Subgroups — #28557928

Order 15104.

610 conjugacy classes of subgroups.

The subgroup lattice has 480 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈×#11745685	C₂	1	1	yes	maximal, characteristic
2	#21432757	C₂	1	2	yes	maximal
3	#21422874	C₂	1	2	yes	maximal, complemented
4	#21422873	C₂	1	2	yes	maximal, complemented
5	#21422865	C₂	1	2	yes	maximal, complemented
6	#21422859	C₂	1	1	yes	maximal, characteristic, complemented
7	#21422858	C₂	1	1	yes	maximal, characteristic, complemented
8	#21422853	C₂	1	1	yes	maximal, characteristic, complemented
9	#21422843	C₂	1	1	yes	maximal, characteristic, complemented
10	#335×D₅₉	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅₉×#1564	C₂	1	1	yes	maximal, characteristic, complemented
12	C₄×#11745685	C₂²	1	1	yes	characteristic
13	C₈×Dic₁₁₈	C₄	1	1	yes	characteristic
14	C₈×Dic₁₁₈	C₄	1	1	yes	characteristic
15	C₈×D₂₃₆	C₄	1	1	yes	characteristic
16	C₈×D₂₃₆	C₄	1	1	yes	characteristic
17	C₈×C₂²⋊D₅₉	C₄	1	1	yes	characteristic
18	C₈×C₂²⋊D₅₉	C₄	1	1	yes	characteristic
19	C₈×C₂²⋊D₅₉	C₄	1	1	yes	characteristic
20	C₈×C₂²⋊D₅₉	C₄	1	1	yes	characteristic
21	#16837461	—	2	2	no	—
22	#16837460	—	2	2	no	—
23	#16837459	C₂²	1	2	yes	—
24	#16837458	C₂²	1	2	yes	—
25	#16837455	C₂²	1	1	yes	characteristic
26	#16837454	C₂²	1	2	yes	—
27	#16837453	C₂²	1	1	yes	characteristic
28	#16837453	C₂²	1	1	yes	characteristic
29	#16837424	C₂²	1	2	yes	—
30	C₄⋊C₈×D₅₉	C₂²	1	2	yes	—
31	#16837367	—	2	2	no	—
32	#16837356	—	2	2	no	—
33	C₄×C₈×D₅₉	C₂²	1	1	yes	characteristic
34	C₄×C₈×D₅₉	C₂²	1	1	yes	characteristic
35	#16837155	C₂²	1	1	yes	characteristic
36	#16837155	C₂²	1	1	yes	characteristic
37	#16837154	C₂²	1	2	yes	—
38	#16837154	C₂²	1	2	yes	—
39	#16837153	C₂²	1	2	yes	—
40	#16837152	C₂²	1	2	yes	—
41	#16837152	C₂²	1	2	yes	—
42	C₅₉×#431	C₂²	1	2	yes	—
43	C₂×C₄×C₈×C₅₉	C₂²	1	1	yes	characteristic
44	C₅₉×#335	C₂²	1	1	yes	characteristic
45	C₅₉×#335	C₂²	1	1	yes	characteristic
46	C₅₉×#334	C₂²	1	2	yes	—
