Subgroups — C₅₉×#23992 #28436101

Order 15104.

1128 conjugacy classes of subgroups.

The subgroup lattice has 556 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅₉×#3509	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅₉×#3028	C₂	1	1	yes	maximal, characteristic
3	C₅₉×#3022	C₂	1	1	yes	maximal, characteristic
4	C₅₉×#2901	C₂	1	1	yes	maximal, characteristic
5	C₅₉×#2031	C₂	1	2	yes	maximal, complemented
6	C₅₉×#2005	C₂	1	2	yes	maximal, complemented
7	C₅₉×#1915	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅₉×#1912	C₂	1	2	yes	maximal, complemented
9	C₅₉×#1909	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅₉×#1905	C₂	1	2	yes	maximal, complemented
11	C₅₉×#1827	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅₉×#585	C₂²	1	1	yes	characteristic
13	C₂×#137×C₅₉	C₂²	1	2	yes	—
14	C₅₉×#568	C₂²	1	1	yes	characteristic
15	C₅₉×#557	—	2	2	no	—
16	C₅₉×#556	—	2	2	no	—
17	C₅₉×#552	—	2	4	no	—
18	C₅₉×#541	—	2	2	no	—
19	C₅₉×#536	C₂²	1	1	yes	characteristic
20	C₅₉×#536	C₂²	1	1	yes	characteristic
21	C₅₉×#536	C₂²	1	2	yes	—
22	C₅₉×#533	—	2	2	no	—
23	C₅₉×#533	C₂²	1	1	yes	characteristic, complemented
24	C₂×C₄⋊Q₈×C₅₉	C₂²	1	1	yes	characteristic, complemented
25	C₅₉×#519	C₂²	1	1	yes	characteristic, complemented
26	C₅₉×#519	C₂²	1	1	yes	characteristic, complemented
27	C₄×#41×C₅₉	C₂²	1	1	yes	characteristic
28	C₅₉×#458	—	2	4	no	—
29	C₅₉×#456	—	2	2	no	—
30	C₅₉×#455	—	2	2	no	—
31	C₅₉×#421	—	2	2	no	—
32	C₅₉×#421	C₂²	1	2	yes	—
33	C₅₉×#421	C₂²	1	2	yes	—
34	C₂×#104×C₅₉	—	2	2	no	—
35	C₂×#104×C₅₉	C₂²	1	2	yes	—
36	C₅₉×#419	C₂²	1	2	yes	complemented
37	C₅₉×#413	C₂²	1	1	yes	characteristic
38	C₂×#101×C₅₉	C₂²	1	2	yes	complemented
39	C₅₉×#410	C₂²	1	2	yes	—
40	C₅₉×#410	C₂²	1	1	yes	characteristic
41	C₅₉×#344	C₂²	1	2	yes	complemented
42	C₅₉×#339	C₂²	1	2	yes	complemented
43	C₅₉×H(3,ℤ/4)	C₂²	1	2	yes	complemented
44	C₅₉×H(3,ℤ/4)	C₂²	1	2	yes	complemented
45	2₋¹⁺⁴×C₅₉	—	2	2	no	—
46	2₋¹⁺⁴×C₅₉	—	2	1	no	—
47	H(5,𝔽₂)×C₅₉	—	2	2	no	—
48	H(5,𝔽₂)×C₅₉	—	2	2	no	—
49	H(5,𝔽₂)×C₅₉	—	2	1	no	—
50	C₂×#41×C₅₉	—	2	2	no	—
51	C₂×#41×C₅₉	—	4	2	no	—
52	C₂×#41×C₅₉	C₂³	1	2	yes	—
