Subgroups — #28610760

Order 15104.

720 conjugacy classes of subgroups.

The subgroup lattice has 490 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#21433045	C₂	1	1	yes	maximal, characteristic, complemented
2	#21432664	C₂	1	1	yes	maximal, characteristic
3	#21425074	C₂	1	1	yes	maximal, characteristic, complemented
4	#21424872	C₂	1	1	yes	maximal, characteristic, complemented
5	#21424845	C₂	1	2	yes	maximal, complemented
6	#21424697	C₂	1	2	yes	maximal, complemented
7	#21424373	C₂	1	2	yes	maximal
8	C₄⋊C₈×Dic₅₉	C₂	1	1	yes	maximal, characteristic, complemented
9	#21423936	C₂	1	2	yes	maximal
10	C₄×#14273654	C₂	1	1	yes	maximal, characteristic
11	C₅₉×#3076	C₂	1	1	yes	maximal, characteristic
12	C₂×#14273734	C₂²	1	2	yes	—
13	#16837533	—	2	1	no	—
14	#16837533	—	2	2	no	—
15	Q₈×C₅₉⋊C₈	—	2	1	no	—
16	C₂×#14273663	C₂²	1	2	yes	—
17	#16837429	—	2	2	no	—
18	#16837429	C₂²	1	2	yes	—
19	#16837429	C₂²	1	2	yes	—
20	#16837426	—	2	1	no	—
21	#16837426	C₂²	1	1	yes	characteristic
22	C₂×C₄⋊(C₅₉⋊C₈)	—	2	1	no	—
23	C₂×C₄⋊(C₅₉⋊C₈)	C₂²	1	1	yes	characteristic
24	C₂×#14273654	C₂²	1	1	yes	characteristic
25	C₂×#14273654	C₂²	1	1	yes	characteristic
26	#16837358	C₂²	1	2	yes	—
27	C₄×#11745664	C₂²	1	1	yes	characteristic
28	C₂×C₈×Dic₅₉	C₂²	1	2	yes	—
29	C₄²×Dic₅₉	C₂²	1	1	yes	characteristic
30	#16837167	C₂²	1	2	yes	—
31	#16837161	C₂²	1	1	yes	characteristic
32	#16837161	C₂²	1	1	yes	characteristic
33	#16837161	C₂²	1	2	yes	—
34	#16837161	C₂²	1	2	yes	—
35	#16837156	C₂²	1	2	yes	—
36	C₅₉×#533	C₂²	1	1	yes	characteristic
37	C₄×#41×C₅₉	C₂²	1	1	yes	characteristic
38	C₅₉×#479	C₄	1	2	yes	complemented
39	C₅₉×#478	C₄	1	2	yes	complemented
40	C₅₉×#477	C₄	1	1	yes	characteristic, complemented
41	C₅₉×#476	C₄	1	1	yes	characteristic, complemented
42	C₅₉×#475	C₄	1	1	yes	characteristic, complemented
43	C₅₉×#474	C₄	1	1	yes	characteristic, complemented
44	C₅₉×#427	C₂²	1	2	yes	—
45	C₂×C₄⋊C₈×C₅₉	C₂²	1	1	yes	characteristic
46	C₅₉×#416	C₂²	1	2	yes	—
47	#14273734	—	2	4	no	—
