Subgroups — #34330870

Order 20224.

830 conjugacy classes of subgroups.

The subgroup lattice has 510 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#23773125	C₂	1	2	yes	maximal, complemented
2	C₂×#19098830	C₂	1	1	yes	maximal, characteristic, complemented
3	#23772301	C₂	1	1	yes	maximal, characteristic, complemented
4	#23772011	C₂	1	1	yes	maximal, characteristic, complemented
5	#23764798	C₂	1	2	yes	maximal, complemented
6	#23764672	C₂	1	2	yes	maximal, complemented
7	#23764311	C₂	1	1	yes	maximal, characteristic, complemented
8	#23764188	C₂	1	1	yes	maximal, characteristic, complemented
9	#23763882	C₂	1	2	yes	maximal, complemented
10	#23763447	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×#472×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
12	#19099361	C₂²	1	1	yes	characteristic
13	C₂×#14579187	C₂²	1	2	yes	—
14	#19099330	C₂²	1	2	yes	—
15	C₂×#14579167	C₂²	1	1	yes	characteristic
16	#19098831	—	2	4	no	—
17	#19098830	—	2	2	no	—
18	#19098830	—	2	2	no	—
19	#19098824	—	2	4	no	—
20	#19098683	—	2	2	no	—
21	#19098678	—	2	2	no	—
22	#19098612	—	2	2	no	—
23	#19098612	C₂²	1	2	yes	—
24	#19098611	C₂²	1	1	yes	characteristic
25	#19098611	C₂²	1	2	yes	—
26	C₂×#14579097	—	2	2	no	—
27	C₂×#14579097	C₂²	1	1	yes	characteristic
28	C₂×#14579097	C₂²	1	1	yes	characteristic
29	#19098580	C₂²	1	1	yes	characteristic
30	#19098579	C₂²	1	1	yes	characteristic
31	#19098568	C₂²	1	2	yes	—
32	#19098545	C₂²	1	2	yes	—
33	C₂×#14579078	C₂²	1	2	yes	—
34	C₂×#14579078	C₂²	1	2	yes	—
35	#19098518	C₂²	1	1	yes	characteristic
36	#19098334	C₂²	1	2	yes	—
37	C₇₉⋊#338	C₂²	1	2	yes	—
38	C₂×AGL(1,ℤ/8)×C₇₉	C₂²	1	2	yes	—
39	C₂²×D₈×C₇₉	C₂²	1	1	yes	characteristic
40	C₂×#131×C₇₉	C₂²	1	1	yes	characteristic
41	#472×C₇₉	—	2	2	no	—
42	#472×C₇₉	—	2	2	no	—
43	C₂×#108×C₇₉	C₂²	1	1	yes	characteristic
44	C₂×#100×C₇₉	C₂²	1	2	yes	—
45	C₂×#11929624	C₂³	1	1	yes	characteristic
46	#14579192	—	2	1	no	—
47	#14579191	D₄	1	2	yes	—
48	#14579187	—	2	1	no	—
49	#14579187	—	2	4	no	—
50	#14579187	—	4	2	no	—
51	#14579186	D₄	1	2	yes	—
52	#14579181	—	2	2	no	—
53	C₂×#11929612	—	2	2	no	—
54	C₂×#11929609	—	2	2	no	—
55	#14579168	—	2	4	no	—
56	#14579168	—	4	2	no	—
