Subgroups — #34292701

Order 20224.

738 conjugacy classes of subgroups.

The subgroup lattice has 536 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#23772198	C₂	1	1	yes	maximal, characteristic
2	#23772052	C₂	1	1	yes	maximal, characteristic, complemented
3	#23772051	C₂	1	1	yes	maximal, characteristic, complemented
4	#23764290	C₂	1	1	yes	maximal, characteristic
5	#23764285	C₂	1	1	yes	maximal, characteristic
6	#23764152	C₂	1	1	yes	maximal, characteristic, complemented
7	#23764147	C₂	1	1	yes	maximal, characteristic, complemented
8	#23764112	C₂	1	1	yes	maximal, characteristic, complemented
9	#23764108	C₂	1	1	yes	maximal, characteristic, complemented
10	#23764105	C₂	1	1	yes	maximal, characteristic, complemented
11	#23764101	C₂	1	1	yes	maximal, characteristic, complemented
12	#23763307	C₂	1	1	yes	maximal, characteristic, complemented
13	C₄×#14579089	C₂	1	1	yes	maximal, characteristic, complemented
14	C₄×#14579072	C₂	1	1	yes	maximal, characteristic, complemented
15	C₄×#104×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#14579181	C₂²	1	1	yes	characteristic
17	C₄×#11929624	C₂²	1	1	yes	characteristic
18	#19098673	C₄	1	2	yes	complemented
19	#19098668	C₄	1	2	yes	complemented
20	#19098663	C₄	1	2	yes	complemented
21	#19098661	C₄	1	2	yes	complemented
22	#19098624	—	2	2	no	—
23	#19098622	—	2	2	no	—
24	#19098620	—	2	2	no	—
25	#19098618	—	2	2	no	—
26	C₂×#14579096	C₂²	1	1	yes	characteristic
27	C₂×#14579096	C₂²	1	1	yes	characteristic
28	#19098599	C₂²	1	1	yes	characteristic
29	#19098591	C₂²	1	1	yes	characteristic
30	#19098591	C₂²	1	1	yes	characteristic
31	#19098590	C₂²	1	1	yes	characteristic
32	#19098590	C₂²	1	1	yes	characteristic
33	C₂×#14579089	C₂²	1	1	yes	characteristic
34	C₂×#14579089	C₂²	1	1	yes	characteristic
35	#19098559	C₂²	1	1	yes	characteristic
36	#19098557	C₂²	1	1	yes	characteristic
37	#19098531	C₂²	1	1	yes	characteristic
38	#19098531	C₂²	1	1	yes	characteristic
39	#19098530	C₂²	1	1	yes	characteristic
40	#19098530	C₂²	1	1	yes	characteristic
41	C₄×#11929608	C₂²	1	1	yes	characteristic
42	C₂×#14579072	C₂²	1	1	yes	characteristic
