Subgroups — #28631300

Order 15104.

810 conjugacy classes of subgroups.

The subgroup lattice has 500 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#21433835	C₂	1	2	yes	maximal
2	C₂×#16837677	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#16837677	C₂	1	1	yes	maximal, characteristic, complemented
4	#21432707	C₂	1	1	yes	maximal, characteristic, complemented
5	#21425496	C₂	1	2	yes	maximal, complemented
6	#21425377	C₂	1	2	yes	maximal, complemented
7	#21425011	C₂	1	1	yes	maximal, characteristic, complemented
8	#21424886	C₂	1	1	yes	maximal, characteristic, complemented
9	#21424567	C₂	1	2	yes	maximal, complemented
10	#21424146	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅₉×#2955	C₂	1	1	yes	maximal, characteristic
12	C₂×#14273757	C₂²	1	2	yes	—
13	C₂×#14273757	C₂²	1	2	yes	—
14	C₂²×Dic₂₃₆	C₂²	1	1	yes	characteristic
15	#16838169	C₂²	1	2	yes	—
16	#16837677	—	2	2	no	—
17	#16837677	—	2	2	no	—
18	#16837677	—	2	2	no	—
19	#16837677	—	2	2	no	—
20	#16837675	—	2	4	no	—
21	#16837663	—	2	4	no	—
22	#16837451	—	2	2	no	—
23	#16837451	C₂²	1	2	yes	—
24	#16837450	C₂²	1	2	yes	—
25	C₂×#14273663	—	2	2	no	—
26	C₂×#14273663	C₂²	1	1	yes	characteristic
27	C₂×#14273663	C₂²	1	1	yes	characteristic
28	C₂×#14273663	C₂²	1	1	yes	characteristic
29	#16837410	C₂²	1	2	yes	—
30	#16837386	C₂²	1	2	yes	—
31	C₂×#14273645	C₂²	1	2	yes	—
32	C₂×#14273645	C₂²	1	2	yes	—
33	C₂×#14273645	C₂²	1	2	yes	—
34	#16837172	C₂²	1	2	yes	—
35	C₅₉⋊#338	C₂²	1	2	yes	—
36	C₅₉×#575	C₂²	1	1	yes	characteristic
37	C₂×#131×C₅₉	C₂²	1	1	yes	characteristic
38	C₂×#131×C₅₉	C₂²	1	1	yes	characteristic
39	C₅₉×#444	—	2	2	no	—
40	C₅₉×#443	—	2	2	no	—
41	C₅₉×#430	C₂²	1	1	yes	characteristic
42	C₅₉×#421	C₂²	1	1	yes	characteristic
43	C₅₉×#421	C₂²	1	1	yes	characteristic
44	C₅₉×#405	C₂²	1	1	yes	characteristic
45	C₂²×Dic₁₁₈	C₂³	1	2	yes	—
46	#14273757	—	2	4	no	—
47	#14273757	—	2	4	no	—
48	#14273757	—	2	4	no	—
49	#14273757	—	4	2	no	—
50	C₂×Dic₂₃₆	—	2	1	no	—
51	C₂×Dic₂₃₆	—	2	1	no	—
52	C₂×Dic₂₃₆	—	2	1	no	—
53	C₂×Dic₂₃₆	—	2	1	no	—
54	C₂×Dic₂₃₆	—	2	1	no	—
55	C₂×Dic₂₃₆	—	2	1	no	—
56	C₂×#11745672	—	2	2	no	—
