Subgroups — #2213×D₇₉ #34442645

Order 20224.

790 conjugacy classes of subgroups.

The subgroup lattice has 534 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#509×D₇₉	C₂	1	2	yes	maximal, complemented
2	#493×D₇₉	C₂	1	1	yes	maximal, characteristic, complemented
3	#443×D₇₉	C₂	1	1	yes	maximal, characteristic, complemented
4	#23765477	C₂	1	1	yes	maximal, characteristic, complemented
5	#23765476	C₂	1	1	yes	maximal, characteristic, complemented
6	#23765475	C₂	1	2	yes	maximal, complemented
7	#23765474	C₂	1	2	yes	maximal, complemented
8	#23765473	C₂	1	1	yes	maximal, characteristic, complemented
9	#364×D₇₉	C₂	1	1	yes	maximal, characteristic, complemented
10	#361×D₇₉	C₂	1	2	yes	maximal, complemented
11	C₇₉×#2213	C₂	1	1	yes	maximal, characteristic, complemented
12	#135×D₇₉	C₂²	1	1	yes	characteristic
13	C₂×D₈×D₇₉	—	2	1	no	—
14	C₂×D₈×D₇₉	C₂²	1	2	yes	—
15	#131×D₇₉	—	2	1	no	—
16	#127×D₇₉	—	2	1	no	—
17	#19099001	C₂²	1	2	yes	complemented
18	#19099000	—	2	2	no	—
19	#19098999	C₂²	1	2	yes	complemented
20	#19098998	C₂²	1	2	yes	complemented
21	#19098997	—	2	2	no	—
22	SD₃₂×D₇₉	—	2	2	no	—
23	D₁₆×D₇₉	—	2	2	no	—
24	M₃₂×D₇₉	C₂²	1	2	yes	—
25	#19098940	C₂²	1	1	yes	characteristic, complemented
26	#19098939	—	2	1	no	—
27	#19098938	—	2	1	no	—
28	#19098938	C₂²	1	2	yes	complemented
29	#19098681	C₂²	1	1	yes	characteristic, complemented
30	#19098680	C₂²	1	1	yes	characteristic, complemented
31	#19098679	C₂²	1	1	yes	characteristic, complemented
32	#19098678	—	2	1	no	—
33	#19098677	—	2	1	no	—
34	#108×D₇₉	C₂²	1	1	yes	characteristic
35	#104×D₇₉	—	2	1	no	—
36	C₄×C₈×D₇₉	C₂²	1	1	yes	characteristic
37	#19098384	C₂²	1	1	yes	characteristic, complemented
38	#19098383	C₂²	1	2	yes	complemented
39	#19098377	C₂²	1	2	yes	complemented
40	#19098376	C₂²	1	2	yes	complemented
41	#19098375	C₂²	1	2	yes	complemented
42	#509×C₇₉	C₂²	1	2	yes	complemented
43	#493×C₇₉	C₂²	1	1	yes	characteristic, complemented
44	#443×C₇₉	C₂²	1	1	yes	characteristic, complemented
45	#364×C₇₉	C₂²	1	1	yes	characteristic, complemented
46	#361×C₇₉	C₂²	1	2	yes	complemented
47	#41×D₇₉	—	2	1	no	—
48	C₂×D₄×D₇₉	—	2	2	no	—
