Subgroups — C₅₉×#35222 #28447331

Order 15104.

7586 conjugacy classes of subgroups.

The subgroup lattice has 516 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂⁴×D₄×C₅₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₅₉×#535	C₂	1	2	yes	maximal, complemented
3	C₂×C₅₉×#525	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅₉×#2846	C₂	1	4	yes	maximal, complemented
5	C₅₉×#2613	C₂	1	4	yes	maximal, complemented
6	C₅₉×#2435	C₂	1	4	yes	maximal, complemented
7	C₅₉×#2433	C₂	1	4	yes	maximal, complemented
8	C₅₉×#2408	C₂	1	8	yes	maximal, complemented
9	C₅₉×#2309	C₂	1	2	yes	maximal, complemented
10	C₅₉×#2280	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂⁶×C₅₉	C₂²	1	2	yes	—
12	C₂²×#41×C₅₉	C₂²	1	1	yes	characteristic, complemented
13	C₂³×D₄×C₅₉	—	2	16	no	—
14	C₂³×D₄×C₅₉	—	2	8	no	—
15	C₂³×D₄×C₅₉	C₂²	1	2	yes	—
16	C₂³×D₄×C₅₉	C₂²	1	4	yes	—
17	C₂³×D₄×C₅₉	C₂²	1	4	yes	—
18	C₂³×D₄×C₅₉	C₂²	1	2	yes	—
19	C₂⁴×C₄×C₅₉	C₂²	1	1	yes	characteristic
20	C₅₉×#535	—	2	16	no	—
21	C₂×#127×C₅₉	C₂²	1	4	yes	complemented
22	C₂×#124×C₅₉	C₂²	1	4	yes	complemented
23	C₅₉×#525	—	2	8	no	—
24	C₂×#123×C₅₉	C₂²	1	2	yes	complemented
25	C₂×C₂²⋊Q₈×C₅₉	C₂²	1	2	yes	complemented
26	C₂×#121×C₅₉	C₂²	1	2	yes	complemented
27	C₂×#121×C₅₉	C₂²	1	8	yes	complemented
28	C₂×#120×C₅₉	C₂²	1	2	yes	—
29	C₂×#120×C₅₉	C₂²	1	8	yes	complemented
30	C₂×#120×C₅₉	C₂²	1	16	yes	complemented
31	C₂×C₄×D₄×C₅₉	C₂²	1	4	yes	complemented
32	C₂×#117×C₅₉	C₂²	1	2	yes	complemented
33	C₂×#117×C₅₉	C₂²	1	1	yes	characteristic, complemented
34	C₅₉×#394	C₂²	1	16	yes	complemented
35	C₅₉×#392	C₂²	1	16	yes	complemented
36	C₅₉×#390	C₂²	1	8	yes	complemented
37	C₅₉×#390	C₂²	1	8	yes	complemented
38	C₅₉×#381	C₂²	1	2	yes	complemented
39	C₅₉×#380	C₂²	1	4	yes	complemented
40	C₅₉×#379	C₂²	1	2	yes	—
41	C₅₉×#379	C₂²	1	8	yes	complemented
42	C₅₉×#379	C₂²	1	16	yes	complemented
43	C₄×C₂²⋊C₄×C₅₉	C₂²	1	4	yes	complemented
44	C₂⁵×C₅₉	—	2	16	no	—
45	C₂⁵×C₅₉	—	2	8	no	—
46	C₂⁵×C₅₉	—	4	16	no	—
47	C₂⁵×C₅₉	C₂³	1	1	yes	characteristic
48	C₂⁵×C₅₉	C₂³	1	8	yes	—
49	C₂⁵×C₅₉	C₂³	1	4	yes	—
50	C₂×#41×C₅₉	—	2	4	no	—
51	C₂×#41×C₅₉	—	2	8	no	—
52	C₂²×Q₈×C₅₉	C₂³	1	1	yes	characteristic, complemented
53	C₂²×D₄×C₅₉	—	2	128	no	—
54	C₂²×D₄×C₅₉	—	2	16	no	—
55	C₂²×D₄×C₅₉	—	2	32	no	—
56	C₂²×D₄×C₅₉	—	2	32	no	—
57	C₂²×D₄×C₅₉	—	2	16	no	—
58	C₂²×D₄×C₅₉	—	2	16	no	—
59	C₂²×D₄×C₅₉	—	2	8	no	—