47	C₂×#11745685	D₄	1	1	yes	characteristic
48	C₂×#11745659	—	2	2	no	—
49	C₂×C₈×D₅₉	—	2	2	no	—
50	C₂×C₈×D₅₉	C₂×C₄	1	1	yes	characteristic
51	C₂×C₈×D₅₉	C₂×C₄	1	1	yes	characteristic
52	C₂×C₈×D₅₉	C₂×C₄	1	1	yes	characteristic
53	C₂×C₈×D₅₉	C₂×C₄	1	1	yes	characteristic
54	C₄×Dic₁₁₈	C₂×C₄	1	1	yes	characteristic
55	C₄×Dic₁₁₈	Q₈	1	1	yes	characteristic
56	C₄×D₂₃₆	C₂×C₄	1	1	yes	characteristic
57	C₄×D₂₃₆	Q₈	1	1	yes	characteristic
58	C₄×C₂²⋊D₅₉	C₂×C₄	1	1	yes	characteristic
59	C₄×C₂²⋊D₅₉	C₂×C₄	1	1	yes	characteristic
60	C₄×C₂²⋊D₅₉	Q₈	1	1	yes	characteristic
61	C₄×C₂²⋊D₅₉	Q₈	1	1	yes	characteristic
62	#14273686	D₄	1	1	yes	characteristic
63	#14273684	D₄	1	1	yes	characteristic
64	#14273684	D₄	1	1	yes	characteristic
65	C₄²×D₅₉	C₂³	1	1	yes	characteristic
66	C₄²×D₅₉	C₂³	1	1	yes	characteristic
67	C₄⋊(C₅₉⋊C₈)	C₂×C₄	1	1	yes	characteristic
68	C₄⋊(C₅₉⋊C₈)	C₂×C₄	1	1	yes	characteristic
69	C₄⋊(C₅₉⋊C₈)	C₂³	1	2	yes	—
70	C₄⋊(C₅₉⋊C₈)	C₂³	1	2	yes	—
71	Dic₅₉⋊C₈	—	2	2	no	—
72	Dic₅₉⋊C₈	—	2	2	no	—
73	Dic₅₉⋊C₈	C₂×C₄	1	1	yes	characteristic
74	Dic₅₉⋊C₈	C₂×C₄	1	1	yes	characteristic
75	Dic₅₉⋊C₈	C₂×C₄	1	1	yes	characteristic
76	Dic₅₉⋊C₈	C₂×C₄	1	1	yes	characteristic
77	C₂²⋊(C₅₉⋊C₈)	—	2	2	no	—
78	C₂²⋊(C₅₉⋊C₈)	C₂×C₄	1	1	yes	characteristic
79	C₂²⋊(C₅₉⋊C₈)	C₂×C₄	1	1	yes	characteristic
80	(C₂×D₅₉)⋊C₈	—	2	2	no	—
81	(C₂×D₅₉)⋊C₈	—	2	2	no	—
82	(C₂×D₅₉)⋊C₈	C₂×C₄	1	1	yes	characteristic
83	(C₂×D₅₉)⋊C₈	C₂×C₄	1	1	yes	characteristic
84	(C₂×D₅₉)⋊C₈	C₂×C₄	1	1	yes	characteristic
85	(C₂×D₅₉)⋊C₈	C₂×C₄	1	1	yes	characteristic
86	#14273638	—	2	2	no	—
87	#14273637	—	2	2	no	—
88	C₄×C₅₉⋊C₈	C₂³	1	1	yes	characteristic
89	C₄×C₅₉⋊C₈	C₂³	1	1	yes	characteristic
90	C₈×Dic₅₉	—	2	2	no	—
91	C₈×Dic₅₉	C₂×C₄	1	1	yes	characteristic
92	C₈×Dic₅₉	C₂×C₄	1	1	yes	characteristic
93	C₈×Dic₅₉	C₂×C₄	1	1	yes	characteristic
94	C₈×Dic₅₉	C₂×C₄	1	1	yes	characteristic
95	C₂²×C₈×C₅₉	C₂×C₄	1	1	yes	characteristic
96	C₂²×C₈×C₅₉	C₂×C₄	1	1	yes	characteristic
97	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
98	C₄⋊C₈×C₅₉	C₂³	1	2	yes	—
