Subgroups — #3292×D₇₉ #35164490

Order 20224.

2766 conjugacy classes of subgroups.

The subgroup lattice has 622 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#576×D₇₉	C₂	1	4	yes	maximal, complemented
2	#23775200	C₂	1	2	yes	maximal, complemented
3	#23775199	C₂	1	1	yes	maximal, characteristic, complemented
4	#23775198	C₂	1	4	yes	maximal, complemented
5	#23775197	C₂	1	4	yes	maximal, complemented
6	#23775196	C₂	1	4	yes	maximal, complemented
7	#493×D₇₉	C₂	1	1	yes	maximal, characteristic, complemented
8	#472×D₇₉	C₂	1	4	yes	maximal, complemented
9	#453×D₇₉	C₂	1	4	yes	maximal, complemented
10	#443×D₇₉	C₂	1	2	yes	maximal, complemented
11	C₇₉×#3292	C₂	1	1	yes	maximal, characteristic, complemented
12	H(5,𝔽₂)×D₇₉	C₂²	1	4	yes	complemented
13	#19099368	C₂²	1	4	yes	complemented
14	#19099367	—	2	8	no	—
15	#19099367	C₂²	1	8	yes	complemented
16	#19099366	C₂²	1	8	yes	complemented
17	#19099365	—	2	4	no	—
18	#19099365	C₂²	1	4	yes	complemented
19	#19099364	—	2	4	no	—
20	#19099364	C₂²	1	4	yes	complemented
21	AGL(1,ℤ/8)×D₇₉	—	2	8	no	—
22	AGL(1,ℤ/8)×D₇₉	C₂²	1	8	yes	complemented
23	#135×D₇₉	—	2	4	no	—
24	#135×D₇₉	C₂²	1	2	yes	—
25	C₂×D₈×D₇₉	—	2	4	no	—
26	C₂×D₈×D₇₉	C₂²	1	4	yes	complemented
27	#131×D₇₉	C₂²	1	4	yes	complemented
28	#127×D₇₉	C₂²	1	2	yes	complemented
29	#19098940	C₂²	1	1	yes	characteristic, complemented
30	#19098939	C₂²	1	2	yes	complemented
31	#19098938	C₂²	1	4	yes	complemented
32	#19098834	C₂²	1	4	yes	complemented
33	#19098833	C₂²	1	4	yes	complemented
34	#19098832	C₂²	1	8	yes	complemented
35	#19098831	C₂²	1	8	yes	complemented
36	#19098830	C₂²	1	4	yes	complemented
37	#19098733	C₂²	1	4	yes	complemented
38	#19098732	C₂²	1	8	yes	complemented
39	#19098731	C₂²	1	4	yes	complemented
40	#19098730	C₂²	1	4	yes	complemented
41	#19098729	C₂²	1	8	yes	complemented
42	#19098681	C₂²	1	2	yes	complemented
43	#19098680	C₂²	1	2	yes	complemented
44	#19098679	C₂²	1	2	yes	complemented
45	#19098678	C₂²	1	4	yes	complemented
46	#19098677	C₂²	1	4	yes	complemented
47	#108×D₇₉	C₂²	1	2	yes	complemented
48	#104×D₇₉	C₂²	1	4	yes	complemented
49	#100×D₇₉	C₂²	1	4	yes	complemented
50	C₄×C₈×D₇₉	C₂²	1	1	yes	characteristic, complemented
51	#576×C₇₉	C₂²	1	4	yes	complemented
52	#493×C₇₉	C₂²	1	1	yes	characteristic, complemented
53	#472×C₇₉	C₂²	1	4	yes	complemented
54	#453×C₇₉	C₂²	1	4	yes	complemented
55	#443×C₇₉	C₂²	1	2	yes	complemented
56	#14579207	—	2	8	no	—
57	#14579207	C₂³	1	8	yes	complemented
58	#14579206	—	2	8	no	—
59	#14579206	—	4	4	no	—
60	#14579206	C₂³	1	4	yes	complemented
61	#41×D₇₉	—	2	8	no	—
62	#41×D₇₉	C₂³	1	4	yes	—
63	C₂×D₄×D₇₉	—	2	8	no	—
64	C₂×D₄×D₇₉	—	4	2	no	—
