Subgroups — C₂²×#16837875 #29495268

Order 15104.

14590 conjugacy classes of subgroups.

The subgroup lattice has 372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂⁴×C₂²⋊D₅₉	C₂	1	1	yes	maximal, characteristic
2	C₂×#16837875	C₂	1	48	yes	maximal, direct product factor
3	C₂²×C₄×C₂²⋊D₅₉	C₂	1	4	yes	maximal, complemented
4	C₂²×(C₂²⋊D₅₉)⋊C₄	C₂	1	4	yes	maximal, complemented
5	C₂²×#14273683	C₂	1	2	yes	maximal, complemented
6	C₂³×C₂²⋊Dic₅₉	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂²×C₂²⋊C₄×D₅₉	C₂	1	2	yes	maximal, complemented
8	C₂³×C₂²⋊C₄×C₅₉	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂⁵×D₅₉	C₂²	1	1	yes	characteristic
10	C₂³×C₂²⋊D₅₉	C₄	1	32	yes	complemented
11	C₂³×C₂²⋊D₅₉	C₂²	1	2	yes	—
12	C₂³×C₂²⋊D₅₉	C₂²	1	2	yes	—
13	C₂³×C₂²⋊D₅₉	C₂²	1	24	yes	—
14	C₂⁴×Dic₅₉	C₂²	1	1	yes	characteristic
15	C₂⁴×Dic₅₉	C₂²	1	2	yes	complemented
16	C₂³×C₄×D₅₉	C₂²	1	4	yes	complemented
17	#16837875	C₂²	1	256	yes	direct product factor
18	C₂×C₄×C₂²⋊D₅₉	C₂²	1	96	yes	complemented
19	C₂×(C₂²⋊D₅₉)⋊C₄	C₂²	1	96	yes	complemented
20	C₂×#14273683	C₂²	1	48	yes	complemented
21	C₂²×Dic₅₉⋊C₄	C₂²	1	4	yes	complemented
22	C₂²×C₂²⋊Dic₅₉	C₂²	1	2	yes	—
23	C₂²×C₂²⋊Dic₅₉	C₂²	1	24	yes	complemented
24	C₂²×C₂²⋊Dic₅₉	C₂²	1	2	yes	complemented
25	C₂²×(C₂×D₅₉)⋊C₄	C₂²	1	4	yes	complemented
26	C₂×C₂²⋊C₄×D₅₉	C₂²	1	48	yes	complemented
27	C₂²×C₄×Dic₅₉	C₂²	1	4	yes	complemented
28	C₂⁶×C₅₉	C₂²	1	1	yes	characteristic
29	C₂⁴×C₄×C₅₉	C₂²	1	2	yes	complemented
30	C₂²×C₂²⋊C₄×C₅₉	C₂²	1	2	yes	—
31	C₂²×C₂²⋊C₄×C₅₉	C₂²	1	24	yes	complemented
32	C₂²×C₂²⋊C₄×C₅₉	C₂²	1	2	yes	complemented
33	C₂⁴×D₅₉	—	4	8	no	—
34	C₂⁴×D₅₉	C₂×C₄	1	16	yes	complemented
35	C₂⁴×D₅₉	C₂³	1	2	yes	—
36	C₂⁴×D₅₉	C₂³	1	12	yes	—
37	C₂²×C₂²⋊D₅₉	C₂×C₄	1	32	yes	complemented
38	C₂²×C₂²⋊D₅₉	C₂×C₄	1	32	yes	complemented
