Subgroups — #34258857

Order 20224.

662 conjugacy classes of subgroups.

The subgroup lattice has 464 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#23773995	C₂	1	1	yes	maximal, characteristic
2	#23772375	C₂	1	1	yes	maximal, characteristic, complemented
3	#23772113	C₂	1	1	yes	maximal, characteristic, complemented
4	#23762315	C₂	1	2	yes	maximal, complemented
5	#23762304	C₂	1	2	yes	maximal, complemented
6	C₈×#11929613	C₂	1	2	yes	maximal, complemented
7	C₈×D₆₃₂	C₂	1	2	yes	maximal, complemented
8	#23762167	C₂	1	1	yes	maximal, characteristic, complemented
9	#23761870	C₂	1	1	yes	maximal, characteristic, complemented
10	#23761866	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈×M₁₆×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#14579167	—	2	1	no	—
13	#19099113	C₂²	1	1	yes	characteristic
14	#19099097	C₂²	1	1	yes	characteristic
15	#19098972	C₄	1	1	yes	characteristic
16	#19098952	C₄	1	1	yes	characteristic
17	#19098928	C₄	1	1	yes	characteristic
18	#19098923	C₄	1	1	yes	characteristic
19	#19098816	C₄	1	2	yes	—
20	#19098809	C₄	1	2	yes	—
21	#19098693	C₂²	1	1	yes	characteristic
22	C₈×Dic₁₅₈	C₂²	1	1	yes	characteristic
23	C₄×#11929613	C₂²	1	2	yes	—
24	C₄×D₆₃₂	C₂²	1	2	yes	—
25	#19098642	—	2	1	no	—
26	#19098642	C₂²	1	2	yes	—
27	#19098642	C₂²	1	1	yes	characteristic
28	#19098634	—	2	1	no	—
29	C₈×D₃₁₆	—	2	1	no	—
30	C₈×D₃₁₆	C₂²	1	1	yes	characteristic
31	C₈×D₃₁₆	C₂²	1	2	yes	—
32	C₈×C₂²⋊D₇₉	—	2	1	no	—
33	#19098622	—	2	1	no	—
34	#19098620	C₂²	1	1	yes	characteristic
35	#19098587	C₂²	1	1	yes	characteristic
36	#19098529	—	2	1	no	—
37	#19098517	—	2	1	no	—
38	#19098316	C₂²	1	2	yes	—
39	#19098314	C₂²	1	2	yes	—
40	#19098295	C₂²	1	2	yes	—
41	#19098292	C₂²	1	2	yes	—
42	#19098292	C₂²	1	2	yes	—
43	#19098292	C₂²	1	2	yes	—
44	#431×C₇₉	C₂²	1	1	yes	characteristic
45	C₄×M₁₆×C₇₉	C₂²	1	1	yes	characteristic
46	C₂×C₄×C₈×C₇₉	C₂²	1	1	yes	characteristic
47	#322×C₇₉	C₂²	1	2	yes	—
48	C₈²×C₇₉	C₂²	1	2	yes	—
49	C₂×#11929624	—	2	1	no	—
50	C₂×#11929613	C₂×C₄	1	2	yes	—
51	C₂×D₆₃₂	C₂×C₄	1	2	yes	—
52	#14579167	—	4	4	no	—
