Subgroups — #28560117

Order 15104.

656 conjugacy classes of subgroups.

The subgroup lattice has 498 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#21433111	C₂	1	1	yes	maximal, characteristic, complemented
2	C₄×#14273747	C₂	1	1	yes	maximal, characteristic
3	#21422991	C₂	1	2	yes	maximal, complemented
4	#21422932	C₂	1	2	yes	maximal, complemented
5	#21422930	C₂	1	2	yes	maximal, complemented
6	C₈×#11745669	C₂	1	2	yes	maximal, complemented
7	#21422857	C₂	1	1	yes	maximal, characteristic, complemented
8	#21422530	C₂	1	1	yes	maximal, characteristic, complemented
9	#21422528	C₂	1	1	yes	maximal, characteristic, complemented
10	M₁₆×C₅₉⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅₉×#2970	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#14273747	C₄	1	1	yes	characteristic
13	C₄×#11745685	C₂²	1	1	yes	characteristic
14	#16837532	C₂²	1	2	yes	—
15	C₄×#11745672	C₄	1	1	yes	characteristic
16	C₄×#11745672	C₂²	1	1	yes	characteristic
17	C₄×#11745671	C₄	1	1	yes	characteristic
18	C₄×#11745671	C₂²	1	1	yes	characteristic
19	C₄×#11745670	C₄	1	1	yes	characteristic
20	C₄×#11745670	C₂²	1	1	yes	characteristic
21	C₄×#11745669	C₄	1	1	yes	characteristic
22	C₄×#11745669	C₂²	1	1	yes	characteristic
23	#16837471	—	2	2	no	—
24	C₈×D₂₃₆	C₂²	1	2	yes	—
25	#16837459	C₂²	1	1	yes	characteristic
26	#16837457	—	2	1	no	—
27	#16837455	C₂²	1	1	yes	characteristic
28	#16837438	C₄	1	1	yes	characteristic
29	#16837398	C₄	1	1	yes	characteristic
30	#16837396	C₄	1	1	yes	characteristic
31	#97×D₅₉	—	2	1	no	—
32	C₂×C₄×C₅₉⋊C₈	C₂²	1	1	yes	characteristic
33	#16837154	C₂²	1	2	yes	—
34	#16837152	C₂²	1	2	yes	—
35	Q₈⋊(C₅₉⋊C₈)	C₂²	1	2	yes	—
36	#16837132	C₂²	1	2	yes	—
37	D₄⋊(C₅₉⋊C₈)	C₂²	1	2	yes	—
38	#16837129	C₂²	1	2	yes	—
39	#16837123	C₂²	1	2	yes	—
40	C₈×C₅₉⋊C₈	C₂²	1	2	yes	—
41	C₄×#41×C₅₉	C₂²	1	1	yes	characteristic
42	C₅₉×#446	C₂²	1	2	yes	—
43	C₅₉×#435	—	2	2	no	—
44	C₈×D₄×C₅₉	C₂²	1	2	yes	—
45	C₅₉×#432	—	2	1	no	—
46	C₅₉×#432	C₂²	1	1	yes	characteristic