57	C₂×#11745672	—	2	2	no	—
58	C₂×#11745670	—	2	2	no	—
59	C₂×#11745670	—	2	2	no	—
60	#14273734	—	2	4	no	—
61	#14273734	—	4	2	no	—
62	C₂×#11745664	—	2	4	no	—
63	C₂×#11745664	C₂³	1	2	yes	—
64	C₂×#11745664	C₂³	1	2	yes	—
65	C₂×#11745664	C₂³	1	2	yes	—
66	#14273663	—	2	1	no	—
67	#14273663	—	2	1	no	—
68	#14273663	—	2	1	no	—
69	#14273663	—	2	1	no	—
70	#14273663	—	2	4	no	—
71	#14273663	D₄	1	2	yes	—
72	#14273663	D₄	1	2	yes	—
73	#14273662	—	2	4	no	—
74	#14273650	—	4	2	no	—
75	#14273646	—	2	2	no	—
76	#14273645	—	2	4	no	—
77	#14273645	—	2	4	no	—
78	#14273645	—	2	4	no	—
79	#14273644	—	2	2	no	—
80	C₂×#41×C₅₉	C₂³	1	1	yes	characteristic
81	C₂×#41×C₅₉	C₂³	1	1	yes	characteristic
82	#137×C₅₉	—	2	1	no	—
83	#137×C₅₉	D₄	1	2	yes	—
84	AGL(1,ℤ/8)×C₅₉	—	2	1	no	—
85	AGL(1,ℤ/8)×C₅₉	D₄	1	2	yes	—
86	#135×C₅₉	—	2	2	no	—
87	#131×C₅₉	—	2	1	no	—
88	#131×C₅₉	—	2	1	no	—
89	#131×C₅₉	—	2	1	no	—
90	#131×C₅₉	—	2	1	no	—
91	#131×C₅₉	—	2	1	no	—
92	#131×C₅₉	—	2	1	no	—
93	#131×C₅₉	D₄	1	2	yes	—
94	#131×C₅₉	D₄	1	2	yes	—
95	C₂×M₁₆×C₅₉	—	2	1	no	—
96	C₂×M₁₆×C₅₉	—	2	1	no	—
97	C₂×M₁₆×C₅₉	C₂³	1	1	yes	characteristic
98	C₂×M₁₆×C₅₉	C₂³	1	1	yes	characteristic
99	C₂×M₁₆×C₅₉	C₂³	1	1	yes	characteristic
100	C₂²×C₈×C₅₉	—	2	1	no	—
101	C₂²×C₈×C₅₉	—	2	1	no	—
102	C₂²×C₈×C₅₉	C₂³	1	1	yes	characteristic
103	#117×C₅₉	C₂³	1	1	yes	characteristic
104	#108×C₅₉	—	2	2	no	—
105	#104×C₅₉	—	2	2	no	—
106	#104×C₅₉	—	2	2	no	—
107	#97×C₅₉	—	2	1	no	—
108	C₄×C₈×C₅₉	—	2	1	no	—
109	#41×C₅₉	—	2	1	no	—
110	#41×C₅₉	—	2	1	no	—
111	#41×C₅₉	—	2	1	no	—
112	#41×C₅₉	—	2	1	no	—
113	#41×C₅₉	—	2	1	no	—
114	#41×C₅₉	—	2	1	no	—
115	#41×C₅₉	C₂×D₄	1	2	yes	—
116	#41×C₅₉	C₂×D₄	1	2	yes	—
117	C₂×Q₈×C₅₉	C₂×D₄	1	1	yes	characteristic
118	C₂×Q₈×C₅₉	#41	1	1	yes	characteristic
119	C₂×D₄×C₅₉	—	2	1	no	—
120	C₂×D₄×C₅₉	—	2	1	no	—
121	C₂×D₄×C₅₉	C₂×D₄	1	1	yes	characteristic
122	C₂×D₄×C₅₉	#41	1	1	yes	characteristic
123	C₂²×C₄×C₅₉	—	2	1	no	—
124	C₂²×C₄×C₅₉	—	2	1	no	—
125	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
126	C₂²×Dic₅₉	—	2	2	no	—
127	C₂×Dic₁₁₈	—	2	2	no	—
128	C₂×Dic₁₁₈	—	2	2	no	—
129	C₂×Dic₁₁₈	—	2	2	no	—
130	C₂×Dic₁₁₈	—	2	2	no	—
131	C₂×Dic₁₁₈	—	2	2	no	—
