Subgroups — #34310347

Order 20224.

708 conjugacy classes of subgroups.

The subgroup lattice has 490 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#23773188	C₂	1	1	yes	maximal, characteristic
2	#23772343	C₂	1	1	yes	maximal, characteristic, complemented
3	#23764376	C₂	1	1	yes	maximal, characteristic, complemented
4	#23764173	C₂	1	1	yes	maximal, characteristic, complemented
5	#23764150	C₂	1	2	yes	maximal, complemented
6	#23763996	C₂	1	2	yes	maximal, complemented
7	#23763675	C₂	1	2	yes	maximal
8	#23763255	C₂	1	1	yes	maximal, characteristic, complemented
9	#23763242	C₂	1	2	yes	maximal
10	C₄×#14579088	C₂	1	1	yes	maximal, characteristic
11	C₇₉×#2906	C₂	1	1	yes	maximal, characteristic
12	#19099120	C₂²	1	1	yes	characteristic
13	#19098870	C₄	1	2	yes	complemented
14	#19098863	C₄	1	2	yes	complemented
15	#19098858	C₄	1	1	yes	characteristic, complemented
16	#19098853	C₄	1	1	yes	characteristic, complemented
17	#19098848	C₄	1	1	yes	characteristic, complemented
18	#19098843	C₄	1	1	yes	characteristic, complemented
19	#19098692	—	2	2	no	—
20	#19098690	—	2	1	no	—
21	#19098687	—	2	1	no	—
22	C₂×#14579096	C₂²	1	2	yes	—
23	#19098599	C₂²	1	2	yes	—
24	#19098589	C₂²	1	2	yes	—
25	C₂×C₄⋊(C₇₉⋊C₈)	C₂²	1	1	yes	characteristic
26	C₂×#14579088	C₂²	1	1	yes	characteristic
27	C₂×#14579088	C₂²	1	1	yes	characteristic
28	#19098559	C₂²	1	2	yes	—
29	#19098518	C₂²	1	2	yes	—
30	C₄×#11929608	C₂²	1	1	yes	characteristic
31	C₂×#14579071	C₂²	1	2	yes	—
32	C₄²×Dic₇₉	C₂²	1	1	yes	characteristic
33	#19098327	C₂²	1	2	yes	—
34	#19098324	C₂²	1	2	yes	—
35	#19098324	C₂²	1	2	yes	—
36	#19098322	C₂²	1	1	yes	characteristic
37	#19098322	C₂²	1	1	yes	characteristic
38	#19098317	C₂²	1	2	yes	—
39	C₂×#131×C₇₉	C₂²	1	2	yes	—
40	C₄×#41×C₇₉	C₂²	1	1	yes	characteristic
41	#424×C₇₉	—	2	2	no	—
42	#424×C₇₉	C₂²	1	2	yes	—
43	#423×C₇₉	—	2	1	no	—
44	#423×C₇₉	C₂²	1	1	yes	characteristic
45	C₂×C₄⋊C₈×C₇₉	—	2	1	no	—
46	C₂×C₄⋊C₈×C₇₉	C₂²	1	1	yes	characteristic
47	C₂×#11929608	C₂³	1	1	yes	characteristic
48	C₂×#11929608	C₂³	1	1	yes	characteristic
49	C₂²×C₇₉⋊C₈	C₂³	1	2	yes	—
50	#14579161	C₂×C₄	1	1	yes	characteristic
51	#14579161	C₂×C₄	1	1	yes	characteristic
52	#14579153	C₂×C₄	1	2	yes	—
