Subgroups — #28602622

Order 15104.

820 conjugacy classes of subgroups.

The subgroup lattice has 450 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#21433013	C₂	1	1	yes	maximal, characteristic, complemented
2	#21432948	C₂	1	1	yes	maximal, characteristic, complemented
3	#21425007	C₂	1	1	yes	maximal, characteristic, complemented
4	#21424995	C₂	1	1	yes	maximal, characteristic, complemented
5	#21424629	C₂	1	2	yes	maximal, complemented
6	#21424624	C₂	1	2	yes	maximal, complemented
7	#21424585	C₂	1	2	yes	maximal, complemented
8	#21424578	C₂	1	2	yes	maximal, complemented
9	#21424220	C₂	1	1	yes	maximal, characteristic, complemented
10	#21423851	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅₉×#3155	C₂	1	1	yes	maximal, characteristic
12	#16838169	C₂²	1	2	yes	—
13	#16837877	C₂²	1	2	yes	—
14	#16837524	—	2	2	no	—
15	#16837519	—	2	2	no	—
16	#16837514	—	2	2	no	—
17	D₈×Dic₅₉	—	2	2	no	—
18	C₂×#14273663	C₂²	1	1	yes	characteristic
19	#16837440	C₂²	1	1	yes	characteristic
20	#16837419	C₂²	1	2	yes	—
21	#16837419	C₂²	1	2	yes	—
22	#16837407	C₂²	1	2	yes	—
23	#16837407	C₂²	1	2	yes	—
24	C₂×#14273644	C₂²	1	2	yes	—
25	#16837376	C₂²	1	2	yes	—
26	#16837357	C₂²	1	1	yes	characteristic
27	#16837357	C₂²	1	1	yes	characteristic
28	#16837173	C₂²	1	2	yes	—
29	C₅₉⋊#338	C₂²	1	1	yes	characteristic
30	#16837159	C₂²	1	1	yes	characteristic
31	#16837158	C₂²	1	2	yes	—
32	#16837158	C₂²	1	1	yes	characteristic
33	#16837158	C₂²	1	1	yes	characteristic
34	C₂×AGL(1,ℤ/8)×C₅₉	C₂²	1	2	yes	—
35	C₂×#135×C₅₉	C₂²	1	1	yes	characteristic
36	C₂²×D₈×C₅₉	C₂²	1	1	yes	characteristic
37	C₅₉×#535	C₂²	1	2	yes	—
38	C₅₉×#496	C₄	1	4	yes	complemented
39	C₅₉×#495	C₄	1	2	yes	complemented
40	C₅₉×#493	C₄	1	2	yes	complemented
41	C₅₉×#405	C₂²	1	1	yes	characteristic
42	#14273734	—	2	4	no	—
43	#14273734	—	4	2	no	—
44	C₂×#11745664	—	4	2	no	—
45	C₂×#11745664	C₂³	1	1	yes	characteristic
46	C₂×#11745664	C₂³	1	2	yes	—
47	C₂×#11745664	C₂³	1	1	yes	characteristic
48	D₄×Dic₅₉	—	2	4	no	—
49	D₄×Dic₅₉	—	4	2	no	—
50	#14273686	C₂³	1	1	yes	characteristic
51	#14273686	C₂³	1	2	yes	—
