Subgroups — #28612051

Order 15104.

662 conjugacy classes of subgroups.

The subgroup lattice has 482 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#21433884	C₂	1	1	yes	maximal, characteristic
2	#21433043	C₂	1	1	yes	maximal, characteristic, complemented
3	#21432762	C₂	1	1	yes	maximal, characteristic
4	#21425073	C₂	1	1	yes	maximal, characteristic, complemented
5	#21424871	C₂	1	1	yes	maximal, characteristic, complemented
6	#21424804	C₂	1	2	yes	maximal
7	#21424747	C₂	1	2	yes	maximal
8	#21424693	C₂	1	2	yes	maximal, complemented
9	#21423979	C₂	1	2	yes	maximal, complemented
10	#21423949	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄×#104×C₅₉	C₂	1	1	yes	maximal, characteristic
12	#16837959	C₂²	1	1	yes	characteristic
13	#16837709	C₄	1	2	yes	complemented
14	#16837702	C₄	1	2	yes	complemented
15	#16837697	C₄	1	1	yes	characteristic, complemented
16	#16837692	C₄	1	1	yes	characteristic, complemented
17	#16837687	C₄	1	1	yes	characteristic, complemented
18	#16837682	C₄	1	1	yes	characteristic, complemented
19	#16837532	—	2	1	no	—
20	#16837530	—	2	2	no	—
21	C₈×Dic₁₁₈	—	2	1	no	—
22	#16837463	—	2	2	no	—
23	#16837459	—	2	1	no	—
24	#16837455	—	2	1	no	—
25	C₂×#14273662	C₂²	1	2	yes	—
26	#16837438	C₂²	1	2	yes	—
27	#16837430	C₂²	1	2	yes	—
28	#16837426	C₂²	1	1	yes	characteristic
29	C₂×C₄⋊(C₅₉⋊C₈)	C₂²	1	1	yes	characteristic
30	C₂×C₄⋊(C₅₉⋊C₈)	C₂²	1	1	yes	characteristic
31	#16837398	C₂²	1	2	yes	—
32	#16837369	C₂²	1	2	yes	—
33	#16837360	C₂²	1	2	yes	—
34	#16837358	C₂²	1	2	yes	—
35	C₂×#14273638	C₂²	1	2	yes	—
36	#16837166	C₂²	1	2	yes	—
37	#16837162	C₂²	1	2	yes	—
38	#16837162	C₂²	1	2	yes	—
39	#16837157	C₂²	1	2	yes	—
40	C₄×#41×C₅₉	C₂²	1	1	yes	characteristic
41	C₂×#104×C₅₉	C₂²	1	1	yes	characteristic
42	C₂×#104×C₅₉	C₂²	1	1	yes	characteristic
43	C₄×M₁₆×C₅₉	C₂²	1	1	yes	characteristic
44	C₄³×C₅₉	C₂²	1	1	yes	characteristic
45	C₅₉×#339	C₂²	1	1	yes	characteristic
46	C₅₉×#339	C₂²	1	1	yes	characteristic
47	C₂×#11745664	C₂³	1	2	yes	—
48	C₂²×C₅₉⋊C₈	C₂³	1	2	yes	—
49	C₂²×C₅₉⋊C₈	C₂³	1	2	yes	—
50	#14273727	C₂×C₄	1	1	yes	characteristic
51	#14273727	C₂×C₄	1	1	yes	characteristic
52	#14273719	C₂×C₄	1	2	yes	—
