Subgroups — #28646794

Order 15104.

710 conjugacy classes of subgroups.

The subgroup lattice has 424 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#21429122	C₂	1	1	yes	maximal, characteristic
2	#21427053	C₂	1	1	yes	maximal, characteristic
3	#21425473	C₂	1	2	yes	maximal
4	#21425235	C₂	1	2	yes	maximal
5	#21425046	C₂	1	2	yes	maximal
6	#21424859	C₂	1	1	yes	maximal, characteristic
7	#21424814	C₂	1	1	yes	maximal, characteristic
8	#21424677	C₂	1	2	yes	maximal
9	#21424224	C₂	1	1	yes	maximal, characteristic
10	#21424101	C₂	1	1	yes	maximal, characteristic
11	C₄×#103×C₅₉	C₂	1	1	yes	maximal, characteristic
12	C₂×#14273727	—	2	1	no	—
13	C₂×#14273726	C₂²	1	2	yes	—
14	C₂×#14273658	C₂²	1	2	yes	—
15	C₂×C₄⋊(C₅₉⋊C₈)	C₂²	1	1	yes	characteristic
16	C₂×Dic₅₉⋊C₈	C₂²	1	2	yes	—
17	C₂×#14273651	C₂²	1	2	yes	—
18	#16837323	—	2	2	no	—
19	#16837309	C₂²	1	2	yes	—
20	#16837301	C₂²	1	2	yes	—
21	#16837300	—	2	1	no	—
22	#16837288	—	2	2	no	—
23	#16837272	C₂²	1	1	yes	characteristic
24	#16837272	C₂²	1	1	yes	characteristic
25	#16837268	—	2	1	no	—
26	C₄⋊C₄×Dic₅₉	C₂²	1	2	yes	—
27	C₄×C₄⋊Dic₅₉	—	2	1	no	—
28	C₄×C₄⋊Dic₅₉	C₂²	1	1	yes	characteristic
29	#16837165	C₂²	1	2	yes	—
30	#16837165	C₂²	1	2	yes	—
31	#16837164	C₂²	1	2	yes	—
32	#16837164	C₂²	1	2	yes	—
33	#16837156	C₂²	1	2	yes	—
34	C₂×C₄×Q₈×C₅₉	C₂²	1	1	yes	characteristic
35	C₂×#103×C₅₉	C₂²	1	1	yes	characteristic
36	C₂×#103×C₅₉	C₂²	1	1	yes	characteristic
37	C₂×C₄×C₈×C₅₉	C₂²	1	1	yes	characteristic
38	C₄×C₄⋊C₄×C₅₉	C₂²	1	1	yes	characteristic
39	C₅₉×#340	C₂²	1	1	yes	characteristic
40	C₅₉×#340	C₂²	1	1	yes	characteristic
41	C₂²×Dic₁₁₈	—	2	2	no	—
42	C₂²×C₅₉⋊C₈	C₂³	1	2	yes	—
43	#14273727	—	4	4	no	—
44	#14273726	—	2	4	no	—
45	#14273726	—	4	2	no	—
46	C₂×C₄⋊Dic₅₉	—	2	1	no	—
47	C₂×C₄⋊Dic₅₉	—	2	1	no	—
48	C₂×C₄⋊Dic₅₉	—	2	2	no	—
49	C₂×C₄⋊Dic₅₉	—	2	1	no	—
50	C₂×C₄⋊Dic₅₉	—	2	1	no	—
51	C₂×C₄⋊Dic₅₉	D₄	1	1	yes	characteristic
52	C₂×C₄⋊Dic₅₉	D₄	1	1	yes	characteristic
53	C₂×C₄⋊Dic₅₉	C₂³	1	2	yes	—
54	C₂×C₄⋊Dic₅₉	C₂³	1	2	yes	—
55	C₂×Dic₅₉⋊C₄	—	2	2	no	—
56	C₂×C₄×Dic₅₉	—	2	2	no	—
57	C₂×C₄×Dic₅₉	C₂³	1	2	yes	—
58	#14273658	—	2	4	no	—
59	C₄⋊(C₅₉⋊C₈)	—	2	2	no	—
60	Dic₅₉⋊C₈	—	4	2	no	—