52	#14273686	C₂³	1	1	yes	characteristic
53	C₂×C₂²⋊Dic₅₉	—	4	2	no	—
54	#14273663	—	2	1	no	—
55	#14273663	—	2	1	no	—
56	#14273661	—	2	1	no	—
57	#14273659	—	2	1	no	—
58	#14273654	—	2	4	no	—
59	#14273654	—	4	2	no	—
60	#14273648	—	2	4	no	—
61	#14273648	—	4	2	no	—
62	#14273644	—	4	2	no	—
63	#14273642	—	4	2	no	—
64	#14273637	—	2	1	no	—
65	#14273637	D₄	1	2	yes	complemented
66	C₈×Dic₅₉	—	2	1	no	—
67	C₈×Dic₅₉	D₄	1	2	yes	complemented
68	C₂×#41×C₅₉	C₂³	1	2	yes	—
69	C₂²×D₄×C₅₉	C₂³	1	2	yes	—
70	AGL(1,ℤ/8)×C₅₉	—	4	2	no	—
71	AGL(1,ℤ/8)×C₅₉	—	4	2	no	—
72	#135×C₅₉	—	2	1	no	—
73	#135×C₅₉	—	2	1	no	—
74	#135×C₅₉	—	2	1	no	—
75	#135×C₅₉	—	2	1	no	—
76	C₂×Q₁₆×C₅₉	C₂×C₄	1	1	yes	characteristic, complemented
77	C₂×SD₁₆×C₅₉	C₂×C₄	1	2	yes	complemented
78	C₂×SD₁₆×C₅₉	C₂×C₄	1	4	yes	complemented
79	C₂×D₈×C₅₉	—	2	1	no	—
80	C₂×D₈×C₅₉	—	2	1	no	—
81	C₂×D₈×C₅₉	—	2	1	no	—
82	C₂×D₈×C₅₉	—	2	1	no	—
83	C₂×D₈×C₅₉	C₂×C₄	1	2	yes	—
84	C₂×D₈×C₅₉	C₂×C₄	1	2	yes	—
85	C₂×D₈×C₅₉	C₂×C₄	1	1	yes	characteristic, complemented
86	C₂×D₈×C₅₉	C₂×C₄	1	4	yes	complemented
87	C₂×M₁₆×C₅₉	C₂³	1	1	yes	characteristic
88	C₂²×C₈×C₅₉	C₂³	1	1	yes	characteristic
89	#127×C₅₉	C₂×C₄	1	4	yes	complemented
90	#124×C₅₉	C₂×C₄	1	4	yes	complemented
91	#121×C₅₉	—	4	2	no	—
92	#120×C₅₉	—	4	2	no	—
93	#117×C₅₉	C₂³	1	1	yes	characteristic
94	#97×C₅₉	C₂×C₄	1	2	yes	complemented
95	C₄×C₈×C₅₉	C₂×C₄	1	2	yes	complemented
96	C₂⁴×C₅₉	—	2	2	no	—
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	—	2	2	no	—
104	C₂×D₄×C₅₉	—	2	2	no	—
105	C₂×D₄×C₅₉	—	2	2	no	—
106	C₂×D₄×C₅₉	—	2	2	no	—
107	C₂×D₄×C₅₉	—	2	2	no	—
108	C₂×D₄×C₅₉	—	4	4	no	—
109	C₂×D₄×C₅₉	C₂²×C₄	1	4	yes	—
110	C₂×D₄×C₅₉	C₂²×C₄	1	2	yes	—
111	C₂²×C₄×C₅₉	—	2	2	no	—
112	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
113	C₂²×Dic₅₉	—	4	4	no	—
114	Q₁₆×C₅₉	—	2	1	no	—
115	Q₁₆×C₅₉	—	2	1	no	—
116	SD₁₆×C₅₉	—	2	2	no	—
117	SD₁₆×C₅₉	—	2	2	no	—
118	SD₁₆×C₅₉	—	4	4	no	—
119	D₈×C₅₉	—	2	2	no	—
120	D₈×C₅₉	—	2	2	no	—
121	D₈×C₅₉	—	2	2	no	—
122	D₈×C₅₉	—	2	2	no	—
123	D₈×C₅₉	—	2	1	no	—
124	D₈×C₅₉	—	2	1	no	—
125	D₈×C₅₉	—	4	4	no	—
126	M₁₆×C₅₉	—	2	1	no	—
127	M₁₆×C₅₉	—	2	1	no	—
