Subgroups — C₅₉×#33840 #28445949

Order 15104.

748 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×#509	C₂	1	2	yes	maximal, complemented
2	C₅₉×#3287	C₂	1	1	yes	maximal, characteristic, complemented
3	D₄×D₈×C₅₉	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅₉×#2246	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅₉×#2218	C₂	1	2	yes	maximal, complemented
6	C₅₉×#2207	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅₉×#2206	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅₉×#2186	C₂	1	2	yes	maximal, complemented
9	C₅₉×#2184	C₂	1	2	yes	maximal, complemented
10	C₄×SD₃₂×C₅₉	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅₉×#2169	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#135×C₅₉	C₂²	1	2	yes	complemented
13	C₂²×D₈×C₅₉	C₂²	1	2	yes	—
14	C₅₉×#550	—	2	1	no	—
15	D₄²×C₅₉	—	2	1	no	—
16	C₅₉×#509	—	2	8	no	—
17	C₂×SD₃₂×C₅₉	C₂²	1	1	yes	characteristic
18	C₂×SD₃₂×C₅₉	C₂²	1	2	yes	complemented
19	C₂×D₁₆×C₅₉	C₂²	1	2	yes	—
20	C₂×D₁₆×C₅₉	C₂²	1	2	yes	complemented
21	C₂×D₁₆×C₅₉	C₂²	1	2	yes	complemented
22	C₂×M₃₂×C₅₉	C₂²	1	2	yes	complemented
23	C₅₉×#493	C₂²	1	1	yes	characteristic
24	C₅₉×#493	C₂²	1	1	yes	characteristic, complemented
25	C₅₉×#466	C₂²	1	2	yes	—
26	C₅₉×#466	C₂²	1	2	yes	complemented
27	C₅₉×#460	—	2	1	no	—
28	C₅₉×#459	—	2	1	no	—
29	C₅₉×#449	—	2	2	no	—
30	C₅₉×#447	—	2	2	no	—
31	C₄×Q₁₆×C₅₉	C₂²	1	1	yes	characteristic, complemented
32	C₄×D₈×C₅₉	C₂²	1	1	yes	characteristic
33	C₈×D₄×C₅₉	C₂²	1	1	yes	characteristic
34	C₅₉×#367	C₂²	1	1	yes	characteristic, complemented
35	C₅₉×C₄⋊C₁₆	C₂²	1	1	yes	characteristic, complemented
36	C₅₉×#358	C₂²	1	1	yes	characteristic, complemented
37	C₅₉×#357	C₂²	1	1	yes	characteristic
38	C₅₉×#357	C₂²	1	2	yes	complemented
39	C₅₉×#357	C₂²	1	2	yes	complemented
40	C₅₉×C₂²⋊C₁₆	C₂²	1	2	yes	complemented
41	C₄×C₁₆×C₅₉	C₂²	1	1	yes	characteristic, complemented
42	C₂×#41×C₅₉	—	2	2	no	—
43	C₂²×D₄×C₅₉	—	2	2	no	—
44	C₂²×D₄×C₅₉	—	4	1	no	—
45	#135×C₅₉	—	2	4	no	—
46	#135×C₅₉	—	4	2	no	—
47	C₂×Q₁₆×C₅₉	C₂³	1	1	yes	characteristic
48	C₂×SD₁₆×C₅₉	—	2	2	no	—
49	C₂×D₈×C₅₉	—	2	4	no	—
