Subgroups — C₅₉×#35574 #28447683

Order 15104.

2590 conjugacy classes of subgroups.

The subgroup lattice has 562 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₄⋊Q₈×C₅₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₅₉×#520	C₂	1	1	yes	maximal, characteristic
3	C₅₉×#2579	C₂	1	4	yes	maximal, complemented
4	C₅₉×#2452	C₂	1	4	yes	maximal, complemented
5	C₅₉×#2451	C₂	1	4	yes	maximal, complemented
6	C₅₉×#2440	C₂	1	4	yes	maximal, complemented
7	C₅₉×#2439	C₂	1	4	yes	maximal, complemented
8	C₅₉×#2409	C₂	1	4	yes	maximal, complemented
9	C₅₉×#2317	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅₉×#2316	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅₉×#2311	C₂	1	1	yes	maximal, characteristic
12	C₅₉×#2297	C₂	1	1	yes	maximal, characteristic
13	C₅₉×#2296	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂²×#41×C₅₉	C₂²	1	1	yes	characteristic
15	C₂³×Q₈×C₅₉	C₂²	1	2	yes	—
16	C₂×C₄⋊Q₈×C₅₉	—	2	8	no	—
17	C₂×C₄⋊Q₈×C₅₉	C₂²	1	4	yes	—
18	C₂×C₄⋊Q₈×C₅₉	C₂²	1	4	yes	—
19	C₂×C₂²⋊Q₈×C₅₉	C₂²	1	8	yes	—
20	C₅₉×#520	—	2	8	no	—
21	C₂×C₄×Q₈×C₅₉	C₂²	1	2	yes	—
22	C₂×C₄×D₄×C₅₉	C₂²	1	4	yes	—
23	C₂×C₄×D₄×C₅₉	C₂²	1	2	yes	—
24	C₂×#117×C₅₉	C₂²	1	1	yes	characteristic
25	C₂×#117×C₅₉	C₂²	1	1	yes	characteristic
26	C₂×#117×C₅₉	C₂²	1	1	yes	characteristic
27	C₂×#117×C₅₉	C₂²	1	2	yes	—
28	C₂²×C₄⋊C₄×C₅₉	C₂²	1	1	yes	characteristic
29	C₂²×C₄⋊C₄×C₅₉	C₂²	1	2	yes	—
30	C₂²×C₄⋊C₄×C₅₉	C₂²	1	2	yes	—
31	C₂²×C₄⋊C₄×C₅₉	C₂²	1	1	yes	characteristic
32	C₂²×C₄²×C₅₉	C₂²	1	1	yes	characteristic
33	C₅₉×#398	C₂²	1	8	yes	—
34	C₅₉×#396	C₂²	1	8	yes	—
35	C₅₉×#395	C₂²	1	8	yes	—
36	C₅₉×#393	C₂²	1	8	yes	—
37	C₅₉×#391	C₂²	1	2	yes	—
38	C₅₉×#391	C₂²	1	2	yes	—
39	C₅₉×#391	C₂²	1	8	yes	—
40	C₅₉×#390	C₂²	1	2	yes	—
41	C₅₉×#390	C₂²	1	2	yes	—
42	C₅₉×#389	C₂²	1	2	yes	—
43	C₅₉×#389	C₂²	1	2	yes	—
44	C₅₉×#389	C₂²	1	4	yes	—
45	C₅₉×#389	C₂²	1	4	yes	—
46	C₅₉×#389	C₂²	1	4	yes	—
47	C₅₉×#387	C₂²	1	8	yes	—
48	C₅₉×#386	C₂²	1	2	yes	—
49	C₅₉×#386	C₂²	1	2	yes	—
50	C₅₉×#386	C₂²	1	4	yes	—
51	C₅₉×#385	C₂²	1	2	yes	—
52	C₅₉×#385	C₂²	1	2	yes	—
53	C₅₉×#385	C₂²	1	4	yes	—
54	C₅₉×#385	C₂²	1	8	yes	—
55	C₅₉×#384	C₂²	1	2	yes	—
56	C₅₉×#382	C₂²	1	2	yes	—
57	C₅₉×#380	C₂²	1	4	yes	—
58	C₅₉×#380	C₂²	1	4	yes	—
59	C₄×C₄⋊C₄×C₅₉	C₂²	1	4	yes	—
60	C₄×C₂²⋊C₄×C₅₉	C₂²	1	4	yes	—
61	C₂×#41×C₅₉	—	2	4	no	—
62	C₂×#41×C₅₉	—	2	4	no	—
63	C₂×#41×C₅₉	Q₈	1	8	yes	complemented
64	C₂²×Q₈×C₅₉	—	2	8	no	—