43	C₂×#14579072	C₂²	1	1	yes	characteristic
44	C₂×#14579072	C₂²	1	1	yes	characteristic
45	C₂×#14579072	C₂²	1	1	yes	characteristic
46	C₂×C₄×C₇₉⋊C₈	C₂²	1	1	yes	characteristic
47	C₂×C₄×C₇₉⋊C₈	C₂²	1	1	yes	characteristic
48	#19098327	C₂²	1	1	yes	characteristic
49	#19098327	C₂²	1	1	yes	characteristic
50	#19098323	C₂²	1	1	yes	characteristic
51	#19098323	C₂²	1	1	yes	characteristic
52	C₄×#41×C₇₉	C₂²	1	1	yes	characteristic
53	C₂×#104×C₇₉	C₂²	1	1	yes	characteristic
54	C₂×#104×C₇₉	C₂²	1	1	yes	characteristic
55	C₄×M₁₆×C₇₉	C₂²	1	1	yes	characteristic
56	C₄³×C₇₉	C₂²	1	1	yes	characteristic
57	#339×C₇₉	C₂²	1	1	yes	characteristic
58	#339×C₇₉	C₂²	1	1	yes	characteristic
59	C₂×#11929624	C₂³	1	1	yes	characteristic
60	#14579181	—	2	2	no	—
61	#14579181	—	2	2	no	—
62	C₂×#11929614	C₂×C₄	1	1	yes	characteristic
63	C₂×#11929612	C₂×C₄	1	1	yes	characteristic
64	C₂×#11929611	C₂×C₄	1	1	yes	characteristic
65	C₂×#11929609	C₂×C₄	1	1	yes	characteristic
66	C₂×#11929608	C₂³	1	1	yes	characteristic
67	C₂×#11929608	C₂³	1	1	yes	characteristic
68	C₂²×C₇₉⋊C₈	C₂³	1	1	yes	characteristic
69	C₂²×C₇₉⋊C₈	C₂³	1	1	yes	characteristic
70	C₂²×C₇₉⋊C₈	C₂³	1	1	yes	characteristic
71	C₂²×C₇₉⋊C₈	C₂³	1	1	yes	characteristic
72	C₄×Dic₁₅₈	C₂×C₄	1	2	yes	—
73	C₄×D₃₁₆	C₂×C₄	1	2	yes	—
74	C₄×C₂²⋊D₇₉	—	2	2	no	—
75	#14579120	C₂³	1	1	yes	characteristic
76	#14579118	—	2	1	no	—
77	C₄²×D₇₉	—	2	1	no	—
78	#14579096	—	2	2	no	—
79	#14579096	—	2	2	no	—
80	#14579094	C₂×C₄	1	2	yes	—
81	#14579092	C₂×C₄	1	2	yes	—
82	C₄⋊(C₇₉⋊C₈)	—	2	2	no	—
83	C₄⋊(C₇₉⋊C₈)	—	2	2	no	—
84	Dic₇₉⋊C₈	—	2	2	no	—
85	Dic₇₉⋊C₈	—	2	2	no	—
86	#14579089	—	2	2	no	—
87	#14579089	—	2	2	no	—
88	#14579085	C₂×C₄	1	2	yes	—
89	#14579084	C₂×C₄	1	2	yes	—
90	#14579082	C₂×C₄	1	2	yes	—
91	#14579081	C₂×C₄	1	2	yes	—
92	C₂²⋊(C₇₉⋊C₈)	—	2	2	no	—
93	C₂²⋊(C₇₉⋊C₈)	—	2	2	no	—
94	(C₂×D₇₉)⋊C₈	—	2	2	no	—
95	(C₂×D₇₉)⋊C₈	—	2	2	no	—
96	#14579072	—	2	1	no	—
97	#14579072	—	2	2	no	—
98	#14579072	—	2	2	no	—
99	#14579072	C₂×C₄	1	2	yes	—
100	#14579072	C₂×C₄	1	2	yes	—
101	#14579072	D₄	1	2	yes	—
102	#14579072	D₄	1	2	yes	—
103	C₄×C₇₉⋊C₈	—	2	1	no	—
104	C₄×C₇₉⋊C₈	—	2	2	no	—
