Subgroups — #34311157

Order 20224.

844 conjugacy classes of subgroups.

The subgroup lattice has 468 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#19098835	C₂	1	1	yes	maximal, characteristic
2	#23772243	C₂	1	2	yes	maximal
3	#23771997	C₂	1	1	yes	maximal, characteristic
4	#23764262	C₂	1	1	yes	maximal, characteristic, complemented
5	#23764185	C₂	1	1	yes	maximal, characteristic, complemented
6	#23764058	C₂	1	2	yes	maximal, complemented
7	#23763766	C₂	1	2	yes	maximal
8	#23763615	C₂	1	2	yes	maximal, complemented
9	#23763281	C₂	1	1	yes	maximal, characteristic, complemented
10	#23763239	C₂	1	1	yes	maximal, characteristic
11	C₇₉×#2950	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#14579192	C₂²	1	2	yes	—
13	C₂×#14579167	C₂²	1	1	yes	characteristic
14	#19099043	C₂²	1	2	yes	—
15	#19098835	C₄	1	8	yes	complemented
16	#19098668	—	2	2	no	—
17	#19098661	—	2	2	no	—
18	C₄×#11929614	—	2	2	no	—
19	C₄×#11929611	—	2	2	no	—
20	C₂×#14579097	C₂²	1	1	yes	characteristic
21	#19098606	C₂²	1	2	yes	—
22	#19098606	C₂²	1	2	yes	—
23	#19098602	—	2	2	no	—
24	#19098600	—	2	1	no	—
25	C₂×#14579095	C₂²	1	1	yes	characteristic
26	#107×D₇₉	—	2	1	no	—
27	C₂×#14579087	C₂²	1	1	yes	characteristic
28	#19098557	C₂²	1	1	yes	characteristic
29	C₂×#14579085	C₂²	1	2	yes	—
30	C₂×#14579080	C₂²	1	2	yes	—
31	#19098519	C₂²	1	2	yes	—
32	C₂×C₈×Dic₇₉	C₂²	1	1	yes	characteristic
33	#19098470	C₂²	1	2	yes	—
34	#19098331	C₂²	1	2	yes	—
35	#19098327	C₂²	1	1	yes	characteristic
36	#19098322	C₂²	1	1	yes	characteristic
37	#19098322	C₂²	1	2	yes	—
38	C₂²×Q₁₆×C₇₉	C₂²	1	1	yes	characteristic
39	#519×C₇₉	C₂²	1	2	yes	—
40	#441×C₇₉	—	2	2	no	—
41	C₄×Q₁₆×C₇₉	—	2	1	no	—
42	C₄×Q₁₆×C₇₉	—	2	1	no	—
43	#427×C₇₉	C₂²	1	1	yes	characteristic
44	#419×C₇₉	C₂²	1	2	yes	—
45	#405×C₇₉	C₂²	1	1	yes	characteristic
46	C₂×#11929624	C₂³	1	1	yes	characteristic
47	#14579192	—	2	4	no	—
48	#14579192	C₂×C₄	1	8	yes	—
49	C₂×#11929614	—	2	2	no	—
50	C₂×#11929611	—	2	2	no	—
51	#14579167	—	2	2	no	—
52	#14579167	C₂×C₄	1	4	yes	—
53	C₂×#11929608	C₂³	1	2	yes	—
