Subgroups — #34296101

Order 20224.

750 conjugacy classes of subgroups.

The subgroup lattice has 506 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#23773190	C₂	1	1	yes	maximal, characteristic
2	#23772334	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄×#14579167	C₂	1	1	yes	maximal, characteristic
4	#23764343	C₂	1	1	yes	maximal, characteristic, complemented
5	#23764176	C₂	1	1	yes	maximal, characteristic, complemented
6	#23764000	C₂	1	2	yes	maximal, complemented
7	#23763678	C₂	1	2	yes	maximal
8	#23763421	C₂	1	1	yes	maximal, characteristic
9	#23763279	C₂	1	2	yes	maximal, complemented
10	#23763237	C₂	1	2	yes	maximal
11	C₈×C₄⋊C₄×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#14579167	C₂²	1	1	yes	characteristic
13	C₂×#14579167	C₂²	1	1	yes	characteristic
14	#19099120	C₂²	1	1	yes	characteristic
15	C₄×#11929624	C₂²	1	1	yes	characteristic
16	#19098871	C₄	1	2	yes	complemented
17	#19098864	C₄	1	2	yes	complemented
18	#19098859	C₄	1	1	yes	characteristic, complemented
19	#19098854	C₄	1	1	yes	characteristic, complemented
20	#19098849	C₄	1	1	yes	characteristic, complemented
21	#19098844	C₄	1	1	yes	characteristic, complemented
22	#19098693	—	2	1	no	—
23	#19098693	—	2	1	no	—
24	C₈×Dic₁₅₈	—	2	1	no	—
25	C₈×Dic₁₅₈	—	2	1	no	—
26	C₂×#14579097	C₂²	1	2	yes	—
27	#19098601	C₂²	1	2	yes	—
28	#19098589	C₂²	1	2	yes	—
29	#19098587	C₂²	1	1	yes	characteristic
30	C₂×#14579089	C₂²	1	2	yes	—
31	#19098560	C₂²	1	2	yes	—
32	#19098518	C₂²	1	1	yes	characteristic
33	#19098518	C₂²	1	2	yes	—
34	#19098518	C₂²	1	1	yes	characteristic
35	#19098517	—	2	1	no	—
36	#19098517	—	2	1	no	—
37	C₄×#11929608	C₂²	1	1	yes	characteristic
38	C₄×#11929607	—	2	1	no	—
39	C₄×C₈×D₇₉	—	2	1	no	—
40	#19098328	C₂²	1	2	yes	—
41	#19098323	C₂²	1	2	yes	—
42	#19098323	C₂²	1	2	yes	—
43	#19098323	C₂²	1	2	yes	—
44	C₂×C₄⋊C₈×C₇₉	C₂²	1	1	yes	characteristic
45	C₂×C₄×C₈×C₇₉	C₂²	1	2	yes	—
46	C₂×C₄×C₈×C₇₉	C₂²	1	1	yes	characteristic
47	C₄×C₄⋊C₄×C₇₉	C₂²	1	1	yes	characteristic
48	#336×C₇₉	C₂²	1	2	yes	—
49	C₂×#11929624	C₂³	1	1	yes	characteristic
50	#14579167	—	2	2	no	—
51	#14579167	—	2	2	no	—
52	#14579167	—	2	2	no	—
53	#14579167	Q₈	1	4	yes	complemented
54	C₂×#11929608	C₂³	1	2	yes	—
55	C₂×#11929608	C₂³	1	1	yes	characteristic
