Subgroups — C₅₉×#19270 #28431379

Order 15104.

670 conjugacy classes of subgroups.

The subgroup lattice has 418 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅₉×#498	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅₉×#3079	C₂	1	1	yes	maximal, characteristic
3	C₅₉×#3039	C₂	1	1	yes	maximal, characteristic
4	C₈×#41×C₅₉	C₂	1	1	yes	maximal, characteristic
5	C₅₉×#1672	C₂	1	4	yes	maximal, complemented
6	C₅₉×#1671	C₂	1	4	yes	maximal, complemented
7	C₅₉×#1566	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅₉×#1548	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅₉×#1546	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#137×C₅₉	—	2	1	no	—
11	C₂×C₄⋊Q₈×C₅₉	C₂²	1	1	yes	characteristic
12	C₂×C₄⋊Q₈×C₅₉	C₂²	1	1	yes	characteristic
13	C₄×#41×C₅₉	C₂²	1	1	yes	characteristic
14	C₅₉×#498	—	2	1	no	—
15	C₅₉×#498	—	2	1	no	—
16	C₅₉×#498	C₂²	1	4	yes	—
17	C₅₉×#477	C₂²	1	2	yes	—
18	C₅₉×#476	C₂²	1	2	yes	—
19	C₅₉×#475	—	2	1	no	—
20	C₅₉×#474	—	2	1	no	—
21	C₅₉×#462	—	2	1	no	—
22	C₅₉×#462	C₂²	1	2	yes	—
23	C₅₉×#461	—	2	1	no	—
24	C₅₉×#461	C₂²	1	2	yes	—
25	C₈×Q₈×C₅₉	C₂²	1	2	yes	—
26	C₈×D₄×C₅₉	—	2	2	no	—
27	C₈×D₄×C₅₉	C₂²	1	2	yes	—
28	C₅₉×#431	—	2	1	no	—
29	C₅₉×#431	C₂²	1	1	yes	characteristic
30	C₅₉×#428	—	2	1	no	—
31	C₂×#106×C₅₉	—	2	2	no	—
32	C₅₉×#423	C₂²	1	1	yes	characteristic
33	C₅₉×#423	C₂²	1	1	yes	characteristic
34	C₅₉×#419	—	2	1	no	—
35	C₅₉×#417	—	2	1	no	—
36	C₂×C₄×C₈×C₅₉	—	2	1	no	—
37	C₂×C₄×C₈×C₅₉	C₂²	1	1	yes	characteristic
38	C₅₉×#334	C₂²	1	4	yes	—
39	C₅₉×#333	C₂²	1	4	yes	—
40	C₅₉×#332	C₂²	1	4	yes	—
41	C₂×#41×C₅₉	D₄	1	1	yes	characteristic
42	C₂²×Q₈×C₅₉	—	2	1	no	—
43	C₂²×Q₈×C₅₉	—	2	1	no	—
44	#137×C₅₉	—	4	4	no	—
45	C₂×Q₁₆×C₅₉	—	2	2	no	—
46	C₂×SD₁₆×C₅₉	—	2	2	no	—
47	C₂×M₁₆×C₅₉	—	2	1	no	—
48	C₂×M₁₆×C₅₉	—	2	1	no	—
49	C₂²×C₈×C₅₉	—	2	2	no	—
50	C₂²×C₈×C₅₉	D₄	1	2	yes	—
51	C₄⋊Q₈×C₅₉	—	2	1	no	—
