Subgroups — C₅₉×#19291 #28431400

Order 15104.

764 conjugacy classes of subgroups.

The subgroup lattice has 448 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅₉×#492	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅₉×#3079	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅₉×#3038	C₂	1	1	yes	maximal, characteristic
4	C₅₉×#2965	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅₉×#1686	C₂	1	4	yes	maximal, complemented
6	C₅₉×#1685	C₂	1	4	yes	maximal, complemented
7	C₅₉×#1567	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅₉×#1549	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅₉×#1545	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×AGL(1,ℤ/8)×C₅₉	—	2	1	no	—
11	C₂²×SD₁₆×C₅₉	—	2	2	no	—
12	C₂×C₄⋊Q₈×C₅₉	C₂²	1	1	yes	characteristic
13	C₂×#127×C₅₉	C₂²	1	1	yes	characteristic
14	C₄×#41×C₅₉	C₂²	1	1	yes	characteristic
15	C₅₉×#492	—	2	1	no	—
16	C₅₉×#492	—	2	1	no	—
17	C₅₉×#492	C₂²	1	4	yes	—
18	C₅₉×#477	—	2	1	no	—
19	C₅₉×#476	—	2	1	no	—
20	C₅₉×#475	C₂²	1	2	yes	complemented
21	C₅₉×#474	C₂²	1	2	yes	complemented
22	C₅₉×#460	—	2	1	no	—
23	C₅₉×#460	C₂²	1	2	yes	—
24	C₅₉×#459	—	2	1	no	—
25	C₅₉×#459	C₂²	1	2	yes	—
26	C₅₉×#446	C₂²	1	2	yes	complemented
27	C₅₉×#436	C₂²	1	2	yes	complemented
28	C₅₉×#435	—	2	2	no	—
29	C₅₉×#431	—	2	1	no	—
30	C₅₉×#431	C₂²	1	1	yes	characteristic
31	C₅₉×#428	—	2	1	no	—
32	C₅₉×#423	C₂²	1	1	yes	characteristic
33	C₅₉×#423	C₂²	1	1	yes	characteristic
34	C₅₉×#418	—	2	1	no	—
35	C₅₉×#417	—	2	1	no	—
36	C₄×M₁₆×C₅₉	—	2	1	no	—
37	C₂×C₄×C₈×C₅₉	C₂²	1	1	yes	characteristic
38	C₅₉×#335	C₂²	1	4	yes	complemented
39	C₅₉×#332	C₂²	1	4	yes	complemented
40	C₅₉×#331	C₂²	1	4	yes	—
41	C₂×#41×C₅₉	D₄	1	1	yes	characteristic
42	C₂²×Q₈×C₅₉	—	2	1	no	—
43	C₂²×D₄×C₅₉	—	2	1	no	—
44	C₂²×D₄×C₅₉	—	2	1	no	—
45	C₂²×D₄×C₅₉	—	2	1	no	—
46	AGL(1,ℤ/8)×C₅₉	—	4	4	no	—
47	C₂×SD₁₆×C₅₉	—	2	2	no	—
48	C₂×SD₁₆×C₅₉	—	2	4	no	—
49	C₂×SD₁₆×C₅₉	—	2	4	no	—
50	C₂×SD₁₆×C₅₉	—	4	8	no	—
51	C₂×D₈×C₅₉	—	2	2	no	—
52	C₂×M₁₆×C₅₉	—	2	1	no	—
53	C₂×M₁₆×C₅₉	—	2	1	no	—
54	C₂×M₁₆×C₅₉	—	2	2	no	—
55	C₂²×C₈×C₅₉	D₄	1	2	yes	—
