Subgroups — C₄×#16837674 #28595574

Order 15104.

882 conjugacy classes of subgroups.

The subgroup lattice has 512 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#16837674	C₂	1	1	yes	maximal, characteristic
2	C₄×#14273758	C₂	1	2	yes	maximal
3	C₄×#14273733	C₂	1	1	yes	maximal, characteristic
4	#21425012	C₂	1	1	yes	maximal, characteristic, complemented
5	#21424879	C₂	1	1	yes	maximal, characteristic, complemented
6	#21424748	C₂	1	2	yes	maximal, complemented
7	#21424614	C₂	1	2	yes	maximal
8	#21424161	C₂	1	1	yes	maximal, characteristic
9	C₄×#14273663	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄×#14273646	C₂	1	2	yes	maximal, complemented
11	C₂×C₄×Q₁₆×C₅₉	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#14273758	C₂²	1	2	yes	—
13	C₂×#14273733	C₂²	1	1	yes	characteristic
14	C₂×#14273733	C₂²	1	1	yes	characteristic
15	C₄×#11745685	C₂²	1	1	yes	characteristic
16	#16837674	C₄	1	8	yes	direct product factor
17	#16837507	—	2	2	no	—
18	#16837500	—	2	2	no	—
19	C₄×#11745672	—	2	2	no	—
20	C₄×#11745671	—	2	2	no	—
21	C₂×#14273663	C₂²	1	1	yes	characteristic
22	C₂×#14273663	C₂²	1	1	yes	characteristic
23	#16837442	C₂²	1	2	yes	—
24	#16837411	C₂²	1	2	yes	—
25	#16837401	C₂²	1	2	yes	—
26	C₂×#14273646	C₂²	1	2	yes	—
27	C₂×#14273646	C₂²	1	2	yes	—
28	#16837357	C₂²	1	1	yes	characteristic
29	#16837357	C₂²	1	1	yes	characteristic
30	#16837356	—	2	1	no	—
31	#16837356	—	2	1	no	—
32	C₄×#11745664	C₂²	1	1	yes	characteristic
33	C₄×#11745664	C₂²	1	2	yes	—
34	C₄×#11745659	—	2	1	no	—
35	C₄×C₈×D₅₉	—	2	1	no	—
36	#16837171	C₂²	1	2	yes	—
37	#16837171	C₂²	1	2	yes	—
38	#16837167	C₂²	1	2	yes	—
39	C₂²×Q₁₆×C₅₉	C₂²	1	1	yes	characteristic
40	C₂×C₄×Q₈×C₅₉	C₂²	1	2	yes	—
41	C₄×Q₁₆×C₅₉	—	2	1	no	—
42	C₄×Q₁₆×C₅₉	—	2	1	no	—
43	C₄×Q₁₆×C₅₉	—	2	1	no	—
44	C₄×Q₁₆×C₅₉	—	2	1	no	—
45	C₂×#107×C₅₉	C₂²	1	1	yes	characteristic
46	C₂×#103×C₅₉	C₂²	1	2	yes	—
47	C₂×C₄×C₈×C₅₉	C₂²	1	1	yes	characteristic
48	C₂×#11745685	C₂³	1	1	yes	characteristic
49	#14273758	—	2	4	no	—
50	#14273758	C₂×C₄	1	8	yes	—
