Subgroups — #34296422

Order 20224.

770 conjugacy classes of subgroups.

The subgroup lattice has 536 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#23773720	C₂	1	1	yes	maximal, characteristic
2	#23772332	C₂	1	1	yes	maximal, characteristic, complemented
3	#23772110	C₂	1	1	yes	maximal, characteristic
4	#23764375	C₂	1	1	yes	maximal, characteristic, complemented
5	#23764226	C₂	1	1	yes	maximal, characteristic
6	#23764106	C₂	1	1	yes	maximal, characteristic, complemented
7	#23764105	C₂	1	1	yes	maximal, characteristic, complemented
8	#23764102	C₂	1	1	yes	maximal, characteristic, complemented
9	#23764101	C₂	1	1	yes	maximal, characteristic, complemented
10	#23763536	C₂	1	1	yes	maximal, characteristic, complemented
11	#23763239	C₂	1	1	yes	maximal, characteristic, complemented
12	#23763237	C₂	1	1	yes	maximal, characteristic, complemented
13	#23763235	C₂	1	1	yes	maximal, characteristic, complemented
14	C₄×C₈×Dic₇₉	C₂	1	1	yes	maximal, characteristic, complemented
15	C₇₉×#1764	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#14579167	C₂²	1	1	yes	characteristic
17	#19099116	C₂²	1	1	yes	characteristic
18	#19099109	C₂²	1	1	yes	characteristic
19	#19098919	C₄	1	2	yes	complemented
20	#19098916	C₄	1	2	yes	complemented
21	#19098912	C₄	1	2	yes	complemented
22	#19098908	C₄	1	2	yes	complemented
23	#19098691	—	2	2	no	—
24	C₈×Dic₁₅₈	—	2	2	no	—
25	#19098639	—	2	2	no	—
26	C₈×C₂²⋊D₇₉	—	2	2	no	—
27	#19098591	C₂²	1	1	yes	characteristic
28	#19098590	C₂²	1	1	yes	characteristic
29	#19098586	C₂²	1	1	yes	characteristic
30	#19098586	C₂²	1	1	yes	characteristic
31	C₂×#14579089	C₂²	1	1	yes	characteristic
32	C₂×#14579088	C₂²	1	1	yes	characteristic
33	C₂×#14579087	C₂²	1	1	yes	characteristic
34	#19098560	C₂²	1	1	yes	characteristic
35	#19098559	C₂²	1	1	yes	characteristic
36	#19098557	C₂²	1	1	yes	characteristic
37	#19098531	C₂²	1	1	yes	characteristic
38	#19098530	C₂²	1	1	yes	characteristic
39	#19098518	C₂²	1	1	yes	characteristic
40	C₂×C₄×C₇₉⋊C₈	C₂²	1	1	yes	characteristic
41	C₂×C₈×Dic₇₉	C₂²	1	1	yes	characteristic
42	C₂×C₈×Dic₇₉	C₂²	1	1	yes	characteristic
