Subgroups — #28557716

Order 15104.

756 conjugacy classes of subgroups.

The subgroup lattice has 412 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#21432729	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×#11745664	C₂	1	1	yes	maximal, characteristic
3	#21422861	C₂	1	4	yes	maximal, complemented
4	#21422854	C₂	1	2	yes	maximal, complemented
5	#21422851	C₂	1	2	yes	maximal, complemented
6	#21422846	C₂	1	4	yes	maximal, complemented
7	C₂×C₅₉×#423	C₂	1	1	yes	maximal, characteristic
8	C₂²×#11745664	C₄	1	2	yes	—
9	#16837459	—	2	1	no	—
10	#16837459	C₂²	1	2	yes	—
11	#16837455	—	2	1	no	—
12	#16837455	C₂²	1	2	yes	—
13	#16837426	C₂²	1	1	yes	characteristic
14	#16837426	C₂²	1	1	yes	characteristic
15	#16837366	—	2	1	no	—
16	C₄×#11745664	—	2	1	no	—
17	C₄×#11745664	C₄	1	2	yes	—
18	C₄×#11745664	C₄	1	1	yes	characteristic
19	C₄×#11745664	C₄	1	1	yes	characteristic
20	C₄×#11745664	C₂²	1	2	yes	—
21	C₄×#11745664	C₂²	1	2	yes	—
22	C₂×#14273638	C₄	1	2	yes	—
23	C₂×C₄×C₅₉⋊C₈	C₂²	1	2	yes	—
24	#16837154	C₂²	1	8	yes	complemented
25	#16837152	C₂²	1	8	yes	complemented
26	C₂²×M₁₆×C₅₉	—	2	1	no	—
27	C₂²×C₄²×C₅₉	C₂²	1	1	yes	characteristic
28	C₅₉×#423	—	2	1	no	—
29	C₅₉×#423	—	2	1	no	—
30	C₅₉×#423	C₂²	1	2	yes	—
31	C₅₉×#423	C₂²	1	2	yes	—
32	C₂×C₄⋊C₈×C₅₉	—	2	1	no	—
33	C₂×C₄⋊C₈×C₅₉	C₂²	1	2	yes	—
34	C₂×#11745664	—	2	8	no	—
35	C₂×#11745664	—	2	1	no	—
36	C₂×#11745664	—	2	1	no	—
37	C₂×#11745664	C₂×C₄	1	2	yes	—
38	C₂×#11745664	C₂×C₄	1	4	yes	—
39	C₂×#11745664	C₂×C₄	1	2	yes	—
40	C₂²×C₅₉⋊C₈	C₂×C₄	1	4	yes	—
41	C₄⋊(C₅₉⋊C₈)	—	2	1	no	—
42	C₄⋊(C₅₉⋊C₈)	—	2	1	no	—
43	C₄⋊(C₅₉⋊C₈)	C₂³	1	2	yes	—
44	C₄⋊(C₅₉⋊C₈)	C₂³	1	2	yes	—
45	C₂²⋊(C₅₉⋊C₈)	—	2	2	no	—
46	C₂²⋊(C₅₉⋊C₈)	—	2	2	no	—
47	#14273638	—	2	2	no	—
48	#14273638	C₂×C₄	1	2	yes	—
49	#14273638	C₂×C₄	1	4	yes	—
50	#14273638	C₂×C₄	1	2	yes	—
51	C₄×C₅₉⋊C₈	—	2	2	no	—
52	C₄×C₅₉⋊C₈	C₂×C₄	1	2	yes	—
53	C₄×C₅₉⋊C₈	C₂×C₄	1	2	yes	—
54	C₄×C₅₉⋊C₈	C₂³	1	4	yes	—
55	C₂³×C₄×C₅₉	C₂×C₄	1	1	yes	characteristic
56	C₂³×C₄×C₅₉	D₄	1	1	yes	characteristic
