Subgroups — #28607146

Order 15104.

858 conjugacy classes of subgroups.

The subgroup lattice has 454 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#16837524	C₂	1	1	yes	maximal, characteristic
2	C₂×#16837519	C₂	1	1	yes	maximal, characteristic
3	#21432664	C₂	1	2	yes	maximal, complemented
4	#21424850	C₂	1	1	yes	maximal, characteristic, complemented
5	#21424845	C₂	1	1	yes	maximal, characteristic, complemented
6	#21424373	C₂	1	2	yes	maximal, complemented
7	#21424373	C₂	1	2	yes	maximal, complemented
8	#21424271	C₂	1	1	yes	maximal, characteristic, complemented
9	#21424116	C₂	1	2	yes	maximal, complemented
10	#21423968	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅₉×#2943	C₂	1	1	yes	maximal, characteristic
12	C₂×#14273734	C₂²	1	2	yes	—
13	C₂×#14273734	C₂²	1	2	yes	—
14	#16837524	—	2	4	no	—
15	#16837519	—	2	4	no	—
16	C₂×#14273663	C₂²	1	1	yes	characteristic
17	C₂×#14273663	C₂²	1	1	yes	characteristic
18	C₂×#14273663	C₂²	1	2	yes	—
19	#16837429	—	2	2	no	—
20	#16837429	—	2	2	no	—
21	#16837429	C₂²	1	2	yes	—
22	#16837429	C₂²	1	2	yes	—
23	#16837426	—	2	2	no	—
24	#16837426	C₂²	1	2	yes	—
25	C₂×C₄⋊(C₅₉⋊C₈)	—	2	2	no	—
26	C₂×C₄⋊(C₅₉⋊C₈)	C₂²	1	1	yes	characteristic
27	C₂×#14273654	C₂²	1	2	yes	—
28	C₂×#14273654	C₂²	1	2	yes	—
29	C₂×#14273637	C₂²	1	1	yes	characteristic
30	C₂×C₈×Dic₅₉	C₂²	1	1	yes	characteristic
31	C₄×C₄⋊Dic₅₉	C₂²	1	1	yes	characteristic
32	#16837161	C₂²	1	2	yes	—
33	#16837161	C₂²	1	2	yes	—
34	#16837156	C₂²	1	1	yes	characteristic
35	#16837156	C₂²	1	1	yes	characteristic
36	C₂×#135×C₅₉	C₂²	1	1	yes	characteristic
37	C₄×#41×C₅₉	C₂²	1	2	yes	—
38	C₅₉×#442	C₄	1	2	yes	complemented
39	C₅₉×#441	C₄	1	2	yes	complemented
40	C₅₉×#440	C₄	1	2	yes	complemented
41	C₅₉×#440	C₄	1	2	yes	complemented
42	C₅₉×#427	C₂²	1	1	yes	characteristic
43	C₅₉×#416	C₂²	1	2	yes	—
44	C₂×#97×C₅₉	C₂²	1	1	yes	characteristic
45	#14273734	—	2	4	no	—
46	#14273734	—	2	4	no	—
47	#14273734	—	4	2	no	—
48	#14273734	—	4	2	no	—
49	C₂×#11745664	—	2	2	no	—
50	C₂×#11745664	—	2	2	no	—
51	C₂×#11745664	C₂³	1	2	yes	—
52	C₂×#11745664	C₂³	1	2	yes	—
