Subgroups — C₅₉×#24232 #28436341

Order 15104.

1488 conjugacy classes of subgroups.

The subgroup lattice has 744 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅₉×#3498	C₂	1	1	yes	maximal, characteristic
2	C₅₉×#3037	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₅₉×#455	C₂	1	2	yes	maximal, complemented
4	C₄×#137×C₅₉	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅₉×#2548	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅₉×#2037	C₂	1	2	yes	maximal, complemented
7	C₅₉×#2004	C₂	1	2	yes	maximal, complemented
8	C₅₉×#1980	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅₉×#1965	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅₉×#1806	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅₉×#1792	C₂	1	2	yes	maximal, complemented
12	C₂×H(5,𝔽₂)×C₅₉	C₂²	1	2	yes	—
13	C₂×#137×C₅₉	C₂²	1	1	yes	characteristic
14	C₂×#137×C₅₉	C₂²	1	2	yes	complemented
15	C₅₉×#550	—	2	1	no	—
16	C₅₉×#550	—	2	1	no	—
17	D₄²×C₅₉	—	2	2	no	—
18	D₄²×C₅₉	—	2	2	no	—
19	D₄²×C₅₉	—	2	1	no	—
20	D₄²×C₅₉	—	2	1	no	—
21	C₅₉×#535	—	2	2	no	—
22	C₅₉×#535	C₂²	1	2	yes	—
23	C₅₉×#532	—	2	1	no	—
24	C₅₉×#532	C₂²	1	1	yes	characteristic
25	C₂×#127×C₅₉	—	2	1	no	—
26	C₂×#127×C₅₉	C₂²	1	1	yes	characteristic
27	C₂×#124×C₅₉	C₂²	1	2	yes	complemented
28	C₄×#41×C₅₉	C₂²	1	1	yes	characteristic
29	C₂×C₄×Q₈×C₅₉	C₂²	1	1	yes	characteristic, complemented
30	C₅₉×#464	—	2	2	no	—
31	C₅₉×#462	—	2	1	no	—
32	C₅₉×#460	—	2	1	no	—
33	C₅₉×#455	—	2	8	no	—
34	C₅₉×#441	—	2	1	no	—
35	C₅₉×#440	—	2	1	no	—
36	C₄×Q₁₆×C₅₉	—	2	1	no	—
37	C₄×SD₁₆×C₅₉	—	2	1	no	—
38	C₅₉×#428	C₂²	1	1	yes	characteristic, complemented
39	C₅₉×#423	C₂²	1	1	yes	characteristic, complemented
40	C₂×#104×C₅₉	C₂²	1	2	yes	—
41	C₂×#104×C₅₉	C₂²	1	2	yes	complemented
42	C₂×#104×C₅₉	C₂²	1	2	yes	complemented
43	C₅₉×#419	C₂²	1	1	yes	characteristic, complemented
44	C₅₉×#417	C₂²	1	1	yes	characteristic
45	C₅₉×#417	C₂²	1	2	yes	complemented
46	C₂×#100×C₅₉	C₂²	1	2	yes	complemented
47	C₂×#100×C₅₉	C₂²	1	2	yes	complemented
48	C₄×M₁₆×C₅₉	C₂²	1	1	yes	characteristic, complemented
49	C₅₉×#394	—	2	2	no	—
50	C₅₉×#390	—	2	2	no	—
51	C₅₉×#390	C₂²	1	2	yes	complemented
52	C₄×C₄⋊C₄×C₅₉	C₂²	1	1	yes	characteristic, complemented
53	C₅₉×#339	C₂²	1	2	yes	complemented
54	H(5,𝔽₂)×C₅₉	—	2	4	no	—
55	H(5,𝔽₂)×C₅₉	—	2	4	no	—
56	H(5,𝔽₂)×C₅₉	—	4	2	no	—
57	H(5,𝔽₂)×C₅₉	—	4	2	no	—
58	C₂×#41×C₅₉	—	2	2	no	—
59	C₂×#41×C₅₉	—	2	2	no	—
60	C₂×#41×C₅₉	C₂³	1	2	yes	—
61	C₂×#41×C₅₉	C₂³	1	1	yes	characteristic
62	C₂²×Q₈×C₅₉	C₂³	1	1	yes	characteristic
63	C₂²×D₄×C₅₉	—	2	4	no	—
64	C₂²×D₄×C₅₉	—	2	2	no	—
65	C₂²×D₄×C₅₉	—	2	2	no	—
66	C₂²×D₄×C₅₉	—	2	2	no	—
67	C₂²×D₄×C₅₉	—	2	2	no	—
68	C₂²×D₄×C₅₉	D₄	1	2	yes	—
69	C₂²×D₄×C₅₉	D₄	1	2	yes	—
70	C₂²×D₄×C₅₉	C₂³	1	2	yes	—
71	#137×C₅₉	—	2	2	no	—
72	#137×C₅₉	—	2	4	no	—
73	#137×C₅₉	—	4	2	no	—
74	#137×C₅₉	D₄	1	4	yes	complemented
75	C₂×Q₁₆×C₅₉	—	2	1	no	—
76	C₂×Q₁₆×C₅₉	—	2	2	no	—
77	C₂×SD₁₆×C₅₉	—	2	1	no	—
