Subgroups — #34180186

Order 20224.

942 conjugacy classes of subgroups.

The subgroup lattice has 548 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#23764353	C₂	1	1	yes	maximal, characteristic, complemented
2	#23763420	C₂	1	1	yes	maximal, characteristic, complemented
3	#23762077	C₂	1	1	yes	maximal, characteristic, complemented
4	#23762072	C₂	1	1	yes	maximal, characteristic, complemented
5	#23761895	C₂	1	1	yes	maximal, characteristic, complemented
6	#23761787	C₂	1	1	yes	maximal, characteristic, complemented
7	C₇₉×#3499	C₂	1	1	yes	maximal, characteristic
8	#19098616	C₂²	1	1	yes	characteristic
9	#19098587	C₂²	1	1	yes	characteristic
10	C₂×C₄⋊(C₇₉⋊C₈)	C₂²	1	1	yes	characteristic
11	C₂×#14579088	—	2	1	no	—
12	C₄×C₄⋊Dic₇₉	C₂²	1	1	yes	characteristic
13	#19098325	—	2	2	no	—
14	#19098322	—	2	1	no	—
15	#19098309	—	2	2	no	—
16	#19098309	—	2	1	no	—
17	#19098307	—	2	1	no	—
18	#19098297	—	2	2	no	—
19	Q₈⋊(C₇₉⋊C₈)	—	2	1	no	—
20	D₄⋊(C₇₉⋊C₈)	—	2	1	no	—
21	C₂×2₋¹⁺⁴×C₇₉	—	2	1	no	—
22	D₄×Q₈×C₇₉	—	2	1	no	—
23	D₄×Q₈×C₇₉	C₄	1	2	yes	complemented
24	#547×C₇₉	—	2	2	no	—
25	#547×C₇₉	—	2	1	no	—
26	#547×C₇₉	—	2	2	no	—
27	#547×C₇₉	C₄	1	2	yes	complemented
28	#536×C₇₉	—	2	2	no	—
29	#536×C₇₉	—	2	1	no	—
30	#532×C₇₉	—	2	1	no	—
31	#532×C₇₉	C₂²	1	1	yes	characteristic
32	C₂×C₄⋊Q₈×C₇₉	—	2	1	no	—
33	C₂×C₄⋊Q₈×C₇₉	C₂²	1	1	yes	characteristic
34	C₄×#41×C₇₉	C₂²	1	1	yes	characteristic
35	C₂×#11929608	—	2	1	no	—
36	C₂²×C₇₉⋊C₈	—	2	1	no	—
37	C₂×C₄⋊Dic₇₉	—	2	1	no	—
38	C₂×C₄×Dic₇₉	—	2	1	no	—
39	C₄⋊(C₇₉⋊C₈)	—	2	1	no	—
40	C₄⋊(C₇₉⋊C₈)	—	2	1	no	—
41	C₄⋊(C₇₉⋊C₈)	—	2	1	no	—
42	C₄⋊(C₇₉⋊C₈)	—	2	1	no	—
43	C₄⋊(C₇₉⋊C₈)	—	2	1	no	—
44	#14579088	—	4	2	no	—
45	C₂²⋊(C₇₉⋊C₈)	—	2	1	no	—
46	C₄×C₇₉⋊C₈	—	2	1	no	—
47	C₇₉⋊#95	—	2	1	no	—
48	2₋¹⁺⁴×C₇₉	—	4	2	no	—
49	2₋¹⁺⁴×C₇₉	—	4	2	no	—
50	2₋¹⁺⁴×C₇₉	—	4	2	no	—
51	2₋¹⁺⁴×C₇₉	—	4	2	no	—
52	C₂×#41×C₇₉	—	2	2	no	—
53	C₂×#41×C₇₉	—	2	4	no	—
54	C₂×#41×C₇₉	—	2	2	no	—
55	C₂×#41×C₇₉	—	2	1	no	—
56	C₂×#41×C₇₉	D₄	1	1	yes	characteristic
57	C₂²×Q₈×C₇₉	—	2	2	no	—
58	C₂²×Q₈×C₇₉	—	2	2	no	—