53	C₂×#41×C₅₉	C₂³	1	1	yes	characteristic
54	C₂²×Q₈×C₅₉	C₂³	1	1	yes	characteristic
55	C₂²×Q₈×C₅₉	C₂³	1	1	yes	characteristic
56	#137×C₅₉	—	2	4	no	—
57	#137×C₅₉	—	4	2	no	—
58	C₂×Q₁₆×C₅₉	—	2	2	no	—
59	C₂×SD₁₆×C₅₉	—	2	2	no	—
60	#131×C₅₉	—	4	2	no	—
61	C₂×M₁₆×C₅₉	—	2	2	no	—
62	C₂×M₁₆×C₅₉	C₂³	1	2	yes	—
63	C₂×M₁₆×C₅₉	C₂³	1	2	yes	—
64	C₄⋊Q₈×C₅₉	—	2	2	no	—
65	C₄⋊Q₈×C₅₉	—	2	1	no	—
66	C₄⋊Q₈×C₅₉	—	2	2	no	—
67	C₄⋊Q₈×C₅₉	—	2	1	no	—
68	C₄⋊Q₈×C₅₉	—	2	1	no	—
69	C₄⋊Q₈×C₅₉	—	2	1	no	—
70	C₄⋊Q₈×C₅₉	D₄	1	2	yes	—
71	#126×C₅₉	—	2	4	no	—
72	#126×C₅₉	—	2	4	no	—
73	#125×C₅₉	—	2	4	no	—
74	#125×C₅₉	—	2	4	no	—
75	#125×C₅₉	—	2	4	no	—
76	#125×C₅₉	—	2	1	no	—
77	#124×C₅₉	—	2	1	no	—
78	#124×C₅₉	—	2	2	no	—
79	#124×C₅₉	D₄	1	2	yes	—
80	#123×C₅₉	—	2	2	no	—
81	#123×C₅₉	—	2	4	no	—
82	#123×C₅₉	D₄	1	4	yes	—
83	C₂²⋊Q₈×C₅₉	—	2	4	no	—
84	C₂²⋊Q₈×C₅₉	—	2	2	no	—
85	C₂²⋊Q₈×C₅₉	—	2	2	no	—
86	C₂²⋊Q₈×C₅₉	—	2	2	no	—
87	C₂²⋊Q₈×C₅₉	—	4	2	no	—
88	C₄×Q₈×C₅₉	—	2	4	no	—
89	C₄×Q₈×C₅₉	—	2	1	no	—
90	C₄×Q₈×C₅₉	—	2	2	no	—
91	C₄×Q₈×C₅₉	—	2	2	no	—
92	C₄×Q₈×C₅₉	—	2	2	no	—
93	C₄×Q₈×C₅₉	—	2	2	no	—
94	C₄×Q₈×C₅₉	—	2	2	no	—
95	C₄×D₄×C₅₉	—	2	2	no	—
96	C₄×D₄×C₅₉	—	2	1	no	—
97	#117×C₅₉	—	2	4	no	—
98	#117×C₅₉	—	2	2	no	—
99	#117×C₅₉	—	2	2	no	—
100	#117×C₅₉	D₄	1	2	yes	—
101	#117×C₅₉	C₂³	1	2	yes	—
102	#117×C₅₉	C₂³	1	1	yes	characteristic
103	#117×C₅₉	C₂³	1	1	yes	characteristic
104	#117×C₅₉	C₂³	1	1	yes	characteristic
105	C₂×C₄⋊C₄×C₅₉	—	2	2	no	—
106	C₂×C₄²×C₅₉	D₄	1	2	yes	—
107	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
108	#104×C₅₉	—	2	2	no	—
109	#104×C₅₉	—	2	4	no	—
110	#104×C₅₉	—	2	2	no	—
111	#104×C₅₉	—	2	4	no	—
112	#103×C₅₉	—	4	2	no	—
113	#101×C₅₉	—	2	1	no	—
114	#101×C₅₉	—	4	2	no	—
115	#100×C₅₉	—	2	1	no	—
116	#99×C₅₉	—	2	2	no	—
117	#99×C₅₉	—	2	4	no	—
118	#41×C₅₉	—	2	2	no	—
119	#41×C₅₉	—	2	2	no	—
120	#41×C₅₉	—	2	4	no	—
121	#41×C₅₉	—	2	2	no	—
122	#41×C₅₉	—	2	2	no	—
123	#41×C₅₉	—	2	2	no	—
124	#41×C₅₉	—	2	2	no	—
125	#41×C₅₉	—	4	4	no	—
126	#41×C₅₉	—	4	2	no	—
127	#41×C₅₉	—	4	2	no	—
128	#41×C₅₉	—	4	2	no	—
129	#41×C₅₉	—	4	2	no	—
130	C₂×Q₈×C₅₉	—	2	2	no	—
131	C₂×Q₈×C₅₉	—	2	1	no	—
132	C₂×Q₈×C₅₉	—	2	1	no	—
133	C₂×Q₈×C₅₉	—	2	1	no	—
