Subgroups — #28608402

Order 15104.

710 conjugacy classes of subgroups.

The subgroup lattice has 434 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#21432762	C₂	1	2	yes	maximal, complemented
2	#21424990	C₂	1	1	yes	maximal, characteristic
3	#21424985	C₂	1	1	yes	maximal, characteristic
4	#21424746	C₂	1	2	yes	maximal, complemented
5	#21424746	C₂	1	2	yes	maximal, complemented
6	#21424271	C₂	1	1	yes	maximal, characteristic, complemented
7	#21424116	C₂	1	2	yes	maximal, complemented
8	#21423982	C₂	1	1	yes	maximal, characteristic, complemented
9	#21423977	C₂	1	1	yes	maximal, characteristic, complemented
10	#21423968	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅₉×#2943	C₂	1	1	yes	maximal, characteristic
12	#16837463	—	2	2	no	—
13	#16837463	—	2	2	no	—
14	#16837459	—	2	2	no	—
15	#16837455	—	2	2	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	#16837426	C₂²	1	2	yes	—
20	C₂×C₄⋊(C₅₉⋊C₈)	C₂²	1	1	yes	characteristic
21	C₂×#14273654	C₂²	1	2	yes	—
22	C₂×#14273654	C₂²	1	2	yes	—
23	#16837369	C₂²	1	2	yes	—
24	#16837369	C₂²	1	2	yes	—
25	#16837358	C₂²	1	2	yes	—
26	#16837358	C₂²	1	2	yes	—
27	C₂×#14273637	C₂²	1	1	yes	characteristic
28	C₂×C₈×Dic₅₉	C₂²	1	1	yes	characteristic
29	C₄×C₄⋊Dic₅₉	C₂²	1	1	yes	characteristic
30	#16837161	C₂²	1	2	yes	—
31	#16837161	C₂²	1	2	yes	—
32	#16837156	C₂²	1	1	yes	characteristic
33	#16837156	C₂²	1	1	yes	characteristic
34	C₂×#135×C₅₉	C₂²	1	1	yes	characteristic
35	C₄×#41×C₅₉	C₂²	1	2	yes	—
36	C₅₉×#442	C₄	1	2	yes	complemented
37	C₅₉×#441	C₄	1	2	yes	complemented
38	C₅₉×#440	C₄	1	2	yes	complemented
39	C₅₉×#440	C₄	1	2	yes	complemented
40	C₅₉×#427	C₂²	1	1	yes	characteristic
41	C₅₉×#416	C₂²	1	2	yes	—
42	C₂×#97×C₅₉	C₂²	1	1	yes	characteristic
43	C₂×#11745664	C₂³	1	2	yes	—
44	C₂×#11745664	C₂³	1	2	yes	—
45	C₂²×C₅₉⋊C₈	C₂³	1	1	yes	characteristic
46	C₂²×C₅₉⋊C₈	C₂³	1	1	yes	characteristic
47	C₂×C₄⋊Dic₅₉	—	2	1	no	—
48	C₂×C₄×Dic₅₉	C₂³	1	1	yes	characteristic
49	C₂×C₄×Dic₅₉	C₂³	1	1	yes	characteristic
50	#14273663	—	2	2	no	—
51	#14273663	—	2	2	no	—
52	#14273663	—	4	2	no	—
53	C₄⋊(C₅₉⋊C₈)	—	2	2	no	—
54	C₄⋊(C₅₉⋊C₈)	—	2	2	no	—
55	C₄⋊(C₅₉⋊C₈)	D₄	1	2	yes	—
56	C₄⋊(C₅₉⋊C₈)	D₄	1	2	yes	—
57	#14273654	—	4	2	no	—
58	#14273654	—	4	2	no	—