51	C₂×#11745672	—	2	2	no	—
52	C₂×#11745671	—	2	2	no	—
53	#14273733	—	2	2	no	—
54	#14273733	—	2	2	no	—
55	#14273733	—	2	2	no	—
56	#14273733	C₂×C₄	1	4	yes	—
57	C₂×#11745664	C₂³	1	2	yes	—
58	C₂×#11745664	C₂³	1	1	yes	characteristic
59	C₂×#11745664	C₂³	1	2	yes	—
60	C₂×#11745664	C₂³	1	1	yes	characteristic
61	C₂×#11745659	—	2	1	no	—
62	C₂×#11745659	—	2	1	no	—
63	C₂×C₈×D₅₉	—	2	1	no	—
64	C₂×C₈×D₅₉	—	2	1	no	—
65	C₄×Dic₁₁₈	D₄	1	1	yes	characteristic
66	C₄×Dic₁₁₈	D₄	1	1	yes	characteristic
67	C₄×D₂₃₆	D₄	1	1	yes	characteristic
68	C₄×D₂₃₆	D₄	1	1	yes	characteristic
69	C₄×C₂²⋊D₅₉	—	2	1	no	—
70	C₄×C₂²⋊D₅₉	—	2	1	no	—
71	#14273686	C₂³	1	1	yes	characteristic
72	#14273684	—	2	1	no	—
73	C₄²×D₅₉	—	2	1	no	—
74	#14273663	—	2	2	no	—
75	#14273663	C₂×C₄	1	4	yes	complemented
76	#14273660	—	2	2	no	—
77	#14273658	—	2	2	no	—
78	#14273651	—	2	2	no	—
79	#14273651	—	2	2	no	—
80	#14273650	—	2	2	no	—
81	#14273647	—	2	2	no	—
82	#14273646	—	2	4	no	—
83	#14273646	C₂×C₄	1	8	yes	complemented
84	#14273638	—	2	2	no	—
85	#14273638	—	2	1	no	—
86	#14273637	—	2	1	no	—
87	#14273637	—	2	1	no	—
88	C₄×C₅₉⋊C₈	—	2	2	no	—
89	C₄×C₅₉⋊C₈	—	2	1	no	—
90	C₈×Dic₅₉	—	2	1	no	—
91	C₈×Dic₅₉	—	2	1	no	—
92	C₂²×Q₈×C₅₉	C₂³	1	2	yes	—
93	C₂×Q₁₆×C₅₉	—	2	1	no	—
94	C₂×Q₁₆×C₅₉	—	2	1	no	—
95	C₂×Q₁₆×C₅₉	—	2	2	no	—
96	C₂×Q₁₆×C₅₉	C₂×C₄	1	4	yes	complemented
97	C₂²×C₈×C₅₉	C₂³	1	1	yes	characteristic
98	C₂²×C₈×C₅₉	C₂³	1	1	yes	characteristic
99	C₄×Q₈×C₅₉	—	2	2	no	—
100	C₄×Q₈×C₅₉	—	2	2	no	—
101	C₄×Q₈×C₅₉	—	2	2	no	—
102	C₄×Q₈×C₅₉	—	2	2	no	—
103	C₂×C₄⋊C₄×C₅₉	—	2	2	no	—
104	C₂×C₄⋊C₄×C₅₉	C₂³	1	2	yes	—
105	C₂×C₄²×C₅₉	—	2	2	no	—
106	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
107	#107×C₅₉	—	2	1	no	—
108	#107×C₅₉	—	2	1	no	—
109	#103×C₅₉	—	2	2	no	—
110	#103×C₅₉	—	2	2	no	—
111	C₄×C₈×C₅₉	D₄	1	1	yes	characteristic
112	C₄×C₈×C₅₉	D₄	1	1	yes	characteristic
113	C₄×C₈×C₅₉	D₄	1	1	yes	characteristic
114	C₄×C₈×C₅₉	D₄	1	1	yes	characteristic
115	C₂×Q₈×C₅₉	—	2	2	no	—
116	C₂×Q₈×C₅₉	—	2	2	no	—
117	C₂×Q₈×C₅₉	—	2	2	no	—