65	C₂²×Q₈×C₅₉	—	4	8	no	—
66	C₂²×Q₈×C₅₉	C₂³	1	8	yes	—
67	C₂²×Q₈×C₅₉	C₂³	1	1	yes	characteristic
68	C₂²×D₄×C₅₉	C₂³	1	2	yes	—
69	C₂²×D₄×C₅₉	C₂³	1	1	yes	characteristic
70	C₂³×C₄×C₅₉	C₂³	1	1	yes	characteristic
71	C₂³×C₄×C₅₉	C₂³	1	1	yes	characteristic
72	C₂³×C₄×C₅₉	C₂³	1	2	yes	—
73	C₂³×C₄×C₅₉	C₂³	1	2	yes	—
74	C₂³×C₄×C₅₉	C₂³	1	4	yes	—
75	C₂³×C₄×C₅₉	C₂³	1	2	yes	—
76	C₂³×C₄×C₅₉	C₂³	1	1	yes	characteristic
77	C₄⋊Q₈×C₅₉	—	2	16	no	—
78	C₄⋊Q₈×C₅₉	—	2	16	no	—
79	C₂²⋊Q₈×C₅₉	—	4	16	no	—
80	C₄×Q₈×C₅₉	—	2	8	no	—
81	C₄×D₄×C₅₉	—	2	16	no	—
82	C₄×D₄×C₅₉	—	2	8	no	—
83	#117×C₅₉	—	2	4	no	—
84	#117×C₅₉	—	2	4	no	—
85	#117×C₅₉	—	2	4	no	—
86	#117×C₅₉	—	2	8	no	—
87	C₂×C₄⋊C₄×C₅₉	—	2	8	no	—
88	C₂×C₄⋊C₄×C₅₉	—	2	4	no	—
89	C₂×C₄⋊C₄×C₅₉	—	2	8	no	—
90	C₂×C₄⋊C₄×C₅₉	D₄	1	8	yes	—
91	C₂×C₄⋊C₄×C₅₉	C₂³	1	4	yes	—
92	C₂×C₄⋊C₄×C₅₉	C₂³	1	4	yes	—
93	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
94	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
95	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
96	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
97	C₂×C₄⋊C₄×C₅₉	C₂³	1	8	yes	—
98	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
99	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
100	C₂×C₄⋊C₄×C₅₉	C₂³	1	4	yes	—
101	C₂×C₄⋊C₄×C₅₉	C₂³	1	8	yes	—
102	C₂×C₄⋊C₄×C₅₉	C₂³	1	8	yes	—
103	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
104	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
105	C₂×C₂²⋊C₄×C₅₉	C₂³	1	4	yes	—
106	C₂×C₂²⋊C₄×C₅₉	C₂³	1	4	yes	—
107	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
108	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
109	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
110	C₂×C₂²⋊C₄×C₅₉	C₂³	1	4	yes	—
111	C₂×C₂²⋊C₄×C₅₉	C₂³	1	8	yes	—
112	C₂×C₄²×C₅₉	—	2	4	no	—
113	C₂×C₄²×C₅₉	C₂³	1	2	yes	—
114	C₂×C₄²×C₅₉	C₂³	1	2	yes	—
115	C₂×C₄²×C₅₉	C₂³	1	2	yes	—
116	C₂×C₄²×C₅₉	C₂³	1	2	yes	—
117	C₂×C₄²×C₅₉	C₂³	1	2	yes	—
118	C₂×C₄²×C₅₉	C₂³	1	4	yes	—
119	#95×C₅₉	C₂³	1	4	yes	—
120	#95×C₅₉	C₂³	1	4	yes	—
121	#95×C₅₉	C₂³	1	4	yes	—
122	#95×C₅₉	C₂³	1	4	yes	—
123	#95×C₅₉	C₂³	1	8	yes	—
124	#95×C₅₉	C₂³	1	8	yes	—
125	#95×C₅₉	C₂³	1	8	yes	—
126	C₂⁴×C₅₉	C₂⁴	1	2	yes	—
127	C₂⁴×C₅₉	C₂⁴	1	1	yes	characteristic
128	#41×C₅₉	—	2	32	no	—
129	C₂×Q₈×C₅₉	—	2	2	no	—
130	C₂×Q₈×C₅₉	—	2	16	no	—
131	C₂×Q₈×C₅₉	—	2	2	no	—
132	C₂×Q₈×C₅₉	—	2	16	no	—
133	C₂×Q₈×C₅₉	—	4	8	no	—
134	C₂×Q₈×C₅₉	—	4	32	no	—
