Subgroups — #28483275

Order 15104.

584 conjugacy classes of subgroups.

The subgroup lattice has 446 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×#11745671	C₂	1	1	yes	maximal, characteristic
2	C₂×#16837479	C₂	1	1	yes	maximal, characteristic
3	#21425033	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#16837131	C₂	1	1	yes	maximal, characteristic
5	#21421930	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅₉⋊#1273	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₅₉×Q₈⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×#11745671	C₄	1	1	yes	characteristic
9	C₂²×#11745659	—	2	1	no	—
10	C₂×C₄×D₂₃₆	C₂²	1	1	yes	characteristic
11	C₄×#11745671	—	2	2	no	—
12	C₄×#11745671	—	2	2	no	—
13	#16837479	—	2	2	no	—
14	#16837479	—	2	2	no	—
15	C₂×#14273658	C₄	1	1	yes	characteristic
16	C₂×C₄⋊(C₅₉⋊C₈)	C₂²	1	1	yes	characteristic
17	C₂×#14273651	C₄	1	1	yes	characteristic
18	C₂×#14273647	C₄	1	1	yes	characteristic
19	C₂×(C₂×D₅₉)⋊C₈	—	2	1	no	—
20	C₂×C₄×C₅₉⋊C₈	C₂²	1	1	yes	characteristic
21	C₂×C₄×C₅₉⋊C₈	C₂²	1	1	yes	characteristic
22	#16837157	—	2	1	no	—
23	#16837157	—	2	1	no	—
24	#16837131	—	2	2	no	—
25	C₂×C₄×Q₈×C₅₉	C₂²	1	1	yes	characteristic
26	C₂×C₄⋊C₈×C₅₉	C₂²	1	1	yes	characteristic
27	C₂×C₄×C₈×C₅₉	C₂²	1	1	yes	characteristic
28	C₅₉×Q₈⋊C₈	—	2	2	no	—
29	C₂²×D₂₃₆	C₂×C₄	1	1	yes	characteristic
30	C₂²×C₄×D₅₉	—	2	1	no	—
31	C₂×#11745671	—	2	2	no	—
32	C₂×#11745671	—	2	2	no	—
33	C₂×#11745671	—	2	2	no	—
34	C₂×#11745659	—	2	4	no	—
35	C₂×#11745659	—	4	2	no	—
36	C₂×#11745659	—	4	2	no	—
37	C₂²×C₅₉⋊C₈	—	2	1	no	—
38	C₂²×C₅₉⋊C₈	C₂×C₄	1	1	yes	characteristic
39	C₂²×C₅₉⋊C₈	C₂×C₄	1	1	yes	characteristic
40	C₂²×C₅₉⋊C₈	D₄	1	1	yes	characteristic
41	C₂²×C₅₉⋊C₈	D₄	1	1	yes	characteristic
42	C₄×D₂₃₆	—	2	1	no	—
43	C₄×D₂₃₆	—	2	1	no	—
44	C₄×D₂₃₆	D₄	1	2	yes	—
45	C₄×D₂₃₆	D₄	1	2	yes	—
46	C₂×C₄⋊Dic₅₉	C₂×C₄	1	1	yes	characteristic
47	C₂×(C₂×D₅₉)⋊C₄	—	2	1	no	—
48	#14273658	—	2	2	no	—
49	C₄⋊(C₅₉⋊C₈)	—	2	1	no	—
50	C₄⋊(C₅₉⋊C₈)	—	2	1	no	—
51	#14273651	—	2	2	no	—