56	C₄⋊Q₈×C₅₉	—	2	1	no	—
57	C₄⋊Q₈×C₅₉	—	2	1	no	—
58	C₄⋊Q₈×C₅₉	—	2	1	no	—
59	C₄⋊Q₈×C₅₉	C₂³	1	2	yes	—
60	#127×C₅₉	—	2	1	no	—
61	#127×C₅₉	—	2	1	no	—
62	#127×C₅₉	—	2	1	no	—
63	#127×C₅₉	C₂³	1	2	yes	—
64	C₄×Q₈×C₅₉	D₄	1	1	yes	characteristic
65	C₄×Q₈×C₅₉	C₂³	1	1	yes	characteristic
66	C₄×D₄×C₅₉	—	2	1	no	—
67	C₄×D₄×C₅₉	—	2	1	no	—
68	C₄×D₄×C₅₉	D₄	1	1	yes	characteristic
69	C₄×D₄×C₅₉	C₂³	1	1	yes	characteristic
70	#117×C₅₉	—	2	1	no	—
71	#117×C₅₉	D₄	1	1	yes	characteristic
72	C₂×C₄⋊C₄×C₅₉	—	2	1	no	—
73	C₂×C₄⋊C₄×C₅₉	—	2	1	no	—
74	C₂×C₄²×C₅₉	—	2	1	no	—
75	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
76	#107×C₅₉	—	2	2	no	—
77	#106×C₅₉	—	2	2	no	—
78	C₄⋊C₈×C₅₉	—	2	2	no	—
79	C₄⋊C₈×C₅₉	—	2	1	no	—
80	C₄⋊C₈×C₅₉	—	2	1	no	—
81	C₄⋊C₈×C₅₉	C₂³	1	2	yes	—
82	C₄⋊C₈×C₅₉	C₂³	1	2	yes	—
83	C₄⋊C₈×C₅₉	C₂³	1	2	yes	—
84	#103×C₅₉	—	2	2	no	—
85	#102×C₅₉	—	2	2	no	—
86	#102×C₅₉	—	2	2	no	—
87	#102×C₅₉	—	2	2	no	—
88	C₂²⋊C₈×C₅₉	—	2	1	no	—
89	C₂²⋊C₈×C₅₉	—	2	2	no	—
90	#97×C₅₉	—	2	2	no	—
91	C₄×C₈×C₅₉	—	2	1	no	—
92	C₄×C₈×C₅₉	D₄	1	1	yes	characteristic
93	C₄×C₈×C₅₉	D₄	1	1	yes	characteristic
94	C₄×C₈×C₅₉	C₂³	1	2	yes	—
95	C₂⁴×C₅₉	—	4	1	no	—
96	#41×C₅₉	—	2	2	no	—
97	#41×C₅₉	—	2	2	no	—
98	C₂×Q₈×C₅₉	—	2	2	no	—
99	C₂×Q₈×C₅₉	—	4	4	no	—
100	C₂×Q₈×C₅₉	—	4	1	no	—
101	C₂×Q₈×C₅₉	C₂×D₄	1	1	yes	characteristic
102	C₂×D₄×C₅₉	—	2	1	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	—	4	4	no	—
107	C₂×D₄×C₅₉	—	4	1	no	—
108	C₂×D₄×C₅₉	—	4	1	no	—
109	C₂×D₄×C₅₉	—	4	1	no	—
110	C₂×D₄×C₅₉	—	4	2	no	—
111	C₂×D₄×C₅₉	—	4	2	no	—
112	C₂×D₄×C₅₉	—	8	2	no	—
113	C₂×D₄×C₅₉	C₂×D₄	1	1	yes	characteristic
114	C₂²×C₄×C₅₉	—	2	1	no	—
115	C₂²×C₄×C₅₉	—	2	1	no	—
116	C₂²×C₄×C₅₉	—	2	1	no	—
117	C₂²×C₄×C₅₉	—	4	1	no	—
118	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
119	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
120	C₂²×C₄×C₅₉	#41	1	1	yes	characteristic
121	SD₁₆×C₅₉	—	4	8	no	—
122	SD₁₆×C₅₉	—	4	4	no	—
123	SD₁₆×C₅₉	—	4	8	no	—
124	D₈×C₅₉	—	4	4	no	—
125	M₁₆×C₅₉	—	4	2	no	—
126	M₁₆×C₅₉	—	4	2	no	—
127	M₁₆×C₅₉	—	4	4	no	—
128	C₂×C₈×C₅₉	—	2	4	no	—
129	C₂×C₈×C₅₉	—	2	2	no	—
