Subgroups — C₅₉×#24229 #28436338

Order 15104.

1330 conjugacy classes of subgroups.

The subgroup lattice has 466 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅₉×#3497	C₂	1	1	yes	maximal, characteristic
2	C₅₉×#3037	C₂	1	2	yes	maximal, complemented
3	C₂×C₅₉×#456	C₂	1	2	yes	maximal, complemented
4	C₅₉×#2327	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅₉×#2040	C₂	1	2	yes	maximal, complemented
6	C₅₉×#2007	C₂	1	2	yes	maximal, complemented
7	C₅₉×#1963	C₂	1	2	yes	maximal, complemented
8	C₅₉×#1801	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅₉×#1793	C₂	1	2	yes	maximal, complemented
10	C₂×2₋¹⁺⁴×C₅₉	C₂²	1	2	yes	—
11	C₂×#137×C₅₉	C₂²	1	4	yes	—
12	C₅₉×#550	—	2	2	no	—
13	D₄×Q₈×C₅₉	—	2	2	no	—
14	C₅₉×#548	—	2	4	no	—
15	C₅₉×#537	—	2	2	no	—
16	C₅₉×#537	C₂²	1	2	yes	—
17	C₅₉×#532	—	2	2	no	—
18	C₅₉×#532	C₂²	1	2	yes	—
19	C₂×C₄⋊Q₈×C₅₉	C₂²	1	1	yes	characteristic
20	C₂×C₄×Q₈×C₅₉	C₂²	1	1	yes	characteristic
21	C₂×C₄×Q₈×C₅₉	C₂²	1	1	yes	characteristic
22	C₅₉×#464	—	2	4	no	—
23	C₅₉×#462	—	2	2	no	—
24	C₅₉×#460	—	2	2	no	—
25	C₅₉×#456	—	2	8	no	—
26	C₅₉×#423	C₂²	1	2	yes	—
27	C₂×#104×C₅₉	C₂²	1	4	yes	—
28	C₂×#104×C₅₉	C₂²	1	4	yes	—
29	C₅₉×#417	C₂²	1	4	yes	—
30	C₂×#101×C₅₉	C₂²	1	2	yes	—
31	C₅₉×#391	C₂²	1	1	yes	characteristic
32	C₅₉×#391	C₂²	1	1	yes	characteristic
33	C₅₉×#387	—	2	2	no	—
34	C₅₉×#387	—	2	2	no	—
35	C₅₉×#382	C₂²	1	1	yes	characteristic
36	C₅₉×#376	C₂²	1	1	yes	characteristic
37	C₅₉×#343	C₂²	1	2	yes	—
38	2₋¹⁺⁴×C₅₉	—	2	4	no	—
39	2₋¹⁺⁴×C₅₉	—	2	4	no	—
40	2₋¹⁺⁴×C₅₉	—	4	4	no	—
41	C₂×#41×C₅₉	—	2	4	no	—
42	C₂×#41×C₅₉	—	2	4	no	—
43	C₂×#41×C₅₉	C₂³	1	4	yes	—
44	C₂²×Q₈×C₅₉	—	2	4	no	—
45	C₂²×Q₈×C₅₉	C₂³	1	1	yes	characteristic
46	C₂²×Q₈×C₅₉	C₂³	1	1	yes	characteristic
47	#137×C₅₉	—	2	8	no	—
48	#137×C₅₉	—	4	4	no	—
49	C₂×Q₁₆×C₅₉	—	2	4	no	—
50	C₂×SD₁₆×C₅₉	—	2	4	no	—
51	C₂×M₁₆×C₅₉	C₂³	1	4	yes	—
52	C₄⋊Q₈×C₅₉	—	2	2	no	—
53	C₄⋊Q₈×C₅₉	—	2	2	no	—
54	C₄⋊Q₈×C₅₉	D₄	1	2	yes	—
55	C₄⋊Q₈×C₅₉	D₄	1	4	yes	complemented
56	#127×C₅₉	—	2	2	no	—
57	#127×C₅₉	D₄	1	2	yes	—