65	C₂×D₄×D₇₉	—	4	4	no	—
66	C₂×D₄×D₇₉	C₂³	1	4	yes	—
67	#14579189	—	2	8	no	—
68	#14579189	C₂³	1	8	yes	complemented
69	#14579188	—	2	8	no	—
70	#14579188	—	2	8	no	—
71	#14579188	—	2	8	no	—
72	#14579187	—	2	8	no	—
73	#14579187	C₂³	1	8	yes	complemented
74	#14579186	—	2	8	no	—
75	#14579186	C₂³	1	8	yes	complemented
76	#14579185	—	2	8	no	—
77	#14579185	—	2	8	no	—
78	#14579185	—	2	8	no	—
79	#14579184	—	2	4	no	—
80	#14579184	D₄	1	2	yes	complemented
81	#14579183	—	2	4	no	—
82	#14579183	C₂³	1	2	yes	—
83	#14579182	—	2	8	no	—
84	#14579182	D₄	1	4	yes	complemented
85	#14579181	—	2	8	no	—
86	#14579181	C₂³	1	4	yes	—
87	#14579180	—	2	4	no	—
88	#14579180	D₄	1	2	yes	complemented
89	Q₁₆×D₇₉	D₄	1	2	yes	complemented
90	SD₁₆×D₇₉	—	2	8	no	—
91	SD₁₆×D₇₉	D₄	1	4	yes	complemented
92	C₂×D₆₃₂	—	2	4	no	—
93	C₂×D₆₃₂	C₂³	1	4	yes	complemented
94	C₂×#11929609	—	2	8	no	—
95	C₂×#11929609	C₂³	1	8	yes	complemented
96	D₈×D₇₉	—	2	4	no	—
97	D₈×D₇₉	—	2	8	no	—
98	D₈×D₇₉	—	2	4	no	—
99	D₈×D₇₉	—	2	8	no	—
100	D₈×D₇₉	—	2	4	no	—
101	D₈×D₇₉	—	2	4	no	—
102	D₈×D₇₉	—	2	4	no	—
103	D₈×D₇₉	—	2	4	no	—
104	D₈×D₇₉	D₄	1	2	yes	complemented
105	#14579169	—	2	4	no	—
106	#14579169	C₂³	1	4	yes	complemented
107	#14579168	C₂³	1	4	yes	complemented
108	#14579167	—	2	4	no	—
109	#14579167	C₂³	1	4	yes	complemented
110	M₁₆×D₇₉	—	2	4	no	—
111	M₁₆×D₇₉	C₂³	1	4	yes	—
112	C₂×C₈×D₇₉	—	2	4	no	—
113	C₂×C₈×D₇₉	C₂³	1	2	yes	—
114	#14579158	C₂³	1	2	yes	complemented
115	#14579157	—	4	2	no	—
116	#14579157	C₂³	1	4	yes	complemented
117	C₄²×D₇₉	C₂³	1	1	yes	characteristic
118	#14579097	C₂³	1	2	yes	complemented
119	#14579096	C₂³	1	4	yes	complemented
120	#14579089	C₂³	1	4	yes	complemented
121	#14579088	C₂³	1	4	yes	complemented
122	#14579087	C₂³	1	4	yes	complemented
123	#14579078	C₂³	1	4	yes	complemented
124	#14579077	C₂³	1	8	yes	complemented
125	C₄×C₇₉⋊C₈	C₂³	1	1	yes	characteristic, complemented
126	C₈×Dic₇₉	C₂³	1	2	yes	complemented
127	H(5,𝔽₂)×C₇₉	C₂³	1	4	yes	complemented
128	AGL(1,ℤ/8)×C₇₉	—	2	8	no	—
129	AGL(1,ℤ/8)×C₇₉	C₂³	1	8	yes	complemented
130	#135×C₇₉	—	2	4	no	—
131	#135×C₇₉	C₂³	1	2	yes	—
132	C₂×D₈×C₇₉	—	2	4	no	—
133	C₂×D₈×C₇₉	C₂³	1	4	yes	complemented
134	#131×C₇₉	C₂³	1	4	yes	complemented
135	#127×C₇₉	C₂³	1	2	yes	complemented
136	#108×C₇₉	C₂³	1	2	yes	complemented
137	#104×C₇₉	C₂³	1	4	yes	complemented
138	#100×C₇₉	C₂³	1	4	yes	complemented
139	C₄×C₈×C₇₉	C₂³	1	1	yes	characteristic, complemented
140	C₂³×D₇₉	—	2	4	no	—
141	C₂³×D₇₉	—	4	4	no	—
142	#11929625	—	2	8	no	—
143	#11929625	C₂×D₄	1	4	yes	—
144	#11929624	—	2	4	no	—
145	#11929624	—	2	8	no	—
146	#11929624	—	4	8	no	—
147	#11929624	C₂⁴	1	4	yes	—
148	#11929623	—	2	4	no	—
