C₂²×C₅₉	1	2	yes	—
327	C₂×#100	C₂²×C₅₉	1	2	yes	—
328	#405	—	2	2	no	—
329	#405	C₂²×C₅₉	1	4	yes	—
330	C₄×M₁₆	—	2	2	no	—
331	C₅₉	#21250	1	1	yes	characteristic, direct product factor, Sylow
332	C₂×#41	—	2	2	no	—
333	C₂×#41	—	2	1	no	—
334	C₂×#41	—	2	1	no	—
335	C₂×#41	—	2	2	no	—
336	C₂×#41	—	2	1	no	—
337	C₂×#41	—	2	1	no	—
338	C₂×#41	—	2	2	no	—
339	C₂×#41	C₂×C₄×C₅₉	1	4	yes	—
340	C₂²×Q₈	—	2	2	no	—
341	C₂²×Q₈	—	2	1	no	—
342	C₂²×Q₈	—	2	1	no	—
343	C₂²×Q₈	—	2	1	no	—
344	C₂²×Q₈	—	2	2	no	—
345	C₂²×Q₈	—	2	1	no	—
346	C₂²×Q₈	—	2	1	no	—
347	C₂²×Q₈	—	2	2	no	—
348	C₂²×Q₈	C₂×C₄×C₅₉	1	4	yes	—
349	C₂²×Q₈	C₂³×C₅₉	1	2	yes	—
350	C₂²×Q₈	C₂³×C₅₉	1	1	yes	characteristic
351	C₂²×D₄	—	2	1	no	—
352	C₂²×D₄	C₂³×C₅₉	1	1	yes	characteristic
353	C₂³×C₄	—	2	1	no	—
354	C₂³×C₄	—	2	1	no	—
355	C₂³×C₄	C₂³×C₅₉	1	1	yes	characteristic
356	#137	—	2	16	no	—
357	#137	—	2	16	no	—
358	C₂×Q₁₆	—	2	4	no	—
359	C₂×Q₁₆	—	2	4	no	—
360	C₂×Q₁₆	C₂×C₄×C₅₉	1	8	yes	complemented
361	C₂×SD₁₆	—	2	4	no	—
362	C₂×SD₁₆	—	2	4	no	—
363	C₂×SD₁₆	C₂×C₄×C₅₉	1	8	yes	complemented
364	C₂×M₁₆	—	2	1	no	—
365	C₂×M₁₆	—	2	2	no	—
366	C₂×M₁₆	—	2	1	no	—
367	C₂×M₁₆	—	2	1	no	—
368	C₂×M₁₆	—	2	2	no	—
369	C₂×M₁₆	—	2	2	no	—
370	C₂×M₁₆	—	2	2	no	—
371	C₂×M₁₆	—	2	2	no	—
372	C₂×M₁₆	C₂×C₄×C₅₉	1	4	yes	—
373	C₂×M₁₆	D₄×C₅₉	1	4	yes	—
374	C₂×M₁₆	D₄×C₅₉	1	2	yes	—
375	C₂×M₁₆	D₄×C₅₉	1	2	yes	—
376	C₂×M₁₆	D₄×C₅₉	1	4	yes	—
377	C₂×M₁₆	C₂³×C₅₉	1	2	yes	—
378	C₂×M₁₆	C₂³×C₅₉	1	2	yes	—
379	C₂×M₁₆	C₂³×C₅₉	1	2	yes	—
380	C₂²×C₈	—	2	1	no	—
381	C₂²×C₈	—	2	1	no	—
382	C₂²×C₈	—	2	1	no	—
383	C₂²×C₈	C₂³×C₅₉	1	2	yes	—
384	#117	—	2	1	no	—
385	#117	—	2	1	no	—
386	#117	D₄×C₅₉	1	2	yes	—
387	#117	C₂³×C₅₉	1	2	yes	—
388	C₂×C₄⋊C₄	D₄×C₅₉	1	2	yes	—
389	C₂×C₂²⋊C₄	—	2	1	no	—
390	C₂×C₄²	—	2	1	no	—
391	#108	—	2	8	no	—
392	#103	—	2	8	no	—
393	#103	—	2	4	no	—
394	#102	—	2	4	no	—
395	#101	—	2	8	no	—
396	#101	—	2	4	no	—
397	#100	—	2	4	no	—
398	#97	—	2	4	no	—
399	C₄×C₈	—	2	4	no	—
400	C₂⁴	—	2	1	no	—