58	#124×C₅₉	—	2	4	no	—
59	#124×C₅₉	D₄	1	4	yes	—
60	C₂²⋊Q₈×C₅₉	—	2	8	no	—
61	C₂²⋊Q₈×C₅₉	—	2	4	no	—
62	#121×C₅₉	—	2	8	no	—
63	#121×C₅₉	—	2	4	no	—
64	#121×C₅₉	—	2	2	no	—
65	#121×C₅₉	—	2	4	no	—
66	#121×C₅₉	—	2	2	no	—
67	C₄×Q₈×C₅₉	—	2	2	no	—
68	C₄×Q₈×C₅₉	—	2	2	no	—
69	C₄×Q₈×C₅₉	—	2	2	no	—
70	C₄×Q₈×C₅₉	—	2	2	no	—
71	C₄×D₄×C₅₉	—	2	4	no	—
72	C₄×D₄×C₅₉	—	2	4	no	—
73	C₄×D₄×C₅₉	—	2	2	no	—
74	C₄×D₄×C₅₉	—	2	2	no	—
75	C₂×C₄⋊C₄×C₅₉	—	2	2	no	—
76	C₂×C₄⋊C₄×C₅₉	—	2	1	no	—
77	C₂×C₄⋊C₄×C₅₉	D₄	1	2	yes	—
78	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
79	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
80	C₂×C₄²×C₅₉	—	2	1	no	—
81	C₂×C₄²×C₅₉	D₄	1	2	yes	—
82	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
83	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
84	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
85	C₄⋊C₈×C₅₉	—	2	2	no	—
86	C₄⋊C₈×C₅₉	—	2	2	no	—
87	#104×C₅₉	—	2	8	no	—
88	#104×C₅₉	—	4	4	no	—
89	#103×C₅₉	—	2	4	no	—
90	#102×C₅₉	—	2	4	no	—
91	#101×C₅₉	—	2	4	no	—
92	#95×C₅₉	—	2	1	no	—
93	#95×C₅₉	—	2	1	no	—
94	#95×C₅₉	—	2	2	no	—
95	#95×C₅₉	—	2	2	no	—
96	#95×C₅₉	—	2	2	no	—
97	#41×C₅₉	—	2	4	no	—
98	#41×C₅₉	—	2	4	no	—
99	#41×C₅₉	—	2	4	no	—
100	#41×C₅₉	—	2	4	no	—
101	#41×C₅₉	—	4	8	no	—
102	#41×C₅₉	—	4	8	no	—
103	#41×C₅₉	—	4	8	no	—
104	#41×C₅₉	—	4	8	no	—
105	C₂×Q₈×C₅₉	—	2	4	no	—
106	C₂×Q₈×C₅₉	—	2	2	no	—
107	C₂×Q₈×C₅₉	—	2	1	no	—
108	C₂×Q₈×C₅₉	—	2	2	no	—
109	C₂×Q₈×C₅₉	—	2	2	no	—
110	C₂×Q₈×C₅₉	—	2	2	no	—
111	C₂×Q₈×C₅₉	—	4	8	no	—
112	C₂×Q₈×C₅₉	—	4	8	no	—
113	C₂×Q₈×C₅₉	C₂×D₄	1	4	yes	—
114	C₂×Q₈×C₅₉	C₂×D₄	1	2	yes	—
115	C₂×Q₈×C₅₉	C₂×D₄	1	2	yes	—
116	C₂×Q₈×C₅₉	#41	1	2	yes	—
117	C₂×D₄×C₅₉	—	2	4	no	—
118	C₂×D₄×C₅₉	—	2	4	no	—
119	C₂×D₄×C₅₉	—	2	4	no	—
120	C₂×D₄×C₅₉	—	2	2	no	—
121	C₂×D₄×C₅₉	—	2	2	no	—
122	C₂×D₄×C₅₉	C₂×D₄	1	4	yes	—
123	C₂²×C₄×C₅₉	—	2	8	no	—
124	C₂²×C₄×C₅₉	—	2	1	no	—
125	C₂²×C₄×C₅₉	—	2	1	no	—
126	C₂²×C₄×C₅₉	—	2	4	no	—
127	C₂²×C₄×C₅₉	—	2	1	no	—
128	C₂²×C₄×C₅₉	—	2	1	no	—
129	C₂²×C₄×C₅₉	C₂×D₄	1	2	yes	—
130	C₂²×C₄×C₅₉	C₂×D₄	1	2	yes	—