59	C₂²×Q₈×C₇₉	—	2	1	no	—
60	C₄⋊Q₈×C₇₉	—	2	2	no	—
61	C₄⋊Q₈×C₇₉	—	2	2	no	—
62	C₄⋊Q₈×C₇₉	—	2	2	no	—
63	C₄⋊Q₈×C₇₉	—	2	1	no	—
64	C₄⋊Q₈×C₇₉	—	2	1	no	—
65	C₄⋊Q₈×C₇₉	C₂×C₄	1	2	yes	—
66	C₄⋊Q₈×C₇₉	D₄	1	1	yes	characteristic
67	C₄⋊Q₈×C₇₉	D₄	1	2	yes	—
68	#127×C₇₉	D₄	1	1	yes	characteristic
69	#124×C₇₉	—	2	2	no	—
70	#124×C₇₉	—	2	1	no	—
71	#123×C₇₉	—	2	4	no	—
72	#123×C₇₉	—	2	4	no	—
73	#123×C₇₉	—	2	4	no	—
74	C₂²⋊Q₈×C₇₉	—	2	4	no	—
75	C₂²⋊Q₈×C₇₉	—	2	2	no	—
76	C₂²⋊Q₈×C₇₉	—	2	4	no	—
77	C₂²⋊Q₈×C₇₉	—	2	2	no	—
78	#121×C₇₉	—	2	2	no	—
79	#121×C₇₉	—	2	2	no	—
80	#121×C₇₉	—	2	1	no	—
81	#121×C₇₉	D₄	1	2	yes	—
82	C₄×Q₈×C₇₉	C₂×C₄	1	1	yes	characteristic
83	C₄×Q₈×C₇₉	D₄	1	1	yes	characteristic
84	C₄×D₄×C₇₉	—	2	2	no	—
85	C₄×D₄×C₇₉	—	2	2	no	—
86	C₄×D₄×C₇₉	—	2	1	no	—
87	C₄×D₄×C₇₉	—	2	1	no	—
88	C₄×D₄×C₇₉	—	2	1	no	—
89	C₄×D₄×C₇₉	C₂×C₄	1	1	yes	characteristic
90	C₄×D₄×C₇₉	C₂×C₄	1	2	yes	—
91	C₄×D₄×C₇₉	D₄	1	1	yes	characteristic
92	#117×C₇₉	—	2	1	no	—
93	#117×C₇₉	D₄	1	1	yes	characteristic
94	C₂×C₄⋊C₄×C₇₉	—	2	2	no	—
95	C₂×C₄⋊C₄×C₇₉	—	2	1	no	—
96	C₂×C₄⋊C₄×C₇₉	—	2	2	no	—
97	C₂×C₄⋊C₄×C₇₉	D₄	1	2	yes	—
98	C₂×C₄²×C₇₉	—	2	1	no	—
99	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
100	C₂²×Dic₇₉	—	4	1	no	—
101	#11929608	—	4	1	no	—
102	#11929608	—	4	1	no	—
103	C₂×C₇₉⋊C₈	—	4	2	no	—
104	C₂×C₇₉⋊C₈	—	4	1	no	—
105	C₂×C₇₉⋊C₈	—	4	1	no	—
106	C₂×C₇₉⋊C₈	—	4	1	no	—
107	C₄⋊Dic₇₉	—	2	2	no	—
108	C₄⋊Dic₇₉	—	4	1	no	—
109	C₄×Dic₇₉	—	4	1	no	—
110	C₄×Dic₇₉	—	4	1	no	—
111	#41×C₇₉	—	2	1	no	—
112	#41×C₇₉	—	2	1	no	—
113	#41×C₇₉	—	4	4	no	—
114	#41×C₇₉	—	4	4	no	—
115	#41×C₇₉	—	4	8	no	—
116	#41×C₇₉	—	4	8	no	—
117	#41×C₇₉	—	4	4	no	—
118	#41×C₇₉	—	4	4	no	—
119	#41×C₇₉	—	4	1	no	—
120	#41×C₇₉	—	4	1	no	—
121	#41×C₇₉	—	4	1	no	—
122	#41×C₇₉	—	4	1	no	—
123	#41×C₇₉	D₈	1	2	yes	—
124	#41×C₇₉	SD₁₆	1	2	yes	—
125	C₂×Q₈×C₇₉	—	2	4	no	—
126	C₂×Q₈×C₇₉	—	2	2	no	—
127	C₂×Q₈×C₇₉	—	2	2	no	—
128	C₂×Q₈×C₇₉	—	2	1	no	—
129	C₂×Q₈×C₇₉	—	4	4	no	—
130	C₂×Q₈×C₇₉	—	4	4	no	—
131	C₂×Q₈×C₇₉	—	4	4	no	—
132	C₂×Q₈×C₇₉	—	4	4	no	—
133	C₂×Q₈×C₇₉	—	4	1	no	—
134	C₂×Q₈×C₇₉	—	4	1	no	—
