Subgroups — #34257389

Order 20224.

602 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	#23772514	C₂	1	1	yes	maximal, characteristic
2	#23772509	C₂	1	1	yes	maximal, characteristic
3	#23772039	C₂	1	1	yes	maximal, characteristic
4	#23762191	C₂	1	1	yes	maximal, characteristic, complemented
5	#23762187	C₂	1	1	yes	maximal, characteristic, complemented
6	#23762183	C₂	1	1	yes	maximal, characteristic, complemented
7	#23762182	C₂	1	1	yes	maximal, characteristic, complemented
8	#23762180	C₂	1	1	yes	maximal, characteristic, complemented
9	#23762177	C₂	1	1	yes	maximal, characteristic, complemented
10	#23762169	C₂	1	1	yes	maximal, characteristic, complemented
11	#23762149	C₂	1	1	yes	maximal, characteristic, complemented
12	#23762149	C₂	1	1	yes	maximal, characteristic, complemented
13	#23762145	C₂	1	1	yes	maximal, characteristic, complemented
14	#334×D₇₉	C₂	1	1	yes	maximal, characteristic, complemented
15	C₇₉×#1570	C₂	1	1	yes	maximal, characteristic, complemented
16	C₄×#11929624	C₂²	1	1	yes	characteristic
17	#19098692	—	2	1	no	—
18	#19098687	—	2	1	no	—
19	#19098639	—	2	1	no	—
20	#19098633	—	2	1	no	—
21	#19098632	—	2	1	no	—
22	#19098628	—	2	1	no	—
23	C₈×C₂²⋊D₇₉	—	2	1	no	—
24	C₈×C₂²⋊D₇₉	—	2	1	no	—
25	#19098623	C₄	1	2	yes	—
26	#19098621	C₄	1	2	yes	—
27	#19098620	C₂²	1	1	yes	characteristic
28	#19098619	C₂²	1	1	yes	characteristic
29	#19098616	C₂²	1	1	yes	characteristic
30	#19098616	C₂²	1	1	yes	characteristic
31	#19098615	C₂²	1	1	yes	characteristic
32	#19098615	C₂²	1	1	yes	characteristic
33	#19098615	C₂²	1	1	yes	characteristic
34	#19098614	C₂²	1	1	yes	characteristic
35	#19098614	C₂²	1	1	yes	characteristic
36	#19098588	C₄	1	2	yes	—
37	#19098585	C₂²	1	1	yes	characteristic
38	C₄⋊C₈×D₇₉	C₂²	1	1	yes	characteristic
39	C₄⋊C₈×D₇₉	C₂²	1	1	yes	characteristic
40	C₄⋊C₈×D₇₉	C₂²	1	1	yes	characteristic
41	#19098528	C₄	1	2	yes	—
42	C₄×#11929607	C₂²	1	1	yes	characteristic
43	C₄×C₈×D₇₉	C₂²	1	1	yes	characteristic
44	#19098316	C₂²	1	1	yes	characteristic
45	#19098316	C₂²	1	1	yes	characteristic
46	#19098315	C₂²	1	1	yes	characteristic