131	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
132	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
133	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
134	Q₁₆×C₅₉	—	4	8	no	—
135	SD₁₆×C₅₉	—	4	8	no	—
136	M₁₆×C₅₉	—	2	4	no	—
137	M₁₆×C₅₉	—	2	4	no	—
138	C₂×C₈×C₅₉	—	2	4	no	—
139	C₄⋊C₄×C₅₉	—	2	4	no	—
140	C₄⋊C₄×C₅₉	—	2	4	no	—
141	C₄⋊C₄×C₅₉	—	2	2	no	—
142	C₄⋊C₄×C₅₉	—	2	2	no	—
143	C₄⋊C₄×C₅₉	—	2	8	no	—
144	C₄⋊C₄×C₅₉	—	2	2	no	—
145	C₄⋊C₄×C₅₉	—	2	2	no	—
146	C₄⋊C₄×C₅₉	—	4	1	no	—
147	C₄⋊C₄×C₅₉	—	4	1	no	—
148	C₂²⋊C₄×C₅₉	—	2	8	no	—
149	C₂²⋊C₄×C₅₉	—	2	4	no	—
150	C₂²⋊C₄×C₅₉	—	2	4	no	—
151	C₄²×C₅₉	—	2	2	no	—
152	C₄²×C₅₉	—	2	2	no	—
153	C₄²×C₅₉	—	2	1	no	—
154	C₄²×C₅₉	—	2	2	no	—
155	C₄²×C₅₉	—	4	2	no	—
156	C₄²×C₅₉	C₂×D₄	1	2	yes	—
157	C₄²×C₅₉	C₂×D₄	1	2	yes	—
158	C₄²×C₅₉	C₂×D₄	1	2	yes	—
159	C₂³×C₅₉	—	2	4	no	—
160	C₂³×C₅₉	C₂²×D₄	1	1	yes	characteristic
161	Q₈×C₅₉	—	2	4	no	—
162	Q₈×C₅₉	—	2	4	no	—
163	Q₈×C₅₉	—	2	4	no	—
164	Q₈×C₅₉	—	2	4	no	—
165	Q₈×C₅₉	—	2	4	no	—
166	Q₈×C₅₉	—	4	8	no	—
167	Q₈×C₅₉	—	4	2	no	—
168	D₄×C₅₉	—	2	4	no	—
169	D₄×C₅₉	—	2	4	no	—
170	D₄×C₅₉	—	4	4	no	—
171	D₄×C₅₉	—	4	8	no	—
172	D₄×C₅₉	—	4	4	no	—
173	D₄×C₅₉	—	4	4	no	—
174	D₄×C₅₉	—	8	2	no	—
175	D₄×C₅₉	—	8	4	no	—
176	C₂×C₄×C₅₉	—	2	2	no	—
177	C₂×C₄×C₅₉	—	2	2	no	—
178	C₂×C₄×C₅₉	—	2	2	no	—
179	C₂×C₄×C₅₉	—	2	4	no	—
180	C₂×C₄×C₅₉	—	2	2	no	—
181	C₂×C₄×C₅₉	—	2	2	no	—
182	C₂×C₄×C₅₉	—	4	1	no	—
183	C₂×C₄×C₅₉	—	4	1	no	—
184	C₂×C₄×C₅₉	—	4	16	no	—
185	C₂×C₄×C₅₉	—	4	1	no	—
186	C₂×C₄×C₅₉	—	4	1	no	—
187	C₂×C₄×C₅₉	—	4	1	no	—
188	C₂×C₄×C₅₉	—	4	1	no	—
189	C₂×C₄×C₅₉	—	4	4	no	—
190	C₂×C₄×C₅₉	—	4	4	no	—
191	C₂×C₄×C₅₉	—	4	2	no	—
192	C₂×C₄×C₅₉	—	4	1	no	—
193	C₂×C₄×C₅₉	—	4	1	no	—
194	C₂×C₄×C₅₉	—	4	2	no	—
195	C₂×C₄×C₅₉	—	4	1	no	—
196	C₂×C₄×C₅₉	—	4	1	no	—
197	C₂×C₄×C₅₉	#120	1	1	yes	characteristic
198	C₂×C₄×C₅₉	#120	1	1	yes	characteristic
199	C₂×C₄×C₅₉	#120	1	2	yes	—
200	C₂×C₄×C₅₉	#121	1	4	yes	—
201	C₂×C₄×C₅₉	C₂²×D₄	1	1	yes	characteristic
202	C₂×C₄×C₅₉	C₂²×D₄	1	2	yes	—
203	C₂×C₄×C₅₉	C₂×#41	1	1	yes	characteristic