47	C₄×M₁₆×C₅₉	C₂²	1	1	yes	characteristic
48	C₂×#97×C₅₉	—	2	1	no	—
49	C₂×#11745685	C₂×C₄	1	1	yes	characteristic
50	#14273747	—	2	4	no	—
51	C₂×#11745672	C₂×C₄	1	1	yes	characteristic
52	C₂×#11745670	C₂×C₄	1	1	yes	characteristic
53	C₂×#11745671	C₂×C₄	1	1	yes	characteristic
54	C₂×#11745669	C₂×C₄	1	1	yes	characteristic
55	C₂²×C₅₉⋊C₈	C₂×C₄	1	1	yes	characteristic
56	C₂²×C₅₉⋊C₈	C₂×C₄	1	1	yes	characteristic
57	C₂×C₈×D₅₉	—	2	2	no	—
58	C₄×Dic₁₁₈	C₂×C₄	1	1	yes	characteristic
59	C₄×Dic₁₁₈	C₂³	1	1	yes	characteristic
60	C₄×D₂₃₆	C₂×C₄	1	1	yes	characteristic
61	C₄×D₂₃₆	C₂³	1	1	yes	characteristic
62	C₄×C₂²⋊D₅₉	—	2	1	no	—
63	C₄×C₂²⋊D₅₉	—	2	1	no	—
64	#14273686	C₂×C₄	1	1	yes	characteristic
65	#14273684	—	2	1	no	—
66	C₄²×D₅₉	—	2	1	no	—
67	#14273660	C₂×C₄	1	1	yes	characteristic
68	#14273660	C₂×C₄	1	1	yes	characteristic
69	#14273658	C₂×C₄	1	1	yes	characteristic
70	#14273658	C₂×C₄	1	1	yes	characteristic
71	C₄⋊(C₅₉⋊C₈)	—	2	1	no	—
72	C₄⋊(C₅₉⋊C₈)	C₂³	1	2	yes	—
73	Dic₅₉⋊C₈	—	2	2	no	—
74	#14273651	C₂×C₄	1	1	yes	characteristic
75	#14273651	C₂×C₄	1	1	yes	characteristic
76	#14273650	C₂×C₄	1	1	yes	characteristic
77	#14273650	C₂×C₄	1	1	yes	characteristic
78	#14273648	C₂×C₄	1	1	yes	characteristic
79	#14273648	C₂×C₄	1	1	yes	characteristic
80	#14273647	C₂×C₄	1	1	yes	characteristic
81	#14273647	C₂×C₄	1	1	yes	characteristic
82	C₂²⋊(C₅₉⋊C₈)	—	2	1	no	—
83	C₂²⋊(C₅₉⋊C₈)	—	2	1	no	—
84	(C₂×D₅₉)⋊C₈	—	2	2	no	—
85	#14273638	—	2	1	no	—
86	#14273637	—	2	2	no	—
87	C₄×C₅₉⋊C₈	C₂×C₄	1	1	yes	characteristic
88	C₄×C₅₉⋊C₈	C₂×C₄	1	1	yes	characteristic
89	C₄×C₅₉⋊C₈	C₂³	1	2	yes	—
90	C₄×C₅₉⋊C₈	C₂³	1	1	yes	characteristic
91	C₄×C₅₉⋊C₈	C₂³	1	1	yes	characteristic
92	C₂×#41×C₅₉	C₂×C₄	1	1	yes	characteristic
93	C₂×M₁₆×C₅₉	D₄	1	2	yes	—
94	C₂²×C₈×C₅₉	—	2	2	no	—
95	C₄×Q₈×C₅₉	C₂×C₄	1	1	yes	characteristic
96	C₄×Q₈×C₅₉	C₂³	1	1	yes	characteristic
97	C₄×D₄×C₅₉	—	2	1	no	—
98	C₄×D₄×C₅₉	—	2	1	no	—
99	C₄×D₄×C₅₉	C₂×C₄	1	1	yes	characteristic