52	#14273647	—	2	2	no	—
53	(C₂×D₅₉)⋊C₈	—	2	4	no	—
54	C₄×C₅₉⋊C₈	—	2	1	no	—
55	C₄×C₅₉⋊C₈	—	2	1	no	—
56	C₄×C₅₉⋊C₈	—	2	1	no	—
57	C₄×C₅₉⋊C₈	—	2	1	no	—
58	C₂²×Q₈×C₅₉	C₂×C₄	1	1	yes	characteristic
59	C₂²×C₈×C₅₉	—	2	1	no	—
60	C₂²×C₈×C₅₉	—	2	1	no	—
61	C₄×Q₈×C₅₉	—	2	1	no	—
62	C₄×Q₈×C₅₉	—	2	1	no	—
63	C₄×Q₈×C₅₉	—	2	1	no	—
64	C₄×Q₈×C₅₉	—	2	1	no	—
65	C₂×C₄⋊C₄×C₅₉	—	2	1	no	—
66	C₂×C₄⋊C₄×C₅₉	C₂×C₄	1	1	yes	characteristic
67	C₂×C₄²×C₅₉	—	2	1	no	—
68	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
69	C₄⋊C₈×C₅₉	—	2	1	no	—
70	C₄⋊C₈×C₅₉	D₄	1	2	yes	—
71	C₄×C₈×C₅₉	—	2	1	no	—
72	C₄×C₈×C₅₉	—	2	1	no	—
73	C₂³×D₅₉	—	2	1	no	—
74	C₂×Q₈×C₅₉	—	2	1	no	—
75	C₂×Q₈×C₅₉	—	2	1	no	—
76	C₂×Q₈×C₅₉	—	2	1	no	—
77	C₂×Q₈×C₅₉	—	2	1	no	—
78	C₂×Q₈×C₅₉	—	2	1	no	—
79	C₂×Q₈×C₅₉	M₁₆	1	2	yes	complemented
80	C₂²×C₄×C₅₉	—	2	1	no	—
81	C₂²×C₄×C₅₉	—	2	1	no	—
82	C₂²×C₄×C₅₉	C₂²×C₄	1	1	yes	characteristic
83	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
84	C₂²×C₄×C₅₉	#41	1	1	yes	characteristic
85	C₂²×Dic₅₉	—	2	1	no	—
86	C₂×D₂₃₆	—	2	1	no	—
87	C₂×D₂₃₆	—	2	1	no	—
88	C₂×D₂₃₆	—	2	1	no	—
89	C₂×D₂₃₆	—	2	1	no	—
90	C₂×D₂₃₆	—	2	1	no	—
91	C₂×D₂₃₆	C₂²⋊C₄	1	2	yes	—
92	C₂×C₄×D₅₉	—	2	2	no	—
93	C₂×C₄×D₅₉	—	2	2	no	—
94	C₂×C₄×D₅₉	—	4	1	no	—
95	C₂×C₄×D₅₉	—	4	1	no	—
96	C₂×C₄×D₅₉	—	4	1	no	—
97	C₂×C₄×D₅₉	—	4	1	no	—
98	C₂×C₈×C₅₉	—	2	2	no	—
99	C₂×C₈×C₅₉	—	2	2	no	—
100	C₂×C₈×C₅₉	—	4	1	no	—
101	C₂×C₈×C₅₉	—	4	1	no	—
102	C₂×C₈×C₅₉	—	4	1	no	—
103	C₂×C₈×C₅₉	—	4	1	no	—
104	C₄⋊C₄×C₅₉	—	2	1	no	—
105	C₄⋊C₄×C₅₉	—	2	1	no	—
106	C₄⋊C₄×C₅₉	—	4	1	no	—
107	C₄⋊C₄×C₅₉	—	4	1	no	—
108	C₄²×C₅₉	—	4	1	no	—
109	C₄²×C₅₉	—	4	1	no	—
110	C₄²×C₅₉	C₂×D₄	1	1	yes	characteristic
111	C₄²×C₅₉	C₂×D₄	1	1	yes	characteristic
112	C₄²×C₅₉	C₂×D₄	1	1	yes	characteristic
113	C₄²×C₅₉	#41	1	1	yes	characteristic
114	#11745671	—	2	8	no	—
115	(C₂×D₅₉)⋊C₄	—	2	2	no	—
116	(C₂×D₅₉)⋊C₄	—	2	2	no	—
117	C₄⋊Dic₅₉	—	2	1	no	—
118	C₄⋊Dic₅₉	C₂²⋊C₄	1	2	yes	—
119	C₂×C₅₉⋊C₈	—	2	1	no	—
120	C₂×C₅₉⋊C₈	—	2	1	no	—
121	C₂×C₅₉⋊C₈	—	2	1	no	—
122	C₂×C₅₉⋊C₈	—	2	1	no	—
123	C₂×C₅₉⋊C₈	—	2	1	no	—
