Subgroups — #34258565

Order 20224.

672 conjugacy classes of subgroups.

The subgroup lattice has 472 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#23772376	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#19098641	C₂	1	1	yes	maximal, characteristic, complemented
3	#23762314	C₂	1	2	yes	maximal, complemented
4	#23762303	C₂	1	2	yes	maximal, complemented
5	#23762244	C₂	1	2	yes	maximal, complemented
6	#23762230	C₂	1	2	yes	maximal, complemented
7	#23762185	C₂	1	1	yes	maximal, characteristic, complemented
8	#23761843	C₂	1	1	yes	maximal, characteristic, complemented
9	#23761813	C₂	1	1	yes	maximal, characteristic, complemented
10	#23761690	C₂	1	1	yes	maximal, characteristic, complemented
11	C₇₉×#3105	C₂	1	1	yes	maximal, characteristic
12	C₂²×#11929608	—	2	1	no	—
13	#19098694	C₂²	1	1	yes	characteristic, complemented
14	Q₈×C₇₉⋊C₈	C₂²	1	1	yes	characteristic, complemented
15	#19098641	—	2	1	no	—
16	#19098641	—	2	1	no	—
17	#19098641	C₂²	1	2	yes	—
18	#19098641	C₂²	1	2	yes	—
19	#19098641	C₂²	1	1	yes	characteristic, complemented
20	#19098635	—	2	1	no	—
21	D₄×C₇₉⋊C₈	—	2	1	no	—
22	D₄×C₇₉⋊C₈	C₂²	1	1	yes	characteristic, complemented
23	#19098624	—	2	1	no	—
24	#19098620	C₂²	1	1	yes	characteristic
25	C₂×C₄⋊(C₇₉⋊C₈)	C₂²	1	1	yes	characteristic
26	C₂×C₂²⋊(C₇₉⋊C₈)	—	2	1	no	—
27	#19098519	—	2	1	no	—
28	C₄×#11929608	C₂²	1	1	yes	characteristic
29	C₂×C₄×C₇₉⋊C₈	C₂²	1	1	yes	characteristic
30	#19098316	C₂²	1	2	yes	complemented
31	#19098314	C₂²	1	2	yes	complemented
32	Q₈⋊(C₇₉⋊C₈)	C₂²	1	2	yes	complemented
33	D₄⋊(C₇₉⋊C₈)	C₂²	1	2	yes	—
34	D₄⋊(C₇₉⋊C₈)	C₂²	1	2	yes	—
35	D₄⋊(C₇₉⋊C₈)	C₂²	1	2	yes	complemented
36	#19098285	C₂²	1	2	yes	complemented
37	#19098284	C₂²	1	2	yes	complemented
38	#529×C₇₉	C₂²	1	1	yes	characteristic
39	C₂×C₄×D₄×C₇₉	C₂²	1	1	yes	characteristic
40	#484×C₇₉	C₄	1	1	yes	characteristic
41	#481×C₇₉	C₄	1	1	yes	characteristic
42	#478×C₇₉	C₄	1	2	yes	—
43	#463×C₇₉	C₄	1	2	yes	—
44	#450×C₇₉	C₄	1	1	yes	characteristic
45	#447×C₇₉	C₄	1	1	yes	characteristic
46	C₄×SD₁₆×C₇₉	C₂²	1	2	yes	—
47	C₄×D₈×C₇₉	C₂²	1	2	yes	—
48	#431×C₇₉	C₂²	1	1	yes	characteristic
49	C₂×#11929608	—	2	1	no	—