105	C₄×C₇₉⋊C₈	—	2	2	no	—
106	C₂×#41×C₇₉	C₂³	1	1	yes	characteristic
107	C₂×M₁₆×C₇₉	C₂³	1	1	yes	characteristic
108	C₂×M₁₆×C₇₉	C₂³	1	1	yes	characteristic
109	C₄×Q₈×C₇₉	C₂×C₄	1	2	yes	—
110	C₄×D₄×C₇₉	—	2	2	no	—
111	C₄×D₄×C₇₉	C₂×C₄	1	2	yes	—
112	#117×C₇₉	—	2	1	no	—
113	#117×C₇₉	C₂³	1	1	yes	characteristic
114	C₂×C₄²×C₇₉	—	2	1	no	—
115	C₂×C₄²×C₇₉	—	2	2	no	—
116	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
117	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
118	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
119	#104×C₇₉	—	2	2	no	—
120	#104×C₇₉	—	2	2	no	—
121	#97×C₇₉	—	2	1	no	—
122	C₄×C₈×C₇₉	—	2	1	no	—
123	#11929624	—	2	1	no	—
124	#11929624	—	2	1	no	—
125	#11929624	—	2	1	no	—
126	#11929624	—	2	1	no	—
127	C₂×Dic₁₅₈	C₂²×C₄	1	1	yes	characteristic
128	C₂×D₃₁₆	C₂²×C₄	1	1	yes	characteristic
129	C₂×C₂²⋊D₇₉	—	2	1	no	—
130	C₂×C₄×D₇₉	—	2	2	no	—
131	C₂×C₄×D₇₉	—	2	1	no	—
132	#11929614	—	2	2	no	—
133	#11929612	—	2	2	no	—
134	#11929611	—	2	2	no	—
135	#11929609	—	2	2	no	—
136	#11929608	—	2	1	no	—
137	#11929608	—	2	1	no	—
138	#11929608	—	2	1	no	—
139	#11929608	—	2	1	no	—
140	C₂×C₇₉⋊C₈	—	2	1	no	—
141	C₂×C₇₉⋊C₈	—	2	1	no	—
142	C₂×C₇₉⋊C₈	—	2	1	no	—
143	C₂×C₇₉⋊C₈	—	2	1	no	—
144	C₂×C₇₉⋊C₈	—	2	1	no	—
145	C₂×C₇₉⋊C₈	—	2	1	no	—
146	C₂×C₇₉⋊C₈	—	2	1	no	—
147	C₂×C₇₉⋊C₈	—	2	1	no	—
148	C₂×C₇₉⋊C₈	C₂²×C₄	1	2	yes	—
149	C₂×C₇₉⋊C₈	C₂²×C₄	1	1	yes	characteristic
150	C₂×C₇₉⋊C₈	C₂²×C₄	1	1	yes	characteristic
151	C₂×C₇₉⋊C₈	C₂×D₄	1	2	yes	—
152	C₂×C₇₉⋊C₈	C₂×D₄	1	2	yes	—
153	C₂×C₇₉⋊C₈	#41	1	2	yes	—
154	C₂×C₇₉⋊C₈	#41	1	2	yes	—
155	C₄⋊Dic₇₉	C₂²×C₄	1	2	yes	—
156	Dic₇₉⋊C₄	—	2	2	no	—
157	C₂²⋊Dic₇₉	—	2	1	no	—
158	(C₂×D₇₉)⋊C₄	—	2	2	no	—
159	C₄×Dic₇₉	—	2	2	no	—
160	C₄×Dic₇₉	—	2	1	no	—
161	#41×C₇₉	—	2	1	no	—
162	#41×C₇₉	—	2	1	no	—
163	#41×C₇₉	—	2	1	no	—
164	#41×C₇₉	—	2	1	no	—
165	C₂×Q₈×C₇₉	C₂²×C₄	1	1	yes	characteristic
166	C₂×D₄×C₇₉	—	2	1	no	—
167	C₂×D₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
168	C₂²×C₄×C₇₉	—	2	1	no	—
169	C₂²×C₄×C₇₉	—	2	1	no	—
170	C₂²×C₄×C₇₉	—	2	1	no	—
171	C₂²×C₄×C₇₉	—	2	2	no	—
172	C₂²×C₄×C₇₉	#41	1	2	yes	—
173	C₂²×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
