Subgroups — #28494685

Order 15104.

782 conjugacy classes of subgroups.

The subgroup lattice has 450 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#16837430	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₄×C₅₉⋊C₈	C₂	1	1	yes	maximal, characteristic
3	C₂×#16837166	C₂	1	1	yes	maximal, characteristic
4	#21423812	C₂	1	1	yes	maximal, characteristic
5	C₂×#16837162	C₂	1	1	yes	maximal, characteristic
6	#21423793	C₂	1	1	yes	maximal, characteristic
7	C₂×C₅₉×#339	C₂	1	1	yes	maximal, characteristic
8	C₂²×#11745664	C₂²	1	1	yes	characteristic
9	C₂³×C₅₉⋊C₈	C₂²	1	1	yes	characteristic
10	C₂³×C₅₉⋊C₈	C₂²	1	1	yes	characteristic
11	C₂×#14273686	C₂²	1	1	yes	characteristic
12	#16837430	—	2	2	no	—
13	#16837430	C₄	1	4	yes	complemented
14	C₂×Dic₅₉⋊C₈	—	2	2	no	—
15	C₂×C₄×C₅₉⋊C₈	—	2	2	no	—
16	C₂×C₄×C₅₉⋊C₈	—	2	2	no	—
17	C₂×C₄×C₅₉⋊C₈	—	2	2	no	—
18	#16837166	—	2	2	no	—
19	#16837164	C₄	1	4	yes	complemented
20	#16837162	C₄	1	4	yes	complemented
21	#16837157	—	2	2	no	—
22	C₂²×M₁₆×C₅₉	C₂²	1	1	yes	characteristic
23	C₂×#117×C₅₉	C₂²	1	1	yes	characteristic
24	C₂²×C₄²×C₅₉	C₂²	1	1	yes	characteristic
25	C₅₉×#339	—	2	2	no	—
26	C₂×#11745664	—	2	1	no	—
27	C₂×#11745664	—	2	1	no	—
28	C₂×#11745664	—	2	1	no	—
29	C₂×#11745664	—	2	1	no	—
30	C₂×#11745664	—	2	1	no	—
31	C₂×#11745664	C₂×C₄	1	2	yes	—
32	C₂²×C₅₉⋊C₈	—	2	1	no	—
33	C₂²×C₅₉⋊C₈	—	2	1	no	—
34	C₂²×C₅₉⋊C₈	—	2	1	no	—
35	C₂²×C₅₉⋊C₈	—	2	1	no	—
36	C₂²×C₅₉⋊C₈	—	2	1	no	—
37	C₂²×C₅₉⋊C₈	—	2	1	no	—
38	C₂²×C₅₉⋊C₈	—	2	1	no	—
39	C₂²×C₅₉⋊C₈	—	2	1	no	—
40	C₂²×C₅₉⋊C₈	—	2	1	no	—
41	C₂²×C₅₉⋊C₈	C₂×C₄	1	2	yes	—
42	C₂²×C₅₉⋊C₈	C₂×C₄	1	2	yes	—
43	C₂²×C₅₉⋊C₈	D₄	1	2	yes	—
44	C₂²×C₅₉⋊C₈	D₄	1	2	yes	—
45	C₂²×C₅₉⋊C₈	D₄	1	2	yes	—
46	C₂²×C₅₉⋊C₈	Q₈	1	2	yes	—
47	#14273686	—	2	1	no	—
48	#14273686	—	2	1	no	—
49	#14273686	C₂×C₄	1	2	yes	—
50	#14273686	C₂×C₄	1	2	yes	—
51	C₂×C₄⋊Dic₅₉	C₂×C₄	1	2	yes	—
52	C₂×C₂²⋊Dic₅₉	—	2	1	no	—
53	C₂×C₄×Dic₅₉	—	2	1	no	—
54	Dic₅₉⋊C₈	—	2	8	no	—
55	C₄×C₅₉⋊C₈	—	2	8	no	—
56	C₂³×C₄×C₅₉	—	2	1	no	—
57	C₂³×C₄×C₅₉	C₂³	1	1	yes	characteristic
58	C₂×M₁₆×C₅₉	—	2	1	no	—
59	C₂×M₁₆×C₅₉	—	2	1	no	—
60	C₂×M₁₆×C₅₉	—	2	1	no	—
61	C₂×M₁₆×C₅₉	—	2	1	no	—
