Subgroups — #28591912

Order 15104.

800 conjugacy classes of subgroups.

The subgroup lattice has 682 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#21432864	C₂	1	1	yes	maximal, characteristic
2	#21432736	C₂	1	1	yes	maximal, characteristic, complemented
3	#21432518	C₂	1	1	yes	maximal, characteristic, complemented
4	#21424746	C₂	1	1	yes	maximal, characteristic, complemented
5	#21424695	C₂	1	1	yes	maximal, characteristic, complemented
6	#21424693	C₂	1	1	yes	maximal, characteristic, complemented
7	#21424426	C₂	1	1	yes	maximal, characteristic
8	#21424420	C₂	1	1	yes	maximal, characteristic
9	#21424374	C₂	1	1	yes	maximal, characteristic, complemented
10	#21424368	C₂	1	1	yes	maximal, characteristic, complemented
11	#108×Dic₅₉	C₂	1	1	yes	maximal, characteristic, complemented
12	#104×Dic₅₉	C₂	1	1	yes	maximal, characteristic, complemented
13	#21423900	C₂	1	1	yes	maximal, characteristic, complemented
14	#21423840	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅₉×#1929	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#14273747	C₂²	1	1	yes	characteristic
17	C₂×#14273735	C₂²	1	1	yes	characteristic
18	C₂×#14273733	C₂²	1	1	yes	characteristic
19	#41×Dic₅₉	C₂²	1	1	yes	characteristic
20	#16837870	C₂²	1	1	yes	characteristic
21	#16837494	C₄	1	1	yes	characteristic, complemented
22	#16837494	C₄	1	1	yes	characteristic, complemented
23	#16837493	C₄	1	1	yes	characteristic, complemented
24	#16837493	C₄	1	1	yes	characteristic, complemented
25	#16837487	C₄	1	1	yes	characteristic, complemented
26	#16837487	C₄	1	1	yes	characteristic, complemented
27	#16837482	C₄	1	1	yes	characteristic, complemented
28	#16837482	C₄	1	1	yes	characteristic, complemented
29	#16837460	—	2	1	no	—
30	#16837460	—	2	1	no	—
31	#16837452	—	2	1	no	—
32	#16837452	—	2	1	no	—
33	C₂×#14273663	C₂²	1	1	yes	characteristic
34	#16837438	C₂²	1	1	yes	characteristic
35	#16837430	C₂²	1	1	yes	characteristic
36	#16837428	C₂²	1	1	yes	characteristic
37	C₂×#14273655	C₂²	1	1	yes	characteristic
38	C₂×#14273654	C₂²	1	1	yes	characteristic
39	C₂×#14273653	C₂²	1	1	yes	characteristic
40	#16837399	C₂²	1	1	yes	characteristic
41	#16837369	C₂²	1	1	yes	characteristic
42	#16837359	—	2	1	no	—
43	#16837358	C₂²	1	1	yes	characteristic
44	#16837356	—	2	1	no	—
45	#16837354	—	2	1	no	—
46	M₁₆×Dic₅₉	C₂²	1	1	yes	characteristic
47	M₁₆×Dic₅₉	C₂²	1	1	yes	characteristic
48	C₂×C₈×Dic₅₉	C₂²	1	1	yes	characteristic
49	C₂×C₈×Dic₅₉	C₂²	1	1	yes	characteristic
50	C₄×C₈×D₅₉	—	2	1	no	—
51	C₄²×Dic₅₉	C₂²	1	1	yes	characteristic
52	#16837166	C₂²	1	1	yes	characteristic
53	#16837166	C₂²	1	1	yes	characteristic
54	#16837163	C₂²	1	1	yes	characteristic