174	M₁₆×C₇₉	—	2	1	no	—
175	M₁₆×C₇₉	—	2	1	no	—
176	M₁₆×C₇₉	—	2	1	no	—
177	M₁₆×C₇₉	—	2	1	no	—
178	C₂×C₈×C₇₉	—	2	1	no	—
179	C₂×C₈×C₇₉	—	2	1	no	—
180	C₄⋊C₄×C₇₉	—	2	2	no	—
181	C₄⋊C₄×C₇₉	C₂²×C₄	1	2	yes	—
182	C₂²⋊C₄×C₇₉	—	2	1	no	—
183	C₂²⋊C₄×C₇₉	—	2	2	no	—
184	C₄²×C₇₉	—	2	2	no	—
185	C₄²×C₇₉	—	2	1	no	—
186	C₄²×C₇₉	—	2	1	no	—
187	C₄²×C₇₉	—	2	1	no	—
188	C₄²×C₇₉	—	4	4	no	—
189	C₄²×C₇₉	C₂²×C₄	1	2	yes	—
190	C₄²×C₇₉	C₂×D₄	1	1	yes	characteristic
191	C₄²×C₇₉	C₂×D₄	1	1	yes	characteristic
192	C₄²×C₇₉	#41	1	2	yes	—
193	C₄²×C₇₉	#41	1	2	yes	—
194	C₂³×C₇₉	—	2	1	no	—
195	C₂³×C₇₉	C₂×#41	1	1	yes	characteristic
196	C₂²×D₇₉	—	2	1	no	—
197	Q₈×C₇₉	—	2	1	no	—
198	Q₈×C₇₉	—	2	1	no	—
199	D₄×C₇₉	—	2	1	no	—
200	D₄×C₇₉	—	2	1	no	—
201	D₄×C₇₉	—	4	1	no	—
202	D₄×C₇₉	—	4	1	no	—
203	C₂×C₄×C₇₉	—	2	4	no	—
204	C₂×C₄×C₇₉	—	2	2	no	—
205	C₂×C₄×C₇₉	—	2	2	no	—
206	C₂×C₄×C₇₉	—	2	1	no	—
207	C₂×C₄×C₇₉	—	2	2	no	—
208	C₂×C₄×C₇₉	—	4	2	no	—
209	C₂×C₄×C₇₉	—	4	2	no	—
210	C₂×C₄×C₇₉	—	4	1	no	—
211	C₂×C₄×C₇₉	—	4	1	no	—
212	C₂×C₄×C₇₉	—	8	2	no	—
213	C₂×C₄×C₇₉	C₄×D₄	1	2	yes	—
214	C₂×C₄×C₇₉	C₄×D₄	1	2	yes	—
215	C₂×C₄×C₇₉	C₂³×C₄	1	1	yes	characteristic
216	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
217	C₂×C₄×C₇₉	C₂×#41	1	1	yes	characteristic
218	C₂×C₄×C₇₉	C₂×#41	1	1	yes	characteristic
219	C₂×C₄×C₇₉	C₂×#41	1	1	yes	characteristic
220	C₂×C₄×C₇₉	C₂×#41	1	1	yes	characteristic
221	C₂²⋊D₇₉	—	4	1	no	—
222	C₂²⋊D₇₉	—	4	1	no	—
223	C₂×Dic₇₉	—	2	2	no	—
224	C₂×Dic₇₉	—	2	1	no	—
225	D₃₁₆	—	2	1	no	—
226	D₃₁₆	—	2	1	no	—
227	C₄×D₇₉	—	4	1	no	—
228	C₄×D₇₉	—	4	1	no	—
229	C₄×D₇₉	—	8	2	no	—
230	Dic₁₅₈	—	2	1	no	—
231	Dic₁₅₈	—	2	1	no	—
232	C₈×C₇₉	—	4	1	no	—
233	C₈×C₇₉	—	4	1	no	—
234	C₇₉⋊C₈	—	2	2	no	—
235	C₇₉⋊C₈	—	2	2	no	—
236	C₇₉⋊C₈	—	2	2	no	—
237	C₇₉⋊C₈	—	4	1	no	—
238	C₇₉⋊C₈	—	4	1	no	—
239	C₇₉⋊C₈	#117	1	2	yes	—
240	C₇₉⋊C₈	#117	1	2	yes	—
241	C₂²×C₇₉	—	2	2	no	—
242	C₂²×C₇₉	—	4	2	no	—
243	C₂²×C₇₉	—	4	1	no	—
244	C₂²×C₇₉	C₂×C₄×D₄	1	1	yes	characteristic
245	C₂²×C₇₉	#529	1	1	yes	characteristic
246	C₂²×C₇₉	#529	1	1	yes	characteristic
247	C₂×D₇₉	—	4	2	no	—
248	C₂×D₇₉	—	4	1	no	—
249	C₄×C₇₉	—	2	4	no	—