100	C₄×D₄×C₅₉	C₂³	1	1	yes	characteristic
101	#117×C₅₉	—	2	1	no	—
102	#117×C₅₉	C₂×C₄	1	1	yes	characteristic
103	C₂×C₄²×C₅₉	—	2	1	no	—
104	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
105	C₄⋊C₈×C₅₉	—	2	2	no	—
106	C₄⋊C₈×C₅₉	C₂³	1	2	yes	—
107	C₂²⋊C₈×C₅₉	—	2	1	no	—
108	C₂²⋊C₈×C₅₉	—	2	2	no	—
109	#97×C₅₉	—	2	2	no	—
110	#97×C₅₉	—	2	1	no	—
111	#97×C₅₉	D₄	1	1	yes	characteristic
112	#97×C₅₉	D₄	1	1	yes	characteristic
113	C₄×C₈×C₅₉	C₂³	1	2	yes	—
114	#41×C₅₉	—	2	2	no	—
115	#41×C₅₉	—	4	1	no	—
116	C₂×Q₈×C₅₉	C₂²×C₄	1	1	yes	characteristic
117	C₂×D₄×C₅₉	—	2	1	no	—
118	C₂×D₄×C₅₉	C₂²×C₄	1	1	yes	characteristic
119	C₂²×C₄×C₅₉	—	2	1	no	—
120	C₂²×C₄×C₅₉	—	2	1	no	—
121	C₂²×C₄×C₅₉	—	2	1	no	—
122	C₂²×C₄×C₅₉	C₂²×C₄	1	1	yes	characteristic
123	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
124	C₂²×C₄×C₅₉	#41	1	1	yes	characteristic
125	C₂×C₂²⋊D₅₉	—	2	1	no	—
126	#11745685	—	2	2	no	—
127	#11745685	—	4	1	no	—
128	C₂×D₂₃₆	C₂²×C₄	1	1	yes	characteristic
129	C₂×C₄×D₅₉	—	2	1	no	—
130	C₂×C₄×D₅₉	—	2	1	no	—
131	C₂×C₄×D₅₉	—	2	1	no	—
132	C₂×Dic₁₁₈	C₂²×C₄	1	1	yes	characteristic
133	M₁₆×C₅₉	—	2	4	no	—
134	C₂×C₈×C₅₉	—	2	2	no	—
135	C₂×C₈×C₅₉	—	4	4	no	—
136	C₂×C₈×C₅₉	C₂×D₄	1	2	yes	—
137	C₂×C₈×C₅₉	C₂×D₄	1	2	yes	—
138	C₄⋊C₄×C₅₉	—	2	1	no	—
139	C₄⋊C₄×C₅₉	—	2	1	no	—
140	C₄⋊C₄×C₅₉	C₂²×C₄	1	1	yes	characteristic
141	C₄⋊C₄×C₅₉	C₂²×C₄	1	1	yes	characteristic
142	C₂²⋊C₄×C₅₉	—	2	1	no	—
143	C₂²⋊C₄×C₅₉	—	2	1	no	—
144	C₂²⋊C₄×C₅₉	—	2	1	no	—
145	C₄²×C₅₉	—	2	1	no	—
146	C₄²×C₅₉	—	2	1	no	—
147	C₄²×C₅₉	—	2	1	no	—
148	C₄²×C₅₉	C₂²×C₄	1	1	yes	characteristic
149	C₄²×C₅₉	C₂×D₄	1	1	yes	characteristic
150	C₄²×C₅₉	#41	1	1	yes	characteristic
151	C₄²×C₅₉	C₂⁴	1	1	yes	characteristic
152	C₂²⋊Dic₅₉	—	2	1	no	—
153	#11745672	—	2	2	no	—
154	#11745671	—	2	2	no	—
155	#11745670	—	2	2	no	—
156	#11745669	M₁₆	1	4	yes	complemented
157	(C₂×D₅₉)⋊C₄	—	2	1	no	—
158	(C₂×D₅₉)⋊C₄	—	2	1	no	—
159	C₄⋊Dic₅₉	C₂²×C₄	1	1	yes	characteristic
160	C₄⋊Dic₅₉	C₂²×C₄	1	1	yes	characteristic
