Subgroups — C₅₉×#26501 #28438610

Order 15104.

724 conjugacy classes of subgroups.

The subgroup lattice has 440 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅₉×#3164	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅₉×#3081	C₂	1	2	yes	maximal, complemented
3	C₅₉×#2948	C₂	1	1	yes	maximal, characteristic
4	C₅₉×#2063	C₂	1	2	yes	maximal, complemented
5	C₅₉×#2027	C₂	1	2	yes	maximal, complemented
6	C₅₉×#1978	C₂	1	1	yes	maximal, characteristic
7	C₅₉×#1970	C₂	1	1	yes	maximal, characteristic
8	C₅₉×#1952	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅₉×#1945	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅₉×#1856	C₂	1	2	yes	maximal, complemented
11	C₅₉×#1772	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×D₈×C₅₉	C₂²	1	1	yes	characteristic
13	C₅₉×#544	C₂²	1	2	yes	—
14	C₅₉×#518	C₂²	1	2	yes	—
15	C₅₉×#501	—	2	2	no	—
16	C₅₉×#500	—	2	1	no	—
17	C₅₉×#499	—	2	1	no	—
18	C₅₉×#478	—	2	2	no	—
19	C₅₉×#478	—	2	2	no	—
20	C₅₉×#476	—	2	2	no	—
21	C₅₉×#474	—	2	2	no	—
22	C₅₉×#442	—	2	2	no	—
23	C₄×D₈×C₅₉	—	2	1	no	—
24	C₄×D₈×C₅₉	—	2	1	no	—
25	C₂×#108×C₅₉	C₂²	1	1	yes	characteristic
26	C₂×#108×C₅₉	C₂²	1	1	yes	characteristic
27	C₅₉×#428	C₂²	1	2	yes	—
28	C₅₉×#428	C₂²	1	2	yes	—
29	C₅₉×#427	C₂²	1	1	yes	characteristic
30	C₅₉×#427	C₂²	1	1	yes	characteristic
31	C₂×#107×C₅₉	C₂²	1	1	yes	characteristic
32	C₅₉×#424	C₂²	1	2	yes	—
33	C₅₉×#418	C₂²	1	2	yes	—
34	C₅₉×#418	C₂²	1	2	yes	—
35	C₂×#102×C₅₉	C₂²	1	2	yes	—
36	C₂×#100×C₅₉	C₂²	1	2	yes	—
37	C₅₉×#405	C₂²	1	1	yes	characteristic
38	C₅₉×#405	C₂²	1	1	yes	characteristic
39	C₂×C₄×C₈×C₅₉	C₂²	1	1	yes	characteristic
40	C₅₉×#390	C₂²	1	2	yes	—
41	C₅₉×#343	C₂²	1	2	yes	—
42	C₅₉×#339	C₂²	1	1	yes	characteristic
43	C₅₉×#339	C₂²	1	2	yes	—
44	C₅₉×#339	C₂²	1	1	yes	characteristic
45	C₂²×D₄×C₅₉	C₂³	1	2	yes	—
46	C₂×D₈×C₅₉	—	2	1	no	—
47	C₂×D₈×C₅₉	—	2	1	no	—
48	C₂×D₈×C₅₉	—	2	2	no	—
49	C₂×D₈×C₅₉	Q₈	1	4	yes	complemented
50	C₂×M₁₆×C₅₉	C₂³	1	1	yes	characteristic
51	C₂×M₁₆×C₅₉	C₂³	1	2	yes	—
52	C₂×M₁₆×C₅₉	C₂³	1	1	yes	characteristic
