Subgroups — C₅₉×#33539 #28445648

Order 15104.

1130 conjugacy classes of subgroups.

The subgroup lattice has 578 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅₉×#576	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅₉×#3414	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₅₉×#509	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅₉×#3067	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅₉×#2194	C₂	1	4	yes	maximal, complemented
6	C₅₉×#2192	C₂	1	4	yes	maximal, complemented
7	C₂×C₅₉×#361	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅₉×#2143	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅₉×#2117	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×H(5,𝔽₂)×C₅₉	—	2	1	no	—
11	C₅₉×#576	—	2	2	no	—
12	C₅₉×#576	—	2	2	no	—
13	C₅₉×#576	—	2	2	no	—
14	C₅₉×#576	C₂²	1	4	yes	—
15	C₅₉×#575	—	2	1	no	—
16	C₂×AGL(1,ℤ/8)×C₅₉	—	2	2	no	—
17	C₂×AGL(1,ℤ/8)×C₅₉	—	2	1	no	—
18	C₂×#135×C₅₉	—	2	1	no	—
19	C₂×#135×C₅₉	C₂²	1	1	yes	characteristic
20	C₂×#135×C₅₉	C₂²	1	1	yes	characteristic, complemented
21	C₂²×D₈×C₅₉	—	2	1	no	—
22	C₂²×D₈×C₅₉	C₂²	1	1	yes	characteristic
23	C₂×#131×C₅₉	C₂²	1	1	yes	characteristic
24	C₅₉×#510	—	2	1	no	—
25	C₅₉×#510	C₂²	1	2	yes	complemented
26	C₅₉×#509	—	2	2	no	—
27	C₅₉×#509	—	2	2	no	—
28	C₅₉×#509	—	2	1	no	—
29	C₅₉×#509	C₂²	1	2	yes	complemented
30	C₅₉×#508	—	2	2	no	—
31	C₂×SD₃₂×C₅₉	C₂²	1	2	yes	complemented
32	C₂×D₁₆×C₅₉	C₂²	1	2	yes	complemented
33	C₂×M₃₂×C₅₉	C₂²	1	1	yes	characteristic, complemented
34	C₂×M₃₂×C₅₉	C₂²	1	1	yes	characteristic, complemented
35	C₅₉×#473	C₂²	1	2	yes	complemented
36	C₅₉×#472	C₂²	1	2	yes	complemented
37	C₅₉×#471	—	2	2	no	—
38	C₂×#108×C₅₉	C₂²	1	1	yes	characteristic, complemented
39	C₅₉×#413	—	2	1	no	—
40	C₅₉×#361	C₂²	1	4	yes	complemented
41	C₅₉×#359	C₂²	1	4	yes	complemented
42	C₅₉×#350	C₂²	1	4	yes	complemented
43	H(5,𝔽₂)×C₅₉	—	2	4	no	—
44	H(5,𝔽₂)×C₅₉	—	2	4	no	—
45	H(5,𝔽₂)×C₅₉	—	4	2	no	—
46	H(5,𝔽₂)×C₅₉	—	4	2	no	—
47	C₂×#41×C₅₉	—	2	2	no	—
48	C₂×#41×C₅₉	—	2	1	no	—
49	C₂×#41×C₅₉	—	2	1	no	—
50	C₂×#41×C₅₉	—	4	1	no	—
51	C₂×#41×C₅₉	D₄	1	1	yes	characteristic
52	C₂²×D₄×C₅₉	—	2	2	no	—
53	C₂²×D₄×C₅₉	—	2	1	no	—
54	C₂²×D₄×C₅₉	—	4	2	no	—
55	C₂²×D₄×C₅₉	—	4	1	no	—
56	#137×C₅₉	—	2	2	no	—
57	#137×C₅₉	—	4	1	no	—
58	AGL(1,ℤ/8)×C₅₉	—	2	4	no	—
59	AGL(1,ℤ/8)×C₅₉	—	2	8	no	—