43	C₂×C₈×Dic₇₉	C₂²	1	1	yes	characteristic
44	C₂×C₈×Dic₇₉	C₂²	1	1	yes	characteristic
45	C₄²×Dic₇₉	C₂²	1	1	yes	characteristic
46	#19098328	C₂²	1	1	yes	characteristic
47	#19098327	C₂²	1	1	yes	characteristic
48	#19098327	C₂²	1	1	yes	characteristic
49	#19098324	C₂²	1	1	yes	characteristic
50	#19098323	C₂²	1	1	yes	characteristic
51	#19098322	C₂²	1	1	yes	characteristic
52	C₂×#131×C₇₉	C₂²	1	1	yes	characteristic
53	C₂×#104×C₇₉	C₂²	1	1	yes	characteristic
54	#416×C₇₉	C₂²	1	1	yes	characteristic
55	#405×C₇₉	C₂²	1	1	yes	characteristic
56	C₂×C₄×C₈×C₇₉	C₂²	1	1	yes	characteristic
57	#341×C₇₉	C₂²	1	1	yes	characteristic
58	#339×C₇₉	C₂²	1	1	yes	characteristic
59	C₂×#11929624	C₂³	1	1	yes	characteristic
60	#14579167	—	2	2	no	—
61	#14579167	—	2	2	no	—
62	C₂×#11929608	C₂³	1	1	yes	characteristic
63	C₂×#11929608	C₂³	1	1	yes	characteristic
64	C₂×#11929607	—	2	1	no	—
65	C₂²×C₇₉⋊C₈	C₂³	1	1	yes	characteristic
66	C₂²×C₇₉⋊C₈	C₂³	1	1	yes	characteristic
67	C₂×C₈×D₇₉	—	2	1	no	—
68	#14579160	C₂×C₄	1	2	yes	—
69	#14579159	C₂×C₄	1	1	yes	characteristic
70	#14579157	C₂×C₄	1	1	yes	characteristic
71	#14579152	C₂×C₄	1	2	yes	—
72	#14579150	C₂×C₄	1	1	yes	characteristic
73	#14579148	C₂×C₄	1	1	yes	characteristic
74	#14579138	—	2	2	no	—
75	#14579133	—	2	2	no	—
76	C₄×Dic₁₅₈	—	2	2	no	—
77	C₄×C₂²⋊D₇₉	—	2	2	no	—
78	#14579120	C₂³	1	1	yes	characteristic
79	C₂×C₄×Dic₇₉	—	2	2	no	—
80	C₂×C₄×Dic₇₉	C₂³	1	1	yes	characteristic
81	C₂×C₄×Dic₇₉	C₂³	1	1	yes	characteristic
82	C₄⋊(C₇₉⋊C₈)	—	2	2	no	—
83	Dic₇₉⋊C₈	—	2	2	no	—
84	Dic₇₉⋊C₈	—	2	2	no	—
85	Dic₇₉⋊C₈	—	2	2	no	—
86	#14579089	—	2	2	no	—
87	#14579088	—	2	2	no	—
88	#14579087	—	2	2	no	—
89	#14579086	C₂×C₄	1	2	yes	—
90	#14579085	C₂×C₄	1	2	yes	—
91	#14579084	C₂×C₄	1	2	yes	—
92	#14579083	C₂×C₄	1	2	yes	—
93	#14579082	C₂×C₄	1	2	yes	—
94	#14579081	C₂×C₄	1	2	yes	—
95	C₂²⋊(C₇₉⋊C₈)	—	2	2	no	—
96	(C₂×D₇₉)⋊C₈	—	2	2	no	—
97	#14579071	—	2	1	no	—
98	C₄×C₇₉⋊C₈	—	2	2	no	—
99	C₈×Dic₇₉	—	2	1	no	—
100	C₈×Dic₇₉	—	2	2	no	—
101	C₈×Dic₇₉	—	2	2	no	—
102	C₈×Dic₇₉	C₂×C₄	1	2	yes	—
103	C₈×Dic₇₉	C₂×C₄	1	2	yes	—
104	C₈×Dic₇₉	D₄	1	2	yes	—
105	C₈×Dic₇₉	D₄	1	2	yes	—