50	C₂×D₈×C₅₉	—	2	2	no	—
51	C₂×D₈×C₅₉	—	2	1	no	—
52	C₂×D₈×C₅₉	—	2	1	no	—
53	C₂×D₈×C₅₉	—	4	2	no	—
54	C₂×D₈×C₅₉	C₂³	1	2	yes	—
55	C₂×D₈×C₅₉	C₂³	1	2	yes	—
56	C₂×D₈×C₅₉	C₂³	1	1	yes	characteristic
57	C₂²×C₈×C₅₉	C₂³	1	2	yes	—
58	#127×C₅₉	—	2	1	no	—
59	#127×C₅₉	—	2	1	no	—
60	#127×C₅₉	—	4	1	no	—
61	#121×C₅₉	—	2	2	no	—
62	#121×C₅₉	—	2	2	no	—
63	#121×C₅₉	—	4	1	no	—
64	#121×C₅₉	—	4	2	no	—
65	#120×C₅₉	—	4	2	no	—
66	C₄×Q₈×C₅₉	—	2	1	no	—
67	C₄×D₄×C₅₉	—	2	1	no	—
68	C₄×D₄×C₅₉	—	4	1	no	—
69	C₄×D₄×C₅₉	D₄	1	1	yes	characteristic
70	SD₃₂×C₅₉	—	2	4	no	—
71	SD₃₂×C₅₉	D₄	1	4	yes	complemented
72	D₁₆×C₅₉	—	2	4	no	—
73	D₁₆×C₅₉	—	2	4	no	—
74	D₁₆×C₅₉	—	4	2	no	—
75	M₃₂×C₅₉	—	2	4	no	—
76	C₂×C₁₆×C₅₉	C₂³	1	1	yes	characteristic
77	C₂×C₁₆×C₅₉	C₂³	1	2	yes	—
78	C₂×C₁₆×C₅₉	C₂³	1	1	yes	characteristic
79	#107×C₅₉	C₂³	1	1	yes	characteristic
80	#107×C₅₉	C₂³	1	1	yes	characteristic
81	C₄⋊C₈×C₅₉	D₄	1	1	yes	characteristic
82	#103×C₅₉	—	2	1	no	—
83	#102×C₅₉	—	2	1	no	—
84	#102×C₅₉	—	2	2	no	—
85	#102×C₅₉	—	2	2	no	—
86	C₂²⋊C₈×C₅₉	D₄	1	2	yes	—
87	C₄×C₈×C₅₉	C₂³	1	1	yes	characteristic
88	C₂⁴×C₅₉	—	4	2	no	—
89	#41×C₅₉	—	4	4	no	—
90	#41×C₅₉	—	8	2	no	—
91	C₂×Q₈×C₅₉	—	2	1	no	—
92	C₂×D₄×C₅₉	—	2	1	no	—
93	C₂×D₄×C₅₉	—	2	2	no	—
94	C₂×D₄×C₅₉	—	2	2	no	—
95	C₂×D₄×C₅₉	—	4	4	no	—
96	C₂×D₄×C₅₉	—	4	2	no	—
97	C₂×D₄×C₅₉	—	4	2	no	—
98	C₂×D₄×C₅₉	—	4	2	no	—
99	C₂×D₄×C₅₉	—	4	1	no	—
100	C₂×D₄×C₅₉	—	4	2	no	—
101	C₂×D₄×C₅₉	—	4	1	no	—
102	C₂×D₄×C₅₉	—	4	1	no	—
103	C₂×D₄×C₅₉	—	4	1	no	—
104	C₂×D₄×C₅₉	—	8	2	no	—
105	C₂×D₄×C₅₉	—	8	4	no	—
106	C₂×D₄×C₅₉	D₈	1	1	yes	characteristic
107	C₂²×C₄×C₅₉	—	4	1	no	—
108	C₂²×C₄×C₅₉	—	4	2	no	—
109	C₂²×C₄×C₅₉	C₂×D₄	1	2	yes	—
110	Q₁₆×C₅₉	—	2	1	no	—
111	Q₁₆×C₅₉	C₂×D₄	1	2	yes	complemented
112	SD₁₆×C₅₉	—	4	4	no	—
113	D₈×C₅₉	—	2	2	no	—
114	D₈×C₅₉	—	2	2	no	—
115	D₈×C₅₉	—	2	1	no	—
116	D₈×C₅₉	—	2	2	no	—
117	D₈×C₅₉	—	2	2	no	—
118	D₈×C₅₉	—	4	4	no	—
119	D₈×C₅₉	—	8	1	no	—
120	D₈×C₅₉	—	8	1	no	—
121	D₈×C₅₉	C₂×D₄	1	2	yes	—
122	C₂×C₈×C₅₉	—	2	2	no	—
123	C₂×C₈×C₅₉	—	2	2	no	—
124	C₂×C₈×C₅₉	C₂×D₄	1	1	yes	characteristic
125	C₂×C₈×C₅₉	C₂×D₄	1	2	yes	—
126	C₂×C₈×C₅₉	C₂⁴	1	1	yes	characteristic