99	C₄⋊C₈×C₅₉	C₂³	1	2	yes	—
100	C₂²⋊C₈×C₅₉	—	2	2	no	—
101	C₄×C₈×C₅₉	—	2	2	no	—
102	C₄×C₈×C₅₉	C₂×C₄	1	1	yes	characteristic
103	C₄×C₈×C₅₉	C₂×C₄	1	1	yes	characteristic
104	C₄×C₈×C₅₉	C₂³	1	1	yes	characteristic
105	C₄×C₈×C₅₉	C₂³	1	1	yes	characteristic
106	C₂²×C₄×C₅₉	C₂²×C₄	1	1	yes	characteristic
107	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
108	C₂²×C₄×C₅₉	C₂×Q₈	1	1	yes	characteristic
109	C₂×C₂²⋊D₅₉	C₄⋊C₄	1	1	yes	characteristic
110	C₂×C₂²⋊D₅₉	C₄⋊C₄	1	1	yes	characteristic
111	#11745685	—	2	2	no	—
112	#11745685	—	2	2	no	—
113	C₂×D₂₃₆	C₄⋊C₄	1	1	yes	characteristic
114	C₂×C₄×D₅₉	C₂²×C₄	1	1	yes	characteristic
115	C₂×C₄×D₅₉	C₂²×C₄	1	1	yes	characteristic
116	C₂×C₄×D₅₉	C₂×D₄	1	1	yes	characteristic
117	C₂×C₄×D₅₉	C₂×D₄	1	1	yes	characteristic
118	C₂×C₄×D₅₉	C₂×Q₈	1	1	yes	characteristic
119	C₂×C₄×D₅₉	C₂×Q₈	1	1	yes	characteristic
120	C₂×Dic₁₁₈	C₄⋊C₄	1	1	yes	characteristic
121	C₂×C₈×C₅₉	—	2	2	no	—
122	C₂×C₈×C₅₉	—	2	2	no	—
123	C₂×C₈×C₅₉	—	2	2	no	—
124	C₂×C₈×C₅₉	—	4	1	no	—
125	C₂×C₈×C₅₉	C₂²×C₄	1	1	yes	characteristic
126	C₂×C₈×C₅₉	C₂²×C₄	1	1	yes	characteristic
127	C₂×C₈×C₅₉	C₂²×C₄	1	1	yes	characteristic
128	C₂×C₈×C₅₉	C₂²×C₄	1	1	yes	characteristic
129	C₄²×C₅₉	C₂²×C₄	1	1	yes	characteristic
130	C₄²×C₅₉	C₂×D₄	1	1	yes	characteristic
131	C₄²×C₅₉	C₂×Q₈	1	1	yes	characteristic
132	C₄²×C₅₉	C₂⁴	1	1	yes	characteristic
133	C₂²⋊Dic₅₉	C₄⋊C₄	1	1	yes	characteristic
134	C₂²⋊Dic₅₉	C₄⋊C₄	1	1	yes	characteristic
135	(C₂×D₅₉)⋊C₄	C₄⋊C₄	1	1	yes	characteristic
136	(C₂×D₅₉)⋊C₄	C₄⋊C₄	1	1	yes	characteristic
137	(C₂×D₅₉)⋊C₄	C₄⋊C₄	1	1	yes	characteristic
138	(C₂×D₅₉)⋊C₄	C₄⋊C₄	1	1	yes	characteristic
139	C₄⋊Dic₅₉	C₄⋊C₄	1	1	yes	characteristic
140	C₄⋊Dic₅₉	C₄⋊C₄	1	1	yes	characteristic
141	Dic₅₉⋊C₄	C₄⋊C₄	1	1	yes	characteristic
142	Dic₅₉⋊C₄	C₄⋊C₄	1	1	yes	characteristic
143	Dic₅₉⋊C₄	C₄⋊C₄	1	1	yes	characteristic
144	Dic₅₉⋊C₄	C₄⋊C₄	1	1	yes	characteristic
145	C₄×Dic₅₉	C₂²×C₄	1	1	yes	characteristic
146	C₄×Dic₅₉	C₂²×C₄	1	1	yes	characteristic
