Subgroups — #34260290

Order 20224.

604 conjugacy classes of subgroups.

The subgroup lattice has 420 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#23772502	C₂	1	1	yes	maximal, characteristic, complemented
2	#23772467	C₂	1	1	yes	maximal, characteristic
3	#23762303	C₂	1	2	yes	maximal, complemented
4	#23762244	C₂	1	2	yes	maximal, complemented
5	#23762237	C₂	1	2	yes	maximal, complemented
6	SD₁₆⋊(C₇₉⋊C₈)	C₂	1	2	yes	maximal, complemented
7	#23762148	C₂	1	1	yes	maximal, characteristic, complemented
8	#23761821	C₂	1	1	yes	maximal, characteristic, complemented
9	#23761817	C₂	1	1	yes	maximal, characteristic
10	#23761689	C₂	1	1	yes	maximal, characteristic, complemented
11	C₇₉×#3167	C₂	1	1	yes	maximal, characteristic
12	#19098694	—	2	1	no	—
13	#19098694	C₂²	1	2	yes	—
14	Q₈×C₇₉⋊C₈	—	2	1	no	—
15	Q₈×C₇₉⋊C₈	C₂²	1	2	yes	—
16	#19098641	—	2	1	no	—
17	#19098641	C₂²	1	2	yes	—
18	D₄×C₇₉⋊C₈	—	2	1	no	—
19	D₄×C₇₉⋊C₈	C₂²	1	2	yes	—
20	#19098624	—	2	2	no	—
21	#19098616	C₂²	1	1	yes	characteristic
22	#19098616	C₂²	1	1	yes	characteristic
23	#19098616	C₂²	1	1	yes	characteristic
24	#19098530	—	2	2	no	—
25	C₄×#11929608	C₂²	1	1	yes	characteristic
26	#19098316	C₂²	1	1	yes	characteristic
27	#19098316	C₂²	1	1	yes	characteristic
28	#19098314	C₂²	1	1	yes	characteristic
29	#19098314	C₂²	1	1	yes	characteristic
30	Q₈⋊(C₇₉⋊C₈)	C₂²	1	2	yes	—
31	Q₈⋊(C₇₉⋊C₈)	C₂²	1	2	yes	—
32	D₄⋊(C₇₉⋊C₈)	C₂²	1	2	yes	—
33	D₄⋊(C₇₉⋊C₈)	C₂²	1	2	yes	—
34	#19098285	C₂²	1	2	yes	—
35	#19098284	C₂²	1	2	yes	—
36	#533×C₇₉	C₂²	1	1	yes	characteristic
37	#532×C₇₉	C₂²	1	1	yes	characteristic
38	#498×C₇₉	C₄	1	1	yes	characteristic
39	#492×C₇₉	C₄	1	1	yes	characteristic
40	#487×C₇₉	C₄	1	1	yes	characteristic
41	#486×C₇₉	C₄	1	1	yes	characteristic
42	#465×C₇₉	C₄	1	2	yes	—
43	#465×C₇₉	C₄	1	2	yes	—
44	C₄×SD₁₆×C₇₉	C₂²	1	2	yes	—
45	C₄×SD₁₆×C₇₉	C₂²	1	2	yes	—
46	C₂×C₄×C₈×C₇₉	C₂²	1	1	yes	characteristic
