Subgroups — #34258783

Order 20224.

750 conjugacy classes of subgroups.

The subgroup lattice has 410 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#23773975	C₂	1	1	yes	maximal, characteristic
2	#23772113	C₂	1	1	yes	maximal, characteristic, complemented
3	#23762283	C₂	1	4	yes	maximal, complemented
4	C₈×#11929609	C₂	1	4	yes	maximal, complemented
5	#23762158	C₂	1	1	yes	maximal, characteristic, complemented
6	#23761851	C₂	1	1	yes	maximal, characteristic, complemented
7	#23761850	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₈×C₇₉⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
9	C₇₉×#2931	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#14579167	—	2	1	no	—
11	#19099113	C₂²	1	1	yes	characteristic
12	#19098966	C₄	1	1	yes	characteristic
13	#19098939	C₄	1	1	yes	characteristic
14	#19098911	C₄	1	1	yes	characteristic
15	#19098909	C₄	1	1	yes	characteristic
16	#19098797	C₄	1	4	yes	—
17	C₄×#11929609	C₂²	1	4	yes	—
18	#19098642	—	2	1	no	—
19	#19098642	C₂²	1	2	yes	—
20	C₈×D₃₁₆	—	2	1	no	—
21	C₈×D₃₁₆	C₂²	1	2	yes	—
22	#19098587	C₂²	1	1	yes	characteristic
23	#19098529	—	2	1	no	—
24	C₂×C₄×C₇₉⋊C₈	C₂²	1	1	yes	characteristic
25	C₂×C₄×C₇₉⋊C₈	C₂²	1	1	yes	characteristic
26	#19098315	C₂²	1	4	yes	—
27	D₄⋊(C₇₉⋊C₈)	C₂²	1	4	yes	—
28	#19098290	C₂²	1	4	yes	—
29	C₈×C₇₉⋊C₈	C₂²	1	2	yes	—
30	C₈×C₇₉⋊C₈	C₂²	1	2	yes	—
31	C₂×#131×C₇₉	—	2	1	no	—
32	#532×C₇₉	C₂²	1	1	yes	characteristic
33	#436×C₇₉	—	2	1	no	—
34	#436×C₇₉	C₂²	1	2	yes	—
35	C₈×D₄×C₇₉	—	2	1	no	—
36	C₈×D₄×C₇₉	C₂²	1	2	yes	—
37	#423×C₇₉	C₂²	1	1	yes	characteristic
38	#408×C₇₉	—	2	1	no	—
39	C₂×C₄×C₈×C₇₉	C₂²	1	1	yes	characteristic
40	C₂×#11929624	—	2	1	no	—
41	C₂×#11929609	C₂×C₄	1	4	yes	—
42	#14579167	—	4	4	no	—
43	C₂×#11929608	—	2	1	no	—
44	C₂×#11929607	—	2	2	no	—
45	C₂²×C₇₉⋊C₈	—	2	1	no	—
46	C₂²×C₇₉⋊C₈	C₂×C₄	1	2	yes	—
47	C₂×C₈×D₇₉	—	2	2	no	—
48	#14579161	C₂×C₄	1	1	yes	characteristic
49	#14579158	C₂×C₄	1	1	yes	characteristic
50	#14579149	—	2	1	no	—
51	#14579135	—	2	1	no	—
52	#14579135	C₂×C₄	1	2	yes	—
53	C₄×D₃₁₆	—	2	1	no	—
54	C₄×D₃₁₆	C₂³	1	2	yes	—
55	#14579094	C₂×C₄	1	4	yes	—
56	C₄⋊(C₇₉⋊C₈)	—	2	1	no	—
57	C₄⋊(C₇₉⋊C₈)	C₂³	1	2	yes	—
58	#14579082	C₂×C₄	1	4	yes	—