204	C₂×C₄×C₅₉	H(5,𝔽₂)	1	2	yes	—
205	C₈×C₅₉	—	4	4	no	—
206	#24229	C₅₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
207	C₂²×C₅₉	—	2	1	no	—
208	C₂²×C₅₉	—	2	1	no	—
209	C₂²×C₅₉	—	4	4	no	—
210	C₂²×C₅₉	—	4	4	no	—
211	C₂²×C₅₉	—	4	4	no	—
212	C₂²×C₅₉	C₂×#120	1	1	yes	characteristic
213	C₂²×C₅₉	C₂×#121	1	1	yes	characteristic
214	C₂²×C₅₉	#535	1	1	yes	characteristic
215	C₄×C₅₉	—	2	4	no	—
216	C₄×C₅₉	—	2	1	no	—
217	C₄×C₅₉	—	2	1	no	—
218	C₄×C₅₉	—	2	2	no	—
219	C₄×C₅₉	—	4	2	no	—
220	C₄×C₅₉	—	4	4	no	—
221	C₄×C₅₉	—	4	2	no	—
222	C₄×C₅₉	—	4	2	no	—
223	C₄×C₅₉	—	8	1	no	—
224	C₄×C₅₉	—	8	1	no	—
225	C₄×C₅₉	D₄²	1	2	yes	—
226	C₄×C₅₉	#546	1	2	yes	—
227	#3497	C₂×C₅₉	1	1	yes	characteristic
228	#3037	C₂×C₅₉	1	2	yes	complemented
229	C₂×#456	C₂×C₅₉	1	2	yes	complemented
230	#2327	C₂×C₅₉	1	1	yes	characteristic, complemented
231	#2040	C₂×C₅₉	1	2	yes	complemented
232	#2007	C₂×C₅₉	1	2	yes	complemented
233	#1963	C₂×C₅₉	1	2	yes	complemented
234	#1801	C₂×C₅₉	1	1	yes	characteristic, complemented
235	#1793	C₂×C₅₉	1	2	yes	complemented
236	C₂×C₅₉	—	2	1	no	—
237	C₂×C₅₉	—	2	1	no	—
238	C₂×C₅₉	—	8	4	no	—
239	C₂×C₅₉	#2408	1	1	yes	characteristic
240	C₂×C₅₉	#3020	1	1	yes	characteristic
241	C₂×C₅₉	#3022	1	1	yes	characteristic
242	C₂×2₋¹⁺⁴	C₂²×C₅₉	1	2	yes	—
243	C₂×#137	C₂²×C₅₉	1	4	yes	—
244	#550	—	2	2	no	—
245	D₄×Q₈	—	2	2	no	—
246	#548	—	2	4	no	—
247	#537	—	2	2	no	—
248	#537	C₂²×C₅₉	1	2	yes	—
249	#532	—	2	2	no	—
250	#532	C₂²×C₅₉	1	2	yes	—
251	C₂×C₄⋊Q₈	C₂²×C₅₉	1	1	yes	characteristic
252	C₂×C₄×Q₈	C₂²×C₅₉	1	1	yes	characteristic
253	C₂×C₄×Q₈	C₂²×C₅₉	1	1	yes	characteristic
254	#464	—	2	4	no	—
255	#462	—	2	2	no	—
256	#460	—	2	2	no	—
257	#456	—	2	8	no	—
258	#423	C₂²×C₅₉	1	2	yes	—
259	C₂×#104	C₂²×C₅₉	1	4	yes	—
260	C₂×#104	C₂²×C₅₉	1	4	yes	—
261	#417	C₂²×C₅₉	1	4	yes	—
262	C₂×#101	C₂²×C₅₉	1	2	yes	—
263	#391	C₂²×C₅₉	1	1	yes	characteristic
264	#391	C₂²×C₅₉	1	1	yes	characteristic
265	#387	—	2	2	no	—
266	#387	—	2	2	no	—
267	#382	C₂²×C₅₉	1	1	yes	characteristic
268	#376	C₂²×C₅₉	1	1	yes	characteristic
