Subgroups — #28611559

Order 15104.

820 conjugacy classes of subgroups.

The subgroup lattice has 460 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#21433013	C₂	1	1	yes	maximal, characteristic, complemented
2	#21433006	C₂	1	2	yes	maximal, complemented
3	#21432707	C₂	1	1	yes	maximal, characteristic, complemented
4	#21424990	C₂	1	1	yes	maximal, characteristic, complemented
5	#21424887	C₂	1	1	yes	maximal, characteristic, complemented
6	#21424767	C₂	1	2	yes	maximal, complemented
7	#21424460	C₂	1	2	yes	maximal, complemented
8	#21424318	C₂	1	2	yes	maximal, complemented
9	#21424004	C₂	1	1	yes	maximal, characteristic, complemented
10	#21423938	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅₉×#3067	C₂	1	1	yes	maximal, characteristic
12	#16838169	C₂²	1	2	yes	—
13	#16838169	C₂²	1	2	yes	—
14	#16837524	—	2	2	no	—
15	#16837524	—	2	4	no	—
16	#16837519	—	2	2	no	—
17	#16837519	—	2	4	no	—
18	#16837451	—	2	2	no	—
19	#16837451	C₂²	1	2	yes	—
20	#16837451	C₂²	1	2	yes	—
21	C₂×#14273663	—	2	2	no	—
22	C₂×#14273663	C₂²	1	1	yes	characteristic
23	C₂×#14273663	C₂²	1	1	yes	characteristic
24	#16837419	C₂²	1	2	yes	—
25	C₂×#14273654	C₂²	1	2	yes	—
26	C₂×#14273654	C₂²	1	1	yes	characteristic
27	#16837398	C₂²	1	1	yes	characteristic
28	#16837369	C₂²	1	2	yes	—
29	#16837357	C₂²	1	1	yes	characteristic
30	M₁₆×Dic₅₉	C₂²	1	2	yes	—
31	C₂×#14273637	C₂²	1	1	yes	characteristic
32	#16837174	C₂²	1	2	yes	—
33	#16837166	C₂²	1	1	yes	characteristic
34	#16837166	C₂²	1	2	yes	—
35	#16837163	C₂²	1	1	yes	characteristic
36	C₅₉×#575	C₂²	1	2	yes	—
37	C₂×#135×C₅₉	C₂²	1	1	yes	characteristic
38	C₂×#131×C₅₉	C₂²	1	1	yes	characteristic
39	C₅₉×#473	C₄	1	2	yes	complemented
40	C₅₉×#472	C₄	1	2	yes	complemented
41	C₅₉×#471	C₄	1	4	yes	complemented
42	C₂×#108×C₅₉	C₂²	1	1	yes	characteristic
43	C₅₉×#413	C₂²	1	2	yes	—
44	#14273734	—	2	4	no	—
45	#14273734	—	2	4	no	—
46	#14273734	—	2	4	no	—
47	#14273734	—	4	2	no	—
48	C₂×#11745664	—	2	4	no	—
49	C₂×#11745664	—	4	2	no	—
50	C₂×#11745664	C₂³	1	2	yes	—