39	C₂²×C₂²⋊D₅₉	C₂×C₄	1	384	yes	complemented
40	C₂²×C₂²⋊D₅₉	C₂³	1	24	yes	—
41	C₂²×C₂²⋊D₅₉	C₂³	1	24	yes	—
42	C₂²×C₂²⋊D₅₉	C₂³	1	64	yes	—
43	C₂³×Dic₅₉	—	4	8	no	—
44	C₂³×Dic₅₉	C₂×C₄	1	16	yes	complemented
45	C₂³×Dic₅₉	C₂³	1	4	yes	—
46	C₂³×Dic₅₉	C₂³	1	2	yes	—
47	C₂³×Dic₅₉	C₂³	1	12	yes	—
48	C₂³×Dic₅₉	C₂³	1	24	yes	complemented
49	C₂²×C₄×D₅₉	—	4	16	no	—
50	C₂²×C₄×D₅₉	C₂³	1	48	yes	complemented
51	C₄×C₂²⋊D₅₉	C₂³	1	256	yes	complemented
52	(C₂²⋊D₅₉)⋊C₄	C₂³	1	256	yes	complemented
53	#14273683	C₂³	1	128	yes	complemented
54	C₂×Dic₅₉⋊C₄	C₂³	1	48	yes	complemented
55	C₂×C₂²⋊Dic₅₉	C₂³	1	24	yes	—
56	C₂×C₂²⋊Dic₅₉	C₂³	1	64	yes	complemented
57	C₂×C₂²⋊Dic₅₉	C₂³	1	24	yes	complemented
58	C₂×(C₂×D₅₉)⋊C₄	C₂³	1	48	yes	complemented
59	C₂²⋊C₄×D₅₉	C₂³	1	128	yes	complemented
60	C₂×C₄×Dic₅₉	C₂³	1	48	yes	complemented
61	C₂⁵×C₅₉	—	4	8	no	—
62	C₂⁵×C₅₉	C₂×C₄	1	16	yes	complemented
63	C₂⁵×C₅₉	C₂³	1	1	yes	characteristic
64	C₂⁵×C₅₉	C₂³	1	1	yes	characteristic
65	C₂⁵×C₅₉	C₂³	1	1	yes	characteristic
66	C₂⁵×C₅₉	C₂³	1	12	yes	—
67	C₂³×C₄×C₅₉	—	4	8	no	—
68	C₂³×C₄×C₅₉	C₂³	1	4	yes	—
69	C₂³×C₄×C₅₉	C₂³	1	24	yes	complemented
70	C₂×C₂²⋊C₄×C₅₉	C₂³	1	24	yes	—
71	C₂×C₂²⋊C₄×C₅₉	C₂³	1	64	yes	complemented
72	C₂×C₂²⋊C₄×C₅₉	C₂³	1	24	yes	complemented
73	C₂⁴×C₅₉	—	2	8	no	—
74	C₂⁴×C₅₉	—	2	8	no	—
75	C₂⁴×C₅₉	—	2	8	no	—
76	C₂⁴×C₅₉	—	4	64	no	—
77	C₂⁴×C₅₉	—	4	48	no	—
78	C₂⁴×C₅₉	C₂²×C₄	1	8	yes	—
79	C₂⁴×C₅₉	C₂²×C₄	1	8	yes	—
80	C₂⁴×C₅₉	C₂²×C₄	1	8	yes	—
81	C₂⁴×C₅₉	C₂²×C₄	1	96	yes	complemented
82	C₂⁴×C₅₉	C₂⁴	1	6	yes	—
83	C₂⁴×C₅₉	C₂⁴	1	6	yes	—
84	C₂⁴×C₅₉	C₂⁴	1	6	yes	—
85	C₂⁴×C₅₉	C₂⁴	1	16	yes	—
86	C₂⁴×C₅₉	C₂⁴	1	1	yes	characteristic
87	C₂³×D₅₉	—	2	16	no	—
88	C₂³×D₅₉	—	4	64	no	—
89	C₂³×D₅₉	—	4	48	no	—
90	C₂³×D₅₉	C₂²×C₄	1	16	yes	—
91	C₂³×D₅₉	C₂²×C₄	1	96	yes	complemented
92	C₂³×D₅₉	C₂⁴	1	12	yes	—
