Subgroups — C₅₉×#60884 #28472993

Order 15104.

1622 conjugacy classes of subgroups.

The subgroup lattice has 496 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅₉×#3509	C₂	1	1	yes	maximal, characteristic
2	C₅₉×#3504	C₂	1	1	yes	maximal, characteristic
3	C₅₉×#3242	C₂	1	8	yes	maximal, complemented
4	C₅₉×#3237	C₂	1	4	yes	maximal, complemented
5	C₅₉×#3236	C₂	1	4	yes	maximal, complemented
6	C₅₉×#3166	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅₉×#3162	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅₉×#3139	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₅₉×#491	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅₉×#3097	C₂	1	4	yes	maximal
11	C₅₉×#3082	C₂	1	4	yes	maximal, complemented
12	C₅₉×#2923	C₂	1	1	yes	maximal, characteristic
13	C₅₉×#557	—	2	2	no	—
14	C₅₉×#557	—	2	2	no	—
15	C₅₉×#556	—	2	2	no	—
16	C₅₉×#554	—	2	4	no	—
17	C₅₉×#554	—	2	2	no	—
18	C₅₉×#552	—	2	4	no	—
19	C₅₉×#544	C₂²	1	2	yes	—
20	C₅₉×#544	C₂²	1	4	yes	—
21	C₅₉×#541	C₂²	1	4	yes	—
22	C₅₉×#536	C₂²	1	2	yes	—
23	C₅₉×#533	C₂²	1	4	yes	—
24	C₅₉×#533	C₂²	1	1	yes	characteristic
25	C₅₉×#533	C₂²	1	1	yes	characteristic
26	C₅₉×#533	C₂²	1	2	yes	—
27	C₂×C₄⋊Q₈×C₅₉	C₂²	1	1	yes	characteristic
28	C₂×#125×C₅₉	C₂²	1	1	yes	characteristic
29	C₂×#125×C₅₉	C₂²	1	2	yes	—
30	C₅₉×#520	C₂²	1	2	yes	—
31	C₅₉×#519	C₂²	1	2	yes	—
32	C₄×#41×C₅₉	C₂²	1	1	yes	characteristic
33	C₅₉×#501	C₂²	1	2	yes	—
34	C₅₉×#501	C₂²	1	2	yes	—
35	C₅₉×#501	C₂²	1	4	yes	—
36	C₅₉×#501	C₂²	1	4	yes	—
37	C₅₉×#499	C₂²	1	4	yes	—
38	C₅₉×#491	C₂²	1	4	yes	—
39	C₅₉×#491	C₂²	1	4	yes	—
40	C₅₉×#491	C₂²	1	2	yes	—
41	C₅₉×#491	C₂²	1	2	yes	—
42	C₅₉×#487	C₂²	1	4	yes	—
43	C₅₉×#485	C₂²	1	8	yes	—
44	C₅₉×#485	C₂²	1	8	yes	—
45	C₅₉×#484	C₂²	1	8	yes	—
46	C₅₉×#483	C₂²	1	8	yes	—
47	C₅₉×#479	C₂²	1	8	yes	—
48	C₅₉×#479	C₂²	1	8	yes	—
49	C₅₉×#477	C₂²	1	8	yes	—
50	C₅₉×#475	C₂²	1	8	yes	—
51	C₅₉×#433	C₂²	1	4	yes	—
52	C₅₉×#432	C₂²	1	4	yes	—
