Subgroups — #28607216

Order 15104.

808 conjugacy classes of subgroups.

The subgroup lattice has 456 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#21433011	C₂	1	2	yes	maximal
2	C₂×#16837522	C₂	1	1	yes	maximal, characteristic
3	#21432704	C₂	1	1	yes	maximal, characteristic, complemented
4	#21424883	C₂	1	2	yes	maximal, complemented
5	#21424336	C₂	1	2	yes	maximal, complemented
6	#21424333	C₂	1	2	yes	maximal, complemented
7	#21424269	C₂	1	1	yes	maximal, characteristic, complemented
8	#21424151	C₂	1	1	yes	maximal, characteristic, complemented
9	#21424150	C₂	1	1	yes	maximal, characteristic, complemented
10	#21423983	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅₉×#2916	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#14273747	C₂²	1	1	yes	characteristic
13	#16838168	C₂²	1	2	yes	—
14	C₂×#14273733	C₂²	1	1	yes	characteristic
15	#16837522	—	2	4	no	—
16	#16837522	C₄	1	4	yes	complemented
17	#16837522	C₄	1	4	yes	complemented
18	#16837517	—	2	4	no	—
19	#16837450	C₂²	1	2	yes	—
20	#16837449	—	2	2	no	—
21	C₂×#14273663	C₂²	1	1	yes	characteristic
22	C₂×#14273662	C₂²	1	2	yes	—
23	C₂×#14273662	C₂²	1	1	yes	characteristic
24	#108×D₅₉	—	2	2	no	—
25	#16837440	C₂²	1	1	yes	characteristic
26	#16837425	C₂²	1	2	yes	—
27	#16837419	C₂²	1	2	yes	—
28	#16837418	C₂²	1	2	yes	—
29	C₂×#14273654	C₂²	1	1	yes	characteristic
30	C₂×#14273653	C₂²	1	1	yes	characteristic
31	#16837360	C₂²	1	2	yes	—
32	C₂×#14273637	C₂²	1	1	yes	characteristic
33	#16837174	C₂²	1	2	yes	—
34	#16837173	C₂²	1	2	yes	—
35	#16837163	C₂²	1	2	yes	—
36	C₅₉×#568	C₂²	1	2	yes	—
37	C₂×#131×C₅₉	C₂²	1	1	yes	characteristic
38	C₅₉×#430	—	2	2	no	—
39	C₅₉×#430	C₂²	1	2	yes	—
40	C₂×#108×C₅₉	—	2	2	no	—
41	C₂×#108×C₅₉	C₂²	1	1	yes	characteristic
42	C₂×#108×C₅₉	C₂²	1	1	yes	characteristic
43	C₂×#11745685	C₂³	1	1	yes	characteristic
44	#14273747	C₂×C₄	1	4	yes	—
45	#14273747	D₄	1	4	yes	—
46	C₂×#11745672	Q₈	1	1	yes	characteristic
47	C₂×#11745670	Q₈	1	1	yes	characteristic
48	C₂×#11745671	Q₈	1	1	yes	characteristic