78	C₂×SD₁₆×C₅₉	—	2	2	no	—
79	C₂×M₁₆×C₅₉	C₂³	1	2	yes	—
80	C₂×M₁₆×C₅₉	C₂³	1	1	yes	characteristic
81	C₂×M₁₆×C₅₉	C₂³	1	1	yes	characteristic
82	C₄⋊Q₈×C₅₉	D₄	1	1	yes	characteristic
83	#127×C₅₉	—	2	2	no	—
84	#127×C₅₉	—	2	2	no	—
85	#127×C₅₉	—	2	2	no	—
86	#127×C₅₉	—	2	1	no	—
87	#127×C₅₉	—	2	1	no	—
88	#127×C₅₉	—	2	1	no	—
89	#127×C₅₉	—	2	1	no	—
90	#127×C₅₉	D₄	1	1	yes	characteristic
91	#124×C₅₉	—	2	2	no	—
92	#124×C₅₉	—	2	4	no	—
93	#124×C₅₉	—	4	2	no	—
94	#124×C₅₉	D₄	1	2	yes	—
95	#121×C₅₉	—	2	2	no	—
96	#121×C₅₉	—	2	2	no	—
97	#121×C₅₉	—	2	4	no	—
98	#121×C₅₉	—	2	4	no	—
99	#121×C₅₉	—	2	1	no	—
100	#121×C₅₉	—	2	1	no	—
101	#121×C₅₉	—	2	2	no	—
102	#121×C₅₉	—	2	2	no	—
103	#120×C₅₉	—	2	4	no	—
104	#120×C₅₉	—	2	4	no	—
105	#120×C₅₉	—	2	4	no	—
106	C₄×Q₈×C₅₉	—	2	1	no	—
107	C₄×Q₈×C₅₉	—	2	1	no	—
108	C₄×Q₈×C₅₉	—	2	1	no	—
109	C₄×Q₈×C₅₉	—	2	1	no	—
110	C₄×Q₈×C₅₉	D₄	1	1	yes	characteristic
111	C₄×Q₈×C₅₉	D₄	1	1	yes	characteristic
112	C₄×D₄×C₅₉	—	2	2	no	—
113	C₄×D₄×C₅₉	—	2	2	no	—
114	C₄×D₄×C₅₉	—	2	1	no	—
115	C₄×D₄×C₅₉	—	2	1	no	—
116	C₄×D₄×C₅₉	—	2	1	no	—
117	C₄×D₄×C₅₉	—	2	1	no	—
118	C₄×D₄×C₅₉	D₄	1	1	yes	characteristic
119	C₄×D₄×C₅₉	D₄	1	1	yes	characteristic
120	#117×C₅₉	—	2	1	no	—
121	#117×C₅₉	C₂³	1	1	yes	characteristic
122	C₂×C₄⋊C₄×C₅₉	—	2	1	no	—
123	C₂×C₄⋊C₄×C₅₉	—	2	1	no	—
124	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
125	C₂×C₂²⋊C₄×C₅₉	—	2	4	no	—
126	C₂×C₂²⋊C₄×C₅₉	—	2	4	no	—
127	C₂×C₄²×C₅₉	—	2	1	no	—
128	C₂×C₄²×C₅₉	—	2	1	no	—
129	C₂×C₄²×C₅₉	C₂³	1	2	yes	—
130	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
131	#107×C₅₉	—	2	1	no	—
132	#106×C₅₉	—	2	1	no	—
133	C₄⋊C₈×C₅₉	—	2	1	no	—
134	C₄⋊C₈×C₅₉	—	2	1	no	—
135	#104×C₅₉	—	2	4	no	—
136	#104×C₅₉	—	2	4	no	—
137	#104×C₅₉	—	4	2	no	—
138	#103×C₅₉	—	2	1	no	—
139	#103×C₅₉	—	2	2	no	—
140	#103×C₅₉	—	2	1	no	—
141	#103×C₅₉	—	2	1	no	—
142	#102×C₅₉	—	2	1	no	—
143	#102×C₅₉	—	2	2	no	—
144	#100×C₅₉	—	2	4	no	—
145	#100×C₅₉	—	4	2	no	—
146	#97×C₅₉	—	2	1	no	—
147	C₄×C₈×C₅₉	—	2	1	no	—
148	#95×C₅₉	—	2	1	no	—
149	C₂⁴×C₅₉	—	2	4	no	—
150	C₂⁴×C₅₉	C₂×D₄	1	4	yes	—
151	#41×C₅₉	—	2	1	no	—
152	#41×C₅₉	—	2	1	no	—
153	#41×C₅₉	—	2	2	no	—
154	#41×C₅₉	—	2	2	no	—
155	#41×C₅₉	—	2	2	no	—
156	#41×C₅₉	—	2	2	no	—
157	#41×C₅₉	—	4	4	no	—
158	#41×C₅₉	—	4	4	no	—
159	#41×C₅₉	—	4	4	no	—
160	#41×C₅₉	—	4	4	no	—
161	#41×C₅₉	C₂×D₄	1	2	yes	—
162	#41×C₅₉	#41	1	2	yes	—
163	C₂×Q₈×C₅₉	—	2	1	no	—
164	C₂×Q₈×C₅₉	—	2	1	no	—
165	C₂×Q₈×C₅₉	—	2	1	no	—
166	C₂×Q₈×C₅₉	—	2	1	no	—
167	C₂×Q₈×C₅₉	—	2	1	no	—
168	C₂×Q₈×C₅₉	C₂×D₄	1	2	yes	—
169	C₂×Q₈×C₅₉	C₂×D₄	1	1	yes	characteristic
170	C₂×Q₈×C₅₉	C₂×D₄	1	2	yes	complemented
171	C₂×D₄×C₅₉	—	2	1	no	—
172	C₂×D₄×C₅₉	—	2	4	no	—
173	C₂×D₄×C₅₉	—	2	4	no	—
174	C₂×D₄×C₅₉	—	2	2	no	—
175	C₂×D₄×C₅₉	—	2	4	no	—
176	C₂×D₄×C₅₉	—	2	4	no	—
177	C₂×D₄×C₅₉	—	2	2	no	—
178	C₂×D₄×C₅₉	—	2	2	no	—
179	C₂×D₄×C₅₉	—	2	1	no	—
180	C₂×D₄×C₅₉	—	2	1	no	—
181	C₂×D₄×C₅₉	—	2	2	no	—
182	C₂×D₄×C₅₉	—	2	2	no	—
183	C₂×D₄×C₅₉	—	2	2	no	—
