Subgroups — #34259242

Order 20224.

740 conjugacy classes of subgroups.

The subgroup lattice has 490 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#23772144	C₂	1	1	yes	maximal, characteristic, complemented
2	D₄×#11929608	C₂	1	1	yes	maximal, characteristic, complemented
3	#23762314	C₂	1	2	yes	maximal, complemented
4	#23762265	C₂	1	2	yes	maximal, complemented
5	#23762265	C₂	1	2	yes	maximal, complemented
6	#23762224	C₂	1	2	yes	maximal, complemented
7	#23762171	C₂	1	1	yes	maximal, characteristic, complemented
8	#23761851	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×D₄⋊(C₇₉⋊C₈)	C₂	1	1	yes	maximal, characteristic, complemented
10	#23761690	C₂	1	1	yes	maximal, characteristic, complemented
11	C₇₉×#3100	C₂	1	1	yes	maximal, characteristic
12	C₂×#14579168	—	2	1	no	—
13	C₂²×#11929608	—	2	1	no	—
14	#19098641	C₂²	1	2	yes	—
15	#19098641	C₂²	1	2	yes	complemented
16	#19098635	—	2	2	no	—
17	#19098635	—	2	2	no	—
18	D₄×C₇₉⋊C₈	C₂²	1	2	yes	—
19	D₄×C₇₉⋊C₈	C₂²	1	2	yes	complemented
20	#19098587	C₂²	1	1	yes	characteristic
21	C₂×C₄⋊(C₇₉⋊C₈)	C₂²	1	1	yes	characteristic
22	#19098530	—	2	1	no	—
23	#19098527	—	2	1	no	—
24	C₄×#11929608	C₂²	1	1	yes	characteristic
25	C₂×C₄×C₇₉⋊C₈	C₂²	1	1	yes	characteristic
26	#19098314	C₂²	1	2	yes	complemented
27	#19098314	C₂²	1	2	yes	complemented
28	D₄⋊(C₇₉⋊C₈)	C₂²	1	1	yes	characteristic
29	D₄⋊(C₇₉⋊C₈)	C₂²	1	1	yes	characteristic
30	D₄⋊(C₇₉⋊C₈)	C₂²	1	1	yes	characteristic
31	D₄⋊(C₇₉⋊C₈)	C₂²	1	1	yes	characteristic
32	D₄⋊(C₇₉⋊C₈)	C₂²	1	2	yes	complemented
33	D₄⋊(C₇₉⋊C₈)	C₂²	1	2	yes	complemented
34	#19098285	C₂²	1	2	yes	complemented
35	#19098284	C₂²	1	2	yes	complemented
36	#532×C₇₉	C₂²	1	1	yes	characteristic
37	C₂×C₄×D₄×C₇₉	C₂²	1	1	yes	characteristic
38	#480×C₇₉	C₄	1	2	yes	—
39	#474×C₇₉	C₄	1	1	yes	characteristic
40	#474×C₇₉	C₄	1	1	yes	characteristic
41	#459×C₇₉	C₄	1	1	yes	characteristic
42	#459×C₇₉	C₄	1	1	yes	characteristic
43	#447×C₇₉	C₄	1	2	yes	—
44	C₄×D₈×C₇₉	C₂²	1	2	yes	—
