Subgroups — C₂×#518×D₅₉ #29495266

Order 15104.

14590 conjugacy classes of subgroups.

The subgroup lattice has 540 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×D₄×D₅₉	C₂	1	1	yes	maximal, characteristic
2	C₂×#16837877	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#16837876	C₂	1	2	yes	maximal, complemented
4	C₂×#16837875	C₂	1	4	yes	maximal, complemented
5	C₂×#16837874	C₂	1	8	yes	maximal, complemented
6	#518×D₅₉	C₂	1	32	yes	maximal, direct product factor
7	C₂×C₄×D₄×D₅₉	C₂	1	8	yes	maximal, complemented
8	C₂×#117×D₅₉	C₂	1	2	yes	maximal, complemented
9	C₂²×C₂²⋊C₄×D₅₉	C₂	1	4	yes	maximal, complemented
10	C₂×C₅₉×#518	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂⁵×D₅₉	C₂²	1	2	yes	—
12	C₂³×D₂₃₆	C₂²	1	1	yes	characteristic
13	C₂³×C₂²⋊D₅₉	C₂²	1	2	yes	—
14	C₂²×D₄×D₅₉	C₄	1	32	yes	complemented
15	C₂²×D₄×D₅₉	C₂²	1	4	yes	—
16	C₂²×D₄×D₅₉	C₂²	1	16	yes	—
17	C₂²×D₄×D₅₉	C₂²	1	4	yes	—
18	C₂³×C₄×D₅₉	C₂²	1	1	yes	characteristic
19	C₂³×C₄×D₅₉	C₂²	1	8	yes	complemented
20	#16837877	C₂²	1	16	yes	complemented
21	#16837876	C₂²	1	32	yes	complemented
22	#16837875	C₂²	1	64	yes	complemented
23	#16837874	C₂²	1	128	yes	complemented
24	C₂×C₄×D₂₃₆	C₂²	1	8	yes	complemented
25	C₂×D₄×Dic₅₉	C₂²	1	8	yes	complemented
26	C₂×#14273689	C₂²	1	8	yes	complemented
27	C₂×C₄×C₂²⋊D₅₉	C₂²	1	16	yes	complemented
28	C₂×(C₂²⋊D₅₉)⋊C₄	C₂²	1	16	yes	complemented
29	C₄×D₄×D₅₉	C₂²	1	128	yes	complemented
30	C₂×#14273686	C₂²	1	2	yes	complemented
31	C₂×#14273685	C₂²	1	4	yes	complemented
32	C₂×#14273684	C₂²	1	4	yes	complemented
33	C₂×#14273683	C₂²	1	4	yes	complemented
34	#117×D₅₉	C₂²	1	32	yes	complemented
35	C₂×C₄⋊C₄×D₅₉	C₂²	1	4	yes	complemented
36	C₂²×C₂²⋊Dic₅₉	C₂²	1	4	yes	complemented
37	C₂²×(C₂×D₅₉)⋊C₄	C₂²	1	8	yes	complemented
38	C₂×C₂²⋊C₄×D₅₉	C₂²	1	4	yes	—
39	C₂×C₂²⋊C₄×D₅₉	C₂²	1	8	yes	complemented
40	C₂×C₂²⋊C₄×D₅₉	C₂²	1	64	yes	complemented
41	C₂×C₂²⋊C₄×D₅₉	C₂²	1	8	yes	complemented
42	C₂×C₂²⋊C₄×D₅₉	C₂²	1	8	yes	complemented
43	C₂×C₄²×D₅₉	C₂²	1	4	yes	complemented
44	C₂³×D₄×C₅₉	C₂²	1	1	yes	characteristic
45	C₅₉×#518	C₂²	1	16	yes	complemented
46	C₂×C₄×D₄×C₅₉	C₂²	1	8	yes	complemented
47	C₂×#117×C₅₉	C₂²	1	2	yes	complemented
48	C₂²×C₂²⋊C₄×C₅₉	C₂²	1	4	yes	complemented
49	C₂⁴×D₅₉	—	4	16	no	—
50	C₂⁴×D₅₉	C₂×C₄	1	32	yes	complemented
51	C₂⁴×D₅₉	C₂³	1	1	yes	characteristic
52	C₂⁴×D₅₉	C₂³	1	4	yes	—
53	C₂⁴×D₅₉	C₂³	1	16	yes	—
54	C₂⁴×D₅₉	C₂³	1	4	yes	—
55	C₂⁴×D₅₉	C₂³	1	2	yes	—
56	C₂²×D₂₃₆	C₂×C₄	1	16	yes	complemented
57	C₂²×D₂₃₆	C₂³	1	4	yes	—
58	C₂²×D₂₃₆	C₂³	1	8	yes	—
59	C₂²×C₂²⋊D₅₉	C₂×C₄	1	32	yes	complemented
60	C₂²×C₂²⋊D₅₉	C₂³	1	8	yes	—
61	C₂²×C₂²⋊D₅₉	C₂³	1	16	yes	—
62	C₂×D₄×D₅₉	C₂×C₄	1	64	yes	complemented
63	C₂×D₄×D₅₉	C₂×C₄	1	256	yes	complemented
64	C₂×D₄×D₅₉	C₂×C₄	1	64	yes	complemented
