Subgroups — C₅₉×#17724 #28429833

Order 15104.

1004 conjugacy classes of subgroups.

The subgroup lattice has 540 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅₉×#3508	C₂	1	1	yes	maximal, characteristic
2	C₅₉×#2988	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅₉×#2925	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅₉×#1553	C₂	1	2	yes	maximal, complemented
5	C₅₉×#1551	C₂	1	2	yes	maximal, complemented
6	C₅₉×#1550	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅₉×#1545	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅₉×#1543	C₂	1	2	yes	maximal, complemented
9	C₅₉×#1542	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅₉×#1540	C₂	1	2	yes	maximal, complemented
11	C₂×C₅₉×#331	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅₉×#559	—	2	1	no	—
13	C₅₉×#559	C₄	1	2	yes	—
14	C₅₉×#550	—	2	1	no	—
15	C₅₉×#550	C₄	1	2	yes	—
16	C₅₉×#546	—	2	2	no	—
17	C₅₉×#546	C₄	1	4	yes	—
18	C₅₉×#540	—	2	2	no	—
19	C₅₉×#535	—	2	1	no	—
20	C₅₉×#533	C₂²	1	1	yes	characteristic
21	C₅₉×#532	C₂²	1	2	yes	—
22	C₅₉×#532	C₂²	1	2	yes	—
23	C₂×#127×C₅₉	C₂²	1	1	yes	characteristic
24	C₅₉×#518	—	2	1	no	—
25	C₄×#41×C₅₉	C₂²	1	1	yes	characteristic
26	C₈×Q₈×C₅₉	—	2	1	no	—
27	C₈×D₄×C₅₉	—	2	1	no	—
28	C₈×D₄×C₅₉	—	2	2	no	—
29	C₅₉×#433	—	2	2	no	—
30	C₅₉×#432	C₂²	1	2	yes	complemented
31	C₅₉×#431	C₂²	1	1	yes	characteristic
32	C₅₉×#431	C₂²	1	2	yes	complemented
33	C₅₉×#431	C₂²	1	2	yes	complemented
34	C₅₉×#423	C₂²	1	1	yes	characteristic
35	C₂×C₄⋊C₈×C₅₉	C₂²	1	1	yes	characteristic
36	C₂×C₄⋊C₈×C₅₉	C₂²	1	1	yes	characteristic
37	C₂×C₄⋊C₈×C₅₉	C₂²	1	2	yes	complemented
38	C₅₉×#408	—	2	1	no	—
39	C₅₉×#405	—	2	1	no	—
40	C₅₉×#333	C₂²	1	1	yes	characteristic, complemented
41	C₅₉×#333	C₂²	1	1	yes	characteristic, complemented
42	C₅₉×#333	C₂²	1	2	yes	complemented
43	C₅₉×#332	C₂²	1	1	yes	characteristic, complemented
44	C₅₉×#332	C₂²	1	2	yes	complemented
45	C₅₉×#332	C₂²	1	1	yes	characteristic, complemented
46	C₅₉×#331	C₂²	1	2	yes	—
47	C₅₉×#331	C₂²	1	2	yes	—
48	C₅₉×#331	C₂²	1	2	yes	—
49	C₅₉×#331	C₂²	1	2	yes	—
50	C₂×#41×C₅₉	—	2	2	no	—
51	C₂×#41×C₅₉	C₂×C₄	1	4	yes	—
52	C₂×#41×C₅₉	D₄	1	1	yes	characteristic
53	C₂²×D₄×C₅₉	—	2	1	no	—
54	C₂²×D₄×C₅₉	—	2	1	no	—
55	C₂²×D₄×C₅₉	C₂×C₄	1	2	yes	—
56	C₂×M₁₆×C₅₉	—	2	1	no	—