59	C₂²⋊(C₅₉⋊C₈)	—	2	2	no	—
60	C₂²⋊(C₅₉⋊C₈)	—	2	2	no	—
61	C₂²⋊(C₅₉⋊C₈)	—	2	2	no	—
62	C₂²⋊(C₅₉⋊C₈)	—	2	2	no	—
63	#14273638	—	2	2	no	—
64	#14273638	—	2	2	no	—
65	#14273637	—	2	2	no	—
66	C₄×C₅₉⋊C₈	—	2	2	no	—
67	C₄×C₅₉⋊C₈	—	2	2	no	—
68	C₈×Dic₅₉	—	2	2	no	—
69	C₅₉⋊#95	—	2	1	no	—
70	C₂×#41×C₅₉	C₂³	1	2	yes	—
71	#135×C₅₉	—	2	2	no	—
72	#135×C₅₉	—	2	2	no	—
73	C₂×Q₁₆×C₅₉	C₂×C₄	1	1	yes	characteristic
74	C₂×SD₁₆×C₅₉	C₂×C₄	1	2	yes	—
75	C₂×D₈×C₅₉	C₂×C₄	1	1	yes	characteristic
76	C₂²×C₈×C₅₉	C₂³	1	1	yes	characteristic
77	C₂²×C₈×C₅₉	C₂³	1	1	yes	characteristic
78	C₄×Q₈×C₅₉	C₂×C₄	1	2	yes	—
79	C₄×Q₈×C₅₉	C₂×C₄	1	2	yes	—
80	C₄×D₄×C₅₉	—	2	2	no	—
81	C₄×D₄×C₅₉	—	2	2	no	—
82	C₄×D₄×C₅₉	C₂×C₄	1	2	yes	—
83	C₄×D₄×C₅₉	C₂×C₄	1	2	yes	—
84	#117×C₅₉	—	2	2	no	—
85	#117×C₅₉	C₂³	1	2	yes	—
86	C₂×C₄²×C₅₉	—	2	2	no	—
87	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
88	#107×C₅₉	C₂×C₄	1	1	yes	characteristic
89	#107×C₅₉	C₂×C₄	1	1	yes	characteristic
90	#106×C₅₉	C₂×C₄	1	2	yes	—
91	#103×C₅₉	C₂×C₄	1	2	yes	—
92	#103×C₅₉	C₂×C₄	1	2	yes	—
93	#102×C₅₉	C₂×C₄	1	2	yes	—
94	#102×C₅₉	C₂×C₄	1	2	yes	—
95	#97×C₅₉	C₂×C₄	1	2	yes	—
96	#97×C₅₉	C₂×C₄	1	2	yes	—
97	#41×C₅₉	—	2	2	no	—
98	#41×C₅₉	—	2	2	no	—
99	#41×C₅₉	—	2	2	no	—
100	#41×C₅₉	—	2	2	no	—
101	C₂×Q₈×C₅₉	C₂²×C₄	1	2	yes	—
102	C₂×D₄×C₅₉	—	2	2	no	—
103	C₂×D₄×C₅₉	C₂²×C₄	1	2	yes	—
104	C₂²×C₄×C₅₉	—	2	2	no	—
105	C₂²×C₄×C₅₉	—	2	2	no	—
106	C₂²×C₄×C₅₉	—	2	2	no	—
107	C₂²×C₄×C₅₉	#41	1	1	yes	characteristic
108	C₂²×C₄×C₅₉	#41	1	1	yes	characteristic
109	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
110	C₂²×Dic₅₉	—	2	1	no	—
111	C₂²×Dic₅₉	—	2	1	no	—
112	Q₁₆×C₅₉	—	2	2	no	—
113	SD₁₆×C₅₉	—	2	4	no	—
114	D₈×C₅₉	—	2	2	no	—
115	C₂×C₈×C₅₉	—	2	1	no	—
116	C₂×C₈×C₅₉	—	2	1	no	—
117	C₂×C₈×C₅₉	C₂²×C₄	1	2	yes	—
118	C₂×C₈×C₅₉	C₂²×C₄	1	1	yes	characteristic
119	C₂×C₈×C₅₉	C₂²×C₄	1	1	yes	characteristic
120	C₂×C₈×C₅₉	#41	1	2	yes	—
121	C₂×C₈×C₅₉	#41	1	2	yes	—
122	C₄⋊C₄×C₅₉	—	2	2	no	—
123	C₄⋊C₄×C₅₉	—	2	2	no	—
124	C₄⋊C₄×C₅₉	C₂²×C₄	1	2	yes	—
125	C₄⋊C₄×C₅₉	C₂²×C₄	1	2	yes	—
126	C₂²⋊C₄×C₅₉	—	2	2	no	—
127	C₂²⋊C₄×C₅₉	—	2	2	no	—
128	C₂²⋊C₄×C₅₉	—	2	2	no	—
129	C₄²×C₅₉	—	2	2	no	—
130	C₄²×C₅₉	—	2	2	no	—
131	C₄²×C₅₉	—	2	2	no	—
132	C₄²×C₅₉	C₂²×C₄	1	2	yes	—
133	C₄²×C₅₉	C₂×D₄	1	2	yes	—
