Subgroups — C₂×C₅₉×#2329 #28446180

Order 15104.

2982 conjugacy classes of subgroups.

The subgroup lattice has 520 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₂²⋊Q₈×C₅₉	C₂	1	1	yes	maximal, characteristic
2	C₅₉×#2329	C₂	1	16	yes	maximal, direct product factor
3	C₂×C₅₉×#391	C₂	1	2	yes	maximal, complemented
4	C₂×C₅₉×#389	C₂	1	2	yes	maximal, complemented
5	C₂×C₅₉×#387	C₂	1	2	yes	maximal, complemented
6	C₂×C₅₉×#387	C₂	1	2	yes	maximal, complemented
7	C₂×C₅₉×#385	C₂	1	2	yes	maximal
8	C₂×C₅₉×#380	C₂	1	1	yes	maximal, characteristic
9	C₂×C₄×C₂²⋊C₄×C₅₉	C₂	1	2	yes	maximal
10	C₂²×#95×C₅₉	C₂	1	1	yes	maximal, characteristic
11	C₂³×Q₈×C₅₉	C₂²	1	1	yes	characteristic
12	C₂⁴×C₄×C₅₉	C₂²	1	1	yes	characteristic
13	C₂⁴×C₄×C₅₉	C₂²	1	1	yes	characteristic
14	C₂⁴×C₄×C₅₉	C₂²	1	1	yes	characteristic
15	C₂×C₂²⋊Q₈×C₅₉	C₄	1	16	yes	complemented
16	C₂×C₂²⋊Q₈×C₅₉	C₂²	1	8	yes	—
17	C₂²×C₄⋊C₄×C₅₉	C₂²	1	1	yes	characteristic
18	C₂²×C₄⋊C₄×C₅₉	C₂²	1	1	yes	characteristic
19	C₂²×C₄⋊C₄×C₅₉	C₂²	1	2	yes	—
20	C₂²×C₄⋊C₄×C₅₉	C₂²	1	2	yes	—
21	C₂²×C₄⋊C₄×C₅₉	C₂²	1	1	yes	characteristic
22	C₂²×C₄⋊C₄×C₅₉	C₂²	1	2	yes	—
23	C₂²×C₂²⋊C₄×C₅₉	C₂²	1	2	yes	—
24	C₂²×C₂²⋊C₄×C₅₉	C₂²	1	2	yes	—
25	C₂²×C₄²×C₅₉	C₂²	1	2	yes	—
26	C₂²×C₄²×C₅₉	C₂²	1	2	yes	—
27	C₅₉×#391	C₂²	1	16	yes	complemented
28	C₅₉×#389	C₂²	1	16	yes	complemented
29	C₅₉×#387	C₂²	1	16	yes	complemented
30	C₅₉×#387	C₂²	1	16	yes	complemented
31	C₅₉×#385	C₂²	1	16	yes	—
32	C₅₉×#380	C₂²	1	8	yes	—
33	C₄×C₂²⋊C₄×C₅₉	C₂²	1	16	yes	—
34	C₂×#95×C₅₉	C₂²	1	2	yes	—
35	C₂×#95×C₅₉	C₂²	1	2	yes	—
36	C₂×#95×C₅₉	C₂²	1	8	yes	—
37	C₂×#95×C₅₉	C₂²	1	2	yes	—
38	C₂×#95×C₅₉	C₂²	1	2	yes	—
39	C₂×#95×C₅₉	C₂²	1	2	yes	—
40	C₂×#95×C₅₉	C₂²	1	2	yes	—
41	C₂×#95×C₅₉	C₂²	1	2	yes	—
42	C₂⁵×C₅₉	C₂³	1	1	yes	characteristic
43	C₂²×Q₈×C₅₉	—	4	2	no	—
44	C₂²×Q₈×C₅₉	—	4	2	no	—
45	C₂²×Q₈×C₅₉	C₂×C₄	1	8	yes	complemented
46	C₂²×Q₈×C₅₉	C₂³	1	4	yes	—
47	C₂³×C₄×C₅₉	—	2	4	no	—
48	C₂³×C₄×C₅₉	—	4	2	no	—
49	C₂³×C₄×C₅₉	—	4	2	no	—
50	C₂³×C₄×C₅₉	—	4	2	no	—
51	C₂³×C₄×C₅₉	—	4	2	no	—
52	C₂³×C₄×C₅₉	—	4	2	no	—
53	C₂³×C₄×C₅₉	—	4	2	no	—
54	C₂³×C₄×C₅₉	C₂×C₄	1	8	yes	—
55	C₂³×C₄×C₅₉	Q₈	1	8	yes	complemented
56	C₂³×C₄×C₅₉	C₂³	1	2	yes	—
57	C₂³×C₄×C₅₉	C₂³	1	2	yes	—