184	C₂×D₄×C₅₉	—	2	2	no	—
185	C₂×D₄×C₅₉	—	2	2	no	—
186	C₂×D₄×C₅₉	—	2	2	no	—
187	C₂×D₄×C₅₉	—	2	2	no	—
188	C₂×D₄×C₅₉	—	2	2	no	—
189	C₂×D₄×C₅₉	—	4	4	no	—
190	C₂×D₄×C₅₉	—	4	4	no	—
191	C₂×D₄×C₅₉	—	4	4	no	—
192	C₂×D₄×C₅₉	—	4	8	no	—
193	C₂×D₄×C₅₉	—	4	8	no	—
194	C₂×D₄×C₅₉	—	4	4	no	—
195	C₂×D₄×C₅₉	—	4	4	no	—
196	C₂×D₄×C₅₉	—	8	4	no	—
197	C₂×D₄×C₅₉	—	8	4	no	—
198	C₂×D₄×C₅₉	—	8	2	no	—
199	C₂×D₄×C₅₉	C₂×D₄	1	2	yes	—
200	C₂×D₄×C₅₉	C₂×D₄	1	1	yes	characteristic
201	C₂²×C₄×C₅₉	—	2	1	no	—
202	C₂²×C₄×C₅₉	—	2	4	no	—
203	C₂²×C₄×C₅₉	—	2	1	no	—
204	C₂²×C₄×C₅₉	—	2	1	no	—
205	C₂²×C₄×C₅₉	—	2	1	no	—
206	C₂²×C₄×C₅₉	—	2	2	no	—
207	C₂²×C₄×C₅₉	—	2	2	no	—
208	C₂²×C₄×C₅₉	—	2	1	no	—
209	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
210	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
211	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
212	Q₁₆×C₅₉	—	2	4	no	—
213	Q₁₆×C₅₉	—	4	4	no	—
214	SD₁₆×C₅₉	—	2	4	no	—
215	SD₁₆×C₅₉	—	4	4	no	—
216	M₁₆×C₅₉	—	2	1	no	—
217	M₁₆×C₅₉	—	2	2	no	—
218	M₁₆×C₅₉	—	2	1	no	—
219	M₁₆×C₅₉	—	2	2	no	—
220	M₁₆×C₅₉	—	2	1	no	—
221	M₁₆×C₅₉	C₂×D₄	1	2	yes	complemented
222	C₂×C₈×C₅₉	—	2	1	no	—
223	C₂×C₈×C₅₉	—	2	1	no	—
224	C₂×C₈×C₅₉	—	2	2	no	—
225	C₄⋊C₄×C₅₉	—	2	1	no	—
226	C₄⋊C₄×C₅₉	—	2	1	no	—
227	C₄⋊C₄×C₅₉	—	2	1	no	—
228	C₄⋊C₄×C₅₉	—	2	1	no	—
229	C₄⋊C₄×C₅₉	—	2	1	no	—
230	C₄⋊C₄×C₅₉	—	2	1	no	—
231	C₄⋊C₄×C₅₉	—	4	2	no	—
232	C₄⋊C₄×C₅₉	—	4	1	no	—
233	C₄⋊C₄×C₅₉	—	4	1	no	—
234	C₄⋊C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
235	C₄⋊C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
236	C₂²⋊C₄×C₅₉	—	2	4	no	—
237	C₂²⋊C₄×C₅₉	—	2	4	no	—
238	C₂²⋊C₄×C₅₉	—	2	1	no	—
239	C₂²⋊C₄×C₅₉	—	2	1	no	—
240	C₂²⋊C₄×C₅₉	—	2	1	no	—
241	C₂²⋊C₄×C₅₉	—	2	2	no	—
242	C₂²⋊C₄×C₅₉	—	2	2	no	—
243	C₂²⋊C₄×C₅₉	—	4	8	no	—
244	C₂²⋊C₄×C₅₉	—	8	4	no	—
245	C₄²×C₅₉	—	2	1	no	—
246	C₄²×C₅₉	—	2	1	no	—
247	C₄²×C₅₉	—	2	1	no	—
248	C₄²×C₅₉	—	2	2	no	—
249	C₄²×C₅₉	—	2	2	no	—
250	C₄²×C₅₉	—	4	1	no	—
251	C₄²×C₅₉	—	4	1	no	—
252	C₄²×C₅₉	C₂×D₄	1	1	yes	characteristic
253	C₄²×C₅₉	C₂×D₄	1	1	yes	characteristic
254	C₄²×C₅₉	C₂×D₄	1	1	yes	characteristic
255	C₄²×C₅₉	C₂×D₄	1	1	yes	characteristic
256	C₂³×C₅₉	—	2	1	no	—
257	C₂³×C₅₉	—	2	4	no	—
258	C₂³×C₅₉	—	2	2	no	—
259	C₂³×C₅₉	—	2	4	no	—
260	C₂³×C₅₉	—	2	4	no	—
261	C₂³×C₅₉	—	4	8	no	—
262	C₂³×C₅₉	—	4	4	no	—
263	C₂³×C₅₉	—	4	4	no	—
264	C₂³×C₅₉	—	8	4	no	—
265	C₂³×C₅₉	—	8	4	no	—
266	C₂³×C₅₉	C₂²×D₄	1	1	yes	characteristic
267	Q₈×C₅₉	—	2	1	no	—
268	Q₈×C₅₉	—	2	2	no	—
269	Q₈×C₅₉	—	2	2	no	—
270	Q₈×C₅₉	—	2	2	no	—
271	Q₈×C₅₉	—	2	2	no	—
272	Q₈×C₅₉	—	4	1	no	—
273	Q₈×C₅₉	—	4	1	no	—
274	Q₈×C₅₉	#121	1	2	yes	—
275	D₄×C₅₉	—	2	2	no	—
276	D₄×C₅₉	—	2	2	no	—
277	D₄×C₅₉	—	2	1	no	—
278	D₄×C₅₉	—	2	2	no	—
279	D₄×C₅₉	—	2	2	no	—
280	D₄×C₅₉	—	4	8	no	—
281	D₄×C₅₉	—	4	4	no	—
282	D₄×C₅₉	—	4	2	no	—
283	D₄×C₅₉	—	4	8	no	—
284	D₄×C₅₉	—	4	2	no	—
285	D₄×C₅₉	—	4	2	no	—
286	D₄×C₅₉	—	4	2	no	—
287	D₄×C₅₉	—	4	2	no	—
288	D₄×C₅₉	—	4	2	no	—