56	C₂×#11929608	C₂³	1	1	yes	characteristic
57	C₂×#11929607	—	2	1	no	—
58	C₂×#11929607	—	2	1	no	—
59	C₂×C₈×D₇₉	—	2	1	no	—
60	C₂×C₈×D₇₉	—	2	1	no	—
61	#14579161	C₂×C₄	1	1	yes	characteristic
62	#14579161	C₂×C₄	1	1	yes	characteristic
63	#14579153	C₂×C₄	1	2	yes	—
64	#14579140	—	2	1	no	—
65	#14579140	—	2	1	no	—
66	C₄×Dic₁₅₈	—	2	1	no	—
67	C₄×Dic₁₅₈	—	2	1	no	—
68	C₄×Dic₁₅₈	C₂×C₄	1	1	yes	characteristic
69	C₄×Dic₁₅₈	C₂×C₄	1	1	yes	characteristic
70	C₄×D₃₁₆	C₂×C₄	1	1	yes	characteristic
71	C₄×D₃₁₆	C₂×C₄	1	1	yes	characteristic
72	C₄×C₂²⋊D₇₉	—	2	1	no	—
73	C₄×C₂²⋊D₇₉	—	2	1	no	—
74	#14579120	C₂³	1	1	yes	characteristic
75	#14579120	C₂³	1	2	yes	—
76	#14579118	—	2	1	no	—
77	C₄²×D₇₉	—	2	1	no	—
78	#14579097	—	2	4	no	—
79	#14579095	C₂×C₄	1	2	yes	—
80	#14579095	C₂×C₄	1	2	yes	—
81	#14579093	C₂×C₄	1	2	yes	—
82	#14579093	C₂×C₄	1	2	yes	—
83	C₄⋊(C₇₉⋊C₈)	—	2	1	no	—
84	C₄⋊(C₇₉⋊C₈)	—	2	1	no	—
85	Dic₇₉⋊C₈	—	2	2	no	—
86	Dic₇₉⋊C₈	—	2	2	no	—
87	#14579089	—	2	4	no	—
88	#14579086	C₂×C₄	1	2	yes	—
89	#14579086	C₂×C₄	1	2	yes	—
90	#14579083	C₂×C₄	1	2	yes	—
91	#14579083	C₂×C₄	1	2	yes	—
92	#14579072	—	2	1	no	—
93	#14579071	—	2	2	no	—
94	#14579071	—	2	1	no	—
95	#14579071	—	2	1	no	—
96	C₄×C₇₉⋊C₈	—	2	1	no	—
97	C₈×Dic₇₉	—	2	2	no	—
98	C₈×Dic₇₉	—	2	1	no	—
99	C₈×Dic₇₉	—	2	1	no	—
100	C₂²×C₈×C₇₉	C₂³	1	2	yes	—
101	C₂²×C₈×C₇₉	C₂³	1	1	yes	characteristic
102	C₂²×C₈×C₇₉	C₂³	1	1	yes	characteristic
103	C₂×C₄⋊C₄×C₇₉	—	2	1	no	—
104	C₂×C₄²×C₇₉	C₂³	1	2	yes	—
105	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
106	C₄⋊C₈×C₇₉	C₂×C₄	1	1	yes	characteristic
107	C₄⋊C₈×C₇₉	C₂×C₄	1	1	yes	characteristic
108	C₄⋊C₈×C₇₉	C₂×C₄	1	2	yes	—
109	C₄×C₈×C₇₉	—	2	4	no	—
110	C₄×C₈×C₇₉	D₄	1	1	yes	characteristic
111	C₄×C₈×C₇₉	D₄	1	1	yes	characteristic
112	C₄×C₈×C₇₉	D₄	1	1	yes	characteristic
113	C₄×C₈×C₇₉	D₄	1	1	yes	characteristic
114	#95×C₇₉	—	2	1	no	—
115	#11929624	—	2	1	no	—
116	#11929624	—	2	1	no	—
117	#11929624	C₂×Q₈	1	2	yes	—
118	#11929624	#41	1	2	yes	—
119	C₂×Dic₁₅₈	—	2	1	no	—
120	C₂×Dic₁₅₈	—	2	1	no	—
121	C₂×Dic₁₅₈	C₂²×C₄	1	1	yes	characteristic
122	C₂×D₃₁₆	C₂²×C₄	1	1	yes	characteristic
123	C₂×C₂²⋊D₇₉	—	2	1	no	—
124	C₂×C₄×D₇₉	—	2	1	no	—
125	C₂×C₄×D₇₉	—	2	1	no	—
126	C₂×C₄×D₇₉	—	2	1	no	—
127	#11929608	—	2	1	no	—