135	C₂×Q₈×C₅₉	C₂×Q₈	1	4	yes	complemented
136	C₂×D₄×C₅₉	—	2	4	no	—
137	C₂×D₄×C₅₉	—	2	4	no	—
138	C₂×D₄×C₅₉	—	2	2	no	—
139	C₂×D₄×C₅₉	—	2	2	no	—
140	C₂×D₄×C₅₉	C₂×Q₈	1	8	yes	—
141	C₂×D₄×C₅₉	C₂×Q₈	1	4	yes	complemented
142	C₂²×C₄×C₅₉	—	2	2	no	—
143	C₂²×C₄×C₅₉	—	2	2	no	—
144	C₂²×C₄×C₅₉	—	2	4	no	—
145	C₂²×C₄×C₅₉	—	2	4	no	—
146	C₂²×C₄×C₅₉	—	2	4	no	—
147	C₂²×C₄×C₅₉	—	2	4	no	—
148	C₂²×C₄×C₅₉	—	2	4	no	—
149	C₂²×C₄×C₅₉	—	2	8	no	—
150	C₂²×C₄×C₅₉	—	4	4	no	—
151	C₂²×C₄×C₅₉	—	4	4	no	—
152	C₂²×C₄×C₅₉	—	4	8	no	—
153	C₂²×C₄×C₅₉	C₂×D₄	1	8	yes	—
154	C₂²×C₄×C₅₉	C₂×D₄	1	4	yes	—
155	C₂²×C₄×C₅₉	C₂×Q₈	1	4	yes	—
156	C₂²×C₄×C₅₉	C₂×Q₈	1	8	yes	complemented
157	C₂²×C₄×C₅₉	#41	1	4	yes	—
158	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
159	C₂²×C₄×C₅₉	C₂⁴	1	4	yes	—
160	C₂²×C₄×C₅₉	C₂⁴	1	4	yes	—
161	C₂²×C₄×C₅₉	C₂⁴	1	4	yes	—
162	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
163	C₂²×C₄×C₅₉	C₂⁴	1	4	yes	—
164	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
165	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
166	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
167	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
168	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
169	C₄⋊C₄×C₅₉	—	2	2	no	—
170	C₄⋊C₄×C₅₉	—	2	8	no	—
171	C₄⋊C₄×C₅₉	—	2	16	no	—
172	C₄⋊C₄×C₅₉	—	2	4	no	—
173	C₄⋊C₄×C₅₉	—	2	4	no	—
174	C₄⋊C₄×C₅₉	—	2	2	no	—
175	C₄⋊C₄×C₅₉	—	2	4	no	—
176	C₄⋊C₄×C₅₉	—	2	4	no	—
177	C₄⋊C₄×C₅₉	—	2	8	no	—
178	C₄⋊C₄×C₅₉	—	2	8	no	—
179	C₄⋊C₄×C₅₉	—	4	8	no	—
180	C₄⋊C₄×C₅₉	—	4	8	no	—
181	C₄⋊C₄×C₅₉	C₂×D₄	1	8	yes	—
182	C₄⋊C₄×C₅₉	C₂×D₄	1	8	yes	—
183	C₂²⋊C₄×C₅₉	—	2	4	no	—
184	C₂²⋊C₄×C₅₉	—	2	4	no	—
185	C₂²⋊C₄×C₅₉	—	2	4	no	—
186	C₂²⋊C₄×C₅₉	—	2	8	no	—
187	C₂²⋊C₄×C₅₉	—	2	8	no	—
188	C₂²⋊C₄×C₅₉	—	2	8	no	—
189	C₂²⋊C₄×C₅₉	—	4	8	no	—
190	C₄²×C₅₉	—	2	4	no	—
191	C₄²×C₅₉	—	2	4	no	—
192	C₄²×C₅₉	—	2	8	no	—
193	C₄²×C₅₉	—	2	4	no	—
194	C₄²×C₅₉	—	2	4	no	—
195	C₄²×C₅₉	—	2	4	no	—
196	C₂³×C₅₉	—	2	2	no	—
197	C₂³×C₅₉	—	2	2	no	—
198	C₂³×C₅₉	—	2	2	no	—
199	C₂³×C₅₉	—	2	2	no	—
200	C₂³×C₅₉	—	2	4	no	—
201	C₂³×C₅₉	—	2	4	no	—
202	C₂³×C₅₉	C₂²×D₄	1	2	yes	—
203	C₂³×C₅₉	C₂²×Q₈	1	4	yes	—
204	C₂³×C₅₉	C₂²×Q₈	1	2	yes	—
205	C₂³×C₅₉	C₂×#41	1	2	yes	—
206	C₂³×C₅₉	C₂⁵	1	1	yes	characteristic
207	Q₈×C₅₉	—	2	8	no	—
208	Q₈×C₅₉	—	4	32	no	—
209	D₄×C₅₉	—	2	16	no	—
210	D₄×C₅₉	—	2	8	no	—
211	C₂×C₄×C₅₉	—	2	8	no	—
212	C₂×C₄×C₅₉	—	2	8	no	—
213	C₂×C₄×C₅₉	—	2	2	no	—