53	#14273706	—	2	1	no	—
54	#14273706	—	2	1	no	—
55	C₄×Dic₁₁₈	—	2	1	no	—
56	C₄×Dic₁₁₈	—	2	1	no	—
57	#14273686	C₂³	1	2	yes	—
58	#14273662	—	2	4	no	—
59	#14273660	C₂×C₄	1	2	yes	—
60	#14273660	C₂×C₄	1	2	yes	—
61	#14273658	C₂×C₄	1	2	yes	—
62	#14273658	C₂×C₄	1	2	yes	—
63	C₄⋊(C₅₉⋊C₈)	—	2	1	no	—
64	C₄⋊(C₅₉⋊C₈)	—	2	1	no	—
65	C₄⋊(C₅₉⋊C₈)	C₂×C₄	1	1	yes	characteristic
66	C₄⋊(C₅₉⋊C₈)	C₂×C₄	1	1	yes	characteristic
67	C₄⋊(C₅₉⋊C₈)	C₂×C₄	1	2	yes	—
68	C₄⋊(C₅₉⋊C₈)	D₄	1	1	yes	characteristic
69	C₄⋊(C₅₉⋊C₈)	D₄	1	1	yes	characteristic
70	C₄⋊(C₅₉⋊C₈)	D₄	1	2	yes	—
71	Dic₅₉⋊C₈	—	2	2	no	—
72	Dic₅₉⋊C₈	—	2	2	no	—
73	#14273651	C₂×C₄	1	2	yes	—
74	#14273651	C₂×C₄	1	2	yes	—
75	#14273648	C₂×C₄	1	2	yes	—
76	#14273648	C₂×C₄	1	2	yes	—
77	C₂²⋊(C₅₉⋊C₈)	—	2	2	no	—
78	C₂²⋊(C₅₉⋊C₈)	—	2	2	no	—
79	#14273638	—	2	4	no	—
80	#14273638	—	2	2	no	—
81	#14273637	—	2	2	no	—
82	C₄×C₅₉⋊C₈	—	2	2	no	—
83	C₈×Dic₅₉	—	2	2	no	—
84	C₂×#41×C₅₉	C₂³	1	1	yes	characteristic
85	C₂×M₁₆×C₅₉	C₂³	1	1	yes	characteristic
86	C₂×M₁₆×C₅₉	C₂³	1	1	yes	characteristic
87	C₄×Q₈×C₅₉	C₂×C₄	1	1	yes	characteristic
88	C₄×Q₈×C₅₉	C₂×C₄	1	1	yes	characteristic
89	C₄×D₄×C₅₉	—	2	1	no	—
90	C₄×D₄×C₅₉	—	2	1	no	—
91	C₄×D₄×C₅₉	C₂×C₄	1	1	yes	characteristic
92	C₄×D₄×C₅₉	C₂×C₄	1	1	yes	characteristic
93	#117×C₅₉	—	2	1	no	—
94	#117×C₅₉	C₂³	1	1	yes	characteristic
95	C₂×C₄²×C₅₉	—	2	1	no	—
96	C₂×C₄²×C₅₉	—	2	1	no	—
97	C₂×C₄²×C₅₉	—	2	1	no	—
98	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
99	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
100	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
101	#104×C₅₉	—	2	2	no	—
102	#104×C₅₉	—	2	2	no	—
103	#97×C₅₉	—	2	1	no	—
104	C₄×C₈×C₅₉	—	2	1	no	—
105	#41×C₅₉	—	2	1	no	—
106	#41×C₅₉	—	2	1	no	—
107	#41×C₅₉	—	2	1	no	—
108	#41×C₅₉	—	2	1	no	—
109	C₂×Q₈×C₅₉	C₂²×C₄	1	1	yes	characteristic
110	C₂×D₄×C₅₉	—	2	1	no	—
111	C₂×D₄×C₅₉	C₂²×C₄	1	1	yes	characteristic
112	C₂²×C₄×C₅₉	—	2	1	no	—
113	C₂²×C₄×C₅₉	—	2	1	no	—
114	C₂²×C₄×C₅₉	—	2	1	no	—
115	C₂²×C₄×C₅₉	—	2	1	no	—
116	C₂²×C₄×C₅₉	—	2	1	no	—
117	C₂²×C₄×C₅₉	#41	1	1	yes	characteristic
118	C₂²×C₄×C₅₉	#41	1	1	yes	characteristic
119	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