53	C₂×#11929608	—	2	1	no	—
54	C₂×#11929607	—	2	1	no	—
55	C₂×#11929607	—	2	2	no	—
56	C₂×C₈×D₇₉	—	2	1	no	—
57	C₂×C₈×D₇₉	—	2	2	no	—
58	#14579161	C₂×C₄	1	1	yes	characteristic
59	#14579158	C₂×C₄	1	1	yes	characteristic
60	#14579155	—	2	1	no	—
61	#14579153	C₂×C₄	1	1	yes	characteristic
62	#14579149	—	2	1	no	—
63	#14579149	C₂×C₄	1	1	yes	characteristic
64	#14579144	—	2	1	no	—
65	#14579140	C₂×C₄	1	1	yes	characteristic
66	#14579135	—	2	1	no	—
67	#14579135	C₂×C₄	1	2	yes	—
68	#14579135	C₂×C₄	1	1	yes	characteristic
69	C₄×Dic₁₅₈	C₂³	1	1	yes	characteristic
70	C₄×D₃₁₆	—	2	1	no	—
71	C₄×D₃₁₆	C₂³	1	1	yes	characteristic
72	C₄×D₃₁₆	C₂³	1	2	yes	—
73	C₄×C₂²⋊D₇₉	—	2	1	no	—
74	#14579118	—	2	1	no	—
75	#14579095	C₂×C₄	1	2	yes	—
76	#14579093	C₂×C₄	1	2	yes	—
77	C₄⋊(C₇₉⋊C₈)	—	2	1	no	—
78	C₄⋊(C₇₉⋊C₈)	C₂³	1	2	yes	—
79	C₄⋊(C₇₉⋊C₈)	C₂³	1	1	yes	characteristic
80	C₄⋊(C₇₉⋊C₈)	C₂³	1	1	yes	characteristic
81	Dic₇₉⋊C₈	—	2	1	no	—
82	Dic₇₉⋊C₈	—	2	1	no	—
83	#14579086	C₂×C₄	1	2	yes	—
84	#14579083	C₂×C₄	1	2	yes	—
85	#14579083	C₂×C₄	1	2	yes	—
86	#14579083	C₂×C₄	1	2	yes	—
87	C₂²⋊(C₇₉⋊C₈)	—	2	1	no	—
88	(C₂×D₇₉)⋊C₈	—	2	1	no	—
89	(C₂×D₇₉)⋊C₈	—	2	2	no	—
90	(C₂×D₇₉)⋊C₈	—	2	1	no	—
91	(C₂×D₇₉)⋊C₈	—	2	2	no	—
92	#14579072	—	2	1	no	—
93	#14579071	—	2	1	no	—
94	C₈×Dic₇₉	—	2	1	no	—
95	C₂×M₁₆×C₇₉	C₂×C₄	1	2	yes	—
96	C₂²×C₈×C₇₉	D₄	1	1	yes	characteristic
97	C₂²×C₈×C₇₉	D₄	1	1	yes	characteristic
98	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
99	C₄⋊C₈×C₇₉	—	2	1	no	—
100	C₂²⋊C₈×C₇₉	—	2	1	no	—
101	#97×C₇₉	C₂×C₄	1	1	yes	characteristic
102	#97×C₇₉	C₂×C₄	1	1	yes	characteristic
103	C₄×C₈×C₇₉	D₄	1	1	yes	characteristic
104	C₄×C₈×C₇₉	D₄	1	1	yes	characteristic
105	C₄×C₈×C₇₉	C₂³	1	2	yes	—
106	C₄×C₈×C₇₉	C₂³	1	2	yes	—
107	C₄×C₈×C₇₉	C₂³	1	1	yes	characteristic
108	C₄×C₈×C₇₉	C₂³	1	1	yes	characteristic
109	#11929624	—	4	2	no	—
110	#11929624	—	4	2	no	—
111	C₂×Dic₁₅₈	—	2	1	no	—
112	C₂×Dic₁₅₈	C₂²×C₄	1	1	yes	characteristic
113	C₂×D₃₁₆	—	2	1	no	—
114	C₂×D₃₁₆	—	2	1	no	—
115	C₂×D₃₁₆	C₂²×C₄	1	1	yes	characteristic
116	C₂×D₃₁₆	C₂²×C₄	1	2	yes	—
117	C₂×C₂²⋊D₇₉	—	2	2	no	—