45	C₄×D₈×C₇₉	C₂²	1	2	yes	—
46	#431×C₇₉	C₂²	1	1	yes	characteristic
47	#14579168	—	4	4	no	—
48	C₂×#11929608	—	2	1	no	—
49	C₂×#11929608	—	2	2	no	—
50	C₂×#11929608	—	2	2	no	—
51	C₂×#11929608	—	4	4	no	—
52	C₂×#11929608	D₄	1	1	yes	characteristic
53	C₂×#11929608	D₄	1	1	yes	characteristic
54	C₂²×C₇₉⋊C₈	—	2	1	no	—
55	C₂²×C₇₉⋊C₈	—	2	1	no	—
56	C₂²×C₇₉⋊C₈	—	2	2	no	—
57	C₂²×C₇₉⋊C₈	—	2	2	no	—
58	C₄⋊(C₇₉⋊C₈)	—	2	1	no	—
59	C₄⋊(C₇₉⋊C₈)	—	2	1	no	—
60	C₄⋊(C₇₉⋊C₈)	C₂³	1	2	yes	—
61	C₄⋊(C₇₉⋊C₈)	C₂³	1	1	yes	characteristic
62	C₄⋊(C₇₉⋊C₈)	C₂³	1	1	yes	characteristic
63	C₂²⋊(C₇₉⋊C₈)	—	2	2	no	—
64	C₂²⋊(C₇₉⋊C₈)	—	2	2	no	—
65	C₂²⋊(C₇₉⋊C₈)	—	2	2	no	—
66	C₂²⋊(C₇₉⋊C₈)	—	2	2	no	—
67	#14579072	D₄	1	2	yes	—
68	C₄×C₇₉⋊C₈	—	2	1	no	—
69	C₄×C₇₉⋊C₈	C₂³	1	1	yes	characteristic
70	C₄×C₇₉⋊C₈	C₂³	1	1	yes	characteristic
71	C₄×C₇₉⋊C₈	C₂³	1	2	yes	—
72	C₂×#41×C₇₉	—	2	1	no	—
73	C₂²×D₄×C₇₉	C₂×C₄	1	1	yes	characteristic
74	C₂³×C₄×C₇₉	—	2	1	no	—
75	C₂×D₈×C₇₉	C₂×C₄	1	2	yes	—
76	C₂×D₈×C₇₉	C₂×C₄	1	2	yes	—
77	C₄⋊Q₈×C₇₉	C₂×C₄	1	1	yes	characteristic
78	#127×C₇₉	C₂×C₄	1	1	yes	characteristic
79	#124×C₇₉	—	2	1	no	—
80	#121×C₇₉	—	2	1	no	—
81	#121×C₇₉	C₂×C₄	1	2	yes	—
82	C₄×D₄×C₇₉	—	2	1	no	—
83	C₄×D₄×C₇₉	—	2	1	no	—
84	C₄×D₄×C₇₉	—	2	1	no	—
85	C₄×D₄×C₇₉	C₂×C₄	1	1	yes	characteristic
86	C₄×D₄×C₇₉	C₂×C₄	1	1	yes	characteristic
87	C₄×D₄×C₇₉	C₂³	1	1	yes	characteristic
88	C₄×D₄×C₇₉	C₂³	1	2	yes	—
89	C₄×D₄×C₇₉	C₂³	1	1	yes	characteristic
90	C₂×C₄⋊C₄×C₇₉	C₂×C₄	1	1	yes	characteristic
91	C₂×C₂²⋊C₄×C₇₉	—	2	1	no	—
92	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
93	#107×C₇₉	C₂×C₄	1	2	yes	—
94	#107×C₇₉	C₂×C₄	1	2	yes	—
95	C₄⋊C₈×C₇₉	C₂×C₄	1	1	yes	characteristic
96	C₄⋊C₈×C₇₉	C₂×C₄	1	1	yes	characteristic
97	#102×C₇₉	C₂×C₄	1	2	yes	—
98	#102×C₇₉	C₂×C₄	1	2	yes	—
99	#102×C₇₉	C₂×C₄	1	2	yes	—
100	#102×C₇₉	C₂×C₄	1	2	yes	—
101	C₂²⋊C₈×C₇₉	C₂×C₄	1	2	yes	—
102	C₄×C₈×C₇₉	C₂³	1	2	yes	—
103	#11929608	—	2	2	no	—
104	#11929608	—	2	2	no	—
105	#11929608	—	4	4	no	—
106	#11929608	—	4	4	no	—
