Subgroups — C₄×C₅₉×#532 #28446147

Order 15104.

3526 conjugacy classes of subgroups.

The subgroup lattice has 458 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅₉×#532	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×#41×C₅₉	C₂	1	2	yes	maximal, complemented
3	C₄×C₄⋊Q₈×C₅₉	C₂	1	2	yes	maximal, complemented
4	C₄×#127×C₅₉	C₂	1	2	yes	maximal, complemented
5	C₄×#124×C₅₉	C₂	1	4	yes	maximal, complemented
6	C₄×#121×C₅₉	C₂	1	8	yes	maximal, complemented
7	C₅₉×#2297	C₂	1	2	yes	maximal, complemented
8	C₅₉×#2293	C₂	1	4	yes	maximal, complemented
9	C₅₉×#2285	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄²×D₄×C₅₉	C₂	1	4	yes	maximal, complemented
11	C₂×C₄³×C₅₉	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×#41×C₅₉	C₂²	1	2	yes	—
13	C₅₉×#532	C₄	1	16	yes	direct product factor
14	C₂×C₄⋊Q₈×C₅₉	C₂²	1	1	yes	characteristic
15	C₂×#127×C₅₉	C₂²	1	1	yes	characteristic
16	C₂×#124×C₅₉	C₂²	1	2	yes	—
17	C₂×#121×C₅₉	C₂²	1	4	yes	—
18	C₄×#41×C₅₉	—	2	16	no	—
19	C₂×C₄×Q₈×C₅₉	C₂²	1	4	yes	—
20	C₂×C₄×D₄×C₅₉	C₂²	1	8	yes	—
21	C₂×C₄×D₄×C₅₉	C₂²	1	8	yes	—
22	C₂×C₄×D₄×C₅₉	C₂²	1	4	yes	—
23	C₂×C₄×D₄×C₅₉	C₂²	1	4	yes	—
24	C₂×#117×C₅₉	C₂²	1	2	yes	—
25	C₂×#117×C₅₉	C₂²	1	4	yes	—
26	C₂²×C₄²×C₅₉	C₂²	1	1	yes	characteristic
27	C₂²×C₄²×C₅₉	C₂²	1	4	yes	—
28	C₂²×C₄²×C₅₉	C₂²	1	4	yes	—
29	C₂²×C₄²×C₅₉	C₂²	1	1	yes	characteristic
30	C₂²×C₄²×C₅₉	C₂²	1	1	yes	characteristic
31	C₅₉×#391	C₂²	1	4	yes	—
32	C₅₉×#390	C₂²	1	8	yes	—
33	C₅₉×#390	C₂²	1	4	yes	—
34	C₅₉×#389	C₂²	1	8	yes	—
35	C₅₉×#388	C₂²	1	16	yes	—
36	C₅₉×#386	C₂²	1	8	yes	—
37	C₅₉×#384	C₂²	1	2	yes	—
38	C₅₉×#382	C₂²	1	2	yes	—
39	C₅₉×#380	C₂²	1	4	yes	—
40	C₄×C₄⋊C₄×C₅₉	C₂²	1	4	yes	—
41	C₄×C₄⋊C₄×C₅₉	C₂²	1	8	yes	—
42	C₄×C₂²⋊C₄×C₅₉	C₂²	1	8	yes	—
43	C₄×C₂²⋊C₄×C₅₉	C₂²	1	16	yes	—
44	C₄³×C₅₉	C₂²	1	2	yes	—
45	C₄³×C₅₉	C₂²	1	2	yes	—
46	C₄³×C₅₉	C₂²	1	2	yes	—
47	C₄³×C₅₉	C₂²	1	2	yes	—
48	C₂×#41×C₅₉	—	2	8	no	—
49	C₂×#41×C₅₉	—	2	8	no	—
50	C₂×#41×C₅₉	C₂×C₄	1	16	yes	complemented
51	C₂²×Q₈×C₅₉	C₂³	1	2	yes	—
52	C₂²×D₄×C₅₉	C₂³	1	4	yes	—
53	C₂²×D₄×C₅₉	C₂³	1	4	yes	—
54	C₂²×D₄×C₅₉	C₂³	1	2	yes	—