52	C₄⋊Q₈×C₅₉	—	2	1	no	—
53	C₄⋊Q₈×C₅₉	—	2	1	no	—
54	C₄⋊Q₈×C₅₉	—	2	1	no	—
55	C₄⋊Q₈×C₅₉	—	2	1	no	—
56	C₄⋊Q₈×C₅₉	—	2	1	no	—
57	C₄⋊Q₈×C₅₉	C₂³	1	2	yes	—
58	C₄⋊Q₈×C₅₉	C₂³	1	2	yes	—
59	C₄×Q₈×C₅₉	D₄	1	1	yes	characteristic
60	C₄×Q₈×C₅₉	C₂³	1	1	yes	characteristic
61	C₄×D₄×C₅₉	—	2	1	no	—
62	C₄×D₄×C₅₉	—	2	1	no	—
63	C₄×D₄×C₅₉	D₄	1	1	yes	characteristic
64	C₄×D₄×C₅₉	C₂³	1	1	yes	characteristic
65	#117×C₅₉	—	2	1	no	—
66	#117×C₅₉	D₄	1	1	yes	characteristic
67	C₂×C₄⋊C₄×C₅₉	—	2	1	no	—
68	C₂×C₄⋊C₄×C₅₉	—	2	1	no	—
69	C₂×C₄⋊C₄×C₅₉	—	2	1	no	—
70	C₂×C₄⋊C₄×C₅₉	—	2	1	no	—
71	C₂×C₄²×C₅₉	—	2	1	no	—
72	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
73	#107×C₅₉	—	2	2	no	—
74	#106×C₅₉	—	2	4	no	—
75	#106×C₅₉	—	2	4	no	—
76	#106×C₅₉	—	2	2	no	—
77	C₄⋊C₈×C₅₉	—	2	2	no	—
78	C₄⋊C₈×C₅₉	—	2	1	no	—
79	C₄⋊C₈×C₅₉	—	2	1	no	—
80	C₄⋊C₈×C₅₉	C₂³	1	2	yes	—
81	C₄⋊C₈×C₅₉	C₂³	1	2	yes	—
82	C₄⋊C₈×C₅₉	C₂³	1	2	yes	—
83	#103×C₅₉	—	2	2	no	—
84	#103×C₅₉	—	2	2	no	—
85	#103×C₅₉	—	2	2	no	—
86	#102×C₅₉	—	2	2	no	—
87	C₂²⋊C₈×C₅₉	—	2	1	no	—
88	C₂²⋊C₈×C₅₉	—	2	2	no	—
89	C₄×C₈×C₅₉	—	2	2	no	—
90	C₄×C₈×C₅₉	—	2	1	no	—
91	C₄×C₈×C₅₉	D₄	1	1	yes	characteristic
92	C₄×C₈×C₅₉	D₄	1	1	yes	characteristic
93	C₄×C₈×C₅₉	C₂³	1	2	yes	—
94	#41×C₅₉	—	2	2	no	—
95	#41×C₅₉	SD₁₆	1	4	yes	—
96	C₂×Q₈×C₅₉	—	2	2	no	—
97	C₂×Q₈×C₅₉	—	2	2	no	—
98	C₂×Q₈×C₅₉	—	4	1	no	—
99	C₂×Q₈×C₅₉	—	4	1	no	—
100	C₂×Q₈×C₅₉	—	4	2	no	—
101	C₂×Q₈×C₅₉	—	4	2	no	—
102	C₂×Q₈×C₅₉	—	8	2	no	—
103	C₂×Q₈×C₅₉	C₂×D₄	1	1	yes	characteristic
104	C₂×D₄×C₅₉	—	2	1	no	—
105	C₂×D₄×C₅₉	C₂×D₄	1	1	yes	characteristic
106	C₂²×C₄×C₅₉	—	2	1	no	—
107	C₂²×C₄×C₅₉	—	2	1	no	—
108	C₂²×C₄×C₅₉	—	2	1	no	—
109	C₂²×C₄×C₅₉	—	4	1	no	—
110	C₂²×C₄×C₅₉	—	4	1	no	—
111	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
112	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
113	C₂²×C₄×C₅₉	#41	1	1	yes	characteristic
114	Q₁₆×C₅₉	—	4	4	no	—
115	SD₁₆×C₅₉	—	4	4	no	—
