Subgroups — C₅₉×#33612 #28445721

Order 15104.

694 conjugacy classes of subgroups.

The subgroup lattice has 424 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	1	yes	maximal, characteristic, complemented
2	C₂×C₅₉×#504	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅₉×#3061	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅₉×#3058	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅₉×#2220	C₂	1	2	yes	maximal, complemented
6	C₅₉×#2218	C₂	1	2	yes	maximal, complemented
7	C₅₉×#2217	C₂	1	2	yes	maximal, complemented
8	C₅₉×#2215	C₂	1	2	yes	maximal, complemented
9	C₅₉×#2159	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅₉×#2138	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₅₉×#357	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#135×C₅₉	C₂²	1	1	yes	characteristic
13	C₂²×D₈×C₅₉	C₂²	1	1	yes	characteristic
14	C₂×#131×C₅₉	C₂²	1	1	yes	characteristic
15	C₅₉×#537	—	2	1	no	—
16	C₅₉×#535	—	2	1	no	—
17	C₅₉×#509	—	2	4	no	—
18	C₂×SD₃₂×C₅₉	C₂²	1	2	yes	—
19	C₂×D₁₆×C₅₉	C₂²	1	2	yes	—
20	C₅₉×#504	—	2	4	no	—
21	C₂×M₃₂×C₅₉	C₂²	1	1	yes	characteristic
22	C₂×M₃₂×C₅₉	C₂²	1	2	yes	complemented
23	C₂²×C₁₆×C₅₉	C₂²	1	1	yes	characteristic
24	C₂²×C₁₆×C₅₉	C₂²	1	2	yes	complemented
25	C₅₉×#469	—	2	2	no	—
26	C₅₉×#468	—	2	2	no	—
27	C₅₉×#467	C₂²	1	2	yes	complemented
28	C₅₉×#466	C₂²	1	2	yes	—
29	C₅₉×#466	C₂²	1	2	yes	—
30	C₅₉×#466	C₂²	1	2	yes	complemented
31	C₅₉×#427	C₂²	1	1	yes	characteristic
32	C₂×#107×C₅₉	C₂²	1	1	yes	characteristic
33	C₅₉×#418	—	2	1	no	—
34	C₅₉×#417	—	2	1	no	—
35	C₅₉×#367	C₂²	1	2	yes	complemented
36	C₅₉×#366	C₂²	1	2	yes	complemented
37	C₅₉×#358	C₂²	1	1	yes	characteristic, complemented
38	C₅₉×#358	C₂²	1	1	yes	characteristic, complemented
39	C₅₉×#357	C₂²	1	2	yes	—
40	C₅₉×#357	C₂²	1	2	yes	—
41	C₅₉×#357	C₂²	1	1	yes	characteristic, complemented
42	C₅₉×#357	C₂²	1	1	yes	characteristic, complemented
43	C₂×#41×C₅₉	—	2	1	no	—
44	C₂×#41×C₅₉	D₄	1	1	yes	characteristic
45	C₂²×D₄×C₅₉	—	2	1	no	—
46	#135×C₅₉	—	2	2	no	—
47	#135×C₅₉	—	2	2	no	—