61	#14273651	—	4	2	no	—
62	C₅₉⋊#95	—	2	2	no	—
63	C₅₉⋊#95	—	2	2	no	—
64	C₅₉⋊#95	—	2	2	no	—
65	C₅₉⋊#95	—	2	2	no	—
66	C₅₉⋊#95	D₄	1	2	yes	—
67	C₂²×Q₈×C₅₉	C₂³	1	1	yes	characteristic
68	C₂²×C₈×C₅₉	C₂³	1	1	yes	characteristic
69	C₂²×C₈×C₅₉	C₂³	1	1	yes	characteristic
70	C₄×Q₈×C₅₉	—	2	2	no	—
71	C₄×Q₈×C₅₉	Q₈	1	4	yes	complemented
72	C₂×C₄⋊C₄×C₅₉	—	2	1	no	—
73	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
74	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
75	C₂×C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
76	C₂×C₄²×C₅₉	—	2	1	no	—
77	C₂×C₄²×C₅₉	—	2	1	no	—
78	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
79	#103×C₅₉	—	2	2	no	—
80	#103×C₅₉	—	2	2	no	—
81	C₄×C₈×C₅₉	—	2	2	no	—
82	#95×C₅₉	—	2	1	no	—
83	C₂×Q₈×C₅₉	—	2	1	no	—
84	C₂×Q₈×C₅₉	—	2	1	no	—
85	C₂×Q₈×C₅₉	—	2	1	no	—
86	C₂×Q₈×C₅₉	—	2	1	no	—
87	C₂×Q₈×C₅₉	—	2	1	no	—
88	C₂×Q₈×C₅₉	C₂×Q₈	1	2	yes	—
89	C₂²×C₄×C₅₉	—	2	1	no	—
90	C₂²×C₄×C₅₉	—	2	1	no	—
91	C₂²×C₄×C₅₉	—	2	1	no	—
92	C₂²×C₄×C₅₉	—	2	1	no	—
93	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
94	C₂²×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
95	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
96	C₂²×Dic₅₉	—	2	2	no	—
97	C₂²×Dic₅₉	—	2	2	no	—
98	C₂²×Dic₅₉	C₂×D₄	1	2	yes	—
99	C₂²×Dic₅₉	C₂×D₄	1	2	yes	—
100	C₂×Dic₁₁₈	—	4	4	no	—
101	C₂×Dic₁₁₈	—	4	4	no	—
102	C₂×Dic₁₁₈	—	8	2	no	—
103	C₂×C₈×C₅₉	—	2	1	no	—
104	C₂×C₈×C₅₉	—	2	1	no	—
105	C₂×C₈×C₅₉	—	2	1	no	—
106	C₂×C₈×C₅₉	—	2	1	no	—
107	C₂×C₈×C₅₉	—	2	1	no	—
108	C₂×C₈×C₅₉	—	2	1	no	—
109	C₄⋊C₄×C₅₉	—	2	4	no	—
110	C₄⋊C₄×C₅₉	—	2	1	no	—
111	C₄⋊C₄×C₅₉	—	2	1	no	—
112	C₄⋊C₄×C₅₉	—	2	1	no	—
113	C₄⋊C₄×C₅₉	C₂×Q₈	1	2	yes	—
114	C₄⋊C₄×C₅₉	#41	1	2	yes	—
115	C₄⋊C₄×C₅₉	#41	1	2	yes	—
116	C₄²×C₅₉	—	2	4	no	—
117	C₄²×C₅₉	—	4	2	no	—
118	C₄²×C₅₉	C₂×Q₈	1	2	yes	—
119	C₄²×C₅₉	#41	1	2	yes	—
120	C₄⋊Dic₅₉	—	2	2	no	—
121	C₄⋊Dic₅₉	—	2	2	no	—
122	C₄⋊Dic₅₉	—	2	2	no	—
123	C₄⋊Dic₅₉	—	2	2	no	—
124	C₄⋊Dic₅₉	—	2	2	no	—
125	C₄⋊Dic₅₉	—	4	2	no	—
126	C₄⋊Dic₅₉	—	4	2	no	—
127	C₄⋊Dic₅₉	—	4	4	no	—
128	C₄⋊Dic₅₉	—	8	1	no	—
129	C₄⋊Dic₅₉	—	8	1	no	—
130	C₄⋊Dic₅₉	SD₁₆	1	4	yes	—
131	Dic₅₉⋊C₄	—	4	4	no	—
132	C₄×Dic₅₉	—	2	2	no	—
133	C₄×Dic₅₉	—	2	2	no	—