116	M₁₆×C₅₉	—	4	2	no	—
117	M₁₆×C₅₉	—	4	2	no	—
118	C₂×C₈×C₅₉	—	2	4	no	—
119	C₂×C₈×C₅₉	—	2	2	no	—
120	C₂×C₈×C₅₉	—	2	2	no	—
121	C₂×C₈×C₅₉	—	2	2	no	—
122	C₂×C₈×C₅₉	—	4	4	no	—
123	C₂×C₈×C₅₉	C₂×D₄	1	2	yes	—
124	C₂×C₈×C₅₉	C₂×D₄	1	2	yes	—
125	C₄⋊C₄×C₅₉	—	2	1	no	—
126	C₄⋊C₄×C₅₉	—	2	1	no	—
127	C₄⋊C₄×C₅₉	—	2	2	no	—
128	C₄⋊C₄×C₅₉	—	2	2	no	—
129	C₄⋊C₄×C₅₉	—	2	2	no	—
130	C₄⋊C₄×C₅₉	—	2	2	no	—
131	C₄⋊C₄×C₅₉	—	4	1	no	—
132	C₄⋊C₄×C₅₉	—	4	1	no	—
133	C₄⋊C₄×C₅₉	—	4	1	no	—
134	C₄⋊C₄×C₅₉	—	4	1	no	—
135	C₄⋊C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
136	C₄⋊C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
137	C₂²⋊C₄×C₅₉	—	2	1	no	—
138	C₂²⋊C₄×C₅₉	—	2	1	no	—
139	C₂²⋊C₄×C₅₉	—	2	1	no	—
140	C₄²×C₅₉	—	2	1	no	—
141	C₄²×C₅₉	—	2	1	no	—
142	C₄²×C₅₉	—	2	1	no	—
143	C₄²×C₅₉	C₂×D₄	1	1	yes	characteristic
144	C₄²×C₅₉	C₂×D₄	1	1	yes	characteristic
145	C₄²×C₅₉	#41	1	1	yes	characteristic
146	C₄²×C₅₉	C₂⁴	1	1	yes	characteristic
147	C₂³×C₅₉	—	2	1	no	—
148	C₂³×C₅₉	#121	1	1	yes	characteristic
149	Q₈×C₅₉	—	2	1	no	—
150	Q₈×C₅₉	—	4	2	no	—
151	Q₈×C₅₉	—	4	2	no	—
152	Q₈×C₅₉	—	8	2	no	—
153	Q₈×C₅₉	—	8	2	no	—
154	Q₈×C₅₉	—	8	2	no	—
155	Q₈×C₅₉	C₂×SD₁₆	1	2	yes	—
156	D₄×C₅₉	—	2	4	no	—
157	D₄×C₅₉	—	2	1	no	—
158	D₄×C₅₉	C₂×SD₁₆	1	2	yes	—
159	C₂×C₄×C₅₉	—	2	1	no	—
160	C₂×C₄×C₅₉	—	2	2	no	—
161	C₂×C₄×C₅₉	—	2	4	no	—
162	C₂×C₄×C₅₉	—	2	2	no	—
163	C₂×C₄×C₅₉	—	2	1	no	—
164	C₂×C₄×C₅₉	—	2	1	no	—
165	C₂×C₄×C₅₉	—	4	2	no	—
166	C₂×C₄×C₅₉	—	4	2	no	—
167	C₂×C₄×C₅₉	—	4	2	no	—
168	C₂×C₄×C₅₉	—	4	2	no	—
169	C₂×C₄×C₅₉	—	8	2	no	—
170	C₂×C₄×C₅₉	—	8	2	no	—
171	C₂×C₄×C₅₉	#121	1	1	yes	characteristic
172	C₂×C₄×C₅₉	#121	1	1	yes	characteristic
173	C₂×C₄×C₅₉	#121	1	1	yes	characteristic
174	C₂×C₄×C₅₉	C₂×SD₁₆	1	2	yes	—
175	C₂×C₄×C₅₉	#135	1	2	yes	—
176	C₂×C₄×C₅₉	C₂²×D₄	1	1	yes	characteristic
177	C₂×C₄×C₅₉	C₂²×D₄	1	1	yes	characteristic
178	C₂×C₄×C₅₉	C₂×#41	1	1	yes	characteristic