49	C₂×D₄×D₇₉	—	4	2	no	—
50	#14579184	D₄	1	1	yes	characteristic, complemented
51	#14579183	C₂³	1	1	yes	characteristic
52	#14579182	—	2	1	no	—
53	#14579181	—	2	1	no	—
54	#14579180	D₄	1	1	yes	characteristic, complemented
55	Q₁₆×D₇₉	D₄	1	1	yes	characteristic, complemented
56	SD₁₆×D₇₉	—	2	1	no	—
57	C₂×D₆₃₂	—	2	1	no	—
58	C₂×D₆₃₂	C₂³	1	2	yes	—
59	C₂×#11929609	—	2	2	no	—
60	C₂×#11929609	—	2	2	no	—
61	D₈×D₇₉	—	2	2	no	—
62	D₈×D₇₉	—	2	2	no	—
63	D₈×D₇₉	—	2	2	no	—
64	D₈×D₇₉	—	2	2	no	—
65	D₈×D₇₉	—	4	1	no	—
66	D₈×D₇₉	—	4	1	no	—
67	D₈×D₇₉	—	4	1	no	—
68	D₈×D₇₉	—	4	1	no	—
69	D₈×D₇₉	D₄	1	1	yes	characteristic, complemented
70	#14579169	—	2	1	no	—
71	#14579169	—	4	1	no	—
72	#14579168	—	2	1	no	—
73	#14579167	—	2	1	no	—
74	#14579167	—	4	1	no	—
75	M₁₆×D₇₉	—	2	1	no	—
76	M₁₆×D₇₉	—	4	1	no	—
77	C₂×C₈×D₇₉	—	4	1	no	—
78	C₂×C₈×D₇₉	D₄	1	1	yes	characteristic
79	C₂×C₈×D₇₉	C₂³	1	1	yes	characteristic
80	#14579158	—	2	1	no	—
81	#14579157	—	2	2	no	—
82	#14579157	—	4	2	no	—
83	C₄²×D₇₉	D₄	1	1	yes	characteristic
84	#14579106	—	2	2	no	—
85	#14579105	—	2	2	no	—
86	#14579104	—	2	2	no	—
87	D₁₂₆₄	—	2	2	no	—
88	#14579102	—	2	2	no	—
89	#14579102	—	2	2	no	—
90	#14579101	C₂³	1	2	yes	—
91	#14579100	—	2	2	no	—
92	C₁₆×D₇₉	—	2	2	no	—
93	#14579097	C₂³	1	1	yes	characteristic
94	#14579096	—	2	1	no	—
95	#14579089	—	2	1	no	—
96	#14579088	—	2	1	no	—
97	#14579087	—	2	1	no	—
98	C₄×C₇₉⋊C₈	D₄	1	1	yes	characteristic
99	C₈×Dic₇₉	D₄	1	1	yes	characteristic
100	C₈×Dic₇₉	C₂³	1	1	yes	characteristic
101	#135×C₇₉	C₂³	1	1	yes	characteristic
102	C₂×D₈×C₇₉	—	2	1	no	—
103	C₂×D₈×C₇₉	C₂³	1	2	yes	—
104	#131×C₇₉	—	2	1	no	—
105	#127×C₇₉	—	2	1	no	—
106	SD₃₂×C₇₉	—	2	2	no	—
107	D₁₆×C₇₉	—	2	2	no	—
108	M₃₂×C₇₉	C₂³	1	2	yes	—
109	#108×C₇₉	C₂³	1	1	yes	characteristic
110	#104×C₇₉	—	2	1	no	—
111	C₄×C₈×C₇₉	C₂³	1	1	yes	characteristic
112	C₂³×D₇₉	—	4	2	no	—
113	#11929625	—	2	1	no	—
114	#11929624	—	2	1	no	—
115	#11929624	—	4	1	no	—
116	#11929623	—	2	1	no	—
117	#11929623	—	4	1	no	—
118	Q₈×D₇₉	—	2	1	no	—
119	C₂×D₃₁₆	—	2	2	no	—
120	C₂×D₃₁₆	—	4	2	no	—
121	C₂×C₂²⋊D₇₉	—	4	4	no	—
122	C₂×C₂²⋊D₇₉	—	4	2	no	—
123	D₄×D₇₉	—	2	1	no	—