134	C₄×Dic₅₉	—	8	2	no	—
135	C₂×C₅₉⋊C₈	—	2	2	no	—
136	C₂×C₅₉⋊C₈	—	2	2	no	—
137	C₂×C₅₉⋊C₈	—	2	2	no	—
138	C₂³×C₅₉	C₂²×D₄	1	1	yes	characteristic
139	Q₈×C₅₉	—	2	2	no	—
140	Q₈×C₅₉	—	2	2	no	—
141	Q₈×C₅₉	—	4	1	no	—
142	Q₈×C₅₉	—	4	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	—	4	1	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	—	4	1	no	—
156	C₂×C₄×C₅₉	—	4	1	no	—
157	C₂×C₄×C₅₉	C₂²⋊Q₈	1	2	yes	—
158	C₂×C₄×C₅₉	C₂²⋊Q₈	1	2	yes	—
159	C₂×C₄×C₅₉	C₂×SD₁₆	1	2	yes	—
160	C₂×C₄×C₅₉	#137	1	2	yes	—
161	C₂×C₄×C₅₉	C₂²×Q₈	1	1	yes	characteristic
162	C₂×C₄×C₅₉	C₂×#41	1	1	yes	characteristic
163	C₂×C₄×C₅₉	C₂×#41	1	1	yes	characteristic
164	C₂×C₄×C₅₉	C₂×#41	1	1	yes	characteristic
165	C₂×C₄×C₅₉	H(5,𝔽₂)	1	1	yes	characteristic
166	C₂×C₄×C₅₉	2₋¹⁺⁴	1	1	yes	characteristic
167	C₂×Dic₅₉	—	2	2	no	—
168	C₂×Dic₅₉	—	2	2	no	—
169	C₂×Dic₅₉	—	2	2	no	—
170	C₂×Dic₅₉	—	2	2	no	—
171	C₂×Dic₅₉	—	2	2	no	—
172	C₂×Dic₅₉	—	4	2	no	—
173	C₂×Dic₅₉	—	4	2	no	—
174	C₂×Dic₅₉	—	4	2	no	—
175	C₂×Dic₅₉	—	4	2	no	—
176	C₂×Dic₅₉	—	4	2	no	—
177	C₂×Dic₅₉	—	4	2	no	—
178	C₂×Dic₅₉	C₂×SD₁₆	1	4	yes	—
179	Dic₁₁₈	—	8	8	no	—
180	C₈×C₅₉	—	4	1	no	—
181	C₈×C₅₉	—	4	1	no	—
182	C₅₉⋊C₈	—	4	2	no	—
183	#26022	—	59	1	no	maximal, Sylow
184	C₂²×C₅₉	C₂×C₂²⋊Q₈	1	1	yes	characteristic
185	C₂²×C₅₉	#546	1	1	yes	characteristic
186	C₂²×C₅₉	#548	1	1	yes	characteristic
187	C₂²×C₅₉	C₂²×SD₁₆	1	1	yes	characteristic
188	C₂²×C₅₉	C₂×#137	1	1	yes	characteristic
189	C₂²×C₅₉	#576	1	1	yes	characteristic
190	C₂²×C₅₉	#578	1	1	yes	characteristic
191	C₄×C₅₉	—	2	2	no	—
192	C₄×C₅₉	—	4	2	no	—
193	C₄×C₅₉	—	4	2	no	—
194	C₄×C₅₉	—	4	2	no	—
195	C₄×C₅₉	—	4	2	no	—
196	C₄×C₅₉	#475	1	4	yes	—
197	C₄×C₅₉	#533	1	1	yes	characteristic
198	C₄×C₅₉	#544	1	1	yes	characteristic
199	C₄×C₅₉	#555	1	1	yes	characteristic
200	C₄×C₅₉	#556	1	1	yes	characteristic
201	Dic₅₉	—	2	4	no	—
202	Dic₅₉	—	4	2	no	—
203	Dic₅₉	—	8	2	no	—
204	Dic₅₉	—	8	2	no	—
205	#2551	—	59	1	no	—
206	#2355	—	59	1	no	—
207	#2066	—	59	2	no	—
208	#2024	—	59	2	no	—
209	#1988	—	59	2	no	—
210	#1948	—	59	1	no	—
211	#1939	—	59	1	no	—
212	#1919	—	59	2	no	—
213	#1834	—	59	1	no	—
214	#1803	—	59	1	no	—
215	C₄×#103	D₅₉	1	1	yes	characteristic