53	#14579140	—	2	1	no	—
54	#14579140	—	2	1	no	—
55	C₄×Dic₁₅₈	—	2	1	no	—
56	C₄×Dic₁₅₈	—	2	1	no	—
57	#14579120	C₂³	1	2	yes	—
58	C₂×C₄×Dic₇₉	—	2	1	no	—
59	C₂×C₄×Dic₇₉	—	2	1	no	—
60	C₂×C₄×Dic₇₉	C₂³	1	1	yes	characteristic
61	C₂×C₄×Dic₇₉	C₂³	1	1	yes	characteristic
62	#14579096	—	4	2	no	—
63	#14579094	C₂×C₄	1	2	yes	—
64	#14579094	C₂×C₄	1	2	yes	—
65	#14579092	C₂×C₄	1	2	yes	—
66	#14579092	C₂×C₄	1	2	yes	—
67	C₄⋊(C₇₉⋊C₈)	C₂×C₄	1	1	yes	characteristic
68	C₄⋊(C₇₉⋊C₈)	C₂×C₄	1	1	yes	characteristic
69	C₄⋊(C₇₉⋊C₈)	C₂×C₄	1	2	yes	—
70	Dic₇₉⋊C₈	—	2	2	no	—
71	Dic₇₉⋊C₈	—	2	2	no	—
72	#14579088	—	2	2	no	—
73	#14579088	Q₈	1	4	yes	complemented
74	#14579085	C₂×C₄	1	2	yes	—
75	#14579085	C₂×C₄	1	2	yes	—
76	#14579082	C₂×C₄	1	2	yes	—
77	#14579082	C₂×C₄	1	2	yes	—
78	#14579072	—	2	1	no	—
79	#14579071	—	2	2	no	—
80	#14579071	—	4	2	no	—
81	C₄×C₇₉⋊C₈	—	2	1	no	—
82	C₈×Dic₇₉	—	2	2	no	—
83	C₂×#41×C₇₉	C₂³	1	1	yes	characteristic
84	#131×C₇₉	—	2	4	no	—
85	#131×C₇₉	—	4	2	no	—
86	C₂×M₁₆×C₇₉	—	2	2	no	—
87	C₂×M₁₆×C₇₉	C₂³	1	2	yes	—
88	C₂²×C₈×C₇₉	—	2	2	no	—
89	C₂²×C₈×C₇₉	C₂³	1	2	yes	—
90	C₄×Q₈×C₇₉	C₂×C₄	1	1	yes	characteristic
91	C₄×Q₈×C₇₉	C₂×C₄	1	1	yes	characteristic
92	C₄×D₄×C₇₉	—	2	1	no	—
93	C₄×D₄×C₇₉	—	2	1	no	—
94	C₄×D₄×C₇₉	C₂×C₄	1	1	yes	characteristic
95	C₄×D₄×C₇₉	C₂×C₄	1	1	yes	characteristic
96	#117×C₇₉	—	2	1	no	—
97	#117×C₇₉	C₂³	1	1	yes	characteristic
98	C₂×C₄²×C₇₉	—	2	1	no	—
99	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
100	C₄⋊C₈×C₇₉	—	2	2	no	—
101	C₄⋊C₈×C₇₉	—	2	2	no	—
102	C₄⋊C₈×C₇₉	—	2	1	no	—
103	C₄⋊C₈×C₇₉	—	2	1	no	—
104	C₄⋊C₈×C₇₉	D₄	1	1	yes	characteristic
105	C₄⋊C₈×C₇₉	D₄	1	1	yes	characteristic
106	C₄⋊C₈×C₇₉	D₄	1	2	yes	—
107	C₂×Dic₁₅₈	—	2	1	no	—
108	C₂×Dic₁₅₈	—	2	1	no	—
109	C₂²×Dic₇₉	—	2	1	no	—
110	C₂²×Dic₇₉	—	2	1	no	—
111	#11929608	—	2	1	no	—
112	#11929608	—	2	1	no	—
113	#11929608	—	2	1	no	—
114	#11929608	C₂×Q₈	1	2	yes	—
115	C₂×C₇₉⋊C₈	—	2	1	no	—
116	C₂×C₇₉⋊C₈	—	2	1	no	—
117	C₂×C₇₉⋊C₈	—	2	2	no	—
118	C₂×C₇₉⋊C₈	—	2	2	no	—
119	C₂×C₇₉⋊C₈	C₂²×C₄	1	2	yes	—
120	C₂×C₇₉⋊C₈	C₂²×C₄	1	2	yes	—
121	C₄⋊Dic₇₉	—	2	1	no	—
122	C₄⋊Dic₇₉	—	2	1	no	—
123	C₄⋊Dic₇₉	C₂²×C₄	1	2	yes	—
124	C₄⋊Dic₇₉	C₂²×C₄	1	2	yes	—
125	Dic₇₉⋊C₄	—	2	2	no	—