132	C₂×Dic₁₁₈	—	2	2	no	—
133	Q₁₆×C₅₉	—	2	2	no	—
134	SD₁₆×C₅₉	—	2	2	no	—
135	SD₁₆×C₅₉	—	2	2	no	—
136	D₈×C₅₉	—	2	2	no	—
137	M₁₆×C₅₉	—	2	1	no	—
138	M₁₆×C₅₉	—	2	1	no	—
139	M₁₆×C₅₉	—	2	2	no	—
140	M₁₆×C₅₉	—	2	2	no	—
141	M₁₆×C₅₉	—	2	1	no	—
142	M₁₆×C₅₉	—	2	1	no	—
143	M₁₆×C₅₉	—	4	1	no	—
144	M₁₆×C₅₉	—	4	1	no	—
145	M₁₆×C₅₉	C₂×D₄	1	2	yes	—
146	M₁₆×C₅₉	C₂×D₄	1	2	yes	—
147	C₂×C₈×C₅₉	—	2	1	no	—
148	C₂×C₈×C₅₉	—	2	1	no	—
149	C₂×C₈×C₅₉	—	2	2	no	—
150	C₂×C₈×C₅₉	—	2	2	no	—
151	C₂×C₈×C₅₉	—	2	1	no	—
152	C₂×C₈×C₅₉	—	4	1	no	—
153	C₂×C₈×C₅₉	—	4	1	no	—
154	C₂×C₈×C₅₉	C₂×D₄	1	1	yes	characteristic
155	C₂×C₈×C₅₉	C₂×D₄	1	1	yes	characteristic
156	C₂×C₈×C₅₉	C₂×D₄	1	1	yes	characteristic
157	C₂×C₈×C₅₉	C₂×D₄	1	1	yes	characteristic
158	C₂×C₈×C₅₉	#41	1	1	yes	characteristic
159	C₂×C₈×C₅₉	#41	1	1	yes	characteristic
160	C₄⋊C₄×C₅₉	—	2	1	no	—
161	C₂²⋊C₄×C₅₉	—	2	1	no	—
162	C₄²×C₅₉	—	2	1	no	—
163	#11745672	—	4	4	no	—
164	#11745672	—	4	4	no	—
165	#11745670	—	4	4	no	—
166	#11745670	—	4	4	no	—
167	#11745664	—	2	2	no	—
168	#11745664	—	2	2	no	—
169	#11745664	—	2	2	no	—
170	#11745664	—	2	2	no	—
171	#11745664	—	2	2	no	—
172	#11745664	—	4	4	no	—
173	#11745664	C₂×D₄	1	4	yes	—
174	C₂×C₅₉⋊C₈	—	2	2	no	—
175	C₂×C₅₉⋊C₈	—	2	2	no	—
176	C₂×C₅₉⋊C₈	—	2	2	no	—
177	C₂×C₅₉⋊C₈	—	4	4	no	—
178	Dic₂₃₆	—	4	1	no	—
179	Dic₂₃₆	—	4	1	no	—
180	Dic₂₃₆	—	4	1	no	—
181	Dic₂₃₆	—	4	1	no	—
182	C₂³×C₅₉	—	2	1	no	—
183	C₂³×C₅₉	—	2	1	no	—
184	C₂³×C₅₉	2₋¹⁺⁴	1	1	yes	characteristic
185	Q₈×C₅₉	—	2	1	no	—
186	Q₈×C₅₉	—	2	1	no	—
187	Q₈×C₅₉	—	2	1	no	—
188	Q₈×C₅₉	#121	1	2	yes	—
189	D₄×C₅₉	—	2	2	no	—
190	D₄×C₅₉	—	2	2	no	—
191	D₄×C₅₉	—	2	1	no	—
192	D₄×C₅₉	—	2	1	no	—
193	D₄×C₅₉	—	2	1	no	—
194	D₄×C₅₉	—	4	1	no	—
195	D₄×C₅₉	—	4	1	no	—
196	D₄×C₅₉	#121	1	2	yes	—
197	C₂×C₄×C₅₉	—	2	1	no	—
198	C₂×C₄×C₅₉	—	2	2	no	—
199	C₂×C₄×C₅₉	—	2	2	no	—
200	C₂×C₄×C₅₉	—	2	1	no	—
201	C₂×C₄×C₅₉	—	4	1	no	—
202	C₂×C₄×C₅₉	—	4	1	no	—
203	C₂×C₄×C₅₉	—	4	1	no	—
204	C₂×C₄×C₅₉	C₂²×D₄	1	1	yes	characteristic
205	C₂×C₄×C₅₉	C₂²×D₄	1	1	yes	characteristic
206	C₂×C₄×C₅₉	C₂²×D₄	1	1	yes	characteristic
207	C₂×C₄×C₅₉	C₂×#41	1	1	yes	characteristic
208	C₂×C₄×C₅₉	C₂×#41	1	1	yes	characteristic
