Subgroups — #28608141

Order 15104.

740 conjugacy classes of subgroups.

The subgroup lattice has 562 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×#14273747	C₂	1	1	yes	maximal, characteristic
2	#21432661	C₂	1	1	yes	maximal, characteristic, complemented
3	#21424810	C₂	1	2	yes	maximal, complemented
4	#21424695	C₂	1	2	yes	maximal, complemented
5	#21424426	C₂	1	2	yes	maximal
6	#21424233	C₂	1	1	yes	maximal, characteristic, complemented
7	#21424116	C₂	1	1	yes	maximal, characteristic, complemented
8	#21424113	C₂	1	1	yes	maximal, characteristic, complemented
9	#21423966	C₂	1	1	yes	maximal, characteristic, complemented
10	#21423942	C₂	1	2	yes	maximal, complemented
11	C₅₉×#2925	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#14273747	C₂²	1	1	yes	characteristic
13	C₂×#14273733	C₂²	1	2	yes	—
14	C₄×#11745685	C₂²	1	1	yes	characteristic
15	C₄×#11745672	C₄	1	1	yes	characteristic, complemented
16	C₄×#11745672	C₄	1	1	yes	characteristic, complemented
17	C₄×#11745671	C₄	1	1	yes	characteristic, complemented
18	C₄×#11745671	C₄	1	1	yes	characteristic, complemented
19	C₄×#11745670	C₄	1	1	yes	characteristic, complemented
20	C₄×#11745670	C₄	1	1	yes	characteristic, complemented
21	C₄×#11745669	C₄	1	1	yes	characteristic, complemented
22	C₄×#11745669	C₄	1	1	yes	characteristic, complemented
23	#16837438	C₂²	1	1	yes	characteristic
24	#16837428	C₂²	1	2	yes	—
25	#16837427	—	2	2	no	—
26	#16837426	C₂²	1	1	yes	characteristic
27	#16837424	—	2	1	no	—
28	C₄⋊C₈×D₅₉	—	2	1	no	—
29	C₂×#14273654	C₂²	1	2	yes	—
30	C₂×#14273653	C₂²	1	2	yes	—
31	#16837398	C₂²	1	1	yes	characteristic
32	#16837396	C₂²	1	1	yes	characteristic
33	C₂×#14273637	C₂²	1	2	yes	—
34	C₂×C₄×C₅₉⋊C₈	C₂²	1	1	yes	characteristic
35	C₄×C₄⋊Dic₅₉	C₂²	1	1	yes	characteristic
36	#16837166	C₂²	1	2	yes	—
37	#16837166	C₂²	1	2	yes	—
38	#16837163	C₂²	1	2	yes	—
39	#16837161	C₂²	1	2	yes	—
40	#16837156	C₂²	1	2	yes	—
41	C₄×#41×C₅₉	C₂²	1	1	yes	characteristic
42	C₅₉×#433	—	2	2	no	—
43	C₅₉×#432	—	2	1	no	—
44	C₅₉×#431	—	2	1	no	—
45	C₅₉×#423	C₂²	1	1	yes	characteristic
46	C₂×C₄⋊C₈×C₅₉	C₂²	1	1	yes	characteristic
47	C₅₉×#408	C₂²	1	2	yes	—
48	C₅₉×#405	C₂²	1	2	yes	—
49	C₂×#11745685	C₂³	1	1	yes	characteristic
50	#14273747	—	2	2	no	—