161	Dic₅₉⋊C₄	—	2	1	no	—
162	Dic₅₉⋊C₄	—	2	1	no	—
163	C₄×Dic₅₉	—	2	1	no	—
164	C₄×Dic₅₉	—	2	1	no	—
165	C₄×Dic₅₉	—	2	1	no	—
166	C₂×C₅₉⋊C₈	—	2	2	no	—
167	C₂×C₅₉⋊C₈	—	2	2	no	—
168	C₂×C₅₉⋊C₈	—	2	2	no	—
169	C₂×C₅₉⋊C₈	—	4	1	no	—
170	C₂×C₅₉⋊C₈	C₂²×C₄	1	1	yes	characteristic
171	C₂×C₅₉⋊C₈	C₂²×C₄	1	1	yes	characteristic
172	C₂×C₅₉⋊C₈	C₂²×C₄	1	1	yes	characteristic
173	C₂×C₅₉⋊C₈	C₂²×C₄	1	1	yes	characteristic
174	C₈×D₅₉	—	4	4	no	—
175	C₂³×C₅₉	—	2	1	no	—
176	C₂³×C₅₉	C₄×D₄	1	1	yes	characteristic
177	C₂²×D₅₉	—	2	1	no	—
178	Q₈×C₅₉	—	2	1	no	—
179	Q₈×C₅₉	—	2	1	no	—
180	D₄×C₅₉	—	2	1	no	—
181	D₄×C₅₉	—	4	2	no	—
182	D₄×C₅₉	C₂×M₁₆	1	2	yes	—
183	C₂×C₄×C₅₉	—	2	1	no	—
184	C₂×C₄×C₅₉	—	2	1	no	—
185	C₂×C₄×C₅₉	—	2	2	no	—
186	C₂×C₄×C₅₉	—	2	1	no	—
187	C₂×C₄×C₅₉	—	2	1	no	—
188	C₂×C₄×C₅₉	—	2	1	no	—
189	C₂×C₄×C₅₉	—	4	1	no	—
190	C₂×C₄×C₅₉	—	4	2	no	—
191	C₂×C₄×C₅₉	—	4	2	no	—
192	C₂×C₄×C₅₉	—	8	1	no	—
193	C₂×C₄×C₅₉	C₄×D₄	1	1	yes	characteristic
194	C₂×C₄×C₅₉	C₄×D₄	1	1	yes	characteristic
195	C₂×C₄×C₅₉	C₄×D₄	1	1	yes	characteristic
196	C₂×C₄×C₅₉	C₂³×C₄	1	1	yes	characteristic
197	C₂×C₄×C₅₉	C₂²×D₄	1	1	yes	characteristic
198	C₂×C₄×C₅₉	C₂×#41	1	1	yes	characteristic
199	C₂²⋊D₅₉	—	4	2	no	—
200	C₂×Dic₅₉	—	2	1	no	—
201	C₂×Dic₅₉	—	2	1	no	—
202	C₂×Dic₅₉	—	2	1	no	—
203	D₂₃₆	—	2	1	no	—
204	D₂₃₆	C₂×M₁₆	1	2	yes	—
205	C₄×D₅₉	—	4	2	no	—
206	C₄×D₅₉	—	4	2	no	—
207	C₄×D₅₉	—	8	1	no	—
208	Dic₁₁₈	—	2	1	no	—
209	Dic₁₁₈	—	2	1	no	—
210	C₈×C₅₉	—	2	2	no	—
211	C₈×C₅₉	—	4	2	no	—
212	C₈×C₅₉	#135	1	4	yes	complemented
213	C₅₉⋊C₈	—	2	1	no	—
214	C₅₉⋊C₈	—	2	1	no	—
215	C₅₉⋊C₈	—	2	1	no	—
216	C₅₉⋊C₈	—	4	2	no	—
217	C₅₉⋊C₈	—	4	2	no	—
218	C₅₉⋊C₈	C₂×M₁₆	1	2	yes	—
219	#18035	—	59	1	no	maximal, Sylow
220	C₂²×C₅₉	—	2	1	no	—
221	C₂²×C₅₉	—	2	2	no	—
222	C₂²×C₅₉	—	2	1	no	—
223	C₂²×C₅₉	—	2	1	no	—
224	C₂²×C₅₉	—	4	1	no	—
225	C₂²×C₅₉	—	4	1	no	—
226	C₂²×C₅₉	C₂×C₄×D₄	1	1	yes	characteristic
227	C₂×D₅₉	—	2	2	no	—
228	C₂×D₅₉	—	4	1	no	—
229	C₂×D₅₉	—	4	1	no	—
230	C₄×C₅₉	—	2	1	no	—
231	C₄×C₅₉	—	2	1	no	—
