Subgroups — C₅₉×#24285 #28436394

Order 15104.

1336 conjugacy classes of subgroups.

The subgroup lattice has 498 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅₉×#3584	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅₉×#3050	C₂	1	2	yes	maximal, complemented
3	C₅₉×#3025	C₂	1	2	yes	maximal, complemented
4	C₅₉×#2929	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅₉×#2053	C₂	1	2	yes	maximal, complemented
6	C₅₉×#2010	C₂	1	2	yes	maximal, complemented
7	C₅₉×#1976	C₂	1	2	yes	maximal, complemented
8	C₅₉×#1812	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅₉×#1794	C₂	1	2	yes	maximal, complemented
10	C₅₉×#585	C₂²	1	2	yes	—
11	C₅₉×#578	—	2	2	no	—
12	C₅₉×#577	—	2	4	no	—
13	C₅₉×#576	—	2	2	no	—
14	C₅₉×#575	—	2	2	no	—
15	C₅₉×#575	C₂²	1	2	yes	—
16	C₂×#135×C₅₉	—	2	2	no	—
17	C₂×#135×C₅₉	C₂²	1	2	yes	—
18	C₂×#131×C₅₉	C₂²	1	1	yes	characteristic
19	C₂³×C₈×C₅₉	C₂²	1	1	yes	characteristic, complemented
20	C₅₉×#525	C₂²	1	1	yes	characteristic
21	C₅₉×#525	C₂²	1	4	yes	complemented
22	C₅₉×#467	—	2	2	no	—
23	C₅₉×#466	—	2	2	no	—
24	C₅₉×#465	—	2	4	no	—
25	C₅₉×#458	—	2	4	no	—
26	C₅₉×B(4,𝔽₂)	—	2	4	no	—
27	C₅₉×#435	—	2	2	no	—
28	C₈×D₄×C₅₉	—	2	2	no	—
29	C₅₉×#427	C₂²	1	2	yes	complemented
30	C₅₉×#424	C₂²	1	1	yes	characteristic, complemented
31	C₅₉×#421	C₂²	1	4	yes	complemented
32	C₅₉×#416	C₂²	1	4	yes	complemented
33	C₅₉×#410	C₂²	1	2	yes	—
34	C₅₉×#410	C₂²	1	4	yes	complemented
35	C₅₉×#408	C₂²	1	1	yes	characteristic
36	C₅₉×#407	C₂²	1	1	yes	characteristic, complemented
37	C₅₉×#405	C₂²	1	1	yes	characteristic, complemented
38	C₅₉×H(3,ℤ/4)	C₂²	1	2	yes	complemented
39	2₋¹⁺⁴×C₅₉	—	2	4	no	—
40	2₋¹⁺⁴×C₅₉	—	2	2	no	—
41	H(5,𝔽₂)×C₅₉	—	2	4	no	—
42	H(5,𝔽₂)×C₅₉	—	2	4	no	—
43	H(5,𝔽₂)×C₅₉	—	2	2	no	—
44	C₂×#41×C₅₉	—	2	4	no	—
45	C₂×#41×C₅₉	—	4	4	no	—
46	C₂×#41×C₅₉	C₂³	1	4	yes	—
47	C₂×#41×C₅₉	C₂³	1	1	yes	characteristic
48	C₂³×C₄×C₅₉	C₂³	1	1	yes	characteristic
49	#137×C₅₉	—	2	8	no	—
50	#137×C₅₉	—	2	4	no	—
51	AGL(1,ℤ/8)×C₅₉	—	2	8	no	—