53	C₂²×C₈×C₅₉	C₂³	1	1	yes	characteristic
54	C₂²×C₈×C₅₉	C₂³	1	1	yes	characteristic
55	C₄⋊Q₈×C₅₉	—	2	2	no	—
56	C₄⋊Q₈×C₅₉	—	2	2	no	—
57	#125×C₅₉	—	2	2	no	—
58	#125×C₅₉	—	2	2	no	—
59	C₂²⋊Q₈×C₅₉	—	4	2	no	—
60	C₄×D₄×C₅₉	—	2	2	no	—
61	C₄×D₄×C₅₉	—	2	2	no	—
62	C₄×D₄×C₅₉	—	2	2	no	—
63	C₄×D₄×C₅₉	—	2	2	no	—
64	#117×C₅₉	C₂³	1	1	yes	characteristic
65	#117×C₅₉	C₂³	1	1	yes	characteristic
66	#117×C₅₉	C₂³	1	2	yes	—
67	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
68	C₂×C₂²⋊C₄×C₅₉	—	4	2	no	—
69	C₂×C₂²⋊C₄×C₅₉	—	4	2	no	—
70	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
71	#108×C₅₉	—	2	2	no	—
72	#108×C₅₉	—	2	2	no	—
73	#107×C₅₉	—	2	1	no	—
74	#107×C₅₉	—	2	1	no	—
75	#107×C₅₉	—	2	2	no	—
76	#107×C₅₉	—	2	2	no	—
77	#107×C₅₉	D₄	1	1	yes	characteristic
78	#107×C₅₉	D₄	1	1	yes	characteristic
79	#107×C₅₉	D₄	1	1	yes	characteristic
80	#107×C₅₉	D₄	1	1	yes	characteristic
81	#106×C₅₉	—	2	2	no	—
82	#106×C₅₉	—	2	2	no	—
83	#106×C₅₉	D₄	1	2	yes	—
84	#106×C₅₉	D₄	1	1	yes	characteristic
85	#106×C₅₉	D₄	1	1	yes	characteristic
86	C₄⋊C₈×C₅₉	—	2	2	no	—
87	C₄⋊C₈×C₅₉	—	2	2	no	—
88	#102×C₅₉	—	2	2	no	—
89	#102×C₅₉	—	2	2	no	—
90	#102×C₅₉	—	2	2	no	—
91	#102×C₅₉	—	2	2	no	—
92	#102×C₅₉	—	2	2	no	—
93	#102×C₅₉	—	2	2	no	—
94	#100×C₅₉	—	2	4	no	—
95	#97×C₅₉	—	2	1	no	—
96	#97×C₅₉	—	2	1	no	—
97	C₄×C₈×C₅₉	—	2	1	no	—
98	C₄×C₈×C₅₉	—	2	1	no	—
99	C₄×C₈×C₅₉	—	2	2	no	—
100	C₂⁴×C₅₉	—	2	2	no	—
101	C₂×Q₈×C₅₉	—	4	2	no	—
102	C₂×D₄×C₅₉	—	2	2	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	C₂×Q₈	1	4	yes	—
108	C₂²×C₄×C₅₉	—	2	1	no	—
109	C₂²×C₄×C₅₉	—	2	2	no	—
110	C₂²×C₄×C₅₉	—	4	2	no	—
111	C₂²×C₄×C₅₉	—	4	2	no	—
112	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
113	D₈×C₅₉	—	2	4	no	—
114	D₈×C₅₉	—	2	4	no	—
115	M₁₆×C₅₉	—	2	1	no	—
116	M₁₆×C₅₉	—	2	2	no	—
117	M₁₆×C₅₉	—	2	2	no	—
118	M₁₆×C₅₉	—	2	1	no	—
119	M₁₆×C₅₉	—	2	1	no	—
120	M₁₆×C₅₉	#41	1	2	yes	—
121	C₂×C₈×C₅₉	—	2	1	no	—
122	C₂×C₈×C₅₉	—	2	1	no	—
123	C₂×C₈×C₅₉	—	2	1	no	—
124	C₂×C₈×C₅₉	—	2	1	no	—
125	C₂×C₈×C₅₉	—	2	2	no	—
126	C₂×C₈×C₅₉	C₂×D₄	1	1	yes	characteristic
127	C₂×C₈×C₅₉	C₂×D₄	1	1	yes	characteristic