401	C₂⁴	#41×C₅₉	1	1	yes	characteristic
402	#41	—	2	4	no	—
403	#41	—	2	4	no	—
404	#41	—	2	4	no	—
405	#41	—	2	4	no	—
406	#41	—	4	2	no	—
407	#41	—	4	2	no	—
408	#41	—	4	2	no	—
409	#41	—	4	2	no	—
410	C₂×Q₈	—	2	4	no	—
411	C₂×Q₈	—	2	2	no	—
412	C₂×Q₈	—	2	1	no	—
413	C₂×Q₈	—	2	4	no	—
414	C₂×Q₈	—	2	4	no	—
415	C₂×Q₈	—	2	4	no	—
416	C₂×Q₈	—	2	4	no	—
417	C₂×Q₈	—	2	2	no	—
418	C₂×Q₈	—	2	1	no	—
419	C₂×Q₈	—	2	2	no	—
420	C₂×Q₈	—	2	2	no	—
421	C₂×Q₈	—	2	1	no	—
422	C₂×Q₈	—	2	1	no	—
423	C₂×Q₈	—	2	2	no	—
424	C₂×Q₈	—	2	1	no	—
425	C₂×Q₈	—	4	2	no	—
426	C₂×Q₈	—	4	2	no	—
427	C₂×Q₈	—	4	1	no	—
428	C₂×Q₈	—	4	1	no	—
429	C₂×Q₈	—	4	2	no	—
430	C₂×Q₈	—	4	2	no	—
431	C₂×Q₈	—	4	2	no	—
432	C₂×Q₈	C₂²×C₄×C₅₉	1	4	yes	—
433	C₂×Q₈	C₂²×C₄×C₅₉	1	2	yes	—
434	C₂×D₄	—	2	4	no	—
435	C₂×D₄	—	2	1	no	—
436	C₂×D₄	—	2	1	no	—
437	C₂×D₄	—	2	1	no	—
438	C₂×D₄	—	2	1	no	—
439	C₂×D₄	—	2	1	no	—
440	C₂×D₄	—	4	1	no	—
441	C₂×D₄	—	4	1	no	—
442	C₂×D₄	—	4	2	no	—
443	C₂×D₄	C₂²×C₄×C₅₉	1	2	yes	—
444	C₂²×C₄	—	2	4	no	—
445	C₂²×C₄	—	2	1	no	—
446	C₂²×C₄	—	2	2	no	—
447	C₂²×C₄	—	2	2	no	—
448	C₂²×C₄	—	2	4	no	—
449	C₂²×C₄	—	4	1	no	—
450	C₂²×C₄	—	4	1	no	—
451	C₂²×C₄	—	4	2	no	—
452	C₂²×C₄	—	4	1	no	—
453	C₂²×C₄	—	4	1	no	—
454	C₂²×C₄	—	4	2	no	—
455	C₂²×C₄	C₂²×C₄×C₅₉	1	2	yes	—
456	C₂²×C₄	C₂×D₄×C₅₉	1	1	yes	characteristic
457	C₂²×C₄	C₂×D₄×C₅₉	1	1	yes	characteristic
458	C₂²×C₄	C₂×D₄×C₅₉	1	2	yes	—
459	C₂²×C₄	C₂×D₄×C₅₉	1	1	yes	characteristic
460	C₂²×C₄	C₂×D₄×C₅₉	1	1	yes	characteristic
461	C₂²×C₄	C₂×D₄×C₅₉	1	2	yes	—
462	C₂²×C₄	#41×C₅₉	1	1	yes	characteristic
463	C₂²×C₄	#41×C₅₉	1	2	yes	—
464	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
465	Q₁₆	—	2	16	no	—
466	SD₁₆	—	2	16	no	—
467	M₁₆	—	2	4	no	—
468	M₁₆	—	2	2	no	—
469	M₁₆	—	2	2	no	—
470	M₁₆	—	2	2	no	—
471	M₁₆	—	2	2	no	—
472	M₁₆	—	2	2	no	—
473	M₁₆	—	4	2	no	—
474	M₁₆	—	4	2	no	—
475	M₁₆	C₂²⋊C₄×C₅₉	1	8	yes	—
476	M₁₆	C₂²⋊C₄×C₅₉	1	8	yes	—
477	M₁₆	C₂×D₄×C₅₉	1	4	yes	—
478	C₂×C₈	—	2	4	no	—
479	C₂×C₈	—	2	2	no	—
480	C₂×C₈	—	2	2	no	—