127	C₄⋊C₄×C₅₉	—	2	1	no	—
128	C₄⋊C₄×C₅₉	—	2	1	no	—
129	C₄⋊C₄×C₅₉	—	4	1	no	—
130	C₄⋊C₄×C₅₉	D₈	1	1	yes	characteristic
131	C₂²⋊C₄×C₅₉	—	4	1	no	—
132	C₂²⋊C₄×C₅₉	—	4	2	no	—
133	C₂²⋊C₄×C₅₉	—	4	2	no	—
134	C₂²⋊C₄×C₅₉	D₈	1	2	yes	—
135	C₄²×C₅₉	—	4	1	no	—
136	C₄²×C₅₉	C₂×D₄	1	1	yes	characteristic
137	C₁₆×C₅₉	—	2	2	no	—
138	C₁₆×C₅₉	—	2	1	no	—
139	C₁₆×C₅₉	C₂×D₄	1	2	yes	complemented
140	C₂³×C₅₉	—	4	1	no	—
141	C₂³×C₅₉	—	4	2	no	—
142	C₂³×C₅₉	—	4	2	no	—
143	C₂³×C₅₉	—	8	4	no	—
144	C₂³×C₅₉	—	8	4	no	—
145	C₂³×C₅₉	—	16	2	no	—
146	C₂³×C₅₉	C₂×D₈	1	2	yes	—
147	Q₈×C₅₉	—	2	2	no	—
148	Q₈×C₅₉	—	4	1	no	—
149	D₄×C₅₉	—	2	2	no	—
150	D₄×C₅₉	—	2	2	no	—
151	D₄×C₅₉	—	4	2	no	—
152	D₄×C₅₉	—	4	2	no	—
153	D₄×C₅₉	—	4	1	no	—
154	D₄×C₅₉	—	4	2	no	—
155	D₄×C₅₉	—	4	2	no	—
156	D₄×C₅₉	—	8	4	no	—
157	D₄×C₅₉	—	8	4	no	—
158	D₄×C₅₉	—	8	4	no	—
159	D₄×C₅₉	—	8	2	no	—
160	D₄×C₅₉	—	8	2	no	—
161	D₄×C₅₉	—	16	1	no	—
162	D₄×C₅₉	—	16	1	no	—
163	D₄×C₅₉	—	16	2	no	—
164	C₂×C₄×C₅₉	—	2	2	no	—
165	C₂×C₄×C₅₉	—	2	2	no	—
166	C₂×C₄×C₅₉	—	4	1	no	—
167	C₂×C₄×C₅₉	—	4	1	no	—
168	C₂×C₄×C₅₉	—	4	1	no	—
169	C₂×C₄×C₅₉	—	8	4	no	—
170	C₂×C₄×C₅₉	—	8	2	no	—
171	C₂×C₄×C₅₉	C₂×D₈	1	1	yes	characteristic
172	C₂×C₄×C₅₉	C₂×D₈	1	2	yes	—
173	C₂×C₄×C₅₉	C₂×D₈	1	1	yes	characteristic
174	C₂×C₄×C₅₉	C₂²×D₄	1	1	yes	characteristic
175	C₈×C₅₉	—	2	2	no	—
176	C₈×C₅₉	—	2	1	no	—
177	C₈×C₅₉	C₂²×D₄	1	1	yes	characteristic
178	C₈×C₅₉	H(5,𝔽₂)	1	1	yes	characteristic
179	#33840	C₅₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
180	C₂²×C₅₉	—	2	2	no	—
181	C₂²×C₅₉	—	2	2	no	—
182	C₂²×C₅₉	—	2	2	no	—
183	C₂²×C₅₉	—	4	2	no	—
184	C₂²×C₅₉	—	8	1	no	—
185	C₂²×C₅₉	—	8	1	no	—
186	C₂²×C₅₉	—	8	2	no	—
187	C₂²×C₅₉	—	8	2	no	—
188	C₂²×C₅₉	—	8	2	no	—
189	C₂²×C₅₉	—	8	2	no	—
190	C₂²×C₅₉	—	8	2	no	—
191	C₂²×C₅₉	—	8	2	no	—
192	C₂²×C₅₉	—	16	8	no	—
193	C₂²×C₅₉	C₂²×D₈	1	1	yes	characteristic
194	C₄×C₅₉	—	2	1	no	—
195	C₄×C₅₉	—	2	2	no	—
196	C₄×C₅₉	—	4	2	no	—
197	C₄×C₅₉	—	8	1	no	—
198	C₄×C₅₉	—	8	1	no	—
199	C₄×C₅₉	#509	1	2	yes	complemented
200	C₄×C₅₉	D₄²	1	1	yes	characteristic
201	C₄×C₅₉	#576	1	1	yes	characteristic
202	C₂×#509	C₂×C₅₉	1	2	yes	complemented