62	C₂×M₁₆×C₅₉	—	2	1	no	—
63	C₂×M₁₆×C₅₉	C₂×C₄	1	2	yes	—
64	C₂²×C₈×C₅₉	—	2	1	no	—
65	#117×C₅₉	—	2	1	no	—
66	#117×C₅₉	—	2	1	no	—
67	#117×C₅₉	—	2	1	no	—
68	#117×C₅₉	—	2	1	no	—
69	C₂×C₄⋊C₄×C₅₉	C₂×C₄	1	2	yes	—
70	C₂×C₂²⋊C₄×C₅₉	—	2	1	no	—
71	C₂×C₄²×C₅₉	—	2	1	no	—
72	C₂×C₄²×C₅₉	—	2	1	no	—
73	C₂×C₄²×C₅₉	—	2	1	no	—
74	C₂×C₄²×C₅₉	—	2	1	no	—
75	C₂×C₄²×C₅₉	C₂×C₄	1	2	yes	—
76	C₂×C₄²×C₅₉	D₄	1	2	yes	—
77	C₂×C₄²×C₅₉	Q₈	1	2	yes	—
78	C₂⁴×C₅₉	#41	1	1	yes	characteristic
79	C₂²×C₄×C₅₉	—	2	8	no	—
80	C₂²×C₄×C₅₉	—	2	2	no	—
81	C₂²×C₄×C₅₉	—	2	2	no	—
82	C₂²×C₄×C₅₉	—	2	2	no	—
83	C₂²×C₄×C₅₉	—	2	2	no	—
84	C₂²×C₄×C₅₉	C₂²×C₄	1	1	yes	characteristic
85	C₂²×C₄×C₅₉	C₂²×C₄	1	1	yes	characteristic
86	C₂²×C₄×C₅₉	C₂²×C₄	1	1	yes	characteristic
87	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
88	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
89	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
90	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
91	C₂²×C₄×C₅₉	C₂×Q₈	1	1	yes	characteristic
92	C₂²×C₄×C₅₉	C₂×Q₈	1	1	yes	characteristic
93	C₂²×C₄×C₅₉	#41	1	1	yes	characteristic
94	C₂²×C₄×C₅₉	#41	1	1	yes	characteristic
95	C₂²×C₄×C₅₉	#41	1	1	yes	characteristic
96	C₂²×C₄×C₅₉	#41	1	1	yes	characteristic
97	C₂²×C₄×C₅₉	#41	1	1	yes	characteristic
98	C₂²×Dic₅₉	—	2	2	no	—
99	M₁₆×C₅₉	—	2	2	no	—
100	M₁₆×C₅₉	—	2	2	no	—
101	M₁₆×C₅₉	—	4	1	no	—
102	M₁₆×C₅₉	—	4	1	no	—
103	C₂×C₈×C₅₉	—	2	2	no	—
104	C₂×C₈×C₅₉	—	4	1	no	—
105	C₂×C₈×C₅₉	—	4	1	no	—
106	C₄⋊C₄×C₅₉	—	2	2	no	—
107	C₄⋊C₄×C₅₉	—	2	2	no	—
108	C₂²⋊C₄×C₅₉	—	4	1	no	—
109	C₂²⋊C₄×C₅₉	—	4	1	no	—
110	C₄²×C₅₉	—	2	2	no	—
111	C₄²×C₅₉	—	2	2	no	—
112	C₄²×C₅₉	—	2	2	no	—
113	C₄²×C₅₉	—	4	1	no	—
114	C₄²×C₅₉	—	4	1	no	—
115	C₄²×C₅₉	C₄⋊C₄	1	4	yes	—
116	C₂²⋊Dic₅₉	—	2	2	no	—
117	C₂²⋊Dic₅₉	—	2	2	no	—
118	C₄⋊Dic₅₉	—	2	2	no	—
119	C₄⋊Dic₅₉	C₄²	1	4	yes	—
120	C₄×Dic₅₉	—	2	2	no	—
121	C₄×Dic₅₉	—	2	2	no	—
122	#11745664	—	2	2	no	—
123	#11745664	—	2	2	no	—
124	#11745664	—	4	1	no	—
125	#11745664	—	4	1	no	—
126	C₂×C₅₉⋊C₈	—	2	2	no	—
127	C₂×C₅₉⋊C₈	—	2	2	no	—
128	C₂×C₅₉⋊C₈	—	2	2	no	—
129	C₂×C₅₉⋊C₈	—	2	2	no	—
130	C₂×C₅₉⋊C₈	—	2	2	no	—
131	C₂×C₅₉⋊C₈	—	2	2	no	—