57	#14579167	—	2	1	no	—
58	#14579167	—	2	1	no	—
59	#14579167	—	2	1	no	—
60	#14579167	—	2	1	no	—
61	C₂×#11929608	—	2	4	no	—
62	C₂×#11929608	C₂³	1	1	yes	characteristic
63	C₂×#11929608	C₂³	1	2	yes	—
64	C₂×#11929608	C₂³	1	1	yes	characteristic
65	C₂×#11929608	C₂³	1	2	yes	—
66	C₂×#11929607	—	2	1	no	—
67	C₂×C₈×D₇₉	—	2	1	no	—
68	#14579120	C₂³	1	1	yes	characteristic
69	#14579097	—	2	1	no	—
70	#14579097	—	2	1	no	—
71	#14579097	—	2	4	no	—
72	#14579097	D₄	1	2	yes	—
73	#14579097	D₄	1	2	yes	—
74	#14579096	—	2	2	no	—
75	#14579096	—	2	4	no	—
76	#14579088	—	2	2	no	—
77	#14579087	—	2	2	no	—
78	#14579082	—	4	2	no	—
79	#14579079	—	2	2	no	—
80	#14579078	—	2	4	no	—
81	#14579078	—	2	4	no	—
82	#14579077	—	2	2	no	—
83	#14579071	—	2	1	no	—
84	C₈×Dic₇₉	—	2	1	no	—
85	C₂×#41×C₇₉	C₂³	1	1	yes	characteristic
86	C₂²×D₄×C₇₉	C₂³	1	2	yes	—
87	AGL(1,ℤ/8)×C₇₉	—	2	4	no	—
88	AGL(1,ℤ/8)×C₇₉	—	2	4	no	—
89	C₂×SD₁₆×C₇₉	—	2	2	no	—
90	C₂×D₈×C₇₉	—	2	2	no	—
91	C₂×D₈×C₇₉	—	2	1	no	—
92	C₂×D₈×C₇₉	—	2	1	no	—
93	C₂×D₈×C₇₉	—	2	1	no	—
94	C₂×D₈×C₇₉	—	2	1	no	—
95	C₂×D₈×C₇₉	—	2	1	no	—
96	C₂×D₈×C₇₉	—	2	1	no	—
97	#131×C₇₉	—	2	1	no	—
98	#131×C₇₉	—	2	1	no	—
99	#131×C₇₉	D₄	1	2	yes	—
100	#131×C₇₉	D₄	1	2	yes	—
101	C₂×M₁₆×C₇₉	—	2	1	no	—
102	C₂×M₁₆×C₇₉	C₂³	1	2	yes	—
103	C₂×M₁₆×C₇₉	C₂³	1	1	yes	characteristic
104	C₂²×C₈×C₇₉	—	2	1	no	—
105	C₂²×C₈×C₇₉	C₂³	1	1	yes	characteristic
106	#108×C₇₉	—	2	1	no	—
107	#108×C₇₉	—	2	1	no	—
108	#100×C₇₉	—	2	4	no	—
109	#11929624	—	2	1	no	—
110	#11929624	—	2	1	no	—
111	#11929624	—	2	1	no	—
112	#11929624	—	2	1	no	—
113	C₂×Dic₁₅₈	C₂×D₄	1	1	yes	characteristic
114	C₂×D₃₁₆	C₂×D₄	1	1	yes	characteristic
115	C₂×C₂²⋊D₇₉	—	2	1	no	—
116	C₂×C₄×D₇₉	—	2	1	no	—
117	#11929614	—	2	2	no	—
118	#11929612	—	2	2	no	—
119	#11929612	—	4	4	no	—
120	#11929611	—	2	2	no	—
121	#11929609	—	2	2	no	—
122	#11929609	—	4	4	no	—
123	#11929608	—	2	2	no	—
124	#11929608	—	2	1	no	—
125	#11929608	—	2	1	no	—
126	#11929608	—	2	2	no	—
127	#11929608	—	2	1	no	—
128	#11929608	—	2	2	no	—
129	#11929608	—	4	4	no	—
130	#11929608	C₂×D₄	1	2	yes	—
131	#11929608	C₂×D₄	1	4	yes	—
132	#11929607	—	4	1	no	—
133	#11929607	—	4	1	no	—
134	C₂×C₇₉⋊C₈	—	2	1	no	—
135	C₂×C₇₉⋊C₈	—	2	2	no	—