250	C₄×C₇₉	—	2	2	no	—
251	C₄×C₇₉	—	2	2	no	—
252	C₄×C₇₉	—	4	2	no	—
253	C₄×C₇₉	—	4	2	no	—
254	C₄×C₇₉	—	4	1	no	—
255	C₄×C₇₉	C₂×#117	1	1	yes	characteristic
256	C₄×C₇₉	C₄×#41	1	1	yes	characteristic
257	C₄×C₇₉	#532	1	1	yes	characteristic
258	C₄×C₇₉	#532	1	1	yes	characteristic
259	Dic₇₉	—	4	2	no	—
260	Dic₇₉	—	4	1	no	—
261	#21297	—	79	1	no	maximal, Sylow
262	C₂×C₇₉	—	2	1	no	—
263	C₂×C₇₉	—	2	1	no	—
264	C₂×C₇₉	—	8	1	no	—
265	C₂×C₇₉	#2293	1	1	yes	characteristic
266	C₂×C₇₉	#2956	1	2	yes	—
267	D₇₉	—	8	1	no	—
268	#2943	—	79	1	no	—
269	#2923	—	79	1	no	—
270	#2923	—	79	1	no	—
271	#1975	—	79	1	no	—
272	#1974	—	79	1	no	—
273	#1946	—	79	1	no	—
274	#1945	—	79	1	no	—
275	#1938	—	79	1	no	—
276	#1938	—	79	1	no	—
277	#1937	—	79	1	no	—
278	#1937	—	79	1	no	—
279	#1778	—	79	1	no	—
280	C₄×#104	—	79	1	no	—
281	C₄×#104	D₇₉	1	1	yes	characteristic, complemented
282	C₄×#97	—	79	1	no	—
283	C₇₉	#21297	1	1	yes	characteristic, complemented, Sylow
284	C₂×#135	—	79	1	no	—
285	C₄×#41	—	79	1	no	—
286	C₄×#41	C₂×D₇₉	1	1	yes	characteristic
287	#442	—	79	2	no	—
288	#441	—	79	2	no	—
289	#440	—	79	2	no	—
290	#440	—	79	2	no	—
291	#433	—	158	2	no	—
292	#433	—	158	2	no	—
293	#432	—	158	2	no	—
294	#432	—	158	2	no	—
295	C₂×#108	—	79	1	no	—
296	C₂×#108	—	79	1	no	—
297	#427	—	79	1	no	—
298	#424	—	79	1	no	—
299	#424	—	79	1	no	—
300	#424	—	79	1	no	—
301	#424	—	79	1	no	—
302	C₂×#104	—	79	1	no	—
303	C₂×#104	—	79	1	no	—
304	C₂×#104	C₂×D₇₉	1	1	yes	characteristic
305	C₂×#104	C₂×D₇₉	1	1	yes	characteristic
306	#416	—	79	1	no	—
307	#416	—	79	1	no	—
308	#408	—	79	1	no	—
309	#408	—	79	1	no	—
310	#408	—	79	1	no	—
311	#408	—	79	1	no	—
312	C₄×M₁₆	—	79	1	no	—
313	C₄×M₁₆	C₂×D₇₉	1	1	yes	characteristic
314	C₂×#97	—	79	1	no	—
315	C₂×#97	—	79	1	no	—
316	C₂×#97	—	79	1	no	—
317	C₂×#97	—	79	1	no	—
318	C₂×C₄×C₈	—	79	1	no	—
319	C₂×C₄×C₈	—	79	1	no	—
320	C₄³	C₂×D₇₉	1	1	yes	characteristic
321	#341	—	79	1	no	—
322	#341	—	79	1	no	—
323	#339	—	79	1	no	—
324	#339	—	79	1	no	—
325	#339	C₂×D₇₉	1	1	yes	characteristic
326	#339	C₂×D₇₉	1	1	yes	characteristic
327	C₂×#41	—	79	1	no	—
328	C₂×#41	C₂²×D₇₉	1	1	yes	characteristic