55	#16837162	C₂²	1	1	yes	characteristic
56	#16837161	C₂²	1	1	yes	characteristic
57	#16837157	C₂²	1	1	yes	characteristic
58	#16837156	C₂²	1	1	yes	characteristic
59	#16837156	C₂²	1	1	yes	characteristic
60	C₂×#108×C₅₉	C₂²	1	1	yes	characteristic
61	C₂×#104×C₅₉	C₂²	1	1	yes	characteristic
62	C₅₉×#416	C₂²	1	1	yes	characteristic
63	C₅₉×#408	C₂²	1	1	yes	characteristic
64	C₅₉×#405	C₂²	1	1	yes	characteristic
65	C₅₉×#339	C₂²	1	1	yes	characteristic
66	C₅₉×#336	C₂²	1	1	yes	characteristic
67	C₂×#11745685	C₂³	1	1	yes	characteristic
68	#14273747	—	2	2	no	—
69	#14273747	—	2	2	no	—
70	C₂×#11745672	C₂×C₄	1	1	yes	characteristic
71	C₂×#11745670	C₂×C₄	1	1	yes	characteristic
72	C₂×#11745671	C₂×C₄	1	1	yes	characteristic
73	C₂×#11745669	C₂×C₄	1	1	yes	characteristic
74	#14273735	—	2	2	no	—
75	#14273735	—	2	2	no	—
76	#14273733	—	2	2	no	—
77	#14273733	—	2	2	no	—
78	C₂×#11745664	C₂³	1	1	yes	characteristic
79	C₂×#11745664	C₂³	1	1	yes	characteristic
80	C₂×#11745659	—	2	1	no	—
81	C₂×#11745659	—	2	1	no	—
82	C₂²×C₅₉⋊C₈	C₂³	1	1	yes	characteristic
83	C₂²×C₅₉⋊C₈	C₂³	1	1	yes	characteristic
84	C₂×C₈×D₅₉	—	2	1	no	—
85	C₂×C₈×D₅₉	—	2	1	no	—
86	Q₈×Dic₅₉	C₂×C₄	1	1	yes	characteristic
87	Q₈×Dic₅₉	C₂×C₄	1	1	yes	characteristic
88	#14273692	C₂×C₄	1	1	yes	characteristic
89	#14273692	C₂×C₄	1	1	yes	characteristic
90	D₄×Dic₅₉	—	2	1	no	—
91	D₄×Dic₅₉	—	2	1	no	—
92	D₄×Dic₅₉	C₂×C₄	1	1	yes	characteristic
93	D₄×Dic₅₉	C₂×C₄	1	1	yes	characteristic
94	#14273689	C₂×C₄	1	1	yes	characteristic
95	#14273689	C₂×C₄	1	1	yes	characteristic
96	(C₂²⋊D₅₉)⋊C₄	—	2	1	no	—
97	(C₂²⋊D₅₉)⋊C₄	—	2	1	no	—
98	#14273686	—	2	1	no	—
99	#14273686	C₂³	1	1	yes	characteristic
100	#14273684	—	2	1	no	—
101	C₂×C₄×Dic₅₉	—	2	1	no	—
102	C₂×C₄×Dic₅₉	—	2	1	no	—
103	C₂×C₄×Dic₅₉	—	2	1	no	—
104	C₂×C₄×Dic₅₉	C₂³	1	1	yes	characteristic
105	C₂×C₄×Dic₅₉	C₂³	1	1	yes	characteristic
106	C₄²×D₅₉	—	2	1	no	—
107	#14273663	—	2	2	no	—
108	#14273660	C₂×C₄	1	1	yes	characteristic
109	#14273660	C₂×C₄	1	1	yes	characteristic
110	#14273658	C₂×C₄	1	1	yes	characteristic
111	#14273658	C₂×C₄	1	1	yes	characteristic
112	Dic₅₉⋊C₈	—	2	1	no	—
113	Dic₅₉⋊C₈	—	2	1	no	—
114	Dic₅₉⋊C₈	—	2	1	no	—
115	Dic₅₉⋊C₈	—	2	1	no	—
116	#14273655	—	2	2	no	—
117	#14273654	—	2	2	no	—
118	#14273653	—	2	2	no	—
119	#14273652	C₂×C₄	1	1	yes	characteristic
120	#14273652	C₂×C₄	1	1	yes	characteristic
121	#14273649	C₂×C₄	1	1	yes	characteristic
122	#14273649	C₂×C₄	1	1	yes	characteristic
123	C₂²⋊(C₅₉⋊C₈)	—	2	1	no	—
124	C₂²⋊(C₅₉⋊C₈)	—	2	1	no	—
125	#14273638	—	2	1	no	—
126	#14273637	—	2	1	no	—
127	#14273637	—	2	1	no	—
128	C₄×C₅₉⋊C₈	—	2	1	no	—
129	C₈×Dic₅₉	—	2	1	no	—
130	C₈×Dic₅₉	—	2	1	no	—
131	C₈×Dic₅₉	C₂×C₄	1	1	yes	characteristic