106	C₂×#41×C₇₉	C₂³	1	1	yes	characteristic
107	#131×C₇₉	—	2	2	no	—
108	#131×C₇₉	—	2	2	no	—
109	C₂×M₁₆×C₇₉	—	2	1	no	—
110	C₂×M₁₆×C₇₉	C₂³	1	1	yes	characteristic
111	C₂×M₁₆×C₇₉	C₂³	1	1	yes	characteristic
112	C₂²×C₈×C₇₉	—	2	1	no	—
113	C₂²×C₈×C₇₉	C₂³	1	1	yes	characteristic
114	C₂²×C₈×C₇₉	C₂³	1	1	yes	characteristic
115	#117×C₇₉	C₂³	1	1	yes	characteristic
116	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
117	#104×C₇₉	—	2	2	no	—
118	#103×C₇₉	C₂×C₄	1	2	yes	—
119	#102×C₇₉	C₂×C₄	1	2	yes	—
120	#97×C₇₉	—	2	1	no	—
121	C₄×C₈×C₇₉	—	2	1	no	—
122	C₄×C₈×C₇₉	—	2	2	no	—
123	#11929624	—	2	1	no	—
124	#11929624	—	2	1	no	—
125	#11929624	—	2	1	no	—
126	#11929624	—	2	1	no	—
127	C₂×Dic₁₅₈	—	2	2	no	—
128	C₂×Dic₁₅₈	C₂²×C₄	1	1	yes	characteristic
129	C₂×D₃₁₆	C₂²×C₄	1	1	yes	characteristic
130	C₂×C₂²⋊D₇₉	—	2	2	no	—
131	C₂×C₂²⋊D₇₉	—	2	1	no	—
132	C₂²×Dic₇₉	—	2	1	no	—
133	C₂²×Dic₇₉	#41	1	2	yes	—
134	C₂×C₄×D₇₉	—	2	1	no	—
135	#11929608	—	2	1	no	—
136	#11929608	—	2	1	no	—
137	#11929608	—	2	1	no	—
138	#11929608	—	2	1	no	—
139	#11929607	—	4	2	no	—
140	C₂×C₇₉⋊C₈	—	2	1	no	—
141	C₂×C₇₉⋊C₈	—	2	1	no	—
142	C₂×C₇₉⋊C₈	—	2	1	no	—
143	C₂×C₇₉⋊C₈	—	2	1	no	—
144	C₂×C₇₉⋊C₈	—	2	1	no	—
145	C₂×C₇₉⋊C₈	—	2	1	no	—
146	C₂×C₇₉⋊C₈	C₂²×C₄	1	2	yes	—
147	C₂×C₇₉⋊C₈	C₂×D₄	1	2	yes	—
148	C₈×D₇₉	—	4	2	no	—
149	C₄⋊Dic₇₉	—	2	2	no	—
150	C₄⋊Dic₇₉	C₂²×C₄	1	2	yes	—
151	Dic₇₉⋊C₄	—	2	2	no	—
152	Dic₇₉⋊C₄	—	2	2	no	—
153	Dic₇₉⋊C₄	—	2	2	no	—
154	C₂²⋊Dic₇₉	—	2	2	no	—
155	C₂²⋊Dic₇₉	—	2	1	no	—
156	(C₂×D₇₉)⋊C₄	—	2	2	no	—
157	C₄×Dic₇₉	—	2	8	no	—
158	C₄×Dic₇₉	—	2	1	no	—
159	C₄×Dic₇₉	—	2	1	no	—
160	C₄×Dic₇₉	C₂²×C₄	1	1	yes	characteristic
161	C₄×Dic₇₉	C₂²×C₄	1	1	yes	characteristic
162	C₄×Dic₇₉	C₂×D₄	1	2	yes	—
163	C₄×Dic₇₉	#41	1	2	yes	—
164	#41×C₇₉	—	2	1	no	—
165	#41×C₇₉	—	2	1	no	—
166	#41×C₇₉	—	2	1	no	—
167	#41×C₇₉	—	2	1	no	—
168	C₂×Q₈×C₇₉	C₂²×C₄	1	1	yes	characteristic
169	C₂×D₄×C₇₉	—	2	1	no	—
170	C₂×D₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
171	C₂²×C₄×C₇₉	—	2	1	no	—
172	C₂²×C₄×C₇₉	—	2	1	no	—
173	C₂²×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
174	M₁₆×C₇₉	—	2	1	no	—