50	C₂×#11929608	—	2	1	no	—
51	C₂×#11929608	—	2	2	no	—
52	C₂×#11929608	—	2	2	no	—
53	C₂×#11929608	—	4	4	no	—
54	C₂²×C₇₉⋊C₈	—	2	1	no	—
55	C₂²×C₇₉⋊C₈	—	2	1	no	—
56	C₂²×C₇₉⋊C₈	D₄	1	1	yes	characteristic
57	C₂²×C₇₉⋊C₈	D₄	1	1	yes	characteristic
58	C₄⋊(C₇₉⋊C₈)	—	2	1	no	—
59	C₄⋊(C₇₉⋊C₈)	—	2	1	no	—
60	C₄⋊(C₇₉⋊C₈)	—	2	1	no	—
61	C₄⋊(C₇₉⋊C₈)	C₂³	1	1	yes	characteristic
62	C₄⋊(C₇₉⋊C₈)	C₂³	1	2	yes	—
63	C₄⋊(C₇₉⋊C₈)	C₂³	1	1	yes	characteristic
64	C₂²⋊(C₇₉⋊C₈)	—	2	1	no	—
65	C₂²⋊(C₇₉⋊C₈)	—	2	1	no	—
66	C₂²⋊(C₇₉⋊C₈)	—	2	1	no	—
67	C₂²⋊(C₇₉⋊C₈)	—	2	2	no	—
68	C₂²⋊(C₇₉⋊C₈)	—	2	2	no	—
69	#14579072	—	2	1	no	—
70	#14579072	—	2	1	no	—
71	#14579072	—	2	1	no	—
72	C₄×C₇₉⋊C₈	—	2	1	no	—
73	C₄×C₇₉⋊C₈	D₄	1	1	yes	characteristic
74	C₄×C₇₉⋊C₈	D₄	1	1	yes	characteristic
75	C₄×C₇₉⋊C₈	C₂³	1	2	yes	—
76	C₄×C₇₉⋊C₈	C₂³	1	1	yes	characteristic
77	C₄×C₇₉⋊C₈	C₂³	1	1	yes	characteristic
78	C₂²×D₄×C₇₉	C₂×C₄	1	1	yes	characteristic
79	C₂³×C₄×C₇₉	—	2	1	no	—
80	C₂×SD₁₆×C₇₉	C₂×C₄	1	2	yes	—
81	C₂×D₈×C₇₉	C₂×C₄	1	2	yes	—
82	#126×C₇₉	—	2	1	no	—
83	#125×C₇₉	C₂×C₄	1	1	yes	characteristic
84	#124×C₇₉	C₂×C₄	1	1	yes	characteristic
85	#123×C₇₉	—	2	1	no	—
86	C₂²⋊Q₈×C₇₉	C₂×C₄	1	1	yes	characteristic
87	#121×C₇₉	C₂×C₄	1	1	yes	characteristic
88	C₄×Q₈×C₇₉	C₂³	1	1	yes	characteristic
89	C₄×D₄×C₇₉	—	2	1	no	—
90	C₄×D₄×C₇₉	—	2	1	no	—
91	C₄×D₄×C₇₉	—	2	1	no	—
92	C₄×D₄×C₇₉	C₂×C₄	1	2	yes	—
93	C₄×D₄×C₇₉	C₂³	1	1	yes	characteristic
94	C₄×D₄×C₇₉	C₂³	1	2	yes	—
95	#117×C₇₉	—	2	1	no	—
96	C₂×C₄⋊C₄×C₇₉	C₂×C₄	1	1	yes	characteristic
97	C₂×C₂²⋊C₄×C₇₉	—	2	1	no	—
98	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
99	#107×C₇₉	C₂×C₄	1	2	yes	—
100	#106×C₇₉	C₂×C₄	1	2	yes	—
101	C₄⋊C₈×C₇₉	C₂×C₄	1	2	yes	—
102	#103×C₇₉	C₂×C₄	1	2	yes	—
103	#102×C₇₉	C₂×C₄	1	2	yes	—
104	#102×C₇₉	C₂×C₄	1	2	yes	—
105	#102×C₇₉	C₂×C₄	1	2	yes	—
106	C₂²⋊C₈×C₇₉	C₂×C₄	1	1	yes	characteristic
107	C₂²⋊C₈×C₇₉	C₂×C₄	1	1	yes	characteristic
108	C₄×C₈×C₇₉	C₂³	1	2	yes	—
109	#11929608	—	4	2	no	—
110	#11929608	—	4	2	no	—
111	#11929608	—	4	4	no	—
112	#11929608	—	4	4	no	—
113	C₂×C₇₉⋊C₈	—	2	2	no	—
114	C₂×C₇₉⋊C₈	—	2	1	no	—
115	C₂×C₇₉⋊C₈	—	2	1	no	—
116	C₂×C₇₉⋊C₈	—	2	2	no	—
117	C₂×C₇₉⋊C₈	—	2	2	no	—
