Subgroups — C₂×C₅₉×#1929 #28433178

Order 15104.

1082 conjugacy classes of subgroups.

The subgroup lattice has 534 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#108×C₅₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×#104×C₅₉	C₂	1	1	yes	maximal, characteristic
3	C₂×C₅₉×#416	C₂	1	1	yes	maximal, characteristic
4	C₂×C₅₉×#408	C₂	1	1	yes	maximal, characteristic
5	C₂×C₅₉×#405	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅₉×#1929	C₂	1	8	yes	maximal, direct product factor
7	C₂×C₅₉×#339	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₅₉×#336	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂²×#41×C₅₉	C₂²	1	1	yes	characteristic
10	C₂²×M₁₆×C₅₉	C₂²	1	1	yes	characteristic
11	C₂²×M₁₆×C₅₉	C₂²	1	1	yes	characteristic
12	C₂³×C₈×C₅₉	C₂²	1	1	yes	characteristic
13	C₂³×C₈×C₅₉	C₂²	1	1	yes	characteristic
14	C₂×#117×C₅₉	C₂²	1	1	yes	characteristic
15	C₂²×C₄²×C₅₉	C₂²	1	1	yes	characteristic
16	C₂×#108×C₅₉	—	2	4	no	—
17	C₂×#108×C₅₉	C₂²	1	4	yes	complemented
18	C₂×#104×C₅₉	—	2	4	no	—
19	C₂×#104×C₅₉	C₂²	1	4	yes	—
20	C₅₉×#416	C₄	1	4	yes	complemented
21	C₅₉×#416	C₂²	1	4	yes	—
22	C₂×#103×C₅₉	C₄	1	1	yes	characteristic, complemented
23	C₂×#103×C₅₉	C₄	1	1	yes	characteristic, complemented
24	C₂×#102×C₅₉	C₄	1	1	yes	characteristic, complemented
25	C₂×#102×C₅₉	C₄	1	1	yes	characteristic, complemented
26	C₅₉×#408	—	2	2	no	—
27	C₅₉×#408	C₂²	1	4	yes	—
28	C₂×C₂²⋊C₈×C₅₉	—	2	1	no	—
29	C₂×C₂²⋊C₈×C₅₉	—	2	1	no	—
30	C₅₉×#405	—	2	2	no	—
31	C₅₉×#405	C₂²	1	4	yes	complemented
32	C₂×#97×C₅₉	—	2	1	no	—
33	C₂×C₄×C₈×C₅₉	—	2	1	no	—
34	C₅₉×#339	C₂²	1	4	yes	complemented
35	C₅₉×#336	C₂²	1	4	yes	complemented
36	C₂×#41×C₅₉	—	2	1	no	—
37	C₂×#41×C₅₉	—	2	1	no	—
38	C₂×#41×C₅₉	—	2	2	no	—
39	C₂×#41×C₅₉	—	2	2	no	—
40	C₂×#41×C₅₉	—	2	2	no	—
41	C₂×#41×C₅₉	—	2	2	no	—
42	C₂×#41×C₅₉	C₂×C₄	1	2	yes	—
43	C₂×#41×C₅₉	C₂³	1	2	yes	—
44	C₂²×Q₈×C₅₉	C₂×C₄	1	1	yes	characteristic
45	C₂²×D₄×C₅₉	—	2	1	no	—
46	C₂²×D₄×C₅₉	C₂×C₄	1	1	yes	characteristic
47	C₂³×C₄×C₅₉	—	2	1	no	—
48	C₂³×C₄×C₅₉	—	2	1	no	—
49	C₂³×C₄×C₅₉	C₂³	1	1	yes	characteristic
50	C₂×M₁₆×C₅₉	—	2	1	no	—
51	C₂×M₁₆×C₅₉	—	2	2	no	—
52	C₂×M₁₆×C₅₉	—	2	1	no	—
53	C₂×M₁₆×C₅₉	—	2	2	no	—
54	C₂×M₁₆×C₅₉	—	2	2	no	—
55	C₂×M₁₆×C₅₉	D₄	1	4	yes	—