147	C₄×Dic₅₉	C₂×D₄	1	1	yes	characteristic
148	C₄×Dic₅₉	C₂×D₄	1	1	yes	characteristic
149	C₄×Dic₅₉	C₂×Q₈	1	1	yes	characteristic
150	C₄×Dic₅₉	C₂×Q₈	1	1	yes	characteristic
151	C₂×C₅₉⋊C₈	—	2	2	no	—
152	C₂×C₅₉⋊C₈	—	2	2	no	—
153	C₂×C₅₉⋊C₈	C₂²×C₄	1	1	yes	characteristic
154	C₂×C₅₉⋊C₈	C₂²×C₄	1	1	yes	characteristic
155	C₂×C₅₉⋊C₈	C₂²×C₄	1	1	yes	characteristic
156	C₂×C₅₉⋊C₈	C₂²×C₄	1	1	yes	characteristic
157	#11745659	—	4	4	no	—
158	C₈×D₅₉	—	2	2	no	—
159	C₈×D₅₉	—	2	2	no	—
160	C₈×D₅₉	—	4	1	no	—
161	C₈×D₅₉	—	4	1	no	—
162	C₈×D₅₉	—	4	4	no	—
163	C₂³×C₅₉	C₂×C₄⋊C₄	1	1	yes	characteristic
164	C₂²×D₅₉	C₂×C₄⋊C₄	1	1	yes	characteristic
165	C₂²×D₅₉	C₂×C₄⋊C₄	1	1	yes	characteristic
166	C₂×C₄×C₅₉	—	2	1	no	—
167	C₂×C₄×C₅₉	—	2	1	no	—
168	C₂×C₄×C₅₉	—	2	1	no	—
169	C₂×C₄×C₅₉	—	2	1	no	—
170	C₂×C₄×C₅₉	—	4	1	no	—
171	C₂×C₄×C₅₉	C₂×C₄⋊C₄	1	1	yes	characteristic
172	C₂×C₄×C₅₉	C₂×C₄⋊C₄	1	1	yes	characteristic
173	C₂×C₄×C₅₉	C₂×C₄⋊C₄	1	1	yes	characteristic
174	C₂×C₄×C₅₉	C₂³×C₄	1	1	yes	characteristic
175	C₂×C₄×C₅₉	C₂²×D₄	1	1	yes	characteristic
176	C₂×C₄×C₅₉	C₂²×Q₈	1	1	yes	characteristic
177	C₂²⋊D₅₉	—	2	2	no	—
178	C₂²⋊D₅₉	—	2	2	no	—
179	C₂×Dic₅₉	C₂×C₄⋊C₄	1	1	yes	characteristic
180	C₂×Dic₅₉	C₂×C₄⋊C₄	1	1	yes	characteristic
181	C₂×Dic₅₉	C₂×C₄⋊C₄	1	1	yes	characteristic
182	C₂×Dic₅₉	C₂×C₄⋊C₄	1	1	yes	characteristic
183	C₂×Dic₅₉	C₂×C₄⋊C₄	1	1	yes	characteristic
184	C₂×Dic₅₉	C₂×C₄⋊C₄	1	1	yes	characteristic
185	D₂₃₆	—	2	2	no	—
186	C₄×D₅₉	—	2	1	no	—
187	C₄×D₅₉	—	2	1	no	—
188	C₄×D₅₉	—	2	1	no	—
189	C₄×D₅₉	—	2	1	no	—
190	C₄×D₅₉	—	2	1	no	—
191	C₄×D₅₉	—	2	1	no	—
192	C₄×D₅₉	—	4	1	no	—
193	C₄×D₅₉	—	4	1	no	—
194	C₄×D₅₉	#135	1	2	yes	—
195	C₄×D₅₉	#135	1	2	yes	—
196	Dic₁₁₈	—	2	2	no	—
197	C₈×C₅₉	—	2	1	no	—
198	C₈×C₅₉	—	2	1	no	—
199	C₈×C₅₉	—	2	1	no	—
200	C₈×C₅₉	—	4	2	no	—
201	C₈×C₅₉	—	4	2	no	—
202	C₈×C₅₉	#131	1	2	yes	—
203	C₅₉⋊C₈	—	2	1	no	—
204	C₅₉⋊C₈	—	2	1	no	—
205	C₅₉⋊C₈	—	2	1	no	—
206	C₅₉⋊C₈	—	2	1	no	—
207	C₅₉⋊C₈	—	4	2	no	—
208	C₅₉⋊C₈	—	4	2	no	—
209	#17829	—	59	1	no	maximal, Sylow