51	#14273747	—	2	2	no	—
52	C₂×#11745672	C₂×C₄	1	1	yes	characteristic
53	C₂×#11745670	C₂×C₄	1	1	yes	characteristic
54	C₂×#11745671	C₂×C₄	1	1	yes	characteristic
55	C₂×#11745669	C₂×C₄	1	1	yes	characteristic
56	#14273733	—	2	4	no	—
57	#14273733	—	4	2	no	—
58	C₂×#11745664	C₂³	1	2	yes	—
59	C₂×#11745659	—	2	2	no	—
60	C₂²×C₅₉⋊C₈	C₂³	1	1	yes	characteristic
61	C₂²×C₅₉⋊C₈	C₂³	1	1	yes	characteristic
62	C₂×C₈×D₅₉	—	2	2	no	—
63	C₄×Dic₁₁₈	C₂×C₄	1	1	yes	characteristic
64	C₄×Dic₁₁₈	C₂×C₄	1	1	yes	characteristic
65	C₄×D₂₃₆	C₂×C₄	1	1	yes	characteristic
66	C₄×D₂₃₆	C₂×C₄	1	1	yes	characteristic
67	C₄×C₂²⋊D₅₉	—	2	1	no	—
68	C₄×C₂²⋊D₅₉	—	2	1	no	—
69	#14273686	C₂³	1	1	yes	characteristic
70	#14273684	—	2	1	no	—
71	C₂×C₄⋊Dic₅₉	—	2	1	no	—
72	C₂×C₄×Dic₅₉	C₂³	1	2	yes	—
73	C₄²×D₅₉	—	2	1	no	—
74	#14273660	C₂×C₄	1	1	yes	characteristic
75	#14273660	C₂×C₄	1	1	yes	characteristic
76	#14273658	C₂×C₄	1	1	yes	characteristic
77	#14273658	C₂×C₄	1	1	yes	characteristic
78	C₄⋊(C₅₉⋊C₈)	—	2	1	no	—
79	C₄⋊(C₅₉⋊C₈)	—	2	1	no	—
80	Dic₅₉⋊C₈	—	2	2	no	—
81	Dic₅₉⋊C₈	—	2	2	no	—
82	#14273654	—	4	2	no	—
83	#14273653	—	2	4	no	—
84	#14273651	C₂×C₄	1	1	yes	characteristic
85	#14273651	C₂×C₄	1	1	yes	characteristic
86	#14273650	C₂×C₄	1	1	yes	characteristic
87	#14273650	C₂×C₄	1	1	yes	characteristic
88	#14273648	C₂×C₄	1	1	yes	characteristic
89	#14273648	C₂×C₄	1	1	yes	characteristic
90	#14273647	C₂×C₄	1	1	yes	characteristic
91	#14273647	C₂×C₄	1	1	yes	characteristic
92	#14273637	—	4	2	no	—
93	C₄×C₅₉⋊C₈	C₂×C₄	1	1	yes	characteristic
94	C₄×C₅₉⋊C₈	C₂×C₄	1	1	yes	characteristic
95	C₄×C₅₉⋊C₈	C₂×C₄	1	1	yes	characteristic
96	C₄×C₅₉⋊C₈	C₂×C₄	1	1	yes	characteristic
97	C₅₉⋊#95	—	2	1	no	—
98	C₂×#41×C₅₉	C₂³	1	1	yes	characteristic
99	C₂×M₁₆×C₅₉	C₂³	1	2	yes	—
100	C₂²×C₈×C₅₉	C₂³	1	2	yes	—
101	C₄×Q₈×C₅₉	C₂×C₄	1	1	yes	characteristic
102	C₄×Q₈×C₅₉	C₂×C₄	1	1	yes	characteristic
103	C₄×D₄×C₅₉	—	2	1	no	—
104	C₄×D₄×C₅₉	—	2	1	no	—
105	C₄×D₄×C₅₉	C₂×C₄	1	1	yes	characteristic
106	C₄×D₄×C₅₉	C₂×C₄	1	1	yes	characteristic
107	#117×C₅₉	—	2	1	no	—
108	#117×C₅₉	C₂³	1	1	yes	characteristic
109	C₂×C₄²×C₅₉	—	2	1	no	—
110	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
111	C₄⋊C₈×C₅₉	—	2	1	no	—
112	C₄⋊C₈×C₅₉	—	2	1	no	—