128	#11929608	—	2	1	no	—
129	#11929608	—	2	2	no	—
130	#11929608	—	2	2	no	—
131	#11929608	C₂×Q₈	1	2	yes	—
132	#11929608	#41	1	2	yes	—
133	#11929607	—	2	4	no	—
134	#11929607	—	2	4	no	—
135	C₂×C₇₉⋊C₈	—	2	1	no	—
136	C₂×C₇₉⋊C₈	—	2	1	no	—
137	C₂×C₇₉⋊C₈	—	2	2	no	—
138	C₈×D₇₉	—	2	4	no	—
139	C₈×D₇₉	—	2	4	no	—
140	C₄⋊Dic₇₉	—	2	1	no	—
141	C₄⋊Dic₇₉	—	2	1	no	—
142	C₄⋊Dic₇₉	C₂²×C₄	1	2	yes	—
143	C₄⋊Dic₇₉	C₂²×C₄	1	2	yes	—
144	C₄⋊Dic₇₉	C₂²×C₄	1	1	yes	characteristic
145	C₄⋊Dic₇₉	C₂²×C₄	1	1	yes	characteristic
146	Dic₇₉⋊C₄	—	2	1	no	—
147	Dic₇₉⋊C₄	—	2	1	no	—
148	Dic₇₉⋊C₄	—	2	2	no	—
149	Dic₇₉⋊C₄	—	2	2	no	—
150	C₂²⋊Dic₇₉	—	2	1	no	—
151	C₂²⋊Dic₇₉	—	2	2	no	—
152	(C₂×D₇₉)⋊C₄	—	2	1	no	—
153	(C₂×D₇₉)⋊C₄	—	2	1	no	—
154	C₄×Dic₇₉	—	2	1	no	—
155	C₄×Dic₇₉	—	2	1	no	—
156	C₄×Dic₇₉	—	2	1	no	—
157	C₄×Dic₇₉	—	2	2	no	—
158	C₂²×C₄×C₇₉	—	2	2	no	—
159	C₂²×C₄×C₇₉	#41	1	1	yes	characteristic
160	C₂²×C₄×C₇₉	#41	1	1	yes	characteristic
161	C₂²×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
162	C₂×C₈×C₇₉	—	2	2	no	—
163	C₂×C₈×C₇₉	—	2	2	no	—
164	C₂×C₈×C₇₉	—	2	1	no	—
165	C₂×C₈×C₇₉	—	2	1	no	—
166	C₂×C₈×C₇₉	C₂²×C₄	1	2	yes	—
167	C₂×C₈×C₇₉	C₂²×C₄	1	2	yes	—
168	C₂×C₈×C₇₉	C₂×D₄	1	1	yes	characteristic
169	C₂×C₈×C₇₉	C₂×D₄	1	1	yes	characteristic
170	C₂×C₈×C₇₉	C₂×D₄	1	1	yes	characteristic
171	C₂×C₈×C₇₉	C₂×D₄	1	1	yes	characteristic
172	C₂×C₈×C₇₉	C₂×Q₈	1	2	yes	—
173	C₂×C₈×C₇₉	#41	1	2	yes	—
174	C₄⋊C₄×C₇₉	—	2	4	no	—
175	C₄²×C₇₉	—	2	2	no	—
176	C₄²×C₇₉	—	2	2	no	—
177	C₄²×C₇₉	C₂²×C₄	1	1	yes	characteristic
178	C₄²×C₇₉	C₂²×C₄	1	1	yes	characteristic
179	C₄²×C₇₉	C₂×D₄	1	1	yes	characteristic
180	C₄²×C₇₉	C₂×D₄	1	1	yes	characteristic
181	C₂³×C₇₉	C₂×#41	1	1	yes	characteristic
182	C₂²×D₇₉	—	2	1	no	—
183	C₂×C₄×C₇₉	—	2	2	no	—
184	C₂×C₄×C₇₉	—	2	4	no	—
185	C₂×C₄×C₇₉	—	4	1	no	—
186	C₂×C₄×C₇₉	—	4	2	no	—
187	C₂×C₄×C₇₉	—	4	2	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	C₂×#41	1	1	yes	characteristic
197	C₂×C₄×C₇₉	C₂×#41	1	1	yes	characteristic
198	C₂²⋊D₇₉	—	2	2	no	—
199	C₂²⋊D₇₉	—	2	2	no	—
200	C₂×Dic₇₉	—	2	1	no	—
201	C₂×Dic₇₉	—	2	1	no	—
202	C₂×Dic₇₉	—	2	1	no	—
203	C₂×Dic₇₉	—	2	2	no	—
204	C₂×Dic₇₉	—	2	2	no	—
205	D₃₁₆	—	2	1	no	—
206	D₃₁₆	C₄×Q₈	1	2	yes	—
207	C₄×D₇₉	—	2	2	no	—
208	C₄×D₇₉	—	2	2	no	—
209	C₄×D₇₉	—	4	2	no	—