53	C₅₉×#428	C₂²	1	4	yes	—
54	C₅₉×#427	C₂²	1	4	yes	—
55	C₅₉×#424	C₂²	1	2	yes	—
56	C₅₉×#419	C₂²	1	4	yes	—
57	C₂×#103×C₅₉	C₂²	1	4	yes	—
58	C₅₉×#408	C₂²	1	2	yes	—
59	C₄×M₁₆×C₅₉	C₂²	1	1	yes	characteristic
60	C₂×#97×C₅₉	C₂²	1	1	yes	characteristic
61	C₂×#41×C₅₉	C₂³	1	1	yes	characteristic
62	C₂²×Q₈×C₅₉	C₂³	1	2	yes	—
63	C₂×M₁₆×C₅₉	C₂³	1	2	yes	—
64	C₂²×C₈×C₅₉	C₂³	1	2	yes	—
65	C₄⋊Q₈×C₅₉	—	2	2	no	—
66	C₄⋊Q₈×C₅₉	—	2	2	no	—
67	C₄⋊Q₈×C₅₉	—	2	4	no	—
68	C₄⋊Q₈×C₅₉	—	2	2	no	—
69	C₄⋊Q₈×C₅₉	C₂³	1	2	yes	—
70	C₄⋊Q₈×C₅₉	C₂³	1	2	yes	—
71	C₄⋊Q₈×C₅₉	C₂³	1	4	yes	—
72	C₄⋊Q₈×C₅₉	C₂³	1	2	yes	—
73	C₄⋊Q₈×C₅₉	C₂³	1	2	yes	—
74	#126×C₅₉	—	2	8	no	—
75	#125×C₅₉	—	2	8	no	—
76	#125×C₅₉	—	2	2	no	—
77	#125×C₅₉	—	2	4	no	—
78	#125×C₅₉	—	2	4	no	—
79	#125×C₅₉	—	2	2	no	—
80	#125×C₅₉	—	2	4	no	—
81	#125×C₅₉	C₂³	1	4	yes	—
82	#125×C₅₉	C₂³	1	2	yes	—
83	#125×C₅₉	C₂³	1	2	yes	—
84	#125×C₅₉	C₂³	1	1	yes	characteristic
85	#125×C₅₉	C₂³	1	1	yes	characteristic
86	#125×C₅₉	C₂³	1	2	yes	—
87	#124×C₅₉	—	2	2	no	—
88	#123×C₅₉	—	2	4	no	—
89	C₂²⋊Q₈×C₅₉	—	2	2	no	—
90	C₂²⋊Q₈×C₅₉	—	2	4	no	—
91	C₂²⋊Q₈×C₅₉	—	2	2	no	—
92	C₂²⋊Q₈×C₅₉	—	2	4	no	—
93	C₂²⋊Q₈×C₅₉	—	2	4	no	—
94	C₂²⋊Q₈×C₅₉	—	2	4	no	—
95	C₂²⋊Q₈×C₅₉	—	2	4	no	—
96	C₂²⋊Q₈×C₅₉	C₂³	1	8	yes	—
97	C₄×Q₈×C₅₉	—	2	2	no	—
98	C₄×Q₈×C₅₉	—	2	4	no	—
99	C₄×Q₈×C₅₉	—	2	4	no	—
100	C₄×Q₈×C₅₉	—	2	4	no	—
101	C₄×Q₈×C₅₉	—	2	2	no	—
102	C₄×Q₈×C₅₉	—	2	2	no	—
103	C₄×Q₈×C₅₉	D₄	1	2	yes	—
104	C₄×Q₈×C₅₉	C₂³	1	8	yes	—
105	C₄×D₄×C₅₉	—	2	4	no	—
106	C₄×D₄×C₅₉	—	2	2	no	—
107	C₄×D₄×C₅₉	D₄	1	4	yes	—
108	C₄×D₄×C₅₉	D₄	1	2	yes	—
109	#117×C₅₉	—	2	4	no	—
110	#117×C₅₉	—	2	4	no	—
111	#117×C₅₉	C₂³	1	2	yes	—
112	#117×C₅₉	C₂³	1	2	yes	—
113	#117×C₅₉	C₂³	1	4	yes	—
114	#117×C₅₉	C₂³	1	1	yes	characteristic
115	#117×C₅₉	C₂³	1	2	yes	—
116	C₂×C₄⋊C₄×C₅₉	—	2	2	no	—
117	C₂×C₄⋊C₄×C₅₉	—	2	4	no	—
118	C₂×C₄⋊C₄×C₅₉	—	2	2	no	—
119	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
120	C₂×C₄⋊C₄×C₅₉	C₂³	1	4	yes	—