124	C₂×C₅₉⋊C₈	—	2	1	no	—
125	C₂×C₅₉⋊C₈	—	2	1	no	—
126	C₂×C₅₉⋊C₈	—	2	1	no	—
127	C₂×C₅₉⋊C₈	—	2	1	no	—
128	C₂×C₅₉⋊C₈	—	2	1	no	—
129	C₂×C₅₉⋊C₈	—	4	1	no	—
130	C₂×C₅₉⋊C₈	—	4	1	no	—
131	C₂×C₅₉⋊C₈	—	4	1	no	—
132	C₂×C₅₉⋊C₈	M₁₆	1	2	yes	complemented
133	C₂×C₅₉⋊C₈	SD₁₆	1	2	yes	complemented
134	#11745659	—	4	8	no	—
135	C₂³×C₅₉	C₄×D₄	1	1	yes	characteristic
136	C₂²×D₅₉	—	2	2	no	—
137	C₂²×D₅₉	—	4	1	no	—
138	C₂²×D₅₉	—	4	1	no	—
139	C₂²×D₅₉	—	4	1	no	—
140	C₂²×D₅₉	—	4	1	no	—
141	C₂²×D₅₉	—	4	1	no	—
142	C₂²×D₅₉	—	4	1	no	—
143	Q₈×C₅₉	—	2	2	no	—
144	Q₈×C₅₉	—	2	2	no	—
145	Q₈×C₅₉	—	4	1	no	—
146	Q₈×C₅₉	—	4	1	no	—
147	C₂×C₄×C₅₉	—	2	1	no	—
148	C₂×C₄×C₅₉	—	2	1	no	—
149	C₂×C₄×C₅₉	—	2	2	no	—
150	C₂×C₄×C₅₉	—	4	1	no	—
151	C₂×C₄×C₅₉	—	4	1	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×C₂²⋊C₄	1	1	yes	characteristic
156	C₂×C₄×C₅₉	C₄×D₄	1	1	yes	characteristic
157	C₂×C₄×C₅₉	#120	1	1	yes	characteristic
158	C₂×C₄×C₅₉	#121	1	1	yes	characteristic
159	C₂×C₄×C₅₉	#121	1	1	yes	characteristic
160	C₂×C₄×C₅₉	#123	1	1	yes	characteristic
161	C₂×C₄×C₅₉	C₂×M₁₆	1	1	yes	characteristic
162	C₂×C₄×C₅₉	C₂×M₁₆	1	1	yes	characteristic
163	C₂×C₄×C₅₉	#131	1	1	yes	characteristic
164	C₂×C₄×C₅₉	#131	1	1	yes	characteristic
165	C₂×C₄×C₅₉	C₂×SD₁₆	1	1	yes	characteristic
166	C₂×C₄×C₅₉	#135	1	1	yes	characteristic
167	C₂×C₄×C₅₉	AGL(1,ℤ/8)	1	1	yes	characteristic
168	C₂×C₄×C₅₉	#137	1	1	yes	characteristic
169	C₂×Dic₅₉	—	2	2	no	—
170	C₂×Dic₅₉	—	4	1	no	—
171	C₂×Dic₅₉	—	4	1	no	—
172	D₂₃₆	—	2	2	no	—
173	D₂₃₆	—	2	2	no	—
174	D₂₃₆	—	4	1	no	—
175	D₂₃₆	—	4	1	no	—
176	C₄×D₅₉	—	4	2	no	—
177	C₄×D₅₉	—	4	2	no	—
178	C₄×D₅₉	—	4	2	no	—
179	C₄×D₅₉	—	4	2	no	—
180	C₈×C₅₉	—	4	2	no	—
181	C₈×C₅₉	—	4	2	no	—
182	C₅₉⋊C₈	—	2	2	no	—
183	C₅₉⋊C₈	—	2	2	no	—
184	C₅₉⋊C₈	—	4	1	no	—
185	C₅₉⋊C₈	—	4	1	no	—
186	C₅₉⋊C₈	—	8	1	no	—
187	#8949	—	59	1	no	maximal, Sylow
188	C₂²×C₅₉	#386	1	1	yes	characteristic
189	C₂²×C₅₉	#435	1	1	yes	characteristic
190	C₂²×C₅₉	#436	1	1	yes	characteristic
191	C₂²×C₅₉	C₄×SD₁₆	1	1	yes	characteristic