149	#11929623	—	2	8	no	—
150	#11929623	—	4	8	no	—
151	#11929623	C₂×D₄	1	4	yes	—
152	Q₈×D₇₉	C₂×D₄	1	4	yes	—
153	C₂×D₃₁₆	—	2	8	no	—
154	C₂×D₃₁₆	—	4	2	no	—
155	C₂×D₃₁₆	—	4	4	no	—
156	C₂×D₃₁₆	C₂⁴	1	4	yes	—
157	C₂×C₂²⋊D₇₉	—	2	4	no	—
158	C₂×C₂²⋊D₇₉	—	4	4	no	—
159	C₂×C₂²⋊D₇₉	—	4	4	no	—
160	C₂×C₂²⋊D₇₉	—	4	8	no	—
161	C₂×C₂²⋊D₇₉	—	4	4	no	—
162	D₄×D₇₉	—	2	4	no	—
163	D₄×D₇₉	—	2	8	no	—
164	D₄×D₇₉	—	2	8	no	—
165	D₄×D₇₉	—	2	8	no	—
166	D₄×D₇₉	—	2	8	no	—
167	D₄×D₇₉	—	4	8	no	—
168	D₄×D₇₉	—	4	8	no	—
169	D₄×D₇₉	—	4	8	no	—
170	D₄×D₇₉	—	4	8	no	—
171	D₄×D₇₉	—	8	8	no	—
172	D₄×D₇₉	C₂×D₄	1	4	yes	—
173	C₂×C₄×D₇₉	—	2	4	no	—
174	C₂×C₄×D₇₉	—	2	1	no	—
175	C₂×C₄×D₇₉	—	4	4	no	—
176	C₂×C₄×D₇₉	C₂⁴	1	1	yes	characteristic
177	Dic₃₁₆	C₂×D₄	1	2	yes	complemented
178	#11929614	C₂×D₄	1	4	yes	complemented
179	#11929613	—	2	8	no	—
180	#11929613	C₂×D₄	1	4	yes	complemented
181	#11929612	—	2	8	no	—
182	#11929612	C₂×D₄	1	4	yes	complemented
183	#11929611	—	2	8	no	—
184	#11929611	C₂×D₄	1	4	yes	complemented
185	D₆₃₂	—	2	8	no	—
186	D₆₃₂	—	2	4	no	—
187	D₆₃₂	—	2	4	no	—
188	D₆₃₂	C₂×D₄	1	2	yes	complemented
189	#11929609	—	2	8	no	—
190	#11929609	—	2	8	no	—
191	#11929609	—	2	8	no	—
192	#11929609	—	2	8	no	—
193	#11929609	C₂×D₄	1	4	yes	complemented
194	#11929608	—	2	4	no	—
195	#11929608	C₂⁴	1	4	yes	—
196	#11929607	—	2	4	no	—
197	#11929607	—	2	4	no	—
198	#11929607	—	2	4	no	—
199	C₂×C₇₉⋊C₈	—	2	4	no	—
200	C₂×C₇₉⋊C₈	C₂⁴	1	2	yes	—
201	C₈×D₇₉	—	2	4	no	—
202	C₈×D₇₉	—	2	4	no	—
203	C₈×D₇₉	—	2	4	no	—
204	C₈×D₇₉	C₂×D₄	1	2	yes	—
205	C₈×D₇₉	C₂×D₄	1	2	yes	—
206	C₈×D₇₉	C₂×D₄	1	2	yes	—
207	C₈×D₇₉	C₂×D₄	1	2	yes	—
208	C₄×Dic₇₉	—	2	1	no	—
209	C₄×Dic₇₉	C₂⁴	1	1	yes	characteristic
210	#41×C₇₉	—	2	8	no	—
211	#41×C₇₉	C₂⁴	1	4	yes	—
212	C₂×D₄×C₇₉	—	2	8	no	—
213	C₂×D₄×C₇₉	—	4	2	no	—
214	C₂×D₄×C₇₉	—	4	4	no	—
215	C₂×D₄×C₇₉	C₂⁴	1	4	yes	—
216	Q₁₆×C₇₉	C₂×D₄	1	2	yes	complemented
217	SD₁₆×C₇₉	—	2	8	no	—
218	SD₁₆×C₇₉	C₂×D₄	1	4	yes	complemented
219	D₈×C₇₉	—	2	4	no	—
220	D₈×C₇₉	—	2	4	no	—
221	D₈×C₇₉	—	2	8	no	—
222	D₈×C₇₉	C₂×D₄	1	2	yes	complemented
223	M₁₆×C₇₉	—	2	4	no	—
224	M₁₆×C₇₉	C₂⁴	1	4	yes	—
225	C₂×C₈×C₇₉	—	2	4	no	—
226	C₂×C₈×C₇₉	C₂⁴	1	2	yes	—
227	C₄²×C₇₉	C₂⁴	1	1	yes	characteristic
228	C₂³×C₇₉	—	2	4	no	—
229	C₂³×C₇₉	—	4	4	no	—
230	C₂²×D₇₉	—	2	4	no	—
231	C₂²×D₇₉	—	2	4	no	—
232	C₂²×D₇₉	—	4	4	no	—
233	C₂²×D₇₉	—	4	8	no	—
234	C₂²×D₇₉	—	4	4	no	—
235	C₂²×D₇₉	—	4	4	no	—
236	C₂²×D₇₉	—	8	8	no	—
237	C₂²×D₇₉	—	16	8	no	—
238	C₂²×D₇₉	H(5,𝔽₂)	1	1	yes	characteristic
239	Q₈×C₇₉	C₂²×D₄	1	4	yes	—
240	D₄×C₇₉	—	2	4	no	—
241	D₄×C₇₉	—	2	8	no	—
242	D₄×C₇₉	—	4	8	no	—
243	D₄×C₇₉	—	8	4	no	—
244	D₄×C₇₉	C₂²×D₄	1	4	yes	—
245	C₂×C₄×C₇₉	—	2	1	no	—