47	#19098315	C₂²	1	1	yes	characteristic
48	#19098315	C₂²	1	1	yes	characteristic
49	#19098315	C₂²	1	1	yes	characteristic
50	#19098314	C₂²	1	1	yes	characteristic
51	#19098314	C₂²	1	1	yes	characteristic
52	#19098313	C₂²	1	1	yes	characteristic
53	#19098313	C₂²	1	1	yes	characteristic
54	#19098313	C₂²	1	1	yes	characteristic
55	#19098313	C₂²	1	1	yes	characteristic
56	#431×C₇₉	C₂²	1	1	yes	characteristic
57	#423×C₇₉	C₂²	1	1	yes	characteristic
58	C₂×C₄⋊C₈×C₇₉	C₂²	1	1	yes	characteristic
59	#334×C₇₉	C₂²	1	1	yes	characteristic
60	#334×C₇₉	C₂²	1	1	yes	characteristic
61	#334×C₇₉	C₂²	1	1	yes	characteristic
62	#334×C₇₉	C₂²	1	1	yes	characteristic
63	C₂×#11929624	C₂×C₄	1	1	yes	characteristic
64	C₂×#11929607	—	2	1	no	—
65	C₂×#11929607	C₂×C₄	1	2	yes	—
66	C₂×C₈×D₇₉	—	2	1	no	—
67	C₂×C₈×D₇₉	—	2	1	no	—
68	C₂×C₈×D₇₉	—	2	1	no	—
69	C₂×C₈×D₇₉	C₂×C₄	1	2	yes	—
70	C₄×Dic₁₅₈	D₄	1	1	yes	characteristic
71	C₄×Dic₁₅₈	Q₈	1	1	yes	characteristic
72	C₄×D₃₁₆	D₄	1	1	yes	characteristic
73	C₄×D₃₁₆	Q₈	1	1	yes	characteristic
74	C₄×C₂²⋊D₇₉	D₄	1	1	yes	characteristic
75	C₄×C₂²⋊D₇₉	D₄	1	1	yes	characteristic
76	C₄×C₂²⋊D₇₉	Q₈	1	1	yes	characteristic
77	C₄×C₂²⋊D₇₉	Q₈	1	1	yes	characteristic
78	#14579120	C₂×C₄	1	1	yes	characteristic
79	#14579118	C₂×C₄	1	1	yes	characteristic
80	#14579118	C₂×C₄	1	1	yes	characteristic
81	C₄²×D₇₉	C₂³	1	1	yes	characteristic
82	C₄²×D₇₉	C₂³	1	1	yes	characteristic
83	C₄⋊(C₇₉⋊C₈)	C₂×C₄	1	2	yes	—
84	C₄⋊(C₇₉⋊C₈)	C₂³	1	1	yes	characteristic
85	C₄⋊(C₇₉⋊C₈)	C₂³	1	1	yes	characteristic
86	C₄⋊(C₇₉⋊C₈)	C₂³	1	1	yes	characteristic
87	C₄⋊(C₇₉⋊C₈)	C₂³	1	1	yes	characteristic
88	Dic₇₉⋊C₈	—	2	1	no	—
89	Dic₇₉⋊C₈	—	2	1	no	—
90	Dic₇₉⋊C₈	—	2	1	no	—
91	Dic₇₉⋊C₈	—	2	1	no	—
92	Dic₇₉⋊C₈	C₂×C₄	1	2	yes	—
93	Dic₇₉⋊C₈	C₂×C₄	1	2	yes	—
94	C₂²⋊(C₇₉⋊C₈)	—	2	1	no	—
95	C₂²⋊(C₇₉⋊C₈)	—	2	1	no	—
96	C₂²⋊(C₇₉⋊C₈)	C₂×C₄	1	2	yes	—
97	(C₂×D₇₉)⋊C₈	—	2	1	no	—
98	(C₂×D₇₉)⋊C₈	—	2	1	no	—
99	(C₂×D₇₉)⋊C₈	—	2	1	no	—
100	(C₂×D₇₉)⋊C₈	—	2	1	no	—
101	(C₂×D₇₉)⋊C₈	C₂×C₄	1	2	yes	—
102	(C₂×D₇₉)⋊C₈	C₂×C₄	1	2	yes	—
103	#14579072	—	2	1	no	—
104	#14579071	—	2	1	no	—
