Subgroups — #34271009

Order 20224.

642 conjugacy classes of subgroups.

The subgroup lattice has 442 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#23773454	C₂	1	2	yes	maximal, complemented
2	#23772366	C₂	1	1	yes	maximal, characteristic, complemented
3	#23762937	C₂	1	2	yes	maximal, complemented
4	#23762930	C₂	1	2	yes	maximal, complemented
5	#23762925	C₂	1	1	yes	maximal, characteristic, complemented
6	#23762920	C₂	1	1	yes	maximal, characteristic, complemented
7	#23762881	C₂	1	1	yes	maximal, characteristic, complemented
8	#23762876	C₂	1	1	yes	maximal, characteristic, complemented
9	#23762148	C₂	1	1	yes	maximal, characteristic, complemented
10	#23762062	C₂	1	2	yes	maximal, complemented
11	C₇₉×#3169	C₂	1	1	yes	maximal, characteristic, complemented
12	C₄×#11929624	C₂²	1	1	yes	characteristic
13	#19098884	—	2	2	no	—
14	#19098855	C₂²	1	2	yes	—
15	#19098850	C₂²	1	2	yes	—
16	#19098760	C₂²	1	2	yes	—
17	#19098755	C₂²	1	2	yes	—
18	#19098706	—	2	2	no	—
19	#19098693	C₂²	1	1	yes	characteristic
20	#19098693	C₂²	1	1	yes	characteristic
21	C₄×#11929612	—	2	2	no	—
22	C₄×#11929609	—	2	2	no	—
23	#19098642	C₂²	1	1	yes	characteristic
24	#19098642	C₂²	1	1	yes	characteristic
25	#19098634	—	2	1	no	—
26	#19098634	—	2	1	no	—
27	#19098616	C₂²	1	2	yes	—
28	#19098616	C₂²	1	1	yes	characteristic
29	#19098614	—	2	1	no	—
30	C₄×#11929607	—	2	1	no	—
31	#19098316	C₂²	1	2	yes	—
32	#19098314	C₂²	1	1	yes	characteristic
33	#19098314	C₂²	1	1	yes	characteristic
34	#19098312	C₂²	1	2	yes	—
35	#19098312	C₂²	1	2	yes	—
36	#19098307	C₂²	1	2	yes	—
37	#19098307	C₂²	1	2	yes	—
38	#532×C₇₉	C₂²	1	2	yes	—
39	#500×C₇₉	C₂²	1	1	yes	characteristic
40	#493×C₇₉	C₂²	1	1	yes	characteristic
41	#486×C₇₉	C₂²	1	2	yes	—
42	#466×C₇₉	—	2	1	no	—
43	#466×C₇₉	—	2	1	no	—
44	C₄×D₈×C₇₉	—	2	1	no	—
45	C₄×D₈×C₇₉	—	2	1	no	—
46	C₂×C₄×C₈×C₇₉	C₂²	1	1	yes	characteristic
47	C₂×#11929624	D₄	1	1	yes	characteristic
48	C₂×#11929612	—	2	2	no	—
49	C₂×#11929609	—	2	2	no	—
50	C₂×#11929607	—	2	1	no	—
51	C₂×#11929607	—	2	1	no	—
52	C₄×Dic₁₅₈	D₄	1	1	yes	characteristic
53	C₄×Dic₁₅₈	C₂³	1	1	yes	characteristic
54	C₄×D₃₁₆	D₄	1	1	yes	characteristic
55	C₄×D₃₁₆	C₂³	1	1	yes	characteristic
56	C₄×C₂²⋊D₇₉	—	2	1	no	—
57	C₄×C₂²⋊D₇₉	—	2	1	no	—
58	#14579120	D₄	1	1	yes	characteristic