132	C₈×Dic₅₉	C₂×C₄	1	1	yes	characteristic
133	C₈×Dic₅₉	C₂×C₄	1	1	yes	characteristic
134	C₈×Dic₅₉	C₂×C₄	1	1	yes	characteristic
135	C₈×Dic₅₉	D₄	1	1	yes	characteristic
136	C₈×Dic₅₉	D₄	1	1	yes	characteristic
137	C₈×Dic₅₉	D₄	1	1	yes	characteristic
138	C₈×Dic₅₉	D₄	1	1	yes	characteristic
139	C₂×#41×C₅₉	C₂³	1	1	yes	characteristic
140	C₂×M₁₆×C₅₉	C₂³	1	1	yes	characteristic
141	C₂×M₁₆×C₅₉	C₂³	1	1	yes	characteristic
142	C₂²×C₈×C₅₉	C₂³	1	1	yes	characteristic
143	C₂²×C₈×C₅₉	C₂³	1	1	yes	characteristic
144	#117×C₅₉	C₂³	1	1	yes	characteristic
145	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
146	#108×C₅₉	—	2	2	no	—
147	#104×C₅₉	—	2	2	no	—
148	#103×C₅₉	C₂×C₄	1	1	yes	characteristic
149	#103×C₅₉	C₂×C₄	1	1	yes	characteristic
150	#102×C₅₉	C₂×C₄	1	1	yes	characteristic
151	#102×C₅₉	C₂×C₄	1	1	yes	characteristic
152	C₂²⋊C₈×C₅₉	—	2	1	no	—
153	C₂²⋊C₈×C₅₉	—	2	1	no	—
154	#97×C₅₉	—	2	1	no	—
155	C₄×C₈×C₅₉	—	2	1	no	—
156	#41×C₅₉	—	2	1	no	—
157	#41×C₅₉	—	2	1	no	—
158	#41×C₅₉	—	2	1	no	—
159	#41×C₅₉	—	2	1	no	—
160	C₂×Q₈×C₅₉	C₂²×C₄	1	1	yes	characteristic
161	C₂×D₄×C₅₉	—	2	1	no	—
162	C₂×D₄×C₅₉	C₂²×C₄	1	1	yes	characteristic
163	C₂²×C₄×C₅₉	—	2	1	no	—
164	C₂²×C₄×C₅₉	—	2	1	no	—
165	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
166	C₂×C₂²⋊D₅₉	—	2	1	no	—
167	C₂²×Dic₅₉	—	2	1	no	—
168	C₂²×Dic₅₉	—	2	1	no	—
169	C₂²×Dic₅₉	—	2	1	no	—
170	C₂²×Dic₅₉	#41	1	1	yes	characteristic
171	C₂²×Dic₅₉	#41	1	1	yes	characteristic
172	#11745685	—	2	1	no	—
173	#11745685	—	2	1	no	—
174	#11745685	#41	1	2	yes	—
175	#11745685	#41	1	2	yes	—
176	C₂×D₂₃₆	C₂²×C₄	1	1	yes	characteristic
177	C₂×C₄×D₅₉	—	2	1	no	—
178	C₂×C₄×D₅₉	—	2	1	no	—
179	C₂×C₄×D₅₉	—	2	1	no	—
180	C₂×Dic₁₁₈	C₂²×C₄	1	1	yes	characteristic
181	M₁₆×C₅₉	—	2	1	no	—
182	M₁₆×C₅₉	—	2	1	no	—
183	M₁₆×C₅₉	—	2	1	no	—
184	M₁₆×C₅₉	#41	1	2	yes	—
185	C₂×C₈×C₅₉	—	2	1	no	—
186	C₂×C₈×C₅₉	—	2	1	no	—
187	C₂×C₈×C₅₉	—	2	1	no	—
188	C₂×C₈×C₅₉	—	2	1	no	—
189	C₂×C₈×C₅₉	—	2	1	no	—
190	C₂×C₈×C₅₉	—	2	1	no	—
191	C₂×C₈×C₅₉	C₂²×C₄	1	1	yes	characteristic
192	C₂×C₈×C₅₉	C₂²×C₄	1	1	yes	characteristic
193	C₂×C₈×C₅₉	C₂×D₄	1	1	yes	characteristic
194	C₂×C₈×C₅₉	C₂×D₄	1	1	yes	characteristic
195	C₄⋊C₄×C₅₉	C₂²×C₄	1	1	yes	characteristic
196	C₄⋊C₄×C₅₉	C₂²×C₄	1	1	yes	characteristic
197	C₂²⋊C₄×C₅₉	—	2	1	no	—
198	C₄²×C₅₉	—	2	1	no	—
199	C₄²×C₅₉	—	2	1	no	—
200	C₄²×C₅₉	—	2	1	no	—
201	C₂²⋊Dic₅₉	—	2	1	no	—
202	C₂²⋊Dic₅₉	—	2	1	no	—
203	C₂²⋊Dic₅₉	—	2	1	no	—
204	#11745672	—	2	2	no	—
205	#11745671	—	2	2	no	—
206	#11745670	—	2	2	no	—
207	#11745669	—	2	2	no	—
208	(C₂×D₅₉)⋊C₄	—	2	1	no	—
209	(C₂×D₅₉)⋊C₄	—	2	1	no	—
210	C₄⋊Dic₅₉	—	2	1	no	—
211	C₄⋊Dic₅₉	—	2	1	no	—
212	C₄⋊Dic₅₉	C₂²×C₄	1	1	yes	characteristic
213	C₄⋊Dic₅₉	C₂²×C₄	1	1	yes	characteristic
