Subgroups — #2209×D₇₉ #34442515

Order 20224.

702 conjugacy classes of subgroups.

The subgroup lattice has 426 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Q₃₂×D₇₉	C₂	1	2	yes	maximal
2	#494×D₇₉	C₂	1	1	yes	maximal, characteristic
3	C₄×Q₁₆×D₇₉	C₂	1	1	yes	maximal, characteristic
4	#23765451	C₂	1	1	yes	maximal, characteristic, complemented
5	#23765450	C₂	1	1	yes	maximal, characteristic, complemented
6	#23765449	C₂	1	2	yes	maximal, complemented
7	#23765448	C₂	1	2	yes	maximal, complemented
8	#23765447	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄⋊C₁₆×D₇₉	C₂	1	1	yes	maximal, characteristic
10	#358×D₇₉	C₂	1	2	yes	maximal
11	C₇₉×#2209	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×Q₁₆×D₇₉	—	2	1	no	—
13	C₂×Q₁₆×D₇₉	C₂²	1	2	yes	—
14	C₂×Q₁₆×D₇₉	C₂²	1	1	yes	characteristic
15	C₄⋊Q₈×D₇₉	—	2	1	no	—
16	C₄×Q₈×D₇₉	—	2	1	no	—
17	C₂×Dic₆₃₂	C₂²	1	2	yes	—
18	C₂×#14579107	C₂²	1	2	yes	—
19	C₂×#14579107	C₂²	1	2	yes	—
20	Q₃₂×D₇₉	—	2	8	no	—
21	C₂×C₁₆×D₇₉	C₂²	1	2	yes	—
22	#19098943	C₂²	1	1	yes	characteristic
23	#19098942	—	2	1	no	—
24	#19098941	—	2	1	no	—
25	#19098941	C₂²	1	2	yes	—
26	C₄×Dic₃₁₆	C₂²	1	1	yes	characteristic
27	Q₁₆×Dic₇₉	C₂²	1	1	yes	characteristic
28	#19098657	C₂²	1	1	yes	characteristic
29	C₄×#11929614	—	2	1	no	—
30	#19098655	—	2	1	no	—
31	#107×D₇₉	C₂²	1	1	yes	characteristic
32	#103×D₇₉	—	2	1	no	—
33	C₄×C₈×D₇₉	C₂²	1	1	yes	characteristic
34	C₄⋊(C₇₉⋊C₁₆)	C₂²	1	1	yes	characteristic
35	Dic₇₉⋊C₁₆	C₂²	1	2	yes	—
36	#19098368	C₂²	1	2	yes	—
37	#19098367	C₂²	1	2	yes	—
38	#19098366	C₂²	1	2	yes	—
39	C₂×Q₃₂×C₇₉	C₂²	1	2	yes	—
40	#494×C₇₉	C₂²	1	1	yes	characteristic
41	C₄×Q₁₆×C₇₉	C₂²	1	1	yes	characteristic
42	C₄⋊C₁₆×C₇₉	C₂²	1	1	yes	characteristic
43	#358×C₇₉	C₂²	1	2	yes	—
44	C₂×Q₈×D₇₉	—	2	1	no	—
45	C₂×Q₈×D₇₉	—	2	2	no	—
46	C₂×Dic₃₁₆	—	2	1	no	—
47	C₂×Dic₃₁₆	C₂³	1	2	yes	—
48	C₂×Dic₃₁₆	C₂³	1	1	yes	characteristic
49	C₂×#11929614	—	2	1	no	—
50	C₂×#11929614	—	2	2	no	—
51	C₂×#11929614	—	2	2	no	—
52	Q₁₆×D₇₉	—	2	4	no	—
53	Q₁₆×D₇₉	—	2	2	no	—
54	Q₁₆×D₇₉	—	2	4	no	—
55	Q₁₆×D₇₉	—	4	4	no	—