329	#135	—	158	2	no	—
330	#135	—	158	2	no	—
331	C₂×Q₁₆	—	79	1	no	—
332	C₂×SD₁₆	—	79	1	no	—
333	C₂×SD₁₆	—	79	1	no	—
334	C₂×D₈	—	79	1	no	—
335	C₂×M₁₆	—	79	1	no	—
336	C₂×M₁₆	—	79	1	no	—
337	C₂×M₁₆	C₂²×D₇₉	1	1	yes	characteristic
338	C₂×M₁₆	C₂²×D₇₉	1	1	yes	characteristic
339	C₂²×C₈	—	79	1	no	—
340	C₂²×C₈	—	79	1	no	—
341	C₂²×C₈	—	79	1	no	—
342	C₂²×C₈	—	79	1	no	—
343	C₄×Q₈	—	79	2	no	—
344	C₄×Q₈	C₄×D₇₉	1	2	yes	—
345	C₄×D₄	—	2	2	no	—
346	C₄×D₄	—	79	2	no	—
347	C₄×D₄	—	158	2	no	—
348	C₄×D₄	C₄×D₇₉	1	2	yes	—
349	#117	—	2	1	no	—
350	#117	—	79	1	no	—
351	#117	—	158	1	no	—
352	#117	C₂²×D₇₉	1	1	yes	characteristic
353	C₂×C₄²	—	2	1	no	—
354	C₂×C₄²	—	2	2	no	—
355	C₂×C₄²	—	158	1	no	—
356	C₂×C₄²	C₂²×D₇₉	1	1	yes	characteristic
357	C₂×C₄²	C₂²×D₇₉	1	1	yes	characteristic
358	C₂×C₄²	C₂²×D₇₉	1	1	yes	characteristic
359	#108	—	158	2	no	—
360	#108	—	158	2	no	—
361	#107	—	79	2	no	—
362	#106	—	79	2	no	—
363	C₄⋊C₈	—	158	2	no	—
364	C₄⋊C₈	—	158	2	no	—
365	C₄⋊C₈	—	158	2	no	—
366	C₄⋊C₈	—	158	2	no	—
367	#104	—	2	2	no	—
368	#104	—	2	2	no	—
369	#104	—	158	2	no	—
370	#104	—	158	2	no	—
371	#103	—	79	2	no	—
372	#103	—	79	2	no	—
373	#102	—	79	2	no	—
374	#102	—	79	2	no	—
375	C₂²⋊C₈	—	158	2	no	—
376	C₂²⋊C₈	—	158	2	no	—
377	C₂²⋊C₈	—	158	2	no	—
378	C₂²⋊C₈	—	158	2	no	—
379	#97	—	2	1	no	—
380	#97	—	79	2	no	—
381	#97	—	79	2	no	—
382	#97	—	79	2	no	—
383	#97	—	79	2	no	—
384	#97	—	158	2	no	—
385	#97	—	158	1	no	—
386	#97	—	158	2	no	—
387	C₄×C₈	—	2	1	no	—
388	C₄×C₈	—	158	2	no	—
389	C₄×C₈	—	158	1	no	—
390	C₄×C₈	—	158	2	no	—
391	#41	—	2	1	no	—
392	#41	—	2	1	no	—
393	#41	—	2	1	no	—
394	#41	—	2	1	no	—
395	#41	—	158	1	no	—
396	#41	—	158	1	no	—
397	#41	—	158	1	no	—
398	#41	—	158	1	no	—
399	C₂×Q₈	—	79	1	no	—
400	C₂×Q₈	C₂×C₄×D₇₉	1	1	yes	characteristic
401	C₂×D₄	—	2	1	no	—
402	C₂×D₄	—	79	1	no	—
403	C₂×D₄	—	158	1	no	—
404	C₂×D₄	C₂×C₄×D₇₉	1	1	yes	characteristic
405	C₂²×C₄	—	2	1	no	—
406	C₂²×C₄	—	2	1	no	—
407	C₂²×C₄	—	2	1	no	—
408	C₂²×C₄	—	2	2	no	—
409	C₂²×C₄	—	158	1	no	—
410	C₂²×C₄	—	158	2	no	—
411	C₂²×C₄	#11929623	1	2	yes	—
412	C₂²×C₄	C₂³×D₇₉	1	1	yes	characteristic
413	Q₁₆	—	158	2	no	—