49	C₂×#11745669	Q₈	1	1	yes	characteristic
50	#14273735	—	4	2	no	—
51	#14273733	—	2	1	no	—
52	#14273733	—	2	1	no	—
53	#14273733	—	2	4	no	—
54	#14273733	C₂×C₄	1	2	yes	—
55	#14273733	C₂×C₄	1	2	yes	—
56	C₂×#11745664	C₂³	1	2	yes	—
57	C₂×#11745664	C₂³	1	1	yes	characteristic
58	C₂×#11745659	—	2	1	no	—
59	M₁₆×D₅₉	—	2	4	no	—
60	C₂²×C₅₉⋊C₈	C₂³	1	1	yes	characteristic
61	C₂×C₈×D₅₉	—	2	1	no	—
62	#14273686	C₂³	1	2	yes	—
63	C₂×C₄×Dic₅₉	C₂³	1	1	yes	characteristic
64	#14273663	—	2	1	no	—
65	#14273663	—	2	1	no	—
66	#14273662	—	2	4	no	—
67	#14273662	—	2	2	no	—
68	#14273662	—	2	2	no	—
69	#14273662	C₂×C₄	1	4	yes	—
70	#14273661	—	2	1	no	—
71	#14273659	—	2	1	no	—
72	Dic₅₉⋊C₈	—	4	2	no	—
73	#14273654	—	2	4	no	—
74	#14273654	C₂×C₄	1	4	yes	—
75	#14273653	—	2	4	no	—
76	#14273653	C₂×C₄	1	4	yes	—
77	#14273637	—	2	2	no	—
78	#14273637	C₂×C₄	1	2	yes	—
79	#14273637	C₂×C₄	1	2	yes	—
80	C₈×Dic₅₉	—	2	2	no	—
81	C₂×#41×C₅₉	C₂³	1	1	yes	characteristic
82	#131×C₅₉	—	2	1	no	—
83	#131×C₅₉	—	2	1	no	—
84	#131×C₅₉	—	2	4	no	—
85	#131×C₅₉	—	4	2	no	—
86	#131×C₅₉	C₂×C₄	1	2	yes	—
87	#131×C₅₉	C₂×C₄	1	2	yes	—
88	C₂×M₁₆×C₅₉	—	2	1	no	—
89	C₂×M₁₆×C₅₉	—	2	4	no	—
90	C₂×M₁₆×C₅₉	C₂³	1	2	yes	—
91	C₂×M₁₆×C₅₉	C₂³	1	1	yes	characteristic
92	C₂×M₁₆×C₅₉	C₂³	1	2	yes	—
93	C₂²×C₈×C₅₉	—	2	1	no	—
94	C₂²×C₈×C₅₉	C₂³	1	1	yes	characteristic
95	#108×C₅₉	—	2	4	no	—
96	#108×C₅₉	—	2	1	no	—
97	#108×C₅₉	—	2	1	no	—
98	#108×C₅₉	D₄	1	2	yes	—
99	#108×C₅₉	D₄	1	2	yes	—
100	#41×C₅₉	—	2	1	no	—
101	#41×C₅₉	—	2	1	no	—
102	#41×C₅₉	C₂²×C₄	1	2	yes	—
103	#41×C₅₉	C₂×D₄	1	2	yes	—
104	C₂×Q₈×C₅₉	C₂×Q₈	1	1	yes	characteristic
105	C₂×D₄×C₅₉	—	2	1	no	—
106	C₂×D₄×C₅₉	C₂×Q₈	1	1	yes	characteristic
107	C₂²×C₄×C₅₉	—	2	1	no	—
108	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
109	C₂×C₂²⋊D₅₉	—	2	1	no	—
110	C₂²×Dic₅₉	—	2	1	no	—
111	#11745685	—	2	1	no	—
112	#11745685	—	2	1	no	—
113	#11745685	C₂²×C₄	1	2	yes	—
114	#11745685	C₂×D₄	1	2	yes	—
115	C₂×D₂₃₆	C₂×Q₈	1	1	yes	characteristic
116	C₂×C₄×D₅₉	—	2	1	no	—
117	C₂×Dic₁₁₈	C₂×Q₈	1	1	yes	characteristic