232	C₄×C₅₉	—	2	1	no	—
233	C₄×C₅₉	—	2	1	no	—
234	C₄×C₅₉	—	4	1	no	—
235	C₄×C₅₉	—	4	1	no	—
236	C₄×C₅₉	—	4	1	no	—
237	C₄×C₅₉	C₂²×M₁₆	1	1	yes	characteristic
238	C₄×C₅₉	#568	1	1	yes	characteristic
239	C₄×C₅₉	C₂×#135	1	2	yes	—
240	Dic₅₉	—	4	1	no	—
241	Dic₅₉	—	4	1	no	—
242	Dic₅₉	—	4	1	no	—
243	#2970	—	59	1	no	—
244	#2970	D₅₉	1	1	yes	characteristic, complemented
245	C₄×#135	—	59	1	no	—
246	#1591	—	59	2	no	—
247	#1582	—	59	2	no	—
248	#1582	—	59	2	no	—
249	C₈×D₈	—	59	2	no	—
250	#1568	—	59	1	no	—
251	#1488	—	59	1	no	—
252	#1488	—	59	1	no	—
253	C₈×M₁₆	—	59	1	no	—
254	C₂×C₅₉	—	4	1	no	—
255	C₂×C₅₉	—	4	2	no	—
256	C₂×C₅₉	D₄×M₁₆	1	1	yes	characteristic
257	C₂×C₅₉	C₄×#135	1	1	yes	characteristic
258	C₂×C₅₉	#2957	1	1	yes	characteristic
259	D₅₉	—	4	2	no	—
260	C₂×#135	—	59	1	no	—
261	C₄×#41	—	59	1	no	—
262	C₄×#41	C₂×D₅₉	1	1	yes	characteristic
263	#446	—	59	2	no	—
264	#446	C₂×D₅₉	1	2	yes	—
265	C₄×Q₁₆	—	59	1	no	—
266	C₄×Q₁₆	—	59	1	no	—
267	C₄×SD₁₆	—	59	1	no	—
268	C₄×SD₁₆	—	59	1	no	—
269	C₄×SD₁₆	—	59	1	no	—
270	C₄×SD₁₆	—	59	1	no	—
271	C₄×D₈	—	59	1	no	—
272	C₄×D₈	—	59	1	no	—
273	#435	—	2	2	no	—
274	#435	—	118	2	no	—
275	C₈×D₄	—	59	2	no	—
276	C₈×D₄	C₂×D₅₉	1	2	yes	—
277	#432	—	2	1	no	—
278	#432	—	59	1	no	—
279	#432	—	118	1	no	—
280	#432	C₂×D₅₉	1	1	yes	characteristic
281	#431	—	59	1	no	—
282	#427	—	59	1	no	—
283	#416	—	59	1	no	—
284	#416	—	59	1	no	—
285	C₄×M₁₆	C₂×D₅₉	1	1	yes	characteristic
286	C₂×#97	—	2	1	no	—
287	C₂×#97	—	118	1	no	—
288	C₂×C₄×C₈	—	59	1	no	—
289	#335	—	59	2	no	—
290	#334	—	59	2	no	—
291	Q₈⋊C₈	—	59	2	no	—
292	Q₈⋊C₈	—	59	2	no	—
293	D₄⋊C₈	—	59	2	no	—
294	D₄⋊C₈	—	59	2	no	—
295	#322	—	59	2	no	—
296	C₈²	—	59	2	no	—
297	C₅₉	#18035	1	1	yes	characteristic, complemented, Sylow
298	C₂×#41	—	59	1	no	—
299	C₂×#41	C₄×D₅₉	1	1	yes	characteristic
300	#135	—	118	4	no	—
301	C₂×Q₁₆	—	59	1	no	—
302	C₂×SD₁₆	—	59	1	no	—
303	C₂×SD₁₆	—	59	1	no	—
304	C₂×D₈	—	59	1	no	—
305	C₂×M₁₆	C₂²⋊D₅₉	1	2	yes	—
306	C₂²×C₈	—	2	2	no	—
