Subgroups — #34295120

Order 20224.

938 conjugacy classes of subgroups.

The subgroup lattice has 626 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#23773006	C₂	1	1	yes	maximal, characteristic
2	C₂×#19098682	C₂	1	1	yes	maximal, characteristic, complemented
3	#23772104	C₂	1	1	yes	maximal, characteristic, complemented
4	#23772099	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₄×#11929608	C₂	1	1	yes	maximal, characteristic, complemented
6	#23764285	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	#23763843	C₂	1	1	yes	maximal, characteristic, complemented
11	#23763440	C₂	1	1	yes	maximal, characteristic, complemented
12	#23763283	C₂	1	1	yes	maximal, characteristic, complemented
13	#23763238	C₂	1	1	yes	maximal, characteristic, complemented
14	#23763234	C₂	1	1	yes	maximal, characteristic, complemented
15	C₇₉×#1896	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#14579181	C₂²	1	1	yes	characteristic
17	C₂×#14579169	C₂²	1	1	yes	characteristic
18	C₂×#14579168	C₂²	1	1	yes	characteristic
19	C₂²×#11929608	C₂²	1	1	yes	characteristic
20	C₂²×#11929608	C₂²	1	1	yes	characteristic
21	#19099074	C₂²	1	1	yes	characteristic
22	#19098819	C₄	1	2	yes	complemented
23	#19098814	C₄	1	2	yes	complemented
24	#19098811	C₄	1	2	yes	complemented
25	#19098807	C₄	1	2	yes	complemented
26	#19098682	—	2	4	no	—
27	#19098641	—	2	2	no	—
28	#19098638	—	2	2	no	—
29	#19098637	—	2	2	no	—
30	#19098635	—	2	2	no	—
31	C₂×#14579096	C₂²	1	1	yes	characteristic
32	C₂×#14579096	C₂²	1	1	yes	characteristic
33	#19098599	C₂²	1	1	yes	characteristic
34	#19098591	C₂²	1	1	yes	characteristic
35	#19098590	C₂²	1	1	yes	characteristic
36	C₂×#14579089	C₂²	1	1	yes	characteristic
37	C₂×#14579089	C₂²	1	1	yes	characteristic
38	#19098559	C₂²	1	1	yes	characteristic
39	#19098557	C₂²	1	1	yes	characteristic
40	#19098531	C₂²	1	1	yes	characteristic
41	#19098530	C₂²	1	1	yes	characteristic
42	#19098527	C₂²	1	1	yes	characteristic
43	#19098521	C₂²	1	1	yes	characteristic
44	#19098519	C₂²	1	1	yes	characteristic
45	C₄×#11929608	—	2	4	no	—
46	C₂×#14579072	C₂²	1	1	yes	characteristic
47	C₂×#14579072	C₂²	1	1	yes	characteristic
48	C₂×C₄×C₇₉⋊C₈	C₂²	1	1	yes	characteristic
49	C₂×C₄×C₇₉⋊C₈	C₂²	1	1	yes	characteristic
50	#19098327	C₂²	1	1	yes	characteristic
51	#19098327	C₂²	1	1	yes	characteristic
52	#19098323	C₂²	1	1	yes	characteristic
53	#19098323	C₂²	1	1	yes	characteristic
54	#525×C₇₉	C₂²	1	1	yes	characteristic