210	C₄×D₇₉	—	4	2	no	—
211	Dic₁₅₈	—	2	1	no	—
212	Dic₁₅₈	—	4	2	no	—
213	Dic₁₅₈	—	4	2	no	—
214	Dic₁₅₈	C₄×Q₈	1	2	yes	—
215	C₈×C₇₉	—	2	2	no	—
216	C₈×C₇₉	—	2	2	no	—
217	C₈×C₇₉	—	2	1	no	—
218	C₈×C₇₉	—	2	1	no	—
219	C₈×C₇₉	C₂²⋊Q₈	1	2	yes	—
220	C₈×C₇₉	C₂²⋊Q₈	1	2	yes	—
221	C₇₉⋊C₈	—	2	2	no	—
222	C₇₉⋊C₈	—	2	2	no	—
223	C₇₉⋊C₈	—	4	2	no	—
224	C₂²×C₇₉	—	2	1	no	—
225	C₂²×C₇₉	—	2	1	no	—
226	C₂²×C₇₉	C₂×C₄×D₄	1	1	yes	characteristic
227	C₂²×C₇₉	#529	1	1	yes	characteristic
228	C₂²×C₇₉	#533	1	1	yes	characteristic
229	C₂×D₇₉	—	2	2	no	—
230	C₂×D₇₉	—	4	1	no	—
231	C₂×D₇₉	—	4	1	no	—
232	C₄×C₇₉	—	2	1	no	—
233	C₄×C₇₉	—	2	1	no	—
234	C₄×C₇₉	—	2	1	no	—
235	C₄×C₇₉	—	4	4	no	—
236	C₄×C₇₉	#443	1	2	yes	—
237	C₄×C₇₉	C₂×C₄×Q₈	1	1	yes	characteristic
238	C₄×C₇₉	C₄×#41	1	1	yes	characteristic
239	C₄×C₇₉	C₂×C₂²⋊Q₈	1	1	yes	characteristic
240	C₄×C₇₉	#525	1	1	yes	characteristic
241	Dic₇₉	—	2	2	no	—
242	Dic₇₉	—	4	2	no	—
243	Dic₇₉	—	4	1	no	—
244	Dic₇₉	—	4	2	no	—
245	Dic₇₉	—	4	1	no	—
246	#21627	—	79	1	no	maximal, Sylow
247	C₂×C₇₉	—	2	1	no	—
248	C₂×C₇₉	—	2	1	no	—
249	C₂×C₇₉	C₄×C₂²⋊Q₈	1	1	yes	characteristic
250	C₂×C₇₉	C₂×#443	1	1	yes	characteristic
251	C₂×C₇₉	#2955	1	1	yes	characteristic
252	D₇₉	—	4	2	no	—
253	#3076	—	79	1	no	—
254	#2960	—	79	1	no	—
255	C₄×#131	—	79	1	no	—
256	#1986	—	79	1	no	—
257	#1950	—	79	1	no	—
258	#1922	—	79	2	no	—
259	#1866	—	79	2	no	—
260	#1806	—	79	1	no	—
261	#1772	—	79	2	no	—
262	C₈×C₄⋊C₄	D₇₉	1	1	yes	characteristic, complemented
263	#1764	—	79	2	no	—
264	C₇₉	#21627	1	1	yes	characteristic, complemented, Sylow
265	C₂×#131	—	79	1	no	—
266	C₂×#131	—	79	1	no	—
267	#533	—	79	1	no	—
268	C₄×#41	—	79	1	no	—
269	#479	—	79	2	no	—
270	#478	—	79	2	no	—
271	#477	—	79	1	no	—
272	#476	—	79	1	no	—
273	#475	—	79	1	no	—
274	#474	—	79	1	no	—
275	#446	—	158	1	no	—
276	#446	—	158	1	no	—
277	C₈×Q₈	—	158	1	no	—
278	C₈×Q₈	—	158	1	no	—
279	C₂×#108	—	79	2	no	—
280	#427	—	79	2	no	—
281	#424	—	79	2	no	—
282	#423	—	79	1	no	—
283	C₂×C₄⋊C₈	C₂×D₇₉	1	1	yes	characteristic
284	C₂×#104	—	79	2	no	—
285	#416	—	79	2	no	—
286	#405	—	79	1	no	—
287	#405	—	79	1	no	—
288	#405	—	79	2	no	—
289	#405	—	158	1	no	—
290	#405	—	158	1	no	—
291	C₄×M₁₆	—	79	1	no	—
292	C₄×M₁₆	—	158	1	no	—
293	C₂×C₄×C₈	—	158	1	no	—
294	C₂×C₄×C₈	C₂×D₇₉	1	2	yes	—