118	C₂×C₂²⋊D₇₉	—	2	1	no	—
119	C₂×C₄×D₇₉	—	2	2	no	—
120	C₂×C₄×D₇₉	—	2	1	no	—
121	#11929613	—	2	4	no	—
122	D₆₃₂	—	2	4	no	—
123	#11929608	—	4	2	no	—
124	#11929607	—	4	2	no	—
125	#11929607	—	4	4	no	—
126	C₂×C₇₉⋊C₈	—	2	1	no	—
127	C₂×C₇₉⋊C₈	—	2	1	no	—
128	C₂×C₇₉⋊C₈	—	2	2	no	—
129	C₈×D₇₉	—	4	2	no	—
130	C₈×D₇₉	—	4	4	no	—
131	C₄⋊Dic₇₉	—	2	1	no	—
132	C₄⋊Dic₇₉	C₂²×C₄	1	1	yes	characteristic
133	C₄⋊Dic₇₉	C₂²×C₄	1	1	yes	characteristic
134	C₄⋊Dic₇₉	C₂²×C₄	1	2	yes	—
135	Dic₇₉⋊C₄	—	2	1	no	—
136	Dic₇₉⋊C₄	—	2	1	no	—
137	Dic₇₉⋊C₄	—	2	1	no	—
138	Dic₇₉⋊C₄	—	2	1	no	—
139	C₂²⋊Dic₇₉	—	2	1	no	—
140	(C₂×D₇₉)⋊C₄	—	2	1	no	—
141	(C₂×D₇₉)⋊C₄	—	2	1	no	—
142	(C₂×D₇₉)⋊C₄	—	2	1	no	—
143	(C₂×D₇₉)⋊C₄	—	2	2	no	—
144	(C₂×D₇₉)⋊C₄	—	2	2	no	—
145	(C₂×D₇₉)⋊C₄	—	2	1	no	—
146	C₄×Dic₇₉	—	2	1	no	—
147	C₂²×C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
148	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
149	C₂²×C₄×C₇₉	#41	1	1	yes	characteristic
150	M₁₆×C₇₉	—	2	4	no	—
151	C₂×C₈×C₇₉	—	2	2	no	—
152	C₂×C₈×C₇₉	—	2	2	no	—
153	C₂×C₈×C₇₉	—	4	1	no	—
154	C₂×C₈×C₇₉	C₂²×C₄	1	2	yes	—
155	C₂×C₈×C₇₉	C₂²×C₄	1	2	yes	—
156	C₂×C₈×C₇₉	C₂×D₄	1	1	yes	characteristic
157	C₂×C₈×C₇₉	C₂×D₄	1	1	yes	characteristic
158	C₂×C₈×C₇₉	C₂×D₄	1	1	yes	characteristic
159	C₂×C₈×C₇₉	C₂×D₄	1	1	yes	characteristic
160	C₄²×C₇₉	C₂²×C₄	1	1	yes	characteristic
161	C₄²×C₇₉	C₂×D₄	1	1	yes	characteristic
162	C₄²×C₇₉	#41	1	1	yes	characteristic
163	C₄²×C₇₉	C₂⁴	1	1	yes	characteristic
164	C₂³×C₇₉	C₄×D₄	1	1	yes	characteristic
165	C₂²×D₇₉	—	2	1	no	—
166	C₂²×D₇₉	—	2	2	no	—
167	C₂×C₄×C₇₉	—	2	2	no	—
168	C₂×C₄×C₇₉	—	2	1	no	—
169	C₂×C₄×C₇₉	—	2	1	no	—
170	C₂×C₄×C₇₉	—	4	1	no	—
171	C₂×C₄×C₇₉	C₄×D₄	1	1	yes	characteristic
172	C₂×C₄×C₇₉	C₄×D₄	1	1	yes	characteristic
173	C₂×C₄×C₇₉	C₄×D₄	1	1	yes	characteristic
174	C₂×C₄×C₇₉	C₂³×C₄	1	1	yes	characteristic
175	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
176	C₂×C₄×C₇₉	C₂×#41	1	1	yes	characteristic
177	C₂²⋊D₇₉	—	4	2	no	—
178	C₂²⋊D₇₉	—	4	4	no	—
179	C₂×Dic₇₉	—	2	1	no	—
180	C₂×Dic₇₉	—	2	1	no	—
181	C₂×Dic₇₉	—	2	2	no	—
182	C₂×Dic₇₉	—	2	1	no	—
183	D₃₁₆	—	2	2	no	—