58	C₂³×C₄×C₅₉	C₂³	1	2	yes	—
59	C₂³×C₄×C₅₉	C₂³	1	1	yes	characteristic
60	C₂³×C₄×C₅₉	C₂³	1	2	yes	—
61	C₂³×C₄×C₅₉	C₂³	1	2	yes	—
62	C₂³×C₄×C₅₉	C₂³	1	1	yes	characteristic
63	C₂³×C₄×C₅₉	C₂³	1	2	yes	—
64	C₂³×C₄×C₅₉	C₂³	1	4	yes	—
65	C₂³×C₄×C₅₉	C₂³	1	4	yes	—
66	C₂³×C₄×C₅₉	C₂³	1	4	yes	—
67	C₂²⋊Q₈×C₅₉	C₂×C₄	1	64	yes	complemented
68	C₂×C₄⋊C₄×C₅₉	—	4	4	no	—
69	C₂×C₄⋊C₄×C₅₉	—	4	2	no	—
70	C₂×C₄⋊C₄×C₅₉	—	4	2	no	—
71	C₂×C₄⋊C₄×C₅₉	—	4	4	no	—
72	C₂×C₄⋊C₄×C₅₉	C₂×C₄	1	8	yes	complemented
73	C₂×C₄⋊C₄×C₅₉	C₂×C₄	1	16	yes	complemented
74	C₂×C₄⋊C₄×C₅₉	C₂³	1	4	yes	—
75	C₂×C₄⋊C₄×C₅₉	C₂³	1	4	yes	—
76	C₂×C₄⋊C₄×C₅₉	C₂³	1	8	yes	—
77	C₂×C₄⋊C₄×C₅₉	C₂³	1	8	yes	—
78	C₂×C₄⋊C₄×C₅₉	C₂³	1	4	yes	—
79	C₂×C₄⋊C₄×C₅₉	C₂³	1	8	yes	—
80	C₂×C₂²⋊C₄×C₅₉	—	2	8	no	—
81	C₂×C₂²⋊C₄×C₅₉	C₂×C₄	1	16	yes	—
82	C₂×C₂²⋊C₄×C₅₉	C₂³	1	8	yes	—
83	C₂×C₂²⋊C₄×C₅₉	C₂³	1	8	yes	—
84	C₂×C₄²×C₅₉	—	4	4	no	—
85	C₂×C₄²×C₅₉	—	4	4	no	—
86	C₂×C₄²×C₅₉	C₂³	1	8	yes	—
87	C₂×C₄²×C₅₉	C₂³	1	8	yes	—
88	#95×C₅₉	C₂³	1	8	yes	—
89	#95×C₅₉	C₂³	1	8	yes	—
90	#95×C₅₉	C₂³	1	8	yes	—
91	#95×C₅₉	C₂³	1	8	yes	—
92	#95×C₅₉	C₂³	1	8	yes	—
93	#95×C₅₉	C₂³	1	8	yes	—
94	#95×C₅₉	C₂³	1	8	yes	—
95	C₂⁴×C₅₉	—	2	2	no	—
96	C₂⁴×C₅₉	—	2	2	no	—
97	C₂⁴×C₅₉	—	2	2	no	—
98	C₂⁴×C₅₉	—	2	2	no	—
99	C₂⁴×C₅₉	C₂²×C₄	1	4	yes	—
100	C₂⁴×C₅₉	C₂×Q₈	1	4	yes	—
101	C₂⁴×C₅₉	#41	1	4	yes	—
102	C₂⁴×C₅₉	C₂⁴	1	2	yes	—
103	C₂⁴×C₅₉	C₂⁴	1	1	yes	characteristic
104	C₂×Q₈×C₅₉	—	4	16	no	—
105	C₂×Q₈×C₅₉	—	4	4	no	—
106	C₂×Q₈×C₅₉	—	4	4	no	—
107	C₂×Q₈×C₅₉	C₂²×C₄	1	16	yes	complemented
108	C₂²×C₄×C₅₉	—	2	4	no	—
109	C₂²×C₄×C₅₉	—	2	4	no	—
110	C₂²×C₄×C₅₉	—	2	4	no	—
111	C₂²×C₄×C₅₉	—	2	4	no	—
112	C₂²×C₄×C₅₉	—	2	2	no	—
113	C₂²×C₄×C₅₉	—	2	2	no	—
114	C₂²×C₄×C₅₉	—	2	4	no	—
115	C₂²×C₄×C₅₉	—	2	2	no	—
116	C₂²×C₄×C₅₉	—	2	2	no	—
117	C₂²×C₄×C₅₉	—	2	4	no	—
118	C₂²×C₄×C₅₉	—	2	4	no	—
119	C₂²×C₄×C₅₉	—	2	4	no	—
120	C₂²×C₄×C₅₉	—	2	8	no	—
121	C₂²×C₄×C₅₉	—	2	4	no	—
122	C₂²×C₄×C₅₉	—	2	4	no	—
123	C₂²×C₄×C₅₉	—	2	4	no	—
124	C₂²×C₄×C₅₉	—	2	4	no	—
125	C₂²×C₄×C₅₉	—	2	4	no	—
126	C₂²×C₄×C₅₉	—	2	4	no	—
127	C₂²×C₄×C₅₉	—	2	4	no	—
128	C₂²×C₄×C₅₉	—	4	16	no	—
129	C₂²×C₄×C₅₉	—	4	16	no	—
130	C₂²×C₄×C₅₉	—	4	4	no	—
131	C₂²×C₄×C₅₉	—	4	4	no	—
132	C₂²×C₄×C₅₉	—	4	4	no	—
133	C₂²×C₄×C₅₉	—	4	4	no	—