113	C₄⋊C₈×C₅₉	D₄	1	1	yes	characteristic
114	C₄⋊C₈×C₅₉	D₄	1	1	yes	characteristic
115	C₄⋊C₈×C₅₉	D₄	1	2	yes	—
116	C₂²⋊C₈×C₅₉	—	2	2	no	—
117	C₂²⋊C₈×C₅₉	—	2	2	no	—
118	#97×C₅₉	—	2	2	no	—
119	C₄×C₈×C₅₉	—	2	2	no	—
120	#41×C₅₉	—	2	1	no	—
121	#41×C₅₉	—	2	1	no	—
122	#41×C₅₉	—	2	1	no	—
123	#41×C₅₉	—	2	1	no	—
124	C₂×Q₈×C₅₉	C₂²×C₄	1	1	yes	characteristic
125	C₂×D₄×C₅₉	—	2	1	no	—
126	C₂×D₄×C₅₉	C₂²×C₄	1	1	yes	characteristic
127	C₂²×C₄×C₅₉	—	2	1	no	—
128	C₂²×C₄×C₅₉	—	2	1	no	—
129	C₂²×C₄×C₅₉	—	2	1	no	—
130	C₂²×C₄×C₅₉	#41	1	1	yes	characteristic
131	C₂²×C₄×C₅₉	#41	1	1	yes	characteristic
132	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
133	C₂×C₂²⋊D₅₉	—	2	1	no	—
134	C₂²×Dic₅₉	—	2	2	no	—
135	#11745685	—	2	1	no	—
136	#11745685	—	2	1	no	—
137	#11745685	#41	1	2	yes	—
138	#11745685	#41	1	2	yes	—
139	C₂×D₂₃₆	C₂²×C₄	1	1	yes	characteristic
140	C₂×C₄×D₅₉	—	2	1	no	—
141	C₂×C₄×D₅₉	—	2	1	no	—
142	C₂×C₄×D₅₉	—	2	1	no	—
143	C₂×Dic₁₁₈	C₂²×C₄	1	1	yes	characteristic
144	M₁₆×C₅₉	—	2	2	no	—
145	M₁₆×C₅₉	—	2	2	no	—
146	C₂×C₈×C₅₉	—	2	2	no	—
147	C₂×C₈×C₅₉	—	2	2	no	—
148	C₂×C₈×C₅₉	—	2	2	no	—
149	C₂×C₈×C₅₉	C₂×D₄	1	2	yes	—
150	C₂×C₈×C₅₉	C₂×D₄	1	2	yes	—
151	C₄⋊C₄×C₅₉	—	2	1	no	—
152	C₄⋊C₄×C₅₉	—	2	1	no	—
153	C₄⋊C₄×C₅₉	C₂²×C₄	1	1	yes	characteristic
154	C₄⋊C₄×C₅₉	C₂²×C₄	1	1	yes	characteristic
155	C₂²⋊C₄×C₅₉	—	2	1	no	—
156	C₂²⋊C₄×C₅₉	—	2	1	no	—
157	C₂²⋊C₄×C₅₉	—	2	1	no	—
158	C₄²×C₅₉	—	2	1	no	—
159	C₄²×C₅₉	—	2	1	no	—
160	C₄²×C₅₉	—	2	1	no	—
161	C₄²×C₅₉	C₂²×C₄	1	1	yes	characteristic
162	C₄²×C₅₉	C₂²×C₄	1	1	yes	characteristic
163	C₄²×C₅₉	C₂×D₄	1	1	yes	characteristic
164	C₄²×C₅₉	C₂×D₄	1	1	yes	characteristic
165	C₂²⋊Dic₅₉	—	2	1	no	—
166	#11745672	—	2	2	no	—
167	#11745671	—	2	2	no	—
168	#11745670	—	2	2	no	—
169	#11745669	—	2	2	no	—
170	(C₂×D₅₉)⋊C₄	—	2	1	no	—
171	(C₂×D₅₉)⋊C₄	—	2	1	no	—
172	C₄⋊Dic₅₉	—	4	2	no	—
173	C₄⋊Dic₅₉	C₂²×C₄	1	1	yes	characteristic
174	C₄⋊Dic₅₉	C₂²×C₄	1	1	yes	characteristic
175	Dic₅₉⋊C₄	—	2	1	no	—
176	Dic₅₉⋊C₄	—	2	1	no	—
177	C₄×Dic₅₉	—	2	1	no	—
178	C₄×Dic₅₉	—	2	1	no	—
179	C₄×Dic₅₉	—	2	1	no	—
180	C₄×Dic₅₉	—	2	2	no	—
181	C₄×Dic₅₉	—	2	2	no	—
182	#11745664	—	2	2	no	—
183	#11745664	—	2	2	no	—
184	C₂×C₅₉⋊C₈	—	2	1	no	—
185	C₂×C₅₉⋊C₈	—	2	1	no	—
186	C₂×C₅₉⋊C₈	—	2	1	no	—
187	C₂×C₅₉⋊C₈	—	2	1	no	—