57	C₂³×C₄×C₅₉	Q₈	1	1	yes	characteristic
58	C₂×M₁₆×C₅₉	—	2	2	no	—
59	C₂×M₁₆×C₅₉	—	2	2	no	—
60	C₂×M₁₆×C₅₉	—	4	4	no	—
61	C₂²×C₈×C₅₉	—	2	2	no	—
62	C₂×C₄²×C₅₉	C₂×C₄	1	1	yes	characteristic
63	C₂×C₄²×C₅₉	C₂×C₄	1	1	yes	characteristic
64	C₂×C₄²×C₅₉	C₂×C₄	1	1	yes	characteristic
65	C₂×C₄²×C₅₉	D₄	1	1	yes	characteristic
66	C₂×C₄²×C₅₉	D₄	1	1	yes	characteristic
67	C₂×C₄²×C₅₉	D₄	1	1	yes	characteristic
68	C₂×C₄²×C₅₉	Q₈	1	1	yes	characteristic
69	C₂×C₄²×C₅₉	Q₈	1	1	yes	characteristic
70	C₂×C₄²×C₅₉	Q₈	1	1	yes	characteristic
71	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
72	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
73	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
74	C₄⋊C₈×C₅₉	—	2	2	no	—
75	C₄⋊C₈×C₅₉	—	2	2	no	—
76	C₄⋊C₈×C₅₉	—	2	2	no	—
77	C₄⋊C₈×C₅₉	C₂³	1	4	yes	—
78	C₂⁴×C₅₉	C₄⋊C₄	1	1	yes	characteristic
79	C₂²×C₄×C₅₉	—	2	4	no	—
80	C₂²×C₄×C₅₉	—	2	2	no	—
81	C₂²×C₄×C₅₉	—	2	2	no	—
82	C₂²×C₄×C₅₉	—	4	2	no	—
83	C₂²×C₄×C₅₉	C₄⋊C₄	1	1	yes	characteristic
84	C₂²×C₄×C₅₉	C₄⋊C₄	1	1	yes	characteristic
85	C₂²×C₄×C₅₉	C₄⋊C₄	1	1	yes	characteristic
86	C₂²×C₄×C₅₉	C₄⋊C₄	1	1	yes	characteristic
87	C₂²×C₄×C₅₉	C₄⋊C₄	1	1	yes	characteristic
88	C₂²×C₄×C₅₉	C₄⋊C₄	1	1	yes	characteristic
89	C₂²×C₄×C₅₉	C₄⋊C₄	1	1	yes	characteristic
90	C₂²×C₄×C₅₉	C₄⋊C₄	1	1	yes	characteristic
91	C₂²×C₄×C₅₉	C₄⋊C₄	1	1	yes	characteristic
92	C₂²×C₄×C₅₉	C₂²×C₄	1	1	yes	characteristic
93	C₂²×C₄×C₅₉	C₂²×C₄	1	1	yes	characteristic
94	C₂²×C₄×C₅₉	C₂²×C₄	1	1	yes	characteristic
95	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
96	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
97	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
98	C₂²×C₄×C₅₉	C₂×Q₈	1	1	yes	characteristic
99	C₂²×C₄×C₅₉	C₂×Q₈	1	1	yes	characteristic
100	C₂²×C₄×C₅₉	C₂×Q₈	1	1	yes	characteristic
101	M₁₆×C₅₉	—	4	4	no	—
102	M₁₆×C₅₉	—	4	4	no	—
103	C₂×C₈×C₅₉	—	2	4	no	—
104	C₂×C₈×C₅₉	—	4	4	no	—
105	C₄²×C₅₉	C₄⋊C₄	1	1	yes	characteristic
106	C₄²×C₅₉	C₄⋊C₄	1	1	yes	characteristic
107	C₄²×C₅₉	C₄⋊C₄	1	1	yes	characteristic
108	C₄²×C₅₉	C₄⋊C₄	1	1	yes	characteristic