51	C₂×#11745664	C₂³	1	1	yes	characteristic
52	C₂×#11745664	C₂³	1	2	yes	—
53	C₂²×C₅₉⋊C₈	C₂³	1	1	yes	characteristic
54	#14273686	C₂³	1	1	yes	characteristic
55	C₂×C₄×Dic₅₉	C₂³	1	1	yes	characteristic
56	#14273663	—	2	1	no	—
57	#14273663	—	2	1	no	—
58	#14273663	—	2	4	no	—
59	#14273663	—	2	4	no	—
60	#14273663	D₄	1	2	yes	—
61	#14273663	D₄	1	2	yes	—
62	#14273654	—	2	2	no	—
63	#14273654	—	2	2	no	—
64	#14273654	—	2	4	no	—
65	#14273654	D₄	1	4	yes	—
66	#14273651	—	2	1	no	—
67	#14273648	—	2	1	no	—
68	C₂²⋊(C₅₉⋊C₈)	—	4	2	no	—
69	#14273637	—	2	1	no	—
70	#14273637	—	2	1	no	—
71	#14273637	—	2	1	no	—
72	#14273637	—	2	2	no	—
73	C₈×Dic₅₉	—	2	1	no	—
74	C₈×Dic₅₉	—	2	2	no	—
75	C₂×#41×C₅₉	C₂³	1	2	yes	—
76	C₂×#41×C₅₉	C₂³	1	1	yes	characteristic
77	#137×C₅₉	—	2	2	no	—
78	#137×C₅₉	C₂×C₄	1	4	yes	—
79	AGL(1,ℤ/8)×C₅₉	—	2	2	no	—
80	AGL(1,ℤ/8)×C₅₉	C₂×C₄	1	4	yes	—
81	#135×C₅₉	—	2	4	no	—
82	#135×C₅₉	—	2	1	no	—
83	#135×C₅₉	—	2	1	no	—
84	#135×C₅₉	—	2	1	no	—
85	#135×C₅₉	—	2	1	no	—
86	C₂×Q₁₆×C₅₉	C₂×C₄	1	1	yes	characteristic
87	C₂×SD₁₆×C₅₉	C₂×C₄	1	2	yes	—
88	C₂×D₈×C₅₉	C₂×C₄	1	1	yes	characteristic
89	#131×C₅₉	—	2	1	no	—
90	#131×C₅₉	—	2	1	no	—
91	#131×C₅₉	C₂×C₄	1	2	yes	—
92	#131×C₅₉	C₂×C₄	1	2	yes	—
93	C₂×M₁₆×C₅₉	—	2	1	no	—
94	C₂×M₁₆×C₅₉	C₂³	1	1	yes	characteristic
95	C₂×M₁₆×C₅₉	C₂³	1	2	yes	—
96	C₂²×C₈×C₅₉	—	2	1	no	—
97	C₂²×C₈×C₅₉	C₂³	1	1	yes	characteristic
98	#108×C₅₉	C₂×C₄	1	2	yes	—
99	#108×C₅₉	C₂×C₄	1	2	yes	—
100	#101×C₅₉	C₂×C₄	1	4	yes	—
101	#100×C₅₉	C₂×C₄	1	4	yes	—
102	#41×C₅₉	—	2	1	no	—
103	#41×C₅₉	—	2	1	no	—
104	#41×C₅₉	—	2	2	no	—
105	#41×C₅₉	—	2	2	no	—
106	#41×C₅₉	—	2	2	no	—
107	#41×C₅₉	—	2	2	no	—
108	#41×C₅₉	C₂²×C₄	1	2	yes	—
109	#41×C₅₉	C₂×D₄	1	2	yes	—
110	C₂×Q₈×C₅₉	C₂²×C₄	1	2	yes	—
111	C₂×Q₈×C₅₉	#41	1	1	yes	characteristic
112	C₂×D₄×C₅₉	—	2	1	no	—
113	C₂×D₄×C₅₉	—	2	2	no	—
114	C₂×D₄×C₅₉	C₂²×C₄	1	2	yes	—
115	C₂×D₄×C₅₉	#41	1	1	yes	characteristic
116	C₂²×C₄×C₅₉	—	2	1	no	—
117	C₂²×C₄×C₅₉	—	2	2	no	—
118	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
119	C₂²×Dic₅₉	—	2	1	no	—
120	Q₁₆×C₅₉	—	2	4	no	—