60	C₂²×D₄×C₅₉	—	2	8	no	—
61	C₂²×D₄×C₅₉	—	2	8	no	—
62	C₂²×D₄×C₅₉	D₄	1	16	yes	complemented
63	C₂²×D₄×C₅₉	C₂³	1	8	yes	—
64	C₂²×D₄×C₅₉	C₂³	1	4	yes	—
65	C₂²×D₄×C₅₉	C₂³	1	2	yes	—
66	C₂²×D₄×C₅₉	C₂³	1	4	yes	—
67	C₂²×D₄×C₅₉	C₂³	1	4	yes	—
68	C₂²×D₄×C₅₉	C₂³	1	1	yes	characteristic, complemented
69	C₂²×D₄×C₅₉	C₂³	1	16	yes	complemented
70	C₂³×C₄×C₅₉	—	2	8	no	—
71	C₂³×C₄×C₅₉	D₄	1	8	yes	complemented
72	C₂³×C₄×C₅₉	C₂³	1	2	yes	—
73	C₂³×C₄×C₅₉	C₂³	1	2	yes	—
74	C₂³×C₄×C₅₉	C₂³	1	1	yes	characteristic
75	C₂³×C₄×C₅₉	C₂³	1	1	yes	characteristic
76	C₂³×C₄×C₅₉	C₂³	1	2	yes	complemented
77	#127×C₅₉	—	2	16	no	—
78	#124×C₅₉	—	2	16	no	—
79	#123×C₅₉	—	2	8	no	—
80	C₂²⋊Q₈×C₅₉	—	2	8	no	—
81	#121×C₅₉	—	2	32	no	—
82	#121×C₅₉	—	2	8	no	—
83	#120×C₅₉	—	2	8	no	—
84	#120×C₅₉	—	2	32	no	—
85	#120×C₅₉	—	4	32	no	—
86	C₄×D₄×C₅₉	—	2	16	no	—
87	#117×C₅₉	—	2	4	no	—
88	#117×C₅₉	—	2	8	no	—
89	C₂×C₄⋊C₄×C₅₉	C₂³	1	4	yes	complemented
90	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	complemented
91	C₂×C₄⋊C₄×C₅₉	C₂³	1	4	yes	complemented
92	C₂×C₂²⋊C₄×C₅₉	C₂³	1	8	yes	—
93	C₂×C₂²⋊C₄×C₅₉	C₂³	1	4	yes	—
94	C₂×C₂²⋊C₄×C₅₉	C₂³	1	2	yes	—
95	C₂×C₂²⋊C₄×C₅₉	C₂³	1	4	yes	—
96	C₂×C₂²⋊C₄×C₅₉	C₂³	1	16	yes	complemented
97	C₂×C₂²⋊C₄×C₅₉	C₂³	1	4	yes	complemented
98	C₂×C₂²⋊C₄×C₅₉	C₂³	1	32	yes	complemented
99	C₂×C₄²×C₅₉	C₂³	1	4	yes	complemented
100	C₂×C₄²×C₅₉	C₂³	1	2	yes	complemented
101	#95×C₅₉	C₂³	1	8	yes	complemented
102	C₂⁴×C₅₉	—	2	4	no	—
103	C₂⁴×C₅₉	—	2	8	no	—
104	C₂⁴×C₅₉	—	2	64	no	—
105	C₂⁴×C₅₉	—	2	32	no	—
106	C₂⁴×C₅₉	—	2	16	no	—
107	C₂⁴×C₅₉	—	2	8	no	—
108	C₂⁴×C₅₉	—	2	8	no	—
109	C₂⁴×C₅₉	—	2	32	no	—
110	C₂⁴×C₅₉	—	4	16	no	—
111	C₂⁴×C₅₉	—	4	16	no	—
112	C₂⁴×C₅₉	—	4	128	no	—
113	C₂⁴×C₅₉	—	4	64	no	—
114	C₂⁴×C₅₉	C₂×D₄	1	4	yes	—
115	C₂⁴×C₅₉	C₂×D₄	1	16	yes	—
116	C₂⁴×C₅₉	C₂⁴	1	2	yes	—
117	C₂⁴×C₅₉	C₂⁴	1	8	yes	—
118	C₂⁴×C₅₉	C₂⁴	1	1	yes	characteristic
119	C₂⁴×C₅₉	C₂⁴	1	2	yes	—
120	#41×C₅₉	—	4	16	no	—
121	C₂×Q₈×C₅₉	—	2	2	no	—
122	C₂×Q₈×C₅₉	—	2	4	no	—
123	C₂×D₄×C₅₉	—	2	64	no	—
124	C₂×D₄×C₅₉	—	2	128	no	—
125	C₂×D₄×C₅₉	—	2	128	no	—
126	C₂×D₄×C₅₉	—	2	32	no	—
127	C₂×D₄×C₅₉	—	2	8	no	—
128	C₂×D₄×C₅₉	—	2	8	no	—
129	C₂×D₄×C₅₉	—	2	4	no	—
130	C₂×D₄×C₅₉	—	2	16	no	—
131	C₂×D₄×C₅₉	—	2	32	no	—
132	C₂×D₄×C₅₉	—	2	64	no	—
133	C₂×D₄×C₅₉	—	2	16	no	—
134	C₂×D₄×C₅₉	—	2	8	no	—
135	C₂×D₄×C₅₉	—	2	8	no	—
136	C₂×D₄×C₅₉	—	2	8	no	—
137	C₂×D₄×C₅₉	—	2	8	no	—
138	C₂×D₄×C₅₉	—	2	2	no	—