414	SD₁₆	—	158	2	no	—
415	SD₁₆	—	158	2	no	—
416	D₈	—	158	2	no	—
417	M₁₆	—	2	1	no	—
418	M₁₆	—	2	1	no	—
419	M₁₆	—	2	1	no	—
420	M₁₆	—	2	1	no	—
421	M₁₆	—	158	1	no	—
422	M₁₆	—	158	1	no	—
423	M₁₆	—	158	1	no	—
424	M₁₆	—	158	1	no	—
425	C₂×C₈	—	2	1	no	—
426	C₂×C₈	—	2	1	no	—
427	C₂×C₈	—	79	2	no	—
428	C₂×C₈	—	79	2	no	—
429	C₂×C₈	—	79	1	no	—
430	C₂×C₈	—	79	1	no	—
431	C₂×C₈	—	79	2	no	—
432	C₂×C₈	—	79	2	no	—
433	C₂×C₈	—	79	2	no	—
434	C₂×C₈	—	158	1	no	—
435	C₂×C₈	—	158	1	no	—
436	C₂×C₈	—	158	1	no	—
437	C₂×C₈	—	158	1	no	—
438	C₂×C₈	—	158	1	no	—
439	C₂×C₈	—	158	1	no	—
440	C₂×C₈	—	158	1	no	—
441	C₂×C₈	—	158	1	no	—
442	C₄⋊C₄	—	2	2	no	—
443	C₄⋊C₄	—	79	2	no	—
444	C₄⋊C₄	—	158	2	no	—
445	C₄⋊C₄	C₂×C₄×D₇₉	1	2	yes	—
446	C₂²⋊C₄	—	2	1	no	—
447	C₂²⋊C₄	—	2	2	no	—
448	C₂²⋊C₄	—	158	1	no	—
449	C₂²⋊C₄	—	158	2	no	—
450	C₄²	—	2	1	no	—
451	C₄²	—	2	1	no	—
452	C₄²	—	2	2	no	—
453	C₄²	—	2	1	no	—
454	C₄²	—	4	4	no	—
455	C₄²	—	158	2	no	—
456	C₄²	—	158	1	no	—
457	C₄²	C₂×C₄×D₇₉	1	2	yes	—
458	C₄²	D₄×D₇₉	1	1	yes	characteristic
459	C₄²	D₄×D₇₉	1	1	yes	characteristic
460	C₄²	#11929624	1	2	yes	—
461	C₄²	#11929624	1	2	yes	—
462	C₂³	—	2	1	no	—
463	C₂³	—	158	1	no	—
464	C₂³	C₂×#11929623	1	1	yes	characteristic
465	Q₈	—	2	1	no	—
466	Q₈	—	2	1	no	—
467	Q₈	—	158	1	no	—
468	Q₈	—	158	1	no	—
469	D₄	—	2	1	no	—
470	D₄	—	2	1	no	—
471	D₄	—	4	1	no	—
472	D₄	—	4	1	no	—
473	D₄	—	316	1	no	—
474	D₄	—	316	1	no	—
475	D₄	—	158	1	no	—
476	D₄	—	158	1	no	—
477	C₂×C₄	—	2	4	no	—
478	C₂×C₄	—	2	2	no	—
479	C₂×C₄	—	2	2	no	—
480	C₂×C₄	—	2	1	no	—
481	C₂×C₄	—	2	2	no	—
482	C₂×C₄	—	4	2	no	—
483	C₂×C₄	—	4	2	no	—
484	C₂×C₄	—	4	1	no	—
485	C₂×C₄	—	4	1	no	—
486	C₂×C₄	—	8	2	no	—
487	C₂×C₄	—	316	1	no	—
488	C₂×C₄	—	316	1	no	—
489	C₂×C₄	—	632	2	no	—
490	C₂×C₄	—	158	2	no	—
491	C₂×C₄	—	158	1	no	—
492	C₂×C₄	(C₂²⋊D₇₉)⋊C₄	1	2	yes	—
493	C₂×C₄	(C₂²⋊D₇₉)⋊C₄	1	2	yes	—
494	C₂×C₄	C₂²×C₄×D₇₉	1	1	yes	characteristic
495	C₂×C₄	C₂×D₄×D₇₉	1	1	yes	characteristic
496	C₂×C₄	#41×D₇₉	1	1	yes	characteristic
497	C₂×C₄	#41×D₇₉	1	1	yes	characteristic
498	C₂×C₄	C₂×#11929624	1	1	yes	characteristic
499	C₂×C₄	C₂×#11929624	1	1	yes	characteristic
500	C₈	—	4	1	no	—