124	D₄×D₇₉	—	4	1	no	—
125	D₄×D₇₉	—	4	2	no	—
126	D₄×D₇₉	—	4	2	no	—
127	D₄×D₇₉	—	4	2	no	—
128	D₄×D₇₉	—	4	2	no	—
129	D₄×D₇₉	—	8	8	no	—
130	C₂×C₄×D₇₉	—	2	1	no	—
131	C₂×C₄×D₇₉	—	4	1	no	—
132	C₂×C₄×D₇₉	C₂×D₄	1	1	yes	characteristic
133	Dic₃₁₆	C₂×D₄	1	1	yes	characteristic, complemented
134	#11929614	—	2	1	no	—
135	#11929613	—	2	1	no	—
136	#11929612	—	2	1	no	—
137	#11929611	—	2	1	no	—
138	D₆₃₂	—	2	2	no	—
139	D₆₃₂	—	2	2	no	—
140	D₆₃₂	—	4	1	no	—
141	D₆₃₂	—	4	1	no	—
142	D₆₃₂	C₂×D₄	1	1	yes	characteristic, complemented
143	#11929609	—	2	1	no	—
144	#11929609	—	4	2	no	—
145	#11929609	—	4	2	no	—
146	#11929609	—	4	2	no	—
147	#11929609	—	4	2	no	—
148	#11929608	—	2	1	no	—
149	#11929608	—	4	1	no	—
150	#11929607	—	4	1	no	—
151	#11929607	—	4	1	no	—
152	#11929607	—	4	1	no	—
153	C₂×C₇₉⋊C₈	—	4	1	no	—
154	C₂×C₇₉⋊C₈	C₂×D₄	1	1	yes	characteristic
155	C₂×C₇₉⋊C₈	C₂×D₄	1	1	yes	characteristic
156	C₈×D₇₉	—	4	1	no	—
157	C₈×D₇₉	—	4	1	no	—
158	C₈×D₇₉	—	4	1	no	—
159	C₈×D₇₉	D₈	1	1	yes	characteristic
160	C₈×D₇₉	D₈	1	1	yes	characteristic
161	C₈×D₇₉	D₈	1	1	yes	characteristic
162	C₈×D₇₉	D₈	1	1	yes	characteristic
163	C₈×D₇₉	C₂×D₄	1	1	yes	characteristic
164	C₈×D₇₉	C₂×D₄	1	1	yes	characteristic
165	C₈×D₇₉	#41	1	1	yes	characteristic
166	C₈×D₇₉	#41	1	1	yes	characteristic
167	C₄×Dic₇₉	—	2	1	no	—
168	C₄×Dic₇₉	C₂×D₄	1	1	yes	characteristic
169	C₇₉⋊C₁₆	—	2	2	no	—
170	#41×C₇₉	—	2	1	no	—
171	C₂×D₄×C₇₉	—	2	2	no	—
172	C₂×D₄×C₇₉	—	4	2	no	—
173	Q₁₆×C₇₉	C₂×D₄	1	1	yes	characteristic, complemented
174	SD₁₆×C₇₉	—	2	1	no	—
175	D₈×C₇₉	—	2	2	no	—
176	D₈×C₇₉	—	2	2	no	—
177	D₈×C₇₉	—	4	1	no	—
178	D₈×C₇₉	—	4	1	no	—
179	D₈×C₇₉	C₂×D₄	1	1	yes	characteristic, complemented
180	M₁₆×C₇₉	—	2	1	no	—
181	M₁₆×C₇₉	—	4	1	no	—
182	C₂×C₈×C₇₉	—	4	1	no	—
183	C₂×C₈×C₇₉	C₂×D₄	1	1	yes	characteristic
184	C₂×C₈×C₇₉	C₂⁴	1	1	yes	characteristic
185	C₄²×C₇₉	C₂×D₄	1	1	yes	characteristic
186	C₁₆×C₇₉	—	2	2	no	—
187	C₂³×C₇₉	—	4	2	no	—
188	C₂²×D₇₉	—	4	1	no	—
189	C₂²×D₇₉	—	4	2	no	—
190	C₂²×D₇₉	—	8	8	no	—
191	C₂²×D₇₉	—	8	2	no	—
192	C₂²×D₇₉	—	8	2	no	—
193	C₂²×D₇₉	AGL(1,ℤ/8)	1	1	yes	characteristic
194	Q₈×C₇₉	—	2	1	no	—