246	C₂×C₄×C₇₉	—	2	4	no	—
247	C₂×C₄×C₇₉	—	4	4	no	—
248	C₂×C₄×C₇₉	C₂⁵	1	1	yes	characteristic
249	C₂²⋊D₇₉	—	2	4	no	—
250	C₂²⋊D₇₉	—	2	4	no	—
251	C₂²⋊D₇₉	—	2	4	no	—
252	C₂²⋊D₇₉	—	4	8	no	—
253	C₂²⋊D₇₉	—	4	8	no	—
254	C₂²⋊D₇₉	—	4	8	no	—
255	C₂²⋊D₇₉	—	8	8	no	—
256	C₂×Dic₇₉	—	2	1	no	—
257	C₂×Dic₇₉	—	2	4	no	—
258	C₂×Dic₇₉	—	4	4	no	—
259	C₂×Dic₇₉	H(5,𝔽₂)	1	1	yes	characteristic
260	D₃₁₆	—	2	4	no	—
261	D₃₁₆	—	2	8	no	—
262	D₃₁₆	—	4	8	no	—
263	D₃₁₆	—	8	4	no	—
264	D₃₁₆	C₂²×D₄	1	4	yes	—
265	C₄×D₇₉	—	2	4	no	—
266	C₄×D₇₉	—	2	4	no	—
267	C₄×D₇₉	—	2	4	no	—
268	C₄×D₇₉	—	2	4	no	—
269	C₄×D₇₉	—	4	8	no	—
270	C₄×D₇₉	C₂²×D₄	1	2	yes	—
271	C₄×D₇₉	C₂²×D₄	1	2	yes	—
272	Dic₁₅₈	—	2	4	no	—
273	Dic₁₅₈	C₂²×D₄	1	4	yes	—
274	C₈×C₇₉	—	2	4	no	—
275	C₈×C₇₉	C₂²×D₄	1	2	yes	—
276	C₈×C₇₉	C₂²×D₄	1	2	yes	—
277	C₇₉⋊C₈	—	2	4	no	—
278	C₇₉⋊C₈	C₂²×D₄	1	2	yes	—
279	C₇₉⋊C₈	C₂²×D₄	1	2	yes	—
280	C₂²×C₇₉	—	2	4	no	—
281	C₂²×C₇₉	—	4	4	no	—
282	C₂²×C₇₉	—	8	4	no	—
283	C₂²×C₇₉	—	16	4	no	—
284	C₂²×C₇₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
285	C₂×D₇₉	—	2	2	no	—
286	C₂×D₇₉	—	2	4	no	—
287	C₂×D₇₉	—	4	8	no	—
288	C₂×D₇₉	—	4	4	no	—
289	C₂×D₇₉	—	8	8	no	—
290	C₂×D₇₉	—	8	4	no	—
291	C₂×D₇₉	—	16	4	no	—
292	C₂×D₇₉	—	16	4	no	—
293	C₂×D₇₉	—	16	8	no	—
294	C₂×D₇₉	D₄²	1	1	yes	characteristic
295	C₂×D₇₉	D₄²	1	1	yes	characteristic
296	C₄×C₇₉	—	2	2	no	—
297	C₄×C₇₉	—	2	4	no	—
298	C₄×C₇₉	C₂³×D₄	1	2	yes	—
299	Dic₇₉	—	2	2	no	—
300	Dic₇₉	—	2	4	no	—
301	Dic₇₉	D₄²	1	2	yes	—
302	C₂×#3292	—	79	1	no	maximal, Sylow
303	C₂×C₇₉	—	2	1	no	—
304	C₂×C₇₉	—	4	4	no	—
305	C₂×C₇₉	—	8	4	no	—
306	C₂×C₇₉	C₂×D₄²	1	1	yes	characteristic
307	D₇₉	—	2	1	no	—
308	D₇₉	—	4	4	no	—
309	D₇₉	—	8	4	no	—
310	D₇₉	#3292	1	2	yes	direct product factor
311	C₂×#576	—	79	4	no	—
312	#3292	—	79	1	no	—
313	#3292	—	79	4	no	—
314	#3292	—	79	4	no	—
315	#3292	—	79	2	no	—
316	#3292	—	79	4	no	—
317	#3292	D₇₉	1	1	yes	characteristic, direct product factor
318	C₂×#493	—	79	1	no	—
319	C₂×#472	—	79	4	no	—
320	C₂×#453	—	79	4	no	—
321	C₂×#443	—	79	2	no	—
322	C₇₉	C₂×#3292	1	1	yes	characteristic, complemented, Sylow
323	C₂×H(5,𝔽₂)	—	79	4	no	—
324	#576	—	79	8	no	—
325	#576	—	79	8	no	—
326	#576	—	79	4	no	—
327	#576	—	79	4	no	—
328	#576	—	79	4	no	—
329	#576	—	158	4	no	—
330	#576	—	158	4	no	—
331	#576	—	158	8	no	—
332	#576	C₂×D₇₉	1	4	yes	complemented
333	C₂×AGL(1,ℤ/8)	—	79	8	no	—
334	C₂×AGL(1,ℤ/8)	—	158	8	no	—
335	C₂×#135	—	79	2	no	—
336	C₂×#135	—	158	4	no	—
337	C₂²×D₈	—	79	4	no	—
338	C₂²×D₈	—	158	4	no	—
339	C₂×#131	—	79	4	no	—
340	C₂×#127	—	79	2	no	—
341	#493	—	79	4	no	—
342	#493	—	79	2	no	—
343	#493	—	79	1	no	—
344	#493	C₂×D₇₉	1	1	yes	characteristic, complemented