139	C₂×D₄×C₅₉	—	2	4	no	—
140	C₂×D₄×C₅₉	—	4	32	no	—
141	C₂×D₄×C₅₉	C₂×D₄	1	16	yes	—
142	C₂×D₄×C₅₉	C₂×D₄	1	16	yes	—
143	C₂²×C₄×C₅₉	—	2	4	no	—
144	C₂²×C₄×C₅₉	—	2	32	no	—
145	C₂²×C₄×C₅₉	—	2	8	no	—
146	C₂²×C₄×C₅₉	—	2	8	no	—
147	C₂²×C₄×C₅₉	—	2	4	no	—
148	C₂²×C₄×C₅₉	—	2	8	no	—
149	C₂²×C₄×C₅₉	C₂×D₄	1	8	yes	—
150	C₂²×C₄×C₅₉	C₂×D₄	1	8	yes	—
151	C₂²×C₄×C₅₉	C₂×D₄	1	4	yes	—
152	C₂²×C₄×C₅₉	C₂×D₄	1	8	yes	—
153	C₂²×C₄×C₅₉	C₂×D₄	1	4	yes	—
154	C₂²×C₄×C₅₉	C₂⁴	1	8	yes	—
155	C₂²×C₄×C₅₉	C₂⁴	1	4	yes	—
156	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
157	C₂²×C₄×C₅₉	C₂⁴	1	2	yes	—
158	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
159	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
160	C₄⋊C₄×C₅₉	—	2	8	no	—
161	C₄⋊C₄×C₅₉	—	2	4	no	—
162	C₄⋊C₄×C₅₉	—	2	8	no	—
163	C₂²⋊C₄×C₅₉	—	2	8	no	—
164	C₂²⋊C₄×C₅₉	—	2	4	no	—
165	C₂²⋊C₄×C₅₉	—	2	8	no	—
166	C₂²⋊C₄×C₅₉	—	2	32	no	—
167	C₂²⋊C₄×C₅₉	—	2	16	no	—
168	C₂²⋊C₄×C₅₉	—	2	8	no	—
169	C₂²⋊C₄×C₅₉	—	4	32	no	—
170	C₄²×C₅₉	—	2	4	no	—
171	C₄²×C₅₉	—	2	8	no	—
172	C₂³×C₅₉	—	2	32	no	—
173	C₂³×C₅₉	—	2	8	no	—
174	C₂³×C₅₉	—	2	16	no	—
175	C₂³×C₅₉	—	2	4	no	—
176	C₂³×C₅₉	—	2	4	no	—
177	C₂³×C₅₉	—	2	4	no	—
178	C₂³×C₅₉	—	2	64	no	—
179	C₂³×C₅₉	—	2	32	no	—
180	C₂³×C₅₉	—	2	8	no	—
181	C₂³×C₅₉	—	2	8	no	—
182	C₂³×C₅₉	—	2	32	no	—
183	C₂³×C₅₉	—	2	2	no	—
184	C₂³×C₅₉	—	2	4	no	—
185	C₂³×C₅₉	—	2	8	no	—
186	C₂³×C₅₉	—	4	32	no	—
187	C₂³×C₅₉	—	4	128	no	—
188	C₂³×C₅₉	—	4	256	no	—
189	C₂³×C₅₉	—	4	32	no	—
190	C₂³×C₅₉	—	4	32	no	—
191	C₂³×C₅₉	—	4	32	no	—
192	C₂³×C₅₉	—	4	32	no	—
193	C₂³×C₅₉	C₂²×D₄	1	16	yes	—
194	C₂³×C₅₉	C₂²×D₄	1	4	yes	—
195	C₂³×C₅₉	C₂²×D₄	1	2	yes	—
196	C₂³×C₅₉	C₂²×D₄	1	4	yes	—
197	C₂³×C₅₉	H(5,𝔽₂)	1	8	yes	—
198	C₂³×C₅₉	C₂⁵	1	1	yes	characteristic
199	Q₈×C₅₉	—	4	4	no	—
200	D₄×C₅₉	—	2	64	no	—
201	D₄×C₅₉	—	2	32	no	—
202	D₄×C₅₉	—	2	32	no	—
203	D₄×C₅₉	—	4	8	no	—
204	D₄×C₅₉	—	4	16	no	—
205	D₄×C₅₉	—	4	4	no	—
206	D₄×C₅₉	—	8	32	no	—
207	C₂×C₄×C₅₉	—	2	8	no	—
208	C₂×C₄×C₅₉	—	2	4	no	—
209	C₂×C₄×C₅₉	—	2	16	no	—
210	C₂×C₄×C₅₉	—	2	16	no	—
211	C₂×C₄×C₅₉	—	2	4	no	—
212	C₂×C₄×C₅₉	—	2	8	no	—
213	C₂×C₄×C₅₉	—	2	4	no	—
214	C₂×C₄×C₅₉	—	2	2	no	—
215	C₂×C₄×C₅₉	—	2	16	no	—
216	C₂×C₄×C₅₉	—	2	8	no	—
217	C₂×C₄×C₅₉	—	4	8	no	—
218	C₂×C₄×C₅₉	#120	1	16	yes	complemented
219	C₂×C₄×C₅₉	C₂²×D₄	1	4	yes	—
220	C₂×C₄×C₅₉	C₂²×D₄	1	2	yes	—
221	C₂×C₄×C₅₉	C₂²×D₄	1	4	yes	—
222	C₂×C₄×C₅₉	C₂²×D₄	1	4	yes	—