48	#14273734	—	4	2	no	—
49	C₂×#11745664	—	2	2	no	—
50	C₂×#11745664	C₂³	1	2	yes	—
51	C₂×#11745664	C₂³	1	1	yes	characteristic
52	C₂×#11745664	C₂³	1	1	yes	characteristic
53	C₂²×C₅₉⋊C₈	—	2	2	no	—
54	C₂²×C₅₉⋊C₈	C₂³	1	2	yes	—
55	C₂×C₄×Dic₅₉	—	2	1	no	—
56	C₂×C₄×Dic₅₉	—	2	1	no	—
57	C₂×C₄×Dic₅₉	C₂³	1	1	yes	characteristic
58	C₂×C₄×Dic₅₉	C₂³	1	1	yes	characteristic
59	#14273663	—	4	2	no	—
60	C₄⋊(C₅₉⋊C₈)	—	2	1	no	—
61	C₄⋊(C₅₉⋊C₈)	—	2	1	no	—
62	C₄⋊(C₅₉⋊C₈)	—	2	2	no	—
63	C₄⋊(C₅₉⋊C₈)	—	2	2	no	—
64	C₄⋊(C₅₉⋊C₈)	—	2	2	no	—
65	C₄⋊(C₅₉⋊C₈)	—	2	2	no	—
66	C₄⋊(C₅₉⋊C₈)	D₄	1	1	yes	characteristic
67	C₄⋊(C₅₉⋊C₈)	D₄	1	1	yes	characteristic
68	C₄⋊(C₅₉⋊C₈)	D₄	1	2	yes	—
69	#14273654	—	2	2	no	—
70	#14273654	Q₈	1	4	yes	complemented
71	#14273638	—	2	1	no	—
72	#14273638	—	2	2	no	—
73	C₄×C₅₉⋊C₈	—	2	1	no	—
74	C₄×C₅₉⋊C₈	—	2	2	no	—
75	C₈×Dic₅₉	—	4	2	no	—
76	C₂×#41×C₅₉	C₂³	1	1	yes	characteristic
77	C₂²×C₈×C₅₉	C₂³	1	2	yes	—
78	C₄⋊Q₈×C₅₉	C₂×C₄	1	1	yes	characteristic
79	C₄⋊Q₈×C₅₉	C₂×C₄	1	1	yes	characteristic
80	#125×C₅₉	C₂×C₄	1	2	yes	—
81	C₂²⋊Q₈×C₅₉	—	2	1	no	—
82	C₂²⋊Q₈×C₅₉	—	2	1	no	—
83	C₄×Q₈×C₅₉	—	2	1	no	—
84	C₄×Q₈×C₅₉	—	2	1	no	—
85	C₄×Q₈×C₅₉	C₂×C₄	1	1	yes	characteristic
86	C₄×Q₈×C₅₉	C₂×C₄	1	1	yes	characteristic
87	C₄×D₄×C₅₉	—	2	1	no	—
88	C₄×D₄×C₅₉	—	2	1	no	—
89	C₄×D₄×C₅₉	C₂×C₄	1	1	yes	characteristic
90	C₄×D₄×C₅₉	C₂×C₄	1	1	yes	characteristic
91	#117×C₅₉	—	2	1	no	—
92	#117×C₅₉	C₂³	1	1	yes	characteristic
93	#117×C₅₉	C₂³	1	2	yes	—
94	C₂×C₄²×C₅₉	—	2	1	no	—
95	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
96	#107×C₅₉	C₂×C₄	1	2	yes	—
97	#107×C₅₉	C₂×C₄	1	2	yes	—
98	#106×C₅₉	C₂×C₄	1	2	yes	—
99	#106×C₅₉	C₂×C₄	1	2	yes	—
100	C₄⋊C₈×C₅₉	C₂×C₄	1	1	yes	characteristic
101	C₄⋊C₈×C₅₉	C₂×C₄	1	1	yes	characteristic
102	C₄⋊C₈×C₅₉	C₂×C₄	1	2	yes	—
103	#103×C₅₉	C₂×C₄	1	2	yes	—
104	#103×C₅₉	C₂×C₄	1	2	yes	—
105	#102×C₅₉	C₂×C₄	1	2	yes	—
106	#102×C₅₉	C₂×C₄	1	2	yes	—
107	#41×C₅₉	—	2	1	no	—
108	#41×C₅₉	—	2	1	no	—
109	#41×C₅₉	C₂×Q₈	1	2	yes	—
110	#41×C₅₉	#41	1	2	yes	—
