Subgroups — #34258014

Order 20224.

682 conjugacy classes of subgroups.

The subgroup lattice has 500 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#23772367	C₂	1	1	yes	maximal, characteristic, complemented
2	#23772361	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄×#14579181	C₂	1	1	yes	maximal, characteristic
4	#23762294	C₂	1	2	yes	maximal, complemented
5	#23762293	C₂	1	2	yes	maximal, complemented
6	#23762287	C₂	1	2	yes	maximal, complemented
7	#23762282	C₂	1	2	yes	maximal, complemented
8	#23762146	C₂	1	1	yes	maximal, characteristic, complemented
9	#23761783	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₈×C₇₉⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
11	C₇₉×#1476	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#14579181	C₄	1	1	yes	characteristic
13	C₄×#11929624	C₂²	1	1	yes	characteristic
14	#19098694	C₂²	1	2	yes	—
15	#19098690	C₂²	1	2	yes	—
16	C₄×#11929614	C₄	1	1	yes	characteristic
17	C₄×#11929614	C₂²	1	1	yes	characteristic
18	C₄×#11929611	C₄	1	1	yes	characteristic
19	C₄×#11929611	C₂²	1	1	yes	characteristic
20	C₄×#11929612	C₄	1	1	yes	characteristic
21	C₄×#11929612	C₂²	1	1	yes	characteristic
22	C₄×#11929609	C₄	1	1	yes	characteristic
23	C₄×#11929609	C₂²	1	1	yes	characteristic
24	#19098641	C₂²	1	2	yes	—
25	#19098640	C₂²	1	2	yes	—
26	#19098635	—	2	2	no	—
27	#19098631	—	2	2	no	—
28	#19098616	—	2	1	no	—
29	#19098616	C₂²	1	1	yes	characteristic
30	#19098614	—	2	1	no	—
31	#19098599	C₄	1	1	yes	characteristic
32	#19098559	C₄	1	1	yes	characteristic
33	#19098557	C₄	1	1	yes	characteristic
34	C₄×#11929608	—	2	1	no	—
35	C₄×#11929607	—	2	1	no	—
36	C₂×C₄×C₇₉⋊C₈	C₂²	1	1	yes	characteristic
37	C₂×C₄×C₇₉⋊C₈	C₂²	1	1	yes	characteristic
38	#19098315	C₂²	1	2	yes	—
39	#19098313	C₂²	1	2	yes	—
40	#19098295	C₂²	1	2	yes	—
41	#19098292	C₂²	1	2	yes	—
42	C₈×C₇₉⋊C₈	C₂²	1	2	yes	—
43	C₈×C₇₉⋊C₈	C₂²	1	2	yes	—
44	C₄×#41×C₇₉	C₂²	1	1	yes	characteristic
45	#431×C₇₉	C₂²	1	1	yes	characteristic