192	C₂²×C₅₉	#440	1	1	yes	characteristic
193	C₂²×C₅₉	#443	1	1	yes	characteristic
194	C₂²×C₅₉	#444	1	1	yes	characteristic
195	C₂×D₅₉	—	4	2	no	—
196	C₂×D₅₉	—	4	2	no	—
197	C₂×D₅₉	—	4	2	no	—
198	C₂×D₅₉	—	8	1	no	—
199	C₂×D₅₉	—	8	1	no	—
200	C₂×D₅₉	—	8	1	no	—
201	C₂×D₅₉	—	8	1	no	—
202	C₄×C₅₉	—	2	1	no	—
203	C₄×C₅₉	—	2	1	no	—
204	C₄×C₅₉	—	4	2	no	—
205	C₄×C₅₉	—	8	1	no	—
206	C₄×C₅₉	#407	1	1	yes	characteristic
207	C₄×C₅₉	#408	1	1	yes	characteristic
208	C₄×C₅₉	#435	1	1	yes	characteristic
209	C₄×C₅₉	#436	1	1	yes	characteristic
210	C₄×C₅₉	#450	1	1	yes	characteristic
211	C₄×C₅₉	#452	1	1	yes	characteristic
212	C₄×C₅₉	#461	1	1	yes	characteristic
213	C₄×C₅₉	#463	1	1	yes	characteristic
214	Dic₅₉	—	4	2	no	—
215	C₂×C₄×SD₁₆	—	59	1	no	—
216	C₂×#436	—	59	1	no	—
217	#1984	—	59	1	no	—
218	C₂×Q₈⋊C₈	D₅₉	1	1	yes	characteristic, complemented
219	C₂×D₄⋊C₈	—	59	1	no	—
220	#1277	—	59	1	no	—
221	#1273	—	59	1	no	—
222	C₂×C₅₉	#1583	1	1	yes	characteristic
223	C₂×C₅₉	#1588	1	1	yes	characteristic
224	C₂×C₅₉	#1590	1	1	yes	characteristic
225	C₂×C₅₉	#1592	1	1	yes	characteristic
226	C₂×C₅₉	#1870	1	1	yes	characteristic
227	C₂×C₅₉	#1876	1	1	yes	characteristic
228	C₂×C₅₉	#1877	1	1	yes	characteristic
229	D₅₉	—	8	2	no	—
230	C₂²×SD₁₆	—	59	1	no	—
231	C₂²×M₁₆	—	118	1	no	—
232	C₂×C₄×Q₈	C₂×D₅₉	1	1	yes	characteristic
233	C₂×C₄×D₄	—	59	1	no	—
234	C₄×SD₁₆	—	118	2	no	—
235	C₄×SD₁₆	—	118	2	no	—
236	#436	—	118	2	no	—
237	#436	—	118	2	no	—
238	C₂×#106	—	59	1	no	—
239	C₂×C₄⋊C₈	—	59	1	no	—
240	C₂×C₄⋊C₈	C₂×D₅₉	1	1	yes	characteristic
241	C₂×#103	—	59	1	no	—
242	C₂×#102	—	59	1	no	—
243	C₂×C₂²⋊C₈	—	118	1	no	—
244	C₂×C₄×C₈	—	59	1	no	—
245	C₂×C₄×C₈	—	59	1	no	—
246	C₂×C₄×C₈	C₂×D₅₉	1	1	yes	characteristic
247	#336	—	118	1	no	—
248	#336	—	118	1	no	—
249	Q₈⋊C₈	—	2	2	no	—
250	D₄⋊C₈	—	118	2	no	—
251	C₅₉	#8949	1	1	yes	characteristic, complemented, Sylow
252	C₂²×Q₈	C₄×D₅₉	1	1	yes	characteristic
253	C₂²×D₄	—	59	1	no	—
254	C₂³×C₄	—	118	1	no	—
255	C₂×SD₁₆	—	118	2	no	—
256	C₂×SD₁₆	—	118	2	no	—
257	C₂×SD₁₆	—	118	2	no	—
