Subgroups — #34257085

Order 20224.

918 conjugacy classes of subgroups.

The subgroup lattice has 732 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#23777311	C₂	1	1	yes	maximal, characteristic
2	#23772066	C₂	1	1	yes	maximal, characteristic, complemented
3	#23762133	C₂	1	1	yes	maximal, characteristic, complemented
4	#23762131	C₂	1	1	yes	maximal, characteristic, complemented
5	#23762125	C₂	1	1	yes	maximal, characteristic, complemented
6	#23762120	C₂	1	1	yes	maximal, characteristic, complemented
7	#23762108	C₂	1	1	yes	maximal, characteristic, complemented
8	#23762106	C₂	1	1	yes	maximal, characteristic, complemented
9	#23762096	C₂	1	1	yes	maximal, characteristic, complemented
10	#23762093	C₂	1	1	yes	maximal, characteristic, complemented
11	#23762091	C₂	1	1	yes	maximal, characteristic, complemented
12	#23762082	C₂	1	1	yes	maximal, characteristic, complemented
13	#23762060	C₂	1	1	yes	maximal, characteristic, complemented
14	#23762058	C₂	1	1	yes	maximal, characteristic, complemented
15	C₇₉×#2989	C₂	1	1	yes	maximal, characteristic, complemented
16	#19099286	C₄	1	2	yes	—
17	#19099278	—	2	1	no	—
18	#19099273	—	2	1	no	—
19	#19099259	—	2	1	no	—
20	#19099259	—	2	1	no	—
21	#19099222	C₄	1	2	yes	—
22	#19099222	C₄	1	2	yes	—
23	#19099218	C₄	1	2	yes	—
24	#19099184	—	2	1	no	—
25	#19099184	—	2	1	no	—
26	#19099141	—	2	1	no	—
27	#19099120	C₂²	1	1	yes	characteristic
28	#19099120	C₂²	1	1	yes	characteristic
29	#19099113	C₂²	1	1	yes	characteristic
30	#19099113	C₂²	1	1	yes	characteristic
31	#19099113	C₂²	1	1	yes	characteristic
32	C₂×#14579161	C₂²	1	1	yes	characteristic
33	#19099043	—	2	1	no	—
34	#19098624	—	2	1	no	—
35	#19098624	—	2	1	no	—
36	#19098620	C₂²	1	1	yes	characteristic
37	#19098620	C₂²	1	1	yes	characteristic
38	#19098616	C₂²	1	1	yes	characteristic
39	#19098616	C₂²	1	1	yes	characteristic
40	#19098587	C₂²	1	1	yes	characteristic
41	C₂×C₄⋊(C₇₉⋊C₈)	C₂²	1	1	yes	characteristic
42	#19098530	—	2	1	no	—
43	#19098519	—	2	1	no	—
44	#19098311	C₂²	1	1	yes	characteristic
45	#19098311	C₂²	1	1	yes	characteristic
46	#19098311	C₂²	1	1	yes	characteristic
47	#19098311	C₂²	1	1	yes	characteristic
48	#19098311	C₂²	1	1	yes	characteristic
49	#19098311	C₂²	1	1	yes	characteristic
50	#19098311	C₂²	1	1	yes	characteristic
51	#19098311	C₂²	1	1	yes	characteristic
52	#19098308	C₂²	1	1	yes	characteristic
53	#19098308	C₂²	1	1	yes	characteristic
54	#19098308	C₂²	1	1	yes	characteristic
55	#19098308	C₂²	1	1	yes	characteristic
56	#19098306	C₂²	1	1	yes	characteristic
57	#19098306	C₂²	1	1	yes	characteristic
58	#19098306	C₂²	1	1	yes	characteristic
59	#19098306	C₂²	1	1	yes	characteristic
60	C₄×#41×C₇₉	C₂²	1	1	yes	characteristic
61	#446×C₇₉	—	2	1	no	—
62	#436×C₇₉	—	2	1	no	—
63	#435×C₇₉	—	2	1	no	—
64	#435×C₇₉	—	2	1	no	—
65	#432×C₇₉	C₂²	1	1	yes	characteristic
66	#432×C₇₉	C₂²	1	1	yes	characteristic
67	#431×C₇₉	C₂²	1	1	yes	characteristic
68	#423×C₇₉	C₂²	1	1	yes	characteristic
69	#423×C₇₉	C₂²	1	1	yes	characteristic