130	C₂×C₈×C₅₉	—	2	2	no	—
131	C₂×C₈×C₅₉	—	2	2	no	—
132	C₂×C₈×C₅₉	C₂×D₄	1	2	yes	—
133	C₂×C₈×C₅₉	C₂×D₄	1	2	yes	—
134	C₄⋊C₄×C₅₉	—	2	1	no	—
135	C₄⋊C₄×C₅₉	—	2	1	no	—
136	C₄⋊C₄×C₅₉	—	2	2	no	—
137	C₄⋊C₄×C₅₉	—	2	2	no	—
138	C₄⋊C₄×C₅₉	—	4	1	no	—
139	C₄⋊C₄×C₅₉	—	4	1	no	—
140	C₄⋊C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
141	C₄⋊C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
142	C₂²⋊C₄×C₅₉	—	2	1	no	—
143	C₂²⋊C₄×C₅₉	—	2	1	no	—
144	C₂²⋊C₄×C₅₉	—	2	1	no	—
145	C₄²×C₅₉	—	2	1	no	—
146	C₄²×C₅₉	—	2	1	no	—
147	C₄²×C₅₉	—	2	1	no	—
148	C₄²×C₅₉	C₂×D₄	1	1	yes	characteristic
149	C₄²×C₅₉	C₂×D₄	1	1	yes	characteristic
150	C₄²×C₅₉	#41	1	1	yes	characteristic
151	C₄²×C₅₉	C₂⁴	1	1	yes	characteristic
152	C₂³×C₅₉	—	2	1	no	—
153	C₂³×C₅₉	—	4	2	no	—
154	C₂³×C₅₉	—	8	2	no	—
155	C₂³×C₅₉	—	8	2	no	—
156	C₂³×C₅₉	—	8	2	no	—
157	C₂³×C₅₉	#121	1	1	yes	characteristic
158	Q₈×C₅₉	—	2	1	no	—
159	Q₈×C₅₉	—	2	1	no	—
160	Q₈×C₅₉	—	4	4	no	—
161	Q₈×C₅₉	—	8	2	no	—
162	D₄×C₅₉	—	2	1	no	—
163	D₄×C₅₉	—	2	1	no	—
164	D₄×C₅₉	—	4	2	no	—
165	D₄×C₅₉	—	4	2	no	—
166	D₄×C₅₉	—	4	4	no	—
167	D₄×C₅₉	—	4	2	no	—
168	D₄×C₅₉	—	8	2	no	—
169	D₄×C₅₉	—	8	2	no	—
170	D₄×C₅₉	—	8	2	no	—
171	D₄×C₅₉	—	8	2	no	—
172	C₂×C₄×C₅₉	—	2	2	no	—
173	C₂×C₄×C₅₉	—	2	2	no	—
174	C₂×C₄×C₅₉	—	2	1	no	—
175	C₂×C₄×C₅₉	—	2	1	no	—
176	C₂×C₄×C₅₉	—	2	1	no	—
177	C₂×C₄×C₅₉	—	4	2	no	—
178	C₂×C₄×C₅₉	—	4	2	no	—
179	C₂×C₄×C₅₉	—	4	2	no	—
180	C₂×C₄×C₅₉	—	4	2	no	—
181	C₂×C₄×C₅₉	—	8	2	no	—
182	C₂×C₄×C₅₉	#121	1	1	yes	characteristic
183	C₂×C₄×C₅₉	#121	1	1	yes	characteristic
184	C₂×C₄×C₅₉	#121	1	1	yes	characteristic
185	C₂×C₄×C₅₉	AGL(1,ℤ/8)	1	2	yes	—
186	C₂×C₄×C₅₉	#137	1	2	yes	—
187	C₂×C₄×C₅₉	C₂²×D₄	1	1	yes	characteristic
188	C₂×C₄×C₅₉	C₂²×D₄	1	1	yes	characteristic
189	C₂×C₄×C₅₉	C₂×#41	1	1	yes	characteristic
190	C₈×C₅₉	—	2	2	no	—
191	C₈×C₅₉	—	4	2	no	—
192	C₈×C₅₉	—	4	2	no	—
193	C₈×C₅₉	—	4	2	no	—
194	C₈×C₅₉	AGL(1,ℤ/8)	1	4	yes	complemented
195	#19291	C₅₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
196	C₂²×C₅₉	—	2	1	no	—
197	C₂²×C₅₉	—	2	1	no	—
198	C₂²×C₅₉	—	4	1	no	—
199	C₂²×C₅₉	—	4	1	no	—
200	C₂²×C₅₉	—	4	1	no	—