56	C₂×M₁₆×C₅₉	C₂³	1	2	yes	—
57	C₂×M₁₆×C₅₉	C₂³	1	2	yes	—
58	C₂²×C₈×C₅₉	—	2	2	no	—
59	C₂²×C₈×C₅₉	—	2	1	no	—
60	C₂²×C₈×C₅₉	—	2	2	no	—
61	C₂²×C₈×C₅₉	—	2	2	no	—
62	C₂²×C₈×C₅₉	—	2	2	no	—
63	C₂²×C₈×C₅₉	—	2	1	no	—
64	C₂²×C₈×C₅₉	C₂×C₄	1	1	yes	characteristic
65	C₂²×C₈×C₅₉	C₂×C₄	1	1	yes	characteristic
66	C₂²×C₈×C₅₉	C₂×C₄	1	2	yes	—
67	C₂²×C₈×C₅₉	D₄	1	2	yes	—
68	C₂²×C₈×C₅₉	D₄	1	1	yes	characteristic
69	C₂²×C₈×C₅₉	D₄	1	1	yes	characteristic
70	C₂²×C₈×C₅₉	C₂³	1	2	yes	—
71	C₂²×C₈×C₅₉	C₂³	1	2	yes	—
72	#117×C₅₉	—	2	1	no	—
73	#117×C₅₉	—	2	1	no	—
74	#117×C₅₉	C₂×C₄	1	2	yes	—
75	#117×C₅₉	C₂³	1	2	yes	—
76	C₂×C₄⋊C₄×C₅₉	C₂×C₄	1	1	yes	characteristic
77	C₂×C₄⋊C₄×C₅₉	C₂×C₄	1	1	yes	characteristic
78	C₂×C₂²⋊C₄×C₅₉	—	2	1	no	—
79	C₂×C₄²×C₅₉	—	2	1	no	—
80	C₂×C₄²×C₅₉	—	2	2	no	—
81	C₂×C₄²×C₅₉	—	2	2	no	—
82	C₂×C₄²×C₅₉	—	2	1	no	—
83	C₂×C₄²×C₅₉	C₂³	1	2	yes	—
84	#108×C₅₉	—	2	8	no	—
85	#104×C₅₉	—	2	8	no	—
86	#103×C₅₉	C₂×C₄	1	4	yes	complemented
87	#103×C₅₉	C₂×C₄	1	4	yes	complemented
88	#102×C₅₉	C₂×C₄	1	4	yes	complemented
89	#102×C₅₉	C₂×C₄	1	4	yes	complemented
90	C₂²⋊C₈×C₅₉	—	2	4	no	—
91	C₂²⋊C₈×C₅₉	—	2	4	no	—
92	#97×C₅₉	—	2	4	no	—
93	C₄×C₈×C₅₉	—	2	4	no	—
94	C₂⁴×C₅₉	—	2	1	no	—
95	C₂⁴×C₅₉	#41	1	1	yes	characteristic
96	#41×C₅₉	—	2	4	no	—
97	#41×C₅₉	—	2	4	no	—
98	#41×C₅₉	—	2	2	no	—
99	#41×C₅₉	—	2	2	no	—
100	#41×C₅₉	—	2	2	no	—
101	#41×C₅₉	—	2	2	no	—
102	#41×C₅₉	—	4	2	no	—
103	#41×C₅₉	—	4	2	no	—
104	#41×C₅₉	—	4	2	no	—
105	#41×C₅₉	—	4	2	no	—
106	C₂×Q₈×C₅₉	—	2	1	no	—
107	C₂×Q₈×C₅₉	—	2	2	no	—
108	C₂×Q₈×C₅₉	—	2	2	no	—
109	C₂×Q₈×C₅₉	C₂²×C₄	1	2	yes	—
110	C₂×D₄×C₅₉	—	2	2	no	—
111	C₂×D₄×C₅₉	—	2	2	no	—
112	C₂×D₄×C₅₉	—	2	2	no	—
113	C₂×D₄×C₅₉	—	2	2	no	—
114	C₂×D₄×C₅₉	—	2	1	no	—
115	C₂×D₄×C₅₉	—	4	2	no	—
116	C₂×D₄×C₅₉	—	4	2	no	—
117	C₂×D₄×C₅₉	C₂²×C₄	1	2	yes	—
118	C₂²×C₄×C₅₉	—	2	4	no	—
119	C₂²×C₄×C₅₉	—	2	1	no	—
120	C₂²×C₄×C₅₉	—	2	1	no	—
121	C₂²×C₄×C₅₉	—	2	1	no	—
122	C₂²×C₄×C₅₉	—	2	2	no	—
123	C₂²×C₄×C₅₉	—	2	2	no	—
124	C₂²×C₄×C₅₉	—	2	2	no	—
125	C₂²×C₄×C₅₉	—	4	2	no	—
126	C₂²×C₄×C₅₉	—	4	2	no	—
127	C₂²×C₄×C₅₉	—	4	2	no	—
128	C₂²×C₄×C₅₉	—	4	2	no	—
129	C₂²×C₄×C₅₉	C₂²×C₄	1	1	yes	characteristic
130	C₂²×C₄×C₅₉	C₂²×C₄	1	1	yes	characteristic
131	C₂²×C₄×C₅₉	C₂×D₄	1	2	yes	—
132	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