210	C₂²×C₅₉	—	2	1	no	—
211	C₂²×C₅₉	—	2	1	no	—
212	C₂²×C₅₉	—	2	1	no	—
213	C₂²×C₅₉	C₂²×C₄⋊C₄	1	1	yes	characteristic
214	C₂×D₅₉	—	2	1	no	—
215	C₂×D₅₉	—	2	1	no	—
216	C₂×D₅₉	—	2	1	no	—
217	C₂×D₅₉	—	2	1	no	—
218	C₂×D₅₉	—	2	1	no	—
219	C₂×D₅₉	#427	1	2	yes	—
220	C₄×C₅₉	—	2	1	no	—
221	C₄×C₅₉	—	2	1	no	—
222	C₄×C₅₉	—	2	1	no	—
223	C₄×C₅₉	—	2	1	no	—
224	C₄×C₅₉	C₂×#131	1	1	yes	characteristic
225	C₄×C₅₉	#568	1	1	yes	characteristic
226	C₄×C₅₉	C₂×#135	1	1	yes	characteristic
227	C₄×C₅₉	C₂×#135	1	1	yes	characteristic
228	Dic₅₉	—	2	1	no	—
229	Dic₅₉	—	2	1	no	—
230	Dic₅₉	—	2	1	no	—
231	Dic₅₉	—	2	1	no	—
232	Dic₅₉	—	2	1	no	—
233	Dic₅₉	#427	1	2	yes	—
234	C₈×#41	—	59	1	no	—
235	#2925	—	59	2	no	—
236	#1572	—	59	2	no	—
237	#1572	—	59	2	no	—
238	#1570	—	59	2	no	—
239	#1568	—	59	1	no	—
240	#1568	—	59	1	no	—
241	#1567	—	59	1	no	—
242	#1564	—	59	1	no	—
243	#1564	D₅₉	1	1	yes	characteristic, complemented
244	C₂×#335	—	59	1	no	—
245	C₂×C₅₉	—	4	1	no	—
246	C₂×C₅₉	#2906	1	1	yes	characteristic
247	C₂×C₅₉	C₂×#427	1	1	yes	characteristic
248	C₂×C₅₉	#2916	1	1	yes	characteristic
249	D₅₉	—	2	2	no	—
250	D₅₉	—	4	1	no	—
251	C₄×#41	—	59	1	no	—
252	C₈×Q₈	—	59	1	no	—
253	C₈×Q₈	—	59	1	no	—
254	C₈×D₄	—	59	1	no	—
255	C₈×D₄	—	59	1	no	—
256	C₈×D₄	—	59	1	no	—
257	C₈×D₄	—	59	1	no	—
258	C₈×D₄	—	59	1	no	—
259	C₈×D₄	—	59	1	no	—
260	#433	—	118	2	no	—
261	#433	—	118	2	no	—
262	#432	—	59	2	no	—
263	#432	—	59	2	no	—
264	#431	—	59	1	no	—
265	#431	—	59	1	no	—
266	#431	—	59	1	no	—
267	#431	—	59	2	no	—
268	#431	C₂×D₅₉	1	2	yes	—
269	#423	—	59	2	no	—
270	C₂×C₄⋊C₈	—	59	2	no	—
271	#408	—	118	2	no	—
272	#405	—	118	2	no	—
273	C₂×C₄×C₈	—	59	1	no	—
274	C₂×C₄×C₈	—	59	1	no	—
275	C₂×C₄×C₈	C₂×D₅₉	1	1	yes	characteristic
276	#335	—	59	2	no	—
277	#335	—	59	2	no	—
278	#335	—	59	1	no	—
279	#335	—	59	1	no	—
280	#335	C₂×D₅₉	1	1	yes	characteristic
281	#335	C₂×D₅₉	1	1	yes	characteristic
282	#334	—	59	2	no	—
283	#334	—	59	2	no	—
284	#334	—	59	2	no	—
285	#334	C₂×D₅₉	1	2	yes	—