121	Q₁₆×C₅₉	—	2	1	no	—
122	Q₁₆×C₅₉	—	2	1	no	—
123	SD₁₆×C₅₉	—	2	4	no	—
124	SD₁₆×C₅₉	—	2	4	no	—
125	SD₁₆×C₅₉	—	2	2	no	—
126	SD₁₆×C₅₉	—	2	2	no	—
127	D₈×C₅₉	—	2	4	no	—
128	D₈×C₅₉	—	2	1	no	—
129	D₈×C₅₉	—	2	1	no	—
130	M₁₆×C₅₉	—	2	1	no	—
131	M₁₆×C₅₉	—	2	2	no	—
132	M₁₆×C₅₉	—	2	2	no	—
133	M₁₆×C₅₉	—	2	2	no	—
134	M₁₆×C₅₉	C₂²×C₄	1	2	yes	—
135	M₁₆×C₅₉	C₂²×C₄	1	4	yes	—
136	C₂×C₈×C₅₉	—	2	1	no	—
137	C₂×C₈×C₅₉	—	2	2	no	—
138	C₂×C₈×C₅₉	—	2	2	no	—
139	C₂×C₈×C₅₉	—	2	2	no	—
140	C₂×C₈×C₅₉	C₂²×C₄	1	1	yes	characteristic
141	C₂×C₈×C₅₉	C₂²×C₄	1	1	yes	characteristic
142	C₂×C₈×C₅₉	C₂×D₄	1	1	yes	characteristic
143	C₂×C₈×C₅₉	C₂×D₄	1	1	yes	characteristic
144	C₂×C₈×C₅₉	#41	1	1	yes	characteristic
145	C₂×C₈×C₅₉	#41	1	1	yes	characteristic
146	C₂²⋊Dic₅₉	—	2	1	no	—
147	C₄⋊Dic₅₉	—	2	1	no	—
148	C₄×Dic₅₉	—	2	1	no	—
149	C₄×Dic₅₉	—	2	1	no	—
150	C₄×Dic₅₉	C₂×D₄	1	2	yes	—
151	#11745664	—	2	1	no	—
152	#11745664	—	2	2	no	—
153	#11745664	—	2	2	no	—
154	#11745664	—	2	2	no	—
155	#11745664	—	4	4	no	—
156	#11745664	—	4	4	no	—
157	#11745664	C₂×D₄	1	4	yes	—
158	#11745664	C₂×D₄	1	2	yes	—
159	C₂×C₅₉⋊C₈	—	2	2	no	—
160	C₂×C₅₉⋊C₈	—	2	1	no	—
161	C₂×C₅₉⋊C₈	—	2	1	no	—
162	C₂×C₅₉⋊C₈	—	2	1	no	—
163	C₂×C₅₉⋊C₈	—	2	1	no	—
164	C₂×C₅₉⋊C₈	—	2	2	no	—
165	C₂×C₅₉⋊C₈	—	4	4	no	—
166	C₂×C₅₉⋊C₈	—	4	4	no	—
167	C₂³×C₅₉	—	2	1	no	—
168	C₂³×C₅₉	—	2	2	no	—
169	C₂³×C₅₉	2₋¹⁺⁴	1	1	yes	characteristic
170	Q₈×C₅₉	—	2	1	no	—
171	Q₈×C₅₉	—	2	2	no	—
172	Q₈×C₅₉	—	2	2	no	—
173	Q₈×C₅₉	C₄×D₄	1	2	yes	—
174	D₄×C₅₉	—	2	2	no	—
175	D₄×C₅₉	—	2	2	no	—
176	D₄×C₅₉	—	2	2	no	—
177	D₄×C₅₉	—	2	2	no	—
178	D₄×C₅₉	—	2	1	no	—
179	D₄×C₅₉	—	4	2	no	—
180	D₄×C₅₉	—	4	2	no	—
181	D₄×C₅₉	C₄×D₄	1	2	yes	—
182	C₂×C₄×C₅₉	—	2	1	no	—
183	C₂×C₄×C₅₉	—	2	2	no	—
184	C₂×C₄×C₅₉	—	2	2	no	—
185	C₂×C₄×C₅₉	—	2	2	no	—
186	C₂×C₄×C₅₉	—	4	2	no	—
187	C₂×C₄×C₅₉	—	4	2	no	—
188	C₂×C₄×C₅₉	C₂³×C₄	1	1	yes	characteristic
189	C₂×C₄×C₅₉	C₂²×D₄	1	1	yes	characteristic
190	C₂×C₄×C₅₉	C₂²×D₄	1	1	yes	characteristic
191	C₂×C₄×C₅₉	C₂×#41	1	1	yes	characteristic
192	C₂×C₄×C₅₉	C₂×#41	1	1	yes	characteristic