223	C₂×C₄×C₅₉	C₂²×D₄	1	2	yes	—
224	#35222	C₅₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
225	C₂²×C₅₉	—	2	32	no	—
226	C₂²×C₅₉	—	2	4	no	—
227	C₂²×C₅₉	—	2	4	no	—
228	C₂²×C₅₉	—	2	4	no	—
229	C₂²×C₅₉	—	2	8	no	—
230	C₂²×C₅₉	—	2	16	no	—
231	C₂²×C₅₉	—	2	16	no	—
232	C₂²×C₅₉	—	2	32	no	—
233	C₂²×C₅₉	—	4	64	no	—
234	C₂²×C₅₉	—	4	128	no	—
235	C₂²×C₅₉	—	4	16	no	—
236	C₂²×C₅₉	—	4	16	no	—
237	C₂²×C₅₉	—	4	2	no	—
238	C₂²×C₅₉	—	4	4	no	—
239	C₂²×C₅₉	—	4	8	no	—
240	C₂²×C₅₉	C₂×#120	1	4	yes	—
241	C₂²×C₅₉	#535	1	8	yes	complemented
242	C₂²×C₅₉	C₂³×D₄	1	1	yes	characteristic
243	C₂²×C₅₉	C₂³×D₄	1	2	yes	—
244	C₂²×C₅₉	C₂×H(5,𝔽₂)	1	4	yes	—
245	C₄×C₅₉	—	2	4	no	—
246	C₄×C₅₉	—	4	2	no	—
247	C₄×C₅₉	—	4	4	no	—
248	C₄×C₅₉	—	4	8	no	—
249	C₄×C₅₉	C₂×#120	1	4	yes	—
250	C₄×C₅₉	C₂×#120	1	4	yes	—
251	C₂⁴×D₄	C₂×C₅₉	1	1	yes	characteristic, complemented
252	C₂×#535	C₂×C₅₉	1	2	yes	complemented
253	C₂×#525	C₂×C₅₉	1	1	yes	characteristic, complemented
254	#2846	C₂×C₅₉	1	4	yes	complemented
255	#2613	C₂×C₅₉	1	4	yes	complemented
256	#2435	C₂×C₅₉	1	4	yes	complemented
257	#2433	C₂×C₅₉	1	4	yes	complemented
258	#2408	C₂×C₅₉	1	8	yes	complemented
259	#2309	C₂×C₅₉	1	2	yes	complemented
260	#2280	C₂×C₅₉	1	1	yes	characteristic, complemented
261	C₂×C₅₉	—	2	4	no	—
262	C₂×C₅₉	—	2	8	no	—
263	C₂×C₅₉	—	4	16	no	—
264	C₂×C₅₉	—	8	2	no	—
265	C₂×C₅₉	C₂²×#120	1	1	yes	characteristic
266	C₂×C₅₉	C₂×#535	1	2	yes	—
267	C₂×C₅₉	#3484	1	4	yes	—
268	C₂⁶	C₂²×C₅₉	1	2	yes	—
269	C₂²×#41	C₂²×C₅₉	1	1	yes	characteristic, complemented
270	C₂³×D₄	—	2	16	no	—
271	C₂³×D₄	—	2	8	no	—
272	C₂³×D₄	C₂²×C₅₉	1	2	yes	—
273	C₂³×D₄	C₂²×C₅₉	1	4	yes	—
274	C₂³×D₄	C₂²×C₅₉	1	4	yes	—
275	C₂³×D₄	C₂²×C₅₉	1	2	yes	—
276	C₂⁴×C₄	C₂²×C₅₉	1	1	yes	characteristic
277	#535	—	2	16	no	—
278	C₂×#127	C₂²×C₅₉	1	4	yes	complemented
279	C₂×#124	C₂²×C₅₉	1	4	yes	complemented
280	#525	—	2	8	no	—
281	C₂×#123	C₂²×C₅₉	1	2	yes	complemented
282	C₂×C₂²⋊Q₈	C₂²×C₅₉	1	2	yes	complemented
283	C₂×#121	C₂²×C₅₉	1	2	yes	complemented
284	C₂×#121	C₂²×C₅₉	1	8	yes	complemented
285	C₂×#120	C₂²×C₅₉	1	2	yes	—
286	C₂×#120	C₂²×C₅₉	1	8	yes	complemented
287	C₂×#120	C₂²×C₅₉	1	16	yes	complemented
288	C₂×C₄×D₄	C₂²×C₅₉	1	4	yes	complemented
289	C₂×#117	C₂²×C₅₉	1	1	yes	characteristic, complemented
290	C₂×#117	C₂²×C₅₉	1	2	yes	complemented
291	#394	C₂²×C₅₉	1	16	yes	complemented
292	#392	C₂²×C₅₉	1	16	yes	complemented