59	#14579118	—	2	1	no	—
60	C₄²×D₇₉	—	2	1	no	—
61	#14579094	—	2	2	no	—
62	#14579092	—	2	2	no	—
63	C₄⋊(C₇₉⋊C₈)	C₂³	1	1	yes	characteristic
64	C₄⋊(C₇₉⋊C₈)	C₂³	1	1	yes	characteristic
65	C₄⋊(C₇₉⋊C₈)	C₂³	1	2	yes	—
66	C₄⋊(C₇₉⋊C₈)	C₂³	1	2	yes	—
67	Dic₇₉⋊C₈	—	2	1	no	—
68	Dic₇₉⋊C₈	—	2	1	no	—
69	#14579084	—	2	2	no	—
70	#14579082	—	2	2	no	—
71	#14579082	—	2	2	no	—
72	#14579081	—	2	2	no	—
73	C₂²⋊(C₇₉⋊C₈)	—	2	2	no	—
74	C₂²⋊(C₇₉⋊C₈)	—	2	1	no	—
75	(C₂×D₇₉)⋊C₈	—	2	1	no	—
76	(C₂×D₇₉)⋊C₈	—	2	1	no	—
77	#14579071	—	2	1	no	—
78	#14579071	—	2	1	no	—
79	C₄×C₇₉⋊C₈	—	2	2	no	—
80	C₄×C₇₉⋊C₈	—	2	1	no	—
81	C₂×#41×C₇₉	—	2	2	no	—
82	C₂×D₈×C₇₉	—	2	1	no	—
83	C₂×D₈×C₇₉	—	2	1	no	—
84	C₂²×C₈×C₇₉	D₄	1	1	yes	characteristic
85	C₂²×C₈×C₇₉	D₄	1	1	yes	characteristic
86	C₄⋊Q₈×C₇₉	C₂³	1	2	yes	—
87	#127×C₇₉	C₂³	1	2	yes	—
88	#124×C₇₉	—	2	2	no	—
89	#121×C₇₉	—	2	2	no	—
90	#121×C₇₉	—	2	2	no	—
91	C₄×D₄×C₇₉	—	2	2	no	—
92	C₄×D₄×C₇₉	—	2	2	no	—
93	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
94	#107×C₇₉	—	2	1	no	—
95	#107×C₇₉	—	2	1	no	—
96	#102×C₇₉	—	2	2	no	—
97	#102×C₇₉	—	2	2	no	—
98	C₄×C₈×C₇₉	D₄	1	1	yes	characteristic
99	C₄×C₈×C₇₉	D₄	1	1	yes	characteristic
100	C₄×C₈×C₇₉	C₂³	1	1	yes	characteristic
101	C₄×C₈×C₇₉	C₂³	1	1	yes	characteristic
102	#11929624	—	4	2	no	—
103	C₂×Dic₁₅₈	C₂×D₄	1	1	yes	characteristic
104	C₂×D₃₁₆	C₂×D₄	1	1	yes	characteristic
105	C₂×C₂²⋊D₇₉	—	2	1	no	—
106	C₂×C₄×D₇₉	—	2	1	no	—
107	C₂×C₄×D₇₉	—	2	1	no	—
108	C₂×C₄×D₇₉	—	2	1	no	—
109	#11929612	—	4	4	no	—
110	#11929609	—	4	4	no	—
111	#11929607	—	4	2	no	—
112	#11929607	—	4	2	no	—
113	C₂×C₇₉⋊C₈	—	2	1	no	—
114	C₂×C₇₉⋊C₈	—	2	1	no	—
115	C₂×C₇₉⋊C₈	—	2	2	no	—
116	C₂×C₇₉⋊C₈	—	2	2	no	—
117	C₄⋊Dic₇₉	C₂×D₄	1	1	yes	characteristic
118	C₄⋊Dic₇₉	C₂×D₄	1	1	yes	characteristic
119	Dic₇₉⋊C₄	—	2	1	no	—
120	Dic₇₉⋊C₄	—	2	1	no	—
121	C₂²⋊Dic₇₉	—	2	1	no	—
122	(C₂×D₇₉)⋊C₄	—	2	1	no	—
123	(C₂×D₇₉)⋊C₄	—	2	1	no	—
124	C₄×Dic₇₉	—	2	1	no	—
125	C₄×Dic₇₉	—	2	1	no	—
126	C₄×Dic₇₉	—	2	1	no	—
127	#41×C₇₉	—	8	4	no	—
128	C₂×Q₈×C₇₉	—	2	2	no	—
129	C₂×D₄×C₇₉	—	2	2	no	—
130	C₂×D₄×C₇₉	—	2	2	no	—
131	C₂×D₄×C₇₉	—	2	2	no	—
132	C₂×D₄×C₇₉	—	4	2	no	—
133	C₂²×C₄×C₇₉	—	4	2	no	—
134	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
135	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