118	C₂×C₇₉⋊C₈	—	4	1	no	—
119	C₂×C₇₉⋊C₈	—	4	2	no	—
120	C₂×C₇₉⋊C₈	—	4	2	no	—
121	C₂×C₇₉⋊C₈	C₂×D₄	1	1	yes	characteristic
122	C₂×C₇₉⋊C₈	C₂×D₄	1	1	yes	characteristic
123	C₂×C₇₉⋊C₈	C₂×D₄	1	1	yes	characteristic
124	C₂×C₇₉⋊C₈	C₂×D₄	1	1	yes	characteristic
125	C₂⁴×C₇₉	—	2	1	no	—
126	C₂×Q₈×C₇₉	C₂²×C₄	1	1	yes	characteristic
127	C₂×D₄×C₇₉	—	2	1	no	—
128	C₂×D₄×C₇₉	—	2	1	no	—
129	C₂×D₄×C₇₉	—	4	2	no	—
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	2	no	—
134	C₂²×C₄×C₇₉	—	2	1	no	—
135	C₂²×C₄×C₇₉	—	2	2	no	—
136	C₂²×C₄×C₇₉	—	4	2	no	—
137	C₂²×C₄×C₇₉	—	4	2	no	—
138	C₂²×C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
139	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
140	C₂²×C₄×C₇₉	#41	1	1	yes	characteristic
141	SD₁₆×C₇₉	—	4	2	no	—
142	D₈×C₇₉	—	4	2	no	—
143	C₂×C₈×C₇₉	C₂²×C₄	1	2	yes	—
144	C₂×C₈×C₇₉	C₂²×C₄	1	2	yes	—
145	C₄⋊C₄×C₇₉	—	2	1	no	—
146	C₄⋊C₄×C₇₉	—	2	1	no	—
147	C₄⋊C₄×C₇₉	—	2	1	no	—
148	C₄⋊C₄×C₇₉	—	2	1	no	—
149	C₄⋊C₄×C₇₉	—	2	1	no	—
150	C₄⋊C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
151	C₄⋊C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
152	C₄⋊C₄×C₇₉	C₂²×C₄	1	2	yes	—
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	1	no	—
158	C₂²⋊C₄×C₇₉	—	2	2	no	—
159	C₂²⋊C₄×C₇₉	—	2	1	no	—
160	C₄²×C₇₉	—	2	1	no	—
161	C₄²×C₇₉	C₂²×C₄	1	1	yes	characteristic
162	C₄²×C₇₉	C₂×D₄	1	1	yes	characteristic
163	C₄²×C₇₉	#41	1	1	yes	characteristic
164	C₄²×C₇₉	C₂⁴	1	1	yes	characteristic
165	C₂³×C₇₉	—	2	1	no	—
166	C₂³×C₇₉	—	2	2	no	—
167	C₂³×C₇₉	—	4	2	no	—
168	C₂³×C₇₉	—	4	2	no	—
169	C₂³×C₇₉	—	4	2	no	—
170	C₂³×C₇₉	C₄×D₄	1	1	yes	characteristic
171	Q₈×C₇₉	—	2	2	no	—
172	D₄×C₇₉	—	2	2	no	—
173	D₄×C₇₉	—	2	2	no	—
174	D₄×C₇₉	—	2	2	no	—
175	D₄×C₇₉	—	4	2	no	—
176	D₄×C₇₉	—	4	2	no	—
177	C₂×C₄×C₇₉	—	2	2	no	—
178	C₂×C₄×C₇₉	—	2	2	no	—
179	C₂×C₄×C₇₉	—	2	1	no	—
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	4	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	2	no	—
191	C₂×C₄×C₇₉	C₄×D₄	1	1	yes	characteristic
192	C₂×C₄×C₇₉	C₄×D₄	1	1	yes	characteristic
193	C₂×C₄×C₇₉	C₄×D₄	1	1	yes	characteristic
194	C₂×C₄×C₇₉	C₂³×C₄	1	1	yes	characteristic
195	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