107	#11929608	—	4	2	no	—
108	C₂×C₇₉⋊C₈	—	2	1	no	—
109	C₂×C₇₉⋊C₈	—	2	2	no	—
110	C₂×C₇₉⋊C₈	—	2	1	no	—
111	C₂×C₇₉⋊C₈	—	2	1	no	—
112	C₂×C₇₉⋊C₈	—	2	1	no	—
113	C₂×C₇₉⋊C₈	—	4	2	no	—
114	C₂×C₇₉⋊C₈	—	4	4	no	—
115	C₂×C₇₉⋊C₈	—	4	4	no	—
116	C₂×C₇₉⋊C₈	—	4	2	no	—
117	C₂×C₇₉⋊C₈	C₂×D₄	1	2	yes	—
118	C₂×C₇₉⋊C₈	C₂×D₄	1	2	yes	—
119	C₂⁴×C₇₉	—	2	1	no	—
120	#41×C₇₉	—	4	2	no	—
121	#41×C₇₉	—	4	2	no	—
122	C₂×Q₈×C₇₉	—	2	1	no	—
123	C₂×D₄×C₇₉	—	2	2	no	—
124	C₂×D₄×C₇₉	—	2	2	no	—
125	C₂×D₄×C₇₉	—	2	1	no	—
126	C₂×D₄×C₇₉	—	2	1	no	—
127	C₂×D₄×C₇₉	—	2	1	no	—
128	C₂×D₄×C₇₉	—	4	1	no	—
129	C₂×D₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
130	C₂×D₄×C₇₉	C₂²×C₄	1	2	yes	—
131	C₂×D₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
132	C₂²×C₄×C₇₉	—	2	1	no	—
133	C₂²×C₄×C₇₉	—	2	1	no	—
134	C₂²×C₄×C₇₉	—	2	1	no	—
135	C₂²×C₄×C₇₉	—	2	1	no	—
136	C₂²×C₄×C₇₉	—	2	1	no	—
137	C₂²×C₄×C₇₉	—	2	2	no	—
138	C₂²×C₄×C₇₉	—	4	2	no	—
139	C₂²×C₄×C₇₉	—	4	2	no	—
140	C₂²×C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
141	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
142	C₂²×C₄×C₇₉	#41	1	1	yes	characteristic
143	D₈×C₇₉	—	2	4	no	—
144	D₈×C₇₉	—	4	2	no	—
145	C₂×C₈×C₇₉	C₂²×C₄	1	2	yes	—
146	C₂×C₈×C₇₉	C₂²×C₄	1	2	yes	—
147	C₄⋊C₄×C₇₉	—	2	1	no	—
148	C₄⋊C₄×C₇₉	—	2	1	no	—
149	C₄⋊C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
150	C₄⋊C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
151	C₄⋊C₄×C₇₉	C₂²×C₄	1	2	yes	—
152	C₂²⋊C₄×C₇₉	—	2	1	no	—
153	C₂²⋊C₄×C₇₉	—	2	1	no	—
154	C₂²⋊C₄×C₇₉	—	2	2	no	—
155	C₂²⋊C₄×C₇₉	—	2	1	no	—
156	C₂²⋊C₄×C₇₉	—	2	1	no	—
157	C₂²⋊C₄×C₇₉	—	2	2	no	—
158	C₄²×C₇₉	C₂²×C₄	1	1	yes	characteristic
159	C₄²×C₇₉	C₂×D₄	1	1	yes	characteristic
160	C₄²×C₇₉	#41	1	1	yes	characteristic
161	C₄²×C₇₉	C₂⁴	1	1	yes	characteristic
162	C₂³×C₇₉	—	2	1	no	—
163	C₂³×C₇₉	—	2	1	no	—
164	C₂³×C₇₉	—	2	2	no	—
165	C₂³×C₇₉	—	4	2	no	—
166	C₂³×C₇₉	—	4	2	no	—
167	C₂³×C₇₉	—	8	1	no	—
168	C₂³×C₇₉	C₄×D₄	1	1	yes	characteristic
169	Q₈×C₇₉	—	4	2	no	—
