Subgroups — #34310332

Order 20224.

720 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	#23773182	C₂	1	1	yes	maximal, characteristic
2	#23771965	C₂	1	1	yes	maximal, characteristic
3	#23764378	C₂	1	1	yes	maximal, characteristic, complemented
4	#23764175	C₂	1	1	yes	maximal, characteristic, complemented
5	#23764145	C₂	1	2	yes	maximal, complemented
6	#23763999	C₂	1	2	yes	maximal, complemented
7	#23763674	C₂	1	2	yes	maximal
8	C₄⋊C₈×Dic₇₉	C₂	1	1	yes	maximal, characteristic, complemented
9	#23763239	C₂	1	2	yes	maximal
10	C₄×#14579087	C₂	1	1	yes	maximal, characteristic
11	C₇₉×#2962	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#14579167	C₂²	1	2	yes	—
13	C₄×#11929624	C₂²	1	1	yes	characteristic
14	#19098867	C₄	1	2	yes	complemented
15	#19098860	C₄	1	2	yes	complemented
16	#19098855	C₄	1	1	yes	characteristic, complemented
17	#19098850	C₄	1	1	yes	characteristic, complemented
18	#19098845	C₄	1	1	yes	characteristic, complemented
19	#19098840	C₄	1	1	yes	characteristic, complemented
20	C₂×#14579096	C₂²	1	2	yes	—
21	#19098599	C₂²	1	2	yes	—
22	#19098589	C₂²	1	2	yes	—
23	#19098588	—	2	2	no	—
24	#19098587	C₂²	1	1	yes	characteristic
25	#19098585	—	2	1	no	—
26	C₂×C₄⋊(C₇₉⋊C₈)	C₂²	1	1	yes	characteristic
27	C₄⋊C₈×D₇₉	—	2	1	no	—
28	C₂×#14579087	C₂²	1	1	yes	characteristic
29	C₂×#14579087	C₂²	1	1	yes	characteristic
30	#19098557	C₂²	1	2	yes	—
31	C₂×C₈×Dic₇₉	C₂²	1	2	yes	—
32	C₄²×Dic₇₉	C₂²	1	1	yes	characteristic
33	#19098327	C₂²	1	2	yes	—
34	#19098324	C₂²	1	1	yes	characteristic
35	#19098324	C₂²	1	1	yes	characteristic
36	#19098322	C₂²	1	2	yes	—
37	#19098322	C₂²	1	2	yes	—
38	#19098317	C₂²	1	2	yes	—
39	#533×C₇₉	C₂²	1	1	yes	characteristic
40	#446×C₇₉	—	2	2	no	—
41	#446×C₇₉	—	2	1	no	—
42	C₈×Q₈×C₇₉	—	2	1	no	—
43	#424×C₇₉	C₂²	1	2	yes	—
44	C₂×C₄⋊C₈×C₇₉	C₂²	1	1	yes	characteristic
45	#405×C₇₉	C₂²	1	2	yes	—
46	C₄×M₁₆×C₇₉	C₂²	1	1	yes	characteristic
47	C₂×#11929624	C₂³	1	1	yes	characteristic
48	#14579167	—	2	4	no	—
49	#14579167	—	4	2	no	—
50	C₂×#11929608	C₂³	1	2	yes	—
51	C₂×#11929607	—	2	2	no	—
52	C₂²×C₇₉⋊C₈	C₂³	1	2	yes	—
53	C₂×C₈×D₇₉	—	2	2	no	—
54	C₄×Dic₁₅₈	C₂×C₄	1	1	yes	characteristic
55	C₄×Dic₁₅₈	C₂×C₄	1	1	yes	characteristic
56	C₄×D₃₁₆	C₂×C₄	1	1	yes	characteristic
57	C₄×D₃₁₆	C₂×C₄	1	1	yes	characteristic
58	C₄×C₂²⋊D₇₉	—	2	1	no	—