289	D₄×C₅₉	—	4	2	no	—
290	D₄×C₅₉	—	4	4	no	—
291	D₄×C₅₉	—	4	2	no	—
292	D₄×C₅₉	—	8	2	no	—
293	D₄×C₅₉	—	8	2	no	—
294	D₄×C₅₉	—	8	4	no	—
295	D₄×C₅₉	—	8	4	no	—
296	D₄×C₅₉	#121	1	2	yes	—
297	C₂×C₄×C₅₉	—	2	1	no	—
298	C₂×C₄×C₅₉	—	2	2	no	—
299	C₂×C₄×C₅₉	—	2	2	no	—
300	C₂×C₄×C₅₉	—	2	2	no	—
301	C₂×C₄×C₅₉	—	2	1	no	—
302	C₂×C₄×C₅₉	—	2	1	no	—
303	C₂×C₄×C₅₉	—	2	2	no	—
304	C₂×C₄×C₅₉	—	2	2	no	—
305	C₂×C₄×C₅₉	—	4	1	no	—
306	C₂×C₄×C₅₉	—	4	8	no	—
307	C₂×C₄×C₅₉	—	4	2	no	—
308	C₂×C₄×C₅₉	—	4	1	no	—
309	C₂×C₄×C₅₉	—	4	1	no	—
310	C₂×C₄×C₅₉	—	4	2	no	—
311	C₂×C₄×C₅₉	—	4	2	no	—
312	C₂×C₄×C₅₉	—	4	2	no	—
313	C₂×C₄×C₅₉	—	4	2	no	—
314	C₂×C₄×C₅₉	—	4	2	no	—
315	C₂×C₄×C₅₉	—	4	2	no	—
316	C₂×C₄×C₅₉	—	4	1	no	—
317	C₂×C₄×C₅₉	—	4	2	no	—
318	C₂×C₄×C₅₉	#120	1	1	yes	characteristic
319	C₂×C₄×C₅₉	#120	1	1	yes	characteristic
320	C₂×C₄×C₅₉	#120	1	1	yes	characteristic
321	C₂×C₄×C₅₉	#120	1	1	yes	characteristic
322	C₂×C₄×C₅₉	C₂²×D₄	1	1	yes	characteristic
323	C₂×C₄×C₅₉	C₂²×D₄	1	1	yes	characteristic
324	C₂×C₄×C₅₉	C₂²×D₄	1	1	yes	characteristic
325	C₂×C₄×C₅₉	C₂×#41	1	1	yes	characteristic
326	C₂×C₄×C₅₉	H(5,𝔽₂)	1	1	yes	characteristic
327	C₂×C₄×C₅₉	H(5,𝔽₂)	1	1	yes	characteristic
328	C₈×C₅₉	—	2	2	no	—
329	C₈×C₅₉	—	4	1	no	—
330	C₈×C₅₉	—	4	2	no	—
331	#24232	C₅₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
332	C₂²×C₅₉	—	2	1	no	—
333	C₂²×C₅₉	—	2	1	no	—
334	C₂²×C₅₉	—	2	2	no	—
335	C₂²×C₅₉	—	4	1	no	—
336	C₂²×C₅₉	—	4	1	no	—
337	C₂²×C₅₉	—	4	2	no	—
338	C₂²×C₅₉	—	4	4	no	—
339	C₂²×C₅₉	—	4	4	no	—
340	C₂²×C₅₉	—	4	2	no	—
341	C₂²×C₅₉	—	4	4	no	—
342	C₂²×C₅₉	—	4	2	no	—
343	C₂²×C₅₉	—	8	4	no	—
344	C₂²×C₅₉	—	8	4	no	—
345	C₂²×C₅₉	—	16	8	no	—
346	C₂²×C₅₉	C₂×#120	1	1	yes	characteristic
347	C₂²×C₅₉	D₄²	1	1	yes	characteristic
348	C₂²×C₅₉	#546	1	1	yes	characteristic
349	C₄×C₅₉	—	2	2	no	—
350	C₄×C₅₉	—	2	1	no	—
351	C₄×C₅₉	—	2	1	no	—
352	C₄×C₅₉	—	2	1	no	—
353	C₄×C₅₉	—	4	2	no	—
354	C₄×C₅₉	—	4	2	no	—
355	C₄×C₅₉	—	4	1	no	—
356	C₄×C₅₉	—	4	1	no	—
357	C₄×C₅₉	—	8	2	no	—
358	C₄×C₅₉	—	8	1	no	—
359	C₄×C₅₉	#455	1	2	yes	complemented
360	C₄×C₅₉	C₂×#121	1	1	yes	characteristic
361	C₄×C₅₉	#535	1	1	yes	characteristic
362	C₄×C₅₉	D₄²	1	1	yes	characteristic
363	C₄×C₅₉	#546	1	1	yes	characteristic
364	#3498	C₂×C₅₉	1	1	yes	characteristic
365	#3037	C₂×C₅₉	1	1	yes	characteristic, complemented
366	C₂×#455	C₂×C₅₉	1	2	yes	complemented
367	C₄×#137	C₂×C₅₉	1	1	yes	characteristic, complemented
368	#2548	C₂×C₅₉	1	1	yes	characteristic, complemented
369	#2037	C₂×C₅₉	1	2	yes	complemented
370	#2004	C₂×C₅₉	1	2	yes	complemented
371	#1980	C₂×C₅₉	1	1	yes	characteristic, complemented
372	#1965	C₂×C₅₉	1	1	yes	characteristic, complemented
373	#1806	C₂×C₅₉	1	1	yes	characteristic, complemented
374	#1792	C₂×C₅₉	1	2	yes	complemented
375	C₂×C₅₉	—	2	1	no	—
376	C₂×C₅₉	—	2	1	no	—
377	C₂×C₅₉	—	4	2	no	—
378	C₂×C₅₉	—	8	4	no	—
379	C₂×C₅₉	—	8	2	no	—
380	C₂×C₅₉	#2408	1	1	yes	characteristic
381	C₂×C₅₉	C₂×#455	1	1	yes	characteristic