307	C₂²×C₈	—	59	1	no	—
308	C₂²×C₈	—	59	1	no	—
309	C₂²×C₈	—	118	2	no	—
310	C₄×Q₈	—	59	1	no	—
311	C₄×Q₈	—	59	1	no	—
312	C₄×Q₈	C₄×D₅₉	1	1	yes	characteristic
313	C₄×Q₈	C₂²×D₅₉	1	1	yes	characteristic
314	C₄×D₄	—	2	1	no	—
315	C₄×D₄	—	2	1	no	—
316	C₄×D₄	—	59	1	no	—
317	C₄×D₄	—	59	1	no	—
318	C₄×D₄	—	118	1	no	—
319	C₄×D₄	—	118	1	no	—
320	C₄×D₄	C₄×D₅₉	1	1	yes	characteristic
321	C₄×D₄	C₂²×D₅₉	1	1	yes	characteristic
322	#117	—	2	1	no	—
323	#117	—	59	1	no	—
324	#117	—	118	1	no	—
325	#117	C₄×D₅₉	1	1	yes	characteristic
326	C₂×C₄²	—	2	1	no	—
327	C₂×C₄²	—	118	1	no	—
328	C₂×C₄²	C₂²×D₅₉	1	1	yes	characteristic
329	#107	—	59	1	no	—
330	#107	—	59	1	no	—
331	#106	—	59	1	no	—
332	#106	—	59	1	no	—
333	C₄⋊C₈	—	2	2	no	—
334	C₄⋊C₈	—	59	2	no	—
335	C₄⋊C₈	—	118	2	no	—
336	C₄⋊C₈	—	118	1	no	—
337	C₄⋊C₈	C₂²×D₅₉	1	2	yes	—
338	#103	—	59	1	no	—
339	#103	—	59	1	no	—
340	#103	—	59	1	no	—
341	#103	—	59	1	no	—
342	#102	—	59	1	no	—
343	#102	—	59	1	no	—
344	#102	—	59	1	no	—
345	#102	—	59	1	no	—
346	C₂²⋊C₈	—	2	1	no	—
347	C₂²⋊C₈	—	2	2	no	—
348	C₂²⋊C₈	—	118	1	no	—
349	C₂²⋊C₈	—	118	1	no	—
350	C₂²⋊C₈	—	118	2	no	—
351	#97	—	2	2	no	—
352	#97	—	2	1	no	—
353	#97	—	118	2	no	—
354	#97	—	118	1	no	—
355	#97	C₂²⋊D₅₉	1	1	yes	characteristic
356	#97	C₂²⋊D₅₉	1	1	yes	characteristic
357	C₄×C₈	—	59	1	no	—
358	C₄×C₈	—	59	1	no	—
359	C₄×C₈	—	59	1	no	—
360	C₄×C₈	—	59	1	no	—
361	C₄×C₈	—	59	2	no	—
362	C₄×C₈	C₂²×D₅₉	1	2	yes	—
363	#41	—	2	2	no	—
364	#41	—	4	1	no	—
365	#41	—	118	2	no	—
366	#41	—	236	1	no	—
367	C₂×Q₈	—	59	1	no	—
368	C₂×Q₈	C₂×C₄×D₅₉	1	1	yes	characteristic
369	C₂×D₄	—	2	1	no	—
370	C₂×D₄	—	59	1	no	—
371	C₂×D₄	—	118	1	no	—
372	C₂×D₄	C₂×C₄×D₅₉	1	1	yes	characteristic
373	C₂²×C₄	—	2	1	no	—
374	C₂²×C₄	—	2	1	no	—
375	C₂²×C₄	—	2	1	no	—
376	C₂²×C₄	—	118	1	no	—
377	C₂²×C₄	—	118	1	no	—
378	C₂²×C₄	—	118	1	no	—
379	C₂²×C₄	C₂×C₄×D₅₉	1	1	yes	characteristic
380	C₂²×C₄	#11745685	1	1	yes	characteristic
381	C₂²×C₄	C₂×C₂²⋊D₅₉	1	1	yes	characteristic
382	Q₁₆	—	118	2	no	—