118	M₁₆×C₅₉	—	2	1	no	—
119	M₁₆×C₅₉	—	2	2	no	—
120	M₁₆×C₅₉	—	2	2	no	—
121	M₁₆×C₅₉	—	2	2	no	—
122	M₁₆×C₅₉	—	2	2	no	—
123	M₁₆×C₅₉	—	2	2	no	—
124	M₁₆×C₅₉	—	4	4	no	—
125	M₁₆×C₅₉	C₂²×C₄	1	2	yes	—
126	M₁₆×C₅₉	C₂×D₄	1	4	yes	—
127	C₂×C₈×C₅₉	—	2	1	no	—
128	C₂×C₈×C₅₉	—	2	2	no	—
129	C₂×C₈×C₅₉	—	2	2	no	—
130	C₂×C₈×C₅₉	—	2	2	no	—
131	C₂×C₈×C₅₉	—	2	2	no	—
132	C₂×C₈×C₅₉	—	4	4	no	—
133	C₂×C₈×C₅₉	C₂²×C₄	1	1	yes	characteristic
134	C₂×C₈×C₅₉	C₂²×C₄	1	1	yes	characteristic
135	C₂×C₈×C₅₉	C₂×D₄	1	1	yes	characteristic
136	C₂×C₈×C₅₉	C₂×D₄	1	1	yes	characteristic
137	C₂×C₈×C₅₉	#41	1	1	yes	characteristic
138	C₂×C₈×C₅₉	#41	1	1	yes	characteristic
139	C₂²⋊Dic₅₉	—	2	2	no	—
140	#11745672	C₄⋊C₄	1	4	yes	—
141	#11745671	C₄⋊C₄	1	4	yes	—
142	#11745670	C₄⋊C₄	1	4	yes	—
143	#11745669	C₄⋊C₄	1	4	yes	—
144	C₄⋊Dic₅₉	—	2	2	no	—
145	C₄×Dic₅₉	—	2	1	no	—
146	C₄×Dic₅₉	—	2	2	no	—
147	C₄×Dic₅₉	C₂²×C₄	1	2	yes	—
148	#11745664	—	2	1	no	—
149	#11745664	—	2	2	no	—
150	#11745664	—	2	2	no	—
151	#11745664	C₂²×C₄	1	2	yes	—
152	C₂×C₅₉⋊C₈	—	2	1	no	—
153	C₂×C₅₉⋊C₈	—	2	2	no	—
154	C₂×C₅₉⋊C₈	C₂²×C₄	1	2	yes	—
155	C₂×C₅₉⋊C₈	C₂×D₄	1	2	yes	—
156	C₂×C₅₉⋊C₈	C₂×Q₈	1	1	yes	characteristic
157	C₂×C₅₉⋊C₈	C₂×Q₈	1	1	yes	characteristic
158	#11745659	—	2	2	no	—
159	#11745659	—	2	2	no	—
160	#11745659	—	4	4	no	—
161	C₈×D₅₉	—	2	2	no	—
162	C₈×D₅₉	—	2	2	no	—
163	C₈×D₅₉	—	4	4	no	—
164	C₂³×C₅₉	—	2	1	no	—
165	C₂³×C₅₉	2₋¹⁺⁴	1	1	yes	characteristic
166	C₂²×D₅₉	—	2	1	no	—
167	Q₈×C₅₉	—	2	1	no	—
168	Q₈×C₅₉	C₂×C₄⋊C₄	1	2	yes	—
169	D₄×C₅₉	—	2	2	no	—
170	D₄×C₅₉	—	2	2	no	—
171	D₄×C₅₉	—	2	1	no	—
172	D₄×C₅₉	C₂×C₄⋊C₄	1	2	yes	—
173	C₂×C₄×C₅₉	—	2	1	no	—
174	C₂×C₄×C₅₉	—	2	2	no	—
175	C₂×C₄×C₅₉	—	2	2	no	—
176	C₂×C₄×C₅₉	C₂³×C₄	1	1	yes	characteristic
177	C₂×C₄×C₅₉	C₂²×D₄	1	1	yes	characteristic
178	C₂×C₄×C₅₉	C₂²×D₄	1	1	yes	characteristic
179	C₂×C₄×C₅₉	C₂²×Q₈	1	1	yes	characteristic
180	C₂×C₄×C₅₉	C₂×#41	1	1	yes	characteristic
181	C₂×C₄×C₅₉	H(5,𝔽₂)	1	1	yes	characteristic
182	C₂²⋊D₅₉	—	2	2	no	—
183	C₂²⋊D₅₉	—	2	2	no	—
184	C₂×Dic₅₉	—	2	1	no	—