65	C₂×D₄×D₅₉	C₂³	1	32	yes	—
66	C₂×D₄×D₅₉	C₂³	1	32	yes	—
67	C₂³×Dic₅₉	C₂³	1	1	yes	characteristic
68	C₂³×Dic₅₉	C₂³	1	8	yes	complemented
69	C₂²×C₄×D₅₉	—	4	32	no	—
70	C₂²×C₄×D₅₉	C₂×C₄	1	16	yes	complemented
71	C₂²×C₄×D₅₉	C₂³	1	8	yes	—
72	C₂²×C₄×D₅₉	C₂³	1	2	yes	—
73	C₂²×C₄×D₅₉	C₂³	1	8	yes	—
74	C₂²×C₄×D₅₉	C₂³	1	2	yes	—
75	C₂²×C₄×D₅₉	C₂³	1	64	yes	complemented
76	C₂²×C₄×D₅₉	C₂³	1	16	yes	complemented
77	C₄×D₂₃₆	C₂³	1	64	yes	complemented
78	D₄×Dic₅₉	C₂³	1	64	yes	complemented
79	#14273689	C₂³	1	64	yes	complemented
80	C₄×C₂²⋊D₅₉	C₂³	1	128	yes	complemented
81	(C₂²⋊D₅₉)⋊C₄	C₂³	1	128	yes	complemented
82	#14273686	C₂³	1	16	yes	complemented
83	#14273685	C₂³	1	32	yes	complemented
84	#14273684	C₂³	1	32	yes	complemented
85	#14273683	C₂³	1	32	yes	complemented
86	C₂×C₄⋊Dic₅₉	C₂³	1	4	yes	complemented
87	C₂×Dic₅₉⋊C₄	C₂³	1	8	yes	complemented
88	C₄⋊C₄×D₅₉	C₂³	1	32	yes	complemented
89	C₂×C₂²⋊Dic₅₉	C₂³	1	4	yes	—
90	C₂×C₂²⋊Dic₅₉	C₂³	1	32	yes	complemented
91	C₂×C₂²⋊Dic₅₉	C₂³	1	8	yes	complemented
92	C₂×(C₂×D₅₉)⋊C₄	C₂³	1	8	yes	—
93	C₂×(C₂×D₅₉)⋊C₄	C₂³	1	64	yes	complemented
94	C₂×(C₂×D₅₉)⋊C₄	C₂³	1	16	yes	complemented
95	C₂²⋊C₄×D₅₉	C₂³	1	32	yes	—
96	C₂²⋊C₄×D₅₉	C₂³	1	64	yes	complemented
97	C₂²⋊C₄×D₅₉	C₂³	1	64	yes	complemented
98	C₂²⋊C₄×D₅₉	C₂³	1	64	yes	complemented
99	C₂×C₄×Dic₅₉	C₂³	1	8	yes	complemented
100	C₂×C₄×Dic₅₉	C₂³	1	4	yes	complemented
101	C₄²×D₅₉	C₂³	1	32	yes	complemented
102	C₂⁵×C₅₉	C₂³	1	2	yes	—
103	C₂²×D₄×C₅₉	C₂×C₄	1	16	yes	complemented
104	C₂²×D₄×C₅₉	C₂³	1	4	yes	—
105	C₂²×D₄×C₅₉	C₂³	1	8	yes	—
106	C₂³×C₄×C₅₉	C₂³	1	1	yes	characteristic
107	C₂³×C₄×C₅₉	C₂³	1	8	yes	complemented
108	C₄×D₄×C₅₉	C₂³	1	64	yes	complemented
109	#117×C₅₉	C₂³	1	16	yes	complemented
110	C₂×C₄⋊C₄×C₅₉	C₂³	1	4	yes	complemented
111	C₂×C₂²⋊C₄×C₅₉	C₂³	1	4	yes	—
112	C₂×C₂²⋊C₄×C₅₉	C₂³	1	32	yes	complemented
113	C₂×C₂²⋊C₄×C₅₉	C₂³	1	8	yes	complemented
114	C₂×C₄²×C₅₉	C₂³	1	4	yes	complemented
115	C₂⁴×C₅₉	—	4	8	no	—
116	C₂⁴×C₅₉	C₂²×C₄	1	16	yes	complemented
117	C₂⁴×C₅₉	C₂⁴	1	1	yes	characteristic
118	C₂⁴×C₅₉	C₂⁴	1	4	yes	—
119	C₂⁴×C₅₉	C₂⁴	1	8	yes	—
120	C₂³×D₅₉	—	2	32	no	—
121	C₂³×D₅₉	—	2	8	no	—
122	C₂³×D₅₉	—	4	128	no	—
123	C₂³×D₅₉	—	4	64	no	—
124	C₂³×D₅₉	—	4	8	no	—
125	C₂³×D₅₉	—	4	16	no	—
126	C₂³×D₅₉	C₂²×C₄	1	8	yes	—
127	C₂³×D₅₉	C₂²×C₄	1	32	yes	—
128	C₂³×D₅₉	C₂²×C₄	1	128	yes	complemented
129	C₂³×D₅₉	C₂²×C₄	1	32	yes	complemented
130	C₂³×D₅₉	C₂²×C₄	1	16	yes	complemented
131	C₂³×D₅₉	C₂⁴	1	4	yes	—
132	C₂³×D₅₉	C₂⁴	1	16	yes	—
133	C₂³×D₅₉	C₂⁴	1	1	yes	characteristic
134	C₂³×D₅₉	C₂⁴	1	4	yes	—
135	C₂³×D₅₉	C₂⁴	1	8	yes	—
136	C₂³×D₅₉	C₂⁴	1	16	yes	—
137	C₂³×D₅₉	C₂⁴	1	1	yes	characteristic
138	C₂×D₄×C₅₉	C₂²×C₄	1	32	yes	complemented
139	C₂×D₄×C₅₉	C₂²×C₄	1	64	yes	complemented
140	C₂×D₄×C₅₉	C₂⁴	1	16	yes	—