46	C₂×C₄×C₈×C₇₉	C₂²	1	1	yes	characteristic
47	Q₈⋊C₈×C₇₉	C₂²	1	2	yes	—
48	D₄⋊C₈×C₇₉	C₂²	1	2	yes	—
49	C₂×#11929624	C₂×C₄	1	1	yes	characteristic
50	#14579181	—	2	4	no	—
51	C₂×#11929614	C₂×C₄	1	1	yes	characteristic
52	C₂×#11929612	C₂×C₄	1	1	yes	characteristic
53	C₂×#11929611	C₂×C₄	1	1	yes	characteristic
54	C₂×#11929609	C₂×C₄	1	1	yes	characteristic
55	C₂×#11929608	—	2	2	no	—
56	C₂×#11929607	—	2	2	no	—
57	C₂²×C₇₉⋊C₈	C₂×C₄	1	1	yes	characteristic
58	C₂²×C₇₉⋊C₈	C₂×C₄	1	1	yes	characteristic
59	C₂²×C₇₉⋊C₈	D₄	1	2	yes	—
60	C₄×Dic₁₅₈	C₂×C₄	1	1	yes	characteristic
61	C₄×Dic₁₅₈	C₂³	1	1	yes	characteristic
62	C₄×D₃₁₆	C₂×C₄	1	1	yes	characteristic
63	C₄×D₃₁₆	C₂³	1	1	yes	characteristic
64	C₄×C₂²⋊D₇₉	—	2	1	no	—
65	C₄×C₂²⋊D₇₉	—	2	1	no	—
66	#14579120	C₂×C₄	1	1	yes	characteristic
67	#14579118	—	2	1	no	—
68	C₄²×D₇₉	—	2	1	no	—
69	#14579094	C₂×C₄	1	1	yes	characteristic
70	#14579094	C₂×C₄	1	1	yes	characteristic
71	#14579092	C₂×C₄	1	1	yes	characteristic
72	#14579092	C₂×C₄	1	1	yes	characteristic
73	C₄⋊(C₇₉⋊C₈)	—	2	2	no	—
74	C₄⋊(C₇₉⋊C₈)	C₂³	1	2	yes	—
75	Dic₇₉⋊C₈	—	2	2	no	—
76	#14579085	C₂×C₄	1	1	yes	characteristic
77	#14579085	C₂×C₄	1	1	yes	characteristic
78	#14579084	C₂×C₄	1	1	yes	characteristic
79	#14579084	C₂×C₄	1	1	yes	characteristic
80	#14579082	C₂×C₄	1	1	yes	characteristic
81	#14579082	C₂×C₄	1	1	yes	characteristic
82	#14579081	C₂×C₄	1	1	yes	characteristic
83	#14579081	C₂×C₄	1	1	yes	characteristic
84	C₂²⋊(C₇₉⋊C₈)	—	2	1	no	—
85	C₂²⋊(C₇₉⋊C₈)	—	2	2	no	—
86	(C₂×D₇₉)⋊C₈	—	2	2	no	—
87	#14579072	—	2	2	no	—
88	#14579071	—	2	2	no	—
89	C₄×C₇₉⋊C₈	—	2	1	no	—
90	C₄×C₇₉⋊C₈	C₂×C₄	1	1	yes	characteristic
91	C₄×C₇₉⋊C₈	C₂×C₄	1	1	yes	characteristic
92	C₄×C₇₉⋊C₈	D₄	1	1	yes	characteristic
93	C₄×C₇₉⋊C₈	D₄	1	1	yes	characteristic
94	C₄×C₇₉⋊C₈	C₂³	1	1	yes	characteristic
95	C₄×C₇₉⋊C₈	C₂³	1	1	yes	characteristic
96	C₄×C₇₉⋊C₈	C₂³	1	2	yes	—
97	C₂×#41×C₇₉	C₂×C₄	1	1	yes	characteristic
98	C₂²×C₈×C₇₉	—	2	1	no	—
99	C₄×Q₈×C₇₉	C₂×C₄	1	1	yes	characteristic
100	C₄×Q₈×C₇₉	C₂³	1	1	yes	characteristic