179	C₈×C₅₉	—	2	2	no	—
180	C₈×C₅₉	—	4	2	no	—
181	C₈×C₅₉	—	4	2	no	—
182	C₈×C₅₉	—	4	2	no	—
183	C₈×C₅₉	#137	1	4	yes	complemented
184	#19270	C₅₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
185	C₂²×C₅₉	—	2	1	no	—
186	C₂²×C₅₉	—	2	1	no	—
187	C₂²×C₅₉	—	2	2	no	—
188	C₂²×C₅₉	—	4	1	no	—
189	C₂²×C₅₉	—	4	1	no	—
190	C₂²×C₅₉	#465	1	2	yes	—
191	C₂²×C₅₉	C₂×#121	1	1	yes	characteristic
192	C₄×C₅₉	—	2	1	no	—
193	C₄×C₅₉	—	2	2	no	—
194	C₄×C₅₉	—	2	1	no	—
195	C₄×C₅₉	—	4	1	no	—
196	C₄×C₅₉	—	4	1	no	—
197	C₄×C₅₉	—	8	2	no	—
198	C₄×C₅₉	—	8	2	no	—
199	C₄×C₅₉	#465	1	2	yes	—
200	C₄×C₅₉	#471	1	2	yes	—
201	C₄×C₅₉	C₂²×SD₁₆	1	1	yes	characteristic
202	C₄×C₅₉	C₂×#135	1	1	yes	characteristic
203	C₄×C₅₉	C₂×#137	1	2	yes	—
204	C₂×#498	C₂×C₅₉	1	1	yes	characteristic, complemented
205	#3079	C₂×C₅₉	1	1	yes	characteristic
206	#3039	C₂×C₅₉	1	1	yes	characteristic
207	C₈×#41	C₂×C₅₉	1	1	yes	characteristic
208	#1672	C₂×C₅₉	1	4	yes	complemented
209	#1671	C₂×C₅₉	1	4	yes	complemented
210	#1566	C₂×C₅₉	1	1	yes	characteristic, complemented
211	#1548	C₂×C₅₉	1	1	yes	characteristic, complemented
212	#1546	C₂×C₅₉	1	1	yes	characteristic, complemented
213	C₂×C₅₉	—	2	2	no	—
214	C₂×C₅₉	—	4	2	no	—
215	C₂×C₅₉	#3039	1	1	yes	characteristic
216	C₂×C₅₉	C₂×#465	1	1	yes	characteristic
217	C₂×C₅₉	C₂×#471	1	1	yes	characteristic
218	C₂×#137	—	2	1	no	—
219	C₂×C₄⋊Q₈	C₂²×C₅₉	1	1	yes	characteristic
220	C₂×C₄⋊Q₈	C₂²×C₅₉	1	1	yes	characteristic
221	C₄×#41	C₂²×C₅₉	1	1	yes	characteristic
222	#498	—	2	1	no	—
223	#498	—	2	1	no	—
224	#498	C₂²×C₅₉	1	4	yes	—
225	#477	C₂²×C₅₉	1	2	yes	—
226	#476	C₂²×C₅₉	1	2	yes	—
227	#475	—	2	1	no	—
228	#474	—	2	1	no	—
229	#462	—	2	1	no	—
230	#462	C₂²×C₅₉	1	2	yes	—
231	#461	—	2	1	no	—
232	#461	C₂²×C₅₉	1	2	yes	—
233	C₈×Q₈	C₂²×C₅₉	1	2	yes	—
234	C₈×D₄	—	2	2	no	—
235	C₈×D₄	C₂²×C₅₉	1	2	yes	—
236	#431	—	2	1	no	—
237	#431	C₂²×C₅₉	1	1	yes	characteristic