170	D₄×C₇₉	—	2	2	no	—
171	D₄×C₇₉	—	2	1	no	—
172	D₄×C₇₉	—	2	1	no	—
173	D₄×C₇₉	—	2	1	no	—
174	D₄×C₇₉	—	2	2	no	—
175	D₄×C₇₉	—	4	2	no	—
176	D₄×C₇₉	—	4	4	no	—
177	D₄×C₇₉	—	4	2	no	—
178	D₄×C₇₉	—	8	1	no	—
179	D₄×C₇₉	#131	1	2	yes	complemented
180	C₂×C₄×C₇₉	—	2	1	no	—
181	C₂×C₄×C₇₉	—	2	1	no	—
182	C₂×C₄×C₇₉	—	2	1	no	—
183	C₂×C₄×C₇₉	—	2	1	no	—
184	C₂×C₄×C₇₉	—	2	2	no	—
185	C₂×C₄×C₇₉	—	4	1	no	—
186	C₂×C₄×C₇₉	—	4	2	no	—
187	C₂×C₄×C₇₉	—	4	1	no	—
188	C₂×C₄×C₇₉	—	4	2	no	—
189	C₂×C₄×C₇₉	—	4	1	no	—
190	C₂×C₄×C₇₉	—	4	1	no	—
191	C₂×C₄×C₇₉	—	4	1	no	—
192	C₂×C₄×C₇₉	—	4	2	no	—
193	C₂×C₄×C₇₉	—	4	2	no	—
194	C₂×C₄×C₇₉	—	4	2	no	—
195	C₂×C₄×C₇₉	C₄×D₄	1	1	yes	characteristic
196	C₂×C₄×C₇₉	C₄×D₄	1	1	yes	characteristic
197	C₂×C₄×C₇₉	C₄×D₄	1	1	yes	characteristic
198	C₂×C₄×C₇₉	AGL(1,ℤ/8)	1	2	yes	—
199	C₂×C₄×C₇₉	AGL(1,ℤ/8)	1	2	yes	—
200	C₂×C₄×C₇₉	C₂³×C₄	1	1	yes	characteristic
201	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
202	C₂×C₄×C₇₉	C₂×#41	1	1	yes	characteristic
203	C₈×C₇₉	—	2	2	no	—
204	C₈×C₇₉	—	2	2	no	—
205	C₇₉⋊C₈	—	2	2	no	—
206	C₇₉⋊C₈	—	2	2	no	—
207	C₇₉⋊C₈	—	2	2	no	—
208	C₇₉⋊C₈	—	4	1	no	—
209	C₇₉⋊C₈	—	4	1	no	—
210	C₇₉⋊C₈	—	4	2	no	—
211	C₇₉⋊C₈	—	4	1	no	—
212	C₂²×C₇₉	—	2	1	no	—
213	C₂²×C₇₉	—	2	1	no	—
214	C₂²×C₇₉	—	2	2	no	—
215	C₂²×C₇₉	—	4	1	no	—
216	C₂²×C₇₉	—	4	1	no	—
217	C₂²×C₇₉	—	4	1	no	—
218	C₂²×C₇₉	—	4	2	no	—
219	C₂²×C₇₉	—	4	1	no	—
220	C₂²×C₇₉	—	4	2	no	—
221	C₂²×C₇₉	—	4	2	no	—
222	C₂²×C₇₉	—	4	1	no	—
223	C₂²×C₇₉	—	8	4	no	—
224	C₂²×C₇₉	#442	1	2	yes	—
225	C₂²×C₇₉	C₂×C₄×D₄	1	1	yes	characteristic
226	C₄×C₇₉	—	2	1	no	—
227	C₄×C₇₉	—	2	1	no	—
228	C₄×C₇₉	—	2	1	no	—
229	C₄×C₇₉	—	4	1	no	—
230	C₄×C₇₉	—	4	1	no	—
231	C₄×C₇₉	—	4	2	no	—
232	C₄×C₇₉	#442	1	2	yes	—
233	C₄×C₇₉	C₂×#131	1	1	yes	characteristic
234	C₄×C₇₉	#568	1	1	yes	characteristic
235	C₄×C₇₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
236	C₄×C₇₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
237	#18001	—	79	1	no	maximal, Sylow
238	C₂×C₇₉	—	2	2	no	—