101	C₄×D₄×C₇₉	—	2	1	no	—
102	C₄×D₄×C₇₉	—	2	1	no	—
103	C₄×D₄×C₇₉	C₂×C₄	1	1	yes	characteristic
104	C₄×D₄×C₇₉	C₂³	1	1	yes	characteristic
105	#117×C₇₉	—	2	1	no	—
106	#117×C₇₉	C₂×C₄	1	1	yes	characteristic
107	C₂×C₄²×C₇₉	—	2	1	no	—
108	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
109	C₄⋊C₈×C₇₉	C₂³	1	2	yes	—
110	C₂²⋊C₈×C₇₉	—	2	1	no	—
111	C₄×C₈×C₇₉	—	2	1	no	—
112	C₄×C₈×C₇₉	—	2	1	no	—
113	C₄×C₈×C₇₉	C₂³	1	2	yes	—
114	#11929624	—	2	2	no	—
115	#11929624	—	2	2	no	—
116	C₂×Dic₁₅₈	C₂²×C₄	1	1	yes	characteristic
117	C₂×D₃₁₆	C₂²×C₄	1	1	yes	characteristic
118	C₂×C₂²⋊D₇₉	—	2	1	no	—
119	C₂×C₄×D₇₉	—	2	1	no	—
120	C₂×C₄×D₇₉	—	2	1	no	—
121	C₂×C₄×D₇₉	—	2	1	no	—
122	#11929614	—	2	2	no	—
123	#11929612	—	2	2	no	—
124	#11929611	—	2	2	no	—
125	#11929609	—	2	2	no	—
126	#11929608	—	4	4	no	—
127	#11929607	—	4	4	no	—
128	C₂×C₇₉⋊C₈	—	2	4	no	—
129	C₂×C₇₉⋊C₈	—	2	2	no	—
130	C₂×C₇₉⋊C₈	—	2	2	no	—
131	C₂×C₇₉⋊C₈	M₁₆	1	4	yes	complemented
132	C₂×C₇₉⋊C₈	C₂²×C₄	1	1	yes	characteristic
133	C₂×C₇₉⋊C₈	C₂²×C₄	1	1	yes	characteristic
134	C₂×C₇₉⋊C₈	C₂²×C₄	1	1	yes	characteristic
135	C₂×C₇₉⋊C₈	C₂²×C₄	1	1	yes	characteristic
136	C₂×C₇₉⋊C₈	C₂×D₄	1	2	yes	—
137	C₂×C₇₉⋊C₈	C₂×D₄	1	2	yes	—
138	C₄⋊Dic₇₉	C₂²×C₄	1	1	yes	characteristic
139	C₄⋊Dic₇₉	C₂²×C₄	1	1	yes	characteristic
140	Dic₇₉⋊C₄	—	2	1	no	—
141	Dic₇₉⋊C₄	—	2	1	no	—
142	C₂²⋊Dic₇₉	—	2	1	no	—
143	(C₂×D₇₉)⋊C₄	—	2	1	no	—
144	(C₂×D₇₉)⋊C₄	—	2	1	no	—
145	C₄×Dic₇₉	—	2	1	no	—
146	C₄×Dic₇₉	—	2	1	no	—
147	C₄×Dic₇₉	—	2	1	no	—
148	#41×C₇₉	—	2	2	no	—
149	#41×C₇₉	—	2	2	no	—
150	C₂×Q₈×C₇₉	C₂²×C₄	1	1	yes	characteristic
151	C₂×D₄×C₇₉	—	2	1	no	—
152	C₂×D₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
153	C₂²×C₄×C₇₉	—	2	1	no	—
154	C₂²×C₄×C₇₉	—	2	1	no	—
155	C₂²×C₄×C₇₉	—	2	1	no	—
156	C₂²×C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
157	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
158	C₂²×C₄×C₇₉	#41	1	1	yes	characteristic
159	C₂×C₈×C₇₉	—	2	4	no	—
160	C₂×C₈×C₇₉	—	2	2	no	—