134	C₂×Q₈×C₅₉	—	2	2	no	—
135	C₂×Q₈×C₅₉	—	2	2	no	—
136	C₂×Q₈×C₅₉	—	2	2	no	—
137	C₂×Q₈×C₅₉	—	2	2	no	—
138	C₂×Q₈×C₅₉	—	2	2	no	—
139	C₂×Q₈×C₅₉	—	4	2	no	—
140	C₂×Q₈×C₅₉	C₂×D₄	1	2	yes	—
141	C₂×Q₈×C₅₉	C₂×D₄	1	1	yes	characteristic
142	C₂×Q₈×C₅₉	#41	1	2	yes	—
143	C₂×D₄×C₅₉	—	2	2	no	—
144	C₂×D₄×C₅₉	—	2	2	no	—
145	C₂×D₄×C₅₉	—	4	2	no	—
146	C₂×D₄×C₅₉	—	4	4	no	—
147	C₂×D₄×C₅₉	—	4	2	no	—
148	C₂×D₄×C₅₉	C₂×D₄	1	2	yes	—
149	C₂×D₄×C₅₉	C₂×D₄	1	1	yes	characteristic
150	C₂×D₄×C₅₉	#41	1	2	yes	—
151	C₂²×C₄×C₅₉	—	2	2	no	—
152	C₂²×C₄×C₅₉	—	2	1	no	—
153	C₂²×C₄×C₅₉	—	2	1	no	—
154	C₂²×C₄×C₅₉	—	2	2	no	—
155	C₂²×C₄×C₅₉	—	4	2	no	—
156	C₂²×C₄×C₅₉	C₂×D₄	1	2	yes	—
157	C₂²×C₄×C₅₉	C₂×D₄	1	2	yes	—
158	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
159	Q₁₆×C₅₉	—	4	4	no	—
160	SD₁₆×C₅₉	—	4	4	no	—
161	M₁₆×C₅₉	—	2	2	no	—
162	M₁₆×C₅₉	—	2	2	no	—
163	M₁₆×C₅₉	—	2	2	no	—
164	M₁₆×C₅₉	—	2	2	no	—
165	M₁₆×C₅₉	—	4	2	no	—
166	C₂×C₈×C₅₉	—	2	2	no	—
167	C₂×C₈×C₅₉	—	2	2	no	—
168	C₂×C₈×C₅₉	—	4	2	no	—
169	C₄⋊C₄×C₅₉	—	2	4	no	—
170	C₄⋊C₄×C₅₉	—	2	4	no	—
171	C₄⋊C₄×C₅₉	—	2	2	no	—
172	C₄⋊C₄×C₅₉	—	2	4	no	—
173	C₄⋊C₄×C₅₉	—	2	4	no	—
174	C₄⋊C₄×C₅₉	—	2	2	no	—
175	C₄⋊C₄×C₅₉	—	2	2	no	—
176	C₄⋊C₄×C₅₉	—	2	2	no	—
177	C₄⋊C₄×C₅₉	—	2	4	no	—
178	C₄⋊C₄×C₅₉	—	2	4	no	—
179	C₄⋊C₄×C₅₉	—	2	1	no	—
180	C₄⋊C₄×C₅₉	—	2	1	no	—
181	C₄⋊C₄×C₅₉	—	2	1	no	—
182	C₄⋊C₄×C₅₉	—	2	2	no	—
183	C₄⋊C₄×C₅₉	—	4	4	no	—
184	C₂²⋊C₄×C₅₉	—	2	4	no	—
185	C₂²⋊C₄×C₅₉	—	2	4	no	—
186	C₂²⋊C₄×C₅₉	—	2	2	no	—
187	C₂²⋊C₄×C₅₉	—	2	1	no	—
188	C₂²⋊C₄×C₅₉	—	2	1	no	—
189	C₂²⋊C₄×C₅₉	—	2	2	no	—
190	C₂²⋊C₄×C₅₉	—	4	4	no	—
191	C₂²⋊C₄×C₅₉	C₂×D₄	1	2	yes	—
192	C₄²×C₅₉	—	2	4	no	—
193	C₄²×C₅₉	—	2	4	no	—
194	C₄²×C₅₉	—	2	2	no	—
195	C₄²×C₅₉	—	2	1	no	—
196	C₄²×C₅₉	—	2	1	no	—
197	C₄²×C₅₉	—	2	2	no	—
198	C₄²×C₅₉	C₂×D₄	1	1	yes	characteristic
199	C₄²×C₅₉	C₂×D₄	1	2	yes	—
200	C₄²×C₅₉	C₂×D₄	1	1	yes	characteristic
201	C₄²×C₅₉	C₂×D₄	1	2	yes	—
202	C₂³×C₅₉	—	2	2	no	—
203	C₂³×C₅₉	—	4	2	no	—
204	C₂³×C₅₉	#120	1	2	yes	—
205	C₂³×C₅₉	C₂²×D₄	1	1	yes	characteristic
206	Q₈×C₅₉	—	2	2	no	—
207	Q₈×C₅₉	—	2	2	no	—
208	Q₈×C₅₉	—	2	4	no	—
209	Q₈×C₅₉	—	2	2	no	—
210	Q₈×C₅₉	—	4	4	no	—
211	Q₈×C₅₉	—	4	2	no	—