216	C₂×C₅₉	#2439	1	1	yes	characteristic
217	C₂×C₅₉	C₂×#475	1	1	yes	characteristic
218	C₂×C₅₉	#3083	1	1	yes	characteristic
219	C₂×C₅₉	#3295	1	1	yes	characteristic
220	C₂×C₅₉	#3328	1	1	yes	characteristic
221	C₂×C₅₉	#3359	1	1	yes	characteristic
222	C₂×C₅₉	#3375	1	1	yes	characteristic
223	C₂×C₄⋊Q₈	—	59	2	no	—
224	C₂×C₄⋊Q₈	—	118	1	no	—
225	C₂×C₄×Q₈	C₂×D₅₉	1	1	yes	characteristic
226	C₂×#106	—	59	2	no	—
227	C₂×C₄⋊C₈	—	59	1	no	—
228	C₂×C₄⋊C₈	—	59	2	no	—
229	C₂×#103	—	59	2	no	—
230	C₂×#103	C₂×D₅₉	1	1	yes	characteristic
231	C₂×#103	C₂×D₅₉	1	1	yes	characteristic
232	C₂×C₄×C₈	C₂×D₅₉	1	1	yes	characteristic
233	#395	—	118	2	no	—
234	#391	—	59	2	no	—
235	#389	—	59	2	no	—
236	#389	—	118	1	no	—
237	#387	—	118	2	no	—
238	#384	—	59	1	no	—
239	#384	—	59	1	no	—
240	#382	—	118	1	no	—
241	C₄×C₄⋊C₄	—	59	1	no	—
242	C₄×C₄⋊C₄	—	59	2	no	—
243	C₄×C₄⋊C₄	—	118	1	no	—
244	C₄×C₄⋊C₄	C₂×D₅₉	1	1	yes	characteristic
245	#340	—	59	2	no	—
246	#340	—	59	2	no	—
247	#340	—	59	2	no	—
248	#340	—	59	2	no	—
249	#340	C₂×D₅₉	1	1	yes	characteristic
250	#340	C₂×D₅₉	1	1	yes	characteristic
251	#336	—	59	2	no	—
252	C₅₉	#26022	1	1	yes	characteristic, complemented, Sylow
253	C₂²×Q₈	—	118	2	no	—
254	C₂²×Q₈	C₂²×D₅₉	1	1	yes	characteristic
255	C₂²×C₈	—	59	2	no	—
256	C₂²×C₈	C₂²×D₅₉	1	1	yes	characteristic
257	C₂²×C₈	C₂²×D₅₉	1	1	yes	characteristic
258	C₄⋊Q₈	—	118	4	no	—
259	C₄⋊Q₈	—	236	4	no	—
260	C₄⋊Q₈	—	236	2	no	—
261	C₄×Q₈	—	2	2	no	—
262	C₄×Q₈	Dic₁₁₈	1	4	yes	complemented
263	C₂×C₄⋊C₄	—	2	1	no	—
264	C₂×C₄⋊C₄	—	59	1	no	—
265	C₂×C₄⋊C₄	—	59	1	no	—
266	C₂×C₄⋊C₄	—	59	2	no	—
267	C₂×C₄⋊C₄	—	59	2	no	—
268	C₂×C₄⋊C₄	—	118	1	no	—
269	C₂×C₄⋊C₄	—	118	1	no	—
270	C₂×C₄⋊C₄	—	118	2	no	—
271	C₂×C₄⋊C₄	—	118	2	no	—
272	C₂×C₄⋊C₄	—	118	1	no	—
273	C₂×C₄⋊C₄	—	118	1	no	—
274	C₂×C₄⋊C₄	C₂²×D₅₉	1	1	yes	characteristic
275	C₂×C₄⋊C₄	C₂²×D₅₉	1	1	yes	characteristic
276	C₂×C₄⋊C₄	C₂²×D₅₉	1	1	yes	characteristic
277	C₂×C₄²	—	2	1	no	—
278	C₂×C₄²	—	2	1	no	—
279	C₂×C₄²	—	59	2	no	—
280	C₂×C₄²	—	118	2	no	—
281	C₂×C₄²	C₂²×D₅₉	1	1	yes	characteristic
282	#106	—	118	4	no	—
283	C₄⋊C₈	—	118	2	no	—
284	C₄⋊C₈	—	236	2	no	—
285	#103	—	2	2	no	—
286	#103	—	2	2	no	—
287	#103	—	236	2	no	—
288	C₄×C₈	—	2	2	no	—