111	C₂×Q₈×C₅₉	—	2	1	no	—
112	C₂×Q₈×C₅₉	—	2	1	no	—
113	C₂×Q₈×C₅₉	C₂²×C₄	1	1	yes	characteristic
114	C₂×D₄×C₅₉	—	2	1	no	—
115	C₂×D₄×C₅₉	C₂²×C₄	1	1	yes	characteristic
116	C₂²×C₄×C₅₉	—	2	1	no	—
117	C₂²×C₄×C₅₉	—	2	1	no	—
118	C₂²×C₄×C₅₉	—	2	1	no	—
119	C₂²×C₄×C₅₉	#41	1	1	yes	characteristic
120	C₂²×C₄×C₅₉	#41	1	1	yes	characteristic
121	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
122	C₂²×Dic₅₉	—	2	1	no	—
123	C₂²×Dic₅₉	—	2	1	no	—
124	C₂×C₈×C₅₉	—	2	2	no	—
125	C₂×C₈×C₅₉	—	2	2	no	—
126	C₂×C₈×C₅₉	C₂²×C₄	1	2	yes	—
127	C₂×C₈×C₅₉	C₂²×C₄	1	2	yes	—
128	C₄⋊C₄×C₅₉	—	2	1	no	—
129	C₄⋊C₄×C₅₉	—	2	1	no	—
130	C₄⋊C₄×C₅₉	—	2	2	no	—
131	C₄⋊C₄×C₅₉	—	2	2	no	—
132	C₄⋊C₄×C₅₉	—	2	1	no	—
133	C₄⋊C₄×C₅₉	—	2	1	no	—
134	C₄⋊C₄×C₅₉	C₂²×C₄	1	2	yes	—
135	C₄⋊C₄×C₅₉	C₂²×C₄	1	2	yes	—
136	C₄⋊C₄×C₅₉	C₂²×C₄	1	1	yes	characteristic
137	C₄⋊C₄×C₅₉	C₂²×C₄	1	1	yes	characteristic
138	C₂²⋊C₄×C₅₉	—	2	1	no	—
139	C₂²⋊C₄×C₅₉	—	2	2	no	—
140	C₂²⋊C₄×C₅₉	—	2	1	no	—
141	C₂²⋊C₄×C₅₉	—	2	1	no	—
142	C₄²×C₅₉	—	2	1	no	—
143	C₄²×C₅₉	—	2	1	no	—
144	C₄²×C₅₉	—	2	1	no	—
145	C₄²×C₅₉	—	2	2	no	—
146	C₄²×C₅₉	C₂²×C₄	1	1	yes	characteristic
147	C₄²×C₅₉	C₂²×C₄	1	1	yes	characteristic
148	C₄²×C₅₉	C₂×D₄	1	1	yes	characteristic
149	C₄²×C₅₉	C₂×D₄	1	1	yes	characteristic
150	C₄×Dic₅₉	—	2	4	no	—
151	C₄×Dic₅₉	—	2	1	no	—
152	C₄×Dic₅₉	—	2	1	no	—
153	C₄×Dic₅₉	—	2	1	no	—
154	C₄×Dic₅₉	—	4	2	no	—
155	C₄×Dic₅₉	C₂×Q₈	1	2	yes	—
156	#11745664	—	2	1	no	—
157	#11745664	—	2	1	no	—
158	#11745664	—	2	2	no	—
159	#11745664	—	2	1	no	—
160	#11745664	—	2	2	no	—
161	#11745664	—	4	4	no	—
162	#11745664	C₂×Q₈	1	2	yes	—
163	C₂×C₅₉⋊C₈	—	2	1	no	—
164	C₂×C₅₉⋊C₈	—	2	2	no	—
165	C₂×C₅₉⋊C₈	—	2	2	no	—
166	C₂×C₅₉⋊C₈	—	2	1	no	—
167	C₂×C₅₉⋊C₈	—	2	2	no	—
168	C₂×C₅₉⋊C₈	—	4	4	no	—
169	C₂×C₅₉⋊C₈	C₂×D₄	1	2	yes	—
170	C₂×C₅₉⋊C₈	C₂×D₄	1	2	yes	—
171	C₂³×C₅₉	—	2	1	no	—
172	C₂³×C₅₉	C₂×#41	1	1	yes	characteristic
173	Q₈×C₅₉	—	2	1	no	—
174	Q₈×C₅₉	—	4	2	no	—
175	Q₈×C₅₉	—	8	1	no	—
176	Q₈×C₅₉	C₄×Q₈	1	2	yes	—
177	D₄×C₅₉	—	2	2	no	—