109	C₄²×C₅₉	C₄⋊C₄	1	1	yes	characteristic
110	C₄²×C₅₉	C₄⋊C₄	1	1	yes	characteristic
111	C₄²×C₅₉	C₂²×C₄	1	1	yes	characteristic
112	C₄²×C₅₉	C₂²×C₄	1	1	yes	characteristic
113	C₄²×C₅₉	C₂²×C₄	1	1	yes	characteristic
114	C₄²×C₅₉	C₂×D₄	1	1	yes	characteristic
115	C₄²×C₅₉	C₂×D₄	1	1	yes	characteristic
116	C₄²×C₅₉	C₂×D₄	1	1	yes	characteristic
117	C₄²×C₅₉	C₂×Q₈	1	1	yes	characteristic
118	C₄²×C₅₉	C₂×Q₈	1	1	yes	characteristic
119	C₄²×C₅₉	C₂×Q₈	1	1	yes	characteristic
120	C₄²×C₅₉	C₂⁴	1	1	yes	characteristic
121	#11745664	—	2	4	no	—
122	#11745664	—	2	8	no	—
123	#11745664	—	4	2	no	—
124	#11745664	—	4	2	no	—
125	#11745664	M₁₆	1	8	yes	complemented
126	C₂×C₅₉⋊C₈	—	2	8	no	—
127	C₂×C₅₉⋊C₈	—	2	2	no	—
128	C₂×C₅₉⋊C₈	—	2	2	no	—
129	C₂×C₅₉⋊C₈	C₂²×C₄	1	4	yes	—
130	C₂×C₅₉⋊C₈	C₂²×C₄	1	4	yes	—
131	C₂³×C₅₉	—	2	2	no	—
132	C₂³×C₅₉	—	2	2	no	—
133	C₂³×C₅₉	—	4	1	no	—
134	C₂³×C₅₉	C₂×C₄⋊C₄	1	1	yes	characteristic
135	C₂³×C₅₉	C₂×C₄⋊C₄	1	1	yes	characteristic
136	C₂³×C₅₉	C₂×C₄⋊C₄	1	1	yes	characteristic
137	C₂×C₄×C₅₉	—	2	2	no	—
138	C₂×C₄×C₅₉	—	2	2	no	—
139	C₂×C₄×C₅₉	—	2	2	no	—
140	C₂×C₄×C₅₉	—	2	2	no	—
141	C₂×C₄×C₅₉	—	2	1	no	—
142	C₂×C₄×C₅₉	—	2	1	no	—
143	C₂×C₄×C₅₉	—	2	1	no	—
144	C₂×C₄×C₅₉	—	2	1	no	—
145	C₂×C₄×C₅₉	—	2	2	no	—
146	C₂×C₄×C₅₉	—	2	2	no	—
147	C₂×C₄×C₅₉	—	2	2	no	—
148	C₂×C₄×C₅₉	—	2	2	no	—
149	C₂×C₄×C₅₉	—	2	2	no	—
150	C₂×C₄×C₅₉	—	2	2	no	—
151	C₂×C₄×C₅₉	—	2	2	no	—
152	C₂×C₄×C₅₉	—	4	1	no	—
153	C₂×C₄×C₅₉	—	4	1	no	—
154	C₂×C₄×C₅₉	—	4	1	no	—
155	C₂×C₄×C₅₉	C₂×C₄⋊C₄	1	1	yes	characteristic
156	C₂×C₄×C₅₉	C₂×C₄⋊C₄	1	1	yes	characteristic
157	C₂×C₄×C₅₉	C₂×C₄⋊C₄	1	1	yes	characteristic
158	C₂×C₄×C₅₉	C₂×C₄⋊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	C₂×C₄⋊C₄	1	1	yes	characteristic
162	C₂×C₄×C₅₉	C₂×C₄⋊C₄	1	1	yes	characteristic
163	C₂×C₄×C₅₉	C₂×C₄⋊C₄	1	1	yes	characteristic
164	C₂×C₄×C₅₉	C₂×M₁₆	1	4	yes	—
165	C₂×C₄×C₅₉	AGL(1,ℤ/8)	1	2	yes	—
166	C₂×C₄×C₅₉	#137	1	2	yes	—
167	C₂×C₄×C₅₉	C₂³×C₄	1	1	yes	characteristic
168	C₂×C₄×C₅₉	C₂²×D₄	1	1	yes	characteristic
169	C₂×C₄×C₅₉	C₂²×Q₈	1	1	yes	characteristic