134	C₂²×C₄×C₅₉	—	4	4	no	—
135	C₂²×C₄×C₅₉	—	4	4	no	—
136	C₂²×C₄×C₅₉	—	4	16	no	—
137	C₂²×C₄×C₅₉	C₂²×C₄	1	8	yes	—
138	C₂²×C₄×C₅₉	C₂²×C₄	1	8	yes	—
139	C₂²×C₄×C₅₉	C₂²×C₄	1	4	yes	—
140	C₂²×C₄×C₅₉	C₂²×C₄	1	4	yes	—
141	C₂²×C₄×C₅₉	C₂²×C₄	1	16	yes	—
142	C₂²×C₄×C₅₉	C₂×Q₈	1	8	yes	—
143	C₂²×C₄×C₅₉	C₂×Q₈	1	16	yes	complemented
144	C₂²×C₄×C₅₉	C₂⁴	1	4	yes	—
145	C₂²×C₄×C₅₉	C₂⁴	1	4	yes	—
146	C₂²×C₄×C₅₉	C₂⁴	1	4	yes	—
147	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
148	C₂²×C₄×C₅₉	C₂⁴	1	4	yes	—
149	C₂²×C₄×C₅₉	C₂⁴	1	4	yes	—
150	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
151	C₂²×C₄×C₅₉	C₂⁴	1	4	yes	—
152	C₄⋊C₄×C₅₉	—	4	8	no	—
153	C₄⋊C₄×C₅₉	—	4	4	no	—
154	C₄⋊C₄×C₅₉	—	4	4	no	—
155	C₄⋊C₄×C₅₉	—	4	8	no	—
156	C₄⋊C₄×C₅₉	C₂²×C₄	1	16	yes	complemented
157	C₄⋊C₄×C₅₉	C₂²×C₄	1	32	yes	complemented
158	C₂²⋊C₄×C₅₉	—	2	16	no	—
159	C₂²⋊C₄×C₅₉	C₂²×C₄	1	32	yes	—
160	C₄²×C₅₉	—	4	8	no	—
161	C₄²×C₅₉	—	4	8	no	—
162	C₂³×C₅₉	—	2	8	no	—
163	C₂³×C₅₉	—	2	8	no	—
164	C₂³×C₅₉	—	2	8	no	—
165	C₂³×C₅₉	—	2	8	no	—
166	C₂³×C₅₉	—	2	8	no	—
167	C₂³×C₅₉	—	2	8	no	—
168	C₂³×C₅₉	—	2	2	no	—
169	C₂³×C₅₉	—	2	2	no	—
170	C₂³×C₅₉	—	2	2	no	—
171	C₂³×C₅₉	—	2	2	no	—
172	C₂³×C₅₉	C₄×Q₈	1	16	yes	—
173	C₂³×C₅₉	C₂³×C₄	1	4	yes	—
174	C₂³×C₅₉	C₂³×C₄	1	2	yes	—
175	C₂³×C₅₉	C₂²×Q₈	1	4	yes	—
176	C₂³×C₅₉	C₂²×Q₈	1	2	yes	—
177	C₂³×C₅₉	C₂×#41	1	4	yes	—
178	C₂³×C₅₉	C₂×#41	1	2	yes	—
179	C₂³×C₅₉	H(5,𝔽₂)	1	2	yes	—
180	C₂³×C₅₉	H(5,𝔽₂)	1	2	yes	—
181	C₂³×C₅₉	H(5,𝔽₂)	1	2	yes	—
182	C₂³×C₅₉	2₋¹⁺⁴	1	2	yes	—
183	C₂³×C₅₉	C₂⁵	1	1	yes	characteristic
184	Q₈×C₅₉	—	4	16	no	—
185	C₂×C₄×C₅₉	—	2	8	no	—
186	C₂×C₄×C₅₉	—	2	8	no	—
187	C₂×C₄×C₅₉	—	2	16	no	—
188	C₂×C₄×C₅₉	—	2	16	no	—
189	C₂×C₄×C₅₉	—	2	16	no	—
190	C₂×C₄×C₅₉	—	2	4	no	—
191	C₂×C₄×C₅₉	—	2	4	no	—
192	C₂×C₄×C₅₉	—	2	4	no	—
193	C₂×C₄×C₅₉	—	2	4	no	—
194	C₂×C₄×C₅₉	—	2	2	no	—
195	C₂×C₄×C₅₉	—	2	2	no	—
196	C₂×C₄×C₅₉	—	2	4	no	—
197	C₂×C₄×C₅₉	—	2	2	no	—
198	C₂×C₄×C₅₉	—	2	2	no	—
199	C₂×C₄×C₅₉	—	2	4	no	—
200	C₂×C₄×C₅₉	—	2	4	no	—
201	C₂×C₄×C₅₉	—	2	4	no	—
202	C₂×C₄×C₅₉	—	2	4	no	—
203	C₂×C₄×C₅₉	—	2	4	no	—
204	C₂×C₄×C₅₉	—	2	4	no	—
205	C₂×C₄×C₅₉	—	2	4	no	—
206	C₂×C₄×C₅₉	—	2	4	no	—
207	C₂×C₄×C₅₉	—	2	4	no	—
208	C₂×C₄×C₅₉	—	2	4	no	—
209	C₂×C₄×C₅₉	—	4	16	no	—