136	C₂²×C₄×C₇₉	#41	1	1	yes	characteristic
137	D₈×C₇₉	—	4	2	no	—
138	D₈×C₇₉	—	4	2	no	—
139	C₂×C₈×C₇₉	—	2	2	no	—
140	C₂×C₈×C₇₉	—	4	1	no	—
141	C₂×C₈×C₇₉	C₂×D₄	1	1	yes	characteristic
142	C₂×C₈×C₇₉	C₂×D₄	1	1	yes	characteristic
143	C₂×C₈×C₇₉	C₂×D₄	1	1	yes	characteristic
144	C₂×C₈×C₇₉	C₂×D₄	1	1	yes	characteristic
145	C₄⋊C₄×C₇₉	—	2	2	no	—
146	C₄⋊C₄×C₇₉	—	2	2	no	—
147	C₂²⋊C₄×C₇₉	—	4	2	no	—
148	C₂²⋊C₄×C₇₉	—	4	2	no	—
149	C₄²×C₇₉	C₂×D₄	1	1	yes	characteristic
150	C₄²×C₇₉	C₂×D₄	1	1	yes	characteristic
151	C₄²×C₇₉	#41	1	1	yes	characteristic
152	C₄²×C₇₉	C₂⁴	1	1	yes	characteristic
153	C₂³×C₇₉	—	4	2	no	—
154	C₂³×C₇₉	#121	1	1	yes	characteristic
155	C₂²×D₇₉	—	2	1	no	—
156	Q₈×C₇₉	—	8	2	no	—
157	D₄×C₇₉	—	4	2	no	—
158	D₄×C₇₉	—	4	2	no	—
159	D₄×C₇₉	—	4	2	no	—
160	D₄×C₇₉	—	4	2	no	—
161	D₄×C₇₉	—	8	2	no	—
162	D₄×C₇₉	—	8	4	no	—
163	C₂×C₄×C₇₉	—	2	1	no	—
164	C₂×C₄×C₇₉	—	2	2	no	—
165	C₂×C₄×C₇₉	—	2	1	no	—
166	C₂×C₄×C₇₉	—	2	2	no	—
167	C₂×C₄×C₇₉	—	4	2	no	—
168	C₂×C₄×C₇₉	—	8	4	no	—
169	C₂×C₄×C₇₉	#121	1	1	yes	characteristic
170	C₂×C₄×C₇₉	#121	1	1	yes	characteristic
171	C₂×C₄×C₇₉	#121	1	1	yes	characteristic
172	C₂×C₄×C₇₉	C₂²×D₄	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	C₂²⋊D₇₉	—	4	2	no	—
176	C₂×Dic₇₉	—	2	1	no	—
177	C₂×Dic₇₉	—	2	1	no	—
178	C₂×Dic₇₉	—	2	1	no	—
179	D₃₁₆	—	2	2	no	—
180	C₄×D₇₉	—	4	2	no	—
181	C₄×D₇₉	—	4	1	no	—
182	C₄×D₇₉	—	4	1	no	—
183	C₄×D₇₉	—	4	2	no	—
184	Dic₁₅₈	—	2	2	no	—
185	C₈×C₇₉	—	2	1	no	—
186	C₈×C₇₉	—	2	1	no	—
187	C₈×C₇₉	—	2	1	no	—
188	C₈×C₇₉	#135	1	2	yes	—
189	C₇₉⋊C₈	—	4	1	no	—
190	C₇₉⋊C₈	—	4	1	no	—
191	C₇₉⋊C₈	—	4	2	no	—
192	C₇₉⋊C₈	—	4	2	no	—
193	C₂²×C₇₉	—	2	1	no	—
194	C₂²×C₇₉	—	2	1	no	—
195	C₂²×C₇₉	—	2	1	no	—
196	C₂²×C₇₉	—	8	2	no	—
197	C₂²×C₇₉	—	8	2	no	—
198	C₂²×C₇₉	—	8	2	no	—
199	C₂²×C₇₉	C₂×#121	1	1	yes	characteristic
200	C₂×D₇₉	—	4	1	no	—
201	C₂×D₇₉	—	4	1	no	—
202	C₂×D₇₉	—	4	1	no	—
203	C₄×C₇₉	—	2	1	no	—
204	C₄×C₇₉	—	2	1	no	—
205	C₄×C₇₉	—	2	1	no	—
206	C₄×C₇₉	—	8	2	no	—
207	C₄×C₇₉	#472	1	2	yes	—
208	C₄×C₇₉	C₂×#135	1	1	yes	characteristic
209	C₄×C₇₉	#575	1	2	yes	—
210	C₄×C₇₉	#575	1	1	yes	characteristic
211	Dic₇₉	—	4	1	no	—
212	Dic₇₉	—	4	1	no	—
213	Dic₇₉	—	4	1	no	—
214	#19160	—	79	1	no	maximal, Sylow
215	C₂×C₇₉	—	4	1	no	—
216	C₂×C₇₉	—	16	2	no	—
217	C₂×C₇₉	#3035	1	1	yes	characteristic