105	#14579071	C₂×C₄	1	2	yes	—
106	C₄×C₇₉⋊C₈	—	2	1	no	—
107	C₄×C₇₉⋊C₈	C₂³	1	1	yes	characteristic
108	C₄×C₇₉⋊C₈	C₂³	1	1	yes	characteristic
109	C₈×Dic₇₉	—	2	1	no	—
110	C₈×Dic₇₉	—	2	1	no	—
111	C₈×Dic₇₉	—	2	1	no	—
112	C₈×Dic₇₉	C₂×C₄	1	2	yes	—
113	C₂×M₁₆×C₇₉	—	2	1	no	—
114	C₂²×C₈×C₇₉	—	2	1	no	—
115	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
116	C₄⋊C₈×C₇₉	—	2	1	no	—
117	C₄⋊C₈×C₇₉	—	2	1	no	—
118	C₄⋊C₈×C₇₉	C₂×C₄	1	2	yes	—
119	C₄⋊C₈×C₇₉	C₂³	1	1	yes	characteristic
120	C₄⋊C₈×C₇₉	C₂³	1	1	yes	characteristic
121	C₄⋊C₈×C₇₉	C₂³	1	1	yes	characteristic
122	C₄⋊C₈×C₇₉	C₂³	1	1	yes	characteristic
123	C₂²⋊C₈×C₇₉	C₂×C₄	1	2	yes	—
124	C₄×C₈×C₇₉	C₂³	1	1	yes	characteristic
125	C₄×C₈×C₇₉	C₂³	1	1	yes	characteristic
126	#11929624	—	2	4	no	—
127	C₂×Dic₁₅₈	C₄⋊C₄	1	1	yes	characteristic
128	C₂×D₃₁₆	C₄⋊C₄	1	1	yes	characteristic
129	C₂×C₂²⋊D₇₉	C₄⋊C₄	1	1	yes	characteristic
130	C₂×C₂²⋊D₇₉	C₄⋊C₄	1	1	yes	characteristic
131	C₂×C₄×D₇₉	C₂²×C₄	1	1	yes	characteristic
132	C₂×C₄×D₇₉	C₂²×C₄	1	1	yes	characteristic
133	C₂×C₄×D₇₉	C₂×D₄	1	1	yes	characteristic
134	C₂×C₄×D₇₉	C₂×D₄	1	1	yes	characteristic
135	C₂×C₄×D₇₉	C₂×Q₈	1	1	yes	characteristic
136	C₂×C₄×D₇₉	C₂×Q₈	1	1	yes	characteristic
137	#11929607	—	2	4	no	—
138	#11929607	—	8	1	no	—
139	C₂×C₇₉⋊C₈	—	2	1	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	C₂²×C₄	1	2	yes	—
144	C₂×C₇₉⋊C₈	C₂²×C₄	1	2	yes	—
145	C₈×D₇₉	—	2	4	no	—
146	C₈×D₇₉	—	8	1	no	—
147	C₈×D₇₉	—	8	1	no	—
148	C₈×D₇₉	—	8	1	no	—
149	C₄⋊Dic₇₉	C₄⋊C₄	1	1	yes	characteristic
150	C₄⋊Dic₇₉	C₄⋊C₄	1	1	yes	characteristic
151	Dic₇₉⋊C₄	C₄⋊C₄	1	1	yes	characteristic
152	Dic₇₉⋊C₄	C₄⋊C₄	1	1	yes	characteristic
153	Dic₇₉⋊C₄	C₄⋊C₄	1	1	yes	characteristic
154	Dic₇₉⋊C₄	C₄⋊C₄	1	1	yes	characteristic
155	C₂²⋊Dic₇₉	C₄⋊C₄	1	1	yes	characteristic
156	C₂²⋊Dic₇₉	C₄⋊C₄	1	1	yes	characteristic
157	(C₂×D₇₉)⋊C₄	C₄⋊C₄	1	1	yes	characteristic
158	(C₂×D₇₉)⋊C₄	C₄⋊C₄	1	1	yes	characteristic
159	(C₂×D₇₉)⋊C₄	C₄⋊C₄	1	1	yes	characteristic
160	(C₂×D₇₉)⋊C₄	C₄⋊C₄	1	1	yes	characteristic
161	C₄×Dic₇₉	C₂²×C₄	1	1	yes	characteristic
162	C₄×Dic₇₉	C₂²×C₄	1	1	yes	characteristic