170	C₈×C₅₉	—	4	4	no	—
171	C₅₉⋊C₈	—	2	4	no	—
172	C₅₉⋊C₈	—	4	2	no	—
173	C₅₉⋊C₈	—	4	2	no	—
174	C₅₉⋊C₈	C₂×M₁₆	1	8	yes	complemented
175	#17796	—	59	1	no	maximal, Sylow
176	C₂²×C₅₉	—	2	1	no	—
177	C₂²×C₅₉	—	2	1	no	—
178	C₂²×C₅₉	—	2	1	no	—
179	C₂²×C₅₉	—	2	1	no	—
180	C₂²×C₅₉	—	2	1	no	—
181	C₂²×C₅₉	—	2	1	no	—
182	C₂²×C₅₉	—	2	1	no	—
183	C₂²×C₅₉	—	4	4	no	—
184	C₂²×C₅₉	#423	1	2	yes	—
185	C₂²×C₅₉	#428	1	2	yes	—
186	C₂²×C₅₉	C₂²×C₄⋊C₄	1	1	yes	characteristic
187	C₄×C₅₉	—	2	1	no	—
188	C₄×C₅₉	—	2	1	no	—
189	C₄×C₅₉	—	2	1	no	—
190	C₄×C₅₉	—	2	1	no	—
191	C₄×C₅₉	—	2	1	no	—
192	C₄×C₅₉	—	2	1	no	—
193	C₄×C₅₉	—	2	1	no	—
194	C₄×C₅₉	#423	1	2	yes	—
195	C₄×C₅₉	#428	1	2	yes	—
196	C₄×C₅₉	#430	1	2	yes	—
197	C₄×C₅₉	C₂²×M₁₆	1	2	yes	—
198	C₄×C₅₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
199	C₄×C₅₉	C₂×#137	1	1	yes	characteristic
200	#2920	—	59	1	no	—
201	C₂×#423	D₅₉	1	1	yes	characteristic
202	C₂×C₄×M₁₆	—	59	1	no	—
203	#1569	—	59	4	no	—
204	#1567	—	59	2	no	—
205	#1566	—	59	2	no	—
206	#1565	—	59	4	no	—
207	C₂×C₅₉	—	2	2	no	—
208	C₂×C₅₉	—	2	2	no	—
209	C₂×C₅₉	—	4	1	no	—
210	C₂×C₅₉	C₂×#423	1	1	yes	characteristic
211	C₂×C₅₉	C₂×#428	1	1	yes	characteristic
212	C₂×C₅₉	C₂×#430	1	1	yes	characteristic
213	C₂²×M₁₆	—	2	1	no	—
214	C₂²×M₁₆	—	59	2	no	—
215	C₂²×C₄²	C₂×D₅₉	1	1	yes	characteristic
216	#432	—	59	2	no	—
217	#432	—	118	1	no	—
218	#431	—	59	2	no	—
219	#431	—	118	1	no	—
220	#423	—	2	1	no	—
221	#423	—	2	1	no	—
222	#423	—	59	1	no	—
223	#423	—	59	1	no	—
224	#423	C₂×D₅₉	1	2	yes	—
225	#423	C₂×D₅₉	1	2	yes	—
226	C₂×C₄⋊C₈	—	2	1	no	—
227	C₂×C₄⋊C₈	C₂×D₅₉	1	2	yes	—
228	#407	—	118	1	no	—
229	C₄×M₁₆	—	59	1	no	—
230	C₄×M₁₆	—	59	2	no	—
231	C₄×M₁₆	—	59	1	no	—
232	C₄×M₁₆	—	59	2	no	—
233	C₄×M₁₆	—	59	2	no	—
234	C₄×M₁₆	—	118	1	no	—
235	C₂×#97	—	59	2	no	—
236	C₂×C₄×C₈	—	59	2	no	—
237	#335	—	59	8	no	—
238	#334	—	59	8	no	—
239	C₅₉	#17796	1	1	yes	characteristic, complemented, Sylow
240	C₂³×C₄	Dic₁₁₈	1	1	yes	characteristic
241	C₂³×C₄	C₄×D₅₉	1	1	yes	characteristic
242	C₂³×C₄	C₂²⋊D₅₉	1	1	yes	characteristic