126	Dic₇₉⋊C₄	—	2	2	no	—
127	C₂²⋊Dic₇₉	—	2	2	no	—
128	C₄×Dic₇₉	—	2	2	no	—
129	C₄×Dic₇₉	—	2	1	no	—
130	C₄×Dic₇₉	—	2	1	no	—
131	C₄×Dic₇₉	—	2	1	no	—
132	C₄×Dic₇₉	—	4	2	no	—
133	C₄×Dic₇₉	—	4	2	no	—
134	C₄×Dic₇₉	C₂×Q₈	1	2	yes	—
135	#41×C₇₉	—	2	1	no	—
136	#41×C₇₉	—	2	1	no	—
137	#41×C₇₉	C₂×Q₈	1	2	yes	—
138	#41×C₇₉	#41	1	2	yes	—
139	C₂×Q₈×C₇₉	C₂²×C₄	1	1	yes	characteristic
140	C₂×D₄×C₇₉	—	2	1	no	—
141	C₂×D₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
142	C₂²×C₄×C₇₉	—	2	1	no	—
143	C₂²×C₄×C₇₉	—	2	1	no	—
144	C₂²×C₄×C₇₉	—	2	1	no	—
145	C₂²×C₄×C₇₉	#41	1	1	yes	characteristic
146	C₂²×C₄×C₇₉	#41	1	1	yes	characteristic
147	C₂²×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
148	M₁₆×C₇₉	—	2	2	no	—
149	M₁₆×C₇₉	—	2	2	no	—
150	M₁₆×C₇₉	—	4	4	no	—
151	C₂×C₈×C₇₉	—	2	2	no	—
152	C₂×C₈×C₇₉	—	2	2	no	—
153	C₂×C₈×C₇₉	—	2	2	no	—
154	C₂×C₈×C₇₉	—	4	4	no	—
155	C₂×C₈×C₇₉	C₂×D₄	1	2	yes	—
156	C₂×C₈×C₇₉	C₂×D₄	1	2	yes	—
157	C₄⋊C₄×C₇₉	—	2	1	no	—
158	C₄⋊C₄×C₇₉	—	2	1	no	—
159	C₄⋊C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
160	C₄⋊C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
161	C₂²⋊C₄×C₇₉	—	2	1	no	—
162	C₂²⋊C₄×C₇₉	—	2	1	no	—
163	C₂²⋊C₄×C₇₉	—	2	1	no	—
164	C₄²×C₇₉	—	2	1	no	—
165	C₄²×C₇₉	—	2	1	no	—
166	C₄²×C₇₉	—	2	1	no	—
167	C₄²×C₇₉	C₂²×C₄	1	1	yes	characteristic
168	C₄²×C₇₉	C₂²×C₄	1	1	yes	characteristic
169	C₄²×C₇₉	C₂×D₄	1	1	yes	characteristic
170	C₄²×C₇₉	C₂×D₄	1	1	yes	characteristic
171	C₂³×C₇₉	—	2	1	no	—
172	C₂³×C₇₉	C₂×#41	1	1	yes	characteristic
173	Q₈×C₇₉	—	2	1	no	—
174	Q₈×C₇₉	C₄×Q₈	1	2	yes	—
175	D₄×C₇₉	—	2	2	no	—
176	D₄×C₇₉	—	2	2	no	—
177	D₄×C₇₉	—	2	1	no	—
178	D₄×C₇₉	C₄×Q₈	1	2	yes	—
179	C₂×C₄×C₇₉	—	2	1	no	—
180	C₂×C₄×C₇₉	—	2	2	no	—
181	C₂×C₄×C₇₉	—	2	2	no	—
182	C₂×C₄×C₇₉	—	2	2	no	—
183	C₂×C₄×C₇₉	—	2	1	no	—
184	C₂×C₄×C₇₉	—	2	1	no	—
185	C₂×C₄×C₇₉	—	4	1	no	—
186	C₂×C₄×C₇₉	—	4	2	no	—
187	C₂×C₄×C₇₉	—	8	1	no	—
188	C₂×C₄×C₇₉	C₄×D₄	1	1	yes	characteristic
189	C₂×C₄×C₇₉	C₄×D₄	1	1	yes	characteristic
190	C₂×C₄×C₇₉	C₄×D₄	1	1	yes	characteristic
191	C₂×C₄×C₇₉	C₄×D₄	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	C₂×C₄×C₇₉	C₂×#41	1	1	yes	characteristic
196	C₂×C₄×C₇₉	H(5,𝔽₂)	1	1	yes	characteristic
197	C₂×C₄×C₇₉	2₋¹⁺⁴	1	1	yes	characteristic