55	C₂³×C₄×C₅₉	C₂³	1	8	yes	—
56	C₂³×C₄×C₅₉	C₂³	1	2	yes	—
57	C₂³×C₄×C₅₉	C₂³	1	4	yes	—
58	C₂³×C₄×C₅₉	C₂³	1	2	yes	—
59	C₂³×C₄×C₅₉	C₂³	1	2	yes	—
60	C₂³×C₄×C₅₉	C₂³	1	1	yes	characteristic
61	C₄⋊Q₈×C₅₉	C₂×C₄	1	8	yes	complemented
62	#127×C₅₉	C₂×C₄	1	8	yes	complemented
63	#124×C₅₉	C₂×C₄	1	16	yes	complemented
64	#121×C₅₉	C₂×C₄	1	32	yes	complemented
65	C₄×Q₈×C₅₉	—	2	16	no	—
66	C₄×D₄×C₅₉	—	2	32	no	—
67	C₄×D₄×C₅₉	—	2	16	no	—
68	C₄×D₄×C₅₉	—	2	32	no	—
69	C₄×D₄×C₅₉	C₂×C₄	1	32	yes	complemented
70	#117×C₅₉	—	2	8	no	—
71	#117×C₅₉	—	2	16	no	—
72	C₂×C₄⋊C₄×C₅₉	C₂³	1	8	yes	—
73	C₂×C₄⋊C₄×C₅₉	C₂³	1	4	yes	—
74	C₂×C₄⋊C₄×C₅₉	C₂³	1	8	yes	—
75	C₂×C₄⋊C₄×C₅₉	C₂³	1	4	yes	—
76	C₂×C₂²⋊C₄×C₅₉	C₂³	1	16	yes	—
77	C₂×C₂²⋊C₄×C₅₉	C₂³	1	4	yes	—
78	C₂×C₂²⋊C₄×C₅₉	C₂³	1	8	yes	—
79	C₂×C₂²⋊C₄×C₅₉	C₂³	1	8	yes	—
80	C₂×C₄²×C₅₉	—	2	4	no	—
81	C₂×C₄²×C₅₉	—	2	16	no	—
82	C₂×C₄²×C₅₉	—	2	16	no	—
83	C₂×C₄²×C₅₉	C₂×C₄	1	8	yes	complemented
84	C₂×C₄²×C₅₉	D₄	1	8	yes	complemented
85	C₂×C₄²×C₅₉	C₂³	1	4	yes	—
86	C₂×C₄²×C₅₉	C₂³	1	2	yes	—
87	C₂×C₄²×C₅₉	C₂³	1	4	yes	—
88	C₂×C₄²×C₅₉	C₂³	1	4	yes	—
89	C₂×C₄²×C₅₉	C₂³	1	2	yes	—
90	C₂×C₄²×C₅₉	C₂³	1	4	yes	—
91	C₂×C₄²×C₅₉	C₂³	1	8	yes	—
92	C₂×C₄²×C₅₉	C₂³	1	2	yes	—
93	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
94	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
95	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
96	C₂×C₄²×C₅₉	C₂³	1	2	yes	—
97	C₂×C₄²×C₅₉	C₂³	1	4	yes	—
98	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
99	#95×C₅₉	C₂³	1	8	yes	—
100	#95×C₅₉	C₂³	1	16	yes	—
101	C₂⁴×C₅₉	C₂⁴	1	4	yes	—
102	C₂⁴×C₅₉	C₂⁴	1	1	yes	characteristic
103	#41×C₅₉	—	2	64	no	—
104	C₂×Q₈×C₅₉	—	2	4	no	—
105	C₂×Q₈×C₅₉	—	2	4	no	—
106	C₂×Q₈×C₅₉	C₂²×C₄	1	8	yes	—
107	C₂×D₄×C₅₉	—	2	8	no	—
108	C₂×D₄×C₅₉	—	2	8	no	—
109	C₂×D₄×C₅₉	—	2	4	no	—
110	C₂×D₄×C₅₉	—	2	16	no	—
111	C₂×D₄×C₅₉	—	2	4	no	—
112	C₂×D₄×C₅₉	C₂²×C₄	1	16	yes	—
113	C₂×D₄×C₅₉	C₂²×C₄	1	16	yes	—
114	C₂×D₄×C₅₉	C₂²×C₄	1	8	yes	—
115	C₂²×C₄×C₅₉	—	2	4	no	—
116	C₂²×C₄×C₅₉	—	2	8	no	—
117	C₂²×C₄×C₅₉	—	2	8	no	—
118	C₂²×C₄×C₅₉	—	2	8	no	—
119	C₂²×C₄×C₅₉	—	2	8	no	—
120	C₂²×C₄×C₅₉	—	2	8	no	—