196	C₂×C₄×C₇₉	C₂×#41	1	1	yes	characteristic
197	C₈×C₇₉	—	2	2	no	—
198	C₈×C₇₉	—	2	2	no	—
199	C₇₉⋊C₈	—	2	1	no	—
200	C₇₉⋊C₈	—	2	1	no	—
201	C₇₉⋊C₈	—	2	1	no	—
202	C₇₉⋊C₈	—	4	2	no	—
203	C₇₉⋊C₈	—	4	1	no	—
204	C₇₉⋊C₈	—	4	2	no	—
205	C₇₉⋊C₈	—	4	1	no	—
206	C₇₉⋊C₈	AGL(1,ℤ/8)	1	2	yes	—
207	C₂²×C₇₉	—	2	1	no	—
208	C₂²×C₇₉	—	2	1	no	—
209	C₂²×C₇₉	—	4	2	no	—
210	C₂²×C₇₉	—	4	1	no	—
211	C₂²×C₇₉	—	4	2	no	—
212	C₂²×C₇₉	—	4	1	no	—
213	C₂²×C₇₉	—	4	1	no	—
214	C₂²×C₇₉	—	4	2	no	—
215	C₂²×C₇₉	—	8	4	no	—
216	C₂²×C₇₉	#444	1	2	yes	—
217	C₂²×C₇₉	C₂×C₄×D₄	1	1	yes	characteristic
218	C₄×C₇₉	—	2	1	no	—
219	C₄×C₇₉	—	2	1	no	—
220	C₄×C₇₉	—	2	1	no	—
221	C₄×C₇₉	—	2	1	no	—
222	C₄×C₇₉	—	4	1	no	—
223	C₄×C₇₉	—	4	1	no	—
224	C₄×C₇₉	—	4	2	no	—
225	C₄×C₇₉	—	4	1	no	—
226	C₄×C₇₉	#568	1	2	yes	—
227	C₄×C₇₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
228	C₄×C₇₉	#575	1	1	yes	characteristic
229	#17938	—	79	1	no	maximal, Sylow
230	C₂×C₇₉	—	2	2	no	—
231	C₂×C₇₉	—	8	1	no	—
232	C₂×C₇₉	—	8	2	no	—
233	C₂×C₇₉	#2930	1	1	yes	characteristic
234	C₂×C₇₉	C₄×AGL(1,ℤ/8)	1	1	yes	characteristic
235	C₂×C₇₉	C₂×#444	1	1	yes	characteristic
236	#3105	D₇₉	1	1	yes	characteristic
237	#2966	—	79	1	no	—
238	C₂×#436	—	79	1	no	—
239	#1594	—	79	2	no	—
240	#1592	—	79	2	no	—
241	#1583	—	79	2	no	—
242	#1581	—	79	2	no	—
243	#1573	—	79	1	no	—
244	#1490	—	79	1	no	—
245	#1483	—	79	1	no	—
246	#1451	—	79	1	no	—
247	C₇₉	#17938	1	1	yes	characteristic, complemented, Sylow
248	C₂²×M₁₆	—	158	1	no	—
249	#529	C₂×D₇₉	1	1	yes	characteristic
250	C₂×C₄×D₄	C₂×D₇₉	1	1	yes	characteristic
251	#484	Dic₇₉	1	1	yes	characteristic
252	#481	Dic₇₉	1	1	yes	characteristic
253	#478	Dic₇₉	1	2	yes	—
254	#463	Dic₇₉	1	2	yes	—
255	#450	Dic₇₉	1	1	yes	characteristic
256	#447	Dic₇₉	1	1	yes	characteristic
257	#446	—	79	1	no	—
258	C₈×Q₈	—	79	1	no	—
259	C₄×SD₁₆	C₂×D₇₉	1	2	yes	—
260	C₄×D₈	C₂×D₇₉	1	2	yes	—
261	#436	—	79	2	no	—
262	#436	—	79	2	no	—
263	#436	—	79	1	no	—
264	#436	—	158	1	no	—
265	#436	—	158	1	no	—
266	#435	—	158	1	no	—
267	C₈×D₄	—	79	1	no	—
268	C₈×D₄	—	158	1	no	—
269	#433	—	158	1	no	—
270	#432	—	79	1	no	—
271	#431	C₂×D₇₉	1	1	yes	characteristic