243	C₂×M₁₆	—	2	2	no	—
244	C₂×M₁₆	—	2	2	no	—
245	C₂×M₁₆	—	4	4	no	—
246	C₂×M₁₆	—	59	2	no	—
247	C₂×M₁₆	—	59	4	no	—
248	C₂×M₁₆	—	59	2	no	—
249	C₂×M₁₆	—	118	8	no	—
250	C₂×M₁₆	—	118	1	no	—
251	C₂×M₁₆	—	118	1	no	—
252	C₂²×C₈	—	2	2	no	—
253	C₂²×C₈	—	59	4	no	—
254	C₂×C₄²	Dic₁₁₈	1	1	yes	characteristic
255	C₂×C₄²	Dic₁₁₈	1	1	yes	characteristic
256	C₂×C₄²	Dic₁₁₈	1	1	yes	characteristic
257	C₂×C₄²	C₄×D₅₉	1	1	yes	characteristic
258	C₂×C₄²	C₄×D₅₉	1	1	yes	characteristic
259	C₂×C₄²	C₄×D₅₉	1	1	yes	characteristic
260	C₂×C₄²	C₂²⋊D₅₉	1	1	yes	characteristic
261	C₂×C₄²	C₂²⋊D₅₉	1	1	yes	characteristic
262	C₂×C₄²	C₂²⋊D₅₉	1	1	yes	characteristic
263	C₂×C₄²	C₂²×D₅₉	1	1	yes	characteristic
264	C₂×C₄²	C₂²×D₅₉	1	1	yes	characteristic
265	C₂×C₄²	C₂²×D₅₉	1	1	yes	characteristic
266	C₄⋊C₈	—	2	2	no	—
267	C₄⋊C₈	—	2	2	no	—
268	C₄⋊C₈	—	2	2	no	—
269	C₄⋊C₈	—	59	2	no	—
270	C₄⋊C₈	—	59	2	no	—
271	C₄⋊C₈	—	118	1	no	—
272	C₄⋊C₈	—	118	1	no	—
273	C₄⋊C₈	C₂²×D₅₉	1	4	yes	—
274	C₂²⋊C₈	—	118	2	no	—
275	C₂²⋊C₈	—	118	2	no	—
276	#97	—	59	2	no	—
277	#97	—	59	4	no	—
278	#97	—	59	2	no	—
279	#97	—	118	2	no	—
280	C₄×C₈	—	59	2	no	—
281	C₄×C₈	—	59	2	no	—
282	C₄×C₈	—	59	4	no	—
283	C₄×C₈	—	118	2	no	—
284	C₂⁴	Dic₅₉⋊C₄	1	1	yes	characteristic
285	C₂²×C₄	—	2	4	no	—
286	C₂²×C₄	—	2	2	no	—
287	C₂²×C₄	—	2	2	no	—
288	C₂²×C₄	—	4	2	no	—
289	C₂²×C₄	Dic₅₉⋊C₄	1	1	yes	characteristic
290	C₂²×C₄	Dic₅₉⋊C₄	1	1	yes	characteristic
291	C₂²×C₄	Dic₅₉⋊C₄	1	1	yes	characteristic
292	C₂²×C₄	Dic₅₉⋊C₄	1	1	yes	characteristic
293	C₂²×C₄	Dic₅₉⋊C₄	1	1	yes	characteristic
294	C₂²×C₄	Dic₅₉⋊C₄	1	1	yes	characteristic
295	C₂²×C₄	Dic₅₉⋊C₄	1	1	yes	characteristic
296	C₂²×C₄	Dic₅₉⋊C₄	1	1	yes	characteristic
297	C₂²×C₄	Dic₅₉⋊C₄	1	1	yes	characteristic
298	C₂²×C₄	C₂×Dic₁₁₈	1	1	yes	characteristic
299	C₂²×C₄	C₂×Dic₁₁₈	1	1	yes	characteristic
300	C₂²×C₄	C₂×Dic₁₁₈	1	1	yes	characteristic
301	C₂²×C₄	C₂×C₄×D₅₉	1	1	yes	characteristic
302	C₂²×C₄	C₂×C₄×D₅₉	1	1	yes	characteristic
303	C₂²×C₄	C₂×C₄×D₅₉	1	1	yes	characteristic
304	C₂²×C₄	C₂×C₂²⋊D₅₉	1	1	yes	characteristic