214	Dic₅₉⋊C₄	—	2	1	no	—
215	Dic₅₉⋊C₄	—	2	1	no	—
216	C₄×Dic₅₉	—	2	4	no	—
217	C₄×Dic₅₉	—	2	1	no	—
218	C₄×Dic₅₉	—	2	1	no	—
219	C₄×Dic₅₉	—	2	1	no	—
220	C₄×Dic₅₉	—	2	1	no	—
221	C₄×Dic₅₉	—	2	1	no	—
222	C₄×Dic₅₉	—	2	1	no	—
223	C₄×Dic₅₉	—	2	1	no	—
224	C₄×Dic₅₉	—	4	2	no	—
225	C₄×Dic₅₉	C₂²×C₄	1	1	yes	characteristic
226	C₄×Dic₅₉	C₂²×C₄	1	1	yes	characteristic
227	C₄×Dic₅₉	C₂×D₄	1	1	yes	characteristic
228	C₄×Dic₅₉	C₂×D₄	1	1	yes	characteristic
229	#11745664	—	2	1	no	—
230	#11745664	—	2	1	no	—
231	#11745664	—	2	1	no	—
232	#11745664	#41	1	2	yes	—
233	C₂×C₅₉⋊C₈	—	2	1	no	—
234	C₂×C₅₉⋊C₈	—	2	1	no	—
235	C₂×C₅₉⋊C₈	—	2	1	no	—
236	C₂×C₅₉⋊C₈	—	2	1	no	—
237	C₂×C₅₉⋊C₈	—	2	1	no	—
238	C₂×C₅₉⋊C₈	—	2	1	no	—
239	C₂×C₅₉⋊C₈	C₂²×C₄	1	1	yes	characteristic
240	C₂×C₅₉⋊C₈	C₂²×C₄	1	1	yes	characteristic
241	C₂×C₅₉⋊C₈	C₂×D₄	1	1	yes	characteristic
242	C₂×C₅₉⋊C₈	C₂×D₄	1	1	yes	characteristic
243	#11745659	—	2	4	no	—
244	#11745659	—	2	4	no	—
245	C₈×D₅₉	—	2	4	no	—
246	C₈×D₅₉	—	2	4	no	—
247	C₂³×C₅₉	—	2	1	no	—
248	C₂³×C₅₉	C₂×#41	1	1	yes	characteristic
249	C₂²×D₅₉	—	2	1	no	—
250	Q₈×C₅₉	—	2	1	no	—
251	Q₈×C₅₉	—	2	1	no	—
252	D₄×C₅₉	—	2	1	no	—
253	D₄×C₅₉	—	2	1	no	—
254	D₄×C₅₉	—	4	1	no	—
255	D₄×C₅₉	—	4	1	no	—
256	C₂×C₄×C₅₉	—	2	2	no	—
257	C₂×C₄×C₅₉	—	2	1	no	—
258	C₂×C₄×C₅₉	—	2	1	no	—
259	C₂×C₄×C₅₉	—	2	1	no	—
260	C₂×C₄×C₅₉	—	4	1	no	—
261	C₂×C₄×C₅₉	—	4	1	no	—
262	C₂×C₄×C₅₉	—	4	1	no	—
263	C₂×C₄×C₅₉	—	4	1	no	—
264	C₂×C₄×C₅₉	C₂³×C₄	1	1	yes	characteristic
265	C₂×C₄×C₅₉	C₂²×D₄	1	1	yes	characteristic
266	C₂×C₄×C₅₉	C₂×#41	1	1	yes	characteristic
267	C₂×C₄×C₅₉	C₂×#41	1	1	yes	characteristic
268	C₂×C₄×C₅₉	C₂×#41	1	1	yes	characteristic
269	C₂×C₄×C₅₉	C₂×#41	1	1	yes	characteristic
270	C₂²⋊D₅₉	—	2	2	no	—
271	C₂²⋊D₅₉	—	2	2	no	—
272	C₂×Dic₅₉	—	2	1	no	—
273	C₂×Dic₅₉	—	2	2	no	—
274	C₂×Dic₅₉	—	2	2	no	—
275	C₂×Dic₅₉	—	2	2	no	—
276	C₂×Dic₅₉	—	2	1	no	—
277	C₂×Dic₅₉	—	2	1	no	—
278	C₂×Dic₅₉	—	4	1	no	—
279	C₂×Dic₅₉	—	4	1	no	—
280	C₂×Dic₅₉	—	4	2	no	—
281	C₂×Dic₅₉	—	4	2	no	—
282	C₂×Dic₅₉	C₄×D₄	1	1	yes	characteristic
283	C₂×Dic₅₉	C₄×D₄	1	1	yes	characteristic
284	C₂×Dic₅₉	C₄×D₄	1	1	yes	characteristic
285	C₂×Dic₅₉	C₄×D₄	1	1	yes	characteristic
286	D₂₃₆	—	2	1	no	—
287	D₂₃₆	#117	1	2	yes	—
288	C₄×D₅₉	—	2	2	no	—
289	C₄×D₅₉	—	2	2	no	—
290	C₄×D₅₉	—	4	2	no	—
291	C₄×D₅₉	—	4	2	no	—
292	Dic₁₁₈	—	2	1	no	—
293	Dic₁₁₈	#117	1	2	yes	—
294	C₈×C₅₉	—	2	1	no	—
295	C₈×C₅₉	—	2	1	no	—
296	C₈×C₅₉	—	2	1	no	—
297	C₈×C₅₉	—	2	2	no	—
298	C₈×C₅₉	—	2	1	no	—
299	C₈×C₅₉	—	4	1	no	—
300	C₅₉⋊C₈	—	2	1	no	—
301	C₅₉⋊C₈	—	2	1	no	—
302	C₅₉⋊C₈	—	2	1	no	—
303	C₅₉⋊C₈	—	2	2	no	—
304	C₅₉⋊C₈	—	2	1	no	—
305	C₅₉⋊C₈	—	4	1	no	—
306	#21137	—	59	1	no	maximal, Sylow
307	C₂²×C₅₉	—	2	1	no	—