238	#428	—	2	1	no	—
239	C₂×#106	—	2	2	no	—
240	#423	C₂²×C₅₉	1	1	yes	characteristic
241	#423	C₂²×C₅₉	1	1	yes	characteristic
242	#419	—	2	1	no	—
243	#417	—	2	1	no	—
244	C₂×C₄×C₈	—	2	1	no	—
245	C₂×C₄×C₈	C₂²×C₅₉	1	1	yes	characteristic
246	#334	C₂²×C₅₉	1	4	yes	—
247	#333	C₂²×C₅₉	1	4	yes	—
248	#332	C₂²×C₅₉	1	4	yes	—
249	C₅₉	#19270	1	1	yes	characteristic, direct product factor, Sylow
250	C₂×#41	D₄×C₅₉	1	1	yes	characteristic
251	C₂²×Q₈	—	2	1	no	—
252	C₂²×Q₈	—	2	1	no	—
253	#137	—	4	4	no	—
254	C₂×Q₁₆	—	2	2	no	—
255	C₂×SD₁₆	—	2	2	no	—
256	C₂×M₁₆	—	2	1	no	—
257	C₂×M₁₆	—	2	1	no	—
258	C₂²×C₈	—	2	2	no	—
259	C₂²×C₈	D₄×C₅₉	1	2	yes	—
260	C₄⋊Q₈	—	2	1	no	—
261	C₄⋊Q₈	—	2	1	no	—
262	C₄⋊Q₈	—	2	1	no	—
263	C₄⋊Q₈	—	2	1	no	—
264	C₄⋊Q₈	—	2	1	no	—
265	C₄⋊Q₈	—	2	1	no	—
266	C₄⋊Q₈	C₂³×C₅₉	1	2	yes	—
267	C₄⋊Q₈	C₂³×C₅₉	1	2	yes	—
268	C₄×Q₈	D₄×C₅₉	1	1	yes	characteristic
269	C₄×Q₈	C₂³×C₅₉	1	1	yes	characteristic
270	C₄×D₄	—	2	1	no	—
271	C₄×D₄	—	2	1	no	—
272	C₄×D₄	D₄×C₅₉	1	1	yes	characteristic
273	C₄×D₄	C₂³×C₅₉	1	1	yes	characteristic
274	#117	—	2	1	no	—
275	#117	D₄×C₅₉	1	1	yes	characteristic
276	C₂×C₄⋊C₄	—	2	1	no	—
277	C₂×C₄⋊C₄	—	2	1	no	—
278	C₂×C₄⋊C₄	—	2	1	no	—
279	C₂×C₄⋊C₄	—	2	1	no	—
280	C₂×C₄²	—	2	1	no	—
281	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
282	#107	—	2	2	no	—
283	#106	—	2	4	no	—
284	#106	—	2	4	no	—
285	#106	—	2	2	no	—
286	C₄⋊C₈	—	2	2	no	—
287	C₄⋊C₈	—	2	1	no	—
288	C₄⋊C₈	—	2	1	no	—
289	C₄⋊C₈	C₂³×C₅₉	1	2	yes	—
290	C₄⋊C₈	C₂³×C₅₉	1	2	yes	—
291	C₄⋊C₈	C₂³×C₅₉	1	2	yes	—
292	#103	—	2	2	no	—
293	#103	—	2	2	no	—
294	#103	—	2	2	no	—
295	#102	—	2	2	no	—
296	C₂²⋊C₈	—	2	1	no	—
297	C₂²⋊C₈	—	2	2	no	—
298	C₄×C₈	—	2	2	no	—
299	C₄×C₈	—	2	1	no	—
300	C₄×C₈	D₄×C₅₉	1	1	yes	characteristic
301	C₄×C₈	D₄×C₅₉	1	1	yes	characteristic
302	C₄×C₈	C₂³×C₅₉	1	2	yes	—
303	#41	—	2	2	no	—
304	#41	SD₁₆×C₅₉	1	4	yes	—
305	C₂×Q₈	—	2	2	no	—