93	C₂³×D₅₉	C₂⁴	1	16	yes	—
94	C₂²×C₄×C₅₉	—	2	16	no	—
95	C₂²×C₄×C₅₉	—	4	48	no	—
96	C₂²×C₄×C₅₉	C₂⁴	1	24	yes	—
97	C₂²×C₄×C₅₉	C₂⁴	1	32	yes	complemented
98	C₂×C₂²⋊D₅₉	C₂²×C₄	1	192	yes	complemented
99	C₂×C₂²⋊D₅₉	C₂²×C₄	1	192	yes	complemented
100	C₂×C₂²⋊D₅₉	C₂²×C₄	1	512	yes	complemented
101	C₂×C₂²⋊D₅₉	C₂⁴	1	32	yes	—
102	C₂×C₂²⋊D₅₉	C₂⁴	1	32	yes	—
103	C₂²×Dic₅₉	—	2	16	no	—
104	C₂²×Dic₅₉	—	4	48	no	—
105	C₂²×Dic₅₉	C₂²×C₄	1	16	yes	—
106	C₂²×Dic₅₉	C₂²×C₄	1	96	yes	complemented
107	C₂²×Dic₅₉	C₂⁴	1	24	yes	—
108	C₂²×Dic₅₉	C₂⁴	1	12	yes	—
109	C₂²×Dic₅₉	C₂⁴	1	16	yes	—
110	C₂²×Dic₅₉	C₂⁴	1	32	yes	complemented
111	C₂×C₄×D₅₉	—	4	96	no	—
112	C₂×C₄×D₅₉	C₂⁴	1	64	yes	complemented
113	C₂²⋊C₄×C₅₉	C₂⁴	1	32	yes	—
114	C₂²⋊C₄×C₅₉	C₂⁴	1	32	yes	complemented
115	C₂²⋊Dic₅₉	C₂⁴	1	32	yes	—
116	C₂²⋊Dic₅₉	C₂⁴	1	32	yes	complemented
117	(C₂×D₅₉)⋊C₄	C₂⁴	1	64	yes	complemented
118	Dic₅₉⋊C₄	C₂⁴	1	64	yes	complemented
119	C₄×Dic₅₉	C₂⁴	1	64	yes	complemented
120	C₂³×C₅₉	—	2	32	no	—
121	C₂³×C₅₉	—	2	32	no	—
122	C₂³×C₅₉	—	2	32	no	—
123	C₂³×C₅₉	—	2	24	no	—
124	C₂³×C₅₉	—	2	24	no	—
125	C₂³×C₅₉	—	2	24	no	—
126	C₂³×C₅₉	—	4	192	no	—
127	C₂³×C₅₉	—	4	32	no	—
128	C₂³×C₅₉	C₂³×C₄	1	24	yes	—
129	C₂³×C₅₉	C₂³×C₄	1	24	yes	—
130	C₂³×C₅₉	C₂³×C₄	1	24	yes	—
131	C₂³×C₅₉	C₂³×C₄	1	4	yes	—
132	C₂³×C₅₉	C₂³×C₄	1	64	yes	complemented
133	C₂³×C₅₉	H(5,𝔽₂)	1	8	yes	—
134	C₂³×C₅₉	C₂⁵	1	4	yes	—
135	C₂³×C₅₉	C₂⁵	1	4	yes	—
136	C₂³×C₅₉	C₂⁵	1	4	yes	—
137	C₂³×C₅₉	C₂⁵	1	3	yes	—
138	C₂²×D₅₉	—	2	64	no	—
139	C₂²×D₅₉	—	2	48	no	—
140	C₂²×D₅₉	—	4	192	no	—
141	C₂²×D₅₉	—	4	32	no	—
142	C₂²×D₅₉	C₂³×C₄	1	48	yes	—
143	C₂²×D₅₉	C₂³×C₄	1	64	yes	complemented
144	C₂²×D₅₉	C₂⁵	1	8	yes	—
145	C₂×C₄×C₅₉	—	2	48	no	—
146	C₂×C₄×C₅₉	—	4	32	no	—
147	C₂×C₄×C₅₉	C₂⁵	1	16	yes	—
148	C₂²⋊D₅₉	C₂³×C₄	1	128	yes	complemented
149	C₂²⋊D₅₉	C₂³×C₄	1	128	yes	complemented