195	D₄×C₇₉	—	2	1	no	—
196	D₄×C₇₉	—	4	1	no	—
197	D₄×C₇₉	—	4	2	no	—
198	D₄×C₇₉	—	4	2	no	—
199	D₄×C₇₉	—	8	4	no	—
200	C₂×C₄×C₇₉	—	2	1	no	—
201	C₂×C₄×C₇₉	—	4	1	no	—
202	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
203	C₂²⋊D₇₉	—	4	1	no	—
204	C₂²⋊D₇₉	—	4	1	no	—
205	C₂²⋊D₇₉	—	4	1	no	—
206	C₂²⋊D₇₉	—	8	8	no	—
207	C₂²⋊D₇₉	—	8	2	no	—
208	C₂²⋊D₇₉	—	8	2	no	—
209	C₂×Dic₇₉	—	2	1	no	—
210	C₂×Dic₇₉	—	4	1	no	—
211	C₂×Dic₇₉	AGL(1,ℤ/8)	1	1	yes	characteristic
212	D₃₁₆	—	2	1	no	—
213	D₃₁₆	—	4	1	no	—
214	D₃₁₆	—	4	2	no	—
215	D₃₁₆	—	4	2	no	—
216	D₃₁₆	—	8	4	no	—
217	C₄×D₇₉	—	2	4	no	—
218	C₄×D₇₉	—	4	1	no	—
219	C₄×D₇₉	—	4	1	no	—
220	C₄×D₇₉	—	4	1	no	—
221	C₄×D₇₉	#121	1	1	yes	characteristic
222	C₄×D₇₉	#121	1	1	yes	characteristic
223	C₄×D₇₉	C₂×D₈	1	1	yes	characteristic
224	C₄×D₇₉	C₂×D₈	1	1	yes	characteristic
225	Dic₁₅₈	—	2	1	no	—
226	Dic₁₅₈	—	4	1	no	—
227	C₈×C₇₉	—	4	1	no	—
228	C₈×C₇₉	C₂×D₈	1	1	yes	characteristic
229	C₈×C₇₉	C₂×D₈	1	1	yes	characteristic
230	C₈×C₇₉	C₂²×D₄	1	1	yes	characteristic
231	C₈×C₇₉	C₂×#41	1	1	yes	characteristic
232	C₇₉⋊C₈	—	4	1	no	—
233	C₇₉⋊C₈	#121	1	1	yes	characteristic
234	C₇₉⋊C₈	#121	1	1	yes	characteristic
235	C₇₉⋊C₈	C₂×D₈	1	1	yes	characteristic
236	C₇₉⋊C₈	C₂×D₈	1	1	yes	characteristic
237	C₂²×C₇₉	—	4	1	no	—
238	C₂²×C₇₉	—	8	4	no	—
239	C₂²×C₇₉	—	8	2	no	—
240	C₂²×C₇₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
241	C₂×D₇₉	—	2	2	no	—
242	C₂×D₇₉	—	4	1	no	—
243	C₂×D₇₉	—	8	2	no	—
244	C₂×D₇₉	—	8	4	no	—
245	C₂×D₇₉	—	8	2	no	—
246	C₂×D₇₉	—	16	4	no	—
247	C₂×D₇₉	—	16	4	no	—
248	C₂×D₇₉	#459	1	1	yes	characteristic
249	C₂×D₇₉	#459	1	1	yes	characteristic
250	C₄×C₇₉	—	2	2	no	—
251	C₄×C₇₉	—	4	1	no	—
252	C₄×C₇₉	C₂×#121	1	1	yes	characteristic
253	C₄×C₇₉	C₂²×D₈	1	1	yes	characteristic
254	Dic₇₉	—	2	2	no	—
255	Dic₇₉	—	4	1	no	—
256	Dic₇₉	#459	1	1	yes	characteristic
257	Dic₇₉	#459	1	1	yes	characteristic
258	C₂×#2213	—	79	1	no	maximal, Sylow
259	C₂×C₇₉	—	2	1	no	—
260	C₂×C₇₉	—	8	1	no	—
261	C₂×C₇₉	—	16	2	no	—
262	C₂×C₇₉	C₂×#459	1	1	yes	characteristic
263	D₇₉	—	2	1	no	—
264	D₇₉	—	8	1	no	—
265	D₇₉	—	16	2	no	—
266	D₇₉	#2213	1	2	yes	direct product factor