269	#343	C₂²×C₅₉	1	2	yes	—
270	C₅₉	#24229	1	1	yes	characteristic, direct product factor, Sylow
271	2₋¹⁺⁴	—	2	4	no	—
272	2₋¹⁺⁴	—	2	4	no	—
273	2₋¹⁺⁴	—	4	4	no	—
274	C₂×#41	—	2	4	no	—
275	C₂×#41	—	2	4	no	—
276	C₂×#41	C₂³×C₅₉	1	4	yes	—
277	C₂²×Q₈	—	2	4	no	—
278	C₂²×Q₈	C₂³×C₅₉	1	1	yes	characteristic
279	C₂²×Q₈	C₂³×C₅₉	1	1	yes	characteristic
280	#137	—	2	8	no	—
281	#137	—	4	4	no	—
282	C₂×Q₁₆	—	2	4	no	—
283	C₂×SD₁₆	—	2	4	no	—
284	C₂×M₁₆	C₂³×C₅₉	1	4	yes	—
285	C₄⋊Q₈	—	2	2	no	—
286	C₄⋊Q₈	—	2	2	no	—
287	C₄⋊Q₈	D₄×C₅₉	1	2	yes	—
288	C₄⋊Q₈	D₄×C₅₉	1	4	yes	complemented
289	#127	—	2	2	no	—
290	#127	D₄×C₅₉	1	2	yes	—
291	#124	—	2	4	no	—
292	#124	D₄×C₅₉	1	4	yes	—
293	C₂²⋊Q₈	—	2	8	no	—
294	C₂²⋊Q₈	—	2	4	no	—
295	#121	—	2	8	no	—
296	#121	—	2	4	no	—
297	#121	—	2	2	no	—
298	#121	—	2	4	no	—
299	#121	—	2	2	no	—
300	C₄×Q₈	—	2	2	no	—
301	C₄×Q₈	—	2	2	no	—
302	C₄×Q₈	—	2	2	no	—
303	C₄×Q₈	—	2	2	no	—
304	C₄×D₄	—	2	4	no	—
305	C₄×D₄	—	2	4	no	—
306	C₄×D₄	—	2	2	no	—
307	C₄×D₄	—	2	2	no	—
308	C₂×C₄⋊C₄	—	2	2	no	—
309	C₂×C₄⋊C₄	—	2	1	no	—
310	C₂×C₄⋊C₄	D₄×C₅₉	1	2	yes	—
311	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
312	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
313	C₂×C₄²	—	2	1	no	—
314	C₂×C₄²	D₄×C₅₉	1	2	yes	—
315	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
316	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
317	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
318	C₄⋊C₈	—	2	2	no	—
319	C₄⋊C₈	—	2	2	no	—
320	#104	—	2	8	no	—
321	#104	—	4	4	no	—
322	#103	—	2	4	no	—
323	#102	—	2	4	no	—
324	#101	—	2	4	no	—
325	#95	—	2	1	no	—
326	#95	—	2	1	no	—
327	#95	—	2	2	no	—
328	#95	—	2	2	no	—
329	#95	—	2	2	no	—
330	#41	—	2	4	no	—
331	#41	—	2	4	no	—
332	#41	—	2	4	no	—
333	#41	—	2	4	no	—
334	#41	—	4	8	no	—
335	#41	—	4	8	no	—
336	#41	—	4	8	no	—
337	#41	—	4	8	no	—
338	C₂×Q₈	—	2	4	no	—
339	C₂×Q₈	—	2	2	no	—
340	C₂×Q₈	—	2	1	no	—
341	C₂×Q₈	—	2	2	no	—
342	C₂×Q₈	—	2	2	no	—
343	C₂×Q₈	—	2	2	no	—
344	C₂×Q₈	—	4	8	no	—
345	C₂×Q₈	—	4	8	no	—
346	C₂×Q₈	C₂×D₄×C₅₉	1	4	yes	—