305	C₂²×C₄	C₂×C₂²⋊D₅₉	1	1	yes	characteristic
306	C₂²×C₄	C₂×C₂²⋊D₅₉	1	1	yes	characteristic
307	M₁₆	—	4	4	no	—
308	M₁₆	—	4	4	no	—
309	M₁₆	—	59	8	no	—
310	M₁₆	—	118	8	no	—
311	M₁₆	—	118	4	no	—
312	M₁₆	—	236	2	no	—
313	M₁₆	—	236	2	no	—
314	C₂×C₈	—	2	4	no	—
315	C₂×C₈	—	4	4	no	—
316	C₂×C₈	—	59	4	no	—
317	C₂×C₈	—	59	4	no	—
318	C₂×C₈	—	118	8	no	—
319	C₂×C₈	—	118	2	no	—
320	C₂×C₈	—	118	2	no	—
321	C₄²	Dic₅₉⋊C₄	1	1	yes	characteristic
322	C₄²	Dic₅₉⋊C₄	1	1	yes	characteristic
323	C₄²	Dic₅₉⋊C₄	1	1	yes	characteristic
324	C₄²	Dic₅₉⋊C₄	1	1	yes	characteristic
325	C₄²	Dic₅₉⋊C₄	1	1	yes	characteristic
326	C₄²	Dic₅₉⋊C₄	1	1	yes	characteristic
327	C₄²	C₂×Dic₁₁₈	1	1	yes	characteristic
328	C₄²	C₂×Dic₁₁₈	1	1	yes	characteristic
329	C₄²	C₂×Dic₁₁₈	1	1	yes	characteristic
330	C₄²	C₂×C₄×D₅₉	1	1	yes	characteristic
331	C₄²	C₂×C₄×D₅₉	1	1	yes	characteristic
332	C₄²	C₂×C₄×D₅₉	1	1	yes	characteristic
333	C₄²	C₂×C₂²⋊D₅₉	1	1	yes	characteristic
334	C₄²	C₂×C₂²⋊D₅₉	1	1	yes	characteristic
335	C₄²	C₂×C₂²⋊D₅₉	1	1	yes	characteristic
336	C₄²	C₂³×D₅₉	1	1	yes	characteristic
337	C₂³	—	2	2	no	—
338	C₂³	—	2	2	no	—
339	C₂³	—	4	1	no	—
340	C₂³	C₂×Dic₅₉⋊C₄	1	1	yes	characteristic
341	C₂³	C₂×Dic₅₉⋊C₄	1	1	yes	characteristic
342	C₂³	C₂×Dic₅₉⋊C₄	1	1	yes	characteristic
343	C₂×C₄	—	2	2	no	—
344	C₂×C₄	—	2	2	no	—
345	C₂×C₄	—	2	2	no	—
346	C₂×C₄	—	2	2	no	—
347	C₂×C₄	—	2	1	no	—
348	C₂×C₄	—	2	1	no	—
349	C₂×C₄	—	2	2	no	—
350	C₂×C₄	—	2	2	no	—
351	C₂×C₄	—	2	1	no	—
352	C₂×C₄	—	2	1	no	—
353	C₂×C₄	—	2	2	no	—
354	C₂×C₄	—	2	2	no	—
355	C₂×C₄	—	2	2	no	—
356	C₂×C₄	—	2	2	no	—
357	C₂×C₄	—	2	2	no	—
358	C₂×C₄	—	4	1	no	—
359	C₂×C₄	—	4	1	no	—
360	C₂×C₄	—	4	1	no	—
361	C₂×C₄	C₂×Dic₅₉⋊C₄	1	1	yes	characteristic
362	C₂×C₄	C₂×Dic₅₉⋊C₄	1	1	yes	characteristic
363	C₂×C₄	C₂×Dic₅₉⋊C₄	1	1	yes	characteristic
364	C₂×C₄	C₂×Dic₅₉⋊C₄	1	1	yes	characteristic
365	C₂×C₄	C₂×Dic₅₉⋊C₄	1	1	yes	characteristic
366	C₂×C₄	C₂×Dic₅₉⋊C₄	1	1	yes	characteristic
367	C₂×C₄	C₂×Dic₅₉⋊C₄	1	1	yes	characteristic
368	C₂×C₄	C₂×Dic₅₉⋊C₄	1	1	yes	characteristic