132	C₂×C₅₉⋊C₈	—	2	2	no	—
133	C₂×C₅₉⋊C₈	—	2	2	no	—
134	C₂×C₅₉⋊C₈	—	2	2	no	—
135	C₂×C₅₉⋊C₈	—	2	2	no	—
136	C₂×C₅₉⋊C₈	—	2	2	no	—
137	C₂×C₅₉⋊C₈	—	2	2	no	—
138	C₂×C₅₉⋊C₈	—	2	2	no	—
139	C₂×C₅₉⋊C₈	—	4	1	no	—
140	C₂×C₅₉⋊C₈	—	4	1	no	—
141	C₂×C₅₉⋊C₈	C₂²⋊C₄	1	4	yes	—
142	C₂×C₅₉⋊C₈	C₄⋊C₄	1	4	yes	—
143	C₂³×C₅₉	—	2	4	no	—
144	C₂³×C₅₉	#117	1	1	yes	characteristic
145	C₂³×C₅₉	C₄×D₄	1	1	yes	characteristic
146	C₂³×C₅₉	C₄×D₄	1	1	yes	characteristic
147	C₂³×C₅₉	C₂²⋊Q₈	1	1	yes	characteristic
148	C₂³×C₅₉	#123	1	1	yes	characteristic
149	C₂³×C₅₉	#125	1	1	yes	characteristic
150	C₂³×C₅₉	#126	1	1	yes	characteristic
151	C₂×C₄×C₅₉	—	2	8	no	—
152	C₂×C₄×C₅₉	—	2	8	no	—
153	C₂×C₄×C₅₉	—	2	8	no	—
154	C₂×C₄×C₅₉	—	2	4	no	—
155	C₂×C₄×C₅₉	—	4	2	no	—
156	C₂×C₄×C₅₉	—	4	4	no	—
157	C₂×C₄×C₅₉	C₂×C₄²	1	1	yes	characteristic
158	C₂×C₄×C₅₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
159	C₂×C₄×C₅₉	C₂×C₄⋊C₄	1	1	yes	characteristic
160	C₂×C₄×C₅₉	C₂×C₄⋊C₄	1	1	yes	characteristic
161	C₂×C₄×C₅₉	#117	1	1	yes	characteristic
162	C₂×C₄×C₅₉	#117	1	1	yes	characteristic
163	C₂×C₄×C₅₉	C₄×D₄	1	1	yes	characteristic
164	C₂×C₄×C₅₉	C₄×D₄	1	1	yes	characteristic
165	C₂×C₄×C₅₉	C₄×D₄	1	1	yes	characteristic
166	C₂×C₄×C₅₉	C₄×D₄	1	1	yes	characteristic
167	C₂×C₄×C₅₉	C₄×D₄	1	1	yes	characteristic
168	C₂×C₄×C₅₉	C₄×D₄	1	1	yes	characteristic
169	C₂×C₄×C₅₉	C₄×Q₈	1	1	yes	characteristic
170	C₂×C₄×C₅₉	C₄×Q₈	1	1	yes	characteristic
171	C₂×C₄×C₅₉	C₄×Q₈	1	1	yes	characteristic
172	C₂×C₄×C₅₉	C₄×Q₈	1	1	yes	characteristic
173	C₂×C₄×C₅₉	#120	1	1	yes	characteristic
174	C₂×C₄×C₅₉	#121	1	1	yes	characteristic
175	C₂×C₄×C₅₉	#121	1	1	yes	characteristic
176	C₂×C₄×C₅₉	C₂²⋊Q₈	1	1	yes	characteristic
177	C₂×C₄×C₅₉	C₂²⋊Q₈	1	1	yes	characteristic
178	C₂×C₄×C₅₉	C₂²⋊Q₈	1	1	yes	characteristic
179	C₂×C₄×C₅₉	#123	1	1	yes	characteristic
180	C₂×C₄×C₅₉	#123	1	1	yes	characteristic
181	C₂×C₄×C₅₉	#124	1	1	yes	characteristic
182	C₂×C₄×C₅₉	#125	1	1	yes	characteristic
183	C₂×C₄×C₅₉	#126	1	1	yes	characteristic
184	C₂×C₄×C₅₉	C₄⋊Q₈	1	1	yes	characteristic
185	C₂×Dic₅₉	—	2	4	no	—
186	C₂×Dic₅₉	—	4	4	no	—
187	C₈×C₅₉	—	4	2	no	—
188	C₅₉⋊C₈	—	2	4	no	—