141	C₂²×C₄×C₅₉	—	4	16	no	—
142	C₂²×C₄×C₅₉	C₂²×C₄	1	8	yes	complemented
143	C₂²×C₄×C₅₉	C₂⁴	1	8	yes	—
144	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
145	C₂²×C₄×C₅₉	C₂⁴	1	4	yes	—
146	C₂²×C₄×C₅₉	C₂⁴	1	32	yes	complemented
147	C₂×C₂²⋊D₅₉	C₂²×C₄	1	64	yes	complemented
148	C₂×C₂²⋊D₅₉	C₂²×C₄	1	128	yes	complemented
149	C₂×C₂²⋊D₅₉	C₂⁴	1	32	yes	—
150	C₂²×Dic₅₉	—	4	16	no	—
151	C₂²×Dic₅₉	C₂²×C₄	1	8	yes	complemented
152	C₂²×Dic₅₉	C₂⁴	1	8	yes	—
153	C₂²×Dic₅₉	C₂⁴	1	2	yes	—
154	C₂²×Dic₅₉	C₂⁴	1	4	yes	—
155	C₂²×Dic₅₉	C₂⁴	1	32	yes	complemented
156	D₄×D₅₉	C₂²×C₄	1	256	yes	complemented
157	D₄×D₅₉	C₂²×C₄	1	256	yes	complemented
158	C₂×D₂₃₆	C₂²×C₄	1	32	yes	complemented
159	C₂×D₂₃₆	C₂²×C₄	1	64	yes	complemented
160	C₂×D₂₃₆	C₂⁴	1	16	yes	—
161	C₂×C₄×D₅₉	—	2	32	no	—
162	C₂×C₄×D₅₉	—	4	128	no	—
163	C₂×C₄×D₅₉	—	4	32	no	—
164	C₂×C₄×D₅₉	C₂²×C₄	1	16	yes	—
165	C₂×C₄×D₅₉	C₂²×C₄	1	64	yes	complemented
166	C₂×C₄×D₅₉	C₂²×C₄	1	16	yes	complemented
167	C₂×C₄×D₅₉	C₂⁴	1	32	yes	—
168	C₂×C₄×D₅₉	C₂⁴	1	8	yes	—
169	C₂×C₄×D₅₉	C₂⁴	1	8	yes	—
170	C₂×C₄×D₅₉	C₂⁴	1	64	yes	complemented
171	C₄⋊C₄×C₅₉	C₂⁴	1	16	yes	complemented
172	C₂²⋊C₄×C₅₉	C₂⁴	1	16	yes	—
173	C₂²⋊C₄×C₅₉	C₂⁴	1	32	yes	complemented
174	C₄²×C₅₉	C₂⁴	1	16	yes	complemented
175	C₂²⋊Dic₅₉	C₂⁴	1	16	yes	—
176	C₂²⋊Dic₅₉	C₂⁴	1	32	yes	complemented
177	(C₂×D₅₉)⋊C₄	C₂⁴	1	32	yes	—
178	(C₂×D₅₉)⋊C₄	C₂⁴	1	64	yes	complemented
179	C₄⋊Dic₅₉	C₂⁴	1	16	yes	complemented
180	Dic₅₉⋊C₄	C₂⁴	1	32	yes	complemented
181	C₄×Dic₅₉	C₂⁴	1	32	yes	complemented
182	C₄×Dic₅₉	C₂⁴	1	16	yes	complemented
183	C₂³×C₅₉	—	2	16	no	—
184	C₂³×C₅₉	—	2	4	no	—
185	C₂³×C₅₉	—	4	32	no	—
186	C₂³×C₅₉	—	4	16	no	—
187	C₂³×C₅₉	C₂³×C₄	1	4	yes	—
188	C₂³×C₅₉	C₂³×C₄	1	16	yes	—
189	C₂³×C₅₉	C₂³×C₄	1	32	yes	complemented
190	C₂³×C₅₉	C₂⁵	1	2	yes	—
191	C₂³×C₅₉	C₂⁵	1	8	yes	—
192	C₂³×C₅₉	C₂⁵	1	1	yes	characteristic
193	C₂²×D₅₉	—	2	16	no	—
194	C₂²×D₅₉	—	2	4	no	—
195	C₂²×D₅₉	—	2	32	no	—
196	C₂²×D₅₉	—	2	128	no	—
197	C₂²×D₅₉	—	2	64	no	—
198	C₂²×D₅₉	—	2	16	no	—
199	C₂²×D₅₉	—	4	256	no	—
200	C₂²×D₅₉	—	4	64	no	—
201	C₂²×D₅₉	—	4	32	no	—
202	C₂²×D₅₉	—	4	16	no	—
203	C₂²×D₅₉	—	4	32	no	—
204	C₂²×D₅₉	C₂³×C₄	1	4	yes	—
205	C₂²×D₅₉	C₂³×C₄	1	16	yes	—
206	C₂²×D₅₉	C₂³×C₄	1	16	yes	—
207	C₂²×D₅₉	C₂³×C₄	1	64	yes	—
208	C₂²×D₅₉	C₂³×C₄	1	4	yes	—
209	C₂²×D₅₉	C₂³×C₄	1	32	yes	complemented
210	C₂²×D₅₉	C₂³×C₄	1	64	yes	complemented
211	C₂²×D₅₉	H(5,𝔽₂)	1	8	yes	—
212	C₂²×D₅₉	C₂⁵	1	2	yes	—
213	C₂²×D₅₉	C₂⁵	1	8	yes	—
214	C₂²×D₅₉	C₂⁵	1	2	yes	—
215	D₄×C₅₉	C₂³×C₄	1	64	yes	complemented
216	C₂×C₄×C₅₉	—	2	16	no	—
217	C₂×C₄×C₅₉	—	4	32	no	—
218	C₂×C₄×C₅₉	C₂³×C₄	1	8	yes	—
219	C₂×C₄×C₅₉	C₂³×C₄	1	16	yes	complemented
220	C₂×C₄×C₅₉	C₂⁵	1	16	yes	—
221	C₂×C₄×C₅₉	C₂⁵	1	4	yes	—
222	C₂²⋊D₅₉	C₂³×C₄	1	128	yes	complemented
223	C₂×Dic₅₉	—	2	16	no	—