59	#14579081	C₂×C₄	1	4	yes	—
60	(C₂×D₇₉)⋊C₈	—	2	2	no	—
61	(C₂×D₇₉)⋊C₈	—	2	2	no	—
62	C₄×C₇₉⋊C₈	—	2	1	no	—
63	C₄×C₇₉⋊C₈	C₂×C₄	1	1	yes	characteristic
64	C₄×C₇₉⋊C₈	C₂×C₄	1	1	yes	characteristic
65	C₄×C₇₉⋊C₈	C₂³	1	2	yes	—
66	C₄×C₇₉⋊C₈	C₂³	1	2	yes	—
67	C₂×#41×C₇₉	—	2	1	no	—
68	#131×C₇₉	—	4	4	no	—
69	C₂×M₁₆×C₇₉	—	2	1	no	—
70	C₂×M₁₆×C₇₉	—	2	2	no	—
71	C₂²×C₈×C₇₉	—	2	2	no	—
72	C₂²×C₈×C₇₉	D₄	1	1	yes	characteristic
73	C₂²×C₈×C₇₉	D₄	1	1	yes	characteristic
74	C₄⋊Q₈×C₇₉	C₂×C₄	1	1	yes	characteristic
75	#127×C₇₉	C₂×C₄	1	1	yes	characteristic
76	#124×C₇₉	—	2	1	no	—
77	#121×C₇₉	—	2	1	no	—
78	#121×C₇₉	C₂×C₄	1	2	yes	—
79	C₄×D₄×C₇₉	—	2	1	no	—
80	C₄×D₄×C₇₉	C₂³	1	2	yes	—
81	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
82	C₄⋊C₈×C₇₉	—	2	1	no	—
83	C₄⋊C₈×C₇₉	C₂³	1	2	yes	—
84	C₂²⋊C₈×C₇₉	—	2	2	no	—
85	C₂²⋊C₈×C₇₉	—	2	2	no	—
86	C₄×C₈×C₇₉	D₄	1	1	yes	characteristic
87	C₄×C₈×C₇₉	D₄	1	1	yes	characteristic
88	C₄×C₈×C₇₉	C₂³	1	1	yes	characteristic
89	C₄×C₈×C₇₉	C₂³	1	1	yes	characteristic
90	#11929624	—	4	2	no	—
91	#11929624	—	4	2	no	—
92	C₂×Dic₁₅₈	—	2	1	no	—
93	C₂×D₃₁₆	—	2	1	no	—
94	C₂×D₃₁₆	—	2	1	no	—
95	C₂×D₃₁₆	C₂²×C₄	1	2	yes	—
96	C₂×C₂²⋊D₇₉	—	2	2	no	—
97	C₂×C₄×D₇₉	—	2	2	no	—
98	#11929609	—	2	8	no	—
99	#11929608	—	4	2	no	—
100	#11929607	—	4	4	no	—
101	C₂×C₇₉⋊C₈	—	2	4	no	—
102	C₂×C₇₉⋊C₈	—	2	4	no	—
103	C₂×C₇₉⋊C₈	—	2	2	no	—
104	C₂×C₇₉⋊C₈	—	2	2	no	—
105	C₂×C₇₉⋊C₈	C₂²×C₄	1	2	yes	—
106	C₂×C₇₉⋊C₈	C₂²×C₄	1	2	yes	—
107	C₈×D₇₉	—	4	4	no	—
108	C₄⋊Dic₇₉	—	2	1	no	—
109	C₄⋊Dic₇₉	C₂²×C₄	1	2	yes	—
110	(C₂×D₇₉)⋊C₄	—	2	2	no	—
111	(C₂×D₇₉)⋊C₄	—	2	2	no	—
112	#41×C₇₉	—	4	2	no	—
113	#41×C₇₉	—	4	2	no	—
114	C₂×Q₈×C₇₉	—	2	1	no	—
115	C₂×D₄×C₇₉	—	2	2	no	—
116	C₂×D₄×C₇₉	—	2	1	no	—
117	C₂×D₄×C₇₉	—	2	1	no	—
118	C₂×D₄×C₇₉	C₂²×C₄	1	2	yes	—
119	C₂²×C₄×C₇₉	—	2	2	no	—
120	C₂²×C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
121	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
122	C₂²×C₄×C₇₉	#41	1	1	yes	characteristic
123	M₁₆×C₇₉	—	4	4	no	—
124	M₁₆×C₇₉	—	4	2	no	—
125	C₂×C₈×C₇₉	—	2	2	no	—
126	C₂×C₈×C₇₉	—	2	2	no	—
127	C₂×C₈×C₇₉	—	4	4	no	—
128	C₂×C₈×C₇₉	D₈	1	4	yes	complemented
129	C₂×C₈×C₇₉	C₂×D₄	1	1	yes	characteristic
130	C₂×C₈×C₇₉	C₂×D₄	1	1	yes	characteristic
