Subgroups — #34273461

Order 20224.

662 conjugacy classes of subgroups.

The subgroup lattice has 434 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#23773495	C₂	1	1	yes	maximal, characteristic, complemented
2	#23773396	C₂	1	1	yes	maximal, characteristic
3	#23772423	C₂	1	1	yes	maximal, characteristic, complemented
4	#23762834	C₂	1	2	yes	maximal, complemented
5	#23762820	C₂	1	2	yes	maximal, complemented
6	#23762762	C₂	1	2	yes	maximal, complemented
7	#23762738	C₂	1	2	yes	maximal, complemented
8	#23762180	C₂	1	1	yes	maximal, characteristic, complemented
9	#23762105	C₂	1	1	yes	maximal, characteristic, complemented
10	#23762065	C₂	1	1	yes	maximal, characteristic, complemented
11	C₇₉×#3210	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₄×D₃₁₆	C₂²	1	1	yes	characteristic
13	#19098896	—	2	1	no	—
14	#19098874	—	2	1	no	—
15	#19098840	C₂²	1	2	yes	—
16	#19098840	C₂²	1	2	yes	—
17	#19098765	C₂²	1	2	yes	—
18	#19098755	C₂²	1	2	yes	—
19	#19098713	—	2	1	no	—
20	#19098696	—	2	1	no	—
21	#19098661	—	2	2	no	—
22	C₄×#11929609	—	2	2	no	—
23	C₈×D₃₁₆	C₂²	1	2	yes	—
24	C₈×D₃₁₆	C₂²	1	2	yes	—
25	#19098628	—	2	2	no	—
26	#19098620	C₂²	1	1	yes	characteristic
27	#19098616	C₂²	1	1	yes	characteristic
28	#19098616	C₂²	1	1	yes	characteristic
29	C₂²⋊C₈×D₇₉	—	2	2	no	—
30	#19098316	C₂²	1	2	yes	complemented
31	#19098314	C₂²	1	2	yes	complemented
32	#19098309	C₂²	1	2	yes	complemented
33	#19098309	C₂²	1	2	yes	complemented
34	#19098309	C₂²	1	2	yes	complemented
35	#19098307	C₂²	1	2	yes	complemented
36	#533×C₇₉	C₂²	1	1	yes	characteristic
37	#532×C₇₉	C₂²	1	1	yes	characteristic
38	#494×C₇₉	C₂²	1	1	yes	characteristic, complemented
39	#492×C₇₉	C₂²	1	1	yes	characteristic, complemented
40	#487×C₇₉	C₂²	1	1	yes	characteristic, complemented
41	#486×C₇₉	C₂²	1	1	yes	characteristic, complemented
42	#464×C₇₉	—	2	2	no	—
43	#452×C₇₉	—	2	2	no	—
44	#431×C₇₉	C₂²	1	1	yes	characteristic
45	C₂²×D₃₁₆	D₄	1	1	yes	characteristic
46	C₂²×C₄×D₇₉	—	2	1	no	—
47	C₂×#11929611	—	2	2	no	—
48	C₂×#11929609	—	2	2	no	—
49	C₂×C₈×D₇₉	—	2	2	no	—
50	C₂×C₈×D₇₉	—	2	2	no	—
51	C₄×D₃₁₆	—	2	1	no	—
52	C₄×D₃₁₆	—	2	1	no	—
53	C₄×D₃₁₆	D₄	1	2	yes	—
54	C₄×D₃₁₆	C₂³	1	2	yes	—
55	C₂×C₄⋊Dic₇₉	D₄	1	1	yes	characteristic
56	C₂×(C₂×D₇₉)⋊C₄	—	2	1	no	—
57	#14579094	—	2	2	no	—