239	C₂×C₇₉	—	4	2	no	—
240	C₂×C₇₉	—	8	2	no	—
241	C₂×C₇₉	—	8	1	no	—
242	C₂×C₇₉	#2933	1	1	yes	characteristic
243	C₂×C₇₉	C₂×#442	1	1	yes	characteristic
244	C₂×C₇₉	#2956	1	1	yes	characteristic
245	#3100	D₇₉	1	1	yes	characteristic
246	#2935	—	79	1	no	—
247	D₄×M₁₆	—	79	1	no	—
248	#1594	—	79	2	no	—
249	#1586	—	79	2	no	—
250	#1586	—	79	2	no	—
251	#1580	—	79	2	no	—
252	#1570	—	79	1	no	—
253	#1492	—	79	1	no	—
254	C₂×D₄⋊C₈	—	79	1	no	—
255	#1451	—	79	1	no	—
256	C₇₉	#18001	1	1	yes	characteristic, complemented, Sylow
257	C₂×#131	—	158	1	no	—
258	C₂²×M₁₆	—	158	1	no	—
259	#532	C₂×D₇₉	1	1	yes	characteristic
260	C₂×C₄×D₄	C₂×D₇₉	1	1	yes	characteristic
261	#480	Dic₇₉	1	2	yes	—
262	#474	Dic₇₉	1	1	yes	characteristic
263	#474	Dic₇₉	1	1	yes	characteristic
264	#459	Dic₇₉	1	1	yes	characteristic
265	#459	Dic₇₉	1	1	yes	characteristic
266	#447	Dic₇₉	1	2	yes	—
267	C₄×D₈	C₂×D₇₉	1	2	yes	—
268	C₄×D₈	C₂×D₇₉	1	2	yes	—
269	#436	—	79	2	no	—
270	#436	—	79	2	no	—
271	#435	—	158	2	no	—
272	#435	—	158	2	no	—
273	C₈×D₄	—	79	2	no	—
274	C₈×D₄	—	79	2	no	—
275	#431	C₂×D₇₉	1	1	yes	characteristic
276	#423	—	79	1	no	—
277	C₂×C₄⋊C₈	—	79	1	no	—
278	#408	—	158	1	no	—
279	#407	—	158	1	no	—
280	C₄×M₁₆	—	79	1	no	—
281	C₂×C₄×C₈	—	79	1	no	—
282	#334	—	79	2	no	—
283	#334	—	79	2	no	—
284	D₄⋊C₈	—	79	1	no	—
285	D₄⋊C₈	—	79	2	no	—
286	D₄⋊C₈	—	79	1	no	—
287	D₄⋊C₈	—	79	1	no	—
288	D₄⋊C₈	—	79	2	no	—
289	D₄⋊C₈	—	79	1	no	—
290	#322	—	79	2	no	—
291	#322	—	79	2	no	—
292	C₂×#41	—	2	1	no	—
293	C₂²×D₄	C₂×Dic₇₉	1	1	yes	characteristic
294	C₂³×C₄	—	2	1	no	—
295	C₂×D₈	C₂×Dic₇₉	1	2	yes	—
296	C₂×D₈	C₂×Dic₇₉	1	2	yes	—
297	#131	—	316	4	no	—
298	C₂×M₁₆	—	316	4	no	—
299	C₂×M₁₆	—	79	1	no	—
300	C₂×M₁₆	—	79	1	no	—
301	C₂×M₁₆	—	158	2	no	—
302	C₂×M₁₆	—	158	2	no	—
303	C₂×M₁₆	—	158	1	no	—
304	C₂²×C₈	—	158	2	no	—
305	C₂²×C₈	—	158	2	no	—
306	C₂²×C₈	—	158	1	no	—
307	C₂²×C₈	—	158	1	no	—
308	C₄⋊Q₈	C₂×Dic₇₉	1	1	yes	characteristic
309	#127	C₂×Dic₇₉	1	1	yes	characteristic