175	M₁₆×C₇₉	—	2	1	no	—
176	M₁₆×C₇₉	—	2	1	no	—
177	M₁₆×C₇₉	—	2	1	no	—
178	M₁₆×C₇₉	—	4	2	no	—
179	C₂×C₈×C₇₉	—	2	1	no	—
180	C₂×C₈×C₇₉	—	2	1	no	—
181	C₂×C₈×C₇₉	—	2	1	no	—
182	C₂×C₈×C₇₉	—	2	1	no	—
183	C₂×C₈×C₇₉	—	4	2	no	—
184	C₂×C₈×C₇₉	C₂²×C₄	1	2	yes	—
185	C₂×C₈×C₇₉	C₂×D₄	1	1	yes	characteristic
186	C₂×C₈×C₇₉	C₂×D₄	1	1	yes	characteristic
187	C₂×C₈×C₇₉	#41	1	2	yes	—
188	C₂×C₈×C₇₉	#41	1	2	yes	—
189	C₄⋊C₄×C₇₉	C₂²×C₄	1	2	yes	—
190	C₂²⋊C₄×C₇₉	—	2	1	no	—
191	C₄²×C₇₉	—	2	1	no	—
192	C₄²×C₇₉	—	2	1	no	—
193	C₄²×C₇₉	#41	1	2	yes	—
194	C₂³×C₇₉	—	2	1	no	—
195	C₂³×C₇₉	C₂×#41	1	1	yes	characteristic
196	C₂²×D₇₉	—	2	1	no	—
197	Q₈×C₇₉	—	2	1	no	—
198	Q₈×C₇₉	—	2	1	no	—
199	D₄×C₇₉	—	2	1	no	—
200	D₄×C₇₉	—	2	1	no	—
201	D₄×C₇₉	—	4	1	no	—
202	D₄×C₇₉	—	4	1	no	—
203	C₂×C₄×C₇₉	—	2	4	no	—
204	C₂×C₄×C₇₉	—	2	2	no	—
205	C₂×C₄×C₇₉	—	2	1	no	—
206	C₂×C₄×C₇₉	—	2	2	no	—
207	C₂×C₄×C₇₉	—	4	1	no	—
208	C₂×C₄×C₇₉	—	4	1	no	—
209	C₂×C₄×C₇₉	C₂³×C₄	1	1	yes	characteristic
210	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
211	C₂×C₄×C₇₉	C₂×#41	1	1	yes	characteristic
212	C₂×C₄×C₇₉	C₂×#41	1	1	yes	characteristic
213	C₂×C₄×C₇₉	C₂×#41	1	1	yes	characteristic
214	C₂×C₄×C₇₉	C₂×#41	1	1	yes	characteristic
215	C₂²⋊D₇₉	—	4	1	no	—
216	C₂²⋊D₇₉	—	4	1	no	—
217	C₂²⋊D₇₉	—	4	4	no	—
218	C₂×Dic₇₉	—	2	4	no	—
219	C₂×Dic₇₉	—	2	2	no	—
220	C₂×Dic₇₉	—	2	4	no	—
221	C₂×Dic₇₉	—	2	2	no	—
222	C₂×Dic₇₉	—	2	1	no	—
223	C₂×Dic₇₉	C₄×D₄	1	2	yes	—
224	C₂×Dic₇₉	C₄×D₄	1	2	yes	—
225	D₃₁₆	—	2	1	no	—
226	D₃₁₆	—	2	1	no	—
227	C₄×D₇₉	—	4	1	no	—
228	C₄×D₇₉	—	4	1	no	—
229	Dic₁₅₈	—	2	1	no	—
230	Dic₁₅₈	—	2	1	no	—
231	Dic₁₅₈	—	4	4	no	—
232	C₈×C₇₉	—	2	2	no	—
233	C₈×C₇₉	—	4	1	no	—
234	C₈×C₇₉	—	4	1	no	—
235	C₈×C₇₉	#124	1	2	yes	—
236	C₈×C₇₉	#124	1	2	yes	—
237	C₇₉⋊C₈	—	2	2	no	—
238	C₇₉⋊C₈	—	2	2	no	—
239	C₇₉⋊C₈	—	4	1	no	—
240	C₇₉⋊C₈	—	4	1	no	—
241	C₂²×C₇₉	—	2	2	no	—
242	C₂²×C₇₉	—	4	2	no	—
243	C₂²×C₇₉	—	4	1	no	—
244	C₂²×C₇₉	C₂×C₄×D₄	1	1	yes	characteristic
245	C₂²×C₇₉	#529	1	1	yes	characteristic
246	C₂²×C₇₉	#529	1	1	yes	characteristic
247	C₂×D₇₉	—	4	2	no	—
248	C₂×D₇₉	—	4	1	no	—
249	C₄×C₇₉	—	2	4	no	—
250	C₄×C₇₉	—	4	2	no	—
251	C₄×C₇₉	—	4	1	no	—