47	C₂×#11929608	—	2	1	no	—
48	C₂×#11929608	—	2	2	no	—
49	C₂²×C₇₉⋊C₈	—	2	2	no	—
50	C₄⋊(C₇₉⋊C₈)	—	2	2	no	—
51	C₄⋊(C₇₉⋊C₈)	—	2	2	no	—
52	C₄⋊(C₇₉⋊C₈)	D₄	1	1	yes	characteristic
53	C₄⋊(C₇₉⋊C₈)	D₄	1	1	yes	characteristic
54	C₄⋊(C₇₉⋊C₈)	C₂³	1	1	yes	characteristic
55	C₄⋊(C₇₉⋊C₈)	C₂³	1	1	yes	characteristic
56	C₄⋊(C₇₉⋊C₈)	C₂³	1	1	yes	characteristic
57	C₄⋊(C₇₉⋊C₈)	C₂³	1	1	yes	characteristic
58	C₂²⋊(C₇₉⋊C₈)	—	2	1	no	—
59	C₂²⋊(C₇₉⋊C₈)	—	2	1	no	—
60	C₂²⋊(C₇₉⋊C₈)	—	2	2	no	—
61	C₂²⋊(C₇₉⋊C₈)	—	2	2	no	—
62	C₂²⋊(C₇₉⋊C₈)	D₄	1	2	yes	—
63	#14579072	—	2	1	no	—
64	#14579072	—	2	2	no	—
65	C₄×C₇₉⋊C₈	—	2	1	no	—
66	C₄×C₇₉⋊C₈	—	2	1	no	—
67	C₄×C₇₉⋊C₈	—	2	2	no	—
68	C₄×C₇₉⋊C₈	C₂³	1	2	yes	—
69	C₄×C₇₉⋊C₈	C₂³	1	2	yes	—
70	C₂×#41×C₇₉	—	2	1	no	—
71	C₂×SD₁₆×C₇₉	C₂×C₄	1	2	yes	—
72	C₂×SD₁₆×C₇₉	C₂×C₄	1	2	yes	—
73	C₂²×C₈×C₇₉	C₂×C₄	1	1	yes	characteristic
74	C₂²×C₈×C₇₉	C₂×C₄	1	1	yes	characteristic
75	C₄⋊Q₈×C₇₉	C₂×C₄	1	1	yes	characteristic
76	C₄⋊Q₈×C₇₉	C₂×C₄	1	1	yes	characteristic
77	C₄⋊Q₈×C₇₉	C₂×C₄	1	1	yes	characteristic
78	#127×C₇₉	C₂×C₄	1	1	yes	characteristic
79	#125×C₇₉	—	2	1	no	—
80	#124×C₇₉	—	2	1	no	—
81	C₂²⋊Q₈×C₇₉	—	2	1	no	—
82	C₂²⋊Q₈×C₇₉	C₂×C₄	1	2	yes	—
83	#121×C₇₉	—	2	1	no	—
84	#121×C₇₉	C₂×C₄	1	2	yes	—
85	C₄×Q₈×C₇₉	—	2	1	no	—
86	C₄×Q₈×C₇₉	C₂³	1	2	yes	—
87	C₄×D₄×C₇₉	—	2	1	no	—
88	C₄×D₄×C₇₉	C₂³	1	2	yes	—
89	#117×C₇₉	—	2	1	no	—
90	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
91	#106×C₇₉	C₂×C₄	1	2	yes	—
92	#106×C₇₉	C₂×C₄	1	2	yes	—
93	#103×C₇₉	C₂×C₄	1	2	yes	—
94	#103×C₇₉	C₂×C₄	1	2	yes	—
95	#102×C₇₉	C₂×C₄	1	2	yes	—
96	#102×C₇₉	C₂×C₄	1	2	yes	—
97	C₄×C₈×C₇₉	C₂×C₄	1	1	yes	characteristic
98	C₄×C₈×C₇₉	C₂×C₄	1	1	yes	characteristic
99	C₄×C₈×C₇₉	C₂³	1	1	yes	characteristic
100	C₄×C₈×C₇₉	C₂³	1	1	yes	characteristic
101	#11929608	—	4	2	no	—
102	#11929608	—	8	2	no	—
103	C₂×C₇₉⋊C₈	—	2	1	no	—
104	C₂×C₇₉⋊C₈	—	2	1	no	—
105	C₂×C₇₉⋊C₈	—	2	1	no	—
106	C₂×C₇₉⋊C₈	—	2	1	no	—