128	C₂×C₈×C₅₉	C₂×D₄	1	1	yes	characteristic
129	C₂×C₈×C₅₉	C₂×D₄	1	1	yes	characteristic
130	C₂×C₈×C₅₉	C₂×Q₈	1	2	yes	—
131	C₂×C₈×C₅₉	#41	1	2	yes	—
132	C₄⋊C₄×C₅₉	—	2	2	no	—
133	C₄⋊C₄×C₅₉	—	2	2	no	—
134	C₄⋊C₄×C₅₉	—	4	2	no	—
135	C₄⋊C₄×C₅₉	—	4	2	no	—
136	C₄⋊C₄×C₅₉	—	4	2	no	—
137	C₄⋊C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
138	C₄⋊C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
139	C₄⋊C₄×C₅₉	C₂×D₄	1	2	yes	—
140	C₄⋊C₄×C₅₉	C₂×D₄	1	2	yes	—
141	C₄⋊C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
142	C₄⋊C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
143	C₂²⋊C₄×C₅₉	—	2	1	no	—
144	C₂²⋊C₄×C₅₉	—	2	2	no	—
145	C₂²⋊C₄×C₅₉	—	2	1	no	—
146	C₂²⋊C₄×C₅₉	—	4	2	no	—
147	C₂²⋊C₄×C₅₉	—	4	2	no	—
148	C₂²⋊C₄×C₅₉	—	8	4	no	—
149	C₄²×C₅₉	—	2	1	no	—
150	C₄²×C₅₉	—	2	1	no	—
151	C₄²×C₅₉	—	2	2	no	—
152	C₄²×C₅₉	—	2	1	no	—
153	C₄²×C₅₉	—	2	1	no	—
154	C₂³×C₅₉	—	2	4	no	—
155	C₂³×C₅₉	—	4	2	no	—
156	C₂³×C₅₉	—	4	2	no	—
157	C₂³×C₅₉	—	8	2	no	—
158	C₂³×C₅₉	—	8	2	no	—
159	C₂³×C₅₉	H(5,𝔽₂)	1	1	yes	characteristic
160	Q₈×C₅₉	—	16	2	no	—
161	D₄×C₅₉	—	2	4	no	—
162	D₄×C₅₉	—	2	4	no	—
163	D₄×C₅₉	—	4	2	no	—
164	D₄×C₅₉	—	4	2	no	—
165	C₂×C₄×C₅₉	—	2	2	no	—
166	C₂×C₄×C₅₉	—	2	1	no	—
167	C₂×C₄×C₅₉	—	2	1	no	—
168	C₂×C₄×C₅₉	—	2	2	no	—
169	C₂×C₄×C₅₉	—	2	2	no	—
170	C₂×C₄×C₅₉	—	2	1	no	—
171	C₂×C₄×C₅₉	—	2	1	no	—
172	C₂×C₄×C₅₉	—	4	1	no	—
173	C₂×C₄×C₅₉	—	4	1	no	—
174	C₂×C₄×C₅₉	—	4	2	no	—
175	C₂×C₄×C₅₉	—	8	2	no	—
176	C₂×C₄×C₅₉	—	16	2	no	—
177	C₂×C₄×C₅₉	—	16	2	no	—
178	C₂×C₄×C₅₉	C₂²×D₄	1	1	yes	characteristic
179	C₂×C₄×C₅₉	C₂²×D₄	1	1	yes	characteristic
180	C₂×C₄×C₅₉	C₂²×Q₈	1	1	yes	characteristic
181	C₂×C₄×C₅₉	C₂×#41	1	1	yes	characteristic
182	C₂×C₄×C₅₉	C₂×#41	1	1	yes	characteristic
183	C₂×C₄×C₅₉	2₋¹⁺⁴	1	1	yes	characteristic
184	C₈×C₅₉	—	2	1	no	—
185	C₈×C₅₉	—	2	1	no	—
186	C₈×C₅₉	—	2	2	no	—
187	C₈×C₅₉	—	4	2	no	—
188	C₈×C₅₉	—	4	1	no	—
189	C₈×C₅₉	C₂²⋊Q₈	1	2	yes	—
190	C₈×C₅₉	C₂²⋊Q₈	1	2	yes	—
191	#26501	C₅₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
192	C₂²×C₅₉	—	2	1	no	—
193	C₂²×C₅₉	—	2	1	no	—