121	C₂²×C₄×C₅₉	—	2	16	no	—
122	C₂²×C₄×C₅₉	—	2	32	no	—
123	C₂²×C₄×C₅₉	C₂²×C₄	1	8	yes	—
124	C₂²×C₄×C₅₉	C₂²×C₄	1	16	yes	—
125	C₂²×C₄×C₅₉	C₂²×C₄	1	4	yes	—
126	C₂²×C₄×C₅₉	C₂×D₄	1	8	yes	—
127	C₂²×C₄×C₅₉	C₂×D₄	1	4	yes	—
128	C₂²×C₄×C₅₉	#41	1	4	yes	—
129	C₂²×C₄×C₅₉	C₂⁴	1	8	yes	—
130	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
131	C₂²×C₄×C₅₉	C₂⁴	1	4	yes	—
132	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
133	C₂²×C₄×C₅₉	C₂⁴	1	4	yes	—
134	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
135	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
136	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
137	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
138	C₄⋊C₄×C₅₉	—	2	16	no	—
139	C₄⋊C₄×C₅₉	—	2	8	no	—
140	C₄⋊C₄×C₅₉	—	2	16	no	—
141	C₄⋊C₄×C₅₉	C₂²×C₄	1	16	yes	—
142	C₂²⋊C₄×C₅₉	—	2	8	no	—
143	C₂²⋊C₄×C₅₉	—	2	16	no	—
144	C₂²⋊C₄×C₅₉	—	2	32	no	—
145	C₂²⋊C₄×C₅₉	C₂²×C₄	1	32	yes	—
146	C₄²×C₅₉	—	2	8	no	—
147	C₄²×C₅₉	—	2	16	no	—
148	C₄²×C₅₉	—	2	8	no	—
149	C₄²×C₅₉	—	2	4	no	—
150	C₄²×C₅₉	—	2	4	no	—
151	C₄²×C₅₉	—	2	8	no	—
152	C₄²×C₅₉	—	2	8	no	—
153	C₄²×C₅₉	C₂²×C₄	1	8	yes	—
154	C₄²×C₅₉	C₂²×C₄	1	4	yes	—
155	C₄²×C₅₉	C₂²×C₄	1	4	yes	—
156	C₄²×C₅₉	C₂×D₄	1	4	yes	—
157	C₄²×C₅₉	C₂×D₄	1	4	yes	—
158	C₄²×C₅₉	C₂×D₄	1	8	yes	—
159	C₄²×C₅₉	#41	1	16	yes	complemented
160	C₂³×C₅₉	—	2	4	no	—
161	C₂³×C₅₉	—	2	4	no	—
162	C₂³×C₅₉	—	2	16	no	—
163	C₂³×C₅₉	—	2	4	no	—
164	C₂³×C₅₉	C₂³×C₄	1	8	yes	—
165	C₂³×C₅₉	C₂³×C₄	1	2	yes	—
166	C₂³×C₅₉	C₂²×D₄	1	2	yes	—
167	C₂³×C₅₉	C₂×#41	1	2	yes	—
168	C₂³×C₅₉	C₂⁵	1	1	yes	characteristic
169	Q₈×C₅₉	—	2	16	no	—
170	D₄×C₅₉	—	2	32	no	—
171	D₄×C₅₉	—	2	16	no	—
172	D₄×C₅₉	—	2	32	no	—
173	C₂×C₄×C₅₉	—	2	16	no	—
174	C₂×C₄×C₅₉	—	2	4	no	—
175	C₂×C₄×C₅₉	—	2	4	no	—
176	C₂×C₄×C₅₉	—	2	4	no	—
177	C₂×C₄×C₅₉	—	2	4	no	—
178	C₂×C₄×C₅₉	—	2	4	no	—
179	C₂×C₄×C₅₉	—	2	4	no	—
180	C₂×C₄×C₅₉	—	2	32	no	—
181	C₂×C₄×C₅₉	—	2	16	no	—
182	C₂×C₄×C₅₉	—	2	16	no	—
183	C₂×C₄×C₅₉	—	2	8	no	—
184	C₂×C₄×C₅₉	—	2	16	no	—
185	C₂×C₄×C₅₉	—	4	32	no	—
186	C₂×C₄×C₅₉	C₄×D₄	1	16	yes	complemented
187	C₂×C₄×C₅₉	C₂³×C₄	1	4	yes	—