345	#472	—	79	8	no	—
346	#472	—	79	4	no	—
347	#472	—	79	4	no	—
348	#472	—	79	4	no	—
349	#472	—	79	8	no	—
350	#472	C₂×D₇₉	1	4	yes	complemented
351	#453	—	79	4	no	—
352	#453	—	79	8	no	—
353	#453	—	79	4	no	—
354	#453	—	79	8	no	—
355	#453	—	79	4	no	—
356	#453	C₂×D₇₉	1	4	yes	complemented
357	#443	—	79	2	no	—
358	#443	—	79	4	no	—
359	#443	—	79	2	no	—
360	#443	—	79	4	no	—
361	#443	—	79	2	no	—
362	#443	C₂×D₇₉	1	2	yes	complemented
363	C₂×#108	—	79	2	no	—
364	C₂×#104	—	79	4	no	—
365	C₂×#100	—	79	4	no	—
366	C₂×C₄×C₈	—	79	1	no	—
367	H(5,𝔽₂)	—	316	4	no	—
368	H(5,𝔽₂)	—	79	8	no	—
369	H(5,𝔽₂)	—	79	4	no	—
370	H(5,𝔽₂)	—	158	8	no	—
371	H(5,𝔽₂)	—	158	8	no	—
372	H(5,𝔽₂)	C₂²×D₇₉	1	4	yes	complemented
373	C₂×#41	—	79	4	no	—
374	C₂×#41	—	158	8	no	—
375	C₂²×D₄	—	316	4	no	—
376	C₂²×D₄	—	316	2	no	—
377	C₂²×D₄	—	79	4	no	—
378	C₂²×D₄	—	158	8	no	—
379	AGL(1,ℤ/8)	—	2	8	no	—
380	AGL(1,ℤ/8)	—	79	8	no	—
381	AGL(1,ℤ/8)	—	79	8	no	—
382	AGL(1,ℤ/8)	—	79	8	no	—
383	AGL(1,ℤ/8)	—	158	8	no	—
384	AGL(1,ℤ/8)	—	158	8	no	—
385	AGL(1,ℤ/8)	—	158	8	no	—
386	AGL(1,ℤ/8)	—	158	8	no	—
387	AGL(1,ℤ/8)	—	158	8	no	—
388	AGL(1,ℤ/8)	—	158	8	no	—
389	AGL(1,ℤ/8)	—	158	8	no	—
390	AGL(1,ℤ/8)	—	158	8	no	—
391	AGL(1,ℤ/8)	—	158	8	no	—
392	AGL(1,ℤ/8)	C₂²×D₇₉	1	8	yes	complemented
393	#135	—	2	4	no	—
394	#135	—	79	4	no	—
395	#135	—	79	2	no	—
396	#135	—	79	4	no	—
397	#135	—	79	2	no	—
398	#135	—	79	2	no	—
399	#135	—	158	4	no	—
400	#135	—	158	4	no	—
401	#135	—	158	8	no	—
402	#135	—	158	8	no	—
403	#135	—	158	4	no	—
404	#135	C₂²×D₇₉	1	2	yes	—
405	C₂×Q₁₆	—	79	2	no	—
406	C₂×SD₁₆	—	79	4	no	—
407	C₂×SD₁₆	—	158	8	no	—
408	C₂×D₈	—	2	4	no	—
409	C₂×D₈	—	79	2	no	—
410	C₂×D₈	—	79	8	no	—
411	C₂×D₈	—	79	4	no	—
412	C₂×D₈	—	158	4	no	—
413	C₂×D₈	—	158	4	no	—
414	C₂×D₈	—	158	4	no	—
415	C₂×D₈	—	158	4	no	—
416	C₂×D₈	—	158	4	no	—
417	C₂×D₈	—	158	8	no	—
418	C₂×D₈	—	158	4	no	—
419	C₂×D₈	—	158	8	no	—
420	C₂×D₈	—	158	8	no	—
421	C₂×D₈	—	158	4	no	—
422	C₂×D₈	C₂²×D₇₉	1	4	yes	complemented
423	#131	—	79	4	no	—
424	#131	—	79	4	no	—
425	#131	—	79	4	no	—
426	#131	—	158	4	no	—
427	#131	—	158	4	no	—
428	#131	C₂²×D₇₉	1	4	yes	complemented
429	C₂×M₁₆	—	79	4	no	—
430	C₂×M₁₆	—	158	4	no	—
431	C₂²×C₈	—	79	2	no	—
432	C₂²×C₈	—	158	4	no	—
433	#127	—	316	2	no	—
434	#127	—	79	4	no	—
435	#127	—	79	2	no	—
436	#127	C₂²×D₇₉	1	2	yes	complemented
437	C₂×C₄²	—	79	1	no	—
438	#108	—	79	4	no	—
439	#108	—	79	2	no	—
440	#108	C₂²×D₇₉	1	2	yes	complemented
441	#104	—	79	4	no	—
442	#104	—	79	4	no	—
443	#104	—	79	4	no	—
444	#104	C₂²×D₇₉	1	4	yes	complemented
445	#100	—	79	4	no	—
446	#100	—	79	8	no	—
447	#100	C₂²×D₇₉	1	4	yes	complemented
448	C₄×C₈	—	79	2	no	—