53	C₂²×C₅₉⋊C₈	—	2	2	no	—
54	C₂²×C₅₉⋊C₈	—	2	2	no	—
55	C₂²×C₅₉⋊C₈	C₂³	1	1	yes	characteristic
56	C₂²×C₅₉⋊C₈	C₂³	1	1	yes	characteristic
57	C₂×C₄⋊Dic₅₉	—	2	1	no	—
58	C₂×C₄×Dic₅₉	C₂³	1	1	yes	characteristic
59	C₂×C₄×Dic₅₉	C₂³	1	1	yes	characteristic
60	#14273663	—	2	2	no	—
61	#14273663	—	2	2	no	—
62	#14273663	—	4	2	no	—
63	C₄⋊(C₅₉⋊C₈)	—	2	2	no	—
64	C₄⋊(C₅₉⋊C₈)	—	2	2	no	—
65	C₄⋊(C₅₉⋊C₈)	—	2	2	no	—
66	C₄⋊(C₅₉⋊C₈)	—	2	2	no	—
67	C₄⋊(C₅₉⋊C₈)	—	2	2	no	—
68	C₄⋊(C₅₉⋊C₈)	—	2	2	no	—
69	C₄⋊(C₅₉⋊C₈)	D₄	1	2	yes	—
70	C₄⋊(C₅₉⋊C₈)	D₄	1	2	yes	—
71	#14273654	—	2	4	no	—
72	#14273654	—	2	4	no	—
73	#14273637	—	2	2	no	—
74	C₈×Dic₅₉	—	2	2	no	—
75	C₅₉⋊#95	—	2	1	no	—
76	C₂×#41×C₅₉	C₂³	1	2	yes	—
77	#135×C₅₉	D₄	1	4	yes	—
78	#135×C₅₉	Q₈	1	4	yes	—
79	C₂×Q₁₆×C₅₉	C₂×C₄	1	1	yes	characteristic
80	C₂×SD₁₆×C₅₉	C₂×C₄	1	2	yes	—
81	C₂×D₈×C₅₉	C₂×C₄	1	1	yes	characteristic
82	C₂²×C₈×C₅₉	C₂³	1	1	yes	characteristic
83	C₂²×C₈×C₅₉	C₂³	1	1	yes	characteristic
84	C₄×Q₈×C₅₉	C₂×C₄	1	2	yes	—
85	C₄×Q₈×C₅₉	C₂×C₄	1	2	yes	—
86	C₄×D₄×C₅₉	—	2	2	no	—
87	C₄×D₄×C₅₉	—	2	2	no	—
88	C₄×D₄×C₅₉	C₂×C₄	1	2	yes	—
89	C₄×D₄×C₅₉	C₂×C₄	1	2	yes	—
90	#117×C₅₉	—	2	2	no	—
91	#117×C₅₉	C₂³	1	2	yes	—
92	C₂×C₄²×C₅₉	—	2	2	no	—
93	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
94	#107×C₅₉	C₂×C₄	1	1	yes	characteristic
95	#107×C₅₉	C₂×C₄	1	1	yes	characteristic
96	#106×C₅₉	C₂×C₄	1	2	yes	—
97	#103×C₅₉	C₂×C₄	1	2	yes	—
98	#103×C₅₉	C₂×C₄	1	2	yes	—
99	#102×C₅₉	C₂×C₄	1	2	yes	—
100	#102×C₅₉	C₂×C₄	1	2	yes	—
101	#97×C₅₉	C₂×C₄	1	2	yes	—
102	#97×C₅₉	C₂×C₄	1	2	yes	—
103	#41×C₅₉	—	2	2	no	—
104	#41×C₅₉	—	2	2	no	—
105	#41×C₅₉	C₂×D₄	1	4	yes	—
106	#41×C₅₉	C₂×Q₈	1	4	yes	—
107	C₂×Q₈×C₅₉	C₂²×C₄	1	2	yes	—
108	C₂×D₄×C₅₉	—	2	2	no	—
109	C₂×D₄×C₅₉	C₂²×C₄	1	2	yes	—
110	C₂²×C₄×C₅₉	—	2	2	no	—
111	C₂²×C₄×C₅₉	—	2	2	no	—
112	C₂²×C₄×C₅₉	—	2	2	no	—
113	C₂²×C₄×C₅₉	#41	1	1	yes	characteristic
114	C₂²×C₄×C₅₉	#41	1	1	yes	characteristic
115	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
116	C₂²×Dic₅₉	—	2	1	no	—
117	C₂²×Dic₅₉	—	2	1	no	—
118	Q₁₆×C₅₉	C₄⋊C₄	1	4	yes	complemented
119	SD₁₆×C₅₉	C₄⋊C₄	1	8	yes	complemented