210	C₂×C₄×C₅₉	—	4	16	no	—
211	C₂×C₄×C₅₉	—	4	16	no	—
212	C₂×C₄×C₅₉	—	4	8	no	—
213	C₂×C₄×C₅₉	—	4	8	no	—
214	C₂×C₄×C₅₉	—	4	8	no	—
215	C₂×C₄×C₅₉	C₂³×C₄	1	8	yes	—
216	C₂×C₄×C₅₉	C₂³×C₄	1	8	yes	—
217	C₂×C₄×C₅₉	C₂³×C₄	1	4	yes	—
218	C₂×C₄×C₅₉	C₂³×C₄	1	4	yes	—
219	C₂×C₄×C₅₉	C₂²×Q₈	1	8	yes	—
220	C₂×#2329	C₅₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
221	C₂²×C₅₉	—	2	32	no	—
222	C₂²×C₅₉	—	2	4	no	—
223	C₂²×C₅₉	—	2	4	no	—
224	C₂²×C₅₉	—	2	4	no	—
225	C₂²×C₅₉	—	2	4	no	—
226	C₂²×C₅₉	—	2	4	no	—
227	C₂²×C₅₉	—	2	4	no	—
228	C₂²×C₅₉	C₂×C₄×Q₈	1	8	yes	—
229	C₂²×C₅₉	C₂×C₄×Q₈	1	4	yes	—
230	C₂²×C₅₉	#518	1	4	yes	—
231	C₂²×C₅₉	#520	1	4	yes	—
232	C₂²×C₅₉	#538	1	4	yes	—
233	C₂²×C₅₉	#539	1	4	yes	—
234	C₂²×C₅₉	#543	1	4	yes	—
235	C₂²×C₅₉	#544	1	4	yes	—
236	C₂²×C₅₉	C₂⁴×C₄	1	1	yes	characteristic
237	C₂²×C₅₉	C₂³×Q₈	1	1	yes	characteristic
238	C₂²×C₅₉	C₂²×#41	1	1	yes	characteristic
239	C₂²×C₅₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
240	C₂²×C₅₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
241	C₂²×C₅₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
242	C₂²×C₅₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
243	C₄×C₅₉	—	2	4	no	—
244	C₄×C₅₉	—	2	4	no	—
245	C₄×C₅₉	—	2	8	no	—
246	C₄×C₅₉	—	2	8	no	—
247	C₄×C₅₉	—	2	8	no	—
248	C₄×C₅₉	—	4	4	no	—
249	C₄×C₅₉	—	4	4	no	—
250	C₄×C₅₉	—	4	4	no	—
251	C₂²×C₂²⋊Q₈	C₂×C₅₉	1	1	yes	characteristic
252	#2329	C₂×C₅₉	1	16	yes	direct product factor
253	C₂×#391	C₂×C₅₉	1	2	yes	complemented
254	C₂×#389	C₂×C₅₉	1	2	yes	complemented
255	C₂×#387	C₂×C₅₉	1	2	yes	complemented
256	C₂×#387	C₂×C₅₉	1	2	yes	complemented
257	C₂×#385	C₂×C₅₉	1	2	yes	—
258	C₂×#380	C₂×C₅₉	1	1	yes	characteristic
259	C₂×C₄×C₂²⋊C₄	C₂×C₅₉	1	2	yes	—
260	C₂²×#95	C₂×C₅₉	1	1	yes	characteristic
261	C₂×C₅₉	—	2	8	no	—
262	C₂×C₅₉	#2329	1	8	yes	direct product factor
263	C₂×C₅₉	C₂²×C₄×Q₈	1	1	yes	characteristic
264	C₂×C₅₉	C₂×#518	1	1	yes	characteristic
265	C₂×C₅₉	C₂×#520	1	1	yes	characteristic
266	C₂×C₅₉	C₂×#538	1	1	yes	characteristic
267	C₂×C₅₉	C₂×#539	1	1	yes	characteristic
268	C₂×C₅₉	C₂×#543	1	1	yes	characteristic
269	C₂×C₅₉	C₂×#544	1	1	yes	characteristic
270	C₂³×Q₈	C₂²×C₅₉	1	1	yes	characteristic
271	C₂⁴×C₄	C₂²×C₅₉	1	1	yes	characteristic