135	C₂×Q₈×C₇₉	—	4	1	no	—
136	C₂×Q₈×C₇₉	—	4	1	no	—
137	C₂×Q₈×C₇₉	C₂²⋊C₄	1	1	yes	characteristic
138	C₂×D₄×C₇₉	—	2	1	no	—
139	C₂×D₄×C₇₉	—	2	4	no	—
140	C₂×D₄×C₇₉	—	2	2	no	—
141	C₂×D₄×C₇₉	—	2	1	no	—
142	C₂×D₄×C₇₉	—	2	1	no	—
143	C₂×D₄×C₇₉	C₂²⋊C₄	1	1	yes	characteristic
144	C₂×D₄×C₇₉	C₂²⋊C₄	1	2	yes	—
145	C₂²×C₄×C₇₉	—	2	1	no	—
146	C₂²×C₄×C₇₉	—	2	4	no	—
147	C₂²×C₄×C₇₉	—	2	4	no	—
148	C₂²×C₄×C₇₉	—	2	2	no	—
149	C₂²×C₄×C₇₉	—	2	1	no	—
150	C₂²×C₄×C₇₉	—	2	2	no	—
151	C₂²×C₄×C₇₉	—	2	1	no	—
152	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
153	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
154	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
155	C₄⋊C₄×C₇₉	—	2	4	no	—
156	C₄⋊C₄×C₇₉	—	2	4	no	—
157	C₄⋊C₄×C₇₉	—	2	2	no	—
158	C₄⋊C₄×C₇₉	—	2	1	no	—
159	C₄⋊C₄×C₇₉	—	2	1	no	—
160	C₄⋊C₄×C₇₉	—	2	2	no	—
161	C₄⋊C₄×C₇₉	—	2	2	no	—
162	C₄⋊C₄×C₇₉	—	2	1	no	—
163	C₄⋊C₄×C₇₉	C₂²⋊C₄	1	2	yes	—
164	C₄⋊C₄×C₇₉	C₂²⋊C₄	1	4	yes	—
165	C₄⋊C₄×C₇₉	C₂²⋊C₄	1	1	yes	characteristic
166	C₄⋊C₄×C₇₉	C₂²⋊C₄	1	1	yes	characteristic
167	C₂²⋊C₄×C₇₉	—	2	4	no	—
168	C₂²⋊C₄×C₇₉	—	2	4	no	—
169	C₂²⋊C₄×C₇₉	—	2	1	no	—
170	C₂²⋊C₄×C₇₉	—	2	1	no	—
171	C₂²⋊C₄×C₇₉	—	2	2	no	—
172	C₂²⋊C₄×C₇₉	—	2	1	no	—
173	C₂²⋊C₄×C₇₉	—	2	2	no	—
174	C₄²×C₇₉	—	2	1	no	—
175	C₄²×C₇₉	—	2	1	no	—
176	C₄²×C₇₉	—	2	1	no	—
177	C₄²×C₇₉	C₂²×C₄	1	1	yes	characteristic
178	C₄²×C₇₉	C₂×D₄	1	1	yes	characteristic
179	C₄²×C₇₉	C₂×D₄	1	1	yes	characteristic
180	C₄²×C₇₉	C₂×D₄	1	1	yes	characteristic
181	C₂³×C₇₉	—	2	1	no	—
182	C₂³×C₇₉	—	2	2	no	—
183	C₂³×C₇₉	#120	1	1	yes	characteristic
184	Q₈×C₇₉	—	2	1	no	—
185	Q₈×C₇₉	—	4	8	no	—
186	Q₈×C₇₉	—	4	2	no	—
187	Q₈×C₇₉	—	4	2	no	—
188	Q₈×C₇₉	—	4	1	no	—
189	Q₈×C₇₉	—	4	2	no	—
190	Q₈×C₇₉	—	4	1	no	—
191	Q₈×C₇₉	—	4	2	no	—
192	Q₈×C₇₉	#102	1	2	yes	—
193	D₄×C₇₉	—	2	2	no	—
194	D₄×C₇₉	—	2	2	no	—
195	D₄×C₇₉	—	2	1	no	—
196	D₄×C₇₉	—	4	2	no	—
197	D₄×C₇₉	—	4	8	no	—
198	D₄×C₇₉	—	4	2	no	—
199	D₄×C₇₉	—	4	2	no	—
200	D₄×C₇₉	—	4	1	no	—
201	D₄×C₇₉	—	4	1	no	—
202	D₄×C₇₉	—	4	1	no	—
203	D₄×C₇₉	—	4	1	no	—
204	D₄×C₇₉	#102	1	2	yes	—