57	C₂²×C₈×C₅₉	—	2	1	no	—
58	C₂²×C₈×C₅₉	—	2	1	no	—
59	C₂²×C₈×C₅₉	—	2	2	no	—
60	C₄⋊Q₈×C₅₉	C₂³	1	1	yes	characteristic
61	C₄⋊Q₈×C₅₉	C₂³	1	1	yes	characteristic
62	#127×C₅₉	—	2	2	no	—
63	#127×C₅₉	—	2	1	no	—
64	#127×C₅₉	—	2	1	no	—
65	#127×C₅₉	C₂×C₄	1	2	yes	—
66	#127×C₅₉	C₂³	1	2	yes	—
67	#125×C₅₉	—	2	1	no	—
68	#124×C₅₉	—	2	2	no	—
69	#124×C₅₉	—	2	2	no	—
70	#124×C₅₉	C₂×C₄	1	4	yes	—
71	#123×C₅₉	—	2	4	no	—
72	#123×C₅₉	—	2	4	no	—
73	C₂²⋊Q₈×C₅₉	—	2	1	no	—
74	C₂²⋊Q₈×C₅₉	C₂×C₄	1	2	yes	—
75	#121×C₅₉	—	2	2	no	—
76	#121×C₅₉	—	2	2	no	—
77	#121×C₅₉	—	2	2	no	—
78	#121×C₅₉	—	2	4	no	—
79	#121×C₅₉	—	2	4	no	—
80	#121×C₅₉	C₂×C₄	1	4	yes	—
81	#120×C₅₉	—	2	4	no	—
82	C₄×Q₈×C₅₉	—	2	1	no	—
83	C₄×Q₈×C₅₉	C₂×C₄	1	2	yes	—
84	C₄×Q₈×C₅₉	C₂×C₄	1	1	yes	characteristic
85	C₄×Q₈×C₅₉	D₄	1	1	yes	characteristic
86	C₄×D₄×C₅₉	—	2	2	no	—
87	C₄×D₄×C₅₉	—	2	2	no	—
88	C₄×D₄×C₅₉	—	2	2	no	—
89	C₄×D₄×C₅₉	—	2	2	no	—
90	C₄×D₄×C₅₉	—	2	2	no	—
91	C₄×D₄×C₅₉	C₂×C₄	1	4	yes	—
92	C₄×D₄×C₅₉	C₂×C₄	1	2	yes	—
93	C₄×D₄×C₅₉	C₂×C₄	1	1	yes	characteristic
94	C₄×D₄×C₅₉	D₄	1	2	yes	—
95	C₄×D₄×C₅₉	D₄	1	1	yes	characteristic
96	#117×C₅₉	—	2	1	no	—
97	#117×C₅₉	D₄	1	1	yes	characteristic
98	#117×C₅₉	D₄	1	2	yes	—
99	C₂×C₂²⋊C₄×C₅₉	—	2	4	no	—
100	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
101	C₂×C₄²×C₅₉	C₂³	1	2	yes	—
102	C₄⋊C₈×C₅₉	—	2	1	no	—
103	C₄⋊C₈×C₅₉	—	2	1	no	—
104	C₄⋊C₈×C₅₉	—	2	2	no	—
105	C₄⋊C₈×C₅₉	—	2	1	no	—
106	C₄⋊C₈×C₅₉	C₂³	1	2	yes	—
107	C₄⋊C₈×C₅₉	C₂³	1	1	yes	characteristic
108	C₄⋊C₈×C₅₉	C₂³	1	1	yes	characteristic
109	C₄⋊C₈×C₅₉	C₂³	1	1	yes	characteristic
110	C₄⋊C₈×C₅₉	C₂³	1	2	yes	—
111	C₄⋊C₈×C₅₉	C₂³	1	1	yes	characteristic
112	C₂²⋊C₈×C₅₉	—	2	2	no	—
113	C₂²⋊C₈×C₅₉	—	2	2	no	—
114	C₂²⋊C₈×C₅₉	—	2	1	no	—
115	C₂²⋊C₈×C₅₉	—	2	2	no	—
116	#97×C₅₉	—	2	2	no	—
117	C₄×C₈×C₅₉	—	2	2	no	—
118	C₄×C₈×C₅₉	—	2	1	no	—
119	C₄×C₈×C₅₉	—	2	2	no	—
120	C₂⁴×C₅₉	—	2	2	no	—
121	#41×C₅₉	—	2	2	no	—
122	#41×C₅₉	—	2	2	no	—
123	#41×C₅₉	—	8	2	no	—
124	#41×C₅₉	—	8	2	no	—
125	#41×C₅₉	—	8	4	no	—
126	C₂×Q₈×C₅₉	—	2	1	no	—
127	C₂×Q₈×C₅₉	C₂²⋊C₄	1	1	yes	characteristic
128	C₂×Q₈×C₅₉	C₂²×C₄	1	2	yes	—
129	C₂×D₄×C₅₉	—	2	4	no	—
130	C₂×D₄×C₅₉	—	2	4	no	—
131	C₂×D₄×C₅₉	—	2	2	no	—
132	C₂×D₄×C₅₉	—	2	2	no	—
133	C₂×D₄×C₅₉	—	2	2	no	—
134	C₂×D₄×C₅₉	—	2	2	no	—