54	C₂×#11929608	C₂³	1	1	yes	characteristic
55	C₂×#11929607	—	2	1	no	—
56	C₂²×C₇₉⋊C₈	C₂³	1	1	yes	characteristic
57	C₂×C₈×D₇₉	—	2	1	no	—
58	C₄×Dic₁₅₈	—	2	2	no	—
59	C₄×D₃₁₆	—	2	2	no	—
60	(C₂²⋊D₇₉)⋊C₄	—	4	2	no	—
61	#14579119	—	2	2	no	—
62	C₂×C₄⋊Dic₇₉	C₂³	1	2	yes	—
63	C₄⋊C₄×D₇₉	—	2	2	no	—
64	C₂×C₄×Dic₇₉	C₂³	1	1	yes	characteristic
65	#14579097	C₂×C₄	1	4	yes	complemented
66	#14579095	—	2	1	no	—
67	#14579095	—	2	1	no	—
68	#14579094	—	2	2	no	—
69	#14579094	—	2	2	no	—
70	#14579092	—	2	2	no	—
71	#14579092	—	2	2	no	—
72	#14579087	—	2	2	no	—
73	#14579085	—	2	2	no	—
74	#14579085	—	2	2	no	—
75	#14579084	D₄	1	1	yes	characteristic
76	#14579084	D₄	1	1	yes	characteristic
77	#14579081	D₄	1	1	yes	characteristic
78	#14579081	D₄	1	1	yes	characteristic
79	#14579080	C₂×C₄	1	8	yes	complemented
80	#14579072	—	2	2	no	—
81	C₄×C₇₉⋊C₈	—	2	2	no	—
82	C₈×Dic₇₉	—	2	2	no	—
83	C₇₉⋊#95	—	4	2	no	—
84	C₂²×Q₈×C₇₉	C₂³	1	2	yes	—
85	C₂×Q₁₆×C₇₉	—	2	1	no	—
86	C₂×Q₁₆×C₇₉	—	2	1	no	—
87	C₂×Q₁₆×C₇₉	—	2	2	no	—
88	C₂×Q₁₆×C₇₉	C₂×C₄	1	4	yes	complemented
89	C₂×M₁₆×C₇₉	C₂³	1	1	yes	characteristic
90	C₂²×C₈×C₇₉	C₂³	1	1	yes	characteristic
91	C₄×Q₈×C₇₉	—	2	2	no	—
92	C₄×Q₈×C₇₉	—	2	2	no	—
93	C₄×Q₈×C₇₉	—	2	2	no	—
94	C₄×Q₈×C₇₉	—	2	2	no	—
95	#117×C₇₉	—	4	2	no	—
96	#117×C₇₉	C₂³	1	2	yes	—
97	#117×C₇₉	C₂³	1	1	yes	characteristic
98	#107×C₇₉	D₄	1	1	yes	characteristic
99	#107×C₇₉	D₄	1	1	yes	characteristic
100	#106×C₇₉	D₄	1	2	yes	—
101	#103×C₇₉	—	2	2	no	—
102	#103×C₇₉	—	2	2	no	—
103	#97×C₇₉	—	2	1	no	—
104	C₄×C₈×C₇₉	—	2	1	no	—
105	#11929624	—	2	1	no	—
106	#11929624	—	2	1	no	—
107	#11929624	C₂²×C₄	1	2	yes	—
108	#11929624	#41	1	2	yes	—
109	C₂×Dic₁₅₈	C₂×D₄	1	1	yes	characteristic
110	C₂×D₃₁₆	C₂×D₄	1	1	yes	characteristic
111	C₂×C₂²⋊D₇₉	—	2	1	no	—
112	C₂²×Dic₇₉	—	2	1	no	—
113	C₂²×Dic₇₉	—	2	2	no	—
114	C₂×C₄×D₇₉	—	2	1	no	—
115	C₂×C₄×D₇₉	—	4	2	no	—
116	#11929614	—	2	8	no	—
117	#11929611	—	2	8	no	—
118	#11929608	—	2	1	no	—
119	#11929608	—	2	2	no	—
120	#11929608	C₂²×C₄	1	2	yes	—
121	#11929608	C₂²×C₄	1	4	yes	—
122	#11929607	—	2	4	no	—