205	C₂×C₄×C₇₉	—	2	1	no	—
206	C₂×C₄×C₇₉	—	2	2	no	—
207	C₂×C₄×C₇₉	—	2	2	no	—
208	C₂×C₄×C₇₉	—	2	1	no	—
209	C₂×C₄×C₇₉	—	2	1	no	—
210	C₂×C₄×C₇₉	—	2	1	no	—
211	C₂×C₄×C₇₉	—	2	1	no	—
212	C₂×C₄×C₇₉	—	2	4	no	—
213	C₂×C₄×C₇₉	—	2	2	no	—
214	C₂×C₄×C₇₉	—	4	1	no	—
215	C₂×C₄×C₇₉	—	4	2	no	—
216	C₂×C₄×C₇₉	—	4	8	no	—
217	C₂×C₄×C₇₉	—	4	8	no	—
218	C₂×C₄×C₇₉	—	4	2	no	—
219	C₂×C₄×C₇₉	—	4	2	no	—
220	C₂×C₄×C₇₉	—	4	2	no	—
221	C₂×C₄×C₇₉	—	4	2	no	—
222	C₂×C₄×C₇₉	—	4	1	no	—
223	C₂×C₄×C₇₉	—	4	1	no	—
224	C₂×C₄×C₇₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
225	C₂×C₄×C₇₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
226	C₂×C₄×C₇₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
227	C₂×C₄×C₇₉	#120	1	1	yes	characteristic
228	C₂×C₄×C₇₉	#120	1	1	yes	characteristic
229	C₂×C₄×C₇₉	#120	1	1	yes	characteristic
230	C₂×C₄×C₇₉	C₂×D₈	1	1	yes	characteristic
231	C₂×C₄×C₇₉	C₂×SD₁₆	1	1	yes	characteristic
232	C₂×C₄×C₇₉	AGL(1,ℤ/8)	1	1	yes	characteristic
233	C₂×C₄×C₇₉	AGL(1,ℤ/8)	1	1	yes	characteristic
234	C₂×Dic₇₉	—	4	2	no	—
235	C₂×Dic₇₉	—	8	1	no	—
236	C₂×Dic₇₉	—	8	1	no	—
237	C₇₉⋊C₈	—	8	1	no	—
238	C₇₉⋊C₈	—	8	1	no	—
239	C₇₉⋊C₈	—	8	1	no	—
240	C₂²×C₇₉	—	2	1	no	—
241	C₂²×C₇₉	—	2	1	no	—
242	C₂²×C₇₉	—	2	2	no	—
243	C₂²×C₇₉	—	4	1	no	—
244	C₂²×C₇₉	—	4	1	no	—
245	C₂²×C₇₉	—	4	2	no	—
246	C₂²×C₇₉	—	4	2	no	—
247	C₂²×C₇₉	—	4	2	no	—
248	C₂²×C₇₉	#379	1	1	yes	characteristic
249	C₂²×C₇₉	#447	1	1	yes	characteristic
250	C₂²×C₇₉	#450	1	1	yes	characteristic
251	C₄×C₇₉	—	2	1	no	—
252	C₄×C₇₉	—	2	1	no	—
253	C₄×C₇₉	—	2	1	no	—
254	C₄×C₇₉	—	2	2	no	—
255	C₄×C₇₉	—	4	1	no	—
256	C₄×C₇₉	—	4	1	no	—
257	C₄×C₇₉	—	4	4	no	—
258	C₄×C₇₉	—	4	2	no	—
259	C₄×C₇₉	C₂×#102	1	1	yes	characteristic
260	C₄×C₇₉	#418	1	1	yes	characteristic
261	C₄×C₇₉	#447	1	1	yes	characteristic
262	C₄×C₇₉	#450	1	1	yes	characteristic
263	C₄×C₇₉	#454	1	1	yes	characteristic
264	C₄×C₇₉	#456	1	1	yes	characteristic
265	Dic₇₉	—	8	2	no	—
266	#8421	—	79	1	no	maximal, Sylow
267	C₂×C₇₉	—	2	1	no	—
268	C₂×C₇₉	—	2	1	no	—
269	C₂×C₇₉	—	4	2	no	—
270	C₂×C₇₉	—	8	2	no	—