59	C₄×C₂²⋊D₇₉	—	2	1	no	—
60	#14579120	C₂³	1	1	yes	characteristic
61	#14579118	—	2	1	no	—
62	C₂×C₄×Dic₇₉	—	2	1	no	—
63	C₂×C₄×Dic₇₉	—	2	1	no	—
64	C₂×C₄×Dic₇₉	C₂³	1	1	yes	characteristic
65	C₂×C₄×Dic₇₉	C₂³	1	1	yes	characteristic
66	C₄²×D₇₉	—	2	1	no	—
67	#14579096	—	4	2	no	—
68	#14579094	C₂×C₄	1	2	yes	—
69	#14579094	C₂×C₄	1	2	yes	—
70	#14579092	C₂×C₄	1	2	yes	—
71	#14579092	C₂×C₄	1	2	yes	—
72	C₄⋊(C₇₉⋊C₈)	—	2	1	no	—
73	C₄⋊(C₇₉⋊C₈)	—	2	1	no	—
74	C₄⋊(C₇₉⋊C₈)	C₂×C₄	1	1	yes	characteristic
75	C₄⋊(C₇₉⋊C₈)	C₂×C₄	1	1	yes	characteristic
76	C₄⋊(C₇₉⋊C₈)	C₂×C₄	1	2	yes	—
77	Dic₇₉⋊C₈	—	2	2	no	—
78	Dic₇₉⋊C₈	—	2	2	no	—
79	#14579087	—	2	2	no	—
80	#14579087	Q₈	1	4	yes	complemented
81	#14579084	C₂×C₄	1	2	yes	—
82	#14579084	C₂×C₄	1	2	yes	—
83	#14579081	C₂×C₄	1	2	yes	—
84	#14579081	C₂×C₄	1	2	yes	—
85	C₈×Dic₇₉	—	4	2	no	—
86	C₂×M₁₆×C₇₉	C₂³	1	1	yes	characteristic
87	C₂×M₁₆×C₇₉	C₂³	1	1	yes	characteristic
88	C₂²×C₈×C₇₉	C₂³	1	2	yes	—
89	C₄⋊Q₈×C₇₉	C₂×C₄	1	1	yes	characteristic
90	C₄⋊Q₈×C₇₉	C₂×C₄	1	1	yes	characteristic
91	#125×C₇₉	C₂×C₄	1	2	yes	—
92	C₂²⋊Q₈×C₇₉	—	2	1	no	—
93	C₂²⋊Q₈×C₇₉	—	2	1	no	—
94	C₄×Q₈×C₇₉	—	2	1	no	—
95	C₄×Q₈×C₇₉	—	2	1	no	—
96	#117×C₇₉	C₂³	1	2	yes	—
97	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
98	C₄⋊C₈×C₇₉	—	2	2	no	—
99	C₄⋊C₈×C₇₉	—	2	2	no	—
100	C₄⋊C₈×C₇₉	D₄	1	1	yes	characteristic
101	C₄⋊C₈×C₇₉	D₄	1	1	yes	characteristic
102	C₄⋊C₈×C₇₉	D₄	1	2	yes	—
103	#97×C₇₉	—	2	2	no	—
104	#97×C₇₉	—	2	1	no	—
105	C₄×C₈×C₇₉	—	2	2	no	—
106	C₄×C₈×C₇₉	—	2	1	no	—
107	#11929624	—	2	1	no	—
108	#11929624	—	2	1	no	—
109	#11929624	C₂×Q₈	1	2	yes	—
110	#11929624	#41	1	2	yes	—
111	C₂×Dic₁₅₈	C₂²×C₄	1	1	yes	characteristic
112	C₂×D₃₁₆	C₂²×C₄	1	1	yes	characteristic
113	C₂×C₂²⋊D₇₉	—	2	1	no	—
114	C₂²×Dic₇₉	—	2	1	no	—
115	C₂²×Dic₇₉	—	2	1	no	—
116	C₂×C₄×D₇₉	—	2	1	no	—
117	C₂×C₄×D₇₉	—	2	1	no	—
118	C₂×C₄×D₇₉	—	2	1	no	—
119	#11929608	—	2	2	no	—
120	#11929608	—	2	2	no	—
121	#11929607	—	4	4	no	—
122	C₂×C₇₉⋊C₈	—	2	2	no	—
123	C₂×C₇₉⋊C₈	—	2	2	no	—
124	C₂×C₇₉⋊C₈	—	2	2	no	—
125	C₂×C₇₉⋊C₈	C₂²×C₄	1	2	yes	—
126	C₂×C₇₉⋊C₈	C₂²×C₄	1	2	yes	—
127	C₈×D₇₉	—	4	4	no	—
128	C₄⋊Dic₇₉	C₂²×C₄	1	1	yes	characteristic
129	C₄⋊Dic₇₉	C₂²×C₄	1	1	yes	characteristic
130	Dic₇₉⋊C₄	—	2	1	no	—
131	Dic₇₉⋊C₄	—	2	1	no	—
132	C₂²⋊Dic₇₉	—	2	1	no	—
133	(C₂×D₇₉)⋊C₄	—	2	1	no	—
134	(C₂×D₇₉)⋊C₄	—	2	1	no	—