134	C₄⋊Dic₅₉	—	4	2	no	—
135	C₄×Dic₅₉	—	2	1	no	—
136	C₄×Dic₅₉	—	2	1	no	—
137	C₄×Dic₅₉	—	2	1	no	—
138	C₄×Dic₅₉	—	2	1	no	—
139	#11745664	—	2	2	no	—
140	#11745664	—	2	2	no	—
141	#11745664	—	2	2	no	—
142	#11745664	—	2	2	no	—
143	C₂×C₅₉⋊C₈	—	2	1	no	—
144	C₂×C₅₉⋊C₈	—	2	1	no	—
145	C₂×C₅₉⋊C₈	—	2	1	no	—
146	C₂×C₅₉⋊C₈	—	2	1	no	—
147	C₂×C₅₉⋊C₈	—	2	2	no	—
148	C₂×C₅₉⋊C₈	—	2	2	no	—
149	C₂×C₅₉⋊C₈	C₂×D₄	1	1	yes	characteristic
150	C₂×C₅₉⋊C₈	C₂×D₄	1	2	yes	—
151	C₂×C₅₉⋊C₈	C₂×D₄	1	1	yes	characteristic
152	C₂³×C₅₉	—	2	2	no	—
153	C₂³×C₅₉	C₂×#41	1	1	yes	characteristic
154	Q₈×C₅₉	—	2	2	no	—
155	Q₈×C₅₉	—	2	2	no	—
156	D₄×C₅₉	—	2	2	no	—
157	D₄×C₅₉	—	2	2	no	—
158	D₄×C₅₉	—	4	2	no	—
159	D₄×C₅₉	—	4	2	no	—
160	C₂×C₄×C₅₉	—	2	2	no	—
161	C₂×C₄×C₅₉	—	2	2	no	—
162	C₂×C₄×C₅₉	—	2	2	no	—
163	C₂×C₄×C₅₉	—	4	1	no	—
164	C₂×C₄×C₅₉	—	4	1	no	—
165	C₂×C₄×C₅₉	—	4	4	no	—
166	C₂×C₄×C₅₉	—	4	2	no	—
167	C₂×C₄×C₅₉	—	4	2	no	—
168	C₂×C₄×C₅₉	—	8	2	no	—
169	C₂×C₄×C₅₉	C₄×D₄	1	2	yes	—
170	C₂×C₄×C₅₉	C₄×D₄	1	2	yes	—
171	C₂×C₄×C₅₉	C₂³×C₄	1	1	yes	characteristic
172	C₂×C₄×C₅₉	C₂²×D₄	1	1	yes	characteristic
173	C₂×C₄×C₅₉	C₂×#41	1	1	yes	characteristic
174	C₂×C₄×C₅₉	C₂×#41	1	1	yes	characteristic
175	C₂×C₄×C₅₉	H(5,𝔽₂)	1	1	yes	characteristic
176	C₂×C₄×C₅₉	2₋¹⁺⁴	1	1	yes	characteristic
177	C₂×Dic₅₉	—	2	2	no	—
178	C₂×Dic₅₉	—	4	1	no	—
179	C₂×Dic₅₉	—	4	1	no	—
180	C₂×Dic₅₉	—	4	1	no	—
181	C₂×Dic₅₉	—	4	1	no	—
182	C₂×Dic₅₉	—	4	1	no	—
183	C₈×C₅₉	—	2	2	no	—
184	C₈×C₅₉	#117	1	2	yes	—
185	C₈×C₅₉	#117	1	2	yes	—
186	C₅₉⋊C₈	—	2	1	no	—
187	C₅₉⋊C₈	—	2	1	no	—
188	C₅₉⋊C₈	—	2	2	no	—
189	C₅₉⋊C₈	—	4	2	no	—
190	C₅₉⋊C₈	—	4	2	no	—
191	#22804	—	59	1	no	maximal, Sylow
192	C₂²×C₅₉	—	2	1	no	—
193	C₂²×C₅₉	—	2	1	no	—
194	C₂²×C₅₉	—	4	2	no	—
195	C₂²×C₅₉	—	4	2	no	—
196	C₂²×C₅₉	—	4	2	no	—
197	C₂²×C₅₉	C₂×C₄×D₄	1	1	yes	characteristic
198	C₂²×C₅₉	#555	1	1	yes	characteristic
199	C₂²×C₅₉	#556	1	1	yes	characteristic
200	C₄×C₅₉	—	2	2	no	—
201	C₄×C₅₉	—	2	2	no	—
202	C₄×C₅₉	—	4	2	no	—
203	C₄×C₅₉	—	4	2	no	—
204	C₄×C₅₉	—	4	2	no	—
205	C₄×C₅₉	C₂×#117	1	1	yes	characteristic
206	C₄×C₅₉	#520	1	1	yes	characteristic
207	C₄×C₅₉	#547	1	1	yes	characteristic
208	C₄×C₅₉	#550	1	1	yes	characteristic
209	Dic₅₉	—	4	2	no	—
210	Dic₅₉	—	8	1	no	—
211	#2943	D₅₉	1	1	yes	characteristic