501	C₈	—	4	1	no	—
502	C₈	—	316	1	no	—
503	C₈	—	316	1	no	—
504	C₈	—	79	2	no	—
505	C₈	—	79	2	no	—
506	C₈	—	158	2	no	—
507	C₈	—	158	2	no	—
508	C₈	—	158	2	no	—
509	C₂²	—	2	2	no	—
510	C₂²	—	4	1	no	—
511	C₂²	—	4	2	no	—
512	C₂²	—	316	1	no	—
513	C₂²	—	316	2	no	—
514	C₂²	C₂×(C₂²⋊D₇₉)⋊C₄	1	1	yes	characteristic
515	C₂²	#19099093	1	1	yes	characteristic
516	C₂²	#19099093	1	1	yes	characteristic
517	C₄	—	2	4	no	—
518	C₄	—	2	2	no	—
519	C₄	—	2	2	no	—
520	C₄	—	4	2	no	—
521	C₄	—	4	1	no	—
522	C₄	—	4	2	no	—
523	C₄	—	316	1	no	—
524	C₄	—	316	2	no	—
525	C₄	#117×D₇₉	1	1	yes	characteristic
526	C₄	C₄×#11929624	1	1	yes	characteristic
527	C₄	#19099110	1	1	yes	characteristic
528	C₄	#19099110	1	1	yes	characteristic
529	C₂	—	2	1	no	—
530	C₂	—	2	1	no	—
531	C₂	—	8	1	no	—
532	C₂	—	632	1	no	—
533	C₂	#23765863	1	1	yes	characteristic
534	C₂	#23772306	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₇₉
commutator	C₂×C₄×C₇₉	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₇₉
Fitting	C₄×#104×C₇₉	C₂
socle	C₂²×C₇₉	C₂×C₄×D₄
prime radical	C₂×#14579181	C₂²
cosocle	C₂²×C₄×C₇₉	C₂⁴
hypercenter	C₄×#104	D₇₉
hypocenter	C₇₉	#21297
LCS	G ▷ C₂×C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ C₄×#104

Complements

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

N	H ≅ G/N	type
2. #23772052	C₂	semidirect
3. #23772051	C₂	semidirect
6. #23764152	C₂	semidirect
7. #23764147	C₂	semidirect
8. #23764112	C₂	semidirect
9. #23764108	C₂	semidirect
10. #23764105	C₂	semidirect
11. #23764101	C₂	semidirect
12. #23763307	C₂	semidirect
13. C₄×#14579089	C₂	semidirect
14. C₄×#14579072	C₂	semidirect
15. C₄×#104×C₇₉	C₂	semidirect
18. #19098673	C₄	semidirect
19. #19098668	C₄	semidirect
20. #19098663	C₄	semidirect
21. #19098661	C₄	semidirect
281. C₄×#104	D₇₉	semidirect
283. C₇₉	#21297	semidirect

Maximal subgroups

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

subgroup	index
#23772198	2
#23772052	2
#23772051	2
#23764290	2
#23764285	2
#23764152	2
#23764147	2
#23764112	2
#23764108	2
#23764105	2
#23764101	2
#23763307	2
C₄×#14579089	2
C₄×#14579072	2
C₄×#104×C₇₉	2
#21297	79