272	C₂×C₄⋊C₈	—	79	1	no	—
273	C₂×C₂²⋊C₈	—	158	1	no	—
274	#405	—	158	1	no	—
275	C₄×M₁₆	—	79	1	no	—
276	C₂×C₄×C₈	—	79	1	no	—
277	#335	—	79	2	no	—
278	#334	—	79	2	no	—
279	Q₈⋊C₈	—	79	2	no	—
280	D₄⋊C₈	—	79	2	no	—
281	D₄⋊C₈	—	79	2	no	—
282	D₄⋊C₈	—	79	2	no	—
283	#322	—	79	2	no	—
284	#322	—	79	2	no	—
285	C₂²×D₄	C₂×Dic₇₉	1	1	yes	characteristic
286	C₂³×C₄	—	2	1	no	—
287	C₂×SD₁₆	C₂×Dic₇₉	1	2	yes	—
288	C₂×D₈	C₂×Dic₇₉	1	2	yes	—
289	C₂×M₁₆	—	316	4	no	—
290	C₂×M₁₆	—	158	2	no	—
291	C₂×M₁₆	—	158	2	no	—
292	C₂×M₁₆	—	158	1	no	—
293	C₂×M₁₆	—	158	1	no	—
294	C₂²×C₈	—	79	1	no	—
295	C₂²×C₈	—	79	1	no	—
296	C₂²×C₈	—	158	1	no	—
297	C₂²×C₈	—	158	1	no	—
298	#126	—	2	1	no	—
299	#125	C₂×Dic₇₉	1	1	yes	characteristic
300	#124	C₂×Dic₇₉	1	1	yes	characteristic
301	#123	—	2	1	no	—
302	C₂²⋊Q₈	C₂×Dic₇₉	1	1	yes	characteristic
303	#121	C₂×Dic₇₉	1	1	yes	characteristic
304	C₄×Q₈	C₂²×D₇₉	1	1	yes	characteristic
305	C₄×D₄	—	2	1	no	—
306	C₄×D₄	—	2	1	no	—
307	C₄×D₄	—	2	1	no	—
308	C₄×D₄	C₂×Dic₇₉	1	2	yes	—
309	C₄×D₄	C₂²×D₇₉	1	2	yes	—
310	C₄×D₄	C₂²×D₇₉	1	1	yes	characteristic
311	#117	—	2	1	no	—
312	C₂×C₄⋊C₄	C₂×Dic₇₉	1	1	yes	characteristic
313	C₂×C₂²⋊C₄	—	2	1	no	—
314	C₂×C₄²	C₂²×D₇₉	1	1	yes	characteristic
315	#107	C₂×Dic₇₉	1	2	yes	—
316	#106	C₂×Dic₇₉	1	2	yes	—
317	C₄⋊C₈	—	79	1	no	—
318	C₄⋊C₈	—	79	1	no	—
319	C₄⋊C₈	—	79	2	no	—
320	C₄⋊C₈	—	158	1	no	—
321	C₄⋊C₈	—	158	1	no	—
322	C₄⋊C₈	—	158	1	no	—
323	C₄⋊C₈	C₂×Dic₇₉	1	2	yes	—
324	#103	C₂×Dic₇₉	1	2	yes	—
325	#102	C₂×Dic₇₉	1	2	yes	—
326	#102	C₂×Dic₇₉	1	2	yes	—
327	#102	C₂×Dic₇₉	1	2	yes	—
328	C₂²⋊C₈	—	158	2	no	—
329	C₂²⋊C₈	—	158	2	no	—
330	C₂²⋊C₈	—	158	1	no	—
331	C₂²⋊C₈	—	158	1	no	—
332	C₂²⋊C₈	—	158	1	no	—
333	C₂²⋊C₈	C₂×Dic₇₉	1	1	yes	characteristic
334	C₂²⋊C₈	C₂×Dic₇₉	1	1	yes	characteristic
335	#97	—	158	1	no	—
336	#97	—	158	1	no	—
337	#97	—	158	1	no	—
338	C₄×C₈	—	79	1	no	—
339	C₄×C₈	—	79	1	no	—
340	C₄×C₈	—	79	1	no	—
341	C₄×C₈	—	79	1	no	—
342	C₄×C₈	—	79	2	no	—
343	C₄×C₈	—	158	1	no	—
344	C₄×C₈	C₂²×D₇₉	1	2	yes	—
345	C₂⁴	—	2	1	no	—
346	C₂×Q₈	C₂²×Dic₇₉	1	1	yes	characteristic
347	C₂×D₄	—	2	1	no	—
348	C₂×D₄	—	2	1	no	—
349	C₂×D₄	—	4	2	no	—
350	C₂×D₄	C₂²×Dic₇₉	1	2	yes	—