188	C₂×C₄×C₅₉	C₂³×C₄	1	8	yes	—
189	C₂×C₄×C₅₉	C₂³×C₄	1	2	yes	—
190	C₂×C₄×C₅₉	C₂³×C₄	1	2	yes	—
191	C₂×C₄×C₅₉	C₂³×C₄	1	4	yes	—
192	C₂×C₄×C₅₉	C₂²×D₄	1	4	yes	—
193	C₂×C₄×C₅₉	C₂²×D₄	1	2	yes	—
194	C₂×C₄×C₅₉	C₂²×D₄	1	2	yes	—
195	C₂×C₄×C₅₉	C₂²×D₄	1	4	yes	—
196	C₂×C₄×C₅₉	C₂×#41	1	8	yes	—
197	C₂×C₄×C₅₉	C₂×#41	1	2	yes	—
198	C₂×C₄×C₅₉	C₂×#41	1	2	yes	—
199	C₂×C₄×C₅₉	C₂×#41	1	8	yes	—
200	C₂×C₄×C₅₉	C₂×#41	1	8	yes	—
201	C₄×#532	C₅₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
202	C₂²×C₅₉	—	2	4	no	—
203	C₂²×C₅₉	—	2	4	no	—
204	C₂²×C₅₉	—	2	4	no	—
205	C₂²×C₅₉	—	2	8	no	—
206	C₂²×C₅₉	—	2	16	no	—
207	C₂²×C₅₉	—	4	8	no	—
208	C₂²×C₅₉	—	4	8	no	—
209	C₂²×C₅₉	C₂×C₄×D₄	1	4	yes	—
210	C₂²×C₅₉	C₂⁴×C₄	1	1	yes	characteristic
211	C₂²×C₅₉	C₂³×D₄	1	1	yes	characteristic
212	C₂²×C₅₉	C₂²×#41	1	1	yes	characteristic
213	C₂²×C₅₉	C₂²×#41	1	4	yes	—
214	C₄×C₅₉	—	2	8	no	—
215	C₄×C₅₉	—	2	4	no	—
216	C₄×C₅₉	—	2	4	no	—
217	C₄×C₅₉	—	2	8	no	—
218	C₄×C₅₉	—	4	8	no	—
219	C₄×C₅₉	C₂×C₄×D₄	1	4	yes	—
220	C₄×C₅₉	C₂×C₄×D₄	1	4	yes	—
221	C₄×C₅₉	C₄×#41	1	8	yes	complemented
222	C₄×C₅₉	#532	1	8	yes	direct product factor
223	C₂×#532	C₂×C₅₉	1	1	yes	characteristic
224	C₂×C₄×#41	C₂×C₅₉	1	2	yes	complemented
225	C₄×C₄⋊Q₈	C₂×C₅₉	1	2	yes	complemented
226	C₄×#127	C₂×C₅₉	1	2	yes	complemented
227	C₄×#124	C₂×C₅₉	1	4	yes	complemented
228	C₄×#121	C₂×C₅₉	1	8	yes	complemented
229	#2297	C₂×C₅₉	1	2	yes	complemented
230	#2293	C₂×C₅₉	1	4	yes	complemented
231	#2285	C₂×C₅₉	1	1	yes	characteristic, complemented
232	C₄²×D₄	C₂×C₅₉	1	4	yes	complemented
233	C₂×C₄³	C₂×C₅₉	1	1	yes	characteristic, complemented
234	C₂×C₅₉	—	2	4	no	—
235	C₂×C₅₉	—	4	8	no	—
236	C₂×C₅₉	C₂²×C₄×D₄	1	1	yes	characteristic
237	C₂×C₅₉	C₂×C₄×#41	1	2	yes	—
238	C₂×C₅₉	C₂×#532	1	2	yes	—
239	C₂×C₅₉	#3444	1	2	yes	—
240	C₂²×#41	C₂²×C₅₉	1	2	yes	—
241	#532	C₄×C₅₉	1	16	yes	direct product factor
242	C₂×C₄⋊Q₈	C₂²×C₅₉	1	1	yes	characteristic
243	C₂×#127	C₂²×C₅₉	1	1	yes	characteristic
244	C₂×#124	C₂²×C₅₉	1	2	yes	—
245	C₂×#121	C₂²×C₅₉	1	4	yes	—
246	C₄×#41	—	2	16	no	—
247	C₂×C₄×Q₈	C₂²×C₅₉	1	4	yes	—
248	C₂×C₄×D₄	C₂²×C₅₉	1	4	yes	—