306	C₂×Q₈	—	2	2	no	—
307	C₂×Q₈	—	4	1	no	—
308	C₂×Q₈	—	4	1	no	—
309	C₂×Q₈	—	4	2	no	—
310	C₂×Q₈	—	4	2	no	—
311	C₂×Q₈	—	8	2	no	—
312	C₂×Q₈	C₂×D₄×C₅₉	1	1	yes	characteristic
313	C₂×D₄	—	2	1	no	—
314	C₂×D₄	C₂×D₄×C₅₉	1	1	yes	characteristic
315	C₂²×C₄	—	2	1	no	—
316	C₂²×C₄	—	2	1	no	—
317	C₂²×C₄	—	2	1	no	—
318	C₂²×C₄	—	4	1	no	—
319	C₂²×C₄	—	4	1	no	—
320	C₂²×C₄	C₂×D₄×C₅₉	1	1	yes	characteristic
321	C₂²×C₄	C₂×D₄×C₅₉	1	1	yes	characteristic
322	C₂²×C₄	#41×C₅₉	1	1	yes	characteristic
323	Q₁₆	—	4	4	no	—
324	SD₁₆	—	4	4	no	—
325	M₁₆	—	4	2	no	—
326	M₁₆	—	4	2	no	—
327	C₂×C₈	—	2	4	no	—
328	C₂×C₈	—	2	2	no	—
329	C₂×C₈	—	2	2	no	—
330	C₂×C₈	—	2	2	no	—
331	C₂×C₈	—	4	4	no	—
332	C₂×C₈	C₂×D₄×C₅₉	1	2	yes	—
333	C₂×C₈	C₂×D₄×C₅₉	1	2	yes	—
334	C₄⋊C₄	—	2	1	no	—
335	C₄⋊C₄	—	2	1	no	—
336	C₄⋊C₄	—	2	2	no	—
337	C₄⋊C₄	—	2	2	no	—
338	C₄⋊C₄	—	2	2	no	—
339	C₄⋊C₄	—	2	2	no	—
340	C₄⋊C₄	—	4	1	no	—
341	C₄⋊C₄	—	4	1	no	—
342	C₄⋊C₄	—	4	1	no	—
343	C₄⋊C₄	—	4	1	no	—
344	C₄⋊C₄	C₂×D₄×C₅₉	1	1	yes	characteristic
345	C₄⋊C₄	C₂×D₄×C₅₉	1	1	yes	characteristic
346	C₂²⋊C₄	—	2	1	no	—
347	C₂²⋊C₄	—	2	1	no	—
348	C₂²⋊C₄	—	2	1	no	—
349	C₄²	—	2	1	no	—
350	C₄²	—	2	1	no	—
351	C₄²	—	2	1	no	—
352	C₄²	C₂×D₄×C₅₉	1	1	yes	characteristic
353	C₄²	C₂×D₄×C₅₉	1	1	yes	characteristic
354	C₄²	#41×C₅₉	1	1	yes	characteristic
355	C₄²	C₂⁴×C₅₉	1	1	yes	characteristic
356	C₂³	—	2	1	no	—
357	C₂³	#121×C₅₉	1	1	yes	characteristic
358	Q₈	—	2	1	no	—
359	Q₈	—	4	2	no	—
360	Q₈	—	4	2	no	—
361	Q₈	—	8	2	no	—
362	Q₈	—	8	2	no	—
363	Q₈	—	8	2	no	—
364	Q₈	C₂×SD₁₆×C₅₉	1	2	yes	—
365	D₄	—	2	4	no	—
366	D₄	—	2	1	no	—
367	D₄	C₂×SD₁₆×C₅₉	1	2	yes	—
368	C₂×C₄	—	2	1	no	—
369	C₂×C₄	—	2	4	no	—
370	C₂×C₄	—	2	2	no	—
371	C₂×C₄	—	2	2	no	—
372	C₂×C₄	—	2	1	no	—
373	C₂×C₄	—	2	1	no	—
374	C₂×C₄	—	4	2	no	—
375	C₂×C₄	—	4	2	no	—
376	C₂×C₄	—	4	2	no	—
377	C₂×C₄	—	4	2	no	—
378	C₂×C₄	—	8	2	no	—
379	C₂×C₄	—	8	2	no	—