55	C₂²×C₄²×C₇₉	C₂²	1	1	yes	characteristic
56	C₂×#104×C₇₉	C₂²	1	1	yes	characteristic
57	C₂×#104×C₇₉	C₂²	1	1	yes	characteristic
58	#407×C₇₉	C₂²	1	1	yes	characteristic
59	#339×C₇₉	C₂²	1	1	yes	characteristic
60	#339×C₇₉	C₂²	1	1	yes	characteristic
61	C₂×#11929624	C₂³	1	1	yes	characteristic
62	#14579181	—	2	2	no	—
63	#14579181	—	2	2	no	—
64	C₂×#11929614	C₂×C₄	1	1	yes	characteristic, complemented
65	C₂×#11929612	C₂×C₄	1	1	yes	characteristic, complemented
66	C₂×#11929611	C₂×C₄	1	1	yes	characteristic, complemented
67	C₂×#11929609	C₂×C₄	1	1	yes	characteristic, complemented
68	#14579169	—	2	2	no	—
69	#14579169	—	2	2	no	—
70	#14579168	—	2	2	no	—
71	#14579168	—	2	2	no	—
72	C₂×#11929608	—	2	2	no	—
73	C₂×#11929608	—	2	2	no	—
74	C₂×#11929608	—	2	1	no	—
75	C₂×#11929608	—	2	2	no	—
76	C₂×#11929608	—	2	2	no	—
77	C₂×#11929608	C₂×C₄	1	2	yes	—
78	C₂×#11929608	C₂×C₄	1	2	yes	—
79	C₂×#11929608	D₄	1	2	yes	—
80	C₂×#11929608	D₄	1	2	yes	—
81	C₂×#11929608	C₂³	1	1	yes	characteristic
82	C₂×#11929608	C₂³	1	1	yes	characteristic
83	C₂×#11929607	—	2	1	no	—
84	C₂²×C₇₉⋊C₈	—	2	1	no	—
85	C₂²×C₇₉⋊C₈	C₂³	1	1	yes	characteristic
86	C₂²×C₇₉⋊C₈	C₂³	1	1	yes	characteristic
87	C₂²×C₇₉⋊C₈	C₂³	1	1	yes	characteristic
88	C₂²×C₇₉⋊C₈	C₂³	1	1	yes	characteristic
89	C₂×C₈×D₇₉	—	2	1	no	—
90	#14579144	—	2	1	no	—
91	#14579140	C₂×C₄	1	2	yes	—
92	#14579135	C₂×C₄	1	2	yes	—
93	#14579130	—	2	1	no	—
94	C₄×C₂²⋊D₇₉	—	2	2	no	—
95	#14579120	C₂³	1	1	yes	characteristic
96	#14579096	—	2	2	no	—
97	#14579096	—	2	2	no	—
98	#14579094	C₂×C₄	1	2	yes	complemented
99	#14579092	C₂×C₄	1	2	yes	complemented
100	C₄⋊(C₇₉⋊C₈)	—	2	2	no	—
101	Dic₇₉⋊C₈	—	2	2	no	—
102	#14579089	—	2	2	no	—
103	#14579089	—	2	2	no	—
104	#14579085	C₂×C₄	1	2	yes	complemented
105	#14579084	C₂×C₄	1	2	yes	complemented
106	#14579082	C₂×C₄	1	2	yes	complemented
107	#14579081	C₂×C₄	1	2	yes	complemented
108	C₂²⋊(C₇₉⋊C₈)	—	2	2	no	—
109	C₂²⋊(C₇₉⋊C₈)	—	2	2	no	—
110	(C₂×D₇₉)⋊C₈	—	2	2	no	—
111	#14579072	—	2	2	no	—
112	#14579072	—	2	1	no	—
113	#14579072	D₄	1	4	yes	complemented
114	#14579071	—	2	1	no	—
115	C₄×C₇₉⋊C₈	—	2	1	no	—
116	C₄×C₇₉⋊C₈	—	2	2	no	—
117	C₄×C₇₉⋊C₈	—	2	2	no	—
118	C₈×Dic₇₉	—	2	1	no	—
119	C₂×#41×C₇₉	C₂³	1	1	yes	characteristic
120	C₂³×C₄×C₇₉	—	2	1	no	—
121	C₂³×C₄×C₇₉	C₂³	1	1	yes	characteristic
122	C₂×M₁₆×C₇₉	C₂³	1	1	yes	characteristic
123	C₂×M₁₆×C₇₉	C₂³	1	1	yes	characteristic
124	#123×C₇₉	—	2	1	no	—
125	C₂²⋊Q₈×C₇₉	C₂×C₄	1	2	yes	—