188	C₂×C₅₉⋊C₈	—	2	2	no	—
189	C₂×C₅₉⋊C₈	C₂²×C₄	1	1	yes	characteristic
190	C₂×C₅₉⋊C₈	C₂²×C₄	1	1	yes	characteristic
191	C₂×C₅₉⋊C₈	C₂²×C₄	1	1	yes	characteristic
192	C₂×C₅₉⋊C₈	C₂²×C₄	1	1	yes	characteristic
193	#11745659	—	4	4	no	—
194	C₈×D₅₉	—	4	4	no	—
195	C₂³×C₅₉	—	2	1	no	—
196	C₂³×C₅₉	C₂×#41	1	1	yes	characteristic
197	C₂²×D₅₉	—	2	1	no	—
198	Q₈×C₅₉	—	2	1	no	—
199	Q₈×C₅₉	—	2	1	no	—
200	D₄×C₅₉	—	2	1	no	—
201	D₄×C₅₉	—	2	1	no	—
202	D₄×C₅₉	—	4	1	no	—
203	D₄×C₅₉	—	4	1	no	—
204	C₂×C₄×C₅₉	—	2	2	no	—
205	C₂×C₄×C₅₉	—	2	1	no	—
206	C₂×C₄×C₅₉	—	2	1	no	—
207	C₂×C₄×C₅₉	—	2	1	no	—
208	C₂×C₄×C₅₉	—	4	1	no	—
209	C₂×C₄×C₅₉	—	4	1	no	—
210	C₂×C₄×C₅₉	—	4	1	no	—
211	C₂×C₄×C₅₉	—	4	2	no	—
212	C₂×C₄×C₅₉	—	8	1	no	—
213	C₂×C₄×C₅₉	C₄×D₄	1	1	yes	characteristic
214	C₂×C₄×C₅₉	C₄×D₄	1	1	yes	characteristic
215	C₂×C₄×C₅₉	C₄×D₄	1	1	yes	characteristic
216	C₂×C₄×C₅₉	C₄×D₄	1	1	yes	characteristic
217	C₂×C₄×C₅₉	C₂³×C₄	1	1	yes	characteristic
218	C₂×C₄×C₅₉	C₂²×D₄	1	1	yes	characteristic
219	C₂×C₄×C₅₉	C₂×#41	1	1	yes	characteristic
220	C₂×C₄×C₅₉	C₂×#41	1	1	yes	characteristic
221	C₂×C₄×C₅₉	H(5,𝔽₂)	1	1	yes	characteristic
222	C₂×C₄×C₅₉	2₋¹⁺⁴	1	1	yes	characteristic
223	C₂²⋊D₅₉	—	2	2	no	—
224	C₂²⋊D₅₉	—	2	2	no	—
225	C₂×Dic₅₉	—	2	1	no	—
226	C₂×Dic₅₉	—	2	1	no	—
227	C₂×Dic₅₉	—	2	1	no	—
228	C₂×Dic₅₉	—	4	2	no	—
229	C₂×Dic₅₉	—	4	2	no	—
230	C₂×Dic₅₉	—	4	2	no	—
231	D₂₃₆	—	2	1	no	—
232	D₂₃₆	#117	1	2	yes	—
233	C₄×D₅₉	—	2	2	no	—
234	C₄×D₅₉	—	2	2	no	—
235	C₄×D₅₉	—	4	2	no	—
236	C₄×D₅₉	—	8	1	no	—
237	Dic₁₁₈	—	2	1	no	—
238	Dic₁₁₈	#117	1	2	yes	—
239	C₈×C₅₉	—	2	2	no	—
240	C₈×C₅₉	—	2	2	no	—
241	C₈×C₅₉	—	4	2	no	—
242	C₅₉⋊C₈	—	2	1	no	—
243	C₅₉⋊C₈	—	2	1	no	—
244	C₅₉⋊C₈	—	2	1	no	—
245	C₅₉⋊C₈	—	2	1	no	—
246	C₅₉⋊C₈	—	4	2	no	—
247	#22782	—	59	1	no	maximal, Sylow
248	C₂²×C₅₉	—	2	1	no	—
249	C₂²×C₅₉	—	2	1	no	—
250	C₂²×C₅₉	—	4	1	no	—
251	C₂²×C₅₉	—	4	1	no	—
252	C₂²×C₅₉	—	4	1	no	—
253	C₂²×C₅₉	C₂×C₄×D₄	1	1	yes	characteristic
254	C₂²×C₅₉	#552	1	1	yes	characteristic
255	C₂²×C₅₉	#553	1	1	yes	characteristic
256	C₂×D₅₉	—	2	2	no	—
257	C₂×D₅₉	—	4	1	no	—
258	C₂×D₅₉	—	4	1	no	—
259	C₄×C₅₉	—	2	1	no	—
260	C₄×C₅₉	—	2	1	no	—
261	C₄×C₅₉	—	2	1	no	—
262	C₄×C₅₉	—	4	1	no	—
263	C₄×C₅₉	—	4	1	no	—
264	C₄×C₅₉	—	4	1	no	—
265	C₄×C₅₉	#444	1	2	yes	—