163	C₄×Dic₇₉	C₂×D₄	1	1	yes	characteristic
164	C₄×Dic₇₉	C₂×D₄	1	1	yes	characteristic
165	C₄×Dic₇₉	C₂×Q₈	1	1	yes	characteristic
166	C₄×Dic₇₉	C₂×Q₈	1	1	yes	characteristic
167	C₂²×C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
168	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
169	C₂²×C₄×C₇₉	C₂×Q₈	1	1	yes	characteristic
170	M₁₆×C₇₉	—	8	1	no	—
171	C₂×C₈×C₇₉	—	2	1	no	—
172	C₂×C₈×C₇₉	—	2	1	no	—
173	C₂×C₈×C₇₉	—	2	1	no	—
174	C₂×C₈×C₇₉	—	2	1	no	—
175	C₂×C₈×C₇₉	—	8	1	no	—
176	C₂×C₈×C₇₉	C₂²×C₄	1	2	yes	—
177	C₂×C₈×C₇₉	C₂²×C₄	1	2	yes	—
178	C₄²×C₇₉	C₂²×C₄	1	1	yes	characteristic
179	C₄²×C₇₉	C₂×D₄	1	1	yes	characteristic
180	C₄²×C₇₉	C₂×Q₈	1	1	yes	characteristic
181	C₄²×C₇₉	C₂⁴	1	1	yes	characteristic
182	C₂³×C₇₉	C₂×C₄⋊C₄	1	1	yes	characteristic
183	C₂²×D₇₉	C₂×C₄⋊C₄	1	1	yes	characteristic
184	C₂²×D₇₉	C₂×C₄⋊C₄	1	1	yes	characteristic
185	C₂×C₄×C₇₉	—	2	2	no	—
186	C₂×C₄×C₇₉	—	2	1	no	—
187	C₂×C₄×C₇₉	—	2	1	no	—
188	C₂×C₄×C₇₉	—	4	1	no	—
189	C₂×C₄×C₇₉	C₂×C₄⋊C₄	1	1	yes	characteristic
190	C₂×C₄×C₇₉	C₂×C₄⋊C₄	1	1	yes	characteristic
191	C₂×C₄×C₇₉	C₂×C₄⋊C₄	1	1	yes	characteristic
192	C₂×C₄×C₇₉	C₂³×C₄	1	1	yes	characteristic
193	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
194	C₂×C₄×C₇₉	C₂²×Q₈	1	1	yes	characteristic
195	C₂²⋊D₇₉	—	2	2	no	—
196	C₂²⋊D₇₉	—	2	2	no	—
197	C₂×Dic₇₉	C₂×C₄⋊C₄	1	1	yes	characteristic
198	C₂×Dic₇₉	C₂×C₄⋊C₄	1	1	yes	characteristic
199	C₂×Dic₇₉	C₂×C₄⋊C₄	1	1	yes	characteristic
200	C₂×Dic₇₉	C₂×C₄⋊C₄	1	1	yes	characteristic
201	C₂×Dic₇₉	C₂×C₄⋊C₄	1	1	yes	characteristic
202	C₂×Dic₇₉	C₂×C₄⋊C₄	1	1	yes	characteristic
203	D₃₁₆	—	2	2	no	—
204	C₄×D₇₉	—	2	2	no	—
205	C₄×D₇₉	—	2	1	no	—
206	C₄×D₇₉	—	2	1	no	—
207	C₄×D₇₉	—	2	1	no	—
208	C₄×D₇₉	—	2	1	no	—
209	C₄×D₇₉	—	4	1	no	—
210	C₄×D₇₉	—	4	1	no	—
211	C₄×D₇₉	#131	1	4	yes	—
212	Dic₁₅₈	—	2	2	no	—
213	C₈×C₇₉	—	2	2	no	—
214	C₈×C₇₉	—	2	2	no	—
215	C₈×C₇₉	—	4	1	no	—
216	C₈×C₇₉	—	4	1	no	—
217	C₈×C₇₉	—	4	1	no	—
218	C₈×C₇₉	—	4	1	no	—
219	C₇₉⋊C₈	—	2	2	no	—
220	C₇₉⋊C₈	—	2	2	no	—
221	C₇₉⋊C₈	—	4	1	no	—
222	C₇₉⋊C₈	—	4	1	no	—
223	C₇₉⋊C₈	—	4	1	no	—