135	C₂×D₄×C₅₉	—	2	2	no	—
136	C₂×D₄×C₅₉	—	4	2	no	—
137	C₂×D₄×C₅₉	—	4	2	no	—
138	C₂×D₄×C₅₉	—	8	1	no	—
139	C₂×D₄×C₅₉	—	8	1	no	—
140	C₂×D₄×C₅₉	—	8	2	no	—
141	C₂×D₄×C₅₉	C₂²⋊C₄	1	2	yes	—
142	C₂×D₄×C₅₉	C₂²⋊C₄	1	1	yes	characteristic
143	C₂×D₄×C₅₉	C₂²×C₄	1	4	yes	—
144	C₂²×C₄×C₅₉	—	2	4	no	—
145	C₂²×C₄×C₅₉	—	2	4	no	—
146	C₂²×C₄×C₅₉	C₂²×C₄	1	2	yes	—
147	C₂²×C₄×C₅₉	C₂²×C₄	1	1	yes	characteristic
148	C₂²×C₄×C₅₉	C₂×D₄	1	2	yes	—
149	C₂²×C₄×C₅₉	C₂×D₄	1	2	yes	—
150	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
151	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
152	M₁₆×C₅₉	—	4	2	no	—
153	C₂×C₈×C₅₉	—	2	1	no	—
154	C₂×C₈×C₅₉	—	2	1	no	—
155	C₂×C₈×C₅₉	—	2	2	no	—
156	C₂×C₈×C₅₉	—	2	1	no	—
157	C₂×C₈×C₅₉	—	2	2	no	—
158	C₂×C₈×C₅₉	—	2	1	no	—
159	C₂×C₈×C₅₉	—	4	2	no	—
160	C₂×C₈×C₅₉	—	8	1	no	—
161	C₂×C₈×C₅₉	—	8	2	no	—
162	C₄⋊C₄×C₅₉	—	2	2	no	—
163	C₄⋊C₄×C₅₉	—	2	2	no	—
164	C₄⋊C₄×C₅₉	—	2	1	no	—
165	C₄⋊C₄×C₅₉	—	2	1	no	—
166	C₄⋊C₄×C₅₉	—	2	1	no	—
167	C₄⋊C₄×C₅₉	C₂²⋊C₄	1	1	yes	characteristic
168	C₄⋊C₄×C₅₉	C₂²⋊C₄	1	1	yes	characteristic
169	C₄⋊C₄×C₅₉	C₂²⋊C₄	1	2	yes	—
170	C₄⋊C₄×C₅₉	C₂²⋊C₄	1	2	yes	—
171	C₄⋊C₄×C₅₉	C₂²×C₄	1	2	yes	—
172	C₂²⋊C₄×C₅₉	—	2	2	no	—
173	C₂²⋊C₄×C₅₉	—	2	4	no	—
174	C₂²⋊C₄×C₅₉	—	2	4	no	—
175	C₂²⋊C₄×C₅₉	—	2	4	no	—
176	C₂²⋊C₄×C₅₉	—	2	4	no	—
177	C₂²⋊C₄×C₅₉	C₂²⋊C₄	1	2	yes	—
178	C₂²⋊C₄×C₅₉	C₂²⋊C₄	1	2	yes	—
179	C₂²⋊C₄×C₅₉	C₂²⋊C₄	1	2	yes	—
180	C₄²×C₅₉	—	2	2	no	—
181	C₄²×C₅₉	C₂²×C₄	1	2	yes	—
182	C₄²×C₅₉	C₂²×C₄	1	1	yes	characteristic
183	C₄²×C₅₉	C₂×D₄	1	2	yes	—
184	C₄²×C₅₉	C₂×D₄	1	2	yes	—
185	C₄²×C₅₉	C₂×D₄	1	1	yes	characteristic
186	C₄²×C₅₉	C₂×D₄	1	1	yes	characteristic
187	C₄²×C₅₉	C₂⁴	1	1	yes	characteristic
188	C₂³×C₅₉	—	2	4	no	—
189	C₂³×C₅₉	—	4	4	no	—
190	C₂³×C₅₉	—	8	2	no	—
191	C₂³×C₅₉	—	8	2	no	—
192	C₂³×C₅₉	C₂×C₂²⋊C₄	1	2	yes	—
193	C₂³×C₅₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
194	Q₈×C₅₉	—	2	2	no	—
195	Q₈×C₅₉	—	4	2	no	—
196	Q₈×C₅₉	—	4	1	no	—
197	Q₈×C₅₉	—	4	1	no	—
198	D₄×C₅₉	—	2	4	no	—
199	D₄×C₅₉	—	2	2	no	—
200	D₄×C₅₉	—	4	4	no	—
201	D₄×C₅₉	—	4	2	no	—
202	D₄×C₅₉	—	4	2	no	—
203	D₄×C₅₉	—	4	2	no	—
204	D₄×C₅₉	—	4	2	no	—
205	D₄×C₅₉	—	4	4	no	—
206	D₄×C₅₉	—	8	2	no	—
207	D₄×C₅₉	—	8	2	no	—
208	D₄×C₅₉	—	8	4	no	—
209	D₄×C₅₉	—	8	4	no	—
210	C₂×C₄×C₅₉	—	2	2	no	—
211	C₂×C₄×C₅₉	—	2	2	no	—
