Subgroups — #28587259

Order 15104.

1022 conjugacy classes of subgroups.

The subgroup lattice has 608 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#16837522	C₂	1	1	yes	maximal, characteristic
2	C₂×#16837521	C₂	1	1	yes	maximal, characteristic
3	#21432864	C₂	1	1	yes	maximal, characteristic
4	#21432518	C₂	1	1	yes	maximal, characteristic, complemented
5	#131×Dic₅₉	C₂	1	1	yes	maximal, characteristic, complemented
6	#21423997	C₂	1	1	yes	maximal, characteristic, complemented
7	#21423981	C₂	1	1	yes	maximal, characteristic, complemented
8	#21423979	C₂	1	1	yes	maximal, characteristic, complemented
9	#21423943	C₂	1	1	yes	maximal, characteristic, complemented
10	#21423940	C₂	1	1	yes	maximal, characteristic, complemented
11	#21423939	C₂	1	1	yes	maximal, characteristic, complemented
12	#104×Dic₅₉	C₂	1	1	yes	maximal, characteristic, complemented
13	#21423900	C₂	1	1	yes	maximal, characteristic, complemented
14	#97×Dic₅₉	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅₉×#1765	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#14273747	C₂²	1	1	yes	characteristic
17	C₂×#14273735	C₂²	1	1	yes	characteristic
18	C₂×#14273734	C₂²	1	1	yes	characteristic
19	C₂×#14273733	C₂²	1	1	yes	characteristic
20	#41×Dic₅₉	C₂²	1	1	yes	characteristic
21	#16837870	C₂²	1	1	yes	characteristic
22	#16837522	C₄	1	8	yes	complemented
23	#16837521	C₄	1	8	yes	complemented
24	#16837494	C₄	1	2	yes	complemented
25	#16837493	C₄	1	2	yes	complemented
26	#16837487	C₄	1	2	yes	complemented
27	#16837482	C₄	1	2	yes	complemented
28	C₂×#14273662	C₂²	1	1	yes	characteristic
29	C₂×#14273662	C₂²	1	1	yes	characteristic
30	#16837438	C₂²	1	1	yes	characteristic
31	C₂×#14273655	C₂²	1	1	yes	characteristic
32	C₂×#14273654	C₂²	1	1	yes	characteristic
33	C₂×#14273653	C₂²	1	1	yes	characteristic
34	#16837399	C₂²	1	1	yes	characteristic
35	#16837360	—	2	1	no	—
36	#16837360	C₂²	1	1	yes	characteristic
37	#16837359	—	2	1	no	—
38	#16837358	C₂²	1	1	yes	characteristic
39	#16837357	—	2	1	no	—
40	#16837357	C₂²	1	1	yes	characteristic
41	#16837356	—	2	1	no	—
42	#16837354	—	2	1	no	—
43	M₁₆×Dic₅₉	—	2	1	no	—
44	M₁₆×Dic₅₉	C₂²	1	1	yes	characteristic
45	M₁₆×Dic₅₉	C₂²	1	1	yes	characteristic
46	C₂×#14273638	C₂²	1	1	yes	characteristic
47	C₂×#14273637	C₂²	1	1	yes	characteristic
48	C₂×#14273637	C₂²	1	1	yes	characteristic
49	C₂×C₈×Dic₅₉	—	2	1	no	—
50	C₂×C₈×Dic₅₉	C₂²	1	1	yes	characteristic
51	C₂×C₈×Dic₅₉	C₂²	1	1	yes	characteristic
52	C₄×C₈×D₅₉	—	2	1	no	—