249	C₂×C₄×D₄	C₂²×C₅₉	1	8	yes	—
250	C₂×C₄×D₄	C₂²×C₅₉	1	8	yes	—
251	C₂×C₄×D₄	C₂²×C₅₉	1	4	yes	—
252	C₂×#117	C₂²×C₅₉	1	2	yes	—
253	C₂×#117	C₂²×C₅₉	1	4	yes	—
254	C₂²×C₄²	C₂²×C₅₉	1	4	yes	—
255	C₂²×C₄²	C₂²×C₅₉	1	1	yes	characteristic
256	C₂²×C₄²	C₂²×C₅₉	1	4	yes	—
257	C₂²×C₄²	C₂²×C₅₉	1	1	yes	characteristic
258	C₂²×C₄²	C₂²×C₅₉	1	1	yes	characteristic
259	#391	C₂²×C₅₉	1	4	yes	—
260	#390	C₂²×C₅₉	1	8	yes	—
261	#390	C₂²×C₅₉	1	4	yes	—
262	#389	C₂²×C₅₉	1	8	yes	—
263	#388	C₂²×C₅₉	1	16	yes	—
264	#386	C₂²×C₅₉	1	8	yes	—
265	#384	C₂²×C₅₉	1	2	yes	—
266	#382	C₂²×C₅₉	1	2	yes	—
267	#380	C₂²×C₅₉	1	4	yes	—
268	C₄×C₄⋊C₄	C₂²×C₅₉	1	8	yes	—
269	C₄×C₄⋊C₄	C₂²×C₅₉	1	4	yes	—
270	C₄×C₂²⋊C₄	C₂²×C₅₉	1	8	yes	—
271	C₄×C₂²⋊C₄	C₂²×C₅₉	1	16	yes	—
272	C₄³	C₂²×C₅₉	1	2	yes	—
273	C₄³	C₂²×C₅₉	1	2	yes	—
274	C₄³	C₂²×C₅₉	1	2	yes	—
275	C₄³	C₂²×C₅₉	1	2	yes	—
276	C₅₉	C₄×#532	1	1	yes	characteristic, direct product factor, Sylow
277	C₂×#41	—	2	8	no	—
278	C₂×#41	—	2	8	no	—
279	C₂×#41	C₂×C₄×C₅₉	1	16	yes	complemented
280	C₂²×Q₈	C₂³×C₅₉	1	2	yes	—
281	C₂²×D₄	C₂³×C₅₉	1	4	yes	—
282	C₂²×D₄	C₂³×C₅₉	1	4	yes	—
283	C₂²×D₄	C₂³×C₅₉	1	2	yes	—
284	C₂³×C₄	C₂³×C₅₉	1	8	yes	—
285	C₂³×C₄	C₂³×C₅₉	1	2	yes	—
286	C₂³×C₄	C₂³×C₅₉	1	4	yes	—
287	C₂³×C₄	C₂³×C₅₉	1	2	yes	—
288	C₂³×C₄	C₂³×C₅₉	1	2	yes	—
289	C₂³×C₄	C₂³×C₅₉	1	1	yes	characteristic
290	C₄⋊Q₈	C₂×C₄×C₅₉	1	8	yes	complemented
291	#127	C₂×C₄×C₅₉	1	8	yes	complemented
292	#124	C₂×C₄×C₅₉	1	16	yes	complemented
293	#121	C₂×C₄×C₅₉	1	32	yes	complemented
294	C₄×Q₈	—	2	16	no	—
295	C₄×D₄	—	2	32	no	—
296	C₄×D₄	—	2	16	no	—
297	C₄×D₄	—	2	32	no	—
298	C₄×D₄	C₂×C₄×C₅₉	1	32	yes	complemented
299	#117	—	2	8	no	—
300	#117	—	2	16	no	—
301	C₂×C₄⋊C₄	C₂³×C₅₉	1	4	yes	—
302	C₂×C₄⋊C₄	C₂³×C₅₉	1	8	yes	—
303	C₂×C₄⋊C₄	C₂³×C₅₉	1	8	yes	—
304	C₂×C₄⋊C₄	C₂³×C₅₉	1	4	yes	—
305	C₂×C₂²⋊C₄	C₂³×C₅₉	1	4	yes	—
306	C₂×C₂²⋊C₄	C₂³×C₅₉	1	8	yes	—
307	C₂×C₂²⋊C₄	C₂³×C₅₉	1	16	yes	—
308	C₂×C₂²⋊C₄	C₂³×C₅₉	1	8	yes	—
309	C₂×C₄²	—	2	4	no	—
310	C₂×C₄²	—	2	16	no	—
311	C₂×C₄²	—	2	16	no	—
312	C₂×C₄²	C₂×C₄×C₅₉	1	8	yes	complemented
313	C₂×C₄²	D₄×C₅₉	1	8	yes	complemented