135	C₄×Dic₇₉	—	2	4	no	—
136	C₄×Dic₇₉	—	2	1	no	—
137	C₄×Dic₇₉	—	2	1	no	—
138	C₄×Dic₇₉	—	2	1	no	—
139	C₄×Dic₇₉	—	2	1	no	—
140	C₄×Dic₇₉	—	2	1	no	—
141	C₄×Dic₇₉	—	2	1	no	—
142	C₄×Dic₇₉	—	4	2	no	—
143	C₄×Dic₇₉	C₂×Q₈	1	2	yes	—
144	C₂×Q₈×C₇₉	—	2	1	no	—
145	C₂×Q₈×C₇₉	—	2	1	no	—
146	C₂²×C₄×C₇₉	#41	1	1	yes	characteristic
147	C₂²×C₄×C₇₉	#41	1	1	yes	characteristic
148	C₂²×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
149	M₁₆×C₇₉	—	2	1	no	—
150	M₁₆×C₇₉	—	2	1	no	—
151	M₁₆×C₇₉	—	2	1	no	—
152	M₁₆×C₇₉	C₂×Q₈	1	2	yes	—
153	C₂×C₈×C₇₉	—	2	1	no	—
154	C₂×C₈×C₇₉	—	2	1	no	—
155	C₂×C₈×C₇₉	—	2	2	no	—
156	C₂×C₈×C₇₉	—	2	2	no	—
157	C₂×C₈×C₇₉	C₂×D₄	1	2	yes	—
158	C₂×C₈×C₇₉	C₂×D₄	1	2	yes	—
159	C₄⋊C₄×C₇₉	—	2	2	no	—
160	C₄⋊C₄×C₇₉	—	2	2	no	—
161	C₄⋊C₄×C₇₉	—	2	1	no	—
162	C₄⋊C₄×C₇₉	—	2	1	no	—
163	C₄⋊C₄×C₇₉	C₂²×C₄	1	2	yes	—
164	C₄⋊C₄×C₇₉	C₂²×C₄	1	2	yes	—
165	C₂²⋊C₄×C₇₉	—	2	2	no	—
166	C₄²×C₇₉	—	2	2	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	C₂×#41	1	1	yes	characteristic
172	C₂²×D₇₉	—	2	1	no	—
173	Q₈×C₇₉	—	4	2	no	—
174	Q₈×C₇₉	—	8	1	no	—
175	C₂×C₄×C₇₉	—	2	2	no	—
176	C₂×C₄×C₇₉	—	2	2	no	—
177	C₂×C₄×C₇₉	—	2	2	no	—
178	C₂×C₄×C₇₉	—	4	1	no	—
179	C₂×C₄×C₇₉	C₄×D₄	1	1	yes	characteristic
180	C₂×C₄×C₇₉	C₄×D₄	1	1	yes	characteristic
181	C₂×C₄×C₇₉	C₄×D₄	1	1	yes	characteristic
182	C₂×C₄×C₇₉	C₄×D₄	1	1	yes	characteristic
183	C₂×C₄×C₇₉	C₂³×C₄	1	1	yes	characteristic
184	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
185	C₂×C₄×C₇₉	C₂²×Q₈	1	1	yes	characteristic
186	C₂×C₄×C₇₉	C₂×#41	1	1	yes	characteristic
187	C₂×C₄×C₇₉	H(5,𝔽₂)	1	1	yes	characteristic
188	C₂×C₄×C₇₉	2₋¹⁺⁴	1	1	yes	characteristic
189	C₂²⋊D₇₉	—	2	2	no	—
190	C₂²⋊D₇₉	—	2	2	no	—
191	C₂×Dic₇₉	—	2	2	no	—
192	C₂×Dic₇₉	—	2	2	no	—
193	C₂×Dic₇₉	—	2	1	no	—
194	C₂×Dic₇₉	—	2	2	no	—
195	C₂×Dic₇₉	—	2	2	no	—
196	C₂×Dic₇₉	—	2	1	no	—
197	C₂×Dic₇₉	—	2	1	no	—
198	C₂×Dic₇₉	—	4	1	no	—
199	C₂×Dic₇₉	—	4	1	no	—
200	D₃₁₆	—	2	1	no	—
201	D₃₁₆	C₄×Q₈	1	2	yes	—
202	C₄×D₇₉	—	2	2	no	—
203	C₄×D₇₉	—	2	2	no	—
204	C₄×D₇₉	—	4	2	no	—
205	C₄×D₇₉	—	8	1	no	—
206	Dic₁₅₈	—	2	1	no	—
207	Dic₁₅₈	C₄×Q₈	1	2	yes	—
208	C₈×C₇₉	—	2	2	no	—
209	C₈×C₇₉	—	2	2	no	—
210	C₈×C₇₉	—	2	2	no	—
211	C₈×C₇₉	—	4	1	no	—
212	C₇₉⋊C₈	—	2	2	no	—
213	C₇₉⋊C₈	—	2	2	no	—
214	C₇₉⋊C₈	—	4	2	no	—
215	C₂²×C₇₉	—	2	1	no	—
216	C₂²×C₇₉	—	2	1	no	—