126	#121×C₇₉	C₂×C₄	1	2	yes	—
127	#120×C₇₉	—	2	1	no	—
128	C₄×D₄×C₇₉	—	2	2	no	—
129	#117×C₇₉	C₂³	1	1	yes	characteristic
130	C₂×C₄²×C₇₉	—	2	1	no	—
131	C₂×C₄²×C₇₉	—	2	2	no	—
132	C₂×C₄²×C₇₉	—	2	2	no	—
133	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
134	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
135	#104×C₇₉	—	2	2	no	—
136	#104×C₇₉	—	2	2	no	—
137	C₂²⋊C₈×C₇₉	—	2	2	no	—
138	#11929624	—	2	1	no	—
139	#11929624	—	2	1	no	—
140	#11929624	—	2	1	no	—
141	#11929624	—	2	1	no	—
142	C₂×Dic₁₅₈	C₂²×C₄	1	1	yes	characteristic
143	C₂×D₃₁₆	C₂²×C₄	1	1	yes	characteristic
144	C₂×C₂²⋊D₇₉	—	2	1	no	—
145	C₂×C₂²⋊D₇₉	—	2	2	no	—
146	C₂×C₄×D₇₉	—	2	1	no	—
147	#11929614	—	2	2	no	—
148	#11929612	—	2	2	no	—
149	#11929611	—	2	2	no	—
150	#11929609	—	2	2	no	—
151	#11929608	—	2	4	no	—
152	#11929608	—	2	4	no	—
153	#11929608	—	2	4	no	—
154	#11929608	—	2	4	no	—
155	#11929608	—	2	1	no	—
156	#11929608	—	2	1	no	—
157	#11929608	—	2	1	no	—
158	#11929608	—	2	1	no	—
159	#11929608	—	4	2	no	—
160	#11929607	—	4	2	no	—
161	C₂×C₇₉⋊C₈	—	2	1	no	—
162	C₂×C₇₉⋊C₈	—	2	1	no	—
163	C₂×C₇₉⋊C₈	—	2	1	no	—
164	C₂×C₇₉⋊C₈	—	2	1	no	—
165	C₂×C₇₉⋊C₈	—	2	1	no	—
166	C₂×C₇₉⋊C₈	—	2	1	no	—
167	C₂×C₇₉⋊C₈	—	4	2	no	—
168	C₂×C₇₉⋊C₈	C₂²×C₄	1	2	yes	—
169	C₂×C₇₉⋊C₈	C₂²×C₄	1	1	yes	characteristic
170	C₂×C₇₉⋊C₈	C₂²×C₄	1	1	yes	characteristic
171	C₂×C₇₉⋊C₈	C₂×D₄	1	2	yes	—
172	C₂×C₇₉⋊C₈	C₂×D₄	1	2	yes	—
173	C₂×C₇₉⋊C₈	C₂×D₄	1	1	yes	characteristic
174	C₂×C₇₉⋊C₈	C₂×D₄	1	1	yes	characteristic
175	C₂×C₇₉⋊C₈	C₂×D₄	1	2	yes	—
176	C₂×C₇₉⋊C₈	#41	1	2	yes	—
177	C₂×C₇₉⋊C₈	#41	1	2	yes	—
178	C₈×D₇₉	—	4	2	no	—
179	C₄⋊Dic₇₉	C₂²×C₄	1	2	yes	—
180	Dic₇₉⋊C₄	—	2	2	no	—
181	C₂²⋊Dic₇₉	—	2	2	no	—
182	C₂²⋊Dic₇₉	—	2	1	no	—
183	(C₂×D₇₉)⋊C₄	—	2	2	no	—
184	C₄×Dic₇₉	—	2	1	no	—
185	C₂⁴×C₇₉	#41	1	1	yes	characteristic
186	#41×C₇₉	—	2	1	no	—
187	#41×C₇₉	—	2	1	no	—
188	#41×C₇₉	—	2	1	no	—
189	#41×C₇₉	—	2	1	no	—
190	C₂×Q₈×C₇₉	C₂²×C₄	1	1	yes	characteristic
191	C₂×D₄×C₇₉	—	2	1	no	—
192	C₂×D₄×C₇₉	—	2	2	no	—
193	C₂×D₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
194	C₂²×C₄×C₇₉	—	2	1	no	—
195	C₂²×C₄×C₇₉	—	2	1	no	—
196	C₂²×C₄×C₇₉	—	2	1	no	—
197	C₂²×C₄×C₇₉	—	2	1	no	—
198	C₂²×C₄×C₇₉	—	2	1	no	—
199	C₂²×C₄×C₇₉	—	2	4	no	—
200	C₂²×C₄×C₇₉	—	2	1	no	—
201	C₂²×C₄×C₇₉	—	2	1	no	—
202	C₂²×C₄×C₇₉	—	4	4	no	—
203	C₂²×C₄×C₇₉	C₂²×C₄	1	2	yes	—
204	C₂²×C₄×C₇₉	C₂×D₄	1	2	yes	—
205	C₂²×C₄×C₇₉	#41	1	1	yes	characteristic
206	C₂²×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