136	C₂×C₇₉⋊C₈	—	2	1	no	—
137	C₂×C₇₉⋊C₈	—	2	2	no	—
138	C₂×C₇₉⋊C₈	—	4	4	no	—
139	C₈×D₇₉	—	4	1	no	—
140	C₈×D₇₉	—	4	1	no	—
141	C₄⋊Dic₇₉	—	2	1	no	—
142	C₂²⋊Dic₇₉	—	2	1	no	—
143	C₄×Dic₇₉	—	2	1	no	—
144	C₂⁴×C₇₉	—	2	2	no	—
145	#41×C₇₉	—	2	1	no	—
146	#41×C₇₉	—	2	1	no	—
147	#41×C₇₉	C₂×D₄	1	2	yes	—
148	#41×C₇₉	C₂×D₄	1	2	yes	—
149	C₂×Q₈×C₇₉	#41	1	1	yes	characteristic
150	C₂×D₄×C₇₉	—	2	1	no	—
151	C₂×D₄×C₇₉	—	2	2	no	—
152	C₂×D₄×C₇₉	—	2	2	no	—
153	C₂×D₄×C₇₉	—	2	2	no	—
154	C₂×D₄×C₇₉	—	2	2	no	—
155	C₂×D₄×C₇₉	—	2	2	no	—
156	C₂×D₄×C₇₉	—	2	2	no	—
157	C₂×D₄×C₇₉	#41	1	1	yes	characteristic
158	C₂²×C₄×C₇₉	—	2	1	no	—
159	C₂²×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
160	SD₁₆×C₇₉	—	4	4	no	—
161	D₈×C₇₉	—	4	1	no	—
162	D₈×C₇₉	—	4	1	no	—
163	D₈×C₇₉	—	4	1	no	—
164	D₈×C₇₉	—	4	1	no	—
165	D₈×C₇₉	—	4	4	no	—
166	M₁₆×C₇₉	—	2	2	no	—
167	M₁₆×C₇₉	—	2	2	no	—
168	M₁₆×C₇₉	—	2	2	no	—
169	M₁₆×C₇₉	—	2	2	no	—
170	M₁₆×C₇₉	—	2	1	no	—
171	M₁₆×C₇₉	C₂×D₄	1	2	yes	—
172	C₂×C₈×C₇₉	—	2	2	no	—
173	C₂×C₈×C₇₉	—	2	2	no	—
174	C₂×C₈×C₇₉	—	2	1	no	—
175	C₂×C₈×C₇₉	—	2	2	no	—
176	C₂×C₈×C₇₉	C₂×D₄	1	1	yes	characteristic
177	C₂×C₈×C₇₉	C₂×D₄	1	1	yes	characteristic
178	C₂×C₈×C₇₉	C₂×D₄	1	1	yes	characteristic
179	C₂×C₈×C₇₉	C₂×D₄	1	1	yes	characteristic
180	C₂×C₈×C₇₉	#41	1	1	yes	characteristic
181	C₂×C₈×C₇₉	#41	1	1	yes	characteristic
182	C₂³×C₇₉	—	2	1	no	—
183	C₂³×C₇₉	—	4	2	no	—
184	C₂³×C₇₉	—	4	2	no	—
185	C₂³×C₇₉	—	4	2	no	—
186	C₂³×C₇₉	—	16	2	no	—
187	C₂³×C₇₉	2₋¹⁺⁴	1	1	yes	characteristic
188	C₂²×D₇₉	—	2	1	no	—
189	Q₈×C₇₉	—	2	1	no	—
190	Q₈×C₇₉	#121	1	2	yes	—
191	D₄×C₇₉	—	2	2	no	—
192	D₄×C₇₉	—	2	2	no	—
193	D₄×C₇₉	—	2	1	no	—
194	D₄×C₇₉	—	4	2	no	—
195	D₄×C₇₉	—	4	2	no	—
196	D₄×C₇₉	—	4	2	no	—
197	D₄×C₇₉	—	4	2	no	—
198	D₄×C₇₉	#121	1	2	yes	—
199	C₂×C₄×C₇₉	—	2	1	no	—
200	C₂×C₄×C₇₉	—	2	2	no	—
201	C₂×C₄×C₇₉	—	2	2	no	—
202	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
203	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
204	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
205	C₂×C₄×C₇₉	C₂×#41	1	1	yes	characteristic
206	C₂×C₄×C₇₉	C₂×#41	1	1	yes	characteristic
207	C₂×C₄×C₇₉	H(5,𝔽₂)	1	1	yes	characteristic
208	C₂²⋊D₇₉	—	4	1	no	—