193	C₂×C₄×C₅₉	H(5,𝔽₂)	1	1	yes	characteristic
194	C₂×Dic₅₉	—	2	2	no	—
195	C₂×Dic₅₉	—	4	1	no	—
196	C₂×Dic₅₉	—	8	1	no	—
197	C₈×C₅₉	—	2	2	no	—
198	C₈×C₅₉	—	2	4	no	—
199	C₈×C₅₉	C₄×D₄	1	1	yes	characteristic
200	C₈×C₅₉	C₄×D₄	1	1	yes	characteristic
201	C₈×C₅₉	C₄×D₄	1	1	yes	characteristic
202	C₈×C₅₉	C₄×D₄	1	1	yes	characteristic
203	C₅₉⋊C₈	—	2	2	no	—
204	C₅₉⋊C₈	—	2	4	no	—
205	C₅₉⋊C₈	—	4	2	no	—
206	C₅₉⋊C₈	—	4	1	no	—
207	#23043	—	59	1	no	maximal, Sylow
208	C₂²×C₅₉	—	2	2	no	—
209	C₂²×C₅₉	—	4	1	no	—
210	C₂²×C₅₉	—	4	2	no	—
211	C₂²×C₅₉	—	8	1	no	—
212	C₂²×C₅₉	—	8	2	no	—
213	C₂²×C₅₉	#520	1	1	yes	characteristic
214	C₂²×C₅₉	#547	1	1	yes	characteristic
215	C₂²×C₅₉	#548	1	1	yes	characteristic
216	C₄×C₅₉	—	2	2	no	—
217	C₄×C₅₉	—	4	2	no	—
218	C₄×C₅₉	C₂×C₄×D₄	1	1	yes	characteristic
219	C₄×C₅₉	C₂×C₄×D₄	1	1	yes	characteristic
220	C₄×C₅₉	D₄²	1	1	yes	characteristic
221	C₄×C₅₉	#553	1	1	yes	characteristic
222	Dic₅₉	—	4	2	no	—
223	Dic₅₉	—	8	1	no	—
224	#3067	D₅₉	1	1	yes	characteristic
225	#2957	—	59	1	no	—
226	#2956	—	59	2	no	—
227	#2916	—	59	1	no	—
228	#1975	—	59	1	no	—
229	#1953	—	59	1	no	—
230	#1932	—	59	2	no	—
231	#1881	—	59	2	no	—
232	#1858	—	59	2	no	—
233	#1778	—	59	1	no	—
234	#1765	—	59	1	no	—
235	C₂×C₅₉	—	2	1	no	—
236	C₂×C₅₉	—	2	1	no	—
237	C₂×C₅₉	—	2	1	no	—
238	C₂×C₅₉	—	4	2	no	—
239	C₂×C₅₉	—	8	2	no	—
240	C₂×C₅₉	#2361	1	1	yes	characteristic
241	#575	C₂×D₅₉	1	2	yes	—
242	C₂×#135	C₂×D₅₉	1	1	yes	characteristic
243	#568	—	59	2	no	—
244	#568	—	59	2	no	—
245	C₂×#131	C₂×D₅₉	1	1	yes	characteristic
246	#473	Dic₅₉	1	2	yes	complemented
247	#472	Dic₅₉	1	2	yes	complemented
248	#471	Dic₅₉	1	4	yes	complemented
249	#444	—	118	4	no	—
250	#444	—	118	2	no	—
251	#443	—	118	4	no	—
252	#443	—	118	2	no	—
253	#430	—	59	2	no	—
254	#430	—	59	2	no	—
255	#430	—	118	2	no	—
256	C₂×#108	—	59	1	no	—
257	C₂×#108	—	59	1	no	—
258	C₂×#108	—	118	2	no	—
259	C₂×#108	C₂×D₅₉	1	1	yes	characteristic
260	#421	—	59	2	no	—
261	C₂×#104	—	59	1	no	—
262	C₂×#104	—	59	2	no	—
263	#416	—	59	1	no	—
264	#413	C₂×D₅₉	1	2	yes	—
265	#408	—	59	2	no	—