121	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
122	C₂×C₄²×C₅₉	C₂³	1	2	yes	—
123	#107×C₅₉	C₂³	1	4	yes	—
124	#107×C₅₉	C₂³	1	4	yes	—
125	#107×C₅₉	C₂³	1	8	yes	—
126	#106×C₅₉	C₂³	1	4	yes	—
127	#106×C₅₉	C₂³	1	4	yes	—
128	#106×C₅₉	C₂³	1	8	yes	—
129	C₄⋊C₈×C₅₉	C₂³	1	8	yes	—
130	#103×C₅₉	C₂³	1	8	yes	—
131	#103×C₅₉	C₂³	1	8	yes	—
132	#103×C₅₉	C₂³	1	8	yes	—
133	#103×C₅₉	C₂³	1	8	yes	—
134	C₂²⋊C₈×C₅₉	C₂³	1	8	yes	—
135	#97×C₅₉	C₂³	1	2	yes	—
136	#97×C₅₉	C₂³	1	2	yes	—
137	#97×C₅₉	C₂³	1	2	yes	—
138	C₄×C₈×C₅₉	C₂³	1	2	yes	—
139	#41×C₅₉	—	2	4	no	—
140	C₂×Q₈×C₅₉	—	2	2	no	—
141	C₂×Q₈×C₅₉	—	2	2	no	—
142	C₂×Q₈×C₅₉	—	2	4	no	—
143	C₂×Q₈×C₅₉	—	2	2	no	—
144	C₂×Q₈×C₅₉	—	2	8	no	—
145	C₂×Q₈×C₅₉	C₂×D₄	1	1	yes	characteristic
146	C₂×Q₈×C₅₉	C₂⁴	1	4	yes	—
147	C₂×D₄×C₅₉	C₂×D₄	1	2	yes	—
148	C₂×D₄×C₅₉	C₂×D₄	1	1	yes	characteristic
149	C₂²×C₄×C₅₉	—	2	2	no	—
150	C₂²×C₄×C₅₉	—	2	4	no	—
151	C₂²×C₄×C₅₉	—	2	2	no	—
152	C₂²×C₄×C₅₉	C₂×D₄	1	2	yes	—
153	C₂²×C₄×C₅₉	C₂×D₄	1	4	yes	—
154	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
155	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
156	M₁₆×C₅₉	—	2	4	no	—
157	C₂×C₈×C₅₉	—	2	4	no	—
158	C₂×C₈×C₅₉	C₂⁴	1	4	yes	—
159	C₂×C₈×C₅₉	C₂⁴	1	4	yes	—
160	C₄⋊C₄×C₅₉	—	2	4	no	—
161	C₄⋊C₄×C₅₉	—	2	2	no	—
162	C₄⋊C₄×C₅₉	—	2	4	no	—
163	C₄⋊C₄×C₅₉	—	2	4	no	—
164	C₄⋊C₄×C₅₉	—	2	4	no	—
165	C₄⋊C₄×C₅₉	—	2	4	no	—
166	C₄⋊C₄×C₅₉	—	2	4	no	—
167	C₄⋊C₄×C₅₉	—	2	4	no	—
168	C₄⋊C₄×C₅₉	—	2	2	no	—
169	C₄⋊C₄×C₅₉	—	2	2	no	—
170	C₄⋊C₄×C₅₉	—	2	8	no	—
171	C₄⋊C₄×C₅₉	—	2	2	no	—
172	C₄⋊C₄×C₅₉	—	2	4	no	—
173	C₄⋊C₄×C₅₉	—	2	2	no	—
174	C₄⋊C₄×C₅₉	—	2	4	no	—
175	C₄⋊C₄×C₅₉	—	2	8	no	—
176	C₄⋊C₄×C₅₉	C₂×D₄	1	2	yes	—
177	C₄⋊C₄×C₅₉	C₂×D₄	1	4	yes	—
178	C₄⋊C₄×C₅₉	C₂⁴	1	4	yes	—
179	C₄⋊C₄×C₅₉	C₂⁴	1	2	yes	—
180	C₄⋊C₄×C₅₉	C₂⁴	1	2	yes	—
181	C₄⋊C₄×C₅₉	C₂⁴	1	4	yes	—
182	C₂²⋊C₄×C₅₉	—	2	2	no	—
183	C₂²⋊C₄×C₅₉	—	2	8	no	—
184	C₂²⋊C₄×C₅₉	—	2	4	no	—
185	C₂²⋊C₄×C₅₉	—	2	2	no	—
186	C₂²⋊C₄×C₅₉	C₂×D₄	1	2	yes	—
187	C₂²⋊C₄×C₅₉	C₂×D₄	1	4	yes	—