212	C₂×C₄×C₅₉	—	2	1	no	—
213	C₂×C₄×C₅₉	—	2	2	no	—
214	C₂×C₄×C₅₉	—	2	1	no	—
215	C₂×C₄×C₅₉	—	2	2	no	—
216	C₂×C₄×C₅₉	—	2	2	no	—
217	C₂×C₄×C₅₉	—	2	2	no	—
218	C₂×C₄×C₅₉	—	4	1	no	—
219	C₂×C₄×C₅₉	—	4	2	no	—
220	C₂×C₄×C₅₉	—	8	4	no	—
221	C₂×C₄×C₅₉	—	8	4	no	—
222	C₂×C₄×C₅₉	C₂×C₂²⋊C₄	1	2	yes	—
223	C₂×C₄×C₅₉	C₂×C₂²⋊C₄	1	2	yes	—
224	C₂×C₄×C₅₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
225	C₂×C₄×C₅₉	C₂×C₂²⋊C₄	1	2	yes	—
226	C₂×C₄×C₅₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
227	C₂×C₄×C₅₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
228	C₂×C₄×C₅₉	#135	1	2	yes	—
229	C₂×C₄×C₅₉	#135	1	2	yes	—
230	C₂×C₄×C₅₉	C₂³×C₄	1	1	yes	characteristic
231	C₂×C₄×C₅₉	C₂²×D₄	1	1	yes	characteristic
232	C₂×C₄×C₅₉	C₂²×D₄	1	1	yes	characteristic
233	C₈×C₅₉	—	4	1	no	—
234	C₈×C₅₉	—	4	1	no	—
235	C₈×C₅₉	—	4	2	no	—
236	C₈×C₅₉	—	4	1	no	—
237	C₈×C₅₉	—	4	2	no	—
238	C₈×C₅₉	—	4	1	no	—
239	#17724	C₅₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
240	C₂²×C₅₉	—	2	1	no	—
241	C₂²×C₅₉	—	2	1	no	—
242	C₂²×C₅₉	—	2	2	no	—
243	C₂²×C₅₉	—	2	2	no	—
244	C₂²×C₅₉	—	2	2	no	—
245	C₂²×C₅₉	—	4	4	no	—
246	C₂²×C₅₉	—	4	4	no	—
247	C₂²×C₅₉	—	4	4	no	—
248	C₂²×C₅₉	—	16	4	no	—
249	C₂²×C₅₉	#416	1	2	yes	—
250	C₂²×C₅₉	C₂²×C₂²⋊C₄	1	1	yes	characteristic
251	C₄×C₅₉	—	2	1	no	—
252	C₄×C₅₉	—	2	2	no	—
253	C₄×C₅₉	—	2	1	no	—
254	C₄×C₅₉	—	2	2	no	—
255	C₄×C₅₉	—	2	2	no	—
256	C₄×C₅₉	—	2	1	no	—
257	C₄×C₅₉	—	4	2	no	—
258	C₄×C₅₉	—	4	2	no	—
259	C₄×C₅₉	#416	1	2	yes	—
260	C₄×C₅₉	C₂×#135	1	1	yes	characteristic
261	C₄×C₅₉	C₂×#135	1	1	yes	characteristic
262	C₄×C₅₉	#576	1	1	yes	characteristic
263	C₄×C₅₉	#577	1	1	yes	characteristic
264	#3508	C₂×C₅₉	1	1	yes	characteristic
265	#2988	C₂×C₅₉	1	1	yes	characteristic, complemented
266	#2925	C₂×C₅₉	1	1	yes	characteristic, complemented
267	#1553	C₂×C₅₉	1	2	yes	complemented
268	#1551	C₂×C₅₉	1	2	yes	complemented
269	#1550	C₂×C₅₉	1	1	yes	characteristic, complemented
270	#1545	C₂×C₅₉	1	1	yes	characteristic, complemented
271	#1543	C₂×C₅₉	1	2	yes	complemented
272	#1542	C₂×C₅₉	1	1	yes	characteristic, complemented
273	#1540	C₂×C₅₉	1	2	yes	complemented
274	C₂×#331	C₂×C₅₉	1	1	yes	characteristic, complemented
275	C₂×C₅₉	—	2	2	no	—
276	C₂×C₅₉	—	4	2	no	—
277	C₂×C₅₉	—	8	4	no	—