107	C₂×C₇₉⋊C₈	—	2	2	no	—
108	C₂×C₇₉⋊C₈	—	8	2	no	—
109	C₂×C₇₉⋊C₈	C₂×D₄	1	2	yes	—
110	C₂×C₇₉⋊C₈	C₂×D₄	1	2	yes	—
111	#41×C₇₉	—	8	1	no	—
112	#41×C₇₉	—	8	1	no	—
113	C₂×Q₈×C₇₉	—	2	1	no	—
114	C₂×Q₈×C₇₉	—	2	1	no	—
115	C₂×Q₈×C₇₉	C₂²×C₄	1	2	yes	—
116	C₂×D₄×C₇₉	—	2	2	no	—
117	C₂×D₄×C₇₉	—	2	1	no	—
118	C₂×D₄×C₇₉	—	2	1	no	—
119	C₂×D₄×C₇₉	C₂²×C₄	1	2	yes	—
120	C₂²×C₄×C₇₉	—	2	2	no	—
121	C₂²×C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
122	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
123	C₂²×C₄×C₇₉	#41	1	1	yes	characteristic
124	SD₁₆×C₇₉	—	2	4	no	—
125	SD₁₆×C₇₉	—	4	2	no	—
126	C₂×C₈×C₇₉	—	2	2	no	—
127	C₂×C₈×C₇₉	—	4	1	no	—
128	C₂×C₈×C₇₉	C₂²×C₄	1	1	yes	characteristic
129	C₂×C₈×C₇₉	C₂²×C₄	1	1	yes	characteristic
130	C₂×C₈×C₇₉	C₂²×C₄	1	1	yes	characteristic
131	C₂×C₈×C₇₉	C₂²×C₄	1	1	yes	characteristic
132	C₄⋊C₄×C₇₉	—	2	1	no	—
133	C₄⋊C₄×C₇₉	—	2	1	no	—
134	C₄⋊C₄×C₇₉	—	2	1	no	—
135	C₄⋊C₄×C₇₉	—	2	1	no	—
136	C₄⋊C₄×C₇₉	—	2	2	no	—
137	C₄⋊C₄×C₇₉	—	2	2	no	—
138	C₄⋊C₄×C₇₉	C₂²×C₄	1	2	yes	—
139	C₄⋊C₄×C₇₉	C₂²×C₄	1	2	yes	—
140	C₂²⋊C₄×C₇₉	—	2	2	no	—
141	C₂²⋊C₄×C₇₉	—	2	2	no	—
142	C₂²⋊C₄×C₇₉	—	2	2	no	—
143	C₄²×C₇₉	—	2	2	no	—
144	C₄²×C₇₉	C₂²×C₄	1	1	yes	characteristic
145	C₄²×C₇₉	C₂×D₄	1	1	yes	characteristic
146	C₄²×C₇₉	#41	1	1	yes	characteristic
147	C₄²×C₇₉	C₂⁴	1	1	yes	characteristic
148	C₂³×C₇₉	—	2	2	no	—
149	C₂³×C₇₉	C₄×D₄	1	1	yes	characteristic
150	Q₈×C₇₉	—	2	2	no	—
151	Q₈×C₇₉	—	2	2	no	—
152	Q₈×C₇₉	—	4	2	no	—
153	Q₈×C₇₉	—	8	1	no	—
154	D₄×C₇₉	—	2	2	no	—
155	D₄×C₇₉	—	2	2	no	—
156	D₄×C₇₉	—	4	2	no	—
157	D₄×C₇₉	—	8	1	no	—
158	D₄×C₇₉	—	8	2	no	—
159	C₂×C₄×C₇₉	—	2	1	no	—
160	C₂×C₄×C₇₉	—	2	1	no	—
161	C₂×C₄×C₇₉	—	2	1	no	—
162	C₂×C₄×C₇₉	—	2	1	no	—
163	C₂×C₄×C₇₉	—	2	2	no	—
164	C₂×C₄×C₇₉	—	2	2	no	—
165	C₂×C₄×C₇₉	—	2	2	no	—
166	C₂×C₄×C₇₉	—	2	2	no	—
167	C₂×C₄×C₇₉	—	4	2	no	—
168	C₂×C₄×C₇₉	—	4	2	no	—
169	C₂×C₄×C₇₉	C₄×D₄	1	1	yes	characteristic
170	C₂×C₄×C₇₉	C₄×D₄	1	1	yes	characteristic