271	C₂×C₇₉	#1786	1	1	yes	characteristic
272	C₂×C₇₉	#1793	1	1	yes	characteristic
273	C₂×C₇₉	#1796	1	1	yes	characteristic
274	#3499	D₇₉	1	1	yes	characteristic
275	#1988	—	79	1	no	—
276	#1806	—	79	1	no	—
277	#1547	—	79	1	no	—
278	#1546	—	79	1	no	—
279	#1502	—	79	1	no	—
280	#1477	—	79	1	no	—
281	C₇₉	#8421	1	1	yes	characteristic, complemented, Sylow
282	C₂×2₋¹⁺⁴	—	2	1	no	—
283	D₄×Q₈	—	2	1	no	—
284	D₄×Q₈	Dic₇₉	1	2	yes	complemented
285	#547	—	2	2	no	—
286	#547	—	2	1	no	—
287	#547	—	2	2	no	—
288	#547	Dic₇₉	1	2	yes	complemented
289	#536	—	2	2	no	—
290	#536	—	2	1	no	—
291	#532	—	2	1	no	—
292	#532	C₂×D₇₉	1	1	yes	characteristic
293	C₂×C₄⋊Q₈	—	2	1	no	—
294	C₂×C₄⋊Q₈	C₂×D₇₉	1	1	yes	characteristic
295	C₄×#41	C₂×D₇₉	1	1	yes	characteristic
296	#431	—	79	1	no	—
297	#423	—	79	1	no	—
298	C₂×C₄⋊C₈	—	79	1	no	—
299	C₂×#104	—	158	1	no	—
300	C₄×C₄⋊C₄	—	79	1	no	—
301	#340	—	158	2	no	—
302	#339	—	158	1	no	—
303	#332	—	158	2	no	—
304	#332	—	158	1	no	—
305	#331	—	158	1	no	—
306	#327	—	158	2	no	—
307	Q₈⋊C₈	—	158	1	no	—
308	D₄⋊C₈	—	158	1	no	—
309	2₋¹⁺⁴	—	4	2	no	—
310	2₋¹⁺⁴	—	4	2	no	—
311	2₋¹⁺⁴	—	4	2	no	—
312	2₋¹⁺⁴	—	4	2	no	—
313	C₂×#41	—	2	2	no	—
314	C₂×#41	—	2	4	no	—
315	C₂×#41	—	2	2	no	—
316	C₂×#41	—	2	1	no	—
317	C₂×#41	C₂²⋊D₇₉	1	1	yes	characteristic
318	C₂²×Q₈	—	2	2	no	—
319	C₂²×Q₈	—	2	2	no	—
320	C₂²×Q₈	—	2	1	no	—
321	C₂×M₁₆	—	158	1	no	—
322	C₂²×C₈	—	158	1	no	—
323	C₄⋊Q₈	—	2	2	no	—
324	C₄⋊Q₈	—	2	2	no	—
325	C₄⋊Q₈	—	2	2	no	—
326	C₄⋊Q₈	—	2	1	no	—
327	C₄⋊Q₈	—	2	1	no	—
328	C₄⋊Q₈	C₂×Dic₇₉	1	2	yes	—
329	C₄⋊Q₈	C₂²⋊D₇₉	1	1	yes	characteristic
330	C₄⋊Q₈	C₂²⋊D₇₉	1	2	yes	—
331	#127	C₂²⋊D₇₉	1	1	yes	characteristic
332	#124	—	2	2	no	—
333	#124	—	2	1	no	—
334	#123	—	2	4	no	—
335	#123	—	2	4	no	—
336	#123	—	2	4	no	—
337	C₂²⋊Q₈	—	2	4	no	—
338	C₂²⋊Q₈	—	2	2	no	—
339	C₂²⋊Q₈	—	2	4	no	—
340	C₂²⋊Q₈	—	2	2	no	—
341	#121	—	2	2	no	—
342	#121	—	2	2	no	—
343	#121	—	2	1	no	—
344	#121	C₂²⋊D₇₉	1	2	yes	—
345	C₄×Q₈	C₂×Dic₇₉	1	1	yes	characteristic
346	C₄×Q₈	C₂²⋊D₇₉	1	1	yes	characteristic
347	C₄×D₄	—	2	2	no	—
348	C₄×D₄	—	2	2	no	—