212	#2925	—	59	2	no	—
213	#1975	—	59	1	no	—
214	#1974	—	59	1	no	—
215	#1929	—	59	2	no	—
216	#1929	—	59	2	no	—
217	#1849	—	59	1	no	—
218	#1806	—	59	2	no	—
219	#1773	—	59	1	no	—
220	#1772	—	59	1	no	—
221	#1771	—	59	1	no	—
222	C₂×C₅₉	—	2	1	no	—
223	C₂×C₅₉	—	2	1	no	—
224	C₂×C₅₉	—	8	2	no	—
225	C₂×C₅₉	#2354	1	1	yes	characteristic
226	C₂×C₅₉	#2955	1	1	yes	characteristic
227	C₂×C₅₉	#2956	1	1	yes	characteristic
228	C₂×#135	C₂×D₅₉	1	1	yes	characteristic
229	C₄×#41	C₂×D₅₉	1	2	yes	—
230	#442	Dic₅₉	1	2	yes	complemented
231	#441	Dic₅₉	1	2	yes	complemented
232	#440	Dic₅₉	1	2	yes	complemented
233	#440	Dic₅₉	1	2	yes	complemented
234	#433	—	118	2	no	—
235	#433	—	118	2	no	—
236	#432	—	118	2	no	—
237	#431	—	118	2	no	—
238	C₂×#108	—	59	1	no	—
239	C₂×#108	—	59	1	no	—
240	C₂×#108	—	59	2	no	—
241	#427	C₂×D₅₉	1	1	yes	characteristic
242	#423	—	59	2	no	—
243	C₂×C₄⋊C₈	—	59	1	no	—
244	C₂×#104	—	59	2	no	—
245	C₂×#104	—	59	2	no	—
246	#416	C₂×D₅₉	1	2	yes	—
247	#408	—	59	2	no	—
248	#408	—	59	2	no	—
249	#405	—	59	2	no	—
250	#405	—	59	2	no	—
251	C₂×#97	—	59	1	no	—
252	C₂×#97	C₂×D₅₉	1	1	yes	characteristic
253	C₂×C₄×C₈	—	59	1	no	—
254	C₄×C₄⋊C₄	—	59	1	no	—
255	#339	—	59	2	no	—
256	#339	—	59	2	no	—
257	#336	—	59	1	no	—
258	#336	—	59	1	no	—
259	C₅₉	#22804	1	1	yes	characteristic, complemented, Sylow
260	C₂×#41	C₂²×D₅₉	1	2	yes	—
261	#135	—	2	2	no	—
262	#135	—	2	2	no	—
263	C₂×Q₁₆	C₂×Dic₅₉	1	1	yes	characteristic
264	C₂×SD₁₆	C₂×Dic₅₉	1	2	yes	—
265	C₂×D₈	C₂×Dic₅₉	1	1	yes	characteristic
266	C₂×M₁₆	—	59	2	no	—
267	C₂×M₁₆	—	59	2	no	—
268	C₂²×C₈	—	59	1	no	—
269	C₂²×C₈	—	59	1	no	—
270	C₂²×C₈	C₂²×D₅₉	1	1	yes	characteristic
271	C₂²×C₈	C₂²×D₅₉	1	1	yes	characteristic
272	C₄×Q₈	C₂×Dic₅₉	1	2	yes	—
273	C₄×Q₈	C₂×Dic₅₉	1	2	yes	—
274	C₄×D₄	—	2	2	no	—
275	C₄×D₄	—	2	2	no	—
276	C₄×D₄	C₂×Dic₅₉	1	2	yes	—
277	C₄×D₄	C₂×Dic₅₉	1	2	yes	—
278	#117	—	2	2	no	—
279	#117	C₂²×D₅₉	1	2	yes	—
280	C₂×C₄⋊C₄	—	118	1	no	—
281	C₂×C₄²	—	2	2	no	—
282	C₂×C₄²	—	59	1	no	—
283	C₂×C₄²	—	59	1	no	—
284	C₂×C₄²	C₂²×D₅₉	1	1	yes	characteristic
285	#108	—	118	2	no	—
286	#108	—	118	2	no	—
287	#108	—	236	2	no	—
288	#107	C₂×Dic₅₉	1	1	yes	characteristic
289	#107	C₂×Dic₅₉	1	1	yes	characteristic
290	#106	C₂×Dic₅₉	1	2	yes	—