308	C₂²×C₅₉	—	2	1	no	—
309	C₂²×C₅₉	—	4	1	no	—
310	C₂²×C₅₉	—	4	1	no	—
311	C₂²×C₅₉	—	4	1	no	—
312	C₂²×C₅₉	C₂×C₄×D₄	1	1	yes	characteristic
313	C₂²×C₅₉	#529	1	1	yes	characteristic
314	C₂²×C₅₉	#529	1	1	yes	characteristic
315	C₂×D₅₉	—	2	2	no	—
316	C₂×D₅₉	—	4	1	no	—
317	C₂×D₅₉	—	4	1	no	—
318	C₄×C₅₉	—	4	2	no	—
319	C₄×C₅₉	—	4	1	no	—
320	C₄×C₅₉	—	4	1	no	—
321	C₄×C₅₉	—	4	1	no	—
322	C₄×C₅₉	C₂×#117	1	1	yes	characteristic
323	C₄×C₅₉	C₄×#41	1	1	yes	characteristic
324	C₄×C₅₉	#525	1	1	yes	characteristic
325	C₄×C₅₉	#525	1	1	yes	characteristic
326	Dic₅₉	—	2	1	no	—
327	Dic₅₉	—	2	1	no	—
328	Dic₅₉	—	2	2	no	—
329	Dic₅₉	—	4	2	no	—
330	Dic₅₉	—	4	1	no	—
331	Dic₅₉	—	4	1	no	—
332	Dic₅₉	#443	1	2	yes	—
333	Dic₅₉	#444	1	2	yes	—
334	C₄×#135	—	59	1	no	—
335	#2922	—	59	1	no	—
336	C₄×#131	—	59	1	no	—
337	#1929	—	59	1	no	—
338	#1929	D₅₉	1	1	yes	characteristic, complemented
339	#1922	—	59	1	no	—
340	#1922	—	59	1	no	—
341	#1876	—	59	1	no	—
342	#1876	—	59	1	no	—
343	#1866	—	59	1	no	—
344	#1866	—	59	1	no	—
345	C₄×#108	—	59	1	no	—
346	C₄×#104	—	59	1	no	—
347	C₄×#104	—	59	1	no	—
348	#1744	—	59	1	no	—
349	C₂×C₅₉	—	2	1	no	—
350	C₂×C₅₉	—	2	1	no	—
351	C₂×C₅₉	—	8	1	no	—
352	C₂×C₅₉	#2290	1	1	yes	characteristic
353	C₂×C₅₉	C₂×#443	1	1	yes	characteristic
354	C₂×C₅₉	C₂×#444	1	1	yes	characteristic
355	D₅₉	—	4	2	no	—
356	C₂×#135	—	59	1	no	—
357	C₂×#131	—	59	1	no	—
358	C₂×#131	—	59	1	no	—
359	C₄×#41	—	59	1	no	—
360	C₄×#41	—	59	1	no	—
361	C₄×Q₁₆	—	59	1	no	—
362	C₄×Q₁₆	—	59	1	no	—
363	C₄×SD₁₆	—	59	1	no	—
364	C₄×SD₁₆	—	59	1	no	—
365	C₄×SD₁₆	—	59	1	no	—
366	C₄×SD₁₆	—	59	1	no	—
367	C₄×D₈	—	59	1	no	—
368	C₄×D₈	—	59	1	no	—
369	#433	—	118	1	no	—
370	#433	—	118	1	no	—
371	#431	—	118	1	no	—
372	#431	—	118	1	no	—
373	C₂×#108	—	59	1	no	—
374	C₂×#108	C₂×D₅₉	1	1	yes	characteristic
375	#427	—	59	1	no	—
376	#424	—	59	1	no	—
377	#424	—	59	1	no	—
378	C₂×#104	—	59	1	no	—
379	C₂×#104	—	59	1	no	—
380	C₂×#104	—	59	1	no	—
381	C₂×#104	C₂×D₅₉	1	1	yes	characteristic
382	#416	—	59	1	no	—
383	#416	C₂×D₅₉	1	1	yes	characteristic
384	#408	—	59	1	no	—
385	#408	C₂×D₅₉	1	1	yes	characteristic
386	#405	—	59	1	no	—
387	#405	—	118	1	no	—
388	#405	—	118	1	no	—
389	#405	C₂×D₅₉	1	1	yes	characteristic
390	C₄×M₁₆	—	59	1	no	—
391	C₄×M₁₆	—	59	1	no	—
392	C₄×M₁₆	—	118	1	no	—
393	C₂×C₄×C₈	—	59	1	no	—
394	C₂×C₄×C₈	—	59	1	no	—
395	C₂×C₄×C₈	—	118	1	no	—
396	C₄³	—	59	1	no	—
397	#341	—	59	1	no	—
398	#341	—	59	1	no	—
399	#339	—	59	1	no	—
400	#339	—	59	1	no	—
401	#339	—	59	1	no	—
402	#339	C₂×D₅₉	1	1	yes	characteristic
403	#336	—	59	1	no	—
404	#336	—	59	1	no	—
405	#336	—	59	1	no	—
406	#336	C₂×D₅₉	1	1	yes	characteristic
407	C₅₉	#21137	1	1	yes	characteristic, complemented, Sylow