218	C₂×C₇₉	#3054	1	1	yes	characteristic
219	C₂×C₇₉	C₂×#472	1	1	yes	characteristic
220	D₇₉	—	8	1	no	—
221	#3169	D₇₉	1	1	yes	characteristic, complemented
222	#3106	—	79	2	no	—
223	#2965	—	79	1	no	—
224	#1698	—	79	2	no	—
225	#1697	—	79	2	no	—
226	#1696	—	79	1	no	—
227	#1695	—	79	1	no	—
228	#1688	—	79	1	no	—
229	#1687	—	79	1	no	—
230	#1564	—	79	1	no	—
231	#1543	—	79	2	no	—
232	C₇₉	#19160	1	1	yes	characteristic, complemented, Sylow
233	#532	C₂×D₇₉	1	2	yes	—
234	C₄×#41	—	79	1	no	—
235	#500	C₂×D₇₉	1	1	yes	characteristic
236	#493	C₂×D₇₉	1	1	yes	characteristic
237	#486	C₂×D₇₉	1	2	yes	—
238	#482	—	158	2	no	—
239	#477	—	79	2	no	—
240	#476	—	79	2	no	—
241	#466	—	2	1	no	—
242	#466	—	2	1	no	—
243	#460	—	79	2	no	—
244	#459	—	79	2	no	—
245	#449	—	158	2	no	—
246	#446	—	79	1	no	—
247	#446	—	79	1	no	—
248	C₄×SD₁₆	—	158	2	no	—
249	C₄×D₈	—	2	1	no	—
250	C₄×D₈	—	2	1	no	—
251	C₄×D₈	—	158	2	no	—
252	#436	—	79	1	no	—
253	#436	—	79	1	no	—
254	#435	—	158	1	no	—
255	#435	—	158	1	no	—
256	#431	—	79	1	no	—
257	#431	—	79	2	no	—
258	#431	—	158	1	no	—
259	C₄×M₁₆	—	158	1	no	—
260	C₂×C₄×C₈	C₂×D₇₉	1	1	yes	characteristic
261	#335	—	79	2	no	—
262	#334	—	79	1	no	—
263	#334	—	79	1	no	—
264	#333	—	79	2	no	—
265	#333	—	79	2	no	—
266	#331	—	79	2	no	—
267	#331	—	79	2	no	—
268	C₂×#41	—	2	2	no	—
269	C₂×#41	—	79	1	no	—
270	C₂×SD₁₆	—	158	2	no	—
271	C₂×D₈	—	2	1	no	—
272	C₂×D₈	—	2	1	no	—
273	C₂×D₈	—	158	2	no	—
274	C₂×M₁₆	—	158	1	no	—
275	C₂×M₁₆	—	158	1	no	—
276	C₂²×C₈	C₂²⋊D₇₉	1	1	yes	characteristic
277	C₂²×C₈	C₂²⋊D₇₉	1	1	yes	characteristic
278	C₄⋊Q₈	C₂²×D₇₉	1	2	yes	—
279	#127	C₂²×D₇₉	1	2	yes	—
280	#124	—	2	2	no	—
281	#121	—	2	2	no	—
282	#121	—	2	2	no	—
283	C₄×Q₈	—	79	1	no	—
284	C₄×Q₈	—	79	1	no	—
285	C₄×D₄	—	2	2	no	—
286	C₄×D₄	—	2	2	no	—
287	C₄×D₄	—	79	1	no	—
288	C₄×D₄	—	79	1	no	—
289	C₄×D₄	—	158	1	no	—
290	C₄×D₄	—	158	1	no	—
291	#117	—	79	1	no	—
292	#117	—	158	1	no	—
293	C₂×C₄²	—	158	1	no	—
294	C₂×C₄²	C₂²×D₇₉	1	1	yes	characteristic
295	#107	—	2	1	no	—
296	#107	—	2	1	no	—
297	#107	—	158	2	no	—
298	#106	—	158	2	no	—
299	C₄⋊C₈	—	79	1	no	—
300	C₄⋊C₈	—	79	1	no	—
301	C₄⋊C₈	—	79	2	no	—
302	C₄⋊C₈	—	79	2	no	—
303	C₄⋊C₈	—	158	1	no	—
304	C₄⋊C₈	—	158	1	no	—
305	#103	—	158	2	no	—
306	#102	—	2	2	no	—
307	#102	—	2	2	no	—
308	#102	—	158	2	no	—