123	C₂×C₇₉⋊C₈	—	2	2	no	—
124	C₂×C₇₉⋊C₈	—	2	1	no	—
125	C₂×C₇₉⋊C₈	—	2	1	no	—
126	C₂×C₇₉⋊C₈	—	2	1	no	—
127	C₂×C₇₉⋊C₈	C₂×D₄	1	1	yes	characteristic
128	C₂×C₇₉⋊C₈	C₂×D₄	1	1	yes	characteristic
129	C₈×D₇₉	—	2	4	no	—
130	C₄⋊Dic₇₉	—	2	2	no	—
131	C₄⋊Dic₇₉	—	2	2	no	—
132	Dic₇₉⋊C₄	—	4	2	no	—
133	(C₂×D₇₉)⋊C₄	—	4	2	no	—
134	C₄×Dic₇₉	—	2	1	no	—
135	C₄×Dic₇₉	—	2	1	no	—
136	C₄×Dic₇₉	—	4	2	no	—
137	C₂×Q₈×C₇₉	—	2	2	no	—
138	C₂×Q₈×C₇₉	—	2	2	no	—
139	C₂×Q₈×C₇₉	—	2	2	no	—
140	C₂×Q₈×C₇₉	—	2	2	no	—
141	C₂×Q₈×C₇₉	—	2	2	no	—
142	C₂×Q₈×C₇₉	C₂²×C₄	1	4	yes	—
143	C₂²×C₄×C₇₉	—	2	2	no	—
144	C₂²×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
145	Q₁₆×C₇₉	—	2	4	no	—
146	Q₁₆×C₇₉	—	2	4	no	—
147	M₁₆×C₇₉	—	2	1	no	—
148	M₁₆×C₇₉	—	2	1	no	—
149	C₂×C₈×C₇₉	—	2	1	no	—
150	C₂×C₈×C₇₉	C₂²×C₄	1	2	yes	—
151	C₂×C₈×C₇₉	C₂×D₄	1	1	yes	characteristic
152	C₂×C₈×C₇₉	C₂×D₄	1	1	yes	characteristic
153	C₂×C₈×C₇₉	#41	1	2	yes	—
154	C₄⋊C₄×C₇₉	—	4	2	no	—
155	C₄⋊C₄×C₇₉	—	4	2	no	—
156	C₄⋊C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
157	C₄⋊C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
158	C₄⋊C₄×C₇₉	C₂×D₄	1	2	yes	—
159	C₄⋊C₄×C₇₉	C₂×D₄	1	2	yes	—
160	C₂²⋊C₄×C₇₉	—	2	1	no	—
161	C₂²⋊C₄×C₇₉	—	2	2	no	—
162	C₄²×C₇₉	—	2	1	no	—
163	C₄²×C₇₉	—	2	2	no	—
164	C₄²×C₇₉	—	4	2	no	—
165	C₄²×C₇₉	—	4	2	no	—
166	C₂³×C₇₉	H(5,𝔽₂)	1	1	yes	characteristic
167	C₂²×D₇₉	—	2	1	no	—
168	Q₈×C₇₉	—	2	4	no	—
169	Q₈×C₇₉	—	2	4	no	—
170	Q₈×C₇₉	—	4	2	no	—
171	Q₈×C₇₉	—	4	2	no	—
172	C₂×C₄×C₇₉	—	2	4	no	—
173	C₂×C₄×C₇₉	—	2	2	no	—
174	C₂×C₄×C₇₉	—	2	2	no	—
175	C₂×C₄×C₇₉	—	2	1	no	—
176	C₂×C₄×C₇₉	—	2	1	no	—
177	C₂×C₄×C₇₉	—	4	2	no	—
178	C₂×C₄×C₇₉	—	4	2	no	—
179	C₂×C₄×C₇₉	C₂³×C₄	1	1	yes	characteristic
180	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
181	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
182	C₂×C₄×C₇₉	C₂×#41	1	1	yes	characteristic
183	C₂×C₄×C₇₉	C₂×#41	1	1	yes	characteristic
184	C₂×C₄×C₇₉	2₋¹⁺⁴	1	1	yes	characteristic
185	C₂²⋊D₇₉	—	2	2	no	—
186	C₂²⋊D₇₉	—	2	2	no	—
187	C₂×Dic₇₉	—	2	1	no	—
188	C₂×Dic₇₉	—	2	2	no	—
189	C₂×Dic₇₉	—	4	1	no	—