171	C₂×C₄×C₇₉	C₄×D₄	1	1	yes	characteristic
172	C₂×C₄×C₇₉	C₂³×C₄	1	1	yes	characteristic
173	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
174	C₂×C₄×C₇₉	C₂×#41	1	1	yes	characteristic
175	C₈×C₇₉	—	2	1	no	—
176	C₈×C₇₉	—	2	1	no	—
177	C₈×C₇₉	—	2	1	no	—
178	C₈×C₇₉	#131	1	2	yes	—
179	C₇₉⋊C₈	—	2	2	no	—
180	C₇₉⋊C₈	—	2	2	no	—
181	C₇₉⋊C₈	—	4	2	no	—
182	C₇₉⋊C₈	—	4	1	no	—
183	C₇₉⋊C₈	—	4	1	no	—
184	C₇₉⋊C₈	—	4	1	no	—
185	C₇₉⋊C₈	—	4	1	no	—
186	C₂²×C₇₉	—	2	1	no	—
187	C₂²×C₇₉	—	2	1	no	—
188	C₂²×C₇₉	—	2	1	no	—
189	C₂²×C₇₉	—	4	2	no	—
190	C₂²×C₇₉	—	4	2	no	—
191	C₂²×C₇₉	—	4	2	no	—
192	C₂²×C₇₉	C₂×C₄×D₄	1	1	yes	characteristic
193	C₄×C₇₉	—	2	1	no	—
194	C₄×C₇₉	—	2	1	no	—
195	C₄×C₇₉	—	2	1	no	—
196	C₄×C₇₉	—	4	2	no	—
197	C₄×C₇₉	—	4	2	no	—
198	C₄×C₇₉	—	4	2	no	—
199	C₄×C₇₉	#444	1	2	yes	—
200	C₄×C₇₉	C₂×#131	1	1	yes	characteristic
201	C₄×C₇₉	#568	1	1	yes	characteristic
202	C₄×C₇₉	#577	1	1	yes	characteristic
203	C₄×C₇₉	#577	1	1	yes	characteristic
204	#18089	—	79	1	no	maximal, Sylow
205	C₂×C₇₉	—	4	1	no	—
206	C₂×C₇₉	—	8	2	no	—
207	C₂×C₇₉	#2935	1	1	yes	characteristic
208	C₂×C₇₉	#2949	1	1	yes	characteristic
209	C₂×C₇₉	C₂×#444	1	1	yes	characteristic
210	#3167	D₇₉	1	1	yes	characteristic
211	#2986	—	79	1	no	—
212	#2979	—	79	1	no	—
213	#1592	—	79	2	no	—
214	#1583	—	79	2	no	—
215	#1582	—	79	2	no	—
216	SD₁₆⋊C₈	—	79	2	no	—
217	#1564	—	79	1	no	—
218	#1485	—	79	1	no	—
219	#1484	—	79	1	no	—
220	#1451	—	79	1	no	—
221	C₇₉	#18089	1	1	yes	characteristic, complemented, Sylow
222	#533	C₂×D₇₉	1	1	yes	characteristic
223	#532	C₂×D₇₉	1	1	yes	characteristic
224	#498	Dic₇₉	1	1	yes	characteristic
225	#492	Dic₇₉	1	1	yes	characteristic
226	#487	Dic₇₉	1	1	yes	characteristic
227	#486	Dic₇₉	1	1	yes	characteristic
228	#465	Dic₇₉	1	2	yes	—
229	#465	Dic₇₉	1	2	yes	—
230	#446	—	79	2	no	—
231	#446	—	158	1	no	—
232	C₈×Q₈	—	79	2	no	—
233	C₈×Q₈	—	158	1	no	—
234	C₄×SD₁₆	C₂×D₇₉	1	2	yes	—