309	#102	—	158	2	no	—
310	#102	—	158	2	no	—
311	C₂²⋊C₈	—	158	2	no	—
312	C₂²⋊C₈	—	158	1	no	—
313	C₂²⋊C₈	—	158	1	no	—
314	C₂²⋊C₈	—	158	1	no	—
315	#97	—	158	1	no	—
316	#97	—	158	1	no	—
317	C₄×C₈	—	158	2	no	—
318	C₄×C₈	—	158	1	no	—
319	C₄×C₈	C₂²⋊D₇₉	1	1	yes	characteristic
320	C₄×C₈	C₂²⋊D₇₉	1	1	yes	characteristic
321	C₄×C₈	C₂²×D₇₉	1	1	yes	characteristic
322	C₄×C₈	C₂²×D₇₉	1	1	yes	characteristic
323	#41	—	8	4	no	—
324	#41	—	316	2	no	—
325	C₂×Q₈	—	2	2	no	—
326	C₂×Q₈	—	79	1	no	—
327	C₂×D₄	—	2	2	no	—
328	C₂×D₄	—	2	2	no	—
329	C₂×D₄	—	2	2	no	—
330	C₂×D₄	—	4	2	no	—
331	C₂×D₄	—	79	1	no	—
332	C₂×D₄	—	158	1	no	—
333	C₂²×C₄	—	4	2	no	—
334	C₂²×C₄	—	158	1	no	—
335	C₂²×C₄	—	158	1	no	—
336	C₂²×C₄	—	158	1	no	—
337	C₂²×C₄	D₄×D₇₉	1	1	yes	characteristic
338	C₂²×C₄	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
339	C₂²×C₄	#11929623	1	1	yes	characteristic
340	SD₁₆	—	316	4	no	—
341	D₈	—	4	2	no	—
342	D₈	—	4	2	no	—
343	D₈	—	316	4	no	—
344	M₁₆	—	316	2	no	—
345	M₁₆	—	316	2	no	—
346	C₂×C₈	—	2	2	no	—
347	C₂×C₈	—	4	1	no	—
348	C₂×C₈	—	158	2	no	—
349	C₂×C₈	—	158	2	no	—
350	C₂×C₈	—	158	1	no	—
351	C₂×C₈	—	158	1	no	—
352	C₂×C₈	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
353	C₂×C₈	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
354	C₂×C₈	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
355	C₂×C₈	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
356	C₄⋊C₄	—	2	2	no	—
357	C₄⋊C₄	—	2	2	no	—
358	C₄⋊C₄	—	79	1	no	—
359	C₄⋊C₄	—	79	1	no	—
360	C₄⋊C₄	—	158	1	no	—
361	C₄⋊C₄	—	158	1	no	—
362	C₂²⋊C₄	—	4	2	no	—
363	C₂²⋊C₄	—	4	2	no	—
364	C₂²⋊C₄	—	158	1	no	—
365	C₂²⋊C₄	—	158	1	no	—
366	C₂²⋊C₄	—	158	1	no	—
367	C₄²	—	158	1	no	—
368	C₄²	—	158	1	no	—
369	C₄²	—	158	1	no	—
370	C₄²	D₄×D₇₉	1	1	yes	characteristic
371	C₄²	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
372	C₄²	#11929623	1	1	yes	characteristic
373	C₄²	C₂³×D₇₉	1	1	yes	characteristic
374	C₂³	—	4	2	no	—
375	C₂³	—	158	1	no	—
376	C₂³	#14579132	1	1	yes	characteristic
377	Q₈	—	8	2	no	—
378	Q₈	—	158	2	no	—
379	D₄	—	4	2	no	—
380	D₄	—	4	2	no	—
381	D₄	—	4	2	no	—
382	D₄	—	4	2	no	—
383	D₄	—	8	2	no	—
384	D₄	—	8	4	no	—
385	D₄	—	316	2	no	—
386	D₄	—	158	2	no	—
387	C₂×C₄	—	2	2	no	—
388	C₂×C₄	—	2	1	no	—
389	C₂×C₄	—	2	2	no	—
390	C₂×C₄	—	2	1	no	—
391	C₂×C₄	—	4	2	no	—