194	C₂²×C₅₉	—	4	4	no	—
195	C₂²×C₅₉	—	8	4	no	—
196	C₂²×C₅₉	—	8	2	no	—
197	C₂²×C₅₉	—	8	2	no	—
198	C₂²×C₅₉	—	16	2	no	—
199	C₂²×C₅₉	#542	1	1	yes	characteristic
200	C₂²×C₅₉	D₄²	1	1	yes	characteristic
201	C₂²×C₅₉	#554	1	1	yes	characteristic
202	C₄×C₅₉	—	4	2	no	—
203	C₄×C₅₉	—	4	1	no	—
204	C₄×C₅₉	—	4	2	no	—
205	C₄×C₅₉	—	4	1	no	—
206	C₄×C₅₉	—	4	1	no	—
207	C₄×C₅₉	—	4	2	no	—
208	C₄×C₅₉	—	4	1	no	—
209	C₄×C₅₉	—	8	2	no	—
210	C₄×C₅₉	C₂×C₂²⋊Q₈	1	1	yes	characteristic
211	C₄×C₅₉	#532	1	1	yes	characteristic
212	C₄×C₅₉	#548	1	1	yes	characteristic
213	C₄×C₅₉	D₄×Q₈	1	1	yes	characteristic
214	#3164	C₂×C₅₉	1	1	yes	characteristic, complemented
215	#3081	C₂×C₅₉	1	2	yes	complemented
216	#2948	C₂×C₅₉	1	1	yes	characteristic
217	#2063	C₂×C₅₉	1	2	yes	complemented
218	#2027	C₂×C₅₉	1	2	yes	complemented
219	#1978	C₂×C₅₉	1	1	yes	characteristic
220	#1970	C₂×C₅₉	1	1	yes	characteristic
221	#1952	C₂×C₅₉	1	1	yes	characteristic, complemented
222	#1945	C₂×C₅₉	1	1	yes	characteristic, complemented
223	#1856	C₂×C₅₉	1	2	yes	complemented
224	#1772	C₂×C₅₉	1	1	yes	characteristic, complemented
225	C₂×C₅₉	—	2	1	no	—
226	C₂×C₅₉	—	2	1	no	—
227	C₂×C₅₉	—	8	4	no	—
228	C₂×C₅₉	#2452	1	1	yes	characteristic
229	C₂×C₅₉	#3290	1	1	yes	characteristic
230	C₂×C₅₉	#3292	1	1	yes	characteristic
231	C₂²×D₈	C₂²×C₅₉	1	1	yes	characteristic
232	#544	C₂²×C₅₉	1	2	yes	—
233	#518	C₂²×C₅₉	1	2	yes	—
234	#501	—	2	2	no	—
235	#500	—	2	1	no	—
236	#499	—	2	1	no	—
237	#478	—	2	2	no	—
238	#478	—	2	2	no	—
239	#476	—	2	2	no	—
240	#474	—	2	2	no	—
241	#442	—	2	2	no	—
242	C₄×D₈	—	2	1	no	—
243	C₄×D₈	—	2	1	no	—
244	C₂×#108	C₂²×C₅₉	1	1	yes	characteristic
245	C₂×#108	C₂²×C₅₉	1	1	yes	characteristic
246	#428	C₂²×C₅₉	1	2	yes	—
247	#428	C₂²×C₅₉	1	2	yes	—
248	#427	C₂²×C₅₉	1	1	yes	characteristic
249	#427	C₂²×C₅₉	1	1	yes	characteristic
250	C₂×#107	C₂²×C₅₉	1	1	yes	characteristic
251	#424	C₂²×C₅₉	1	2	yes	—
252	#418	C₂²×C₅₉	1	2	yes	—
253	#418	C₂²×C₅₉	1	2	yes	—
254	C₂×#102	C₂²×C₅₉	1	2	yes	—
255	C₂×#100	C₂²×C₅₉	1	2	yes	—
256	#405	C₂²×C₅₉	1	1	yes	characteristic