70	C₂×C₄⋊C₈×C₇₉	C₂²	1	1	yes	characteristic
71	C₂×#11929624	—	2	1	no	—
72	C₂×#11929624	C₂×C₄	1	2	yes	—
73	C₂×#11929624	C₂×C₄	1	2	yes	—
74	C₂²×Dic₁₅₈	C₂×C₄	1	2	yes	—
75	C₂×#11929608	—	2	1	no	—
76	C₂²×C₇₉⋊C₈	—	2	1	no	—
77	#14579161	—	2	1	no	—
78	#14579161	—	2	1	no	—
79	#14579161	C₂×C₄	1	2	yes	—
80	#14579161	C₂³	1	1	yes	characteristic
81	#14579161	C₂³	1	1	yes	characteristic
82	#14579161	C₂³	1	1	yes	characteristic
83	#14579158	C₂³	1	1	yes	characteristic
84	#14579156	—	2	2	no	—
85	#14579156	—	2	2	no	—
86	#14579153	—	2	1	no	—
87	#14579153	—	2	1	no	—
88	#14579149	—	2	1	no	—
89	#14579149	C₂×C₄	1	2	yes	—
90	#14579149	C₂×C₄	1	2	yes	—
91	#14579147	—	2	2	no	—
92	#14579147	—	2	2	no	—
93	#14579143	—	2	2	no	—
94	#14579143	—	2	2	no	—
95	#14579140	—	2	1	no	—
96	#14579140	—	2	1	no	—
97	#14579140	C₂×C₄	1	2	yes	—
98	#14579140	C₂×C₄	1	2	yes	—
99	#14579139	—	2	2	no	—
100	#14579139	—	2	2	no	—
101	#14579137	—	2	2	no	—
102	#14579135	—	2	1	no	—
103	#14579135	—	2	1	no	—
104	#14579135	—	2	1	no	—
105	#14579135	—	2	1	no	—
106	#14579135	—	2	1	no	—
107	#14579135	C₂×C₄	1	2	yes	—
108	#14579133	—	2	2	no	—
109	#14579133	—	2	2	no	—
110	#14579132	—	2	2	no	—
111	C₄×Dic₁₅₈	—	2	1	no	—
112	C₄×Dic₁₅₈	—	2	1	no	—
113	C₄×Dic₁₅₈	C₂×C₄	1	2	yes	—
114	C₄×Dic₁₅₈	C₂×C₄	1	2	yes	—
115	C₄×D₃₁₆	—	2	1	no	—
116	C₄×D₃₁₆	—	2	1	no	—
117	C₄×D₃₁₆	—	2	1	no	—
118	C₄×D₃₁₆	—	2	1	no	—
119	C₄×D₃₁₆	—	2	1	no	—
120	C₄×D₃₁₆	C₂×C₄	1	2	yes	—
121	(C₂²⋊D₇₉)⋊C₄	—	2	2	no	—
122	(C₂²⋊D₇₉)⋊C₄	—	2	2	no	—
123	#14579120	—	2	1	no	—
124	#14579120	—	2	1	no	—
125	#14579119	—	2	2	no	—
126	C₂×C₄⋊Dic₇₉	—	2	1	no	—
127	C₂×C₄⋊Dic₇₉	—	2	1	no	—
128	C₄⋊C₄×D₇₉	—	2	2	no	—
129	C₄⋊(C₇₉⋊C₈)	—	2	1	no	—
130	C₄⋊(C₇₉⋊C₈)	—	2	1	no	—
131	C₄⋊(C₇₉⋊C₈)	C₂³	1	1	yes	characteristic
132	C₄⋊(C₇₉⋊C₈)	C₂³	1	1	yes	characteristic
133	C₄⋊(C₇₉⋊C₈)	C₂³	1	1	yes	characteristic
134	C₄⋊(C₇₉⋊C₈)	C₂³	1	1	yes	characteristic
135	C₂²⋊(C₇₉⋊C₈)	—	2	1	no	—
136	C₂²⋊(C₇₉⋊C₈)	—	2	1	no	—
137	C₂²⋊(C₇₉⋊C₈)	—	2	1	no	—
138	C₂²⋊(C₇₉⋊C₈)	—	2	1	no	—
139	#14579072	—	2	1	no	—
140	#14579072	—	2	1	no	—
141	C₄×C₇₉⋊C₈	—	2	1	no	—
142	C₄×C₇₉⋊C₈	—	2	1	no	—
143	C₂×#41×C₇₉	D₄	1	1	yes	characteristic
144	C₂×M₁₆×C₇₉	—	2	1	no	—
145	C₂×M₁₆×C₇₉	—	2	1	no	—
146	C₂²×C₈×C₇₉	—	2	1	no	—
147	C₄×Q₈×C₇₉	C₂×C₄	1	1	yes	characteristic
148	C₄×Q₈×C₇₉	D₄	1	1	yes	characteristic
149	C₄×D₄×C₇₉	C₂×C₄	1	1	yes	characteristic
150	C₄×D₄×C₇₉	C₂×C₄	1	1	yes	characteristic
151	C₄×D₄×C₇₉	C₂×C₄	1	1	yes	characteristic
152	C₄×D₄×C₇₉	D₄	1	1	yes	characteristic
153	C₄×D₄×C₇₉	D₄	1	1	yes	characteristic
154	C₄×D₄×C₇₉	D₄	1	1	yes	characteristic
155	#117×C₇₉	D₄	1	1	yes	characteristic
156	#117×C₇₉	D₄	1	1	yes	characteristic
157	#117×C₇₉	D₄	1	1	yes	characteristic
158	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
159	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
160	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
161	C₄⋊C₈×C₇₉	—	2	1	no	—
162	C₄⋊C₈×C₇₉	—	2	1	no	—
163	C₄⋊C₈×C₇₉	—	2	1	no	—
164	C₄⋊C₈×C₇₉	C₂³	1	1	yes	characteristic