184	D₃₁₆	—	2	2	no	—
185	D₃₁₆	—	2	2	no	—
186	D₃₁₆	—	4	2	no	—
187	D₃₁₆	—	4	2	no	—
188	C₄×D₇₉	—	4	2	no	—
189	C₄×D₇₉	—	4	1	no	—
190	C₄×D₇₉	—	4	1	no	—
191	C₄×D₇₉	—	4	2	no	—
192	Dic₁₅₈	—	2	2	no	—
193	Dic₁₅₈	—	4	2	no	—
194	C₈×C₇₉	—	2	2	no	—
195	C₈×C₇₉	—	2	1	no	—
196	C₈×C₇₉	—	2	1	no	—
197	C₈×C₇₉	—	2	1	no	—
198	C₈×C₇₉	—	4	2	no	—
199	C₈×C₇₉	#131	1	4	yes	complemented
200	C₈×C₇₉	AGL(1,ℤ/8)	1	2	yes	—
201	C₇₉⋊C₈	—	4	1	no	—
202	C₇₉⋊C₈	—	4	2	no	—
203	C₇₉⋊C₈	—	4	1	no	—
204	C₂²×C₇₉	—	2	1	no	—
205	C₂²×C₇₉	—	2	1	no	—
206	C₂²×C₇₉	—	2	1	no	—
207	C₂²×C₇₉	C₂×C₄×D₄	1	1	yes	characteristic
208	C₂×D₇₉	—	4	1	no	—
209	C₂×D₇₉	—	4	2	no	—
210	C₂×D₇₉	—	4	2	no	—
211	C₂×D₇₉	—	4	1	no	—
212	C₂×D₇₉	—	4	1	no	—
213	C₂×D₇₉	—	4	2	no	—
214	C₄×C₇₉	—	2	1	no	—
215	C₄×C₇₉	—	2	1	no	—
216	C₄×C₇₉	—	2	1	no	—
217	C₄×C₇₉	—	2	1	no	—
218	C₄×C₇₉	C₂×#131	1	2	yes	—
219	C₄×C₇₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
220	C₄×C₇₉	#575	1	1	yes	characteristic
221	Dic₇₉	—	4	1	no	—
222	Dic₇₉	—	4	2	no	—
223	Dic₇₉	—	4	1	no	—
224	Dic₇₉	—	4	1	no	—
225	#17964	—	79	1	no	maximal, Sylow
226	C₂×C₇₉	—	4	1	no	—
227	C₂×C₇₉	#2931	1	1	yes	characteristic
228	C₂×C₇₉	C₄×AGL(1,ℤ/8)	1	1	yes	characteristic
229	C₂×C₇₉	#2955	1	1	yes	characteristic
230	D₇₉	—	8	2	no	—
231	D₇₉	—	8	1	no	—
232	#3171	—	79	1	no	—
233	#2966	—	79	1	no	—
234	#2931	—	79	1	no	—
235	#1594	—	79	2	no	—
236	#1592	—	79	2	no	—
237	C₈×SD₁₆	—	79	2	no	—
238	C₈×D₈	—	79	2	no	—
239	#1569	—	79	1	no	—
240	#1496	—	79	1	no	—
241	#1495	—	79	1	no	—
242	C₈×M₁₆	D₇₉	1	1	yes	characteristic, complemented
243	C₇₉	#17964	1	1	yes	characteristic, complemented, Sylow
244	C₂×#131	—	158	1	no	—
245	#532	—	79	1	no	—
246	#529	—	79	1	no	—
247	#501	—	79	1	no	—
248	#496	—	79	1	no	—
249	#490	—	79	1	no	—
250	#489	—	79	1	no	—
251	#469	—	79	2	no	—
252	#468	—	79	2	no	—
253	#446	—	79	1	no	—
254	C₈×Q₈	—	79	1	no	—
255	C₄×SD₁₆	—	79	2	no	—
256	C₄×D₈	—	79	2	no	—
257	#436	—	79	2	no	—
258	#436	—	79	1	no	—
259	#436	—	158	1	no	—
260	#435	—	158	1	no	—
261	C₈×D₄	—	79	1	no	—
262	C₈×D₄	—	79	2	no	—
263	C₈×D₄	—	158	1	no	—
264	C₈×D₄	—	158	1	no	—