201	C₂²×C₅₉	—	8	2	no	—
202	C₂²×C₅₉	—	8	2	no	—
203	C₂²×C₅₉	—	8	2	no	—
204	C₂²×C₅₉	—	16	4	no	—
205	C₂²×C₅₉	#468	1	2	yes	—
206	C₂²×C₅₉	C₂×#121	1	1	yes	characteristic
207	C₄×C₅₉	—	2	1	no	—
208	C₄×C₅₉	—	2	1	no	—
209	C₄×C₅₉	—	4	1	no	—
210	C₄×C₅₉	—	4	1	no	—
211	C₄×C₅₉	—	4	1	no	—
212	C₄×C₅₉	—	8	2	no	—
213	C₄×C₅₉	#468	1	2	yes	—
214	C₄×C₅₉	#471	1	2	yes	—
215	C₄×C₅₉	C₂×AGL(1,ℤ/8)	1	2	yes	—
216	C₄×C₅₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
217	C₄×C₅₉	C₂×#137	1	1	yes	characteristic
218	C₂×#492	C₂×C₅₉	1	1	yes	characteristic, complemented
219	#3079	C₂×C₅₉	1	1	yes	characteristic, complemented
220	#3038	C₂×C₅₉	1	1	yes	characteristic
221	#2965	C₂×C₅₉	1	1	yes	characteristic, complemented
222	#1686	C₂×C₅₉	1	4	yes	complemented
223	#1685	C₂×C₅₉	1	4	yes	complemented
224	#1567	C₂×C₅₉	1	1	yes	characteristic, complemented
225	#1549	C₂×C₅₉	1	1	yes	characteristic, complemented
226	#1545	C₂×C₅₉	1	1	yes	characteristic, complemented
227	C₂×C₅₉	—	2	2	no	—
228	C₂×C₅₉	—	8	1	no	—
229	C₂×C₅₉	—	16	2	no	—
230	C₂×C₅₉	#3038	1	1	yes	characteristic
231	C₂×C₅₉	C₂×#468	1	1	yes	characteristic
232	C₂×C₅₉	C₂×#471	1	1	yes	characteristic
233	C₂×AGL(1,ℤ/8)	—	2	1	no	—
234	C₂²×SD₁₆	—	2	2	no	—
235	C₂×C₄⋊Q₈	C₂²×C₅₉	1	1	yes	characteristic
236	C₂×#127	C₂²×C₅₉	1	1	yes	characteristic
237	C₄×#41	C₂²×C₅₉	1	1	yes	characteristic
238	#492	—	2	1	no	—
239	#492	—	2	1	no	—
240	#492	C₂²×C₅₉	1	4	yes	—
241	#477	—	2	1	no	—
242	#476	—	2	1	no	—
243	#475	C₂²×C₅₉	1	2	yes	complemented
244	#474	C₂²×C₅₉	1	2	yes	complemented
245	#460	—	2	1	no	—
246	#460	C₂²×C₅₉	1	2	yes	—
247	#459	—	2	1	no	—
248	#459	C₂²×C₅₉	1	2	yes	—
249	#446	C₂²×C₅₉	1	2	yes	complemented
250	#436	C₂²×C₅₉	1	2	yes	complemented
251	#435	—	2	2	no	—
252	#431	—	2	1	no	—
253	#431	C₂²×C₅₉	1	1	yes	characteristic
254	#428	—	2	1	no	—
255	#423	C₂²×C₅₉	1	1	yes	characteristic
256	#423	C₂²×C₅₉	1	1	yes	characteristic
257	#418	—	2	1	no	—
258	#417	—	2	1	no	—
259	C₄×M₁₆	—	2	1	no	—
260	C₂×C₄×C₈	C₂²×C₅₉	1	1	yes	characteristic
261	#335	C₂²×C₅₉	1	4	yes	complemented
262	#332	C₂²×C₅₉	1	4	yes	complemented