52	AGL(1,ℤ/8)×C₅₉	—	2	4	no	—
53	#135×C₅₉	—	2	4	no	—
54	#135×C₅₉	—	2	4	no	—
55	#135×C₅₉	—	2	2	no	—
56	#135×C₅₉	—	2	4	no	—
57	#135×C₅₉	—	2	2	no	—
58	#135×C₅₉	—	2	2	no	—
59	#135×C₅₉	—	2	2	no	—
60	C₂×Q₁₆×C₅₉	—	2	2	no	—
61	C₂×Q₁₆×C₅₉	D₄	1	2	yes	complemented
62	C₂×SD₁₆×C₅₉	—	2	4	no	—
63	C₂×SD₁₆×C₅₉	D₄	1	4	yes	complemented
64	C₂×D₈×C₅₉	—	2	2	no	—
65	C₂×D₈×C₅₉	D₄	1	2	yes	complemented
66	#131×C₅₉	—	2	2	no	—
67	#131×C₅₉	—	2	2	no	—
68	C₂×M₁₆×C₅₉	D₄	1	2	yes	complemented
69	C₂×M₁₆×C₅₉	C₂³	1	1	yes	characteristic
70	C₂×M₁₆×C₅₉	C₂³	1	1	yes	characteristic
71	C₂²×C₈×C₅₉	—	2	1	no	—
72	C₂²×C₈×C₅₉	—	2	1	no	—
73	C₂²×C₈×C₅₉	—	2	2	no	—
74	C₂²×C₈×C₅₉	—	2	2	no	—
75	C₂²×C₈×C₅₉	D₄	1	2	yes	complemented
76	C₂²×C₈×C₅₉	C₂³	1	1	yes	characteristic
77	C₂²×C₈×C₅₉	C₂³	1	1	yes	characteristic
78	#123×C₅₉	—	2	4	no	—
79	#123×C₅₉	D₄	1	2	yes	—
80	C₂²⋊Q₈×C₅₉	—	2	1	no	—
81	C₂²⋊Q₈×C₅₉	—	2	4	no	—
82	#121×C₅₉	—	2	1	no	—
83	#121×C₅₉	—	2	4	no	—
84	#120×C₅₉	—	2	4	no	—
85	#120×C₅₉	D₄	1	2	yes	—
86	C₄×D₄×C₅₉	—	2	2	no	—
87	C₄×D₄×C₅₉	—	4	4	no	—
88	#117×C₅₉	C₂³	1	4	yes	—
89	#117×C₅₉	C₂³	1	1	yes	characteristic
90	#107×C₅₉	—	2	2	no	—
91	#106×C₅₉	—	2	2	no	—
92	C₄⋊C₈×C₅₉	—	2	2	no	—
93	#104×C₅₉	—	4	4	no	—
94	#103×C₅₉	—	2	4	no	—
95	#102×C₅₉	—	2	4	no	—
96	#99×C₅₉	—	2	4	no	—
97	#99×C₅₉	—	2	8	no	—
98	C₂²⋊C₈×C₅₉	—	2	2	no	—
99	C₂²⋊C₈×C₅₉	—	2	2	no	—
100	#97×C₅₉	—	2	1	no	—
101	C₄×C₈×C₅₉	—	2	1	no	—
102	C₂⁴×C₅₉	C₂×D₄	1	1	yes	characteristic
103	#41×C₅₉	—	2	2	no	—
104	#41×C₅₉	—	2	2	no	—
105	#41×C₅₉	—	2	8	no	—
106	#41×C₅₉	—	2	4	no	—
107	#41×C₅₉	—	2	4	no	—
108	#41×C₅₉	—	2	4	no	—
109	#41×C₅₉	—	2	4	no	—
110	#41×C₅₉	—	4	8	no	—
111	#41×C₅₉	—	4	4	no	—
112	#41×C₅₉	—	4	4	no	—
113	#41×C₅₉	—	4	4	no	—
114	#41×C₅₉	—	4	4	no	—
115	C₂×Q₈×C₅₉	—	2	4	no	—
116	C₂×Q₈×C₅₉	—	4	4	no	—
117	C₂×Q₈×C₅₉	C₂×D₄	1	4	yes	—
118	C₂×Q₈×C₅₉	#41	1	1	yes	characteristic
119	C₂×D₄×C₅₉	—	2	4	no	—
120	C₂×D₄×C₅₉	—	2	2	no	—
121	C₂×D₄×C₅₉	—	2	4	no	—
122	C₂×D₄×C₅₉	—	4	4	no	—
123	C₂×D₄×C₅₉	—	4	8	no	—
124	C₂×D₄×C₅₉	—	4	4	no	—
125	C₂×D₄×C₅₉	—	4	4	no	—