190	C₂×Dic₇₉	—	4	1	no	—
191	C₂×Dic₇₉	—	4	2	no	—
192	C₂×Dic₇₉	—	8	2	no	—
193	D₃₁₆	—	2	1	no	—
194	D₃₁₆	C₄×D₄	1	2	yes	—
195	C₄×D₇₉	—	2	2	no	—
196	C₄×D₇₉	—	2	2	no	—
197	C₄×D₇₉	—	16	2	no	—
198	Dic₁₅₈	—	2	1	no	—
199	Dic₁₅₈	C₄×D₄	1	2	yes	—
200	C₈×C₇₉	—	4	1	no	—
201	C₈×C₇₉	C₄×D₄	1	2	yes	—
202	C₈×C₇₉	C₄×D₄	1	2	yes	—
203	C₇₉⋊C₈	—	2	2	no	—
204	C₇₉⋊C₈	—	2	4	no	—
205	C₇₉⋊C₈	—	2	1	no	—
206	C₇₉⋊C₈	—	2	1	no	—
207	C₂²×C₇₉	—	2	1	no	—
208	C₂²×C₇₉	—	2	1	no	—
209	C₂²×C₇₉	#520	1	1	yes	characteristic
210	C₂²×C₇₉	D₄²	1	1	yes	characteristic
211	C₂²×C₇₉	#553	1	1	yes	characteristic
212	C₂×D₇₉	—	2	2	no	—
213	C₂×D₇₉	—	4	1	no	—
214	C₂×D₇₉	—	4	1	no	—
215	C₄×C₇₉	—	4	4	no	—
216	C₄×C₇₉	—	4	1	no	—
217	C₄×C₇₉	—	4	2	no	—
218	C₄×C₇₉	—	4	2	no	—
219	C₄×C₇₉	—	4	1	no	—
220	C₄×C₇₉	C₂×C₄×D₄	1	1	yes	characteristic
221	C₄×C₇₉	C₂×C₄×D₄	1	1	yes	characteristic
222	C₄×C₇₉	#547	1	1	yes	characteristic
223	C₄×C₇₉	#548	1	1	yes	characteristic
224	Dic₇₉	—	2	2	no	—
225	Dic₇₉	—	4	2	no	—
226	Dic₇₉	—	8	2	no	—
227	#23045	—	79	1	no	maximal, Sylow
228	C₂×C₇₉	—	2	1	no	—
229	C₂×C₇₉	—	2	1	no	—
230	C₂×C₇₉	#2361	1	1	yes	characteristic
231	C₂×C₇₉	#3290	1	1	yes	characteristic
232	C₂×C₇₉	#3293	1	1	yes	characteristic
233	D₇₉	—	4	2	no	—
234	C₂×#473	—	79	1	no	—
235	#2950	D₇₉	1	1	yes	characteristic, complemented
236	#2947	—	79	2	no	—
237	#2913	—	79	1	no	—
238	#1969	—	79	1	no	—
239	#1952	—	79	1	no	—
240	#1930	—	79	2	no	—
241	#1882	—	79	2	no	—
242	#1857	—	79	2	no	—
243	#1772	—	79	1	no	—
244	#1764	—	79	1	no	—
245	C₇₉	#23045	1	1	yes	characteristic, complemented, Sylow
246	C₂×#137	—	79	2	no	—
247	C₂²×Q₁₆	C₂×D₇₉	1	1	yes	characteristic
248	C₂×#131	—	79	1	no	—
249	#520	—	79	2	no	—
250	#519	C₂×D₇₉	1	2	yes	—
251	#473	—	79	8	no	—
252	#441	—	2	2	no	—
253	#441	—	158	2	no	—
254	#440	—	158	2	no	—
255	C₄×Q₁₆	—	2	1	no	—
256	C₄×Q₁₆	—	2	1	no	—
257	C₄×Q₁₆	—	158	2	no	—
258	C₄×SD₁₆	—	158	2	no	—
259	C₂×#108	—	79	1	no	—
260	#428	—	79	2	no	—
261	#428	—	79	2	no	—
262	#428	—	158	2	no	—
263	#427	—	158	1	no	—
264	#427	C₂×D₇₉	1	1	yes	characteristic