349	C₄×D₄	—	2	1	no	—
350	C₄×D₄	—	2	1	no	—
351	C₄×D₄	—	2	1	no	—
352	C₄×D₄	C₂×Dic₇₉	1	1	yes	characteristic
353	C₄×D₄	C₂×Dic₇₉	1	2	yes	—
354	C₄×D₄	C₂²⋊D₇₉	1	1	yes	characteristic
355	#117	—	2	1	no	—
356	#117	C₂²⋊D₇₉	1	1	yes	characteristic
357	C₂×C₄⋊C₄	—	2	2	no	—
358	C₂×C₄⋊C₄	—	2	1	no	—
359	C₂×C₄⋊C₄	—	2	2	no	—
360	C₂×C₄⋊C₄	—	158	1	no	—
361	C₂×C₄⋊C₄	C₂²⋊D₇₉	1	2	yes	—
362	C₂×C₄²	—	2	1	no	—
363	C₂×C₄²	—	158	1	no	—
364	C₂×C₄²	C₂²×D₇₉	1	1	yes	characteristic
365	C₄⋊C₈	—	158	1	no	—
366	C₄⋊C₈	—	158	1	no	—
367	C₄⋊C₈	—	158	1	no	—
368	C₄⋊C₈	—	158	1	no	—
369	C₄⋊C₈	—	158	1	no	—
370	#104	—	316	2	no	—
371	C₂²⋊C₈	—	158	1	no	—
372	C₄×C₈	—	158	1	no	—
373	#95	—	158	1	no	—
374	#41	—	2	1	no	—
375	#41	—	2	1	no	—
376	#41	—	4	4	no	—
377	#41	—	4	4	no	—
378	#41	—	4	8	no	—
379	#41	—	4	8	no	—
380	#41	—	4	4	no	—
381	#41	—	4	4	no	—
382	#41	—	4	1	no	—
383	#41	—	4	1	no	—
384	#41	—	4	1	no	—
385	#41	—	4	1	no	—
386	#41	#11929609	1	2	yes	—
387	#41	#11929612	1	2	yes	—
388	C₂×Q₈	—	2	4	no	—
389	C₂×Q₈	—	2	2	no	—
390	C₂×Q₈	—	2	2	no	—
391	C₂×Q₈	—	2	1	no	—
392	C₂×Q₈	—	4	4	no	—
393	C₂×Q₈	—	4	4	no	—
394	C₂×Q₈	—	4	4	no	—
395	C₂×Q₈	—	4	4	no	—
396	C₂×Q₈	—	4	1	no	—
397	C₂×Q₈	—	4	1	no	—
398	C₂×Q₈	—	4	1	no	—
399	C₂×Q₈	—	4	1	no	—
400	C₂×Q₈	C₂²⋊Dic₇₉	1	1	yes	characteristic
401	C₂×D₄	—	2	1	no	—
402	C₂×D₄	—	2	4	no	—
403	C₂×D₄	—	2	2	no	—
404	C₂×D₄	—	2	1	no	—
405	C₂×D₄	—	2	1	no	—
406	C₂×D₄	C₂²⋊Dic₇₉	1	1	yes	characteristic
407	C₂×D₄	C₂²⋊Dic₇₉	1	2	yes	—
408	C₂²×C₄	—	2	1	no	—
409	C₂²×C₄	—	2	4	no	—
410	C₂²×C₄	—	2	4	no	—
411	C₂²×C₄	—	2	2	no	—
412	C₂²×C₄	—	2	1	no	—
413	C₂²×C₄	—	2	2	no	—
414	C₂²×C₄	—	2	1	no	—
415	C₂²×C₄	—	316	1	no	—
416	C₂²×C₄	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
417	C₂²×C₄	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
418	C₂²×C₄	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
419	M₁₆	—	316	1	no	—
420	M₁₆	—	316	1	no	—
421	C₂×C₈	—	316	2	no	—
422	C₂×C₈	—	316	1	no	—
423	C₂×C₈	—	316	1	no	—
424	C₂×C₈	—	316	1	no	—
425	C₄⋊C₄	—	2	4	no	—
426	C₄⋊C₄	—	2	4	no	—
427	C₄⋊C₄	—	2	2	no	—