161	C₂×C₈×C₇₉	—	2	2	no	—
162	C₄⋊C₄×C₇₉	—	2	1	no	—
163	C₄⋊C₄×C₇₉	—	2	1	no	—
164	C₄⋊C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
165	C₄⋊C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
166	C₂²⋊C₄×C₇₉	—	2	1	no	—
167	C₂²⋊C₄×C₇₉	—	2	1	no	—
168	C₂²⋊C₄×C₇₉	—	2	1	no	—
169	C₄²×C₇₉	—	2	1	no	—
170	C₄²×C₇₉	—	2	1	no	—
171	C₄²×C₇₉	—	2	1	no	—
172	C₄²×C₇₉	C₂²×C₄	1	1	yes	characteristic
173	C₄²×C₇₉	C₂×D₄	1	1	yes	characteristic
174	C₄²×C₇₉	#41	1	1	yes	characteristic
175	C₄²×C₇₉	C₂⁴	1	1	yes	characteristic
176	C₂³×C₇₉	—	2	1	no	—
177	C₂³×C₇₉	C₄×D₄	1	1	yes	characteristic
178	C₂²×D₇₉	—	2	1	no	—
179	Q₈×C₇₉	—	2	1	no	—
180	Q₈×C₇₉	—	2	1	no	—
181	D₄×C₇₉	—	2	1	no	—
182	D₄×C₇₉	—	2	1	no	—
183	D₄×C₇₉	—	4	2	no	—
184	C₂×C₄×C₇₉	—	2	2	no	—
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	—	2	1	no	—
189	C₂×C₄×C₇₉	—	4	2	no	—
190	C₂×C₄×C₇₉	—	4	2	no	—
191	C₂×C₄×C₇₉	—	4	2	no	—
192	C₂×C₄×C₇₉	C₄×D₄	1	1	yes	characteristic
193	C₂×C₄×C₇₉	C₄×D₄	1	1	yes	characteristic
194	C₂×C₄×C₇₉	C₄×D₄	1	1	yes	characteristic
195	C₂×C₄×C₇₉	C₂×M₁₆	1	2	yes	—
196	C₂×C₄×C₇₉	#131	1	2	yes	—
197	C₂×C₄×C₇₉	C₂³×C₄	1	1	yes	characteristic
198	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
199	C₂×C₄×C₇₉	C₂×#41	1	1	yes	characteristic
200	C₂²⋊D₇₉	—	4	2	no	—
201	C₂×Dic₇₉	—	2	1	no	—
202	C₂×Dic₇₉	—	2	1	no	—
203	C₂×Dic₇₉	—	2	1	no	—
204	D₃₁₆	—	2	1	no	—
205	D₃₁₆	—	2	1	no	—
206	C₄×D₇₉	—	4	2	no	—
207	C₄×D₇₉	—	4	2	no	—
208	C₄×D₇₉	—	4	2	no	—
209	Dic₁₅₈	—	2	1	no	—
210	Dic₁₅₈	—	2	1	no	—
211	C₈×C₇₉	—	2	4	no	—
212	C₈×C₇₉	—	4	2	no	—
213	C₇₉⋊C₈	—	2	1	no	—
214	C₇₉⋊C₈	—	2	1	no	—
215	C₇₉⋊C₈	—	2	2	no	—
216	C₇₉⋊C₈	—	4	2	no	—
217	C₇₉⋊C₈	C₂×M₁₆	1	2	yes	—
218	C₇₉⋊C₈	C₂×M₁₆	1	2	yes	—
219	C₇₉⋊C₈	#135	1	4	yes	complemented
220	C₂²×C₇₉	—	2	1	no	—
221	C₂²×C₇₉	—	2	1	no	—
222	C₂²×C₇₉	—	4	1	no	—
223	C₂²×C₇₉	—	4	1	no	—
224	C₂²×C₇₉	—	4	1	no	—
225	C₂²×C₇₉	#436	1	2	yes	—
226	C₂²×C₇₉	C₂×C₄×D₄	1	1	yes	characteristic
227	C₂×D₇₉	—	4	1	no	—
228	C₂×D₇₉	—	4	1	no	—
229	C₂×D₇₉	—	4	1	no	—
230	C₄×C₇₉	—	2	1	no	—