118	C₂×Q₈×C₅₉	—	2	2	no	—
119	C₂×Q₈×C₅₉	—	2	2	no	—
120	C₂×Q₈×C₅₉	C₂²×C₄	1	4	yes	—
121	C₂²×C₄×C₅₉	—	2	2	no	—
122	C₂²×C₄×C₅₉	—	2	2	no	—
123	C₂²×C₄×C₅₉	#41	1	1	yes	characteristic
124	C₂²×C₄×C₅₉	#41	1	1	yes	characteristic
125	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
126	C₂×C₂²⋊D₅₉	—	2	1	no	—
127	#11745685	—	2	1	no	—
128	#11745685	—	2	1	no	—
129	#11745685	C₂²×C₄	1	2	yes	—
130	#11745685	#41	1	2	yes	—
131	C₂×D₂₃₆	C₂×D₄	1	1	yes	characteristic
132	C₂×C₄×D₅₉	—	2	1	no	—
133	C₂×C₄×D₅₉	—	2	1	no	—
134	C₂×C₄×D₅₉	—	2	1	no	—
135	C₂×Dic₁₁₈	C₂×D₄	1	1	yes	characteristic
136	Q₁₆×C₅₉	—	2	4	no	—
137	Q₁₆×C₅₉	—	2	4	no	—
138	C₂×C₈×C₅₉	—	2	1	no	—
139	C₂×C₈×C₅₉	—	2	1	no	—
140	C₂×C₈×C₅₉	C₂²×C₄	1	2	yes	—
141	C₂×C₈×C₅₉	C₂×D₄	1	1	yes	characteristic
142	C₂×C₈×C₅₉	C₂×D₄	1	1	yes	characteristic
143	C₂×C₈×C₅₉	C₂×D₄	1	1	yes	characteristic
144	C₂×C₈×C₅₉	C₂×D₄	1	1	yes	characteristic
145	C₂×C₈×C₅₉	#41	1	2	yes	—
146	C₄⋊C₄×C₅₉	—	2	2	no	—
147	C₄⋊C₄×C₅₉	—	2	2	no	—
148	C₄⋊C₄×C₅₉	—	4	2	no	—
149	C₄⋊C₄×C₅₉	—	4	2	no	—
150	C₄²×C₅₉	—	4	2	no	—
151	C₄²×C₅₉	—	4	2	no	—
152	C₄²×C₅₉	C₂×D₄	1	1	yes	characteristic
153	C₄²×C₅₉	C₂×D₄	1	1	yes	characteristic
154	C₄²×C₅₉	C₂×D₄	1	1	yes	characteristic
155	C₄²×C₅₉	C₂×D₄	1	1	yes	characteristic
156	C₂²⋊Dic₅₉	—	2	1	no	—
157	#11745672	—	2	8	no	—
158	#11745671	—	2	8	no	—
159	(C₂×D₅₉)⋊C₄	—	2	1	no	—
160	(C₂×D₅₉)⋊C₄	—	2	1	no	—
161	C₄⋊Dic₅₉	C₂×D₄	1	1	yes	characteristic
162	C₄⋊Dic₅₉	C₂×D₄	1	1	yes	characteristic
163	Dic₅₉⋊C₄	—	2	1	no	—
164	Dic₅₉⋊C₄	—	2	1	no	—
165	C₄×Dic₅₉	—	2	1	no	—
166	C₄×Dic₅₉	—	2	1	no	—
167	C₄×Dic₅₉	—	2	1	no	—
168	#11745664	—	2	1	no	—
169	#11745664	—	2	1	no	—
170	#11745664	—	2	2	no	—
171	#11745664	—	2	2	no	—
172	#11745664	—	2	2	no	—
173	#11745664	C₂²×C₄	1	2	yes	—
174	#11745664	C₂²×C₄	1	4	yes	—
175	#11745664	#41	1	2	yes	—
176	C₂×C₅₉⋊C₈	—	2	1	no	—
177	C₂×C₅₉⋊C₈	—	2	1	no	—
178	C₂×C₅₉⋊C₈	—	2	2	no	—
179	C₂×C₅₉⋊C₈	—	2	2	no	—
180	#11745659	—	2	4	no	—
181	#11745659	—	2	4	no	—
182	C₈×D₅₉	—	2	4	no	—
183	C₈×D₅₉	—	2	4	no	—
184	C₂³×C₅₉	C₂×#41	1	1	yes	characteristic