258	C₂×M₁₆	—	118	4	no	—
259	C₂×M₁₆	—	236	2	no	—
260	C₂×M₁₆	—	236	2	no	—
261	C₂²×C₈	—	2	1	no	—
262	C₂²×C₈	—	2	1	no	—
263	C₂²×C₈	—	59	1	no	—
264	C₂²×C₈	—	59	1	no	—
265	C₂²×C₈	—	59	1	no	—
266	C₂²×C₈	—	59	1	no	—
267	C₂²×C₈	—	118	1	no	—
268	C₄×Q₈	—	2	1	no	—
269	C₄×Q₈	—	2	1	no	—
270	C₄×Q₈	—	2	1	no	—
271	C₄×Q₈	—	2	1	no	—
272	C₄×D₄	—	59	2	no	—
273	C₄×D₄	—	59	2	no	—
274	C₄×D₄	—	118	1	no	—
275	C₄×D₄	—	118	1	no	—
276	C₂×C₄⋊C₄	—	2	1	no	—
277	C₂×C₄⋊C₄	—	59	1	no	—
278	C₂×C₄⋊C₄	C₄×D₅₉	1	1	yes	characteristic
279	C₂×C₂²⋊C₄	—	118	1	no	—
280	C₂×C₄²	—	2	1	no	—
281	C₂×C₄²	C₂²×D₅₉	1	1	yes	characteristic
282	#106	—	118	2	no	—
283	C₄⋊C₈	—	2	1	no	—
284	C₄⋊C₈	—	118	1	no	—
285	C₄⋊C₈	—	118	1	no	—
286	C₄⋊C₈	C₂²⋊D₅₉	1	2	yes	—
287	#103	—	118	2	no	—
288	#102	—	118	2	no	—
289	C₂²⋊C₈	—	118	4	no	—
290	C₄×C₈	—	2	1	no	—
291	C₄×C₈	—	2	1	no	—
292	C₄×C₈	—	118	1	no	—
293	C₄×C₈	—	118	1	no	—
294	C₄×C₈	—	118	1	no	—
295	C₄×C₈	—	118	1	no	—
296	C₂⁴	—	118	1	no	—
297	C₂×Q₈	—	2	1	no	—
298	C₂×Q₈	—	2	1	no	—
299	C₂×Q₈	—	2	1	no	—
300	C₂×Q₈	—	2	1	no	—
301	C₂×Q₈	—	2	1	no	—
302	C₂×Q₈	#11745659	1	2	yes	complemented
303	C₂×D₄	—	59	2	no	—
304	C₂×D₄	—	118	1	no	—
305	C₂×D₄	—	118	1	no	—
306	C₂×D₄	—	118	1	no	—
307	C₂×D₄	—	118	1	no	—
308	C₂×D₄	—	118	1	no	—
309	C₂²×C₄	—	2	1	no	—
310	C₂²×C₄	—	2	1	no	—
311	C₂²×C₄	—	118	1	no	—
312	C₂²×C₄	—	118	2	no	—
313	C₂²×C₄	—	118	2	no	—
314	C₂²×C₄	—	236	1	no	—
315	C₂²×C₄	—	236	1	no	—
316	C₂²×C₄	—	236	1	no	—
317	C₂²×C₄	—	236	1	no	—
318	C₂²×C₄	C₂×C₄×D₅₉	1	1	yes	characteristic
319	C₂²×C₄	D₄×D₅₉	1	1	yes	characteristic
320	C₂²×C₄	#11745687	1	1	yes	characteristic
321	SD₁₆	—	118	8	no	—
322	M₁₆	—	236	8	no	—
323	C₂×C₈	—	2	2	no	—
324	C₂×C₈	—	2	2	no	—
325	C₂×C₈	—	4	1	no	—
326	C₂×C₈	—	4	1	no	—
327	C₂×C₈	—	4	1	no	—
328	C₂×C₈	—	4	1	no	—
329	C₂×C₈	—	59	2	no	—
330	C₂×C₈	—	59	2	no	—
331	C₂×C₈	—	118	1	no	—
332	C₂×C₈	—	118	1	no	—
333	C₂×C₈	—	118	1	no	—
334	C₂×C₈	—	118	1	no	—
335	C₂×C₈	—	118	1	no	—
336	C₂×C₈	—	118	1	no	—
337	C₂×C₈	—	118	1	no	—
338	C₂×C₈	—	118	1	no	—