165	C₄⋊C₈×C₇₉	C₂³	1	1	yes	characteristic
166	C₄⋊C₈×C₇₉	C₂³	1	1	yes	characteristic
167	C₄⋊C₈×C₇₉	C₂³	1	1	yes	characteristic
168	C₂²⋊C₈×C₇₉	—	2	1	no	—
169	C₂²⋊C₈×C₇₉	—	2	1	no	—
170	C₂²⋊C₈×C₇₉	—	2	1	no	—
171	#97×C₇₉	—	2	1	no	—
172	#97×C₇₉	—	2	1	no	—
173	C₄×C₈×C₇₉	—	2	1	no	—
174	#11929624	—	4	2	no	—
175	#11929624	—	4	2	no	—
176	#11929624	—	8	2	no	—
177	#11929624	—	8	2	no	—
178	C₂×Dic₁₅₈	—	2	2	no	—
179	C₂×Dic₁₅₈	—	2	1	no	—
180	C₂×Dic₁₅₈	—	8	2	no	—
181	C₂×Dic₁₅₈	C₂²×C₄	1	2	yes	—
182	C₂×Dic₁₅₈	C₂²×C₄	1	2	yes	—
183	C₂×D₃₁₆	—	2	1	no	—
184	C₂×D₃₁₆	—	2	1	no	—
185	C₂×D₃₁₆	C₂²×C₄	1	2	yes	—
186	C₂×C₂²⋊D₇₉	—	2	2	no	—
187	C₂×C₂²⋊D₇₉	—	2	2	no	—
188	C₂×C₂²⋊D₇₉	—	2	2	no	—
189	C₂²×Dic₇₉	—	2	2	no	—
190	C₂×C₄×D₇₉	—	2	2	no	—
191	C₂×C₄×D₇₉	—	2	2	no	—
192	C₂×C₄×D₇₉	—	2	2	no	—
193	#11929608	—	4	2	no	—
194	C₂×C₇₉⋊C₈	—	2	1	no	—
195	C₂×C₇₉⋊C₈	—	2	1	no	—
196	C₂×C₇₉⋊C₈	—	2	1	no	—
197	C₂×C₇₉⋊C₈	—	2	1	no	—
198	C₂×C₇₉⋊C₈	—	4	2	no	—
199	C₄⋊Dic₇₉	—	2	2	no	—
200	C₄⋊Dic₇₉	—	2	2	no	—
201	C₄⋊Dic₇₉	—	2	1	no	—
202	C₄⋊Dic₇₉	—	2	1	no	—
203	C₄⋊Dic₇₉	—	2	1	no	—
204	C₄⋊Dic₇₉	—	2	1	no	—
205	C₄⋊Dic₇₉	—	2	1	no	—
206	C₄⋊Dic₇₉	C₂²×C₄	1	2	yes	—
207	Dic₇₉⋊C₄	—	2	2	no	—
208	Dic₇₉⋊C₄	—	2	2	no	—
209	Dic₇₉⋊C₄	—	2	2	no	—
210	Dic₇₉⋊C₄	—	2	2	no	—
211	C₂²⋊Dic₇₉	—	2	2	no	—
212	C₂²⋊Dic₇₉	—	2	2	no	—
213	(C₂×D₇₉)⋊C₄	—	2	2	no	—
214	(C₂×D₇₉)⋊C₄	—	2	2	no	—
215	(C₂×D₇₉)⋊C₄	—	2	2	no	—
216	(C₂×D₇₉)⋊C₄	—	2	2	no	—
217	(C₂×D₇₉)⋊C₄	—	2	2	no	—
218	(C₂×D₇₉)⋊C₄	—	2	2	no	—
219	C₄×Dic₇₉	—	2	2	no	—
220	C₄×Dic₇₉	—	2	2	no	—
221	#41×C₇₉	—	4	1	no	—
222	#41×C₇₉	—	4	1	no	—
223	C₂×Q₈×C₇₉	C₂²⋊C₄	1	1	yes	characteristic
224	C₂×D₄×C₇₉	C₂²⋊C₄	1	1	yes	characteristic
225	C₂×D₄×C₇₉	C₂²⋊C₄	1	1	yes	characteristic
226	C₂×D₄×C₇₉	C₂²⋊C₄	1	1	yes	characteristic
227	C₂²×C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
228	C₂²×C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
229	C₂²×C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
230	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
231	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
232	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
233	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
234	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
235	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
236	M₁₆×C₇₉	—	8	1	no	—
237	M₁₆×C₇₉	—	8	1	no	—
238	C₂×C₈×C₇₉	—	2	1	no	—
239	C₂×C₈×C₇₉	—	2	1	no	—
240	C₂×C₈×C₇₉	—	2	1	no	—
241	C₂×C₈×C₇₉	—	2	1	no	—
242	C₂×C₈×C₇₉	—	8	1	no	—
243	C₄⋊C₄×C₇₉	C₂²⋊C₄	1	1	yes	characteristic
244	C₄⋊C₄×C₇₉	C₂²⋊C₄	1	1	yes	characteristic
245	C₄⋊C₄×C₇₉	C₂²⋊C₄	1	1	yes	characteristic
246	C₄⋊C₄×C₇₉	C₂²⋊C₄	1	1	yes	characteristic
247	C₄⋊C₄×C₇₉	C₂²⋊C₄	1	1	yes	characteristic
248	C₄⋊C₄×C₇₉	C₂²⋊C₄	1	1	yes	characteristic
249	C₂²⋊C₄×C₇₉	C₂²⋊C₄	1	1	yes	characteristic
250	C₂²⋊C₄×C₇₉	C₂²⋊C₄	1	1	yes	characteristic
251	C₂²⋊C₄×C₇₉	C₂²⋊C₄	1	1	yes	characteristic
252	C₂²⋊C₄×C₇₉	C₂²⋊C₄	1	1	yes	characteristic
253	C₂²⋊C₄×C₇₉	C₂²⋊C₄	1	1	yes	characteristic