428	C₄⋊C₄	—	2	1	no	—
429	C₄⋊C₄	—	2	1	no	—
430	C₄⋊C₄	—	2	2	no	—
431	C₄⋊C₄	—	2	2	no	—
432	C₄⋊C₄	—	2	1	no	—
433	C₄⋊C₄	—	316	1	no	—
434	C₄⋊C₄	—	158	2	no	—
435	C₄⋊C₄	C₂²⋊Dic₇₉	1	2	yes	—
436	C₄⋊C₄	C₂²⋊Dic₇₉	1	4	yes	—
437	C₄⋊C₄	C₂²⋊Dic₇₉	1	1	yes	characteristic
438	C₄⋊C₄	C₂²⋊Dic₇₉	1	1	yes	characteristic
439	C₂²⋊C₄	—	2	4	no	—
440	C₂²⋊C₄	—	2	4	no	—
441	C₂²⋊C₄	—	2	1	no	—
442	C₂²⋊C₄	—	2	1	no	—
443	C₂²⋊C₄	—	2	2	no	—
444	C₂²⋊C₄	—	2	1	no	—
445	C₂²⋊C₄	—	2	2	no	—
446	C₄²	—	2	1	no	—
447	C₄²	—	2	1	no	—
448	C₄²	—	2	1	no	—
449	C₄²	—	316	1	no	—
450	C₄²	—	316	1	no	—
451	C₄²	C₂²×Dic₇₉	1	1	yes	characteristic
452	C₄²	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
453	C₄²	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
454	C₄²	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
455	C₂³	—	2	1	no	—
456	C₂³	—	2	2	no	—
457	C₂³	#14579130	1	1	yes	characteristic
458	Q₈	—	2	1	no	—
459	Q₈	—	4	8	no	—
460	Q₈	—	4	1	no	—
461	Q₈	—	4	2	no	—
462	Q₈	—	4	1	no	—
463	Q₈	—	4	2	no	—
464	Q₈	—	4	2	no	—
465	Q₈	—	4	2	no	—
466	Q₈	#14579082	1	2	yes	—
467	D₄	—	2	2	no	—
468	D₄	—	2	2	no	—
469	D₄	—	2	1	no	—
470	D₄	—	4	2	no	—
471	D₄	—	4	8	no	—
472	D₄	—	4	2	no	—
473	D₄	—	4	2	no	—
474	D₄	—	4	1	no	—
475	D₄	—	4	1	no	—
476	D₄	—	4	1	no	—
477	D₄	—	4	1	no	—
478	D₄	#14579082	1	2	yes	—
479	C₂×C₄	—	2	1	no	—
480	C₂×C₄	—	2	2	no	—
481	C₂×C₄	—	2	2	no	—
482	C₂×C₄	—	2	1	no	—
483	C₂×C₄	—	2	1	no	—
484	C₂×C₄	—	2	1	no	—
485	C₂×C₄	—	2	1	no	—
486	C₂×C₄	—	2	4	no	—
487	C₂×C₄	—	2	2	no	—
488	C₂×C₄	—	4	1	no	—
489	C₂×C₄	—	4	2	no	—
490	C₂×C₄	—	4	8	no	—
491	C₂×C₄	—	4	8	no	—
492	C₂×C₄	—	4	2	no	—
493	C₂×C₄	—	4	2	no	—
494	C₂×C₄	—	4	1	no	—
495	C₂×C₄	—	4	1	no	—
496	C₂×C₄	—	4	2	no	—
497	C₂×C₄	—	4	2	no	—
498	C₂×C₄	—	316	2	no	—
499	C₂×C₄	—	632	1	no	—
500	C₂×C₄	—	632	1	no	—
501	C₂×C₄	C₂×C₂²⋊Dic₇₉	1	1	yes	characteristic
502	C₂×C₄	C₂×C₂²⋊Dic₇₉	1	1	yes	characteristic
503	C₂×C₄	C₂×C₂²⋊Dic₇₉	1	1	yes	characteristic
504	C₂×C₄	#14579130	1	1	yes	characteristic
505	C₂×C₄	#14579130	1	1	yes	characteristic
506	C₂×C₄	#14579130	1	1	yes	characteristic