133	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
134	C₂²×C₄×C₅₉	#41	1	2	yes	—
135	C₂²×C₄×C₅₉	#41	1	2	yes	—
136	C₂²×C₄×C₅₉	#41	1	2	yes	—
137	C₂²×C₄×C₅₉	#41	1	1	yes	characteristic
138	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
139	M₁₆×C₅₉	—	2	4	no	—
140	M₁₆×C₅₉	—	2	2	no	—
141	M₁₆×C₅₉	—	2	2	no	—
142	M₁₆×C₅₉	—	2	2	no	—
143	M₁₆×C₅₉	—	4	2	no	—
144	M₁₆×C₅₉	C₂×D₄	1	4	yes	—
145	C₂×C₈×C₅₉	—	2	2	no	—
146	C₂×C₈×C₅₉	—	2	2	no	—
147	C₂×C₈×C₅₉	—	2	4	no	—
148	C₂×C₈×C₅₉	—	2	4	no	—
149	C₂×C₈×C₅₉	—	2	2	no	—
150	C₂×C₈×C₅₉	—	2	2	no	—
151	C₂×C₈×C₅₉	—	2	4	no	—
152	C₂×C₈×C₅₉	—	2	2	no	—
153	C₂×C₈×C₅₉	—	2	2	no	—
154	C₂×C₈×C₅₉	—	2	2	no	—
155	C₂×C₈×C₅₉	—	2	2	no	—
156	C₂×C₈×C₅₉	—	2	2	no	—
157	C₂×C₈×C₅₉	—	2	2	no	—
158	C₂×C₈×C₅₉	—	4	2	no	—
159	C₂×C₈×C₅₉	C₂²×C₄	1	2	yes	—
160	C₂×C₈×C₅₉	C₂²×C₄	1	2	yes	—
161	C₂×C₈×C₅₉	C₂×D₄	1	2	yes	—
162	C₂×C₈×C₅₉	C₂×D₄	1	2	yes	—
163	C₄⋊C₄×C₅₉	—	2	1	no	—
164	C₄⋊C₄×C₅₉	—	2	1	no	—
165	C₄⋊C₄×C₅₉	C₂²×C₄	1	2	yes	—
166	C₄⋊C₄×C₅₉	C₂²×C₄	1	2	yes	—
167	C₂²⋊C₄×C₅₉	—	2	2	no	—
168	C₂²⋊C₄×C₅₉	—	2	2	no	—
169	C₄²×C₅₉	—	2	2	no	—
170	C₄²×C₅₉	—	2	2	no	—
171	C₄²×C₅₉	—	2	2	no	—
172	C₄²×C₅₉	—	2	2	no	—
173	C₄²×C₅₉	—	4	2	no	—
174	C₂³×C₅₉	—	2	2	no	—
175	C₂³×C₅₉	—	2	2	no	—
176	C₂³×C₅₉	—	2	2	no	—
177	C₂³×C₅₉	—	4	2	no	—
178	C₂³×C₅₉	—	4	2	no	—
179	C₂³×C₅₉	—	4	2	no	—
180	C₂³×C₅₉	C₄×D₄	1	1	yes	characteristic
181	C₂³×C₅₉	C₄×D₄	1	1	yes	characteristic
182	C₂³×C₅₉	#124	1	2	yes	—
183	C₂³×C₅₉	#126	1	2	yes	—
184	C₂³×C₅₉	C₂×#41	1	1	yes	characteristic
185	Q₈×C₅₉	—	2	2	no	—
186	Q₈×C₅₉	—	2	2	no	—
187	Q₈×C₅₉	—	4	2	no	—
188	D₄×C₅₉	—	2	2	no	—
189	D₄×C₅₉	—	2	2	no	—
190	D₄×C₅₉	—	4	2	no	—
191	D₄×C₅₉	—	4	2	no	—
192	D₄×C₅₉	—	4	4	no	—
193	D₄×C₅₉	—	4	2	no	—
194	C₂×C₄×C₅₉	—	2	4	no	—
195	C₂×C₄×C₅₉	—	2	2	no	—
196	C₂×C₄×C₅₉	—	2	2	no	—
197	C₂×C₄×C₅₉	—	2	2	no	—
198	C₂×C₄×C₅₉	—	4	8	no	—
199	C₂×C₄×C₅₉	—	4	2	no	—
200	C₂×C₄×C₅₉	—	4	2	no	—
201	C₂×C₄×C₅₉	—	4	2	no	—
202	C₂×C₄×C₅₉	—	4	2	no	—
203	C₂×C₄×C₅₉	—	4	2	no	—
204	C₂×C₄×C₅₉	—	4	2	no	—
205	C₂×C₄×C₅₉	—	4	2	no	—
206	C₂×C₄×C₅₉	—	4	4	no	—
207	C₂×C₄×C₅₉	#117	1	2	yes	—
208	C₂×C₄×C₅₉	#117	1	2	yes	—
209	C₂×C₄×C₅₉	C₄×D₄	1	2	yes	—
210	C₂×C₄×C₅₉	C₄×D₄	1	2	yes	—
211	C₂×C₄×C₅₉	C₄×D₄	1	1	yes	characteristic
212	C₂×C₄×C₅₉	C₄×D₄	1	1	yes	characteristic