235	C₄×SD₁₆	C₂×D₇₉	1	2	yes	—
236	#436	—	79	2	no	—
237	#436	—	158	1	no	—
238	C₈×D₄	—	79	2	no	—
239	C₈×D₄	—	158	1	no	—
240	#433	—	158	2	no	—
241	#431	—	79	1	no	—
242	#431	—	79	1	no	—
243	#431	—	79	1	no	—
244	#408	—	158	2	no	—
245	C₄×M₁₆	—	79	1	no	—
246	C₂×C₄×C₈	C₂×D₇₉	1	1	yes	characteristic
247	#335	—	79	1	no	—
248	#335	—	79	1	no	—
249	#334	—	79	1	no	—
250	#334	—	79	1	no	—
251	Q₈⋊C₈	—	79	2	no	—
252	Q₈⋊C₈	—	79	2	no	—
253	D₄⋊C₈	—	79	2	no	—
254	D₄⋊C₈	—	79	2	no	—
255	#322	—	79	2	no	—
256	#322	—	79	2	no	—
257	C₂×#41	—	2	1	no	—
258	C₂×SD₁₆	C₂×Dic₇₉	1	2	yes	—
259	C₂×SD₁₆	C₂×Dic₇₉	1	2	yes	—
260	C₂×M₁₆	—	158	2	no	—
261	C₂×M₁₆	—	158	1	no	—
262	C₂²×C₈	—	158	2	no	—
263	C₂²×C₈	C₂×Dic₇₉	1	1	yes	characteristic
264	C₂²×C₈	C₂×Dic₇₉	1	1	yes	characteristic
265	C₄⋊Q₈	C₂×Dic₇₉	1	1	yes	characteristic
266	C₄⋊Q₈	C₂×Dic₇₉	1	1	yes	characteristic
267	C₄⋊Q₈	C₂×Dic₇₉	1	1	yes	characteristic
268	#127	C₂×Dic₇₉	1	1	yes	characteristic
269	#125	—	2	1	no	—
270	#124	—	2	1	no	—
271	C₂²⋊Q₈	—	2	1	no	—
272	C₂²⋊Q₈	C₂×Dic₇₉	1	2	yes	—
273	#121	—	2	1	no	—
274	#121	C₂×Dic₇₉	1	2	yes	—
275	C₄×Q₈	—	2	1	no	—
276	C₄×Q₈	C₂²×D₇₉	1	2	yes	—
277	C₄×D₄	—	2	1	no	—
278	C₄×D₄	C₂²×D₇₉	1	2	yes	—
279	#117	—	2	1	no	—
280	C₂×C₄²	C₂²×D₇₉	1	1	yes	characteristic
281	#106	C₂×Dic₇₉	1	2	yes	—
282	#106	C₂×Dic₇₉	1	2	yes	—
283	C₄⋊C₈	—	79	1	no	—
284	C₄⋊C₈	—	79	1	no	—
285	C₄⋊C₈	—	79	1	no	—
286	C₄⋊C₈	—	79	1	no	—
287	C₄⋊C₈	—	79	1	no	—
288	C₄⋊C₈	—	79	1	no	—
289	C₄⋊C₈	—	158	2	no	—
290	C₄⋊C₈	—	158	2	no	—
291	#103	C₂×Dic₇₉	1	2	yes	—
292	#103	C₂×Dic₇₉	1	2	yes	—
293	#102	C₂×Dic₇₉	1	2	yes	—
294	#102	C₂×Dic₇₉	1	2	yes	—
295	C₂²⋊C₈	—	79	2	no	—
296	C₂²⋊C₈	—	158	2	no	—
297	C₂²⋊C₈	—	158	2	no	—
298	C₂²⋊C₈	—	158	1	no	—
299	C₂²⋊C₈	—	158	1	no	—
300	#97	—	158	2	no	—
301	#97	—	158	1	no	—
302	C₄×C₈	—	79	2	no	—
303	C₄×C₈	—	79	2	no	—
304	C₄×C₈	—	158	2	no	—
305	C₄×C₈	—	158	1	no	—
306	C₄×C₈	—	158	1	no	—