382	C₂×C₅₉	#3019	1	1	yes	characteristic
383	C₂×H(5,𝔽₂)	C₂²×C₅₉	1	2	yes	—
384	C₂×#137	C₂²×C₅₉	1	1	yes	characteristic
385	C₂×#137	C₂²×C₅₉	1	2	yes	complemented
386	#550	—	2	1	no	—
387	#550	—	2	1	no	—
388	D₄²	—	2	2	no	—
389	D₄²	—	2	2	no	—
390	D₄²	—	2	1	no	—
391	D₄²	—	2	1	no	—
392	#535	—	2	2	no	—
393	#535	C₂²×C₅₉	1	2	yes	—
394	#532	—	2	1	no	—
395	#532	C₂²×C₅₉	1	1	yes	characteristic
396	C₂×#127	—	2	1	no	—
397	C₂×#127	C₂²×C₅₉	1	1	yes	characteristic
398	C₂×#124	C₂²×C₅₉	1	2	yes	complemented
399	C₄×#41	C₂²×C₅₉	1	1	yes	characteristic
400	C₂×C₄×Q₈	C₂²×C₅₉	1	1	yes	characteristic, complemented
401	#464	—	2	2	no	—
402	#462	—	2	1	no	—
403	#460	—	2	1	no	—
404	#455	—	2	8	no	—
405	#441	—	2	1	no	—
406	#440	—	2	1	no	—
407	C₄×Q₁₆	—	2	1	no	—
408	C₄×SD₁₆	—	2	1	no	—
409	#428	C₂²×C₅₉	1	1	yes	characteristic, complemented
410	#423	C₂²×C₅₉	1	1	yes	characteristic, complemented
411	C₂×#104	C₂²×C₅₉	1	2	yes	—
412	C₂×#104	C₂²×C₅₉	1	2	yes	complemented
413	C₂×#104	C₂²×C₅₉	1	2	yes	complemented
414	#419	C₂²×C₅₉	1	1	yes	characteristic, complemented
415	#417	C₂²×C₅₉	1	1	yes	characteristic
416	#417	C₂²×C₅₉	1	2	yes	complemented
417	C₂×#100	C₂²×C₅₉	1	2	yes	complemented
418	C₂×#100	C₂²×C₅₉	1	2	yes	complemented
419	C₄×M₁₆	C₂²×C₅₉	1	1	yes	characteristic, complemented
420	#394	—	2	2	no	—
421	#390	—	2	2	no	—
422	#390	C₂²×C₅₉	1	2	yes	complemented
423	C₄×C₄⋊C₄	C₂²×C₅₉	1	1	yes	characteristic, complemented
424	#339	C₂²×C₅₉	1	2	yes	complemented
425	C₅₉	#24232	1	1	yes	characteristic, direct product factor, Sylow
426	H(5,𝔽₂)	—	2	4	no	—
427	H(5,𝔽₂)	—	2	4	no	—
428	H(5,𝔽₂)	—	4	2	no	—
429	H(5,𝔽₂)	—	4	2	no	—
430	C₂×#41	—	2	2	no	—
431	C₂×#41	—	2	2	no	—
432	C₂×#41	C₂³×C₅₉	1	2	yes	—
433	C₂×#41	C₂³×C₅₉	1	1	yes	characteristic
434	C₂²×Q₈	C₂³×C₅₉	1	1	yes	characteristic
435	C₂²×D₄	—	2	4	no	—
436	C₂²×D₄	—	2	2	no	—
437	C₂²×D₄	—	2	2	no	—
438	C₂²×D₄	—	2	2	no	—
439	C₂²×D₄	—	2	2	no	—
440	C₂²×D₄	D₄×C₅₉	1	2	yes	—
441	C₂²×D₄	D₄×C₅₉	1	2	yes	—
442	C₂²×D₄	C₂³×C₅₉	1	2	yes	—
443	#137	—	2	2	no	—
444	#137	—	2	4	no	—
445	#137	—	4	2	no	—
446	#137	D₄×C₅₉	1	4	yes	complemented
447	C₂×Q₁₆	—	2	1	no	—
448	C₂×Q₁₆	—	2	2	no	—
449	C₂×SD₁₆	—	2	1	no	—
450	C₂×SD₁₆	—	2	2	no	—
451	C₂×M₁₆	C₂³×C₅₉	1	2	yes	—
452	C₂×M₁₆	C₂³×C₅₉	1	1	yes	characteristic
453	C₂×M₁₆	C₂³×C₅₉	1	1	yes	characteristic
454	C₄⋊Q₈	D₄×C₅₉	1	1	yes	characteristic
455	#127	—	2	2	no	—
456	#127	—	2	2	no	—
457	#127	—	2	2	no	—
458	#127	—	2	1	no	—
459	#127	—	2	1	no	—
460	#127	—	2	1	no	—
461	#127	—	2	1	no	—
462	#127	D₄×C₅₉	1	1	yes	characteristic
463	#124	—	2	2	no	—
464	#124	—	2	4	no	—
465	#124	—	4	2	no	—
466	#124	D₄×C₅₉	1	2	yes	—
467	#121	—	2	2	no	—
468	#121	—	2	2	no	—
469	#121	—	2	4	no	—
470	#121	—	2	4	no	—
471	#121	—	2	1	no	—
472	#121	—	2	1	no	—
473	#121	—	2	2	no	—
474	#121	—	2	2	no	—
475	#120	—	2	4	no	—
476	#120	—	2	4	no	—
477	#120	—	2	4	no	—
478	C₄×Q₈	—	2	1	no	—
479	C₄×Q₈	—	2	1	no	—
480	C₄×Q₈	—	2	1	no	—