449	C₄×C₈	—	79	1	no	—
450	C₄×C₈	C₂²×D₇₉	1	1	yes	characteristic, complemented
451	C₂⁴	—	316	4	no	—
452	C₂⁴	—	158	4	no	—
453	#41	—	2	8	no	—
454	#41	—	316	8	no	—
455	#41	—	316	8	no	—
456	#41	—	79	4	no	—
457	#41	—	79	4	no	—
458	#41	—	79	4	no	—
459	#41	—	158	8	no	—
460	#41	—	158	4	no	—
461	#41	—	158	8	no	—
462	#41	—	158	8	no	—
463	#41	—	158	4	no	—
464	#41	C₂³×D₇₉	1	4	yes	—
465	C₂×Q₈	—	79	4	no	—
466	C₂×D₄	—	2	8	no	—
467	C₂×D₄	—	4	2	no	—
468	C₂×D₄	—	4	4	no	—
469	C₂×D₄	—	316	2	no	—
470	C₂×D₄	—	316	4	no	—
471	C₂×D₄	—	316	8	no	—
472	C₂×D₄	—	316	8	no	—
473	C₂×D₄	—	316	4	no	—
474	C₂×D₄	—	316	4	no	—
475	C₂×D₄	—	316	8	no	—
476	C₂×D₄	—	316	8	no	—
477	C₂×D₄	—	316	8	no	—
478	C₂×D₄	—	316	4	no	—
479	C₂×D₄	—	79	4	no	—
480	C₂×D₄	—	79	4	no	—
481	C₂×D₄	—	632	8	no	—
482	C₂×D₄	—	158	8	no	—
483	C₂×D₄	—	158	8	no	—
484	C₂×D₄	—	158	8	no	—
485	C₂×D₄	—	158	4	no	—
486	C₂×D₄	—	158	8	no	—
487	C₂×D₄	—	158	4	no	—
488	C₂×D₄	—	158	8	no	—
489	C₂×D₄	C₂³×D₇₉	1	4	yes	—
490	C₂²×C₄	—	316	4	no	—
491	C₂²×C₄	—	79	1	no	—
492	C₂²×C₄	—	158	4	no	—
493	C₂²×C₄	—	158	1	no	—
494	Q₁₆	—	79	4	no	—
495	Q₁₆	—	79	2	no	—
496	Q₁₆	D₄×D₇₉	1	2	yes	complemented
497	SD₁₆	—	2	8	no	—
498	SD₁₆	—	79	4	no	—
499	SD₁₆	—	79	4	no	—
500	SD₁₆	—	79	4	no	—
501	SD₁₆	—	158	8	no	—
502	SD₁₆	—	158	8	no	—
503	SD₁₆	—	158	8	no	—
504	SD₁₆	D₄×D₇₉	1	4	yes	complemented
505	D₈	—	2	8	no	—
506	D₈	—	2	4	no	—
507	D₈	—	2	4	no	—
508	D₈	—	79	4	no	—
509	D₈	—	79	2	no	—
510	D₈	—	158	8	no	—
511	D₈	—	158	8	no	—
512	D₈	—	158	8	no	—
513	D₈	—	158	8	no	—
514	D₈	—	158	8	no	—
515	D₈	—	158	4	no	—
516	D₈	—	158	4	no	—
517	D₈	D₄×D₇₉	1	2	yes	complemented
518	M₁₆	—	2	4	no	—
519	M₁₆	—	79	4	no	—
520	M₁₆	—	158	4	no	—
521	M₁₆	—	158	4	no	—
522	M₁₆	—	158	4	no	—
523	M₁₆	—	158	4	no	—
524	M₁₆	C₂³×D₇₉	1	4	yes	—
525	C₂×C₈	—	2	4	no	—
526	C₂×C₈	—	79	2	no	—
527	C₂×C₈	—	79	2	no	—
528	C₂×C₈	—	79	2	no	—
529	C₂×C₈	—	79	2	no	—
530	C₂×C₈	—	79	2	no	—
531	C₂×C₈	—	158	4	no	—
532	C₂×C₈	—	158	4	no	—
533	C₂×C₈	—	158	4	no	—
534	C₂×C₈	—	158	4	no	—
535	C₂×C₈	C₂³×D₇₉	1	2	yes	—
536	C₄²	—	79	1	no	—
537	C₄²	—	158	1	no	—
538	C₄²	C₂³×D₇₉	1	1	yes	characteristic
539	C₂³	—	2	4	no	—
540	C₂³	—	4	4	no	—
541	C₂³	—	316	8	no	—
542	C₂³	—	316	4	no	—
543	C₂³	—	316	4	no	—
544	C₂³	—	316	4	no	—
545	C₂³	—	79	1	no	—
546	C₂³	—	632	8	no	—
547	C₂³	—	158	4	no	—
548	C₂³	—	158	4	no	—
549	C₂³	—	1264	8	no	—
550	Q₈	—	79	4	no	—
551	Q₈	—	158	4	no	—
552	Q₈	C₂×D₄×D₇₉	1	4	yes	—
553	D₄	—	2	4	no	—
554	D₄	—	2	8	no	—
555	D₄	—	4	8	no	—
556	D₄	—	8	4	no	—
557	D₄	—	316	8	no	—
558	D₄	—	316	8	no	—
559	D₄	—	316	8	no	—
560	D₄	—	316	8	no	—
561	D₄	—	79	4	no	—
562	D₄	—	632	4	no	—
563	D₄	—	632	8	no	—
564	D₄	—	158	4	no	—
565	D₄	—	158	4	no	—