53	C₄²×Dic₅₉	C₂²	1	1	yes	characteristic
54	#16837167	C₂²	1	1	yes	characteristic
55	#16837163	C₂²	1	1	yes	characteristic
56	#16837162	C₂²	1	1	yes	characteristic
57	#16837161	C₂²	1	1	yes	characteristic
58	C₂×#131×C₅₉	C₂²	1	1	yes	characteristic
59	C₂×#104×C₅₉	C₂²	1	1	yes	characteristic
60	C₅₉×#416	C₂²	1	1	yes	characteristic
61	C₅₉×#405	C₂²	1	1	yes	characteristic
62	C₂×#97×C₅₉	C₂²	1	1	yes	characteristic
63	C₅₉×#341	C₂²	1	1	yes	characteristic
64	C₅₉×#339	C₂²	1	1	yes	characteristic
65	C₂×#11745685	C₂³	1	1	yes	characteristic
66	#14273747	C₂×C₄	1	4	yes	—
67	#14273747	C₂×C₄	1	4	yes	—
68	C₂×#11745672	C₂×C₄	1	1	yes	characteristic
69	C₂×#11745670	C₂×C₄	1	1	yes	characteristic
70	C₂×#11745671	C₂×C₄	1	1	yes	characteristic
71	C₂×#11745669	C₂×C₄	1	1	yes	characteristic
72	#14273735	—	2	2	no	—
73	#14273735	C₂×C₄	1	4	yes	complemented
74	#14273734	—	2	2	no	—
75	#14273734	C₂×C₄	1	4	yes	complemented
76	#14273733	—	2	2	no	—
77	#14273733	C₂×C₄	1	4	yes	complemented
78	C₂×#11745664	—	2	1	no	—
79	C₂×#11745664	C₂³	1	1	yes	characteristic
80	C₂×#11745664	C₂³	1	1	yes	characteristic
81	C₂×#11745659	—	2	1	no	—
82	C₂×#11745659	—	2	1	no	—
83	C₂²×C₅₉⋊C₈	—	2	1	no	—
84	C₂²×C₅₉⋊C₈	C₂³	1	1	yes	characteristic
85	C₂²×C₅₉⋊C₈	C₂³	1	1	yes	characteristic
86	C₂×C₈×D₅₉	—	2	1	no	—
87	C₂×C₈×D₅₉	—	2	1	no	—
88	Q₈×Dic₅₉	C₂×C₄	1	2	yes	—
89	#14273692	C₂×C₄	1	2	yes	—
90	D₄×Dic₅₉	—	2	2	no	—
91	D₄×Dic₅₉	C₂×C₄	1	2	yes	—
92	#14273689	C₂×C₄	1	2	yes	—
93	(C₂²⋊D₅₉)⋊C₄	—	2	2	no	—
94	#14273686	—	2	1	no	—
95	#14273686	C₂³	1	1	yes	characteristic
96	#14273684	—	2	1	no	—
97	C₂×C₄×Dic₅₉	—	2	1	no	—
98	C₂×C₄×Dic₅₉	—	2	2	no	—
99	C₂×C₄×Dic₅₉	C₂³	1	1	yes	characteristic
100	C₂×C₄×Dic₅₉	C₂³	1	1	yes	characteristic
101	C₄²×D₅₉	—	2	1	no	—
102	#14273662	C₂×C₄	1	4	yes	complemented
103	#14273662	C₂×C₄	1	4	yes	complemented
104	#14273660	C₂×C₄	1	2	yes	—
105	#14273658	C₂×C₄	1	2	yes	—
106	#14273655	C₂×C₄	1	4	yes	complemented
107	#14273654	C₂×C₄	1	4	yes	complemented
108	#14273653	C₂×C₄	1	4	yes	complemented
109	#14273652	C₂×C₄	1	2	yes	—
110	#14273649	C₂×C₄	1	2	yes	—
111	#14273638	—	2	1	no	—
112	#14273638	C₂×C₄	1	4	yes	complemented
113	#14273637	—	2	1	no	—
114	#14273637	—	2	1	no	—
115	#14273637	—	2	1	no	—
116	#14273637	—	2	1	no	—
117	#14273637	—	2	2	no	—
118	#14273637	C₂×C₄	1	4	yes	complemented
119	C₄×C₅₉⋊C₈	—	2	1	no	—
120	C₈×Dic₅₉	—	2	1	no	—
121	C₈×Dic₅₉	—	2	1	no	—
122	C₈×Dic₅₉	—	2	1	no	—
123	C₈×Dic₅₉	—	2	1	no	—
124	C₈×Dic₅₉	C₂×C₄	1	2	yes	—
125	C₈×Dic₅₉	C₂×C₄	1	2	yes	—