293	#390	C₂²×C₅₉	1	8	yes	complemented
294	#390	C₂²×C₅₉	1	8	yes	complemented
295	#381	C₂²×C₅₉	1	2	yes	complemented
296	#380	C₂²×C₅₉	1	4	yes	complemented
297	#379	C₂²×C₅₉	1	2	yes	—
298	#379	C₂²×C₅₉	1	8	yes	complemented
299	#379	C₂²×C₅₉	1	16	yes	complemented
300	C₄×C₂²⋊C₄	C₂²×C₅₉	1	4	yes	complemented
301	C₅₉	#35222	1	1	yes	characteristic, direct product factor, Sylow
302	C₂⁵	—	2	16	no	—
303	C₂⁵	—	2	8	no	—
304	C₂⁵	—	4	16	no	—
305	C₂⁵	C₂³×C₅₉	1	1	yes	characteristic
306	C₂⁵	C₂³×C₅₉	1	8	yes	—
307	C₂⁵	C₂³×C₅₉	1	4	yes	—
308	C₂×#41	—	2	4	no	—
309	C₂×#41	—	2	8	no	—
310	C₂²×Q₈	C₂³×C₅₉	1	1	yes	characteristic, complemented
311	C₂²×D₄	—	2	128	no	—
312	C₂²×D₄	—	2	16	no	—
313	C₂²×D₄	—	2	32	no	—
314	C₂²×D₄	—	2	32	no	—
315	C₂²×D₄	—	2	16	no	—
316	C₂²×D₄	—	2	16	no	—
317	C₂²×D₄	—	2	8	no	—
318	C₂²×D₄	—	2	8	no	—
319	C₂²×D₄	—	2	8	no	—
320	C₂²×D₄	D₄×C₅₉	1	16	yes	complemented
321	C₂²×D₄	C₂³×C₅₉	1	4	yes	—
322	C₂²×D₄	C₂³×C₅₉	1	2	yes	—
323	C₂²×D₄	C₂³×C₅₉	1	8	yes	—
324	C₂²×D₄	C₂³×C₅₉	1	4	yes	—
325	C₂²×D₄	C₂³×C₅₉	1	4	yes	—
326	C₂²×D₄	C₂³×C₅₉	1	1	yes	characteristic, complemented
327	C₂²×D₄	C₂³×C₅₉	1	16	yes	complemented
328	C₂³×C₄	—	2	8	no	—
329	C₂³×C₄	D₄×C₅₉	1	8	yes	complemented
330	C₂³×C₄	C₂³×C₅₉	1	2	yes	—
331	C₂³×C₄	C₂³×C₅₉	1	2	yes	—
332	C₂³×C₄	C₂³×C₅₉	1	1	yes	characteristic
333	C₂³×C₄	C₂³×C₅₉	1	1	yes	characteristic
334	C₂³×C₄	C₂³×C₅₉	1	2	yes	complemented
335	#127	—	2	16	no	—
336	#124	—	2	16	no	—
337	#123	—	2	8	no	—
338	C₂²⋊Q₈	—	2	8	no	—
339	#121	—	2	32	no	—
340	#121	—	2	8	no	—
341	#120	—	2	8	no	—
342	#120	—	2	32	no	—
343	#120	—	4	32	no	—
344	C₄×D₄	—	2	16	no	—
345	#117	—	2	4	no	—
346	#117	—	2	8	no	—
347	C₂×C₄⋊C₄	C₂³×C₅₉	1	4	yes	complemented
348	C₂×C₄⋊C₄	C₂³×C₅₉	1	2	yes	complemented
349	C₂×C₄⋊C₄	C₂³×C₅₉	1	4	yes	complemented
350	C₂×C₂²⋊C₄	C₂³×C₅₉	1	2	yes	—
351	C₂×C₂²⋊C₄	C₂³×C₅₉	1	4	yes	—
352	C₂×C₂²⋊C₄	C₂³×C₅₉	1	4	yes	—
353	C₂×C₂²⋊C₄	C₂³×C₅₉	1	8	yes	—
354	C₂×C₂²⋊C₄	C₂³×C₅₉	1	4	yes	complemented
355	C₂×C₂²⋊C₄	C₂³×C₅₉	1	16	yes	complemented
356	C₂×C₂²⋊C₄	C₂³×C₅₉	1	32	yes	complemented
357	C₂×C₄²	C₂³×C₅₉	1	2	yes	complemented
358	C₂×C₄²	C₂³×C₅₉	1	4	yes	complemented
359	#95	C₂³×C₅₉	1	8	yes	complemented
360	C₂⁴	—	2	4	no	—
361	C₂⁴	—	2	8	no	—
362	C₂⁴	—	2	64	no	—
363	C₂⁴	—	2	32	no	—
364	C₂⁴	—	2	16	no	—
365	C₂⁴	—	2	8	no	—
366	C₂⁴	—	2	8	no	—
367	C₂⁴	—	2	32	no	—
368	C₂⁴	—	4	16	no	—
369	C₂⁴	—	4	16	no	—
370	C₂⁴	—	4	128	no	—