278	C₂×C₅₉	#2888	1	1	yes	characteristic
279	C₂×C₅₉	C₂×#416	1	1	yes	characteristic
280	C₂×C₅₉	#2897	1	1	yes	characteristic
281	#559	—	2	1	no	—
282	#559	C₄×C₅₉	1	2	yes	—
283	#550	—	2	1	no	—
284	#550	C₄×C₅₉	1	2	yes	—
285	#546	—	2	2	no	—
286	#546	C₄×C₅₉	1	4	yes	—
287	#540	—	2	2	no	—
288	#535	—	2	1	no	—
289	#533	C₂²×C₅₉	1	1	yes	characteristic
290	#532	C₂²×C₅₉	1	2	yes	—
291	#532	C₂²×C₅₉	1	2	yes	—
292	C₂×#127	C₂²×C₅₉	1	1	yes	characteristic
293	#518	—	2	1	no	—
294	C₄×#41	C₂²×C₅₉	1	1	yes	characteristic
295	C₈×Q₈	—	2	1	no	—
296	C₈×D₄	—	2	1	no	—
297	C₈×D₄	—	2	2	no	—
298	#433	—	2	2	no	—
299	#432	C₂²×C₅₉	1	2	yes	complemented
300	#431	C₂²×C₅₉	1	1	yes	characteristic
301	#431	C₂²×C₅₉	1	2	yes	complemented
302	#431	C₂²×C₅₉	1	2	yes	complemented
303	#423	C₂²×C₅₉	1	1	yes	characteristic
304	C₂×C₄⋊C₈	C₂²×C₅₉	1	1	yes	characteristic
305	C₂×C₄⋊C₈	C₂²×C₅₉	1	1	yes	characteristic
306	C₂×C₄⋊C₈	C₂²×C₅₉	1	2	yes	complemented
307	#408	—	2	1	no	—
308	#405	—	2	1	no	—
309	#333	C₂²×C₅₉	1	1	yes	characteristic, complemented
310	#333	C₂²×C₅₉	1	1	yes	characteristic, complemented
311	#333	C₂²×C₅₉	1	2	yes	complemented
312	#332	C₂²×C₅₉	1	1	yes	characteristic, complemented
313	#332	C₂²×C₅₉	1	2	yes	complemented
314	#332	C₂²×C₅₉	1	1	yes	characteristic, complemented
315	#331	C₂²×C₅₉	1	2	yes	—
316	#331	C₂²×C₅₉	1	2	yes	—
317	#331	C₂²×C₅₉	1	2	yes	—
318	#331	C₂²×C₅₉	1	2	yes	—
319	C₅₉	#17724	1	1	yes	characteristic, direct product factor, Sylow
320	C₂×#41	—	2	2	no	—
321	C₂×#41	C₂×C₄×C₅₉	1	4	yes	—
322	C₂×#41	D₄×C₅₉	1	1	yes	characteristic
323	C₂²×D₄	—	2	1	no	—
324	C₂²×D₄	—	2	1	no	—
325	C₂²×D₄	C₂×C₄×C₅₉	1	2	yes	—
326	C₂×M₁₆	—	2	1	no	—
327	C₂²×C₈	—	2	1	no	—
328	C₂²×C₈	—	2	1	no	—
329	C₂²×C₈	—	2	2	no	—
330	C₄⋊Q₈	C₂³×C₅₉	1	1	yes	characteristic
331	C₄⋊Q₈	C₂³×C₅₉	1	1	yes	characteristic
332	#127	—	2	2	no	—
333	#127	—	2	1	no	—
334	#127	—	2	1	no	—
335	#127	C₂×C₄×C₅₉	1	2	yes	—
336	#127	C₂³×C₅₉	1	2	yes	—
337	#125	—	2	1	no	—
338	#124	—	2	2	no	—
339	#124	—	2	2	no	—
340	#124	C₂×C₄×C₅₉	1	4	yes	—
341	#123	—	2	4	no	—
342	#123	—	2	4	no	—
343	C₂²⋊Q₈	—	2	1	no	—
344	C₂²⋊Q₈	C₂×C₄×C₅₉	1	2	yes	—
345	#121	—	2	2	no	—
346	#121	—	2	2	no	—
347	#121	—	2	2	no	—
348	#121	—	2	4	no	—
349	#121	—	2	4	no	—
350	#121	C₂×C₄×C₅₉	1	4	yes	—
351	#120	—	2	4	no	—