214	C₂×C₄×C₅₉	—	2	2	no	—
215	C₂×C₄×C₅₉	—	2	2	no	—
216	C₂×C₄×C₅₉	—	2	2	no	—
217	C₂×C₄×C₅₉	—	2	8	no	—
218	C₂×C₄×C₅₉	—	2	2	no	—
219	C₂×C₄×C₅₉	—	2	2	no	—
220	C₂×C₄×C₅₉	—	2	16	no	—
221	C₂×C₄×C₅₉	—	2	2	no	—
222	C₂×C₄×C₅₉	—	2	2	no	—
223	C₂×C₄×C₅₉	—	2	4	no	—
224	C₂×C₄×C₅₉	—	2	4	no	—
225	C₂×C₄×C₅₉	—	2	4	no	—
226	C₂×C₄×C₅₉	—	2	4	no	—
227	C₂×C₄×C₅₉	—	2	4	no	—
228	C₂×C₄×C₅₉	—	2	8	no	—
229	C₂×C₄×C₅₉	—	2	4	no	—
230	C₂×C₄×C₅₉	—	2	4	no	—
231	C₂×C₄×C₅₉	—	2	4	no	—
232	C₂×C₄×C₅₉	—	2	4	no	—
233	C₂×C₄×C₅₉	—	4	8	no	—
234	C₂×C₄×C₅₉	—	4	8	no	—
235	C₂×C₄×C₅₉	—	8	8	no	—
236	C₂×C₄×C₅₉	C₂²⋊Q₈	1	16	yes	complemented
237	C₂×C₄×C₅₉	C₂²×D₄	1	8	yes	—
238	C₂×C₄×C₅₉	C₂²×D₄	1	2	yes	—
239	C₂×C₄×C₅₉	C₂²×D₄	1	2	yes	—
240	C₂×C₄×C₅₉	C₂²×Q₈	1	4	yes	—
241	C₂×C₄×C₅₉	C₂²×Q₈	1	2	yes	—
242	C₂×C₄×C₅₉	C₂²×Q₈	1	2	yes	—
243	C₂×C₄×C₅₉	C₂×#41	1	2	yes	—
244	C₂×C₄×C₅₉	C₂×#41	1	2	yes	—
245	C₂×C₄×C₅₉	H(5,𝔽₂)	1	4	yes	—
246	C₂×C₄×C₅₉	2₋¹⁺⁴	1	4	yes	—
247	#35574	C₅₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
248	C₂²×C₅₉	—	2	2	no	—
249	C₂²×C₅₉	—	2	2	no	—
250	C₂²×C₅₉	—	2	4	no	—
251	C₂²×C₅₉	—	2	4	no	—
252	C₂²×C₅₉	—	2	4	no	—
253	C₂²×C₅₉	—	2	8	no	—
254	C₂²×C₅₉	—	4	2	no	—
255	C₂²×C₅₉	—	4	2	no	—
256	C₂²×C₅₉	—	4	4	no	—
257	C₂²×C₅₉	C₂×C₂²⋊Q₈	1	4	yes	—
258	C₂²×C₅₉	C₂³×D₄	1	1	yes	characteristic
259	C₂²×C₅₉	C₂³×Q₈	1	1	yes	characteristic
260	C₂²×C₅₉	C₂²×#41	1	1	yes	characteristic
261	C₂²×C₅₉	C₂×H(5,𝔽₂)	1	2	yes	—
262	C₂²×C₅₉	C₂×2₋¹⁺⁴	1	2	yes	—
263	C₄×C₅₉	—	2	4	no	—
264	C₄×C₅₉	—	2	4	no	—
265	C₄×C₅₉	—	2	8	no	—
266	C₄×C₅₉	—	2	4	no	—
267	C₄×C₅₉	—	4	4	no	—
268	C₄×C₅₉	—	4	2	no	—
269	C₄×C₅₉	—	4	2	no	—
270	C₄×C₅₉	—	4	4	no	—
271	C₄×C₅₉	—	4	4	no	—
272	C₄×C₅₉	C₂×C₂²⋊Q₈	1	4	yes	—
273	C₄×C₅₉	C₂×C₂²⋊Q₈	1	4	yes	—
274	C₂²×C₄⋊Q₈	C₂×C₅₉	1	1	yes	characteristic, complemented
275	C₂×#520	C₂×C₅₉	1	1	yes	characteristic
276	#2579	C₂×C₅₉	1	4	yes	complemented
277	#2452	C₂×C₅₉	1	4	yes	complemented
278	#2451	C₂×C₅₉	1	4	yes	complemented
279	#2440	C₂×C₅₉	1	4	yes	complemented
280	#2439	C₂×C₅₉	1	4	yes	complemented
281	#2409	C₂×C₅₉	1	4	yes	complemented
282	#2317	C₂×C₅₉	1	1	yes	characteristic, complemented
283	#2316	C₂×C₅₉	1	1	yes	characteristic, complemented
284	#2311	C₂×C₅₉	1	1	yes	characteristic
285	#2297	C₂×C₅₉	1	1	yes	characteristic
286	#2296	C₂×C₅₉	1	1	yes	characteristic, complemented
287	C₂×C₅₉	—	2	4	no	—
288	C₂×C₅₉	—	4	4	no	—
289	C₂×C₅₉	C₂²×C₂²⋊Q₈	1	1	yes	characteristic