150	C₂×Dic₅₉	—	2	48	no	—
151	C₂×Dic₅₉	—	4	32	no	—
152	C₂×Dic₅₉	C₂³×C₄	1	48	yes	—
153	C₂×Dic₅₉	C₂³×C₄	1	64	yes	complemented
154	C₂×Dic₅₉	C₂⁵	1	16	yes	—
155	C₂×Dic₅₉	C₂⁵	1	8	yes	—
156	C₄×D₅₉	—	4	64	no	—
157	C₂²×#518	—	59	1	no	maximal, Sylow
158	C₂²×C₅₉	—	2	8	no	—
159	C₂²×C₅₉	—	2	8	no	—
160	C₂²×C₅₉	—	2	8	no	—
161	C₂²×C₅₉	—	2	48	no	—
162	C₂²×C₅₉	—	2	48	no	—
163	C₂²×C₅₉	—	2	48	no	—
164	C₂²×C₅₉	—	4	64	no	—
165	C₂²×C₅₉	#518	1	16	yes	complemented
166	C₂²×C₅₉	C₂⁴×C₄	1	8	yes	—
167	C₂²×C₅₉	C₂⁴×C₄	1	8	yes	—
168	C₂²×C₅₉	C₂⁴×C₄	1	8	yes	—
169	C₂²×C₅₉	C₂⁴×C₄	1	6	yes	—
170	C₂²×C₅₉	C₂×H(5,𝔽₂)	1	12	yes	—
171	C₂²×C₅₉	C₂⁶	1	1	yes	characteristic
172	C₂×D₅₉	—	2	16	no	—
173	C₂×D₅₉	—	2	96	no	—
174	C₂×D₅₉	—	4	64	no	—
175	C₂×D₅₉	C₂⁴×C₄	1	16	yes	—
176	C₄×C₅₉	—	2	16	no	—
177	Dic₅₉	—	2	16	no	—
178	Dic₅₉	C₂⁴×C₄	1	16	yes	—
179	C₂⁴×D₄	—	59	1	no	—
180	C₂×#518	—	59	48	no	—
181	C₂²×C₄×D₄	—	59	4	no	—
182	C₂²×C₄×D₄	—	59	4	no	—
183	C₂²×#117	—	59	2	no	—
184	C₂³×C₂²⋊C₄	—	59	1	no	—
185	C₂³×C₂²⋊C₄	—	59	2	no	—
186	C₂³×C₂²⋊C₄	D₅₉	1	1	yes	characteristic, complemented
187	C₂×C₅₉	—	2	8	no	—
188	C₂×C₅₉	—	2	8	no	—
189	C₂×C₅₉	—	2	8	no	—
190	C₂×C₅₉	C₂×#518	1	12	yes	complemented
191	C₂×C₅₉	C₂⁵×C₄	1	1	yes	characteristic
192	C₂×C₅₉	C₂²×H(5,𝔽₂)	1	2	yes	—
193	D₅₉	—	2	16	no	—
194	C₂⁶	—	59	1	no	—
195	C₂⁶	C₂×D₅₉	1	1	yes	characteristic
196	C₂³×D₄	—	59	32	no	—
197	C₂³×D₄	—	59	2	no	—
198	C₂³×D₄	—	59	2	no	—
199	C₂³×D₄	—	59	24	no	—
200	C₂⁴×C₄	—	59	1	no	—
201	C₂⁴×C₄	—	59	2	no	—
202	C₂⁴×C₄	—	59	4	no	—
203	C₂⁴×C₄	C₂×D₅₉	1	2	yes	complemented
204	#518	—	59	256	no	—
205	C₂×C₄×D₄	—	59	96	no	—
206	C₂×C₄×D₄	—	59	96	no	—
207	C₂×#117	—	59	48	no	—
208	C₂²×C₄⋊C₄	—	59	4	no	—
209	C₂²×C₂²⋊C₄	—	59	2	no	—
210	C₂²×C₂²⋊C₄	—	59	2	no	—
211	C₂²×C₂²⋊C₄	—	59	24	no	—
212	C₂²×C₂²⋊C₄	—	59	4	no	—
213	C₂²×C₂²⋊C₄	—	59	48	no	—