408	C₂×#41	—	59	1	no	—
409	C₂×#41	C₂²×D₅₉	1	1	yes	characteristic
410	#135	—	118	2	no	—
411	#135	—	118	2	no	—
412	C₂×Q₁₆	—	59	1	no	—
413	C₂×SD₁₆	—	59	1	no	—
414	C₂×SD₁₆	—	59	1	no	—
415	C₂×D₈	—	59	1	no	—
416	#131	—	118	2	no	—
417	#131	—	118	2	no	—
418	#131	—	118	2	no	—
419	#131	—	118	2	no	—
420	C₂×M₁₆	—	59	1	no	—
421	C₂×M₁₆	—	59	1	no	—
422	C₂×M₁₆	—	118	1	no	—
423	C₂×M₁₆	—	118	1	no	—
424	C₂×M₁₆	C₂²×D₅₉	1	1	yes	characteristic
425	C₂×M₁₆	C₂²×D₅₉	1	1	yes	characteristic
426	C₂²×C₈	—	59	1	no	—
427	C₂²×C₈	—	59	1	no	—
428	C₂²×C₈	—	118	1	no	—
429	C₂²×C₈	—	118	1	no	—
430	C₂²×C₈	C₂²×D₅₉	1	1	yes	characteristic
431	C₂²×C₈	C₂²×D₅₉	1	1	yes	characteristic
432	C₄×Q₈	—	59	1	no	—
433	C₄×Q₈	—	59	1	no	—
434	C₄×Q₈	—	59	1	no	—
435	C₄×Q₈	—	59	1	no	—
436	C₄×D₄	—	59	1	no	—
437	C₄×D₄	—	59	1	no	—
438	C₄×D₄	—	59	1	no	—
439	C₄×D₄	—	59	1	no	—
440	C₄×D₄	—	118	1	no	—
441	C₄×D₄	—	118	1	no	—
442	C₄×D₄	—	118	1	no	—
443	C₄×D₄	—	118	1	no	—
444	#117	—	59	1	no	—
445	#117	—	118	1	no	—
446	#117	—	118	1	no	—
447	#117	C₂²×D₅₉	1	1	yes	characteristic
448	C₂×C₄²	—	59	1	no	—
449	C₂×C₄²	—	59	1	no	—
450	C₂×C₄²	—	118	1	no	—
451	C₂×C₄²	—	118	1	no	—
452	C₂×C₄²	—	118	1	no	—
453	C₂×C₄²	—	118	1	no	—
454	C₂×C₄²	C₂²×D₅₉	1	1	yes	characteristic
455	#108	—	2	2	no	—
456	#108	—	118	2	no	—
457	#107	—	59	1	no	—
458	#107	—	59	1	no	—
459	#106	—	59	1	no	—
460	#106	—	59	1	no	—
461	C₄⋊C₈	—	118	1	no	—
462	C₄⋊C₈	—	118	1	no	—
463	C₄⋊C₈	—	118	1	no	—
464	C₄⋊C₈	—	118	1	no	—
465	#104	—	2	2	no	—
466	#104	—	118	2	no	—
467	#104	—	118	2	no	—
468	#104	—	118	2	no	—
469	#103	—	59	1	no	—
470	#103	—	59	1	no	—
471	#103	C₄×D₅₉	1	1	yes	characteristic
472	#103	C₄×D₅₉	1	1	yes	characteristic
473	#102	—	59	1	no	—
474	#102	—	59	1	no	—
475	#102	C₄×D₅₉	1	1	yes	characteristic
476	#102	C₄×D₅₉	1	1	yes	characteristic
477	C₂²⋊C₈	—	2	1	no	—
478	C₂²⋊C₈	—	2	1	no	—
479	C₂²⋊C₈	—	118	1	no	—
480	C₂²⋊C₈	—	118	1	no	—
481	#97	—	2	1	no	—
482	#97	—	118	1	no	—
483	#97	—	118	1	no	—
484	#97	—	118	1	no	—
485	C₄×C₈	—	2	1	no	—
486	C₄×C₈	—	59	1	no	—
487	C₄×C₈	—	59	1	no	—
488	C₄×C₈	—	59	1	no	—
489	C₄×C₈	—	59	1	no	—
490	C₄×C₈	—	59	1	no	—
491	C₄×C₈	—	59	1	no	—
492	C₄×C₈	—	59	1	no	—
493	C₄×C₈	—	59	1	no	—
494	C₄×C₈	—	118	1	no	—
495	C₄×C₈	—	118	1	no	—
496	C₄×C₈	—	118	1	no	—
497	#41	—	2	1	no	—
498	#41	—	2	1	no	—
499	#41	—	2	1	no	—
500	#41	—	2	1	no	—
501	#41	—	59	2	no	—
502	#41	—	59	2	no	—
503	#41	—	118	1	no	—
504	#41	—	118	1	no	—
505	C₂×Q₈	—	59	1	no	—
506	C₂×Q₈	C₂×C₄×D₅₉	1	1	yes	characteristic
507	C₂×D₄	—	2	1	no	—
508	C₂×D₄	—	59	1	no	—
509	C₂×D₄	—	118	1	no	—
510	C₂×D₄	C₂×C₄×D₅₉	1	1	yes	characteristic
511	C₂²×C₄	—	2	1	no	—
512	C₂²×C₄	—	2	1	no	—
513	C₂²×C₄	—	59	1	no	—