290	C₂×C₅₉	#3484	1	1	yes	characteristic
291	C₂×C₅₉	#3486	1	1	yes	characteristic
292	C₂×C₅₉	#3503	1	2	yes	—
293	C₂×C₅₉	#3511	1	2	yes	—
294	C₂²×#41	C₂²×C₅₉	1	1	yes	characteristic
295	C₂³×Q₈	C₂²×C₅₉	1	2	yes	—
296	C₂×C₄⋊Q₈	—	2	8	no	—
297	C₂×C₄⋊Q₈	C₂²×C₅₉	1	4	yes	—
298	C₂×C₄⋊Q₈	C₂²×C₅₉	1	4	yes	—
299	C₂×C₂²⋊Q₈	C₂²×C₅₉	1	8	yes	—
300	#520	—	2	8	no	—
301	C₂×C₄×Q₈	C₂²×C₅₉	1	2	yes	—
302	C₂×C₄×D₄	C₂²×C₅₉	1	4	yes	—
303	C₂×C₄×D₄	C₂²×C₅₉	1	2	yes	—
304	C₂×#117	C₂²×C₅₉	1	1	yes	characteristic
305	C₂×#117	C₂²×C₅₉	1	1	yes	characteristic
306	C₂×#117	C₂²×C₅₉	1	1	yes	characteristic
307	C₂×#117	C₂²×C₅₉	1	2	yes	—
308	C₂²×C₄⋊C₄	C₂²×C₅₉	1	1	yes	characteristic
309	C₂²×C₄⋊C₄	C₂²×C₅₉	1	2	yes	—
310	C₂²×C₄⋊C₄	C₂²×C₅₉	1	2	yes	—
311	C₂²×C₄⋊C₄	C₂²×C₅₉	1	1	yes	characteristic
312	C₂²×C₄²	C₂²×C₅₉	1	1	yes	characteristic
313	#398	C₂²×C₅₉	1	8	yes	—
314	#396	C₂²×C₅₉	1	8	yes	—
315	#395	C₂²×C₅₉	1	8	yes	—
316	#393	C₂²×C₅₉	1	8	yes	—
317	#391	C₂²×C₅₉	1	2	yes	—
318	#391	C₂²×C₅₉	1	8	yes	—
319	#391	C₂²×C₅₉	1	2	yes	—
320	#390	C₂²×C₅₉	1	2	yes	—
321	#390	C₂²×C₅₉	1	2	yes	—
322	#389	C₂²×C₅₉	1	4	yes	—
323	#389	C₂²×C₅₉	1	4	yes	—
324	#389	C₂²×C₅₉	1	4	yes	—
325	#389	C₂²×C₅₉	1	2	yes	—
326	#389	C₂²×C₅₉	1	2	yes	—
327	#387	C₂²×C₅₉	1	8	yes	—
328	#386	C₂²×C₅₉	1	4	yes	—
329	#386	C₂²×C₅₉	1	2	yes	—
330	#386	C₂²×C₅₉	1	2	yes	—
331	#385	C₂²×C₅₉	1	4	yes	—
332	#385	C₂²×C₅₉	1	2	yes	—
333	#385	C₂²×C₅₉	1	8	yes	—
334	#385	C₂²×C₅₉	1	2	yes	—
335	#384	C₂²×C₅₉	1	2	yes	—
336	#382	C₂²×C₅₉	1	2	yes	—
337	#380	C₂²×C₅₉	1	4	yes	—
338	#380	C₂²×C₅₉	1	4	yes	—
339	C₄×C₄⋊C₄	C₂²×C₅₉	1	4	yes	—
340	C₄×C₂²⋊C₄	C₂²×C₅₉	1	4	yes	—
341	C₅₉	#35574	1	1	yes	characteristic, direct product factor, Sylow
342	C₂×#41	—	2	4	no	—
343	C₂×#41	—	2	4	no	—
344	C₂×#41	Q₈×C₅₉	1	8	yes	complemented
345	C₂²×Q₈	—	2	8	no	—
346	C₂²×Q₈	—	4	8	no	—
347	C₂²×Q₈	C₂³×C₅₉	1	8	yes	—
348	C₂²×Q₈	C₂³×C₅₉	1	1	yes	characteristic
349	C₂²×D₄	C₂³×C₅₉	1	2	yes	—
350	C₂²×D₄	C₂³×C₅₉	1	1	yes	characteristic
351	C₂³×C₄	C₂³×C₅₉	1	1	yes	characteristic
352	C₂³×C₄	C₂³×C₅₉	1	1	yes	characteristic
353	C₂³×C₄	C₂³×C₅₉	1	2	yes	—
354	C₂³×C₄	C₂³×C₅₉	1	2	yes	—
355	C₂³×C₄	C₂³×C₅₉	1	4	yes	—
356	C₂³×C₄	C₂³×C₅₉	1	2	yes	—
357	C₂³×C₄	C₂³×C₅₉	1	1	yes	characteristic
358	C₄⋊Q₈	—	2	16	no	—
359	C₄⋊Q₈	—	2	16	no	—
360	C₂²⋊Q₈	—	4	16	no	—
361	C₄×Q₈	—	2	8	no	—
362	C₄×D₄	—	2	16	no	—
363	C₄×D₄	—	2	8	no	—
364	#117	—	2	4	no	—
365	#117	—	2	4	no	—
366	#117	—	2	4	no	—