198	C₂×Dic₇₉	—	2	2	no	—
199	C₂×Dic₇₉	—	2	2	no	—
200	C₂×Dic₇₉	—	2	2	no	—
201	C₂×Dic₇₉	—	2	2	no	—
202	C₂×Dic₇₉	—	4	1	no	—
203	C₂×Dic₇₉	—	4	1	no	—
204	C₂×Dic₇₉	—	4	1	no	—
205	C₂×Dic₇₉	—	4	1	no	—
206	Dic₁₅₈	—	4	2	no	—
207	Dic₁₅₈	—	8	1	no	—
208	C₈×C₇₉	—	2	2	no	—
209	C₈×C₇₉	—	2	2	no	—
210	C₈×C₇₉	—	4	2	no	—
211	C₇₉⋊C₈	—	2	2	no	—
212	C₇₉⋊C₈	—	2	2	no	—
213	C₇₉⋊C₈	—	2	2	no	—
214	C₇₉⋊C₈	—	4	1	no	—
215	C₂²×C₇₉	—	2	1	no	—
216	C₂²×C₇₉	—	2	1	no	—
217	C₂²×C₇₉	—	2	2	no	—
218	C₂²×C₇₉	—	4	1	no	—
219	C₂²×C₇₉	—	4	1	no	—
220	C₂²×C₇₉	C₂×C₄×D₄	1	1	yes	characteristic
221	C₂²×C₇₉	#552	1	1	yes	characteristic
222	C₂²×C₇₉	#554	1	1	yes	characteristic
223	C₄×C₇₉	—	2	2	no	—
224	C₄×C₇₉	—	2	1	no	—
225	C₄×C₇₉	—	2	1	no	—
226	C₄×C₇₉	—	2	1	no	—
227	C₄×C₇₉	—	4	1	no	—
228	C₄×C₇₉	—	4	1	no	—
229	C₄×C₇₉	#444	1	2	yes	—
230	C₄×C₇₉	C₂×C₄×Q₈	1	1	yes	characteristic
231	C₄×C₇₉	#520	1	1	yes	characteristic
232	C₄×C₇₉	#546	1	1	yes	characteristic
233	C₄×C₇₉	D₄×Q₈	1	1	yes	characteristic
234	Dic₇₉	—	4	2	no	—
235	Dic₇₉	—	4	2	no	—
236	Dic₇₉	—	4	2	no	—
237	Dic₇₉	—	4	2	no	—
238	#22983	—	79	1	no	maximal, Sylow
239	C₂×C₇₉	—	2	1	no	—
240	C₂×C₇₉	—	2	1	no	—
241	C₂×C₇₉	—	4	2	no	—
242	C₂×C₇₉	#2360	1	1	yes	characteristic
243	C₂×C₇₉	C₂×#444	1	1	yes	characteristic
244	C₂×C₇₉	#2956	1	1	yes	characteristic
245	#3076	—	79	1	no	—
246	#2962	—	79	1	no	—
247	#2906	D₇₉	1	1	yes	characteristic
248	#1994	—	79	1	no	—
249	#1950	—	79	1	no	—
250	#1946	—	79	2	no	—
251	#1922	—	79	2	no	—
252	#1866	—	79	2	no	—
253	#1767	—	79	1	no	—
254	#1765	—	79	2	no	—
255	C₄×#104	—	79	1	no	—
256	C₇₉	#22983	1	1	yes	characteristic, complemented, Sylow
257	C₂×#131	C₂×D₇₉	1	2	yes	—
258	#533	—	79	1	no	—
259	C₄×#41	C₂×D₇₉	1	1	yes	characteristic
260	#479	—	79	2	no	—
261	#478	—	79	2	no	—
262	#477	—	79	1	no	—
263	#476	—	79	1	no	—
264	#475	—	79	1	no	—
265	#474	—	79	1	no	—
266	#446	—	158	1	no	—
267	#446	—	158	2	no	—
268	C₈×Q₈	—	158	1	no	—
269	C₂×#108	—	79	2	no	—
270	#427	—	79	2	no	—
271	#424	—	2	2	no	—
272	#424	—	79	2	no	—
273	#424	C₂×D₇₉	1	2	yes	—
274	#423	—	2	1	no	—
275	#423	C₂×D₇₉	1	1	yes	characteristic
276	C₂×C₄⋊C₈	—	2	1	no	—
277	C₂×C₄⋊C₈	—	79	1	no	—
278	C₂×C₄⋊C₈	C₂×D₇₉	1	1	yes	characteristic