48	C₂×Q₁₆×C₅₉	C₂³	1	1	yes	characteristic
49	C₂×SD₁₆×C₅₉	—	2	1	no	—
50	C₂×D₈×C₅₉	—	2	2	no	—
51	C₂×D₈×C₅₉	—	2	1	no	—
52	C₂×D₈×C₅₉	—	2	2	no	—
53	C₂×D₈×C₅₉	C₂³	1	2	yes	—
54	C₂×D₈×C₅₉	C₂³	1	1	yes	characteristic
55	#131×C₅₉	—	2	2	no	—
56	#131×C₅₉	—	2	2	no	—
57	C₂×M₁₆×C₅₉	D₄	1	1	yes	characteristic
58	C₂×M₁₆×C₅₉	D₄	1	2	yes	—
59	C₂²×C₈×C₅₉	C₂³	1	2	yes	—
60	C₂²×C₈×C₅₉	C₂³	1	1	yes	characteristic
61	#127×C₅₉	—	4	1	no	—
62	#124×C₅₉	—	4	1	no	—
63	C₂²⋊Q₈×C₅₉	—	2	2	no	—
64	C₂²⋊Q₈×C₅₉	—	4	1	no	—
65	#121×C₅₉	—	2	2	no	—
66	#121×C₅₉	—	2	2	no	—
67	#121×C₅₉	—	2	2	no	—
68	#121×C₅₉	—	4	1	no	—
69	#121×C₅₉	—	4	2	no	—
70	#120×C₅₉	—	4	2	no	—
71	#117×C₅₉	—	2	1	no	—
72	C₂×C₄⋊C₄×C₅₉	—	2	1	no	—
73	SD₃₂×C₅₉	—	2	4	no	—
74	D₁₆×C₅₉	—	2	4	no	—
75	M₃₂×C₅₉	—	2	4	no	—
76	M₃₂×C₅₉	D₄	1	4	yes	complemented
77	C₂×C₁₆×C₅₉	—	2	2	no	—
78	C₂×C₁₆×C₅₉	—	2	4	no	—
79	C₂×C₁₆×C₅₉	C₂³	1	1	yes	characteristic
80	C₂×C₁₆×C₅₉	C₂³	1	1	yes	characteristic
81	C₂×C₁₆×C₅₉	C₂³	1	2	yes	—
82	#107×C₅₉	—	2	1	no	—
83	#107×C₅₉	C₂³	1	2	yes	—
84	#107×C₅₉	C₂³	1	1	yes	characteristic
85	#107×C₅₉	C₂³	1	1	yes	characteristic
86	#106×C₅₉	—	2	1	no	—
87	#103×C₅₉	—	2	2	no	—
88	#102×C₅₉	—	2	2	no	—
89	#102×C₅₉	—	2	2	no	—
90	#102×C₅₉	—	2	2	no	—
91	C₂⁴×C₅₉	—	4	1	no	—
92	#41×C₅₉	—	2	2	no	—
93	#41×C₅₉	—	2	2	no	—
94	#41×C₅₉	—	4	2	no	—
95	#41×C₅₉	—	4	2	no	—
96	C₂×Q₈×C₅₉	—	2	1	no	—
97	C₂×Q₈×C₅₉	D₈	1	1	yes	characteristic
98	C₂×D₄×C₅₉	—	2	2	no	—
99	C₂×D₄×C₅₉	—	2	1	no	—
100	C₂×D₄×C₅₉	—	4	1	no	—
101	C₂×D₄×C₅₉	—	4	2	no	—
102	C₂×D₄×C₅₉	—	4	2	no	—
103	C₂×D₄×C₅₉	—	4	2	no	—
104	C₂×D₄×C₅₉	—	4	2	no	—
105	C₂×D₄×C₅₉	—	4	1	no	—
106	C₂×D₄×C₅₉	—	4	2	no	—
107	C₂×D₄×C₅₉	D₈	1	2	yes	—
108	C₂×D₄×C₅₉	D₈	1	1	yes	characteristic
109	C₂²×C₄×C₅₉	—	4	1	no	—
110	C₂²×C₄×C₅₉	—	4	1	no	—
111	C₂²×C₄×C₅₉	C₂×D₄	1	2	yes	—
112	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
113	Q₁₆×C₅₉	—	2	1	no	—
114	Q₁₆×C₅₉	—	2	1	no	—
115	SD₁₆×C₅₉	—	4	2	no	—
116	D₈×C₅₉	—	2	1	no	—
117	D₈×C₅₉	—	2	2	no	—
118	D₈×C₅₉	—	2	2	no	—
119	D₈×C₅₉	—	2	1	no	—
120	D₈×C₅₉	—	4	2	no	—
121	M₁₆×C₅₉	—	2	2	no	—