224	C₂×Dic₅₉	—	4	32	no	—
225	C₂×Dic₅₉	C₂³×C₄	1	8	yes	—
226	C₂×Dic₅₉	C₂³×C₄	1	16	yes	complemented
227	C₂×Dic₅₉	C₂⁵	1	16	yes	—
228	C₂×Dic₅₉	C₂⁵	1	4	yes	—
229	D₂₃₆	C₂³×C₄	1	64	yes	complemented
230	C₄×D₅₉	—	2	64	no	—
231	C₄×D₅₉	—	4	64	no	—
232	C₄×D₅₉	C₂³×C₄	1	32	yes	—
233	C₄×D₅₉	C₂³×C₄	1	32	yes	complemented
234	C₂²×#518	—	59	1	no	maximal, Sylow
235	C₂²×C₅₉	—	2	16	no	—
236	C₂²×C₅₉	—	2	4	no	—
237	C₂²×C₅₉	—	2	8	no	—
238	C₂²×C₅₉	—	2	32	no	—
239	C₂²×C₅₉	—	4	32	no	—
240	C₂²×C₅₉	C₂⁴×C₄	1	4	yes	—
241	C₂²×C₅₉	C₂⁴×C₄	1	16	yes	—
242	C₂²×C₅₉	C₂⁴×C₄	1	2	yes	—
243	C₂²×C₅₉	C₂×H(5,𝔽₂)	1	4	yes	—
244	C₂²×C₅₉	C₂⁶	1	1	yes	characteristic
245	C₂×D₅₉	—	2	16	no	—
246	C₂×D₅₉	—	2	4	no	—
247	C₂×D₅₉	—	2	8	no	—
248	C₂×D₅₉	—	2	32	no	—
249	C₂×D₅₉	—	2	32	no	—
250	C₂×D₅₉	—	2	128	no	—
251	C₂×D₅₉	—	4	64	no	—
252	C₂×D₅₉	—	4	32	no	—
253	C₂×D₅₉	#518	1	16	yes	direct product factor
254	C₂×D₅₉	C₂⁴×C₄	1	4	yes	—
255	C₂×D₅₉	C₂⁴×C₄	1	16	yes	—
256	C₂×D₅₉	C₂⁴×C₄	1	4	yes	—
257	C₂×D₅₉	C₂×H(5,𝔽₂)	1	8	yes	—
258	C₄×C₅₉	—	2	16	no	—
259	C₄×C₅₉	C₂⁴×C₄	1	8	yes	—
260	Dic₅₉	—	2	16	no	—
261	Dic₅₉	C₂⁴×C₄	1	8	yes	—
262	C₂⁴×D₄	—	59	1	no	—
263	C₂×#518	—	59	1	no	—
264	C₂×#518	—	59	32	no	—
265	C₂×#518	—	59	8	no	—
266	C₂×#518	—	59	2	no	—
267	C₂×#518	—	59	4	no	—
268	C₂×#518	D₅₉	1	1	yes	characteristic, direct product factor
269	C₂²×C₄×D₄	—	59	8	no	—
270	C₂²×#117	—	59	2	no	—
271	C₂³×C₂²⋊C₄	—	59	4	no	—
272	C₂×C₅₉	—	2	4	no	—
273	C₂×C₅₉	—	2	16	no	—
274	C₂×C₅₉	C₂×#518	1	4	yes	complemented
275	C₂×C₅₉	C₂⁵×C₄	1	1	yes	characteristic
276	C₂×C₅₉	C₂²×H(5,𝔽₂)	1	2	yes	—
277	D₅₉	—	2	4	no	—
278	D₅₉	—	2	16	no	—
279	D₅₉	C₂×#518	1	8	yes	direct product factor
280	C₂⁶	—	59	2	no	—
281	C₂³×D₄	—	59	2	no	—
282	C₂³×D₄	—	59	32	no	—
283	C₂³×D₄	—	59	4	no	—
284	C₂³×D₄	—	59	4	no	—
285	C₂³×D₄	—	59	16	no	—
286	C₂³×D₄	—	59	1	no	—
287	C₂³×D₄	C₂×D₅₉	1	1	yes	characteristic
288	C₂⁴×C₄	—	59	1	no	—
289	C₂⁴×C₄	—	59	8	no	—
290	#518	—	59	16	no	—
291	#518	—	59	128	no	—
292	#518	—	59	32	no	—
293	#518	—	59	64	no	—
294	#518	C₂×D₅₉	1	16	yes	direct product factor
295	C₂×C₄×D₄	—	59	8	no	—
296	C₂×C₄×D₄	—	59	16	no	—
297	C₂×C₄×D₄	—	59	128	no	—
298	C₂×C₄×D₄	—	59	8	no	—
299	C₂×C₄×D₄	—	59	16	no	—
300	C₂×C₄×D₄	—	59	8	no	—
301	C₂×C₄×D₄	C₂×D₅₉	1	8	yes	complemented
302	C₂×#117	—	59	2	no	—
303	C₂×#117	—	59	32	no	—
304	C₂×#117	—	59	4	no	—
305	C₂×#117	—	59	4	no	—
306	C₂×#117	—	59	4	no	—
307	C₂×#117	C₂×D₅₉	1	2	yes	complemented
308	C₂²×C₄⋊C₄	—	59	4	no	—
309	C₂²×C₂²⋊C₄	—	59	4	no	—
310	C₂²×C₂²⋊C₄	—	59	8	no	—
311	C₂²×C₂²⋊C₄	—	59	4	no	—
312	C₂²×C₂²⋊C₄	—	59	8	no	—
313	C₂²×C₂²⋊C₄	—	59	8	no	—
314	C₂²×C₂²⋊C₄	—	59	8	no	—
315	C₂²×C₂²⋊C₄	—	59	64	no	—
316	C₂²×C₂²⋊C₄	C₂×D₅₉	1	4	yes	complemented
317	C₂²×C₄²	—	59	4	no	—
318	C₅₉	C₂²×#518	1	1	yes	characteristic, complemented, Sylow