203	#3287	C₂×C₅₉	1	1	yes	characteristic, complemented
204	D₄×D₈	C₂×C₅₉	1	1	yes	characteristic, complemented
205	#2246	C₂×C₅₉	1	1	yes	characteristic, complemented
206	#2218	C₂×C₅₉	1	2	yes	complemented
207	#2207	C₂×C₅₉	1	1	yes	characteristic, complemented
208	#2206	C₂×C₅₉	1	1	yes	characteristic, complemented
209	#2186	C₂×C₅₉	1	2	yes	complemented
210	#2184	C₂×C₅₉	1	2	yes	complemented
211	C₄×SD₃₂	C₂×C₅₉	1	1	yes	characteristic, complemented
212	#2169	C₂×C₅₉	1	1	yes	characteristic, complemented
213	C₂×C₅₉	—	4	2	no	—
214	C₂×C₅₉	—	8	2	no	—
215	C₂×C₅₉	—	16	2	no	—
216	C₂×C₅₉	—	16	2	no	—
217	C₂×C₅₉	D₄×D₈	1	1	yes	characteristic
218	C₂×C₅₉	C₂×#509	1	1	yes	characteristic
219	C₂×C₅₉	#3415	1	1	yes	characteristic
220	C₂×#135	C₂²×C₅₉	1	2	yes	complemented
221	C₂²×D₈	C₂²×C₅₉	1	2	yes	—
222	#550	—	2	1	no	—
223	D₄²	—	2	1	no	—
224	#509	—	2	8	no	—
225	C₂×SD₃₂	C₂²×C₅₉	1	1	yes	characteristic
226	C₂×SD₃₂	C₂²×C₅₉	1	2	yes	complemented
227	C₂×D₁₆	C₂²×C₅₉	1	2	yes	—
228	C₂×D₁₆	C₂²×C₅₉	1	2	yes	complemented
229	C₂×D₁₆	C₂²×C₅₉	1	2	yes	complemented
230	C₂×M₃₂	C₂²×C₅₉	1	2	yes	complemented
231	#493	C₂²×C₅₉	1	1	yes	characteristic
232	#493	C₂²×C₅₉	1	1	yes	characteristic, complemented
233	#466	C₂²×C₅₉	1	2	yes	—
234	#466	C₂²×C₅₉	1	2	yes	complemented
235	#460	—	2	1	no	—
236	#459	—	2	1	no	—
237	#449	—	2	2	no	—
238	#447	—	2	2	no	—
239	C₄×Q₁₆	C₂²×C₅₉	1	1	yes	characteristic, complemented
240	C₄×D₈	C₂²×C₅₉	1	1	yes	characteristic
241	C₈×D₄	C₂²×C₅₉	1	1	yes	characteristic
242	#367	C₂²×C₅₉	1	1	yes	characteristic, complemented
243	C₄⋊C₁₆	C₂²×C₅₉	1	1	yes	characteristic, complemented
244	#358	C₂²×C₅₉	1	1	yes	characteristic, complemented
245	#357	C₂²×C₅₉	1	1	yes	characteristic
246	#357	C₂²×C₅₉	1	2	yes	complemented
247	#357	C₂²×C₅₉	1	2	yes	complemented
248	C₂²⋊C₁₆	C₂²×C₅₉	1	2	yes	complemented
249	C₄×C₁₆	C₂²×C₅₉	1	1	yes	characteristic, complemented
250	C₅₉	#33840	1	1	yes	characteristic, direct product factor, Sylow
251	C₂×#41	—	2	2	no	—
252	C₂²×D₄	—	2	2	no	—
253	C₂²×D₄	—	4	1	no	—
254	#135	—	2	4	no	—
255	#135	—	4	2	no	—
256	C₂×Q₁₆	C₂³×C₅₉	1	1	yes	characteristic