120	D₈×C₅₉	C₄⋊C₄	1	4	yes	complemented
121	C₂×C₈×C₅₉	—	2	1	no	—
122	C₂×C₈×C₅₉	—	2	1	no	—
123	C₂×C₈×C₅₉	C₂²×C₄	1	2	yes	—
124	C₂×C₈×C₅₉	C₂²×C₄	1	1	yes	characteristic
125	C₂×C₈×C₅₉	C₂²×C₄	1	1	yes	characteristic
126	C₂×C₈×C₅₉	C₂×D₄	1	2	yes	—
127	C₂×C₈×C₅₉	C₂×Q₈	1	2	yes	—
128	C₄⋊C₄×C₅₉	—	2	2	no	—
129	C₄⋊C₄×C₅₉	—	2	2	no	—
130	C₄⋊C₄×C₅₉	C₂²×C₄	1	2	yes	—
131	C₄⋊C₄×C₅₉	C₂²×C₄	1	2	yes	—
132	C₂²⋊C₄×C₅₉	—	2	2	no	—
133	C₂²⋊C₄×C₅₉	—	2	2	no	—
134	C₂²⋊C₄×C₅₉	—	2	2	no	—
135	C₄²×C₅₉	—	2	2	no	—
136	C₄²×C₅₉	—	2	2	no	—
137	C₄²×C₅₉	—	2	2	no	—
138	C₄²×C₅₉	C₂²×C₄	1	2	yes	—
139	C₄²×C₅₉	C₂×D₄	1	2	yes	—
140	C₄⋊Dic₅₉	—	4	2	no	—
141	C₄×Dic₅₉	—	2	1	no	—
142	C₄×Dic₅₉	—	2	1	no	—
143	C₄×Dic₅₉	—	2	1	no	—
144	C₄×Dic₅₉	—	2	1	no	—
145	#11745664	—	2	2	no	—
146	#11745664	—	2	2	no	—
147	#11745664	—	2	2	no	—
148	#11745664	—	2	2	no	—
149	#11745664	—	4	4	no	—
150	#11745664	—	4	4	no	—
151	C₂×C₅₉⋊C₈	—	2	1	no	—
152	C₂×C₅₉⋊C₈	—	2	1	no	—
153	C₂×C₅₉⋊C₈	—	2	1	no	—
154	C₂×C₅₉⋊C₈	—	2	1	no	—
155	C₂×C₅₉⋊C₈	—	2	2	no	—
156	C₂×C₅₉⋊C₈	—	2	2	no	—
157	C₂×C₅₉⋊C₈	—	4	4	no	—
158	C₂×C₅₉⋊C₈	—	4	4	no	—
159	C₂×C₅₉⋊C₈	C₂×D₄	1	1	yes	characteristic
160	C₂×C₅₉⋊C₈	C₂×D₄	1	2	yes	—
161	C₂×C₅₉⋊C₈	C₂×D₄	1	1	yes	characteristic
162	C₂³×C₅₉	—	2	2	no	—
163	C₂³×C₅₉	C₂×#41	1	1	yes	characteristic
164	Q₈×C₅₉	—	2	2	no	—
165	Q₈×C₅₉	C₂×C₄⋊C₄	1	4	yes	—
166	D₄×C₅₉	—	2	4	no	—
167	D₄×C₅₉	—	2	4	no	—
168	D₄×C₅₉	—	2	2	no	—
169	D₄×C₅₉	C₂×C₄⋊C₄	1	4	yes	—
170	C₂×C₄×C₅₉	—	2	2	no	—
171	C₂×C₄×C₅₉	—	2	4	no	—
172	C₂×C₄×C₅₉	—	2	4	no	—
173	C₂×C₄×C₅₉	—	2	2	no	—
174	C₂×C₄×C₅₉	—	2	2	no	—
175	C₂×C₄×C₅₉	—	4	1	no	—
176	C₂×C₄×C₅₉	—	4	1	no	—
177	C₂×C₄×C₅₉	—	4	4	no	—
178	C₂×C₄×C₅₉	—	8	2	no	—
179	C₂×C₄×C₅₉	C₄×D₄	1	2	yes	—
180	C₂×C₄×C₅₉	C₄×D₄	1	2	yes	—
181	C₂×C₄×C₅₉	C₂³×C₄	1	1	yes	characteristic
182	C₂×C₄×C₅₉	C₂²×D₄	1	1	yes	characteristic
183	C₂×C₄×C₅₉	C₂²×D₄	1	1	yes	characteristic
184	C₂×C₄×C₅₉	C₂²×Q₈	1	1	yes	characteristic
185	C₂×C₄×C₅₉	H(5,𝔽₂)	1	1	yes	characteristic
186	C₂×C₄×C₅₉	2₋¹⁺⁴	1	1	yes	characteristic
187	C₂×Dic₅₉	—	2	2	no	—
188	C₂×Dic₅₉	—	4	1	no	—
189	C₂×Dic₅₉	—	4	1	no	—
190	C₂×Dic₅₉	—	4	1	no	—
191	C₂×Dic₅₉	—	4	1	no	—