60	AGL(1,ℤ/8)×C₅₉	—	2	8	no	—
61	AGL(1,ℤ/8)×C₅₉	—	2	2	no	—
62	AGL(1,ℤ/8)×C₅₉	—	2	4	no	—
63	AGL(1,ℤ/8)×C₅₉	—	4	1	no	—
64	#135×C₅₉	—	2	4	no	—
65	#135×C₅₉	—	2	4	no	—
66	#135×C₅₉	—	2	1	no	—
67	#135×C₅₉	—	2	1	no	—
68	#135×C₅₉	—	2	1	no	—
69	#135×C₅₉	—	2	1	no	—
70	#135×C₅₉	—	2	1	no	—
71	#135×C₅₉	—	2	1	no	—
72	#135×C₅₉	—	4	2	no	—
73	#135×C₅₉	D₄	1	2	yes	—
74	#135×C₅₉	C₂³	1	2	yes	—
75	C₂×Q₁₆×C₅₉	D₄	1	1	yes	characteristic
76	C₂×Q₁₆×C₅₉	C₂³	1	1	yes	characteristic, complemented
77	C₂×SD₁₆×C₅₉	—	2	2	no	—
78	C₂×SD₁₆×C₅₉	—	2	1	no	—
79	C₂×SD₁₆×C₅₉	—	2	1	no	—
80	C₂×D₈×C₅₉	—	2	2	no	—
81	C₂×D₈×C₅₉	—	2	4	no	—
82	C₂×D₈×C₅₉	—	2	4	no	—
83	C₂×D₈×C₅₉	—	2	1	no	—
84	C₂×D₈×C₅₉	—	2	1	no	—
85	C₂×D₈×C₅₉	—	2	1	no	—
86	C₂×D₈×C₅₉	D₄	1	1	yes	characteristic
87	C₂×D₈×C₅₉	D₄	1	2	yes	—
88	C₂×D₈×C₅₉	D₄	1	2	yes	—
89	C₂×D₈×C₅₉	C₂³	1	2	yes	—
90	C₂×D₈×C₅₉	C₂³	1	1	yes	characteristic, complemented
91	#131×C₅₉	—	2	1	no	—
92	#131×C₅₉	—	2	1	no	—
93	#131×C₅₉	D₄	1	2	yes	—
94	#131×C₅₉	C₂³	1	2	yes	—
95	C₂×M₁₆×C₅₉	—	2	1	no	—
96	C₂×M₁₆×C₅₉	—	2	1	no	—
97	C₂×M₁₆×C₅₉	D₄	1	1	yes	characteristic
98	C₂²×C₈×C₅₉	—	2	1	no	—
99	C₂²×C₈×C₅₉	C₂³	1	1	yes	characteristic
100	Q₃₂×C₅₉	—	2	2	no	—
101	SD₃₂×C₅₉	—	2	2	no	—
102	SD₃₂×C₅₉	—	2	4	no	—
103	SD₃₂×C₅₉	—	2	2	no	—
104	D₁₆×C₅₉	—	2	4	no	—
105	D₁₆×C₅₉	—	2	2	no	—
106	M₃₂×C₅₉	—	2	1	no	—
107	M₃₂×C₅₉	—	2	1	no	—
108	M₃₂×C₅₉	—	2	1	no	—
109	M₃₂×C₅₉	C₂³	1	2	yes	complemented
110	C₂×C₁₆×C₅₉	—	2	1	no	—
111	C₂×C₁₆×C₅₉	C₂³	1	2	yes	complemented
112	#108×C₅₉	—	2	1	no	—
113	#108×C₅₉	C₂³	1	2	yes	complemented
114	#101×C₅₉	—	2	2	no	—
115	#100×C₅₉	—	2	2	no	—
116	C₂⁴×C₅₉	—	4	2	no	—
117	C₂⁴×C₅₉	—	4	1	no	—
118	#41×C₅₉	—	2	1	no	—
119	#41×C₅₉	—	2	1	no	—
120	#41×C₅₉	—	2	8	no	—
121	#41×C₅₉	—	2	2	no	—
122	#41×C₅₉	—	2	2	no	—
123	#41×C₅₉	—	4	4	no	—
124	#41×C₅₉	—	4	4	no	—
125	#41×C₅₉	—	4	4	no	—
126	#41×C₅₉	—	4	1	no	—
127	#41×C₅₉	—	4	1	no	—
128	#41×C₅₉	—	4	1	no	—
129	#41×C₅₉	—	4	1	no	—
130	#41×C₅₉	—	4	1	no	—
131	#41×C₅₉	—	4	1	no	—
132	#41×C₅₉	D₈	1	2	yes	—
133	#41×C₅₉	C₂×D₄	1	2	yes	—
134	C₂×Q₈×C₅₉	—	2	1	no	—
135	C₂×Q₈×C₅₉	—	2	1	no	—
136	C₂×Q₈×C₅₉	D₈	1	1	yes	characteristic
137	C₂×D₄×C₅₉	—	2	1	no	—
138	C₂×D₄×C₅₉	—	2	8	no	—
139	C₂×D₄×C₅₉	—	2	1	no	—
140	C₂×D₄×C₅₉	—	2	2	no	—
141	C₂×D₄×C₅₉	—	2	2	no	—
142	C₂×D₄×C₅₉	—	2	2	no	—
143	C₂×D₄×C₅₉	—	2	1	no	—
144	C₂×D₄×C₅₉	—	4	2	no	—
145	C₂×D₄×C₅₉	—	4	4	no	—