185	C₂²×D₅₉	—	2	1	no	—
186	Q₈×C₅₉	—	2	4	no	—
187	Q₈×C₅₉	—	2	4	no	—
188	Q₈×C₅₉	—	4	2	no	—
189	Q₈×C₅₉	—	4	2	no	—
190	C₂×C₄×C₅₉	—	2	2	no	—
191	C₂×C₄×C₅₉	—	2	4	no	—
192	C₂×C₄×C₅₉	—	4	1	no	—
193	C₂×C₄×C₅₉	—	4	2	no	—
194	C₂×C₄×C₅₉	—	4	2	no	—
195	C₂×C₄×C₅₉	—	4	2	no	—
196	C₂×C₄×C₅₉	—	8	2	no	—
197	C₂×C₄×C₅₉	#121	1	1	yes	characteristic
198	C₂×C₄×C₅₉	#121	1	1	yes	characteristic
199	C₂×C₄×C₅₉	#121	1	1	yes	characteristic
200	C₂×C₄×C₅₉	#121	1	1	yes	characteristic
201	C₂×C₄×C₅₉	C₂³×C₄	1	1	yes	characteristic
202	C₂×C₄×C₅₉	C₂²×D₄	1	1	yes	characteristic
203	C₂×C₄×C₅₉	C₂²×D₄	1	1	yes	characteristic
204	C₂×C₄×C₅₉	C₂×#41	1	1	yes	characteristic
205	C₂×C₄×C₅₉	C₂×#41	1	1	yes	characteristic
206	C₂×C₄×C₅₉	C₂×#41	1	1	yes	characteristic
207	C₂²⋊D₅₉	—	2	2	no	—
208	C₂²⋊D₅₉	—	2	2	no	—
209	C₂×Dic₅₉	—	2	1	no	—
210	C₂×Dic₅₉	—	2	1	no	—
211	C₂×Dic₅₉	—	2	1	no	—
212	D₂₃₆	—	2	1	no	—
213	D₂₃₆	C₄×D₄	1	2	yes	—
214	C₄×D₅₉	—	2	2	no	—
215	C₄×D₅₉	—	2	2	no	—
216	C₄×D₅₉	—	4	2	no	—
217	C₄×D₅₉	—	4	2	no	—
218	Dic₁₁₈	—	2	1	no	—
219	Dic₁₁₈	C₄×D₄	1	2	yes	—
220	C₈×C₅₉	—	2	1	no	—
221	C₈×C₅₉	—	2	1	no	—
222	C₈×C₅₉	C₄×D₄	1	2	yes	—
223	C₈×C₅₉	C₄×D₄	1	2	yes	—
224	C₅₉⋊C₈	—	2	2	no	—
225	C₅₉⋊C₈	—	2	4	no	—
226	C₅₉⋊C₈	—	2	2	no	—
227	C₅₉⋊C₈	—	4	2	no	—
228	C₄×#473	—	59	1	no	maximal, Sylow
229	C₂²×C₅₉	—	2	1	no	—
230	C₂²×C₅₉	—	2	1	no	—
231	C₂²×C₅₉	C₄×#41	1	1	yes	characteristic
232	C₂²×C₅₉	C₂×#121	1	1	yes	characteristic
233	C₂²×C₅₉	#529	1	1	yes	characteristic
234	C₂×D₅₉	—	2	2	no	—
235	C₂×D₅₉	—	4	1	no	—
236	C₂×D₅₉	—	4	1	no	—
237	C₄×C₅₉	—	2	1	no	—
238	C₄×C₅₉	—	2	1	no	—
239	C₄×C₅₉	—	2	1	no	—
240	C₄×C₅₉	—	4	4	no	—
241	C₄×C₅₉	—	8	2	no	—
242	C₄×C₅₉	#473	1	2	yes	complemented
243	C₄×C₅₉	C₂×C₄×D₄	1	1	yes	characteristic
244	C₄×C₅₉	C₂×C₄×D₄	1	1	yes	characteristic
245	C₄×C₅₉	#525	1	1	yes	characteristic
246	C₄×C₅₉	#532	1	1	yes	characteristic
247	Dic₅₉	—	2	2	no	—
248	Dic₅₉	—	4	1	no	—
249	Dic₅₉	—	4	1	no	—
250	C₂×#473	—	59	1	no	—
251	C₄×#137	—	59	2	no	—
252	C₂×C₄×Q₁₆	D₅₉	1	1	yes	characteristic, complemented