224	C₇₉⋊C₈	—	4	1	no	—
225	C₂²×C₇₉	—	2	1	no	—
226	C₂²×C₇₉	—	2	1	no	—
227	C₂²×C₇₉	—	2	1	no	—
228	C₂²×C₇₉	C₂²×C₄⋊C₄	1	1	yes	characteristic
229	C₂×D₇₉	—	2	1	no	—
230	C₂×D₇₉	—	2	1	no	—
231	C₂×D₇₉	—	2	1	no	—
232	C₂×D₇₉	—	2	1	no	—
233	C₂×D₇₉	—	2	1	no	—
234	C₂×D₇₉	#424	1	2	yes	—
235	C₄×C₇₉	—	2	1	no	—
236	C₄×C₇₉	—	2	1	no	—
237	C₄×C₇₉	—	2	1	no	—
238	C₄×C₇₉	—	2	1	no	—
239	C₄×C₇₉	C₂×#131	1	2	yes	—
240	C₄×C₇₉	#577	1	1	yes	characteristic
241	C₄×C₇₉	#577	1	1	yes	characteristic
242	Dic₇₉	—	2	1	no	—
243	Dic₇₉	—	2	1	no	—
244	Dic₇₉	—	2	1	no	—
245	Dic₇₉	—	2	1	no	—
246	Dic₇₉	—	2	1	no	—
247	Dic₇₉	#424	1	2	yes	—
248	#17811	—	79	1	no	maximal, Sylow
249	C₂×C₇₉	—	4	1	no	—
250	C₂×C₇₉	C₂×#424	1	1	yes	characteristic
251	C₂×C₇₉	#2912	1	1	yes	characteristic
252	C₂×C₇₉	#2916	1	1	yes	characteristic
253	D₇₉	—	2	2	no	—
254	D₇₉	—	4	1	no	—
255	#2989	—	79	1	no	—
256	#2988	—	79	1	no	—
257	#2922	—	79	1	no	—
258	#1574	—	79	1	no	—
259	#1574	—	79	1	no	—
260	#1573	—	79	1	no	—
261	#1573	—	79	1	no	—
262	#1572	—	79	1	no	—
263	#1572	—	79	1	no	—
264	#1570	—	79	1	no	—
265	#1570	D₇₉	1	1	yes	characteristic, complemented
266	#1565	—	79	1	no	—
267	#1565	—	79	1	no	—
268	#1564	—	79	1	no	—
269	C₂×#334	—	79	1	no	—
270	C₇₉	#17811	1	1	yes	characteristic, complemented, Sylow
271	C₄×#41	—	79	1	no	—
272	#446	—	158	1	no	—
273	C₈×Q₈	—	158	1	no	—
274	#436	—	158	1	no	—
275	#435	—	158	1	no	—
276	#435	—	158	1	no	—
277	C₈×D₄	—	158	1	no	—
278	C₈×D₄	—	158	1	no	—
279	C₈×D₄	—	158	1	no	—
280	#433	—	79	2	no	—
281	#433	—	79	2	no	—
282	#432	—	79	1	no	—
283	#432	—	79	1	no	—
284	#431	—	79	1	no	—
285	#431	—	79	1	no	—
286	#431	—	79	1	no	—
287	#431	—	79	1	no	—
288	#431	—	79	1	no	—
289	#431	—	79	1	no	—
290	#431	—	79	1	no	—
291	#431	C₂×D₇₉	1	1	yes	characteristic
292	#424	—	79	2	no	—
293	#423	—	79	1	no	—
294	#423	C₂×D₇₉	1	1	yes	characteristic
295	C₂×C₄⋊C₈	—	79	1	no	—
296	C₂×C₄⋊C₈	—	79	1	no	—
297	C₂×C₄⋊C₈	—	79	1	no	—
298	C₂×C₄⋊C₈	C₂×D₇₉	1	1	yes	characteristic
299	#408	—	79	2	no	—
300	C₄×M₁₆	—	79	1	no	—
301	C₂×C₄×C₈	—	79	1	no	—
302	#335	—	79	1	no	—
303	#335	—	79	1	no	—