207	M₁₆×C₇₉	—	2	1	no	—
208	M₁₆×C₇₉	—	2	1	no	—
209	M₁₆×C₇₉	—	2	1	no	—
210	M₁₆×C₇₉	—	2	1	no	—
211	C₂×C₈×C₇₉	—	2	1	no	—
212	C₂×C₈×C₇₉	—	2	1	no	—
213	C₄⋊C₄×C₇₉	—	2	2	no	—
214	C₄⋊C₄×C₇₉	C₂²×C₄	1	2	yes	—
215	C₂²⋊C₄×C₇₉	—	2	2	no	—
216	C₂²⋊C₄×C₇₉	—	2	1	no	—
217	C₂²⋊C₄×C₇₉	—	2	2	no	—
218	C₄²×C₇₉	—	2	4	no	—
219	C₄²×C₇₉	—	2	1	no	—
220	C₄²×C₇₉	—	2	1	no	—
221	C₄²×C₇₉	—	2	1	no	—
222	C₄²×C₇₉	C₂×D₄	1	2	yes	—
223	C₄²×C₇₉	#41	1	2	yes	—
224	C₂³×C₇₉	—	2	1	no	—
225	C₂³×C₇₉	—	2	1	no	—
226	C₂³×C₇₉	—	2	1	no	—
227	C₂³×C₇₉	—	4	2	no	—
228	C₂³×C₇₉	C₄×D₄	1	2	yes	—
229	C₂³×C₇₉	C₂×#41	1	1	yes	characteristic
230	C₂²×D₇₉	—	2	1	no	—
231	Q₈×C₇₉	—	2	1	no	—
232	Q₈×C₇₉	—	2	1	no	—
233	D₄×C₇₉	—	2	1	no	—
234	D₄×C₇₉	—	2	1	no	—
235	D₄×C₇₉	—	4	1	no	—
236	D₄×C₇₉	—	4	1	no	—
237	D₄×C₇₉	—	8	2	no	—
238	C₂×C₄×C₇₉	—	2	4	no	—
239	C₂×C₄×C₇₉	—	2	1	no	—
240	C₂×C₄×C₇₉	—	2	2	no	—
241	C₂×C₄×C₇₉	—	2	1	no	—
242	C₂×C₄×C₇₉	—	2	2	no	—
243	C₂×C₄×C₇₉	—	2	2	no	—
244	C₂×C₄×C₇₉	—	2	2	no	—
245	C₂×C₄×C₇₉	—	2	2	no	—
246	C₂×C₄×C₇₉	—	2	2	no	—
247	C₂×C₄×C₇₉	—	2	1	no	—
248	C₂×C₄×C₇₉	—	2	2	no	—
249	C₂×C₄×C₇₉	—	4	8	no	—
250	C₂×C₄×C₇₉	—	4	2	no	—
251	C₂×C₄×C₇₉	—	4	1	no	—
252	C₂×C₄×C₇₉	—	4	1	no	—
253	C₂×C₄×C₇₉	C₄×D₄	1	2	yes	—
254	C₂×C₄×C₇₉	C₂³×C₄	1	1	yes	characteristic
255	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
256	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
257	C₂×C₄×C₇₉	C₂×#41	1	1	yes	characteristic
258	C₂×C₄×C₇₉	C₂×#41	1	1	yes	characteristic
259	C₂×C₄×C₇₉	C₂×#41	1	1	yes	characteristic
260	C₂²⋊D₇₉	—	4	1	no	—
261	C₂²⋊D₇₉	—	4	1	no	—
262	C₂²⋊D₇₉	—	8	2	no	—
263	C₂×Dic₇₉	—	2	2	no	—
264	C₂×Dic₇₉	—	2	1	no	—
265	D₃₁₆	—	2	1	no	—
266	D₃₁₆	—	2	1	no	—
267	C₄×D₇₉	—	4	1	no	—
268	C₄×D₇₉	—	4	1	no	—
269	Dic₁₅₈	—	2	1	no	—
270	Dic₁₅₈	—	2	1	no	—
271	C₈×C₇₉	—	4	1	no	—
272	C₈×C₇₉	—	4	1	no	—
273	C₇₉⋊C₈	—	2	2	no	—
274	C₇₉⋊C₈	—	2	2	no	—
275	C₇₉⋊C₈	—	4	1	no	—
276	C₇₉⋊C₈	—	4	1	no	—
277	C₇₉⋊C₈	C₄×D₄	1	2	yes	—
278	C₇₉⋊C₈	C₄×D₄	1	2	yes	—
279	C₇₉⋊C₈	#121	1	2	yes	—
280	C₇₉⋊C₈	#121	1	2	yes	—
281	C₂²×C₇₉	—	2	2	no	—
282	C₂²×C₇₉	—	2	2	no	—
283	C₂²×C₇₉	—	2	2	no	—
284	C₂²×C₇₉	—	2	2	no	—
285	C₂²×C₇₉	—	4	2	no	—
286	C₂²×C₇₉	—	4	2	no	—
287	C₂²×C₇₉	—	4	2	no	—
288	C₂²×C₇₉	—	4	1	no	—
289	C₂²×C₇₉	C₂×C₄×D₄	1	1	yes	characteristic
290	C₂²×C₇₉	#525	1	1	yes	characteristic
291	C₂²×C₇₉	#529	1	1	yes	characteristic
292	C₂×D₇₉	—	4	2	no	—
293	C₂×D₇₉	—	4	1	no	—
294	C₄×C₇₉	—	2	4	no	—
295	C₄×C₇₉	—	2	2	no	—
296	C₄×C₇₉	—	4	2	no	—