126	C₂×D₄×C₅₉	C₂×D₄	1	2	yes	—
127	C₂×D₄×C₅₉	C₂×D₄	1	4	yes	—
128	C₂×D₄×C₅₉	#41	1	1	yes	characteristic
129	C₂²×C₄×C₅₉	—	2	1	no	—
130	C₂²×C₄×C₅₉	—	2	2	no	—
131	C₂²×C₄×C₅₉	—	2	1	no	—
132	C₂²×C₄×C₅₉	—	2	2	no	—
133	C₂²×C₄×C₅₉	—	2	4	no	—
134	C₂²×C₄×C₅₉	—	4	4	no	—
135	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
136	C₂²×C₄×C₅₉	C₂×D₄	1	2	yes	—
137	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
138	Q₁₆×C₅₉	—	2	4	no	—
139	Q₁₆×C₅₉	—	2	2	no	—
140	Q₁₆×C₅₉	—	2	2	no	—
141	SD₁₆×C₅₉	—	2	8	no	—
142	SD₁₆×C₅₉	—	2	4	no	—
143	SD₁₆×C₅₉	—	2	4	no	—
144	D₈×C₅₉	—	2	4	no	—
145	D₈×C₅₉	—	2	2	no	—
146	D₈×C₅₉	—	2	2	no	—
147	M₁₆×C₅₉	—	2	2	no	—
148	M₁₆×C₅₉	—	2	4	no	—
149	M₁₆×C₅₉	—	2	2	no	—
150	C₂×C₈×C₅₉	—	2	2	no	—
151	C₂×C₈×C₅₉	—	2	2	no	—
152	C₂×C₈×C₅₉	—	2	1	no	—
153	C₂×C₈×C₅₉	—	2	1	no	—
154	C₂×C₈×C₅₉	—	2	2	no	—
155	C₂×C₈×C₅₉	—	4	1	no	—
156	C₂×C₈×C₅₉	—	4	1	no	—
157	C₂×C₈×C₅₉	—	4	2	no	—
158	C₂×C₈×C₅₉	C₂×D₄	1	2	yes	—
159	C₂×C₈×C₅₉	C₂×D₄	1	1	yes	characteristic
160	C₂×C₈×C₅₉	C₂×D₄	1	1	yes	characteristic
161	C₂×C₈×C₅₉	C₂×D₄	1	2	yes	—
162	C₂×C₈×C₅₉	C₂×D₄	1	2	yes	—
163	C₄⋊C₄×C₅₉	—	2	2	no	—
164	C₄⋊C₄×C₅₉	—	2	1	no	—
165	C₄⋊C₄×C₅₉	—	2	4	no	—
166	C₄⋊C₄×C₅₉	—	4	4	no	—
167	C₂²⋊C₄×C₅₉	—	2	2	no	—
168	C₂²⋊C₄×C₅₉	—	2	2	no	—
169	C₂²⋊C₄×C₅₉	—	2	4	no	—
170	C₂²⋊C₄×C₅₉	—	4	4	no	—
171	C₂²⋊C₄×C₅₉	—	4	4	no	—
172	C₂²⋊C₄×C₅₉	C₂×D₄	1	2	yes	—
173	C₄²×C₅₉	—	2	1	no	—
174	C₄²×C₅₉	—	2	4	no	—
175	C₂³×C₅₉	—	2	1	no	—
176	C₂³×C₅₉	—	2	2	no	—
177	C₂³×C₅₉	—	2	4	no	—
178	C₂³×C₅₉	—	4	2	no	—
179	C₂³×C₅₉	—	4	4	no	—
180	C₂³×C₅₉	#121	1	2	yes	—
181	C₂³×C₅₉	C₂²×D₄	1	1	yes	characteristic
182	Q₈×C₅₉	—	2	2	no	—
183	Q₈×C₅₉	—	2	4	no	—
184	Q₈×C₅₉	—	2	4	no	—
185	Q₈×C₅₉	—	4	4	no	—
186	D₄×C₅₉	—	2	4	no	—
187	D₄×C₅₉	—	2	4	no	—
188	D₄×C₅₉	—	2	2	no	—
189	D₄×C₅₉	—	2	4	no	—
190	D₄×C₅₉	—	4	4	no	—
191	D₄×C₅₉	—	4	4	no	—
192	D₄×C₅₉	—	4	8	no	—
193	D₄×C₅₉	—	4	4	no	—
194	D₄×C₅₉	—	4	4	no	—
195	D₄×C₅₉	—	8	8	no	—
196	C₂×C₄×C₅₉	—	2	2	no	—
197	C₂×C₄×C₅₉	—	2	2	no	—
198	C₂×C₄×C₅₉	—	2	2	no	—