263	#331	C₂²×C₅₉	1	4	yes	—
264	C₅₉	#19291	1	1	yes	characteristic, direct product factor, Sylow
265	C₂×#41	D₄×C₅₉	1	1	yes	characteristic
266	C₂²×Q₈	—	2	1	no	—
267	C₂²×D₄	—	2	1	no	—
268	C₂²×D₄	—	2	1	no	—
269	C₂²×D₄	—	2	1	no	—
270	AGL(1,ℤ/8)	—	4	4	no	—
271	C₂×SD₁₆	—	2	2	no	—
272	C₂×SD₁₆	—	2	4	no	—
273	C₂×SD₁₆	—	2	4	no	—
274	C₂×SD₁₆	—	4	8	no	—
275	C₂×D₈	—	2	2	no	—
276	C₂×M₁₆	—	2	1	no	—
277	C₂×M₁₆	—	2	1	no	—
278	C₂×M₁₆	—	2	2	no	—
279	C₂²×C₈	D₄×C₅₉	1	2	yes	—
280	C₄⋊Q₈	—	2	1	no	—
281	C₄⋊Q₈	—	2	1	no	—
282	C₄⋊Q₈	—	2	1	no	—
283	C₄⋊Q₈	C₂³×C₅₉	1	2	yes	—
284	#127	—	2	1	no	—
285	#127	—	2	1	no	—
286	#127	—	2	1	no	—
287	#127	C₂³×C₅₉	1	2	yes	—
288	C₄×Q₈	D₄×C₅₉	1	1	yes	characteristic
289	C₄×Q₈	C₂³×C₅₉	1	1	yes	characteristic
290	C₄×D₄	—	2	1	no	—
291	C₄×D₄	—	2	1	no	—
292	C₄×D₄	D₄×C₅₉	1	1	yes	characteristic
293	C₄×D₄	C₂³×C₅₉	1	1	yes	characteristic
294	#117	—	2	1	no	—
295	#117	D₄×C₅₉	1	1	yes	characteristic
296	C₂×C₄⋊C₄	—	2	1	no	—
297	C₂×C₄⋊C₄	—	2	1	no	—
298	C₂×C₄²	—	2	1	no	—
299	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
300	#107	—	2	2	no	—
301	#106	—	2	2	no	—
302	C₄⋊C₈	—	2	2	no	—
303	C₄⋊C₈	—	2	1	no	—
304	C₄⋊C₈	—	2	1	no	—
305	C₄⋊C₈	C₂³×C₅₉	1	2	yes	—
306	C₄⋊C₈	C₂³×C₅₉	1	2	yes	—
307	C₄⋊C₈	C₂³×C₅₉	1	2	yes	—
308	#103	—	2	2	no	—
309	#102	—	2	2	no	—
310	#102	—	2	2	no	—
311	#102	—	2	2	no	—
312	C₂²⋊C₈	—	2	1	no	—
313	C₂²⋊C₈	—	2	2	no	—
314	#97	—	2	2	no	—
315	C₄×C₈	—	2	1	no	—
316	C₄×C₈	D₄×C₅₉	1	1	yes	characteristic
317	C₄×C₈	D₄×C₅₉	1	1	yes	characteristic
318	C₄×C₈	C₂³×C₅₉	1	2	yes	—
319	C₂⁴	—	4	1	no	—
320	#41	—	2	2	no	—
321	#41	—	2	2	no	—
322	C₂×Q₈	—	2	2	no	—
323	C₂×Q₈	—	4	4	no	—
324	C₂×Q₈	—	4	1	no	—
325	C₂×Q₈	C₂×D₄×C₅₉	1	1	yes	characteristic
326	C₂×D₄	—	2	1	no	—
327	C₂×D₄	—	2	2	no	—
328	C₂×D₄	—	2	2	no	—
329	C₂×D₄	—	2	2	no	—
330	C₂×D₄	—	4	4	no	—
331	C₂×D₄	—	4	1	no	—
332	C₂×D₄	—	4	1	no	—
333	C₂×D₄	—	4	1	no	—
334	C₂×D₄	—	4	2	no	—
335	C₂×D₄	—	4	2	no	—
336	C₂×D₄	—	8	2	no	—
337	C₂×D₄	C₂×D₄×C₅₉	1	1	yes	characteristic
338	C₂²×C₄	—	2	1	no	—
339	C₂²×C₄	—	2	1	no	—
340	C₂²×C₄	—	2	1	no	—
341	C₂²×C₄	—	4	1	no	—