213	C₂×C₄×C₅₉	#121	1	2	yes	—
214	C₂×C₄×C₅₉	#121	1	2	yes	—
215	C₂×C₄×C₅₉	#123	1	2	yes	—
216	C₂×C₄×C₅₉	#123	1	2	yes	—
217	C₂×C₄×C₅₉	#124	1	2	yes	—
218	C₂×C₄×C₅₉	#126	1	2	yes	—
219	C₂×C₄×C₅₉	C₂³×C₄	1	1	yes	characteristic
220	C₂×C₄×C₅₉	C₂²×D₄	1	1	yes	characteristic
221	C₂×C₄×C₅₉	C₂²×D₄	1	1	yes	characteristic
222	C₂×C₄×C₅₉	C₂×#41	1	1	yes	characteristic
223	C₂×C₄×C₅₉	C₂×#41	1	1	yes	characteristic
224	C₂×C₄×C₅₉	C₂×#41	1	1	yes	characteristic
225	C₈×C₅₉	—	2	2	no	—
226	C₈×C₅₉	—	2	2	no	—
227	C₈×C₅₉	—	2	4	no	—
228	C₈×C₅₉	—	2	2	no	—
229	C₈×C₅₉	—	2	2	no	—
230	C₈×C₅₉	—	4	2	no	—
231	C₂×#1929	C₅₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
232	C₂²×C₅₉	—	2	4	no	—
233	C₂²×C₅₉	—	2	4	no	—
234	C₂²×C₅₉	—	2	1	no	—
235	C₂²×C₅₉	—	2	1	no	—
236	C₂²×C₅₉	—	2	1	no	—
237	C₂²×C₅₉	—	2	1	no	—
238	C₂²×C₅₉	—	4	2	no	—
239	C₂²×C₅₉	—	4	2	no	—
240	C₂²×C₅₉	—	4	2	no	—
241	C₂²×C₅₉	—	8	4	no	—
242	C₂²×C₅₉	#388	1	2	yes	—
243	C₂²×C₅₉	#388	1	2	yes	—
244	C₂²×C₅₉	#443	1	2	yes	—
245	C₂²×C₅₉	#444	1	2	yes	—
246	C₂²×C₅₉	C₂×C₄×D₄	1	1	yes	characteristic
247	C₂²×C₅₉	C₂×#124	1	1	yes	characteristic
248	C₂²×C₅₉	C₂×#126	1	1	yes	characteristic
249	C₄×C₅₉	—	4	4	no	—
250	C₄×C₅₉	—	4	2	no	—
251	C₄×C₅₉	—	4	2	no	—
252	C₄×C₅₉	—	4	2	no	—
253	C₄×C₅₉	#388	1	2	yes	—
254	C₄×C₅₉	#388	1	2	yes	—
255	C₄×C₅₉	C₂×#117	1	1	yes	characteristic
256	C₄×C₅₉	C₂×C₄×D₄	1	1	yes	characteristic
257	C₄×C₅₉	C₂×#121	1	1	yes	characteristic
258	C₄×C₅₉	C₂×#123	1	1	yes	characteristic
259	C₂²×#108	C₂×C₅₉	1	1	yes	characteristic, complemented
260	C₂²×#104	C₂×C₅₉	1	1	yes	characteristic
261	C₂×#416	C₂×C₅₉	1	1	yes	characteristic
262	C₂×#408	C₂×C₅₉	1	1	yes	characteristic
263	C₂×#405	C₂×C₅₉	1	1	yes	characteristic, complemented
264	#1929	C₂×C₅₉	1	8	yes	direct product factor
265	C₂×#339	C₂×C₅₉	1	1	yes	characteristic, complemented
266	C₂×#336	C₂×C₅₉	1	1	yes	characteristic, complemented
267	C₂×C₅₉	—	2	1	no	—
268	C₂×C₅₉	—	2	1	no	—
269	C₂×C₅₉	—	2	2	no	—
270	C₂×C₅₉	—	8	2	no	—
271	C₂×C₅₉	#1929	1	4	yes	direct product factor
272	C₂×C₅₉	C₂×#388	1	1	yes	characteristic
273	C₂×C₅₉	C₂×#443	1	1	yes	characteristic
274	C₂×C₅₉	C₂×#444	1	1	yes	characteristic
275	C₂²×#41	C₂²×C₅₉	1	1	yes	characteristic
276	C₂²×M₁₆	C₂²×C₅₉	1	1	yes	characteristic