122	M₁₆×C₅₉	—	2	4	no	—
123	C₂×C₈×C₅₉	—	2	2	no	—
124	C₂×C₈×C₅₉	—	2	2	no	—
125	C₂×C₈×C₅₉	C₂×D₄	1	2	yes	—
126	C₂×C₈×C₅₉	C₂×D₄	1	1	yes	characteristic
127	C₂×C₈×C₅₉	C₂×D₄	1	2	yes	—
128	C₂×C₈×C₅₉	#41	1	2	yes	—
129	C₂×C₈×C₅₉	C₂⁴	1	1	yes	characteristic
130	C₄⋊C₄×C₅₉	—	2	1	no	—
131	C₄⋊C₄×C₅₉	—	2	1	no	—
132	C₄⋊C₄×C₅₉	—	2	2	no	—
133	C₄⋊C₄×C₅₉	—	4	1	no	—
134	C₄⋊C₄×C₅₉	—	4	2	no	—
135	C₂²⋊C₄×C₅₉	—	4	1	no	—
136	C₂²⋊C₄×C₅₉	—	4	2	no	—
137	C₂²⋊C₄×C₅₉	—	4	2	no	—
138	C₂²⋊C₄×C₅₉	—	4	2	no	—
139	C₂²⋊C₄×C₅₉	—	4	2	no	—
140	C₄²×C₅₉	—	4	1	no	—
141	C₁₆×C₅₉	—	2	1	no	—
142	C₁₆×C₅₉	—	2	1	no	—
143	C₁₆×C₅₉	C₂×D₄	1	4	yes	—
144	C₂³×C₅₉	—	4	1	no	—
145	C₂³×C₅₉	—	4	2	no	—
146	C₂³×C₅₉	—	8	2	no	—
147	C₂³×C₅₉	—	16	1	no	—
148	C₂³×C₅₉	—	16	1	no	—
149	C₂³×C₅₉	C₂×D₈	1	2	yes	—
150	C₂³×C₅₉	C₂×D₈	1	1	yes	characteristic
151	Q₈×C₅₉	—	2	2	no	—
152	Q₈×C₅₉	—	4	1	no	—
153	Q₈×C₅₉	—	4	1	no	—
154	D₄×C₅₉	—	2	4	no	—
155	D₄×C₅₉	—	2	2	no	—
156	D₄×C₅₉	—	4	2	no	—
157	D₄×C₅₉	—	4	1	no	—
158	D₄×C₅₉	—	4	2	no	—
159	D₄×C₅₉	—	4	1	no	—
160	D₄×C₅₉	—	8	2	no	—
161	D₄×C₅₉	—	8	2	no	—
162	D₄×C₅₉	—	16	2	no	—
163	D₄×C₅₉	—	16	2	no	—
164	D₄×C₅₉	—	16	2	no	—
165	C₂×C₄×C₅₉	—	2	2	no	—
166	C₂×C₄×C₅₉	—	2	2	no	—
167	C₂×C₄×C₅₉	—	4	1	no	—
168	C₂×C₄×C₅₉	—	4	1	no	—
169	C₂×C₄×C₅₉	—	4	2	no	—
170	C₂×C₄×C₅₉	—	4	1	no	—
171	C₂×C₄×C₅₉	—	8	2	no	—
172	C₂×C₄×C₅₉	—	16	1	no	—
173	C₂×C₄×C₅₉	#121	1	2	yes	—
174	C₂×C₄×C₅₉	C₂×D₈	1	2	yes	—
175	C₂×C₄×C₅₉	C₂×D₈	1	1	yes	characteristic
176	C₂×C₄×C₅₉	#135	1	2	yes	—
177	C₂×C₄×C₅₉	C₂²×D₄	1	1	yes	characteristic
178	C₈×C₅₉	—	2	2	no	—
179	C₈×C₅₉	#121	1	2	yes	—
180	C₈×C₅₉	C₂²×D₄	1	1	yes	characteristic
181	C₈×C₅₉	C₂×#41	1	1	yes	characteristic
182	#33612	C₅₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
183	C₂²×C₅₉	—	2	1	no	—
184	C₂²×C₅₉	—	2	1	no	—
185	C₂²×C₅₉	—	2	2	no	—
186	C₂²×C₅₉	—	2	2	no	—
187	C₂²×C₅₉	—	2	2	no	—
188	C₂²×C₅₉	—	8	1	no	—
189	C₂²×C₅₉	—	8	2	no	—
190	C₂²×C₅₉	—	8	2	no	—
191	C₂²×C₅₉	—	8	1	no	—
192	C₂²×C₅₉	—	8	1	no	—
193	C₂²×C₅₉	—	8	2	no	—
194	C₂²×C₅₉	—	16	4	no	—
195	C₂²×C₅₉	#466	1	2	yes	—