272	C₂⁴×C₄	C₂²×C₅₉	1	1	yes	characteristic
273	C₂⁴×C₄	C₂²×C₅₉	1	1	yes	characteristic
274	C₂×C₂²⋊Q₈	C₄×C₅₉	1	16	yes	complemented
275	C₂×C₂²⋊Q₈	C₂²×C₅₉	1	8	yes	—
276	C₂²×C₄⋊C₄	C₂²×C₅₉	1	1	yes	characteristic
277	C₂²×C₄⋊C₄	C₂²×C₅₉	1	1	yes	characteristic
278	C₂²×C₄⋊C₄	C₂²×C₅₉	1	2	yes	—
279	C₂²×C₄⋊C₄	C₂²×C₅₉	1	2	yes	—
280	C₂²×C₄⋊C₄	C₂²×C₅₉	1	1	yes	characteristic
281	C₂²×C₄⋊C₄	C₂²×C₅₉	1	2	yes	—
282	C₂²×C₂²⋊C₄	C₂²×C₅₉	1	2	yes	—
283	C₂²×C₂²⋊C₄	C₂²×C₅₉	1	2	yes	—
284	C₂²×C₄²	C₂²×C₅₉	1	2	yes	—
285	C₂²×C₄²	C₂²×C₅₉	1	2	yes	—
286	#391	C₂²×C₅₉	1	16	yes	complemented
287	#389	C₂²×C₅₉	1	16	yes	complemented
288	#387	C₂²×C₅₉	1	16	yes	complemented
289	#387	C₂²×C₅₉	1	16	yes	complemented
290	#385	C₂²×C₅₉	1	16	yes	—
291	#380	C₂²×C₅₉	1	8	yes	—
292	C₄×C₂²⋊C₄	C₂²×C₅₉	1	16	yes	—
293	C₂×#95	C₂²×C₅₉	1	8	yes	—
294	C₂×#95	C₂²×C₅₉	1	2	yes	—
295	C₂×#95	C₂²×C₅₉	1	2	yes	—
296	C₂×#95	C₂²×C₅₉	1	2	yes	—
297	C₂×#95	C₂²×C₅₉	1	2	yes	—
298	C₂×#95	C₂²×C₅₉	1	2	yes	—
299	C₂×#95	C₂²×C₅₉	1	2	yes	—
300	C₂×#95	C₂²×C₅₉	1	2	yes	—
301	C₅₉	C₂×#2329	1	1	yes	characteristic, direct product factor, Sylow
302	C₂⁵	C₂³×C₅₉	1	1	yes	characteristic
303	C₂²×Q₈	—	4	2	no	—
304	C₂²×Q₈	—	4	2	no	—
305	C₂²×Q₈	C₂×C₄×C₅₉	1	8	yes	complemented
306	C₂²×Q₈	C₂³×C₅₉	1	4	yes	—
307	C₂³×C₄	—	2	4	no	—
308	C₂³×C₄	—	4	2	no	—
309	C₂³×C₄	—	4	2	no	—
310	C₂³×C₄	—	4	2	no	—
311	C₂³×C₄	—	4	2	no	—
312	C₂³×C₄	—	4	2	no	—
313	C₂³×C₄	—	4	2	no	—
314	C₂³×C₄	C₂×C₄×C₅₉	1	8	yes	—
315	C₂³×C₄	Q₈×C₅₉	1	8	yes	complemented
316	C₂³×C₄	C₂³×C₅₉	1	2	yes	—
317	C₂³×C₄	C₂³×C₅₉	1	2	yes	—
318	C₂³×C₄	C₂³×C₅₉	1	2	yes	—
319	C₂³×C₄	C₂³×C₅₉	1	2	yes	—
320	C₂³×C₄	C₂³×C₅₉	1	2	yes	—
321	C₂³×C₄	C₂³×C₅₉	1	1	yes	characteristic
322	C₂³×C₄	C₂³×C₅₉	1	1	yes	characteristic
323	C₂³×C₄	C₂³×C₅₉	1	2	yes	—
324	C₂³×C₄	C₂³×C₅₉	1	4	yes	—
325	C₂³×C₄	C₂³×C₅₉	1	4	yes	—
326	C₂³×C₄	C₂³×C₅₉	1	4	yes	—
327	C₂²⋊Q₈	C₂×C₄×C₅₉	1	64	yes	complemented
328	C₂×C₄⋊C₄	—	4	4	no	—
329	C₂×C₄⋊C₄	—	4	2	no	—
330	C₂×C₄⋊C₄	—	4	2	no	—
331	C₂×C₄⋊C₄	—	4	4	no	—
332	C₂×C₄⋊C₄	C₂×C₄×C₅₉	1	8	yes	complemented
333	C₂×C₄⋊C₄	C₂×C₄×C₅₉	1	16	yes	complemented
334	C₂×C₄⋊C₄	C₂³×C₅₉	1	4	yes	—
335	C₂×C₄⋊C₄	C₂³×C₅₉	1	4	yes	—
336	C₂×C₄⋊C₄	C₂³×C₅₉	1	8	yes	—
337	C₂×C₄⋊C₄	C₂³×C₅₉	1	8	yes	—