231	C₄×C₇₉	—	2	1	no	—
232	C₄×C₇₉	—	4	1	no	—
233	C₄×C₇₉	—	4	1	no	—
234	C₄×C₇₉	—	4	1	no	—
235	C₄×C₇₉	#436	1	2	yes	—
236	C₄×C₇₉	#443	1	2	yes	—
237	C₄×C₇₉	C₂²×M₁₆	1	1	yes	characteristic
238	C₄×C₇₉	C₂×#131	1	1	yes	characteristic
239	C₄×C₇₉	C₂×#135	1	2	yes	—
240	Dic₇₉	—	4	1	no	—
241	Dic₇₉	—	4	1	no	—
242	Dic₇₉	—	4	1	no	—
243	#17886	—	79	1	no	maximal, Sylow
244	C₂×C₇₉	—	2	2	no	—
245	C₂×C₇₉	—	8	1	no	—
246	C₂×C₇₉	C₂×#436	1	1	yes	characteristic
247	C₂×C₇₉	C₄×#135	1	1	yes	characteristic
248	C₂×C₇₉	C₂×#443	1	1	yes	characteristic
249	D₇₉	—	8	1	no	—
250	#2965	—	79	1	no	—
251	#2965	—	79	1	no	—
252	C₄×#135	—	79	1	no	—
253	#1591	—	79	2	no	—
254	#1590	—	79	2	no	—
255	#1590	—	79	2	no	—
256	#1589	—	79	2	no	—
257	#1564	—	79	1	no	—
258	#1476	—	79	1	no	—
259	#1476	D₇₉	1	1	yes	characteristic, complemented
260	C₂×C₈²	—	79	1	no	—
261	C₇₉	#17886	1	1	yes	characteristic, complemented, Sylow
262	C₂×#135	—	79	1	no	—
263	C₄×#41	—	79	1	no	—
264	C₄×#41	C₂×D₇₉	1	1	yes	characteristic
265	#446	—	79	2	no	—
266	#446	—	79	2	no	—
267	C₄×Q₁₆	—	79	1	no	—
268	C₄×Q₁₆	—	79	1	no	—
269	C₄×SD₁₆	—	79	1	no	—
270	C₄×SD₁₆	—	79	1	no	—
271	C₄×SD₁₆	—	79	1	no	—
272	C₄×SD₁₆	—	79	1	no	—
273	C₄×D₈	—	79	1	no	—
274	C₄×D₈	—	79	1	no	—
275	#436	—	79	2	no	—
276	#436	—	79	2	no	—
277	#435	—	158	2	no	—
278	#435	—	158	2	no	—
279	#431	—	79	1	no	—
280	#431	—	158	1	no	—
281	#431	—	158	1	no	—
282	#431	C₂×D₇₉	1	1	yes	characteristic
283	#427	—	79	1	no	—
284	#416	—	79	1	no	—
285	#416	—	79	1	no	—
286	C₄×M₁₆	—	158	1	no	—
287	C₄×M₁₆	—	158	1	no	—
288	C₂×C₄×C₈	—	79	1	no	—
289	C₂×C₄×C₈	—	79	1	no	—
290	C₂×C₄×C₈	C₂×D₇₉	1	1	yes	characteristic
291	#335	—	79	2	no	—
292	#334	—	79	2	no	—
293	Q₈⋊C₈	—	79	2	no	—
294	Q₈⋊C₈	C₂×D₇₉	1	2	yes	—
295	D₄⋊C₈	—	79	2	no	—
296	D₄⋊C₈	C₂×D₇₉	1	2	yes	—
297	C₈²	—	79	2	no	—
298	C₈²	—	79	2	no	—
299	C₂×#41	—	79	1	no	—
300	C₂×#41	C₄×D₇₉	1	1	yes	characteristic
301	#135	—	158	4	no	—
302	C₂×Q₁₆	—	79	1	no	—
303	C₂×SD₁₆	—	79	1	no	—
304	C₂×SD₁₆	—	79	1	no	—