265	#433	—	158	1	no	—
266	#432	—	79	1	no	—
267	#431	C₂×D₇₉	1	1	yes	characteristic
268	#423	—	79	1	no	—
269	#408	—	158	1	no	—
270	#405	—	158	1	no	—
271	C₄×M₁₆	C₂×D₇₉	1	1	yes	characteristic
272	C₂×C₄×C₈	C₂×D₇₉	1	1	yes	characteristic
273	#335	—	79	2	no	—
274	#334	—	79	2	no	—
275	Q₈⋊C₈	—	79	2	no	—
276	D₄⋊C₈	—	79	2	no	—
277	D₄⋊C₈	—	79	2	no	—
278	D₄⋊C₈	—	79	2	no	—
279	#322	C₂×D₇₉	1	2	yes	—
280	C₈²	C₂×D₇₉	1	2	yes	—
281	C₂×#41	—	158	1	no	—
282	C₂×SD₁₆	—	79	2	no	—
283	C₂×D₈	—	79	2	no	—
284	#131	—	316	4	no	—
285	C₂×M₁₆	—	158	1	no	—
286	C₂×M₁₆	—	158	2	no	—
287	C₂×M₁₆	—	158	1	no	—
288	C₂×M₁₆	C₄×D₇₉	1	2	yes	—
289	C₂²×C₈	—	158	2	no	—
290	C₂²×C₈	—	158	1	no	—
291	C₂²×C₈	D₃₁₆	1	1	yes	characteristic
292	C₂²×C₈	D₃₁₆	1	1	yes	characteristic
293	C₄⋊Q₈	—	79	1	no	—
294	#127	—	79	1	no	—
295	#126	—	158	1	no	—
296	#125	—	79	1	no	—
297	#124	—	79	1	no	—
298	#124	—	158	1	no	—
299	#123	—	158	1	no	—
300	C₂²⋊Q₈	—	79	1	no	—
301	#121	—	79	1	no	—
302	#121	—	79	2	no	—
303	#121	—	158	1	no	—
304	C₄×Q₈	—	79	1	no	—
305	C₄×D₄	—	79	1	no	—
306	C₄×D₄	—	79	2	no	—
307	C₄×D₄	—	158	1	no	—
308	C₄×D₄	—	158	1	no	—
309	#117	—	158	1	no	—
310	C₂×C₄²	C₂²×D₇₉	1	1	yes	characteristic
311	#107	—	79	2	no	—
312	#106	—	79	2	no	—
313	C₄⋊C₈	—	2	1	no	—
314	C₄⋊C₈	—	79	1	no	—
315	C₄⋊C₈	—	79	1	no	—
316	C₄⋊C₈	—	79	2	no	—
317	C₄⋊C₈	—	158	1	no	—
318	C₄⋊C₈	—	158	1	no	—
319	C₄⋊C₈	—	158	1	no	—
320	#103	—	79	2	no	—
321	#102	—	79	2	no	—
322	#102	—	79	2	no	—
323	#102	—	79	2	no	—
324	C₂²⋊C₈	—	2	1	no	—
325	C₂²⋊C₈	—	158	1	no	—
326	C₂²⋊C₈	—	158	2	no	—
327	C₂²⋊C₈	—	158	2	no	—
328	C₂²⋊C₈	—	158	1	no	—
329	C₂²⋊C₈	—	158	1	no	—
330	#97	—	158	1	no	—
331	#97	—	158	1	no	—
332	#97	C₄×D₇₉	1	1	yes	characteristic
333	#97	C₄×D₇₉	1	1	yes	characteristic
334	C₄×C₈	—	158	1	no	—
335	C₄×C₈	D₃₁₆	1	1	yes	characteristic
336	C₄×C₈	D₃₁₆	1	1	yes	characteristic
337	C₄×C₈	C₂²×D₇₉	1	2	yes	—
338	C₄×C₈	C₂²×D₇₉	1	2	yes	—
339	C₄×C₈	C₂²×D₇₉	1	1	yes	characteristic
340	C₄×C₈	C₂²×D₇₉	1	1	yes	characteristic
341	#41	—	316	2	no	—
342	#41	—	316	2	no	—
343	C₂×Q₈	—	79	1	no	—
344	C₂×Q₈	—	158	1	no	—