196	C₂²×C₅₉	C₂²×D₈	1	1	yes	characteristic
197	C₄×C₅₉	—	2	2	no	—
198	C₄×C₅₉	—	8	2	no	—
199	C₄×C₅₉	—	8	1	no	—
200	C₄×C₅₉	—	8	1	no	—
201	C₄×C₅₉	—	8	1	no	—
202	C₄×C₅₉	#466	1	2	yes	—
203	C₄×C₅₉	C₂×#121	1	1	yes	characteristic
204	C₄×C₅₉	C₂×#135	1	1	yes	characteristic
205	C₂×#509	C₂×C₅₉	1	1	yes	characteristic, complemented
206	C₂×#504	C₂×C₅₉	1	1	yes	characteristic, complemented
207	#3061	C₂×C₅₉	1	1	yes	characteristic, complemented
208	#3058	C₂×C₅₉	1	1	yes	characteristic, complemented
209	#2220	C₂×C₅₉	1	2	yes	complemented
210	#2218	C₂×C₅₉	1	2	yes	complemented
211	#2217	C₂×C₅₉	1	2	yes	complemented
212	#2215	C₂×C₅₉	1	2	yes	complemented
213	#2159	C₂×C₅₉	1	1	yes	characteristic, complemented
214	#2138	C₂×C₅₉	1	1	yes	characteristic, complemented
215	C₂×#357	C₂×C₅₉	1	1	yes	characteristic, complemented
216	C₂×C₅₉	—	2	2	no	—
217	C₂×C₅₉	—	4	2	no	—
218	C₂×C₅₉	—	16	1	no	—
219	C₂×C₅₉	—	16	2	no	—
220	C₂×C₅₉	C₂×#466	1	1	yes	characteristic
221	C₂×C₅₉	#3415	1	1	yes	characteristic
222	C₂×C₅₉	#3416	1	1	yes	characteristic
223	C₂×#135	C₂²×C₅₉	1	1	yes	characteristic
224	C₂²×D₈	C₂²×C₅₉	1	1	yes	characteristic
225	C₂×#131	C₂²×C₅₉	1	1	yes	characteristic
226	#537	—	2	1	no	—
227	#535	—	2	1	no	—
228	#509	—	2	4	no	—
229	C₂×SD₃₂	C₂²×C₅₉	1	2	yes	—
230	C₂×D₁₆	C₂²×C₅₉	1	2	yes	—
231	#504	—	2	4	no	—
232	C₂×M₃₂	C₂²×C₅₉	1	1	yes	characteristic
233	C₂×M₃₂	C₂²×C₅₉	1	2	yes	complemented
234	C₂²×C₁₆	C₂²×C₅₉	1	1	yes	characteristic
235	C₂²×C₁₆	C₂²×C₅₉	1	2	yes	complemented
236	#469	—	2	2	no	—
237	#468	—	2	2	no	—
238	#467	C₂²×C₅₉	1	2	yes	complemented
239	#466	C₂²×C₅₉	1	2	yes	—
240	#466	C₂²×C₅₉	1	2	yes	—
241	#466	C₂²×C₅₉	1	2	yes	complemented
242	#427	C₂²×C₅₉	1	1	yes	characteristic
243	C₂×#107	C₂²×C₅₉	1	1	yes	characteristic
244	#418	—	2	1	no	—
245	#417	—	2	1	no	—
246	#367	C₂²×C₅₉	1	2	yes	complemented
247	#366	C₂²×C₅₉	1	2	yes	complemented
248	#358	C₂²×C₅₉	1	1	yes	characteristic, complemented
249	#358	C₂²×C₅₉	1	1	yes	characteristic, complemented
250	#357	C₂²×C₅₉	1	2	yes	—
251	#357	C₂²×C₅₉	1	2	yes	—