120	C₂×Dic₁₁₈	—	2	1	no	—
121	C₂×Dic₁₁₈	—	2	1	no	—
122	M₁₆×C₅₉	—	2	1	no	—
123	M₁₆×C₅₉	—	2	1	no	—
124	M₁₆×C₅₉	—	2	1	no	—
125	M₁₆×C₅₉	#41	1	2	yes	—
126	C₂×C₈×C₅₉	—	2	1	no	—
127	C₂×C₈×C₅₉	—	2	1	no	—
128	C₄⋊C₄×C₅₉	—	2	1	no	—
129	C₄⋊C₄×C₅₉	—	2	1	no	—
130	C₄⋊C₄×C₅₉	C₂²×C₄	1	1	yes	characteristic
131	C₄⋊C₄×C₅₉	C₂²×C₄	1	1	yes	characteristic
132	C₂²⋊C₄×C₅₉	—	2	1	no	—
133	C₂²⋊C₄×C₅₉	—	2	1	no	—
134	C₂²⋊C₄×C₅₉	—	2	1	no	—
135	C₄²×C₅₉	—	2	1	no	—
136	C₄²×C₅₉	—	2	1	no	—
137	C₄²×C₅₉	—	2	1	no	—
138	C₄²×C₅₉	—	2	1	no	—
139	C₄²×C₅₉	—	2	1	no	—
140	C₄²×C₅₉	—	2	1	no	—
141	C₄²×C₅₉	—	4	2	no	—
142	C₄²×C₅₉	—	4	2	no	—
143	C₄²×C₅₉	C₂²×C₄	1	1	yes	characteristic
144	C₄²×C₅₉	C₂²×C₄	1	1	yes	characteristic
145	C₄²×C₅₉	C₂×D₄	1	1	yes	characteristic
146	C₄²×C₅₉	C₂×D₄	1	1	yes	characteristic
147	C₄²×C₅₉	#41	1	2	yes	—
148	C₂²⋊Dic₅₉	—	2	2	no	—
149	C₄⋊Dic₅₉	—	2	1	no	—
150	C₄⋊Dic₅₉	—	2	1	no	—
151	C₄⋊Dic₅₉	C₂²×C₄	1	2	yes	—
152	C₄⋊Dic₅₉	C₂²×C₄	1	2	yes	—
153	Dic₅₉⋊C₄	—	2	2	no	—
154	Dic₅₉⋊C₄	—	2	2	no	—
155	C₄×Dic₅₉	—	2	2	no	—
156	#11745664	—	2	2	no	—
157	#11745664	—	2	2	no	—
158	C₂×C₅₉⋊C₈	—	2	2	no	—
159	C₂×C₅₉⋊C₈	—	2	2	no	—
160	C₂×C₅₉⋊C₈	—	2	2	no	—
161	C₂×C₅₉⋊C₈	—	2	2	no	—
162	C₂×C₅₉⋊C₈	—	2	2	no	—
163	C₂×C₅₉⋊C₈	C₂²×C₄	1	2	yes	—
164	C₂×C₅₉⋊C₈	C₂²×C₄	1	2	yes	—
165	C₂×C₅₉⋊C₈	C₂×D₄	1	2	yes	—
166	C₂×C₅₉⋊C₈	C₂×D₄	1	2	yes	—
167	C₂³×C₅₉	—	2	1	no	—
168	C₂³×C₅₉	C₂×#41	1	1	yes	characteristic
169	Q₈×C₅₉	—	2	1	no	—
170	Q₈×C₅₉	—	2	1	no	—
171	D₄×C₅₉	—	2	1	no	—
172	D₄×C₅₉	—	2	1	no	—
173	D₄×C₅₉	—	4	1	no	—
174	D₄×C₅₉	—	4	1	no	—
175	C₂×C₄×C₅₉	—	2	2	no	—
176	C₂×C₄×C₅₉	—	2	2	no	—
177	C₂×C₄×C₅₉	—	2	1	no	—
178	C₂×C₄×C₅₉	—	2	1	no	—
179	C₂×C₄×C₅₉	—	2	1	no	—
180	C₂×C₄×C₅₉	—	2	2	no	—
181	C₂×C₄×C₅₉	—	4	1	no	—
182	C₂×C₄×C₅₉	—	4	1	no	—
183	C₂×C₄×C₅₉	—	4	1	no	—
184	C₂×C₄×C₅₉	—	4	1	no	—
185	C₂×C₄×C₅₉	—	4	1	no	—
186	C₂×C₄×C₅₉	—	4	1	no	—
187	C₂×C₄×C₅₉	—	4	1	no	—
188	C₂×C₄×C₅₉	—	4	2	no	—
189	C₂×C₄×C₅₉	—	8	1	no	—
190	C₂×C₄×C₅₉	C₄×D₄	1	1	yes	characteristic
191	C₂×C₄×C₅₉	C₄×D₄	1	1	yes	characteristic
192	C₂×C₄×C₅₉	C₄×D₄	1	1	yes	characteristic
193	C₂×C₄×C₅₉	C₄×D₄	1	1	yes	characteristic
194	C₂×C₄×C₅₉	C₂³×C₄	1	1	yes	characteristic
195	C₂×C₄×C₅₉	C₂²×D₄	1	1	yes	characteristic