345	C₂×D₄	—	79	1	no	—
346	C₂×D₄	—	79	2	no	—
347	C₂×D₄	—	158	1	no	—
348	C₂×D₄	—	158	2	no	—
349	C₂×D₄	—	158	1	no	—
350	C₂×D₄	—	158	1	no	—
351	C₂²×C₄	—	158	1	no	—
352	C₂²×C₄	—	158	2	no	—
353	C₂²×C₄	C₂×C₄×D₇₉	1	1	yes	characteristic
354	C₂²×C₄	C₂×D₃₁₆	1	1	yes	characteristic
355	C₂²×C₄	#11929624	1	1	yes	characteristic
356	SD₁₆	—	158	4	no	—
357	D₈	—	158	4	no	—
358	M₁₆	—	2	4	no	—
359	M₁₆	—	316	2	no	—
360	M₁₆	—	316	4	no	—
361	M₁₆	—	316	2	no	—
362	C₂×C₈	—	2	2	no	—
363	C₂×C₈	—	2	2	no	—
364	C₂×C₈	—	4	1	no	—
365	C₂×C₈	—	316	2	no	—
366	C₂×C₈	—	316	4	no	—
367	C₂×C₈	—	158	1	no	—
368	C₂×C₈	—	158	1	no	—
369	C₂×C₈	—	158	2	no	—
370	C₂×C₈	C₂×C₄×D₇₉	1	2	yes	—
371	C₂×C₈	C₂×C₄×D₇₉	1	2	yes	—
372	C₂×C₈	C₂×D₃₁₆	1	1	yes	characteristic
373	C₂×C₈	C₂×D₃₁₆	1	1	yes	characteristic
374	C₂×C₈	C₂×D₃₁₆	1	1	yes	characteristic
375	C₂×C₈	C₂×D₃₁₆	1	1	yes	characteristic
376	C₄⋊C₄	—	79	1	no	—
377	C₄⋊C₄	—	79	1	no	—
378	C₄⋊C₄	—	79	2	no	—
379	C₄⋊C₄	—	158	1	no	—
380	C₄⋊C₄	—	158	1	no	—
381	C₄⋊C₄	—	158	1	no	—
382	C₄⋊C₄	—	158	1	no	—
383	C₄⋊C₄	—	158	1	no	—
384	C₂²⋊C₄	—	158	1	no	—
385	C₂²⋊C₄	—	158	2	no	—
386	C₂²⋊C₄	—	158	1	no	—
387	C₂²⋊C₄	—	158	1	no	—
388	C₂²⋊C₄	—	158	1	no	—
389	C₂²⋊C₄	—	158	2	no	—
390	C₂²⋊C₄	—	158	1	no	—
391	C₄²	—	158	1	no	—
392	C₄²	C₂×C₄×D₇₉	1	1	yes	characteristic
393	C₄²	C₂×D₃₁₆	1	1	yes	characteristic
394	C₄²	#11929624	1	1	yes	characteristic
395	C₄²	C₂³×D₇₉	1	1	yes	characteristic
396	C₂³	—	158	1	no	—
397	C₂³	—	158	2	no	—
398	C₂³	C₄×D₃₁₆	1	1	yes	characteristic
399	Q₈	—	316	2	no	—
400	Q₈	—	158	2	no	—
401	D₄	—	316	2	no	—
402	D₄	—	316	2	no	—
403	D₄	—	316	2	no	—
404	D₄	—	316	4	no	—
405	D₄	—	158	2	no	—
406	D₄	—	158	2	no	—
407	D₄	—	158	2	no	—
408	C₂×C₄	—	2	2	no	—
409	C₂×C₄	—	2	1	no	—
410	C₂×C₄	—	2	1	no	—
411	C₂×C₄	—	4	1	no	—
412	C₂×C₄	—	316	2	no	—
413	C₂×C₄	—	316	1	no	—
414	C₂×C₄	—	316	1	no	—
415	C₂×C₄	—	316	2	no	—
416	C₂×C₄	—	158	1	no	—
417	C₂×C₄	—	158	1	no	—
418	C₂×C₄	—	158	1	no	—
419	C₂×C₄	—	158	2	no	—
420	C₂×C₄	C₄×D₃₁₆	1	1	yes	characteristic
421	C₂×C₄	C₄×D₃₁₆	1	1	yes	characteristic
422	C₂×C₄	C₄×D₃₁₆	1	1	yes	characteristic