310	#124	—	2	1	no	—
311	#121	—	2	1	no	—
312	#121	C₂×Dic₇₉	1	2	yes	—
313	C₄×D₄	—	2	1	no	—
314	C₄×D₄	—	2	1	no	—
315	C₄×D₄	—	2	1	no	—
316	C₄×D₄	C₂×Dic₇₉	1	1	yes	characteristic
317	C₄×D₄	C₂×Dic₇₉	1	1	yes	characteristic
318	C₄×D₄	C₂²×D₇₉	1	1	yes	characteristic
319	C₄×D₄	C₂²×D₇₉	1	1	yes	characteristic
320	C₄×D₄	C₂²×D₇₉	1	2	yes	—
321	C₂×C₄⋊C₄	C₂×Dic₇₉	1	1	yes	characteristic
322	C₂×C₂²⋊C₄	—	2	1	no	—
323	C₂×C₄²	C₂²×D₇₉	1	1	yes	characteristic
324	#107	C₂×Dic₇₉	1	2	yes	—
325	#107	C₂×Dic₇₉	1	2	yes	—
326	C₄⋊C₈	—	79	1	no	—
327	C₄⋊C₈	—	79	1	no	—
328	C₄⋊C₈	—	79	2	no	—
329	C₄⋊C₈	—	158	1	no	—
330	C₄⋊C₈	—	158	1	no	—
331	C₄⋊C₈	C₂×Dic₇₉	1	1	yes	characteristic
332	C₄⋊C₈	C₂×Dic₇₉	1	1	yes	characteristic
333	#102	C₂×Dic₇₉	1	2	yes	—
334	#102	C₂×Dic₇₉	1	2	yes	—
335	#102	C₂×Dic₇₉	1	2	yes	—
336	#102	C₂×Dic₇₉	1	2	yes	—
337	C₂²⋊C₈	—	158	2	no	—
338	C₂²⋊C₈	—	158	2	no	—
339	C₂²⋊C₈	—	158	2	no	—
340	C₂²⋊C₈	—	158	2	no	—
341	C₂²⋊C₈	C₂×Dic₇₉	1	2	yes	—
342	#97	—	79	2	no	—
343	C₄×C₈	—	79	2	no	—
344	C₄×C₈	—	79	1	no	—
345	C₄×C₈	—	79	1	no	—
346	C₄×C₈	—	158	1	no	—
347	C₄×C₈	C₂²×D₇₉	1	2	yes	—
348	C₂⁴	—	2	1	no	—
349	#41	—	4	2	no	—
350	#41	—	4	2	no	—
351	C₂×Q₈	—	2	1	no	—
352	C₂×D₄	—	2	2	no	—
353	C₂×D₄	—	2	2	no	—
354	C₂×D₄	—	2	1	no	—
355	C₂×D₄	—	2	1	no	—
356	C₂×D₄	—	2	1	no	—
357	C₂×D₄	—	4	1	no	—
358	C₂×D₄	C₂²×Dic₇₉	1	1	yes	characteristic
359	C₂×D₄	C₂²×Dic₇₉	1	2	yes	—
360	C₂×D₄	C₂²×Dic₇₉	1	1	yes	characteristic
361	C₂²×C₄	—	2	1	no	—
362	C₂²×C₄	—	2	1	no	—
363	C₂²×C₄	—	2	1	no	—
364	C₂²×C₄	—	2	1	no	—
365	C₂²×C₄	—	2	2	no	—
366	C₂²×C₄	—	2	1	no	—
367	C₂²×C₄	—	4	2	no	—
368	C₂²×C₄	—	4	2	no	—
369	C₂²×C₄	C₂²×Dic₇₉	1	1	yes	characteristic
370	C₂²×C₄	D₄×D₇₉	1	1	yes	characteristic
371	C₂²×C₄	#11929623	1	1	yes	characteristic
372	D₈	—	2	4	no	—
373	D₈	—	4	2	no	—
374	M₁₆	—	316	2	no	—
375	M₁₆	—	316	4	no	—
376	M₁₆	—	316	4	no	—
377	M₁₆	—	158	2	no	—
378	M₁₆	—	158	2	no	—
379	C₂×C₈	—	316	2	no	—
380	C₂×C₈	—	316	2	no	—
381	C₂×C₈	—	316	4	no	—
382	C₂×C₈	—	316	4	no	—