279	C₂×#104	—	79	1	no	—
280	C₂×#104	—	79	1	no	—
281	#416	—	79	2	no	—
282	#405	—	79	2	no	—
283	C₄×M₁₆	—	79	1	no	—
284	C₂×#97	—	79	2	no	—
285	C₄³	—	79	1	no	—
286	#341	—	79	2	no	—
287	#339	—	79	2	no	—
288	#339	—	79	2	no	—
289	#339	—	79	1	no	—
290	#339	—	79	1	no	—
291	#336	—	79	2	no	—
292	C₂×#41	C₂²×D₇₉	1	1	yes	characteristic
293	#131	—	2	4	no	—
294	#131	—	4	2	no	—
295	C₂×M₁₆	—	2	2	no	—
296	C₂×M₁₆	—	79	1	no	—
297	C₂×M₁₆	—	79	1	no	—
298	C₂×M₁₆	C₂²×D₇₉	1	2	yes	—
299	C₂²×C₈	—	2	2	no	—
300	C₂²×C₈	—	79	2	no	—
301	C₂²×C₈	C₂²×D₇₉	1	2	yes	—
302	C₄⋊Q₈	—	79	1	no	—
303	C₄⋊Q₈	—	79	1	no	—
304	#125	—	79	2	no	—
305	C₂²⋊Q₈	—	158	1	no	—
306	C₂²⋊Q₈	—	158	1	no	—
307	C₄×Q₈	—	158	1	no	—
308	C₄×Q₈	—	158	1	no	—
309	C₄×Q₈	C₄×D₇₉	1	1	yes	characteristic
310	C₄×Q₈	C₄×D₇₉	1	1	yes	characteristic
311	C₄×D₄	—	2	1	no	—
312	C₄×D₄	—	2	1	no	—
313	C₄×D₄	C₄×D₇₉	1	1	yes	characteristic
314	C₄×D₄	C₄×D₇₉	1	1	yes	characteristic
315	#117	—	2	1	no	—
316	#117	—	79	2	no	—
317	#117	C₂²×D₇₉	1	1	yes	characteristic
318	C₂×C₄²	—	2	1	no	—
319	C₂×C₄²	—	79	1	no	—
320	C₂×C₄²	—	79	1	no	—
321	C₂×C₄²	—	158	1	no	—
322	C₂×C₄²	—	158	1	no	—
323	C₂×C₄²	C₂²×D₇₉	1	1	yes	characteristic
324	#108	—	316	2	no	—
325	#107	—	79	2	no	—
326	#107	—	79	2	no	—
327	#106	—	79	2	no	—
328	#106	—	79	2	no	—
329	C₄⋊C₈	—	2	2	no	—
330	C₄⋊C₈	—	2	2	no	—
331	C₄⋊C₈	—	2	1	no	—
332	C₄⋊C₈	—	2	1	no	—
333	C₄⋊C₈	—	79	1	no	—
334	C₄⋊C₈	—	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	1	yes	characteristic
339	C₄⋊C₈	C₂²⋊D₇₉	1	1	yes	characteristic
340	C₄⋊C₈	C₂²⋊D₇₉	1	2	yes	—
341	#104	—	79	4	no	—
342	#104	—	158	2	no	—
343	#103	—	79	2	no	—
344	#103	—	79	2	no	—
345	#102	—	79	2	no	—
346	#102	—	79	2	no	—
347	#97	—	316	2	no	—
348	#97	—	158	2	no	—
349	#97	—	158	1	no	—
350	C₄×C₈	—	158	2	no	—
351	C₄×C₈	—	158	1	no	—
352	#41	—	2	1	no	—
353	#41	—	2	1	no	—
354	#41	Q₈×D₇₉	1	2	yes	—
355	#41	#11929623	1	2	yes	—
356	C₂×Q₈	—	158	1	no	—
357	C₂×Q₈	—	158	1	no	—
358	C₂×Q₈	C₂×C₄×D₇₉	1	1	yes	characteristic
359	C₂×D₄	—	2	1	no	—
360	C₂×D₄	C₂×C₄×D₇₉	1	1	yes	characteristic
361	C₂²×C₄	—	2	1	no	—
362	C₂²×C₄	—	2	1	no	—
363	C₂²×C₄	—	2	1	no	—
364	C₂²×C₄	—	158	1	no	—
365	C₂²×C₄	—	158	1	no	—
366	C₂²×C₄	#11929624	1	1	yes	characteristic