128	C₂×C₈×C₅₉	C₂²×C₄	1	2	yes	—
129	C₂×C₈×C₅₉	C₂²×C₄	1	1	yes	characteristic
130	C₂×C₈×C₅₉	C₂²×C₄	1	1	yes	characteristic
131	C₂×C₈×C₅₉	C₂×D₄	1	1	yes	characteristic
132	C₂×C₈×C₅₉	C₂×D₄	1	1	yes	characteristic
133	C₂×C₈×C₅₉	#41	1	1	yes	characteristic
134	C₂×C₈×C₅₉	#41	1	1	yes	characteristic
135	C₄⋊C₄×C₅₉	—	2	1	no	—
136	C₂²⋊C₄×C₅₉	—	2	1	no	—
137	C₂²⋊C₄×C₅₉	—	4	4	no	—
138	C₄²×C₅₉	C₂²×C₄	1	2	yes	—
139	C₂²⋊Dic₅₉	—	2	1	no	—
140	C₂²⋊Dic₅₉	—	2	1	no	—
141	C₂²⋊Dic₅₉	—	2	2	no	—
142	C₂²⋊Dic₅₉	—	4	4	no	—
143	C₄⋊Dic₅₉	—	2	1	no	—
144	C₄⋊Dic₅₉	—	2	2	no	—
145	C₄⋊Dic₅₉	—	2	1	no	—
146	C₄×Dic₅₉	—	2	1	no	—
147	C₄×Dic₅₉	—	2	2	no	—
148	C₄×Dic₅₉	C₂×D₄	1	2	yes	—
149	#11745664	—	2	1	no	—
150	#11745664	—	2	1	no	—
151	#11745664	—	2	2	no	—
152	#11745664	—	2	1	no	—
153	#11745664	—	2	2	no	—
154	#11745664	—	2	1	no	—
155	#11745664	—	4	4	no	—
156	C₂×C₅₉⋊C₈	—	2	1	no	—
157	C₂×C₅₉⋊C₈	—	2	2	no	—
158	C₂×C₅₉⋊C₈	—	4	4	no	—
159	C₂×C₅₉⋊C₈	C₂×D₄	1	2	yes	—
160	C₂³×C₅₉	—	2	4	no	—
161	C₂³×C₅₉	—	2	2	no	—
162	C₂³×C₅₉	—	4	2	no	—
163	C₂³×C₅₉	—	4	2	no	—
164	C₂³×C₅₉	—	16	2	no	—
165	C₂³×C₅₉	H(5,𝔽₂)	1	1	yes	characteristic
166	Q₈×C₅₉	—	2	2	no	—
167	Q₈×C₅₉	—	2	2	no	—
168	D₄×C₅₉	—	2	4	no	—
169	D₄×C₅₉	—	2	2	no	—
170	D₄×C₅₉	—	2	2	no	—
171	D₄×C₅₉	—	2	4	no	—
172	D₄×C₅₉	—	4	2	no	—
173	D₄×C₅₉	—	4	2	no	—
174	D₄×C₅₉	—	4	2	no	—
175	D₄×C₅₉	—	4	2	no	—
176	D₄×C₅₉	—	16	4	no	—
177	C₂×C₄×C₅₉	—	2	2	no	—
178	C₂×C₄×C₅₉	—	2	2	no	—
179	C₂×C₄×C₅₉	—	4	2	no	—
180	C₂×C₄×C₅₉	—	4	2	no	—
181	C₂×C₄×C₅₉	C₂³×C₄	1	1	yes	characteristic
182	C₂×C₄×C₅₉	C₂²×D₄	1	1	yes	characteristic
183	C₂×C₄×C₅₉	C₂×#41	1	1	yes	characteristic
184	C₂×C₄×C₅₉	H(5,𝔽₂)	1	1	yes	characteristic
185	C₂×C₄×C₅₉	H(5,𝔽₂)	1	1	yes	characteristic
186	C₂×C₄×C₅₉	H(5,𝔽₂)	1	1	yes	characteristic
187	C₂×Dic₅₉	—	2	2	no	—
188	C₂×Dic₅₉	—	4	2	no	—
189	C₂×Dic₅₉	—	4	1	no	—
190	C₂×Dic₅₉	—	16	4	no	—
191	C₈×C₅₉	—	2	2	no	—
192	C₈×C₅₉	C₄×D₄	1	1	yes	characteristic
193	C₈×C₅₉	C₄×D₄	1	1	yes	characteristic
194	C₈×C₅₉	C₄×D₄	1	1	yes	characteristic
195	C₈×C₅₉	C₄×D₄	1	1	yes	characteristic
196	C₅₉⋊C₈	—	2	2	no	—
197	C₅₉⋊C₈	—	4	2	no	—
198	C₅₉⋊C₈	—	4	1	no	—