146	C₂×D₄×C₅₉	—	4	8	no	—
147	C₂×D₄×C₅₉	—	4	8	no	—
148	C₂×D₄×C₅₉	—	4	4	no	—
149	C₂×D₄×C₅₉	—	4	2	no	—
150	C₂×D₄×C₅₉	—	4	1	no	—
151	C₂×D₄×C₅₉	—	4	4	no	—
152	C₂×D₄×C₅₉	—	4	1	no	—
153	C₂×D₄×C₅₉	—	4	1	no	—
154	C₂×D₄×C₅₉	—	4	1	no	—
155	C₂×D₄×C₅₉	—	4	1	no	—
156	C₂×D₄×C₅₉	D₈	1	1	yes	characteristic
157	C₂²×C₄×C₅₉	—	2	1	no	—
158	C₂²×C₄×C₅₉	—	4	2	no	—
159	C₂²×C₄×C₅₉	—	4	1	no	—
160	C₂²×C₄×C₅₉	—	4	1	no	—
161	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
162	Q₁₆×C₅₉	—	2	1	no	—
163	Q₁₆×C₅₉	—	2	1	no	—
164	Q₁₆×C₅₉	—	2	1	no	—
165	Q₁₆×C₅₉	—	4	2	no	—
166	Q₁₆×C₅₉	C₂×D₄	1	2	yes	—
167	SD₁₆×C₅₉	—	2	8	no	—
168	SD₁₆×C₅₉	—	2	2	no	—
169	SD₁₆×C₅₉	—	2	2	no	—
170	SD₁₆×C₅₉	—	4	2	no	—
171	SD₁₆×C₅₉	—	4	2	no	—
172	SD₁₆×C₅₉	—	4	1	no	—
173	SD₁₆×C₅₉	—	4	1	no	—
174	D₈×C₅₉	—	2	8	no	—
175	D₈×C₅₉	—	2	1	no	—
176	D₈×C₅₉	—	2	2	no	—
177	D₈×C₅₉	—	2	2	no	—
178	D₈×C₅₉	—	2	2	no	—
179	D₈×C₅₉	—	2	1	no	—
180	D₈×C₅₉	—	2	1	no	—
181	D₈×C₅₉	—	4	2	no	—
182	D₈×C₅₉	C₂×D₄	1	2	yes	—
183	D₈×C₅₉	C₂×D₄	1	4	yes	—
184	M₁₆×C₅₉	—	2	1	no	—
185	M₁₆×C₅₉	—	2	2	no	—
186	M₁₆×C₅₉	—	2	2	no	—
187	M₁₆×C₅₉	—	2	2	no	—
188	M₁₆×C₅₉	—	4	1	no	—
189	M₁₆×C₅₉	C₂×D₄	1	2	yes	—
190	C₂×C₈×C₅₉	—	2	1	no	—
191	C₂×C₈×C₅₉	—	2	2	no	—
192	C₂×C₈×C₅₉	—	2	2	no	—
193	C₂×C₈×C₅₉	—	4	1	no	—
194	C₂×C₈×C₅₉	C₂×D₄	1	1	yes	characteristic
195	C₂×C₈×C₅₉	C₂×D₄	1	1	yes	characteristic
196	C₂×C₈×C₅₉	C₂×D₄	1	1	yes	characteristic
197	C₂×C₈×C₅₉	C₂×D₄	1	1	yes	characteristic
198	C₂×C₈×C₅₉	C₂×D₄	1	1	yes	characteristic
199	C₂×C₈×C₅₉	C₂⁴	1	1	yes	characteristic
200	C₁₆×C₅₉	—	2	2	no	—
201	C₁₆×C₅₉	—	2	2	no	—
202	C₂³×C₅₉	—	2	1	no	—
203	C₂³×C₅₉	—	4	8	no	—
204	C₂³×C₅₉	—	4	2	no	—
205	C₂³×C₅₉	—	4	1	no	—
206	C₂³×C₅₉	—	4	2	no	—
207	C₂³×C₅₉	—	4	2	no	—
208	C₂³×C₅₉	—	4	1	no	—
209	C₂³×C₅₉	—	16	2	no	—
210	C₂³×C₅₉	—	16	4	no	—
211	C₂³×C₅₉	AGL(1,ℤ/8)	1	1	yes	characteristic
212	Q₈×C₅₉	—	2	1	no	—
213	Q₈×C₅₉	—	2	2	no	—
214	Q₈×C₅₉	—	4	1	no	—
215	Q₈×C₅₉	—	4	1	no	—
216	Q₈×C₅₉	—	4	1	no	—
217	Q₈×C₅₉	C₂×D₈	1	2	yes	—
218	D₄×C₅₉	—	2	2	no	—
219	D₄×C₅₉	—	2	2	no	—
220	D₄×C₅₉	—	2	2	no	—
221	D₄×C₅₉	—	2	4	no	—
222	D₄×C₅₉	—	2	1	no	—
223	D₄×C₅₉	—	4	8	no	—
224	D₄×C₅₉	—	4	8	no	—
225	D₄×C₅₉	—	4	2	no	—
226	D₄×C₅₉	—	4	2	no	—
227	D₄×C₅₉	—	4	1	no	—
228	D₄×C₅₉	—	4	2	no	—
229	D₄×C₅₉	—	4	1	no	—
230	D₄×C₅₉	—	4	1	no	—
231	D₄×C₅₉	—	4	2	no	—
232	D₄×C₅₉	—	4	2	no	—