58	#14579094	—	2	2	no	—
59	C₄⋊(C₇₉⋊C₈)	C₂³	1	2	yes	—
60	C₄⋊(C₇₉⋊C₈)	C₂³	1	2	yes	—
61	C₄⋊(C₇₉⋊C₈)	C₂³	1	2	yes	—
62	#14579085	—	2	2	no	—
63	#14579082	—	2	2	no	—
64	#14579081	—	2	2	no	—
65	#14579081	—	2	2	no	—
66	C₂²⋊(C₇₉⋊C₈)	—	2	1	no	—
67	C₂²⋊(C₇₉⋊C₈)	—	2	1	no	—
68	C₂²⋊(C₇₉⋊C₈)	—	2	1	no	—
69	(C₂×D₇₉)⋊C₈	—	2	2	no	—
70	(C₂×D₇₉)⋊C₈	—	2	2	no	—
71	#14579072	—	2	1	no	—
72	C₄×C₇₉⋊C₈	—	2	1	no	—
73	C₄×C₇₉⋊C₈	—	2	1	no	—
74	C₂×#41×C₇₉	—	2	1	no	—
75	C₂×Q₁₆×C₇₉	—	2	2	no	—
76	C₂×SD₁₆×C₇₉	—	2	2	no	—
77	C₄⋊Q₈×C₇₉	C₂³	1	1	yes	characteristic
78	C₄⋊Q₈×C₇₉	C₂³	1	1	yes	characteristic
79	C₄⋊Q₈×C₇₉	C₂³	1	1	yes	characteristic
80	#127×C₇₉	C₂³	1	1	yes	characteristic
81	#125×C₇₉	—	2	1	no	—
82	#124×C₇₉	—	2	1	no	—
83	C₂²⋊Q₈×C₇₉	—	2	1	no	—
84	C₂²⋊Q₈×C₇₉	—	2	1	no	—
85	#121×C₇₉	—	2	1	no	—
86	#121×C₇₉	—	2	1	no	—
87	C₄×Q₈×C₇₉	—	2	1	no	—
88	C₄×Q₈×C₇₉	—	2	1	no	—
89	C₄×D₄×C₇₉	—	2	1	no	—
90	C₄×D₄×C₇₉	—	2	1	no	—
91	#117×C₇₉	—	2	1	no	—
92	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
93	C₄⋊C₈×C₇₉	D₄	1	2	yes	—
94	#103×C₇₉	—	2	2	no	—
95	#102×C₇₉	—	2	2	no	—
96	C₂²⋊C₈×C₇₉	D₄	1	2	yes	—
97	C₄×C₈×C₇₉	C₂³	1	1	yes	characteristic
98	C₄×C₈×C₇₉	C₂³	1	1	yes	characteristic
99	C₂³×D₇₉	—	2	1	no	—
100	C₂×D₃₁₆	—	2	4	no	—
101	C₂×D₃₁₆	—	2	1	no	—
102	C₂×D₃₁₆	C₂×D₄	1	2	yes	—
103	C₂²×Dic₇₉	—	2	1	no	—
104	C₂×C₄×D₇₉	—	2	2	no	—
105	C₂×C₄×D₇₉	—	2	2	no	—
106	C₂×C₄×D₇₉	—	8	2	no	—
107	#11929611	—	4	4	no	—
108	#11929609	—	4	4	no	—
109	C₂×C₇₉⋊C₈	—	2	2	no	—
110	C₂×C₇₉⋊C₈	—	2	2	no	—
111	C₂×C₇₉⋊C₈	—	2	2	no	—
112	C₈×D₇₉	—	8	2	no	—
113	C₈×D₇₉	—	8	2	no	—
114	C₄⋊Dic₇₉	—	2	1	no	—
115	C₄⋊Dic₇₉	C₂×D₄	1	2	yes	—
116	(C₂×D₇₉)⋊C₄	—	2	2	no	—
117	(C₂×D₇₉)⋊C₄	—	2	2	no	—
118	#41×C₇₉	—	8	2	no	—
119	C₂×Q₈×C₇₉	—	2	1	no	—
120	C₂×Q₈×C₇₉	—	2	1	no	—
121	C₂×Q₈×C₇₉	—	2	1	no	—
122	C₂×D₄×C₇₉	—	2	1	no	—
123	C₂×D₄×C₇₉	—	2	1	no	—
124	C₂×D₄×C₇₉	—	2	1	no	—
125	C₂×D₄×C₇₉	—	4	1	no	—
126	C₂²×C₄×C₇₉	—	4	1	no	—
127	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
128	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
129	C₂²×C₄×C₇₉	#41	1	1	yes	characteristic
130	Q₁₆×C₇₉	—	8	2	no	—
131	SD₁₆×C₇₉	—	8	2	no	—
132	C₂×C₈×C₇₉	C₂×D₄	1	2	yes	—
133	C₂×C₈×C₇₉	C₂×D₄	1	2	yes	—
134	C₄⋊C₄×C₇₉	—	2	1	no	—
135	C₄⋊C₄×C₇₉	—	2	1	no	—
136	C₄⋊C₄×C₇₉	—	2	1	no	—
137	C₄⋊C₄×C₇₉	—	2	1	no	—
138	C₄⋊C₄×C₇₉	—	2	1	no	—