217	C₂²×C₇₉	C₂×C₄×D₄	1	1	yes	characteristic
218	C₂²×C₇₉	#552	1	1	yes	characteristic
219	C₂²×C₇₉	#554	1	1	yes	characteristic
220	C₂×D₇₉	—	2	2	no	—
221	C₂×D₇₉	—	4	1	no	—
222	C₂×D₇₉	—	4	1	no	—
223	C₄×C₇₉	—	2	1	no	—
224	C₄×C₇₉	—	2	1	no	—
225	C₄×C₇₉	—	2	1	no	—
226	C₄×C₇₉	—	4	2	no	—
227	C₄×C₇₉	—	4	2	no	—
228	C₄×C₇₉	#443	1	2	yes	—
229	C₄×C₇₉	C₂×C₄×Q₈	1	1	yes	characteristic
230	C₄×C₇₉	#520	1	1	yes	characteristic
231	C₄×C₇₉	#546	1	1	yes	characteristic
232	C₄×C₇₉	D₄×Q₈	1	1	yes	characteristic
233	Dic₇₉	—	2	4	no	—
234	Dic₇₉	—	2	2	no	—
235	Dic₇₉	—	4	2	no	—
236	Dic₇₉	—	4	1	no	—
237	Dic₇₉	—	4	1	no	—
238	#22982	—	79	1	no	maximal, Sylow
239	C₂×C₇₉	—	2	1	no	—
240	C₂×C₇₉	—	2	1	no	—
241	C₂×C₇₉	#2360	1	1	yes	characteristic
242	C₂×C₇₉	C₂×#443	1	1	yes	characteristic
243	C₂×C₇₉	#2956	1	1	yes	characteristic
244	D₇₉	—	4	2	no	—
245	#3076	—	79	1	no	—
246	#2962	D₇₉	1	1	yes	characteristic, complemented
247	#2906	—	79	1	no	—
248	#1994	—	79	1	no	—
249	#1950	—	79	1	no	—
250	#1945	—	79	2	no	—
251	#1922	—	79	2	no	—
252	#1866	—	79	2	no	—
253	C₄×C₄⋊C₈	—	79	1	no	—
254	#1764	—	79	2	no	—
255	C₄×#104	—	79	1	no	—
256	C₇₉	#22982	1	1	yes	characteristic, complemented, Sylow
257	C₂×#131	—	79	2	no	—
258	#533	C₂×D₇₉	1	1	yes	characteristic
259	C₄×#41	—	79	1	no	—
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	—	2	2	no	—
267	#446	—	2	1	no	—
268	C₈×Q₈	—	2	1	no	—
269	C₂×#108	—	79	2	no	—
270	#427	—	79	2	no	—
271	#424	—	79	2	no	—
272	#424	—	158	2	no	—
273	#424	C₂×D₇₉	1	2	yes	—
274	#423	—	79	1	no	—
275	#423	—	158	1	no	—
276	C₂×C₄⋊C₈	—	79	1	no	—
277	C₂×C₄⋊C₈	—	158	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	C₂×D₇₉	1	2	yes	—
283	C₄×M₁₆	C₂×D₇₉	1	1	yes	characteristic
284	C₂×C₄×C₈	—	79	2	no	—
285	C₄³	—	79	1	no	—
286	#341	—	79	2	no	—
287	#339	—	79	1	no	—
288	#339	—	79	1	no	—
289	#339	—	79	2	no	—
290	#339	—	79	2	no	—
291	#336	—	79	2	no	—
292	C₂×#41	—	79	1	no	—
293	#131	—	316	2	no	—
294	#131	—	158	4	no	—
295	C₂×M₁₆	—	79	2	no	—
296	C₂×M₁₆	—	158	2	no	—
297	C₂×M₁₆	C₂²×D₇₉	1	1	yes	characteristic
298	C₂×M₁₆	C₂²×D₇₉	1	1	yes	characteristic
299	C₂²×C₈	—	79	2	no	—
300	C₂²×C₈	—	158	2	no	—
301	C₂²×C₈	C₂²×D₇₉	1	2	yes	—
302	C₄⋊Q₈	C₄×D₇₉	1	1	yes	characteristic
303	C₄⋊Q₈	C₄×D₇₉	1	1	yes	characteristic
304	#125	C₄×D₇₉	1	2	yes	—
305	C₂²⋊Q₈	—	2	1	no	—
306	C₂²⋊Q₈	—	2	1	no	—