266	C₄×C₅₉	C₂×#117	1	1	yes	characteristic
267	C₄×C₅₉	#520	1	1	yes	characteristic
268	C₄×C₅₉	#546	1	1	yes	characteristic
269	C₄×C₅₉	#548	1	1	yes	characteristic
270	Dic₅₉	—	2	2	no	—
271	Dic₅₉	—	4	1	no	—
272	Dic₅₉	—	4	1	no	—
273	Dic₅₉	—	8	2	no	—
274	C₄×#135	—	59	1	no	—
275	#2925	D₅₉	1	1	yes	characteristic, complemented
276	#2906	—	59	1	no	—
277	#1938	—	59	2	no	—
278	#1922	—	59	2	no	—
279	#1876	—	59	2	no	—
280	#1837	—	59	1	no	—
281	#1806	—	59	1	no	—
282	#1806	—	59	1	no	—
283	#1770	—	59	1	no	—
284	#1765	—	59	2	no	—
285	C₂×C₅₉	—	2	1	no	—
286	C₂×C₅₉	—	2	1	no	—
287	C₂×C₅₉	—	8	1	no	—
288	C₂×C₅₉	#2352	1	1	yes	characteristic
289	C₂×C₅₉	C₂×#444	1	1	yes	characteristic
290	C₂×C₅₉	#2957	1	1	yes	characteristic
291	D₅₉	—	4	2	no	—
292	C₂×#135	—	59	1	no	—
293	C₂×#131	—	59	2	no	—
294	C₄×#41	—	59	1	no	—
295	C₄×#41	C₂×D₅₉	1	1	yes	characteristic
296	C₄×Q₁₆	—	59	1	no	—
297	C₄×Q₁₆	—	59	1	no	—
298	C₄×SD₁₆	—	59	1	no	—
299	C₄×SD₁₆	—	59	1	no	—
300	C₄×SD₁₆	—	59	1	no	—
301	C₄×SD₁₆	—	59	1	no	—
302	C₄×D₈	—	59	1	no	—
303	C₄×D₈	—	59	1	no	—
304	#433	—	2	2	no	—
305	#432	—	2	1	no	—
306	#431	—	2	1	no	—
307	#427	—	59	1	no	—
308	#424	—	59	2	no	—
309	#424	—	118	2	no	—
310	#423	—	59	1	no	—
311	#423	—	118	1	no	—
312	#423	C₂×D₅₉	1	1	yes	characteristic
313	C₂×C₄⋊C₈	—	118	1	no	—
314	C₂×C₄⋊C₈	C₂×D₅₉	1	1	yes	characteristic
315	C₂×#104	—	59	2	no	—
316	C₂×#104	—	59	2	no	—
317	#416	—	59	1	no	—
318	#416	—	59	1	no	—
319	#408	C₂×D₅₉	1	2	yes	—
320	#405	C₂×D₅₉	1	2	yes	—
321	C₂×#97	—	59	2	no	—
322	C₂×C₄×C₈	—	59	1	no	—
323	C₄×C₄⋊C₄	—	59	1	no	—
324	#341	—	59	2	no	—
325	#341	—	59	2	no	—
326	#339	—	59	2	no	—
327	#339	—	59	2	no	—
328	#336	—	59	2	no	—
329	C₅₉	#22782	1	1	yes	characteristic, complemented, Sylow
330	C₂×#41	—	59	1	no	—
331	C₂×#41	C₂²×D₅₉	1	1	yes	characteristic
332	#135	—	118	2	no	—
333	#135	—	118	2	no	—
334	C₂×Q₁₆	—	59	1	no	—
335	C₂×SD₁₆	—	59	1	no	—
336	C₂×SD₁₆	—	59	1	no	—
337	C₂×D₈	—	59	1	no	—
338	#131	—	118	4	no	—
339	#131	—	236	2	no	—
340	C₂×M₁₆	—	59	2	no	—
341	C₂×M₁₆	—	118	2	no	—
342	C₂×M₁₆	C₂²×D₅₉	1	2	yes	—
343	C₂²×C₈	—	59	1	no	—
344	C₂²×C₈	—	59	1	no	—
345	C₂²×C₈	—	118	2	no	—
346	C₂²×C₈	C₂²×D₅₉	1	2	yes	—
347	C₄×Q₈	—	59	1	no	—
348	C₄×Q₈	—	59	1	no	—
349	C₄×Q₈	C₄×D₅₉	1	1	yes	characteristic