212	Q₈×C₅₉	—	4	1	no	—
213	Q₈×C₅₉	—	4	1	no	—
214	Q₈×C₅₉	—	4	1	no	—
215	Q₈×C₅₉	—	4	1	no	—
216	Q₈×C₅₉	—	4	2	no	—
217	D₄×C₅₉	—	2	4	no	—
218	D₄×C₅₉	—	2	2	no	—
219	D₄×C₅₉	—	2	2	no	—
220	D₄×C₅₉	—	2	2	no	—
221	D₄×C₅₉	—	4	2	no	—
222	D₄×C₅₉	—	4	4	no	—
223	D₄×C₅₉	—	4	2	no	—
224	D₄×C₅₉	—	4	2	no	—
225	C₂×C₄×C₅₉	—	2	1	no	—
226	C₂×C₄×C₅₉	—	2	2	no	—
227	C₂×C₄×C₅₉	—	2	2	no	—
228	C₂×C₄×C₅₉	—	2	2	no	—
229	C₂×C₄×C₅₉	—	2	2	no	—
230	C₂×C₄×C₅₉	—	2	2	no	—
231	C₂×C₄×C₅₉	—	2	2	no	—
232	C₂×C₄×C₅₉	—	2	2	no	—
233	C₂×C₄×C₅₉	—	2	1	no	—
234	C₂×C₄×C₅₉	—	2	4	no	—
235	C₂×C₄×C₅₉	—	2	2	no	—
236	C₂×C₄×C₅₉	—	4	2	no	—
237	C₂×C₄×C₅₉	—	4	4	no	—
238	C₂×C₄×C₅₉	—	4	4	no	—
239	C₂×C₄×C₅₉	—	4	2	no	—
240	C₂×C₄×C₅₉	—	4	2	no	—
241	C₂×C₄×C₅₉	—	4	2	no	—
242	C₂×C₄×C₅₉	—	4	2	no	—
243	C₂×C₄×C₅₉	—	4	2	no	—
244	C₂×C₄×C₅₉	#120	1	2	yes	—
245	C₂×C₄×C₅₉	C₂²×D₄	1	1	yes	characteristic
246	C₂×C₄×C₅₉	C₂²×D₄	1	1	yes	characteristic
247	C₂×C₄×C₅₉	C₂×#41	1	2	yes	—
248	C₂×C₄×C₅₉	H(5,𝔽₂)	1	2	yes	—
249	C₈×C₅₉	—	4	2	no	—
250	C₈×C₅₉	—	4	2	no	—
251	#23992	C₅₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
252	C₂²×C₅₉	—	2	2	no	—
253	C₂²×C₅₉	—	4	1	no	—
254	C₂²×C₅₉	—	4	2	no	—
255	C₂²×C₅₉	—	4	2	no	—
256	C₂²×C₅₉	—	8	2	no	—
257	C₂²×C₅₉	—	16	2	no	—
258	C₂²×C₅₉	C₂×#120	1	1	yes	characteristic
259	C₂²×C₅₉	#546	1	2	yes	—
260	C₄×C₅₉	—	2	2	no	—
261	C₄×C₅₉	—	2	2	no	—
262	C₄×C₅₉	—	4	2	no	—
263	C₄×C₅₉	—	4	1	no	—
264	C₄×C₅₉	—	4	2	no	—
265	C₄×C₅₉	—	4	2	no	—
266	C₄×C₅₉	—	4	2	no	—
267	C₄×C₅₉	—	4	2	no	—
268	C₄×C₅₉	—	4	2	no	—
269	C₄×C₅₉	—	8	2	no	—
270	C₄×C₅₉	#525	1	1	yes	characteristic
271	C₄×C₅₉	#535	1	1	yes	characteristic
272	C₄×C₅₉	#546	1	2	yes	—
273	#3509	C₂×C₅₉	1	1	yes	characteristic, complemented
274	#3028	C₂×C₅₉	1	1	yes	characteristic
275	#3022	C₂×C₅₉	1	1	yes	characteristic
276	#2901	C₂×C₅₉	1	1	yes	characteristic
277	#2031	C₂×C₅₉	1	2	yes	complemented
278	#2005	C₂×C₅₉	1	2	yes	complemented
279	#1915	C₂×C₅₉	1	1	yes	characteristic, complemented
280	#1912	C₂×C₅₉	1	2	yes	complemented
281	#1909	C₂×C₅₉	1	1	yes	characteristic, complemented
282	#1905	C₂×C₅₉	1	2	yes	complemented
283	#1827	C₂×C₅₉	1	1	yes	characteristic, complemented