380	C₂×C₄	#121×C₅₉	1	1	yes	characteristic
381	C₂×C₄	#121×C₅₉	1	1	yes	characteristic
382	C₂×C₄	#121×C₅₉	1	1	yes	characteristic
383	C₂×C₄	C₂×SD₁₆×C₅₉	1	2	yes	—
384	C₂×C₄	#135×C₅₉	1	2	yes	—
385	C₂×C₄	C₂²×D₄×C₅₉	1	1	yes	characteristic
386	C₂×C₄	C₂²×D₄×C₅₉	1	1	yes	characteristic
387	C₂×C₄	C₂×#41×C₅₉	1	1	yes	characteristic
388	C₈	—	2	2	no	—
389	C₈	—	4	2	no	—
390	C₈	—	4	2	no	—
391	C₈	—	4	2	no	—
392	C₈	#137×C₅₉	1	4	yes	complemented
393	C₂²	—	2	1	no	—
394	C₂²	—	2	1	no	—
395	C₂²	—	2	2	no	—
396	C₂²	—	4	1	no	—
397	C₂²	—	4	1	no	—
398	C₂²	C₅₉×#465	1	2	yes	—
399	C₂²	C₂×#121×C₅₉	1	1	yes	characteristic
400	C₄	—	2	1	no	—
401	C₄	—	2	2	no	—
402	C₄	—	2	1	no	—
403	C₄	—	4	1	no	—
404	C₄	—	4	1	no	—
405	C₄	—	8	2	no	—
406	C₄	—	8	2	no	—
407	C₄	C₅₉×#465	1	2	yes	—
408	C₄	C₅₉×#471	1	2	yes	—
409	C₄	C₂²×SD₁₆×C₅₉	1	1	yes	characteristic
410	C₄	C₂×#135×C₅₉	1	1	yes	characteristic
411	C₄	C₂×#137×C₅₉	1	2	yes	—
412	C₂	—	2	2	no	—
413	C₂	—	4	2	no	—
414	C₂	C₅₉×#3039	1	1	yes	characteristic
415	C₂	C₂×C₅₉×#465	1	1	yes	characteristic
416	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	C₂×#41×C₅₉	D₄
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×#498	C₂	semidirect
5. C₅₉×#1672	C₂	semidirect
6. C₅₉×#1671	C₂	semidirect
7. C₅₉×#1566	C₂	semidirect
8. C₅₉×#1548	C₂	semidirect
9. C₅₉×#1546	C₂	semidirect
183. C₈×C₅₉	#137	semidirect
184. #19270	C₅₉	direct (N × H)
204. C₂×#498	C₂×C₅₉	semidirect
208. #1672	C₂×C₅₉	semidirect
209. #1671	C₂×C₅₉	semidirect
210. #1566	C₂×C₅₉	semidirect
211. #1548	C₂×C₅₉	semidirect
212. #1546	C₂×C₅₉	semidirect
249. C₅₉	#19270	direct (N × H)
392. C₈	#137×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×#498	2
C₅₉×#3079	2
C₅₉×#3039	2
C₈×#41×C₅₉	2
C₅₉×#1672	2
C₅₉×#1671	2
C₅₉×#1566	2
C₅₉×#1548	2
C₅₉×#1546	2
#19270	59

Subgroups — C59×#19270 #28431379

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₉×#19270 #28431379