350	C₄×Q₈	C₄×D₅₉	1	1	yes	characteristic
351	C₄×D₄	—	2	1	no	—
352	C₄×D₄	—	2	1	no	—
353	C₄×D₄	—	59	1	no	—
354	C₄×D₄	—	59	1	no	—
355	C₄×D₄	—	118	1	no	—
356	C₄×D₄	—	118	1	no	—
357	C₄×D₄	C₄×D₅₉	1	1	yes	characteristic
358	C₄×D₄	C₄×D₅₉	1	1	yes	characteristic
359	#117	—	2	1	no	—
360	#117	—	59	1	no	—
361	#117	—	118	1	no	—
362	#117	C₂²×D₅₉	1	1	yes	characteristic
363	C₂×C₄⋊C₄	—	118	1	no	—
364	C₂×C₄²	—	2	1	no	—
365	C₂×C₄²	—	59	2	no	—
366	C₂×C₄²	—	118	1	no	—
367	C₂×C₄²	C₂²×D₅₉	1	1	yes	characteristic
368	#107	—	59	1	no	—
369	#107	—	59	1	no	—
370	#106	—	59	1	no	—
371	#106	—	59	1	no	—
372	C₄⋊C₈	—	2	1	no	—
373	C₄⋊C₈	—	2	1	no	—
374	C₄⋊C₈	—	118	2	no	—
375	C₄⋊C₈	—	118	2	no	—
376	C₄⋊C₈	—	118	1	no	—
377	C₄⋊C₈	—	118	1	no	—
378	C₄⋊C₈	C₂²⋊D₅₉	1	1	yes	characteristic
379	C₄⋊C₈	C₂²⋊D₅₉	1	1	yes	characteristic
380	C₄⋊C₈	C₂²⋊D₅₉	1	2	yes	—
381	#104	—	118	4	no	—
382	#104	—	236	2	no	—
383	#103	—	59	1	no	—
384	#103	—	59	1	no	—
385	#103	—	59	1	no	—
386	#103	—	59	1	no	—
387	#102	—	59	1	no	—
388	#102	—	59	1	no	—
389	#102	—	59	1	no	—
390	#102	—	59	1	no	—
391	C₂²⋊C₈	—	2	2	no	—
392	C₂²⋊C₈	—	2	2	no	—
393	#97	—	2	2	no	—
394	#97	—	236	2	no	—
395	C₄×C₈	—	2	2	no	—
396	C₄×C₈	—	59	1	no	—
397	C₄×C₈	—	59	1	no	—
398	C₄×C₈	—	59	1	no	—
399	C₄×C₈	—	59	1	no	—
400	#95	—	118	1	no	—
401	#41	—	2	1	no	—
402	#41	—	2	1	no	—
403	#41	—	2	1	no	—
404	#41	—	2	1	no	—
405	#41	—	59	2	no	—
406	#41	—	59	2	no	—
407	#41	—	118	1	no	—
408	#41	—	118	1	no	—
409	C₂×Q₈	—	59	1	no	—
410	C₂×Q₈	C₂×C₄×D₅₉	1	1	yes	characteristic
411	C₂×D₄	—	2	1	no	—
412	C₂×D₄	—	59	1	no	—
413	C₂×D₄	—	118	1	no	—
414	C₂×D₄	C₂×C₄×D₅₉	1	1	yes	characteristic
415	C₂²×C₄	—	2	1	no	—
416	C₂²×C₄	—	2	1	no	—
417	C₂²×C₄	—	2	1	no	—
418	C₂²×C₄	—	118	1	no	—
419	C₂²×C₄	—	118	1	no	—
420	C₂²×C₄	—	118	1	no	—
421	C₂²×C₄	—	118	2	no	—
422	C₂²×C₄	#11745685	1	1	yes	characteristic
423	C₂²×C₄	#11745685	1	1	yes	characteristic
424	C₂²×C₄	C₂³×D₅₉	1	1	yes	characteristic
425	Q₁₆	—	118	2	no	—
426	SD₁₆	—	118	2	no	—
427	SD₁₆	—	118	2	no	—
428	D₈	—	118	2	no	—
429	M₁₆	—	2	2	no	—
430	M₁₆	—	2	2	no	—
431	M₁₆	—	118	2	no	—
432	M₁₆	—	118	2	no	—
433	M₁₆	—	236	4	no	—
434	C₂×C₈	—	2	2	no	—
435	C₂×C₈	—	2	2	no	—
436	C₂×C₈	—	2	2	no	—
437	C₂×C₈	—	59	1	no	—
438	C₂×C₈	—	59	1	no	—