347	C₂×Q₈	C₂×D₄×C₅₉	1	2	yes	—
348	C₂×Q₈	C₂×D₄×C₅₉	1	2	yes	—
349	C₂×Q₈	#41×C₅₉	1	2	yes	—
350	C₂×D₄	—	2	4	no	—
351	C₂×D₄	—	2	4	no	—
352	C₂×D₄	—	2	4	no	—
353	C₂×D₄	—	2	2	no	—
354	C₂×D₄	—	2	2	no	—
355	C₂×D₄	C₂×D₄×C₅₉	1	4	yes	—
356	C₂²×C₄	—	2	8	no	—
357	C₂²×C₄	—	2	1	no	—
358	C₂²×C₄	—	2	1	no	—
359	C₂²×C₄	—	2	4	no	—
360	C₂²×C₄	—	2	1	no	—
361	C₂²×C₄	—	2	1	no	—
362	C₂²×C₄	C₂×D₄×C₅₉	1	2	yes	—
363	C₂²×C₄	C₂×D₄×C₅₉	1	2	yes	—
364	C₂²×C₄	C₂×D₄×C₅₉	1	1	yes	characteristic
365	C₂²×C₄	C₂×D₄×C₅₉	1	1	yes	characteristic
366	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
367	Q₁₆	—	4	8	no	—
368	SD₁₆	—	4	8	no	—
369	M₁₆	—	2	4	no	—
370	M₁₆	—	2	4	no	—
371	C₂×C₈	—	2	4	no	—
372	C₄⋊C₄	—	2	4	no	—
373	C₄⋊C₄	—	2	4	no	—
374	C₄⋊C₄	—	2	2	no	—
375	C₄⋊C₄	—	2	2	no	—
376	C₄⋊C₄	—	2	8	no	—
377	C₄⋊C₄	—	2	2	no	—
378	C₄⋊C₄	—	2	2	no	—
379	C₄⋊C₄	—	4	1	no	—
380	C₄⋊C₄	—	4	1	no	—
381	C₂²⋊C₄	—	2	8	no	—
382	C₂²⋊C₄	—	2	4	no	—
383	C₂²⋊C₄	—	2	4	no	—
384	C₄²	—	2	2	no	—
385	C₄²	—	2	2	no	—
386	C₄²	—	2	1	no	—
387	C₄²	—	2	2	no	—
388	C₄²	—	4	2	no	—
389	C₄²	C₂×D₄×C₅₉	1	2	yes	—
390	C₄²	C₂×D₄×C₅₉	1	2	yes	—
391	C₄²	C₂×D₄×C₅₉	1	2	yes	—
392	C₂³	—	2	4	no	—
393	C₂³	C₂²×D₄×C₅₉	1	1	yes	characteristic
394	Q₈	—	2	4	no	—
395	Q₈	—	2	4	no	—
396	Q₈	—	2	4	no	—
397	Q₈	—	2	4	no	—
398	Q₈	—	2	4	no	—
399	Q₈	—	4	8	no	—
400	Q₈	—	4	2	no	—
401	D₄	—	2	4	no	—
402	D₄	—	2	4	no	—
403	D₄	—	4	4	no	—
404	D₄	—	4	8	no	—
405	D₄	—	4	4	no	—
406	D₄	—	4	4	no	—
407	D₄	—	8	2	no	—
408	D₄	—	8	4	no	—
409	C₂×C₄	—	2	2	no	—
410	C₂×C₄	—	2	2	no	—
411	C₂×C₄	—	2	2	no	—
412	C₂×C₄	—	2	4	no	—
413	C₂×C₄	—	2	2	no	—
414	C₂×C₄	—	2	2	no	—
415	C₂×C₄	—	4	1	no	—
416	C₂×C₄	—	4	1	no	—
417	C₂×C₄	—	4	16	no	—
418	C₂×C₄	—	4	1	no	—
419	C₂×C₄	—	4	1	no	—
420	C₂×C₄	—	4	1	no	—
421	C₂×C₄	—	4	1	no	—
422	C₂×C₄	—	4	4	no	—
423	C₂×C₄	—	4	4	no	—
424	C₂×C₄	—	4	2	no	—
425	C₂×C₄	—	4	1	no	—
426	C₂×C₄	—	4	1	no	—
427	C₂×C₄	—	4	2	no	—
428	C₂×C₄	—	4	1	no	—
429	C₂×C₄	—	4	1	no	—
430	C₂×C₄	#120×C₅₉	1	1	yes	characteristic
431	C₂×C₄	#120×C₅₉	1	1	yes	characteristic