286	C₅₉	#17829	1	1	yes	characteristic, complemented, Sylow
287	C₂×#41	—	59	1	no	—
288	C₂×M₁₆	—	118	2	no	—
289	C₂²×C₈	—	59	1	no	—
290	C₂²×C₈	—	59	1	no	—
291	C₂²×C₈	—	59	1	no	—
292	C₂²×C₈	—	59	1	no	—
293	C₂²×C₈	—	118	2	no	—
294	C₂²×C₈	C₄×D₅₉	1	1	yes	characteristic
295	C₂²×C₈	C₄×D₅₉	1	1	yes	characteristic
296	C₄×Q₈	—	59	1	no	—
297	C₄×Q₈	—	59	1	no	—
298	C₄×D₄	—	59	1	no	—
299	C₄×D₄	—	59	1	no	—
300	C₄×D₄	—	59	1	no	—
301	C₄×D₄	—	59	1	no	—
302	C₄×D₄	—	59	1	no	—
303	C₄×D₄	—	59	1	no	—
304	#117	—	59	1	no	—
305	#117	—	59	1	no	—
306	#117	—	59	1	no	—
307	C₂×C₄²	—	59	1	no	—
308	C₂×C₄²	—	59	1	no	—
309	C₂×C₄²	C₂²×D₅₉	1	1	yes	characteristic
310	C₄⋊C₈	—	59	1	no	—
311	C₄⋊C₈	—	59	1	no	—
312	C₄⋊C₈	—	59	1	no	—
313	C₄⋊C₈	—	59	1	no	—
314	C₄⋊C₈	—	59	1	no	—
315	C₄⋊C₈	—	59	1	no	—
316	C₄⋊C₈	—	59	2	no	—
317	C₄⋊C₈	—	59	2	no	—
318	C₄⋊C₈	—	118	2	no	—
319	C₄⋊C₈	—	118	2	no	—
320	C₄⋊C₈	C₂²×D₅₉	1	2	yes	—
321	C₄⋊C₈	C₂²×D₅₉	1	2	yes	—
322	C₂²⋊C₈	—	2	2	no	—
323	C₂²⋊C₈	—	59	1	no	—
324	C₂²⋊C₈	—	59	1	no	—
325	C₂²⋊C₈	—	59	1	no	—
326	C₂²⋊C₈	—	59	1	no	—
327	C₂²⋊C₈	—	59	1	no	—
328	C₂²⋊C₈	—	59	1	no	—
329	C₂²⋊C₈	—	118	2	no	—
330	C₂²⋊C₈	—	118	2	no	—
331	C₂²⋊C₈	—	118	2	no	—
332	#97	—	118	2	no	—
333	#97	—	118	2	no	—
334	C₄×C₈	—	2	2	no	—
335	C₄×C₈	—	59	1	no	—
336	C₄×C₈	—	59	1	no	—
337	C₄×C₈	—	59	1	no	—
338	C₄×C₈	—	59	1	no	—
339	C₄×C₈	—	59	1	no	—
340	C₄×C₈	—	59	1	no	—
341	C₄×C₈	—	118	2	no	—
342	C₄×C₈	C₄×D₅₉	1	1	yes	characteristic
343	C₄×C₈	C₄×D₅₉	1	1	yes	characteristic
344	C₄×C₈	C₂²×D₅₉	1	1	yes	characteristic
345	C₄×C₈	C₂²×D₅₉	1	1	yes	characteristic
346	#41	—	118	2	no	—
347	#41	—	118	2	no	—
348	C₂×Q₈	—	59	1	no	—
349	C₂×D₄	—	59	1	no	—
350	C₂×D₄	—	59	1	no	—
351	C₂×D₄	—	59	1	no	—
352	C₂²×C₄	—	59	1	no	—
353	C₂²×C₄	—	59	1	no	—
354	C₂²×C₄	—	59	1	no	—
355	C₂²×C₄	—	59	1	no	—
356	C₂²×C₄	—	59	1	no	—
357	C₂²×C₄	—	59	1	no	—
358	C₂²×C₄	C₂×C₄×D₅₉	1	1	yes	characteristic
359	C₂²×C₄	D₄×D₅₉	1	1	yes	characteristic
360	C₂²×C₄	Q₈×D₅₉	1	1	yes	characteristic
361	M₁₆	—	236	4	no	—