307	C₄×Q₈	—	2	1	no	—
308	C₄×Q₈	—	2	1	no	—
309	C₄×Q₈	—	79	1	no	—
310	C₄×Q₈	—	79	1	no	—
311	C₄×D₄	—	79	1	no	—
312	C₄×D₄	—	79	1	no	—
313	C₄×D₄	—	158	1	no	—
314	C₄×D₄	—	158	1	no	—
315	#117	—	79	1	no	—
316	#117	—	158	1	no	—
317	#117	C₂²×D₇₉	1	2	yes	—
318	C₂×C₄²	—	79	1	no	—
319	C₂×C₄²	—	79	1	no	—
320	C₂×C₄²	—	158	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	—	79	1	no	—
332	C₄⋊C₈	—	79	1	no	—
333	C₄⋊C₈	—	79	2	no	—
334	C₄⋊C₈	—	158	2	no	—
335	C₄⋊C₈	—	158	2	no	—
336	C₄⋊C₈	—	158	1	no	—
337	C₄⋊C₈	—	158	1	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	—	2	2	no	—
348	#97	—	2	1	no	—
349	C₄×C₈	—	2	2	no	—
350	C₄×C₈	—	2	1	no	—
351	C₄×C₈	—	316	2	no	—
352	#41	—	79	2	no	—
353	#41	—	79	2	no	—
354	#41	—	158	1	no	—
355	#41	—	158	1	no	—
356	C₂×Q₈	—	2	1	no	—
357	C₂×Q₈	—	2	1	no	—
358	C₂×Q₈	—	79	1	no	—
359	C₂×D₄	—	79	1	no	—
360	C₂×D₄	—	158	1	no	—
361	C₂²×C₄	—	158	1	no	—
362	C₂²×C₄	—	158	1	no	—
363	C₂²×C₄	—	158	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	1	no	—
370	M₁₆	—	2	1	no	—
371	M₁₆	—	2	1	no	—
372	M₁₆	—	316	4	no	—
373	M₁₆	—	158	2	no	—
374	M₁₆	—	158	2	no	—
375	M₁₆	Q₈×D₇₉	1	2	yes	—
376	C₂×C₈	—	2	2	no	—
377	C₂×C₈	—	2	2	no	—
378	C₂×C₈	—	2	1	no	—
379	C₂×C₈	—	2	1	no	—
380	C₂×C₈	—	316	4	no	—
381	C₂×C₈	—	79	2	no	—
382	C₂×C₈	—	79	2	no	—
383	C₂×C₈	—	158	2	no	—
384	C₂×C₈	—	158	2	no	—
385	C₂×C₈	—	158	2	no	—
386	C₂×C₈	C₂×C₂²⋊D₇₉	1	2	yes	—
387	C₂×C₈	C₂×C₂²⋊D₇₉	1	2	yes	—
388	C₄⋊C₄	—	2	2	no	—
389	C₄⋊C₄	—	2	2	no	—
390	C₄⋊C₄	—	2	1	no	—
391	C₄⋊C₄	—	2	1	no	—
392	C₄⋊C₄	—	79	1	no	—
393	C₄⋊C₄	—	79	1	no	—
394	C₄⋊C₄	—	158	1	no	—
395	C₄⋊C₄	—	158	1	no	—
396	C₄⋊C₄	C₂×C₄×D₇₉	1	2	yes	—
397	C₄⋊C₄	C₂×C₄×D₇₉	1	2	yes	—
398	C₂²⋊C₄	—	2	2	no	—
399	C₂²⋊C₄	—	158	1	no	—
400	C₂²⋊C₄	—	158	1	no	—
401	C₂²⋊C₄	—	158	1	no	—
402	C₄²	—	2	2	no	—
403	C₄²	—	316	2	no	—
404	C₄²	—	79	2	no	—
405	C₄²	—	158	4	no	—
406	C₄²	—	158	1	no	—
407	C₄²	—	158	1	no	—
408	C₄²	—	158	1	no	—
409	C₄²	—	158	1	no	—
410	C₄²	—	158	1	no	—
411	C₄²	—	158	1	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	—	158	1	no	—
417	C₂³	C₂×#11929624	1	1	yes	characteristic
418	Q₈	—	4	2	no	—
419	Q₈	—	8	1	no	—
420	Q₈	—	79	2	no	—
421	Q₈	—	158	1	no	—
422	D₄	—	79	2	no	—
423	D₄	—	158	2	no	—
424	D₄	—	158	2	no	—
425	D₄	—	158	1	no	—
426	C₂×C₄	—	2	2	no	—
427	C₂×C₄	—	2	2	no	—
428	C₂×C₄	—	2	2	no	—