192	C₂×Dic₅₉	—	4	1	no	—
193	C₈×C₅₉	—	2	2	no	—
194	C₈×C₅₉	C₂×C₄⋊C₄	1	2	yes	—
195	C₈×C₅₉	C₂×C₄⋊C₄	1	2	yes	—
196	C₅₉⋊C₈	—	2	1	no	—
197	C₅₉⋊C₈	—	2	2	no	—
198	C₅₉⋊C₈	—	2	1	no	—
199	C₅₉⋊C₈	—	4	2	no	—
200	C₅₉⋊C₈	—	4	2	no	—
201	#22687	—	59	1	no	maximal, Sylow
202	C₂²×C₅₉	—	2	1	no	—
203	C₂²×C₅₉	—	2	1	no	—
204	C₂²×C₅₉	—	2	4	no	—
205	C₂²×C₅₉	—	4	2	no	—
206	C₂²×C₅₉	—	4	2	no	—
207	C₂²×C₅₉	C₂×C₄×D₄	1	1	yes	characteristic
208	C₂²×C₅₉	#547	1	1	yes	characteristic
209	C₂²×C₅₉	#554	1	1	yes	characteristic
210	C₄×C₅₉	—	2	4	no	—
211	C₄×C₅₉	—	2	2	no	—
212	C₄×C₅₉	—	2	2	no	—
213	C₄×C₅₉	—	4	2	no	—
214	C₄×C₅₉	—	4	2	no	—
215	C₄×C₅₉	C₂²×C₄⋊C₄	1	1	yes	characteristic
216	C₄×C₅₉	#520	1	1	yes	characteristic
217	C₄×C₅₉	D₄²	1	1	yes	characteristic
218	C₄×C₅₉	D₄×Q₈	1	1	yes	characteristic
219	Dic₅₉	—	4	2	no	—
220	Dic₅₉	—	8	1	no	—
221	C₂×#444	—	59	1	no	—
222	C₂×#443	—	59	1	no	—
223	#2943	D₅₉	1	1	yes	characteristic
224	#2906	—	59	2	no	—
225	#1946	—	59	1	no	—
226	#1945	—	59	1	no	—
227	#1866	—	59	2	no	—
228	#1866	—	59	2	no	—
229	#1849	—	59	1	no	—
230	#1806	—	59	2	no	—
231	#1771	—	59	1	no	—
232	C₂×C₅₉	—	2	1	no	—
233	C₂×C₅₉	—	2	1	no	—
234	C₂×C₅₉	—	4	4	no	—
235	C₂×C₅₉	D₄×C₄⋊C₄	1	1	yes	characteristic
236	C₂×C₅₉	#2955	1	1	yes	characteristic
237	C₂×C₅₉	#2956	1	1	yes	characteristic
238	C₂×#135	C₂×D₅₉	1	1	yes	characteristic
239	C₂×#131	—	59	2	no	—
240	C₂×#131	—	59	2	no	—
241	C₄×#41	C₂×D₅₉	1	2	yes	—
242	#444	—	118	4	no	—
243	#443	—	118	4	no	—
244	#442	Dic₅₉	1	2	yes	complemented
245	#441	Dic₅₉	1	2	yes	complemented
246	#440	Dic₅₉	1	2	yes	complemented
247	#440	Dic₅₉	1	2	yes	complemented
248	C₂×#108	—	59	1	no	—
249	C₂×#108	—	59	1	no	—
250	C₂×#108	—	59	2	no	—
251	#427	C₂×D₅₉	1	1	yes	characteristic
252	#424	—	59	2	no	—
253	#424	—	59	2	no	—
254	#424	—	118	2	no	—
255	#424	—	118	2	no	—
256	#423	—	59	2	no	—
257	#423	—	118	2	no	—
258	C₂×C₄⋊C₈	—	59	1	no	—
259	C₂×C₄⋊C₈	—	118	2	no	—
260	C₂×#104	—	59	2	no	—
261	C₂×#104	—	59	2	no	—
262	#416	C₂×D₅₉	1	2	yes	—
263	C₂×#97	—	59	1	no	—
264	C₂×#97	C₂×D₅₉	1	1	yes	characteristic
265	C₂×C₄×C₈	—	59	1	no	—
266	C₄×C₄⋊C₄	—	59	1	no	—