352	C₄×Q₈	—	2	1	no	—
353	C₄×Q₈	C₂×C₄×C₅₉	1	2	yes	—
354	C₄×Q₈	C₂×C₄×C₅₉	1	1	yes	characteristic
355	C₄×Q₈	D₄×C₅₉	1	1	yes	characteristic
356	C₄×D₄	—	2	2	no	—
357	C₄×D₄	—	2	2	no	—
358	C₄×D₄	—	2	2	no	—
359	C₄×D₄	—	2	2	no	—
360	C₄×D₄	—	2	2	no	—
361	C₄×D₄	C₂×C₄×C₅₉	1	4	yes	—
362	C₄×D₄	C₂×C₄×C₅₉	1	2	yes	—
363	C₄×D₄	C₂×C₄×C₅₉	1	1	yes	characteristic
364	C₄×D₄	D₄×C₅₉	1	2	yes	—
365	C₄×D₄	D₄×C₅₉	1	1	yes	characteristic
366	#117	—	2	1	no	—
367	#117	D₄×C₅₉	1	1	yes	characteristic
368	#117	D₄×C₅₉	1	2	yes	—
369	C₂×C₂²⋊C₄	—	2	4	no	—
370	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
371	C₂×C₄²	C₂³×C₅₉	1	2	yes	—
372	C₄⋊C₈	—	2	1	no	—
373	C₄⋊C₈	—	2	1	no	—
374	C₄⋊C₈	—	2	2	no	—
375	C₄⋊C₈	—	2	1	no	—
376	C₄⋊C₈	C₂³×C₅₉	1	2	yes	—
377	C₄⋊C₈	C₂³×C₅₉	1	1	yes	characteristic
378	C₄⋊C₈	C₂³×C₅₉	1	1	yes	characteristic
379	C₄⋊C₈	C₂³×C₅₉	1	1	yes	characteristic
380	C₄⋊C₈	C₂³×C₅₉	1	2	yes	—
381	C₄⋊C₈	C₂³×C₅₉	1	1	yes	characteristic
382	C₂²⋊C₈	—	2	2	no	—
383	C₂²⋊C₈	—	2	2	no	—
384	C₂²⋊C₈	—	2	1	no	—
385	C₂²⋊C₈	—	2	2	no	—
386	#97	—	2	2	no	—
387	C₄×C₈	—	2	2	no	—
388	C₄×C₈	—	2	1	no	—
389	C₄×C₈	—	2	2	no	—
390	C₂⁴	—	2	2	no	—
391	#41	—	2	2	no	—
392	#41	—	2	2	no	—
393	#41	—	8	2	no	—
394	#41	—	8	2	no	—
395	#41	—	8	4	no	—
396	C₂×Q₈	—	2	1	no	—
397	C₂×Q₈	C₂²⋊C₄×C₅₉	1	1	yes	characteristic
398	C₂×Q₈	C₂²×C₄×C₅₉	1	2	yes	—
399	C₂×D₄	—	2	4	no	—
400	C₂×D₄	—	2	4	no	—
401	C₂×D₄	—	2	2	no	—
402	C₂×D₄	—	2	2	no	—
403	C₂×D₄	—	2	2	no	—
404	C₂×D₄	—	2	2	no	—
405	C₂×D₄	—	2	2	no	—
406	C₂×D₄	—	4	2	no	—
407	C₂×D₄	—	4	2	no	—
408	C₂×D₄	—	8	1	no	—
409	C₂×D₄	—	8	1	no	—
410	C₂×D₄	—	8	2	no	—
411	C₂×D₄	C₂²⋊C₄×C₅₉	1	2	yes	—
412	C₂×D₄	C₂²⋊C₄×C₅₉	1	1	yes	characteristic
413	C₂×D₄	C₂²×C₄×C₅₉	1	4	yes	—
414	C₂²×C₄	—	2	4	no	—
415	C₂²×C₄	—	2	4	no	—
416	C₂²×C₄	C₂²×C₄×C₅₉	1	2	yes	—
417	C₂²×C₄	C₂²×C₄×C₅₉	1	1	yes	characteristic
418	C₂²×C₄	C₂×D₄×C₅₉	1	2	yes	—
419	C₂²×C₄	C₂×D₄×C₅₉	1	2	yes	—
420	C₂²×C₄	C₂×D₄×C₅₉	1	1	yes	characteristic
421	C₂²×C₄	C₂×D₄×C₅₉	1	1	yes	characteristic
422	M₁₆	—	4	2	no	—
423	C₂×C₈	—	2	1	no	—
424	C₂×C₈	—	2	1	no	—
425	C₂×C₈	—	2	2	no	—
426	C₂×C₈	—	2	1	no	—
427	C₂×C₈	—	2	2	no	—
428	C₂×C₈	—	2	1	no	—
429	C₂×C₈	—	4	2	no	—
430	C₂×C₈	—	8	1	no	—
431	C₂×C₈	—	8	2	no	—
432	C₄⋊C₄	—	2	2	no	—
433	C₄⋊C₄	—	2	2	no	—
434	C₄⋊C₄	—	2	1	no	—