304	#335	—	79	1	no	—
305	#335	—	79	1	no	—
306	#335	—	79	1	no	—
307	#335	—	79	1	no	—
308	#334	—	79	1	no	—
309	#334	—	79	1	no	—
310	#334	—	79	1	no	—
311	#334	—	79	1	no	—
312	#334	—	79	1	no	—
313	#334	—	79	1	no	—
314	#334	C₂×D₇₉	1	1	yes	characteristic
315	#334	C₂×D₇₉	1	1	yes	characteristic
316	#334	C₂×D₇₉	1	1	yes	characteristic
317	#334	C₂×D₇₉	1	1	yes	characteristic
318	C₂×#41	—	79	1	no	—
319	C₂×M₁₆	—	2	1	no	—
320	C₂×M₁₆	—	79	2	no	—
321	C₂×M₁₆	—	158	1	no	—
322	C₂²×C₈	—	2	1	no	—
323	C₂²×C₈	—	79	2	no	—
324	C₂²×C₈	—	158	1	no	—
325	C₂²×C₈	—	158	1	no	—
326	C₂²×C₈	—	158	1	no	—
327	C₄×Q₈	—	79	1	no	—
328	C₄×Q₈	—	79	1	no	—
329	C₄×D₄	—	79	1	no	—
330	C₄×D₄	—	79	1	no	—
331	C₄×D₄	—	79	1	no	—
332	C₄×D₄	—	79	1	no	—
333	C₄×D₄	—	79	1	no	—
334	C₄×D₄	—	79	1	no	—
335	#117	—	79	1	no	—
336	#117	—	79	1	no	—
337	#117	—	79	1	no	—
338	C₂×C₄²	—	79	1	no	—
339	C₂×C₄²	—	79	1	no	—
340	C₂×C₄²	C₂²×D₇₉	1	1	yes	characteristic
341	C₄⋊C₈	—	2	1	no	—
342	C₄⋊C₈	—	2	1	no	—
343	C₄⋊C₈	—	79	2	no	—
344	C₄⋊C₈	—	79	2	no	—
345	C₄⋊C₈	—	79	2	no	—
346	C₄⋊C₈	—	79	1	no	—
347	C₄⋊C₈	—	79	1	no	—
348	C₄⋊C₈	—	79	1	no	—
349	C₄⋊C₈	—	79	1	no	—
350	C₄⋊C₈	—	158	1	no	—
351	C₄⋊C₈	—	158	1	no	—
352	C₄⋊C₈	—	158	1	no	—
353	C₄⋊C₈	—	158	1	no	—
354	C₄⋊C₈	C₄×D₇₉	1	2	yes	—
355	C₄⋊C₈	C₂²×D₇₉	1	1	yes	characteristic
356	C₄⋊C₈	C₂²×D₇₉	1	1	yes	characteristic
357	C₄⋊C₈	C₂²×D₇₉	1	1	yes	characteristic
358	C₄⋊C₈	C₂²×D₇₉	1	1	yes	characteristic
359	C₂²⋊C₈	—	79	2	no	—
360	C₂²⋊C₈	—	79	2	no	—
361	C₂²⋊C₈	—	79	2	no	—
362	C₂²⋊C₈	—	158	1	no	—
363	C₂²⋊C₈	—	158	1	no	—
364	C₂²⋊C₈	—	158	1	no	—
365	C₂²⋊C₈	—	158	1	no	—
366	C₂²⋊C₈	—	158	1	no	—
367	C₂²⋊C₈	—	158	1	no	—
368	C₂²⋊C₈	C₄×D₇₉	1	2	yes	—
369	#97	—	79	2	no	—
370	#97	—	158	1	no	—
371	#97	—	158	1	no	—
372	C₄×C₈	—	79	2	no	—
373	C₄×C₈	—	79	1	no	—
374	C₄×C₈	—	79	1	no	—
375	C₄×C₈	—	158	1	no	—
376	C₄×C₈	—	158	1	no	—
377	C₄×C₈	—	158	1	no	—
378	C₄×C₈	—	158	1	no	—
379	C₄×C₈	C₂²×D₇₉	1	1	yes	characteristic
380	C₄×C₈	C₂²×D₇₉	1	1	yes	characteristic
381	#41	—	158	4	no	—
382	C₂×Q₈	—	79	1	no	—
383	C₂×D₄	—	79	1	no	—
384	C₂×D₄	—	79	1	no	—
385	C₂×D₄	—	79	1	no	—