267	#339	—	59	2	no	—
268	#339	—	59	2	no	—
269	#336	—	59	1	no	—
270	#336	—	59	1	no	—
271	C₅₉	#22687	1	1	yes	characteristic, complemented, Sylow
272	C₂×#41	C₂²×D₅₉	1	2	yes	—
273	#135	Dic₁₁₈	1	4	yes	—
274	#135	D₂₃₆	1	4	yes	—
275	C₂×Q₁₆	C₂×Dic₅₉	1	1	yes	characteristic
276	C₂×SD₁₆	C₂×Dic₅₉	1	2	yes	—
277	C₂×D₈	C₂×Dic₅₉	1	1	yes	characteristic
278	#131	—	118	4	no	—
279	#131	—	118	4	no	—
280	#131	—	236	2	no	—
281	#131	—	236	2	no	—
282	C₂×M₁₆	—	59	2	no	—
283	C₂×M₁₆	—	59	2	no	—
284	C₂×M₁₆	—	118	2	no	—
285	C₂×M₁₆	—	118	2	no	—
286	C₂²×C₈	—	59	1	no	—
287	C₂²×C₈	—	59	1	no	—
288	C₂²×C₈	—	118	2	no	—
289	C₂²×C₈	—	118	2	no	—
290	C₂²×C₈	C₂²×D₅₉	1	1	yes	characteristic
291	C₂²×C₈	C₂²×D₅₉	1	1	yes	characteristic
292	C₄×Q₈	C₂×Dic₅₉	1	2	yes	—
293	C₄×Q₈	C₂×Dic₅₉	1	2	yes	—
294	C₄×D₄	—	2	2	no	—
295	C₄×D₄	—	2	2	no	—
296	C₄×D₄	C₂×Dic₅₉	1	2	yes	—
297	C₄×D₄	C₂×Dic₅₉	1	2	yes	—
298	#117	—	2	2	no	—
299	#117	C₂²×D₅₉	1	2	yes	—
300	C₂×C₄⋊C₄	—	118	1	no	—
301	C₂×C₄²	—	2	2	no	—
302	C₂×C₄²	—	59	1	no	—
303	C₂×C₄²	—	59	1	no	—
304	C₂×C₄²	C₂²×D₅₉	1	1	yes	characteristic
305	#108	—	118	2	no	—
306	#108	—	118	2	no	—
307	#108	—	236	2	no	—
308	#107	C₂×Dic₅₉	1	1	yes	characteristic
309	#107	C₂×Dic₅₉	1	1	yes	characteristic
310	#106	C₂×Dic₅₉	1	2	yes	—
311	C₄⋊C₈	—	59	2	no	—
312	C₄⋊C₈	—	59	2	no	—
313	C₄⋊C₈	—	118	2	no	—
314	C₄⋊C₈	—	118	2	no	—
315	C₄⋊C₈	—	118	2	no	—
316	C₄⋊C₈	—	118	2	no	—
317	C₄⋊C₈	—	118	2	no	—
318	C₄⋊C₈	—	118	2	no	—
319	#104	—	118	4	no	—
320	#104	—	118	4	no	—
321	#103	C₂×Dic₅₉	1	2	yes	—
322	#103	C₂×Dic₅₉	1	2	yes	—
323	#102	C₂×Dic₅₉	1	2	yes	—
324	#102	C₂×Dic₅₉	1	2	yes	—
325	#97	—	118	2	no	—
326	#97	C₂×Dic₅₉	1	2	yes	—
327	#97	C₂×Dic₅₉	1	2	yes	—
328	C₄×C₈	—	118	2	no	—
329	#95	—	118	1	no	—
330	#41	—	2	2	no	—
331	#41	—	2	2	no	—
332	#41	C₂×Dic₁₁₈	1	4	yes	—
333	#41	C₂×D₂₃₆	1	4	yes	—
334	C₂×Q₈	C₂²×Dic₅₉	1	2	yes	—
335	C₂×D₄	—	2	2	no	—
336	C₂×D₄	C₂²×Dic₅₉	1	2	yes	—
337	C₂²×C₄	—	2	2	no	—
338	C₂²×C₄	—	2	2	no	—
339	C₂²×C₄	—	2	2	no	—
340	C₂²×C₄	—	118	1	no	—
341	C₂²×C₄	—	118	1	no	—
342	C₂²×C₄	#11745687	1	1	yes	characteristic
343	C₂²×C₄	#11745687	1	1	yes	characteristic