253	C₄×#131	—	59	1	no	—
254	#1979	—	59	1	no	—
255	#1952	—	59	1	no	—
256	#1930	—	59	2	no	—
257	#1908	—	59	2	no	—
258	#1816	—	59	1	no	—
259	C₄×#108	—	59	1	no	—
260	C₄×#101	—	59	2	no	—
261	C₂×C₅₉	—	2	1	no	—
262	C₂×C₅₉	—	2	1	no	—
263	C₂×C₅₉	C₄×#121	1	1	yes	characteristic
264	C₂×C₅₉	C₂×#473	1	1	yes	characteristic
265	C₂×C₅₉	#3067	1	1	yes	characteristic
266	D₅₉	—	4	2	no	—
267	C₂×#137	—	59	2	no	—
268	C₂²×Q₁₆	C₂×D₅₉	1	1	yes	characteristic
269	C₂×#131	—	59	1	no	—
270	C₂×#131	—	59	1	no	—
271	C₄×#41	—	59	1	no	—
272	C₂×C₄×Q₈	C₂×D₅₉	1	2	yes	—
273	#473	—	59	8	no	—
274	#441	—	118	2	no	—
275	#440	—	118	2	no	—
276	C₄×Q₁₆	—	2	1	no	—
277	C₄×Q₁₆	—	2	1	no	—
278	C₄×Q₁₆	—	2	1	no	—
279	C₄×Q₁₆	—	2	1	no	—
280	C₄×Q₁₆	—	118	2	no	—
281	C₄×SD₁₆	—	118	2	no	—
282	C₂×#108	—	59	1	no	—
283	C₂×#108	—	59	1	no	—
284	#428	—	59	2	no	—
285	C₂×#107	C₂×D₅₉	1	1	yes	characteristic
286	#419	—	59	2	no	—
287	#417	—	59	2	no	—
288	C₂×#103	C₂×D₅₉	1	2	yes	—
289	C₂×#101	—	59	2	no	—
290	C₂×#101	—	59	2	no	—
291	#405	—	59	1	no	—
292	#405	—	59	1	no	—
293	#405	—	118	1	no	—
294	#405	—	118	1	no	—
295	C₄×M₁₆	—	59	1	no	—
296	C₄×M₁₆	—	59	2	no	—
297	C₄×M₁₆	—	118	1	no	—
298	C₂×C₄×C₈	—	118	1	no	—
299	C₂×C₄×C₈	C₂×D₅₉	1	1	yes	characteristic
300	#343	—	59	2	no	—
301	#343	—	59	2	no	—
302	#341	—	59	2	no	—
303	C₅₉	C₄×#473	1	1	yes	characteristic, complemented, Sylow
304	C₂×#41	—	59	1	no	—
305	C₂²×Q₈	C₂²×D₅₉	1	2	yes	—
306	#137	—	59	8	no	—
307	#137	—	118	4	no	—
308	C₂×Q₁₆	—	2	2	no	—
309	C₂×Q₁₆	—	2	1	no	—
310	C₂×Q₁₆	—	2	1	no	—
311	C₂×Q₁₆	—	118	2	no	—
312	C₂×Q₁₆	C₄×D₅₉	1	4	yes	complemented
313	C₂×SD₁₆	—	118	2	no	—
314	#131	—	59	4	no	—
315	#131	—	118	2	no	—
316	#131	—	118	2	no	—
317	#131	—	118	2	no	—
318	C₂×M₁₆	—	59	1	no	—
319	C₂×M₁₆	—	59	1	no	—
320	C₂×M₁₆	—	59	2	no	—
321	C₂×M₁₆	—	59	2	no	—
322	C₂×M₁₆	—	118	1	no	—
323	C₂×M₁₆	—	118	1	no	—
324	C₂²×C₈	—	118	1	no	—
325	C₂²×C₈	—	118	1	no	—
326	C₂²×C₈	C₂²×D₅₉	1	1	yes	characteristic
327	C₂²×C₈	C₂²×D₅₉	1	1	yes	characteristic
328	C₄×Q₈	—	2	2	no	—
329	C₄×Q₈	—	2	2	no	—