297	C₄×C₇₉	—	4	2	no	—
298	C₄×C₇₉	—	4	1	no	—
299	C₄×C₇₉	C₂×C₄×D₄	1	1	yes	characteristic
300	C₄×C₇₉	C₄×#41	1	1	yes	characteristic
301	C₄×C₇₉	C₂×#121	1	1	yes	characteristic
302	C₄×C₇₉	#532	1	1	yes	characteristic
303	Dic₇₉	—	4	2	no	—
304	Dic₇₉	—	4	1	no	—
305	#21551	—	79	1	no	maximal, Sylow
306	C₂×C₇₉	—	2	1	no	—
307	C₂×C₇₉	—	2	1	no	—
308	C₂×C₇₉	—	4	2	no	—
309	C₂×C₇₉	—	8	1	no	—
310	C₂×C₇₉	C₄×#121	1	1	yes	characteristic
311	C₂×C₇₉	#2956	1	2	yes	—
312	D₇₉	—	8	1	no	—
313	#3054	—	79	1	no	—
314	C₂×#444	—	79	1	no	—
315	#2930	—	79	1	no	—
316	#2930	—	79	1	no	—
317	C₂×C₄×M₁₆	—	79	1	no	—
318	#1974	—	79	1	no	—
319	#1945	—	79	1	no	—
320	#1938	—	79	1	no	—
321	#1938	—	79	1	no	—
322	#1896	—	79	1	no	—
323	#1896	D₇₉	1	1	yes	characteristic, complemented
324	#1811	—	79	1	no	—
325	#1773	—	79	1	no	—
326	#1764	—	79	1	no	—
327	#1764	—	79	1	no	—
328	C₇₉	#21551	1	1	yes	characteristic, complemented, Sylow
329	C₂×#135	—	79	1	no	—
330	C₂×#131	—	79	1	no	—
331	C₂×#131	—	79	1	no	—
332	C₂²×M₁₆	—	79	1	no	—
333	C₂²×M₁₆	—	79	1	no	—
334	#525	—	79	1	no	—
335	#525	C₂×D₇₉	1	1	yes	characteristic
336	C₂²×C₄²	C₂×D₇₉	1	1	yes	characteristic
337	#470	—	79	2	no	—
338	#469	—	79	2	no	—
339	#468	—	79	2	no	—
340	#468	—	79	2	no	—
341	#444	—	158	4	no	—
342	#436	—	158	2	no	—
343	#436	—	158	2	no	—
344	#435	—	158	2	no	—
345	#435	—	158	2	no	—
346	C₂×#108	—	79	1	no	—
347	C₂×#108	—	79	1	no	—
348	#427	—	79	1	no	—
349	#424	—	79	1	no	—
350	#424	—	79	1	no	—
351	C₂×#104	—	79	1	no	—
352	C₂×#104	—	79	1	no	—
353	C₂×#104	C₂×D₇₉	1	1	yes	characteristic
354	C₂×#104	C₂×D₇₉	1	1	yes	characteristic
355	#416	—	79	1	no	—
356	#416	—	79	1	no	—
357	#408	—	79	1	no	—
358	#408	—	79	1	no	—
359	#407	—	79	1	no	—
360	#407	C₂×D₇₉	1	1	yes	characteristic
361	#405	—	79	1	no	—
362	#405	—	79	1	no	—
363	C₄×M₁₆	—	158	4	no	—
364	C₂×#97	—	79	1	no	—
365	C₂×#97	—	79	1	no	—
366	C₂×C₄×C₈	—	79	1	no	—
367	C₂×C₄×C₈	—	79	1	no	—
368	#341	—	79	1	no	—
369	#341	—	79	1	no	—
370	#339	—	79	1	no	—
371	#339	—	79	1	no	—
372	#339	C₂×D₇₉	1	1	yes	characteristic
373	#339	C₂×D₇₉	1	1	yes	characteristic
374	C₂×#41	—	79	1	no	—
375	C₂×#41	C₂²×D₇₉	1	1	yes	characteristic
376	C₂³×C₄	—	2	1	no	—
377	C₂³×C₄	C₂²×D₇₉	1	1	yes	characteristic
378	#135	—	158	2	no	—
379	#135	—	158	2	no	—
380	C₂×Q₁₆	—	79	1	no	—
381	C₂×SD₁₆	—	79	1	no	—
382	C₂×SD₁₆	—	79	1	no	—
383	C₂×D₈	—	79	1	no	—
384	#131	—	158	2	no	—
385	#131	—	158	2	no	—
386	#131	—	158	2	no	—
387	#131	—	158	2	no	—