383	C₂×C₈	—	79	2	no	—
384	C₂×C₈	—	79	2	no	—
385	C₂×C₈	—	158	1	no	—
386	C₂×C₈	—	158	1	no	—
387	C₂×C₈	—	158	2	no	—
388	C₂×C₈	—	158	1	no	—
389	C₂×C₈	—	158	1	no	—
390	C₂×C₈	C₂²×Dic₇₉	1	2	yes	—
391	C₂×C₈	C₂²×Dic₇₉	1	2	yes	—
392	C₄⋊C₄	—	2	1	no	—
393	C₄⋊C₄	—	2	1	no	—
394	C₄⋊C₄	C₂²×Dic₇₉	1	1	yes	characteristic
395	C₄⋊C₄	C₂²×Dic₇₉	1	1	yes	characteristic
396	C₄⋊C₄	C₂²×Dic₇₉	1	2	yes	—
397	C₂²⋊C₄	—	2	1	no	—
398	C₂²⋊C₄	—	2	1	no	—
399	C₂²⋊C₄	—	2	2	no	—
400	C₂²⋊C₄	—	2	1	no	—
401	C₂²⋊C₄	—	2	1	no	—
402	C₂²⋊C₄	—	2	2	no	—
403	C₄²	C₂²×Dic₇₉	1	1	yes	characteristic
404	C₄²	D₄×D₇₉	1	1	yes	characteristic
405	C₄²	#11929623	1	1	yes	characteristic
406	C₄²	C₂³×D₇₉	1	1	yes	characteristic
407	C₂³	—	2	1	no	—
408	C₂³	—	2	1	no	—
409	C₂³	—	2	2	no	—
410	C₂³	—	4	2	no	—
411	C₂³	—	4	2	no	—
412	C₂³	—	8	1	no	—
413	C₂³	D₄×Dic₇₉	1	1	yes	characteristic
414	Q₈	—	4	2	no	—
415	D₄	—	2	2	no	—
416	D₄	—	2	1	no	—
417	D₄	—	2	1	no	—
418	D₄	—	2	1	no	—
419	D₄	—	2	2	no	—
420	D₄	—	4	2	no	—
421	D₄	—	4	4	no	—
422	D₄	—	4	2	no	—
423	D₄	—	8	1	no	—
424	D₄	#14579168	1	2	yes	complemented
425	C₂×C₄	—	2	1	no	—
426	C₂×C₄	—	2	1	no	—
427	C₂×C₄	—	2	1	no	—
428	C₂×C₄	—	2	1	no	—
429	C₂×C₄	—	2	2	no	—
430	C₂×C₄	—	4	1	no	—
431	C₂×C₄	—	4	2	no	—
432	C₂×C₄	—	4	2	no	—
433	C₂×C₄	—	4	2	no	—
434	C₂×C₄	—	4	1	no	—
435	C₂×C₄	—	4	2	no	—
436	C₂×C₄	—	4	1	no	—
437	C₂×C₄	—	4	1	no	—
438	C₂×C₄	—	4	1	no	—
439	C₂×C₄	—	4	2	no	—
440	C₂×C₄	D₄×Dic₇₉	1	1	yes	characteristic
441	C₂×C₄	D₄×Dic₇₉	1	1	yes	characteristic
442	C₂×C₄	D₄×Dic₇₉	1	1	yes	characteristic
443	C₂×C₄	#14579185	1	2	yes	—
444	C₂×C₄	#14579185	1	2	yes	—
445	C₂×C₄	C₂³×Dic₇₉	1	1	yes	characteristic
446	C₂×C₄	C₂×D₄×D₇₉	1	1	yes	characteristic
447	C₂×C₄	C₂×#11929623	1	1	yes	characteristic
448	C₈	—	2	2	no	—
449	C₈	—	2	2	no	—
450	C₈	—	316	1	no	—
451	C₈	—	316	1	no	—
452	C₈	—	316	1	no	—
453	C₈	—	316	2	no	—
454	C₈	—	158	2	no	—
455	C₈	—	158	2	no	—
456	C₈	—	158	2	no	—
457	C₂²	—	2	1	no	—
458	C₂²	—	2	1	no	—
459	C₂²	—	2	2	no	—