126	C₈×Dic₅₉	D₄	1	1	yes	characteristic
127	C₈×Dic₅₉	D₄	1	1	yes	characteristic
128	C₈×Dic₅₉	D₄	1	1	yes	characteristic
129	C₈×Dic₅₉	D₄	1	1	yes	characteristic
130	C₂×#41×C₅₉	C₂³	1	1	yes	characteristic
131	#131×C₅₉	—	2	2	no	—
132	#131×C₅₉	C₂×C₄	1	4	yes	complemented
133	C₂×M₁₆×C₅₉	—	2	1	no	—
134	C₂×M₁₆×C₅₉	C₂³	1	1	yes	characteristic
135	C₂×M₁₆×C₅₉	C₂³	1	1	yes	characteristic
136	C₂²×C₈×C₅₉	—	2	1	no	—
137	C₂²×C₈×C₅₉	C₂³	1	1	yes	characteristic
138	C₂²×C₈×C₅₉	C₂³	1	1	yes	characteristic
139	#117×C₅₉	C₂³	1	1	yes	characteristic
140	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
141	#104×C₅₉	C₂×C₄	1	4	yes	complemented
142	#103×C₅₉	C₂×C₄	1	2	yes	—
143	#102×C₅₉	C₂×C₄	1	2	yes	—
144	#97×C₅₉	—	2	1	no	—
145	#97×C₅₉	—	2	2	no	—
146	C₄×C₈×C₅₉	—	2	1	no	—
147	#41×C₅₉	—	2	1	no	—
148	#41×C₅₉	—	2	1	no	—
149	#41×C₅₉	C₂²×C₄	1	2	yes	—
150	#41×C₅₉	C₂²×C₄	1	2	yes	—
151	C₂×Q₈×C₅₉	C₂²×C₄	1	1	yes	characteristic
152	C₂×D₄×C₅₉	—	2	1	no	—
153	C₂×D₄×C₅₉	C₂²×C₄	1	1	yes	characteristic
154	C₂²×C₄×C₅₉	—	2	1	no	—
155	C₂²×C₄×C₅₉	—	2	1	no	—
156	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
157	C₂×C₂²⋊D₅₉	—	2	1	no	—
158	C₂²×Dic₅₉	—	2	1	no	—
159	C₂²×Dic₅₉	—	2	2	no	—
160	C₂²×Dic₅₉	#41	1	2	yes	—
161	#11745685	—	2	1	no	—
162	#11745685	—	2	1	no	—
163	#11745685	C₂²×C₄	1	2	yes	—
164	#11745685	C₂²×C₄	1	2	yes	—
165	C₂×D₂₃₆	C₂²×C₄	1	1	yes	characteristic
166	C₂×C₄×D₅₉	—	2	1	no	—
167	C₂×C₄×D₅₉	—	2	2	no	—
168	C₂×Dic₁₁₈	C₂²×C₄	1	1	yes	characteristic
169	M₁₆×C₅₉	—	2	1	no	—
170	M₁₆×C₅₉	—	2	1	no	—
171	M₁₆×C₅₉	—	2	4	no	—
172	M₁₆×C₅₉	C₂²×C₄	1	2	yes	—
173	M₁₆×C₅₉	C₂²×C₄	1	2	yes	—
174	C₂×C₈×C₅₉	—	2	1	no	—
175	C₂×C₈×C₅₉	—	2	1	no	—
176	C₂×C₈×C₅₉	—	2	1	no	—
177	C₂×C₈×C₅₉	—	2	1	no	—
178	C₂×C₈×C₅₉	—	2	4	no	—
179	C₂×C₈×C₅₉	C₂²×C₄	1	2	yes	—
180	C₂×C₈×C₅₉	C₂²×C₄	1	2	yes	—
181	C₂×C₈×C₅₉	C₂×D₄	1	1	yes	characteristic
182	C₂×C₈×C₅₉	C₂×D₄	1	1	yes	characteristic
183	C₂×C₈×C₅₉	#41	1	2	yes	—
184	C₄⋊C₄×C₅₉	C₂²×C₄	1	2	yes	—
185	C₂²⋊C₄×C₅₉	—	2	1	no	—
186	C₄²×C₅₉	—	2	1	no	—
187	C₄²×C₅₉	—	2	1	no	—
188	C₄²×C₅₉	C₂²×C₄	1	2	yes	—
189	C₂²⋊Dic₅₉	—	2	1	no	—
190	C₂²⋊Dic₅₉	—	2	2	no	—
191	#11745672	C₄²	1	4	yes	complemented
192	#11745671	C₄²	1	4	yes	complemented
193	#11745670	C₄²	1	4	yes	complemented
194	#11745669	C₄²	1	4	yes	complemented
195	(C₂×D₅₉)⋊C₄	—	2	2	no	—
196	C₄⋊Dic₅₉	—	2	2	no	—
197	C₄⋊Dic₅₉	C₂²×C₄	1	2	yes	—
198	Dic₅₉⋊C₄	—	2	2	no	—
199	C₄×Dic₅₉	—	2	1	no	—
200	C₄×Dic₅₉	—	2	1	no	—
201	C₄×Dic₅₉	—	2	2	no	—
202	C₄×Dic₅₉	—	2	2	no	—
203	C₄×Dic₅₉	—	4	4	no	—