199	C₂×C₄×C₅₉	—	2	1	no	—
200	C₂×C₄×C₅₉	—	2	2	no	—
201	C₂×C₄×C₅₉	—	2	4	no	—
202	C₂×C₄×C₅₉	—	4	8	no	—
203	C₂×C₄×C₅₉	—	4	4	no	—
204	C₂×C₄×C₅₉	—	4	1	no	—
205	C₂×C₄×C₅₉	—	4	1	no	—
206	C₂×C₄×C₅₉	—	4	4	no	—
207	C₂×C₄×C₅₉	—	4	2	no	—
208	C₂×C₄×C₅₉	—	4	4	no	—
209	C₂×C₄×C₅₉	—	4	4	no	—
210	C₂×C₄×C₅₉	#121	1	2	yes	—
211	C₂×C₄×C₅₉	C₂²×D₄	1	1	yes	characteristic
212	C₂×C₄×C₅₉	C₂²×D₄	1	2	yes	—
213	C₂×C₄×C₅₉	C₂×#41	1	1	yes	characteristic
214	C₂×C₄×C₅₉	H(5,𝔽₂)	1	2	yes	—
215	C₈×C₅₉	—	2	2	no	—
216	C₈×C₅₉	—	4	1	no	—
217	C₈×C₅₉	—	4	1	no	—
218	C₈×C₅₉	#120	1	1	yes	characteristic
219	C₈×C₅₉	#120	1	1	yes	characteristic
220	C₈×C₅₉	#120	1	2	yes	—
221	#24285	C₅₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
222	C₂²×C₅₉	—	2	2	no	—
223	C₂²×C₅₉	—	2	4	no	—
224	C₂²×C₅₉	—	2	2	no	—
225	C₂²×C₅₉	—	4	1	no	—
226	C₂²×C₅₉	—	4	2	no	—
227	C₂²×C₅₉	—	4	1	no	—
228	C₂²×C₅₉	—	4	2	no	—
229	C₂²×C₅₉	—	4	1	no	—
230	C₂²×C₅₉	—	4	4	no	—
231	C₂²×C₅₉	—	8	4	no	—
232	C₂²×C₅₉	—	16	4	no	—
233	C₂²×C₅₉	C₂×#121	1	1	yes	characteristic
234	C₂²×C₅₉	D₄²	1	2	yes	—
235	C₄×C₅₉	—	2	2	no	—
236	C₄×C₅₉	—	4	2	no	—
237	C₄×C₅₉	—	4	1	no	—
238	C₄×C₅₉	—	4	4	no	—
239	C₄×C₅₉	—	8	4	no	—
240	C₄×C₅₉	C₂×#120	1	1	yes	characteristic
241	C₄×C₅₉	#535	1	1	yes	characteristic
242	C₄×C₅₉	#546	1	2	yes	—
243	#3584	C₂×C₅₉	1	1	yes	characteristic, complemented
244	#3050	C₂×C₅₉	1	2	yes	complemented
245	#3025	C₂×C₅₉	1	2	yes	complemented
246	#2929	C₂×C₅₉	1	1	yes	characteristic, complemented
247	#2053	C₂×C₅₉	1	2	yes	complemented
248	#2010	C₂×C₅₉	1	2	yes	complemented
249	#1976	C₂×C₅₉	1	2	yes	complemented
250	#1812	C₂×C₅₉	1	1	yes	characteristic, complemented
251	#1794	C₂×C₅₉	1	2	yes	complemented
252	C₂×C₅₉	—	2	1	no	—
253	C₂×C₅₉	—	2	2	no	—
254	C₂×C₅₉	—	4	2	no	—
255	C₂×C₅₉	—	4	2	no	—
256	C₂×C₅₉	—	8	4	no	—
257	C₂×C₅₉	#2408	1	1	yes	characteristic
258	#585	C₂²×C₅₉	1	2	yes	—
259	#578	—	2	2	no	—
260	#577	—	2	4	no	—
261	#576	—	2	2	no	—
262	#575	—	2	2	no	—
263	#575	C₂²×C₅₉	1	2	yes	—
264	C₂×#135	—	2	2	no	—
265	C₂×#135	C₂²×C₅₉	1	2	yes	—