257	#405	C₂²×C₅₉	1	1	yes	characteristic
258	C₂×C₄×C₈	C₂²×C₅₉	1	1	yes	characteristic
259	#390	C₂²×C₅₉	1	2	yes	—
260	#343	C₂²×C₅₉	1	2	yes	—
261	#339	C₂²×C₅₉	1	1	yes	characteristic
262	#339	C₂²×C₅₉	1	2	yes	—
263	#339	C₂²×C₅₉	1	1	yes	characteristic
264	C₅₉	#26501	1	1	yes	characteristic, direct product factor, Sylow
265	C₂²×D₄	C₂³×C₅₉	1	2	yes	—
266	C₂×D₈	—	2	1	no	—
267	C₂×D₈	—	2	1	no	—
268	C₂×D₈	—	2	2	no	—
269	C₂×D₈	Q₈×C₅₉	1	4	yes	complemented
270	C₂×M₁₆	C₂³×C₅₉	1	1	yes	characteristic
271	C₂×M₁₆	C₂³×C₅₉	1	2	yes	—
272	C₂×M₁₆	C₂³×C₅₉	1	1	yes	characteristic
273	C₂²×C₈	C₂³×C₅₉	1	1	yes	characteristic
274	C₂²×C₈	C₂³×C₅₉	1	1	yes	characteristic
275	C₄⋊Q₈	—	2	2	no	—
276	C₄⋊Q₈	—	2	2	no	—
277	#125	—	2	2	no	—
278	#125	—	2	2	no	—
279	C₂²⋊Q₈	—	4	2	no	—
280	C₄×D₄	—	2	2	no	—
281	C₄×D₄	—	2	2	no	—
282	C₄×D₄	—	2	2	no	—
283	C₄×D₄	—	2	2	no	—
284	#117	C₂³×C₅₉	1	1	yes	characteristic
285	#117	C₂³×C₅₉	1	2	yes	—
286	#117	C₂³×C₅₉	1	1	yes	characteristic
287	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
288	C₂×C₂²⋊C₄	—	4	2	no	—
289	C₂×C₂²⋊C₄	—	4	2	no	—
290	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
291	#108	—	2	2	no	—
292	#108	—	2	2	no	—
293	#107	—	2	1	no	—
294	#107	—	2	1	no	—
295	#107	—	2	2	no	—
296	#107	—	2	2	no	—
297	#107	D₄×C₅₉	1	1	yes	characteristic
298	#107	D₄×C₅₉	1	1	yes	characteristic
299	#107	D₄×C₅₉	1	1	yes	characteristic
300	#107	D₄×C₅₉	1	1	yes	characteristic
301	#106	—	2	2	no	—
302	#106	—	2	2	no	—
303	#106	D₄×C₅₉	1	2	yes	—
304	#106	D₄×C₅₉	1	1	yes	characteristic
305	#106	D₄×C₅₉	1	1	yes	characteristic
306	C₄⋊C₈	—	2	2	no	—
307	C₄⋊C₈	—	2	2	no	—
308	#102	—	2	2	no	—
309	#102	—	2	2	no	—
310	#102	—	2	2	no	—
311	#102	—	2	2	no	—
312	#102	—	2	2	no	—
313	#102	—	2	2	no	—
314	#100	—	2	4	no	—
315	#97	—	2	1	no	—
316	#97	—	2	1	no	—
317	C₄×C₈	—	2	1	no	—
318	C₄×C₈	—	2	1	no	—
319	C₄×C₈	—	2	2	no	—
320	C₂⁴	—	2	2	no	—
321	C₂×Q₈	—	4	2	no	—
322	C₂×D₄	—	2	2	no	—
323	C₂×D₄	—	2	2	no	—
324	C₂×D₄	—	2	2	no	—
325	C₂×D₄	—	2	2	no	—
326	C₂×D₄	—	2	2	no	—
327	C₂×D₄	C₂×Q₈×C₅₉	1	4	yes	—