131	C₂×C₈×C₇₉	C₂×D₄	1	1	yes	characteristic
132	C₂×C₈×C₇₉	C₂×D₄	1	1	yes	characteristic
133	C₄⋊C₄×C₇₉	—	2	1	no	—
134	C₄⋊C₄×C₇₉	C₂²×C₄	1	2	yes	—
135	C₂²⋊C₄×C₇₉	—	2	2	no	—
136	C₂²⋊C₄×C₇₉	—	2	2	no	—
137	C₄²×C₇₉	C₂²×C₄	1	1	yes	characteristic
138	C₄²×C₇₉	C₂×D₄	1	1	yes	characteristic
139	C₄²×C₇₉	#41	1	1	yes	characteristic
140	C₄²×C₇₉	C₂⁴	1	1	yes	characteristic
141	C₂³×C₇₉	—	2	2	no	—
142	C₂³×C₇₉	C₄×D₄	1	1	yes	characteristic
143	C₂²×D₇₉	—	2	2	no	—
144	Q₈×C₇₉	—	4	2	no	—
145	D₄×C₇₉	—	2	4	no	—
146	D₄×C₇₉	—	4	4	no	—
147	D₄×C₇₉	—	4	2	no	—
148	D₄×C₇₉	—	4	2	no	—
149	C₂×C₄×C₇₉	—	2	2	no	—
150	C₂×C₄×C₇₉	—	2	2	no	—
151	C₂×C₄×C₇₉	—	2	2	no	—
152	C₂×C₄×C₇₉	—	4	2	no	—
153	C₂×C₄×C₇₉	—	4	2	no	—
154	C₂×C₄×C₇₉	C₄×D₄	1	1	yes	characteristic
155	C₂×C₄×C₇₉	C₄×D₄	1	1	yes	characteristic
156	C₂×C₄×C₇₉	C₄×D₄	1	1	yes	characteristic
157	C₂×C₄×C₇₉	C₂×D₈	1	2	yes	—
158	C₂×C₄×C₇₉	#135	1	2	yes	—
159	C₂×C₄×C₇₉	C₂³×C₄	1	1	yes	characteristic
160	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
161	C₂×C₄×C₇₉	C₂×#41	1	1	yes	characteristic
162	C₂²⋊D₇₉	—	4	4	no	—
163	C₂×Dic₇₉	—	2	2	no	—
164	D₃₁₆	—	2	4	no	—
165	D₃₁₆	—	4	2	no	—
166	D₃₁₆	—	4	2	no	—
167	C₄×D₇₉	—	4	2	no	—
168	C₄×D₇₉	—	4	2	no	—
169	Dic₁₅₈	—	4	2	no	—
170	C₈×C₇₉	—	2	1	no	—
171	C₈×C₇₉	—	2	1	no	—
172	C₈×C₇₉	—	4	2	no	—
173	C₈×C₇₉	C₂×D₈	1	2	yes	—
174	C₈×C₇₉	C₂×D₈	1	2	yes	—
175	C₇₉⋊C₈	—	2	4	no	—
176	C₇₉⋊C₈	—	2	2	no	—
177	C₇₉⋊C₈	—	4	2	no	—
178	C₇₉⋊C₈	#131	1	4	yes	complemented
179	C₂²×C₇₉	—	2	1	no	—
180	C₂²×C₇₉	—	2	1	no	—
181	C₂²×C₇₉	—	4	2	no	—
182	C₂²×C₇₉	—	4	2	no	—
183	C₂²×C₇₉	—	4	2	no	—
184	C₂²×C₇₉	C₄×D₈	1	2	yes	—
185	C₂²×C₇₉	C₂×C₄×D₄	1	1	yes	characteristic
186	C₂×D₇₉	—	4	2	no	—
187	C₂×D₇₉	—	4	2	no	—
188	C₂×D₇₉	—	4	2	no	—
189	C₄×C₇₉	—	2	1	no	—
190	C₄×C₇₉	—	2	1	no	—
191	C₄×C₇₉	—	4	2	no	—
192	C₄×C₇₉	C₄×D₈	1	2	yes	—
193	C₄×C₇₉	#443	1	2	yes	—
194	C₄×C₇₉	C₂×#131	1	2	yes	—
195	C₄×C₇₉	C₂²×D₈	1	1	yes	characteristic
196	C₄×C₇₉	C₂×#135	1	1	yes	characteristic
197	Dic₇₉	—	4	2	no	—
198	#17956	—	79	1	no	maximal, Sylow
199	C₂×C₇₉	—	2	2	no	—
200	C₂×C₇₉	—	8	2	no	—
201	C₂×C₇₉	#2931	1	1	yes	characteristic
202	C₂×C₇₉	C₂×C₄×D₈	1	1	yes	characteristic
203	C₂×C₇₉	C₂×#443	1	1	yes	characteristic
204	D₇₉	—	8	2	no	—