267	C₂×#509	—	79	2	no	—
268	C₂×#493	—	79	1	no	—
269	C₂×#443	—	79	1	no	—
270	#2213	—	79	2	no	—
271	#2213	—	79	1	no	—
272	#2213	—	79	1	no	—
273	#2213	—	79	1	no	—
274	#2213	—	79	2	no	—
275	#2213	D₇₉	1	1	yes	characteristic, direct product factor
276	C₂×#364	—	79	1	no	—
277	C₂×#361	—	79	2	no	—
278	C₇₉	C₂×#2213	1	1	yes	characteristic, complemented, Sylow
279	C₂×#135	—	79	1	no	—
280	C₂²×D₈	—	79	2	no	—
281	C₂²×D₈	—	158	1	no	—
282	C₂×#131	—	158	1	no	—
283	C₂×#127	—	158	1	no	—
284	#509	—	79	2	no	—
285	#509	—	79	2	no	—
286	#509	—	79	2	no	—
287	#509	—	158	2	no	—
288	#509	—	158	2	no	—
289	#509	C₂×D₇₉	1	2	yes	complemented
290	C₂×SD₃₂	—	158	2	no	—
291	C₂×D₁₆	—	158	2	no	—
292	C₂×M₃₂	—	79	2	no	—
293	#493	—	79	2	no	—
294	#493	—	79	1	no	—
295	#493	—	158	1	no	—
296	#493	—	158	1	no	—
297	#493	C₂×D₇₉	1	1	yes	characteristic, complemented
298	#443	—	79	1	no	—
299	#443	—	79	1	no	—
300	#443	—	79	1	no	—
301	#443	—	158	1	no	—
302	#443	—	158	1	no	—
303	#443	C₂×D₇₉	1	1	yes	characteristic, complemented
304	C₂×#108	—	79	1	no	—
305	C₂×#104	—	158	1	no	—
306	C₂×C₄×C₈	—	79	1	no	—
307	#364	—	79	2	no	—
308	#364	—	79	1	no	—
309	#364	C₂×D₇₉	1	1	yes	characteristic, complemented
310	#361	—	79	2	no	—
311	#361	—	79	2	no	—
312	#361	—	79	2	no	—
313	#361	C₂×D₇₉	1	2	yes	complemented
314	C₂×#41	—	158	1	no	—
315	C₂²×D₄	—	316	2	no	—
316	C₂²×D₄	—	158	2	no	—
317	#135	—	79	1	no	—
318	#135	—	79	1	no	—
319	#135	—	79	1	no	—
320	#135	—	158	1	no	—
321	#135	—	158	1	no	—
322	#135	C₂²×D₇₉	1	1	yes	characteristic
323	C₂×Q₁₆	—	79	1	no	—
324	C₂×SD₁₆	—	158	1	no	—
325	C₂×D₈	—	2	1	no	—
326	C₂×D₈	—	316	1	no	—
327	C₂×D₈	—	316	1	no	—
328	C₂×D₈	—	316	1	no	—
329	C₂×D₈	—	316	1	no	—
330	C₂×D₈	—	79	1	no	—
331	C₂×D₈	—	79	2	no	—
332	C₂×D₈	—	158	2	no	—
333	C₂×D₈	—	158	2	no	—
334	C₂×D₈	—	158	2	no	—
335	C₂×D₈	—	158	2	no	—
336	C₂×D₈	—	158	2	no	—
337	C₂×D₈	—	158	2	no	—
338	C₂×D₈	—	158	1	no	—
339	C₂×D₈	C₂²×D₇₉	1	2	yes	—
340	#131	—	2	1	no	—
341	#131	—	316	1	no	—
342	#131	—	316	1	no	—
343	#131	—	158	1	no	—
344	#131	—	158	1	no	—
345	#131	—	158	1	no	—
346	C₂×M₁₆	—	316	1	no	—
347	C₂×M₁₆	—	158	1	no	—
348	C₂²×C₈	—	316	1	no	—