199	#22286	—	59	1	no	maximal, Sylow
200	C₂²×C₅₉	—	4	1	no	—
201	C₂²×C₅₉	—	4	2	no	—
202	C₂²×C₅₉	—	4	4	no	—
203	C₂²×C₅₉	—	8	2	no	—
204	C₂²×C₅₉	—	8	4	no	—
205	C₂²×C₅₉	—	8	4	no	—
206	C₂²×C₅₉	—	16	2	no	—
207	C₂²×C₅₉	#518	1	1	yes	characteristic
208	C₂²×C₅₉	#535	1	1	yes	characteristic
209	C₂²×C₅₉	#540	1	1	yes	characteristic
210	C₄×C₅₉	—	4	2	no	—
211	C₄×C₅₉	—	4	2	no	—
212	C₄×C₅₉	C₂×C₄×D₄	1	1	yes	characteristic
213	C₄×C₅₉	#518	1	1	yes	characteristic
214	C₄×C₅₉	#535	1	1	yes	characteristic
215	C₄×C₅₉	#540	1	1	yes	characteristic
216	Dic₅₉	—	4	2	no	—
217	Dic₅₉	—	8	1	no	—
218	Dic₅₉	—	8	2	no	—
219	#3155	D₅₉	1	1	yes	characteristic
220	#2957	—	59	1	no	—
221	#2948	—	59	1	no	—
222	#1978	—	59	1	no	—
223	#1976	—	59	1	no	—
224	#1911	—	59	2	no	—
225	#1910	—	59	2	no	—
226	#1904	—	59	2	no	—
227	#1903	—	59	2	no	—
228	#1833	—	59	1	no	—
229	#1747	—	59	1	no	—
230	C₂×C₅₉	—	2	1	no	—
231	C₂×C₅₉	—	2	1	no	—
232	C₂×C₅₉	—	2	1	no	—
233	C₂×C₅₉	—	8	2	no	—
234	C₂×C₅₉	—	8	4	no	—
235	C₂×C₅₉	#2328	1	1	yes	characteristic
236	C₂×AGL(1,ℤ/8)	C₂×D₅₉	1	2	yes	—
237	C₂×#135	C₂×D₅₉	1	1	yes	characteristic
238	C₂²×D₈	C₂×D₅₉	1	1	yes	characteristic
239	#568	—	59	2	no	—
240	#535	C₂×D₅₉	1	2	yes	—
241	#518	—	59	2	no	—
242	#496	Dic₅₉	1	4	yes	complemented
243	#495	Dic₅₉	1	2	yes	complemented
244	#493	Dic₅₉	1	2	yes	complemented
245	#444	—	118	2	no	—
246	#443	—	118	2	no	—
247	#442	—	118	2	no	—
248	C₄×D₈	—	118	2	no	—
249	C₂×#108	—	59	1	no	—
250	#427	—	59	1	no	—
251	#421	—	59	2	no	—
252	#421	—	59	2	no	—
253	#418	—	59	2	no	—
254	#418	—	59	2	no	—
255	C₂×#100	—	59	2	no	—
256	#410	—	59	2	no	—
257	#405	—	59	1	no	—
258	#405	—	59	1	no	—
259	#405	C₂×D₅₉	1	1	yes	characteristic
260	#344	—	59	2	no	—
261	#338	—	59	1	no	—
262	H(3,ℤ/4)	—	59	1	no	—
263	H(3,ℤ/4)	—	59	2	no	—
264	H(3,ℤ/4)	—	59	1	no	—
265	H(3,ℤ/4)	—	59	1	no	—
266	C₅₉	#22286	1	1	yes	characteristic, complemented, Sylow
267	C₂×#41	C₂²×D₅₉	1	2	yes	—
268	C₂²×D₄	C₂²×D₅₉	1	2	yes	—
269	AGL(1,ℤ/8)	—	4	2	no	—
270	AGL(1,ℤ/8)	—	4	2	no	—
271	#135	—	2	1	no	—
272	#135	—	2	1	no	—
273	#135	—	2	1	no	—
274	#135	—	2	1	no	—