139	C₄⋊C₄×C₇₉	—	2	1	no	—
140	C₄⋊C₄×C₇₉	—	4	1	no	—
141	C₄⋊C₄×C₇₉	—	4	1	no	—
142	C₂²⋊C₄×C₇₉	—	4	1	no	—
143	C₂²⋊C₄×C₇₉	—	4	1	no	—
144	C₂²⋊C₄×C₇₉	—	4	1	no	—
145	C₄²×C₇₉	—	4	1	no	—
146	C₄²×C₇₉	C₂×D₄	1	1	yes	characteristic
147	C₄²×C₇₉	C₂×D₄	1	1	yes	characteristic
148	C₄²×C₇₉	#41	1	1	yes	characteristic
149	C₄²×C₇₉	C₂⁴	1	1	yes	characteristic
150	C₂³×C₇₉	—	4	1	no	—
151	C₂³×C₇₉	#121	1	1	yes	characteristic
152	C₂²×D₇₉	—	2	2	no	—
153	C₂²×D₇₉	—	2	4	no	—
154	C₂²×D₇₉	—	8	1	no	—
155	C₂²×D₇₉	—	8	1	no	—
156	Q₈×C₇₉	—	4	2	no	—
157	Q₈×C₇₉	—	4	2	no	—
158	Q₈×C₇₉	—	4	2	no	—
159	D₄×C₇₉	—	4	2	no	—
160	D₄×C₇₉	—	4	2	no	—
161	D₄×C₇₉	—	8	1	no	—
162	D₄×C₇₉	—	8	2	no	—
163	C₂×C₄×C₇₉	—	2	2	no	—
164	C₂×C₄×C₇₉	—	2	2	no	—
165	C₂×C₄×C₇₉	—	4	1	no	—
166	C₂×C₄×C₇₉	—	4	1	no	—
167	C₂×C₄×C₇₉	—	4	1	no	—
168	C₂×C₄×C₇₉	—	4	1	no	—
169	C₂×C₄×C₇₉	—	8	2	no	—
170	C₂×C₄×C₇₉	#121	1	1	yes	characteristic
171	C₂×C₄×C₇₉	#121	1	1	yes	characteristic
172	C₂×C₄×C₇₉	#121	1	1	yes	characteristic
173	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
174	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
175	C₂×C₄×C₇₉	C₂×#41	1	1	yes	characteristic
176	C₂×Dic₇₉	—	2	2	no	—
177	C₂×Dic₇₉	—	8	1	no	—
178	D₃₁₆	—	2	4	no	—
179	D₃₁₆	—	2	2	no	—
180	D₃₁₆	#135	1	4	yes	—
181	C₄×D₇₉	—	4	2	no	—
182	C₄×D₇₉	—	4	2	no	—
183	C₄×D₇₉	—	8	2	no	—
184	C₈×C₇₉	—	2	2	no	—
185	C₈×C₇₉	—	2	2	no	—
186	C₇₉⋊C₈	—	4	2	no	—
187	C₇₉⋊C₈	—	4	2	no	—
188	C₇₉⋊C₈	—	4	2	no	—
189	C₂²×C₇₉	—	2	1	no	—
190	C₂²×C₇₉	—	2	1	no	—
191	C₂²×C₇₉	—	2	1	no	—
192	C₂²×C₇₉	—	8	1	no	—
193	C₂²×C₇₉	—	8	1	no	—
194	C₂²×C₇₉	—	8	1	no	—
195	C₂²×C₇₉	C₂×#121	1	1	yes	characteristic
196	C₂×D₇₉	—	2	4	no	—
197	C₂×D₇₉	—	4	2	no	—
198	C₂×D₇₉	—	4	2	no	—
199	C₂×D₇₉	—	8	4	no	—
200	C₄×C₇₉	—	2	1	no	—
201	C₄×C₇₉	—	2	1	no	—
202	C₄×C₇₉	—	2	1	no	—
203	C₄×C₇₉	—	2	1	no	—
204	C₄×C₇₉	—	8	1	no	—
205	C₄×C₇₉	—	8	1	no	—
206	C₄×C₇₉	—	8	1	no	—
207	C₄×C₇₉	C₂×#135	1	2	yes	—
208	C₄×C₇₉	#576	1	2	yes	—
209	Dic₇₉	—	4	2	no	—
210	#19388	—	79	1	no	maximal, Sylow
211	C₂×C₇₉	—	4	1	no	—
212	C₂×C₇₉	—	16	1	no	—
213	C₂×C₇₉	#3041	1	1	yes	characteristic
214	C₂×C₇₉	#3050	1	1	yes	characteristic
215	C₂×C₇₉	#3069	1	1	yes	characteristic
216	D₇₉	—	4	4	no	—
217	#3210	D₇₉	1	1	yes	characteristic, complemented
218	#3110	—	79	1	no	—
219	#3100	—	79	1	no	—
220	#2972	—	79	1	no	—