254	C₂²⋊C₄×C₇₉	C₂²⋊C₄	1	1	yes	characteristic
255	C₄²×C₇₉	C₂²×C₄	1	1	yes	characteristic
256	C₄²×C₇₉	C₂²×C₄	1	1	yes	characteristic
257	C₄²×C₇₉	C₂²×C₄	1	1	yes	characteristic
258	C₄²×C₇₉	C₂×D₄	1	1	yes	characteristic
259	C₄²×C₇₉	C₂×D₄	1	1	yes	characteristic
260	C₄²×C₇₉	C₂×D₄	1	1	yes	characteristic
261	C₄²×C₇₉	C₂×D₄	1	1	yes	characteristic
262	C₄²×C₇₉	C₂×D₄	1	1	yes	characteristic
263	C₄²×C₇₉	C₂×D₄	1	1	yes	characteristic
264	C₄²×C₇₉	C₂⁴	1	1	yes	characteristic
265	C₂³×C₇₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
266	C₂³×C₇₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
267	C₂³×C₇₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
268	C₂²×D₇₉	—	2	2	no	—
269	Q₈×C₇₉	—	4	1	no	—
270	D₄×C₇₉	—	4	1	no	—
271	D₄×C₇₉	—	4	1	no	—
272	D₄×C₇₉	—	4	1	no	—
273	C₂×C₄×C₇₉	—	2	1	no	—
274	C₂×C₄×C₇₉	—	2	1	no	—
275	C₂×C₄×C₇₉	—	2	1	no	—
276	C₂×C₄×C₇₉	—	2	1	no	—
277	C₂×C₄×C₇₉	—	2	1	no	—
278	C₂×C₄×C₇₉	—	2	1	no	—
279	C₂×C₄×C₇₉	—	2	1	no	—
280	C₂×C₄×C₇₉	—	2	1	no	—
281	C₂×C₄×C₇₉	—	2	1	no	—
282	C₂×C₄×C₇₉	—	2	1	no	—
283	C₂×C₄×C₇₉	—	2	1	no	—
284	C₂×C₄×C₇₉	—	2	1	no	—
285	C₂×C₄×C₇₉	—	4	1	no	—
286	C₂×C₄×C₇₉	—	4	1	no	—
287	C₂×C₄×C₇₉	—	4	1	no	—
288	C₂×C₄×C₇₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
289	C₂×C₄×C₇₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
290	C₂×C₄×C₇₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
291	C₂×C₄×C₇₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
292	C₂×C₄×C₇₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
293	C₂×C₄×C₇₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
294	C₂×C₄×C₇₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
295	C₂×C₄×C₇₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
296	C₂×C₄×C₇₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
297	C₂×C₄×C₇₉	C₂³×C₄	1	1	yes	characteristic
298	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
299	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
300	C₂²⋊D₇₉	—	4	4	no	—
301	C₂²⋊D₇₉	—	8	2	no	—
302	C₂²⋊D₇₉	—	8	2	no	—
303	C₂×Dic₇₉	—	2	2	no	—
304	C₂×Dic₇₉	—	2	2	no	—
305	C₂×Dic₇₉	—	2	2	no	—
306	C₂×Dic₇₉	—	8	2	no	—
307	D₃₁₆	—	4	2	no	—
308	D₃₁₆	—	4	1	no	—
309	D₃₁₆	—	4	1	no	—
310	D₃₁₆	—	4	1	no	—
311	D₃₁₆	—	4	1	no	—
312	C₄×D₇₉	—	4	4	no	—
313	C₄×D₇₉	—	8	2	no	—
314	C₄×D₇₉	—	8	2	no	—
315	Dic₁₅₈	—	4	1	no	—
316	Dic₁₅₈	—	4	1	no	—
317	Dic₁₅₈	—	4	2	no	—
318	Dic₁₅₈	—	4	2	no	—
319	Dic₁₅₈	—	8	2	no	—
320	C₈×C₇₉	—	4	1	no	—
321	C₈×C₇₉	—	4	1	no	—
322	C₈×C₇₉	—	4	1	no	—
323	C₈×C₇₉	—	4	1	no	—
324	C₇₉⋊C₈	—	4	1	no	—
325	C₇₉⋊C₈	—	4	1	no	—
326	C₇₉⋊C₈	—	4	1	no	—
327	C₇₉⋊C₈	—	4	1	no	—
328	C₂²×C₇₉	—	2	1	no	—
329	C₂²×C₇₉	—	2	1	no	—
330	C₂²×C₇₉	—	2	1	no	—
331	C₂²×C₇₉	—	2	1	no	—
332	C₂²×C₇₉	—	2	1	no	—
333	C₂²×C₇₉	—	2	1	no	—
334	C₂²×C₇₉	—	2	1	no	—
335	C₂²×C₇₉	—	2	1	no	—
336	C₂²×C₇₉	—	2	1	no	—
337	C₂²×C₇₉	C₂²×C₂²⋊C₄	1	1	yes	characteristic
338	C₂×D₇₉	—	4	2	no	—
339	C₂×D₇₉	—	4	2	no	—
340	C₂×D₇₉	—	4	2	no	—
341	C₄×C₇₉	—	2	1	no	—
342	C₄×C₇₉	—	2	1	no	—
343	C₄×C₇₉	—	2	1	no	—