319	C₂⁵	—	59	1	no	—
320	C₂⁵	—	59	4	no	—
321	C₂⁵	—	59	32	no	—
322	C₂⁵	—	59	16	no	—
323	C₂⁵	—	59	4	no	—
324	C₂⁵	—	59	2	no	—
325	C₂⁵	—	236	16	no	—
326	C₂⁵	C₂²×D₅₉	1	2	yes	—
327	C₂²×D₄	—	59	32	no	—
328	C₂²×D₄	—	59	8	no	—
329	C₂²×D₄	—	59	16	no	—
330	C₂²×D₄	—	59	64	no	—
331	C₂²×D₄	—	59	64	no	—
332	C₂²×D₄	—	59	256	no	—
333	C₂²×D₄	—	59	32	no	—
334	C₂²×D₄	—	59	32	no	—
335	C₂²×D₄	—	59	16	no	—
336	C₂²×D₄	—	59	4	no	—
337	C₂²×D₄	—	59	8	no	—
338	C₂²×D₄	C₄×D₅₉	1	16	yes	complemented
339	C₂²×D₄	C₂²×D₅₉	1	4	yes	—
340	C₂²×D₄	C₂²×D₅₉	1	8	yes	—
341	C₂³×C₄	—	59	1	no	—
342	C₂³×C₄	—	59	16	no	—
343	C₂³×C₄	—	59	2	no	—
344	C₂³×C₄	—	59	8	no	—
345	C₂³×C₄	—	59	2	no	—
346	C₂³×C₄	—	59	8	no	—
347	C₂³×C₄	—	59	8	no	—
348	C₂³×C₄	—	59	16	no	—
349	C₂³×C₄	—	59	64	no	—
350	C₂³×C₄	—	236	32	no	—
351	C₂³×C₄	C₂²×D₅₉	1	1	yes	characteristic
352	C₂³×C₄	C₂²×D₅₉	1	8	yes	complemented
353	C₄×D₄	—	59	64	no	—
354	C₄×D₄	—	59	128	no	—
355	C₄×D₄	—	59	64	no	—
356	C₄×D₄	—	59	128	no	—
357	C₄×D₄	—	59	64	no	—
358	C₄×D₄	C₂²×D₅₉	1	64	yes	complemented
359	#117	—	59	16	no	—
360	#117	—	59	32	no	—
361	#117	—	59	32	no	—
362	#117	—	59	32	no	—
363	#117	C₂²×D₅₉	1	16	yes	complemented
364	C₂×C₄⋊C₄	—	59	8	no	—
365	C₂×C₄⋊C₄	—	59	4	no	—
366	C₂×C₄⋊C₄	—	59	32	no	—
367	C₂×C₄⋊C₄	C₂²×D₅₉	1	4	yes	complemented
368	C₂×C₂²⋊C₄	—	59	4	no	—
369	C₂×C₂²⋊C₄	—	59	8	no	—
370	C₂×C₂²⋊C₄	—	59	32	no	—
371	C₂×C₂²⋊C₄	—	59	8	no	—
372	C₂×C₂²⋊C₄	—	59	16	no	—
373	C₂×C₂²⋊C₄	—	59	64	no	—
374	C₂×C₂²⋊C₄	—	59	32	no	—
375	C₂×C₂²⋊C₄	—	59	64	no	—
376	C₂×C₂²⋊C₄	—	59	64	no	—
377	C₂×C₂²⋊C₄	—	59	64	no	—
378	C₂×C₂²⋊C₄	C₂²×D₅₉	1	4	yes	—
379	C₂×C₂²⋊C₄	C₂²×D₅₉	1	32	yes	complemented
380	C₂×C₂²⋊C₄	C₂²×D₅₉	1	8	yes	complemented
381	C₂×C₄²	—	59	8	no	—
382	C₂×C₄²	—	59	4	no	—
383	C₂×C₄²	—	59	32	no	—
384	C₂×C₄²	C₂²×D₅₉	1	4	yes	complemented
385	C₂⁴	—	4	8	no	—
386	C₂⁴	—	59	1	no	—
387	C₂⁴	—	59	8	no	—
388	C₂⁴	—	59	32	no	—
389	C₂⁴	—	59	4	no	—
390	C₂⁴	—	59	16	no	—
391	C₂⁴	—	59	1	no	—
392	C₂⁴	—	59	4	no	—
393	C₂⁴	—	59	32	no	—
394	C₂⁴	—	59	16	no	—
395	C₂⁴	—	59	128	no	—
396	C₂⁴	—	59	16	no	—
397	C₂⁴	—	59	8	no	—
398	C₂⁴	—	118	32	no	—
399	C₂⁴	—	118	8	no	—
400	C₂⁴	—	236	16	no	—
401	C₂⁴	—	236	8	no	—
402	C₂⁴	—	236	128	no	—
403	C₂⁴	—	236	64	no	—
404	C₂⁴	C₂×C₄×D₅₉	1	16	yes	complemented
405	C₂⁴	C₂³×D₅₉	1	1	yes	characteristic
406	C₂⁴	C₂³×D₅₉	1	4	yes	—
407	C₂⁴	C₂³×D₅₉	1	8	yes	—
408	C₂×D₄	—	59	64	no	—
409	C₂×D₄	—	59	128	no	—
410	C₂×D₄	—	59	32	no	—
411	C₂×D₄	—	59	256	no	—
412	C₂×D₄	—	59	256	no	—
413	C₂×D₄	—	59	32	no	—
414	C₂×D₄	—	59	64	no	—
415	C₂×D₄	—	59	16	no	—
416	C₂×D₄	C₂×C₄×D₅₉	1	32	yes	complemented
417	C₂×D₄	C₂×C₄×D₅₉	1	64	yes	complemented
418	C₂×D₄	C₂³×D₅₉	1	16	yes	—
419	C₂²×C₄	—	4	16	no	—
420	C₂²×C₄	—	59	8	no	—
421	C₂²×C₄	—	59	4	no	—