277	C₂²×M₁₆	C₂²×C₅₉	1	1	yes	characteristic
278	C₂³×C₈	C₂²×C₅₉	1	1	yes	characteristic
279	C₂³×C₈	C₂²×C₅₉	1	1	yes	characteristic
280	C₂×#117	C₂²×C₅₉	1	1	yes	characteristic
281	C₂²×C₄²	C₂²×C₅₉	1	1	yes	characteristic
282	C₂×#108	—	2	4	no	—
283	C₂×#108	C₂²×C₅₉	1	4	yes	complemented
284	C₂×#104	—	2	4	no	—
285	C₂×#104	C₂²×C₅₉	1	4	yes	—
286	#416	C₄×C₅₉	1	4	yes	complemented
287	#416	C₂²×C₅₉	1	4	yes	—
288	C₂×#103	C₄×C₅₉	1	1	yes	characteristic, complemented
289	C₂×#103	C₄×C₅₉	1	1	yes	characteristic, complemented
290	C₂×#102	C₄×C₅₉	1	1	yes	characteristic, complemented
291	C₂×#102	C₄×C₅₉	1	1	yes	characteristic, complemented
292	#408	—	2	2	no	—
293	#408	C₂²×C₅₉	1	4	yes	—
294	C₂×C₂²⋊C₈	—	2	1	no	—
295	C₂×C₂²⋊C₈	—	2	1	no	—
296	#405	—	2	2	no	—
297	#405	C₂²×C₅₉	1	4	yes	complemented
298	C₂×#97	—	2	1	no	—
299	C₂×C₄×C₈	—	2	1	no	—
300	#339	C₂²×C₅₉	1	4	yes	complemented
301	#336	C₂²×C₅₉	1	4	yes	complemented
302	C₅₉	C₂×#1929	1	1	yes	characteristic, direct product factor, Sylow
303	C₂×#41	—	2	1	no	—
304	C₂×#41	—	2	1	no	—
305	C₂×#41	—	2	2	no	—
306	C₂×#41	—	2	2	no	—
307	C₂×#41	—	2	2	no	—
308	C₂×#41	—	2	2	no	—
309	C₂×#41	C₂×C₄×C₅₉	1	2	yes	—
310	C₂×#41	C₂³×C₅₉	1	2	yes	—
311	C₂²×Q₈	C₂×C₄×C₅₉	1	1	yes	characteristic
312	C₂²×D₄	—	2	1	no	—
313	C₂²×D₄	C₂×C₄×C₅₉	1	1	yes	characteristic
314	C₂³×C₄	—	2	1	no	—
315	C₂³×C₄	—	2	1	no	—
316	C₂³×C₄	C₂³×C₅₉	1	1	yes	characteristic
317	C₂×M₁₆	—	2	1	no	—
318	C₂×M₁₆	—	2	2	no	—
319	C₂×M₁₆	—	2	1	no	—
320	C₂×M₁₆	—	2	2	no	—
321	C₂×M₁₆	—	2	2	no	—
322	C₂×M₁₆	D₄×C₅₉	1	4	yes	—
323	C₂×M₁₆	C₂³×C₅₉	1	2	yes	—
324	C₂×M₁₆	C₂³×C₅₉	1	2	yes	—
325	C₂²×C₈	—	2	2	no	—
326	C₂²×C₈	—	2	1	no	—
327	C₂²×C₈	—	2	2	no	—
328	C₂²×C₈	—	2	2	no	—
329	C₂²×C₈	—	2	2	no	—
330	C₂²×C₈	—	2	1	no	—
331	C₂²×C₈	C₂×C₄×C₅₉	1	1	yes	characteristic
332	C₂²×C₈	C₂×C₄×C₅₉	1	1	yes	characteristic
333	C₂²×C₈	C₂×C₄×C₅₉	1	2	yes	—
334	C₂²×C₈	D₄×C₅₉	1	1	yes	characteristic
335	C₂²×C₈	D₄×C₅₉	1	1	yes	characteristic
336	C₂²×C₈	D₄×C₅₉	1	2	yes	—
337	C₂²×C₈	C₂³×C₅₉	1	2	yes	—
338	C₂²×C₈	C₂³×C₅₉	1	2	yes	—
339	#117	—	2	1	no	—
340	#117	—	2	1	no	—
341	#117	C₂×C₄×C₅₉	1	2	yes	—
342	#117	C₂³×C₅₉	1	2	yes	—
343	C₂×C₄⋊C₄	C₂×C₄×C₅₉	1	1	yes	characteristic
344	C₂×C₄⋊C₄	C₂×C₄×C₅₉	1	1	yes	characteristic
345	C₂×C₂²⋊C₄	—	2	1	no	—