233	D₄×C₅₉	—	8	1	no	—
234	D₄×C₅₉	—	8	1	no	—
235	D₄×C₅₉	C₂×D₈	1	2	yes	—
236	C₂×C₄×C₅₉	—	2	1	no	—
237	C₂×C₄×C₅₉	—	2	2	no	—
238	C₂×C₄×C₅₉	—	2	2	no	—
239	C₂×C₄×C₅₉	—	4	8	no	—
240	C₂×C₄×C₅₉	—	4	1	no	—
241	C₂×C₄×C₅₉	—	4	2	no	—
242	C₂×C₄×C₅₉	—	4	2	no	—
243	C₂×C₄×C₅₉	—	4	1	no	—
244	C₂×C₄×C₅₉	—	8	1	no	—
245	C₂×C₄×C₅₉	—	8	1	no	—
246	C₂×C₄×C₅₉	#120	1	1	yes	characteristic
247	C₂×C₄×C₅₉	#120	1	1	yes	characteristic
248	C₂×C₄×C₅₉	C₂×D₈	1	1	yes	characteristic
249	C₂×C₄×C₅₉	C₂×D₈	1	1	yes	characteristic
250	C₂×C₄×C₅₉	AGL(1,ℤ/8)	1	1	yes	characteristic
251	C₂×C₄×C₅₉	C₂²×D₄	1	1	yes	characteristic
252	C₈×C₅₉	—	2	2	no	—
253	C₈×C₅₉	—	4	2	no	—
254	C₈×C₅₉	#120	1	1	yes	characteristic
255	C₈×C₅₉	#120	1	1	yes	characteristic
256	C₈×C₅₉	C₂²×D₄	1	1	yes	characteristic
257	C₈×C₅₉	C₂²×D₄	1	1	yes	characteristic
258	#33539	C₅₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
259	C₂²×C₅₉	—	2	2	no	—
260	C₂²×C₅₉	—	4	1	no	—
261	C₂²×C₅₉	—	4	2	no	—
262	C₂²×C₅₉	—	4	4	no	—
263	C₂²×C₅₉	—	4	2	no	—
264	C₂²×C₅₉	—	8	4	no	—
265	C₂²×C₅₉	—	8	2	no	—
266	C₂²×C₅₉	—	8	1	no	—
267	C₂²×C₅₉	—	16	2	no	—
268	C₂²×C₅₉	—	16	2	no	—
269	C₂²×C₅₉	—	16	1	no	—
270	C₂²×C₅₉	—	16	8	no	—
271	C₂²×C₅₉	#447	1	1	yes	characteristic
272	C₂²×C₅₉	#447	1	1	yes	characteristic
273	C₂²×C₅₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
274	C₄×C₅₉	—	2	2	no	—
275	C₄×C₅₉	—	4	2	no	—
276	C₄×C₅₉	—	8	1	no	—
277	C₄×C₅₉	#447	1	1	yes	characteristic
278	C₄×C₅₉	#447	1	1	yes	characteristic
279	C₄×C₅₉	C₂×#120	1	1	yes	characteristic
280	C₄×C₅₉	C₂²×D₈	1	1	yes	characteristic
281	C₂×#576	C₂×C₅₉	1	1	yes	characteristic, complemented
282	#3414	C₂×C₅₉	1	1	yes	characteristic, complemented
283	C₂×#509	C₂×C₅₉	1	1	yes	characteristic, complemented
284	#3067	C₂×C₅₉	1	1	yes	characteristic, complemented
285	#2194	C₂×C₅₉	1	4	yes	complemented
286	#2192	C₂×C₅₉	1	4	yes	complemented
287	C₂×#361	C₂×C₅₉	1	1	yes	characteristic, complemented
288	#2143	C₂×C₅₉	1	1	yes	characteristic, complemented
289	#2117	C₂×C₅₉	1	1	yes	characteristic, complemented
290	C₂×C₅₉	—	2	1	no	—
291	C₂×C₅₉	—	2	1	no	—
292	C₂×C₅₉	—	2	1	no	—
293	C₂×C₅₉	—	4	2	no	—
294	C₂×C₅₉	—	8	4	no	—
295	C₂×C₅₉	—	8	2	no	—
296	C₂×C₅₉	—	16	1	no	—
297	C₂×C₅₉	C₂×#447	1	1	yes	characteristic
298	C₂×H(5,𝔽₂)	—	2	1	no	—
299	#576	—	2	2	no	—
300	#576	—	2	2	no	—
301	#576	—	2	2	no	—
302	#576	C₂²×C₅₉	1	4	yes	—