178	D₄×C₅₉	—	2	2	no	—
179	D₄×C₅₉	—	2	1	no	—
180	D₄×C₅₉	C₄×Q₈	1	2	yes	—
181	C₂×C₄×C₅₉	—	2	1	no	—
182	C₂×C₄×C₅₉	—	2	2	no	—
183	C₂×C₄×C₅₉	—	2	2	no	—
184	C₂×C₄×C₅₉	—	2	2	no	—
185	C₂×C₄×C₅₉	—	2	1	no	—
186	C₂×C₄×C₅₉	—	2	1	no	—
187	C₂×C₄×C₅₉	—	2	2	no	—
188	C₂×C₄×C₅₉	—	2	2	no	—
189	C₂×C₄×C₅₉	—	4	1	no	—
190	C₂×C₄×C₅₉	—	4	2	no	—
191	C₂×C₄×C₅₉	—	8	1	no	—
192	C₂×C₄×C₅₉	C₄×D₄	1	1	yes	characteristic
193	C₂×C₄×C₅₉	C₄×D₄	1	1	yes	characteristic
194	C₂×C₄×C₅₉	C₄×D₄	1	1	yes	characteristic
195	C₂×C₄×C₅₉	C₄×D₄	1	1	yes	characteristic
196	C₂×C₄×C₅₉	C₂³×C₄	1	1	yes	characteristic
197	C₂×C₄×C₅₉	C₂²×D₄	1	1	yes	characteristic
198	C₂×C₄×C₅₉	C₂²×Q₈	1	1	yes	characteristic
199	C₂×C₄×C₅₉	C₂×#41	1	1	yes	characteristic
200	C₂×C₄×C₅₉	H(5,𝔽₂)	1	1	yes	characteristic
201	C₂×C₄×C₅₉	2₋¹⁺⁴	1	1	yes	characteristic
202	C₂×Dic₅₉	—	2	2	no	—
203	C₂×Dic₅₉	—	2	2	no	—
204	C₂×Dic₅₉	—	2	2	no	—
205	C₂×Dic₅₉	—	2	2	no	—
206	C₂×Dic₅₉	—	4	1	no	—
207	C₂×Dic₅₉	—	4	1	no	—
208	C₈×C₅₉	—	2	2	no	—
209	C₈×C₅₉	—	2	2	no	—
210	C₅₉⋊C₈	—	2	2	no	—
211	C₅₉⋊C₈	—	2	2	no	—
212	C₅₉⋊C₈	—	2	2	no	—
213	C₅₉⋊C₈	—	4	2	no	—
214	C₅₉⋊C₈	—	4	1	no	—
215	#22982	—	59	1	no	maximal, Sylow
216	C₂²×C₅₉	—	2	1	no	—
217	C₂²×C₅₉	—	2	1	no	—
218	C₂²×C₅₉	—	2	2	no	—
219	C₂²×C₅₉	—	4	1	no	—
220	C₂²×C₅₉	—	4	1	no	—
221	C₂²×C₅₉	C₂×C₄×D₄	1	1	yes	characteristic
222	C₂²×C₅₉	#552	1	1	yes	characteristic
223	C₂²×C₅₉	#554	1	1	yes	characteristic
224	C₄×C₅₉	—	2	2	no	—
225	C₄×C₅₉	—	2	1	no	—
226	C₄×C₅₉	—	2	1	no	—
227	C₄×C₅₉	—	2	1	no	—
228	C₄×C₅₉	—	4	1	no	—
229	C₄×C₅₉	—	4	2	no	—
230	C₄×C₅₉	—	4	1	no	—
231	C₄×C₅₉	—	4	2	no	—
232	C₄×C₅₉	#443	1	2	yes	—
233	C₄×C₅₉	C₂×C₄×Q₈	1	1	yes	characteristic
234	C₄×C₅₉	#520	1	1	yes	characteristic
235	C₄×C₅₉	#546	1	1	yes	characteristic
236	C₄×C₅₉	D₄×Q₈	1	1	yes	characteristic
237	Dic₅₉	—	2	4	no	—
238	Dic₅₉	—	4	2	no	—
239	#3076	D₅₉	1	1	yes	characteristic
240	#2962	—	59	1	no	—
241	#2906	—	59	1	no	—
242	#1994	—	59	1	no	—
243	#1950	—	59	1	no	—
244	#1945	—	59	2	no	—
245	#1922	—	59	2	no	—