275	C₂×Q₁₆	C₂×Dic₅₉	1	1	yes	characteristic, complemented
276	C₂×SD₁₆	C₂×Dic₅₉	1	2	yes	complemented
277	C₂×SD₁₆	C₂×Dic₅₉	1	4	yes	complemented
278	C₂×D₈	—	2	1	no	—
279	C₂×D₈	—	2	1	no	—
280	C₂×D₈	—	2	1	no	—
281	C₂×D₈	—	2	1	no	—
282	C₂×D₈	C₂×Dic₅₉	1	2	yes	—
283	C₂×D₈	C₂×Dic₅₉	1	2	yes	—
284	C₂×D₈	C₂×Dic₅₉	1	1	yes	characteristic, complemented
285	C₂×D₈	C₂×Dic₅₉	1	4	yes	complemented
286	#131	—	118	4	no	—
287	#131	—	236	2	no	—
288	C₂×M₁₆	—	59	1	no	—
289	C₂×M₁₆	—	59	2	no	—
290	C₂×M₁₆	—	59	1	no	—
291	C₂×M₁₆	—	236	2	no	—
292	C₂×M₁₆	C₂²×D₅₉	1	1	yes	characteristic
293	C₂²×C₈	C₂²×D₅₉	1	1	yes	characteristic
294	#127	C₂×Dic₅₉	1	4	yes	complemented
295	#124	C₂×Dic₅₉	1	4	yes	complemented
296	#121	—	4	2	no	—
297	#120	—	4	2	no	—
298	C₄×D₄	—	118	4	no	—
299	C₄×D₄	—	236	2	no	—
300	#117	—	59	1	no	—
301	#117	—	59	2	no	—
302	#117	—	59	1	no	—
303	#117	C₂²×D₅₉	1	1	yes	characteristic
304	C₂×C₂²⋊C₄	—	236	2	no	—
305	#108	—	118	1	no	—
306	#108	—	118	1	no	—
307	#107	—	118	1	no	—
308	#106	—	118	1	no	—
309	#104	—	118	4	no	—
310	#104	—	236	2	no	—
311	#102	—	118	4	no	—
312	#102	—	236	2	no	—
313	#100	—	236	2	no	—
314	#99	—	236	2	no	—
315	#97	—	59	2	no	—
316	#97	—	118	1	no	—
317	#97	C₂×Dic₅₉	1	2	yes	complemented
318	C₄×C₈	—	59	2	no	—
319	C₄×C₈	—	118	1	no	—
320	C₄×C₈	C₂×Dic₅₉	1	2	yes	complemented
321	C₂⁴	—	2	2	no	—
322	#41	—	2	2	no	—
323	#41	—	2	2	no	—
324	#41	—	2	2	no	—
325	#41	—	2	2	no	—
326	C₂×Q₈	C₂²×Dic₅₉	1	2	yes	—
327	C₂×D₄	—	2	2	no	—
328	C₂×D₄	—	2	2	no	—
329	C₂×D₄	—	2	2	no	—
330	C₂×D₄	—	2	2	no	—
331	C₂×D₄	—	2	2	no	—
332	C₂×D₄	—	2	2	no	—
333	C₂×D₄	—	4	4	no	—
334	C₂×D₄	C₂²×Dic₅₉	1	4	yes	—
335	C₂×D₄	C₂²×Dic₅₉	1	2	yes	—
336	C₂²×C₄	—	2	2	no	—
337	C₂²×C₄	—	236	4	no	—
338	C₂²×C₄	C₂³×D₅₉	1	1	yes	characteristic
339	Q₁₆	—	2	1	no	—
340	Q₁₆	—	2	1	no	—
341	SD₁₆	—	2	2	no	—
342	SD₁₆	—	2	2	no	—
343	SD₁₆	—	4	4	no	—
344	D₈	—	2	2	no	—
345	D₈	—	2	2	no	—
346	D₈	—	2	2	no	—
347	D₈	—	2	2	no	—
348	D₈	—	2	1	no	—
349	D₈	—	2	1	no	—
350	D₈	—	4	4	no	—
351	M₁₆	—	2	1	no	—
352	M₁₆	—	2	1	no	—
353	M₁₆	—	118	1	no	—
354	M₁₆	—	118	1	no	—
355	M₁₆	—	118	2	no	—
356	M₁₆	—	118	1	no	—
357	M₁₆	—	118	2	no	—