383	SD₁₆	—	118	2	no	—
384	SD₁₆	—	118	2	no	—
385	D₈	—	59	4	no	—
386	M₁₆	—	2	4	no	—
387	C₂×C₈	—	2	2	no	—
388	C₂×C₈	—	4	4	no	—
389	C₂×C₈	—	59	1	no	—
390	C₂×C₈	—	59	1	no	—
391	C₂×C₈	—	59	1	no	—
392	C₂×C₈	—	59	1	no	—
393	C₂×C₈	—	118	2	no	—
394	C₂×C₈	—	118	2	no	—
395	C₂×C₈	—	118	2	no	—
396	C₂×C₈	—	236	1	no	—
397	C₂×C₈	—	236	4	no	—
398	C₂×C₈	C₂×C₂²⋊D₅₉	1	2	yes	—
399	C₂×C₈	C₂×C₂²⋊D₅₉	1	2	yes	—
400	C₄⋊C₄	—	2	1	no	—
401	C₄⋊C₄	—	2	1	no	—
402	C₄⋊C₄	—	59	1	no	—
403	C₄⋊C₄	—	59	1	no	—
404	C₄⋊C₄	—	118	1	no	—
405	C₄⋊C₄	—	118	1	no	—
406	C₄⋊C₄	C₂×C₄×D₅₉	1	1	yes	characteristic
407	C₄⋊C₄	C₂×C₄×D₅₉	1	1	yes	characteristic
408	C₂²⋊C₄	—	2	1	no	—
409	C₂²⋊C₄	—	2	1	no	—
410	C₂²⋊C₄	—	2	1	no	—
411	C₂²⋊C₄	—	118	1	no	—
412	C₂²⋊C₄	—	118	1	no	—
413	C₂²⋊C₄	—	118	1	no	—
414	C₄²	—	2	1	no	—
415	C₄²	—	2	1	no	—
416	C₄²	—	2	1	no	—
417	C₄²	—	118	1	no	—
418	C₄²	—	118	1	no	—
419	C₄²	—	118	1	no	—
420	C₄²	C₂×C₄×D₅₉	1	1	yes	characteristic
421	C₄²	#11745685	1	1	yes	characteristic
422	C₄²	C₂×C₂²⋊D₅₉	1	1	yes	characteristic
423	C₄²	C₂³×D₅₉	1	1	yes	characteristic
424	C₂³	—	2	1	no	—
425	C₂³	—	118	1	no	—
426	C₂³	C₄×C₂²⋊D₅₉	1	1	yes	characteristic
427	Q₈	—	2	1	no	—
428	Q₈	—	2	1	no	—
429	Q₈	—	118	1	no	—
430	Q₈	—	118	1	no	—
431	D₄	—	2	1	no	—
432	D₄	—	4	2	no	—
433	D₄	—	59	2	no	—
434	D₄	—	118	1	no	—
435	D₄	—	236	2	no	—
436	D₄	M₁₆×D₅₉	1	2	yes	—
437	C₂×C₄	—	2	1	no	—
438	C₂×C₄	—	2	1	no	—
439	C₂×C₄	—	2	2	no	—
440	C₂×C₄	—	2	1	no	—
441	C₂×C₄	—	2	1	no	—
442	C₂×C₄	—	2	1	no	—
443	C₂×C₄	—	4	1	no	—
444	C₂×C₄	—	4	2	no	—
445	C₂×C₄	—	4	2	no	—
446	C₂×C₄	—	8	1	no	—
447	C₂×C₄	—	118	1	no	—
448	C₂×C₄	—	118	1	no	—
449	C₂×C₄	—	118	1	no	—
450	C₂×C₄	—	472	1	no	—
451	C₂×C₄	—	236	2	no	—
452	C₂×C₄	—	236	2	no	—
453	C₂×C₄	C₄×C₂²⋊D₅₉	1	1	yes	characteristic
454	C₂×C₄	C₄×C₂²⋊D₅₉	1	1	yes	characteristic
455	C₂×C₄	C₄×C₂²⋊D₅₉	1	1	yes	characteristic
456	C₂×C₄	C₂²×C₄×D₅₉	1	1	yes	characteristic
457	C₂×C₄	C₂²×C₂²⋊D₅₉	1	1	yes	characteristic
458	C₂×C₄	C₂×#11745685	1	1	yes	characteristic