367	#117	—	2	8	no	—
368	C₂×C₄⋊C₄	—	2	8	no	—
369	C₂×C₄⋊C₄	—	2	4	no	—
370	C₂×C₄⋊C₄	—	2	8	no	—
371	C₂×C₄⋊C₄	D₄×C₅₉	1	8	yes	—
372	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
373	C₂×C₄⋊C₄	C₂³×C₅₉	1	4	yes	—
374	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
375	C₂×C₄⋊C₄	C₂³×C₅₉	1	8	yes	—
376	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
377	C₂×C₄⋊C₄	C₂³×C₅₉	1	1	yes	characteristic
378	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
379	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
380	C₂×C₄⋊C₄	C₂³×C₅₉	1	4	yes	—
381	C₂×C₄⋊C₄	C₂³×C₅₉	1	4	yes	—
382	C₂×C₄⋊C₄	C₂³×C₅₉	1	8	yes	—
383	C₂×C₄⋊C₄	C₂³×C₅₉	1	8	yes	—
384	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
385	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	—
386	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
387	C₂×C₂²⋊C₄	C₂³×C₅₉	1	4	yes	—
388	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
389	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
390	C₂×C₂²⋊C₄	C₂³×C₅₉	1	4	yes	—
391	C₂×C₂²⋊C₄	C₂³×C₅₉	1	4	yes	—
392	C₂×C₂²⋊C₄	C₂³×C₅₉	1	8	yes	—
393	C₂×C₄²	—	2	4	no	—
394	C₂×C₄²	C₂³×C₅₉	1	2	yes	—
395	C₂×C₄²	C₂³×C₅₉	1	4	yes	—
396	C₂×C₄²	C₂³×C₅₉	1	2	yes	—
397	C₂×C₄²	C₂³×C₅₉	1	2	yes	—
398	C₂×C₄²	C₂³×C₅₉	1	2	yes	—
399	C₂×C₄²	C₂³×C₅₉	1	2	yes	—
400	#95	C₂³×C₅₉	1	4	yes	—
401	#95	C₂³×C₅₉	1	4	yes	—
402	#95	C₂³×C₅₉	1	4	yes	—
403	#95	C₂³×C₅₉	1	4	yes	—
404	#95	C₂³×C₅₉	1	8	yes	—
405	#95	C₂³×C₅₉	1	8	yes	—
406	#95	C₂³×C₅₉	1	8	yes	—
407	C₂⁴	C₂⁴×C₅₉	1	2	yes	—
408	C₂⁴	C₂⁴×C₅₉	1	1	yes	characteristic
409	#41	—	2	32	no	—
410	C₂×Q₈	—	2	2	no	—
411	C₂×Q₈	—	2	16	no	—
412	C₂×Q₈	—	2	2	no	—
413	C₂×Q₈	—	2	16	no	—
414	C₂×Q₈	—	4	8	no	—
415	C₂×Q₈	—	4	32	no	—
416	C₂×Q₈	C₂×Q₈×C₅₉	1	4	yes	complemented
417	C₂×D₄	—	2	4	no	—
418	C₂×D₄	—	2	4	no	—
419	C₂×D₄	—	2	2	no	—
420	C₂×D₄	—	2	2	no	—
421	C₂×D₄	C₂×Q₈×C₅₉	1	8	yes	—
422	C₂×D₄	C₂×Q₈×C₅₉	1	4	yes	complemented
423	C₂²×C₄	—	2	2	no	—
424	C₂²×C₄	—	2	2	no	—
425	C₂²×C₄	—	2	4	no	—
426	C₂²×C₄	—	2	4	no	—
427	C₂²×C₄	—	2	4	no	—
428	C₂²×C₄	—	2	4	no	—
429	C₂²×C₄	—	2	4	no	—
430	C₂²×C₄	—	2	8	no	—
431	C₂²×C₄	—	4	4	no	—
432	C₂²×C₄	—	4	4	no	—
433	C₂²×C₄	—	4	8	no	—
434	C₂²×C₄	C₂×D₄×C₅₉	1	8	yes	—
435	C₂²×C₄	C₂×D₄×C₅₉	1	4	yes	—
436	C₂²×C₄	C₂×Q₈×C₅₉	1	4	yes	—
437	C₂²×C₄	C₂×Q₈×C₅₉	1	8	yes	complemented
438	C₂²×C₄	#41×C₅₉	1	4	yes	—
439	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