257	C₂×SD₁₆	—	2	2	no	—
258	C₂×D₈	—	2	4	no	—
259	C₂×D₈	—	2	2	no	—
260	C₂×D₈	—	2	1	no	—
261	C₂×D₈	—	2	1	no	—
262	C₂×D₈	—	4	2	no	—
263	C₂×D₈	C₂³×C₅₉	1	2	yes	—
264	C₂×D₈	C₂³×C₅₉	1	2	yes	—
265	C₂×D₈	C₂³×C₅₉	1	1	yes	characteristic
266	C₂²×C₈	C₂³×C₅₉	1	2	yes	—
267	#127	—	2	1	no	—
268	#127	—	2	1	no	—
269	#127	—	4	1	no	—
270	#121	—	2	2	no	—
271	#121	—	2	2	no	—
272	#121	—	4	1	no	—
273	#121	—	4	2	no	—
274	#120	—	4	2	no	—
275	C₄×Q₈	—	2	1	no	—
276	C₄×D₄	—	2	1	no	—
277	C₄×D₄	—	4	1	no	—
278	C₄×D₄	D₄×C₅₉	1	1	yes	characteristic
279	SD₃₂	—	2	4	no	—
280	SD₃₂	D₄×C₅₉	1	4	yes	complemented
281	D₁₆	—	2	4	no	—
282	D₁₆	—	2	4	no	—
283	D₁₆	—	4	2	no	—
284	M₃₂	—	2	4	no	—
285	C₂×C₁₆	C₂³×C₅₉	1	1	yes	characteristic
286	C₂×C₁₆	C₂³×C₅₉	1	2	yes	—
287	C₂×C₁₆	C₂³×C₅₉	1	1	yes	characteristic
288	#107	C₂³×C₅₉	1	1	yes	characteristic
289	#107	C₂³×C₅₉	1	1	yes	characteristic
290	C₄⋊C₈	D₄×C₅₉	1	1	yes	characteristic
291	#103	—	2	1	no	—
292	#102	—	2	1	no	—
293	#102	—	2	2	no	—
294	#102	—	2	2	no	—
295	C₂²⋊C₈	D₄×C₅₉	1	2	yes	—
296	C₄×C₈	C₂³×C₅₉	1	1	yes	characteristic
297	C₂⁴	—	4	2	no	—
298	#41	—	4	4	no	—
299	#41	—	8	2	no	—
300	C₂×Q₈	—	2	1	no	—
301	C₂×D₄	—	2	1	no	—
302	C₂×D₄	—	2	2	no	—
303	C₂×D₄	—	2	2	no	—
304	C₂×D₄	—	4	4	no	—
305	C₂×D₄	—	4	2	no	—
306	C₂×D₄	—	4	2	no	—
307	C₂×D₄	—	4	2	no	—
308	C₂×D₄	—	4	1	no	—
309	C₂×D₄	—	4	2	no	—
310	C₂×D₄	—	4	1	no	—
311	C₂×D₄	—	4	1	no	—
312	C₂×D₄	—	4	1	no	—
313	C₂×D₄	—	8	2	no	—
314	C₂×D₄	—	8	4	no	—
315	C₂×D₄	D₈×C₅₉	1	1	yes	characteristic
316	C₂²×C₄	—	4	1	no	—
317	C₂²×C₄	—	4	2	no	—
318	C₂²×C₄	C₂×D₄×C₅₉	1	2	yes	—
319	Q₁₆	—	2	1	no	—
320	Q₁₆	C₂×D₄×C₅₉	1	2	yes	complemented
321	SD₁₆	—	4	4	no	—
322	D₈	—	2	2	no	—
323	D₈	—	2	2	no	—
324	D₈	—	2	1	no	—
325	D₈	—	2	2	no	—
326	D₈	—	2	2	no	—
327	D₈	—	4	4	no	—
328	D₈	—	8	1	no	—
329	D₈	—	8	1	no	—
330	D₈	C₂×D₄×C₅₉	1	2	yes	—
331	C₂×C₈	—	2	2	no	—
332	C₂×C₈	—	2	2	no	—
333	C₂×C₈	C₂×D₄×C₅₉	1	1	yes	characteristic
334	C₂×C₈	C₂×D₄×C₅₉	1	2	yes	—
335	C₂×C₈	C₂⁴×C₅₉	1	1	yes	characteristic
336	C₄⋊C₄	—	2	1	no	—
337	C₄⋊C₄	—	2	1	no	—
338	C₄⋊C₄	—	4	1	no	—
339	C₄⋊C₄	D₈×C₅₉	1	1	yes	characteristic
340	C₂²⋊C₄	—	4	1	no	—