481	C₄×Q₈	—	2	1	no	—
482	C₄×Q₈	D₄×C₅₉	1	1	yes	characteristic
483	C₄×Q₈	D₄×C₅₉	1	1	yes	characteristic
484	C₄×D₄	—	2	2	no	—
485	C₄×D₄	—	2	2	no	—
486	C₄×D₄	—	2	1	no	—
487	C₄×D₄	—	2	1	no	—
488	C₄×D₄	—	2	1	no	—
489	C₄×D₄	—	2	1	no	—
490	C₄×D₄	D₄×C₅₉	1	1	yes	characteristic
491	C₄×D₄	D₄×C₅₉	1	1	yes	characteristic
492	#117	—	2	1	no	—
493	#117	C₂³×C₅₉	1	1	yes	characteristic
494	C₂×C₄⋊C₄	—	2	1	no	—
495	C₂×C₄⋊C₄	—	2	1	no	—
496	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
497	C₂×C₂²⋊C₄	—	2	4	no	—
498	C₂×C₂²⋊C₄	—	2	4	no	—
499	C₂×C₄²	—	2	1	no	—
500	C₂×C₄²	—	2	1	no	—
501	C₂×C₄²	C₂³×C₅₉	1	2	yes	—
502	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
503	#107	—	2	1	no	—
504	#106	—	2	1	no	—
505	C₄⋊C₈	—	2	1	no	—
506	C₄⋊C₈	—	2	1	no	—
507	#104	—	2	4	no	—
508	#104	—	2	4	no	—
509	#104	—	4	2	no	—
510	#103	—	2	1	no	—
511	#103	—	2	2	no	—
512	#103	—	2	1	no	—
513	#103	—	2	1	no	—
514	#102	—	2	1	no	—
515	#102	—	2	2	no	—
516	#100	—	2	4	no	—
517	#100	—	4	2	no	—
518	#97	—	2	1	no	—
519	C₄×C₈	—	2	1	no	—
520	#95	—	2	1	no	—
521	C₂⁴	—	2	4	no	—
522	C₂⁴	C₂×D₄×C₅₉	1	4	yes	—
523	#41	—	2	1	no	—
524	#41	—	2	1	no	—
525	#41	—	2	2	no	—
526	#41	—	2	2	no	—
527	#41	—	2	2	no	—
528	#41	—	2	2	no	—
529	#41	—	4	4	no	—
530	#41	—	4	4	no	—
531	#41	—	4	4	no	—
532	#41	—	4	4	no	—
533	#41	C₂×D₄×C₅₉	1	2	yes	—
534	#41	#41×C₅₉	1	2	yes	—
535	C₂×Q₈	—	2	1	no	—
536	C₂×Q₈	—	2	1	no	—
537	C₂×Q₈	—	2	1	no	—
538	C₂×Q₈	—	2	1	no	—
539	C₂×Q₈	—	2	1	no	—
540	C₂×Q₈	C₂×D₄×C₅₉	1	2	yes	—
541	C₂×Q₈	C₂×D₄×C₅₉	1	1	yes	characteristic
542	C₂×Q₈	C₂×D₄×C₅₉	1	2	yes	complemented
543	C₂×D₄	—	2	1	no	—
544	C₂×D₄	—	2	4	no	—
545	C₂×D₄	—	2	4	no	—
546	C₂×D₄	—	2	2	no	—
547	C₂×D₄	—	2	4	no	—
548	C₂×D₄	—	2	4	no	—
549	C₂×D₄	—	2	2	no	—
550	C₂×D₄	—	2	2	no	—
551	C₂×D₄	—	2	1	no	—
552	C₂×D₄	—	2	1	no	—
553	C₂×D₄	—	2	2	no	—
554	C₂×D₄	—	2	2	no	—
555	C₂×D₄	—	2	2	no	—
556	C₂×D₄	—	2	2	no	—
557	C₂×D₄	—	2	2	no	—
558	C₂×D₄	—	2	2	no	—
559	C₂×D₄	—	2	2	no	—
560	C₂×D₄	—	2	2	no	—
561	C₂×D₄	—	4	4	no	—
562	C₂×D₄	—	4	4	no	—
563	C₂×D₄	—	4	4	no	—
564	C₂×D₄	—	4	8	no	—
565	C₂×D₄	—	4	8	no	—
566	C₂×D₄	—	4	4	no	—
567	C₂×D₄	—	4	4	no	—
568	C₂×D₄	—	8	4	no	—
569	C₂×D₄	—	8	4	no	—
570	C₂×D₄	—	8	2	no	—
571	C₂×D₄	C₂×D₄×C₅₉	1	2	yes	—
572	C₂×D₄	C₂×D₄×C₅₉	1	1	yes	characteristic
573	C₂²×C₄	—	2	1	no	—
574	C₂²×C₄	—	2	4	no	—
575	C₂²×C₄	—	2	1	no	—
576	C₂²×C₄	—	2	1	no	—
577	C₂²×C₄	—	2	1	no	—
578	C₂²×C₄	—	2	2	no	—
579	C₂²×C₄	—	2	2	no	—
580	C₂²×C₄	—	2	1	no	—
581	C₂²×C₄	C₂×D₄×C₅₉	1	1	yes	characteristic
582	C₂²×C₄	C₂×D₄×C₅₉	1	1	yes	characteristic
583	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
584	Q₁₆	—	2	4	no	—
585	Q₁₆	—	4	4	no	—
586	SD₁₆	—	2	4	no	—
587	SD₁₆	—	4	4	no	—
588	M₁₆	—	2	1	no	—
589	M₁₆	—	2	2	no	—
590	M₁₆	—	2	1	no	—
591	M₁₆	—	2	2	no	—
592	M₁₆	—	2	1	no	—
593	M₁₆	C₂×D₄×C₅₉	1	2	yes	complemented
594	C₂×C₈	—	2	1	no	—
595	C₂×C₈	—	2	1	no	—
596	C₂×C₈	—	2	2	no	—
597	C₄⋊C₄	—	2	1	no	—
598	C₄⋊C₄	—	2	1	no	—
599	C₄⋊C₄	—	2	1	no	—