349	C₂²×C₈	—	79	1	no	—
350	C₂²×C₈	—	79	1	no	—
351	#127	—	2	1	no	—
352	#127	—	316	2	no	—
353	#127	—	158	2	no	—
354	#127	—	158	1	no	—
355	C₂×C₄²	—	79	1	no	—
356	SD₃₂	—	2	2	no	—
357	SD₃₂	—	158	2	no	—
358	SD₃₂	—	158	2	no	—
359	SD₃₂	—	158	2	no	—
360	D₁₆	—	2	2	no	—
361	D₁₆	—	158	2	no	—
362	D₁₆	—	158	2	no	—
363	D₁₆	—	158	2	no	—
364	M₃₂	—	79	2	no	—
365	M₃₂	—	158	2	no	—
366	M₃₂	C₂²×D₇₉	1	2	yes	—
367	C₂×C₁₆	—	158	2	no	—
368	#108	—	79	1	no	—
369	#108	—	158	1	no	—
370	#108	C₂²×D₇₉	1	1	yes	characteristic
371	#104	—	2	1	no	—
372	#104	—	158	1	no	—
373	#104	—	158	1	no	—
374	#104	—	158	1	no	—
375	C₄×C₈	—	79	1	no	—
376	C₄×C₈	—	79	1	no	—
377	C₄×C₈	—	79	1	no	—
378	C₄×C₈	C₂²×D₇₉	1	1	yes	characteristic
379	C₂⁴	—	316	2	no	—
380	#41	—	2	1	no	—
381	#41	—	316	1	no	—
382	#41	—	316	1	no	—
383	#41	—	158	1	no	—
384	#41	—	158	1	no	—
385	#41	—	158	1	no	—
386	C₂×Q₈	—	158	1	no	—
387	C₂×D₄	—	2	2	no	—
388	C₂×D₄	—	4	2	no	—
389	C₂×D₄	—	316	2	no	—
390	C₂×D₄	—	316	1	no	—
391	C₂×D₄	—	316	2	no	—
392	C₂×D₄	—	316	2	no	—
393	C₂×D₄	—	316	2	no	—
394	C₂×D₄	—	316	2	no	—
395	C₂×D₄	—	316	2	no	—
396	C₂×D₄	—	316	4	no	—
397	C₂×D₄	—	632	8	no	—
398	C₂×D₄	—	158	1	no	—
399	C₂×D₄	—	158	2	no	—
400	C₂²×C₄	—	316	1	no	—
401	C₂²×C₄	—	79	1	no	—
402	C₂²×C₄	—	158	1	no	—
403	Q₁₆	—	79	1	no	—
404	Q₁₆	—	158	1	no	—
405	Q₁₆	D₄×D₇₉	1	1	yes	characteristic, complemented
406	SD₁₆	—	2	1	no	—
407	SD₁₆	—	158	1	no	—
408	SD₁₆	—	158	1	no	—
409	SD₁₆	—	158	1	no	—
410	D₈	—	2	2	no	—
411	D₈	—	2	2	no	—
412	D₈	—	4	1	no	—
413	D₈	—	4	1	no	—
414	D₈	—	316	2	no	—
415	D₈	—	316	2	no	—
416	D₈	—	316	2	no	—
417	D₈	—	316	2	no	—
418	D₈	—	316	1	no	—
419	D₈	—	316	1	no	—
420	D₈	—	79	1	no	—
421	D₈	—	158	1	no	—
422	D₈	—	158	2	no	—
423	D₈	—	158	2	no	—
424	D₈	D₄×D₇₉	1	1	yes	characteristic, complemented
425	M₁₆	—	2	1	no	—
426	M₁₆	—	4	1	no	—
427	M₁₆	—	316	1	no	—
428	M₁₆	—	316	1	no	—
429	M₁₆	—	316	1	no	—
430	M₁₆	—	316	1	no	—
431	M₁₆	—	158	1	no	—
432	C₂×C₈	—	4	1	no	—
433	C₂×C₈	—	316	1	no	—
434	C₂×C₈	—	316	1	no	—
435	C₂×C₈	—	316	1	no	—
436	C₂×C₈	—	316	1	no	—
437	C₂×C₈	—	79	1	no	—
438	C₂×C₈	—	79	1	no	—
439	C₂×C₈	—	79	1	no	—