351	C₂×D₄	C₂²×Dic₇₉	1	1	yes	characteristic
352	C₂²×C₄	—	2	1	no	—
353	C₂²×C₄	—	2	2	no	—
354	C₂²×C₄	—	2	1	no	—
355	C₂²×C₄	—	2	2	no	—
356	C₂²×C₄	—	4	2	no	—
357	C₂²×C₄	—	4	2	no	—
358	C₂²×C₄	C₂²×Dic₇₉	1	1	yes	characteristic
359	C₂²×C₄	D₄×D₇₉	1	1	yes	characteristic
360	C₂²×C₄	#11929623	1	1	yes	characteristic
361	SD₁₆	—	4	2	no	—
362	D₈	—	4	2	no	—
363	M₁₆	—	316	2	no	—
364	M₁₆	—	316	4	no	—
365	M₁₆	—	316	4	no	—
366	M₁₆	—	316	2	no	—
367	C₂×C₈	—	316	2	no	—
368	C₂×C₈	—	316	2	no	—
369	C₂×C₈	—	316	1	no	—
370	C₂×C₈	—	79	1	no	—
371	C₂×C₈	—	79	1	no	—
372	C₂×C₈	—	79	1	no	—
373	C₂×C₈	—	79	1	no	—
374	C₂×C₈	—	158	2	no	—
375	C₂×C₈	—	158	1	no	—
376	C₂×C₈	—	158	1	no	—
377	C₂×C₈	—	158	2	no	—
378	C₂×C₈	—	158	2	no	—
379	C₂×C₈	C₂²×Dic₇₉	1	2	yes	—
380	C₂×C₈	C₂²×Dic₇₉	1	2	yes	—
381	C₄⋊C₄	—	2	1	no	—
382	C₄⋊C₄	—	2	1	no	—
383	C₄⋊C₄	—	2	1	no	—
384	C₄⋊C₄	—	2	1	no	—
385	C₄⋊C₄	—	2	1	no	—
386	C₄⋊C₄	C₂²×Dic₇₉	1	1	yes	characteristic
387	C₄⋊C₄	C₂²×Dic₇₉	1	1	yes	characteristic
388	C₄⋊C₄	C₂²×Dic₇₉	1	2	yes	—
389	C₂²⋊C₄	—	2	1	no	—
390	C₂²⋊C₄	—	2	2	no	—
391	C₂²⋊C₄	—	2	1	no	—
392	C₂²⋊C₄	—	2	2	no	—
393	C₂²⋊C₄	—	2	1	no	—
394	C₂²⋊C₄	—	2	1	no	—
395	C₂²⋊C₄	—	2	1	no	—
396	C₄²	—	2	1	no	—
397	C₄²	C₂²×Dic₇₉	1	1	yes	characteristic
398	C₄²	D₄×D₇₉	1	1	yes	characteristic
399	C₄²	#11929623	1	1	yes	characteristic
400	C₄²	C₂³×D₇₉	1	1	yes	characteristic
401	C₂³	—	2	1	no	—
402	C₂³	—	2	2	no	—
403	C₂³	—	4	2	no	—
404	C₂³	—	4	2	no	—
405	C₂³	—	4	2	no	—
406	C₂³	D₄×Dic₇₉	1	1	yes	characteristic
407	Q₈	—	2	2	no	—
408	D₄	—	2	2	no	—
409	D₄	—	2	2	no	—
410	D₄	—	2	2	no	—
411	D₄	—	4	2	no	—
412	D₄	—	4	2	no	—
413	C₂×C₄	—	2	2	no	—
414	C₂×C₄	—	2	2	no	—
415	C₂×C₄	—	2	1	no	—
416	C₂×C₄	—	2	1	no	—
417	C₂×C₄	—	2	1	no	—
418	C₂×C₄	—	2	1	no	—
419	C₂×C₄	—	2	1	no	—
420	C₂×C₄	—	2	2	no	—
421	C₂×C₄	—	4	4	no	—
422	C₂×C₄	—	4	2	no	—
423	C₂×C₄	—	4	1	no	—
424	C₂×C₄	—	4	2	no	—
425	C₂×C₄	—	4	1	no	—
426	C₂×C₄	—	4	2	no	—
427	C₂×C₄	D₄×Dic₇₉	1	1	yes	characteristic
428	C₂×C₄	D₄×Dic₇₉	1	1	yes	characteristic
429	C₂×C₄	D₄×Dic₇₉	1	1	yes	characteristic
430	C₂×C₄	C₂³×Dic₇₉	1	1	yes	characteristic
431	C₂×C₄	C₂×D₄×D₇₉	1	1	yes	characteristic
432	C₂×C₄	C₂×#11929623	1	1	yes	characteristic