205	#3169	—	79	1	no	—
206	#2931	—	79	1	no	—
207	#2931	D₇₉	1	1	yes	characteristic, complemented
208	#1589	—	79	4	no	—
209	C₈×D₈	—	79	4	no	—
210	#1567	—	79	1	no	—
211	#1492	—	79	1	no	—
212	#1492	—	79	1	no	—
213	C₂×C₈²	—	79	1	no	—
214	C₇₉	#17956	1	1	yes	characteristic, complemented, Sylow
215	C₂×#131	—	2	1	no	—
216	C₂×#131	—	158	1	no	—
217	#532	—	79	1	no	—
218	#532	C₂×D₇₉	1	1	yes	characteristic
219	#500	—	79	1	no	—
220	#493	—	79	1	no	—
221	#486	—	79	1	no	—
222	#486	—	79	1	no	—
223	#466	—	79	4	no	—
224	C₄×D₈	—	79	4	no	—
225	#436	—	2	1	no	—
226	#436	—	79	2	no	—
227	#436	—	158	1	no	—
228	#436	C₂×D₇₉	1	2	yes	—
229	C₈×D₄	—	2	1	no	—
230	C₈×D₄	—	79	2	no	—
231	C₈×D₄	—	158	1	no	—
232	C₈×D₄	C₂×D₇₉	1	2	yes	—
233	#423	—	79	1	no	—
234	#423	C₂×D₇₉	1	1	yes	characteristic
235	#408	—	2	1	no	—
236	#408	—	158	1	no	—
237	C₂×C₄×C₈	—	79	1	no	—
238	C₂×C₄×C₈	—	79	1	no	—
239	C₂×C₄×C₈	C₂×D₇₉	1	1	yes	characteristic
240	#335	—	79	4	no	—
241	D₄⋊C₈	—	79	4	no	—
242	D₄⋊C₈	—	79	4	no	—
243	C₈²	—	79	2	no	—
244	C₈²	—	79	2	no	—
245	C₂×#41	—	2	1	no	—
246	C₂×#41	—	158	1	no	—
247	C₂×D₈	—	79	4	no	—
248	#131	—	4	4	no	—
249	#131	—	316	4	no	—
250	C₂×M₁₆	—	2	1	no	—
251	C₂×M₁₆	—	2	2	no	—
252	C₂×M₁₆	—	158	1	no	—
253	C₂×M₁₆	—	158	2	no	—
254	C₂²×C₈	—	2	2	no	—
255	C₂²×C₈	—	79	2	no	—
256	C₂²×C₈	—	158	2	no	—
257	C₂²×C₈	—	158	1	no	—
258	C₂²×C₈	C₂²⋊D₇₉	1	1	yes	characteristic
259	C₂²×C₈	C₂²⋊D₇₉	1	1	yes	characteristic
260	C₄⋊Q₈	—	79	1	no	—
261	C₄⋊Q₈	C₄×D₇₉	1	1	yes	characteristic
262	#127	—	79	1	no	—
263	#127	C₄×D₇₉	1	1	yes	characteristic
264	#124	—	2	1	no	—
265	#124	—	158	1	no	—
266	#121	—	2	1	no	—
267	#121	—	79	2	no	—
268	#121	—	158	1	no	—
269	#121	C₄×D₇₉	1	2	yes	—
270	C₄×D₄	—	2	1	no	—
271	C₄×D₄	—	79	2	no	—
272	C₄×D₄	—	158	1	no	—
273	C₄×D₄	C₂²×D₇₉	1	2	yes	—
274	C₂×C₄²	C₂²×D₇₉	1	1	yes	characteristic
275	#107	—	79	4	no	—
276	C₄⋊C₈	—	2	1	no	—
277	C₄⋊C₈	—	79	2	no	—
278	C₄⋊C₈	—	158	1	no	—
279	C₄⋊C₈	C₂²×D₇₉	1	2	yes	—
280	#102	—	79	4	no	—
281	#102	—	79	4	no	—
282	C₂²⋊C₈	—	2	2	no	—
283	C₂²⋊C₈	—	2	2	no	—
284	C₂²⋊C₈	—	158	2	no	—
285	C₂²⋊C₈	—	158	2	no	—
286	C₄×C₈	—	79	1	no	—
287	C₄×C₈	—	79	1	no	—
288	C₄×C₈	—	79	2	no	—
289	C₄×C₈	—	79	2	no	—
290	C₄×C₈	—	158	1	no	—