252	#357	C₂²×C₅₉	1	1	yes	characteristic, complemented
253	#357	C₂²×C₅₉	1	1	yes	characteristic, complemented
254	C₅₉	#33612	1	1	yes	characteristic, direct product factor, Sylow
255	C₂×#41	—	2	1	no	—
256	C₂×#41	D₄×C₅₉	1	1	yes	characteristic
257	C₂²×D₄	—	2	1	no	—
258	#135	—	2	2	no	—
259	#135	—	2	2	no	—
260	C₂×Q₁₆	C₂³×C₅₉	1	1	yes	characteristic
261	C₂×SD₁₆	—	2	1	no	—
262	C₂×D₈	—	2	2	no	—
263	C₂×D₈	—	2	1	no	—
264	C₂×D₈	—	2	2	no	—
265	C₂×D₈	C₂³×C₅₉	1	2	yes	—
266	C₂×D₈	C₂³×C₅₉	1	1	yes	characteristic
267	#131	—	2	2	no	—
268	#131	—	2	2	no	—
269	C₂×M₁₆	D₄×C₅₉	1	1	yes	characteristic
270	C₂×M₁₆	D₄×C₅₉	1	2	yes	—
271	C₂²×C₈	C₂³×C₅₉	1	2	yes	—
272	C₂²×C₈	C₂³×C₅₉	1	1	yes	characteristic
273	#127	—	4	1	no	—
274	#124	—	4	1	no	—
275	C₂²⋊Q₈	—	2	2	no	—
276	C₂²⋊Q₈	—	4	1	no	—
277	#121	—	2	2	no	—
278	#121	—	2	2	no	—
279	#121	—	2	2	no	—
280	#121	—	4	1	no	—
281	#121	—	4	2	no	—
282	#120	—	4	2	no	—
283	#117	—	2	1	no	—
284	C₂×C₄⋊C₄	—	2	1	no	—
285	SD₃₂	—	2	4	no	—
286	D₁₆	—	2	4	no	—
287	M₃₂	—	2	4	no	—
288	M₃₂	D₄×C₅₉	1	4	yes	complemented
289	C₂×C₁₆	—	2	2	no	—
290	C₂×C₁₆	—	2	4	no	—
291	C₂×C₁₆	C₂³×C₅₉	1	1	yes	characteristic
292	C₂×C₁₆	C₂³×C₅₉	1	1	yes	characteristic
293	C₂×C₁₆	C₂³×C₅₉	1	2	yes	—
294	#107	—	2	1	no	—
295	#107	C₂³×C₅₉	1	2	yes	—
296	#107	C₂³×C₅₉	1	1	yes	characteristic
297	#107	C₂³×C₅₉	1	1	yes	characteristic
298	#106	—	2	1	no	—
299	#103	—	2	2	no	—
300	#102	—	2	2	no	—
301	#102	—	2	2	no	—
302	#102	—	2	2	no	—
303	C₂⁴	—	4	1	no	—
304	#41	—	2	2	no	—
305	#41	—	2	2	no	—
306	#41	—	4	2	no	—
307	#41	—	4	2	no	—
308	C₂×Q₈	—	2	1	no	—
309	C₂×Q₈	D₈×C₅₉	1	1	yes	characteristic
310	C₂×D₄	—	2	2	no	—
311	C₂×D₄	—	2	1	no	—
312	C₂×D₄	—	4	1	no	—
313	C₂×D₄	—	4	2	no	—
314	C₂×D₄	—	4	2	no	—
315	C₂×D₄	—	4	2	no	—
316	C₂×D₄	—	4	2	no	—
317	C₂×D₄	—	4	1	no	—
318	C₂×D₄	—	4	2	no	—
319	C₂×D₄	D₈×C₅₉	1	2	yes	—
320	C₂×D₄	D₈×C₅₉	1	1	yes	characteristic
321	C₂²×C₄	—	4	1	no	—
322	C₂²×C₄	—	4	1	no	—
323	C₂²×C₄	C₂×D₄×C₅₉	1	2	yes	—
324	C₂²×C₄	C₂×D₄×C₅₉	1	1	yes	characteristic
325	Q₁₆	—	2	1	no	—