196	C₂×C₄×C₅₉	C₂×#41	1	1	yes	characteristic
197	C₂×C₄×C₅₉	C₂×#41	1	1	yes	characteristic
198	C₂×C₄×C₅₉	2₋¹⁺⁴	1	1	yes	characteristic
199	C₂×C₄×C₅₉	2₋¹⁺⁴	1	1	yes	characteristic
200	C₂×Dic₅₉	—	2	2	no	—
201	C₂×Dic₅₉	—	2	2	no	—
202	Dic₁₁₈	—	4	2	no	—
203	Dic₁₁₈	—	8	1	no	—
204	C₈×C₅₉	—	2	2	no	—
205	C₈×C₅₉	—	4	1	no	—
206	C₅₉⋊C₈	—	2	2	no	—
207	C₅₉⋊C₈	—	2	2	no	—
208	C₅₉⋊C₈	—	2	2	no	—
209	C₅₉⋊C₈	—	2	2	no	—
210	C₅₉⋊C₈	—	4	2	no	—
211	#23081	—	59	1	no	maximal, Sylow
212	C₂²×C₅₉	—	2	1	no	—
213	C₂²×C₅₉	—	2	1	no	—
214	C₂²×C₅₉	—	4	1	no	—
215	C₂²×C₅₉	—	4	1	no	—
216	C₂²×C₅₉	—	4	1	no	—
217	C₂²×C₅₉	C₂×C₄×D₄	1	1	yes	characteristic
218	C₂²×C₅₉	#552	1	1	yes	characteristic
219	C₂²×C₅₉	#556	1	1	yes	characteristic
220	C₄×C₅₉	—	2	1	no	—
221	C₄×C₅₉	—	2	1	no	—
222	C₄×C₅₉	—	2	1	no	—
223	C₄×C₅₉	—	4	2	no	—
224	C₄×C₅₉	—	4	2	no	—
225	C₄×C₅₉	—	4	1	no	—
226	C₄×C₅₉	—	4	1	no	—
227	C₄×C₅₉	—	4	1	no	—
228	C₄×C₅₉	#444	1	2	yes	—
229	C₄×C₅₉	C₄×#41	1	1	yes	characteristic
230	C₄×C₅₉	#519	1	1	yes	characteristic
231	C₄×C₅₉	#547	1	1	yes	characteristic
232	C₄×C₅₉	#548	1	1	yes	characteristic
233	Dic₅₉	—	4	2	no	—
234	Dic₅₉	—	4	2	no	—
235	#3076	—	59	1	no	—
236	#2962	—	59	1	no	—
237	#2925	—	59	1	no	—
238	#1994	—	59	1	no	—
239	#1950	—	59	1	no	—
240	#1938	—	59	2	no	—
241	#1929	—	59	2	no	—
242	#1922	—	59	2	no	—
243	#1773	—	59	2	no	—
244	#1767	—	59	1	no	—
245	C₄×#104	D₅₉	1	1	yes	characteristic
246	C₂×C₅₉	—	2	1	no	—
247	C₂×C₅₉	—	2	1	no	—
248	C₂×C₅₉	—	8	1	no	—
249	C₂×C₅₉	#2362	1	1	yes	characteristic
250	C₂×C₅₉	C₂×#444	1	1	yes	characteristic
251	C₂×C₅₉	#2956	1	1	yes	characteristic
252	#533	—	59	1	no	—
253	C₄×#41	C₂×D₅₉	1	1	yes	characteristic
254	#479	—	59	2	no	—
255	#478	—	59	2	no	—
256	#477	—	59	1	no	—
257	#476	—	59	1	no	—
258	#475	—	59	1	no	—
259	#474	—	59	1	no	—
260	#446	—	118	1	no	—
261	#446	—	118	2	no	—
262	C₈×Q₈	—	118	1	no	—
263	#433	—	118	2	no	—
264	#432	—	118	1	no	—
265	#431	—	118	1	no	—
266	C₂×#108	—	59	2	no	—
267	#427	—	59	2	no	—
268	#424	—	59	2	no	—
269	#423	—	59	1	no	—
270	C₂×C₄⋊C₈	—	59	1	no	—
271	C₂×C₄⋊C₈	—	59	1	no	—
272	C₂×#104	C₂×D₅₉	1	1	yes	characteristic
273	C₂×#104	C₂×D₅₉	1	1	yes	characteristic