338	C₂×C₄⋊C₄	C₂³×C₅₉	1	4	yes	—
339	C₂×C₄⋊C₄	C₂³×C₅₉	1	8	yes	—
340	C₂×C₂²⋊C₄	—	2	8	no	—
341	C₂×C₂²⋊C₄	C₂×C₄×C₅₉	1	16	yes	—
342	C₂×C₂²⋊C₄	C₂³×C₅₉	1	8	yes	—
343	C₂×C₂²⋊C₄	C₂³×C₅₉	1	8	yes	—
344	C₂×C₄²	—	4	4	no	—
345	C₂×C₄²	—	4	4	no	—
346	C₂×C₄²	C₂³×C₅₉	1	8	yes	—
347	C₂×C₄²	C₂³×C₅₉	1	8	yes	—
348	#95	C₂³×C₅₉	1	8	yes	—
349	#95	C₂³×C₅₉	1	8	yes	—
350	#95	C₂³×C₅₉	1	8	yes	—
351	#95	C₂³×C₅₉	1	8	yes	—
352	#95	C₂³×C₅₉	1	8	yes	—
353	#95	C₂³×C₅₉	1	8	yes	—
354	#95	C₂³×C₅₉	1	8	yes	—
355	C₂⁴	—	2	2	no	—
356	C₂⁴	—	2	2	no	—
357	C₂⁴	—	2	2	no	—
358	C₂⁴	—	2	2	no	—
359	C₂⁴	C₂²×C₄×C₅₉	1	4	yes	—
360	C₂⁴	C₂×Q₈×C₅₉	1	4	yes	—
361	C₂⁴	#41×C₅₉	1	4	yes	—
362	C₂⁴	C₂⁴×C₅₉	1	2	yes	—
363	C₂⁴	C₂⁴×C₅₉	1	1	yes	characteristic
364	C₂×Q₈	—	4	16	no	—
365	C₂×Q₈	—	4	4	no	—
366	C₂×Q₈	—	4	4	no	—
367	C₂×Q₈	C₂²×C₄×C₅₉	1	16	yes	complemented
368	C₂²×C₄	—	2	4	no	—
369	C₂²×C₄	—	2	4	no	—
370	C₂²×C₄	—	2	4	no	—
371	C₂²×C₄	—	2	4	no	—
372	C₂²×C₄	—	2	2	no	—
373	C₂²×C₄	—	2	2	no	—
374	C₂²×C₄	—	2	4	no	—
375	C₂²×C₄	—	2	2	no	—
376	C₂²×C₄	—	2	2	no	—
377	C₂²×C₄	—	2	4	no	—
378	C₂²×C₄	—	2	4	no	—
379	C₂²×C₄	—	2	4	no	—
380	C₂²×C₄	—	2	8	no	—
381	C₂²×C₄	—	2	4	no	—
382	C₂²×C₄	—	2	4	no	—
383	C₂²×C₄	—	2	4	no	—
384	C₂²×C₄	—	2	4	no	—
385	C₂²×C₄	—	2	4	no	—
386	C₂²×C₄	—	2	4	no	—
387	C₂²×C₄	—	2	4	no	—
388	C₂²×C₄	—	4	16	no	—
389	C₂²×C₄	—	4	16	no	—
390	C₂²×C₄	—	4	4	no	—
391	C₂²×C₄	—	4	4	no	—
392	C₂²×C₄	—	4	4	no	—
393	C₂²×C₄	—	4	4	no	—
394	C₂²×C₄	—	4	4	no	—
395	C₂²×C₄	—	4	4	no	—
396	C₂²×C₄	—	4	16	no	—
397	C₂²×C₄	C₂²×C₄×C₅₉	1	8	yes	—
398	C₂²×C₄	C₂²×C₄×C₅₉	1	8	yes	—
399	C₂²×C₄	C₂²×C₄×C₅₉	1	4	yes	—
400	C₂²×C₄	C₂²×C₄×C₅₉	1	4	yes	—
401	C₂²×C₄	C₂²×C₄×C₅₉	1	16	yes	—
402	C₂²×C₄	C₂×Q₈×C₅₉	1	8	yes	—
403	C₂²×C₄	C₂×Q₈×C₅₉	1	16	yes	complemented
404	C₂²×C₄	C₂⁴×C₅₉	1	4	yes	—
405	C₂²×C₄	C₂⁴×C₅₉	1	4	yes	—
406	C₂²×C₄	C₂⁴×C₅₉	1	4	yes	—
407	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
408	C₂²×C₄	C₂⁴×C₅₉	1	4	yes	—
409	C₂²×C₄	C₂⁴×C₅₉	1	4	yes	—
410	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
411	C₂²×C₄	C₂⁴×C₅₉	1	4	yes	—
412	C₄⋊C₄	—	4	8	no	—
413	C₄⋊C₄	—	4	4	no	—
414	C₄⋊C₄	—	4	4	no	—
415	C₄⋊C₄	—	4	8	no	—
416	C₄⋊C₄	C₂²×C₄×C₅₉	1	16	yes	complemented
417	C₄⋊C₄	C₂²×C₄×C₅₉	1	32	yes	complemented