371	C₂⁴	—	4	64	no	—
372	C₂⁴	C₂×D₄×C₅₉	1	4	yes	—
373	C₂⁴	C₂×D₄×C₅₉	1	16	yes	—
374	C₂⁴	C₂⁴×C₅₉	1	2	yes	—
375	C₂⁴	C₂⁴×C₅₉	1	8	yes	—
376	C₂⁴	C₂⁴×C₅₉	1	1	yes	characteristic
377	C₂⁴	C₂⁴×C₅₉	1	2	yes	—
378	#41	—	4	16	no	—
379	C₂×Q₈	—	2	2	no	—
380	C₂×Q₈	—	2	4	no	—
381	C₂×D₄	—	2	64	no	—
382	C₂×D₄	—	2	128	no	—
383	C₂×D₄	—	2	128	no	—
384	C₂×D₄	—	2	32	no	—
385	C₂×D₄	—	2	8	no	—
386	C₂×D₄	—	2	8	no	—
387	C₂×D₄	—	2	4	no	—
388	C₂×D₄	—	2	16	no	—
389	C₂×D₄	—	2	32	no	—
390	C₂×D₄	—	2	64	no	—
391	C₂×D₄	—	2	16	no	—
392	C₂×D₄	—	2	8	no	—
393	C₂×D₄	—	2	8	no	—
394	C₂×D₄	—	2	8	no	—
395	C₂×D₄	—	2	8	no	—
396	C₂×D₄	—	2	2	no	—
397	C₂×D₄	—	2	4	no	—
398	C₂×D₄	—	4	32	no	—
399	C₂×D₄	C₂×D₄×C₅₉	1	16	yes	—
400	C₂×D₄	C₂×D₄×C₅₉	1	16	yes	—
401	C₂²×C₄	—	2	4	no	—
402	C₂²×C₄	—	2	32	no	—
403	C₂²×C₄	—	2	8	no	—
404	C₂²×C₄	—	2	8	no	—
405	C₂²×C₄	—	2	4	no	—
406	C₂²×C₄	—	2	8	no	—
407	C₂²×C₄	C₂×D₄×C₅₉	1	8	yes	—
408	C₂²×C₄	C₂×D₄×C₅₉	1	8	yes	—
409	C₂²×C₄	C₂×D₄×C₅₉	1	4	yes	—
410	C₂²×C₄	C₂×D₄×C₅₉	1	8	yes	—
411	C₂²×C₄	C₂×D₄×C₅₉	1	4	yes	—
412	C₂²×C₄	C₂⁴×C₅₉	1	8	yes	—
413	C₂²×C₄	C₂⁴×C₅₉	1	4	yes	—
414	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
415	C₂²×C₄	C₂⁴×C₅₉	1	2	yes	—
416	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
417	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
418	C₄⋊C₄	—	2	8	no	—
419	C₄⋊C₄	—	2	4	no	—
420	C₄⋊C₄	—	2	8	no	—
421	C₂²⋊C₄	—	2	8	no	—
422	C₂²⋊C₄	—	2	4	no	—
423	C₂²⋊C₄	—	2	8	no	—
424	C₂²⋊C₄	—	2	32	no	—
425	C₂²⋊C₄	—	2	16	no	—
426	C₂²⋊C₄	—	2	8	no	—
427	C₂²⋊C₄	—	4	32	no	—
428	C₄²	—	2	4	no	—
429	C₄²	—	2	8	no	—
430	C₂³	—	2	32	no	—
431	C₂³	—	2	8	no	—
432	C₂³	—	2	16	no	—
433	C₂³	—	2	4	no	—
434	C₂³	—	2	4	no	—
435	C₂³	—	2	4	no	—
436	C₂³	—	2	64	no	—
437	C₂³	—	2	32	no	—
438	C₂³	—	2	8	no	—
439	C₂³	—	2	8	no	—
440	C₂³	—	2	32	no	—
441	C₂³	—	2	2	no	—
442	C₂³	—	2	4	no	—
443	C₂³	—	2	8	no	—
444	C₂³	—	4	32	no	—
445	C₂³	—	4	128	no	—
446	C₂³	—	4	256	no	—
447	C₂³	—	4	32	no	—
448	C₂³	—	4	32	no	—
449	C₂³	—	4	32	no	—
450	C₂³	—	4	32	no	—
451	C₂³	C₂²×D₄×C₅₉	1	16	yes	—
452	C₂³	C₂²×D₄×C₅₉	1	4	yes	—
453	C₂³	C₂²×D₄×C₅₉	1	2	yes	—
454	C₂³	C₂²×D₄×C₅₉	1	4	yes	—
455	C₂³	H(5,𝔽₂)×C₅₉	1	8	yes	—
456	C₂³	C₂⁵×C₅₉	1	1	yes	characteristic
457	Q₈	—	4	4	no	—
458	D₄	—	2	64	no	—
459	D₄	—	2	32	no	—
460	D₄	—	2	32	no	—
461	D₄	—	4	8	no	—
462	D₄	—	4	16	no	—
463	D₄	—	4	4	no	—
464	D₄	—	8	32	no	—
465	C₂×C₄	—	2	8	no	—
466	C₂×C₄	—	2	4	no	—