189	C₅₉⋊C₈	—	2	4	no	—
190	C₅₉⋊C₈	—	4	2	no	—
191	#10882	—	59	1	no	maximal, Sylow
192	C₂²×C₅₉	—	2	2	no	—
193	C₂²×C₅₉	—	2	2	no	—
194	C₂²×C₅₉	—	2	2	no	—
195	C₂²×C₅₉	—	2	2	no	—
196	C₂²×C₅₉	—	2	2	no	—
197	C₂²×C₅₉	—	2	2	no	—
198	C₂²×C₅₉	C₄×C₂²⋊C₄	1	1	yes	characteristic
199	C₂²×C₅₉	#385	1	1	yes	characteristic
200	C₂²×C₅₉	#387	1	1	yes	characteristic
201	C₂²×C₅₉	#387	1	1	yes	characteristic
202	C₂²×C₅₉	#387	1	1	yes	characteristic
203	C₂²×C₅₉	#388	1	1	yes	characteristic
204	C₂²×C₅₉	#389	1	1	yes	characteristic
205	C₂²×C₅₉	#443	1	4	yes	—
206	C₄×C₅₉	—	2	8	no	—
207	C₄×C₅₉	—	8	2	no	—
208	C₄×C₅₉	C₄×C₄⋊C₄	1	1	yes	characteristic
209	C₄×C₅₉	C₄×C₄⋊C₄	1	1	yes	characteristic
210	C₄×C₅₉	#385	1	1	yes	characteristic
211	C₄×C₅₉	#386	1	1	yes	characteristic
212	C₄×C₅₉	#387	1	1	yes	characteristic
213	C₄×C₅₉	#388	1	1	yes	characteristic
214	C₄×C₅₉	#389	1	1	yes	characteristic
215	C₄×C₅₉	#391	1	1	yes	characteristic
216	Dic₅₉	—	4	4	no	—
217	C₂×#424	—	59	1	no	—
218	C₂²×C₄×C₈	—	59	1	no	—
219	C₂×#341	—	59	1	no	—
220	#1735	—	59	1	no	—
221	C₂×#339	—	59	1	no	—
222	C₂×#339	D₅₉	1	1	yes	characteristic
223	#1729	—	59	1	no	—
224	C₂×C₅₉	—	2	1	no	—
225	C₂×C₅₉	—	2	1	no	—
226	C₂×C₅₉	—	2	1	no	—
227	C₂×C₅₉	—	2	1	no	—
228	C₂×C₅₉	#1436	1	1	yes	characteristic
229	C₂×C₅₉	#1764	1	2	yes	—
230	C₂×C₅₉	#1937	1	2	yes	—
231	C₂×C₅₉	#1945	1	2	yes	—
232	C₂²×M₁₆	—	59	1	no	—
233	C₂²×M₁₆	C₂×D₅₉	1	1	yes	characteristic
234	C₂³×C₈	—	59	1	no	—
235	C₂³×C₈	—	59	1	no	—
236	C₂×#117	—	59	1	no	—
237	C₂×#117	C₂×D₅₉	1	1	yes	characteristic
238	C₂²×C₄²	C₂×D₅₉	1	1	yes	characteristic
239	#424	—	59	4	no	—
240	#424	—	118	2	no	—
241	C₂×C₄⋊C₈	—	118	2	no	—
242	C₂×C₄×C₈	—	118	2	no	—
243	C₂×C₄×C₈	—	118	2	no	—
244	C₂×C₄×C₈	—	118	2	no	—
245	#341	—	118	2	no	—
246	#340	—	59	4	no	—
247	#339	—	2	2	no	—
248	#339	—	59	4	no	—
249	#336	—	118	2	no	—
250	C₅₉	#10882	1	1	yes	characteristic, complemented, Sylow
251	C₂³×C₄	—	2	1	no	—
252	C₂³×C₄	C₂²×D₅₉	1	1	yes	characteristic
253	C₂×M₁₆	—	2	1	no	—
254	C₂×M₁₆	—	2	1	no	—
255	C₂×M₁₆	—	2	1	no	—
256	C₂×M₁₆	—	2	1	no	—
257	C₂×M₁₆	—	2	1	no	—
258	C₂×M₁₆	—	59	2	no	—
259	C₂×M₁₆	—	118	1	no	—
260	C₂×M₁₆	—	118	1	no	—