440	C₂²×C₄	C₂⁴×C₅₉	1	4	yes	—
441	C₂²×C₄	C₂⁴×C₅₉	1	4	yes	—
442	C₂²×C₄	C₂⁴×C₅₉	1	4	yes	—
443	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
444	C₂²×C₄	C₂⁴×C₅₉	1	4	yes	—
445	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
446	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
447	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
448	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
449	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
450	C₄⋊C₄	—	2	2	no	—
451	C₄⋊C₄	—	2	8	no	—
452	C₄⋊C₄	—	2	16	no	—
453	C₄⋊C₄	—	2	4	no	—
454	C₄⋊C₄	—	2	4	no	—
455	C₄⋊C₄	—	2	2	no	—
456	C₄⋊C₄	—	2	4	no	—
457	C₄⋊C₄	—	2	4	no	—
458	C₄⋊C₄	—	2	8	no	—
459	C₄⋊C₄	—	2	8	no	—
460	C₄⋊C₄	—	4	8	no	—
461	C₄⋊C₄	—	4	8	no	—
462	C₄⋊C₄	C₂×D₄×C₅₉	1	8	yes	—
463	C₄⋊C₄	C₂×D₄×C₅₉	1	8	yes	—
464	C₂²⋊C₄	—	2	4	no	—
465	C₂²⋊C₄	—	2	4	no	—
466	C₂²⋊C₄	—	2	4	no	—
467	C₂²⋊C₄	—	2	8	no	—
468	C₂²⋊C₄	—	2	8	no	—
469	C₂²⋊C₄	—	2	8	no	—
470	C₂²⋊C₄	—	4	8	no	—
471	C₄²	—	2	4	no	—
472	C₄²	—	2	4	no	—
473	C₄²	—	2	8	no	—
474	C₄²	—	2	4	no	—
475	C₄²	—	2	4	no	—
476	C₄²	—	2	4	no	—
477	C₂³	—	2	2	no	—
478	C₂³	—	2	2	no	—
479	C₂³	—	2	2	no	—
480	C₂³	—	2	2	no	—
481	C₂³	—	2	4	no	—
482	C₂³	—	2	4	no	—
483	C₂³	C₂²×D₄×C₅₉	1	2	yes	—
484	C₂³	C₂²×Q₈×C₅₉	1	4	yes	—
485	C₂³	C₂²×Q₈×C₅₉	1	2	yes	—
486	C₂³	C₂×#41×C₅₉	1	2	yes	—
487	C₂³	C₂⁵×C₅₉	1	1	yes	characteristic
488	Q₈	—	2	8	no	—
489	Q₈	—	4	32	no	—
490	D₄	—	2	16	no	—
491	D₄	—	2	8	no	—
492	C₂×C₄	—	2	8	no	—
493	C₂×C₄	—	2	8	no	—
494	C₂×C₄	—	2	2	no	—
495	C₂×C₄	—	2	2	no	—
496	C₂×C₄	—	2	2	no	—
497	C₂×C₄	—	2	2	no	—
498	C₂×C₄	—	2	8	no	—
499	C₂×C₄	—	2	2	no	—
500	C₂×C₄	—	2	2	no	—
501	C₂×C₄	—	2	16	no	—
502	C₂×C₄	—	2	2	no	—
503	C₂×C₄	—	2	2	no	—
504	C₂×C₄	—	2	4	no	—
505	C₂×C₄	—	2	4	no	—
506	C₂×C₄	—	2	4	no	—
507	C₂×C₄	—	2	4	no	—
508	C₂×C₄	—	2	4	no	—
509	C₂×C₄	—	2	8	no	—
510	C₂×C₄	—	2	4	no	—
511	C₂×C₄	—	2	4	no	—
512	C₂×C₄	—	2	4	no	—
513	C₂×C₄	—	2	4	no	—
514	C₂×C₄	—	4	8	no	—
515	C₂×C₄	—	4	8	no	—
516	C₂×C₄	—	8	8	no	—
517	C₂×C₄	C₂²⋊Q₈×C₅₉	1	16	yes	complemented
518	C₂×C₄	C₂²×D₄×C₅₉	1	8	yes	—
519	C₂×C₄	C₂²×D₄×C₅₉	1	2	yes	—
520	C₂×C₄	C₂²×D₄×C₅₉	1	2	yes	—
521	C₂×C₄	C₂²×Q₈×C₅₉	1	4	yes	—
522	C₂×C₄	C₂²×Q₈×C₅₉	1	2	yes	—
523	C₂×C₄	C₂²×Q₈×C₅₉	1	2	yes	—
524	C₂×C₄	C₂×#41×C₅₉	1	2	yes	—
525	C₂×C₄	C₂×#41×C₅₉	1	2	yes	—
526	C₂×C₄	H(5,𝔽₂)×C₅₉	1	4	yes	—
527	C₂×C₄	2₋¹⁺⁴×C₅₉	1	4	yes	—
528	C₂²	—	2	4	no	—
529	C₂²	—	2	2	no	—
530	C₂²	—	2	2	no	—