314	C₂×C₄²	C₂³×C₅₉	1	4	yes	—
315	C₂×C₄²	C₂³×C₅₉	1	8	yes	—
316	C₂×C₄²	C₂³×C₅₉	1	4	yes	—
317	C₂×C₄²	C₂³×C₅₉	1	2	yes	—
318	C₂×C₄²	C₂³×C₅₉	1	4	yes	—
319	C₂×C₄²	C₂³×C₅₉	1	4	yes	—
320	C₂×C₄²	C₂³×C₅₉	1	2	yes	—
321	C₂×C₄²	C₂³×C₅₉	1	2	yes	—
322	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
323	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
324	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
325	C₂×C₄²	C₂³×C₅₉	1	2	yes	—
326	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
327	C₂×C₄²	C₂³×C₅₉	1	4	yes	—
328	#95	C₂³×C₅₉	1	8	yes	—
329	#95	C₂³×C₅₉	1	16	yes	—
330	C₂⁴	C₂⁴×C₅₉	1	4	yes	—
331	C₂⁴	C₂⁴×C₅₉	1	1	yes	characteristic
332	#41	—	2	64	no	—
333	C₂×Q₈	—	2	4	no	—
334	C₂×Q₈	—	2	4	no	—
335	C₂×Q₈	C₂²×C₄×C₅₉	1	8	yes	—
336	C₂×D₄	—	2	8	no	—
337	C₂×D₄	—	2	8	no	—
338	C₂×D₄	—	2	4	no	—
339	C₂×D₄	—	2	16	no	—
340	C₂×D₄	—	2	4	no	—
341	C₂×D₄	C₂²×C₄×C₅₉	1	16	yes	—
342	C₂×D₄	C₂²×C₄×C₅₉	1	16	yes	—
343	C₂×D₄	C₂²×C₄×C₅₉	1	8	yes	—
344	C₂²×C₄	—	2	4	no	—
345	C₂²×C₄	—	2	8	no	—
346	C₂²×C₄	—	2	8	no	—
347	C₂²×C₄	—	2	8	no	—
348	C₂²×C₄	—	2	8	no	—
349	C₂²×C₄	—	2	8	no	—
350	C₂²×C₄	—	2	16	no	—
351	C₂²×C₄	—	2	32	no	—
352	C₂²×C₄	C₂²×C₄×C₅₉	1	8	yes	—
353	C₂²×C₄	C₂²×C₄×C₅₉	1	16	yes	—
354	C₂²×C₄	C₂²×C₄×C₅₉	1	4	yes	—
355	C₂²×C₄	C₂×D₄×C₅₉	1	8	yes	—
356	C₂²×C₄	C₂×D₄×C₅₉	1	4	yes	—
357	C₂²×C₄	#41×C₅₉	1	4	yes	—
358	C₂²×C₄	C₂⁴×C₅₉	1	8	yes	—
359	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
360	C₂²×C₄	C₂⁴×C₅₉	1	4	yes	—
361	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
362	C₂²×C₄	C₂⁴×C₅₉	1	4	yes	—
363	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
364	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
365	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
366	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
367	C₄⋊C₄	—	2	16	no	—
368	C₄⋊C₄	—	2	8	no	—
369	C₄⋊C₄	—	2	16	no	—
370	C₄⋊C₄	C₂²×C₄×C₅₉	1	16	yes	—
371	C₂²⋊C₄	—	2	8	no	—
372	C₂²⋊C₄	—	2	16	no	—
373	C₂²⋊C₄	—	2	32	no	—
374	C₂²⋊C₄	C₂²×C₄×C₅₉	1	32	yes	—
375	C₄²	—	2	8	no	—
376	C₄²	—	2	16	no	—
377	C₄²	—	2	8	no	—
378	C₄²	—	2	4	no	—
379	C₄²	—	2	4	no	—