188	C₄²×C₅₉	—	2	8	no	—
189	C₄²×C₅₉	—	2	4	no	—
190	C₄²×C₅₉	—	2	2	no	—
191	C₄²×C₅₉	—	2	2	no	—
192	C₄²×C₅₉	C₂×D₄	1	4	yes	—
193	C₄²×C₅₉	C₂×D₄	1	2	yes	—
194	C₄²×C₅₉	C₂⁴	1	1	yes	characteristic
195	C₄²×C₅₉	C₂⁴	1	1	yes	characteristic
196	C₄²×C₅₉	C₂⁴	1	2	yes	—
197	C₂³×C₅₉	C₂²×D₄	1	2	yes	—
198	C₂³×C₅₉	C₂²×D₄	1	1	yes	characteristic
199	Q₈×C₅₉	—	2	2	no	—
200	Q₈×C₅₉	—	2	8	no	—
201	Q₈×C₅₉	—	4	4	no	—
202	Q₈×C₅₉	—	4	4	no	—
203	Q₈×C₅₉	—	8	4	no	—
204	Q₈×C₅₉	—	8	2	no	—
205	D₄×C₅₉	—	2	4	no	—
206	D₄×C₅₉	—	2	2	no	—
207	C₂×C₄×C₅₉	—	2	4	no	—
208	C₂×C₄×C₅₉	—	2	4	no	—
209	C₂×C₄×C₅₉	—	2	2	no	—
210	C₂×C₄×C₅₉	—	2	4	no	—
211	C₂×C₄×C₅₉	—	2	4	no	—
212	C₂×C₄×C₅₉	—	2	2	no	—
213	C₂×C₄×C₅₉	—	4	2	no	—
214	C₂×C₄×C₅₉	—	4	4	no	—
215	C₂×C₄×C₅₉	—	4	4	no	—
216	C₂×C₄×C₅₉	—	8	2	no	—
217	C₂×C₄×C₅₉	—	8	4	no	—
218	C₂×C₄×C₅₉	C₂²×D₄	1	2	yes	—
219	C₂×C₄×C₅₉	C₂²×D₄	1	4	yes	—
220	C₂×C₄×C₅₉	C₂²×D₄	1	2	yes	—
221	C₂×C₄×C₅₉	C₂²×D₄	1	2	yes	—
222	C₂×C₄×C₅₉	C₂²×D₄	1	1	yes	characteristic
223	C₂×C₄×C₅₉	2₋¹⁺⁴	1	4	yes	—
224	C₂×C₄×C₅₉	C₂⁵	1	1	yes	characteristic
225	C₈×C₅₉	—	2	4	no	—
226	C₈×C₅₉	—	2	4	no	—
227	#60884	C₅₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
228	C₂²×C₅₉	—	2	2	no	—
229	C₂²×C₅₉	—	2	4	no	—
230	C₂²×C₅₉	—	2	2	no	—
231	C₂²×C₅₉	#536	1	2	yes	—
232	C₂²×C₅₉	C₂³×D₄	1	1	yes	characteristic
233	C₄×C₅₉	—	2	2	no	—
234	C₄×C₅₉	—	2	4	no	—
235	C₄×C₅₉	—	2	2	no	—
236	C₄×C₅₉	—	2	2	no	—
237	C₄×C₅₉	—	4	4	no	—
238	C₄×C₅₉	—	4	2	no	—
239	C₄×C₅₉	—	4	4	no	—
240	C₄×C₅₉	—	4	2	no	—
241	C₄×C₅₉	—	4	4	no	—
242	C₄×C₅₉	#536	1	2	yes	—
243	C₄×C₅₉	C₂×2₋¹⁺⁴	1	2	yes	—
244	#3509	C₂×C₅₉	1	1	yes	characteristic
245	#3504	C₂×C₅₉	1	1	yes	characteristic
246	#3242	C₂×C₅₉	1	8	yes	complemented
247	#3237	C₂×C₅₉	1	4	yes	complemented
248	#3236	C₂×C₅₉	1	4	yes	complemented
249	#3166	C₂×C₅₉	1	1	yes	characteristic, complemented
250	#3162	C₂×C₅₉	1	1	yes	characteristic, complemented
251	#3139	C₂×C₅₉	1	1	yes	characteristic, complemented