388	C₂×M₁₆	—	79	2	no	—
389	C₂×M₁₆	—	79	2	no	—
390	C₂×M₁₆	—	79	2	no	—
391	C₂×M₁₆	—	79	2	no	—
392	C₂×M₁₆	—	79	1	no	—
393	C₂×M₁₆	—	79	1	no	—
394	C₂×M₁₆	—	158	1	no	—
395	C₂×M₁₆	—	158	1	no	—
396	C₂×M₁₆	—	158	2	no	—
397	C₂×M₁₆	—	158	2	no	—
398	C₂×M₁₆	—	158	2	no	—
399	C₂×M₁₆	—	158	2	no	—
400	C₂×M₁₆	C₂²×D₇₉	1	1	yes	characteristic
401	C₂×M₁₆	C₂²×D₇₉	1	1	yes	characteristic
402	C₂²×C₈	—	79	1	no	—
403	C₂²×C₈	—	79	1	no	—
404	C₂²×C₈	—	79	1	no	—
405	C₂²×C₈	—	79	1	no	—
406	C₂²×C₈	—	158	1	no	—
407	C₂²×C₈	—	158	1	no	—
408	#123	—	2	1	no	—
409	#123	—	158	1	no	—
410	C₂²⋊Q₈	—	79	2	no	—
411	C₂²⋊Q₈	C₄×D₇₉	1	2	yes	—
412	#121	—	79	2	no	—
413	#121	C₄×D₇₉	1	2	yes	—
414	#120	—	2	1	no	—
415	#120	—	158	1	no	—
416	C₄×D₄	—	2	2	no	—
417	C₄×D₄	—	158	2	no	—
418	#117	—	79	1	no	—
419	#117	C₂²×D₇₉	1	1	yes	characteristic
420	C₂×C₄²	—	2	1	no	—
421	C₂×C₄²	—	2	2	no	—
422	C₂×C₄²	—	2	2	no	—
423	C₂×C₄²	C₂²×D₇₉	1	1	yes	characteristic
424	C₂×C₄²	C₂²×D₇₉	1	1	yes	characteristic
425	#108	—	158	2	no	—
426	#108	—	158	2	no	—
427	#107	—	79	2	no	—
428	#106	—	79	2	no	—
429	C₄⋊C₈	—	158	2	no	—
430	C₄⋊C₈	—	158	2	no	—
431	#104	—	2	2	no	—
432	#104	—	2	2	no	—
433	#104	—	158	2	no	—
434	#104	—	158	2	no	—
435	#103	—	79	2	no	—
436	#103	—	79	2	no	—
437	#102	—	79	2	no	—
438	#102	—	79	2	no	—
439	C₂²⋊C₈	—	2	2	no	—
440	C₂²⋊C₈	—	158	2	no	—
441	C₂²⋊C₈	—	158	2	no	—
442	C₂²⋊C₈	—	158	2	no	—
443	#97	—	79	4	no	—
444	#97	—	158	1	no	—
445	#97	—	158	1	no	—
446	#97	—	158	2	no	—
447	C₄×C₈	—	158	2	no	—
448	C₄×C₈	—	158	2	no	—
449	C₄×C₈	—	158	1	no	—
450	C₄×C₈	—	158	1	no	—
451	C₂⁴	#11929623	1	1	yes	characteristic
452	#41	—	2	1	no	—
453	#41	—	2	1	no	—
454	#41	—	2	1	no	—
455	#41	—	2	1	no	—
456	#41	—	158	1	no	—
457	#41	—	158	1	no	—
458	#41	—	158	1	no	—
459	#41	—	158	1	no	—
460	C₂×Q₈	—	79	1	no	—
461	C₂×Q₈	C₂×C₄×D₇₉	1	1	yes	characteristic
462	C₂×D₄	—	2	1	no	—
463	C₂×D₄	—	2	2	no	—
464	C₂×D₄	—	79	1	no	—
465	C₂×D₄	—	158	1	no	—
466	C₂×D₄	—	158	2	no	—
467	C₂×D₄	C₂×C₄×D₇₉	1	1	yes	characteristic
468	C₂²×C₄	—	2	1	no	—
469	C₂²×C₄	—	2	1	no	—
470	C₂²×C₄	—	2	1	no	—
471	C₂²×C₄	—	2	1	no	—
472	C₂²×C₄	—	2	1	no	—
473	C₂²×C₄	—	2	4	no	—
474	C₂²×C₄	—	2	1	no	—
475	C₂²×C₄	—	2	1	no	—
476	C₂²×C₄	—	4	4	no	—
477	C₂²×C₄	—	158	1	no	—
478	C₂²×C₄	C₂×C₄×D₇₉	1	2	yes	—
479	C₂²×C₄	D₄×D₇₉	1	2	yes	—
480	C₂²×C₄	#11929623	1	1	yes	characteristic
481	C₂²×C₄	C₂³×D₇₉	1	1	yes	characteristic
482	Q₁₆	—	158	2	no	—
483	SD₁₆	—	158	2	no	—
484	SD₁₆	—	158	2	no	—
485	D₈	—	158	2	no	—