467	C₂×C₄	—	2	16	no	—
468	C₂×C₄	—	2	16	no	—
469	C₂×C₄	—	2	4	no	—
470	C₂×C₄	—	2	8	no	—
471	C₂×C₄	—	2	4	no	—
472	C₂×C₄	—	2	2	no	—
473	C₂×C₄	—	2	16	no	—
474	C₂×C₄	—	2	8	no	—
475	C₂×C₄	—	4	8	no	—
476	C₂×C₄	#120×C₅₉	1	16	yes	complemented
477	C₂×C₄	C₂²×D₄×C₅₉	1	4	yes	—
478	C₂×C₄	C₂²×D₄×C₅₉	1	2	yes	—
479	C₂×C₄	C₂²×D₄×C₅₉	1	4	yes	—
480	C₂×C₄	C₂²×D₄×C₅₉	1	4	yes	—
481	C₂×C₄	C₂²×D₄×C₅₉	1	2	yes	—
482	C₂²	—	2	32	no	—
483	C₂²	—	2	4	no	—
484	C₂²	—	2	4	no	—
485	C₂²	—	2	4	no	—
486	C₂²	—	2	8	no	—
487	C₂²	—	2	16	no	—
488	C₂²	—	2	16	no	—
489	C₂²	—	2	32	no	—
490	C₂²	—	4	64	no	—
491	C₂²	—	4	128	no	—
492	C₂²	—	4	16	no	—
493	C₂²	—	4	16	no	—
494	C₂²	—	4	2	no	—
495	C₂²	—	4	4	no	—
496	C₂²	—	4	8	no	—
497	C₂²	C₂×#120×C₅₉	1	4	yes	—
498	C₂²	C₅₉×#535	1	8	yes	complemented
499	C₂²	C₂³×D₄×C₅₉	1	1	yes	characteristic
500	C₂²	C₂³×D₄×C₅₉	1	2	yes	—
501	C₂²	C₂×H(5,𝔽₂)×C₅₉	1	4	yes	—
502	C₄	—	2	4	no	—
503	C₄	—	4	2	no	—
504	C₄	—	4	4	no	—
505	C₄	—	4	8	no	—
506	C₄	C₂×#120×C₅₉	1	4	yes	—
507	C₄	C₂×#120×C₅₉	1	4	yes	—
508	C₂	—	2	4	no	—
509	C₂	—	2	8	no	—
510	C₂	—	4	16	no	—
511	C₂	—	8	2	no	—
512	C₂	C₂²×#120×C₅₉	1	1	yes	characteristic
513	C₂	C₂×C₅₉×#535	1	2	yes	—
514	C₂	C₅₉×#3484	1	4	yes	—

	subgroup	G/H
center, socle	C₂³×C₅₉	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₅₉
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. C₂⁴×D₄×C₅₉	C₂	semidirect
2. C₂×C₅₉×#535	C₂	semidirect
3. C₂×C₅₉×#525	C₂	semidirect
4. C₅₉×#2846	C₂	semidirect
5. C₅₉×#2613	C₂	semidirect
6. C₅₉×#2435	C₂	semidirect
7. C₅₉×#2433	C₂	semidirect
8. C₅₉×#2408	C₂	semidirect
9. C₅₉×#2309	C₂	semidirect
10. C₅₉×#2280	C₂	semidirect
12. C₂²×#41×C₅₉	C₂²	semidirect
21. C₂×#127×C₅₉	C₂²	semidirect
22. C₂×#124×C₅₉	C₂²	semidirect
24. C₂×#123×C₅₉	C₂²	semidirect
25. C₂×C₂²⋊Q₈×C₅₉	C₂²	semidirect
26. C₂×#121×C₅₉	C₂²	semidirect
27. C₂×#121×C₅₉	C₂²	semidirect
29. C₂×#120×C₅₉	C₂²	semidirect
30. C₂×#120×C₅₉	C₂²	semidirect
31. C₂×C₄×D₄×C₅₉	C₂²	semidirect
32. C₂×#117×C₅₉	C₂²	semidirect
33. C₂×#117×C₅₉	C₂²	semidirect
34. C₅₉×#394	C₂²	semidirect
35. C₅₉×#392	C₂²	semidirect
36. C₅₉×#390	C₂²	semidirect
37. C₅₉×#390	C₂²	semidirect
38. C₅₉×#381	C₂²	semidirect
39. C₅₉×#380	C₂²	semidirect
41. C₅₉×#379	C₂²	semidirect
42. C₅₉×#379	C₂²	semidirect
43. C₄×C₂²⋊C₄×C₅₉	C₂²	semidirect
52. C₂²×Q₈×C₅₉	C₂³	semidirect
62. C₂²×D₄×C₅₉	D₄	semidirect
68. C₂²×D₄×C₅₉	C₂³	semidirect