284	C₂×C₅₉	—	2	1	no	—
285	C₂×C₅₉	—	2	2	no	—
286	C₂×C₅₉	—	4	2	no	—
287	C₂×C₅₉	—	8	2	no	—
288	C₂×C₅₉	#2404	1	1	yes	characteristic
289	#585	C₂²×C₅₉	1	1	yes	characteristic
290	C₂×#137	C₂²×C₅₉	1	2	yes	—
291	#568	C₂²×C₅₉	1	1	yes	characteristic
292	#557	—	2	2	no	—
293	#556	—	2	2	no	—
294	#552	—	2	4	no	—
295	#541	—	2	2	no	—
296	#536	C₂²×C₅₉	1	1	yes	characteristic
297	#536	C₂²×C₅₉	1	1	yes	characteristic
298	#536	C₂²×C₅₉	1	2	yes	—
299	#533	—	2	2	no	—
300	#533	C₂²×C₅₉	1	1	yes	characteristic, complemented
301	C₂×C₄⋊Q₈	C₂²×C₅₉	1	1	yes	characteristic, complemented
302	#519	C₂²×C₅₉	1	1	yes	characteristic, complemented
303	#519	C₂²×C₅₉	1	1	yes	characteristic, complemented
304	C₄×#41	C₂²×C₅₉	1	1	yes	characteristic
305	#458	—	2	4	no	—
306	#456	—	2	2	no	—
307	#455	—	2	2	no	—
308	#421	—	2	2	no	—
309	#421	C₂²×C₅₉	1	2	yes	—
310	#421	C₂²×C₅₉	1	2	yes	—
311	C₂×#104	—	2	2	no	—
312	C₂×#104	C₂²×C₅₉	1	2	yes	—
313	#419	C₂²×C₅₉	1	2	yes	complemented
314	#413	C₂²×C₅₉	1	1	yes	characteristic
315	C₂×#101	C₂²×C₅₉	1	2	yes	complemented
316	#410	C₂²×C₅₉	1	1	yes	characteristic
317	#410	C₂²×C₅₉	1	2	yes	—
318	#344	C₂²×C₅₉	1	2	yes	complemented
319	#339	C₂²×C₅₉	1	2	yes	complemented
320	H(3,ℤ/4)	C₂²×C₅₉	1	2	yes	complemented
321	H(3,ℤ/4)	C₂²×C₅₉	1	2	yes	complemented
322	C₅₉	#23992	1	1	yes	characteristic, direct product factor, Sylow
323	2₋¹⁺⁴	—	2	2	no	—
324	2₋¹⁺⁴	—	2	1	no	—
325	H(5,𝔽₂)	—	2	2	no	—
326	H(5,𝔽₂)	—	2	2	no	—
327	H(5,𝔽₂)	—	2	1	no	—
328	C₂×#41	—	2	2	no	—
329	C₂×#41	—	4	2	no	—
330	C₂×#41	C₂³×C₅₉	1	2	yes	—
331	C₂×#41	C₂³×C₅₉	1	1	yes	characteristic
332	C₂²×Q₈	C₂³×C₅₉	1	1	yes	characteristic
333	C₂²×Q₈	C₂³×C₅₉	1	1	yes	characteristic
334	#137	—	2	4	no	—
335	#137	—	4	2	no	—
336	C₂×Q₁₆	—	2	2	no	—
337	C₂×SD₁₆	—	2	2	no	—
338	#131	—	4	2	no	—
339	C₂×M₁₆	—	2	2	no	—
340	C₂×M₁₆	C₂³×C₅₉	1	2	yes	—
341	C₂×M₁₆	C₂³×C₅₉	1	2	yes	—
342	C₄⋊Q₈	—	2	2	no	—
343	C₄⋊Q₈	—	2	1	no	—
344	C₄⋊Q₈	—	2	2	no	—
345	C₄⋊Q₈	—	2	1	no	—
346	C₄⋊Q₈	—	2	1	no	—
347	C₄⋊Q₈	—	2	1	no	—
348	C₄⋊Q₈	D₄×C₅₉	1	2	yes	—
349	#126	—	2	4	no	—
350	#126	—	2	4	no	—
351	#125	—	2	4	no	—
352	#125	—	2	4	no	—
353	#125	—	2	4	no	—
354	#125	—	2	1	no	—