435	C₄⋊C₄	—	2	1	no	—
436	C₄⋊C₄	—	2	1	no	—
437	C₄⋊C₄	C₂²⋊C₄×C₅₉	1	1	yes	characteristic
438	C₄⋊C₄	C₂²⋊C₄×C₅₉	1	1	yes	characteristic
439	C₄⋊C₄	C₂²⋊C₄×C₅₉	1	2	yes	—
440	C₄⋊C₄	C₂²⋊C₄×C₅₉	1	2	yes	—
441	C₄⋊C₄	C₂²×C₄×C₅₉	1	2	yes	—
442	C₂²⋊C₄	—	2	2	no	—
443	C₂²⋊C₄	—	2	4	no	—
444	C₂²⋊C₄	—	2	4	no	—
445	C₂²⋊C₄	—	2	4	no	—
446	C₂²⋊C₄	—	2	4	no	—
447	C₂²⋊C₄	C₂²⋊C₄×C₅₉	1	2	yes	—
448	C₂²⋊C₄	C₂²⋊C₄×C₅₉	1	2	yes	—
449	C₂²⋊C₄	C₂²⋊C₄×C₅₉	1	2	yes	—
450	C₄²	—	2	2	no	—
451	C₄²	C₂²×C₄×C₅₉	1	2	yes	—
452	C₄²	C₂²×C₄×C₅₉	1	1	yes	characteristic
453	C₄²	C₂×D₄×C₅₉	1	2	yes	—
454	C₄²	C₂×D₄×C₅₉	1	2	yes	—
455	C₄²	C₂×D₄×C₅₉	1	1	yes	characteristic
456	C₄²	C₂×D₄×C₅₉	1	1	yes	characteristic
457	C₄²	C₂⁴×C₅₉	1	1	yes	characteristic
458	C₂³	—	2	4	no	—
459	C₂³	—	4	4	no	—
460	C₂³	—	8	2	no	—
461	C₂³	—	8	2	no	—
462	C₂³	C₂×C₂²⋊C₄×C₅₉	1	2	yes	—
463	C₂³	C₂×C₂²⋊C₄×C₅₉	1	1	yes	characteristic
464	Q₈	—	2	2	no	—
465	Q₈	—	4	2	no	—
466	Q₈	—	4	1	no	—
467	Q₈	—	4	1	no	—
468	D₄	—	2	4	no	—
469	D₄	—	2	2	no	—
470	D₄	—	4	4	no	—
471	D₄	—	4	4	no	—
472	D₄	—	4	2	no	—
473	D₄	—	4	2	no	—
474	D₄	—	4	2	no	—
475	D₄	—	4	2	no	—
476	D₄	—	8	2	no	—
477	D₄	—	8	2	no	—
478	D₄	—	8	4	no	—
479	D₄	—	8	4	no	—
480	C₂×C₄	—	2	2	no	—
481	C₂×C₄	—	2	2	no	—
482	C₂×C₄	—	2	1	no	—
483	C₂×C₄	—	2	2	no	—
484	C₂×C₄	—	2	1	no	—
485	C₂×C₄	—	2	2	no	—
486	C₂×C₄	—	2	2	no	—
487	C₂×C₄	—	2	2	no	—
488	C₂×C₄	—	4	1	no	—
489	C₂×C₄	—	4	2	no	—
490	C₂×C₄	—	8	4	no	—
491	C₂×C₄	—	8	4	no	—
492	C₂×C₄	C₂×C₂²⋊C₄×C₅₉	1	2	yes	—
493	C₂×C₄	C₂×C₂²⋊C₄×C₅₉	1	2	yes	—
494	C₂×C₄	C₂×C₂²⋊C₄×C₅₉	1	1	yes	characteristic
495	C₂×C₄	C₂×C₂²⋊C₄×C₅₉	1	2	yes	—
496	C₂×C₄	C₂×C₂²⋊C₄×C₅₉	1	1	yes	characteristic
497	C₂×C₄	C₂×C₂²⋊C₄×C₅₉	1	1	yes	characteristic
498	C₂×C₄	#135×C₅₉	1	2	yes	—
499	C₂×C₄	#135×C₅₉	1	2	yes	—
500	C₂×C₄	C₂³×C₄×C₅₉	1	1	yes	characteristic
501	C₂×C₄	C₂²×D₄×C₅₉	1	1	yes	characteristic
502	C₂×C₄	C₂²×D₄×C₅₉	1	1	yes	characteristic
503	C₈	—	4	1	no	—
504	C₈	—	4	1	no	—
505	C₈	—	4	2	no	—
506	C₈	—	4	1	no	—
507	C₈	—	4	2	no	—
508	C₈	—	4	1	no	—
509	C₂²	—	2	1	no	—
510	C₂²	—	2	1	no	—
511	C₂²	—	2	2	no	—
512	C₂²	—	2	2	no	—
513	C₂²	—	2	2	no	—
514	C₂²	—	4	4	no	—
515	C₂²	—	4	4	no	—
516	C₂²	—	4	4	no	—
517	C₂²	—	16	4	no	—
518	C₂²	C₅₉×#416	1	2	yes	—
519	C₂²	C₂²×C₂²⋊C₄×C₅₉	1	1	yes	characteristic
520	C₄	—	2	1	no	—