295	C₂×C₄×C₈	C₂×D₇₉	1	1	yes	characteristic
296	C₄×C₄⋊C₄	C₂×D₇₉	1	1	yes	characteristic
297	#341	—	79	2	no	—
298	#339	—	79	2	no	—
299	#339	—	79	2	no	—
300	#339	—	79	2	no	—
301	#336	C₂×D₇₉	1	2	yes	—
302	C₂×#41	—	79	1	no	—
303	#131	—	79	4	no	—
304	#131	—	158	2	no	—
305	#131	—	158	2	no	—
306	#131	—	158	2	no	—
307	C₂×M₁₆	—	79	1	no	—
308	C₂×M₁₆	—	79	1	no	—
309	C₂×M₁₆	—	79	2	no	—
310	C₂×M₁₆	—	158	1	no	—
311	C₂×M₁₆	—	158	1	no	—
312	C₂²×C₈	—	158	1	no	—
313	C₂²×C₈	—	158	1	no	—
314	C₂²×C₈	C₂²×D₇₉	1	2	yes	—
315	C₂²×C₈	C₂²×D₇₉	1	1	yes	characteristic
316	C₂²×C₈	C₂²×D₇₉	1	1	yes	characteristic
317	C₄⋊Q₈	—	79	1	no	—
318	C₄⋊Q₈	—	79	1	no	—
319	#125	—	79	2	no	—
320	C₂²⋊Q₈	—	158	1	no	—
321	C₂²⋊Q₈	—	158	1	no	—
322	C₄×Q₈	—	79	1	no	—
323	C₄×Q₈	—	79	1	no	—
324	C₄×Q₈	—	158	1	no	—
325	C₄×Q₈	—	158	1	no	—
326	C₄×D₄	—	79	1	no	—
327	C₄×D₄	—	79	1	no	—
328	C₄×D₄	—	158	1	no	—
329	C₄×D₄	—	158	1	no	—
330	#117	—	79	1	no	—
331	#117	—	79	2	no	—
332	#117	—	158	1	no	—
333	C₂×C₄⋊C₄	—	2	1	no	—
334	C₂×C₄²	—	158	1	no	—
335	C₂×C₄²	C₂²×D₇₉	1	2	yes	—
336	C₂×C₄²	C₂²×D₇₉	1	1	yes	characteristic
337	#108	—	158	4	no	—
338	#107	—	79	2	no	—
339	#107	—	79	2	no	—
340	#106	—	79	2	no	—
341	#106	—	79	2	no	—
342	C₄⋊C₈	—	158	2	no	—
343	C₄⋊C₈	—	158	2	no	—
344	C₄⋊C₈	—	158	1	no	—
345	C₄⋊C₈	—	158	1	no	—
346	C₄⋊C₈	C₄×D₇₉	1	1	yes	characteristic
347	C₄⋊C₈	C₄×D₇₉	1	1	yes	characteristic
348	C₄⋊C₈	C₄×D₇₉	1	2	yes	—
349	#104	—	158	4	no	—
350	#103	—	79	2	no	—
351	#103	—	79	2	no	—
352	#102	—	79	2	no	—
353	#102	—	79	2	no	—
354	#97	—	158	1	no	—
355	#97	—	158	1	no	—
356	#97	—	158	2	no	—
357	#97	—	158	1	no	—
358	C₄×C₈	—	2	4	no	—
359	C₄×C₈	—	158	1	no	—
360	C₄×C₈	—	158	1	no	—
361	C₄×C₈	—	158	2	no	—
362	C₄×C₈	—	158	1	no	—
363	C₄×C₈	D₃₁₆	1	1	yes	characteristic
364	C₄×C₈	D₃₁₆	1	1	yes	characteristic
365	C₄×C₈	D₃₁₆	1	1	yes	characteristic
366	C₄×C₈	D₃₁₆	1	1	yes	characteristic
367	#95	—	2	1	no	—
368	#41	—	79	2	no	—
369	#41	—	79	2	no	—
370	#41	—	158	1	no	—
371	#41	—	158	1	no	—
372	C₂×Q₈	—	79	1	no	—
373	C₂×Q₈	—	158	1	no	—
374	C₂×Q₈	—	158	1	no	—
375	C₂×D₄	—	79	1	no	—
376	C₂×D₄	—	158	1	no	—
377	C₂²×C₄	—	2	2	no	—
378	C₂²×C₄	—	158	1	no	—
379	C₂²×C₄	—	158	1	no	—
380	C₂²×C₄	—	158	1	no	—
381	C₂²×C₄	#11929624	1	1	yes	characteristic