204	C₄×Dic₅₉	C₂²×C₄	1	2	yes	—
205	C₄×Dic₅₉	C₂²×C₄	1	2	yes	—
206	C₄×Dic₅₉	C₂×D₄	1	1	yes	characteristic
207	C₄×Dic₅₉	C₂×D₄	1	1	yes	characteristic
208	#11745664	—	2	1	no	—
209	#11745664	—	2	1	no	—
210	#11745664	—	2	4	no	—
211	#11745664	C₂²×C₄	1	2	yes	—
212	#11745664	C₂²×C₄	1	2	yes	—
213	C₂×C₅₉⋊C₈	—	2	1	no	—
214	C₂×C₅₉⋊C₈	—	2	1	no	—
215	C₂×C₅₉⋊C₈	—	2	4	no	—
216	C₂×C₅₉⋊C₈	C₂²×C₄	1	1	yes	characteristic
217	C₂×C₅₉⋊C₈	C₂²×C₄	1	1	yes	characteristic
218	C₂×C₅₉⋊C₈	C₂²×C₄	1	2	yes	—
219	C₂×C₅₉⋊C₈	C₂²×C₄	1	2	yes	—
220	C₂×C₅₉⋊C₈	C₂²×C₄	1	2	yes	—
221	C₂×C₅₉⋊C₈	C₂×D₄	1	1	yes	characteristic
222	C₂×C₅₉⋊C₈	C₂×D₄	1	1	yes	characteristic
223	C₂×C₅₉⋊C₈	#41	1	2	yes	—
224	#11745659	—	2	4	no	—
225	#11745659	—	2	4	no	—
226	C₈×D₅₉	—	2	4	no	—
227	C₈×D₅₉	—	2	4	no	—
228	C₂³×C₅₉	—	2	1	no	—
229	C₂³×C₅₉	C₂×#41	1	1	yes	characteristic
230	C₂²×D₅₉	—	2	1	no	—
231	Q₈×C₅₉	—	2	1	no	—
232	Q₈×C₅₉	C₂×C₄²	1	2	yes	—
233	D₄×C₅₉	—	2	2	no	—
234	D₄×C₅₉	—	2	2	no	—
235	D₄×C₅₉	—	2	1	no	—
236	D₄×C₅₉	C₂×C₄²	1	2	yes	—
237	C₂×C₄×C₅₉	—	2	1	no	—
238	C₂×C₄×C₅₉	—	2	2	no	—
239	C₂×C₄×C₅₉	—	2	2	no	—
240	C₂×C₄×C₅₉	—	2	2	no	—
241	C₂×C₄×C₅₉	—	2	2	no	—
242	C₂×C₄×C₅₉	—	4	2	no	—
243	C₂×C₄×C₅₉	C₂³×C₄	1	1	yes	characteristic
244	C₂×C₄×C₅₉	C₂³×C₄	1	1	yes	characteristic
245	C₂×C₄×C₅₉	C₂³×C₄	1	1	yes	characteristic
246	C₂×C₄×C₅₉	C₂²×D₄	1	1	yes	characteristic
247	C₂×C₄×C₅₉	C₂×#41	1	1	yes	characteristic
248	C₂×C₄×C₅₉	C₂×#41	1	1	yes	characteristic
249	C₂²⋊D₅₉	—	2	2	no	—
250	C₂²⋊D₅₉	—	2	2	no	—
251	C₂×Dic₅₉	—	2	1	no	—
252	C₂×Dic₅₉	—	2	4	no	—
253	C₂×Dic₅₉	—	2	2	no	—
254	C₂×Dic₅₉	—	2	2	no	—
255	C₂×Dic₅₉	—	4	2	no	—
256	C₂×Dic₅₉	—	4	4	no	—
257	C₂×Dic₅₉	C₄×D₄	1	2	yes	—
258	C₂×Dic₅₉	C₄×D₄	1	2	yes	—
259	D₂₃₆	—	2	1	no	—
260	D₂₃₆	C₂×C₄²	1	2	yes	—
261	C₄×D₅₉	—	2	2	no	—
262	C₄×D₅₉	—	2	2	no	—
263	C₄×D₅₉	—	4	4	no	—
264	Dic₁₁₈	—	2	1	no	—
265	Dic₁₁₈	C₂×C₄²	1	2	yes	—
266	C₈×C₅₉	—	2	2	no	—
267	C₈×C₅₉	—	2	2	no	—
268	C₈×C₅₉	—	2	2	no	—
269	C₈×C₅₉	C₄×D₄	1	2	yes	—
270	C₈×C₅₉	C₄×D₄	1	2	yes	—
271	C₅₉⋊C₈	—	2	2	no	—
272	C₅₉⋊C₈	—	2	2	no	—
273	C₅₉⋊C₈	C₂×C₄²	1	2	yes	—
274	C₅₉⋊C₈	C₂×C₄²	1	2	yes	—
275	C₅₉⋊C₈	C₄×D₄	1	2	yes	—
276	C₅₉⋊C₈	C₄×D₄	1	2	yes	—
277	C₄×#444	—	59	1	no	maximal, Sylow
278	C₂²×C₅₉	—	2	2	no	—
279	C₂²×C₅₉	—	2	2	no	—
280	C₂²×C₅₉	—	4	2	no	—
281	C₂²×C₅₉	C₂×C₄×D₄	1	1	yes	characteristic
282	C₂²×C₅₉	C₄×#41	1	1	yes	characteristic
283	C₂²×C₅₉	C₄×#41	1	1	yes	characteristic
284	C₂×D₅₉	—	2	2	no	—
285	C₂×D₅₉	—	4	2	no	—
286	C₄×C₅₉	—	2	2	no	—
287	C₄×C₅₉	—	4	2	no	—
288	C₄×C₅₉	—	4	2	no	—