303	#575	—	2	1	no	—
304	C₂×AGL(1,ℤ/8)	—	2	2	no	—
305	C₂×AGL(1,ℤ/8)	—	2	1	no	—
306	C₂×#135	—	2	1	no	—
307	C₂×#135	C₂²×C₅₉	1	1	yes	characteristic
308	C₂×#135	C₂²×C₅₉	1	1	yes	characteristic, complemented
309	C₂²×D₈	—	2	1	no	—
310	C₂²×D₈	C₂²×C₅₉	1	1	yes	characteristic
311	C₂×#131	C₂²×C₅₉	1	1	yes	characteristic
312	#510	—	2	1	no	—
313	#510	C₂²×C₅₉	1	2	yes	complemented
314	#509	—	2	2	no	—
315	#509	—	2	2	no	—
316	#509	—	2	1	no	—
317	#509	C₂²×C₅₉	1	2	yes	complemented
318	#508	—	2	2	no	—
319	C₂×SD₃₂	C₂²×C₅₉	1	2	yes	complemented
320	C₂×D₁₆	C₂²×C₅₉	1	2	yes	complemented
321	C₂×M₃₂	C₂²×C₅₉	1	1	yes	characteristic, complemented
322	C₂×M₃₂	C₂²×C₅₉	1	1	yes	characteristic, complemented
323	#473	C₂²×C₅₉	1	2	yes	complemented
324	#472	C₂²×C₅₉	1	2	yes	complemented
325	#471	—	2	2	no	—
326	C₂×#108	C₂²×C₅₉	1	1	yes	characteristic, complemented
327	#413	—	2	1	no	—
328	#361	C₂²×C₅₉	1	4	yes	complemented
329	#359	C₂²×C₅₉	1	4	yes	complemented
330	#350	C₂²×C₅₉	1	4	yes	complemented
331	C₅₉	#33539	1	1	yes	characteristic, direct product factor, Sylow
332	H(5,𝔽₂)	—	2	4	no	—
333	H(5,𝔽₂)	—	2	4	no	—
334	H(5,𝔽₂)	—	4	2	no	—
335	H(5,𝔽₂)	—	4	2	no	—
336	C₂×#41	—	2	2	no	—
337	C₂×#41	—	2	1	no	—
338	C₂×#41	—	2	1	no	—
339	C₂×#41	—	4	1	no	—
340	C₂×#41	D₄×C₅₉	1	1	yes	characteristic
341	C₂²×D₄	—	2	2	no	—
342	C₂²×D₄	—	2	1	no	—
343	C₂²×D₄	—	4	2	no	—
344	C₂²×D₄	—	4	1	no	—
345	#137	—	2	2	no	—
346	#137	—	4	1	no	—
347	AGL(1,ℤ/8)	—	2	4	no	—
348	AGL(1,ℤ/8)	—	2	8	no	—
349	AGL(1,ℤ/8)	—	2	8	no	—
350	AGL(1,ℤ/8)	—	2	2	no	—
351	AGL(1,ℤ/8)	—	2	4	no	—
352	AGL(1,ℤ/8)	—	4	1	no	—
353	#135	—	2	4	no	—
354	#135	—	2	4	no	—
355	#135	—	2	1	no	—
356	#135	—	2	1	no	—
357	#135	—	2	1	no	—
358	#135	—	2	1	no	—
359	#135	—	2	1	no	—
360	#135	—	2	1	no	—
361	#135	—	4	2	no	—
362	#135	D₄×C₅₉	1	2	yes	—
363	#135	C₂³×C₅₉	1	2	yes	—
364	C₂×Q₁₆	D₄×C₅₉	1	1	yes	characteristic
365	C₂×Q₁₆	C₂³×C₅₉	1	1	yes	characteristic, complemented
366	C₂×SD₁₆	—	2	2	no	—
367	C₂×SD₁₆	—	2	1	no	—
368	C₂×SD₁₆	—	2	1	no	—
369	C₂×D₈	—	2	2	no	—
370	C₂×D₈	—	2	4	no	—
371	C₂×D₈	—	2	4	no	—
372	C₂×D₈	—	2	1	no	—
373	C₂×D₈	—	2	1	no	—
374	C₂×D₈	—	2	1	no	—
375	C₂×D₈	D₄×C₅₉	1	1	yes	characteristic
376	C₂×D₈	D₄×C₅₉	1	2	yes	—
377	C₂×D₈	D₄×C₅₉	1	2	yes	—
378	C₂×D₈	C₂³×C₅₉	1	2	yes	—
379	C₂×D₈	C₂³×C₅₉	1	1	yes	characteristic, complemented