367	C₂²×C₄	#11929624	1	1	yes	characteristic
368	C₂²×C₄	C₂³×D₇₉	1	1	yes	characteristic
369	M₁₆	—	2	2	no	—
370	M₁₆	—	2	2	no	—
371	M₁₆	—	4	4	no	—
372	M₁₆	—	79	2	no	—
373	M₁₆	—	158	1	no	—
374	M₁₆	—	158	1	no	—
375	M₁₆	—	158	1	no	—
376	C₂×C₈	—	2	2	no	—
377	C₂×C₈	—	2	2	no	—
378	C₂×C₈	—	2	2	no	—
379	C₂×C₈	—	4	4	no	—
380	C₂×C₈	—	79	2	no	—
381	C₂×C₈	—	79	2	no	—
382	C₂×C₈	—	158	1	no	—
383	C₂×C₈	—	158	2	no	—
384	C₂×C₈	—	158	2	no	—
385	C₂×C₈	—	158	1	no	—
386	C₂×C₈	C₂×C₂²⋊D₇₉	1	2	yes	—
387	C₂×C₈	C₂×C₂²⋊D₇₉	1	2	yes	—
388	C₄⋊C₄	—	2	1	no	—
389	C₄⋊C₄	—	2	1	no	—
390	C₄⋊C₄	—	79	2	no	—
391	C₄⋊C₄	—	79	2	no	—
392	C₄⋊C₄	—	158	2	no	—
393	C₄⋊C₄	—	158	2	no	—
394	C₄⋊C₄	—	158	1	no	—
395	C₄⋊C₄	—	158	1	no	—
396	C₄⋊C₄	C₂×C₄×D₇₉	1	1	yes	characteristic
397	C₄⋊C₄	C₂×C₄×D₇₉	1	1	yes	characteristic
398	C₂²⋊C₄	—	2	1	no	—
399	C₂²⋊C₄	—	2	1	no	—
400	C₂²⋊C₄	—	2	1	no	—
401	C₂²⋊C₄	—	158	2	no	—
402	C₄²	—	2	1	no	—
403	C₄²	—	2	1	no	—
404	C₄²	—	2	1	no	—
405	C₄²	—	316	2	no	—
406	C₄²	—	316	2	no	—
407	C₄²	—	79	2	no	—
408	C₄²	—	158	1	no	—
409	C₄²	—	158	1	no	—
410	C₄²	—	158	1	no	—
411	C₄²	—	158	2	no	—
412	C₄²	C₂×C₄×D₇₉	1	1	yes	characteristic
413	C₄²	C₂×C₄×D₇₉	1	1	yes	characteristic
414	C₄²	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
415	C₄²	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
416	C₂³	—	2	1	no	—
417	C₂³	C₂×#11929624	1	1	yes	characteristic
418	Q₈	—	2	1	no	—
419	Q₈	—	316	2	no	—
420	Q₈	—	632	1	no	—
421	Q₈	#14579126	1	2	yes	—
422	D₄	—	2	2	no	—
423	D₄	—	2	2	no	—
424	D₄	—	2	1	no	—
425	D₄	#14579126	1	2	yes	—
426	C₂×C₄	—	2	1	no	—
427	C₂×C₄	—	2	2	no	—
428	C₂×C₄	—	2	2	no	—
429	C₂×C₄	—	2	2	no	—
430	C₂×C₄	—	2	1	no	—
431	C₂×C₄	—	2	1	no	—
432	C₂×C₄	—	4	1	no	—
433	C₂×C₄	—	4	2	no	—
434	C₂×C₄	—	8	1	no	—
435	C₂×C₄	—	316	1	no	—
436	C₂×C₄	—	316	1	no	—
437	C₂×C₄	—	316	1	no	—
438	C₂×C₄	—	316	1	no	—
439	C₂×C₄	—	158	2	no	—
440	C₂×C₄	—	158	2	no	—
441	C₂×C₄	—	158	2	no	—
442	C₂×C₄	—	158	2	no	—
443	C₂×C₄	C₄×C₂²⋊D₇₉	1	1	yes	characteristic
444	C₂×C₄	C₄×C₂²⋊D₇₉	1	1	yes	characteristic
445	C₂×C₄	C₄×C₂²⋊D₇₉	1	1	yes	characteristic
446	C₂×C₄	C₄×C₂²⋊D₇₉	1	1	yes	characteristic
447	C₂×C₄	C₂²×C₄×D₇₉	1	1	yes	characteristic
448	C₂×C₄	C₂²×C₂²⋊D₇₉	1	1	yes	characteristic