265	C₂×#107	—	79	1	no	—
266	C₂×#107	—	158	1	no	—
267	C₂×#104	—	79	1	no	—
268	#419	C₂×D₇₉	1	2	yes	—
269	#416	—	79	1	no	—
270	C₂×#103	—	79	2	no	—
271	C₂×#101	—	79	2	no	—
272	#405	—	79	2	no	—
273	#405	C₂×D₇₉	1	1	yes	characteristic
274	C₂×C₄×C₈	—	79	1	no	—
275	#391	—	79	2	no	—
276	#343	—	79	2	no	—
277	#341	—	79	1	no	—
278	#339	—	79	1	no	—
279	#339	—	79	2	no	—
280	C₂×#41	—	79	1	no	—
281	C₂²×Q₈	C₂²×D₇₉	1	2	yes	—
282	#137	—	79	8	no	—
283	#137	—	158	4	no	—
284	C₂×Q₁₆	—	2	1	no	—
285	C₂×Q₁₆	—	2	1	no	—
286	C₂×Q₁₆	—	2	2	no	—
287	C₂×Q₁₆	—	158	2	no	—
288	C₂×Q₁₆	C₄×D₇₉	1	4	yes	complemented
289	C₂×SD₁₆	—	158	2	no	—
290	#131	—	79	4	no	—
291	#131	—	158	2	no	—
292	C₂×M₁₆	—	79	1	no	—
293	C₂×M₁₆	—	79	2	no	—
294	C₂×M₁₆	—	158	1	no	—
295	C₂×M₁₆	C₂²×D₇₉	1	1	yes	characteristic
296	C₂²×C₈	—	79	1	no	—
297	C₂²×C₈	—	158	1	no	—
298	C₂²×C₈	C₂²×D₇₉	1	1	yes	characteristic
299	C₄×Q₈	—	2	2	no	—
300	C₄×Q₈	—	2	2	no	—
301	C₄×Q₈	—	2	2	no	—
302	C₄×Q₈	—	2	2	no	—
303	C₄×Q₈	—	158	2	no	—
304	C₄×D₄	—	316	2	no	—
305	C₄×D₄	—	158	2	no	—
306	#117	—	4	2	no	—
307	#117	—	158	2	no	—
308	#117	C₂²×D₇₉	1	1	yes	characteristic
309	#117	C₂²×D₇₉	1	2	yes	—
310	C₂×C₄⋊C₄	—	79	2	no	—
311	C₂×C₄⋊C₄	—	158	2	no	—
312	C₂×C₄²	—	79	1	no	—
313	#108	—	79	4	no	—
314	#107	—	158	1	no	—
315	#107	—	158	1	no	—
316	#107	—	158	2	no	—
317	#107	—	158	2	no	—
318	#107	C₂²⋊D₇₉	1	1	yes	characteristic
319	#107	C₂²⋊D₇₉	1	1	yes	characteristic
320	#106	—	158	2	no	—
321	#106	—	158	2	no	—
322	#106	C₂²⋊D₇₉	1	2	yes	—
323	#104	—	158	2	no	—
324	#103	—	2	2	no	—
325	#103	—	2	2	no	—
326	#103	—	79	1	no	—
327	#103	—	79	1	no	—
328	#103	—	158	2	no	—
329	#103	—	158	2	no	—
330	#102	—	79	1	no	—
331	#102	—	79	1	no	—
332	#101	—	79	8	no	—
333	#97	—	2	1	no	—
334	#97	—	158	2	no	—
335	C₄×C₈	—	2	1	no	—
336	C₄×C₈	—	158	2	no	—
337	C₄×C₈	—	158	2	no	—
338	#95	—	316	2	no	—
339	#41	—	79	2	no	—
340	#41	—	79	2	no	—
341	#41	—	158	1	no	—
342	#41	—	158	1	no	—
343	C₂×Q₈	—	2	2	no	—
344	C₂×Q₈	—	2	2	no	—
345	C₂×Q₈	—	2	2	no	—
346	C₂×Q₈	—	2	2	no	—
347	C₂×Q₈	—	2	2	no	—
348	C₂×Q₈	—	79	1	no	—