185	C₂×Dic₅₉	—	2	2	no	—
186	C₂×Dic₅₉	—	4	2	no	—
187	C₂×Dic₅₉	—	8	1	no	—
188	D₂₃₆	—	2	1	no	—
189	D₂₃₆	C₂×C₄⋊C₄	1	2	yes	—
190	C₄×D₅₉	—	2	2	no	—
191	C₄×D₅₉	—	2	2	no	—
192	Dic₁₁₈	—	2	1	no	—
193	Dic₁₁₈	C₂×C₄⋊C₄	1	2	yes	—
194	C₈×C₅₉	—	2	2	no	—
195	C₈×C₅₉	—	2	4	no	—
196	C₈×C₅₉	—	4	2	no	—
197	C₈×C₅₉	C₄×D₄	1	1	yes	characteristic
198	C₈×C₅₉	C₄×D₄	1	1	yes	characteristic
199	C₈×C₅₉	C₄×D₄	1	1	yes	characteristic
200	C₈×C₅₉	C₄×D₄	1	1	yes	characteristic
201	C₅₉⋊C₈	—	2	2	no	—
202	C₅₉⋊C₈	—	4	2	no	—
203	C₅₉⋊C₈	C₂×C₄⋊C₄	1	2	yes	—
204	C₅₉⋊C₈	C₂×C₄⋊C₄	1	2	yes	—
205	#22695	—	59	1	no	maximal, Sylow
206	C₂²×C₅₉	—	2	2	no	—
207	C₂²×C₅₉	—	4	1	no	—
208	C₂²×C₅₉	—	8	1	no	—
209	C₂²×C₅₉	#520	1	1	yes	characteristic
210	C₂²×C₅₉	#547	1	1	yes	characteristic
211	C₂²×C₅₉	D₄×Q₈	1	1	yes	characteristic
212	C₂×D₅₉	—	2	2	no	—
213	C₂×D₅₉	—	8	1	no	—
214	C₄×C₅₉	—	2	2	no	—
215	C₄×C₅₉	C₂²×C₄⋊C₄	1	1	yes	characteristic
216	C₄×C₅₉	C₂×C₄×D₄	1	1	yes	characteristic
217	C₄×C₅₉	D₄²	1	1	yes	characteristic
218	C₄×C₅₉	#554	1	1	yes	characteristic
219	Dic₅₉	—	2	2	no	—
220	Dic₅₉	—	4	2	no	—
221	Dic₅₉	—	8	2	no	—
222	#2957	—	59	2	no	—
223	C₂×#444	—	59	1	no	—
224	#2916	—	59	1	no	—
225	#2916	D₅₉	1	1	yes	characteristic, complemented
226	#1953	—	59	2	no	—
227	#1861	—	59	2	no	—
228	#1861	—	59	2	no	—
229	#1849	—	59	1	no	—
230	#1814	—	59	1	no	—
231	#1814	—	59	1	no	—
232	#1773	—	59	1	no	—
233	C₂×C₅₉	—	2	1	no	—
234	C₂×C₅₉	—	2	1	no	—
235	C₂×C₅₉	—	2	1	no	—
236	C₂×C₅₉	—	4	2	no	—
237	C₂×C₅₉	D₄×C₄⋊C₄	1	1	yes	characteristic
238	D₅₉	—	4	2	no	—
239	C₂×#135	—	59	1	no	—
240	#568	—	59	2	no	—
241	#568	C₂×D₅₉	1	2	yes	—
242	C₂×#131	—	59	1	no	—
243	C₂×#131	C₂×D₅₉	1	1	yes	characteristic
244	#444	—	59	4	no	—
245	#444	—	59	4	no	—
246	#444	—	118	4	no	—
247	#443	—	118	4	no	—
248	#430	—	2	2	no	—
249	#430	—	59	2	no	—
250	#430	—	118	2	no	—
251	#430	C₂×D₅₉	1	2	yes	—
252	C₂×#108	—	2	2	no	—
253	C₂×#108	—	59	1	no	—
254	C₂×#108	—	59	2	no	—
255	C₂×#108	—	59	1	no	—
256	C₂×#108	—	118	2	no	—
257	C₂×#108	C₂×D₅₉	1	1	yes	characteristic