486	M₁₆	—	2	1	no	—
487	M₁₆	—	2	1	no	—
488	M₁₆	—	2	1	no	—
489	M₁₆	—	2	1	no	—
490	M₁₆	—	316	2	no	—
491	M₁₆	—	316	2	no	—
492	M₁₆	—	158	1	no	—
493	M₁₆	—	158	1	no	—
494	M₁₆	—	158	1	no	—
495	M₁₆	—	158	1	no	—
496	M₁₆	—	158	4	no	—
497	M₁₆	—	158	4	no	—
498	M₁₆	—	158	4	no	—
499	M₁₆	—	158	4	no	—
500	C₂×C₈	—	2	1	no	—
501	C₂×C₈	—	2	1	no	—
502	C₂×C₈	—	316	2	no	—
503	C₂×C₈	—	316	2	no	—
504	C₂×C₈	—	79	2	no	—
505	C₂×C₈	—	79	2	no	—
506	C₂×C₈	—	79	1	no	—
507	C₂×C₈	—	79	1	no	—
508	C₂×C₈	—	79	2	no	—
509	C₂×C₈	—	79	2	no	—
510	C₂×C₈	—	79	1	no	—
511	C₂×C₈	—	79	1	no	—
512	C₂×C₈	—	79	2	no	—
513	C₂×C₈	—	79	2	no	—
514	C₂×C₈	—	158	1	no	—
515	C₂×C₈	—	158	1	no	—
516	C₂×C₈	—	158	1	no	—
517	C₂×C₈	—	158	1	no	—
518	C₂×C₈	—	158	1	no	—
519	C₂×C₈	—	158	1	no	—
520	C₄⋊C₄	—	2	2	no	—
521	C₄⋊C₄	—	79	2	no	—
522	C₄⋊C₄	—	158	2	no	—
523	C₄⋊C₄	C₂×C₄×D₇₉	1	2	yes	—
524	C₂²⋊C₄	—	2	1	no	—
525	C₂²⋊C₄	—	2	2	no	—
526	C₂²⋊C₄	—	2	2	no	—
527	C₂²⋊C₄	—	158	1	no	—
528	C₂²⋊C₄	—	158	2	no	—
529	C₂²⋊C₄	—	158	2	no	—
530	C₄²	—	2	4	no	—
531	C₄²	—	2	1	no	—
532	C₄²	—	2	1	no	—
533	C₄²	—	2	1	no	—
534	C₄²	—	158	1	no	—
535	C₄²	D₄×D₇₉	1	2	yes	—
536	C₄²	#11929623	1	2	yes	—
537	C₂³	—	2	1	no	—
538	C₂³	—	2	1	no	—
539	C₂³	—	2	1	no	—
540	C₂³	—	4	2	no	—
541	C₂³	—	158	1	no	—
542	C₂³	(C₂²⋊D₇₉)⋊C₄	1	2	yes	—
543	C₂³	C₂×#11929623	1	1	yes	characteristic
544	Q₈	—	2	1	no	—
545	Q₈	—	2	1	no	—
546	Q₈	—	158	1	no	—
547	Q₈	—	158	1	no	—
548	D₄	—	2	1	no	—
549	D₄	—	2	1	no	—
550	D₄	—	4	1	no	—
551	D₄	—	4	1	no	—
552	D₄	—	8	2	no	—
553	D₄	—	316	1	no	—
554	D₄	—	316	1	no	—
555	D₄	—	632	2	no	—
556	D₄	—	158	1	no	—
557	D₄	—	158	1	no	—
558	C₂×C₄	—	2	4	no	—
559	C₂×C₄	—	2	1	no	—
560	C₂×C₄	—	2	2	no	—
561	C₂×C₄	—	2	1	no	—
562	C₂×C₄	—	2	2	no	—
563	C₂×C₄	—	2	2	no	—
564	C₂×C₄	—	2	2	no	—
565	C₂×C₄	—	2	2	no	—
566	C₂×C₄	—	2	2	no	—
567	C₂×C₄	—	2	1	no	—
568	C₂×C₄	—	2	2	no	—
569	C₂×C₄	—	4	8	no	—
570	C₂×C₄	—	4	2	no	—
571	C₂×C₄	—	4	1	no	—
572	C₂×C₄	—	4	1	no	—
573	C₂×C₄	—	316	1	no	—
574	C₂×C₄	—	316	1	no	—
575	C₂×C₄	—	158	2	no	—
576	C₂×C₄	—	158	1	no	—
577	C₂×C₄	(C₂²⋊D₇₉)⋊C₄	1	2	yes	—
578	C₂×C₄	C₂²×C₄×D₇₉	1	1	yes	characteristic
579	C₂×C₄	C₂×D₄×D₇₉	1	1	yes	characteristic
580	C₂×C₄	C₂×D₄×D₇₉	1	1	yes	characteristic
581	C₂×C₄	#41×D₇₉	1	1	yes	characteristic
582	C₂×C₄	#41×D₇₉	1	1	yes	characteristic
583	C₂×C₄	C₂×#11929623	1	1	yes	characteristic
584	C₈	—	4	1	no	—
585	C₈	—	4	1	no	—
586	C₈	—	316	1	no	—
587	C₈	—	316	1	no	—
588	C₈	—	79	2	no	—
589	C₈	—	79	2	no	—