440	C₂×C₈	—	79	1	no	—
441	C₂×C₈	—	79	1	no	—
442	C₂×C₈	—	79	1	no	—
443	C₂×C₈	—	79	1	no	—
444	C₂×C₈	—	79	1	no	—
445	C₂×C₈	—	79	1	no	—
446	C₂×C₈	—	79	1	no	—
447	C₂×C₈	D₄×D₇₉	1	1	yes	characteristic
448	C₂×C₈	C₂³×D₇₉	1	1	yes	characteristic
449	C₄²	—	79	1	no	—
450	C₄²	—	158	1	no	—
451	C₄²	D₄×D₇₉	1	1	yes	characteristic
452	C₁₆	—	2	2	no	—
453	C₁₆	—	158	2	no	—
454	C₂³	—	4	2	no	—
455	C₂³	—	316	1	no	—
456	C₂³	—	316	2	no	—
457	C₂³	—	79	1	no	—
458	C₂³	—	632	2	no	—
459	C₂³	—	632	2	no	—
460	C₂³	—	632	8	no	—
461	Q₈	—	2	1	no	—
462	Q₈	—	316	1	no	—
463	Q₈	—	158	1	no	—
464	D₄	—	2	1	no	—
465	D₄	—	4	1	no	—
466	D₄	—	4	2	no	—
467	D₄	—	4	2	no	—
468	D₄	—	8	4	no	—
469	D₄	—	316	1	no	—
470	D₄	—	316	1	no	—
471	D₄	—	316	1	no	—
472	D₄	—	316	1	no	—
473	D₄	—	316	2	no	—
474	D₄	—	316	2	no	—
475	D₄	—	632	4	no	—
476	D₄	—	632	2	no	—
477	D₄	—	632	2	no	—
478	D₄	—	632	8	no	—
479	D₄	—	158	1	no	—
480	C₂×C₄	—	2	1	no	—
481	C₂×C₄	—	4	1	no	—
482	C₂×C₄	—	316	1	no	—
483	C₂×C₄	—	316	1	no	—
484	C₂×C₄	—	316	1	no	—
485	C₂×C₄	—	316	1	no	—
486	C₂×C₄	—	79	1	no	—
487	C₂×C₄	—	79	1	no	—
488	C₂×C₄	—	79	1	no	—
489	C₂×C₄	—	79	1	no	—
490	C₂×C₄	—	79	1	no	—
491	C₂×C₄	—	158	4	no	—
492	C₂×C₄	—	158	1	no	—
493	C₂×C₄	C₂×D₄×D₇₉	1	1	yes	characteristic
494	C₈	—	4	1	no	—
495	C₈	—	316	1	no	—
496	C₈	—	79	1	no	—
497	C₈	—	79	1	no	—
498	C₈	—	79	1	no	—
499	C₈	—	79	1	no	—
500	C₈	D₈×D₇₉	1	1	yes	characteristic
501	C₈	D₈×D₇₉	1	1	yes	characteristic
502	C₈	C₂×D₄×D₇₉	1	1	yes	characteristic
503	C₈	#41×D₇₉	1	1	yes	characteristic
504	C₂²	—	4	1	no	—
505	C₂²	—	8	4	no	—
506	C₂²	—	8	2	no	—
507	C₂²	—	316	1	no	—
508	C₂²	—	79	1	no	—
509	C₂²	—	79	1	no	—
510	C₂²	—	632	4	no	—
511	C₂²	—	632	2	no	—
512	C₂²	—	632	2	no	—
513	C₂²	—	158	2	no	—
514	C₂²	—	1264	4	no	—
515	C₂²	—	1264	4	no	—
516	C₂²	AGL(1,ℤ/8)×D₇₉	1	1	yes	characteristic
517	C₄	—	2	2	no	—
518	C₄	—	4	1	no	—
519	C₄	—	316	1	no	—
520	C₄	—	79	1	no	—
521	C₄	—	79	1	no	—
522	C₄	—	158	2	no	—
523	C₄	#121×D₇₉	1	1	yes	characteristic
524	C₄	C₂×D₈×D₇₉	1	1	yes	characteristic
525	C₂	—	2	1	no	—
526	C₂	—	8	1	no	—
527	C₂	—	16	2	no	—
528	C₂	—	79	2	no	—
529	C₂	—	632	1	no	—
530	C₂	—	158	1	no	—