392	C₂×C₄	—	8	4	no	—
393	C₂×C₄	—	316	2	no	—
394	C₂×C₄	—	316	2	no	—
395	C₂×C₄	—	316	1	no	—
396	C₂×C₄	—	316	1	no	—
397	C₂×C₄	—	158	1	no	—
398	C₂×C₄	—	158	1	no	—
399	C₂×C₄	—	158	1	no	—
400	C₂×C₄	#14579132	1	1	yes	characteristic
401	C₂×C₄	#14579132	1	1	yes	characteristic
402	C₂×C₄	#14579132	1	1	yes	characteristic
403	C₂×C₄	C₂×D₄×D₇₉	1	1	yes	characteristic
404	C₂×C₄	C₂²×C₂²⋊D₇₉	1	1	yes	characteristic
405	C₂×C₄	C₂×#11929623	1	1	yes	characteristic
406	C₈	—	2	1	no	—
407	C₈	—	2	1	no	—
408	C₈	—	2	1	no	—
409	C₈	—	316	1	no	—
410	C₈	—	316	2	no	—
411	C₈	—	316	2	no	—
412	C₈	—	316	1	no	—
413	C₈	#14579181	1	2	yes	—
414	C₂²	—	2	1	no	—
415	C₂²	—	2	1	no	—
416	C₂²	—	2	1	no	—
417	C₂²	—	8	2	no	—
418	C₂²	—	8	2	no	—
419	C₂²	—	8	2	no	—
420	C₂²	—	316	1	no	—
421	C₂²	—	316	1	no	—
422	C₂²	—	316	1	no	—
423	C₂²	C₂×#14579132	1	1	yes	characteristic
424	C₄	—	2	1	no	—
425	C₄	—	2	1	no	—
426	C₄	—	2	1	no	—
427	C₄	—	8	2	no	—
428	C₄	—	316	1	no	—
429	C₄	—	316	1	no	—
430	C₄	—	316	1	no	—
431	C₄	#19098830	1	2	yes	—
432	C₄	C₂×#14579181	1	1	yes	characteristic
433	C₄	#19099360	1	2	yes	—
434	C₄	#19099361	1	1	yes	characteristic
435	C₂	—	4	1	no	—
436	C₂	—	16	2	no	—
437	C₂	—	632	1	no	—
438	C₂	#23772849	1	1	yes	characteristic
439	C₂	#23773005	1	1	yes	characteristic
440	C₂	C₂×#19098830	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	#14579132
commutator, cosocle	C₄²×C₇₉	C₂⁴
Frattini	C₄²	C₂³×D₇₉
Fitting	C₇₉×#3169	C₂
socle	C₂²×C₇₉	C₂×#121
hypercenter	#3169	D₇₉
hypocenter	C₇₉	#19160
LCS	G ▷ C₄²×C₇₉ ▷ C₂²×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #3169

Complements

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

N	H ≅ G/N	type
1. #23773454	C₂	semidirect
2. #23772366	C₂	semidirect
3. #23762937	C₂	semidirect
4. #23762930	C₂	semidirect
5. #23762925	C₂	semidirect
6. #23762920	C₂	semidirect
7. #23762881	C₂	semidirect
8. #23762876	C₂	semidirect
9. #23762148	C₂	semidirect
10. #23762062	C₂	semidirect
11. C₇₉×#3169	C₂	semidirect
221. #3169	D₇₉	semidirect
232. C₇₉	#19160	semidirect

Maximal subgroups

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

subgroup	index
#23773454	2
#23772366	2
#23762937	2
#23762930	2
#23762925	2
#23762920	2
#23762881	2
#23762876	2
#23762148	2
#23762062	2
C₇₉×#3169	2
#19160	79