214	C₂²×C₂²⋊C₄	C₂×D₅₉	1	2	yes	—
215	C₂²×C₂²⋊C₄	C₂×D₅₉	1	24	yes	complemented
216	C₂²×C₂²⋊C₄	C₂×D₅₉	1	2	yes	complemented
217	C₂²×C₄²	—	59	4	no	—
218	C₅₉	C₂²×#518	1	1	yes	characteristic, complemented, Sylow
219	C₂⁵	—	4	8	no	—
220	C₂⁵	—	59	2	no	—
221	C₂⁵	—	59	16	no	—
222	C₂⁵	—	59	12	no	—
223	C₂⁵	—	236	8	no	—
224	C₂⁵	C₄×D₅₉	1	16	yes	complemented
225	C₂⁵	C₂²×D₅₉	1	1	yes	characteristic
226	C₂⁵	C₂²×D₅₉	1	1	yes	characteristic
227	C₂⁵	C₂²×D₅₉	1	1	yes	characteristic
228	C₂⁵	C₂²×D₅₉	1	12	yes	—
229	C₂²×D₄	—	59	32	no	—
230	C₂²×D₄	—	59	32	no	—
231	C₂²×D₄	—	59	384	no	—
232	C₂²×D₄	—	59	24	no	—
233	C₂²×D₄	—	59	24	no	—
234	C₂²×D₄	—	59	64	no	—
235	C₂³×C₄	—	4	8	no	—
236	C₂³×C₄	—	59	16	no	—
237	C₂³×C₄	—	59	12	no	—
238	C₂³×C₄	—	59	2	no	—
239	C₂³×C₄	—	59	4	no	—
240	C₂³×C₄	—	59	24	no	—
241	C₂³×C₄	—	59	48	no	—
242	C₂³×C₄	—	236	16	no	—
243	C₂³×C₄	—	236	8	no	—
244	C₂³×C₄	C₂²×D₅₉	1	4	yes	—
245	C₂³×C₄	C₂²×D₅₉	1	24	yes	complemented
246	C₄×D₄	—	59	256	no	—
247	C₄×D₄	—	59	256	no	—
248	#117	—	59	128	no	—
249	C₂×C₄⋊C₄	—	59	48	no	—
250	C₂×C₂²⋊C₄	—	59	24	no	—
251	C₂×C₂²⋊C₄	—	59	24	no	—
252	C₂×C₂²⋊C₄	—	59	64	no	—
253	C₂×C₂²⋊C₄	—	59	48	no	—
254	C₂×C₂²⋊C₄	—	59	128	no	—
255	C₂×C₂²⋊C₄	C₂²×D₅₉	1	24	yes	—
256	C₂×C₂²⋊C₄	C₂²×D₅₉	1	64	yes	complemented
257	C₂×C₂²⋊C₄	C₂²×D₅₉	1	24	yes	complemented
258	C₂×C₄²	—	59	48	no	—
259	C₂⁴	—	2	8	no	—
260	C₂⁴	—	2	8	no	—
261	C₂⁴	—	2	8	no	—
262	C₂⁴	—	4	64	no	—
263	C₂⁴	—	4	48	no	—
264	C₂⁴	—	59	16	no	—
265	C₂⁴	—	59	12	no	—
266	C₂⁴	—	59	96	no	—
267	C₂⁴	—	59	16	no	—
268	C₂⁴	—	118	16	no	—
269	C₂⁴	—	236	48	no	—
270	C₂⁴	—	236	64	no	—
271	C₂⁴	C₂×C₄×D₅₉	1	8	yes	—
272	C₂⁴	C₂×C₄×D₅₉	1	8	yes	—
273	C₂⁴	C₂×C₄×D₅₉	1	8	yes	—
274	C₂⁴	C₂×C₄×D₅₉	1	96	yes	complemented
275	C₂⁴	C₂³×D₅₉	1	6	yes	—
276	C₂⁴	C₂³×D₅₉	1	6	yes	—
277	C₂⁴	C₂³×D₅₉	1	6	yes	—