246	#1866	—	59	2	no	—
247	C₄×C₄⋊C₈	—	59	1	no	—
248	#1764	—	59	2	no	—
249	C₄×#104	—	59	1	no	—
250	C₂×C₅₉	—	2	1	no	—
251	C₂×C₅₉	—	2	1	no	—
252	C₂×C₅₉	—	4	2	no	—
253	C₂×C₅₉	#2360	1	1	yes	characteristic
254	C₂×C₅₉	C₂×#443	1	1	yes	characteristic
255	C₂×C₅₉	#2956	1	1	yes	characteristic
256	C₂×#131	—	59	2	no	—
257	#533	C₂×D₅₉	1	1	yes	characteristic
258	C₄×#41	C₂×D₅₉	1	1	yes	characteristic
259	#479	Dic₅₉	1	2	yes	complemented
260	#478	Dic₅₉	1	2	yes	complemented
261	#477	Dic₅₉	1	1	yes	characteristic, complemented
262	#476	Dic₅₉	1	1	yes	characteristic, complemented
263	#475	Dic₅₉	1	1	yes	characteristic, complemented
264	#474	Dic₅₉	1	1	yes	characteristic, complemented
265	#446	—	118	2	no	—
266	#446	—	118	1	no	—
267	C₈×Q₈	—	118	1	no	—
268	C₂×#108	—	59	2	no	—
269	#427	C₂×D₅₉	1	2	yes	—
270	#424	—	59	2	no	—
271	#424	—	59	2	no	—
272	#424	—	118	2	no	—
273	#423	—	59	1	no	—
274	#423	—	118	1	no	—
275	C₂×C₄⋊C₈	—	59	1	no	—
276	C₂×C₄⋊C₈	—	118	1	no	—
277	C₂×C₄⋊C₈	C₂×D₅₉	1	1	yes	characteristic
278	C₂×#104	—	59	1	no	—
279	C₂×#104	—	59	1	no	—
280	#416	C₂×D₅₉	1	2	yes	—
281	#405	—	59	2	no	—
282	C₄×M₁₆	—	59	1	no	—
283	C₂×C₄×C₈	—	59	2	no	—
284	C₄³	—	59	1	no	—
285	#341	—	59	2	no	—
286	#339	—	59	2	no	—
287	#339	—	59	1	no	—
288	#339	—	59	1	no	—
289	#339	—	59	2	no	—
290	#336	—	59	2	no	—
291	C₅₉	#22982	1	1	yes	characteristic, complemented, Sylow
292	C₂×#41	C₂²×D₅₉	1	1	yes	characteristic
293	#131	—	118	4	no	—
294	#131	—	236	2	no	—
295	C₂×M₁₆	—	59	1	no	—
296	C₂×M₁₆	—	59	2	no	—
297	C₂×M₁₆	—	59	1	no	—
298	C₂×M₁₆	—	118	2	no	—
299	C₂²×C₈	—	59	2	no	—
300	C₂²×C₈	—	118	2	no	—
301	C₂²×C₈	C₂²×D₅₉	1	2	yes	—
302	C₄⋊Q₈	C₂×Dic₅₉	1	1	yes	characteristic
303	C₄⋊Q₈	C₂×Dic₅₉	1	1	yes	characteristic
304	#125	C₂×Dic₅₉	1	2	yes	—
305	C₂²⋊Q₈	—	2	1	no	—
306	C₂²⋊Q₈	—	2	1	no	—
307	C₄×Q₈	—	2	1	no	—
308	C₄×Q₈	—	2	1	no	—
309	C₄×Q₈	C₂×Dic₅₉	1	1	yes	characteristic
310	C₄×Q₈	C₂×Dic₅₉	1	1	yes	characteristic
311	C₄×D₄	—	2	1	no	—
312	C₄×D₄	—	2	1	no	—