274	#416	—	59	2	no	—
275	#408	—	59	2	no	—
276	#405	—	59	2	no	—
277	#405	—	59	2	no	—
278	C₄×M₁₆	C₂×D₅₉	1	1	yes	characteristic
279	C₂×#97	—	59	2	no	—
280	C₄³	C₂×D₅₉	1	1	yes	characteristic
281	#341	—	59	2	no	—
282	#339	—	59	2	no	—
283	#339	—	59	2	no	—
284	#339	C₂×D₅₉	1	1	yes	characteristic
285	#339	C₂×D₅₉	1	1	yes	characteristic
286	#336	—	59	2	no	—
287	C₅₉	#23081	1	1	yes	characteristic, complemented, Sylow
288	C₂×#41	C₂²×D₅₉	1	1	yes	characteristic
289	C₂×M₁₆	—	59	2	no	—
290	C₂×M₁₆	C₂²×D₅₉	1	1	yes	characteristic
291	C₂×M₁₆	C₂²×D₅₉	1	1	yes	characteristic
292	C₂²×C₈	—	59	2	no	—
293	C₂²×C₈	—	59	2	no	—
294	C₄⋊Q₈	—	59	1	no	—
295	C₄⋊Q₈	—	59	1	no	—
296	#125	—	59	2	no	—
297	C₂²⋊Q₈	—	118	1	no	—
298	C₂²⋊Q₈	—	118	1	no	—
299	C₄×Q₈	—	118	1	no	—
300	C₄×Q₈	—	118	1	no	—
301	C₄×Q₈	C₄×D₅₉	1	1	yes	characteristic
302	C₄×Q₈	C₄×D₅₉	1	1	yes	characteristic
303	C₄×D₄	—	2	1	no	—
304	C₄×D₄	—	2	1	no	—
305	C₄×D₄	C₄×D₅₉	1	1	yes	characteristic
306	C₄×D₄	C₄×D₅₉	1	1	yes	characteristic
307	#117	—	2	1	no	—
308	#117	—	59	2	no	—
309	#117	C₂²×D₅₉	1	1	yes	characteristic
310	C₂×C₄²	—	2	1	no	—
311	C₂×C₄²	—	2	1	no	—
312	C₂×C₄²	—	2	1	no	—
313	C₂×C₄²	C₂²×D₅₉	1	1	yes	characteristic
314	C₂×C₄²	C₂²×D₅₉	1	1	yes	characteristic
315	C₂×C₄²	C₂²×D₅₉	1	1	yes	characteristic
316	#108	—	118	4	no	—
317	#107	—	59	2	no	—
318	#107	—	59	2	no	—
319	#106	—	59	2	no	—
320	#106	—	59	2	no	—
321	C₄⋊C₈	—	59	1	no	—
322	C₄⋊C₈	—	59	1	no	—
323	C₄⋊C₈	—	59	2	no	—
324	C₄⋊C₈	—	59	1	no	—
325	C₄⋊C₈	—	59	1	no	—
326	C₄⋊C₈	—	59	2	no	—
327	C₄⋊C₈	—	118	2	no	—
328	C₄⋊C₈	—	118	2	no	—
329	C₄⋊C₈	—	118	1	no	—
330	C₄⋊C₈	—	118	1	no	—
331	#104	—	2	2	no	—
332	#104	—	2	2	no	—
333	#103	—	59	2	no	—
334	#103	—	59	2	no	—
335	#102	—	59	2	no	—
336	#102	—	59	2	no	—
337	C₂²⋊C₈	—	118	2	no	—
338	C₂²⋊C₈	—	118	2	no	—
339	#97	—	2	1	no	—
340	#97	—	118	2	no	—
341	#97	—	118	2	no	—
342	#97	—	118	4	no	—
343	C₄×C₈	—	2	1	no	—
344	C₄×C₈	—	118	2	no	—
345	C₄×C₈	—	118	2	no	—
346	#41	—	2	1	no	—
347	#41	—	2	1	no	—
348	#41	—	2	1	no	—
349	#41	—	2	1	no	—
350	C₂×Q₈	—	118	1	no	—
351	C₂×Q₈	—	118	1	no	—
352	C₂×Q₈	C₂×C₄×D₅₉	1	1	yes	characteristic
353	C₂×D₄	—	2	1	no	—
354	C₂×D₄	C₂×C₄×D₅₉	1	1	yes	characteristic