433	C₈	—	2	2	no	—
434	C₈	—	2	2	no	—
435	C₈	—	316	2	no	—
436	C₈	—	316	2	no	—
437	C₈	—	316	1	no	—
438	C₈	—	316	1	no	—
439	C₈	—	79	2	no	—
440	C₈	—	158	1	no	—
441	C₈	—	158	1	no	—
442	C₈	—	158	1	no	—
443	C₂²	—	2	1	no	—
444	C₂²	—	2	1	no	—
445	C₂²	—	4	2	no	—
446	C₂²	—	4	1	no	—
447	C₂²	—	4	1	no	—
448	C₂²	—	4	2	no	—
449	C₂²	—	4	2	no	—
450	C₂²	—	4	1	no	—
451	C₂²	—	8	4	no	—
452	C₂²	#19098685	1	2	yes	—
453	C₂²	C₂×D₄×Dic₇₉	1	1	yes	characteristic
454	C₄	—	2	1	no	—
455	C₄	—	2	1	no	—
456	C₄	—	2	1	no	—
457	C₄	—	2	1	no	—
458	C₄	—	4	2	no	—
459	C₄	—	4	1	no	—
460	C₄	—	4	1	no	—
461	C₄	—	4	1	no	—
462	C₄	#19099330	1	2	yes	—
463	C₄	AGL(1,ℤ/8)×D₇₉	1	1	yes	characteristic
464	C₄	#19099359	1	1	yes	characteristic
465	C₂	—	2	2	no	—
466	C₂	—	8	2	no	—
467	C₂	—	8	1	no	—
468	C₂	#23772104	1	1	yes	characteristic
469	C₂	AGL(1,ℤ/8)×Dic₇₉	1	1	yes	characteristic
470	C₂	C₂×#19098685	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₇₉
commutator	C₂×C₄×C₇₉	C₂³×C₄
Frattini	C₄²	C₂³×D₇₉
Fitting	C₇₉×#3105	C₂
socle	C₂²×C₇₉	C₂×C₄×D₄
prime radical	#447×C₇₉	C₄
cosocle	C₄²×C₇₉	C₂⁴
hypercenter	#3105	D₇₉
hypocenter	C₇₉	#17938
LCS	G ▷ C₂×C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #3105

Complements

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

N	H ≅ G/N	type
1. #23772376	C₂	semidirect
2. C₂×#19098641	C₂	semidirect
3. #23762314	C₂	semidirect
4. #23762303	C₂	semidirect
5. #23762244	C₂	semidirect
6. #23762230	C₂	semidirect
7. #23762185	C₂	semidirect
8. #23761843	C₂	semidirect
9. #23761813	C₂	semidirect
10. #23761690	C₂	semidirect
13. #19098694	C₂²	semidirect
14. Q₈×C₇₉⋊C₈	C₂²	semidirect
19. #19098641	C₂²	semidirect
22. D₄×C₇₉⋊C₈	C₂²	semidirect
30. #19098316	C₂²	semidirect
31. #19098314	C₂²	semidirect
32. Q₈⋊(C₇₉⋊C₈)	C₂²	semidirect
35. D₄⋊(C₇₉⋊C₈)	C₂²	semidirect
36. #19098285	C₂²	semidirect
37. #19098284	C₂²	semidirect
247. C₇₉	#17938	semidirect

Maximal subgroups

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

subgroup	index
#23772376	2
C₂×#19098641	2
#23762314	2
#23762303	2
#23762244	2
#23762230	2
#23762185	2
#23761843	2
#23761813	2
#23761690	2
C₇₉×#3105	2
#17938	79