209	C₂²⋊D₇₉	—	4	1	no	—
210	C₂×Dic₇₉	—	2	1	no	—
211	C₂×Dic₇₉	—	4	1	no	—
212	D₃₁₆	—	2	1	no	—
213	D₃₁₆	—	2	1	no	—
214	C₄×D₇₉	—	4	1	no	—
215	C₄×D₇₉	—	4	1	no	—
216	Dic₁₅₈	—	2	1	no	—
217	Dic₁₅₈	—	2	1	no	—
218	C₈×C₇₉	—	2	2	no	—
219	C₈×C₇₉	—	4	2	no	—
220	C₈×C₇₉	#121	1	1	yes	characteristic
221	C₈×C₇₉	#121	1	1	yes	characteristic
222	C₈×C₇₉	#121	1	1	yes	characteristic
223	C₈×C₇₉	#121	1	1	yes	characteristic
224	C₇₉⋊C₈	—	2	2	no	—
225	C₇₉⋊C₈	—	2	4	no	—
226	C₇₉⋊C₈	—	4	1	no	—
227	C₇₉⋊C₈	—	4	2	no	—
228	C₂²×C₇₉	—	2	2	no	—
229	C₂²×C₇₉	—	4	1	no	—
230	C₂²×C₇₉	—	8	1	no	—
231	C₂²×C₇₉	—	8	2	no	—
232	C₂²×C₇₉	—	16	2	no	—
233	C₂²×C₇₉	—	16	2	no	—
234	C₂²×C₇₉	—	16	2	no	—
235	C₂²×C₇₉	#537	1	1	yes	characteristic
236	C₂²×C₇₉	#547	1	1	yes	characteristic
237	C₂²×C₇₉	#548	1	1	yes	characteristic
238	C₂×D₇₉	—	4	1	no	—
239	C₂×D₇₉	—	8	1	no	—
240	C₄×C₇₉	—	2	2	no	—
241	C₄×C₇₉	C₂×#121	1	1	yes	characteristic
242	C₄×C₇₉	C₂×#121	1	1	yes	characteristic
243	C₄×C₇₉	D₄²	1	1	yes	characteristic
244	C₄×C₇₉	#553	1	1	yes	characteristic
245	Dic₇₉	—	4	1	no	—
246	Dic₇₉	—	8	1	no	—
247	#24809	—	79	1	no	maximal, Sylow
248	C₂×C₇₉	—	2	1	no	—
249	C₂×C₇₉	—	2	1	no	—
250	C₂×C₇₉	—	2	1	no	—
251	C₂×C₇₉	—	4	2	no	—
252	C₂×C₇₉	—	16	2	no	—
253	C₂×C₇₉	#2416	1	1	yes	characteristic
254	D₇₉	—	8	1	no	—
255	#3068	—	79	2	no	—
256	C₂×#472	—	79	1	no	—
257	C₂×#472	D₇₉	1	1	yes	characteristic, complemented
258	#2955	—	79	1	no	—
259	#2916	—	79	1	no	—
260	#2069	—	79	2	no	—
261	#2048	—	79	2	no	—
262	#1978	—	79	1	no	—
263	#1953	—	79	1	no	—
264	#1903	—	79	2	no	—
265	#1813	—	79	1	no	—
266	C₇₉	#24809	1	1	yes	characteristic, complemented, Sylow
267	#575	—	79	1	no	—
268	C₂×AGL(1,ℤ/8)	—	79	2	no	—
269	C₂×AGL(1,ℤ/8)	C₂×D₇₉	1	2	yes	—
270	C₂²×D₈	C₂×D₇₉	1	1	yes	characteristic
271	#568	—	79	2	no	—
272	C₂×#131	—	79	1	no	—
273	C₂×#131	C₂×D₇₉	1	1	yes	characteristic
274	#472	—	2	2	no	—
275	#472	—	2	2	no	—
276	#472	—	158	2	no	—
277	#472	—	158	2	no	—
278	#472	—	158	4	no	—
279	#471	—	158	4	no	—
280	#444	—	158	2	no	—
281	#443	—	158	2	no	—
282	#430	—	79	2	no	—
283	#430	—	79	1	no	—
284	#430	—	79	2	no	—
285	#430	—	158	2	no	—
286	C₂×#108	—	79	1	no	—
287	C₂×#108	—	79	1	no	—
288	C₂×#108	—	158	2	no	—