289	C₄×C₅₉	C₂²×C₄²	1	1	yes	characteristic
290	C₄×C₅₉	C₂×C₄×D₄	1	1	yes	characteristic
291	C₄×C₅₉	C₂×C₄×D₄	1	1	yes	characteristic
292	C₄×C₅₉	C₄×#41	1	1	yes	characteristic
293	Dic₅₉	—	2	2	no	—
294	Dic₅₉	—	2	2	no	—
295	Dic₅₉	—	4	2	no	—
296	Dic₅₉	—	4	2	no	—
297	Dic₅₉	#444	1	4	yes	complemented
298	C₂×#444	—	59	1	no	—
299	C₂×#444	—	59	1	no	—
300	C₄×#135	—	59	1	no	—
301	C₄×#131	—	59	1	no	—
302	C₄×#131	—	59	1	no	—
303	C₄×#108	—	59	1	no	—
304	#1773	—	59	1	no	—
305	#1773	—	59	1	no	—
306	#1765	—	59	1	no	—
307	#1765	—	59	1	no	—
308	#1765	—	59	1	no	—
309	#1765	D₅₉	1	1	yes	characteristic, complemented
310	C₄×#104	—	59	1	no	—
311	C₄×#104	—	59	1	no	—
312	C₄×#97	—	59	1	no	—
313	C₂×C₅₉	—	2	1	no	—
314	C₂×C₅₉	—	2	1	no	—
315	C₂×C₅₉	—	4	2	no	—
316	C₂×C₅₉	C₄²×D₄	1	1	yes	characteristic
317	C₂×C₅₉	C₂×#444	1	2	yes	—
318	D₅₉	—	4	2	no	—
319	C₂×#135	—	59	1	no	—
320	C₂×#131	—	59	1	no	—
321	C₂×#131	—	59	1	no	—
322	C₂×#131	—	59	1	no	—
323	C₂×#131	C₂×D₅₉	1	1	yes	characteristic
324	C₄×#41	—	59	1	no	—
325	C₄×#41	—	59	1	no	—
326	#444	—	59	8	no	—
327	#444	—	59	8	no	—
328	C₄×Q₁₆	—	59	2	no	—
329	C₄×SD₁₆	—	59	2	no	—
330	C₄×SD₁₆	—	59	2	no	—
331	C₄×D₈	—	59	2	no	—
332	C₂×#108	—	59	1	no	—
333	C₂×#108	—	59	1	no	—
334	#427	—	59	1	no	—
335	C₂×#104	—	59	1	no	—
336	C₂×#104	—	59	1	no	—
337	C₂×#104	—	59	1	no	—
338	C₂×#104	C₂×D₅₉	1	1	yes	characteristic
339	#416	—	59	1	no	—
340	#416	C₂×D₅₉	1	1	yes	characteristic
341	#405	—	59	1	no	—
342	#405	—	59	1	no	—
343	#405	—	59	1	no	—
344	#405	—	118	1	no	—
345	#405	—	118	1	no	—
346	#405	—	118	1	no	—
347	#405	—	118	1	no	—
348	#405	C₂×D₅₉	1	1	yes	characteristic
349	C₄×M₁₆	—	59	1	no	—
350	C₄×M₁₆	—	59	1	no	—
351	C₄×M₁₆	—	118	1	no	—
352	C₄×M₁₆	—	118	1	no	—
353	C₂×#97	—	59	1	no	—
354	C₂×#97	—	59	1	no	—
355	C₂×#97	—	59	1	no	—
356	C₂×#97	C₂×D₅₉	1	1	yes	characteristic
357	C₂×C₄×C₈	—	59	1	no	—
358	C₂×C₄×C₈	—	59	1	no	—
359	C₂×C₄×C₈	—	118	1	no	—
360	C₂×C₄×C₈	—	118	1	no	—
361	C₄³	—	59	1	no	—
362	#341	—	59	1	no	—
363	#341	C₂×D₅₉	1	1	yes	characteristic
364	#339	—	59	1	no	—
365	#339	—	59	1	no	—
366	#339	—	59	1	no	—
367	#339	C₂×D₅₉	1	1	yes	characteristic
368	C₅₉	C₄×#444	1	1	yes	characteristic, complemented, Sylow
369	C₂×#41	—	59	1	no	—
370	C₂×#41	C₂²×D₅₉	1	1	yes	characteristic
371	#135	—	59	4	no	—
372	#135	—	59	4	no	—
373	C₂×Q₁₆	—	59	1	no	—
374	C₂×SD₁₆	—	59	1	no	—
375	C₂×SD₁₆	—	59	1	no	—
376	C₂×D₈	—	59	1	no	—
377	#131	—	2	2	no	—
378	#131	—	59	4	no	—
379	#131	—	59	4	no	—
380	#131	—	59	4	no	—
381	#131	—	118	2	no	—