328	C₂²×C₄	—	2	1	no	—
329	C₂²×C₄	—	2	2	no	—
330	C₂²×C₄	—	4	2	no	—
331	C₂²×C₄	—	4	2	no	—
332	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
333	D₈	—	2	4	no	—
334	D₈	—	2	4	no	—
335	M₁₆	—	2	1	no	—
336	M₁₆	—	2	2	no	—
337	M₁₆	—	2	2	no	—
338	M₁₆	—	2	1	no	—
339	M₁₆	—	2	1	no	—
340	M₁₆	#41×C₅₉	1	2	yes	—
341	C₂×C₈	—	2	1	no	—
342	C₂×C₈	—	2	1	no	—
343	C₂×C₈	—	2	1	no	—
344	C₂×C₈	—	2	1	no	—
345	C₂×C₈	—	2	2	no	—
346	C₂×C₈	C₂×D₄×C₅₉	1	1	yes	characteristic
347	C₂×C₈	C₂×D₄×C₅₉	1	1	yes	characteristic
348	C₂×C₈	C₂×D₄×C₅₉	1	1	yes	characteristic
349	C₂×C₈	C₂×D₄×C₅₉	1	1	yes	characteristic
350	C₂×C₈	C₂×Q₈×C₅₉	1	2	yes	—
351	C₂×C₈	#41×C₅₉	1	2	yes	—
352	C₄⋊C₄	—	2	2	no	—
353	C₄⋊C₄	—	2	2	no	—
354	C₄⋊C₄	—	4	2	no	—
355	C₄⋊C₄	—	4	2	no	—
356	C₄⋊C₄	—	4	2	no	—
357	C₄⋊C₄	C₂×D₄×C₅₉	1	1	yes	characteristic
358	C₄⋊C₄	C₂×D₄×C₅₉	1	1	yes	characteristic
359	C₄⋊C₄	C₂×D₄×C₅₉	1	2	yes	—
360	C₄⋊C₄	C₂×D₄×C₅₉	1	2	yes	—
361	C₄⋊C₄	C₂×D₄×C₅₉	1	1	yes	characteristic
362	C₄⋊C₄	C₂×D₄×C₅₉	1	1	yes	characteristic
363	C₂²⋊C₄	—	2	1	no	—
364	C₂²⋊C₄	—	2	2	no	—
365	C₂²⋊C₄	—	2	1	no	—
366	C₂²⋊C₄	—	4	2	no	—
367	C₂²⋊C₄	—	4	2	no	—
368	C₂²⋊C₄	—	8	4	no	—
369	C₄²	—	2	1	no	—
370	C₄²	—	2	1	no	—
371	C₄²	—	2	2	no	—
372	C₄²	—	2	1	no	—
373	C₄²	—	2	1	no	—
374	C₂³	—	2	4	no	—
375	C₂³	—	4	2	no	—
376	C₂³	—	4	2	no	—
377	C₂³	—	8	2	no	—
378	C₂³	—	8	2	no	—
379	C₂³	H(5,𝔽₂)×C₅₉	1	1	yes	characteristic
380	Q₈	—	16	2	no	—
381	D₄	—	2	4	no	—
382	D₄	—	2	4	no	—
383	D₄	—	4	2	no	—
384	D₄	—	4	2	no	—
385	C₂×C₄	—	2	2	no	—
386	C₂×C₄	—	2	1	no	—
387	C₂×C₄	—	2	1	no	—
388	C₂×C₄	—	2	2	no	—
389	C₂×C₄	—	2	2	no	—
390	C₂×C₄	—	2	1	no	—
391	C₂×C₄	—	2	1	no	—
392	C₂×C₄	—	4	1	no	—
393	C₂×C₄	—	4	1	no	—
394	C₂×C₄	—	4	2	no	—
395	C₂×C₄	—	8	2	no	—
396	C₂×C₄	—	16	2	no	—
397	C₂×C₄	—	16	2	no	—
398	C₂×C₄	C₂²×D₄×C₅₉	1	1	yes	characteristic
399	C₂×C₄	C₂²×D₄×C₅₉	1	1	yes	characteristic
400	C₂×C₄	C₂²×Q₈×C₅₉	1	1	yes	characteristic
401	C₂×C₄	C₂×#41×C₅₉	1	1	yes	characteristic
402	C₂×C₄	C₂×#41×C₅₉	1	1	yes	characteristic
403	C₂×C₄	2₋¹⁺⁴×C₅₉	1	1	yes	characteristic
404	C₈	—	2	1	no	—
405	C₈	—	2	1	no	—