252	C₄×C₇₉	C₄×#41	1	1	yes	characteristic
253	C₄×C₇₉	C₄×#41	1	1	yes	characteristic
254	C₄×C₇₉	C₂×#124	1	1	yes	characteristic
255	C₄×C₇₉	#532	1	1	yes	characteristic
256	Dic₇₉	—	2	4	no	—
257	Dic₇₉	—	2	2	no	—
258	Dic₇₉	—	4	2	no	—
259	Dic₇₉	—	4	1	no	—
260	Dic₇₉	#443	1	4	yes	—
261	#21658	—	79	1	no	maximal, Sylow
262	C₂×C₇₉	—	2	1	no	—
263	C₂×C₇₉	—	2	1	no	—
264	C₂×C₇₉	—	8	1	no	—
265	C₂×C₇₉	C₄×#124	1	1	yes	characteristic
266	C₂×C₇₉	C₂×#443	1	2	yes	—
267	D₇₉	—	8	1	no	—
268	#3131	—	79	1	no	—
269	#2960	—	79	1	no	—
270	#2931	—	79	1	no	—
271	#1994	—	79	1	no	—
272	#1962	—	79	1	no	—
273	#1937	—	79	1	no	—
274	#1937	—	79	1	no	—
275	#1937	—	79	1	no	—
276	#1937	—	79	1	no	—
277	#1837	—	79	1	no	—
278	#1764	—	79	1	no	—
279	#1764	—	79	1	no	—
280	#1764	—	79	1	no	—
281	#1764	D₇₉	1	1	yes	characteristic, complemented
282	C₄²×C₈	—	79	1	no	—
283	C₇₉	#21658	1	1	yes	characteristic, complemented, Sylow
284	C₂×#131	—	79	1	no	—
285	C₂×#131	C₂×D₇₉	1	1	yes	characteristic
286	#533	—	79	1	no	—
287	#532	—	79	1	no	—
288	#488	—	79	2	no	—
289	#488	—	79	2	no	—
290	#487	—	79	2	no	—
291	#486	—	79	2	no	—
292	#446	—	158	2	no	—
293	C₈×Q₈	—	158	2	no	—
294	#436	—	158	2	no	—
295	C₈×D₄	—	158	2	no	—
296	#424	—	79	1	no	—
297	#424	—	79	1	no	—
298	#423	—	79	1	no	—
299	#423	—	79	1	no	—
300	C₂×#104	—	79	1	no	—
301	C₂×#104	—	79	1	no	—
302	C₂×#104	—	79	1	no	—
303	C₂×#104	C₂×D₇₉	1	1	yes	characteristic
304	#416	—	79	1	no	—
305	#416	—	79	1	no	—
306	#416	—	79	1	no	—
307	#416	C₂×D₇₉	1	1	yes	characteristic
308	#408	—	79	1	no	—
309	#408	—	79	1	no	—
310	#405	—	79	1	no	—
311	#405	C₂×D₇₉	1	1	yes	characteristic
312	C₂×C₄×C₈	—	79	1	no	—
313	C₂×C₄×C₈	—	79	1	no	—
314	C₂×C₄×C₈	—	79	1	no	—
315	C₂×C₄×C₈	—	79	1	no	—
316	C₂×C₄×C₈	—	79	1	no	—
317	C₂×C₄×C₈	C₂×D₇₉	1	1	yes	characteristic
318	C₄³	—	79	1	no	—
319	#341	—	79	1	no	—
320	#341	—	79	1	no	—
321	#341	—	79	1	no	—
322	#341	C₂×D₇₉	1	1	yes	characteristic
323	#339	—	79	1	no	—
324	#339	—	79	1	no	—
325	#339	—	79	1	no	—
326	#339	C₂×D₇₉	1	1	yes	characteristic
327	C₂×#41	—	79	1	no	—
328	C₂×#41	C₂²×D₇₉	1	1	yes	characteristic
329	#131	—	2	2	no	—