346	C₂×C₄²	—	2	1	no	—
347	C₂×C₄²	—	2	2	no	—
348	C₂×C₄²	—	2	2	no	—
349	C₂×C₄²	—	2	1	no	—
350	C₂×C₄²	C₂³×C₅₉	1	2	yes	—
351	#108	—	2	8	no	—
352	#104	—	2	8	no	—
353	#103	C₂×C₄×C₅₉	1	4	yes	complemented
354	#103	C₂×C₄×C₅₉	1	4	yes	complemented
355	#102	C₂×C₄×C₅₉	1	4	yes	complemented
356	#102	C₂×C₄×C₅₉	1	4	yes	complemented
357	C₂²⋊C₈	—	2	4	no	—
358	C₂²⋊C₈	—	2	4	no	—
359	#97	—	2	4	no	—
360	C₄×C₈	—	2	4	no	—
361	C₂⁴	—	2	1	no	—
362	C₂⁴	#41×C₅₉	1	1	yes	characteristic
363	#41	—	2	4	no	—
364	#41	—	2	4	no	—
365	#41	—	2	2	no	—
366	#41	—	2	2	no	—
367	#41	—	2	2	no	—
368	#41	—	2	2	no	—
369	#41	—	4	2	no	—
370	#41	—	4	2	no	—
371	#41	—	4	2	no	—
372	#41	—	4	2	no	—
373	C₂×Q₈	—	2	1	no	—
374	C₂×Q₈	—	2	2	no	—
375	C₂×Q₈	—	2	2	no	—
376	C₂×Q₈	C₂²×C₄×C₅₉	1	2	yes	—
377	C₂×D₄	—	2	2	no	—
378	C₂×D₄	—	2	2	no	—
379	C₂×D₄	—	2	2	no	—
380	C₂×D₄	—	2	2	no	—
381	C₂×D₄	—	2	1	no	—
382	C₂×D₄	—	4	2	no	—
383	C₂×D₄	—	4	2	no	—
384	C₂×D₄	C₂²×C₄×C₅₉	1	2	yes	—
385	C₂²×C₄	—	2	4	no	—
386	C₂²×C₄	—	2	1	no	—
387	C₂²×C₄	—	2	1	no	—
388	C₂²×C₄	—	2	1	no	—
389	C₂²×C₄	—	2	2	no	—
390	C₂²×C₄	—	2	2	no	—
391	C₂²×C₄	—	2	2	no	—
392	C₂²×C₄	—	4	2	no	—
393	C₂²×C₄	—	4	2	no	—
394	C₂²×C₄	—	4	2	no	—
395	C₂²×C₄	—	4	2	no	—
396	C₂²×C₄	C₂²×C₄×C₅₉	1	1	yes	characteristic
397	C₂²×C₄	C₂²×C₄×C₅₉	1	1	yes	characteristic
398	C₂²×C₄	C₂×D₄×C₅₉	1	2	yes	—
399	C₂²×C₄	C₂×D₄×C₅₉	1	1	yes	characteristic
400	C₂²×C₄	C₂×D₄×C₅₉	1	1	yes	characteristic
401	C₂²×C₄	#41×C₅₉	1	2	yes	—
402	C₂²×C₄	#41×C₅₉	1	2	yes	—
403	C₂²×C₄	#41×C₅₉	1	2	yes	—
404	C₂²×C₄	#41×C₅₉	1	1	yes	characteristic
405	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
406	M₁₆	—	2	4	no	—
407	M₁₆	—	2	2	no	—
408	M₁₆	—	2	2	no	—
409	M₁₆	—	2	2	no	—
410	M₁₆	—	4	2	no	—
411	M₁₆	C₂×D₄×C₅₉	1	4	yes	—
412	C₂×C₈	—	2	2	no	—
413	C₂×C₈	—	2	2	no	—
414	C₂×C₈	—	2	4	no	—
415	C₂×C₈	—	2	4	no	—
416	C₂×C₈	—	2	2	no	—
417	C₂×C₈	—	2	2	no	—
418	C₂×C₈	—	2	4	no	—
419	C₂×C₈	—	2	2	no	—
420	C₂×C₈	—	2	2	no	—
421	C₂×C₈	—	2	2	no	—
422	C₂×C₈	—	2	2	no	—
423	C₂×C₈	—	2	2	no	—
424	C₂×C₈	—	2	2	no	—
425	C₂×C₈	—	4	2	no	—
426	C₂×C₈	C₂²×C₄×C₅₉	1	2	yes	—
427	C₂×C₈	C₂²×C₄×C₅₉	1	2	yes	—
428	C₂×C₈	C₂×D₄×C₅₉	1	2	yes	—
429	C₂×C₈	C₂×D₄×C₅₉	1	2	yes	—
430	C₄⋊C₄	—	2	1	no	—
431	C₄⋊C₄	—	2	1	no	—
432	C₄⋊C₄	C₂²×C₄×C₅₉	1	2	yes	—