289	C₂×#108	C₂×D₇₉	1	1	yes	characteristic
290	#421	—	79	1	no	—
291	#421	—	79	1	no	—
292	#418	—	79	2	no	—
293	#413	—	79	2	no	—
294	C₂×#100	—	79	2	no	—
295	C₂×#100	—	79	2	no	—
296	C₂×#100	C₂×D₇₉	1	2	yes	—
297	#405	—	79	1	no	—
298	#344	—	79	2	no	—
299	#338	—	79	2	no	—
300	C₂×#41	—	79	1	no	—
301	C₂×#41	C₂²×D₇₉	1	1	yes	characteristic
302	C₂²×D₄	C₂²×D₇₉	1	2	yes	—
303	#137	—	79	2	no	—
304	#137	—	158	1	no	—
305	AGL(1,ℤ/8)	—	2	4	no	—
306	AGL(1,ℤ/8)	—	2	4	no	—
307	AGL(1,ℤ/8)	—	316	2	no	—
308	AGL(1,ℤ/8)	—	79	2	no	—
309	AGL(1,ℤ/8)	—	158	4	no	—
310	AGL(1,ℤ/8)	—	158	1	no	—
311	#135	—	158	2	no	—
312	C₂×SD₁₆	—	2	2	no	—
313	C₂×SD₁₆	—	158	2	no	—
314	C₂×D₈	—	2	2	no	—
315	C₂×D₈	—	2	1	no	—
316	C₂×D₈	—	2	1	no	—
317	C₂×D₈	—	2	1	no	—
318	C₂×D₈	—	2	1	no	—
319	C₂×D₈	—	2	1	no	—
320	C₂×D₈	—	2	1	no	—
321	C₂×D₈	—	158	2	no	—
322	#131	—	2	1	no	—
323	#131	—	2	1	no	—
324	#131	—	316	2	no	—
325	#131	—	158	4	no	—
326	#131	—	158	1	no	—
327	#131	—	158	1	no	—
328	#131	—	158	1	no	—
329	#131	—	158	1	no	—
330	#131	C₂²⋊D₇₉	1	2	yes	—
331	#131	C₂²⋊D₇₉	1	2	yes	—
332	C₂×M₁₆	—	2	1	no	—
333	C₂×M₁₆	—	79	2	no	—
334	C₂×M₁₆	—	79	1	no	—
335	C₂×M₁₆	—	79	1	no	—
336	C₂×M₁₆	—	79	2	no	—
337	C₂×M₁₆	—	158	4	no	—
338	C₂×M₁₆	—	158	1	no	—
339	C₂×M₁₆	C₂²×D₇₉	1	2	yes	—
340	C₂×M₁₆	C₂²×D₇₉	1	1	yes	characteristic
341	C₂²×C₈	—	2	1	no	—
342	C₂²×C₈	—	158	1	no	—
343	C₂²×C₈	C₂²×D₇₉	1	1	yes	characteristic
344	#117	—	79	1	no	—
345	#108	—	2	1	no	—
346	#108	—	2	1	no	—
347	#108	—	79	2	no	—
348	#108	—	79	2	no	—
349	#108	—	158	4	no	—
350	#108	—	158	4	no	—
351	#108	—	158	2	no	—
352	#108	—	158	1	no	—
353	#108	—	158	1	no	—
354	#104	—	158	2	no	—
355	#104	—	158	2	no	—
356	#102	—	316	2	no	—
357	#101	—	158	2	no	—
358	#100	—	2	4	no	—
359	#100	—	158	2	no	—
360	#100	—	158	4	no	—
361	#100	—	158	4	no	—
362	#97	—	158	1	no	—
363	C₄×C₈	—	158	1	no	—
364	C₂⁴	—	2	2	no	—
365	#41	—	2	1	no	—
366	#41	—	2	1	no	—
367	#41	—	158	1	no	—
368	#41	—	158	1	no	—
369	#41	—	158	1	no	—
370	#41	—	158	1	no	—
371	#41	D₄×D₇₉	1	2	yes	—
372	#41	C₂×C₂²⋊D₇₉	1	2	yes	—
373	C₂×Q₈	—	79	1	no	—
374	C₂×Q₈	#11929623	1	1	yes	characteristic
375	C₂×D₄	—	2	1	no	—
376	C₂×D₄	—	2	2	no	—
377	C₂×D₄	—	2	2	no	—
378	C₂×D₄	—	2	2	no	—