330	#131	—	2	2	no	—
331	#131	—	158	2	no	—
332	#131	—	158	2	no	—
333	C₂×M₁₆	—	2	1	no	—
334	C₂×M₁₆	—	79	1	no	—
335	C₂×M₁₆	—	79	1	no	—
336	C₂×M₁₆	—	158	1	no	—
337	C₂×M₁₆	C₂²×D₇₉	1	1	yes	characteristic
338	C₂×M₁₆	C₂²×D₇₉	1	1	yes	characteristic
339	C₂²×C₈	—	2	1	no	—
340	C₂²×C₈	—	79	1	no	—
341	C₂²×C₈	—	79	1	no	—
342	C₂²×C₈	—	158	1	no	—
343	C₂²×C₈	C₂²×D₇₉	1	1	yes	characteristic
344	C₂²×C₈	C₂²×D₇₉	1	1	yes	characteristic
345	C₄⋊Q₈	—	79	2	no	—
346	C₄⋊Q₈	—	79	1	no	—
347	#127	—	79	1	no	—
348	#125	—	79	2	no	—
349	#124	—	79	1	no	—
350	#124	—	79	1	no	—
351	C₂²⋊Q₈	—	158	2	no	—
352	#121	—	158	2	no	—
353	C₄×Q₈	—	158	2	no	—
354	C₄×D₄	—	158	2	no	—
355	#117	—	79	1	no	—
356	#117	C₂²×D₇₉	1	1	yes	characteristic
357	C₂×C₄²	—	79	1	no	—
358	C₂×C₄²	—	79	1	no	—
359	C₂×C₄²	—	158	2	no	—
360	C₂×C₄²	C₂²×D₇₉	1	1	yes	characteristic
361	C₄⋊C₈	—	158	2	no	—
362	C₄⋊C₈	—	158	2	no	—
363	C₄⋊C₈	—	158	2	no	—
364	C₄⋊C₈	—	158	2	no	—
365	#104	—	2	2	no	—
366	#104	—	158	2	no	—
367	#104	—	158	2	no	—
368	#104	—	158	2	no	—
369	#103	—	79	2	no	—
370	#103	—	79	2	no	—
371	#103	—	79	2	no	—
372	#103	C₄×D₇₉	1	2	yes	—
373	#102	—	79	2	no	—
374	#102	—	79	2	no	—
375	#102	—	79	2	no	—
376	#102	C₄×D₇₉	1	2	yes	—
377	C₂²⋊C₈	—	158	2	no	—
378	C₂²⋊C₈	—	158	2	no	—
379	#97	—	2	1	no	—
380	#97	—	158	1	no	—
381	C₄×C₈	—	2	1	no	—
382	C₄×C₈	—	2	2	no	—
383	C₄×C₈	—	79	2	no	—
384	C₄×C₈	—	79	2	no	—
385	C₄×C₈	—	79	2	no	—
386	C₄×C₈	—	79	2	no	—
387	C₄×C₈	—	158	2	no	—
388	C₄×C₈	—	158	1	no	—
389	C₄×C₈	—	158	2	no	—
390	C₄×C₈	—	158	2	no	—
391	#41	—	2	1	no	—
392	#41	—	2	1	no	—
393	#41	—	2	1	no	—
394	#41	—	2	1	no	—
395	#41	—	158	1	no	—
396	#41	—	158	1	no	—
397	#41	—	158	1	no	—
398	#41	—	158	1	no	—
399	C₂×Q₈	—	79	1	no	—
400	C₂×Q₈	—	158	2	no	—
401	C₂×Q₈	C₂×C₄×D₇₉	1	1	yes	characteristic
402	C₂×D₄	—	2	1	no	—
403	C₂×D₄	—	79	1	no	—
404	C₂×D₄	—	158	2	no	—
405	C₂×D₄	—	158	1	no	—
406	C₂×D₄	C₂×C₄×D₇₉	1	1	yes	characteristic
407	C₂²×C₄	—	2	1	no	—
408	C₂²×C₄	—	2	1	no	—
409	C₂²×C₄	—	79	2	no	—
410	C₂²×C₄	—	158	1	no	—
411	C₂²×C₄	—	158	1	no	—
412	C₂²×C₄	C₂³×D₇₉	1	1	yes	characteristic
413	M₁₆	—	2	1	no	—
414	M₁₆	—	2	1	no	—