266	C₂×#131	C₂²×C₅₉	1	1	yes	characteristic
267	C₂³×C₈	C₂²×C₅₉	1	1	yes	characteristic, complemented
268	#525	C₂²×C₅₉	1	1	yes	characteristic
269	#525	C₂²×C₅₉	1	4	yes	complemented
270	#467	—	2	2	no	—
271	#466	—	2	2	no	—
272	#465	—	2	4	no	—
273	#458	—	2	4	no	—
274	B(4,𝔽₂)	—	2	4	no	—
275	#435	—	2	2	no	—
276	C₈×D₄	—	2	2	no	—
277	#427	C₂²×C₅₉	1	2	yes	complemented
278	#424	C₂²×C₅₉	1	1	yes	characteristic, complemented
279	#421	C₂²×C₅₉	1	4	yes	complemented
280	#416	C₂²×C₅₉	1	4	yes	complemented
281	#410	C₂²×C₅₉	1	2	yes	—
282	#410	C₂²×C₅₉	1	4	yes	complemented
283	#408	C₂²×C₅₉	1	1	yes	characteristic
284	#407	C₂²×C₅₉	1	1	yes	characteristic, complemented
285	#405	C₂²×C₅₉	1	1	yes	characteristic, complemented
286	H(3,ℤ/4)	C₂²×C₅₉	1	2	yes	complemented
287	C₅₉	#24285	1	1	yes	characteristic, direct product factor, Sylow
288	2₋¹⁺⁴	—	2	4	no	—
289	2₋¹⁺⁴	—	2	2	no	—
290	H(5,𝔽₂)	—	2	4	no	—
291	H(5,𝔽₂)	—	2	4	no	—
292	H(5,𝔽₂)	—	2	2	no	—
293	C₂×#41	—	2	4	no	—
294	C₂×#41	—	4	4	no	—
295	C₂×#41	C₂³×C₅₉	1	4	yes	—
296	C₂×#41	C₂³×C₅₉	1	1	yes	characteristic
297	C₂³×C₄	C₂³×C₅₉	1	1	yes	characteristic
298	#137	—	2	8	no	—
299	#137	—	2	4	no	—
300	AGL(1,ℤ/8)	—	2	8	no	—
301	AGL(1,ℤ/8)	—	2	4	no	—
302	#135	—	2	4	no	—
303	#135	—	2	4	no	—
304	#135	—	2	2	no	—
305	#135	—	2	4	no	—
306	#135	—	2	2	no	—
307	#135	—	2	2	no	—
308	#135	—	2	2	no	—
309	C₂×Q₁₆	—	2	2	no	—
310	C₂×Q₁₆	D₄×C₅₉	1	2	yes	complemented
311	C₂×SD₁₆	—	2	4	no	—
312	C₂×SD₁₆	D₄×C₅₉	1	4	yes	complemented
313	C₂×D₈	—	2	2	no	—
314	C₂×D₈	D₄×C₅₉	1	2	yes	complemented
315	#131	—	2	2	no	—
316	#131	—	2	2	no	—
317	C₂×M₁₆	D₄×C₅₉	1	2	yes	complemented
318	C₂×M₁₆	C₂³×C₅₉	1	1	yes	characteristic
319	C₂×M₁₆	C₂³×C₅₉	1	1	yes	characteristic
320	C₂²×C₈	—	2	1	no	—
321	C₂²×C₈	—	2	1	no	—
322	C₂²×C₈	—	2	2	no	—
323	C₂²×C₈	—	2	2	no	—
324	C₂²×C₈	D₄×C₅₉	1	2	yes	complemented
325	C₂²×C₈	C₂³×C₅₉	1	1	yes	characteristic
326	C₂²×C₈	C₂³×C₅₉	1	1	yes	characteristic
327	#123	—	2	4	no	—
328	#123	D₄×C₅₉	1	2	yes	—
329	C₂²⋊Q₈	—	2	1	no	—