433	C₄⋊C₄	C₂²×C₄×C₅₉	1	2	yes	—
434	C₂²⋊C₄	—	2	2	no	—
435	C₂²⋊C₄	—	2	2	no	—
436	C₄²	—	2	2	no	—
437	C₄²	—	2	2	no	—
438	C₄²	—	2	2	no	—
439	C₄²	—	2	2	no	—
440	C₄²	—	4	2	no	—
441	C₂³	—	2	2	no	—
442	C₂³	—	2	2	no	—
443	C₂³	—	2	2	no	—
444	C₂³	—	4	2	no	—
445	C₂³	—	4	2	no	—
446	C₂³	—	4	2	no	—
447	C₂³	C₄×D₄×C₅₉	1	1	yes	characteristic
448	C₂³	C₄×D₄×C₅₉	1	1	yes	characteristic
449	C₂³	#124×C₅₉	1	2	yes	—
450	C₂³	#126×C₅₉	1	2	yes	—
451	C₂³	C₂×#41×C₅₉	1	1	yes	characteristic
452	Q₈	—	2	2	no	—
453	Q₈	—	2	2	no	—
454	Q₈	—	4	2	no	—
455	D₄	—	2	2	no	—
456	D₄	—	2	2	no	—
457	D₄	—	4	4	no	—
458	D₄	—	4	2	no	—
459	D₄	—	4	2	no	—
460	D₄	—	4	2	no	—
461	C₂×C₄	—	2	4	no	—
462	C₂×C₄	—	2	2	no	—
463	C₂×C₄	—	2	2	no	—
464	C₂×C₄	—	2	2	no	—
465	C₂×C₄	—	4	8	no	—
466	C₂×C₄	—	4	2	no	—
467	C₂×C₄	—	4	2	no	—
468	C₂×C₄	—	4	2	no	—
469	C₂×C₄	—	4	2	no	—
470	C₂×C₄	—	4	2	no	—
471	C₂×C₄	—	4	4	no	—
472	C₂×C₄	—	4	2	no	—
473	C₂×C₄	—	4	2	no	—
474	C₂×C₄	#117×C₅₉	1	2	yes	—
475	C₂×C₄	#117×C₅₉	1	2	yes	—
476	C₂×C₄	C₄×D₄×C₅₉	1	1	yes	characteristic
477	C₂×C₄	C₄×D₄×C₅₉	1	1	yes	characteristic
478	C₂×C₄	C₄×D₄×C₅₉	1	2	yes	—
479	C₂×C₄	C₄×D₄×C₅₉	1	2	yes	—
480	C₂×C₄	#121×C₅₉	1	2	yes	—
481	C₂×C₄	#121×C₅₉	1	2	yes	—
482	C₂×C₄	#123×C₅₉	1	2	yes	—
483	C₂×C₄	#123×C₅₉	1	2	yes	—
484	C₂×C₄	#124×C₅₉	1	2	yes	—
485	C₂×C₄	#126×C₅₉	1	2	yes	—
486	C₂×C₄	C₂³×C₄×C₅₉	1	1	yes	characteristic
487	C₂×C₄	C₂²×D₄×C₅₉	1	1	yes	characteristic
488	C₂×C₄	C₂²×D₄×C₅₉	1	1	yes	characteristic
489	C₂×C₄	C₂×#41×C₅₉	1	1	yes	characteristic
490	C₂×C₄	C₂×#41×C₅₉	1	1	yes	characteristic
491	C₂×C₄	C₂×#41×C₅₉	1	1	yes	characteristic
492	C₈	—	2	2	no	—
493	C₈	—	2	2	no	—
494	C₈	—	2	4	no	—
495	C₈	—	2	2	no	—
496	C₈	—	2	2	no	—
497	C₈	—	4	2	no	—
498	C₂²	—	2	4	no	—
499	C₂²	—	2	4	no	—
500	C₂²	—	2	1	no	—
501	C₂²	—	2	1	no	—
502	C₂²	—	2	1	no	—
503	C₂²	—	2	1	no	—
504	C₂²	—	4	2	no	—
505	C₂²	—	4	2	no	—
506	C₂²	—	4	2	no	—
507	C₂²	—	8	4	no	—
508	C₂²	C₅₉×#388	1	2	yes	—
509	C₂²	C₅₉×#388	1	2	yes	—
510	C₂²	C₅₉×#443	1	2	yes	—
511	C₂²	C₅₉×#444	1	2	yes	—
512	C₂²	C₂×C₄×D₄×C₅₉	1	1	yes	characteristic
513	C₂²	C₂×#124×C₅₉	1	1	yes	characteristic
514	C₂²	C₂×#126×C₅₉	1	1	yes	characteristic
515	C₄	—	4	4	no	—
516	C₄	—	4	2	no	—
517	C₄	—	4	2	no	—
518	C₄	—	4	2	no	—
519	C₄	C₅₉×#388	1	2	yes	—