386	C₂²×C₄	—	79	1	no	—
387	C₂²×C₄	—	79	1	no	—
388	C₂²×C₄	—	79	1	no	—
389	C₂²×C₄	—	79	1	no	—
390	C₂²×C₄	—	79	1	no	—
391	C₂²×C₄	—	79	1	no	—
392	C₂²×C₄	C₂×C₄×D₇₉	1	1	yes	characteristic
393	C₂²×C₄	D₄×D₇₉	1	1	yes	characteristic
394	C₂²×C₄	Q₈×D₇₉	1	1	yes	characteristic
395	M₁₆	—	8	1	no	—
396	M₁₆	—	632	1	no	—
397	M₁₆	—	158	4	no	—
398	C₂×C₈	—	2	1	no	—
399	C₂×C₈	—	2	1	no	—
400	C₂×C₈	—	2	1	no	—
401	C₂×C₈	—	2	1	no	—
402	C₂×C₈	—	8	1	no	—
403	C₂×C₈	—	79	2	no	—
404	C₂×C₈	—	79	2	no	—
405	C₂×C₈	—	632	1	no	—
406	C₂×C₈	—	632	1	no	—
407	C₂×C₈	—	632	1	no	—
408	C₂×C₈	—	158	4	no	—
409	C₂×C₈	—	158	1	no	—
410	C₂×C₈	—	158	1	no	—
411	C₂×C₈	—	158	1	no	—
412	C₂×C₈	—	158	1	no	—
413	C₂×C₈	C₂×C₄×D₇₉	1	2	yes	—
414	C₂×C₈	C₂×C₄×D₇₉	1	2	yes	—
415	C₄⋊C₄	—	79	1	no	—
416	C₄⋊C₄	—	79	1	no	—
417	C₄⋊C₄	—	79	1	no	—
418	C₄⋊C₄	—	79	1	no	—
419	C₄⋊C₄	—	79	1	no	—
420	C₄⋊C₄	—	79	1	no	—
421	C₂²⋊C₄	—	79	1	no	—
422	C₂²⋊C₄	—	79	1	no	—
423	C₂²⋊C₄	—	79	1	no	—
424	C₂²⋊C₄	—	79	1	no	—
425	C₂²⋊C₄	—	79	1	no	—
426	C₂²⋊C₄	—	79	1	no	—
427	C₄²	—	79	1	no	—
428	C₄²	—	79	1	no	—
429	C₄²	—	79	1	no	—
430	C₄²	—	79	1	no	—
431	C₄²	—	79	1	no	—
432	C₄²	—	79	1	no	—
433	C₄²	C₂×C₄×D₇₉	1	1	yes	characteristic
434	C₄²	D₄×D₇₉	1	1	yes	characteristic
435	C₄²	Q₈×D₇₉	1	1	yes	characteristic
436	C₄²	C₂³×D₇₉	1	1	yes	characteristic
437	C₂³	—	79	1	no	—
438	C₂³	—	79	1	no	—
439	C₂³	C₄⋊C₄×D₇₉	1	1	yes	characteristic
440	Q₈	—	158	2	no	—
441	D₄	—	158	2	no	—
442	D₄	—	158	2	no	—
443	D₄	—	158	2	no	—
444	C₂×C₄	—	2	2	no	—
445	C₂×C₄	—	2	1	no	—
446	C₂×C₄	—	2	1	no	—
447	C₂×C₄	—	4	1	no	—
448	C₂×C₄	—	316	1	no	—
449	C₂×C₄	—	316	1	no	—
450	C₂×C₄	—	79	1	no	—
451	C₂×C₄	—	79	4	no	—
452	C₂×C₄	—	79	1	no	—
453	C₂×C₄	—	79	1	no	—
454	C₂×C₄	—	79	1	no	—
455	C₂×C₄	—	79	1	no	—
456	C₂×C₄	—	79	1	no	—
457	C₂×C₄	—	158	2	no	—
458	C₂×C₄	—	158	1	no	—
459	C₂×C₄	—	158	1	no	—
460	C₂×C₄	—	158	1	no	—
461	C₂×C₄	—	158	1	no	—
462	C₂×C₄	C₄⋊C₄×D₇₉	1	1	yes	characteristic
463	C₂×C₄	C₄⋊C₄×D₇₉	1	1	yes	characteristic
464	C₂×C₄	C₄⋊C₄×D₇₉	1	1	yes	characteristic
465	C₂×C₄	C₂²×C₄×D₇₉	1	1	yes	characteristic