600	C₄⋊C₄	—	2	1	no	—
601	C₄⋊C₄	—	2	1	no	—
602	C₄⋊C₄	—	2	1	no	—
603	C₄⋊C₄	—	4	2	no	—
604	C₄⋊C₄	—	4	1	no	—
605	C₄⋊C₄	—	4	1	no	—
606	C₄⋊C₄	C₂×D₄×C₅₉	1	1	yes	characteristic
607	C₄⋊C₄	C₂×D₄×C₅₉	1	1	yes	characteristic
608	C₂²⋊C₄	—	2	4	no	—
609	C₂²⋊C₄	—	2	4	no	—
610	C₂²⋊C₄	—	2	1	no	—
611	C₂²⋊C₄	—	2	1	no	—
612	C₂²⋊C₄	—	2	1	no	—
613	C₂²⋊C₄	—	2	2	no	—
614	C₂²⋊C₄	—	2	2	no	—
615	C₂²⋊C₄	—	4	8	no	—
616	C₂²⋊C₄	—	8	4	no	—
617	C₄²	—	2	1	no	—
618	C₄²	—	2	1	no	—
619	C₄²	—	2	1	no	—
620	C₄²	—	2	2	no	—
621	C₄²	—	2	2	no	—
622	C₄²	—	4	1	no	—
623	C₄²	—	4	1	no	—
624	C₄²	C₂×D₄×C₅₉	1	1	yes	characteristic
625	C₄²	C₂×D₄×C₅₉	1	1	yes	characteristic
626	C₄²	C₂×D₄×C₅₉	1	1	yes	characteristic
627	C₄²	C₂×D₄×C₅₉	1	1	yes	characteristic
628	C₂³	—	2	1	no	—
629	C₂³	—	2	4	no	—
630	C₂³	—	2	2	no	—
631	C₂³	—	2	4	no	—
632	C₂³	—	2	4	no	—
633	C₂³	—	4	8	no	—
634	C₂³	—	4	4	no	—
635	C₂³	—	4	4	no	—
636	C₂³	—	8	4	no	—
637	C₂³	—	8	4	no	—
638	C₂³	C₂²×D₄×C₅₉	1	1	yes	characteristic
639	Q₈	—	2	1	no	—
640	Q₈	—	2	2	no	—
641	Q₈	—	2	2	no	—
642	Q₈	—	2	2	no	—
643	Q₈	—	2	2	no	—
644	Q₈	—	4	1	no	—
645	Q₈	—	4	1	no	—
646	Q₈	#121×C₅₉	1	2	yes	—
647	D₄	—	2	2	no	—
648	D₄	—	2	2	no	—
649	D₄	—	2	1	no	—
650	D₄	—	2	2	no	—
651	D₄	—	2	2	no	—
652	D₄	—	4	8	no	—
653	D₄	—	4	4	no	—
654	D₄	—	4	2	no	—
655	D₄	—	4	8	no	—
656	D₄	—	4	2	no	—
657	D₄	—	4	2	no	—
658	D₄	—	4	4	no	—
659	D₄	—	4	2	no	—
660	D₄	—	4	2	no	—
661	D₄	—	4	2	no	—
662	D₄	—	4	2	no	—
663	D₄	—	4	2	no	—
664	D₄	—	8	2	no	—
665	D₄	—	8	2	no	—
666	D₄	—	8	4	no	—
667	D₄	—	8	4	no	—
668	D₄	#121×C₅₉	1	2	yes	—
669	C₂×C₄	—	2	1	no	—
670	C₂×C₄	—	2	2	no	—
671	C₂×C₄	—	2	2	no	—
672	C₂×C₄	—	2	2	no	—
673	C₂×C₄	—	2	1	no	—
674	C₂×C₄	—	2	1	no	—
675	C₂×C₄	—	2	2	no	—
676	C₂×C₄	—	2	2	no	—
677	C₂×C₄	—	4	1	no	—
678	C₂×C₄	—	4	8	no	—
679	C₂×C₄	—	4	2	no	—
680	C₂×C₄	—	4	1	no	—
681	C₂×C₄	—	4	1	no	—
682	C₂×C₄	—	4	2	no	—
683	C₂×C₄	—	4	2	no	—
684	C₂×C₄	—	4	2	no	—
685	C₂×C₄	—	4	2	no	—
686	C₂×C₄	—	4	2	no	—
687	C₂×C₄	—	4	2	no	—
688	C₂×C₄	—	4	1	no	—
689	C₂×C₄	—	4	2	no	—
690	C₂×C₄	#120×C₅₉	1	1	yes	characteristic
691	C₂×C₄	#120×C₅₉	1	1	yes	characteristic
692	C₂×C₄	#120×C₅₉	1	1	yes	characteristic
693	C₂×C₄	#120×C₅₉	1	1	yes	characteristic
694	C₂×C₄	C₂²×D₄×C₅₉	1	1	yes	characteristic
695	C₂×C₄	C₂²×D₄×C₅₉	1	1	yes	characteristic
696	C₂×C₄	C₂²×D₄×C₅₉	1	1	yes	characteristic
697	C₂×C₄	C₂×#41×C₅₉	1	1	yes	characteristic
698	C₂×C₄	H(5,𝔽₂)×C₅₉	1	1	yes	characteristic
699	C₂×C₄	H(5,𝔽₂)×C₅₉	1	1	yes	characteristic
700	C₈	—	2	2	no	—
701	C₈	—	4	1	no	—
702	C₈	—	4	2	no	—
703	C₂²	—	2	1	no	—
704	C₂²	—	2	1	no	—
705	C₂²	—	2	2	no	—
706	C₂²	—	4	1	no	—
707	C₂²	—	4	1	no	—
708	C₂²	—	4	4	no	—
709	C₂²	—	4	2	no	—
710	C₂²	—	4	4	no	—
711	C₂²	—	4	2	no	—
712	C₂²	—	4	2	no	—
713	C₂²	—	4	4	no	—
714	C₂²	—	8	4	no	—
715	C₂²	—	8	4	no	—
716	C₂²	—	16	8	no	—
717	C₂²	C₂×#120×C₅₉	1	1	yes	characteristic
718	C₂²	D₄²×C₅₉	1	1	yes	characteristic
719	C₂²	C₅₉×#546	1	1	yes	characteristic
720	C₄	—	2	1	no	—