344	C₄×C₇₉	—	2	1	no	—
345	C₄×C₇₉	—	2	1	no	—
346	C₄×C₇₉	—	2	1	no	—
347	C₄×C₇₉	—	2	1	no	—
348	C₄×C₇₉	—	2	1	no	—
349	C₄×C₇₉	—	2	1	no	—
350	C₄×C₇₉	—	2	1	no	—
351	C₄×C₇₉	#575	1	1	yes	characteristic
352	C₄×C₇₉	#575	1	1	yes	characteristic
353	C₄×C₇₉	#577	1	1	yes	characteristic
354	C₄×C₇₉	#578	1	1	yes	characteristic
355	Dic₇₉	—	4	2	no	—
356	Dic₇₉	—	4	2	no	—
357	Dic₇₉	—	4	2	no	—
358	#17768	—	79	1	no	maximal, Sylow
359	C₂×C₇₉	—	4	1	no	—
360	C₂×C₇₉	—	4	1	no	—
361	C₂×C₇₉	—	4	1	no	—
362	C₂×C₇₉	#2888	1	1	yes	characteristic
363	C₂×C₇₉	#2896	1	1	yes	characteristic
364	C₂×C₇₉	#2898	1	1	yes	characteristic
365	D₇₉	—	8	2	no	—
366	#3511	—	79	1	no	—
367	#2989	D₇₉	1	1	yes	characteristic, complemented
368	#2925	—	79	1	no	—
369	#1560	—	79	1	no	—
370	#1559	—	79	1	no	—
371	#1558	—	79	1	no	—
372	#1557	—	79	1	no	—
373	#1554	—	79	1	no	—
374	#1553	—	79	1	no	—
375	#1551	—	79	1	no	—
376	#1551	—	79	1	no	—
377	#1550	—	79	1	no	—
378	#1548	—	79	1	no	—
379	#1543	—	79	1	no	—
380	#1542	—	79	1	no	—
381	C₇₉	#17768	1	1	yes	characteristic, complemented, Sylow
382	#556	—	79	2	no	—
383	#555	—	158	1	no	—
384	#554	—	158	1	no	—
385	#553	—	158	1	no	—
386	#553	—	158	1	no	—
387	#548	—	79	2	no	—
388	#548	—	79	2	no	—
389	#547	—	79	2	no	—
390	#542	—	158	1	no	—
391	#542	—	158	1	no	—
392	#537	—	158	1	no	—
393	#533	—	79	1	no	—
394	#533	—	79	1	no	—
395	#532	—	79	1	no	—
396	#532	—	79	1	no	—
397	#532	—	79	1	no	—
398	C₂×C₄⋊Q₈	—	79	1	no	—
399	#520	—	158	1	no	—
400	C₄×#41	C₂×D₇₉	1	1	yes	characteristic
401	#446	—	2	1	no	—
402	#436	—	2	1	no	—
403	#435	—	2	1	no	—
404	#435	—	2	1	no	—
405	#433	—	158	1	no	—
406	#433	—	158	1	no	—
407	#432	—	79	1	no	—
408	#432	—	79	1	no	—
409	#432	C₂×D₇₉	1	1	yes	characteristic
410	#432	C₂×D₇₉	1	1	yes	characteristic
411	#431	—	79	1	no	—
412	#431	—	79	1	no	—
413	#431	C₂×D₇₉	1	1	yes	characteristic
414	#423	—	79	1	no	—
415	#423	C₂×D₇₉	1	1	yes	characteristic
416	#423	C₂×D₇₉	1	1	yes	characteristic
417	C₂×C₄⋊C₈	—	79	1	no	—
418	C₂×C₄⋊C₈	C₂×D₇₉	1	1	yes	characteristic
419	#408	—	158	1	no	—
420	#405	—	158	1	no	—
421	#333	—	79	1	no	—
422	#333	—	79	1	no	—
423	#333	—	79	1	no	—
424	#333	—	79	1	no	—
425	#333	—	79	1	no	—
426	#333	—	79	1	no	—
427	#333	—	79	1	no	—
428	#333	—	79	1	no	—
429	#332	—	79	1	no	—
430	#332	—	79	1	no	—
431	#332	—	79	1	no	—
432	#332	—	79	1	no	—
433	#331	—	79	1	no	—
434	#331	—	79	1	no	—
435	#331	—	79	1	no	—
436	#331	—	79	1	no	—
437	C₂×#41	—	79	2	no	—
438	C₂×#41	—	79	2	no	—
439	C₂×#41	—	158	1	no	—
440	C₂×#41	D₃₁₆	1	1	yes	characteristic
441	C₂²×Q₈	—	79	2	no	—
442	C₂×M₁₆	—	2	1	no	—
443	C₂×M₁₆	—	2	1	no	—
444	C₂×M₁₆	—	158	1	no	—
445	C₂²×C₈	—	2	1	no	—
446	C₂²×C₈	—	158	1	no	—
447	C₄⋊Q₈	—	79	2	no	—
448	C₄⋊Q₈	—	79	1	no	—
449	C₄⋊Q₈	—	79	1	no	—
450	C₄⋊Q₈	—	79	1	no	—
451	C₄⋊Q₈	—	158	1	no	—
452	C₄⋊Q₈	—	158	1	no	—
453	#127	—	79	1	no	—
454	#126	—	158	2	no	—
455	#126	—	158	2	no	—
456	#125	—	158	1	no	—
457	#125	—	158	1	no	—
458	#124	—	79	2	no	—
459	#124	—	79	2	no	—
460	#124	—	158	2	no	—