209	C₂×C₄×C₅₉	H(5,𝔽₂)	1	1	yes	characteristic
210	C₂×Dic₅₉	—	4	2	no	—
211	C₂×Dic₅₉	—	4	2	no	—
212	C₂×Dic₅₉	—	4	2	no	—
213	Dic₁₁₈	—	4	2	no	—
214	Dic₁₁₈	—	4	2	no	—
215	Dic₁₁₈	—	4	2	no	—
216	Dic₁₁₈	—	4	2	no	—
217	C₈×C₅₉	—	2	2	no	—
218	C₈×C₅₉	—	2	2	no	—
219	C₈×C₅₉	—	4	1	no	—
220	C₈×C₅₉	#121	1	1	yes	characteristic
221	C₈×C₅₉	#121	1	1	yes	characteristic
222	C₈×C₅₉	#121	1	1	yes	characteristic
223	C₈×C₅₉	#121	1	1	yes	characteristic
224	C₅₉⋊C₈	—	2	4	no	—
225	C₅₉⋊C₈	—	4	2	no	—
226	C₅₉⋊C₈	—	4	2	no	—
227	#24810	—	59	1	no	maximal, Sylow
228	C₂²×C₅₉	—	2	2	no	—
229	C₂²×C₅₉	—	4	1	no	—
230	C₂²×C₅₉	—	4	1	no	—
231	C₂²×C₅₉	—	8	1	no	—
232	C₂²×C₅₉	—	8	1	no	—
233	C₂²×C₅₉	#537	1	1	yes	characteristic
234	C₂²×C₅₉	#547	1	1	yes	characteristic
235	C₂²×C₅₉	#548	1	1	yes	characteristic
236	C₄×C₅₉	—	2	2	no	—
237	C₄×C₅₉	—	4	1	no	—
238	C₄×C₅₉	—	8	1	no	—
239	C₄×C₅₉	C₂×#121	1	1	yes	characteristic
240	C₄×C₅₉	C₂×#121	1	1	yes	characteristic
241	C₄×C₅₉	D₄²	1	1	yes	characteristic
242	C₄×C₅₉	#553	1	1	yes	characteristic
243	Dic₅₉	—	8	2	no	—
244	#3069	—	59	2	no	—
245	C₂×#473	—	59	1	no	—
246	C₂×#473	—	59	1	no	—
247	#2955	D₅₉	1	1	yes	characteristic
248	#2916	—	59	1	no	—
249	#2070	—	59	2	no	—
250	#2049	—	59	2	no	—
251	#1979	—	59	1	no	—
252	#1953	—	59	1	no	—
253	#1902	—	59	2	no	—
254	#1813	—	59	1	no	—
255	C₂×C₅₉	—	2	1	no	—
256	C₂×C₅₉	—	2	1	no	—
257	C₂×C₅₉	—	2	1	no	—
258	C₂×C₅₉	—	4	2	no	—
259	C₂×C₅₉	—	8	1	no	—
260	C₂×C₅₉	#2416	1	1	yes	characteristic
261	#575	C₂×D₅₉	1	1	yes	characteristic
262	C₂×#137	—	59	2	no	—
263	C₂×#137	—	59	2	no	—
264	C₂²×Q₁₆	—	59	1	no	—
265	#568	—	59	2	no	—
266	C₂×#131	C₂×D₅₉	1	1	yes	characteristic
267	C₂×#131	C₂×D₅₉	1	1	yes	characteristic
268	#473	—	118	2	no	—
269	#473	—	118	2	no	—
270	#473	—	118	4	no	—
271	#473	—	118	2	no	—
272	#473	—	118	2	no	—
273	#471	—	118	4	no	—
274	#444	—	2	2	no	—
275	#443	—	2	2	no	—
276	#430	—	59	2	no	—
277	#430	—	59	2	no	—
278	#430	—	118	2	no	—
279	#430	C₂×D₅₉	1	1	yes	characteristic
280	C₂×#108	—	59	1	no	—
281	C₂×#108	—	59	1	no	—
282	C₂×#108	—	59	1	no	—
283	C₂×#108	—	118	2	no	—
284	#421	C₂×D₅₉	1	1	yes	characteristic