521	C₄	—	2	2	no	—
522	C₄	—	2	1	no	—
523	C₄	—	2	2	no	—
524	C₄	—	2	2	no	—
525	C₄	—	2	1	no	—
526	C₄	—	4	2	no	—
527	C₄	—	4	2	no	—
528	C₄	C₅₉×#416	1	2	yes	—
529	C₄	C₂×#135×C₅₉	1	1	yes	characteristic
530	C₄	C₂×#135×C₅₉	1	1	yes	characteristic
531	C₄	C₅₉×#576	1	1	yes	characteristic
532	C₄	C₅₉×#577	1	1	yes	characteristic
533	C₂	—	2	2	no	—
534	C₂	—	4	2	no	—
535	C₂	—	8	4	no	—
536	C₂	C₅₉×#2888	1	1	yes	characteristic
537	C₂	C₂×C₅₉×#416	1	1	yes	characteristic
538	C₂	C₅₉×#2897	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₅₉	C₂²×C₂²⋊C₄
commutator	C₂×C₄	C₂³×C₄×C₅₉
Frattini, cosocle	C₄²	C₂⁴×C₅₉
prime radical	C₅₉×#3508	C₂
LCS	G ▷ C₂×C₄ ▷ C₂² ▷ 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
2. C₅₉×#2988	C₂	semidirect
3. C₅₉×#2925	C₂	semidirect
4. C₅₉×#1553	C₂	semidirect
5. C₅₉×#1551	C₂	semidirect
6. C₅₉×#1550	C₂	semidirect
7. C₅₉×#1545	C₂	semidirect
8. C₅₉×#1543	C₂	semidirect
9. C₅₉×#1542	C₂	semidirect
10. C₅₉×#1540	C₂	semidirect
11. C₂×C₅₉×#331	C₂	semidirect
30. C₅₉×#432	C₂²	semidirect
32. C₅₉×#431	C₂²	semidirect
33. C₅₉×#431	C₂²	semidirect
37. C₂×C₄⋊C₈×C₅₉	C₂²	semidirect
40. C₅₉×#333	C₂²	semidirect
41. C₅₉×#333	C₂²	semidirect
42. C₅₉×#333	C₂²	semidirect
43. C₅₉×#332	C₂²	semidirect
44. C₅₉×#332	C₂²	semidirect
45. C₅₉×#332	C₂²	semidirect
239. #17724	C₅₉	direct (N × H)
265. #2988	C₂×C₅₉	semidirect
266. #2925	C₂×C₅₉	semidirect
267. #1553	C₂×C₅₉	semidirect
268. #1551	C₂×C₅₉	semidirect
269. #1550	C₂×C₅₉	semidirect
270. #1545	C₂×C₅₉	semidirect
271. #1543	C₂×C₅₉	semidirect
272. #1542	C₂×C₅₉	semidirect
273. #1540	C₂×C₅₉	semidirect
274. C₂×#331	C₂×C₅₉	semidirect
299. #432	C₂²×C₅₉	semidirect
301. #431	C₂²×C₅₉	semidirect
302. #431	C₂²×C₅₉	semidirect
306. C₂×C₄⋊C₈	C₂²×C₅₉	semidirect
309. #333	C₂²×C₅₉	semidirect
310. #333	C₂²×C₅₉	semidirect
311. #333	C₂²×C₅₉	semidirect
312. #332	C₂²×C₅₉	semidirect
313. #332	C₂²×C₅₉	semidirect
314. #332	C₂²×C₅₉	semidirect
319. C₅₉	#17724	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×#3508	2
C₅₉×#2988	2
C₅₉×#2925	2
C₅₉×#1553	2
C₅₉×#1551	2
C₅₉×#1550	2
C₅₉×#1545	2
C₅₉×#1543	2
C₅₉×#1542	2
C₅₉×#1540	2
C₂×C₅₉×#331	2
#17724	59

Subgroups — C59×#17724 #28429833

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₉×#17724 #28429833