566	D₄	—	158	4	no	—
567	D₄	—	158	4	no	—
568	D₄	—	158	8	no	—
569	D₄	C₂×D₄×D₇₉	1	4	yes	—
570	C₂×C₄	—	2	1	no	—
571	C₂×C₄	—	2	4	no	—
572	C₂×C₄	—	4	4	no	—
573	C₂×C₄	—	316	8	no	—
574	C₂×C₄	—	316	4	no	—
575	C₂×C₄	—	79	1	no	—
576	C₂×C₄	—	79	2	no	—
577	C₂×C₄	—	79	2	no	—
578	C₂×C₄	—	158	4	no	—
579	C₂×C₄	—	158	4	no	—
580	C₂×C₄	—	158	4	no	—
581	C₂×C₄	—	158	4	no	—
582	C₂×C₄	—	158	1	no	—
583	C₂×C₄	—	158	4	no	—
584	C₂×C₄	C₂⁴×D₇₉	1	1	yes	characteristic
585	C₈	—	2	4	no	—
586	C₈	—	79	2	no	—
587	C₈	—	79	2	no	—
588	C₈	—	158	4	no	—
589	C₈	C₂×D₄×D₇₉	1	2	yes	—
590	C₈	C₂×D₄×D₇₉	1	2	yes	—
591	C₂²	—	2	4	no	—
592	C₂²	—	4	4	no	—
593	C₂²	—	8	4	no	—
594	C₂²	—	16	4	no	—
595	C₂²	—	316	8	no	—
596	C₂²	—	316	4	no	—
597	C₂²	—	79	1	no	—
598	C₂²	—	79	1	no	—
599	C₂²	—	632	4	no	—
600	C₂²	—	632	8	no	—
601	C₂²	—	158	2	no	—
602	C₂²	—	158	4	no	—
603	C₂²	—	1264	8	no	—
604	C₂²	—	1264	4	no	—
605	C₂²	—	1264	4	no	—
606	C₂²	H(5,𝔽₂)×D₇₉	1	1	yes	characteristic
607	C₄	—	2	2	no	—
608	C₄	—	2	4	no	—
609	C₄	—	79	2	no	—
610	C₄	—	158	2	no	—
611	C₄	—	158	4	no	—
612	C₄	C₂²×D₄×D₇₉	1	2	yes	—
613	C₂	—	2	1	no	—
614	C₂	—	4	4	no	—
615	C₂	—	8	4	no	—
616	C₂	—	316	4	no	—
617	C₂	—	79	2	no	—
618	C₂	—	632	4	no	—
619	C₂	—	158	1	no	—
620	C₂	D₄²×D₇₉	1	1	yes	characteristic

	subgroup	G/H
center	C₂	D₄²×D₇₉
commutator, cosocle	C₂×C₄×C₇₉	C₂⁵
Frattini	C₂×C₄	C₂⁴×D₇₉
Fitting	C₇₉×#3292	C₂
socle	C₂×C₇₉	C₂×D₄²
hypercenter	#3292	D₇₉
hypocenter	C₇₉	C₂×#3292
LCS	G ▷ C₂×C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ #3292

Complements

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

N	H ≅ G/N	type
1. #576×D₇₉	C₂	semidirect
2. #23775200	C₂	semidirect
3. #23775199	C₂	semidirect
4. #23775198	C₂	semidirect
5. #23775197	C₂	semidirect
6. #23775196	C₂	semidirect
7. #493×D₇₉	C₂	semidirect
8. #472×D₇₉	C₂	semidirect
9. #453×D₇₉	C₂	semidirect
10. #443×D₇₉	C₂	semidirect
11. C₇₉×#3292	C₂	semidirect
12. H(5,𝔽₂)×D₇₉	C₂²	semidirect
13. #19099368	C₂²	semidirect
15. #19099367	C₂²	semidirect
16. #19099366	C₂²	semidirect
18. #19099365	C₂²	semidirect
20. #19099364	C₂²	semidirect
22. AGL(1,ℤ/8)×D₇₉	C₂²	semidirect
26. C₂×D₈×D₇₉	C₂²	semidirect
27. #131×D₇₉	C₂²	semidirect
28. #127×D₇₉	C₂²	semidirect
29. #19098940	C₂²	semidirect
30. #19098939	C₂²	semidirect
31. #19098938	C₂²	semidirect
32. #19098834	C₂²	semidirect
33. #19098833	C₂²	semidirect
34. #19098832	C₂²	semidirect
35. #19098831	C₂²	semidirect
36. #19098830	C₂²	semidirect
37. #19098733	C₂²	semidirect
38. #19098732	C₂²	semidirect
39. #19098731	C₂²	semidirect
40. #19098730	C₂²	semidirect
41. #19098729	C₂²	semidirect
42. #19098681	C₂²	semidirect
43. #19098680	C₂²	semidirect