379	C₂×D₄	—	2	2	no	—
380	C₂×D₄	—	2	2	no	—
381	C₂×D₄	—	2	2	no	—
382	C₂×D₄	—	79	1	no	—
383	C₂×D₄	—	158	1	no	—
384	C₂×D₄	#11929623	1	1	yes	characteristic
385	C₂²×C₄	—	2	1	no	—
386	C₂²×C₄	—	158	1	no	—
387	C₂²×C₄	C₂³×D₇₉	1	1	yes	characteristic
388	Q₁₆	—	158	2	no	—
389	SD₁₆	—	4	4	no	—
390	SD₁₆	—	316	4	no	—
391	SD₁₆	—	158	2	no	—
392	SD₁₆	—	158	2	no	—
393	D₈	—	4	4	no	—
394	D₈	—	4	1	no	—
395	D₈	—	4	1	no	—
396	D₈	—	4	1	no	—
397	D₈	—	4	1	no	—
398	D₈	—	316	4	no	—
399	D₈	—	158	2	no	—
400	M₁₆	—	2	1	no	—
401	M₁₆	—	2	2	no	—
402	M₁₆	—	2	2	no	—
403	M₁₆	—	2	2	no	—
404	M₁₆	—	2	2	no	—
405	M₁₆	—	316	4	no	—
406	M₁₆	—	316	1	no	—
407	M₁₆	—	316	1	no	—
408	M₁₆	—	79	2	no	—
409	M₁₆	—	79	4	no	—
410	M₁₆	—	158	1	no	—
411	M₁₆	—	158	2	no	—
412	M₁₆	—	158	2	no	—
413	M₁₆	—	158	1	no	—
414	M₁₆	—	158	1	no	—
415	M₁₆	—	158	2	no	—
416	M₁₆	C₂×C₂²⋊D₇₉	1	2	yes	—
417	C₂×C₈	—	2	1	no	—
418	C₂×C₈	—	2	2	no	—
419	C₂×C₈	—	2	2	no	—
420	C₂×C₈	—	2	2	no	—
421	C₂×C₈	—	316	4	no	—
422	C₂×C₈	—	316	1	no	—
423	C₂×C₈	—	316	1	no	—
424	C₂×C₈	—	158	1	no	—
425	C₂×C₈	—	158	2	no	—
426	C₂×C₈	—	158	2	no	—
427	C₂×C₈	—	158	1	no	—
428	C₂×C₈	D₄×D₇₉	1	1	yes	characteristic
429	C₂×C₈	D₄×D₇₉	1	1	yes	characteristic
430	C₂×C₈	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
431	C₂×C₈	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
432	C₂×C₈	#11929623	1	1	yes	characteristic
433	C₂×C₈	#11929623	1	1	yes	characteristic
434	C₄⋊C₄	—	158	1	no	—
435	C₂²⋊C₄	—	158	1	no	—
436	C₄²	—	158	1	no	—
437	C₂³	—	2	1	no	—
438	C₂³	—	4	2	no	—
439	C₂³	—	4	2	no	—
440	C₂³	—	4	2	no	—
441	C₂³	—	16	2	no	—
442	C₂³	—	158	1	no	—
443	C₂³	#14579208	1	1	yes	characteristic
444	Q₈	—	2	1	no	—
445	Q₈	—	158	1	no	—
446	Q₈	—	158	1	no	—
447	Q₈	#14579132	1	2	yes	—
448	D₄	—	2	2	no	—
449	D₄	—	2	2	no	—
450	D₄	—	2	1	no	—
451	D₄	—	4	2	no	—
452	D₄	—	4	2	no	—
453	D₄	—	4	2	no	—
454	D₄	—	4	2	no	—
455	D₄	—	316	1	no	—
456	D₄	—	316	1	no	—
457	D₄	—	158	1	no	—
458	D₄	—	158	1	no	—
459	D₄	#14579132	1	2	yes	—
460	C₂×C₄	—	2	1	no	—
461	C₂×C₄	—	2	2	no	—
462	C₂×C₄	—	2	2	no	—
463	C₂×C₄	—	316	1	no	—
464	C₂×C₄	—	316	1	no	—
465	C₂×C₄	—	316	1	no	—
466	C₂×C₄	—	158	1	no	—
467	C₂×C₄	C₂×D₄×D₇₉	1	1	yes	characteristic