380	C₄²	—	2	8	no	—
381	C₄²	—	2	8	no	—
382	C₄²	C₂²×C₄×C₅₉	1	8	yes	—
383	C₄²	C₂²×C₄×C₅₉	1	4	yes	—
384	C₄²	C₂²×C₄×C₅₉	1	4	yes	—
385	C₄²	C₂×D₄×C₅₉	1	4	yes	—
386	C₄²	C₂×D₄×C₅₉	1	4	yes	—
387	C₄²	C₂×D₄×C₅₉	1	8	yes	—
388	C₄²	#41×C₅₉	1	16	yes	complemented
389	C₂³	—	2	4	no	—
390	C₂³	—	2	4	no	—
391	C₂³	—	2	16	no	—
392	C₂³	—	2	4	no	—
393	C₂³	C₂³×C₄×C₅₉	1	8	yes	—
394	C₂³	C₂³×C₄×C₅₉	1	2	yes	—
395	C₂³	C₂²×D₄×C₅₉	1	2	yes	—
396	C₂³	C₂×#41×C₅₉	1	2	yes	—
397	C₂³	C₂⁵×C₅₉	1	1	yes	characteristic
398	Q₈	—	2	16	no	—
399	D₄	—	2	32	no	—
400	D₄	—	2	16	no	—
401	D₄	—	2	32	no	—
402	C₂×C₄	—	2	16	no	—
403	C₂×C₄	—	2	4	no	—
404	C₂×C₄	—	2	4	no	—
405	C₂×C₄	—	2	4	no	—
406	C₂×C₄	—	2	4	no	—
407	C₂×C₄	—	2	4	no	—
408	C₂×C₄	—	2	4	no	—
409	C₂×C₄	—	2	32	no	—
410	C₂×C₄	—	2	16	no	—
411	C₂×C₄	—	2	16	no	—
412	C₂×C₄	—	2	8	no	—
413	C₂×C₄	—	2	16	no	—
414	C₂×C₄	—	4	32	no	—
415	C₂×C₄	C₄×D₄×C₅₉	1	16	yes	complemented
416	C₂×C₄	C₂³×C₄×C₅₉	1	4	yes	—
417	C₂×C₄	C₂³×C₄×C₅₉	1	8	yes	—
418	C₂×C₄	C₂³×C₄×C₅₉	1	2	yes	—
419	C₂×C₄	C₂³×C₄×C₅₉	1	2	yes	—
420	C₂×C₄	C₂³×C₄×C₅₉	1	4	yes	—
421	C₂×C₄	C₂²×D₄×C₅₉	1	4	yes	—
422	C₂×C₄	C₂²×D₄×C₅₉	1	2	yes	—
423	C₂×C₄	C₂²×D₄×C₅₉	1	2	yes	—
424	C₂×C₄	C₂²×D₄×C₅₉	1	4	yes	—
425	C₂×C₄	C₂×#41×C₅₉	1	8	yes	—
426	C₂×C₄	C₂×#41×C₅₉	1	2	yes	—
427	C₂×C₄	C₂×#41×C₅₉	1	2	yes	—
428	C₂×C₄	C₂×#41×C₅₉	1	8	yes	—
429	C₂×C₄	C₂×#41×C₅₉	1	8	yes	—
430	C₂²	—	2	4	no	—
431	C₂²	—	2	4	no	—
432	C₂²	—	2	4	no	—
433	C₂²	—	2	8	no	—
434	C₂²	—	2	16	no	—
435	C₂²	—	4	8	no	—
436	C₂²	—	4	8	no	—
437	C₂²	C₂×C₄×D₄×C₅₉	1	4	yes	—
438	C₂²	C₂⁴×C₄×C₅₉	1	1	yes	characteristic
439	C₂²	C₂³×D₄×C₅₉	1	1	yes	characteristic
440	C₂²	C₂²×#41×C₅₉	1	1	yes	characteristic
441	C₂²	C₂²×#41×C₅₉	1	4	yes	—
442	C₄	—	2	8	no	—
443	C₄	—	2	4	no	—
444	C₄	—	2	4	no	—
445	C₄	—	2	8	no	—
446	C₄	—	4	8	no	—
447	C₄	C₂×C₄×D₄×C₅₉	1	4	yes	—
448	C₄	C₂×C₄×D₄×C₅₉	1	4	yes	—
449	C₄	C₄×#41×C₅₉	1	8	yes	complemented
450	C₄	C₅₉×#532	1	8	yes	direct product factor
451	C₂	—	2	4	no	—
452	C₂	—	4	8	no	—
453	C₂	C₂²×C₄×D₄×C₅₉	1	1	yes	characteristic
454	C₂	C₂×C₄×#41×C₅₉	1	2	yes	—
455	C₂	C₂×C₅₉×#532	1	2	yes	—