481	C₂×C₈	—	2	2	no	—
482	C₂×C₈	—	4	2	no	—
483	C₂×C₈	—	4	2	no	—
484	C₂×C₈	C₂²×C₄×C₅₉	1	4	yes	—
485	C₂×C₈	C₂×D₄×C₅₉	1	4	yes	—
486	C₂×C₈	C₂×D₄×C₅₉	1	4	yes	—
487	C₄⋊C₄	—	2	2	no	—
488	C₄⋊C₄	C₂×D₄×C₅₉	1	4	yes	—
489	C₂²⋊C₄	—	2	2	no	—
490	C₂²⋊C₄	—	2	2	no	—
491	C₄²	—	2	2	no	—
492	C₄²	—	2	2	no	—
493	C₂³	—	2	2	no	—
494	C₂³	—	4	2	no	—
495	C₂³	—	4	1	no	—
496	C₂³	—	4	1	no	—
497	C₂³	—	8	2	no	—
498	C₂³	C₄×D₄×C₅₉	1	2	yes	—
499	C₂³	#121×C₅₉	1	1	yes	characteristic
500	C₂³	#121×C₅₉	1	1	yes	characteristic
501	C₂³	#124×C₅₉	1	2	yes	—
502	C₂³	C₂×#41×C₅₉	1	1	yes	characteristic
503	Q₈	—	2	4	no	—
504	Q₈	—	2	2	no	—
505	Q₈	—	2	4	no	—
506	Q₈	—	2	2	no	—
507	Q₈	—	4	4	no	—
508	Q₈	—	4	4	no	—
509	Q₈	—	4	2	no	—
510	Q₈	—	4	1	no	—
511	Q₈	—	4	2	no	—
512	Q₈	—	4	1	no	—
513	D₄	—	2	2	no	—
514	D₄	—	2	2	no	—
515	D₄	—	4	4	no	—
516	D₄	—	4	4	no	—
517	D₄	—	4	1	no	—
518	D₄	—	4	1	no	—
519	C₂×C₄	—	2	2	no	—
520	C₂×C₄	—	2	4	no	—
521	C₂×C₄	—	2	4	no	—
522	C₂×C₄	—	4	4	no	—
523	C₂×C₄	—	4	4	no	—
524	C₂×C₄	—	4	1	no	—
525	C₂×C₄	—	4	2	no	—
526	C₂×C₄	—	4	1	no	—
527	C₂×C₄	—	4	2	no	—
528	C₂×C₄	—	4	4	no	—
529	C₂×C₄	—	4	4	no	—
530	C₂×C₄	—	8	2	no	—
531	C₂×C₄	C₂×C₂²⋊C₄×C₅₉	1	2	yes	—
532	C₂×C₄	C₂×C₂²⋊C₄×C₅₉	1	2	yes	—
533	C₂×C₄	C₄×D₄×C₅₉	1	2	yes	—
534	C₂×C₄	C₄×D₄×C₅₉	1	2	yes	—
535	C₂×C₄	C₄×D₄×C₅₉	1	2	yes	—
536	C₂×C₄	#121×C₅₉	1	1	yes	characteristic
537	C₂×C₄	#121×C₅₉	1	1	yes	characteristic
538	C₂×C₄	#121×C₅₉	1	2	yes	—
539	C₂×C₄	#121×C₅₉	1	2	yes	—
540	C₂×C₄	#124×C₅₉	1	2	yes	—
541	C₂×C₄	#127×C₅₉	1	2	yes	—
542	C₂×C₄	#127×C₅₉	1	2	yes	—
543	C₂×C₄	C₂³×C₄×C₅₉	1	1	yes	characteristic
544	C₂×C₄	C₂²×D₄×C₅₉	1	1	yes	characteristic
545	C₂×C₄	C₂²×D₄×C₅₉	1	1	yes	characteristic
546	C₂×C₄	C₂²×D₄×C₅₉	1	1	yes	characteristic
547	C₂×C₄	C₂²×D₄×C₅₉	1	1	yes	characteristic
548	C₂×C₄	C₂×#41×C₅₉	1	1	yes	characteristic
549	C₈	—	2	4	no	—
550	C₈	—	4	2	no	—
551	C₈	—	4	2	no	—
552	C₈	C₂×C₂²⋊C₄×C₅₉	1	8	yes	—
553	C₂²	—	2	2	no	—
554	C₂²	—	2	2	no	—
555	C₂²	—	2	2	no	—
556	C₂²	—	4	2	no	—