285	#421	C₂×D₅₉	1	1	yes	characteristic
286	#419	—	59	2	no	—
287	#413	—	59	2	no	—
288	C₂×#101	—	59	2	no	—
289	C₂×#101	—	59	2	no	—
290	C₂×#101	—	59	2	no	—
291	#405	C₂×D₅₉	1	1	yes	characteristic
292	#344	—	59	2	no	—
293	#338	—	59	2	no	—
294	C₅₉	#24810	1	1	yes	characteristic, complemented, Sylow
295	C₂×#41	C₂²×D₅₉	1	1	yes	characteristic
296	C₂×#41	C₂²×D₅₉	1	1	yes	characteristic
297	C₂²×Q₈	—	59	2	no	—
298	#137	—	2	1	no	—
299	#137	—	118	4	no	—
300	#137	—	118	4	no	—
301	#137	—	118	4	no	—
302	#137	—	236	2	no	—
303	#137	D₂₃₆	1	2	yes	—
304	AGL(1,ℤ/8)	—	2	1	no	—
305	AGL(1,ℤ/8)	D₂₃₆	1	2	yes	—
306	#135	—	2	2	no	—
307	C₂×Q₁₆	—	118	2	no	—
308	C₂×Q₁₆	—	118	2	no	—
309	C₂×Q₁₆	—	118	1	no	—
310	C₂×Q₁₆	—	118	1	no	—
311	C₂×Q₁₆	—	118	1	no	—
312	C₂×Q₁₆	—	118	1	no	—
313	C₂×Q₁₆	—	118	1	no	—
314	C₂×Q₁₆	—	118	1	no	—
315	C₂×SD₁₆	—	118	2	no	—
316	C₂×SD₁₆	—	118	2	no	—
317	#131	—	2	1	no	—
318	#131	—	2	1	no	—
319	#131	—	2	1	no	—
320	#131	—	2	1	no	—
321	#131	—	2	1	no	—
322	#131	—	2	1	no	—
323	#131	—	118	4	no	—
324	#131	—	236	2	no	—
325	#131	C₂²⋊D₅₉	1	2	yes	—
326	#131	C₂²⋊D₅₉	1	2	yes	—
327	C₂×M₁₆	—	2	1	no	—
328	C₂×M₁₆	—	2	1	no	—
329	C₂×M₁₆	—	59	2	no	—
330	C₂×M₁₆	—	59	2	no	—
331	C₂×M₁₆	—	59	2	no	—
332	C₂×M₁₆	—	118	4	no	—
333	C₂×M₁₆	C₂²×D₅₉	1	1	yes	characteristic
334	C₂×M₁₆	C₂²×D₅₉	1	1	yes	characteristic
335	C₂×M₁₆	C₂²×D₅₉	1	1	yes	characteristic
336	C₂²×C₈	—	2	1	no	—
337	C₂²×C₈	—	2	1	no	—
338	C₂²×C₈	C₂²×D₅₉	1	1	yes	characteristic
339	#117	C₂²×D₅₉	1	1	yes	characteristic
340	#108	—	2	2	no	—
341	#108	—	59	2	no	—
342	#108	—	59	2	no	—
343	#108	—	118	4	no	—
344	#108	—	118	4	no	—
345	#108	—	118	1	no	—
346	#108	—	118	1	no	—
347	#108	—	118	1	no	—
348	#108	—	118	1	no	—
349	#104	—	2	2	no	—
350	#104	—	2	2	no	—
351	#103	—	236	2	no	—
352	#101	—	118	4	no	—
353	#101	—	118	2	no	—
354	#101	—	118	4	no	—
355	#101	—	118	4	no	—
356	#100	—	118	2	no	—
357	#97	—	2	1	no	—
358	C₄×C₈	—	2	1	no	—
359	#41	—	2	1	no	—
360	#41	—	2	1	no	—
361	#41	—	2	1	no	—
362	#41	—	2	1	no	—
363	#41	—	2	1	no	—
364	#41	—	2	1	no	—
365	#41	C₂×D₂₃₆	1	2	yes	—
366	#41	C₂×C₂²⋊D₅₉	1	2	yes	—
367	C₂×Q₈	—	118	2	no	—
368	C₂×Q₈	—	118	2	no	—