261	C₂×M₁₆	—	118	1	no	—
262	C₂×M₁₆	—	118	1	no	—
263	C₂×M₁₆	—	118	1	no	—
264	C₂×M₁₆	C₄×D₅₉	1	2	yes	—
265	C₂²×C₈	—	2	1	no	—
266	C₂²×C₈	—	59	2	no	—
267	C₂²×C₈	—	59	2	no	—
268	C₂²×C₈	—	59	2	no	—
269	C₂²×C₈	—	59	2	no	—
270	C₂²×C₈	—	59	2	no	—
271	C₂²×C₈	—	59	2	no	—
272	C₂²×C₈	—	118	1	no	—
273	C₂²×C₈	—	118	1	no	—
274	C₂²×C₈	—	118	1	no	—
275	C₂²×C₈	—	118	1	no	—
276	C₂²×C₈	—	118	1	no	—
277	C₂²×C₈	—	118	1	no	—
278	C₂²×C₈	—	118	1	no	—
279	C₂²×C₈	—	118	1	no	—
280	C₂²×C₈	—	118	1	no	—
281	#117	—	2	1	no	—
282	#117	—	2	1	no	—
283	#117	—	2	1	no	—
284	#117	—	2	1	no	—
285	#117	—	59	2	no	—
286	#117	—	59	2	no	—
287	#117	—	118	1	no	—
288	#117	—	118	1	no	—
289	C₂×C₄⋊C₄	—	59	2	no	—
290	C₂×C₄⋊C₄	C₄×D₅₉	1	2	yes	—
291	C₂×C₂²⋊C₄	—	2	1	no	—
292	C₂×C₂²⋊C₄	—	118	1	no	—
293	C₂×C₄²	—	2	1	no	—
294	C₂×C₄²	—	2	1	no	—
295	C₂×C₄²	—	2	1	no	—
296	C₂×C₄²	—	2	1	no	—
297	C₂×C₄²	—	118	1	no	—
298	C₂×C₄²	Dic₁₁₈	1	2	yes	—
299	C₂×C₄²	C₄×D₅₉	1	2	yes	—
300	C₂×C₄²	C₂²⋊D₅₉	1	2	yes	—
301	C₄⋊C₈	—	118	8	no	—
302	C₄×C₈	—	118	8	no	—
303	C₂⁴	#11745687	1	1	yes	characteristic
304	C₂²×C₄	—	2	8	no	—
305	C₂²×C₄	—	2	2	no	—
306	C₂²×C₄	—	2	2	no	—
307	C₂²×C₄	—	2	2	no	—
308	C₂²×C₄	—	2	2	no	—
309	C₂²×C₄	—	118	2	no	—
310	C₂²×C₄	C₂×Dic₁₁₈	1	1	yes	characteristic
311	C₂²×C₄	C₂×C₄×D₅₉	1	1	yes	characteristic
312	C₂²×C₄	C₂×C₄×D₅₉	1	1	yes	characteristic
313	C₂²×C₄	C₂×C₄×D₅₉	1	1	yes	characteristic
314	C₂²×C₄	#11745685	1	1	yes	characteristic
315	C₂²×C₄	#11745685	1	1	yes	characteristic
316	C₂²×C₄	D₄×D₅₉	1	1	yes	characteristic
317	C₂²×C₄	D₄×D₅₉	1	1	yes	characteristic
318	C₂²×C₄	D₄×D₅₉	1	1	yes	characteristic
319	C₂²×C₄	#11745687	1	1	yes	characteristic
320	C₂²×C₄	#11745687	1	1	yes	characteristic
321	C₂²×C₄	Q₈×D₅₉	1	1	yes	characteristic
322	C₂²×C₄	#11745689	1	1	yes	characteristic
323	C₂²×C₄	C₂×C₂²⋊D₅₉	1	1	yes	characteristic
324	M₁₆	—	2	2	no	—
325	M₁₆	—	2	2	no	—
326	M₁₆	—	4	1	no	—
327	M₁₆	—	4	1	no	—
328	M₁₆	—	118	2	no	—
329	M₁₆	—	118	2	no	—
330	M₁₆	—	236	1	no	—
331	M₁₆	—	236	1	no	—
332	C₂×C₈	—	2	2	no	—
333	C₂×C₈	—	4	1	no	—
334	C₂×C₈	—	4	1	no	—
335	C₂×C₈	—	59	4	no	—
336	C₂×C₈	—	59	4	no	—
337	C₂×C₈	—	118	2	no	—