330	C₂²⋊Q₈	—	2	4	no	—
331	#121	—	2	1	no	—
332	#121	—	2	4	no	—
333	#120	—	2	4	no	—
334	#120	D₄×C₅₉	1	2	yes	—
335	C₄×D₄	—	2	2	no	—
336	C₄×D₄	—	4	4	no	—
337	#117	C₂³×C₅₉	1	4	yes	—
338	#117	C₂³×C₅₉	1	1	yes	characteristic
339	#107	—	2	2	no	—
340	#106	—	2	2	no	—
341	C₄⋊C₈	—	2	2	no	—
342	#104	—	4	4	no	—
343	#103	—	2	4	no	—
344	#102	—	2	4	no	—
345	#99	—	2	4	no	—
346	#99	—	2	8	no	—
347	C₂²⋊C₈	—	2	2	no	—
348	C₂²⋊C₈	—	2	2	no	—
349	#97	—	2	1	no	—
350	C₄×C₈	—	2	1	no	—
351	C₂⁴	C₂×D₄×C₅₉	1	1	yes	characteristic
352	#41	—	2	2	no	—
353	#41	—	2	2	no	—
354	#41	—	2	8	no	—
355	#41	—	2	4	no	—
356	#41	—	2	4	no	—
357	#41	—	2	4	no	—
358	#41	—	2	4	no	—
359	#41	—	4	8	no	—
360	#41	—	4	4	no	—
361	#41	—	4	4	no	—
362	#41	—	4	4	no	—
363	#41	—	4	4	no	—
364	C₂×Q₈	—	2	4	no	—
365	C₂×Q₈	—	4	4	no	—
366	C₂×Q₈	C₂×D₄×C₅₉	1	4	yes	—
367	C₂×Q₈	#41×C₅₉	1	1	yes	characteristic
368	C₂×D₄	—	2	4	no	—
369	C₂×D₄	—	2	2	no	—
370	C₂×D₄	—	2	4	no	—
371	C₂×D₄	—	4	4	no	—
372	C₂×D₄	—	4	8	no	—
373	C₂×D₄	—	4	4	no	—
374	C₂×D₄	—	4	4	no	—
375	C₂×D₄	C₂×D₄×C₅₉	1	2	yes	—
376	C₂×D₄	C₂×D₄×C₅₉	1	4	yes	—
377	C₂×D₄	#41×C₅₉	1	1	yes	characteristic
378	C₂²×C₄	—	2	1	no	—
379	C₂²×C₄	—	2	2	no	—
380	C₂²×C₄	—	2	1	no	—
381	C₂²×C₄	—	2	2	no	—
382	C₂²×C₄	—	2	4	no	—
383	C₂²×C₄	—	4	4	no	—
384	C₂²×C₄	C₂×D₄×C₅₉	1	1	yes	characteristic
385	C₂²×C₄	C₂×D₄×C₅₉	1	2	yes	—
386	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
387	Q₁₆	—	2	4	no	—
388	Q₁₆	—	2	2	no	—
389	Q₁₆	—	2	2	no	—
390	SD₁₆	—	2	8	no	—
391	SD₁₆	—	2	4	no	—
392	SD₁₆	—	2	4	no	—
393	D₈	—	2	4	no	—
394	D₈	—	2	2	no	—
395	D₈	—	2	2	no	—
396	M₁₆	—	2	2	no	—
397	M₁₆	—	2	4	no	—
398	M₁₆	—	2	2	no	—
399	C₂×C₈	—	2	2	no	—
400	C₂×C₈	—	2	2	no	—
401	C₂×C₈	—	2	1	no	—
402	C₂×C₈	—	2	1	no	—
403	C₂×C₈	—	2	2	no	—
404	C₂×C₈	—	4	1	no	—
405	C₂×C₈	—	4	1	no	—
406	C₂×C₈	—	4	2	no	—
407	C₂×C₈	C₂×D₄×C₅₉	1	2	yes	—
408	C₂×C₈	C₂×D₄×C₅₉	1	1	yes	characteristic
409	C₂×C₈	C₂×D₄×C₅₉	1	1	yes	characteristic
410	C₂×C₈	C₂×D₄×C₅₉	1	2	yes	—
411	C₂×C₈	C₂×D₄×C₅₉	1	2	yes	—
412	C₄⋊C₄	—	2	2	no	—