291	C₄×C₈	C₂²⋊D₇₉	1	1	yes	characteristic
292	C₄×C₈	C₂²⋊D₇₉	1	1	yes	characteristic
293	C₄×C₈	C₂²×D₇₉	1	1	yes	characteristic
294	C₄×C₈	C₂²×D₇₉	1	1	yes	characteristic
295	#41	—	4	2	no	—
296	#41	—	4	2	no	—
297	#41	—	316	2	no	—
298	#41	—	316	2	no	—
299	C₂×Q₈	—	2	1	no	—
300	C₂×Q₈	—	158	1	no	—
301	C₂×D₄	—	2	2	no	—
302	C₂×D₄	—	2	1	no	—
303	C₂×D₄	—	2	1	no	—
304	C₂×D₄	—	79	2	no	—
305	C₂×D₄	—	158	2	no	—
306	C₂×D₄	—	158	1	no	—
307	C₂×D₄	—	158	1	no	—
308	C₂×D₄	C₂×C₄×D₇₉	1	2	yes	—
309	C₂²×C₄	—	2	2	no	—
310	C₂²×C₄	—	158	2	no	—
311	C₂²×C₄	C₂×C₄×D₇₉	1	1	yes	characteristic
312	C₂²×C₄	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
313	C₂²×C₄	#11929624	1	1	yes	characteristic
314	D₈	—	158	8	no	—
315	M₁₆	—	4	2	no	—
316	M₁₆	—	4	4	no	—
317	M₁₆	—	316	2	no	—
318	M₁₆	—	316	4	no	—
319	C₂×C₈	—	2	2	no	—
320	C₂×C₈	—	2	2	no	—
321	C₂×C₈	—	4	4	no	—
322	C₂×C₈	—	316	4	no	—
323	C₂×C₈	—	79	2	no	—
324	C₂×C₈	—	79	2	no	—
325	C₂×C₈	—	158	2	no	—
326	C₂×C₈	—	158	4	no	—
327	C₂×C₈	—	158	4	no	—
328	C₂×C₈	—	158	2	no	—
329	C₂×C₈	#11929609	1	4	yes	complemented
330	C₂×C₈	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
331	C₂×C₈	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
332	C₂×C₈	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
333	C₂×C₈	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
334	C₄⋊C₄	—	2	1	no	—
335	C₄⋊C₄	—	79	2	no	—
336	C₄⋊C₄	—	158	1	no	—
337	C₄⋊C₄	C₂×C₄×D₇₉	1	2	yes	—
338	C₂²⋊C₄	—	2	2	no	—
339	C₂²⋊C₄	—	2	2	no	—
340	C₂²⋊C₄	—	158	2	no	—
341	C₂²⋊C₄	—	158	2	no	—
342	C₄²	C₂×C₄×D₇₉	1	1	yes	characteristic
343	C₄²	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
344	C₄²	#11929624	1	1	yes	characteristic
345	C₄²	C₂³×D₇₉	1	1	yes	characteristic
346	C₂³	—	2	2	no	—
347	C₂³	—	158	2	no	—
348	C₂³	C₄×C₂²⋊D₇₉	1	1	yes	characteristic
349	Q₈	—	4	2	no	—
350	Q₈	—	316	2	no	—
351	D₄	—	2	4	no	—
352	D₄	—	4	4	no	—
353	D₄	—	4	2	no	—
354	D₄	—	4	2	no	—
355	D₄	—	316	4	no	—
356	D₄	—	316	2	no	—
357	D₄	—	316	2	no	—
358	D₄	—	158	4	no	—
359	C₂×C₄	—	2	2	no	—
360	C₂×C₄	—	2	2	no	—
361	C₂×C₄	—	2	2	no	—
362	C₂×C₄	—	4	2	no	—
363	C₂×C₄	—	4	2	no	—
364	C₂×C₄	—	316	2	no	—
365	C₂×C₄	—	316	2	no	—
366	C₂×C₄	—	158	2	no	—
367	C₂×C₄	C₄×C₂²⋊D₇₉	1	1	yes	characteristic