355	#124	—	2	1	no	—
356	#124	—	2	2	no	—
357	#124	D₄×C₅₉	1	2	yes	—
358	#123	—	2	2	no	—
359	#123	—	2	4	no	—
360	#123	D₄×C₅₉	1	4	yes	—
361	C₂²⋊Q₈	—	2	4	no	—
362	C₂²⋊Q₈	—	2	2	no	—
363	C₂²⋊Q₈	—	2	2	no	—
364	C₂²⋊Q₈	—	2	2	no	—
365	C₂²⋊Q₈	—	4	2	no	—
366	C₄×Q₈	—	2	4	no	—
367	C₄×Q₈	—	2	1	no	—
368	C₄×Q₈	—	2	2	no	—
369	C₄×Q₈	—	2	2	no	—
370	C₄×Q₈	—	2	2	no	—
371	C₄×Q₈	—	2	2	no	—
372	C₄×Q₈	—	2	2	no	—
373	C₄×D₄	—	2	2	no	—
374	C₄×D₄	—	2	1	no	—
375	#117	—	2	4	no	—
376	#117	—	2	2	no	—
377	#117	—	2	2	no	—
378	#117	D₄×C₅₉	1	2	yes	—
379	#117	C₂³×C₅₉	1	2	yes	—
380	#117	C₂³×C₅₉	1	1	yes	characteristic
381	#117	C₂³×C₅₉	1	1	yes	characteristic
382	#117	C₂³×C₅₉	1	1	yes	characteristic
383	C₂×C₄⋊C₄	—	2	2	no	—
384	C₂×C₄²	D₄×C₅₉	1	2	yes	—
385	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
386	#104	—	2	2	no	—
387	#104	—	2	4	no	—
388	#104	—	2	2	no	—
389	#104	—	2	4	no	—
390	#103	—	4	2	no	—
391	#101	—	2	1	no	—
392	#101	—	4	2	no	—
393	#100	—	2	1	no	—
394	#99	—	2	2	no	—
395	#99	—	2	4	no	—
396	#41	—	2	2	no	—
397	#41	—	2	2	no	—
398	#41	—	2	4	no	—
399	#41	—	2	2	no	—
400	#41	—	2	2	no	—
401	#41	—	2	2	no	—
402	#41	—	2	2	no	—
403	#41	—	4	4	no	—
404	#41	—	4	2	no	—
405	#41	—	4	2	no	—
406	#41	—	4	2	no	—
407	#41	—	4	2	no	—
408	C₂×Q₈	—	2	2	no	—
409	C₂×Q₈	—	2	1	no	—
410	C₂×Q₈	—	2	1	no	—
411	C₂×Q₈	—	2	1	no	—
412	C₂×Q₈	—	2	2	no	—
413	C₂×Q₈	—	2	2	no	—
414	C₂×Q₈	—	2	2	no	—
415	C₂×Q₈	—	2	2	no	—
416	C₂×Q₈	—	2	2	no	—
417	C₂×Q₈	—	4	2	no	—
418	C₂×Q₈	C₂×D₄×C₅₉	1	2	yes	—
419	C₂×Q₈	C₂×D₄×C₅₉	1	1	yes	characteristic
420	C₂×Q₈	#41×C₅₉	1	2	yes	—
421	C₂×D₄	—	2	2	no	—
422	C₂×D₄	—	2	2	no	—
423	C₂×D₄	—	4	2	no	—
424	C₂×D₄	—	4	4	no	—
425	C₂×D₄	—	4	2	no	—
426	C₂×D₄	C₂×D₄×C₅₉	1	2	yes	—
427	C₂×D₄	C₂×D₄×C₅₉	1	1	yes	characteristic
428	C₂×D₄	#41×C₅₉	1	2	yes	—
429	C₂²×C₄	—	2	2	no	—
430	C₂²×C₄	—	2	1	no	—
431	C₂²×C₄	—	2	1	no	—
432	C₂²×C₄	—	2	2	no	—
433	C₂²×C₄	—	4	2	no	—
434	C₂²×C₄	C₂×D₄×C₅₉	1	2	yes	—
435	C₂²×C₄	C₂×D₄×C₅₉	1	2	yes	—
436	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
437	Q₁₆	—	4	4	no	—
438	SD₁₆	—	4	4	no	—
439	M₁₆	—	2	2	no	—
440	M₁₆	—	2	2	no	—
441	M₁₆	—	2	2	no	—
442	M₁₆	—	2	2	no	—
443	M₁₆	—	4	2	no	—