344	C₂²×C₄	C₂³×D₅₉	1	1	yes	characteristic
345	Q₁₆	C₄⋊Dic₅₉	1	4	yes	complemented
346	SD₁₆	C₄⋊Dic₅₉	1	8	yes	complemented
347	D₈	C₄⋊Dic₅₉	1	4	yes	complemented
348	M₁₆	—	118	2	no	—
349	M₁₆	—	118	2	no	—
350	M₁₆	—	118	2	no	—
351	M₁₆	—	118	2	no	—
352	M₁₆	—	236	4	no	—
353	M₁₆	—	236	4	no	—
354	C₂×C₈	—	2	1	no	—
355	C₂×C₈	—	2	1	no	—
356	C₂×C₈	—	59	1	no	—
357	C₂×C₈	—	59	2	no	—
358	C₂×C₈	—	59	1	no	—
359	C₂×C₈	—	118	1	no	—
360	C₂×C₈	—	118	1	no	—
361	C₂×C₈	—	118	1	no	—
362	C₂×C₈	—	118	1	no	—
363	C₂×C₈	—	118	2	no	—
364	C₂×C₈	—	118	2	no	—
365	C₂×C₈	—	236	4	no	—
366	C₂×C₈	—	236	4	no	—
367	C₂×C₈	C₂×Dic₁₁₈	1	2	yes	—
368	C₂×C₈	C₂×D₂₃₆	1	2	yes	—
369	C₂×C₈	C₂²×Dic₅₉	1	2	yes	—
370	C₂×C₈	C₂²×Dic₅₉	1	1	yes	characteristic
371	C₂×C₈	C₂²×Dic₅₉	1	1	yes	characteristic
372	C₄⋊C₄	—	2	2	no	—
373	C₄⋊C₄	—	2	2	no	—
374	C₄⋊C₄	—	236	2	no	—
375	C₄⋊C₄	C₂²×Dic₅₉	1	2	yes	—
376	C₄⋊C₄	C₂²×Dic₅₉	1	2	yes	—
377	C₂²⋊C₄	—	2	2	no	—
378	C₂²⋊C₄	—	2	2	no	—
379	C₂²⋊C₄	—	2	2	no	—
380	C₄²	—	2	2	no	—
381	C₄²	—	2	2	no	—
382	C₄²	—	2	2	no	—
383	C₄²	—	118	1	no	—
384	C₄²	—	118	1	no	—
385	C₄²	—	118	1	no	—
386	C₄²	—	118	1	no	—
387	C₄²	D₄×D₅₉	1	2	yes	—
388	C₄²	C₂²×Dic₅₉	1	2	yes	—
389	C₂³	—	2	2	no	—
390	C₂³	C₂×#11745687	1	1	yes	characteristic
391	Q₈	—	2	2	no	—
392	Q₈	C₂×C₄⋊Dic₅₉	1	4	yes	—
393	D₄	—	2	4	no	—
394	D₄	—	2	4	no	—
395	D₄	—	2	2	no	—
396	D₄	C₂×C₄⋊Dic₅₉	1	4	yes	—
397	C₂×C₄	—	2	2	no	—
398	C₂×C₄	—	2	4	no	—
399	C₂×C₄	—	2	4	no	—
400	C₂×C₄	—	2	2	no	—
401	C₂×C₄	—	2	2	no	—
402	C₂×C₄	—	4	1	no	—
403	C₂×C₄	—	4	1	no	—
404	C₂×C₄	—	4	4	no	—
405	C₂×C₄	—	8	2	no	—
406	C₂×C₄	—	118	2	no	—
407	C₂×C₄	—	236	1	no	—
408	C₂×C₄	—	236	1	no	—
409	C₂×C₄	—	236	1	no	—
410	C₂×C₄	—	236	1	no	—
411	C₂×C₄	—	236	1	no	—
412	C₂×C₄	D₄×Dic₅₉	1	2	yes	—
413	C₂×C₄	D₄×Dic₅₉	1	2	yes	—
414	C₂×C₄	C₂³×Dic₅₉	1	1	yes	characteristic
415	C₂×C₄	C₂×D₄×D₅₉	1	1	yes	characteristic
416	C₂×C₄	C₂²×D₂₃₆	1	1	yes	characteristic
417	C₂×C₄	C₂²×Dic₁₁₈	1	1	yes	characteristic
418	C₂×C₄	#14273773	1	1	yes	characteristic
419	C₂×C₄	#14273774	1	1	yes	characteristic
420	C₈	—	2	2	no	—
421	C₈	—	118	1	no	—
422	C₈	—	118	2	no	—