461	#124	—	158	2	no	—
462	#124	—	158	1	no	—
463	#123	—	158	2	no	—
464	#123	—	158	2	no	—
465	C₂²⋊Q₈	—	79	2	no	—
466	C₂²⋊Q₈	—	79	2	no	—
467	C₂²⋊Q₈	—	158	2	no	—
468	C₂²⋊Q₈	—	158	1	no	—
469	C₂²⋊Q₈	—	158	1	no	—
470	C₂²⋊Q₈	—	158	2	no	—
471	C₂²⋊Q₈	—	158	2	no	—
472	#121	—	79	2	no	—
473	#121	—	158	2	no	—
474	#121	—	158	2	no	—
475	#121	—	158	2	no	—
476	#121	—	158	1	no	—
477	#121	—	158	1	no	—
478	#121	—	158	1	no	—
479	#121	—	158	1	no	—
480	#121	—	158	1	no	—
481	C₄×Q₈	—	79	2	no	—
482	C₄×Q₈	—	79	2	no	—
483	C₄×Q₈	—	158	1	no	—
484	C₄×Q₈	—	158	1	no	—
485	C₄×Q₈	C₄×D₇₉	1	1	yes	characteristic
486	C₄×Q₈	C₂²⋊D₇₉	1	1	yes	characteristic
487	C₄×D₄	—	79	2	no	—
488	C₄×D₄	—	158	2	no	—
489	C₄×D₄	—	158	2	no	—
490	C₄×D₄	—	158	1	no	—
491	C₄×D₄	—	158	1	no	—
492	C₄×D₄	—	158	1	no	—
493	C₄×D₄	—	158	1	no	—
494	C₄×D₄	—	158	1	no	—
495	C₄×D₄	C₄×D₇₉	1	1	yes	characteristic
496	C₄×D₄	C₄×D₇₉	1	1	yes	characteristic
497	C₄×D₄	C₄×D₇₉	1	1	yes	characteristic
498	C₄×D₄	C₂²⋊D₇₉	1	1	yes	characteristic
499	C₄×D₄	C₂²⋊D₇₉	1	1	yes	characteristic
500	C₄×D₄	C₂²⋊D₇₉	1	1	yes	characteristic
501	#117	—	158	1	no	—
502	#117	—	158	1	no	—
503	#117	—	158	2	no	—
504	#117	D₃₁₆	1	1	yes	characteristic
505	#117	D₃₁₆	1	1	yes	characteristic
506	#117	D₃₁₆	1	1	yes	characteristic
507	C₂×C₄⋊C₄	—	158	1	no	—
508	C₂×C₄⋊C₄	—	158	1	no	—
509	C₂×C₄⋊C₄	—	158	2	no	—
510	C₂×C₄²	C₂²×D₇₉	1	1	yes	characteristic
511	C₂×C₄²	C₂²×D₇₉	1	1	yes	characteristic
512	C₂×C₄²	C₂²×D₇₉	1	1	yes	characteristic
513	C₄⋊C₈	—	2	1	no	—
514	C₄⋊C₈	—	2	1	no	—
515	C₄⋊C₈	—	2	1	no	—
516	C₄⋊C₈	—	79	1	no	—
517	C₄⋊C₈	—	79	1	no	—
518	C₄⋊C₈	—	79	1	no	—
519	C₄⋊C₈	—	79	1	no	—
520	C₄⋊C₈	—	158	1	no	—
521	C₄⋊C₈	—	158	1	no	—
522	C₄⋊C₈	C₂²×D₇₉	1	1	yes	characteristic
523	C₄⋊C₈	C₂²×D₇₉	1	1	yes	characteristic
524	C₄⋊C₈	C₂²×D₇₉	1	1	yes	characteristic
525	C₄⋊C₈	C₂²×D₇₉	1	1	yes	characteristic
526	C₂²⋊C₈	—	2	1	no	—
527	C₂²⋊C₈	—	2	1	no	—
528	C₂²⋊C₈	—	2	1	no	—
529	C₂²⋊C₈	—	158	1	no	—
530	C₂²⋊C₈	—	158	1	no	—
531	C₂²⋊C₈	—	158	1	no	—
532	C₂²⋊C₈	—	158	1	no	—
533	#97	—	2	1	no	—
534	#97	—	2	1	no	—
535	#97	—	158	1	no	—
536	#97	—	158	1	no	—
537	C₄×C₈	—	2	1	no	—
538	C₄×C₈	—	158	1	no	—
539	C₄×C₈	—	158	1	no	—
540	#41	—	4	1	no	—
541	#41	—	4	1	no	—
542	#41	—	316	2	no	—
543	#41	—	316	2	no	—
544	#41	—	632	2	no	—
545	#41	—	632	2	no	—
546	C₂×Q₈	—	79	2	no	—
547	C₂×Q₈	—	79	2	no	—
548	C₂×Q₈	—	632	2	no	—
549	C₂×Q₈	—	158	2	no	—
550	C₂×Q₈	—	158	1	no	—
551	C₂×Q₈	(C₂×D₇₉)⋊C₄	1	1	yes	characteristic
552	C₂×D₄	—	79	2	no	—
553	C₂×D₄	—	158	2	no	—
554	C₂×D₄	—	158	2	no	—
555	C₂×D₄	—	158	2	no	—
556	C₂×D₄	—	158	1	no	—
557	C₂×D₄	—	158	1	no	—
558	C₂×D₄	(C₂×D₇₉)⋊C₄	1	1	yes	characteristic
559	C₂×D₄	(C₂×D₇₉)⋊C₄	1	1	yes	characteristic
560	C₂×D₄	(C₂×D₇₉)⋊C₄	1	1	yes	characteristic
561	C₂²×C₄	—	158	2	no	—
562	C₂²×C₄	—	158	2	no	—
563	C₂²×C₄	—	158	2	no	—
564	C₂²×C₄	—	158	2	no	—
565	C₂²×C₄	C₂×C₄×D₇₉	1	1	yes	characteristic
566	C₂²×C₄	C₂×C₄×D₇₉	1	1	yes	characteristic
567	C₂²×C₄	C₂×C₄×D₇₉	1	1	yes	characteristic