444	C₂×C₈	—	2	2	no	—
445	C₂×C₈	—	2	2	no	—
446	C₂×C₈	—	4	2	no	—
447	C₄⋊C₄	—	2	4	no	—
448	C₄⋊C₄	—	2	4	no	—
449	C₄⋊C₄	—	2	2	no	—
450	C₄⋊C₄	—	2	4	no	—
451	C₄⋊C₄	—	2	4	no	—
452	C₄⋊C₄	—	2	2	no	—
453	C₄⋊C₄	—	2	2	no	—
454	C₄⋊C₄	—	2	2	no	—
455	C₄⋊C₄	—	2	4	no	—
456	C₄⋊C₄	—	2	4	no	—
457	C₄⋊C₄	—	2	1	no	—
458	C₄⋊C₄	—	2	1	no	—
459	C₄⋊C₄	—	2	1	no	—
460	C₄⋊C₄	—	2	2	no	—
461	C₄⋊C₄	—	4	4	no	—
462	C₂²⋊C₄	—	2	4	no	—
463	C₂²⋊C₄	—	2	4	no	—
464	C₂²⋊C₄	—	2	2	no	—
465	C₂²⋊C₄	—	2	1	no	—
466	C₂²⋊C₄	—	2	1	no	—
467	C₂²⋊C₄	—	2	2	no	—
468	C₂²⋊C₄	—	4	4	no	—
469	C₂²⋊C₄	C₂×D₄×C₅₉	1	2	yes	—
470	C₄²	—	2	4	no	—
471	C₄²	—	2	4	no	—
472	C₄²	—	2	2	no	—
473	C₄²	—	2	1	no	—
474	C₄²	—	2	1	no	—
475	C₄²	—	2	2	no	—
476	C₄²	C₂×D₄×C₅₉	1	1	yes	characteristic
477	C₄²	C₂×D₄×C₅₉	1	2	yes	—
478	C₄²	C₂×D₄×C₅₉	1	1	yes	characteristic
479	C₄²	C₂×D₄×C₅₉	1	2	yes	—
480	C₂³	—	2	2	no	—
481	C₂³	—	4	2	no	—
482	C₂³	#120×C₅₉	1	2	yes	—
483	C₂³	C₂²×D₄×C₅₉	1	1	yes	characteristic
484	Q₈	—	2	2	no	—
485	Q₈	—	2	2	no	—
486	Q₈	—	2	4	no	—
487	Q₈	—	2	2	no	—
488	Q₈	—	4	4	no	—
489	Q₈	—	4	2	no	—
490	Q₈	—	4	1	no	—
491	Q₈	—	4	1	no	—
492	Q₈	—	4	1	no	—
493	Q₈	—	4	1	no	—
494	Q₈	—	4	2	no	—
495	D₄	—	2	4	no	—
496	D₄	—	2	2	no	—
497	D₄	—	2	2	no	—
498	D₄	—	2	2	no	—
499	D₄	—	4	2	no	—
500	D₄	—	4	4	no	—
501	D₄	—	4	2	no	—
502	D₄	—	4	2	no	—
503	C₂×C₄	—	2	1	no	—
504	C₂×C₄	—	2	2	no	—
505	C₂×C₄	—	2	2	no	—
506	C₂×C₄	—	2	2	no	—
507	C₂×C₄	—	2	2	no	—
508	C₂×C₄	—	2	2	no	—
509	C₂×C₄	—	2	2	no	—
510	C₂×C₄	—	2	2	no	—
511	C₂×C₄	—	2	1	no	—
512	C₂×C₄	—	2	4	no	—
513	C₂×C₄	—	2	2	no	—
514	C₂×C₄	—	4	2	no	—
515	C₂×C₄	—	4	4	no	—
516	C₂×C₄	—	4	4	no	—
517	C₂×C₄	—	4	2	no	—
518	C₂×C₄	—	4	2	no	—
519	C₂×C₄	—	4	2	no	—
520	C₂×C₄	—	4	2	no	—
521	C₂×C₄	—	4	2	no	—
522	C₂×C₄	#120×C₅₉	1	2	yes	—
523	C₂×C₄	C₂²×D₄×C₅₉	1	1	yes	characteristic
524	C₂×C₄	C₂²×D₄×C₅₉	1	1	yes	characteristic
525	C₂×C₄	C₂×#41×C₅₉	1	2	yes	—
526	C₂×C₄	H(5,𝔽₂)×C₅₉	1	2	yes	—
527	C₈	—	4	2	no	—
528	C₈	—	4	2	no	—
529	C₂²	—	2	2	no	—
530	C₂²	—	4	1	no	—
531	C₂²	—	4	2	no	—
532	C₂²	—	4	2	no	—
533	C₂²	—	8	2	no	—
534	C₂²	—	16	2	no	—
535	C₂²	C₂×#120×C₅₉	1	1	yes	characteristic
536	C₂²	C₅₉×#546	1	2	yes	—
537	C₄	—	2	2	no	—