252	C₂×#491	C₂×C₅₉	1	1	yes	characteristic, complemented
253	#3097	C₂×C₅₉	1	4	yes	—
254	#3082	C₂×C₅₉	1	4	yes	complemented
255	#2923	C₂×C₅₉	1	1	yes	characteristic
256	C₂×C₅₉	—	2	2	no	—
257	C₂×C₅₉	—	4	2	no	—
258	C₂×C₅₉	C₂×#536	1	1	yes	characteristic
259	C₂×C₅₉	#3586	1	2	yes	—
260	#557	—	2	2	no	—
261	#557	—	2	2	no	—
262	#556	—	2	2	no	—
263	#554	—	2	4	no	—
264	#554	—	2	2	no	—
265	#552	—	2	4	no	—
266	#544	C₂²×C₅₉	1	2	yes	—
267	#544	C₂²×C₅₉	1	4	yes	—
268	#541	C₂²×C₅₉	1	4	yes	—
269	#536	C₂²×C₅₉	1	2	yes	—
270	#533	C₂²×C₅₉	1	4	yes	—
271	#533	C₂²×C₅₉	1	1	yes	characteristic
272	#533	C₂²×C₅₉	1	1	yes	characteristic
273	#533	C₂²×C₅₉	1	2	yes	—
274	C₂×C₄⋊Q₈	C₂²×C₅₉	1	1	yes	characteristic
275	C₂×#125	C₂²×C₅₉	1	1	yes	characteristic
276	C₂×#125	C₂²×C₅₉	1	2	yes	—
277	#520	C₂²×C₅₉	1	2	yes	—
278	#519	C₂²×C₅₉	1	2	yes	—
279	C₄×#41	C₂²×C₅₉	1	1	yes	characteristic
280	#501	C₂²×C₅₉	1	2	yes	—
281	#501	C₂²×C₅₉	1	2	yes	—
282	#501	C₂²×C₅₉	1	4	yes	—
283	#501	C₂²×C₅₉	1	4	yes	—
284	#499	C₂²×C₅₉	1	4	yes	—
285	#491	C₂²×C₅₉	1	4	yes	—
286	#491	C₂²×C₅₉	1	4	yes	—
287	#491	C₂²×C₅₉	1	2	yes	—
288	#491	C₂²×C₅₉	1	2	yes	—
289	#487	C₂²×C₅₉	1	4	yes	—
290	#485	C₂²×C₅₉	1	8	yes	—
291	#485	C₂²×C₅₉	1	8	yes	—
292	#484	C₂²×C₅₉	1	8	yes	—
293	#483	C₂²×C₅₉	1	8	yes	—
294	#479	C₂²×C₅₉	1	8	yes	—
295	#479	C₂²×C₅₉	1	8	yes	—
296	#477	C₂²×C₅₉	1	8	yes	—
297	#475	C₂²×C₅₉	1	8	yes	—
298	#433	C₂²×C₅₉	1	4	yes	—
299	#432	C₂²×C₅₉	1	4	yes	—
300	#428	C₂²×C₅₉	1	4	yes	—
301	#427	C₂²×C₅₉	1	4	yes	—
302	#424	C₂²×C₅₉	1	2	yes	—
303	#419	C₂²×C₅₉	1	4	yes	—
304	C₂×#103	C₂²×C₅₉	1	4	yes	—
305	#408	C₂²×C₅₉	1	2	yes	—
306	C₄×M₁₆	C₂²×C₅₉	1	1	yes	characteristic
307	C₂×#97	C₂²×C₅₉	1	1	yes	characteristic
308	C₅₉	#60884	1	1	yes	characteristic, direct product factor, Sylow
309	C₂×#41	C₂³×C₅₉	1	1	yes	characteristic
310	C₂²×Q₈	C₂³×C₅₉	1	2	yes	—
311	C₂×M₁₆	C₂³×C₅₉	1	2	yes	—
312	C₂²×C₈	C₂³×C₅₉	1	2	yes	—
313	C₄⋊Q₈	—	2	2	no	—