468	C₂×C₄	C₂×D₄×D₇₉	1	1	yes	characteristic
469	C₂×C₄	C₂²×C₂²⋊D₇₉	1	1	yes	characteristic
470	C₂×C₄	C₂×#11929623	1	1	yes	characteristic
471	C₂×C₄	C₂×#11929623	1	1	yes	characteristic
472	C₂×C₄	#14579207	1	1	yes	characteristic
473	C₈	—	2	2	no	—
474	C₈	—	4	2	no	—
475	C₈	—	316	2	no	—
476	C₈	—	316	1	no	—
477	C₈	—	158	4	no	—
478	C₈	—	158	2	no	—
479	C₈	#14579133	1	1	yes	characteristic
480	C₈	#14579133	1	1	yes	characteristic
481	C₈	#14579133	1	1	yes	characteristic
482	C₈	#14579133	1	1	yes	characteristic
483	C₂²	—	2	2	no	—
484	C₂²	—	4	1	no	—
485	C₂²	—	8	1	no	—
486	C₂²	—	8	2	no	—
487	C₂²	—	16	2	no	—
488	C₂²	—	16	2	no	—
489	C₂²	—	16	2	no	—
490	C₂²	—	316	1	no	—
491	C₂²	—	632	1	no	—
492	C₂²	#19099141	1	1	yes	characteristic
493	C₂²	#19099213	1	1	yes	characteristic
494	C₂²	#19099219	1	1	yes	characteristic
495	C₄	—	2	2	no	—
496	C₄	—	316	1	no	—
497	C₄	—	632	1	no	—
498	C₄	C₂×#14579132	1	1	yes	characteristic
499	C₄	C₂×#14579133	1	1	yes	characteristic
500	C₄	#19099197	1	1	yes	characteristic
501	C₄	#19099265	1	1	yes	characteristic
502	C₂	—	2	1	no	—
503	C₂	—	2	1	no	—
504	C₂	—	2	1	no	—
505	C₂	—	4	2	no	—
506	C₂	—	16	2	no	—
507	C₂	—	632	1	no	—
508	C₂	#23766841	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#23766841
commutator, cosocle	C₂²×C₄×C₇₉	C₂⁴
Frattini	C₂²×C₄	C₂³×D₇₉
Fitting	C₂×#472×C₇₉	C₂
socle	C₂×C₇₉	#2416
hypercenter	C₂×#472	D₇₉
hypocenter	C₇₉	#24809
LCS	G ▷ C₂²×C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂ ◁ C₂²×C₄ ◁ C₂×#472

Complements

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

N	H ≅ G/N	type
1. #23773125	C₂	semidirect
2. C₂×#19098830	C₂	semidirect
3. #23772301	C₂	semidirect
4. #23772011	C₂	semidirect
5. #23764798	C₂	semidirect
6. #23764672	C₂	semidirect
7. #23764311	C₂	semidirect
8. #23764188	C₂	semidirect
9. #23763882	C₂	semidirect
10. #23763447	C₂	semidirect
11. C₂×#472×C₇₉	C₂	semidirect
257. C₂×#472	D₇₉	semidirect
266. C₇₉	#24809	semidirect

Maximal subgroups

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

subgroup	index
#23773125	2
C₂×#19098830	2
#23772301	2
#23772011	2
#23764798	2
#23764672	2
#23764311	2
#23764188	2
#23763882	2
#23763447	2
C₂×#472×C₇₉	2
#24809	79