557	C₂²	—	4	2	no	—
558	C₂²	—	4	2	no	—
559	C₂²	—	8	2	no	—
560	C₂²	—	8	2	no	—
561	C₂²	—	8	2	no	—
562	C₂²	C₅₉×#390	1	2	yes	—
563	C₂²	C₅₉×#390	1	2	yes	—
564	C₂²	C₂×C₄×D₄×C₅₉	1	1	yes	characteristic
565	C₂²	C₂×#121×C₅₉	1	1	yes	characteristic
566	C₂²	C₂×#124×C₅₉	1	1	yes	characteristic
567	C₄	—	4	2	no	—
568	C₄	—	4	4	no	—
569	C₄	—	4	4	no	—
570	C₄	C₅₉×#390	1	2	yes	—
571	C₄	C₅₉×#390	1	2	yes	—
572	C₄	C₂²×C₂²⋊C₄×C₅₉	1	1	yes	characteristic
573	C₄	C₂×C₄×D₄×C₅₉	1	1	yes	characteristic
574	C₄	C₂×#121×C₅₉	1	1	yes	characteristic
575	C₄	C₂×#127×C₅₉	1	1	yes	characteristic
576	C₂	—	2	1	no	—
577	C₂	—	2	1	no	—
578	C₂	—	2	2	no	—
579	C₂	—	2	2	no	—
580	C₂	—	8	2	no	—
581	C₂	C₂×C₅₉×#390	1	1	yes	characteristic
582	C₂	C₅₉×#3069	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₅₉	C₂×#121
commutator	C₂×C₄	C₂³×C₄×C₅₉
Frattini, cosocle	C₂²×C₄	C₂⁴×C₅₉
prime radical	C₂²×#41×C₅₉	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₅₉ ◁ C₂³×C₄×C₅₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₅₉×#430	C₂	semidirect
4. C₂×C₅₉×#419	C₂	semidirect
6. C₂²×#101×C₅₉	C₂	semidirect
7. C₅₉×#2873	C₂	semidirect
8. C₅₉×#1979	C₂	semidirect
9. C₅₉×#1977	C₂	semidirect
15. C₂×#137×C₅₉	C₄	semidirect
68. C₂×Q₁₆×C₅₉	C₂×C₄	semidirect
71. C₂×SD₁₆×C₅₉	C₂×C₄	semidirect
261. #21250	C₅₉	direct (N × H)
286. C₂×#430	C₂×C₅₉	semidirect
288. C₂×#419	C₂×C₅₉	semidirect
290. C₂²×#101	C₂×C₅₉	semidirect
291. #2873	C₂×C₅₉	semidirect
292. #1979	C₂×C₅₉	semidirect
293. #1977	C₂×C₅₉	semidirect
306. C₂×#137	C₄×C₅₉	semidirect
331. C₅₉	#21250	direct (N × H)
360. C₂×Q₁₆	C₂×C₄×C₅₉	semidirect
363. C₂×SD₁₆	C₂×C₄×C₅₉	semidirect

Maximal subgroups

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

subgroup	index
C₂²×#137×C₅₉	2
C₂×C₅₉×#430	2
C₅₉×#2896	2
C₂×C₅₉×#419	2
C₂×C₅₉×#413	2
C₂²×#101×C₅₉	2
C₅₉×#2873	2
C₅₉×#1979	2
C₅₉×#1977	2
#21250	59

Subgroups — C59×#21250 #28433359

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₉×#21250 #28433359