291	C₄⋊C₈	—	59	2	no	—
292	C₄⋊C₈	—	59	2	no	—
293	C₄⋊C₈	—	118	2	no	—
294	C₄⋊C₈	—	118	2	no	—
295	#104	—	236	2	no	—
296	#104	—	236	2	no	—
297	#103	C₂×Dic₅₉	1	2	yes	—
298	#103	C₂×Dic₅₉	1	2	yes	—
299	#102	C₂×Dic₅₉	1	2	yes	—
300	#102	C₂×Dic₅₉	1	2	yes	—
301	C₂²⋊C₈	—	118	2	no	—
302	C₂²⋊C₈	—	118	2	no	—
303	C₂²⋊C₈	—	118	2	no	—
304	C₂²⋊C₈	—	118	2	no	—
305	#97	—	118	2	no	—
306	#97	—	118	2	no	—
307	#97	—	118	2	no	—
308	#97	C₂×Dic₅₉	1	2	yes	—
309	#97	C₂×Dic₅₉	1	2	yes	—
310	C₄×C₈	—	118	2	no	—
311	C₄×C₈	—	118	2	no	—
312	C₄×C₈	—	118	2	no	—
313	#95	—	118	1	no	—
314	#41	—	2	2	no	—
315	#41	—	2	2	no	—
316	#41	—	2	2	no	—
317	#41	—	2	2	no	—
318	C₂×Q₈	C₂²×Dic₅₉	1	2	yes	—
319	C₂×D₄	—	2	2	no	—
320	C₂×D₄	C₂²×Dic₅₉	1	2	yes	—
321	C₂²×C₄	—	2	2	no	—
322	C₂²×C₄	—	2	2	no	—
323	C₂²×C₄	—	2	2	no	—
324	C₂²×C₄	—	118	1	no	—
325	C₂²×C₄	—	118	1	no	—
326	C₂²×C₄	#11745687	1	1	yes	characteristic
327	C₂²×C₄	#11745687	1	1	yes	characteristic
328	C₂²×C₄	C₂³×D₅₉	1	1	yes	characteristic
329	Q₁₆	—	2	2	no	—
330	SD₁₆	—	2	4	no	—
331	D₈	—	2	2	no	—
332	M₁₆	—	118	2	no	—
333	M₁₆	—	118	2	no	—
334	M₁₆	—	118	2	no	—
335	M₁₆	—	118	2	no	—
336	C₂×C₈	—	2	1	no	—
337	C₂×C₈	—	2	1	no	—
338	C₂×C₈	—	59	1	no	—
339	C₂×C₈	—	59	2	no	—
340	C₂×C₈	—	59	1	no	—
341	C₂×C₈	—	118	1	no	—
342	C₂×C₈	—	118	1	no	—
343	C₂×C₈	—	118	1	no	—
344	C₂×C₈	—	118	1	no	—
345	C₂×C₈	—	118	2	no	—
346	C₂×C₈	—	118	2	no	—
347	C₂×C₈	#11745685	1	2	yes	—
348	C₂×C₈	#11745685	1	2	yes	—
349	C₂×C₈	C₂²×Dic₅₉	1	2	yes	—
350	C₂×C₈	C₂²×Dic₅₉	1	1	yes	characteristic
351	C₂×C₈	C₂²×Dic₅₉	1	1	yes	characteristic
352	C₄⋊C₄	—	2	2	no	—
353	C₄⋊C₄	—	2	2	no	—
354	C₄⋊C₄	—	236	2	no	—
355	C₄⋊C₄	C₂²×Dic₅₉	1	2	yes	—
356	C₄⋊C₄	C₂²×Dic₅₉	1	2	yes	—
357	C₂²⋊C₄	—	2	2	no	—
358	C₂²⋊C₄	—	2	2	no	—
359	C₂²⋊C₄	—	2	2	no	—
360	C₄²	—	2	2	no	—
361	C₄²	—	2	2	no	—
362	C₄²	—	2	2	no	—
363	C₄²	—	118	1	no	—
364	C₄²	—	118	1	no	—
365	C₄²	—	118	1	no	—
366	C₄²	—	118	1	no	—
367	C₄²	D₄×D₅₉	1	2	yes	—
368	C₄²	C₂²×Dic₅₉	1	2	yes	—
369	C₂³	—	2	2	no	—
370	C₂³	C₂×#11745687	1	1	yes	characteristic
371	Q₈	—	2	2	no	—
372	Q₈	—	2	2	no	—
373	D₄	—	2	2	no	—
374	D₄	—	2	2	no	—
375	D₄	—	4	2	no	—
376	D₄	—	4	2	no	—
377	C₂×C₄	—	2	2	no	—
378	C₂×C₄	—	2	2	no	—
379	C₂×C₄	—	2	2	no	—
380	C₂×C₄	—	4	1	no	—
381	C₂×C₄	—	4	1	no	—