382	#131	—	118	2	no	—
383	#131	—	118	2	no	—
384	#131	C₄×D₅₉	1	4	yes	complemented
385	C₂×M₁₆	—	2	1	no	—
386	C₂×M₁₆	—	59	1	no	—
387	C₂×M₁₆	—	59	1	no	—
388	C₂×M₁₆	—	118	1	no	—
389	C₂×M₁₆	—	118	1	no	—
390	C₂×M₁₆	—	118	1	no	—
391	C₂×M₁₆	C₂²×D₅₉	1	1	yes	characteristic
392	C₂×M₁₆	C₂²×D₅₉	1	1	yes	characteristic
393	C₂²×C₈	—	2	1	no	—
394	C₂²×C₈	—	59	1	no	—
395	C₂²×C₈	—	59	1	no	—
396	C₂²×C₈	—	118	1	no	—
397	C₂²×C₈	—	118	1	no	—
398	C₂²×C₈	—	118	1	no	—
399	C₂²×C₈	C₂²×D₅₉	1	1	yes	characteristic
400	C₂²×C₈	C₂²×D₅₉	1	1	yes	characteristic
401	C₄×Q₈	—	59	2	no	—
402	C₄×Q₈	—	59	2	no	—
403	C₄×D₄	—	59	2	no	—
404	C₄×D₄	—	59	2	no	—
405	C₄×D₄	—	118	2	no	—
406	C₄×D₄	—	118	2	no	—
407	#117	—	59	1	no	—
408	#117	—	118	1	no	—
409	#117	—	118	1	no	—
410	#117	C₂²×D₅₉	1	1	yes	characteristic
411	C₂×C₄²	—	59	1	no	—
412	C₂×C₄²	—	59	1	no	—
413	C₂×C₄²	—	118	1	no	—
414	C₂×C₄²	—	118	1	no	—
415	C₂×C₄²	—	118	2	no	—
416	C₂×C₄²	C₂²×D₅₉	1	1	yes	characteristic
417	#108	—	59	4	no	—
418	#108	—	59	4	no	—
419	#107	—	59	2	no	—
420	#106	—	59	2	no	—
421	#104	—	59	4	no	—
422	#104	—	59	4	no	—
423	#104	—	59	4	no	—
424	#104	C₄×D₅₉	1	4	yes	complemented
425	#103	—	59	2	no	—
426	#103	C₄×D₅₉	1	2	yes	—
427	#102	—	59	2	no	—
428	#102	C₄×D₅₉	1	2	yes	—
429	#97	—	2	1	no	—
430	#97	—	2	2	no	—
431	#97	—	59	4	no	—
432	#97	—	59	4	no	—
433	#97	—	118	1	no	—
434	#97	—	118	1	no	—
435	#97	—	118	1	no	—
436	#97	—	118	2	no	—
437	#97	—	118	1	no	—
438	#97	—	118	1	no	—
439	C₄×C₈	—	2	1	no	—
440	C₄×C₈	—	59	2	no	—
441	C₄×C₈	—	59	2	no	—
442	C₄×C₈	—	59	1	no	—
443	C₄×C₈	—	59	1	no	—
444	C₄×C₈	—	59	1	no	—
445	C₄×C₈	—	59	1	no	—
446	C₄×C₈	—	118	1	no	—
447	C₄×C₈	—	118	1	no	—
448	C₄×C₈	—	118	1	no	—
449	C₄×C₈	—	118	1	no	—
450	C₄×C₈	—	118	1	no	—
451	#41	—	2	1	no	—
452	#41	—	2	1	no	—
453	#41	—	59	2	no	—
454	#41	—	59	2	no	—
455	#41	—	118	1	no	—
456	#41	—	118	1	no	—
457	#41	C₂×C₄×D₅₉	1	2	yes	—
458	#41	C₂×C₄×D₅₉	1	2	yes	—
459	C₂×Q₈	—	59	1	no	—
460	C₂×Q₈	C₂×C₄×D₅₉	1	1	yes	characteristic
461	C₂×D₄	—	2	1	no	—
462	C₂×D₄	—	59	1	no	—
463	C₂×D₄	—	118	1	no	—
464	C₂×D₄	C₂×C₄×D₅₉	1	1	yes	characteristic
465	C₂²×C₄	—	2	1	no	—
466	C₂²×C₄	—	2	1	no	—
467	C₂²×C₄	—	59	2	no	—
468	C₂²×C₄	—	118	2	no	—
469	C₂²×C₄	—	118	2	no	—
470	C₂²×C₄	—	118	1	no	—
471	C₂²×C₄	—	118	1	no	—
472	C₂²×C₄	C₂³×D₅₉	1	1	yes	characteristic
473	Q₁₆	—	59	4	no	—
474	SD₁₆	—	59	4	no	—
475	SD₁₆	—	59	4	no	—
476	D₈	—	59	4	no	—
477	M₁₆	—	2	1	no	—
478	M₁₆	—	2	1	no	—
479	M₁₆	—	2	4	no	—
480	M₁₆	—	59	2	no	—
481	M₁₆	—	59	2	no	—