342	C₂²×C₄	C₂×D₄×C₅₉	1	1	yes	characteristic
343	C₂²×C₄	C₂×D₄×C₅₉	1	1	yes	characteristic
344	C₂²×C₄	#41×C₅₉	1	1	yes	characteristic
345	SD₁₆	—	4	8	no	—
346	SD₁₆	—	4	4	no	—
347	SD₁₆	—	4	8	no	—
348	D₈	—	4	4	no	—
349	M₁₆	—	4	2	no	—
350	M₁₆	—	4	2	no	—
351	M₁₆	—	4	4	no	—
352	C₂×C₈	—	2	4	no	—
353	C₂×C₈	—	2	2	no	—
354	C₂×C₈	—	2	2	no	—
355	C₂×C₈	—	2	2	no	—
356	C₂×C₈	C₂×D₄×C₅₉	1	2	yes	—
357	C₂×C₈	C₂×D₄×C₅₉	1	2	yes	—
358	C₄⋊C₄	—	2	1	no	—
359	C₄⋊C₄	—	2	1	no	—
360	C₄⋊C₄	—	2	2	no	—
361	C₄⋊C₄	—	2	2	no	—
362	C₄⋊C₄	—	4	1	no	—
363	C₄⋊C₄	—	4	1	no	—
364	C₄⋊C₄	C₂×D₄×C₅₉	1	1	yes	characteristic
365	C₄⋊C₄	C₂×D₄×C₅₉	1	1	yes	characteristic
366	C₂²⋊C₄	—	2	1	no	—
367	C₂²⋊C₄	—	2	1	no	—
368	C₂²⋊C₄	—	2	1	no	—
369	C₄²	—	2	1	no	—
370	C₄²	—	2	1	no	—
371	C₄²	—	2	1	no	—
372	C₄²	C₂×D₄×C₅₉	1	1	yes	characteristic
373	C₄²	C₂×D₄×C₅₉	1	1	yes	characteristic
374	C₄²	#41×C₅₉	1	1	yes	characteristic
375	C₄²	C₂⁴×C₅₉	1	1	yes	characteristic
376	C₂³	—	2	1	no	—
377	C₂³	—	4	2	no	—
378	C₂³	—	8	2	no	—
379	C₂³	—	8	2	no	—
380	C₂³	—	8	2	no	—
381	C₂³	#121×C₅₉	1	1	yes	characteristic
382	Q₈	—	2	1	no	—
383	Q₈	—	2	1	no	—
384	Q₈	—	4	4	no	—
385	Q₈	—	8	2	no	—
386	D₄	—	2	1	no	—
387	D₄	—	2	1	no	—
388	D₄	—	4	2	no	—
389	D₄	—	4	2	no	—
390	D₄	—	4	4	no	—
391	D₄	—	4	2	no	—
392	D₄	—	8	2	no	—
393	D₄	—	8	2	no	—
394	D₄	—	8	2	no	—
395	D₄	—	8	2	no	—
396	C₂×C₄	—	2	2	no	—
397	C₂×C₄	—	2	2	no	—
398	C₂×C₄	—	2	1	no	—
399	C₂×C₄	—	2	1	no	—
400	C₂×C₄	—	2	1	no	—
401	C₂×C₄	—	4	2	no	—
402	C₂×C₄	—	4	2	no	—
403	C₂×C₄	—	4	2	no	—
404	C₂×C₄	—	4	2	no	—
405	C₂×C₄	—	8	2	no	—
406	C₂×C₄	#121×C₅₉	1	1	yes	characteristic
407	C₂×C₄	#121×C₅₉	1	1	yes	characteristic
408	C₂×C₄	#121×C₅₉	1	1	yes	characteristic
409	C₂×C₄	AGL(1,ℤ/8)×C₅₉	1	2	yes	—
410	C₂×C₄	#137×C₅₉	1	2	yes	—
411	C₂×C₄	C₂²×D₄×C₅₉	1	1	yes	characteristic
412	C₂×C₄	C₂²×D₄×C₅₉	1	1	yes	characteristic
413	C₂×C₄	C₂×#41×C₅₉	1	1	yes	characteristic
414	C₈	—	2	2	no	—
415	C₈	—	4	2	no	—
416	C₈	—	4	2	no	—
417	C₈	—	4	2	no	—
418	C₈	AGL(1,ℤ/8)×C₅₉	1	4	yes	complemented
419	C₂²	—	2	1	no	—
420	C₂²	—	2	1	no	—
421	C₂²	—	4	1	no	—
422	C₂²	—	4	1	no	—
423	C₂²	—	4	1	no	—