418	C₂²⋊C₄	—	2	16	no	—
419	C₂²⋊C₄	C₂²×C₄×C₅₉	1	32	yes	—
420	C₄²	—	4	8	no	—
421	C₄²	—	4	8	no	—
422	C₂³	—	2	8	no	—
423	C₂³	—	2	8	no	—
424	C₂³	—	2	8	no	—
425	C₂³	—	2	8	no	—
426	C₂³	—	2	8	no	—
427	C₂³	—	2	8	no	—
428	C₂³	—	2	2	no	—
429	C₂³	—	2	2	no	—
430	C₂³	—	2	2	no	—
431	C₂³	—	2	2	no	—
432	C₂³	C₄×Q₈×C₅₉	1	16	yes	—
433	C₂³	C₂³×C₄×C₅₉	1	4	yes	—
434	C₂³	C₂³×C₄×C₅₉	1	2	yes	—
435	C₂³	C₂²×Q₈×C₅₉	1	4	yes	—
436	C₂³	C₂²×Q₈×C₅₉	1	2	yes	—
437	C₂³	C₂×#41×C₅₉	1	4	yes	—
438	C₂³	C₂×#41×C₅₉	1	2	yes	—
439	C₂³	H(5,𝔽₂)×C₅₉	1	2	yes	—
440	C₂³	H(5,𝔽₂)×C₅₉	1	2	yes	—
441	C₂³	H(5,𝔽₂)×C₅₉	1	2	yes	—
442	C₂³	2₋¹⁺⁴×C₅₉	1	2	yes	—
443	C₂³	C₂⁵×C₅₉	1	1	yes	characteristic
444	Q₈	—	4	16	no	—
445	C₂×C₄	—	2	8	no	—
446	C₂×C₄	—	2	8	no	—
447	C₂×C₄	—	2	16	no	—
448	C₂×C₄	—	2	16	no	—
449	C₂×C₄	—	2	16	no	—
450	C₂×C₄	—	2	4	no	—
451	C₂×C₄	—	2	4	no	—
452	C₂×C₄	—	2	4	no	—
453	C₂×C₄	—	2	4	no	—
454	C₂×C₄	—	2	2	no	—
455	C₂×C₄	—	2	2	no	—
456	C₂×C₄	—	2	4	no	—
457	C₂×C₄	—	2	2	no	—
458	C₂×C₄	—	2	2	no	—
459	C₂×C₄	—	2	4	no	—
460	C₂×C₄	—	2	4	no	—
461	C₂×C₄	—	2	4	no	—
462	C₂×C₄	—	2	4	no	—
463	C₂×C₄	—	2	4	no	—
464	C₂×C₄	—	2	4	no	—
465	C₂×C₄	—	2	4	no	—
466	C₂×C₄	—	2	4	no	—
467	C₂×C₄	—	2	4	no	—
468	C₂×C₄	—	2	4	no	—
469	C₂×C₄	—	4	16	no	—
470	C₂×C₄	—	4	16	no	—
471	C₂×C₄	—	4	16	no	—
472	C₂×C₄	—	4	8	no	—
473	C₂×C₄	—	4	8	no	—
474	C₂×C₄	—	4	8	no	—
475	C₂×C₄	C₂³×C₄×C₅₉	1	8	yes	—
476	C₂×C₄	C₂³×C₄×C₅₉	1	8	yes	—
477	C₂×C₄	C₂³×C₄×C₅₉	1	4	yes	—
478	C₂×C₄	C₂³×C₄×C₅₉	1	4	yes	—
479	C₂×C₄	C₂²×Q₈×C₅₉	1	8	yes	—
480	C₂²	—	2	32	no	—
481	C₂²	—	2	4	no	—
482	C₂²	—	2	4	no	—
483	C₂²	—	2	4	no	—
484	C₂²	—	2	4	no	—
485	C₂²	—	2	4	no	—
486	C₂²	—	2	4	no	—
487	C₂²	C₂×C₄×Q₈×C₅₉	1	8	yes	—
488	C₂²	C₂×C₄×Q₈×C₅₉	1	4	yes	—
489	C₂²	C₅₉×#518	1	4	yes	—
490	C₂²	C₅₉×#520	1	4	yes	—
491	C₂²	C₅₉×#538	1	4	yes	—
492	C₂²	C₅₉×#539	1	4	yes	—
493	C₂²	C₅₉×#543	1	4	yes	—
494	C₂²	C₅₉×#544	1	4	yes	—
495	C₂²	C₂⁴×C₄×C₅₉	1	1	yes	characteristic
496	C₂²	C₂³×Q₈×C₅₉	1	1	yes	characteristic
497	C₂²	C₂²×#41×C₅₉	1	1	yes	characteristic
498	C₂²	C₂×H(5,𝔽₂)×C₅₉	1	1	yes	characteristic
499	C₂²	C₂×H(5,𝔽₂)×C₅₉	1	1	yes	characteristic
500	C₂²	C₂×H(5,𝔽₂)×C₅₉	1	1	yes	characteristic
501	C₂²	C₂×2₋¹⁺⁴×C₅₉	1	1	yes	characteristic