423	C₈	—	118	1	no	—
424	C₈	—	236	2	no	—
425	C₈	—	236	2	no	—
426	C₈	C₂×C₄⋊Dic₅₉	1	2	yes	—
427	C₈	C₂×C₄⋊Dic₅₉	1	2	yes	—
428	C₂²	—	2	1	no	—
429	C₂²	—	2	1	no	—
430	C₂²	—	2	4	no	—
431	C₂²	—	4	2	no	—
432	C₂²	—	4	2	no	—
433	C₂²	C₂×D₄×Dic₅₉	1	1	yes	characteristic
434	C₂²	#16838056	1	1	yes	characteristic
435	C₂²	#16838109	1	1	yes	characteristic
436	C₄	—	2	4	no	—
437	C₄	—	2	2	no	—
438	C₄	—	2	2	no	—
439	C₄	—	4	2	no	—
440	C₄	—	4	2	no	—
441	C₄	—	472	1	no	—
442	C₄	—	236	2	no	—
443	C₄	C₂²×C₄⋊Dic₅₉	1	1	yes	characteristic
444	C₄	#16837885	1	1	yes	characteristic
445	C₄	D₄×D₂₃₆	1	1	yes	characteristic
446	C₄	D₄×Dic₁₁₈	1	1	yes	characteristic
447	C₂	—	2	1	no	—
448	C₂	—	2	1	no	—
449	C₂	—	4	4	no	—
450	C₂	D₄×C₄⋊Dic₅₉	1	1	yes	characteristic
451	C₂	#21432999	1	1	yes	characteristic
452	C₂	#21433006	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₅₉
commutator	C₂×C₄×C₅₉	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₅₉
Fitting	C₅₉×#2943	C₂
socle	C₂²×C₅₉	C₂×C₄×D₄
prime radical	C₂×#135×C₅₉	C₂²
cosocle	C₂²×C₄×C₅₉	C₂⁴
hypercenter	#2943	D₅₉
hypocenter	C₅₉	#22687
LCS	G ▷ C₂×C₄×C₅₉ ▷ C₂×C₅₉ ▷ C₅₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #2943

Complements

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

N	H ≅ G/N	type
3. #21432664	C₂	semidirect
4. #21424850	C₂	semidirect
5. #21424845	C₂	semidirect
6. #21424373	C₂	semidirect
7. #21424373	C₂	semidirect
8. #21424271	C₂	semidirect
9. #21424116	C₂	semidirect
10. #21423968	C₂	semidirect
38. C₅₉×#442	C₄	semidirect
39. C₅₉×#441	C₄	semidirect
40. C₅₉×#440	C₄	semidirect
41. C₅₉×#440	C₄	semidirect
118. Q₁₆×C₅₉	C₄⋊C₄	semidirect
119. SD₁₆×C₅₉	C₄⋊C₄	semidirect
120. D₈×C₅₉	C₄⋊C₄	semidirect
244. #442	Dic₅₉	semidirect
245. #441	Dic₅₉	semidirect
246. #440	Dic₅₉	semidirect
247. #440	Dic₅₉	semidirect
271. C₅₉	#22687	semidirect
345. Q₁₆	C₄⋊Dic₅₉	semidirect
346. SD₁₆	C₄⋊Dic₅₉	semidirect
347. D₈	C₄⋊Dic₅₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×#16837524	2
C₂×#16837519	2
#21432664	2
#21424850	2
#21424845	2
#21424373	2
#21424271	2
#21424116	2
#21423968	2
C₅₉×#2943	2
#22687	59