422	C₂²×C₄	—	59	2	no	—
423	C₂²×C₄	—	59	16	no	—
424	C₂²×C₄	—	59	16	no	—
425	C₂²×C₄	—	59	64	no	—
426	C₂²×C₄	—	59	8	no	—
427	C₂²×C₄	—	59	8	no	—
428	C₂²×C₄	—	59	8	no	—
429	C₂²×C₄	—	59	32	no	—
430	C₂²×C₄	—	59	32	no	—
431	C₂²×C₄	—	59	64	no	—
432	C₂²×C₄	—	118	32	no	—
433	C₂²×C₄	—	236	32	no	—
434	C₂²×C₄	—	236	128	no	—
435	C₂²×C₄	—	236	16	no	—
436	C₂²×C₄	C₂×C₄×D₅₉	1	8	yes	complemented
437	C₂²×C₄	C₂³×D₅₉	1	8	yes	—
438	C₂²×C₄	C₂³×D₅₉	1	2	yes	—
439	C₂²×C₄	C₂³×D₅₉	1	4	yes	—
440	C₂²×C₄	C₂³×D₅₉	1	32	yes	complemented
441	C₄⋊C₄	—	59	32	no	—
442	C₄⋊C₄	—	59	16	no	—
443	C₄⋊C₄	C₂³×D₅₉	1	16	yes	complemented
444	C₂²⋊C₄	—	59	16	no	—
445	C₂²⋊C₄	—	59	32	no	—
446	C₂²⋊C₄	—	59	32	no	—
447	C₂²⋊C₄	—	59	64	no	—
448	C₂²⋊C₄	C₂³×D₅₉	1	16	yes	—
449	C₂²⋊C₄	C₂³×D₅₉	1	32	yes	complemented
450	C₄²	—	59	32	no	—
451	C₄²	—	59	16	no	—
452	C₄²	C₂³×D₅₉	1	16	yes	complemented
453	C₂³	—	2	16	no	—
454	C₂³	—	2	4	no	—
455	C₂³	—	4	32	no	—
456	C₂³	—	4	16	no	—
457	C₂³	—	59	4	no	—
458	C₂³	—	59	8	no	—
459	C₂³	—	59	2	no	—
460	C₂³	—	59	16	no	—
461	C₂³	—	59	4	no	—
462	C₂³	—	59	64	no	—
463	C₂³	—	59	16	no	—
464	C₂³	—	59	2	no	—
465	C₂³	—	59	8	no	—
466	C₂³	—	59	64	no	—
467	C₂³	—	59	32	no	—
468	C₂³	—	118	64	no	—
469	C₂³	—	118	128	no	—
470	C₂³	—	118	32	no	—
471	C₂³	—	118	16	no	—
472	C₂³	—	118	16	no	—
473	C₂³	—	118	4	no	—
474	C₂³	—	236	32	no	—
475	C₂³	—	236	64	no	—
476	C₂³	—	236	32	no	—
477	C₂³	—	236	16	no	—
478	C₂³	—	236	256	no	—
479	C₂³	C₂²×C₄×D₅₉	1	4	yes	—
480	C₂³	C₂²×C₄×D₅₉	1	16	yes	—
481	C₂³	C₂²×C₄×D₅₉	1	32	yes	complemented
482	C₂³	C₂⁴×D₅₉	1	2	yes	—
483	C₂³	C₂⁴×D₅₉	1	8	yes	—
484	C₂³	C₂⁴×D₅₉	1	1	yes	characteristic
485	D₄	—	59	128	no	—
486	D₄	—	59	64	no	—
487	D₄	C₂²×C₄×D₅₉	1	64	yes	complemented
488	C₂×C₄	—	2	16	no	—
489	C₂×C₄	—	4	32	no	—
490	C₂×C₄	—	59	8	no	—
491	C₂×C₄	—	59	16	no	—
492	C₂×C₄	—	59	4	no	—
493	C₂×C₄	—	59	32	no	—
494	C₂×C₄	—	59	32	no	—
495	C₂×C₄	—	59	16	no	—
496	C₂×C₄	—	118	64	no	—
497	C₂×C₄	—	118	16	no	—
498	C₂×C₄	—	236	64	no	—
499	C₂×C₄	—	236	32	no	—
500	C₂×C₄	C₂²×C₄×D₅₉	1	8	yes	—
501	C₂×C₄	C₂²×C₄×D₅₉	1	16	yes	complemented
502	C₂×C₄	C₂⁴×D₅₉	1	16	yes	—
503	C₂×C₄	C₂⁴×D₅₉	1	4	yes	—
504	C₂²	—	2	8	no	—
505	C₂²	—	2	32	no	—
506	C₂²	—	2	16	no	—
507	C₂²	—	2	4	no	—
508	C₂²	—	4	32	no	—
509	C₂²	—	59	16	no	—
510	C₂²	—	59	4	no	—
511	C₂²	—	59	8	no	—
512	C₂²	—	59	4	no	—
513	C₂²	—	59	16	no	—
514	C₂²	—	118	32	no	—
515	C₂²	—	118	128	no	—
516	C₂²	—	118	8	no	—
517	C₂²	—	118	32	no	—
518	C₂²	—	118	16	no	—
519	C₂²	—	118	4	no	—
520	C₂²	—	236	32	no	—
521	C₂²	—	236	64	no	—
522	C₂²	C₂³×C₄×D₅₉	1	4	yes	—
523	C₂²	C₂³×C₄×D₅₉	1	16	yes	—
524	C₂²	C₂³×C₄×D₅₉	1	2	yes	—
525	C₂²	H(5,𝔽₂)×D₅₉	1	4	yes	—
526	C₂²	C₂⁵×D₅₉	1	1	yes	characteristic
527	C₄	—	2	16	no	—
528	C₄	—	59	8	no	—
529	C₄	—	118	16	no	—
530	C₄	C₂³×C₄×D₅₉	1	8	yes	—