423	C₂×C₄	C₂²×C₄×D₇₉	1	1	yes	characteristic
424	C₂×C₄	C₂²×D₃₁₆	1	1	yes	characteristic
425	C₂×C₄	C₂×#11929624	1	1	yes	characteristic
426	C₈	—	2	2	no	—
427	C₈	—	2	1	no	—
428	C₈	—	2	1	no	—
429	C₈	—	2	1	no	—
430	C₈	—	4	2	no	—
431	C₈	—	316	2	no	—
432	C₈	—	316	1	no	—
433	C₈	—	316	1	no	—
434	C₈	#14579167	1	4	yes	complemented
435	C₈	#14579189	1	2	yes	—
436	C₂²	—	2	1	no	—
437	C₂²	—	2	1	no	—
438	C₂²	—	2	1	no	—
439	C₂²	—	316	2	no	—
440	C₂²	—	316	1	no	—
441	C₂²	—	316	2	no	—
442	C₂²	—	316	1	no	—
443	C₂²	—	316	1	no	—
444	C₂²	—	316	2	no	—
445	C₂²	C₂×C₄×D₃₁₆	1	1	yes	characteristic
446	C₄	—	2	1	no	—
447	C₄	—	2	1	no	—
448	C₄	—	2	1	no	—
449	C₄	—	2	1	no	—
450	C₄	—	316	2	no	—
451	C₄	—	316	1	no	—
452	C₄	—	316	1	no	—
453	C₄	—	316	1	no	—
454	C₄	C₂×#14579167	1	2	yes	—
455	C₄	C₂×#14579189	1	1	yes	characteristic
456	C₄	#19099363	1	1	yes	characteristic
457	C₂	—	4	1	no	—
458	C₂	—	632	2	no	—
459	C₂	—	632	1	no	—
460	C₂	#23772113	1	1	yes	characteristic
461	C₂	C₄×#14579189	1	1	yes	characteristic
462	C₂	#23772304	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₈	C₂×D₃₁₆
commutator	C₂×C₄×C₇₉	C₂³×C₄
Frattini	C₄²	C₂³×D₇₉
Fitting	C₈×M₁₆×C₇₉	C₂
socle	C₂²×C₇₉	C₂×C₄×D₄
prime radical	#23773995	C₂
cosocle	C₄²×C₇₉	C₂⁴
hypercenter	C₈×M₁₆	D₇₉
hypocenter	C₇₉	#17964
LCS	G ▷ C₂×C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂×C₈ ◁ C₂×C₄×C₈ ◁ C₈×M₁₆

Complements

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

N	H ≅ G/N	type
2. #23772375	C₂	semidirect
3. #23772113	C₂	semidirect
4. #23762315	C₂	semidirect
5. #23762304	C₂	semidirect
6. C₈×#11929613	C₂	semidirect
7. C₈×D₆₃₂	C₂	semidirect
8. #23762167	C₂	semidirect
9. #23761870	C₂	semidirect
10. #23761866	C₂	semidirect
11. C₈×M₁₆×C₇₉	C₂	semidirect
199. C₈×C₇₉	#131	semidirect
242. C₈×M₁₆	D₇₉	semidirect
243. C₇₉	#17964	semidirect
434. C₈	#14579167	semidirect

Maximal subgroups

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

subgroup	index
#23773995	2
#23772375	2
#23772113	2
#23762315	2
#23762304	2
C₈×#11929613	2
C₈×D₆₃₂	2
#23762167	2
#23761870	2
#23761866	2
C₈×M₁₆×C₇₉	2
#17964	79