305	C₂×D₈	—	79	1	no	—
306	C₂×M₁₆	—	158	2	no	—
307	C₂×M₁₆	—	158	2	no	—
308	C₂²×C₈	—	2	1	no	—
309	C₂²×C₈	—	79	1	no	—
310	C₂²×C₈	—	79	1	no	—
311	C₂²×C₈	—	79	2	no	—
312	C₄×Q₈	—	79	1	no	—
313	C₄×Q₈	—	79	1	no	—
314	C₄×Q₈	C₄×D₇₉	1	1	yes	characteristic
315	C₄×Q₈	C₂²×D₇₉	1	1	yes	characteristic
316	C₄×D₄	—	2	1	no	—
317	C₄×D₄	—	2	1	no	—
318	C₄×D₄	—	79	1	no	—
319	C₄×D₄	—	79	1	no	—
320	C₄×D₄	—	158	1	no	—
321	C₄×D₄	—	158	1	no	—
322	C₄×D₄	C₄×D₇₉	1	1	yes	characteristic
323	C₄×D₄	C₂²×D₇₉	1	1	yes	characteristic
324	#117	—	2	1	no	—
325	#117	—	79	1	no	—
326	#117	—	158	1	no	—
327	#117	C₄×D₇₉	1	1	yes	characteristic
328	C₂×C₄²	—	2	1	no	—
329	C₂×C₄²	—	158	1	no	—
330	C₂×C₄²	C₂²×D₇₉	1	1	yes	characteristic
331	#107	—	79	1	no	—
332	#107	—	79	1	no	—
333	#106	—	79	1	no	—
334	#106	—	79	1	no	—
335	C₄⋊C₈	—	79	2	no	—
336	C₄⋊C₈	—	158	2	no	—
337	C₄⋊C₈	—	158	2	no	—
338	C₄⋊C₈	C₂²×D₇₉	1	2	yes	—
339	#103	—	79	1	no	—
340	#103	—	79	1	no	—
341	#103	—	79	1	no	—
342	#103	—	79	1	no	—
343	#102	—	79	1	no	—
344	#102	—	79	1	no	—
345	#102	—	79	1	no	—
346	#102	—	79	1	no	—
347	C₂²⋊C₈	—	2	1	no	—
348	C₂²⋊C₈	—	158	2	no	—
349	C₂²⋊C₈	—	158	2	no	—
350	C₂²⋊C₈	—	158	1	no	—
351	#97	—	158	2	no	—
352	#97	—	158	2	no	—
353	C₄×C₈	—	2	1	no	—
354	C₄×C₈	—	2	1	no	—
355	C₄×C₈	—	79	1	no	—
356	C₄×C₈	—	79	1	no	—
357	C₄×C₈	—	79	1	no	—
358	C₄×C₈	—	79	1	no	—
359	C₄×C₈	—	79	1	no	—
360	C₄×C₈	—	79	1	no	—
361	C₄×C₈	—	79	2	no	—
362	C₄×C₈	—	158	1	no	—
363	C₄×C₈	C₂²×D₇₉	1	2	yes	—
364	#41	—	2	2	no	—
365	#41	—	2	2	no	—
366	#41	—	158	2	no	—
367	#41	—	158	2	no	—
368	C₂×Q₈	—	79	1	no	—
369	C₂×Q₈	C₂×C₄×D₇₉	1	1	yes	characteristic
370	C₂×D₄	—	2	1	no	—
371	C₂×D₄	—	79	1	no	—
372	C₂×D₄	—	158	1	no	—
373	C₂×D₄	C₂×C₄×D₇₉	1	1	yes	characteristic
374	C₂²×C₄	—	2	1	no	—
375	C₂²×C₄	—	2	1	no	—
376	C₂²×C₄	—	2	1	no	—
377	C₂²×C₄	—	158	1	no	—
378	C₂²×C₄	—	158	1	no	—
379	C₂²×C₄	—	158	1	no	—
380	C₂²×C₄	C₂×C₄×D₇₉	1	1	yes	characteristic
381	C₂²×C₄	D₄×D₇₉	1	1	yes	characteristic
382	C₂²×C₄	#11929623	1	1	yes	characteristic