424	C₂²	—	8	2	no	—
425	C₂²	—	8	2	no	—
426	C₂²	—	8	2	no	—
427	C₂²	—	16	4	no	—
428	C₂²	C₅₉×#468	1	2	yes	—
429	C₂²	C₂×#121×C₅₉	1	1	yes	characteristic
430	C₄	—	2	1	no	—
431	C₄	—	2	1	no	—
432	C₄	—	4	1	no	—
433	C₄	—	4	1	no	—
434	C₄	—	4	1	no	—
435	C₄	—	8	2	no	—
436	C₄	C₅₉×#468	1	2	yes	—
437	C₄	C₅₉×#471	1	2	yes	—
438	C₄	C₂×AGL(1,ℤ/8)×C₅₉	1	2	yes	—
439	C₄	C₂×AGL(1,ℤ/8)×C₅₉	1	1	yes	characteristic
440	C₄	C₂×#137×C₅₉	1	1	yes	characteristic
441	C₂	—	2	2	no	—
442	C₂	—	8	1	no	—
443	C₂	—	16	2	no	—
444	C₂	C₅₉×#3038	1	1	yes	characteristic
445	C₂	C₂×C₅₉×#468	1	1	yes	characteristic
446	C₂	C₂×C₅₉×#471	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₅₉	C₂×#121
commutator, Frattini, cosocle	C₄²	C₂⁴×C₅₉
prime radical	C₅₉×#3038	C₂
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₅₉ ◁ C₂×C₄²×C₅₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₅₉×#492	C₂	semidirect
2. C₅₉×#3079	C₂	semidirect
4. C₅₉×#2965	C₂	semidirect
5. C₅₉×#1686	C₂	semidirect
6. C₅₉×#1685	C₂	semidirect
7. C₅₉×#1567	C₂	semidirect
8. C₅₉×#1549	C₂	semidirect
9. C₅₉×#1545	C₂	semidirect
20. C₅₉×#475	C₂²	semidirect
21. C₅₉×#474	C₂²	semidirect
26. C₅₉×#446	C₂²	semidirect
27. C₅₉×#436	C₂²	semidirect
38. C₅₉×#335	C₂²	semidirect
39. C₅₉×#332	C₂²	semidirect
194. C₈×C₅₉	AGL(1,ℤ/8)	semidirect
195. #19291	C₅₉	direct (N × H)
218. C₂×#492	C₂×C₅₉	semidirect
219. #3079	C₂×C₅₉	semidirect
221. #2965	C₂×C₅₉	semidirect
222. #1686	C₂×C₅₉	semidirect
223. #1685	C₂×C₅₉	semidirect
224. #1567	C₂×C₅₉	semidirect
225. #1549	C₂×C₅₉	semidirect
226. #1545	C₂×C₅₉	semidirect
243. #475	C₂²×C₅₉	semidirect
244. #474	C₂²×C₅₉	semidirect
249. #446	C₂²×C₅₉	semidirect
250. #436	C₂²×C₅₉	semidirect
261. #335	C₂²×C₅₉	semidirect
262. #332	C₂²×C₅₉	semidirect
264. C₅₉	#19291	direct (N × H)
418. C₈	AGL(1,ℤ/8)×C₅₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₅₉×#492	2
C₅₉×#3079	2
C₅₉×#3038	2
C₅₉×#2965	2
C₅₉×#1686	2
C₅₉×#1685	2
C₅₉×#1567	2
C₅₉×#1549	2
C₅₉×#1545	2
#19291	59

Subgroups — C59×#19291 #28431400

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₉×#19291 #28431400