507	C₂×C₄	C₂×#11929609	1	1	yes	characteristic
508	C₂×C₄	C₂×#11929612	1	1	yes	characteristic
509	C₂×C₄	#14579187	1	1	yes	characteristic
510	C₂×C₄	#14579187	1	1	yes	characteristic
511	C₈	—	632	1	no	—
512	C₈	—	632	1	no	—
513	C₈	—	632	1	no	—
514	C₂²	—	2	1	no	—
515	C₂²	—	2	1	no	—
516	C₂²	—	2	2	no	—
517	C₂²	—	4	1	no	—
518	C₂²	—	4	1	no	—
519	C₂²	—	4	2	no	—
520	C₂²	—	4	2	no	—
521	C₂²	—	4	2	no	—
522	C₂²	#19098419	1	1	yes	characteristic
523	C₂²	#19098697	1	1	yes	characteristic
524	C₂²	#19098714	1	1	yes	characteristic
525	C₄	—	2	2	no	—
526	C₄	—	2	1	no	—
527	C₄	—	2	1	no	—
528	C₄	—	2	1	no	—
529	C₄	—	4	4	no	—
530	C₄	—	4	2	no	—
531	C₄	—	4	1	no	—
532	C₄	—	4	1	no	—
533	C₄	—	632	2	no	—
534	C₄	C₂×#14579082	1	1	yes	characteristic
535	C₄	#19098568	1	1	yes	characteristic
536	C₄	#19098697	1	1	yes	characteristic
537	C₄	#19098714	1	1	yes	characteristic
538	C₄	#19098736	1	1	yes	characteristic
539	C₄	#19098746	1	1	yes	characteristic
540	C₂	—	2	1	no	—
541	C₂	—	2	1	no	—
542	C₂	—	4	2	no	—
543	C₂	—	8	2	no	—
544	C₂	#23763331	1	1	yes	characteristic
545	C₂	#23763359	1	1	yes	characteristic
546	C₂	#23763375	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#19098419
commutator	C₄²×C₇₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₇₉
Fitting, prime radical	C₇₉×#3499	C₂
socle	C₂²×C₇₉	#379
cosocle	C₂×C₄²×C₇₉	C₂³
hypercenter	#3499	D₇₉
hypocenter	C₇₉	#8421
LCS	G ▷ C₄²×C₇₉ ▷ C₂²×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #3499

Complements

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

N	H ≅ G/N	type
1. #23764353	C₂	semidirect
2. #23763420	C₂	semidirect
3. #23762077	C₂	semidirect
4. #23762072	C₂	semidirect
5. #23761895	C₂	semidirect
6. #23761787	C₂	semidirect
23. D₄×Q₈×C₇₉	C₄	semidirect
27. #547×C₇₉	C₄	semidirect
281. C₇₉	#8421	semidirect
284. D₄×Q₈	Dic₇₉	semidirect
288. #547	Dic₇₉	semidirect

Maximal subgroups

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

subgroup	index
#23764353	2
#23763420	2
#23762077	2
#23762072	2
#23761895	2
#23761787	2
C₇₉×#3499	2
#8421	79