358	M₁₆	—	118	1	no	—
359	M₁₆	—	236	4	no	—
360	C₂×C₈	—	59	2	no	—
361	C₂×C₈	—	118	1	no	—
362	C₂×C₈	—	118	2	no	—
363	C₂×C₈	—	236	4	no	—
364	C₂×C₈	D₄×D₅₉	1	1	yes	characteristic
365	C₂×C₈	D₄×D₅₉	1	1	yes	characteristic
366	C₂×C₈	#11745687	1	1	yes	characteristic
367	C₂×C₈	#11745687	1	1	yes	characteristic
368	C₂×C₈	C₂²×Dic₅₉	1	2	yes	—
369	C₂×C₈	C₂²×Dic₅₉	1	1	yes	characteristic
370	C₂×C₈	C₂²×Dic₅₉	1	1	yes	characteristic
371	C₄⋊C₄	—	2	1	no	—
372	C₄⋊C₄	—	118	1	no	—
373	C₄⋊C₄	—	118	2	no	—
374	C₄⋊C₄	—	118	1	no	—
375	C₂²⋊C₄	—	2	1	no	—
376	C₂²⋊C₄	—	4	4	no	—
377	C₂²⋊C₄	—	118	1	no	—
378	C₂²⋊C₄	—	118	1	no	—
379	C₂²⋊C₄	—	118	2	no	—
380	C₂²⋊C₄	—	236	4	no	—
381	C₄²	—	59	2	no	—
382	C₄²	—	118	1	no	—
383	C₄²	—	118	2	no	—
384	C₄²	C₂²×Dic₅₉	1	2	yes	—
385	C₂³	—	2	4	no	—
386	C₂³	—	2	2	no	—
387	C₂³	—	4	2	no	—
388	C₂³	—	4	2	no	—
389	C₂³	—	16	2	no	—
390	C₂³	#14273772	1	1	yes	characteristic
391	Q₈	—	2	2	no	—
392	Q₈	—	2	2	no	—
393	D₄	—	2	4	no	—
394	D₄	—	2	2	no	—
395	D₄	—	2	2	no	—
396	D₄	—	2	4	no	—
397	D₄	—	4	2	no	—
398	D₄	—	4	2	no	—
399	D₄	—	4	2	no	—
400	D₄	—	4	2	no	—
401	D₄	—	16	4	no	—
402	C₂×C₄	—	2	2	no	—
403	C₂×C₄	—	2	2	no	—
404	C₂×C₄	—	4	2	no	—
405	C₂×C₄	—	4	2	no	—
406	C₂×C₄	—	118	2	no	—
407	C₂×C₄	—	944	4	no	—
408	C₂×C₄	—	236	2	no	—
409	C₂×C₄	—	236	1	no	—
410	C₂×C₄	C₂³×Dic₅₉	1	1	yes	characteristic
411	C₂×C₄	C₂×D₄×D₅₉	1	1	yes	characteristic
412	C₂×C₄	C₂×#11745687	1	1	yes	characteristic
413	C₂×C₄	#14273772	1	1	yes	characteristic
414	C₂×C₄	#14273772	1	1	yes	characteristic
415	C₂×C₄	#14273772	1	1	yes	characteristic
416	C₈	—	2	2	no	—
417	C₈	—	118	2	no	—
418	C₈	—	236	2	no	—
419	C₈	—	236	1	no	—
420	C₈	D₄×Dic₅₉	1	1	yes	characteristic
421	C₈	D₄×Dic₅₉	1	1	yes	characteristic
422	C₈	D₄×Dic₅₉	1	1	yes	characteristic
423	C₈	D₄×Dic₅₉	1	1	yes	characteristic
424	C₂²	—	4	1	no	—
425	C₂²	—	4	2	no	—
426	C₂²	—	4	4	no	—
427	C₂²	—	8	2	no	—
428	C₂²	—	8	4	no	—
429	C₂²	—	8	4	no	—
430	C₂²	—	16	2	no	—
431	C₂²	#16837877	1	1	yes	characteristic
432	C₂²	#16837965	1	1	yes	characteristic
433	C₂²	#16838006	1	1	yes	characteristic
434	C₄	—	4	2	no	—
435	C₄	—	4	2	no	—