531	C₂	—	1264	2	no	—
532	C₂	#459×D₇₉	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#459×D₇₉
commutator, cosocle	C₂×C₈×C₇₉	C₂⁴
Frattini	C₂×C₈	C₂³×D₇₉
Fitting	C₇₉×#2213	C₂
socle	C₂×C₇₉	C₂×#459
hypercenter	#2213	D₇₉
hypocenter	C₇₉	C₂×#2213
LCS	G ▷ C₂×C₈×C₇₉ ▷ C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₄×C₈ ◁ #2213

Complements

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

N	H ≅ G/N	type
1. #509×D₇₉	C₂	semidirect
2. #493×D₇₉	C₂	semidirect
3. #443×D₇₉	C₂	semidirect
4. #23765477	C₂	semidirect
5. #23765476	C₂	semidirect
6. #23765475	C₂	semidirect
7. #23765474	C₂	semidirect
8. #23765473	C₂	semidirect
9. #364×D₇₉	C₂	semidirect
10. #361×D₇₉	C₂	semidirect
11. C₇₉×#2213	C₂	semidirect
17. #19099001	C₂²	semidirect
19. #19098999	C₂²	semidirect
20. #19098998	C₂²	semidirect
25. #19098940	C₂²	semidirect
28. #19098938	C₂²	semidirect
29. #19098681	C₂²	semidirect
30. #19098680	C₂²	semidirect
31. #19098679	C₂²	semidirect
37. #19098384	C₂²	semidirect
38. #19098383	C₂²	semidirect
39. #19098377	C₂²	semidirect
40. #19098376	C₂²	semidirect
41. #19098375	C₂²	semidirect
42. #509×C₇₉	C₂²	semidirect
43. #493×C₇₉	C₂²	semidirect
44. #443×C₇₉	C₂²	semidirect
45. #364×C₇₉	C₂²	semidirect
46. #361×C₇₉	C₂²	semidirect
50. #14579184	D₄	semidirect
54. #14579180	D₄	semidirect
55. Q₁₆×D₇₉	D₄	semidirect
69. D₈×D₇₉	D₄	semidirect
133. Dic₃₁₆	C₂×D₄	semidirect
142. D₆₃₂	C₂×D₄	semidirect
173. Q₁₆×C₇₉	C₂×D₄	semidirect
179. D₈×C₇₉	C₂×D₄	semidirect
266. D₇₉	#2213	direct (N × H)
275. #2213	D₇₉	direct (N × H)
278. C₇₉	C₂×#2213	semidirect
289. #509	C₂×D₇₉	semidirect
297. #493	C₂×D₇₉	semidirect
303. #443	C₂×D₇₉	semidirect
309. #364	C₂×D₇₉	semidirect
313. #361	C₂×D₇₉	semidirect
405. Q₁₆	D₄×D₇₉	semidirect
424. D₈	D₄×D₇₉	semidirect

Maximal subgroups

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

subgroup	index
#509×D₇₉	2
#493×D₇₉	2
#443×D₇₉	2
#23765477	2
#23765476	2
#23765475	2
#23765474	2
#23765473	2
#364×D₇₉	2
#361×D₇₉	2
C₇₉×#2213	2
C₂×#2213	79

Subgroups — #2213×D79 #34442645

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #2213×D₇₉ #34442645