380	#131	—	2	1	no	—
381	#131	—	2	1	no	—
382	#131	D₄×C₅₉	1	2	yes	—
383	#131	C₂³×C₅₉	1	2	yes	—
384	C₂×M₁₆	—	2	1	no	—
385	C₂×M₁₆	—	2	1	no	—
386	C₂×M₁₆	D₄×C₅₉	1	1	yes	characteristic
387	C₂²×C₈	—	2	1	no	—
388	C₂²×C₈	C₂³×C₅₉	1	1	yes	characteristic
389	Q₃₂	—	2	2	no	—
390	SD₃₂	—	2	2	no	—
391	SD₃₂	—	2	4	no	—
392	SD₃₂	—	2	2	no	—
393	D₁₆	—	2	4	no	—
394	D₁₆	—	2	2	no	—
395	M₃₂	—	2	1	no	—
396	M₃₂	—	2	1	no	—
397	M₃₂	—	2	1	no	—
398	M₃₂	C₂³×C₅₉	1	2	yes	complemented
399	C₂×C₁₆	—	2	1	no	—
400	C₂×C₁₆	C₂³×C₅₉	1	2	yes	complemented
401	#108	—	2	1	no	—
402	#108	C₂³×C₅₉	1	2	yes	complemented
403	#101	—	2	2	no	—
404	#100	—	2	2	no	—
405	C₂⁴	—	4	2	no	—
406	C₂⁴	—	4	1	no	—
407	#41	—	2	1	no	—
408	#41	—	2	1	no	—
409	#41	—	2	8	no	—
410	#41	—	2	2	no	—
411	#41	—	2	2	no	—
412	#41	—	4	4	no	—
413	#41	—	4	4	no	—
414	#41	—	4	4	no	—
415	#41	—	4	1	no	—
416	#41	—	4	1	no	—
417	#41	—	4	1	no	—
418	#41	—	4	1	no	—
419	#41	—	4	1	no	—
420	#41	—	4	1	no	—
421	#41	D₈×C₅₉	1	2	yes	—
422	#41	C₂×D₄×C₅₉	1	2	yes	—
423	C₂×Q₈	—	2	1	no	—
424	C₂×Q₈	—	2	1	no	—
425	C₂×Q₈	D₈×C₅₉	1	1	yes	characteristic
426	C₂×D₄	—	2	1	no	—
427	C₂×D₄	—	2	8	no	—
428	C₂×D₄	—	2	1	no	—
429	C₂×D₄	—	2	2	no	—
430	C₂×D₄	—	2	2	no	—
431	C₂×D₄	—	2	2	no	—
432	C₂×D₄	—	2	1	no	—
433	C₂×D₄	—	4	2	no	—
434	C₂×D₄	—	4	4	no	—
435	C₂×D₄	—	4	8	no	—
436	C₂×D₄	—	4	8	no	—
437	C₂×D₄	—	4	4	no	—
438	C₂×D₄	—	4	2	no	—
439	C₂×D₄	—	4	1	no	—
440	C₂×D₄	—	4	4	no	—
441	C₂×D₄	—	4	1	no	—
442	C₂×D₄	—	4	1	no	—
443	C₂×D₄	—	4	1	no	—
444	C₂×D₄	—	4	1	no	—
445	C₂×D₄	D₈×C₅₉	1	1	yes	characteristic
446	C₂²×C₄	—	2	1	no	—
447	C₂²×C₄	—	4	2	no	—
448	C₂²×C₄	—	4	1	no	—
449	C₂²×C₄	—	4	1	no	—
450	C₂²×C₄	C₂×D₄×C₅₉	1	1	yes	characteristic
451	Q₁₆	—	2	1	no	—
452	Q₁₆	—	2	1	no	—
453	Q₁₆	—	2	1	no	—
454	Q₁₆	—	4	2	no	—
455	Q₁₆	C₂×D₄×C₅₉	1	2	yes	—
456	SD₁₆	—	2	8	no	—
457	SD₁₆	—	2	2	no	—
458	SD₁₆	—	2	2	no	—
459	SD₁₆	—	4	2	no	—
460	SD₁₆	—	4	2	no	—
461	SD₁₆	—	4	1	no	—
462	SD₁₆	—	4	1	no	—
463	D₈	—	2	8	no	—
464	D₈	—	2	1	no	—
465	D₈	—	2	2	no	—
466	D₈	—	2	2	no	—
467	D₈	—	2	2	no	—
468	D₈	—	2	1	no	—
469	D₈	—	2	1	no	—
470	D₈	—	4	2	no	—
471	D₈	C₂×D₄×C₅₉	1	2	yes	—
472	D₈	C₂×D₄×C₅₉	1	4	yes	—
473	M₁₆	—	2	1	no	—
474	M₁₆	—	2	2	no	—
475	M₁₆	—	2	2	no	—
476	M₁₆	—	2	2	no	—
477	M₁₆	—	4	1	no	—
478	M₁₆	C₂×D₄×C₅₉	1	2	yes	—
479	C₂×C₈	—	2	1	no	—
480	C₂×C₈	—	2	2	no	—
481	C₂×C₈	—	2	2	no	—