383	Q₁₆	—	158	2	no	—
384	SD₁₆	—	158	2	no	—
385	SD₁₆	—	158	2	no	—
386	D₈	—	158	2	no	—
387	M₁₆	—	316	4	no	—
388	M₁₆	—	316	4	no	—
389	C₂×C₈	—	2	4	no	—
390	C₂×C₈	—	2	2	no	—
391	C₂×C₈	—	2	2	no	—
392	C₂×C₈	—	79	4	no	—
393	C₂×C₈	—	79	1	no	—
394	C₂×C₈	—	79	1	no	—
395	C₂×C₈	—	79	2	no	—
396	C₂×C₈	—	79	1	no	—
397	C₂×C₈	—	79	1	no	—
398	C₂×C₈	—	79	2	no	—
399	C₂×C₈	—	158	2	no	—
400	C₂×C₈	—	158	4	no	—
401	C₂×C₈	—	158	2	no	—
402	C₄⋊C₄	—	2	1	no	—
403	C₄⋊C₄	—	2	1	no	—
404	C₄⋊C₄	—	79	1	no	—
405	C₄⋊C₄	—	79	1	no	—
406	C₄⋊C₄	—	158	1	no	—
407	C₄⋊C₄	—	158	1	no	—
408	C₄⋊C₄	C₂×C₄×D₇₉	1	1	yes	characteristic
409	C₄⋊C₄	C₂×C₄×D₇₉	1	1	yes	characteristic
410	C₂²⋊C₄	—	2	1	no	—
411	C₂²⋊C₄	—	2	1	no	—
412	C₂²⋊C₄	—	2	1	no	—
413	C₂²⋊C₄	—	158	1	no	—
414	C₂²⋊C₄	—	158	1	no	—
415	C₂²⋊C₄	—	158	1	no	—
416	C₄²	—	2	1	no	—
417	C₄²	—	2	1	no	—
418	C₄²	—	2	1	no	—
419	C₄²	—	158	1	no	—
420	C₄²	—	158	1	no	—
421	C₄²	—	158	1	no	—
422	C₄²	C₂×C₄×D₇₉	1	1	yes	characteristic
423	C₄²	D₄×D₇₉	1	1	yes	characteristic
424	C₄²	#11929623	1	1	yes	characteristic
425	C₄²	C₂³×D₇₉	1	1	yes	characteristic
426	C₂³	—	2	1	no	—
427	C₂³	—	158	1	no	—
428	C₂³	(C₂²⋊D₇₉)⋊C₄	1	1	yes	characteristic
429	Q₈	—	2	1	no	—
430	Q₈	—	2	1	no	—
431	Q₈	—	158	1	no	—
432	Q₈	—	158	1	no	—
433	D₄	—	2	1	no	—
434	D₄	—	2	1	no	—
435	D₄	—	4	2	no	—
436	D₄	—	316	2	no	—
437	D₄	—	158	1	no	—
438	D₄	—	158	1	no	—
439	C₂×C₄	—	2	2	no	—
440	C₂×C₄	—	2	2	no	—
441	C₂×C₄	—	2	1	no	—
442	C₂×C₄	—	2	1	no	—
443	C₂×C₄	—	2	1	no	—
444	C₂×C₄	—	4	2	no	—
445	C₂×C₄	—	4	2	no	—
446	C₂×C₄	—	4	2	no	—
447	C₂×C₄	—	316	2	no	—
448	C₂×C₄	—	316	2	no	—
449	C₂×C₄	—	316	2	no	—
450	C₂×C₄	—	158	1	no	—
451	C₂×C₄	—	158	1	no	—
452	C₂×C₄	—	158	1	no	—
453	C₂×C₄	(C₂²⋊D₇₉)⋊C₄	1	1	yes	characteristic
454	C₂×C₄	(C₂²⋊D₇₉)⋊C₄	1	1	yes	characteristic
455	C₂×C₄	(C₂²⋊D₇₉)⋊C₄	1	1	yes	characteristic
456	C₂×C₄	M₁₆×D₇₉	1	2	yes	—
457	C₂×C₄	#14579167	1	2	yes	—
458	C₂×C₄	C₂²×C₄×D₇₉	1	1	yes	characteristic
459	C₂×C₄	C₂×D₄×D₇₉	1	1	yes	characteristic
460	C₂×C₄	C₂×#11929623	1	1	yes	characteristic