313	C₄×D₄	C₂×Dic₅₉	1	1	yes	characteristic
314	C₄×D₄	C₂×Dic₅₉	1	1	yes	characteristic
315	#117	—	2	1	no	—
316	#117	C₂²×D₅₉	1	1	yes	characteristic
317	#117	C₂²×D₅₉	1	2	yes	—
318	C₂×C₄²	—	2	1	no	—
319	C₂×C₄²	—	59	1	no	—
320	C₂×C₄²	—	59	1	no	—
321	C₂×C₄²	—	118	1	no	—
322	C₂×C₄²	—	118	1	no	—
323	C₂×C₄²	C₂²×D₅₉	1	1	yes	characteristic
324	#108	—	236	2	no	—
325	#107	C₂×Dic₅₉	1	2	yes	—
326	#107	C₂×Dic₅₉	1	2	yes	—
327	#106	C₂×Dic₅₉	1	2	yes	—
328	#106	C₂×Dic₅₉	1	2	yes	—
329	C₄⋊C₈	—	59	1	no	—
330	C₄⋊C₈	—	59	1	no	—
331	C₄⋊C₈	—	59	2	no	—
332	C₄⋊C₈	—	118	2	no	—
333	C₄⋊C₈	—	118	2	no	—
334	C₄⋊C₈	—	118	2	no	—
335	C₄⋊C₈	—	118	2	no	—
336	C₄⋊C₈	—	118	1	no	—
337	C₄⋊C₈	—	118	1	no	—
338	C₄⋊C₈	C₂×Dic₅₉	1	1	yes	characteristic
339	C₄⋊C₈	C₂×Dic₅₉	1	1	yes	characteristic
340	C₄⋊C₈	C₂×Dic₅₉	1	2	yes	—
341	#104	—	59	4	no	—
342	#104	—	118	2	no	—
343	#103	C₂×Dic₅₉	1	2	yes	—
344	#103	C₂×Dic₅₉	1	2	yes	—
345	#102	C₂×Dic₅₉	1	2	yes	—
346	#102	C₂×Dic₅₉	1	2	yes	—
347	#97	—	118	2	no	—
348	#97	—	118	1	no	—
349	C₄×C₈	—	118	2	no	—
350	C₄×C₈	—	118	1	no	—
351	C₄×C₈	—	236	2	no	—
352	#41	—	2	1	no	—
353	#41	—	2	1	no	—
354	#41	Q₈×D₅₉	1	2	yes	—
355	#41	#11745689	1	2	yes	—
356	C₂×Q₈	—	2	1	no	—
357	C₂×Q₈	—	2	1	no	—
358	C₂×Q₈	C₂²×Dic₅₉	1	1	yes	characteristic
359	C₂×D₄	—	2	1	no	—
360	C₂×D₄	C₂²×Dic₅₉	1	1	yes	characteristic
361	C₂²×C₄	—	2	1	no	—
362	C₂²×C₄	—	2	1	no	—
363	C₂²×C₄	—	2	1	no	—
364	C₂²×C₄	—	118	1	no	—
365	C₂²×C₄	—	118	1	no	—
366	C₂²×C₄	#11745687	1	1	yes	characteristic
367	C₂²×C₄	#11745687	1	1	yes	characteristic
368	C₂²×C₄	C₂³×D₅₉	1	1	yes	characteristic
369	M₁₆	—	59	2	no	—
370	M₁₆	—	118	1	no	—
371	M₁₆	—	118	1	no	—
372	M₁₆	—	118	2	no	—
373	M₁₆	—	118	1	no	—
374	M₁₆	—	118	2	no	—
375	M₁₆	—	236	4	no	—
376	C₂×C₈	—	2	2	no	—
377	C₂×C₈	—	2	2	no	—
378	C₂×C₈	—	59	2	no	—
379	C₂×C₈	—	59	2	no	—
380	C₂×C₈	—	118	1	no	—
381	C₂×C₈	—	118	2	no	—
382	C₂×C₈	—	118	2	no	—
383	C₂×C₈	—	118	1	no	—
384	C₂×C₈	—	118	2	no	—
385	C₂×C₈	—	236	4	no	—
386	C₂×C₈	C₂²×Dic₅₉	1	2	yes	—
387	C₂×C₈	C₂²×Dic₅₉	1	2	yes	—