349	C₂×Q₈	C₂×C₄×D₇₉	1	4	yes	—
350	C₂×D₄	—	79	1	no	—
351	C₂×D₄	—	158	1	no	—
352	C₂²×C₄	—	2	2	no	—
353	C₂²×C₄	—	316	2	no	—
354	C₂²×C₄	—	158	1	no	—
355	C₂²×C₄	—	158	2	no	—
356	C₂²×C₄	—	158	1	no	—
357	C₂²×C₄	C₂³×D₇₉	1	1	yes	characteristic
358	Q₁₆	—	2	4	no	—
359	Q₁₆	—	2	4	no	—
360	Q₁₆	—	158	8	no	—
361	SD₁₆	—	158	8	no	—
362	M₁₆	—	2	1	no	—
363	M₁₆	—	2	1	no	—
364	M₁₆	—	79	2	no	—
365	M₁₆	—	79	4	no	—
366	M₁₆	—	158	2	no	—
367	M₁₆	—	158	1	no	—
368	M₁₆	—	158	4	no	—
369	C₂×C₈	—	2	1	no	—
370	C₂×C₈	—	79	1	no	—
371	C₂×C₈	—	79	1	no	—
372	C₂×C₈	—	158	1	no	—
373	C₂×C₈	—	158	1	no	—
374	C₂×C₈	—	158	2	no	—
375	C₂×C₈	—	158	1	no	—
376	C₂×C₈	—	158	4	no	—
377	C₂×C₈	C₂×C₄×D₇₉	1	2	yes	—
378	C₂×C₈	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
379	C₂×C₈	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
380	C₂×C₈	#11929624	1	2	yes	—
381	C₄⋊C₄	—	4	2	no	—
382	C₄⋊C₄	—	4	2	no	—
383	C₄⋊C₄	—	316	2	no	—
384	C₄⋊C₄	—	158	2	no	—
385	C₄⋊C₄	—	158	2	no	—
386	C₄⋊C₄	D₄×D₇₉	1	1	yes	characteristic
387	C₄⋊C₄	D₄×D₇₉	1	1	yes	characteristic
388	C₄⋊C₄	C₂×C₂²⋊D₇₉	1	2	yes	—
389	C₄⋊C₄	C₂×C₂²⋊D₇₉	1	2	yes	—
390	C₂²⋊C₄	—	2	1	no	—
391	C₂²⋊C₄	—	2	2	no	—
392	C₂²⋊C₄	—	316	2	no	—
393	C₄²	—	2	2	no	—
394	C₄²	—	2	1	no	—
395	C₄²	—	4	2	no	—
396	C₄²	—	4	2	no	—
397	C₄²	—	316	2	no	—
398	C₄²	—	158	1	no	—
399	C₄²	—	158	1	no	—
400	C₂³	—	158	1	no	—
401	C₂³	#14579206	1	1	yes	characteristic
402	Q₈	—	2	4	no	—
403	Q₈	—	2	4	no	—
404	Q₈	—	4	2	no	—
405	Q₈	—	4	2	no	—
406	Q₈	—	79	2	no	—
407	Q₈	—	158	1	no	—
408	D₄	—	79	2	no	—
409	D₄	—	158	2	no	—
410	D₄	—	158	2	no	—
411	D₄	—	158	1	no	—
412	C₂×C₄	—	2	1	no	—
413	C₂×C₄	—	2	1	no	—
414	C₂×C₄	—	2	2	no	—
415	C₂×C₄	—	2	2	no	—
416	C₂×C₄	—	2	4	no	—
417	C₂×C₄	—	4	2	no	—
418	C₂×C₄	—	4	2	no	—
419	C₂×C₄	—	316	1	no	—
420	C₂×C₄	—	316	1	no	—
421	C₂×C₄	—	316	2	no	—
422	C₂×C₄	—	632	2	no	—
423	C₂×C₄	—	158	2	no	—
424	C₂×C₄	—	158	1	no	—
425	C₂×C₄	—	158	2	no	—
426	C₂×C₄	—	158	2	no	—
427	C₂×C₄	—	1264	2	no	—
428	C₂×C₄	C₂²×C₄×D₇₉	1	1	yes	characteristic
429	C₂×C₄	C₂×D₄×D₇₉	1	1	yes	characteristic