502	C₄	—	2	4	no	—
503	C₄	—	2	4	no	—
504	C₄	—	2	8	no	—
505	C₄	—	2	8	no	—
506	C₄	—	2	8	no	—
507	C₄	—	4	4	no	—
508	C₄	—	4	4	no	—
509	C₄	—	4	4	no	—
510	C₂	—	2	8	no	—
511	C₂	C₅₉×#2329	1	8	yes	direct product factor
512	C₂	C₂²×C₄×Q₈×C₅₉	1	1	yes	characteristic
513	C₂	C₂×C₅₉×#518	1	1	yes	characteristic
514	C₂	C₂×C₅₉×#520	1	1	yes	characteristic
515	C₂	C₂×C₅₉×#538	1	1	yes	characteristic
516	C₂	C₂×C₅₉×#539	1	1	yes	characteristic
517	C₂	C₂×C₅₉×#543	1	1	yes	characteristic
518	C₂	C₂×C₅₉×#544	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
2. C₅₉×#2329	C₂	direct (N × H)
3. C₂×C₅₉×#391	C₂	semidirect
4. C₂×C₅₉×#389	C₂	semidirect
5. C₂×C₅₉×#387	C₂	semidirect
6. C₂×C₅₉×#387	C₂	semidirect
15. C₂×C₂²⋊Q₈×C₅₉	C₄	semidirect
27. C₅₉×#391	C₂²	semidirect
28. C₅₉×#389	C₂²	semidirect
29. C₅₉×#387	C₂²	semidirect
30. C₅₉×#387	C₂²	semidirect
45. C₂²×Q₈×C₅₉	C₂×C₄	semidirect
55. C₂³×C₄×C₅₉	Q₈	semidirect
67. C₂²⋊Q₈×C₅₉	C₂×C₄	semidirect
72. C₂×C₄⋊C₄×C₅₉	C₂×C₄	semidirect
73. C₂×C₄⋊C₄×C₅₉	C₂×C₄	semidirect
107. C₂×Q₈×C₅₉	C₂²×C₄	semidirect
143. C₂²×C₄×C₅₉	C₂×Q₈	semidirect
156. C₄⋊C₄×C₅₉	C₂²×C₄	semidirect
157. C₄⋊C₄×C₅₉	C₂²×C₄	semidirect
220. C₂×#2329	C₅₉	direct (N × H)
252. #2329	C₂×C₅₉	direct (N × H)
253. C₂×#391	C₂×C₅₉	semidirect
254. C₂×#389	C₂×C₅₉	semidirect
255. C₂×#387	C₂×C₅₉	semidirect
256. C₂×#387	C₂×C₅₉	semidirect
262. C₂×C₅₉	#2329	direct (N × H)
274. C₂×C₂²⋊Q₈	C₄×C₅₉	semidirect
286. #391	C₂²×C₅₉	semidirect
287. #389	C₂²×C₅₉	semidirect
288. #387	C₂²×C₅₉	semidirect
289. #387	C₂²×C₅₉	semidirect
301. C₅₉	C₂×#2329	direct (N × H)
305. C₂²×Q₈	C₂×C₄×C₅₉	semidirect
315. C₂³×C₄	Q₈×C₅₉	semidirect
327. C₂²⋊Q₈	C₂×C₄×C₅₉	semidirect
332. C₂×C₄⋊C₄	C₂×C₄×C₅₉	semidirect
333. C₂×C₄⋊C₄	C₂×C₄×C₅₉	semidirect
367. C₂×Q₈	C₂²×C₄×C₅₉	semidirect
403. C₂²×C₄	C₂×Q₈×C₅₉	semidirect
416. C₄⋊C₄	C₂²×C₄×C₅₉	semidirect
417. C₄⋊C₄	C₂²×C₄×C₅₉	semidirect
511. C₂	C₅₉×#2329	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×C₂²⋊Q₈×C₅₉	2
C₅₉×#2329	2
C₂×C₅₉×#391	2
C₂×C₅₉×#389	2
C₂×C₅₉×#387	2
C₂×C₅₉×#385	2
C₂×C₅₉×#380	2
C₂×C₄×C₂²⋊C₄×C₅₉	2
C₂²×#95×C₅₉	2
C₂×#2329	59

Subgroups — C2×C59×#2329 #28446180

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅₉×#2329 #28446180