289	#95	—	2	1	no	—
290	#95	—	59	2	no	—
291	#95	—	118	2	no	—
292	#95	—	118	2	no	—
293	#95	—	118	2	no	—
294	#95	—	118	2	no	—
295	C₂×Q₈	—	2	1	no	—
296	C₂×Q₈	—	2	1	no	—
297	C₂×Q₈	—	2	1	no	—
298	C₂×Q₈	—	2	1	no	—
299	C₂×Q₈	—	2	1	no	—
300	C₂×Q₈	—	472	2	no	—
301	C₂×Q₈	—	236	4	no	—
302	C₂×Q₈	—	236	4	no	—
303	C₂×Q₈	C₂×Dic₁₁₈	1	2	yes	—
304	C₂²×C₄	—	2	1	no	—
305	C₂²×C₄	—	2	1	no	—
306	C₂²×C₄	—	2	1	no	—
307	C₂²×C₄	—	2	1	no	—
308	C₂²×C₄	—	59	2	no	—
309	C₂²×C₄	—	59	2	no	—
310	C₂²×C₄	—	118	2	no	—
311	C₂²×C₄	—	118	2	no	—
312	C₂²×C₄	D₄×D₅₉	1	1	yes	characteristic
313	C₂²×C₄	D₄×D₅₉	1	1	yes	characteristic
314	C₂²×C₄	C₂³×D₅₉	1	1	yes	characteristic
315	C₂×C₈	—	2	1	no	—
316	C₂×C₈	—	2	1	no	—
317	C₂×C₈	—	2	1	no	—
318	C₂×C₈	—	2	1	no	—
319	C₂×C₈	—	2	1	no	—
320	C₂×C₈	—	2	1	no	—
321	C₂×C₈	—	118	2	no	—
322	C₂×C₈	—	118	2	no	—
323	C₂×C₈	—	118	2	no	—
324	C₄⋊C₄	—	2	4	no	—
325	C₄⋊C₄	—	2	1	no	—
326	C₄⋊C₄	—	2	1	no	—
327	C₄⋊C₄	—	2	1	no	—
328	C₄⋊C₄	—	59	4	no	—
329	C₄⋊C₄	—	118	2	no	—
330	C₄⋊C₄	—	118	2	no	—
331	C₄⋊C₄	—	118	2	no	—
332	C₄⋊C₄	—	118	2	no	—
333	C₄⋊C₄	—	118	2	no	—
334	C₄⋊C₄	—	472	1	no	—
335	C₄⋊C₄	—	472	1	no	—
336	C₄⋊C₄	—	236	4	no	—
337	C₄⋊C₄	—	236	4	no	—
338	C₄⋊C₄	—	236	2	no	—
339	C₄⋊C₄	—	236	2	no	—
340	C₄⋊C₄	C₂×Dic₁₁₈	1	2	yes	—
341	C₄⋊C₄	#11745685	1	2	yes	—
342	C₄⋊C₄	#11745685	1	2	yes	—
343	C₄²	—	2	4	no	—
344	C₄²	—	4	2	no	—
345	C₄²	—	118	2	no	—
346	C₄²	—	118	2	no	—
347	C₄²	—	472	2	no	—
348	C₄²	C₂×Dic₁₁₈	1	2	yes	—
349	C₄²	#11745687	1	2	yes	—
350	C₂³	C₂×D₄×D₅₉	1	1	yes	characteristic
351	Q₈	—	2	2	no	—
352	Q₈	—	2	2	no	—
353	Q₈	—	4	1	no	—
354	Q₈	—	4	1	no	—
355	Q₈	—	472	8	no	—
356	C₂×C₄	—	2	1	no	—
357	C₂×C₄	—	2	1	no	—
358	C₂×C₄	—	2	2	no	—
359	C₂×C₄	—	2	2	no	—
360	C₂×C₄	—	2	2	no	—
361	C₂×C₄	—	2	2	no	—
362	C₂×C₄	—	4	1	no	—
363	C₂×C₄	—	4	1	no	—
364	C₂×C₄	—	4	1	no	—
365	C₂×C₄	—	4	1	no	—
366	C₂×C₄	—	4	1	no	—
367	C₂×C₄	—	4	1	no	—
368	C₂×C₄	—	4	1	no	—
369	C₂×C₄	—	4	1	no	—
370	C₂×C₄	—	59	4	no	—
371	C₂×C₄	—	118	2	no	—
372	C₂×C₄	—	118	2	no	—
373	C₂×C₄	—	118	2	no	—
374	C₂×C₄	—	118	2	no	—
375	C₂×C₄	—	118	2	no	—
376	C₂×C₄	—	236	2	no	—
377	C₂×C₄	—	236	2	no	—
378	C₂×C₄	—	236	2	no	—
379	C₂×C₄	—	236	2	no	—
380	C₂×C₄	—	236	2	no	—