258	C₂×#108	C₂×D₅₉	1	1	yes	characteristic
259	#427	—	59	1	no	—
260	#423	—	59	2	no	—
261	#421	—	59	2	no	—
262	#421	—	59	2	no	—
263	C₂×#104	—	59	1	no	—
264	C₂×#104	—	59	1	no	—
265	#405	—	59	2	no	—
266	C₂×#97	—	59	1	no	—
267	#344	—	59	2	no	—
268	#344	—	59	2	no	—
269	#339	—	59	2	no	—
270	C₅₉	#22695	1	1	yes	characteristic, complemented, Sylow
271	C₂×#41	—	59	1	no	—
272	C₂×#41	C₂²×D₅₉	1	1	yes	characteristic
273	#135	—	59	4	no	—
274	#135	—	59	4	no	—
275	C₂×Q₁₆	—	59	1	no	—
276	C₂×SD₁₆	—	59	1	no	—
277	C₂×SD₁₆	—	59	1	no	—
278	C₂×D₈	—	59	1	no	—
279	#131	—	2	1	no	—
280	#131	—	2	1	no	—
281	#131	—	2	4	no	—
282	#131	—	4	2	no	—
283	#131	—	59	2	no	—
284	#131	—	59	2	no	—
285	#131	—	118	4	no	—
286	#131	—	118	1	no	—
287	#131	—	118	1	no	—
288	#131	—	236	2	no	—
289	#131	C₄×D₅₉	1	2	yes	—
290	#131	C₄×D₅₉	1	2	yes	—
291	C₂×M₁₆	—	2	1	no	—
292	C₂×M₁₆	—	2	4	no	—
293	C₂×M₁₆	—	59	1	no	—
294	C₂×M₁₆	—	59	2	no	—
295	C₂×M₁₆	—	118	1	no	—
296	C₂×M₁₆	—	118	4	no	—
297	C₂×M₁₆	C₂²×D₅₉	1	2	yes	—
298	C₂×M₁₆	C₂²×D₅₉	1	1	yes	characteristic
299	C₂×M₁₆	C₂²×D₅₉	1	2	yes	—
300	C₂²×C₈	—	2	1	no	—
301	C₂²×C₈	—	59	1	no	—
302	C₂²×C₈	—	118	1	no	—
303	C₂²×C₈	C₂²×D₅₉	1	1	yes	characteristic
304	#117	—	59	2	no	—
305	C₂×C₄²	—	59	1	no	—
306	#108	—	2	4	no	—
307	#108	—	2	1	no	—
308	#108	—	2	1	no	—
309	#108	—	59	4	no	—
310	#108	—	118	2	no	—
311	#108	—	118	2	no	—
312	#108	—	118	4	no	—
313	#108	—	118	1	no	—
314	#108	—	118	1	no	—
315	#108	C₂²⋊D₅₉	1	2	yes	—
316	#108	C₂²⋊D₅₉	1	2	yes	—
317	#107	—	118	1	no	—
318	#106	—	118	1	no	—
319	C₄⋊C₈	—	236	2	no	—
320	#104	—	59	4	no	—
321	#104	—	59	4	no	—
322	#104	—	118	4	no	—
323	#104	—	118	4	no	—
324	#97	—	59	2	no	—
325	#97	—	59	2	no	—
326	#97	—	118	2	no	—
327	C₄×C₈	—	118	2	no	—
328	#41	—	2	1	no	—
329	#41	—	2	1	no	—
330	#41	—	59	2	no	—
331	#41	—	59	2	no	—
332	#41	—	118	1	no	—
333	#41	—	118	1	no	—
334	#41	C₂×C₄×D₅₉	1	2	yes	—
335	#41	D₄×D₅₉	1	2	yes	—
336	C₂×Q₈	—	59	1	no	—
337	C₂×Q₈	Q₈×D₅₉	1	1	yes	characteristic
338	C₂×D₄	—	2	1	no	—
339	C₂×D₄	—	59	1	no	—
340	C₂×D₄	—	118	1	no	—