568	C₂²×C₄	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
569	C₂²×C₄	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
570	C₂²×C₄	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
571	C₂²×C₄	C₂×D₃₁₆	1	1	yes	characteristic
572	C₂²×C₄	C₂×D₃₁₆	1	1	yes	characteristic
573	C₂²×C₄	C₂×D₃₁₆	1	1	yes	characteristic
574	M₁₆	—	8	1	no	—
575	M₁₆	—	8	1	no	—
576	M₁₆	—	316	2	no	—
577	C₂×C₈	—	2	1	no	—
578	C₂×C₈	—	2	1	no	—
579	C₂×C₈	—	2	1	no	—
580	C₂×C₈	—	2	1	no	—
581	C₂×C₈	—	8	1	no	—
582	C₂×C₈	—	316	2	no	—
583	C₂×C₈	—	158	1	no	—
584	C₂×C₈	—	158	1	no	—
585	C₂×C₈	—	158	1	no	—
586	C₂×C₈	—	158	1	no	—
587	C₄⋊C₄	—	79	2	no	—
588	C₄⋊C₄	—	158	2	no	—
589	C₄⋊C₄	—	158	2	no	—
590	C₄⋊C₄	—	158	2	no	—
591	C₄⋊C₄	—	158	2	no	—
592	C₄⋊C₄	—	158	2	no	—
593	C₄⋊C₄	—	158	2	no	—
594	C₄⋊C₄	—	158	1	no	—
595	C₄⋊C₄	—	158	1	no	—
596	C₄⋊C₄	—	158	1	no	—
597	C₄⋊C₄	—	158	1	no	—
598	C₄⋊C₄	—	158	1	no	—
599	C₄⋊C₄	(C₂×D₇₉)⋊C₄	1	1	yes	characteristic
600	C₄⋊C₄	(C₂×D₇₉)⋊C₄	1	1	yes	characteristic
601	C₄⋊C₄	(C₂×D₇₉)⋊C₄	1	1	yes	characteristic
602	C₄⋊C₄	(C₂×D₇₉)⋊C₄	1	1	yes	characteristic
603	C₄⋊C₄	(C₂×D₇₉)⋊C₄	1	1	yes	characteristic
604	C₄⋊C₄	(C₂×D₇₉)⋊C₄	1	1	yes	characteristic
605	C₂²⋊C₄	—	158	2	no	—
606	C₂²⋊C₄	—	158	2	no	—
607	C₂²⋊C₄	—	158	2	no	—
608	C₂²⋊C₄	—	158	2	no	—
609	C₂²⋊C₄	—	158	2	no	—
610	C₂²⋊C₄	—	158	2	no	—
611	C₂²⋊C₄	—	158	2	no	—
612	C₂²⋊C₄	—	158	2	no	—
613	C₂²⋊C₄	(C₂×D₇₉)⋊C₄	1	1	yes	characteristic
614	C₂²⋊C₄	(C₂×D₇₉)⋊C₄	1	1	yes	characteristic
615	C₂²⋊C₄	(C₂×D₇₉)⋊C₄	1	1	yes	characteristic
616	C₂²⋊C₄	(C₂×D₇₉)⋊C₄	1	1	yes	characteristic
617	C₂²⋊C₄	(C₂×D₇₉)⋊C₄	1	1	yes	characteristic
618	C₂²⋊C₄	(C₂×D₇₉)⋊C₄	1	1	yes	characteristic
619	C₄²	—	158	2	no	—
620	C₄²	—	158	2	no	—
621	C₄²	C₂×C₄×D₇₉	1	1	yes	characteristic
622	C₄²	C₂×C₄×D₇₉	1	1	yes	characteristic
623	C₄²	C₂×C₄×D₇₉	1	1	yes	characteristic
624	C₄²	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
625	C₄²	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
626	C₄²	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
627	C₄²	C₂×D₃₁₆	1	1	yes	characteristic
628	C₄²	C₂×D₃₁₆	1	1	yes	characteristic
629	C₄²	C₂×D₃₁₆	1	1	yes	characteristic
630	C₄²	C₂³×D₇₉	1	1	yes	characteristic
631	C₂³	—	158	2	no	—
632	C₂³	C₂×(C₂×D₇₉)⋊C₄	1	1	yes	characteristic
633	C₂³	C₂×(C₂×D₇₉)⋊C₄	1	1	yes	characteristic
634	C₂³	C₂×(C₂×D₇₉)⋊C₄	1	1	yes	characteristic
635	Q₈	—	4	1	no	—
636	Q₈	—	316	2	no	—
637	Q₈	—	316	2	no	—
638	Q₈	—	316	1	no	—
639	Q₈	—	316	1	no	—
640	Q₈	—	632	2	no	—
641	D₄	—	4	1	no	—
642	D₄	—	4	1	no	—
643	D₄	—	4	1	no	—
644	D₄	—	316	2	no	—
645	D₄	—	316	4	no	—
646	D₄	—	316	1	no	—
647	D₄	—	316	1	no	—
648	D₄	—	316	1	no	—
649	D₄	—	316	1	no	—
650	D₄	—	632	2	no	—
651	D₄	—	632	2	no	—
652	C₂×C₄	—	2	1	no	—
653	C₂×C₄	—	2	1	no	—
654	C₂×C₄	—	2	1	no	—
655	C₂×C₄	—	2	1	no	—
656	C₂×C₄	—	2	1	no	—
657	C₂×C₄	—	2	1	no	—
658	C₂×C₄	—	2	1	no	—
659	C₂×C₄	—	2	1	no	—
660	C₂×C₄	—	2	1	no	—
661	C₂×C₄	—	2	1	no	—
662	C₂×C₄	—	2	1	no	—
663	C₂×C₄	—	2	1	no	—
664	C₂×C₄	—	4	1	no	—
665	C₂×C₄	—	4	1	no	—