388	C₄⋊C₄	—	2	1	no	—
389	C₄⋊C₄	—	2	1	no	—
390	C₄⋊C₄	—	2	2	no	—
391	C₄⋊C₄	—	2	2	no	—
392	C₄⋊C₄	—	2	1	no	—
393	C₄⋊C₄	—	2	1	no	—
394	C₄⋊C₄	C₂²×Dic₅₉	1	2	yes	—
395	C₄⋊C₄	C₂²×Dic₅₉	1	2	yes	—
396	C₄⋊C₄	C₂²×Dic₅₉	1	1	yes	characteristic
397	C₄⋊C₄	C₂²×Dic₅₉	1	1	yes	characteristic
398	C₂²⋊C₄	—	2	1	no	—
399	C₂²⋊C₄	—	2	2	no	—
400	C₂²⋊C₄	—	2	1	no	—
401	C₂²⋊C₄	—	2	1	no	—
402	C₄²	—	2	1	no	—
403	C₄²	—	2	1	no	—
404	C₄²	—	2	2	no	—
405	C₄²	—	2	1	no	—
406	C₄²	—	59	2	no	—
407	C₄²	—	118	4	no	—
408	C₄²	—	118	1	no	—
409	C₄²	—	118	1	no	—
410	C₄²	—	118	1	no	—
411	C₄²	—	236	2	no	—
412	C₄²	D₄×D₅₉	1	1	yes	characteristic
413	C₄²	D₄×D₅₉	1	1	yes	characteristic
414	C₄²	C₂²×Dic₅₉	1	1	yes	characteristic
415	C₄²	C₂²×Dic₅₉	1	1	yes	characteristic
416	C₂³	—	2	1	no	—
417	C₂³	C₂×#11745687	1	1	yes	characteristic
418	Q₈	—	2	1	no	—
419	Q₈	—	4	2	no	—
420	Q₈	—	8	1	no	—
421	Q₈	Q₈×Dic₅₉	1	2	yes	—
422	D₄	—	2	2	no	—
423	D₄	—	2	2	no	—
424	D₄	—	2	1	no	—
425	D₄	Q₈×Dic₅₉	1	2	yes	—
426	C₂×C₄	—	2	1	no	—
427	C₂×C₄	—	2	2	no	—
428	C₂×C₄	—	2	2	no	—
429	C₂×C₄	—	2	2	no	—
430	C₂×C₄	—	2	1	no	—
431	C₂×C₄	—	2	1	no	—
432	C₂×C₄	—	2	2	no	—
433	C₂×C₄	—	2	2	no	—
434	C₂×C₄	—	4	1	no	—
435	C₂×C₄	—	4	2	no	—
436	C₂×C₄	—	8	1	no	—
437	C₂×C₄	—	118	2	no	—
438	C₂×C₄	—	118	2	no	—
439	C₂×C₄	—	118	2	no	—
440	C₂×C₄	—	118	2	no	—
441	C₂×C₄	—	236	1	no	—
442	C₂×C₄	—	236	1	no	—
443	C₂×C₄	D₄×Dic₅₉	1	1	yes	characteristic
444	C₂×C₄	D₄×Dic₅₉	1	1	yes	characteristic
445	C₂×C₄	D₄×Dic₅₉	1	1	yes	characteristic
446	C₂×C₄	D₄×Dic₅₉	1	1	yes	characteristic
447	C₂×C₄	C₂³×Dic₅₉	1	1	yes	characteristic
448	C₂×C₄	C₂×D₄×D₅₉	1	1	yes	characteristic
449	C₂×C₄	C₂×Q₈×D₅₉	1	1	yes	characteristic
450	C₂×C₄	C₂×#11745689	1	1	yes	characteristic
451	C₂×C₄	#14273773	1	1	yes	characteristic
452	C₂×C₄	#14273774	1	1	yes	characteristic
453	C₈	—	2	2	no	—
454	C₈	—	2	2	no	—
455	C₈	—	118	2	no	—
456	C₈	—	118	2	no	—
457	C₈	—	118	2	no	—
458	C₈	—	236	2	no	—
459	C₈	—	236	1	no	—
460	C₂²	—	2	1	no	—
461	C₂²	—	2	1	no	—