466	C₂×C₄	C₂×D₄×D₇₉	1	1	yes	characteristic
467	C₂×C₄	C₂×Q₈×D₇₉	1	1	yes	characteristic
468	C₈	—	2	2	no	—
469	C₈	—	2	2	no	—
470	C₈	—	4	1	no	—
471	C₈	—	4	1	no	—
472	C₈	—	4	1	no	—
473	C₈	—	4	1	no	—
474	C₈	—	316	1	no	—
475	C₈	—	316	1	no	—
476	C₈	—	316	1	no	—
477	C₈	—	316	1	no	—
478	C₈	—	158	2	no	—
479	C₈	—	158	2	no	—
480	C₂²	—	2	1	no	—
481	C₂²	—	2	1	no	—
482	C₂²	—	2	1	no	—
483	C₂²	—	79	2	no	—
484	C₂²	—	158	1	no	—
485	C₂²	—	158	1	no	—
486	C₂²	—	158	1	no	—
487	C₂²	—	158	1	no	—
488	C₂²	—	158	1	no	—
489	C₂²	C₂×C₄⋊C₄×D₇₉	1	1	yes	characteristic
490	C₄	—	2	1	no	—
491	C₄	—	2	1	no	—
492	C₄	—	2	1	no	—
493	C₄	—	2	1	no	—
494	C₄	—	79	2	no	—
495	C₄	—	158	1	no	—
496	C₄	—	158	1	no	—
497	C₄	—	158	1	no	—
498	C₄	—	158	1	no	—
499	C₄	—	158	1	no	—
500	C₄	#131×D₇₉	1	2	yes	—
501	C₄	#19099369	1	1	yes	characteristic
502	C₄	#19099369	1	1	yes	characteristic
503	C₂	—	4	1	no	—
504	C₂	—	316	1	no	—
505	C₂	—	158	2	no	—
506	C₂	#424×D₇₉	1	1	yes	characteristic
507	C₂	#23771991	1	1	yes	characteristic
508	C₂	#23772010	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₇₉
commutator	C₂×C₄×C₇₉	C₂³×C₄
Frattini	C₄²	C₂³×D₇₉
Fitting	C₇₉×#1570	C₂
socle	C₂²×C₇₉	C₂²×C₄⋊C₄
prime radical	C₂×#11929624	C₂×C₄
cosocle	C₄²×C₇₉	C₂⁴
hypercenter	#1570	D₇₉
hypocenter	C₇₉	#17811
LCS	G ▷ C₂×C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1570

Complements

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

N	H ≅ G/N	type
4. #23762191	C₂	semidirect
5. #23762187	C₂	semidirect
6. #23762183	C₂	semidirect
7. #23762182	C₂	semidirect
8. #23762180	C₂	semidirect
9. #23762177	C₂	semidirect
10. #23762169	C₂	semidirect
11. #23762149	C₂	semidirect
12. #23762149	C₂	semidirect
13. #23762145	C₂	semidirect
14. #334×D₇₉	C₂	semidirect
15. C₇₉×#1570	C₂	semidirect
265. #1570	D₇₉	semidirect
270. C₇₉	#17811	semidirect

Maximal subgroups

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

subgroup	index
#23772514	2
#23772509	2
#23772039	2
#23762191	2
#23762187	2
#23762183	2
#23762182	2
#23762180	2
#23762177	2
#23762169	2
#23762149	2
#23762145	2
#334×D₇₉	2
C₇₉×#1570	2
#17811	79