456	C₂	C₅₉×#3444	1	2	yes	—

	subgroup	G/H
center	C₂×C₄²×C₅₉	C₂³
commutator	C₂²	C₂⁴×C₄×C₅₉
Frattini, cosocle	C₂³	C₂⁵×C₅₉
socle	C₂³×C₅₉	C₂⁵
prime radical	C₂×C₅₉×#532	C₂
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₄²×C₅₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₄×#41×C₅₉	C₂	semidirect
3. C₄×C₄⋊Q₈×C₅₉	C₂	semidirect
4. C₄×#127×C₅₉	C₂	semidirect
5. C₄×#124×C₅₉	C₂	semidirect
6. C₄×#121×C₅₉	C₂	semidirect
7. C₅₉×#2297	C₂	semidirect
8. C₅₉×#2293	C₂	semidirect
9. C₅₉×#2285	C₂	semidirect
10. C₄²×D₄×C₅₉	C₂	semidirect
11. C₂×C₄³×C₅₉	C₂	semidirect
13. C₅₉×#532	C₄	direct (N × H)
50. C₂×#41×C₅₉	C₂×C₄	semidirect
61. C₄⋊Q₈×C₅₉	C₂×C₄	semidirect
62. #127×C₅₉	C₂×C₄	semidirect
63. #124×C₅₉	C₂×C₄	semidirect
64. #121×C₅₉	C₂×C₄	semidirect
69. C₄×D₄×C₅₉	C₂×C₄	semidirect
83. C₂×C₄²×C₅₉	C₂×C₄	semidirect
84. C₂×C₄²×C₅₉	D₄	semidirect
159. C₄²×C₅₉	#41	semidirect
186. C₂×C₄×C₅₉	C₄×D₄	semidirect
201. C₄×#532	C₅₉	direct (N × H)
221. C₄×C₅₉	C₄×#41	semidirect
222. C₄×C₅₉	#532	direct (N × H)
224. C₂×C₄×#41	C₂×C₅₉	semidirect
225. C₄×C₄⋊Q₈	C₂×C₅₉	semidirect
226. C₄×#127	C₂×C₅₉	semidirect
227. C₄×#124	C₂×C₅₉	semidirect
228. C₄×#121	C₂×C₅₉	semidirect
229. #2297	C₂×C₅₉	semidirect
230. #2293	C₂×C₅₉	semidirect
231. #2285	C₂×C₅₉	semidirect
232. C₄²×D₄	C₂×C₅₉	semidirect
233. C₂×C₄³	C₂×C₅₉	semidirect
241. #532	C₄×C₅₉	direct (N × H)
276. C₅₉	C₄×#532	direct (N × H)
279. C₂×#41	C₂×C₄×C₅₉	semidirect
290. C₄⋊Q₈	C₂×C₄×C₅₉	semidirect
291. #127	C₂×C₄×C₅₉	semidirect
292. #124	C₂×C₄×C₅₉	semidirect
293. #121	C₂×C₄×C₅₉	semidirect
298. C₄×D₄	C₂×C₄×C₅₉	semidirect
312. C₂×C₄²	C₂×C₄×C₅₉	semidirect
313. C₂×C₄²	D₄×C₅₉	semidirect
388. C₄²	#41×C₅₉	semidirect
415. C₂×C₄	C₄×D₄×C₅₉	semidirect
449. C₄	C₄×#41×C₅₉	semidirect
450. C₄	C₅₉×#532	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×#532	2
C₂×C₄×#41×C₅₉	2
C₄×C₄⋊Q₈×C₅₉	2
C₄×#127×C₅₉	2
C₄×#124×C₅₉	2
C₄×#121×C₅₉	2
C₅₉×#2297	2
C₅₉×#2293	2
C₅₉×#2285	2
C₄²×D₄×C₅₉	2
C₂×C₄³×C₅₉	2
C₄×#532	59

Subgroups — C4×C59×#532 #28446147

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×C₅₉×#532 #28446147