482	C₂×C₈	—	4	1	no	—
483	C₂×C₈	C₂×D₄×C₅₉	1	1	yes	characteristic
484	C₂×C₈	C₂×D₄×C₅₉	1	1	yes	characteristic
485	C₂×C₈	C₂×D₄×C₅₉	1	1	yes	characteristic
486	C₂×C₈	C₂×D₄×C₅₉	1	1	yes	characteristic
487	C₂×C₈	C₂×D₄×C₅₉	1	1	yes	characteristic
488	C₂×C₈	C₂⁴×C₅₉	1	1	yes	characteristic
489	C₁₆	—	2	2	no	—
490	C₁₆	—	2	2	no	—
491	C₂³	—	2	1	no	—
492	C₂³	—	4	8	no	—
493	C₂³	—	4	2	no	—
494	C₂³	—	4	1	no	—
495	C₂³	—	4	2	no	—
496	C₂³	—	4	2	no	—
497	C₂³	—	4	1	no	—
498	C₂³	—	16	2	no	—
499	C₂³	—	16	4	no	—
500	C₂³	AGL(1,ℤ/8)×C₅₉	1	1	yes	characteristic
501	Q₈	—	2	1	no	—
502	Q₈	—	2	2	no	—
503	Q₈	—	4	1	no	—
504	Q₈	—	4	1	no	—
505	Q₈	—	4	1	no	—
506	Q₈	C₂×D₈×C₅₉	1	2	yes	—
507	D₄	—	2	2	no	—
508	D₄	—	2	2	no	—
509	D₄	—	2	1	no	—
510	D₄	—	2	2	no	—
511	D₄	—	2	4	no	—
512	D₄	—	4	8	no	—
513	D₄	—	4	8	no	—
514	D₄	—	4	2	no	—
515	D₄	—	4	2	no	—
516	D₄	—	4	1	no	—
517	D₄	—	4	2	no	—
518	D₄	—	4	2	no	—
519	D₄	—	4	1	no	—
520	D₄	—	4	2	no	—
521	D₄	—	4	1	no	—
522	D₄	—	8	1	no	—
523	D₄	—	8	1	no	—
524	D₄	C₂×D₈×C₅₉	1	2	yes	—
525	C₂×C₄	—	2	1	no	—
526	C₂×C₄	—	2	2	no	—
527	C₂×C₄	—	2	2	no	—
528	C₂×C₄	—	4	8	no	—
529	C₂×C₄	—	4	1	no	—
530	C₂×C₄	—	4	2	no	—
531	C₂×C₄	—	4	2	no	—
532	C₂×C₄	—	4	1	no	—
533	C₂×C₄	—	8	1	no	—
534	C₂×C₄	—	8	1	no	—
535	C₂×C₄	#120×C₅₉	1	1	yes	characteristic
536	C₂×C₄	#120×C₅₉	1	1	yes	characteristic
537	C₂×C₄	C₂×D₈×C₅₉	1	1	yes	characteristic
538	C₂×C₄	C₂×D₈×C₅₉	1	1	yes	characteristic
539	C₂×C₄	AGL(1,ℤ/8)×C₅₉	1	1	yes	characteristic
540	C₂×C₄	C₂²×D₄×C₅₉	1	1	yes	characteristic
541	C₈	—	2	2	no	—
542	C₈	—	4	2	no	—
543	C₈	#120×C₅₉	1	1	yes	characteristic
544	C₈	#120×C₅₉	1	1	yes	characteristic
545	C₈	C₂²×D₄×C₅₉	1	1	yes	characteristic
546	C₈	C₂²×D₄×C₅₉	1	1	yes	characteristic
547	C₂²	—	2	2	no	—
548	C₂²	—	4	1	no	—
549	C₂²	—	4	2	no	—
550	C₂²	—	4	4	no	—
551	C₂²	—	4	2	no	—
552	C₂²	—	8	4	no	—
553	C₂²	—	8	2	no	—
554	C₂²	—	8	1	no	—
555	C₂²	—	16	2	no	—
556	C₂²	—	16	2	no	—
557	C₂²	—	16	1	no	—
558	C₂²	—	16	8	no	—
559	C₂²	C₅₉×#447	1	1	yes	characteristic
560	C₂²	C₅₉×#447	1	1	yes	characteristic
561	C₂²	C₂×AGL(1,ℤ/8)×C₅₉	1	1	yes	characteristic
562	C₄	—	2	2	no	—
563	C₄	—	4	2	no	—
564	C₄	—	8	1	no	—
565	C₄	C₅₉×#447	1	1	yes	characteristic
566	C₄	C₅₉×#447	1	1	yes	characteristic
567	C₄	C₂×#120×C₅₉	1	1	yes	characteristic
568	C₄	C₂²×D₈×C₅₉	1	1	yes	characteristic
569	C₂	—	2	1	no	—
570	C₂	—	2	1	no	—