449	C₂×C₄	C₂×Q₈×D₇₉	1	1	yes	characteristic
450	C₂×C₄	C₂×#11929623	1	1	yes	characteristic
451	C₂×C₄	#14579206	1	1	yes	characteristic
452	C₂×C₄	#14579209	1	1	yes	characteristic
453	C₈	—	2	2	no	—
454	C₈	—	2	2	no	—
455	C₈	—	4	2	no	—
456	C₈	—	316	1	no	—
457	C₈	—	158	2	no	—
458	C₈	—	158	2	no	—
459	C₈	—	158	2	no	—
460	C₂²	—	2	1	no	—
461	C₂²	—	2	1	no	—
462	C₂²	—	2	2	no	—
463	C₂²	—	4	1	no	—
464	C₂²	—	4	1	no	—
465	C₂²	C₂×C₄×C₂²⋊D₇₉	1	1	yes	characteristic
466	C₂²	#19099248	1	1	yes	characteristic
467	C₂²	#19099268	1	1	yes	characteristic
468	C₄	—	2	2	no	—
469	C₄	—	2	1	no	—
470	C₄	—	2	1	no	—
471	C₄	—	2	1	no	—
472	C₄	—	4	1	no	—
473	C₄	—	4	1	no	—
474	C₄	—	316	2	no	—
475	C₄	—	316	2	no	—
476	C₄	—	316	2	no	—
477	C₄	—	316	2	no	—
478	C₄	#19098683	1	2	yes	—
479	C₄	C₂×#14579126	1	1	yes	characteristic
480	C₄	#19099044	1	1	yes	characteristic
481	C₄	#19099207	1	1	yes	characteristic
482	C₄	Q₈×C₂²⋊D₇₉	1	1	yes	characteristic
483	C₂	—	2	1	no	—
484	C₂	—	2	1	no	—
485	C₂	—	4	2	no	—
486	C₂	#23766405	1	1	yes	characteristic
487	C₂	C₂×#19098683	1	1	yes	characteristic
488	C₂	#23772307	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²×C₂²⋊D₇₉
commutator	C₂×C₄×C₇₉	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₇₉
Fitting	C₇₉×#2906	C₂
socle	C₂²×C₇₉	C₂×C₄×D₄
prime radical	C₂×#41×C₇₉	C₂³
cosocle	C₂²×C₄×C₇₉	C₂⁴
hypercenter	#2906	D₇₉
hypocenter	C₇₉	#22983
LCS	G ▷ C₂×C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄⋊C₈ ◁ #2906

Complements

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

N	H ≅ G/N	type
2. #23772343	C₂	semidirect
3. #23764376	C₂	semidirect
4. #23764173	C₂	semidirect
5. #23764150	C₂	semidirect
6. #23763996	C₂	semidirect
8. #23763255	C₂	semidirect
13. #19098870	C₄	semidirect
14. #19098863	C₄	semidirect
15. #19098858	C₄	semidirect
16. #19098853	C₄	semidirect
17. #19098848	C₄	semidirect
18. #19098843	C₄	semidirect
73. #14579088	Q₈	semidirect
256. C₇₉	#22983	semidirect

Maximal subgroups

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

subgroup	index
#23773188	2
#23772343	2
#23764376	2
#23764173	2
#23764150	2
#23763996	2
#23763675	2
#23763255	2
#23763242	2
C₄×#14579088	2
C₇₉×#2906	2
#22983	79