338	C₂×C₈	—	118	2	no	—
339	C₂×C₈	—	118	2	no	—
340	C₂×C₈	—	118	2	no	—
341	C₂×C₈	—	118	2	no	—
342	C₂×C₈	—	118	2	no	—
343	C₂×C₈	—	118	2	no	—
344	C₂×C₈	—	118	2	no	—
345	C₂×C₈	—	118	2	no	—
346	C₂×C₈	—	118	2	no	—
347	C₂×C₈	—	118	2	no	—
348	C₂×C₈	—	118	2	no	—
349	C₂×C₈	—	118	2	no	—
350	C₂×C₈	—	236	1	no	—
351	C₂×C₈	—	236	1	no	—
352	C₄⋊C₄	—	2	2	no	—
353	C₄⋊C₄	—	2	2	no	—
354	C₄⋊C₄	—	59	4	no	—
355	C₄⋊C₄	—	118	2	no	—
356	C₂²⋊C₄	—	4	1	no	—
357	C₂²⋊C₄	—	4	1	no	—
358	C₂²⋊C₄	—	118	2	no	—
359	C₂²⋊C₄	—	118	2	no	—
360	C₄²	—	2	2	no	—
361	C₄²	—	2	2	no	—
362	C₄²	—	2	2	no	—
363	C₄²	—	4	1	no	—
364	C₄²	—	4	1	no	—
365	C₄²	—	118	2	no	—
366	C₄²	—	118	2	no	—
367	C₄²	Dic₅₉⋊C₄	1	4	yes	—
368	C₂³	—	2	4	no	—
369	C₂³	#14273685	1	1	yes	characteristic
370	C₂³	(C₂²⋊D₅₉)⋊C₄	1	1	yes	characteristic
371	C₂³	(C₂²⋊D₅₉)⋊C₄	1	1	yes	characteristic
372	C₂³	#14273704	1	1	yes	characteristic
373	C₂³	#14273708	1	1	yes	characteristic
374	C₂³	#14273717	1	1	yes	characteristic
375	C₂³	#14273720	1	1	yes	characteristic
376	C₂×C₄	—	2	8	no	—
377	C₂×C₄	—	2	8	no	—
378	C₂×C₄	—	2	8	no	—
379	C₂×C₄	—	2	4	no	—
380	C₂×C₄	—	4	4	no	—
381	C₂×C₄	—	4	2	no	—
382	C₂×C₄	—	118	4	no	—
383	C₂×C₄	—	236	4	no	—
384	C₂×C₄	C₄²×D₅₉	1	1	yes	characteristic
385	C₂×C₄	C₂²⋊C₄×D₅₉	1	1	yes	characteristic
386	C₂×C₄	C₄⋊C₄×D₅₉	1	1	yes	characteristic
387	C₂×C₄	C₂×Dic₅₉⋊C₄	1	1	yes	characteristic
388	C₂×C₄	#14273683	1	1	yes	characteristic
389	C₂×C₄	#14273684	1	1	yes	characteristic
390	C₂×C₄	(C₂²⋊D₅₉)⋊C₄	1	1	yes	characteristic
391	C₂×C₄	(C₂²⋊D₅₉)⋊C₄	1	1	yes	characteristic
392	C₂×C₄	C₄×C₂²⋊D₅₉	1	1	yes	characteristic
393	C₂×C₄	C₄×C₂²⋊D₅₉	1	1	yes	characteristic
394	C₂×C₄	#14273689	1	1	yes	characteristic
395	C₂×C₄	#14273689	1	1	yes	characteristic
396	C₂×C₄	#14273692	1	1	yes	characteristic
397	C₂×C₄	#14273692	1	1	yes	characteristic
398	C₂×C₄	C₄×Dic₁₁₈	1	1	yes	characteristic
399	C₂×C₄	C₄×Dic₁₁₈	1	1	yes	characteristic
400	C₂×C₄	#14273695	1	1	yes	characteristic
401	C₂×C₄	#14273698	1	1	yes	characteristic
402	C₂×C₄	#14273700	1	1	yes	characteristic
403	C₂×C₄	#14273703	1	1	yes	characteristic
404	C₂×C₄	#14273704	1	1	yes	characteristic