69. C₂²×D₄×C₅₉	C₂³	semidirect
71. C₂³×C₄×C₅₉	D₄	semidirect
76. C₂³×C₄×C₅₉	C₂³	semidirect
89. C₂×C₄⋊C₄×C₅₉	C₂³	semidirect
90. C₂×C₄⋊C₄×C₅₉	C₂³	semidirect
91. C₂×C₄⋊C₄×C₅₉	C₂³	semidirect
96. C₂×C₂²⋊C₄×C₅₉	C₂³	semidirect
97. C₂×C₂²⋊C₄×C₅₉	C₂³	semidirect
98. C₂×C₂²⋊C₄×C₅₉	C₂³	semidirect
99. C₂×C₄²×C₅₉	C₂³	semidirect
100. C₂×C₄²×C₅₉	C₂³	semidirect
101. #95×C₅₉	C₂³	semidirect
218. C₂×C₄×C₅₉	#120	semidirect
224. #35222	C₅₉	direct (N × H)
241. C₂²×C₅₉	#535	semidirect
251. C₂⁴×D₄	C₂×C₅₉	semidirect
252. C₂×#535	C₂×C₅₉	semidirect
253. C₂×#525	C₂×C₅₉	semidirect
254. #2846	C₂×C₅₉	semidirect
255. #2613	C₂×C₅₉	semidirect
256. #2435	C₂×C₅₉	semidirect
257. #2433	C₂×C₅₉	semidirect
258. #2408	C₂×C₅₉	semidirect
259. #2309	C₂×C₅₉	semidirect
260. #2280	C₂×C₅₉	semidirect
269. C₂²×#41	C₂²×C₅₉	semidirect
278. C₂×#127	C₂²×C₅₉	semidirect
279. C₂×#124	C₂²×C₅₉	semidirect
281. C₂×#123	C₂²×C₅₉	semidirect
282. C₂×C₂²⋊Q₈	C₂²×C₅₉	semidirect
283. C₂×#121	C₂²×C₅₉	semidirect
284. C₂×#121	C₂²×C₅₉	semidirect
286. C₂×#120	C₂²×C₅₉	semidirect
287. C₂×#120	C₂²×C₅₉	semidirect
288. C₂×C₄×D₄	C₂²×C₅₉	semidirect
289. C₂×#117	C₂²×C₅₉	semidirect
290. C₂×#117	C₂²×C₅₉	semidirect
291. #394	C₂²×C₅₉	semidirect
292. #392	C₂²×C₅₉	semidirect
293. #390	C₂²×C₅₉	semidirect
294. #390	C₂²×C₅₉	semidirect
295. #381	C₂²×C₅₉	semidirect
296. #380	C₂²×C₅₉	semidirect
298. #379	C₂²×C₅₉	semidirect
299. #379	C₂²×C₅₉	semidirect
300. C₄×C₂²⋊C₄	C₂²×C₅₉	semidirect
301. C₅₉	#35222	direct (N × H)
310. C₂²×Q₈	C₂³×C₅₉	semidirect
320. C₂²×D₄	D₄×C₅₉	semidirect
326. C₂²×D₄	C₂³×C₅₉	semidirect
327. C₂²×D₄	C₂³×C₅₉	semidirect
329. C₂³×C₄	D₄×C₅₉	semidirect
334. C₂³×C₄	C₂³×C₅₉	semidirect
347. C₂×C₄⋊C₄	C₂³×C₅₉	semidirect
348. C₂×C₄⋊C₄	C₂³×C₅₉	semidirect
349. C₂×C₄⋊C₄	C₂³×C₅₉	semidirect
354. C₂×C₂²⋊C₄	C₂³×C₅₉	semidirect
355. C₂×C₂²⋊C₄	C₂³×C₅₉	semidirect
356. C₂×C₂²⋊C₄	C₂³×C₅₉	semidirect
357. C₂×C₄²	C₂³×C₅₉	semidirect
358. C₂×C₄²	C₂³×C₅₉	semidirect
359. #95	C₂³×C₅₉	semidirect
476. C₂×C₄	#120×C₅₉	semidirect
498. C₂²	C₅₉×#535	semidirect

Maximal subgroups

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

subgroup	index
C₂⁴×D₄×C₅₉	2
C₂×C₅₉×#535	2
C₂×C₅₉×#525	2
C₅₉×#2846	2
C₅₉×#2613	2
C₅₉×#2435	2
C₅₉×#2433	2
C₅₉×#2408	2
C₅₉×#2309	2
C₅₉×#2280	2
#35222	59

Subgroups — C59×#35222 #28447331

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₉×#35222 #28447331