44. #19098679	C₂²	semidirect
45. #19098678	C₂²	semidirect
46. #19098677	C₂²	semidirect
47. #108×D₇₉	C₂²	semidirect
48. #104×D₇₉	C₂²	semidirect
49. #100×D₇₉	C₂²	semidirect
50. C₄×C₈×D₇₉	C₂²	semidirect
51. #576×C₇₉	C₂²	semidirect
52. #493×C₇₉	C₂²	semidirect
53. #472×C₇₉	C₂²	semidirect
54. #453×C₇₉	C₂²	semidirect
55. #443×C₇₉	C₂²	semidirect
57. #14579207	C₂³	semidirect
60. #14579206	C₂³	semidirect
68. #14579189	C₂³	semidirect
73. #14579187	C₂³	semidirect
75. #14579186	C₂³	semidirect
80. #14579184	D₄	semidirect
84. #14579182	D₄	semidirect
88. #14579180	D₄	semidirect
89. Q₁₆×D₇₉	D₄	semidirect
91. SD₁₆×D₇₉	D₄	semidirect
93. C₂×D₆₃₂	C₂³	semidirect
95. C₂×#11929609	C₂³	semidirect
104. D₈×D₇₉	D₄	semidirect
106. #14579169	C₂³	semidirect
107. #14579168	C₂³	semidirect
109. #14579167	C₂³	semidirect
114. #14579158	C₂³	semidirect
116. #14579157	C₂³	semidirect
118. #14579097	C₂³	semidirect
119. #14579096	C₂³	semidirect
120. #14579089	C₂³	semidirect
121. #14579088	C₂³	semidirect
122. #14579087	C₂³	semidirect
123. #14579078	C₂³	semidirect
124. #14579077	C₂³	semidirect
125. C₄×C₇₉⋊C₈	C₂³	semidirect
126. C₈×Dic₇₉	C₂³	semidirect
127. H(5,𝔽₂)×C₇₉	C₂³	semidirect
129. AGL(1,ℤ/8)×C₇₉	C₂³	semidirect
133. C₂×D₈×C₇₉	C₂³	semidirect
134. #131×C₇₉	C₂³	semidirect
135. #127×C₇₉	C₂³	semidirect
136. #108×C₇₉	C₂³	semidirect
137. #104×C₇₉	C₂³	semidirect
138. #100×C₇₉	C₂³	semidirect
139. C₄×C₈×C₇₉	C₂³	semidirect
177. Dic₃₁₆	C₂×D₄	semidirect
178. #11929614	C₂×D₄	semidirect
180. #11929613	C₂×D₄	semidirect
182. #11929612	C₂×D₄	semidirect
184. #11929611	C₂×D₄	semidirect
188. D₆₃₂	C₂×D₄	semidirect
193. #11929609	C₂×D₄	semidirect
216. Q₁₆×C₇₉	C₂×D₄	semidirect
218. SD₁₆×C₇₉	C₂×D₄	semidirect
222. D₈×C₇₉	C₂×D₄	semidirect
310. D₇₉	#3292	direct (N × H)
317. #3292	D₇₉	direct (N × H)
322. C₇₉	C₂×#3292	semidirect
332. #576	C₂×D₇₉	semidirect
344. #493	C₂×D₇₉	semidirect
350. #472	C₂×D₇₉	semidirect
356. #453	C₂×D₇₉	semidirect
362. #443	C₂×D₇₉	semidirect
372. H(5,𝔽₂)	C₂²×D₇₉	semidirect
392. AGL(1,ℤ/8)	C₂²×D₇₉	semidirect
422. C₂×D₈	C₂²×D₇₉	semidirect
428. #131	C₂²×D₇₉	semidirect
436. #127	C₂²×D₇₉	semidirect
440. #108	C₂²×D₇₉	semidirect
444. #104	C₂²×D₇₉	semidirect
447. #100	C₂²×D₇₉	semidirect
450. C₄×C₈	C₂²×D₇₉	semidirect
496. Q₁₆	D₄×D₇₉	semidirect
504. SD₁₆	D₄×D₇₉	semidirect
517. 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
#576×D₇₉	2
#23775200	2
#23775199	2
#23775198	2
#23775197	2
#23775196	2
#493×D₇₉	2
#472×D₇₉	2
#453×D₇₉	2
#443×D₇₉	2
C₇₉×#3292	2
C₂×#3292	79

Subgroups — #3292×D79 #35164490

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #3292×D₇₉ #35164490