368	C₂×C₄	C₄×C₂²⋊D₇₉	1	1	yes	characteristic
369	C₂×C₄	C₄×C₂²⋊D₇₉	1	1	yes	characteristic
370	C₂×C₄	C₂×#11929609	1	2	yes	—
371	C₂×C₄	#14579181	1	2	yes	—
372	C₂×C₄	C₂²×C₄×D₇₉	1	1	yes	characteristic
373	C₂×C₄	C₂²×C₂²⋊D₇₉	1	1	yes	characteristic
374	C₂×C₄	C₂×#11929624	1	1	yes	characteristic
375	C₈	—	2	1	no	—
376	C₈	—	2	1	no	—
377	C₈	—	4	2	no	—
378	C₈	—	316	2	no	—
379	C₈	—	79	4	no	—
380	C₈	—	158	4	no	—
381	C₈	—	158	2	no	—
382	C₈	C₂×#11929609	1	2	yes	—
383	C₈	C₂×#11929609	1	2	yes	—
384	C₂²	—	2	1	no	—
385	C₂²	—	2	1	no	—
386	C₂²	—	4	2	no	—
387	C₂²	—	4	2	no	—
388	C₂²	—	4	2	no	—
389	C₂²	—	316	2	no	—
390	C₂²	—	316	2	no	—
391	C₂²	—	316	2	no	—
392	C₂²	C₄×#11929609	1	2	yes	—
393	C₂²	C₂×C₄×C₂²⋊D₇₉	1	1	yes	characteristic
394	C₄	—	2	1	no	—
395	C₄	—	2	1	no	—
396	C₄	—	4	2	no	—
397	C₄	—	316	2	no	—
398	C₄	C₄×#11929609	1	2	yes	—
399	C₄	#19098678	1	2	yes	—
400	C₄	#131×D₇₉	1	2	yes	—
401	C₄	C₂²×#11929609	1	1	yes	characteristic
402	C₄	C₂×#14579181	1	1	yes	characteristic
403	C₂	—	2	2	no	—
404	C₂	—	8	2	no	—
405	C₂	—	632	2	no	—
406	C₂	#23772110	1	1	yes	characteristic
407	C₂	C₂×C₄×#11929609	1	1	yes	characteristic
408	C₂	C₂×#19098678	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₈	C₂×C₂²⋊D₇₉
commutator	C₂×C₄×C₇₉	C₂³×C₄
Frattini	C₄²	C₂³×D₇₉
Fitting	C₇₉×#2931	C₂
socle	C₂²×C₇₉	C₂×C₄×D₄
prime radical	#23773975	C₂
cosocle	C₄²×C₇₉	C₂⁴
hypercenter	#2931	D₇₉
hypocenter	C₇₉	#17956
LCS	G ▷ C₂×C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂×C₈ ◁ C₂×C₄×C₈ ◁ #2931

Complements

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

N	H ≅ G/N	type
2. #23772113	C₂	semidirect
3. #23762283	C₂	semidirect
4. C₈×#11929609	C₂	semidirect
5. #23762158	C₂	semidirect
6. #23761851	C₂	semidirect
7. #23761850	C₂	semidirect
8. C₂×C₈×C₇₉⋊C₈	C₂	semidirect
9. C₇₉×#2931	C₂	semidirect
128. C₂×C₈×C₇₉	D₈	semidirect
178. C₇₉⋊C₈	#131	semidirect
207. #2931	D₇₉	semidirect
214. C₇₉	#17956	semidirect
329. C₂×C₈	#11929609	semidirect

Maximal subgroups

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

subgroup	index
#23773975	2
#23772113	2
#23762283	2
C₈×#11929609	2
#23762158	2
#23761851	2
#23761850	2
C₂×C₈×C₇₉⋊C₈	2
C₇₉×#2931	2
#17956	79