413	C₄⋊C₄	—	2	1	no	—
414	C₄⋊C₄	—	2	4	no	—
415	C₄⋊C₄	—	4	4	no	—
416	C₂²⋊C₄	—	2	2	no	—
417	C₂²⋊C₄	—	2	2	no	—
418	C₂²⋊C₄	—	2	4	no	—
419	C₂²⋊C₄	—	4	4	no	—
420	C₂²⋊C₄	—	4	4	no	—
421	C₂²⋊C₄	C₂×D₄×C₅₉	1	2	yes	—
422	C₄²	—	2	1	no	—
423	C₄²	—	2	4	no	—
424	C₂³	—	2	1	no	—
425	C₂³	—	2	2	no	—
426	C₂³	—	2	4	no	—
427	C₂³	—	4	2	no	—
428	C₂³	—	4	4	no	—
429	C₂³	#121×C₅₉	1	2	yes	—
430	C₂³	C₂²×D₄×C₅₉	1	1	yes	characteristic
431	Q₈	—	2	2	no	—
432	Q₈	—	2	4	no	—
433	Q₈	—	2	4	no	—
434	Q₈	—	4	4	no	—
435	D₄	—	2	4	no	—
436	D₄	—	2	4	no	—
437	D₄	—	2	2	no	—
438	D₄	—	2	4	no	—
439	D₄	—	4	4	no	—
440	D₄	—	4	4	no	—
441	D₄	—	4	8	no	—
442	D₄	—	4	4	no	—
443	D₄	—	4	4	no	—
444	D₄	—	8	8	no	—
445	C₂×C₄	—	2	2	no	—
446	C₂×C₄	—	2	2	no	—
447	C₂×C₄	—	2	2	no	—
448	C₂×C₄	—	2	1	no	—
449	C₂×C₄	—	2	2	no	—
450	C₂×C₄	—	2	4	no	—
451	C₂×C₄	—	4	8	no	—
452	C₂×C₄	—	4	4	no	—
453	C₂×C₄	—	4	1	no	—
454	C₂×C₄	—	4	1	no	—
455	C₂×C₄	—	4	4	no	—
456	C₂×C₄	—	4	2	no	—
457	C₂×C₄	—	4	4	no	—
458	C₂×C₄	—	4	4	no	—
459	C₂×C₄	#121×C₅₉	1	2	yes	—
460	C₂×C₄	C₂²×D₄×C₅₉	1	1	yes	characteristic
461	C₂×C₄	C₂²×D₄×C₅₉	1	2	yes	—
462	C₂×C₄	C₂×#41×C₅₉	1	1	yes	characteristic
463	C₂×C₄	H(5,𝔽₂)×C₅₉	1	2	yes	—
464	C₈	—	2	2	no	—
465	C₈	—	4	1	no	—
466	C₈	—	4	1	no	—
467	C₈	#120×C₅₉	1	1	yes	characteristic
468	C₈	#120×C₅₉	1	1	yes	characteristic
469	C₈	#120×C₅₉	1	2	yes	—
470	C₂²	—	2	2	no	—
471	C₂²	—	2	4	no	—
472	C₂²	—	2	2	no	—
473	C₂²	—	4	1	no	—
474	C₂²	—	4	2	no	—
475	C₂²	—	4	1	no	—
476	C₂²	—	4	2	no	—
477	C₂²	—	4	1	no	—
478	C₂²	—	4	4	no	—
479	C₂²	—	8	4	no	—
480	C₂²	—	16	4	no	—
481	C₂²	C₂×#121×C₅₉	1	1	yes	characteristic
482	C₂²	D₄²×C₅₉	1	2	yes	—
483	C₄	—	2	2	no	—
484	C₄	—	4	2	no	—
485	C₄	—	4	1	no	—
486	C₄	—	4	4	no	—
487	C₄	—	8	4	no	—
488	C₄	C₂×#120×C₅₉	1	1	yes	characteristic
489	C₄	C₅₉×#535	1	1	yes	characteristic
490	C₄	C₅₉×#546	1	2	yes	—
491	C₂	—	2	1	no	—
492	C₂	—	2	2	no	—
493	C₂	—	4	2	no	—
494	C₂	—	4	2	no	—
495	C₂	—	8	4	no	—
496	C₂	C₅₉×#2408	1	1	yes	characteristic

	subgroup	G/H
center	C₄×C₅₉	#535