221	#1681	—	79	2	no	—
222	#1679	—	79	2	no	—
223	#1669	—	79	2	no	—
224	#1665	—	79	2	no	—
225	#1572	—	79	1	no	—
226	#1553	—	79	1	no	—
227	#1544	—	79	1	no	—
228	C₇₉	#19388	1	1	yes	characteristic, complemented, Sylow
229	#533	C₂×D₇₉	1	1	yes	characteristic
230	#532	C₂×D₇₉	1	1	yes	characteristic
231	C₂×C₄×D₄	—	79	1	no	—
232	#494	C₂×D₇₉	1	1	yes	characteristic, complemented
233	#492	C₂×D₇₉	1	1	yes	characteristic, complemented
234	#487	C₂×D₇₉	1	1	yes	characteristic, complemented
235	#486	C₂×D₇₉	1	1	yes	characteristic, complemented
236	#484	—	158	1	no	—
237	#480	—	158	1	no	—
238	#474	—	79	2	no	—
239	#474	—	79	2	no	—
240	#464	—	2	2	no	—
241	#461	—	79	2	no	—
242	#459	—	79	2	no	—
243	#452	—	2	2	no	—
244	#450	—	158	1	no	—
245	#447	—	158	1	no	—
246	#440	—	158	2	no	—
247	C₄×D₈	—	158	2	no	—
248	C₈×D₄	—	79	2	no	—
249	C₈×D₄	—	79	2	no	—
250	C₈×D₄	—	158	2	no	—
251	#432	—	79	1	no	—
252	#431	—	79	1	no	—
253	#431	—	79	1	no	—
254	#431	C₂×D₇₉	1	1	yes	characteristic
255	C₂×C₂²⋊C₈	—	158	2	no	—
256	#335	—	79	2	no	—
257	#334	—	79	2	no	—
258	#332	—	79	2	no	—
259	#332	—	79	2	no	—
260	#332	—	79	2	no	—
261	#331	—	79	2	no	—
262	C₂×#41	—	2	1	no	—
263	C₂²×D₄	—	79	1	no	—
264	C₂³×C₄	—	158	1	no	—
265	C₂×Q₁₆	—	2	2	no	—
266	C₂×SD₁₆	—	2	2	no	—
267	C₂×SD₁₆	—	158	2	no	—
268	C₂×D₈	—	158	2	no	—
269	C₂²×C₈	—	158	2	no	—
270	C₂²×C₈	—	158	2	no	—
271	C₄⋊Q₈	C₂²×D₇₉	1	1	yes	characteristic
272	C₄⋊Q₈	C₂²×D₇₉	1	1	yes	characteristic
273	C₄⋊Q₈	C₂²×D₇₉	1	1	yes	characteristic
274	#127	C₂²×D₇₉	1	1	yes	characteristic
275	#125	—	2	1	no	—
276	#124	—	2	1	no	—
277	C₂²⋊Q₈	—	2	1	no	—
278	C₂²⋊Q₈	—	2	1	no	—
279	#121	—	2	1	no	—
280	#121	—	2	1	no	—
281	C₄×Q₈	—	2	1	no	—
282	C₄×Q₈	—	2	1	no	—
283	C₄×D₄	—	2	1	no	—
284	C₄×D₄	—	2	1	no	—
285	C₄×D₄	—	79	2	no	—
286	C₄×D₄	—	79	2	no	—
287	C₄×D₄	—	158	1	no	—
288	C₄×D₄	—	158	1	no	—
289	#117	—	2	1	no	—
290	C₂×C₄⋊C₄	—	79	1	no	—
291	C₂×C₂²⋊C₄	—	158	1	no	—
292	C₂×C₄²	C₂²×D₇₉	1	1	yes	characteristic
293	#107	—	158	2	no	—
294	#107	—	158	2	no	—
295	C₄⋊C₈	—	79	2	no	—
296	C₄⋊C₈	—	79	2	no	—
297	C₄⋊C₈	—	79	2	no	—
298	C₄⋊C₈	C₂²⋊D₇₉	1	2	yes	—
299	#103	—	2	2	no	—
300	#103	—	158	2	no	—
301	#102	—	2	2	no	—
302	#102	—	158	2	no	—
303	#102	—	158	2	no	—
304	#102	—	158	2	no	—
305	C₂²⋊C₈	—	158	1	no	—
306	C₂²⋊C₈	—	158	1	no	—