721	C₄	—	2	1	no	—
722	C₄	—	2	1	no	—
723	C₄	—	2	2	no	—
724	C₄	—	4	1	no	—
725	C₄	—	4	1	no	—
726	C₄	—	4	2	no	—
727	C₄	—	4	2	no	—
728	C₄	—	8	2	no	—
729	C₄	—	8	1	no	—
730	C₄	C₅₉×#455	1	2	yes	complemented
731	C₄	C₂×#121×C₅₉	1	1	yes	characteristic
732	C₄	C₅₉×#535	1	1	yes	characteristic
733	C₄	D₄²×C₅₉	1	1	yes	characteristic
734	C₄	C₅₉×#546	1	1	yes	characteristic
735	C₂	—	2	1	no	—
736	C₂	—	2	1	no	—
737	C₂	—	4	2	no	—
738	C₂	—	8	4	no	—
739	C₂	—	8	2	no	—
740	C₂	C₅₉×#2408	1	1	yes	characteristic
741	C₂	C₂×C₅₉×#455	1	1	yes	characteristic
742	C₂	C₅₉×#3019	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₅₉	C₂×#120
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₅₉
prime radical	C₅₉×#3498	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×#455	C₂	semidirect
4. C₄×#137×C₅₉	C₂	semidirect
5. C₅₉×#2548	C₂	semidirect
6. C₅₉×#2037	C₂	semidirect
7. C₅₉×#2004	C₂	semidirect
8. C₅₉×#1980	C₂	semidirect
9. C₅₉×#1965	C₂	semidirect
10. C₅₉×#1806	C₂	semidirect
11. C₅₉×#1792	C₂	semidirect
14. C₂×#137×C₅₉	C₂²	semidirect
27. C₂×#124×C₅₉	C₂²	semidirect
29. C₂×C₄×Q₈×C₅₉	C₂²	semidirect
38. C₅₉×#428	C₂²	semidirect
39. C₅₉×#423	C₂²	semidirect
41. C₂×#104×C₅₉	C₂²	semidirect
42. C₂×#104×C₅₉	C₂²	semidirect
43. C₅₉×#419	C₂²	semidirect
45. C₅₉×#417	C₂²	semidirect
46. C₂×#100×C₅₉	C₂²	semidirect
47. C₂×#100×C₅₉	C₂²	semidirect
48. C₄×M₁₆×C₅₉	C₂²	semidirect
51. C₅₉×#390	C₂²	semidirect
52. C₄×C₄⋊C₄×C₅₉	C₂²	semidirect
53. C₅₉×#339	C₂²	semidirect
74. #137×C₅₉	D₄	semidirect
170. C₂×Q₈×C₅₉	C₂×D₄	semidirect
221. M₁₆×C₅₉	C₂×D₄	semidirect
331. #24232	C₅₉	direct (N × H)
359. C₄×C₅₉	#455	semidirect
365. #3037	C₂×C₅₉	semidirect
366. C₂×#455	C₂×C₅₉	semidirect
367. C₄×#137	C₂×C₅₉	semidirect
368. #2548	C₂×C₅₉	semidirect
369. #2037	C₂×C₅₉	semidirect
370. #2004	C₂×C₅₉	semidirect
371. #1980	C₂×C₅₉	semidirect
372. #1965	C₂×C₅₉	semidirect
373. #1806	C₂×C₅₉	semidirect
374. #1792	C₂×C₅₉	semidirect
385. C₂×#137	C₂²×C₅₉	semidirect
398. C₂×#124	C₂²×C₅₉	semidirect
400. C₂×C₄×Q₈	C₂²×C₅₉	semidirect
409. #428	C₂²×C₅₉	semidirect
410. #423	C₂²×C₅₉	semidirect
412. C₂×#104	C₂²×C₅₉	semidirect
413. C₂×#104	C₂²×C₅₉	semidirect
414. #419	C₂²×C₅₉	semidirect
416. #417	C₂²×C₅₉	semidirect
417. C₂×#100	C₂²×C₅₉	semidirect
418. C₂×#100	C₂²×C₅₉	semidirect
419. C₄×M₁₆	C₂²×C₅₉	semidirect
422. #390	C₂²×C₅₉	semidirect
423. C₄×C₄⋊C₄	C₂²×C₅₉	semidirect
424. #339	C₂²×C₅₉	semidirect
425. C₅₉	#24232	direct (N × H)
446. #137	D₄×C₅₉	semidirect
542. C₂×Q₈	C₂×D₄×C₅₉	semidirect
593. M₁₆	C₂×D₄×C₅₉	semidirect
730. C₄	C₅₉×#455	semidirect

Maximal subgroups

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

subgroup	index
C₅₉×#3498	2
C₅₉×#3037	2
C₂×C₅₉×#455	2
C₄×#137×C₅₉	2
C₅₉×#2548	2
C₅₉×#2037	2
C₅₉×#2004	2
C₅₉×#1980	2
C₅₉×#1965	2
C₅₉×#1806	2
C₅₉×#1792	2
#24232	59

Subgroups — C59×#24232 #28436341

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₉×#24232 #28436341