326	Q₁₆	—	2	1	no	—
327	SD₁₆	—	4	2	no	—
328	D₈	—	2	1	no	—
329	D₈	—	2	2	no	—
330	D₈	—	2	2	no	—
331	D₈	—	2	1	no	—
332	D₈	—	4	2	no	—
333	M₁₆	—	2	2	no	—
334	M₁₆	—	2	4	no	—
335	C₂×C₈	—	2	2	no	—
336	C₂×C₈	—	2	2	no	—
337	C₂×C₈	C₂×D₄×C₅₉	1	2	yes	—
338	C₂×C₈	C₂×D₄×C₅₉	1	1	yes	characteristic
339	C₂×C₈	C₂×D₄×C₅₉	1	2	yes	—
340	C₂×C₈	#41×C₅₉	1	2	yes	—
341	C₂×C₈	C₂⁴×C₅₉	1	1	yes	characteristic
342	C₄⋊C₄	—	2	1	no	—
343	C₄⋊C₄	—	2	1	no	—
344	C₄⋊C₄	—	2	2	no	—
345	C₄⋊C₄	—	4	1	no	—
346	C₄⋊C₄	—	4	2	no	—
347	C₂²⋊C₄	—	4	1	no	—
348	C₂²⋊C₄	—	4	2	no	—
349	C₂²⋊C₄	—	4	2	no	—
350	C₂²⋊C₄	—	4	2	no	—
351	C₂²⋊C₄	—	4	2	no	—
352	C₄²	—	4	1	no	—
353	C₁₆	—	2	1	no	—
354	C₁₆	—	2	1	no	—
355	C₁₆	C₂×D₄×C₅₉	1	4	yes	—
356	C₂³	—	4	1	no	—
357	C₂³	—	4	2	no	—
358	C₂³	—	8	2	no	—
359	C₂³	—	16	1	no	—
360	C₂³	—	16	1	no	—
361	C₂³	C₂×D₈×C₅₉	1	2	yes	—
362	C₂³	C₂×D₈×C₅₉	1	1	yes	characteristic
363	Q₈	—	2	2	no	—
364	Q₈	—	4	1	no	—
365	Q₈	—	4	1	no	—
366	D₄	—	2	4	no	—
367	D₄	—	2	2	no	—
368	D₄	—	4	2	no	—
369	D₄	—	4	1	no	—
370	D₄	—	4	2	no	—
371	D₄	—	4	1	no	—
372	D₄	—	8	2	no	—
373	D₄	—	8	2	no	—
374	D₄	—	16	2	no	—
375	D₄	—	16	2	no	—
376	D₄	—	16	2	no	—
377	C₂×C₄	—	2	2	no	—
378	C₂×C₄	—	2	2	no	—
379	C₂×C₄	—	4	1	no	—
380	C₂×C₄	—	4	1	no	—
381	C₂×C₄	—	4	2	no	—
382	C₂×C₄	—	4	1	no	—
383	C₂×C₄	—	8	2	no	—
384	C₂×C₄	—	16	1	no	—
385	C₂×C₄	#121×C₅₉	1	2	yes	—
386	C₂×C₄	C₂×D₈×C₅₉	1	2	yes	—
387	C₂×C₄	C₂×D₈×C₅₉	1	1	yes	characteristic
388	C₂×C₄	#135×C₅₉	1	2	yes	—
389	C₂×C₄	C₂²×D₄×C₅₉	1	1	yes	characteristic
390	C₈	—	2	2	no	—
391	C₈	#121×C₅₉	1	2	yes	—
392	C₈	C₂²×D₄×C₅₉	1	1	yes	characteristic
393	C₈	C₂×#41×C₅₉	1	1	yes	characteristic
394	C₂²	—	2	1	no	—
395	C₂²	—	2	1	no	—
396	C₂²	—	2	2	no	—
397	C₂²	—	2	2	no	—
398	C₂²	—	2	2	no	—
399	C₂²	—	8	1	no	—
400	C₂²	—	8	2	no	—
401	C₂²	—	8	1	no	—
402	C₂²	—	8	2	no	—
403	C₂²	—	8	2	no	—
404	C₂²	—	8	1	no	—
405	C₂²	—	16	4	no	—
406	C₂²	C₅₉×#466	1	2	yes	—
407	C₂²	C₂²×D₈×C₅₉	1	1	yes	characteristic
408	C₄	—	2	2	no	—
409	C₄	—	8	1	no	—
410	C₄	—	8	2	no	—
411	C₄	—	8	1	no	—
412	C₄	—	8	1	no	—
413	C₄	C₅₉×#466	1	2	yes	—