405	C₂×C₄	#14273705	1	1	yes	characteristic
406	C₂×C₄	#14273709	1	1	yes	characteristic
407	C₂×C₄	#14273712	1	1	yes	characteristic
408	C₂×C₄	#14273713	1	1	yes	characteristic
409	C₂×C₄	#14273718	1	1	yes	characteristic
410	C₂×C₄	#14273722	1	1	yes	characteristic
411	C₂×C₄	#14273726	1	1	yes	characteristic
412	C₈	—	4	2	no	—
413	C₈	—	118	4	no	—
414	C₈	—	118	4	no	—
415	C₈	—	236	2	no	—
416	C₂²	—	2	2	no	—
417	C₂²	—	2	2	no	—
418	C₂²	—	2	2	no	—
419	C₂²	—	2	2	no	—
420	C₂²	—	2	2	no	—
421	C₂²	—	2	2	no	—
422	C₂²	#16837249	1	1	yes	characteristic
423	C₂²	#16837274	1	1	yes	characteristic
424	C₂²	#16837283	1	1	yes	characteristic
425	C₂²	#16837284	1	1	yes	characteristic
426	C₂²	#16837289	1	1	yes	characteristic
427	C₂²	#16837290	1	1	yes	characteristic
428	C₂²	#16837299	1	1	yes	characteristic
429	C₂²	#16837516	1	4	yes	—
430	C₄	—	2	8	no	—
431	C₄	—	8	2	no	—
432	C₄	—	236	4	no	—
433	C₄	#16837253	1	1	yes	characteristic
434	C₄	C₄×Dic₅₉⋊C₄	1	1	yes	characteristic
435	C₄	#16837273	1	1	yes	characteristic
436	C₄	#16837278	1	1	yes	characteristic
437	C₄	#16837285	1	1	yes	characteristic
438	C₄	#16837291	1	1	yes	characteristic
439	C₄	#16837298	1	1	yes	characteristic
440	C₄	#16837306	1	1	yes	characteristic
441	C₂	—	2	1	no	—
442	C₂	—	2	1	no	—
443	C₂	—	2	1	no	—
444	C₂	—	2	1	no	—
445	C₂	#21422327	1	1	yes	characteristic
446	C₂	#21423930	1	2	yes	—
447	C₂	#21424797	1	2	yes	—
448	C₂	#21424843	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄	D₄×D₅₉
commutator	C₂×C₄×C₅₉	C₂×C₄²
Frattini	C₂³×C₄	C₂²×D₅₉
Fitting	C₂×C₅₉×#339	C₂
socle	C₂³×C₅₉	C₄×D₄
prime radical	C₂⁴×C₅₉	#41
cosocle	C₂³×C₄×C₅₉	C₂³
hypercenter	C₂×#339	D₅₉
hypocenter	C₅₉	#10882
LCS	G ▷ C₂×C₄×C₅₉ ▷ C₂×C₅₉ ▷ C₅₉
UCS	C₁ ◁ C₂²×C₄ ◁ C₂³×C₄ ◁ C₂×#339

Complements

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

N	H ≅ G/N	type
13. #16837430	C₄	semidirect
19. #16837164	C₄	semidirect
20. #16837162	C₄	semidirect
250. C₅₉	#10882	semidirect

Maximal subgroups

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

subgroup	index
C₂×#16837430	2
C₂²×C₄×C₅₉⋊C₈	2
C₂×#16837166	2
#21423812	2
C₂×#16837162	2
#21423793	2
C₂×C₅₉×#339	2
#10882	59