330	C₄×Q₈	—	2	2	no	—
331	C₄×Q₈	—	2	2	no	—
332	C₄×Q₈	—	59	1	no	—
333	C₄×Q₈	—	59	1	no	—
334	C₄×D₄	—	59	1	no	—
335	C₄×D₄	—	59	1	no	—
336	C₄×D₄	—	118	1	no	—
337	C₄×D₄	—	118	1	no	—
338	#117	—	59	1	no	—
339	#117	—	118	1	no	—
340	C₂×C₄⋊C₄	—	2	2	no	—
341	C₂×C₄⋊C₄	C₂²×D₅₉	1	2	yes	—
342	C₂×C₄²	—	2	2	no	—
343	C₂×C₄²	—	118	1	no	—
344	C₂×C₄²	C₂²×D₅₉	1	1	yes	characteristic
345	#108	—	59	4	no	—
346	#108	—	118	2	no	—
347	#107	—	2	1	no	—
348	#107	—	2	1	no	—
349	#107	—	118	2	no	—
350	#106	—	118	2	no	—
351	#103	—	2	2	no	—
352	#103	—	2	2	no	—
353	#103	—	118	2	no	—
354	#103	—	118	2	no	—
355	#103	—	118	2	no	—
356	#102	—	118	2	no	—
357	#101	—	59	8	no	—
358	#101	—	118	4	no	—
359	#97	—	118	1	no	—
360	#97	—	118	1	no	—
361	#97	—	118	2	no	—
362	#97	—	118	1	no	—
363	C₄×C₈	—	118	1	no	—
364	C₄×C₈	—	118	1	no	—
365	C₄×C₈	—	118	2	no	—
366	C₄×C₈	—	118	1	no	—
367	C₄×C₈	C₂²⋊D₅₉	1	1	yes	characteristic
368	C₄×C₈	C₂²⋊D₅₉	1	1	yes	characteristic
369	C₄×C₈	C₂²⋊D₅₉	1	1	yes	characteristic
370	C₄×C₈	C₂²⋊D₅₉	1	1	yes	characteristic
371	#41	—	59	2	no	—
372	#41	—	59	2	no	—
373	#41	—	118	1	no	—
374	#41	—	118	1	no	—
375	C₂×Q₈	—	2	2	no	—
376	C₂×Q₈	—	2	2	no	—
377	C₂×Q₈	—	2	2	no	—
378	C₂×Q₈	—	2	2	no	—
379	C₂×Q₈	—	2	2	no	—
380	C₂×Q₈	—	59	1	no	—
381	C₂×Q₈	C₂×C₄×D₅₉	1	4	yes	—
382	C₂×D₄	—	59	1	no	—
383	C₂×D₄	—	118	1	no	—
384	C₂²×C₄	—	2	2	no	—
385	C₂²×C₄	—	2	2	no	—
386	C₂²×C₄	—	118	1	no	—
387	C₂²×C₄	—	118	1	no	—
388	C₂²×C₄	—	118	1	no	—
389	C₂²×C₄	#11745687	1	1	yes	characteristic
390	C₂²×C₄	#11745687	1	1	yes	characteristic
391	C₂²×C₄	C₂³×D₅₉	1	1	yes	characteristic
392	Q₁₆	—	2	4	no	—
393	Q₁₆	—	2	4	no	—
394	Q₁₆	—	118	8	no	—
395	SD₁₆	—	118	8	no	—
396	M₁₆	—	59	2	no	—
397	M₁₆	—	59	4	no	—
398	M₁₆	—	59	2	no	—
399	M₁₆	—	118	4	no	—
400	M₁₆	—	118	1	no	—
401	M₁₆	—	118	2	no	—
402	M₁₆	—	118	1	no	—
403	M₁₆	—	118	4	no	—
404	M₁₆	—	118	2	no	—
405	M₁₆	—	118	2	no	—
406	C₂×C₈	—	2	1	no	—
407	C₂×C₈	—	2	1	no	—
408	C₂×C₈	—	118	4	no	—
409	C₂×C₈	—	118	2	no	—
410	C₂×C₈	—	118	1	no	—
411	C₂×C₈	—	118	1	no	—