415	M₁₆	—	2	1	no	—
416	M₁₆	—	2	1	no	—
417	M₁₆	—	4	2	no	—
418	M₁₆	—	316	2	no	—
419	M₁₆	—	158	1	no	—
420	M₁₆	—	158	1	no	—
421	M₁₆	—	158	1	no	—
422	M₁₆	—	158	1	no	—
423	C₂×C₈	—	2	1	no	—
424	C₂×C₈	—	2	1	no	—
425	C₂×C₈	—	2	1	no	—
426	C₂×C₈	—	2	1	no	—
427	C₂×C₈	—	4	2	no	—
428	C₂×C₈	—	316	2	no	—
429	C₂×C₈	—	79	2	no	—
430	C₂×C₈	—	79	2	no	—
431	C₂×C₈	—	158	1	no	—
432	C₂×C₈	—	158	1	no	—
433	C₂×C₈	—	158	1	no	—
434	C₂×C₈	—	158	1	no	—
435	C₂×C₈	—	158	1	no	—
436	C₂×C₈	—	158	1	no	—
437	C₂×C₈	C₂×C₄×D₇₉	1	2	yes	—
438	C₂×C₈	D₄×D₇₉	1	1	yes	characteristic
439	C₂×C₈	D₄×D₇₉	1	1	yes	characteristic
440	C₂×C₈	#11929623	1	2	yes	—
441	C₂×C₈	#11929624	1	2	yes	—
442	C₄⋊C₄	—	79	2	no	—
443	C₄⋊C₄	—	158	2	no	—
444	C₄⋊C₄	—	158	2	no	—
445	C₄⋊C₄	—	158	2	no	—
446	C₄⋊C₄	—	158	2	no	—
447	C₄⋊C₄	C₂×C₄×D₇₉	1	2	yes	—
448	C₂²⋊C₄	—	2	1	no	—
449	C₂²⋊C₄	—	158	2	no	—
450	C₂²⋊C₄	—	158	2	no	—
451	C₂²⋊C₄	—	158	1	no	—
452	C₄²	—	2	1	no	—
453	C₄²	—	2	1	no	—
454	C₄²	—	79	1	no	—
455	C₄²	—	79	1	no	—
456	C₄²	—	79	2	no	—
457	C₄²	—	79	2	no	—
458	C₄²	—	158	8	no	—
459	C₄²	—	158	1	no	—
460	C₄²	—	158	1	no	—
461	C₄²	#11929624	1	2	yes	—
462	C₂³	—	2	1	no	—
463	C₂³	—	158	1	no	—
464	C₂³	#41×D₇₉	1	1	yes	characteristic
465	Q₈	—	2	1	no	—
466	Q₈	—	2	1	no	—
467	Q₈	—	316	4	no	—
468	Q₈	—	158	1	no	—
469	Q₈	—	158	1	no	—
470	D₄	—	2	1	no	—
471	D₄	—	2	1	no	—
472	D₄	—	4	1	no	—
473	D₄	—	4	1	no	—
474	D₄	—	316	1	no	—
475	D₄	—	316	1	no	—
476	D₄	—	316	4	no	—
477	D₄	—	158	1	no	—
478	D₄	—	158	1	no	—
479	C₂×C₄	—	2	4	no	—
480	C₂×C₄	—	2	2	no	—
481	C₂×C₄	—	2	2	no	—
482	C₂×C₄	—	2	1	no	—
483	C₂×C₄	—	4	1	no	—
484	C₂×C₄	—	4	1	no	—
485	C₂×C₄	—	316	1	no	—
486	C₂×C₄	—	316	1	no	—
487	C₂×C₄	—	79	2	no	—
488	C₂×C₄	—	79	2	no	—
489	C₂×C₄	—	158	2	no	—
490	C₂×C₄	—	158	1	no	—
491	C₂×C₄	—	158	4	no	—
492	C₂×C₄	—	158	4	no	—
493	C₂×C₄	—	158	2	no	—
494	C₂×C₄	C₂²×C₄×D₇₉	1	1	yes	characteristic
495	C₂×C₄	C₂×D₄×D₇₉	1	1	yes	characteristic
496	C₂×C₄	#41×D₇₉	1	1	yes	characteristic
497	C₂×C₄	C₂×#11929623	1	1	yes	characteristic
498	C₂×C₄	C₂×#11929624	1	1	yes	characteristic
499	C₂×C₄	C₂×#11929624	1	1	yes	characteristic
500	C₈	—	2	2	no	—