666	C₂×C₄	—	4	1	no	—
667	C₂×C₄	—	316	4	no	—
668	C₂×C₄	—	632	2	no	—
669	C₂×C₄	—	632	2	no	—
670	C₂×C₄	—	632	2	no	—
671	C₂×C₄	—	158	2	no	—
672	C₂×C₄	—	158	2	no	—
673	C₂×C₄	—	158	2	no	—
674	C₂×C₄	C₂×(C₂×D₇₉)⋊C₄	1	1	yes	characteristic
675	C₂×C₄	C₂×(C₂×D₇₉)⋊C₄	1	1	yes	characteristic
676	C₂×C₄	C₂×(C₂×D₇₉)⋊C₄	1	1	yes	characteristic
677	C₂×C₄	C₂×(C₂×D₇₉)⋊C₄	1	1	yes	characteristic
678	C₂×C₄	C₂×(C₂×D₇₉)⋊C₄	1	1	yes	characteristic
679	C₂×C₄	C₂×(C₂×D₇₉)⋊C₄	1	1	yes	characteristic
680	C₂×C₄	C₂×(C₂×D₇₉)⋊C₄	1	1	yes	characteristic
681	C₂×C₄	C₂×(C₂×D₇₉)⋊C₄	1	1	yes	characteristic
682	C₂×C₄	C₂×(C₂×D₇₉)⋊C₄	1	1	yes	characteristic
683	C₂×C₄	C₂²×C₄×D₇₉	1	1	yes	characteristic
684	C₂×C₄	C₂²×C₂²⋊D₇₉	1	1	yes	characteristic
685	C₂×C₄	C₂²×D₃₁₆	1	1	yes	characteristic
686	C₈	—	4	1	no	—
687	C₈	—	4	1	no	—
688	C₈	—	4	1	no	—
689	C₈	—	4	1	no	—
690	C₈	—	316	1	no	—
691	C₈	—	316	1	no	—
692	C₈	—	316	1	no	—
693	C₈	—	316	1	no	—
694	C₂²	—	2	1	no	—
695	C₂²	—	2	1	no	—
696	C₂²	—	2	1	no	—
697	C₂²	—	2	1	no	—
698	C₂²	—	2	1	no	—
699	C₂²	—	2	1	no	—
700	C₂²	—	2	1	no	—
701	C₂²	—	2	1	no	—
702	C₂²	—	2	1	no	—
703	C₂²	—	316	2	no	—
704	C₂²	—	316	2	no	—
705	C₂²	—	316	2	no	—
706	C₂²	C₂²×(C₂×D₇₉)⋊C₄	1	1	yes	characteristic
707	C₄	—	2	1	no	—
708	C₄	—	2	1	no	—
709	C₄	—	2	1	no	—
710	C₄	—	2	1	no	—
711	C₄	—	2	1	no	—
712	C₄	—	2	1	no	—
713	C₄	—	2	1	no	—
714	C₄	—	2	1	no	—
715	C₄	—	2	1	no	—
716	C₄	—	2	1	no	—
717	C₄	—	316	2	no	—
718	C₄	—	316	2	no	—
719	C₄	—	316	2	no	—
720	C₄	#19099363	1	1	yes	characteristic
721	C₄	#19099363	1	1	yes	characteristic
722	C₄	#19099374	1	1	yes	characteristic
723	C₄	#19099378	1	1	yes	characteristic
724	C₂	—	4	1	no	—
725	C₂	—	4	1	no	—
726	C₂	—	4	1	no	—
727	C₂	—	632	2	no	—
728	C₂	#23771878	1	1	yes	characteristic
729	C₂	#23771920	1	1	yes	characteristic
730	C₂	#23771930	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂²×(C₂×D₇₉)⋊C₄
commutator	C₂×C₄×C₇₉	C₂³×C₄
Frattini	C₄²	C₂³×D₇₉
Fitting	C₇₉×#2989	C₂
socle	C₂²×C₇₉	C₂²×C₂²⋊C₄
prime radical	#23777311	C₂
cosocle	C₄²×C₇₉	C₂⁴
hypercenter	#2989	D₇₉
hypocenter	C₇₉	#17768
LCS	G ▷ C₂×C₄×C₇₉ ▷ C₂²×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂² ◁ C₄×#41 ◁ #2989

Complements

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

N	H ≅ G/N	type
2. #23772066	C₂	semidirect
3. #23762133	C₂	semidirect
4. #23762131	C₂	semidirect
5. #23762125	C₂	semidirect
6. #23762120	C₂	semidirect
7. #23762108	C₂	semidirect
8. #23762106	C₂	semidirect
9. #23762096	C₂	semidirect
10. #23762093	C₂	semidirect
11. #23762091	C₂	semidirect
12. #23762082	C₂	semidirect
13. #23762060	C₂	semidirect
14. #23762058	C₂	semidirect
15. C₇₉×#2989	C₂	semidirect
367. #2989	D₇₉	semidirect
381. C₇₉	#17768	semidirect

Maximal subgroups

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

subgroup	index
#23777311	2
#23772066	2
#23762133	2
#23762131	2
#23762125	2
#23762120	2
#23762108	2
#23762106	2
#23762096	2
#23762093	2
#23762091	2
#23762082	2
#23762060	2
#23762058	2
C₇₉×#2989	2
#17768	79