412	C₂×C₈	—	118	4	no	—
413	C₂×C₈	—	118	2	no	—
414	C₂×C₈	C₂×C₄×D₅₉	1	2	yes	—
415	C₂×C₈	#11745685	1	2	yes	—
416	C₂×C₈	C₂×C₂²⋊D₅₉	1	1	yes	characteristic
417	C₂×C₈	C₂×C₂²⋊D₅₉	1	1	yes	characteristic
418	C₂×C₈	C₂×C₂²⋊D₅₉	1	1	yes	characteristic
419	C₂×C₈	C₂×C₂²⋊D₅₉	1	1	yes	characteristic
420	C₄⋊C₄	—	2	2	no	—
421	C₄⋊C₄	—	2	2	no	—
422	C₄⋊C₄	—	4	2	no	—
423	C₄⋊C₄	—	4	2	no	—
424	C₄⋊C₄	—	59	1	no	—
425	C₄⋊C₄	—	59	1	no	—
426	C₄⋊C₄	—	118	1	no	—
427	C₄⋊C₄	—	118	1	no	—
428	C₂²⋊C₄	—	118	1	no	—
429	C₂²⋊C₄	—	118	1	no	—
430	C₂²⋊C₄	—	118	1	no	—
431	C₄²	—	4	2	no	—
432	C₄²	—	4	2	no	—
433	C₄²	—	118	1	no	—
434	C₄²	—	118	1	no	—
435	C₄²	—	118	1	no	—
436	C₄²	D₄×D₅₉	1	1	yes	characteristic
437	C₄²	D₄×D₅₉	1	1	yes	characteristic
438	C₄²	C₂×C₂²⋊D₅₉	1	1	yes	characteristic
439	C₄²	C₂×C₂²⋊D₅₉	1	1	yes	characteristic
440	C₂³	—	118	1	no	—
441	C₂³	C₂×#11745687	1	1	yes	characteristic
442	Q₈	—	2	4	no	—
443	Q₈	—	2	4	no	—
444	Q₈	—	4	2	no	—
445	Q₈	—	4	2	no	—
446	Q₈	—	59	2	no	—
447	Q₈	—	118	1	no	—
448	D₄	—	59	2	no	—
449	D₄	—	118	2	no	—
450	D₄	—	118	2	no	—
451	D₄	—	118	1	no	—
452	C₂×C₄	—	2	2	no	—
453	C₂×C₄	—	2	4	no	—
454	C₂×C₄	—	4	1	no	—
455	C₂×C₄	—	4	2	no	—
456	C₂×C₄	—	4	2	no	—
457	C₂×C₄	—	4	2	no	—
458	C₂×C₄	—	8	2	no	—
459	C₂×C₄	—	118	1	no	—
460	C₂×C₄	—	118	2	no	—
461	C₂×C₄	—	118	2	no	—
462	C₂×C₄	—	118	1	no	—
463	C₂×C₄	—	118	1	no	—
464	C₂×C₄	—	236	2	no	—
465	C₂×C₄	—	236	2	no	—
466	C₂×C₄	#14273698	1	1	yes	characteristic
467	C₂×C₄	#14273698	1	1	yes	characteristic
468	C₂×C₄	#14273698	1	1	yes	characteristic
469	C₂×C₄	#14273698	1	1	yes	characteristic
470	C₂×C₄	C₂²×C₄×D₅₉	1	1	yes	characteristic
471	C₂×C₄	C₂×D₄×D₅₉	1	1	yes	characteristic
472	C₂×C₄	C₂²×C₂²⋊D₅₉	1	1	yes	characteristic
473	C₂×C₄	#41×D₅₉	1	1	yes	characteristic
474	C₂×C₄	#41×D₅₉	1	1	yes	characteristic
475	C₂×C₄	C₂×#11745685	1	1	yes	characteristic
476	C₈	—	2	1	no	—
477	C₈	—	2	1	no	—
478	C₈	—	118	2	no	—
479	C₈	—	118	4	no	—
480	C₈	—	118	2	no	—
481	C₈	—	236	2	no	—
482	C₈	C₄×C₂²⋊D₅₉	1	2	yes	—
483	C₈	C₄×C₂²⋊D₅₉	1	2	yes	—
484	C₂²	—	2	1	no	—