531	C₂	—	2	4	no	—
532	C₂	—	2	16	no	—
533	C₂	—	59	8	no	—
534	C₂	—	118	4	no	—
535	C₂	—	118	16	no	—
536	C₂	#518×D₅₉	1	4	yes	direct product factor
537	C₂	C₂⁴×C₄×D₅₉	1	1	yes	characteristic
538	C₂	C₂×H(5,𝔽₂)×D₅₉	1	2	yes	—

	subgroup	G/H
center	C₂³	C₂⁴×D₅₉
commutator	C₂×C₅₉	C₂⁵×C₄
Frattini	C₂²	C₂⁵×D₅₉
Fitting	C₂×C₅₉×#518	C₂
socle	C₂³×C₅₉	C₂⁵
prime radical	C₂³×D₄×D₅₉	C₂
cosocle	C₂²×C₅₉	C₂⁶
hypercenter	C₂×#518	D₅₉
hypocenter	C₅₉	C₂²×#518
LCS	G ▷ C₂×C₅₉ ▷ C₅₉
UCS	C₁ ◁ C₂³ ◁ C₂×#518

Complements

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

N	H ≅ G/N	type
2. C₂×#16837877	C₂	semidirect
3. C₂×#16837876	C₂	semidirect
4. C₂×#16837875	C₂	semidirect
5. C₂×#16837874	C₂	semidirect
6. #518×D₅₉	C₂	direct (N × H)
7. C₂×C₄×D₄×D₅₉	C₂	semidirect
8. C₂×#117×D₅₉	C₂	semidirect
9. C₂²×C₂²⋊C₄×D₅₉	C₂	semidirect
10. C₂×C₅₉×#518	C₂	semidirect
14. C₂²×D₄×D₅₉	C₄	semidirect
19. C₂³×C₄×D₅₉	C₂²	semidirect
20. #16837877	C₂²	semidirect
21. #16837876	C₂²	semidirect
22. #16837875	C₂²	semidirect
23. #16837874	C₂²	semidirect
24. C₂×C₄×D₂₃₆	C₂²	semidirect
25. C₂×D₄×Dic₅₉	C₂²	semidirect
26. C₂×#14273689	C₂²	semidirect
27. C₂×C₄×C₂²⋊D₅₉	C₂²	semidirect
28. C₂×(C₂²⋊D₅₉)⋊C₄	C₂²	semidirect
29. C₄×D₄×D₅₉	C₂²	semidirect
30. C₂×#14273686	C₂²	semidirect
31. C₂×#14273685	C₂²	semidirect
32. C₂×#14273684	C₂²	semidirect
33. C₂×#14273683	C₂²	semidirect
34. #117×D₅₉	C₂²	semidirect
35. C₂×C₄⋊C₄×D₅₉	C₂²	semidirect
36. C₂²×C₂²⋊Dic₅₉	C₂²	semidirect
37. C₂²×(C₂×D₅₉)⋊C₄	C₂²	semidirect
39. C₂×C₂²⋊C₄×D₅₉	C₂²	semidirect
40. C₂×C₂²⋊C₄×D₅₉	C₂²	semidirect
41. C₂×C₂²⋊C₄×D₅₉	C₂²	semidirect
42. C₂×C₂²⋊C₄×D₅₉	C₂²	semidirect
43. C₂×C₄²×D₅₉	C₂²	semidirect
45. C₅₉×#518	C₂²	semidirect
46. C₂×C₄×D₄×C₅₉	C₂²	semidirect
47. C₂×#117×C₅₉	C₂²	semidirect
48. C₂²×C₂²⋊C₄×C₅₉	C₂²	semidirect
50. C₂⁴×D₅₉	C₂×C₄	semidirect
56. C₂²×D₂₃₆	C₂×C₄	semidirect
59. C₂²×C₂²⋊D₅₉	C₂×C₄	semidirect
62. C₂×D₄×D₅₉	C₂×C₄	semidirect
63. C₂×D₄×D₅₉	C₂×C₄	semidirect
64. C₂×D₄×D₅₉	C₂×C₄	semidirect
68. C₂³×Dic₅₉	C₂³	semidirect
70. C₂²×C₄×D₅₉	C₂×C₄	semidirect
75. C₂²×C₄×D₅₉	C₂³	semidirect
76. C₂²×C₄×D₅₉	C₂³	semidirect
77. C₄×D₂₃₆	C₂³	semidirect
78. D₄×Dic₅₉	C₂³	semidirect
79. #14273689	C₂³	semidirect
80. C₄×C₂²⋊D₅₉	C₂³	semidirect
81. (C₂²⋊D₅₉)⋊C₄	C₂³	semidirect
82. #14273686	C₂³	semidirect
83. #14273685	C₂³	semidirect
84. #14273684	C₂³	semidirect
85. #14273683	C₂³	semidirect
86. C₂×C₄⋊Dic₅₉	C₂³	semidirect
87. C₂×Dic₅₉⋊C₄	C₂³	semidirect
88. C₄⋊C₄×D₅₉	C₂³	semidirect
90. C₂×C₂²⋊Dic₅₉	C₂³	semidirect
91. C₂×C₂²⋊Dic₅₉	C₂³	semidirect
93. C₂×(C₂×D₅₉)⋊C₄	C₂³	semidirect
94. C₂×(C₂×D₅₉)⋊C₄	C₂³	semidirect
96. C₂²⋊C₄×D₅₉	C₂³	semidirect
97. C₂²⋊C₄×D₅₉	C₂³	semidirect
98. C₂²⋊C₄×D₅₉	C₂³	semidirect
99. C₂×C₄×Dic₅₉	C₂³	semidirect