369	C₂×C₄	C₂×Dic₅₉⋊C₄	1	1	yes	characteristic
370	C₂×C₄	M₁₆×D₅₉	1	4	yes	—
371	C₂×C₄	#14273753	1	2	yes	—
372	C₂×C₄	#14273758	1	2	yes	—
373	C₂×C₄	C₂²×C₄×D₅₉	1	1	yes	characteristic
374	C₂×C₄	C₂²×C₂²⋊D₅₉	1	1	yes	characteristic
375	C₂×C₄	C₂²×Dic₁₁₈	1	1	yes	characteristic
376	C₈	—	4	4	no	—
377	C₈	—	59	8	no	—
378	C₈	—	118	4	no	—
379	C₈	—	236	2	no	—
380	C₈	—	236	2	no	—
381	C₂²	—	2	1	no	—
382	C₂²	—	2	1	no	—
383	C₂²	—	2	1	no	—
384	C₂²	—	2	1	no	—
385	C₂²	—	2	1	no	—
386	C₂²	—	2	1	no	—
387	C₂²	—	2	1	no	—
388	C₂²	—	4	4	no	—
389	C₂²	#16837425	1	2	yes	—
390	C₂²	#16837442	1	2	yes	—
391	C₂²	C₂²×Dic₅₉⋊C₄	1	1	yes	characteristic
392	C₄	—	2	1	no	—
393	C₄	—	2	1	no	—
394	C₄	—	2	1	no	—
395	C₄	—	2	1	no	—
396	C₄	—	2	1	no	—
397	C₄	—	2	1	no	—
398	C₄	—	2	1	no	—
399	C₄	#16837425	1	2	yes	—
400	C₄	#16837442	1	2	yes	—
401	C₄	#16837450	1	2	yes	—
402	C₄	C₂×M₁₆×D₅₉	1	2	yes	—
403	C₄	C₂×#14273753	1	1	yes	characteristic
404	C₄	C₂×#14273758	1	1	yes	characteristic
405	C₂	—	2	2	no	—
406	C₂	—	2	2	no	—
407	C₂	—	4	1	no	—
408	C₂	C₂×#16837425	1	1	yes	characteristic
409	C₂	C₂×#16837442	1	1	yes	characteristic
410	C₂	C₂×#16837450	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²×C₂²⋊D₅₉
commutator	C₂×C₄×C₅₉	C₂³×C₄
Frattini	C₄²	C₂³×D₅₉
Fitting	C₂×C₅₉×#423	C₂
socle	C₂²×C₅₉	C₂²×C₄⋊C₄
prime radical	C₂⁴×C₅₉	C₄⋊C₄
cosocle	C₄²×C₅₉	C₂⁴
hypercenter	C₂×#423	D₅₉
hypocenter	C₅₉	#17796
LCS	G ▷ C₂×C₄×C₅₉ ▷ C₂×C₅₉ ▷ C₅₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₄² ◁ C₂×#423

Complements

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

N	H ≅ G/N	type
3. #21422861	C₂	semidirect
4. #21422854	C₂	semidirect
5. #21422851	C₂	semidirect
6. #21422846	C₂	semidirect
24. #16837154	C₂²	semidirect
25. #16837152	C₂²	semidirect
125. #11745664	M₁₆	semidirect
174. C₅₉⋊C₈	C₂×M₁₆	semidirect
239. C₅₉	#17796	semidirect

Maximal subgroups

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

subgroup	index
#21432729	2
C₂×C₄×#11745664	2
#21422861	2
#21422854	2
#21422851	2
#21422846	2
C₂×C₅₉×#423	2
#17796	59