Subgroups — C₂×C₅₉×#2192 #28445643

Order 15104.

1150 conjugacy classes of subgroups.

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

	subgroup	G/H
center, socle	C₂²×C₅₉	#447
commutator, Frattini, cosocle	C₂×C₈	C₂⁴×C₅₉
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×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. C₂×C₅₉×#509	C₂	semidirect
3. C₂²×D₁₆×C₅₉	C₂	semidirect
4. C₂×C₅₉×#472	C₂	semidirect
5. C₅₉×#2192	C₂	direct (N × H)
6. C₂×C₅₉×#361	C₂	semidirect
7. C₂×C₅₉×#359	C₂	semidirect
8. C₂×C₅₉×#350	C₂	semidirect
13. C₅₉×#576	C₂²	semidirect
21. C₂²×D₈×C₅₉	C₂²	semidirect
24. C₅₉×#509	C₂²	semidirect
29. C₂×D₁₆×C₅₉	C₂²	semidirect
30. C₂×M₃₂×C₅₉	C₂²	semidirect
31. C₂²×C₁₆×C₅₉	C₂²	semidirect
33. C₅₉×#472	C₂²	semidirect
34. C₂×#108×C₅₉	C₂²	semidirect
36. C₅₉×#361	C₂²	semidirect
37. C₅₉×#359	C₂²	semidirect
38. C₅₉×#350	C₂²	semidirect
84. C₂×D₈×C₅₉	C₂³	semidirect
98. M₃₂×C₅₉	C₂³	semidirect
102. C₂×C₁₆×C₅₉	C₂³	semidirect
104. #108×C₅₉	C₂³	semidirect
241. C₂×#2192	C₅₉	direct (N × H)
265. C₂×#576	C₂×C₅₉	semidirect
266. C₂×#509	C₂×C₅₉	semidirect
267. C₂²×D₁₆	C₂×C₅₉	semidirect
268. C₂×#472	C₂×C₅₉	semidirect
269. #2192	C₂×C₅₉	direct (N × H)
270. C₂×#361	C₂×C₅₉	semidirect
271. C₂×#359	C₂×C₅₉	semidirect
272. C₂×#350	C₂×C₅₉	semidirect
279. C₂×C₅₉	#2192	direct (N × H)
285. #576	C₂²×C₅₉	semidirect
293. C₂²×D₈	C₂²×C₅₉	semidirect
296. #509	C₂²×C₅₉	semidirect
301. C₂×D₁₆	C₂²×C₅₉	semidirect
302. C₂×M₃₂	C₂²×C₅₉	semidirect
303. C₂²×C₁₆	C₂²×C₅₉	semidirect
305. #472	C₂²×C₅₉	semidirect
306. C₂×#108	C₂²×C₅₉	semidirect
308. #361	C₂²×C₅₉	semidirect
309. #359	C₂²×C₅₉	semidirect
310. #350	C₂²×C₅₉	semidirect
311. C₅₉	C₂×#2192	direct (N × H)
357. C₂×D₈	C₂³×C₅₉	semidirect
371. M₃₂	C₂³×C₅₉	semidirect
375. C₂×C₁₆	C₂³×C₅₉	semidirect
377. #108	C₂³×C₅₉	semidirect
543. C₂	C₅₉×#2192	direct (N × H)

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
C₂×C₅₉×#509	2
C₂²×D₁₆×C₅₉	2
C₂×C₅₉×#472	2
C₅₉×#2192	2
C₂×C₅₉×#361	2
C₂×C₅₉×#359	2
C₂×C₅₉×#350	2
C₂×#2192	59

Subgroups — C2×C59×#2192 #28445643

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅₉×#2192 #28445643