571	C₂	—	2	1	no	—
572	C₂	—	4	2	no	—
573	C₂	—	8	4	no	—
574	C₂	—	8	2	no	—
575	C₂	—	16	1	no	—
576	C₂	C₂×C₅₉×#447	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂×C₅₉	C₂×#447
commutator, Frattini, cosocle	C₂×C₈	C₂⁴×C₅₉
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₅₉ ◁ C₂²×C₄×C₅₉ ◁ C₂×#131×C₅₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₅₉×#576	C₂	semidirect
2. C₅₉×#3414	C₂	semidirect
3. C₂×C₅₉×#509	C₂	semidirect
4. C₅₉×#3067	C₂	semidirect
5. C₅₉×#2194	C₂	semidirect
6. C₅₉×#2192	C₂	semidirect
7. C₂×C₅₉×#361	C₂	semidirect
8. C₅₉×#2143	C₂	semidirect
9. C₅₉×#2117	C₂	semidirect
20. C₂×#135×C₅₉	C₂²	semidirect
25. C₅₉×#510	C₂²	semidirect
29. C₅₉×#509	C₂²	semidirect
31. C₂×SD₃₂×C₅₉	C₂²	semidirect
32. C₂×D₁₆×C₅₉	C₂²	semidirect
33. C₂×M₃₂×C₅₉	C₂²	semidirect
34. C₂×M₃₂×C₅₉	C₂²	semidirect
35. C₅₉×#473	C₂²	semidirect
36. C₅₉×#472	C₂²	semidirect
38. C₂×#108×C₅₉	C₂²	semidirect
40. C₅₉×#361	C₂²	semidirect
41. C₅₉×#359	C₂²	semidirect
42. C₅₉×#350	C₂²	semidirect
76. C₂×Q₁₆×C₅₉	C₂³	semidirect
90. C₂×D₈×C₅₉	C₂³	semidirect
109. M₃₂×C₅₉	C₂³	semidirect
111. C₂×C₁₆×C₅₉	C₂³	semidirect
113. #108×C₅₉	C₂³	semidirect
258. #33539	C₅₉	direct (N × H)
281. C₂×#576	C₂×C₅₉	semidirect
282. #3414	C₂×C₅₉	semidirect
283. C₂×#509	C₂×C₅₉	semidirect
284. #3067	C₂×C₅₉	semidirect
285. #2194	C₂×C₅₉	semidirect
286. #2192	C₂×C₅₉	semidirect
287. C₂×#361	C₂×C₅₉	semidirect
288. #2143	C₂×C₅₉	semidirect
289. #2117	C₂×C₅₉	semidirect
308. C₂×#135	C₂²×C₅₉	semidirect
313. #510	C₂²×C₅₉	semidirect
317. #509	C₂²×C₅₉	semidirect
319. C₂×SD₃₂	C₂²×C₅₉	semidirect
320. C₂×D₁₆	C₂²×C₅₉	semidirect
321. C₂×M₃₂	C₂²×C₅₉	semidirect
322. C₂×M₃₂	C₂²×C₅₉	semidirect
323. #473	C₂²×C₅₉	semidirect
324. #472	C₂²×C₅₉	semidirect
326. C₂×#108	C₂²×C₅₉	semidirect
328. #361	C₂²×C₅₉	semidirect
329. #359	C₂²×C₅₉	semidirect
330. #350	C₂²×C₅₉	semidirect
331. C₅₉	#33539	direct (N × H)
365. C₂×Q₁₆	C₂³×C₅₉	semidirect
379. C₂×D₈	C₂³×C₅₉	semidirect
398. M₃₂	C₂³×C₅₉	semidirect
400. C₂×C₁₆	C₂³×C₅₉	semidirect
402. #108	C₂³×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×#576	2
C₅₉×#3414	2
C₂×C₅₉×#509	2
C₅₉×#3067	2
C₅₉×#2194	2
C₅₉×#2192	2
C₂×C₅₉×#361	2
C₅₉×#2143	2
C₅₉×#2117	2
#33539	59

Subgroups — C59×#33539 #28445648

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₉×#33539 #28445648