307	C₂²⋊C₈	—	158	1	no	—
308	C₂²⋊C₈	—	158	2	no	—
309	C₂²⋊C₈	—	158	2	no	—
310	C₂²⋊C₈	C₂²⋊D₇₉	1	2	yes	—
311	#97	—	158	1	no	—
312	C₄×C₈	—	158	1	no	—
313	C₄×C₈	—	158	1	no	—
314	C₄×C₈	C₂²×D₇₉	1	1	yes	characteristic
315	C₄×C₈	C₂²×D₇₉	1	1	yes	characteristic
316	C₂⁴	—	158	1	no	—
317	#41	—	8	2	no	—
318	C₂×Q₈	—	2	1	no	—
319	C₂×Q₈	—	2	1	no	—
320	C₂×Q₈	—	2	1	no	—
321	C₂×D₄	—	2	1	no	—
322	C₂×D₄	—	2	1	no	—
323	C₂×D₄	—	2	1	no	—
324	C₂×D₄	—	4	1	no	—
325	C₂×D₄	—	79	2	no	—
326	C₂×D₄	—	158	4	no	—
327	C₂×D₄	—	158	1	no	—
328	C₂²×C₄	—	4	1	no	—
329	C₂²×C₄	—	632	2	no	—
330	C₂²×C₄	—	158	2	no	—
331	C₂²×C₄	—	158	1	no	—
332	C₂²×C₄	—	158	2	no	—
333	C₂²×C₄	D₄×D₇₉	1	1	yes	characteristic
334	C₂²×C₄	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
335	C₂²×C₄	#11929623	1	1	yes	characteristic
336	Q₁₆	—	8	2	no	—
337	SD₁₆	—	8	2	no	—
338	SD₁₆	—	316	4	no	—
339	D₈	—	316	4	no	—
340	C₂×C₈	—	632	2	no	—
341	C₂×C₈	—	632	2	no	—
342	C₂×C₈	—	158	2	no	—
343	C₂×C₈	—	158	2	no	—
344	C₂×C₈	—	158	2	no	—
345	C₂×C₈	C₂×C₂²⋊D₇₉	1	2	yes	—
346	C₂×C₈	C₂×C₂²⋊D₇₉	1	2	yes	—
347	C₄⋊C₄	—	2	1	no	—
348	C₄⋊C₄	—	2	1	no	—
349	C₄⋊C₄	—	2	1	no	—
350	C₄⋊C₄	—	2	1	no	—
351	C₄⋊C₄	—	2	1	no	—
352	C₄⋊C₄	—	2	1	no	—
353	C₄⋊C₄	—	4	1	no	—
354	C₄⋊C₄	—	4	1	no	—
355	C₄⋊C₄	—	79	2	no	—
356	C₄⋊C₄	—	158	1	no	—
357	C₂²⋊C₄	—	4	1	no	—
358	C₂²⋊C₄	—	4	1	no	—
359	C₂²⋊C₄	—	4	1	no	—
360	C₂²⋊C₄	—	158	2	no	—
361	C₂²⋊C₄	—	158	2	no	—
362	C₄²	—	4	1	no	—
363	C₄²	D₄×D₇₉	1	1	yes	characteristic
364	C₄²	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
365	C₄²	#11929623	1	1	yes	characteristic
366	C₄²	C₂³×D₇₉	1	1	yes	characteristic
367	C₂³	—	4	1	no	—
368	C₂³	—	632	1	no	—
369	C₂³	—	632	1	no	—
370	C₂³	—	158	4	no	—
371	C₂³	—	158	2	no	—
372	C₂³	#14579132	1	1	yes	characteristic
373	Q₈	—	4	2	no	—
374	Q₈	—	4	2	no	—
375	Q₈	—	4	2	no	—
376	D₄	—	4	2	no	—
377	D₄	—	4	2	no	—
378	D₄	—	8	1	no	—
379	D₄	—	8	2	no	—
380	D₄	—	79	4	no	—
381	D₄	—	158	4	no	—
382	D₄	—	158	2	no	—
383	C₂×C₄	—	2	2	no	—
384	C₂×C₄	—	2	2	no	—
385	C₂×C₄	—	4	1	no	—
386	C₂×C₄	—	4	1	no	—
387	C₂×C₄	—	4	1	no	—
388	C₂×C₄	—	4	1	no	—
389	C₂×C₄	—	8	2	no	—
390	C₂×C₄	—	316	2	no	—
391	C₂×C₄	—	316	2	no	—
392	C₂×C₄	—	632	2	no	—
393	C₂×C₄	—	632	1	no	—
394	C₂×C₄	—	158	2	no	—
395	C₂×C₄	#14579132	1	1	yes	characteristic
396	C₂×C₄	#14579132	1	1	yes	characteristic