520	C₄	C₅₉×#388	1	2	yes	—
521	C₄	C₂×#117×C₅₉	1	1	yes	characteristic
522	C₄	C₂×C₄×D₄×C₅₉	1	1	yes	characteristic
523	C₄	C₂×#121×C₅₉	1	1	yes	characteristic
524	C₄	C₂×#123×C₅₉	1	1	yes	characteristic
525	C₂	—	2	1	no	—
526	C₂	—	2	2	no	—
527	C₂	—	2	1	no	—
528	C₂	—	8	2	no	—
529	C₂	C₅₉×#1929	1	4	yes	direct product factor
530	C₂	C₂×C₅₉×#388	1	1	yes	characteristic
531	C₂	C₂×C₅₉×#443	1	1	yes	characteristic
532	C₂	C₂×C₅₉×#444	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄×C₅₉	C₂×D₄
commutator	C₂×C₄	C₂³×C₄×C₅₉
Frattini, cosocle	C₂²×C₄	C₂⁴×C₅₉
socle	C₂³×C₅₉	C₄×D₄
prime radical	C₂²×#41×C₅₉	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₅₉ ◁ C₂³×C₈×C₅₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂²×#108×C₅₉	C₂	semidirect
5. C₂×C₅₉×#405	C₂	semidirect
6. C₅₉×#1929	C₂	direct (N × H)
7. C₂×C₅₉×#339	C₂	semidirect
8. C₂×C₅₉×#336	C₂	semidirect
17. C₂×#108×C₅₉	C₂²	semidirect
20. C₅₉×#416	C₄	semidirect
22. C₂×#103×C₅₉	C₄	semidirect
23. C₂×#103×C₅₉	C₄	semidirect
24. C₂×#102×C₅₉	C₄	semidirect
25. C₂×#102×C₅₉	C₄	semidirect
31. C₅₉×#405	C₂²	semidirect
34. C₅₉×#339	C₂²	semidirect
35. C₅₉×#336	C₂²	semidirect
86. #103×C₅₉	C₂×C₄	semidirect
87. #103×C₅₉	C₂×C₄	semidirect
88. #102×C₅₉	C₂×C₄	semidirect
89. #102×C₅₉	C₂×C₄	semidirect
231. C₂×#1929	C₅₉	direct (N × H)
259. C₂²×#108	C₂×C₅₉	semidirect
263. C₂×#405	C₂×C₅₉	semidirect
264. #1929	C₂×C₅₉	direct (N × H)
265. C₂×#339	C₂×C₅₉	semidirect
266. C₂×#336	C₂×C₅₉	semidirect
271. C₂×C₅₉	#1929	direct (N × H)
283. C₂×#108	C₂²×C₅₉	semidirect
286. #416	C₄×C₅₉	semidirect
288. C₂×#103	C₄×C₅₉	semidirect
289. C₂×#103	C₄×C₅₉	semidirect
290. C₂×#102	C₄×C₅₉	semidirect
291. C₂×#102	C₄×C₅₉	semidirect
297. #405	C₂²×C₅₉	semidirect
300. #339	C₂²×C₅₉	semidirect
301. #336	C₂²×C₅₉	semidirect
302. C₅₉	C₂×#1929	direct (N × H)
353. #103	C₂×C₄×C₅₉	semidirect
354. #103	C₂×C₄×C₅₉	semidirect
355. #102	C₂×C₄×C₅₉	semidirect
356. #102	C₂×C₄×C₅₉	semidirect
529. C₂	C₅₉×#1929	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×#108×C₅₉	2
C₂²×#104×C₅₉	2
C₂×C₅₉×#416	2
C₂×C₅₉×#408	2
C₂×C₅₉×#405	2
C₅₉×#1929	2
C₂×C₅₉×#339	2
C₂×C₅₉×#336	2
C₂×#1929	59

Subgroups — C2×C59×#1929 #28433178

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅₉×#1929 #28433178