355	C₂²×C₄	—	2	1	no	—
356	C₂²×C₄	—	2	1	no	—
357	C₂²×C₄	—	2	1	no	—
358	C₂²×C₄	—	2	1	no	—
359	C₂²×C₄	—	2	1	no	—
360	C₂²×C₄	#11745687	1	1	yes	characteristic
361	C₂²×C₄	#11745687	1	1	yes	characteristic
362	C₂²×C₄	C₂³×D₅₉	1	1	yes	characteristic
363	M₁₆	—	2	1	no	—
364	M₁₆	—	2	1	no	—
365	M₁₆	—	2	1	no	—
366	M₁₆	—	118	2	no	—
367	M₁₆	—	118	2	no	—
368	M₁₆	#11745685	1	2	yes	—
369	C₂×C₈	—	2	1	no	—
370	C₂×C₈	—	2	1	no	—
371	C₂×C₈	—	59	2	no	—
372	C₂×C₈	—	59	2	no	—
373	C₂×C₈	—	59	2	no	—
374	C₂×C₈	—	59	2	no	—
375	C₂×C₈	—	118	2	no	—
376	C₂×C₈	—	118	2	no	—
377	C₂×C₈	—	118	2	no	—
378	C₂×C₈	—	118	2	no	—
379	C₂×C₈	—	118	2	no	—
380	C₄⋊C₄	—	2	1	no	—
381	C₄⋊C₄	—	2	1	no	—
382	C₄⋊C₄	—	59	2	no	—
383	C₄⋊C₄	—	59	2	no	—
384	C₄⋊C₄	—	118	2	no	—
385	C₄⋊C₄	—	118	2	no	—
386	C₄⋊C₄	—	118	1	no	—
387	C₄⋊C₄	—	118	1	no	—
388	C₄⋊C₄	C₂×C₄×D₅₉	1	1	yes	characteristic
389	C₄⋊C₄	C₂×C₄×D₅₉	1	1	yes	characteristic
390	C₂²⋊C₄	—	2	1	no	—
391	C₂²⋊C₄	—	2	1	no	—
392	C₂²⋊C₄	—	2	1	no	—
393	C₂²⋊C₄	—	118	2	no	—
394	C₄²	—	2	1	no	—
395	C₄²	—	2	1	no	—
396	C₄²	—	2	1	no	—
397	C₄²	—	2	1	no	—
398	C₄²	—	2	1	no	—
399	C₄²	—	2	1	no	—
400	C₄²	—	4	2	no	—
401	C₄²	—	4	2	no	—
402	C₄²	—	118	2	no	—
403	C₄²	C₂×C₄×D₅₉	1	1	yes	characteristic
404	C₄²	C₂×C₄×D₅₉	1	1	yes	characteristic
405	C₄²	#11745685	1	2	yes	—
406	C₄²	D₄×D₅₉	1	1	yes	characteristic
407	C₄²	D₄×D₅₉	1	1	yes	characteristic
408	C₂³	—	2	1	no	—
409	C₂³	C₂×#11745687	1	1	yes	characteristic
410	Q₈	—	2	1	no	—
411	Q₈	—	2	1	no	—
412	Q₈	—	472	1	no	—
413	Q₈	—	236	2	no	—
414	D₄	—	2	1	no	—
415	D₄	—	2	1	no	—
416	D₄	—	4	1	no	—
417	D₄	—	4	1	no	—
418	C₂×C₄	—	2	2	no	—
419	C₂×C₄	—	2	2	no	—
420	C₂×C₄	—	2	2	no	—
421	C₂×C₄	—	2	1	no	—
422	C₂×C₄	—	2	1	no	—
423	C₂×C₄	—	2	1	no	—
424	C₂×C₄	—	4	1	no	—
425	C₂×C₄	—	4	1	no	—
426	C₂×C₄	—	4	1	no	—
427	C₂×C₄	—	4	1	no	—
428	C₂×C₄	—	4	1	no	—
429	C₂×C₄	—	4	2	no	—
430	C₂×C₄	—	4	1	no	—
431	C₂×C₄	—	4	1	no	—
432	C₂×C₄	—	8	1	no	—
433	C₂×C₄	—	118	2	no	—
434	C₂×C₄	—	118	2	no	—
435	C₂×C₄	(C₂²⋊D₅₉)⋊C₄	1	1	yes	characteristic
436	C₂×C₄	(C₂²⋊D₅₉)⋊C₄	1	1	yes	characteristic
437	C₂×C₄	(C₂²⋊D₅₉)⋊C₄	1	1	yes	characteristic
438	C₂×C₄	(C₂²⋊D₅₉)⋊C₄	1	1	yes	characteristic