278	C₂⁴	C₂³×D₅₉	1	16	yes	—
279	C₂⁴	C₂³×D₅₉	1	1	yes	characteristic
280	C₂×D₄	—	59	192	no	—
281	C₂×D₄	—	59	192	no	—
282	C₂×D₄	—	59	512	no	—
283	C₂×D₄	—	59	32	no	—
284	C₂×D₄	—	59	32	no	—
285	C₂²×C₄	—	2	16	no	—
286	C₂²×C₄	—	4	48	no	—
287	C₂²×C₄	—	59	16	no	—
288	C₂²×C₄	—	59	96	no	—
289	C₂²×C₄	—	59	12	no	—
290	C₂²×C₄	—	59	16	no	—
291	C₂²×C₄	—	59	24	no	—
292	C₂²×C₄	—	59	32	no	—
293	C₂²×C₄	—	59	64	no	—
294	C₂²×C₄	—	118	16	no	—
295	C₂²×C₄	—	236	96	no	—
296	C₂²×C₄	—	236	48	no	—
297	C₂²×C₄	C₂³×D₅₉	1	24	yes	—
298	C₂²×C₄	C₂³×D₅₉	1	32	yes	complemented
299	C₄⋊C₄	—	59	64	no	—
300	C₂²⋊C₄	—	59	32	no	—
301	C₂²⋊C₄	—	59	32	no	—
302	C₂²⋊C₄	—	59	64	no	—
303	C₂²⋊C₄	C₂³×D₅₉	1	32	yes	—
304	C₂²⋊C₄	C₂³×D₅₉	1	32	yes	complemented
305	C₄²	—	59	64	no	—
306	C₂³	—	2	24	no	—
307	C₂³	—	2	24	no	—
308	C₂³	—	2	24	no	—
309	C₂³	—	2	32	no	—
310	C₂³	—	2	32	no	—
311	C₂³	—	2	32	no	—
312	C₂³	—	4	192	no	—
313	C₂³	—	4	32	no	—
314	C₂³	—	59	48	no	—
315	C₂³	—	59	8	no	—
316	C₂³	—	59	64	no	—
317	C₂³	—	118	48	no	—
318	C₂³	—	118	64	no	—
319	C₂³	—	236	192	no	—
320	C₂³	—	236	32	no	—
321	C₂³	C₂²×C₄×D₅₉	1	24	yes	—
322	C₂³	C₂²×C₄×D₅₉	1	24	yes	—
323	C₂³	C₂²×C₄×D₅₉	1	24	yes	—
324	C₂³	C₂²×C₄×D₅₉	1	4	yes	—
325	C₂³	C₂²×C₄×D₅₉	1	64	yes	complemented
326	C₂³	#14273772	1	8	yes	—
327	C₂³	C₂⁴×D₅₉	1	4	yes	—
328	C₂³	C₂⁴×D₅₉	1	4	yes	—
329	C₂³	C₂⁴×D₅₉	1	4	yes	—
330	C₂³	C₂⁴×D₅₉	1	3	yes	—
331	D₄	—	59	128	no	—
332	D₄	—	59	128	no	—
333	C₂×C₄	—	2	48	no	—
334	C₂×C₄	—	4	32	no	—
335	C₂×C₄	—	59	48	no	—
336	C₂×C₄	—	59	64	no	—
337	C₂×C₄	—	59	8	no	—
338	C₂×C₄	—	59	16	no	—
339	C₂×C₄	—	118	48	no	—
340	C₂×C₄	—	236	64	no	—
341	C₂×C₄	—	236	32	no	—
342	C₂×C₄	C₂⁴×D₅₉	1	16	yes	—
343	C₂²	—	2	48	no	—
344	C₂²	—	2	48	no	—
345	C₂²	—	2	48	no	—
346	C₂²	—	2	8	no	—
347	C₂²	—	2	8	no	—
348	C₂²	—	2	8	no	—
349	C₂²	—	4	64	no	—