341	C₂×D₄	Q₈×D₅₉	1	1	yes	characteristic
342	C₂²×C₄	—	2	1	no	—
343	C₂²×C₄	—	118	1	no	—
344	C₂²×C₄	—	118	1	no	—
345	C₂²×C₄	C₂³×D₅₉	1	1	yes	characteristic
346	Q₁₆	—	59	4	no	—
347	SD₁₆	—	59	4	no	—
348	SD₁₆	—	59	4	no	—
349	D₈	—	59	4	no	—
350	M₁₆	—	2	1	no	—
351	M₁₆	—	2	2	no	—
352	M₁₆	—	2	2	no	—
353	M₁₆	—	2	2	no	—
354	M₁₆	—	2	2	no	—
355	M₁₆	—	2	2	no	—
356	M₁₆	—	4	4	no	—
357	M₁₆	—	59	2	no	—
358	M₁₆	—	118	1	no	—
359	M₁₆	—	118	2	no	—
360	M₁₆	—	118	2	no	—
361	M₁₆	—	118	2	no	—
362	M₁₆	—	118	2	no	—
363	M₁₆	—	236	4	no	—
364	M₁₆	C₂×C₄×D₅₉	1	2	yes	—
365	M₁₆	C₂×C₂²⋊D₅₉	1	4	yes	—
366	C₂×C₈	—	2	2	no	—
367	C₂×C₈	—	2	1	no	—
368	C₂×C₈	—	2	2	no	—
369	C₂×C₈	—	2	2	no	—
370	C₂×C₈	—	2	2	no	—
371	C₂×C₈	—	4	4	no	—
372	C₂×C₈	—	59	2	no	—
373	C₂×C₈	—	59	2	no	—
374	C₂×C₈	—	59	1	no	—
375	C₂×C₈	—	59	1	no	—
376	C₂×C₈	—	118	1	no	—
377	C₂×C₈	—	118	2	no	—
378	C₂×C₈	—	118	2	no	—
379	C₂×C₈	—	118	2	no	—
380	C₂×C₈	—	236	4	no	—
381	C₂×C₈	C₂×C₄×D₅₉	1	1	yes	characteristic
382	C₂×C₈	C₂×C₄×D₅₉	1	1	yes	characteristic
383	C₂×C₈	#11745685	1	1	yes	characteristic
384	C₂×C₈	#11745685	1	1	yes	characteristic
385	C₂×C₈	C₂×C₂²⋊D₅₉	1	1	yes	characteristic
386	C₂×C₈	C₂×C₂²⋊D₅₉	1	1	yes	characteristic
387	C₄⋊C₄	—	118	2	no	—
388	C₂²⋊C₄	—	118	2	no	—
389	C₄²	—	59	2	no	—
390	C₄²	—	118	1	no	—
391	C₄²	—	118	2	no	—
392	C₂³	—	2	1	no	—
393	C₂³	—	118	1	no	—
394	C₂³	#14273775	1	1	yes	characteristic
395	Q₈	—	2	1	no	—
396	Q₈	—	59	2	no	—
397	Q₈	—	118	1	no	—
398	Q₈	C₄⋊C₄×D₅₉	1	2	yes	—
399	D₄	—	2	2	no	—
400	D₄	—	2	2	no	—
401	D₄	—	2	1	no	—
402	D₄	—	59	2	no	—
403	D₄	—	118	2	no	—
404	D₄	—	118	2	no	—
405	D₄	—	118	1	no	—
406	D₄	C₄⋊C₄×D₅₉	1	2	yes	—
407	C₂×C₄	—	2	1	no	—
408	C₂×C₄	—	2	2	no	—
409	C₂×C₄	—	2	2	no	—
410	C₂×C₄	—	118	1	no	—
411	C₂×C₄	—	118	2	no	—
412	C₂×C₄	—	118	2	no	—
413	C₂×C₄	—	118	2	no	—
414	C₂×C₄	—	472	1	no	—
415	C₂×C₄	—	236	2	no	—
416	C₂×C₄	C₂²×C₄×D₅₉	1	1	yes	characteristic
417	C₂×C₄	C₂×D₄×D₅₉	1	1	yes	characteristic
418	C₂×C₄	C₂²×C₂²⋊D₅₉	1	1	yes	characteristic
419	C₂×C₄	C₂×Q₈×D₅₉	1	1	yes	characteristic