307	C₄×C₈	C₂×Dic₇₉	1	1	yes	characteristic
308	C₄×C₈	C₂×Dic₇₉	1	1	yes	characteristic
309	C₄×C₈	C₂²×D₇₉	1	1	yes	characteristic
310	C₄×C₈	C₂²×D₇₉	1	1	yes	characteristic
311	#41	—	8	1	no	—
312	#41	—	8	1	no	—
313	C₂×Q₈	—	2	1	no	—
314	C₂×Q₈	—	2	1	no	—
315	C₂×Q₈	C₂²×Dic₇₉	1	2	yes	—
316	C₂×D₄	—	2	2	no	—
317	C₂×D₄	—	2	1	no	—
318	C₂×D₄	—	2	1	no	—
319	C₂×D₄	C₂²×Dic₇₉	1	2	yes	—
320	C₂²×C₄	—	2	2	no	—
321	C₂²×C₄	C₂²×Dic₇₉	1	1	yes	characteristic
322	C₂²×C₄	D₄×D₇₉	1	1	yes	characteristic
323	C₂²×C₄	#11929623	1	1	yes	characteristic
324	SD₁₆	—	2	4	no	—
325	SD₁₆	—	4	2	no	—
326	M₁₆	—	316	2	no	—
327	M₁₆	—	632	2	no	—
328	C₂×C₈	—	2	2	no	—
329	C₂×C₈	—	4	1	no	—
330	C₂×C₈	—	79	2	no	—
331	C₂×C₈	—	79	2	no	—
332	C₂×C₈	—	632	2	no	—
333	C₂×C₈	—	158	2	no	—
334	C₂×C₈	—	158	1	no	—
335	C₂×C₈	—	158	1	no	—
336	C₂×C₈	—	158	1	no	—
337	C₂×C₈	—	158	1	no	—
338	C₂×C₈	C₂²×Dic₇₉	1	1	yes	characteristic
339	C₂×C₈	C₂²×Dic₇₉	1	1	yes	characteristic
340	C₂×C₈	C₂²×Dic₇₉	1	1	yes	characteristic
341	C₂×C₈	C₂²×Dic₇₉	1	1	yes	characteristic
342	C₄⋊C₄	—	2	2	no	—
343	C₄⋊C₄	—	2	1	no	—
344	C₄⋊C₄	—	2	1	no	—
345	C₄⋊C₄	—	2	1	no	—
346	C₄⋊C₄	—	2	1	no	—
347	C₄⋊C₄	—	2	2	no	—
348	C₄⋊C₄	C₂²×Dic₇₉	1	2	yes	—
349	C₄⋊C₄	C₂²×Dic₇₉	1	2	yes	—
350	C₂²⋊C₄	—	2	2	no	—
351	C₂²⋊C₄	—	2	2	no	—
352	C₂²⋊C₄	—	2	2	no	—
353	C₄²	—	2	2	no	—
354	C₄²	C₂²×Dic₇₉	1	1	yes	characteristic
355	C₄²	D₄×D₇₉	1	1	yes	characteristic
356	C₄²	#11929623	1	1	yes	characteristic
357	C₄²	C₂³×D₇₉	1	1	yes	characteristic
358	C₂³	—	2	2	no	—
359	C₂³	D₄×Dic₇₉	1	1	yes	characteristic
360	Q₈	—	2	2	no	—
361	Q₈	—	2	2	no	—
362	Q₈	—	4	2	no	—
363	Q₈	—	8	1	no	—
364	D₄	—	2	2	no	—
365	D₄	—	2	2	no	—
366	D₄	—	4	2	no	—
367	D₄	—	8	1	no	—
368	D₄	—	8	2	no	—
369	C₂×C₄	—	2	2	no	—
370	C₂×C₄	—	2	1	no	—
371	C₂×C₄	—	2	1	no	—
372	C₂×C₄	—	2	1	no	—
373	C₂×C₄	—	2	1	no	—
374	C₂×C₄	—	2	2	no	—
375	C₂×C₄	—	2	2	no	—
376	C₂×C₄	—	2	2	no	—
377	C₂×C₄	—	4	2	no	—
378	C₂×C₄	—	4	2	no	—