314	C₄⋊Q₈	—	2	2	no	—
315	C₄⋊Q₈	—	2	4	no	—
316	C₄⋊Q₈	—	2	2	no	—
317	C₄⋊Q₈	C₂³×C₅₉	1	2	yes	—
318	C₄⋊Q₈	C₂³×C₅₉	1	2	yes	—
319	C₄⋊Q₈	C₂³×C₅₉	1	2	yes	—
320	C₄⋊Q₈	C₂³×C₅₉	1	4	yes	—
321	C₄⋊Q₈	C₂³×C₅₉	1	2	yes	—
322	#126	—	2	8	no	—
323	#125	—	2	8	no	—
324	#125	—	2	2	no	—
325	#125	—	2	4	no	—
326	#125	—	2	4	no	—
327	#125	—	2	2	no	—
328	#125	—	2	4	no	—
329	#125	C₂³×C₅₉	1	2	yes	—
330	#125	C₂³×C₅₉	1	1	yes	characteristic
331	#125	C₂³×C₅₉	1	4	yes	—
332	#125	C₂³×C₅₉	1	2	yes	—
333	#125	C₂³×C₅₉	1	1	yes	characteristic
334	#125	C₂³×C₅₉	1	2	yes	—
335	#124	—	2	2	no	—
336	#123	—	2	4	no	—
337	C₂²⋊Q₈	—	2	2	no	—
338	C₂²⋊Q₈	—	2	4	no	—
339	C₂²⋊Q₈	—	2	2	no	—
340	C₂²⋊Q₈	—	2	4	no	—
341	C₂²⋊Q₈	—	2	4	no	—
342	C₂²⋊Q₈	—	2	4	no	—
343	C₂²⋊Q₈	—	2	4	no	—
344	C₂²⋊Q₈	C₂³×C₅₉	1	8	yes	—
345	C₄×Q₈	—	2	2	no	—
346	C₄×Q₈	—	2	4	no	—
347	C₄×Q₈	—	2	4	no	—
348	C₄×Q₈	—	2	4	no	—
349	C₄×Q₈	—	2	2	no	—
350	C₄×Q₈	—	2	2	no	—
351	C₄×Q₈	D₄×C₅₉	1	2	yes	—
352	C₄×Q₈	C₂³×C₅₉	1	8	yes	—
353	C₄×D₄	—	2	4	no	—
354	C₄×D₄	—	2	2	no	—
355	C₄×D₄	D₄×C₅₉	1	4	yes	—
356	C₄×D₄	D₄×C₅₉	1	2	yes	—
357	#117	—	2	4	no	—
358	#117	—	2	4	no	—
359	#117	C₂³×C₅₉	1	2	yes	—
360	#117	C₂³×C₅₉	1	2	yes	—
361	#117	C₂³×C₅₉	1	4	yes	—
362	#117	C₂³×C₅₉	1	1	yes	characteristic
363	#117	C₂³×C₅₉	1	2	yes	—
364	C₂×C₄⋊C₄	—	2	2	no	—
365	C₂×C₄⋊C₄	—	2	4	no	—
366	C₂×C₄⋊C₄	—	2	2	no	—
367	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
368	C₂×C₄⋊C₄	C₂³×C₅₉	1	4	yes	—
369	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
370	C₂×C₄²	C₂³×C₅₉	1	2	yes	—
371	#107	C₂³×C₅₉	1	4	yes	—
372	#107	C₂³×C₅₉	1	4	yes	—
373	#107	C₂³×C₅₉	1	8	yes	—
374	#106	C₂³×C₅₉	1	4	yes	—
375	#106	C₂³×C₅₉	1	4	yes	—
376	#106	C₂³×C₅₉	1	8	yes	—
377	C₄⋊C₈	C₂³×C₅₉	1	8	yes	—
378	#103	C₂³×C₅₉	1	8	yes	—
379	#103	C₂³×C₅₉	1	8	yes	—
380	#103	C₂³×C₅₉	1	8	yes	—
381	#103	C₂³×C₅₉	1	8	yes	—
382	C₂²⋊C₈	C₂³×C₅₉	1	8	yes	—
383	#97	C₂³×C₅₉	1	2	yes	—
384	#97	C₂³×C₅₉	1	2	yes	—
385	#97	C₂³×C₅₉	1	2	yes	—