436	C₄	—	472	2	no	—
437	C₄	—	472	1	no	—
438	C₄	—	236	2	no	—
439	C₄	C₂×D₄×Dic₅₉	1	1	yes	characteristic
440	C₄	#16837877	1	1	yes	characteristic
441	C₄	#16837965	1	1	yes	characteristic
442	C₄	#16838006	1	1	yes	characteristic
443	C₂	—	2	1	no	—
444	C₂	—	2	1	no	—
445	C₂	—	2	1	no	—
446	C₂	—	8	4	no	—
447	C₂	—	8	2	no	—
448	C₂	#21426822	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#21426822
commutator	C₂×C₄×C₅₉	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₅₉
Fitting, prime radical	C₅₉×#3155	C₂
socle	C₂×C₅₉	#2328
cosocle	C₂²×C₄×C₅₉	C₂⁴
hypercenter	#3155	D₅₉
hypocenter	C₅₉	#22286
LCS	G ▷ C₂×C₄×C₅₉ ▷ C₂×C₅₉ ▷ C₅₉
UCS	C₁ ◁ C₂ ◁ C₂²×C₄ ◁ #3155

Complements

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

N	H ≅ G/N	type
1. #21433013	C₂	semidirect
2. #21432948	C₂	semidirect
3. #21425007	C₂	semidirect
4. #21424995	C₂	semidirect
5. #21424629	C₂	semidirect
6. #21424624	C₂	semidirect
7. #21424585	C₂	semidirect
8. #21424578	C₂	semidirect
9. #21424220	C₂	semidirect
10. #21423851	C₂	semidirect
38. C₅₉×#496	C₄	semidirect
39. C₅₉×#495	C₄	semidirect
40. C₅₉×#493	C₄	semidirect
65. #14273637	D₄	semidirect
67. C₈×Dic₅₉	D₄	semidirect
76. C₂×Q₁₆×C₅₉	C₂×C₄	semidirect
77. C₂×SD₁₆×C₅₉	C₂×C₄	semidirect
78. C₂×SD₁₆×C₅₉	C₂×C₄	semidirect
85. C₂×D₈×C₅₉	C₂×C₄	semidirect
86. C₂×D₈×C₅₉	C₂×C₄	semidirect
89. #127×C₅₉	C₂×C₄	semidirect
90. #124×C₅₉	C₂×C₄	semidirect
94. #97×C₅₉	C₂×C₄	semidirect
95. C₄×C₈×C₅₉	C₂×C₄	semidirect
242. #496	Dic₅₉	semidirect
243. #495	Dic₅₉	semidirect
244. #493	Dic₅₉	semidirect
266. C₅₉	#22286	semidirect
275. C₂×Q₁₆	C₂×Dic₅₉	semidirect
276. C₂×SD₁₆	C₂×Dic₅₉	semidirect
277. C₂×SD₁₆	C₂×Dic₅₉	semidirect
284. C₂×D₈	C₂×Dic₅₉	semidirect
285. C₂×D₈	C₂×Dic₅₉	semidirect
294. #127	C₂×Dic₅₉	semidirect
295. #124	C₂×Dic₅₉	semidirect
317. #97	C₂×Dic₅₉	semidirect
320. C₄×C₈	C₂×Dic₅₉	semidirect

Maximal subgroups

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

subgroup	index
#21433013	2
#21432948	2
#21425007	2
#21424995	2
#21424629	2
#21424624	2
#21424585	2
#21424578	2
#21424220	2
#21423851	2
C₅₉×#3155	2
#22286	59