382	C₂×C₄	—	4	4	no	—
383	C₂×C₄	—	4	2	no	—
384	C₂×C₄	—	4	2	no	—
385	C₂×C₄	—	8	2	no	—
386	C₂×C₄	—	118	2	no	—
387	C₂×C₄	—	236	1	no	—
388	C₂×C₄	—	236	1	no	—
389	C₂×C₄	—	236	1	no	—
390	C₂×C₄	—	236	1	no	—
391	C₂×C₄	—	236	1	no	—
392	C₂×C₄	D₄×Dic₅₉	1	2	yes	—
393	C₂×C₄	D₄×Dic₅₉	1	2	yes	—
394	C₂×C₄	C₂³×Dic₅₉	1	1	yes	characteristic
395	C₂×C₄	C₂×D₄×D₅₉	1	1	yes	characteristic
396	C₂×C₄	C₂×#11745685	1	1	yes	characteristic
397	C₂×C₄	C₂×#11745685	1	1	yes	characteristic
398	C₂×C₄	#14273773	1	1	yes	characteristic
399	C₂×C₄	#14273774	1	1	yes	characteristic
400	C₈	—	2	2	no	—
401	C₈	—	118	1	no	—
402	C₈	—	118	2	no	—
403	C₈	—	118	1	no	—
404	C₈	—	236	2	no	—
405	C₈	—	236	2	no	—
406	C₈	#14273686	1	2	yes	—
407	C₈	#14273686	1	2	yes	—
408	C₂²	—	2	1	no	—
409	C₂²	—	2	1	no	—
410	C₂²	—	4	2	no	—
411	C₂²	—	4	2	no	—
412	C₂²	—	4	2	no	—
413	C₂²	C₂×D₄×Dic₅₉	1	1	yes	characteristic
414	C₂²	#16838117	1	1	yes	characteristic
415	C₂²	#16838122	1	1	yes	characteristic
416	C₄	—	2	2	no	—
417	C₄	—	2	2	no	—
418	C₄	—	4	2	no	—
419	C₄	—	4	2	no	—
420	C₄	—	4	2	no	—
421	C₄	—	472	1	no	—
422	C₄	—	236	2	no	—
423	C₄	C₂×#14273686	1	1	yes	characteristic
424	C₄	#16837885	1	1	yes	characteristic
425	C₄	#16838057	1	1	yes	characteristic
426	C₄	#16838073	1	1	yes	characteristic
427	C₂	—	2	1	no	—
428	C₂	—	2	1	no	—
429	C₂	—	8	2	no	—
430	C₂	#21427045	1	1	yes	characteristic
431	C₂	#21432999	1	1	yes	characteristic
432	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	#22804
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
1. #21432762	C₂	semidirect
4. #21424746	C₂	semidirect
5. #21424746	C₂	semidirect
6. #21424271	C₂	semidirect
7. #21424116	C₂	semidirect
8. #21423982	C₂	semidirect
9. #21423977	C₂	semidirect
10. #21423968	C₂	semidirect
36. C₅₉×#442	C₄	semidirect
37. C₅₉×#441	C₄	semidirect
38. C₅₉×#440	C₄	semidirect
39. C₅₉×#440	C₄	semidirect
230. #442	Dic₅₉	semidirect
231. #441	Dic₅₉	semidirect
232. #440	Dic₅₉	semidirect
233. #440	Dic₅₉	semidirect
259. C₅₉	#22804	semidirect

Maximal subgroups

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

subgroup	index
#21432762	2
#21424990	2
#21424985	2
#21424746	2
#21424271	2
#21424116	2
#21423982	2
#21423977	2
#21423968	2
C₅₉×#2943	2
#22804	59