462	C₂²	—	2	2	no	—
463	C₂²	—	4	1	no	—
464	C₂²	—	4	1	no	—
465	C₂²	C₂×D₄×Dic₅₉	1	1	yes	characteristic
466	C₂²	#16838094	1	1	yes	characteristic
467	C₂²	#16838110	1	1	yes	characteristic
468	C₄	—	2	1	no	—
469	C₄	—	2	2	no	—
470	C₄	—	2	1	no	—
471	C₄	—	2	1	no	—
472	C₄	—	4	1	no	—
473	C₄	—	4	2	no	—
474	C₄	—	4	1	no	—
475	C₄	—	4	2	no	—
476	C₄	—	118	4	no	—
477	C₄	—	236	2	no	—
478	C₄	#16837519	1	2	yes	—
479	C₄	C₂×Q₈×Dic₅₉	1	1	yes	characteristic
480	C₄	#16837885	1	1	yes	characteristic
481	C₄	#16838043	1	1	yes	characteristic
482	C₄	#16838065	1	1	yes	characteristic
483	C₂	—	2	1	no	—
484	C₂	—	2	1	no	—
485	C₂	—	4	2	no	—
486	C₂	#21427105	1	1	yes	characteristic
487	C₂	C₂×#16837519	1	1	yes	characteristic
488	C₂	#21433006	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₅₉
commutator	C₂×C₄×C₅₉	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₅₉
Fitting	C₅₉×#3076	C₂
socle	C₂²×C₅₉	C₂×C₄×D₄
prime radical	C₂×#41×C₅₉	C₂³
cosocle	C₂²×C₄×C₅₉	C₂⁴
hypercenter	#3076	D₅₉
hypocenter	C₅₉	#22982
LCS	G ▷ C₂×C₄×C₅₉ ▷ C₂×C₅₉ ▷ C₅₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #3076

Complements

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

N	H ≅ G/N	type
1. #21433045	C₂	semidirect
3. #21425074	C₂	semidirect
4. #21424872	C₂	semidirect
5. #21424845	C₂	semidirect
6. #21424697	C₂	semidirect
8. C₄⋊C₈×Dic₅₉	C₂	semidirect
38. C₅₉×#479	C₄	semidirect
39. C₅₉×#478	C₄	semidirect
40. C₅₉×#477	C₄	semidirect
41. C₅₉×#476	C₄	semidirect
42. C₅₉×#475	C₄	semidirect
43. C₅₉×#474	C₄	semidirect
70. #14273654	Q₈	semidirect
259. #479	Dic₅₉	semidirect
260. #478	Dic₅₉	semidirect
261. #477	Dic₅₉	semidirect
262. #476	Dic₅₉	semidirect
263. #475	Dic₅₉	semidirect
264. #474	Dic₅₉	semidirect
291. C₅₉	#22982	semidirect

Maximal subgroups

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

subgroup	index
#21433045	2
#21432664	2
#21425074	2
#21424872	2
#21424845	2
#21424697	2
#21424373	2
C₄⋊C₈×Dic₅₉	2
#21423936	2
C₄×#14273654	2
C₅₉×#3076	2
#22982	59