386	C₄×C₈	C₂³×C₅₉	1	2	yes	—
387	#41	—	2	4	no	—
388	C₂×Q₈	—	2	2	no	—
389	C₂×Q₈	—	2	2	no	—
390	C₂×Q₈	—	2	4	no	—
391	C₂×Q₈	—	2	2	no	—
392	C₂×Q₈	—	2	8	no	—
393	C₂×Q₈	C₂×D₄×C₅₉	1	1	yes	characteristic
394	C₂×Q₈	C₂⁴×C₅₉	1	4	yes	—
395	C₂×D₄	C₂×D₄×C₅₉	1	2	yes	—
396	C₂×D₄	C₂×D₄×C₅₉	1	1	yes	characteristic
397	C₂²×C₄	—	2	2	no	—
398	C₂²×C₄	—	2	4	no	—
399	C₂²×C₄	—	2	2	no	—
400	C₂²×C₄	C₂×D₄×C₅₉	1	2	yes	—
401	C₂²×C₄	C₂×D₄×C₅₉	1	4	yes	—
402	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
403	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
404	M₁₆	—	2	4	no	—
405	C₂×C₈	—	2	4	no	—
406	C₂×C₈	C₂⁴×C₅₉	1	4	yes	—
407	C₂×C₈	C₂⁴×C₅₉	1	4	yes	—
408	C₄⋊C₄	—	2	4	no	—
409	C₄⋊C₄	—	2	2	no	—
410	C₄⋊C₄	—	2	4	no	—
411	C₄⋊C₄	—	2	4	no	—
412	C₄⋊C₄	—	2	4	no	—
413	C₄⋊C₄	—	2	4	no	—
414	C₄⋊C₄	—	2	4	no	—
415	C₄⋊C₄	—	2	4	no	—
416	C₄⋊C₄	—	2	2	no	—
417	C₄⋊C₄	—	2	2	no	—
418	C₄⋊C₄	—	2	8	no	—
419	C₄⋊C₄	—	2	2	no	—
420	C₄⋊C₄	—	2	4	no	—
421	C₄⋊C₄	—	2	2	no	—
422	C₄⋊C₄	—	2	4	no	—
423	C₄⋊C₄	—	2	8	no	—
424	C₄⋊C₄	C₂×D₄×C₅₉	1	2	yes	—
425	C₄⋊C₄	C₂×D₄×C₅₉	1	4	yes	—
426	C₄⋊C₄	C₂⁴×C₅₉	1	4	yes	—
427	C₄⋊C₄	C₂⁴×C₅₉	1	2	yes	—
428	C₄⋊C₄	C₂⁴×C₅₉	1	2	yes	—
429	C₄⋊C₄	C₂⁴×C₅₉	1	4	yes	—
430	C₂²⋊C₄	—	2	2	no	—
431	C₂²⋊C₄	—	2	8	no	—
432	C₂²⋊C₄	—	2	4	no	—
433	C₂²⋊C₄	—	2	2	no	—
434	C₂²⋊C₄	C₂×D₄×C₅₉	1	2	yes	—
435	C₂²⋊C₄	C₂×D₄×C₅₉	1	4	yes	—
436	C₄²	—	2	8	no	—
437	C₄²	—	2	4	no	—
438	C₄²	—	2	2	no	—
439	C₄²	—	2	2	no	—
440	C₄²	C₂×D₄×C₅₉	1	4	yes	—
441	C₄²	C₂×D₄×C₅₉	1	2	yes	—
442	C₄²	C₂⁴×C₅₉	1	1	yes	characteristic
443	C₄²	C₂⁴×C₅₉	1	1	yes	characteristic
444	C₄²	C₂⁴×C₅₉	1	2	yes	—
445	C₂³	C₂²×D₄×C₅₉	1	2	yes	—
446	C₂³	C₂²×D₄×C₅₉	1	1	yes	characteristic
447	Q₈	—	2	2	no	—
448	Q₈	—	2	8	no	—
449	Q₈	—	4	4	no	—
450	Q₈	—	4	4	no	—
451	Q₈	—	8	4	no	—
452	Q₈	—	8	2	no	—
453	D₄	—	2	4	no	—
454	D₄	—	2	2	no	—
455	C₂×C₄	—	2	4	no	—
456	C₂×C₄	—	2	4	no	—
457	C₂×C₄	—	2	2	no	—
458	C₂×C₄	—	2	4	no	—
459	C₂×C₄	—	2	4	no	—
460	C₂×C₄	—	2	2	no	—
461	C₂×C₄	—	4	2	no	—