439	C₂×C₈	—	59	1	no	—
440	C₂×C₈	—	59	1	no	—
441	C₂×C₈	—	118	1	no	—
442	C₂×C₈	—	118	1	no	—
443	C₂×C₈	—	118	1	no	—
444	C₂×C₈	—	118	1	no	—
445	C₂×C₈	—	118	2	no	—
446	C₂×C₈	—	236	4	no	—
447	C₂×C₈	C₂×C₂²⋊D₅₉	1	2	yes	—
448	C₂×C₈	C₂×C₂²⋊D₅₉	1	2	yes	—
449	C₄⋊C₄	—	2	1	no	—
450	C₄⋊C₄	—	2	1	no	—
451	C₄⋊C₄	—	59	1	no	—
452	C₄⋊C₄	—	59	1	no	—
453	C₄⋊C₄	—	118	1	no	—
454	C₄⋊C₄	—	118	1	no	—
455	C₄⋊C₄	—	236	2	no	—
456	C₄⋊C₄	C₂×C₄×D₅₉	1	1	yes	characteristic
457	C₄⋊C₄	C₂×C₄×D₅₉	1	1	yes	characteristic
458	C₂²⋊C₄	—	2	1	no	—
459	C₂²⋊C₄	—	2	1	no	—
460	C₂²⋊C₄	—	2	1	no	—
461	C₂²⋊C₄	—	118	1	no	—
462	C₂²⋊C₄	—	118	1	no	—
463	C₂²⋊C₄	—	118	1	no	—
464	C₄²	—	2	1	no	—
465	C₄²	—	2	1	no	—
466	C₄²	—	2	1	no	—
467	C₄²	—	118	1	no	—
468	C₄²	—	118	1	no	—
469	C₄²	—	118	1	no	—
470	C₄²	—	118	2	no	—
471	C₄²	—	118	2	no	—
472	C₄²	C₂×C₄×D₅₉	1	1	yes	characteristic
473	C₄²	C₂×C₄×D₅₉	1	1	yes	characteristic
474	C₄²	C₂×C₂²⋊D₅₉	1	1	yes	characteristic
475	C₄²	C₂×C₂²⋊D₅₉	1	1	yes	characteristic
476	C₂³	—	2	1	no	—
477	C₂³	—	118	1	no	—
478	C₂³	C₂×#11745685	1	1	yes	characteristic
479	Q₈	—	2	1	no	—
480	Q₈	—	2	1	no	—
481	Q₈	—	59	2	no	—
482	Q₈	—	118	1	no	—
483	D₄	—	2	1	no	—
484	D₄	—	2	1	no	—
485	D₄	—	4	1	no	—
486	D₄	—	4	1	no	—
487	D₄	—	59	2	no	—
488	D₄	—	118	2	no	—
489	D₄	—	118	2	no	—
490	D₄	—	118	1	no	—
491	C₂×C₄	—	2	2	no	—
492	C₂×C₄	—	2	1	no	—
493	C₂×C₄	—	2	1	no	—
494	C₂×C₄	—	2	1	no	—
495	C₂×C₄	—	4	1	no	—
496	C₂×C₄	—	4	2	no	—
497	C₂×C₄	—	4	1	no	—
498	C₂×C₄	—	4	1	no	—
499	C₂×C₄	—	8	1	no	—
500	C₂×C₄	—	118	1	no	—
501	C₂×C₄	—	118	2	no	—
502	C₂×C₄	—	118	2	no	—
503	C₂×C₄	—	118	1	no	—
504	C₂×C₄	—	118	1	no	—
505	C₂×C₄	—	472	1	no	—
506	C₂×C₄	—	236	2	no	—
507	C₂×C₄	—	236	2	no	—
508	C₂×C₄	—	236	2	no	—
509	C₂×C₄	—	236	2	no	—
510	C₂×C₄	C₄×C₂²⋊D₅₉	1	1	yes	characteristic
511	C₂×C₄	C₄×C₂²⋊D₅₉	1	1	yes	characteristic
512	C₂×C₄	C₄×C₂²⋊D₅₉	1	1	yes	characteristic
513	C₂×C₄	C₄×C₂²⋊D₅₉	1	1	yes	characteristic
514	C₂×C₄	C₂²×C₄×D₅₉	1	1	yes	characteristic
515	C₂×C₄	C₂²×C₂²⋊D₅₉	1	1	yes	characteristic
516	C₂×C₄	#41×D₅₉	1	1	yes	characteristic
517	C₂×C₄	#41×D₅₉	1	1	yes	characteristic
518	C₂×C₄	#14273773	1	1	yes	characteristic
519	C₂×C₄	#14273774	1	1	yes	characteristic
520	C₈	—	2	2	no	—
521	C₈	—	2	2	no	—
522	C₈	—	4	2	no	—