362	C₂×C₈	—	2	2	no	—
363	C₂×C₈	—	2	2	no	—
364	C₂×C₈	—	2	2	no	—
365	C₂×C₈	—	4	1	no	—
366	C₂×C₈	—	59	1	no	—
367	C₂×C₈	—	59	1	no	—
368	C₂×C₈	—	59	1	no	—
369	C₂×C₈	—	59	1	no	—
370	C₂×C₈	—	118	2	no	—
371	C₂×C₈	—	118	2	no	—
372	C₂×C₈	—	118	2	no	—
373	C₂×C₈	—	118	2	no	—
374	C₂×C₈	—	236	1	no	—
375	C₂×C₈	—	236	1	no	—
376	C₂×C₈	—	236	4	no	—
377	C₂×C₈	C₂×C₄×D₅₉	1	1	yes	characteristic
378	C₂×C₈	C₂×C₄×D₅₉	1	1	yes	characteristic
379	C₂×C₈	C₂×C₄×D₅₉	1	1	yes	characteristic
380	C₂×C₈	C₂×C₄×D₅₉	1	1	yes	characteristic
381	C₄⋊C₄	—	59	1	no	—
382	C₄⋊C₄	—	59	1	no	—
383	C₄⋊C₄	—	59	1	no	—
384	C₄⋊C₄	—	59	1	no	—
385	C₄⋊C₄	—	59	1	no	—
386	C₄⋊C₄	—	59	1	no	—
387	C₂²⋊C₄	—	59	1	no	—
388	C₂²⋊C₄	—	59	1	no	—
389	C₂²⋊C₄	—	59	1	no	—
390	C₂²⋊C₄	—	59	1	no	—
391	C₂²⋊C₄	—	59	1	no	—
392	C₂²⋊C₄	—	59	1	no	—
393	C₄²	—	59	1	no	—
394	C₄²	—	59	1	no	—
395	C₄²	—	59	1	no	—
396	C₄²	—	59	1	no	—
397	C₄²	—	59	1	no	—
398	C₄²	—	59	1	no	—
399	C₄²	C₂×C₄×D₅₉	1	1	yes	characteristic
400	C₄²	D₄×D₅₉	1	1	yes	characteristic
401	C₄²	Q₈×D₅₉	1	1	yes	characteristic
402	C₄²	C₂³×D₅₉	1	1	yes	characteristic
403	C₂³	—	59	1	no	—
404	C₂³	—	59	1	no	—
405	C₂³	C₄⋊C₄×D₅₉	1	1	yes	characteristic
406	Q₈	—	118	2	no	—
407	D₄	—	118	2	no	—
408	D₄	—	118	2	no	—
409	D₄	—	118	2	no	—
410	C₂×C₄	—	2	1	no	—
411	C₂×C₄	—	2	1	no	—
412	C₂×C₄	—	2	1	no	—
413	C₂×C₄	—	2	1	no	—
414	C₂×C₄	—	4	1	no	—
415	C₂×C₄	—	59	1	no	—
416	C₂×C₄	—	59	2	no	—
417	C₂×C₄	—	59	2	no	—
418	C₂×C₄	—	59	1	no	—
419	C₂×C₄	—	59	1	no	—
420	C₂×C₄	—	59	1	no	—
421	C₂×C₄	—	59	1	no	—
422	C₂×C₄	—	59	1	no	—
423	C₂×C₄	—	118	1	no	—
424	C₂×C₄	—	118	1	no	—
425	C₂×C₄	—	118	1	no	—
426	C₂×C₄	—	118	1	no	—
427	C₂×C₄	—	118	1	no	—
428	C₂×C₄	—	118	1	no	—
429	C₂×C₄	—	236	1	no	—
430	C₂×C₄	—	236	1	no	—
431	C₂×C₄	C₄⋊C₄×D₅₉	1	1	yes	characteristic
432	C₂×C₄	C₄⋊C₄×D₅₉	1	1	yes	characteristic
433	C₂×C₄	C₄⋊C₄×D₅₉	1	1	yes	characteristic
434	C₂×C₄	C₂²×C₄×D₅₉	1	1	yes	characteristic
435	C₂×C₄	C₂×D₄×D₅₉	1	1	yes	characteristic
436	C₂×C₄	C₂×Q₈×D₅₉	1	1	yes	characteristic