266	#405	—	59	1	no	—
267	C₄×M₁₆	—	59	2	no	—
268	C₂×#97	—	59	1	no	—
269	#344	—	59	2	no	—
270	#341	—	59	1	no	—
271	#341	—	59	2	no	—
272	#339	—	59	1	no	—
273	C₅₉	#23043	1	1	yes	characteristic, complemented, Sylow
274	C₂×#41	C₂²×D₅₉	1	1	yes	characteristic
275	C₂×#41	C₂²×D₅₉	1	2	yes	—
276	#137	—	2	2	no	—
277	#137	C₂×Dic₅₉	1	4	yes	—
278	AGL(1,ℤ/8)	—	2	2	no	—
279	AGL(1,ℤ/8)	C₂×Dic₅₉	1	4	yes	—
280	#135	—	2	4	no	—
281	#135	—	2	1	no	—
282	#135	—	2	1	no	—
283	#135	—	2	1	no	—
284	#135	—	2	1	no	—
285	C₂×Q₁₆	C₂×Dic₅₉	1	1	yes	characteristic
286	C₂×SD₁₆	C₂×Dic₅₉	1	2	yes	—
287	C₂×D₈	C₂×Dic₅₉	1	1	yes	characteristic
288	#131	—	2	1	no	—
289	#131	—	2	1	no	—
290	#131	—	118	4	no	—
291	#131	—	118	4	no	—
292	#131	—	118	4	no	—
293	#131	—	236	2	no	—
294	#131	C₂×Dic₅₉	1	2	yes	—
295	#131	C₂×Dic₅₉	1	2	yes	—
296	C₂×M₁₆	—	2	1	no	—
297	C₂×M₁₆	—	59	2	no	—
298	C₂×M₁₆	—	59	1	no	—
299	C₂×M₁₆	—	59	2	no	—
300	C₂×M₁₆	—	118	4	no	—
301	C₂×M₁₆	—	236	2	no	—
302	C₂×M₁₆	C₂²×D₅₉	1	1	yes	characteristic
303	C₂×M₁₆	C₂²×D₅₉	1	2	yes	—
304	C₂²×C₈	—	2	1	no	—
305	C₂²×C₈	—	59	1	no	—
306	C₂²×C₈	C₂²×D₅₉	1	1	yes	characteristic
307	#117	—	59	1	no	—
308	C₂×C₄²	—	59	1	no	—
309	#108	—	59	2	no	—
310	#108	—	59	2	no	—
311	#108	—	118	4	no	—
312	#108	—	118	4	no	—
313	#108	—	118	1	no	—
314	#108	—	118	1	no	—
315	#108	C₂×Dic₅₉	1	2	yes	—
316	#108	C₂×Dic₅₉	1	2	yes	—
317	#104	—	59	4	no	—
318	#104	—	118	2	no	—
319	#104	—	118	2	no	—
320	#104	—	118	4	no	—
321	#103	—	118	1	no	—
322	#102	—	118	1	no	—
323	#101	C₂×Dic₅₉	1	4	yes	—
324	#100	C₂×Dic₅₉	1	4	yes	—
325	C₂²⋊C₈	—	236	2	no	—
326	#97	—	118	2	no	—
327	#97	—	118	1	no	—
328	#97	—	118	1	no	—
329	#97	—	118	1	no	—
330	C₄×C₈	—	118	2	no	—
331	C₄×C₈	—	118	1	no	—
332	#41	—	2	1	no	—
333	#41	—	2	1	no	—
334	#41	—	2	2	no	—
335	#41	—	2	2	no	—
336	#41	—	2	2	no	—
337	#41	—	2	2	no	—
338	#41	D₄×D₅₉	1	2	yes	—
339	#41	C₂²×Dic₅₉	1	2	yes	—
340	C₂×Q₈	#11745687	1	1	yes	characteristic
341	C₂×Q₈	C₂²×Dic₅₉	1	2	yes	—
342	C₂×D₄	—	2	1	no	—
343	C₂×D₄	—	2	2	no	—
344	C₂×D₄	#11745687	1	1	yes	characteristic