100. C₂×C₄×Dic₅₉	C₂³	semidirect
101. C₄²×D₅₉	C₂³	semidirect
103. C₂²×D₄×C₅₉	C₂×C₄	semidirect
107. C₂³×C₄×C₅₉	C₂³	semidirect
108. C₄×D₄×C₅₉	C₂³	semidirect
109. #117×C₅₉	C₂³	semidirect
110. C₂×C₄⋊C₄×C₅₉	C₂³	semidirect
112. C₂×C₂²⋊C₄×C₅₉	C₂³	semidirect
113. C₂×C₂²⋊C₄×C₅₉	C₂³	semidirect
114. C₂×C₄²×C₅₉	C₂³	semidirect
116. C₂⁴×C₅₉	C₂²×C₄	semidirect
128. C₂³×D₅₉	C₂²×C₄	semidirect
129. C₂³×D₅₉	C₂²×C₄	semidirect
130. C₂³×D₅₉	C₂²×C₄	semidirect
138. C₂×D₄×C₅₉	C₂²×C₄	semidirect
139. C₂×D₄×C₅₉	C₂²×C₄	semidirect
142. C₂²×C₄×C₅₉	C₂²×C₄	semidirect
146. C₂²×C₄×C₅₉	C₂⁴	semidirect
147. C₂×C₂²⋊D₅₉	C₂²×C₄	semidirect
148. C₂×C₂²⋊D₅₉	C₂²×C₄	semidirect
151. C₂²×Dic₅₉	C₂²×C₄	semidirect
155. C₂²×Dic₅₉	C₂⁴	semidirect
156. D₄×D₅₉	C₂²×C₄	semidirect
157. D₄×D₅₉	C₂²×C₄	semidirect
158. C₂×D₂₃₆	C₂²×C₄	semidirect
159. C₂×D₂₃₆	C₂²×C₄	semidirect
165. C₂×C₄×D₅₉	C₂²×C₄	semidirect
166. C₂×C₄×D₅₉	C₂²×C₄	semidirect
170. C₂×C₄×D₅₉	C₂⁴	semidirect
171. C₄⋊C₄×C₅₉	C₂⁴	semidirect
173. C₂²⋊C₄×C₅₉	C₂⁴	semidirect
174. C₄²×C₅₉	C₂⁴	semidirect
176. C₂²⋊Dic₅₉	C₂⁴	semidirect
178. (C₂×D₅₉)⋊C₄	C₂⁴	semidirect
179. C₄⋊Dic₅₉	C₂⁴	semidirect
180. Dic₅₉⋊C₄	C₂⁴	semidirect
181. C₄×Dic₅₉	C₂⁴	semidirect
182. C₄×Dic₅₉	C₂⁴	semidirect
189. C₂³×C₅₉	C₂³×C₄	semidirect
209. C₂²×D₅₉	C₂³×C₄	semidirect
210. C₂²×D₅₉	C₂³×C₄	semidirect
215. D₄×C₅₉	C₂³×C₄	semidirect
219. C₂×C₄×C₅₉	C₂³×C₄	semidirect
222. C₂²⋊D₅₉	C₂³×C₄	semidirect
226. C₂×Dic₅₉	C₂³×C₄	semidirect
229. D₂₃₆	C₂³×C₄	semidirect
233. C₄×D₅₉	C₂³×C₄	semidirect
253. C₂×D₅₉	#518	direct (N × H)
268. C₂×#518	D₅₉	direct (N × H)
274. C₂×C₅₉	C₂×#518	semidirect
279. D₅₉	C₂×#518	direct (N × H)
294. #518	C₂×D₅₉	direct (N × H)
301. C₂×C₄×D₄	C₂×D₅₉	semidirect
307. C₂×#117	C₂×D₅₉	semidirect
316. C₂²×C₂²⋊C₄	C₂×D₅₉	semidirect
318. C₅₉	C₂²×#518	semidirect
338. C₂²×D₄	C₄×D₅₉	semidirect
352. C₂³×C₄	C₂²×D₅₉	semidirect
358. C₄×D₄	C₂²×D₅₉	semidirect
363. #117	C₂²×D₅₉	semidirect
367. C₂×C₄⋊C₄	C₂²×D₅₉	semidirect
379. C₂×C₂²⋊C₄	C₂²×D₅₉	semidirect
380. C₂×C₂²⋊C₄	C₂²×D₅₉	semidirect
384. C₂×C₄²	C₂²×D₅₉	semidirect
404. C₂⁴	C₂×C₄×D₅₉	semidirect
416. C₂×D₄	C₂×C₄×D₅₉	semidirect
417. C₂×D₄	C₂×C₄×D₅₉	semidirect
436. C₂²×C₄	C₂×C₄×D₅₉	semidirect
440. C₂²×C₄	C₂³×D₅₉	semidirect
443. C₄⋊C₄	C₂³×D₅₉	semidirect
449. C₂²⋊C₄	C₂³×D₅₉	semidirect
452. C₄²	C₂³×D₅₉	semidirect
481. C₂³	C₂²×C₄×D₅₉	semidirect
487. D₄	C₂²×C₄×D₅₉	semidirect
501. C₂×C₄	C₂²×C₄×D₅₉	semidirect
536. C₂	#518×D₅₉	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂³×D₄×D₅₉	2
C₂×#16837877	2
C₂×#16837876	2
C₂×#16837875	2
C₂×#16837874	2
#518×D₅₉	2
C₂×C₄×D₄×D₅₉	2
C₂×#117×D₅₉	2
C₂²×C₂²⋊C₄×D₅₉	2
C₂×C₅₉×#518	2
C₂²×#518	59

Subgroups — C2×#518×D59 #29495266

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#518×D₅₉ #29495266