414	C₄	C₂×#121×C₅₉	1	1	yes	characteristic
415	C₄	C₂×#135×C₅₉	1	1	yes	characteristic
416	C₂	—	2	2	no	—
417	C₂	—	4	2	no	—
418	C₂	—	16	2	no	—
419	C₂	—	16	1	no	—
420	C₂	C₂×C₅₉×#466	1	1	yes	characteristic
421	C₂	C₅₉×#3415	1	1	yes	characteristic
422	C₂	C₅₉×#3416	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 ◁ C₂×#41×C₅₉ ◁ C₂×#131×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. C₂×C₅₉×#504	C₂	semidirect
3. C₅₉×#3061	C₂	semidirect
4. C₅₉×#3058	C₂	semidirect
5. C₅₉×#2220	C₂	semidirect
6. C₅₉×#2218	C₂	semidirect
7. C₅₉×#2217	C₂	semidirect
8. C₅₉×#2215	C₂	semidirect
9. C₅₉×#2159	C₂	semidirect
10. C₅₉×#2138	C₂	semidirect
11. C₂×C₅₉×#357	C₂	semidirect
22. C₂×M₃₂×C₅₉	C₂²	semidirect
24. C₂²×C₁₆×C₅₉	C₂²	semidirect
27. C₅₉×#467	C₂²	semidirect
30. C₅₉×#466	C₂²	semidirect
35. C₅₉×#367	C₂²	semidirect
36. C₅₉×#366	C₂²	semidirect
37. C₅₉×#358	C₂²	semidirect
38. C₅₉×#358	C₂²	semidirect
41. C₅₉×#357	C₂²	semidirect
42. C₅₉×#357	C₂²	semidirect
76. M₃₂×C₅₉	D₄	semidirect
182. #33612	C₅₉	direct (N × H)
205. C₂×#509	C₂×C₅₉	semidirect
206. C₂×#504	C₂×C₅₉	semidirect
207. #3061	C₂×C₅₉	semidirect
208. #3058	C₂×C₅₉	semidirect
209. #2220	C₂×C₅₉	semidirect
210. #2218	C₂×C₅₉	semidirect
211. #2217	C₂×C₅₉	semidirect
212. #2215	C₂×C₅₉	semidirect
213. #2159	C₂×C₅₉	semidirect
214. #2138	C₂×C₅₉	semidirect
215. C₂×#357	C₂×C₅₉	semidirect
233. C₂×M₃₂	C₂²×C₅₉	semidirect
235. C₂²×C₁₆	C₂²×C₅₉	semidirect
238. #467	C₂²×C₅₉	semidirect
241. #466	C₂²×C₅₉	semidirect
246. #367	C₂²×C₅₉	semidirect
247. #366	C₂²×C₅₉	semidirect
248. #358	C₂²×C₅₉	semidirect
249. #358	C₂²×C₅₉	semidirect
252. #357	C₂²×C₅₉	semidirect
253. #357	C₂²×C₅₉	semidirect
254. C₅₉	#33612	direct (N × H)
288. M₃₂	D₄×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×#509	2
C₂×C₅₉×#504	2
C₅₉×#3061	2
C₅₉×#3058	2
C₅₉×#2220	2
C₅₉×#2218	2
C₅₉×#2217	2
C₅₉×#2215	2
C₅₉×#2159	2
C₅₉×#2138	2
C₂×C₅₉×#357	2
#33612	59

Subgroups — C59×#33612 #28445721

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₉×#33612 #28445721