523	C₈	—	118	1	no	—
524	C₈	—	118	1	no	—
525	C₈	—	118	1	no	—
526	C₈	—	118	1	no	—
527	C₈	—	236	2	no	—
528	C₂²	—	2	1	no	—
529	C₂²	—	2	1	no	—
530	C₂²	—	4	1	no	—
531	C₂²	—	4	1	no	—
532	C₂²	—	4	1	no	—
533	C₂²	—	118	2	no	—
534	C₂²	—	236	1	no	—
535	C₂²	—	236	1	no	—
536	C₂²	C₂×C₄×C₂²⋊D₅₉	1	1	yes	characteristic
537	C₂²	#16838091	1	1	yes	characteristic
538	C₂²	#16838096	1	1	yes	characteristic
539	C₄	—	2	1	no	—
540	C₄	—	2	1	no	—
541	C₄	—	2	1	no	—
542	C₄	—	4	1	no	—
543	C₄	—	4	1	no	—
544	C₄	—	4	1	no	—
545	C₄	—	118	2	no	—
546	C₄	—	472	2	no	—
547	C₄	—	236	1	no	—
548	C₄	—	236	1	no	—
549	C₄	#16837522	1	2	yes	—
550	C₄	#117×D₅₉	1	1	yes	characteristic
551	C₄	#16837882	1	1	yes	characteristic
552	C₄	#16838040	1	1	yes	characteristic
553	C₄	#16838059	1	1	yes	characteristic
554	C₂	—	2	1	no	—
555	C₂	—	2	1	no	—
556	C₂	—	8	1	no	—
557	C₂	—	236	2	no	—
558	C₂	#21427026	1	1	yes	characteristic
559	C₂	C₂×#16837522	1	1	yes	characteristic
560	C₂	#21433011	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²×C₂²⋊D₅₉
commutator	C₂×C₄×C₅₉	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₅₉
Fitting	C₅₉×#2925	C₂
socle	C₂²×C₅₉	C₂×C₄×D₄
prime radical	C₂×#14273747	C₂²
cosocle	C₂²×C₄×C₅₉	C₂⁴
hypercenter	#2925	D₅₉
hypocenter	C₅₉	#22782
LCS	G ▷ C₂×C₄×C₅₉ ▷ C₂×C₅₉ ▷ C₅₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄⋊C₈ ◁ #2925

Complements

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

N	H ≅ G/N	type
2. #21432661	C₂	semidirect
3. #21424810	C₂	semidirect
4. #21424695	C₂	semidirect
6. #21424233	C₂	semidirect
7. #21424116	C₂	semidirect
8. #21424113	C₂	semidirect
9. #21423966	C₂	semidirect
10. #21423942	C₂	semidirect
11. C₅₉×#2925	C₂	semidirect
15. C₄×#11745672	C₄	semidirect
16. C₄×#11745672	C₄	semidirect
17. C₄×#11745671	C₄	semidirect
18. C₄×#11745671	C₄	semidirect
19. C₄×#11745670	C₄	semidirect
20. C₄×#11745670	C₄	semidirect
21. C₄×#11745669	C₄	semidirect
22. C₄×#11745669	C₄	semidirect
275. #2925	D₅₉	semidirect
329. C₅₉	#22782	semidirect

Maximal subgroups

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

subgroup	index
C₄×#14273747	2
#21432661	2
#21424810	2
#21424695	2
#21424426	2
#21424233	2
#21424116	2
#21424113	2
#21423966	2
#21423942	2
C₅₉×#2925	2
#22782	59