406	C₈	—	2	2	no	—
407	C₈	—	4	2	no	—
408	C₈	—	4	1	no	—
409	C₈	C₂²⋊Q₈×C₅₉	1	2	yes	—
410	C₈	C₂²⋊Q₈×C₅₉	1	2	yes	—
411	C₂²	—	2	1	no	—
412	C₂²	—	2	1	no	—
413	C₂²	—	4	4	no	—
414	C₂²	—	8	4	no	—
415	C₂²	—	8	2	no	—
416	C₂²	—	8	2	no	—
417	C₂²	—	16	2	no	—
418	C₂²	C₅₉×#542	1	1	yes	characteristic
419	C₂²	D₄²×C₅₉	1	1	yes	characteristic
420	C₂²	C₅₉×#554	1	1	yes	characteristic
421	C₄	—	4	2	no	—
422	C₄	—	4	1	no	—
423	C₄	—	4	2	no	—
424	C₄	—	4	1	no	—
425	C₄	—	4	1	no	—
426	C₄	—	4	2	no	—
427	C₄	—	4	1	no	—
428	C₄	—	8	2	no	—
429	C₄	C₂×C₂²⋊Q₈×C₅₉	1	1	yes	characteristic
430	C₄	C₅₉×#532	1	1	yes	characteristic
431	C₄	C₅₉×#548	1	1	yes	characteristic
432	C₄	D₄×Q₈×C₅₉	1	1	yes	characteristic
433	C₂	—	2	1	no	—
434	C₂	—	2	1	no	—
435	C₂	—	8	4	no	—
436	C₂	C₅₉×#2452	1	1	yes	characteristic
437	C₂	C₅₉×#3290	1	1	yes	characteristic
438	C₂	C₅₉×#3292	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₅₉	D₄²
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₅₉
prime radical	C₂²×D₈×C₅₉	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₅₉ ◁ C₂²×C₄×C₅₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₅₉×#3164	C₂	semidirect
2. C₅₉×#3081	C₂	semidirect
4. C₅₉×#2063	C₂	semidirect
5. C₅₉×#2027	C₂	semidirect
8. C₅₉×#1952	C₂	semidirect
9. C₅₉×#1945	C₂	semidirect
10. C₅₉×#1856	C₂	semidirect
11. C₅₉×#1772	C₂	semidirect
49. C₂×D₈×C₅₉	Q₈	semidirect
191. #26501	C₅₉	direct (N × H)
214. #3164	C₂×C₅₉	semidirect
215. #3081	C₂×C₅₉	semidirect
217. #2063	C₂×C₅₉	semidirect
218. #2027	C₂×C₅₉	semidirect
221. #1952	C₂×C₅₉	semidirect
222. #1945	C₂×C₅₉	semidirect
223. #1856	C₂×C₅₉	semidirect
224. #1772	C₂×C₅₉	semidirect
264. C₅₉	#26501	direct (N × H)
269. C₂×D₈	Q₈×C₅₉	semidirect

Maximal subgroups

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

subgroup	index
C₅₉×#3164	2
C₅₉×#3081	2
C₅₉×#2948	2
C₅₉×#2063	2
C₅₉×#2027	2
C₅₉×#1978	2
C₅₉×#1970	2
C₅₉×#1952	2
C₅₉×#1945	2
C₅₉×#1856	2
C₅₉×#1772	2
#26501	59

Subgroups — C59×#26501 #28438610

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₉×#26501 #28438610