339	C₂×C₈	—	118	1	no	—
340	C₂×C₈	—	118	1	no	—
341	C₂×C₈	—	236	1	no	—
342	C₂×C₈	—	236	1	no	—
343	C₂×C₈	—	236	1	no	—
344	C₄⋊C₄	—	2	1	no	—
345	C₄⋊C₄	—	2	1	no	—
346	C₄⋊C₄	—	4	1	no	—
347	C₄⋊C₄	—	4	1	no	—
348	C₄⋊C₄	—	59	2	no	—
349	C₄⋊C₄	—	118	1	no	—
350	C₂²⋊C₄	—	118	2	no	—
351	C₂²⋊C₄	—	118	2	no	—
352	C₄²	—	4	1	no	—
353	C₄²	—	4	1	no	—
354	C₄²	#11745685	1	1	yes	characteristic
355	C₄²	D₄×D₅₉	1	1	yes	characteristic
356	C₄²	D₄×D₅₉	1	1	yes	characteristic
357	C₄²	C₂×C₂²⋊D₅₉	1	1	yes	characteristic
358	C₂³	—	118	2	no	—
359	C₂³	—	236	1	no	—
360	C₂³	—	236	1	no	—
361	C₂³	—	236	1	no	—
362	C₂³	—	236	1	no	—
363	C₂³	—	236	1	no	—
364	C₂³	—	236	1	no	—
365	C₂³	(C₂²⋊D₅₉)⋊C₄	1	1	yes	characteristic
366	Q₈	—	2	2	no	—
367	Q₈	—	2	2	no	—
368	Q₈	—	4	1	no	—
369	Q₈	—	4	1	no	—
370	D₄	—	118	2	no	—
371	D₄	—	118	2	no	—
372	D₄	—	236	1	no	—
373	D₄	—	236	1	no	—
374	C₂×C₄	—	2	1	no	—
375	C₂×C₄	—	2	1	no	—
376	C₂×C₄	—	2	2	no	—
377	C₂×C₄	—	4	1	no	—
378	C₂×C₄	—	4	1	no	—
379	C₂×C₄	—	4	1	no	—
380	C₂×C₄	—	4	1	no	—
381	C₂×C₄	—	4	1	no	—
382	C₂×C₄	—	118	2	no	—
383	C₂×C₄	—	236	1	no	—
384	C₂×C₄	—	236	1	no	—
385	C₂×C₄	—	236	2	no	—
386	C₂×C₄	—	236	2	no	—
387	C₂×C₄	—	236	2	no	—
388	C₂×C₄	—	236	2	no	—
389	C₂×C₄	C₂²⋊C₄×D₅₉	1	1	yes	characteristic
390	C₂×C₄	C₄×C₂²⋊D₅₉	1	1	yes	characteristic
391	C₂×C₄	#14273695	1	1	yes	characteristic
392	C₂×C₄	#14273698	1	1	yes	characteristic
393	C₂×C₄	#14273700	1	1	yes	characteristic
394	C₂×C₄	#14273709	1	1	yes	characteristic
395	C₂×C₄	M₁₆×D₅₉	1	1	yes	characteristic
396	C₂×C₄	C₂×#11745659	1	1	yes	characteristic
397	C₂×C₄	#14273733	1	1	yes	characteristic
398	C₂×C₄	#14273735	1	1	yes	characteristic
399	C₂×C₄	SD₁₆×D₅₉	1	1	yes	characteristic
400	C₂×C₄	#14273750	1	1	yes	characteristic
401	C₂×C₄	#14273754	1	1	yes	characteristic
402	C₂×C₄	#14273759	1	1	yes	characteristic
403	C₈	—	4	2	no	—
404	C₈	—	4	2	no	—
405	C₈	—	118	2	no	—
406	C₈	—	118	2	no	—
407	C₈	—	472	1	no	—
408	C₈	—	236	1	no	—
409	C₈	—	236	1	no	—
410	C₂²	—	472	1	no	—
411	C₂²	—	472	1	no	—
412	C₂²	—	472	1	no	—