462	C₂×C₄	—	4	4	no	—
463	C₂×C₄	—	4	4	no	—
464	C₂×C₄	—	8	2	no	—
465	C₂×C₄	—	8	4	no	—
466	C₂×C₄	C₂²×D₄×C₅₉	1	2	yes	—
467	C₂×C₄	C₂²×D₄×C₅₉	1	4	yes	—
468	C₂×C₄	C₂²×D₄×C₅₉	1	2	yes	—
469	C₂×C₄	C₂²×D₄×C₅₉	1	2	yes	—
470	C₂×C₄	C₂²×D₄×C₅₉	1	1	yes	characteristic
471	C₂×C₄	2₋¹⁺⁴×C₅₉	1	4	yes	—
472	C₂×C₄	C₂⁵×C₅₉	1	1	yes	characteristic
473	C₈	—	2	4	no	—
474	C₈	—	2	4	no	—
475	C₂²	—	2	2	no	—
476	C₂²	—	2	4	no	—
477	C₂²	—	2	2	no	—
478	C₂²	C₅₉×#536	1	2	yes	—
479	C₂²	C₂³×D₄×C₅₉	1	1	yes	characteristic
480	C₄	—	2	2	no	—
481	C₄	—	2	4	no	—
482	C₄	—	2	2	no	—
483	C₄	—	2	2	no	—
484	C₄	—	4	4	no	—
485	C₄	—	4	2	no	—
486	C₄	—	4	4	no	—
487	C₄	—	4	2	no	—
488	C₄	—	4	4	no	—
489	C₄	C₅₉×#536	1	2	yes	—
490	C₄	C₂×2₋¹⁺⁴×C₅₉	1	2	yes	—
491	C₂	—	2	2	no	—
492	C₂	—	4	2	no	—
493	C₂	C₂×C₅₉×#536	1	1	yes	characteristic
494	C₂	C₅₉×#3586	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₅₉	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₅₉
prime radical	C₂×#41×C₅₉	C₂³
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₅₉ ◁ C₄×#41×C₅₉ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₅₉×#3242	C₂	semidirect
4. C₅₉×#3237	C₂	semidirect
5. C₅₉×#3236	C₂	semidirect
6. C₅₉×#3166	C₂	semidirect
7. C₅₉×#3162	C₂	semidirect
8. C₅₉×#3139	C₂	semidirect
9. C₂×C₅₉×#491	C₂	semidirect
11. C₅₉×#3082	C₂	semidirect
227. #60884	C₅₉	direct (N × H)
246. #3242	C₂×C₅₉	semidirect
247. #3237	C₂×C₅₉	semidirect
248. #3236	C₂×C₅₉	semidirect
249. #3166	C₂×C₅₉	semidirect
250. #3162	C₂×C₅₉	semidirect
251. #3139	C₂×C₅₉	semidirect
252. C₂×#491	C₂×C₅₉	semidirect
254. #3082	C₂×C₅₉	semidirect
308. C₅₉	#60884	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×#3509	2
C₅₉×#3504	2
C₅₉×#3242	2
C₅₉×#3237	2
C₅₉×#3236	2
C₅₉×#3166	2
C₅₉×#3162	2
C₅₉×#3139	2
C₂×C₅₉×#491	2
C₅₉×#3097	2
C₅₉×#3082	2
C₅₉×#2923	2
#60884	59

Subgroups — C59×#60884 #28472993

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₉×#60884 #28472993