382	C₂²×C₄	#11929624	1	1	yes	characteristic
383	C₂²×C₄	C₂³×D₇₉	1	1	yes	characteristic
384	M₁₆	—	79	2	no	—
385	M₁₆	—	79	2	no	—
386	M₁₆	—	158	4	no	—
387	M₁₆	—	158	2	no	—
388	M₁₆	—	158	2	no	—
389	M₁₆	—	158	1	no	—
390	M₁₆	—	158	1	no	—
391	M₁₆	—	158	4	no	—
392	C₂×C₈	—	2	2	no	—
393	C₂×C₈	—	2	1	no	—
394	C₂×C₈	—	2	1	no	—
395	C₂×C₈	—	2	2	no	—
396	C₂×C₈	—	158	4	no	—
397	C₂×C₈	—	158	2	no	—
398	C₂×C₈	—	158	1	no	—
399	C₂×C₈	—	158	1	no	—
400	C₂×C₈	—	158	4	no	—
401	C₂×C₈	C₂×C₄×D₇₉	1	2	yes	—
402	C₂×C₈	C₂×C₄×D₇₉	1	2	yes	—
403	C₂×C₈	C₂×D₃₁₆	1	1	yes	characteristic
404	C₂×C₈	C₂×D₃₁₆	1	1	yes	characteristic
405	C₂×C₈	C₂×D₃₁₆	1	1	yes	characteristic
406	C₂×C₈	C₂×D₃₁₆	1	1	yes	characteristic
407	C₂×C₈	Q₈×D₇₉	1	2	yes	—
408	C₂×C₈	#11929623	1	2	yes	—
409	C₄⋊C₄	—	2	4	no	—
410	C₄⋊C₄	—	79	2	no	—
411	C₄⋊C₄	—	79	2	no	—
412	C₄⋊C₄	—	79	1	no	—
413	C₄⋊C₄	—	79	1	no	—
414	C₄⋊C₄	—	158	1	no	—
415	C₄⋊C₄	—	158	1	no	—
416	C₄⋊C₄	—	158	2	no	—
417	C₄⋊C₄	—	158	2	no	—
418	C₄⋊C₄	—	158	1	no	—
419	C₄⋊C₄	—	158	1	no	—
420	C₂²⋊C₄	—	158	1	no	—
421	C₂²⋊C₄	—	158	2	no	—
422	C₂²⋊C₄	—	158	1	no	—
423	C₂²⋊C₄	—	158	1	no	—
424	C₄²	—	2	2	no	—
425	C₄²	—	2	2	no	—
426	C₄²	—	158	1	no	—
427	C₄²	—	158	1	no	—
428	C₄²	—	158	1	no	—
429	C₄²	—	158	2	no	—
430	C₄²	C₂×C₄×D₇₉	1	1	yes	characteristic
431	C₄²	C₂×C₄×D₇₉	1	1	yes	characteristic
432	C₄²	C₂×D₃₁₆	1	1	yes	characteristic
433	C₄²	C₂×D₃₁₆	1	1	yes	characteristic
434	C₂³	—	158	1	no	—
435	C₂³	C₂×#11929624	1	1	yes	characteristic
436	Q₈	—	316	2	no	—
437	Q₈	—	316	2	no	—
438	Q₈	—	79	2	no	—
439	Q₈	—	158	1	no	—
440	D₄	—	79	2	no	—
441	D₄	—	158	2	no	—
442	D₄	—	158	2	no	—
443	D₄	—	158	1	no	—
444	C₂×C₄	—	2	2	no	—
445	C₂×C₄	—	2	4	no	—
446	C₂×C₄	—	4	1	no	—
447	C₂×C₄	—	4	2	no	—
448	C₂×C₄	—	4	2	no	—
449	C₂×C₄	—	316	2	no	—
450	C₂×C₄	—	316	2	no	—
451	C₂×C₄	—	158	1	no	—
452	C₂×C₄	—	158	1	no	—
453	C₂×C₄	—	158	2	no	—
454	C₂×C₄	—	158	2	no	—
455	C₂×C₄	—	158	1	no	—
456	C₂×C₄	—	158	2	no	—
457	C₂×C₄	—	158	2	no	—
458	C₂×C₄	C₄×D₃₁₆	1	1	yes	characteristic
459	C₂×C₄	C₄×D₃₁₆	1	1	yes	characteristic
460	C₂×C₄	C₄×D₃₁₆	1	1	yes	characteristic
461	C₂×C₄	C₄×D₃₁₆	1	1	yes	characteristic
462	C₂×C₄	C₂²×C₄×D₇₉	1	1	yes	characteristic
463	C₂×C₄	C₂²×D₃₁₆	1	1	yes	characteristic
464	C₂×C₄	C₂×Q₈×D₇₉	1	1	yes	characteristic