420	C₂×C₄	C₂×#11745685	1	1	yes	characteristic
421	C₂×C₄	#14273772	1	1	yes	characteristic
422	C₈	—	2	4	no	—
423	C₈	—	2	2	no	—
424	C₈	—	4	2	no	—
425	C₈	—	59	2	no	—
426	C₈	—	59	2	no	—
427	C₈	—	118	2	no	—
428	C₈	—	236	2	no	—
429	C₈	C₄×C₂²⋊D₅₉	1	1	yes	characteristic
430	C₈	C₄×C₂²⋊D₅₉	1	1	yes	characteristic
431	C₈	C₄×C₂²⋊D₅₉	1	1	yes	characteristic
432	C₈	C₄×C₂²⋊D₅₉	1	1	yes	characteristic
433	C₂²	—	2	2	no	—
434	C₂²	—	4	1	no	—
435	C₂²	—	8	1	no	—
436	C₂²	—	118	2	no	—
437	C₂²	—	472	1	no	—
438	C₂²	#16837883	1	1	yes	characteristic
439	C₂²	#16838053	1	1	yes	characteristic
440	C₂²	Q₈×C₂²⋊D₅₉	1	1	yes	characteristic
441	C₄	—	2	2	no	—
442	C₄	—	118	2	no	—
443	C₄	—	472	2	no	—
444	C₄	—	236	2	no	—
445	C₄	C₂×C₄⋊C₄×D₅₉	1	1	yes	characteristic
446	C₄	C₂×C₄×C₂²⋊D₅₉	1	1	yes	characteristic
447	C₄	D₄×C₂²⋊D₅₉	1	1	yes	characteristic
448	C₄	#16838107	1	1	yes	characteristic
449	C₂	—	2	1	no	—
450	C₂	—	2	1	no	—
451	C₂	—	2	1	no	—
452	C₂	—	4	2	no	—
453	C₂	—	236	2	no	—
454	C₂	C₄⋊C₄×C₂²⋊D₅₉	1	1	yes	characteristic

	subgroup	G/H
center	C₄	D₄×C₂²⋊D₅₉
commutator	C₂×C₄×C₅₉	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₅₉
Fitting	C₅₉×#2916	C₂
socle	C₂×C₅₉	D₄×C₄⋊C₄
prime radical	C₂×#14273747	C₂²
cosocle	C₂²×C₄×C₅₉	C₂⁴
hypercenter	#2916	D₅₉
hypocenter	C₅₉	#22695
LCS	G ▷ C₂×C₄×C₅₉ ▷ C₂×C₅₉ ▷ C₅₉
UCS	C₁ ◁ C₄ ◁ C₂²×C₄ ◁ #2916

Complements

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

N	H ≅ G/N	type
3. #21432704	C₂	semidirect
4. #21424883	C₂	semidirect
5. #21424336	C₂	semidirect
6. #21424333	C₂	semidirect
7. #21424269	C₂	semidirect
8. #21424151	C₂	semidirect
9. #21424150	C₂	semidirect
10. #21423983	C₂	semidirect
11. C₅₉×#2916	C₂	semidirect
16. #16837522	C₄	semidirect
17. #16837522	C₄	semidirect
225. #2916	D₅₉	semidirect
270. C₅₉	#22695	semidirect

Maximal subgroups

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

subgroup	index
#21433011	2
C₂×#16837522	2
#21432704	2
#21424883	2
#21424336	2
#21424333	2
#21424269	2
#21424151	2
#21424150	2
#21423983	2
C₅₉×#2916	2
#22695	59