379	C₂×C₄	D₄×Dic₇₉	1	1	yes	characteristic
380	C₂×C₄	D₄×Dic₇₉	1	1	yes	characteristic
381	C₂×C₄	D₄×Dic₇₉	1	1	yes	characteristic
382	C₂×C₄	C₂³×Dic₇₉	1	1	yes	characteristic
383	C₂×C₄	C₂×D₄×D₇₉	1	1	yes	characteristic
384	C₂×C₄	C₂×#11929623	1	1	yes	characteristic
385	C₈	—	2	1	no	—
386	C₈	—	2	1	no	—
387	C₈	—	2	1	no	—
388	C₈	—	316	2	no	—
389	C₈	—	316	1	no	—
390	C₈	—	316	1	no	—
391	C₈	—	316	1	no	—
392	C₈	—	316	1	no	—
393	C₈	—	158	2	no	—
394	C₈	—	158	2	no	—
395	C₈	#14579168	1	2	yes	—
396	C₂²	—	2	1	no	—
397	C₂²	—	2	1	no	—
398	C₂²	—	2	1	no	—
399	C₂²	—	4	2	no	—
400	C₂²	—	4	2	no	—
401	C₂²	—	4	2	no	—
402	C₂²	C₂×D₄×Dic₇₉	1	1	yes	characteristic
403	C₄	—	2	1	no	—
404	C₄	—	2	1	no	—
405	C₄	—	2	1	no	—
406	C₄	—	4	2	no	—
407	C₄	—	4	2	no	—
408	C₄	—	4	2	no	—
409	C₄	#19098685	1	2	yes	—
410	C₄	C₂×#14579168	1	1	yes	characteristic
411	C₄	#19099330	1	1	yes	characteristic
412	C₄	#19099369	1	1	yes	characteristic
413	C₄	#19099369	1	1	yes	characteristic
414	C₂	—	4	1	no	—
415	C₂	—	8	2	no	—
416	C₂	#23772144	1	1	yes	characteristic
417	C₂	#23772260	1	1	yes	characteristic
418	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×#3167	C₂
socle	C₂²×C₇₉	C₂×C₄×D₄
prime radical	#532×C₇₉	C₂²
cosocle	C₄²×C₇₉	C₂⁴
hypercenter	#3167	D₇₉
hypocenter	C₇₉	#18089
LCS	G ▷ C₂×C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #3167

Complements

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

N	H ≅ G/N	type
1. #23772502	C₂	semidirect
3. #23762303	C₂	semidirect
4. #23762244	C₂	semidirect
5. #23762237	C₂	semidirect
6. SD₁₆⋊(C₇₉⋊C₈)	C₂	semidirect
7. #23762148	C₂	semidirect
8. #23761821	C₂	semidirect
10. #23761689	C₂	semidirect
221. C₇₉	#18089	semidirect

Maximal subgroups

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

subgroup	index
#23772502	2
#23772467	2
#23762303	2
#23762244	2
#23762237	2
SD₁₆⋊(C₇₉⋊C₈)	2
#23762148	2
#23761821	2
#23761817	2
#23761689	2
C₇₉×#3167	2
#18089	79