350	C₂²	—	59	16	no	—
351	C₂²	—	118	96	no	—
352	C₂²	—	118	16	no	—
353	C₂²	—	236	64	no	—
354	C₂²	#16837875	1	16	yes	direct product factor
355	C₂²	C₂³×C₄×D₅₉	1	8	yes	—
356	C₂²	C₂³×C₄×D₅₉	1	8	yes	—
357	C₂²	C₂³×C₄×D₅₉	1	8	yes	—
358	C₂²	C₂³×C₄×D₅₉	1	6	yes	—
359	C₂²	C₂×#14273772	1	12	yes	—
360	C₂²	C₂⁵×D₅₉	1	1	yes	characteristic
361	C₄	—	2	16	no	—
362	C₄	—	59	16	no	—
363	C₄	—	118	16	no	—
364	C₂	—	2	8	no	—
365	C₂	—	2	8	no	—
366	C₂	—	2	8	no	—
367	C₂	—	118	16	no	—
368	C₂	C₂×#16837875	1	12	yes	direct product factor
369	C₂	C₂⁴×C₄×D₅₉	1	1	yes	characteristic
370	C₂	C₂²×#14273772	1	2	yes	—

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

Complements

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

N	H ≅ G/N	type
2. C₂×#16837875	C₂	direct (N × H)
3. C₂²×C₄×C₂²⋊D₅₉	C₂	semidirect
4. C₂²×(C₂²⋊D₅₉)⋊C₄	C₂	semidirect
5. C₂²×#14273683	C₂	semidirect
6. C₂³×C₂²⋊Dic₅₉	C₂	semidirect
7. C₂²×C₂²⋊C₄×D₅₉	C₂	semidirect
8. C₂³×C₂²⋊C₄×C₅₉	C₂	semidirect
10. C₂³×C₂²⋊D₅₉	C₄	semidirect
15. C₂⁴×Dic₅₉	C₂²	semidirect
16. C₂³×C₄×D₅₉	C₂²	semidirect
17. #16837875	C₂²	direct (N × H)
18. C₂×C₄×C₂²⋊D₅₉	C₂²	semidirect
19. C₂×(C₂²⋊D₅₉)⋊C₄	C₂²	semidirect
20. C₂×#14273683	C₂²	semidirect
21. C₂²×Dic₅₉⋊C₄	C₂²	semidirect
23. C₂²×C₂²⋊Dic₅₉	C₂²	semidirect
24. C₂²×C₂²⋊Dic₅₉	C₂²	semidirect
25. C₂²×(C₂×D₅₉)⋊C₄	C₂²	semidirect
26. C₂×C₂²⋊C₄×D₅₉	C₂²	semidirect
27. C₂²×C₄×Dic₅₉	C₂²	semidirect
29. C₂⁴×C₄×C₅₉	C₂²	semidirect
31. C₂²×C₂²⋊C₄×C₅₉	C₂²	semidirect
32. C₂²×C₂²⋊C₄×C₅₉	C₂²	semidirect
34. C₂⁴×D₅₉	C₂×C₄	semidirect
37. C₂²×C₂²⋊D₅₉	C₂×C₄	semidirect
38. C₂²×C₂²⋊D₅₉	C₂×C₄	semidirect
39. C₂²×C₂²⋊D₅₉	C₂×C₄	semidirect
44. C₂³×Dic₅₉	C₂×C₄	semidirect
48. C₂³×Dic₅₉	C₂³	semidirect
50. C₂²×C₄×D₅₉	C₂³	semidirect
51. C₄×C₂²⋊D₅₉	C₂³	semidirect
52. (C₂²⋊D₅₉)⋊C₄	C₂³	semidirect