531	C₂²	—	2	4	no	—
532	C₂²	—	2	4	no	—
533	C₂²	—	2	8	no	—
534	C₂²	—	4	4	no	—
535	C₂²	—	4	2	no	—
536	C₂²	—	4	2	no	—
537	C₂²	C₂×C₂²⋊Q₈×C₅₉	1	4	yes	—
538	C₂²	C₂³×D₄×C₅₉	1	1	yes	characteristic
539	C₂²	C₂³×Q₈×C₅₉	1	1	yes	characteristic
540	C₂²	C₂²×#41×C₅₉	1	1	yes	characteristic
541	C₂²	C₂×H(5,𝔽₂)×C₅₉	1	2	yes	—
542	C₂²	C₂×2₋¹⁺⁴×C₅₉	1	2	yes	—
543	C₄	—	2	4	no	—
544	C₄	—	2	4	no	—
545	C₄	—	2	8	no	—
546	C₄	—	2	4	no	—
547	C₄	—	4	4	no	—
548	C₄	—	4	4	no	—
549	C₄	—	4	4	no	—
550	C₄	—	4	2	no	—
551	C₄	—	4	2	no	—
552	C₄	C₂×C₂²⋊Q₈×C₅₉	1	4	yes	—
553	C₄	C₂×C₂²⋊Q₈×C₅₉	1	4	yes	—
554	C₂	—	2	4	no	—
555	C₂	—	4	4	no	—
556	C₂	C₂²×C₂²⋊Q₈×C₅₉	1	1	yes	characteristic
557	C₂	C₅₉×#3484	1	1	yes	characteristic
558	C₂	C₅₉×#3486	1	1	yes	characteristic
559	C₂	C₅₉×#3503	1	2	yes	—
560	C₂	C₅₉×#3511	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₅₉	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₅₉
prime radical	C₂²×#41×C₅₉	C₂²
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₅₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂²×C₄⋊Q₈×C₅₉	C₂	semidirect
3. C₅₉×#2579	C₂	semidirect
4. C₅₉×#2452	C₂	semidirect
5. C₅₉×#2451	C₂	semidirect
6. C₅₉×#2440	C₂	semidirect
7. C₅₉×#2439	C₂	semidirect
8. C₅₉×#2409	C₂	semidirect
9. C₅₉×#2317	C₂	semidirect
10. C₅₉×#2316	C₂	semidirect
13. C₅₉×#2296	C₂	semidirect
63. C₂×#41×C₅₉	Q₈	semidirect
135. C₂×Q₈×C₅₉	C₂×Q₈	semidirect
141. C₂×D₄×C₅₉	C₂×Q₈	semidirect
156. C₂²×C₄×C₅₉	C₂×Q₈	semidirect
236. C₂×C₄×C₅₉	C₂²⋊Q₈	semidirect
247. #35574	C₅₉	direct (N × H)
274. C₂²×C₄⋊Q₈	C₂×C₅₉	semidirect
276. #2579	C₂×C₅₉	semidirect
277. #2452	C₂×C₅₉	semidirect
278. #2451	C₂×C₅₉	semidirect
279. #2440	C₂×C₅₉	semidirect
280. #2439	C₂×C₅₉	semidirect
281. #2409	C₂×C₅₉	semidirect
282. #2317	C₂×C₅₉	semidirect
283. #2316	C₂×C₅₉	semidirect
286. #2296	C₂×C₅₉	semidirect
341. C₅₉	#35574	direct (N × H)
344. C₂×#41	Q₈×C₅₉	semidirect
416. C₂×Q₈	C₂×Q₈×C₅₉	semidirect
422. C₂×D₄	C₂×Q₈×C₅₉	semidirect
437. C₂²×C₄	C₂×Q₈×C₅₉	semidirect
517. C₂×C₄	C₂²⋊Q₈×C₅₉	semidirect

Maximal subgroups

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

subgroup	index
C₂²×C₄⋊Q₈×C₅₉	2
C₂×C₅₉×#520	2
C₅₉×#2579	2
C₅₉×#2452	2
C₅₉×#2451	2
C₅₉×#2440	2
C₅₉×#2439	2
C₅₉×#2409	2
C₅₉×#2317	2
C₅₉×#2316	2
C₅₉×#2311	2
C₅₉×#2297	2
C₅₉×#2296	2
#35574	59

Subgroups — C59×#35574 #28447683

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₉×#35574 #28447683