514	C₂²×C₄	—	59	1	no	—
515	C₂²×C₄	—	118	1	no	—
516	C₂²×C₄	—	118	1	no	—
517	C₂²×C₄	—	118	1	no	—
518	C₂²×C₄	—	118	1	no	—
519	C₂²×C₄	—	118	1	no	—
520	C₂²×C₄	—	118	1	no	—
521	C₂²×C₄	C₂³×D₅₉	1	1	yes	characteristic
522	Q₁₆	—	118	2	no	—
523	SD₁₆	—	118	2	no	—
524	SD₁₆	—	118	2	no	—
525	D₈	—	118	2	no	—
526	M₁₆	—	2	1	no	—
527	M₁₆	—	2	1	no	—
528	M₁₆	—	2	1	no	—
529	M₁₆	—	59	2	no	—
530	M₁₆	—	118	4	no	—
531	M₁₆	—	118	4	no	—
532	M₁₆	—	118	1	no	—
533	M₁₆	—	118	1	no	—
534	M₁₆	—	118	1	no	—
535	M₁₆	#11745687	1	2	yes	—
536	C₂×C₈	—	2	1	no	—
537	C₂×C₈	—	2	1	no	—
538	C₂×C₈	—	2	1	no	—
539	C₂×C₈	—	2	1	no	—
540	C₂×C₈	—	2	1	no	—
541	C₂×C₈	—	2	1	no	—
542	C₂×C₈	—	59	1	no	—
543	C₂×C₈	—	59	1	no	—
544	C₂×C₈	—	59	1	no	—
545	C₂×C₈	—	59	1	no	—
546	C₂×C₈	—	118	4	no	—
547	C₂×C₈	—	118	4	no	—
548	C₂×C₈	—	118	1	no	—
549	C₂×C₈	—	118	1	no	—
550	C₂×C₈	—	118	1	no	—
551	C₂×C₈	—	118	1	no	—
552	C₂×C₈	—	118	1	no	—
553	C₂×C₈	—	118	1	no	—
554	C₂×C₈	C₂×C₄×D₅₉	1	1	yes	characteristic
555	C₂×C₈	C₂×C₄×D₅₉	1	1	yes	characteristic
556	C₂×C₈	D₄×D₅₉	1	1	yes	characteristic
557	C₂×C₈	D₄×D₅₉	1	1	yes	characteristic
558	C₄⋊C₄	—	59	1	no	—
559	C₄⋊C₄	—	59	1	no	—
560	C₄⋊C₄	—	118	1	no	—
561	C₄⋊C₄	—	118	1	no	—
562	C₄⋊C₄	—	118	1	no	—
563	C₄⋊C₄	—	118	1	no	—
564	C₄⋊C₄	C₂×C₄×D₅₉	1	1	yes	characteristic
565	C₄⋊C₄	C₂×C₄×D₅₉	1	1	yes	characteristic
566	C₂²⋊C₄	—	2	1	no	—
567	C₂²⋊C₄	—	118	1	no	—
568	C₂²⋊C₄	—	118	1	no	—
569	C₂²⋊C₄	—	118	1	no	—
570	C₂²⋊C₄	—	118	1	no	—
571	C₂²⋊C₄	—	118	1	no	—
572	C₄²	—	2	1	no	—
573	C₄²	—	2	1	no	—
574	C₄²	—	2	1	no	—
575	C₄²	—	59	1	no	—
576	C₄²	—	59	1	no	—
577	C₄²	—	59	1	no	—
578	C₄²	—	59	1	no	—
579	C₄²	—	118	1	no	—
580	C₄²	—	118	1	no	—
581	C₄²	—	118	1	no	—
582	C₄²	—	118	1	no	—
583	C₄²	—	118	4	no	—
584	C₄²	—	118	1	no	—
585	C₄²	—	118	1	no	—
586	C₄²	—	118	1	no	—
587	C₄²	—	236	2	no	—
588	C₂³	—	2	1	no	—
589	C₂³	—	118	1	no	—
590	C₂³	#41×D₅₉	1	1	yes	characteristic
591	Q₈	—	2	1	no	—
592	Q₈	—	2	1	no	—
593	Q₈	—	59	2	no	—
594	Q₈	—	118	1	no	—
595	D₄	—	2	1	no	—
596	D₄	—	2	1	no	—
597	D₄	—	4	1	no	—
598	D₄	—	4	1	no	—
599	D₄	—	59	2	no	—
600	D₄	—	118	2	no	—
601	D₄	—	118	2	no	—
602	D₄	—	118	1	no	—
603	C₂×C₄	—	2	2	no	—
604	C₂×C₄	—	2	1	no	—
605	C₂×C₄	—	2	1	no	—
606	C₂×C₄	—	2	1	no	—
607	C₂×C₄	—	4	1	no	—
608	C₂×C₄	—	4	1	no	—
609	C₂×C₄	—	4	1	no	—
610	C₂×C₄	—	4	1	no	—
611	C₂×C₄	—	59	1	no	—
612	C₂×C₄	—	59	1	no	—
613	C₂×C₄	—	59	1	no	—
614	C₂×C₄	—	59	1	no	—
615	C₂×C₄	—	118	2	no	—
616	C₂×C₄	—	118	2	no	—
617	C₂×C₄	—	118	1	no	—
618	C₂×C₄	—	118	2	no	—
619	C₂×C₄	—	118	2	no	—
620	C₂×C₄	—	118	2	no	—
621	C₂×C₄	—	118	1	no	—
622	C₂×C₄	—	118	1	no	—
623	C₂×C₄	—	236	2	no	—
624	C₂×C₄	—	236	2	no	—
625	C₂×C₄	—	236	2	no	—
626	C₂×C₄	—	236	2	no	—
627	C₂×C₄	—	236	1	no	—