429	C₂×C₄	—	4	1	no	—
430	C₂×C₄	—	316	1	no	—
431	C₂×C₄	—	316	1	no	—
432	C₂×C₄	—	316	2	no	—
433	C₂×C₄	—	632	1	no	—
434	C₂×C₄	—	158	2	no	—
435	C₂×C₄	—	158	1	no	—
436	C₂×C₄	—	158	1	no	—
437	C₂×C₄	—	158	2	no	—
438	C₂×C₄	—	158	2	no	—
439	C₂×C₄	—	158	2	no	—
440	C₂×C₄	—	158	1	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	#41×D₇₉	1	1	yes	characteristic
451	C₂×C₄	#14579207	1	1	yes	characteristic
452	C₂×C₄	#14579209	1	1	yes	characteristic
453	C₈	—	2	2	no	—
454	C₈	—	2	2	no	—
455	C₈	—	2	2	no	—
456	C₈	—	4	1	no	—
457	C₈	—	316	2	no	—
458	C₈	—	158	2	no	—
459	C₈	—	158	2	no	—
460	C₂²	—	2	1	no	—
461	C₂²	—	2	1	no	—
462	C₂²	—	316	1	no	—
463	C₂²	—	316	1	no	—
464	C₂²	—	158	2	no	—
465	C₂²	C₂×C₄×C₂²⋊D₇₉	1	1	yes	characteristic
466	C₂²	#19099254	1	1	yes	characteristic
467	C₂²	#19099273	1	1	yes	characteristic
468	C₄	—	2	1	no	—
469	C₄	—	2	1	no	—
470	C₄	—	2	1	no	—
471	C₄	—	4	2	no	—
472	C₄	—	4	2	no	—
473	C₄	—	316	2	no	—
474	C₄	—	316	1	no	—
475	C₄	—	316	1	no	—
476	C₄	—	158	4	no	—
477	C₄	—	158	2	no	—
478	C₄	#19098678	1	2	yes	—
479	C₄	C₄×Q₈×D₇₉	1	1	yes	characteristic
480	C₄	#19099045	1	1	yes	characteristic
481	C₄	#19099201	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	—	316	2	no	—
486	C₂	#23766401	1	1	yes	characteristic
487	C₂	C₂×#19098678	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×#2962	C₂
socle	C₂²×C₇₉	C₂×C₄×D₄
prime radical	C₂×#11929624	C₂³
cosocle	C₂²×C₄×C₇₉	C₂⁴
hypercenter	#2962	D₇₉
hypocenter	C₇₉	#22982
LCS	G ▷ C₂×C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄⋊C₈ ◁ #2962

Complements

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

N	H ≅ G/N	type
3. #23764378	C₂	semidirect
4. #23764175	C₂	semidirect
5. #23764145	C₂	semidirect
6. #23763999	C₂	semidirect
8. C₄⋊C₈×Dic₇₉	C₂	semidirect
11. C₇₉×#2962	C₂	semidirect
14. #19098867	C₄	semidirect
15. #19098860	C₄	semidirect
16. #19098855	C₄	semidirect
17. #19098850	C₄	semidirect
18. #19098845	C₄	semidirect
19. #19098840	C₄	semidirect
80. #14579087	Q₈	semidirect
246. #2962	D₇₉	semidirect
256. C₇₉	#22982	semidirect

Maximal subgroups

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

subgroup	index
#23773182	2
#23771965	2
#23764378	2
#23764175	2
#23764145	2
#23763999	2
#23763674	2
C₄⋊C₈×Dic₇₉	2
#23763239	2
C₄×#14579087	2
C₇₉×#2962	2
#22982	79