413	C₂²	—	472	1	no	—
414	C₂²	—	236	2	no	—
415	C₂²	—	236	2	no	—
416	C₂²	—	236	2	no	—
417	C₂²	#16837278	1	1	yes	characteristic
418	C₂²	#16837470	1	1	yes	characteristic
419	C₂²	#16837477	1	1	yes	characteristic
420	C₂²	#16837487	1	1	yes	characteristic
421	C₂²	#16837505	1	1	yes	characteristic
422	C₂²	#16837516	1	1	yes	characteristic
423	C₂²	#16837521	1	1	yes	characteristic
424	C₄	—	2	1	no	—
425	C₄	—	2	1	no	—
426	C₄	—	4	2	no	—
427	C₄	—	8	1	no	—
428	C₄	—	236	2	no	—
429	C₄	#16837364	1	1	yes	characteristic
430	C₄	#16837367	1	1	yes	characteristic
431	C₄	#16837473	1	1	yes	characteristic
432	C₄	#16837478	1	1	yes	characteristic
433	C₄	#16837551	1	1	yes	characteristic
434	C₄	#16837563	1	1	yes	characteristic
435	C₄	#16837606	1	1	yes	characteristic
436	C₄	#16837620	1	1	yes	characteristic
437	C₂	—	472	2	no	—
438	C₂	#21422936	1	1	yes	characteristic
439	C₂	#21422971	1	1	yes	characteristic
440	C₂	#21422983	1	1	yes	characteristic
441	C₂	#21423001	1	1	yes	characteristic
442	C₂	#21424390	1	1	yes	characteristic
443	C₂	#21424420	1	1	yes	characteristic
444	C₂	#21424427	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	D₄×D₅₉
commutator	C₂²×C₄×C₅₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₅₉
Fitting	C₂×C₅₉×Q₈⋊C₈	C₂
socle	C₂³×C₅₉	C₄×D₄
prime radical	C₂²×D₂₃₆	C₂×C₄
cosocle	C₂×C₄²×C₅₉	C₂³
hypercenter	C₂×Q₈⋊C₈	D₅₉
hypocenter	C₅₉	#8949
LCS	G ▷ C₂²×C₄×C₅₉ ▷ C₂×C₅₉ ▷ C₅₉
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×C₄² ◁ C₂×Q₈⋊C₈

Complements

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

N	H ≅ G/N	type
3. #21425033	C₂	semidirect
5. #21421930	C₂	semidirect
6. C₅₉⋊#1273	C₂	semidirect
7. C₂×C₅₉×Q₈⋊C₈	C₂	semidirect
79. C₂×Q₈×C₅₉	M₁₆	semidirect
132. C₂×C₅₉⋊C₈	M₁₆	semidirect
133. C₂×C₅₉⋊C₈	SD₁₆	semidirect
218. C₂×Q₈⋊C₈	D₅₉	semidirect
251. C₅₉	#8949	semidirect
302. C₂×Q₈	#11745659	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄×#11745671	2
C₂×#16837479	2
#21425033	2
C₂×#16837131	2
#21421930	2
C₅₉⋊#1273	2
C₂×C₅₉×Q₈⋊C₈	2
#8949	59