53. #14273683	C₂³	semidirect
54. C₂×Dic₅₉⋊C₄	C₂³	semidirect
56. C₂×C₂²⋊Dic₅₉	C₂³	semidirect
57. C₂×C₂²⋊Dic₅₉	C₂³	semidirect
58. C₂×(C₂×D₅₉)⋊C₄	C₂³	semidirect
59. C₂²⋊C₄×D₅₉	C₂³	semidirect
60. C₂×C₄×Dic₅₉	C₂³	semidirect
62. C₂⁵×C₅₉	C₂×C₄	semidirect
69. C₂³×C₄×C₅₉	C₂³	semidirect
71. C₂×C₂²⋊C₄×C₅₉	C₂³	semidirect
72. C₂×C₂²⋊C₄×C₅₉	C₂³	semidirect
81. C₂⁴×C₅₉	C₂²×C₄	semidirect
91. C₂³×D₅₉	C₂²×C₄	semidirect
97. C₂²×C₄×C₅₉	C₂⁴	semidirect
98. C₂×C₂²⋊D₅₉	C₂²×C₄	semidirect
99. C₂×C₂²⋊D₅₉	C₂²×C₄	semidirect
100. C₂×C₂²⋊D₅₉	C₂²×C₄	semidirect
106. C₂²×Dic₅₉	C₂²×C₄	semidirect
110. C₂²×Dic₅₉	C₂⁴	semidirect
112. C₂×C₄×D₅₉	C₂⁴	semidirect
114. C₂²⋊C₄×C₅₉	C₂⁴	semidirect
116. C₂²⋊Dic₅₉	C₂⁴	semidirect
117. (C₂×D₅₉)⋊C₄	C₂⁴	semidirect
118. Dic₅₉⋊C₄	C₂⁴	semidirect
119. C₄×Dic₅₉	C₂⁴	semidirect
132. C₂³×C₅₉	C₂³×C₄	semidirect
143. C₂²×D₅₉	C₂³×C₄	semidirect
148. C₂²⋊D₅₉	C₂³×C₄	semidirect
149. C₂²⋊D₅₉	C₂³×C₄	semidirect
153. C₂×Dic₅₉	C₂³×C₄	semidirect
165. C₂²×C₅₉	#518	semidirect
186. C₂³×C₂²⋊C₄	D₅₉	semidirect
190. C₂×C₅₉	C₂×#518	semidirect
203. C₂⁴×C₄	C₂×D₅₉	semidirect
215. C₂²×C₂²⋊C₄	C₂×D₅₉	semidirect
216. C₂²×C₂²⋊C₄	C₂×D₅₉	semidirect
218. C₅₉	C₂²×#518	semidirect
224. C₂⁵	C₄×D₅₉	semidirect
245. C₂³×C₄	C₂²×D₅₉	semidirect
256. C₂×C₂²⋊C₄	C₂²×D₅₉	semidirect
257. C₂×C₂²⋊C₄	C₂²×D₅₉	semidirect
274. C₂⁴	C₂×C₄×D₅₉	semidirect
298. C₂²×C₄	C₂³×D₅₉	semidirect
304. C₂²⋊C₄	C₂³×D₅₉	semidirect
325. C₂³	C₂²×C₄×D₅₉	semidirect
354. C₂²	#16837875	direct (N × H)
368. C₂	C₂×#16837875	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂⁴×C₂²⋊D₅₉	2
C₂×#16837875	2
C₂²×C₄×C₂²⋊D₅₉	2
C₂²×(C₂²⋊D₅₉)⋊C₄	2
C₂²×#14273683	2
C₂³×C₂²⋊Dic₅₉	2
C₂²×C₂²⋊C₄×D₅₉	2
C₂³×C₂²⋊C₄×C₅₉	2
C₂²×#518	59

Subgroups — C22×#16837875 #29495268

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×#16837875 #29495268