485	C₂²	—	2	1	no	—
486	C₂²	—	118	2	no	—
487	C₂²	—	236	1	no	—
488	C₂²	—	236	1	no	—
489	C₂²	C₄×#11745687	1	1	yes	characteristic
490	C₂²	C₂×#14273698	1	1	yes	characteristic
491	C₂²	#16837934	1	1	yes	characteristic
492	C₄	—	2	1	no	—
493	C₄	—	2	1	no	—
494	C₄	—	2	1	no	—
495	C₄	—	4	4	no	—
496	C₄	—	8	2	no	—
497	C₄	—	118	2	no	—
498	C₄	—	236	1	no	—
499	C₄	—	236	1	no	—
500	C₄	#16837674	1	2	yes	direct product factor
501	C₄	C₄×D₄×D₅₉	1	1	yes	characteristic
502	C₄	C₂×C₄×C₂²⋊D₅₉	1	1	yes	characteristic
503	C₄	#16837909	1	1	yes	characteristic
504	C₄	#16837949	1	1	yes	characteristic
505	C₂	—	2	1	no	—
506	C₂	—	2	1	no	—
507	C₂	—	236	2	no	—
508	C₂	C₄×#14273698	1	1	yes	characteristic
509	C₂	C₂×#16837674	1	1	yes	characteristic
510	C₂	#21433812	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	#14273698
commutator	C₂×C₄×C₅₉	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₅₉
Fitting	C₂×C₄×Q₁₆×C₅₉	C₂
socle	C₂²×C₅₉	C₂×#121
prime radical	C₂×#11745685	C₂³
cosocle	C₂²×C₄×C₅₉	C₂⁴
hypercenter	C₂×C₄×Q₁₆	D₅₉
hypocenter	C₅₉	C₄×#473
LCS	G ▷ C₂×C₄×C₅₉ ▷ C₂×C₅₉ ▷ C₅₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ C₂×C₄×Q₁₆

Complements

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

N	H ≅ G/N	type
4. #21425012	C₂	semidirect
5. #21424879	C₂	semidirect
6. #21424748	C₂	semidirect
9. C₄×#14273663	C₂	semidirect
10. C₄×#14273646	C₂	semidirect
11. C₂×C₄×Q₁₆×C₅₉	C₂	semidirect
16. #16837674	C₄	direct (N × H)
75. #14273663	C₂×C₄	semidirect
83. #14273646	C₂×C₄	semidirect
96. C₂×Q₁₆×C₅₉	C₂×C₄	semidirect
242. C₄×C₅₉	#473	semidirect
252. C₂×C₄×Q₁₆	D₅₉	semidirect
303. C₅₉	C₄×#473	semidirect
312. C₂×Q₁₆	C₄×D₅₉	semidirect
500. C₄	#16837674	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×#16837674	2
C₄×#14273758	2
C₄×#14273733	2
#21425012	2
#21424879	2
#21424748	2
#21424614	2
#21424161	2
C₄×#14273663	2
C₄×#14273646	2
C₂×C₄×Q₁₆×C₅₉	2
C₄×#473	59

Subgroups — C4×#16837674 #28595574

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×#16837674 #28595574