501	C₈	—	4	1	no	—
502	C₈	—	4	1	no	—
503	C₈	—	316	1	no	—
504	C₈	—	316	1	no	—
505	C₈	—	158	2	no	—
506	C₈	—	158	2	no	—
507	C₈	#14579147	1	2	yes	—
508	C₈	#14579147	1	2	yes	—
509	C₂²	—	2	2	no	—
510	C₂²	—	4	2	no	—
511	C₂²	—	4	1	no	—
512	C₂²	—	316	2	no	—
513	C₂²	—	316	1	no	—
514	C₂²	C₄×D₄×D₇₉	1	1	yes	characteristic
515	C₂²	#19099091	1	1	yes	characteristic
516	C₂²	#19099093	1	1	yes	characteristic
517	C₄	—	2	4	no	—
518	C₄	—	4	2	no	—
519	C₄	—	4	1	no	—
520	C₄	—	316	2	no	—
521	C₄	—	316	1	no	—
522	C₄	—	79	4	no	—
523	C₄	—	158	4	no	—
524	C₄	—	158	2	no	—
525	C₄	C₄×#11929623	1	1	yes	characteristic
526	C₄	C₄×#11929624	1	1	yes	characteristic
527	C₄	C₂×#14579147	1	1	yes	characteristic
528	C₄	#19099110	1	1	yes	characteristic
529	C₂	—	2	1	no	—
530	C₂	—	2	1	no	—
531	C₂	—	8	1	no	—
532	C₂	—	632	1	no	—
533	C₂	C₄×#14579147	1	1	yes	characteristic
534	C₂	#443×D₇₉	1	2	yes	—

	subgroup	G/H
center	C₂×C₈	D₄×D₇₉
commutator	C₂×C₄×C₇₉	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₇₉
Fitting	C₇₉×#1764	C₂
socle	C₂²×C₇₉	C₂×C₄×D₄
prime radical	#19099109	C₂²
cosocle	C₂²×C₄×C₇₉	C₂⁴
hypercenter	#1764	D₇₉
hypocenter	C₇₉	#21658
LCS	G ▷ C₂×C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂×C₈ ◁ C₂²×C₈ ◁ #1764

Complements

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

N	H ≅ G/N	type
2. #23772332	C₂	semidirect
4. #23764375	C₂	semidirect
6. #23764106	C₂	semidirect
7. #23764105	C₂	semidirect
8. #23764102	C₂	semidirect
9. #23764101	C₂	semidirect
10. #23763536	C₂	semidirect
11. #23763239	C₂	semidirect
12. #23763237	C₂	semidirect
13. #23763235	C₂	semidirect
14. C₄×C₈×Dic₇₉	C₂	semidirect
15. C₇₉×#1764	C₂	semidirect
19. #19098919	C₄	semidirect
20. #19098916	C₄	semidirect
21. #19098912	C₄	semidirect
22. #19098908	C₄	semidirect
281. #1764	D₇₉	semidirect
283. C₇₉	#21658	semidirect

Maximal subgroups

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

subgroup	index
#23773720	2
#23772332	2
#23772110	2
#23764375	2
#23764226	2
#23764106	2
#23764105	2
#23764102	2
#23764101	2
#23763536	2
#23763239	2
#23763237	2
#23763235	2
C₄×C₈×Dic₇₉	2
C₇₉×#1764	2
#21658	79