628	C₂×C₄	—	236	1	no	—
629	C₂×C₄	C₂²×C₄×D₅₉	1	1	yes	characteristic
630	C₂×C₄	C₂×D₄×D₅₉	1	1	yes	characteristic
631	C₂×C₄	#41×D₅₉	1	1	yes	characteristic
632	C₂×C₄	#41×D₅₉	1	1	yes	characteristic
633	C₂×C₄	#41×D₅₉	1	1	yes	characteristic
634	C₂×C₄	C₂×#11745687	1	1	yes	characteristic
635	C₈	—	2	1	no	—
636	C₈	—	2	1	no	—
637	C₈	—	2	2	no	—
638	C₈	—	2	1	no	—
639	C₈	—	2	1	no	—
640	C₈	—	4	1	no	—
641	C₈	—	118	2	no	—
642	C₈	—	118	1	no	—
643	C₈	—	118	1	no	—
644	C₈	—	118	1	no	—
645	C₈	—	118	1	no	—
646	C₈	—	236	1	no	—
647	C₂²	—	2	1	no	—
648	C₂²	—	2	1	no	—
649	C₂²	—	4	1	no	—
650	C₂²	—	4	1	no	—
651	C₂²	—	4	1	no	—
652	C₂²	—	118	2	no	—
653	C₂²	—	236	1	no	—
654	C₂²	—	236	1	no	—
655	C₂²	C₄×D₄×D₅₉	1	1	yes	characteristic
656	C₂²	#16837931	1	1	yes	characteristic
657	C₂²	#16837935	1	1	yes	characteristic
658	C₄	—	4	2	no	—
659	C₄	—	4	1	no	—
660	C₄	—	4	1	no	—
661	C₄	—	4	1	no	—
662	C₄	—	59	2	no	—
663	C₄	—	59	2	no	—
664	C₄	—	118	2	no	—
665	C₄	—	118	1	no	—
666	C₄	—	118	1	no	—
667	C₄	—	236	2	no	—
668	C₄	—	236	1	no	—
669	C₄	—	236	1	no	—
670	C₄	#117×D₅₉	1	1	yes	characteristic
671	C₄	C₄×#11745687	1	1	yes	characteristic
672	C₄	#16837910	1	1	yes	characteristic
673	C₄	#16837912	1	1	yes	characteristic
674	C₂	—	2	1	no	—
675	C₂	—	2	1	no	—
676	C₂	—	8	1	no	—
677	C₂	—	236	2	no	—
678	C₂	#21426538	1	1	yes	characteristic
679	C₂	#443×D₅₉	1	1	yes	characteristic
680	C₂	#444×D₅₉	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×#1929	C₂
socle	C₂²×C₅₉	C₂×C₄×D₄
prime radical	C₂×#14273747	C₂²
cosocle	C₂²×C₄×C₅₉	C₂⁴
hypercenter	#1929	D₅₉
hypocenter	C₅₉	#21137
LCS	G ▷ C₂×C₄×C₅₉ ▷ C₂×C₅₉ ▷ C₅₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₈ ◁ #1929

Complements

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

N	H ≅ G/N	type
2. #21432736	C₂	semidirect
3. #21432518	C₂	semidirect
4. #21424746	C₂	semidirect
5. #21424695	C₂	semidirect
6. #21424693	C₂	semidirect
9. #21424374	C₂	semidirect
10. #21424368	C₂	semidirect
11. #108×Dic₅₉	C₂	semidirect
12. #104×Dic₅₉	C₂	semidirect
13. #21423900	C₂	semidirect
14. #21423840	C₂	semidirect
15. C₅₉×#1929	C₂	semidirect
21. #16837494	C₄	semidirect
22. #16837494	C₄	semidirect
23. #16837493	C₄	semidirect
24. #16837493	C₄	semidirect
25. #16837487	C₄	semidirect
26. #16837487	C₄	semidirect
27. #16837482	C₄	semidirect
28. #16837482	C₄	semidirect
338. #1929	D₅₉	semidirect
407. C₅₉	#21137	semidirect

Maximal subgroups

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

subgroup	index
#21432864	2
#21432736	2
#21432518	2
#21424746	2
#21424695	2
#21424693	2
#21424426	2
#21424420	2
#21424374	2
#21424368	2
#108×Dic₅₉	2
#104×Dic₅₉	2
#21423900	2
#21423840	2
C₅₉×#1929	2
#21137	59