437	C₈	—	2	1	no	—
438	C₈	—	2	1	no	—
439	C₈	—	2	1	no	—
440	C₈	—	4	2	no	—
441	C₈	—	4	2	no	—
442	C₈	—	118	1	no	—
443	C₈	—	118	1	no	—
444	C₈	—	118	1	no	—
445	C₈	—	118	1	no	—
446	C₈	—	236	2	no	—
447	C₈	—	236	2	no	—
448	C₈	#14273733	1	2	yes	—
449	C₂²	—	2	1	no	—
450	C₂²	—	2	1	no	—
451	C₂²	—	2	1	no	—
452	C₂²	—	59	2	no	—
453	C₂²	—	118	1	no	—
454	C₂²	—	118	1	no	—
455	C₂²	—	118	1	no	—
456	C₂²	—	118	1	no	—
457	C₂²	—	118	1	no	—
458	C₂²	C₂×C₄⋊C₄×D₅₉	1	1	yes	characteristic
459	C₄	—	2	1	no	—
460	C₄	—	2	1	no	—
461	C₄	—	2	1	no	—
462	C₄	—	2	1	no	—
463	C₄	—	59	2	no	—
464	C₄	—	118	1	no	—
465	C₄	—	118	1	no	—
466	C₄	—	118	1	no	—
467	C₄	—	118	1	no	—
468	C₄	—	118	1	no	—
469	C₄	C₂×#14273733	1	1	yes	characteristic
470	C₄	#16838168	1	1	yes	characteristic
471	C₄	#135×D₅₉	1	1	yes	characteristic
472	C₄	#135×D₅₉	1	1	yes	characteristic
473	C₂	—	4	1	no	—
474	C₂	—	118	2	no	—
475	C₂	—	236	1	no	—
476	C₂	#21432661	1	1	yes	characteristic
477	C₂	#427×D₅₉	1	1	yes	characteristic
478	C₂	#21432704	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₅₉
commutator	C₂×C₄×C₅₉	C₂³×C₄
Frattini	C₄²	C₂³×D₅₉
Fitting	C₅₉×#1564	C₂
socle	C₂²×C₅₉	C₂²×C₄⋊C₄
prime radical	C₂×#11745685	D₄
cosocle	C₄²×C₅₉	C₂⁴
hypercenter	#1564	D₅₉
hypocenter	C₅₉	#17829
LCS	G ▷ C₂×C₄×C₅₉ ▷ C₂×C₅₉ ▷ C₅₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1564

Complements

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

N	H ≅ G/N	type
3. #21422874	C₂	semidirect
4. #21422873	C₂	semidirect
5. #21422865	C₂	semidirect
6. #21422859	C₂	semidirect
7. #21422858	C₂	semidirect
8. #21422853	C₂	semidirect
9. #21422843	C₂	semidirect
10. #335×D₅₉	C₂	semidirect
11. C₅₉×#1564	C₂	semidirect
243. #1564	D₅₉	semidirect
286. C₅₉	#17829	semidirect

Maximal subgroups

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

subgroup	index
C₈×#11745685	2
#21432757	2
#21422874	2
#21422873	2
#21422865	2
#21422859	2
#21422858	2
#21422853	2
#21422843	2
#335×D₅₉	2
C₅₉×#1564	2
#17829	59