341	C₂²⋊C₄	—	4	2	no	—
342	C₂²⋊C₄	—	4	2	no	—
343	C₂²⋊C₄	D₈×C₅₉	1	2	yes	—
344	C₄²	—	4	1	no	—
345	C₄²	C₂×D₄×C₅₉	1	1	yes	characteristic
346	C₁₆	—	2	2	no	—
347	C₁₆	—	2	1	no	—
348	C₁₆	C₂×D₄×C₅₉	1	2	yes	complemented
349	C₂³	—	4	1	no	—
350	C₂³	—	4	2	no	—
351	C₂³	—	4	2	no	—
352	C₂³	—	8	4	no	—
353	C₂³	—	8	4	no	—
354	C₂³	—	16	2	no	—
355	C₂³	C₂×D₈×C₅₉	1	2	yes	—
356	Q₈	—	2	2	no	—
357	Q₈	—	4	1	no	—
358	D₄	—	2	2	no	—
359	D₄	—	2	2	no	—
360	D₄	—	4	2	no	—
361	D₄	—	4	2	no	—
362	D₄	—	4	1	no	—
363	D₄	—	4	2	no	—
364	D₄	—	4	2	no	—
365	D₄	—	8	4	no	—
366	D₄	—	8	4	no	—
367	D₄	—	8	4	no	—
368	D₄	—	8	2	no	—
369	D₄	—	8	2	no	—
370	D₄	—	16	1	no	—
371	D₄	—	16	1	no	—
372	D₄	—	16	2	no	—
373	C₂×C₄	—	2	2	no	—
374	C₂×C₄	—	2	2	no	—
375	C₂×C₄	—	4	1	no	—
376	C₂×C₄	—	4	1	no	—
377	C₂×C₄	—	4	1	no	—
378	C₂×C₄	—	8	4	no	—
379	C₂×C₄	—	8	2	no	—
380	C₂×C₄	C₂×D₈×C₅₉	1	1	yes	characteristic
381	C₂×C₄	C₂×D₈×C₅₉	1	2	yes	—
382	C₂×C₄	C₂×D₈×C₅₉	1	1	yes	characteristic
383	C₂×C₄	C₂²×D₄×C₅₉	1	1	yes	characteristic
384	C₈	—	2	2	no	—
385	C₈	—	2	1	no	—
386	C₈	C₂²×D₄×C₅₉	1	1	yes	characteristic
387	C₈	H(5,𝔽₂)×C₅₉	1	1	yes	characteristic
388	C₂²	—	2	2	no	—
389	C₂²	—	2	2	no	—
390	C₂²	—	2	2	no	—
391	C₂²	—	4	2	no	—
392	C₂²	—	8	1	no	—
393	C₂²	—	8	1	no	—
394	C₂²	—	8	2	no	—
395	C₂²	—	8	2	no	—
396	C₂²	—	8	2	no	—
397	C₂²	—	8	2	no	—
398	C₂²	—	8	2	no	—
399	C₂²	—	8	2	no	—
400	C₂²	—	16	8	no	—
401	C₂²	C₂²×D₈×C₅₉	1	1	yes	characteristic
402	C₄	—	2	2	no	—
403	C₄	—	2	1	no	—
404	C₄	—	4	2	no	—
405	C₄	—	8	1	no	—
406	C₄	—	8	1	no	—
407	C₄	C₅₉×#509	1	2	yes	complemented
408	C₄	D₄²×C₅₉	1	1	yes	characteristic
409	C₄	C₅₉×#576	1	1	yes	characteristic
410	C₂	—	4	2	no	—
411	C₂	—	8	2	no	—
412	C₂	—	16	2	no	—
413	C₂	—	16	2	no	—
414	C₂	D₄×D₈×C₅₉	1	1	yes	characteristic
415	C₂	C₂×C₅₉×#509	1	1	yes	characteristic
416	C₂	C₅₉×#3415	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₅₉	C₂²×D₈
commutator, Frattini, cosocle	C₂×C₈	C₂⁴×C₅₉
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₅₉ ◁ C₄×D₄×C₅₉ ◁ C₈×D₄×C₅₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₅₉×#509	C₂	semidirect
2. C₅₉×#3287	C₂	semidirect