461	C₈	—	2	4	no	—
462	C₈	—	4	2	no	—
463	C₈	—	316	2	no	—
464	C₈	—	79	2	no	—
465	C₈	—	79	2	no	—
466	C₈	—	79	4	no	—
467	C₈	—	158	1	no	—
468	C₈	—	158	1	no	—
469	C₈	—	158	2	no	—
470	C₂²	—	2	1	no	—
471	C₂²	—	2	1	no	—
472	C₂²	—	4	1	no	—
473	C₂²	—	4	1	no	—
474	C₂²	—	4	1	no	—
475	C₂²	—	316	1	no	—
476	C₂²	—	316	1	no	—
477	C₂²	—	316	1	no	—
478	C₂²	#19098638	1	2	yes	—
479	C₂²	C₂×(C₂²⋊D₇₉)⋊C₄	1	1	yes	characteristic
480	C₄	—	2	1	no	—
481	C₄	—	2	1	no	—
482	C₄	—	4	1	no	—
483	C₄	—	4	1	no	—
484	C₄	—	4	1	no	—
485	C₄	—	316	1	no	—
486	C₄	—	316	1	no	—
487	C₄	—	316	1	no	—
488	C₄	#19098638	1	2	yes	—
489	C₄	#19098677	1	2	yes	—
490	C₄	C₂×M₁₆×D₇₉	1	1	yes	characteristic
491	C₄	C₂×#14579167	1	1	yes	characteristic
492	C₄	#135×D₇₉	1	2	yes	—
493	C₂	—	2	2	no	—
494	C₂	—	8	1	no	—
495	C₂	—	632	1	no	—
496	C₂	C₂×#19098638	1	1	yes	characteristic
497	C₂	#23772168	1	1	yes	characteristic
498	C₂	C₂×#19098677	1	1	yes	characteristic

	subgroup	G/H
center	C₄²	D₄×D₇₉
commutator	C₂×C₄×C₇₉	C₂³×C₄
Frattini	C₄²	C₂³×D₇₉
Fitting	C₇₉×#1476	C₂
socle	C₂²×C₇₉	C₂×C₄×D₄
prime radical	C₂×#14579181	C₄
cosocle	C₄²×C₇₉	C₂⁴
hypercenter	#1476	D₇₉
hypocenter	C₇₉	#17886
LCS	G ▷ C₂×C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₄² ◁ C₂×C₄² ◁ #1476

Complements

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

N	H ≅ G/N	type
1. #23772367	C₂	semidirect
2. #23772361	C₂	semidirect
4. #23762294	C₂	semidirect
5. #23762293	C₂	semidirect
6. #23762287	C₂	semidirect
7. #23762282	C₂	semidirect
8. #23762146	C₂	semidirect
9. #23761783	C₂	semidirect
10. C₂×C₈×C₇₉⋊C₈	C₂	semidirect
11. C₇₉×#1476	C₂	semidirect
131. C₂×C₇₉⋊C₈	M₁₆	semidirect
219. C₇₉⋊C₈	#135	semidirect
259. #1476	D₇₉	semidirect
261. C₇₉	#17886	semidirect

Maximal subgroups

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

subgroup	index
#23772367	2
#23772361	2
C₄×#14579181	2
#23762294	2
#23762293	2
#23762287	2
#23762282	2
#23762146	2
#23761783	2
C₂×C₈×C₇₉⋊C₈	2
C₇₉×#1476	2
#17886	79