439	C₂×C₄	C₂²×C₄×D₅₉	1	1	yes	characteristic
440	C₂×C₄	C₂×D₄×D₅₉	1	1	yes	characteristic
441	C₂×C₄	C₂×#11745685	1	1	yes	characteristic
442	C₂×C₄	C₂×#11745685	1	1	yes	characteristic
443	C₂×C₄	#14273774	1	1	yes	characteristic
444	C₂×C₄	#14273774	1	1	yes	characteristic
445	C₈	—	2	2	no	—
446	C₈	—	4	1	no	—
447	C₈	—	118	2	no	—
448	C₈	—	118	2	no	—
449	C₈	—	118	2	no	—
450	C₈	—	118	2	no	—
451	C₈	—	236	2	no	—
452	C₂²	—	2	1	no	—
453	C₂²	—	2	1	no	—
454	C₂²	—	4	1	no	—
455	C₂²	—	4	1	no	—
456	C₂²	—	4	1	no	—
457	C₂²	C₂×(C₂²⋊D₅₉)⋊C₄	1	1	yes	characteristic
458	C₂²	#16838092	1	1	yes	characteristic
459	C₂²	#16838122	1	1	yes	characteristic
460	C₄	—	2	1	no	—
461	C₄	—	2	1	no	—
462	C₄	—	2	1	no	—
463	C₄	—	4	2	no	—
464	C₄	—	4	2	no	—
465	C₄	—	4	1	no	—
466	C₄	—	4	1	no	—
467	C₄	—	4	1	no	—
468	C₄	—	236	2	no	—
469	C₄	—	236	2	no	—
470	C₄	#16837521	1	2	yes	—
471	C₄	C₄×#11745685	1	1	yes	characteristic
472	C₄	#16837879	1	1	yes	characteristic
473	C₄	#16838057	1	1	yes	characteristic
474	C₄	#16838061	1	1	yes	characteristic
475	C₂	—	2	1	no	—
476	C₂	—	2	1	no	—
477	C₂	—	8	1	no	—
478	C₂	#21427121	1	1	yes	characteristic
479	C₂	C₂×#16837521	1	1	yes	characteristic
480	C₂	#21433002	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	C₄×#104×C₅₉	C₂
socle	C₂²×C₅₉	C₂×C₄×D₄
prime radical	C₂×#41×C₅₉	C₂³
cosocle	C₂²×C₄×C₅₉	C₂⁴
hypercenter	C₄×#104	D₅₉
hypocenter	C₅₉	#23081
LCS	G ▷ C₂×C₄×C₅₉ ▷ C₂×C₅₉ ▷ C₅₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ C₄×#104

Complements

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

N	H ≅ G/N	type
2. #21433043	C₂	semidirect
4. #21425073	C₂	semidirect
5. #21424871	C₂	semidirect
8. #21424693	C₂	semidirect
9. #21423979	C₂	semidirect
10. #21423949	C₂	semidirect
13. #16837709	C₄	semidirect
14. #16837702	C₄	semidirect
15. #16837697	C₄	semidirect
16. #16837692	C₄	semidirect
17. #16837687	C₄	semidirect
18. #16837682	C₄	semidirect
287. C₅₉	#23081	semidirect

Maximal subgroups

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

subgroup	index
#21433884	2
#21433043	2
#21432762	2
#21425073	2
#21424871	2
#21424804	2
#21424747	2
#21424693	2
#21423979	2
#21423949	2
C₄×#104×C₅₉	2
#23081	59