590	C₈	—	79	2	no	—
591	C₈	—	79	2	no	—
592	C₈	—	158	2	no	—
593	C₈	—	158	2	no	—
594	C₂²	—	2	2	no	—
595	C₂²	—	2	2	no	—
596	C₂²	—	2	2	no	—
597	C₂²	—	2	2	no	—
598	C₂²	—	4	2	no	—
599	C₂²	—	4	2	no	—
600	C₂²	—	4	2	no	—
601	C₂²	—	4	1	no	—
602	C₂²	—	316	2	no	—
603	C₂²	—	316	1	no	—
604	C₂²	C₂×(C₂²⋊D₇₉)⋊C₄	1	1	yes	characteristic
605	C₂²	#19099069	1	1	yes	characteristic
606	C₂²	#19099090	1	1	yes	characteristic
607	C₄	—	2	4	no	—
608	C₄	—	2	2	no	—
609	C₄	—	4	2	no	—
610	C₄	—	4	2	no	—
611	C₄	—	4	1	no	—
612	C₄	—	316	2	no	—
613	C₄	—	316	1	no	—
614	C₄	C₄×D₄×D₇₉	1	1	yes	characteristic
615	C₄	C₄×#11929623	1	1	yes	characteristic
616	C₄	#121×D₇₉	1	1	yes	characteristic
617	C₄	#19099108	1	1	yes	characteristic
618	C₂	—	2	1	no	—
619	C₂	—	2	1	no	—
620	C₂	—	4	2	no	—
621	C₂	—	8	1	no	—
622	C₂	—	632	1	no	—
623	C₂	#23765910	1	1	yes	characteristic
624	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	C₇₉×#1896	C₂
socle	C₂²×C₇₉	C₂×C₄×D₄
prime radical	#23773006	C₂
cosocle	C₂²×C₄×C₇₉	C₂⁴
hypercenter	#1896	D₇₉
hypocenter	C₇₉	#21551
LCS	G ▷ C₂×C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂³×C₄ ◁ #1896

Complements

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

N	H ≅ G/N	type
2. C₂×#19098682	C₂	semidirect
3. #23772104	C₂	semidirect
4. #23772099	C₂	semidirect
5. C₂×C₄×#11929608	C₂	semidirect
6. #23764285	C₂	semidirect
7. #23764147	C₂	semidirect
8. #23764112	C₂	semidirect
9. #23764108	C₂	semidirect
10. #23763843	C₂	semidirect
11. #23763440	C₂	semidirect
12. #23763283	C₂	semidirect
13. #23763238	C₂	semidirect
14. #23763234	C₂	semidirect
15. C₇₉×#1896	C₂	semidirect
22. #19098819	C₄	semidirect
23. #19098814	C₄	semidirect
24. #19098811	C₄	semidirect
25. #19098807	C₄	semidirect
64. C₂×#11929614	C₂×C₄	semidirect
65. C₂×#11929612	C₂×C₄	semidirect
66. C₂×#11929611	C₂×C₄	semidirect
67. C₂×#11929609	C₂×C₄	semidirect
98. #14579094	C₂×C₄	semidirect
99. #14579092	C₂×C₄	semidirect
104. #14579085	C₂×C₄	semidirect
105. #14579084	C₂×C₄	semidirect
106. #14579082	C₂×C₄	semidirect
107. #14579081	C₂×C₄	semidirect
113. #14579072	D₄	semidirect
323. #1896	D₇₉	semidirect
328. C₇₉	#21551	semidirect

Maximal subgroups

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

subgroup	index
#23773006	2
C₂×#19098682	2
#23772104	2
#23772099	2
C₂×C₄×#11929608	2
#23764285	2
#23764147	2
#23764112	2
#23764108	2
#23763843	2
#23763440	2
#23763283	2
#23763238	2
#23763234	2
C₇₉×#1896	2
#21551	79