345	C₂×D₄	C₂²×Dic₅₉	1	2	yes	—
346	C₂²×C₄	—	2	1	no	—
347	C₂²×C₄	—	2	2	no	—
348	C₂²×C₄	—	118	1	no	—
349	C₂²×C₄	C₂³×D₅₉	1	1	yes	characteristic
350	Q₁₆	—	2	4	no	—
351	Q₁₆	—	2	1	no	—
352	Q₁₆	—	2	1	no	—
353	SD₁₆	—	2	4	no	—
354	SD₁₆	—	2	4	no	—
355	SD₁₆	—	2	2	no	—
356	SD₁₆	—	2	2	no	—
357	D₈	—	2	4	no	—
358	D₈	—	2	1	no	—
359	D₈	—	2	1	no	—
360	M₁₆	—	2	1	no	—
361	M₁₆	—	2	2	no	—
362	M₁₆	—	2	2	no	—
363	M₁₆	—	2	2	no	—
364	M₁₆	—	59	2	no	—
365	M₁₆	—	59	4	no	—
366	M₁₆	—	118	1	no	—
367	M₁₆	—	118	2	no	—
368	M₁₆	—	118	2	no	—
369	M₁₆	—	118	2	no	—
370	M₁₆	—	236	4	no	—
371	M₁₆	—	236	4	no	—
372	M₁₆	C₂²×Dic₅₉	1	2	yes	—
373	M₁₆	C₂²×Dic₅₉	1	4	yes	—
374	C₂×C₈	—	2	2	no	—
375	C₂×C₈	—	2	1	no	—
376	C₂×C₈	—	2	2	no	—
377	C₂×C₈	—	2	2	no	—
378	C₂×C₈	—	118	2	no	—
379	C₂×C₈	—	118	1	no	—
380	C₂×C₈	—	118	1	no	—
381	C₂×C₈	—	118	1	no	—
382	C₂×C₈	—	118	1	no	—
383	C₂×C₈	—	118	2	no	—
384	C₂×C₈	—	236	4	no	—
385	C₂×C₈	—	236	4	no	—
386	C₂×C₈	D₄×D₅₉	1	1	yes	characteristic
387	C₂×C₈	D₄×D₅₉	1	1	yes	characteristic
388	C₂×C₈	#11745687	1	1	yes	characteristic
389	C₂×C₈	#11745687	1	1	yes	characteristic
390	C₂×C₈	C₂²×Dic₅₉	1	1	yes	characteristic
391	C₂×C₈	C₂²×Dic₅₉	1	1	yes	characteristic
392	C₄⋊C₄	—	118	1	no	—
393	C₂²⋊C₄	—	118	1	no	—
394	C₄²	—	59	2	no	—
395	C₄²	—	118	1	no	—
396	C₄²	—	118	1	no	—
397	C₂³	—	2	1	no	—
398	C₂³	—	2	2	no	—
399	C₂³	#14273774	1	1	yes	characteristic
400	Q₈	—	2	1	no	—
401	Q₈	—	2	2	no	—
402	Q₈	—	2	2	no	—
403	Q₈	D₄×Dic₅₉	1	2	yes	—
404	D₄	—	2	2	no	—
405	D₄	—	2	2	no	—
406	D₄	—	2	1	no	—
407	D₄	—	2	2	no	—
408	D₄	—	2	2	no	—
409	D₄	—	4	2	no	—
410	D₄	—	4	2	no	—
411	D₄	D₄×Dic₅₉	1	2	yes	—
412	C₂×C₄	—	2	1	no	—
413	C₂×C₄	—	2	2	no	—
414	C₂×C₄	—	2	2	no	—
415	C₂×C₄	—	2	2	no	—
416	C₂×C₄	—	4	2	no	—
417	C₂×C₄	—	4	2	no	—
418	C₂×C₄	—	118	2	no	—
419	C₂×C₄	—	472	1	no	—
420	C₂×C₄	—	236	1	no	—
421	C₂×C₄	C₂³×Dic₅₉	1	1	yes	characteristic
422	C₂×C₄	C₂×D₄×D₅₉	1	1	yes	characteristic
423	C₂×C₄	C₂×D₄×D₅₉	1	1	yes	characteristic
424	C₂×C₄	C₂×#11745687	1	1	yes	characteristic
425	C₂×C₄	C₂×#11745687	1	1	yes	characteristic