432	C₂×C₄	#120×C₅₉	1	2	yes	—
433	C₂×C₄	#121×C₅₉	1	4	yes	—
434	C₂×C₄	C₂²×D₄×C₅₉	1	1	yes	characteristic
435	C₂×C₄	C₂²×D₄×C₅₉	1	2	yes	—
436	C₂×C₄	C₂×#41×C₅₉	1	1	yes	characteristic
437	C₂×C₄	H(5,𝔽₂)×C₅₉	1	2	yes	—
438	C₈	—	4	4	no	—
439	C₂²	—	2	1	no	—
440	C₂²	—	2	1	no	—
441	C₂²	—	4	4	no	—
442	C₂²	—	4	4	no	—
443	C₂²	—	4	4	no	—
444	C₂²	C₂×#120×C₅₉	1	1	yes	characteristic
445	C₂²	C₂×#121×C₅₉	1	1	yes	characteristic
446	C₂²	C₅₉×#535	1	1	yes	characteristic
447	C₄	—	2	1	no	—
448	C₄	—	2	1	no	—
449	C₄	—	2	2	no	—
450	C₄	—	2	4	no	—
451	C₄	—	4	2	no	—
452	C₄	—	4	2	no	—
453	C₄	—	4	4	no	—
454	C₄	—	4	2	no	—
455	C₄	—	8	1	no	—
456	C₄	—	8	1	no	—
457	C₄	D₄²×C₅₉	1	2	yes	—
458	C₄	C₅₉×#546	1	2	yes	—
459	C₂	—	2	1	no	—
460	C₂	—	2	1	no	—
461	C₂	—	8	4	no	—
462	C₂	C₅₉×#2408	1	1	yes	characteristic
463	C₂	C₅₉×#3020	1	1	yes	characteristic
464	C₂	C₅₉×#3022	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₅₉	C₂×#120
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₅₉
prime radical	C₅₉×#3497	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ 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
2. C₅₉×#3037	C₂	semidirect
3. C₂×C₅₉×#456	C₂	semidirect
4. C₅₉×#2327	C₂	semidirect
5. C₅₉×#2040	C₂	semidirect
6. C₅₉×#2007	C₂	semidirect
7. C₅₉×#1963	C₂	semidirect
8. C₅₉×#1801	C₂	semidirect
9. C₅₉×#1793	C₂	semidirect
55. C₄⋊Q₈×C₅₉	D₄	semidirect
206. #24229	C₅₉	direct (N × H)
228. #3037	C₂×C₅₉	semidirect
229. C₂×#456	C₂×C₅₉	semidirect
230. #2327	C₂×C₅₉	semidirect
231. #2040	C₂×C₅₉	semidirect
232. #2007	C₂×C₅₉	semidirect
233. #1963	C₂×C₅₉	semidirect
234. #1801	C₂×C₅₉	semidirect
235. #1793	C₂×C₅₉	semidirect
270. C₅₉	#24229	direct (N × H)
288. C₄⋊Q₈	D₄×C₅₉	semidirect

Maximal subgroups

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

subgroup	index
C₅₉×#3497	2
C₅₉×#3037	2
C₂×C₅₉×#456	2
C₅₉×#2327	2
C₅₉×#2040	2
C₅₉×#2007	2
C₅₉×#1963	2
C₅₉×#1801	2
C₅₉×#1793	2
#24229	59

Subgroups — C59×#24229 #28436338

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₉×#24229 #28436338