381	C₂×C₄	—	236	2	no	—
382	C₂×C₄	#14273704	1	2	yes	—
383	C₂×C₄	#14273704	1	2	yes	—
384	C₂×C₄	SD₁₆×D₅₉	1	2	yes	—
385	C₂×C₄	#14273759	1	2	yes	—
386	C₂×C₄	C₂²×Dic₁₁₈	1	1	yes	characteristic
387	C₂×C₄	C₂×#11745687	1	1	yes	characteristic
388	C₂×C₄	C₂×#11745685	1	1	yes	characteristic
389	C₂×C₄	C₂×#11745685	1	1	yes	characteristic
390	C₂×C₄	#14273773	1	1	yes	characteristic
391	C₂×C₄	#14273774	1	1	yes	characteristic
392	C₈	—	4	1	no	—
393	C₈	—	4	1	no	—
394	C₈	—	236	2	no	—
395	C₂²	C₂×#14273704	1	1	yes	characteristic
396	C₂²	#16838048	1	1	yes	characteristic
397	C₂²	#16838061	1	1	yes	characteristic
398	C₂²	C₂×SD₁₆×D₅₉	1	1	yes	characteristic
399	C₂²	C₂×#14273759	1	1	yes	characteristic
400	C₂²	#16838204	1	1	yes	characteristic
401	C₂²	#16838216	1	1	yes	characteristic
402	C₄	—	2	2	no	—
403	C₄	—	4	2	no	—
404	C₄	—	4	2	no	—
405	C₄	—	4	2	no	—
406	C₄	—	4	2	no	—
407	C₄	—	118	4	no	—
408	C₄	—	472	2	no	—
409	C₄	—	472	2	no	—
410	C₄	—	236	2	no	—
411	C₄	#16837685	1	4	yes	—
412	C₄	#16837959	1	1	yes	characteristic
413	C₄	#16838030	1	1	yes	characteristic
414	C₄	#16838117	1	1	yes	characteristic
415	C₄	#16838122	1	1	yes	characteristic
416	C₂	#21427787	1	1	yes	characteristic
417	C₂	C₂×#16837685	1	1	yes	characteristic
418	C₂	#21433945	1	1	yes	characteristic
419	C₂	#21435922	1	1	yes	characteristic
420	C₂	#21436381	1	1	yes	characteristic
421	C₂	#21436736	1	1	yes	characteristic
422	C₂	#21436908	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂×D₄×D₅₉
commutator, cosocle	C₂²×C₄×C₅₉	C₂⁴
Frattini	C₂²×C₄	C₂³×D₅₉
Fitting	C₄×#103×C₅₉	C₂
socle, prime radical	C₂³×C₅₉	C₂²×D₄
hypercenter	C₄×#103	D₅₉
hypocenter	C₅₉	#26022
LCS	G ▷ C₂²×C₄×C₅₉ ▷ C₂×C₅₉ ▷ C₅₉
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₄×#103

Complements

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

N	H ≅ G/N	type
71. C₄×Q₈×C₅₉	Q₈	semidirect
252. C₅₉	#26022	semidirect
262. C₄×Q₈	Dic₁₁₈	semidirect

Maximal subgroups

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

subgroup	index
#21429122	2
#21427053	2
#21425473	2
#21425235	2
#21425046	2
#21424859	2
#21424814	2
#21424677	2
#21424224	2
#21424101	2
C₄×#103×C₅₉	2
#26022	59