459	C₈	—	2	2	no	—
460	C₈	—	4	2	no	—
461	C₈	—	59	2	no	—
462	C₈	—	118	1	no	—
463	C₈	—	118	1	no	—
464	C₈	—	118	1	no	—
465	C₈	—	236	2	no	—
466	C₈	—	236	2	no	—
467	C₈	#14273747	1	4	yes	complemented
468	C₂²	—	2	1	no	—
469	C₂²	—	2	1	no	—
470	C₂²	—	2	1	no	—
471	C₂²	—	2	2	no	—
472	C₂²	—	4	1	no	—
473	C₂²	—	4	1	no	—
474	C₂²	—	118	2	no	—
475	C₂²	—	236	1	no	—
476	C₂²	—	236	1	no	—
477	C₂²	C₂×C₄×C₂²⋊D₅₉	1	1	yes	characteristic
478	C₄	—	2	1	no	—
479	C₄	—	2	1	no	—
480	C₄	—	2	1	no	—
481	C₄	—	2	1	no	—
482	C₄	—	4	1	no	—
483	C₄	—	4	1	no	—
484	C₄	—	4	1	no	—
485	C₄	—	236	1	no	—
486	C₄	—	236	1	no	—
487	C₄	—	236	1	no	—
488	C₄	C₂×M₁₆×D₅₉	1	1	yes	characteristic
489	C₄	#16838168	1	1	yes	characteristic
490	C₄	C₂×#14273747	1	2	yes	—
491	C₂	—	4	1	no	—
492	C₂	—	4	2	no	—
493	C₂	—	236	2	no	—
494	C₂	M₁₆×C₂²⋊D₅₉	1	1	yes	characteristic
495	C₂	C₄×#14273747	1	1	yes	characteristic
496	C₂	#21433011	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²×C₂²⋊D₅₉
commutator	C₂×C₄×C₅₉	C₂³×C₄
Frattini	C₄²	C₂³×D₅₉
Fitting	C₅₉×#2970	C₂
socle	C₂²×C₅₉	C₂×C₄×D₄
prime radical	C₂×#14273747	C₄
cosocle	C₄²×C₅₉	C₂⁴
hypercenter	#2970	D₅₉
hypocenter	C₅₉	#18035
LCS	G ▷ C₂×C₄×C₅₉ ▷ C₂×C₅₉ ▷ C₅₉
UCS	C₁ ◁ C₂×C₄ ◁ C₄×M₁₆ ◁ #2970

Complements

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

N	H ≅ G/N	type
1. #21433111	C₂	semidirect
3. #21422991	C₂	semidirect
4. #21422932	C₂	semidirect
5. #21422930	C₂	semidirect
6. C₈×#11745669	C₂	semidirect
7. #21422857	C₂	semidirect
8. #21422530	C₂	semidirect
9. #21422528	C₂	semidirect
10. M₁₆×C₅₉⋊C₈	C₂	semidirect
11. C₅₉×#2970	C₂	semidirect
156. #11745669	M₁₆	semidirect
212. C₈×C₅₉	#135	semidirect
244. #2970	D₅₉	semidirect
297. C₅₉	#18035	semidirect
467. C₈	#14273747	semidirect

Maximal subgroups

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

subgroup	index
#21433111	2
C₄×#14273747	2
#21422991	2
#21422932	2
#21422930	2
C₈×#11745669	2
#21422857	2
#21422530	2
#21422528	2
M₁₆×C₅₉⋊C₈	2
C₅₉×#2970	2
#18035	59