538	C₄	—	2	2	no	—
539	C₄	—	4	2	no	—
540	C₄	—	4	1	no	—
541	C₄	—	4	2	no	—
542	C₄	—	4	2	no	—
543	C₄	—	4	2	no	—
544	C₄	—	4	2	no	—
545	C₄	—	4	2	no	—
546	C₄	—	8	2	no	—
547	C₄	C₅₉×#525	1	1	yes	characteristic
548	C₄	C₅₉×#535	1	1	yes	characteristic
549	C₄	C₅₉×#546	1	2	yes	—
550	C₂	—	2	1	no	—
551	C₂	—	2	2	no	—
552	C₂	—	4	2	no	—
553	C₂	—	8	2	no	—
554	C₂	C₅₉×#2404	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂×C₅₉	#2404
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₅₉
prime radical	C₅₉×#585	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₅₉ ◁ C₂²×C₄×C₅₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₅₉×#3509	C₂	semidirect
5. C₅₉×#2031	C₂	semidirect
6. C₅₉×#2005	C₂	semidirect
7. C₅₉×#1915	C₂	semidirect
8. C₅₉×#1912	C₂	semidirect
9. C₅₉×#1909	C₂	semidirect
10. C₅₉×#1905	C₂	semidirect
11. C₅₉×#1827	C₂	semidirect
23. C₅₉×#533	C₂²	semidirect
24. C₂×C₄⋊Q₈×C₅₉	C₂²	semidirect
25. C₅₉×#519	C₂²	semidirect
26. C₅₉×#519	C₂²	semidirect
36. C₅₉×#419	C₂²	semidirect
38. C₂×#101×C₅₉	C₂²	semidirect
41. C₅₉×#344	C₂²	semidirect
42. C₅₉×#339	C₂²	semidirect
43. C₅₉×H(3,ℤ/4)	C₂²	semidirect
44. C₅₉×H(3,ℤ/4)	C₂²	semidirect
251. #23992	C₅₉	direct (N × H)
273. #3509	C₂×C₅₉	semidirect
277. #2031	C₂×C₅₉	semidirect
278. #2005	C₂×C₅₉	semidirect
279. #1915	C₂×C₅₉	semidirect
280. #1912	C₂×C₅₉	semidirect
281. #1909	C₂×C₅₉	semidirect
282. #1905	C₂×C₅₉	semidirect
283. #1827	C₂×C₅₉	semidirect
300. #533	C₂²×C₅₉	semidirect
301. C₂×C₄⋊Q₈	C₂²×C₅₉	semidirect
302. #519	C₂²×C₅₉	semidirect
303. #519	C₂²×C₅₉	semidirect
313. #419	C₂²×C₅₉	semidirect
315. C₂×#101	C₂²×C₅₉	semidirect
318. #344	C₂²×C₅₉	semidirect
319. #339	C₂²×C₅₉	semidirect
320. H(3,ℤ/4)	C₂²×C₅₉	semidirect
321. H(3,ℤ/4)	C₂²×C₅₉	semidirect
322. C₅₉	#23992	direct (N × H)

Maximal subgroups

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

subgroup	index
C₅₉×#3509	2
C₅₉×#3028	2
C₅₉×#3022	2
C₅₉×#2901	2
C₅₉×#2031	2
C₅₉×#2005	2
C₅₉×#1915	2
C₅₉×#1912	2
C₅₉×#1909	2
C₅₉×#1905	2
C₅₉×#1827	2
#23992	59

Subgroups — C59×#23992 #28436101

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₉×#23992 #28436101