482	M₁₆	—	118	4	no	—
483	M₁₆	—	118	4	no	—
484	M₁₆	—	118	1	no	—
485	M₁₆	—	118	1	no	—
486	M₁₆	—	118	4	no	—
487	M₁₆	C₂×C₄×D₅₉	1	2	yes	—
488	M₁₆	C₂×C₄×D₅₉	1	2	yes	—
489	C₂×C₈	—	2	1	no	—
490	C₂×C₈	—	2	1	no	—
491	C₂×C₈	—	2	1	no	—
492	C₂×C₈	—	2	1	no	—
493	C₂×C₈	—	2	4	no	—
494	C₂×C₈	—	59	1	no	—
495	C₂×C₈	—	59	1	no	—
496	C₂×C₈	—	59	2	no	—
497	C₂×C₈	—	59	2	no	—
498	C₂×C₈	—	59	2	no	—
499	C₂×C₈	—	59	1	no	—
500	C₂×C₈	—	59	1	no	—
501	C₂×C₈	—	59	2	no	—
502	C₂×C₈	—	118	4	no	—
503	C₂×C₈	—	118	4	no	—
504	C₂×C₈	—	118	1	no	—
505	C₂×C₈	—	118	1	no	—
506	C₂×C₈	—	118	4	no	—
507	C₂×C₈	C₂×C₄×D₅₉	1	2	yes	—
508	C₂×C₈	C₂×C₄×D₅₉	1	2	yes	—
509	C₂×C₈	D₄×D₅₉	1	1	yes	characteristic
510	C₂×C₈	D₄×D₅₉	1	1	yes	characteristic
511	C₂×C₈	#11745687	1	2	yes	—
512	C₄⋊C₄	—	59	2	no	—
513	C₄⋊C₄	—	118	2	no	—
514	C₄⋊C₄	—	118	2	no	—
515	C₄⋊C₄	C₂×C₄×D₅₉	1	2	yes	—
516	C₂²⋊C₄	—	2	1	no	—
517	C₂²⋊C₄	—	118	2	no	—
518	C₂²⋊C₄	—	118	2	no	—
519	C₂²⋊C₄	—	118	1	no	—
520	C₄²	—	2	1	no	—
521	C₄²	—	2	1	no	—
522	C₄²	—	59	2	no	—
523	C₄²	—	59	1	no	—
524	C₄²	—	59	1	no	—
525	C₄²	—	59	2	no	—
526	C₄²	—	118	2	no	—
527	C₄²	—	118	2	no	—
528	C₄²	—	118	1	no	—
529	C₄²	—	118	1	no	—
530	C₄²	—	236	4	no	—
531	C₄²	C₂×C₄×D₅₉	1	2	yes	—
532	C₂³	—	2	1	no	—
533	C₂³	—	118	1	no	—
534	C₂³	#41×D₅₉	1	1	yes	characteristic
535	Q₈	—	2	1	no	—
536	Q₈	—	59	2	no	—
537	Q₈	—	118	1	no	—
538	Q₈	C₄²×D₅₉	1	2	yes	—
539	D₄	—	2	2	no	—
540	D₄	—	2	2	no	—
541	D₄	—	2	1	no	—
542	D₄	—	59	2	no	—
543	D₄	—	118	2	no	—
544	D₄	—	118	2	no	—
545	D₄	—	118	1	no	—
546	D₄	C₄²×D₅₉	1	2	yes	—
547	C₂×C₄	—	2	1	no	—
548	C₂×C₄	—	2	2	no	—
549	C₂×C₄	—	2	2	no	—
550	C₂×C₄	—	2	2	no	—
551	C₂×C₄	—	2	2	no	—
552	C₂×C₄	—	4	2	no	—
553	C₂×C₄	—	59	2	no	—
554	C₂×C₄	—	59	2	no	—
555	C₂×C₄	—	118	4	no	—
556	C₂×C₄	—	118	1	no	—
557	C₂×C₄	—	118	2	no	—
558	C₂×C₄	—	118	2	no	—
559	C₂×C₄	—	118	2	no	—
560	C₂×C₄	—	118	2	no	—
561	C₂×C₄	—	236	4	no	—
562	C₂×C₄	—	236	4	no	—
563	C₂×C₄	—	236	2	no	—
564	C₂×C₄	C₂²×C₄×D₅₉	1	1	yes	characteristic
565	C₂×C₄	C₂²×C₄×D₅₉	1	1	yes	characteristic
566	C₂×C₄	C₂²×C₄×D₅₉	1	1	yes	characteristic
567	C₂×C₄	C₂×D₄×D₅₉	1	1	yes	characteristic
568	C₂×C₄	#41×D₅₉	1	1	yes	characteristic
569	C₂×C₄	C₂×#11745687	1	1	yes	characteristic
570	C₈	—	2	2	no	—
571	C₈	—	2	2	no	—
572	C₈	—	2	2	no	—
573	C₈	—	59	2	no	—
574	C₈	—	59	2	no	—
575	C₈	—	59	2	no	—
576	C₈	—	59	2	no	—
577	C₈	—	118	2	no	—
578	C₈	—	118	2	no	—
579	C₈	(C₂²⋊D₅₉)⋊C₄	1	2	yes	—
580	C₈	(C₂²⋊D₅₉)⋊C₄	1	2	yes	—
581	C₂²	—	2	2	no	—
582	C₂²	—	2	2	no	—
583	C₂²	—	4	2	no	—