397	C₂×C₄	#14579132	1	1	yes	characteristic
398	C₂×C₄	C₂×D₄×D₇₉	1	1	yes	characteristic
399	C₂×C₄	C₂²×C₂²⋊D₇₉	1	1	yes	characteristic
400	C₂×C₄	C₂×#11929623	1	1	yes	characteristic
401	C₈	—	2	2	no	—
402	C₈	—	2	2	no	—
403	C₈	—	316	2	no	—
404	C₈	—	316	2	no	—
405	C₈	—	316	2	no	—
406	C₂²	—	2	1	no	—
407	C₂²	—	2	1	no	—
408	C₂²	—	2	1	no	—
409	C₂²	—	8	1	no	—
410	C₂²	—	8	1	no	—
411	C₂²	—	8	1	no	—
412	C₂²	—	316	2	no	—
413	C₂²	—	316	2	no	—
414	C₂²	—	632	4	no	—
415	C₂²	—	158	4	no	—
416	C₂²	C₂×#14579132	1	1	yes	characteristic
417	C₄	—	2	1	no	—
418	C₄	—	2	1	no	—
419	C₄	—	2	1	no	—
420	C₄	—	2	1	no	—
421	C₄	—	8	1	no	—
422	C₄	—	8	1	no	—
423	C₄	—	8	1	no	—
424	C₄	—	316	2	no	—
425	C₄	#135×D₇₉	1	2	yes	—
426	C₄	#19099366	1	2	yes	—
427	C₂	—	4	1	no	—
428	C₂	—	16	1	no	—
429	C₂	—	316	4	no	—
430	C₂	#23772899	1	1	yes	characteristic
431	C₂	#23772977	1	1	yes	characteristic
432	C₂	#23773133	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×#14579132
commutator, cosocle	C₄²×C₇₉	C₂⁴
Frattini	C₄²	C₂³×D₇₉
Fitting	C₇₉×#3210	C₂
socle	C₂²×C₇₉	C₂×#121
prime radical	#23773396	C₂
hypercenter	#3210	D₇₉
hypocenter	C₇₉	#19388
LCS	G ▷ C₄²×C₇₉ ▷ C₂²×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #3210

Complements

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

N	H ≅ G/N	type
1. #23773495	C₂	semidirect
3. #23772423	C₂	semidirect
4. #23762834	C₂	semidirect
5. #23762820	C₂	semidirect
6. #23762762	C₂	semidirect
7. #23762738	C₂	semidirect
8. #23762180	C₂	semidirect
9. #23762105	C₂	semidirect
10. #23762065	C₂	semidirect
11. C₇₉×#3210	C₂	semidirect
30. #19098316	C₂²	semidirect
31. #19098314	C₂²	semidirect
32. #19098309	C₂²	semidirect
33. #19098309	C₂²	semidirect
34. #19098309	C₂²	semidirect
35. #19098307	C₂²	semidirect
38. #494×C₇₉	C₂²	semidirect
39. #492×C₇₉	C₂²	semidirect
40. #487×C₇₉	C₂²	semidirect
41. #486×C₇₉	C₂²	semidirect
217. #3210	D₇₉	semidirect
228. C₇₉	#19388	semidirect
232. #494	C₂×D₇₉	semidirect
233. #492	C₂×D₇₉	semidirect
234. #487	C₂×D₇₉	semidirect
235. #486	C₂×D₇₉	semidirect

Maximal subgroups

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

subgroup	index
#23773495	2
#23773396	2
#23772423	2
#23762834	2
#23762820	2
#23762762	2
#23762738	2
#23762180	2
#23762105	2
#23762065	2
C₇₉×#3210	2
#19388	79