369	C₂×Q₈	—	118	2	no	—
370	C₂×Q₈	—	118	2	no	—
371	C₂×Q₈	—	118	2	no	—
372	C₂×Q₈	—	118	2	no	—
373	C₂×Q₈	C₂×D₂₃₆	1	1	yes	characteristic
374	C₂×Q₈	#11745685	1	1	yes	characteristic
375	C₂×D₄	—	2	1	no	—
376	C₂×D₄	—	2	1	no	—
377	C₂×D₄	C₂×D₂₃₆	1	1	yes	characteristic
378	C₂×D₄	#11745685	1	1	yes	characteristic
379	C₂²×C₄	—	2	1	no	—
380	C₂²×C₄	—	2	1	no	—
381	C₂²×C₄	—	118	2	no	—
382	C₂²×C₄	C₂³×D₅₉	1	1	yes	characteristic
383	Q₁₆	—	2	2	no	—
384	Q₁₆	—	236	4	no	—
385	Q₁₆	—	236	4	no	—
386	Q₁₆	—	236	1	no	—
387	Q₁₆	—	236	1	no	—
388	Q₁₆	—	236	1	no	—
389	Q₁₆	—	236	1	no	—
390	SD₁₆	—	2	2	no	—
391	SD₁₆	—	2	2	no	—
392	SD₁₆	—	236	4	no	—
393	SD₁₆	—	236	4	no	—
394	D₈	—	2	2	no	—
395	M₁₆	—	2	1	no	—
396	M₁₆	—	2	1	no	—
397	M₁₆	—	2	2	no	—
398	M₁₆	—	2	2	no	—
399	M₁₆	—	2	1	no	—
400	M₁₆	—	2	1	no	—
401	M₁₆	—	4	1	no	—
402	M₁₆	—	4	1	no	—
403	M₁₆	—	59	4	no	—
404	M₁₆	—	118	2	no	—
405	M₁₆	—	118	2	no	—
406	M₁₆	—	118	2	no	—
407	M₁₆	—	118	2	no	—
408	M₁₆	—	118	2	no	—
409	M₁₆	—	236	4	no	—
410	M₁₆	C₂×D₂₃₆	1	2	yes	—
411	M₁₆	C₂×C₂²⋊D₅₉	1	2	yes	—
412	C₂×C₈	—	2	1	no	—
413	C₂×C₈	—	2	1	no	—
414	C₂×C₈	—	2	2	no	—
415	C₂×C₈	—	2	2	no	—
416	C₂×C₈	—	2	1	no	—
417	C₂×C₈	—	4	1	no	—
418	C₂×C₈	—	4	1	no	—
419	C₂×C₈	—	118	2	no	—
420	C₂×C₈	—	118	2	no	—
421	C₂×C₈	—	118	2	no	—
422	C₂×C₈	—	236	4	no	—
423	C₂×C₈	D₄×D₅₉	1	1	yes	characteristic
424	C₂×C₈	D₄×D₅₉	1	1	yes	characteristic
425	C₂×C₈	#11745687	1	1	yes	characteristic
426	C₂×C₈	#11745687	1	1	yes	characteristic
427	C₂×C₈	C₂×C₂²⋊D₅₉	1	1	yes	characteristic
428	C₂×C₈	C₂×C₂²⋊D₅₉	1	1	yes	characteristic
429	C₄⋊C₄	—	2	1	no	—
430	C₂²⋊C₄	—	2	1	no	—
431	C₄²	—	2	1	no	—
432	C₂³	—	2	1	no	—
433	C₂³	—	2	1	no	—
434	C₂³	#14273774	1	1	yes	characteristic
435	Q₈	—	2	1	no	—
436	Q₈	—	2	1	no	—
437	Q₈	—	2	1	no	—
438	Q₈	—	236	2	no	—
439	Q₈	—	236	2	no	—
440	Q₈	—	236	2	no	—
441	Q₈	—	236	2	no	—
442	Q₈	#14273701	1	2	yes	—
443	D₄	—	2	2	no	—
444	D₄	—	2	2	no	—
445	D₄	—	2	1	no	—
446	D₄	—	2	1	no	—
447	D₄	—	2	1	no	—
448	D₄	—	4	1	no	—
449	D₄	—	4	1	no	—
450	D₄	#14273701	1	2	yes	—
451	C₂×C₄	—	2	1	no	—
452	C₂×C₄	—	2	2	no	—
453	C₂×C₄	—	2	2	no	—
454	C₂×C₄	—	2	1	no	—
455	C₂×C₄	—	4	1	no	—
456	C₂×C₄	—	4	1	no	—