3. D₄×D₈×C₅₉	C₂	semidirect
4. C₅₉×#2246	C₂	semidirect
5. C₅₉×#2218	C₂	semidirect
6. C₅₉×#2207	C₂	semidirect
7. C₅₉×#2206	C₂	semidirect
8. C₅₉×#2186	C₂	semidirect
9. C₅₉×#2184	C₂	semidirect
10. C₄×SD₃₂×C₅₉	C₂	semidirect
11. C₅₉×#2169	C₂	semidirect
12. C₂×#135×C₅₉	C₂²	semidirect
18. C₂×SD₃₂×C₅₉	C₂²	semidirect
20. C₂×D₁₆×C₅₉	C₂²	semidirect
21. C₂×D₁₆×C₅₉	C₂²	semidirect
22. C₂×M₃₂×C₅₉	C₂²	semidirect
24. C₅₉×#493	C₂²	semidirect
26. C₅₉×#466	C₂²	semidirect
31. C₄×Q₁₆×C₅₉	C₂²	semidirect
34. C₅₉×#367	C₂²	semidirect
35. C₅₉×C₄⋊C₁₆	C₂²	semidirect
36. C₅₉×#358	C₂²	semidirect
38. C₅₉×#357	C₂²	semidirect
39. C₅₉×#357	C₂²	semidirect
40. C₅₉×C₂²⋊C₁₆	C₂²	semidirect
41. C₄×C₁₆×C₅₉	C₂²	semidirect
71. SD₃₂×C₅₉	D₄	semidirect
111. Q₁₆×C₅₉	C₂×D₄	semidirect
139. C₁₆×C₅₉	C₂×D₄	semidirect
179. #33840	C₅₉	direct (N × H)
199. C₄×C₅₉	#509	semidirect
202. C₂×#509	C₂×C₅₉	semidirect
203. #3287	C₂×C₅₉	semidirect
204. D₄×D₈	C₂×C₅₉	semidirect
205. #2246	C₂×C₅₉	semidirect
206. #2218	C₂×C₅₉	semidirect
207. #2207	C₂×C₅₉	semidirect
208. #2206	C₂×C₅₉	semidirect
209. #2186	C₂×C₅₉	semidirect
210. #2184	C₂×C₅₉	semidirect
211. C₄×SD₃₂	C₂×C₅₉	semidirect
212. #2169	C₂×C₅₉	semidirect
220. C₂×#135	C₂²×C₅₉	semidirect
226. C₂×SD₃₂	C₂²×C₅₉	semidirect
228. C₂×D₁₆	C₂²×C₅₉	semidirect
229. C₂×D₁₆	C₂²×C₅₉	semidirect
230. C₂×M₃₂	C₂²×C₅₉	semidirect
232. #493	C₂²×C₅₉	semidirect
234. #466	C₂²×C₅₉	semidirect
239. C₄×Q₁₆	C₂²×C₅₉	semidirect
242. #367	C₂²×C₅₉	semidirect
243. C₄⋊C₁₆	C₂²×C₅₉	semidirect
244. #358	C₂²×C₅₉	semidirect
246. #357	C₂²×C₅₉	semidirect
247. #357	C₂²×C₅₉	semidirect
248. C₂²⋊C₁₆	C₂²×C₅₉	semidirect
249. C₄×C₁₆	C₂²×C₅₉	semidirect
250. C₅₉	#33840	direct (N × H)
280. SD₃₂	D₄×C₅₉	semidirect
320. Q₁₆	C₂×D₄×C₅₉	semidirect
348. C₁₆	C₂×D₄×C₅₉	semidirect
407. C₄	C₅₉×#509	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₅₉×#509	2
C₅₉×#3287	2
D₄×D₈×C₅₉	2
C₅₉×#2246	2
C₅₉×#2218	2
C₅₉×#2207	2
C₅₉×#2206	2
C₅₉×#2186	2
C₅₉×#2184	2
C₄×SD₃₂×C₅₉	2
C₅₉×#2169	2
#33840	59

Subgroups — C59×#33840 #28445949

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₉×#33840 #28445949