465	C₂×C₄	#41×D₇₉	1	1	yes	characteristic
466	C₂×C₄	#41×D₇₉	1	1	yes	characteristic
467	C₂×C₄	C₂×#11929623	1	1	yes	characteristic
468	C₈	—	2	2	no	—
469	C₈	—	2	2	no	—
470	C₈	—	2	1	no	—
471	C₈	—	2	1	no	—
472	C₈	—	316	2	no	—
473	C₈	—	158	2	no	—
474	C₈	—	158	2	no	—
475	C₈	#14579141	1	2	yes	—
476	C₈	#14579141	1	2	yes	—
477	C₂²	—	2	1	no	—
478	C₂²	—	2	1	no	—
479	C₂²	—	316	1	no	—
480	C₂²	—	316	1	no	—
481	C₂²	—	158	2	no	—
482	C₂²	C₂×C₄×D₃₁₆	1	1	yes	characteristic
483	C₂²	#19099095	1	1	yes	characteristic
484	C₂²	#19099117	1	1	yes	characteristic
485	C₄	—	2	1	no	—
486	C₄	—	2	1	no	—
487	C₄	—	2	1	no	—
488	C₄	—	4	4	no	—
489	C₄	—	316	1	no	—
490	C₄	—	316	2	no	—
491	C₄	—	316	1	no	—
492	C₄	—	316	2	no	—
493	C₄	—	158	2	no	—
494	C₄	#19098681	1	2	yes	—
495	C₄	C₄×Q₈×D₇₉	1	1	yes	characteristic
496	C₄	C₄×#11929623	1	1	yes	characteristic
497	C₄	C₂×#14579141	1	1	yes	characteristic
498	C₄	#19099075	1	1	yes	characteristic
499	C₂	—	2	1	no	—
500	C₂	—	2	1	no	—
501	C₂	—	316	2	no	—
502	C₂	C₄×#14579141	1	1	yes	characteristic
503	C₂	C₂×#19098681	1	1	yes	characteristic
504	C₂	#23772304	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₈	C₂×D₃₁₆
commutator	C₂×C₄×C₇₉	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₇₉
Fitting	C₈×C₄⋊C₄×C₇₉	C₂
socle	C₂²×C₇₉	C₂×C₄×D₄
prime radical	C₂×#11929624	C₂³
cosocle	C₂²×C₄×C₇₉	C₂⁴
hypercenter	C₈×C₄⋊C₄	D₇₉
hypocenter	C₇₉	#21627
LCS	G ▷ C₂×C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂×C₈ ◁ C₂×C₄×C₈ ◁ C₈×C₄⋊C₄

Complements

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

N	H ≅ G/N	type
2. #23772334	C₂	semidirect
4. #23764343	C₂	semidirect
5. #23764176	C₂	semidirect
6. #23764000	C₂	semidirect
9. #23763279	C₂	semidirect
11. C₈×C₄⋊C₄×C₇₉	C₂	semidirect
16. #19098871	C₄	semidirect
17. #19098864	C₄	semidirect
18. #19098859	C₄	semidirect
19. #19098854	C₄	semidirect
20. #19098849	C₄	semidirect
21. #19098844	C₄	semidirect
53. #14579167	Q₈	semidirect
262. C₈×C₄⋊C₄	D₇₉	semidirect
264. C₇₉	#21627	semidirect

Maximal subgroups

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

subgroup	index
#23773190	2
#23772334	2
C₄×#14579167	2
#23764343	2
#23764176	2
#23764000	2
#23763678	2
#23763421	2
#23763279	2
#23763237	2
C₈×C₄⋊C₄×C₇₉	2
#21627	79