457	C₂×C₄	—	4	1	no	—
458	C₂×C₄	—	236	2	no	—
459	C₂×C₄	—	236	2	no	—
460	C₂×C₄	—	236	2	no	—
461	C₂×C₄	C₂×D₄×D₅₉	1	1	yes	characteristic
462	C₂×C₄	C₂²×C₂²⋊D₅₉	1	1	yes	characteristic
463	C₂×C₄	C₂²×D₂₃₆	1	1	yes	characteristic
464	C₂×C₄	C₂×#11745687	1	1	yes	characteristic
465	C₂×C₄	C₂×#11745685	1	1	yes	characteristic
466	C₂×C₄	#14273773	1	1	yes	characteristic
467	C₈	—	2	2	no	—
468	C₈	—	2	2	no	—
469	C₈	—	4	1	no	—
470	C₈	—	118	4	no	—
471	C₈	—	236	2	no	—
472	C₈	—	236	2	no	—
473	C₈	#14273699	1	1	yes	characteristic
474	C₈	#14273699	1	1	yes	characteristic
475	C₈	#14273699	1	1	yes	characteristic
476	C₈	#14273699	1	1	yes	characteristic
477	C₂²	—	2	2	no	—
478	C₂²	—	4	1	no	—
479	C₂²	—	4	1	no	—
480	C₂²	—	8	1	no	—
481	C₂²	—	8	1	no	—
482	C₂²	#16837980	1	1	yes	characteristic
483	C₂²	#16838056	1	1	yes	characteristic
484	C₂²	#16838061	1	1	yes	characteristic
485	C₄	—	2	2	no	—
486	C₄	—	4	1	no	—
487	C₄	—	8	1	no	—
488	C₄	—	472	2	no	—
489	C₄	C₂×#14273699	1	1	yes	characteristic
490	C₄	C₂×#14273701	1	1	yes	characteristic
491	C₄	D₄×D₂₃₆	1	1	yes	characteristic
492	C₄	#16838098	1	1	yes	characteristic
493	C₂	—	2	1	no	—
494	C₂	—	2	1	no	—
495	C₂	—	2	1	no	—
496	C₂	—	4	2	no	—
497	C₂	—	8	1	no	—
498	C₂	#21427536	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#21427536
commutator, cosocle	C₂²×C₄×C₅₉	C₂⁴
Frattini	C₂²×C₄	C₂³×D₅₉
Fitting	C₅₉×#2955	C₂
socle	C₂×C₅₉	#2416
prime radical	C₅₉×#575	C₂²
hypercenter	#2955	D₅₉
hypocenter	C₅₉	#24810
LCS	G ▷ C₂²×C₄×C₅₉ ▷ C₂×C₅₉ ▷ C₅₉
UCS	C₁ ◁ C₂ ◁ C₂²×C₄ ◁ #2955

Complements

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

N	H ≅ G/N	type
2. C₂×#16837677	C₂	semidirect
3. C₂×#16837677	C₂	semidirect
4. #21432707	C₂	semidirect
5. #21425496	C₂	semidirect
6. #21425377	C₂	semidirect
7. #21425011	C₂	semidirect
8. #21424886	C₂	semidirect
9. #21424567	C₂	semidirect
10. #21424146	C₂	semidirect
294. C₅₉	#24810	semidirect

Maximal subgroups

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

subgroup	index
#21433835	2
C₂×#16837677	2
#21432707	2
#21425496	2
#21425377	2
#21425011	2
#21424886	2
#21424567	2
#21424146	2
C₅₉×#2955	2
#24810	59