584	C₂²	—	118	2	no	—
585	C₂²	—	236	2	no	—
586	C₂²	C₄×D₄×D₅₉	1	1	yes	characteristic
587	C₂²	C₄×#11745687	1	1	yes	characteristic
588	C₂²	#16837870	1	1	yes	characteristic
589	C₄	—	2	2	no	—
590	C₄	—	4	2	no	—
591	C₄	—	4	2	no	—
592	C₄	—	59	4	no	—
593	C₄	—	118	2	no	—
594	C₄	—	118	2	no	—
595	C₄	—	236	2	no	—
596	C₄	—	236	2	no	—
597	C₄	C₂×C₄²×D₅₉	1	1	yes	characteristic
598	C₄	C₄×D₄×D₅₉	1	1	yes	characteristic
599	C₄	C₂×(C₂²⋊D₅₉)⋊C₄	1	1	yes	characteristic
600	C₄	C₄×#11745687	1	1	yes	characteristic
601	C₂	—	2	1	no	—
602	C₂	—	2	1	no	—
603	C₂	—	4	2	no	—
604	C₂	—	236	2	no	—
605	C₂	C₄×(C₂²⋊D₅₉)⋊C₄	1	1	yes	characteristic
606	C₂	#444×D₅₉	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₅₉
commutator	C₄×C₅₉	C₂²×C₄²
Frattini	C₂²×C₄	C₂³×D₅₉
Fitting	C₅₉×#1765	C₂
socle	C₂²×C₅₉	C₂×C₄×D₄
prime radical	C₂×#14273747	C₂²
cosocle	C₂²×C₄×C₅₉	C₂⁴
hypercenter	#1765	D₅₉
hypocenter	C₅₉	C₄×#444
LCS	G ▷ C₄×C₅₉ ▷ C₂×C₅₉ ▷ C₅₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₈ ◁ #1765

Complements

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

N	H ≅ G/N	type
4. #21432518	C₂	semidirect
5. #131×Dic₅₉	C₂	semidirect
6. #21423997	C₂	semidirect
7. #21423981	C₂	semidirect
8. #21423979	C₂	semidirect
9. #21423943	C₂	semidirect
10. #21423940	C₂	semidirect
11. #21423939	C₂	semidirect
12. #104×Dic₅₉	C₂	semidirect
13. #21423900	C₂	semidirect
14. #97×Dic₅₉	C₂	semidirect
15. C₅₉×#1765	C₂	semidirect
22. #16837522	C₄	semidirect
23. #16837521	C₄	semidirect
24. #16837494	C₄	semidirect
25. #16837493	C₄	semidirect
26. #16837487	C₄	semidirect
27. #16837482	C₄	semidirect
73. #14273735	C₂×C₄	semidirect
75. #14273734	C₂×C₄	semidirect
77. #14273733	C₂×C₄	semidirect
102. #14273662	C₂×C₄	semidirect
103. #14273662	C₂×C₄	semidirect
106. #14273655	C₂×C₄	semidirect
107. #14273654	C₂×C₄	semidirect
108. #14273653	C₂×C₄	semidirect
112. #14273638	C₂×C₄	semidirect
118. #14273637	C₂×C₄	semidirect
132. #131×C₅₉	C₂×C₄	semidirect
141. #104×C₅₉	C₂×C₄	semidirect
191. #11745672	C₄²	semidirect
192. #11745671	C₄²	semidirect
193. #11745670	C₄²	semidirect
194. #11745669	C₄²	semidirect
297. Dic₅₉	#444	semidirect
309. #1765	D₅₉	semidirect
368. C₅₉	C₄×#444	semidirect
384. #131	C₄×D₅₉	semidirect
424. #104	C₄×D₅₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×#16837522	2
C₂×#16837521	2
#21432864	2
#21432518	2
#131×Dic₅₉	2
#21423997	2
#21423981	2
#21423979	2
#21423943	2
#21423940	2
#21423939	2
#104×Dic₅₉	2
#21423900	2
#97×Dic₅₉	2
C₅₉×#1765	2
C₄×#444	59