426	C₂×C₄	#14273773	1	1	yes	characteristic
427	C₈	—	2	2	no	—
428	C₈	—	2	4	no	—
429	C₈	—	118	2	no	—
430	C₈	—	118	4	no	—
431	C₈	—	236	2	no	—
432	C₈	—	236	1	no	—
433	C₈	D₄×Dic₅₉	1	1	yes	characteristic
434	C₈	D₄×Dic₅₉	1	1	yes	characteristic
435	C₈	D₄×Dic₅₉	1	1	yes	characteristic
436	C₈	D₄×Dic₅₉	1	1	yes	characteristic
437	C₂²	—	2	2	no	—
438	C₂²	—	4	1	no	—
439	C₂²	—	4	2	no	—
440	C₂²	—	8	1	no	—
441	C₂²	—	8	2	no	—
442	C₂²	#16837885	1	1	yes	characteristic
443	C₂²	#16838052	1	1	yes	characteristic
444	C₂²	#16838058	1	1	yes	characteristic
445	C₄	—	2	2	no	—
446	C₄	—	4	2	no	—
447	C₄	—	472	1	no	—
448	C₄	—	236	2	no	—
449	C₄	C₂×D₄×Dic₅₉	1	1	yes	characteristic
450	C₄	C₂×D₄×Dic₅₉	1	1	yes	characteristic
451	C₄	#16838036	1	1	yes	characteristic
452	C₄	#16838104	1	1	yes	characteristic
453	C₂	—	2	1	no	—
454	C₂	—	2	1	no	—
455	C₂	—	2	1	no	—
456	C₂	—	4	2	no	—
457	C₂	—	8	2	no	—
458	C₂	#21427116	1	1	yes	characteristic

	subgroup	G/H
center	C₄	#16838036
commutator	C₂×C₄×C₅₉	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₅₉
Fitting, prime radical	C₅₉×#3067	C₂
socle	C₂×C₅₉	#2361
cosocle	C₂²×C₄×C₅₉	C₂⁴
hypercenter	#3067	D₅₉
hypocenter	C₅₉	#23043
LCS	G ▷ C₂×C₄×C₅₉ ▷ C₂×C₅₉ ▷ C₅₉
UCS	C₁ ◁ C₄ ◁ C₂²×C₄ ◁ #3067

Complements

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

N	H ≅ G/N	type
1. #21433013	C₂	semidirect
2. #21433006	C₂	semidirect
3. #21432707	C₂	semidirect
4. #21424990	C₂	semidirect
5. #21424887	C₂	semidirect
6. #21424767	C₂	semidirect
7. #21424460	C₂	semidirect
8. #21424318	C₂	semidirect
9. #21424004	C₂	semidirect
10. #21423938	C₂	semidirect
39. C₅₉×#473	C₄	semidirect
40. C₅₉×#472	C₄	semidirect
41. C₅₉×#471	C₄	semidirect
246. #473	Dic₅₉	semidirect
247. #472	Dic₅₉	semidirect
248. #471	Dic₅₉	semidirect
273. C₅₉	#23043	semidirect

Maximal subgroups

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

subgroup	index
#21433013	2
#21433006	2
#21432707	2
#21424990	2
#21424887	2
#21424767	2
#21424460	2
#21424318	2
#21424004	2
#21423938	2
C₅₉×#3067	2
#23043	59