460	C₂²	—	4	1	no	—
461	C₂²	—	4	1	no	—
462	C₂²	—	4	1	no	—
463	C₂²	—	4	2	no	—
464	C₂²	—	4	2	no	—
465	C₂²	—	4	1	no	—
466	C₂²	—	4	1	no	—
467	C₂²	—	4	2	no	—
468	C₂²	—	8	4	no	—
469	C₂²	#19098675	1	2	yes	—
470	C₂²	C₂×D₄×Dic₇₉	1	1	yes	characteristic
471	C₄	—	2	1	no	—
472	C₄	—	2	1	no	—
473	C₄	—	2	1	no	—
474	C₄	—	4	1	no	—
475	C₄	—	4	1	no	—
476	C₄	—	4	2	no	—
477	C₄	#19098675	1	2	yes	—
478	C₄	C₂×#14579168	1	1	yes	characteristic
479	C₄	#19099330	1	1	yes	characteristic
480	C₄	C₂×#14579185	1	1	yes	characteristic
481	C₄	C₂×#14579185	1	1	yes	characteristic
482	C₂	—	2	2	no	—
483	C₂	—	4	2	no	—
484	C₂	—	8	1	no	—
485	C₂	—	8	2	no	—
486	C₂	#23772127	1	1	yes	characteristic
487	C₂	C₂×#19098675	1	1	yes	characteristic
488	C₂	#23772310	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₇₉
commutator	C₂×C₄×C₇₉	C₂³×C₄
Frattini	C₄²	C₂³×D₇₉
Fitting, prime radical	C₇₉×#3100	C₂
socle	C₂²×C₇₉	C₂×C₄×D₄
cosocle	C₄²×C₇₉	C₂⁴
hypercenter	#3100	D₇₉
hypocenter	C₇₉	#18001
LCS	G ▷ C₂×C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #3100

Complements

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

N	H ≅ G/N	type
1. #23772144	C₂	semidirect
2. D₄×#11929608	C₂	semidirect
3. #23762314	C₂	semidirect
4. #23762265	C₂	semidirect
5. #23762265	C₂	semidirect
6. #23762224	C₂	semidirect
7. #23762171	C₂	semidirect
8. #23761851	C₂	semidirect
9. C₂×D₄⋊(C₇₉⋊C₈)	C₂	semidirect
10. #23761690	C₂	semidirect
15. #19098641	C₂²	semidirect
19. D₄×C₇₉⋊C₈	C₂²	semidirect
26. #19098314	C₂²	semidirect
27. #19098314	C₂²	semidirect
32. D₄⋊(C₇₉⋊C₈)	C₂²	semidirect
33. D₄⋊(C₇₉⋊C₈)	C₂²	semidirect
34. #19098285	C₂²	semidirect
35. #19098284	C₂²	semidirect
179. D₄×C₇₉	#131	semidirect
256. C₇₉	#18001	semidirect
424. D₄	#14579168	semidirect

Maximal subgroups

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

subgroup	index
#23772144	2
D₄×#11929608	2
#23762314	2
#23762265	2
#23762224	2
#23762171	2
#23761851	2
C₂×D₄⋊(C₇₉⋊C₈)	2
#23761690	2
C₇₉×#3100	2
#18001	79