430	C₂×C₄	C₂²×C₂²⋊D₇₉	1	1	yes	characteristic
431	C₂×C₄	#41×D₇₉	1	1	yes	characteristic
432	C₂×C₄	C₂×#11929624	1	1	yes	characteristic
433	C₂×C₄	#14579208	1	1	yes	characteristic
434	C₈	—	4	1	no	—
435	C₈	—	158	1	no	—
436	C₈	—	158	1	no	—
437	C₈	—	158	4	no	—
438	C₈	—	158	2	no	—
439	C₈	C₄×C₂²⋊D₇₉	1	2	yes	—
440	C₈	C₄×C₂²⋊D₇₉	1	2	yes	—
441	C₂²	—	2	1	no	—
442	C₂²	—	2	1	no	—
443	C₂²	—	316	1	no	—
444	C₂²	—	316	1	no	—
445	C₂²	—	158	2	no	—
446	C₂²	#19099042	1	1	yes	characteristic
447	C₂²	D₄×C₂²⋊D₇₉	1	1	yes	characteristic
448	C₂²	#19099263	1	1	yes	characteristic
449	C₄	—	4	4	no	—
450	C₄	—	4	2	no	—
451	C₄	—	4	1	no	—
452	C₄	—	4	1	no	—
453	C₄	—	4	2	no	—
454	C₄	—	316	2	no	—
455	C₄	—	632	2	no	—
456	C₄	—	158	2	no	—
457	C₄	C₄×D₄×D₇₉	1	1	yes	characteristic
458	C₄	C₂×C₄×C₂²⋊D₇₉	1	1	yes	characteristic
459	C₄	#19099218	1	1	yes	characteristic
460	C₄	#19099220	1	1	yes	characteristic
461	C₂	—	2	1	no	—
462	C₂	—	2	1	no	—
463	C₂	—	316	2	no	—
464	C₂	#23766412	1	1	yes	characteristic
465	C₂	#23775186	1	1	yes	characteristic
466	C₂	#23775202	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	D₄×C₂²⋊D₇₉
commutator	C₂×C₄×C₇₉	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₇₉
Fitting	C₇₉×#2950	C₂
socle	C₂²×C₇₉	D₄²
prime radical	C₂×#11929624	C₂³
cosocle	C₂²×C₄×C₇₉	C₂⁴
hypercenter	#2950	D₇₉
hypocenter	C₇₉	#23045
LCS	G ▷ C₂×C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ #2950

Complements

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

N	H ≅ G/N	type
4. #23764262	C₂	semidirect
5. #23764185	C₂	semidirect
6. #23764058	C₂	semidirect
8. #23763615	C₂	semidirect
9. #23763281	C₂	semidirect
11. C₇₉×#2950	C₂	semidirect
15. #19098835	C₄	semidirect
65. #14579097	C₂×C₄	semidirect
79. #14579080	C₂×C₄	semidirect
88. C₂×Q₁₆×C₇₉	C₂×C₄	semidirect
235. #2950	D₇₉	semidirect
245. C₇₉	#23045	semidirect
288. C₂×Q₁₆	C₄×D₇₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×#19098835	2
#23772243	2
#23771997	2
#23764262	2
#23764185	2
#23764058	2
#23763766	2
#23763615	2
#23763281	2
#23763239	2
C₇₉×#2950	2
#23045	79