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₅₉
socle	C₂×C₅₉	#2408
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₅₉ ◁ C₂²×C₄×C₅₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₅₉×#3584	C₂	semidirect
2. C₅₉×#3050	C₂	semidirect
3. C₅₉×#3025	C₂	semidirect
4. C₅₉×#2929	C₂	semidirect
5. C₅₉×#2053	C₂	semidirect
6. C₅₉×#2010	C₂	semidirect
7. C₅₉×#1976	C₂	semidirect
8. C₅₉×#1812	C₂	semidirect
9. C₅₉×#1794	C₂	semidirect
19. C₂³×C₈×C₅₉	C₂²	semidirect
21. C₅₉×#525	C₂²	semidirect
29. C₅₉×#427	C₂²	semidirect
30. C₅₉×#424	C₂²	semidirect
31. C₅₉×#421	C₂²	semidirect
32. C₅₉×#416	C₂²	semidirect
34. C₅₉×#410	C₂²	semidirect
36. C₅₉×#407	C₂²	semidirect
37. C₅₉×#405	C₂²	semidirect
38. C₅₉×H(3,ℤ/4)	C₂²	semidirect
61. C₂×Q₁₆×C₅₉	D₄	semidirect
63. C₂×SD₁₆×C₅₉	D₄	semidirect
65. C₂×D₈×C₅₉	D₄	semidirect
68. C₂×M₁₆×C₅₉	D₄	semidirect
75. C₂²×C₈×C₅₉	D₄	semidirect
221. #24285	C₅₉	direct (N × H)
243. #3584	C₂×C₅₉	semidirect
244. #3050	C₂×C₅₉	semidirect
245. #3025	C₂×C₅₉	semidirect
246. #2929	C₂×C₅₉	semidirect
247. #2053	C₂×C₅₉	semidirect
248. #2010	C₂×C₅₉	semidirect
249. #1976	C₂×C₅₉	semidirect
250. #1812	C₂×C₅₉	semidirect
251. #1794	C₂×C₅₉	semidirect
267. C₂³×C₈	C₂²×C₅₉	semidirect
269. #525	C₂²×C₅₉	semidirect
277. #427	C₂²×C₅₉	semidirect
278. #424	C₂²×C₅₉	semidirect
279. #421	C₂²×C₅₉	semidirect
280. #416	C₂²×C₅₉	semidirect
282. #410	C₂²×C₅₉	semidirect
284. #407	C₂²×C₅₉	semidirect
285. #405	C₂²×C₅₉	semidirect
286. H(3,ℤ/4)	C₂²×C₅₉	semidirect
287. C₅₉	#24285	direct (N × H)
310. C₂×Q₁₆	D₄×C₅₉	semidirect
312. C₂×SD₁₆	D₄×C₅₉	semidirect
314. C₂×D₈	D₄×C₅₉	semidirect
317. C₂×M₁₆	D₄×C₅₉	semidirect
324. C₂²×C₈	D₄×C₅₉	semidirect

Maximal subgroups

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

subgroup	index
C₅₉×#3584	2
C₅₉×#3050	2
C₅₉×#3025	2
C₅₉×#2929	2
C₅₉×#2053	2
C₅₉×#2010	2
C₅₉×#1976	2
C₅₉×#1812	2
C₅₉×#1794	2
#24285	59

Subgroups — C59×#24285 #28436394

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₉×#24285 #28436394