56	Q₁₆×D₇₉	D₄	1	4	yes	—
57	C₂×C₈×D₇₉	D₄	1	1	yes	characteristic
58	C₂×C₈×D₇₉	C₂³	1	1	yes	characteristic
59	#14579161	—	2	1	no	—
60	#14579160	—	4	1	no	—
61	#14579160	—	4	1	no	—
62	#14579159	—	2	2	no	—
63	Q₈×Dic₇₉	—	2	1	no	—
64	C₄×Dic₁₅₈	—	2	1	no	—
65	C₄×Dic₁₅₈	—	4	1	no	—
66	#14579126	—	2	1	no	—
67	#14579126	—	4	1	no	—
68	C₄⋊C₄×D₇₉	—	2	1	no	—
69	C₄⋊C₄×D₇₉	—	4	1	no	—
70	C₄⋊C₄×D₇₉	—	4	1	no	—
71	C₄⋊C₄×D₇₉	—	4	1	no	—
72	C₄²×D₇₉	—	4	1	no	—
73	C₄²×D₇₉	D₄	1	1	yes	characteristic
74	Dic₆₃₂	—	2	4	no	—
75	#14579107	—	2	4	no	—
76	#14579107	—	2	4	no	—
77	C₂×C₇₉⋊C₁₆	C₂³	1	2	yes	—
78	C₁₆×D₇₉	—	2	4	no	—
79	#14579095	C₂³	1	1	yes	characteristic
80	#14579094	—	2	1	no	—
81	#14579086	—	2	1	no	—
82	#14579085	—	2	1	no	—
83	#14579084	—	2	1	no	—
84	C₄×C₇₉⋊C₈	D₄	1	1	yes	characteristic
85	C₈×Dic₇₉	D₄	1	1	yes	characteristic
86	C₈×Dic₇₉	C₂³	1	1	yes	characteristic
87	C₂×Q₁₆×C₇₉	—	2	1	no	—
88	C₂×Q₁₆×C₇₉	C₂³	1	2	yes	—
89	C₂×Q₁₆×C₇₉	C₂³	1	1	yes	characteristic
90	C₄⋊Q₈×C₇₉	—	2	1	no	—
91	C₄×Q₈×C₇₉	—	2	1	no	—
92	Q₃₂×C₇₉	—	2	4	no	—
93	C₂×C₁₆×C₇₉	C₂³	1	2	yes	—
94	#107×C₇₉	C₂³	1	1	yes	characteristic
95	#103×C₇₉	—	2	1	no	—
96	C₄×C₈×C₇₉	C₂³	1	1	yes	characteristic
97	C₂×Dic₁₅₈	—	2	1	no	—
98	C₂×Dic₁₅₈	—	2	2	no	—
99	C₂×Dic₁₅₈	—	4	1	no	—
100	C₂×Dic₁₅₈	—	4	2	no	—
101	Q₈×D₇₉	—	2	4	no	—
102	Q₈×D₇₉	—	4	2	no	—
103	Q₈×D₇₉	—	4	4	no	—
104	Q₈×D₇₉	—	4	4	no	—
105	C₂×C₄×D₇₉	—	4	1	no	—
106	C₂×C₄×D₇₉	—	4	2	no	—
107	C₂×C₄×D₇₉	—	4	1	no	—
108	C₂×C₄×D₇₉	D₈	1	1	yes	characteristic
109	C₂×C₄×D₇₉	D₈	1	1	yes	characteristic
110	C₂×C₄×D₇₉	C₂×D₄	1	1	yes	characteristic
111	Dic₃₁₆	—	2	2	no	—
112	Dic₃₁₆	—	2	1	no	—
113	Dic₃₁₆	—	2	2	no	—
114	Dic₃₁₆	—	4	2	no	—
115	Dic₃₁₆	C₂×D₄	1	2	yes	—
116	#11929614	—	2	4	no	—
117	#11929614	—	4	4	no	—
118	#11929614	—	4	4	no	—
119	C₂×C₇₉⋊C₈	C₂×D₄	1	1	yes	characteristic
120	C₂×C₇₉⋊C₈	C₂×D₄	1	1	yes	characteristic
121	C₈×D₇₉	—	2	2	no	—
122	C₈×D₇₉	C₂×D₄	1	2	yes	—
123	C₈×D₇₉	#41	1	2	yes	—
124	C₄⋊Dic₇₉	—	2	1	no	—
125	C₄⋊Dic₇₉	—	4	1	no	—
126	C₄⋊Dic₇₉	—	4	1	no	—
127	C₄⋊Dic₇₉	—	4	1	no	—
128	Dic₇₉⋊C₄	—	4	1	no	—
129	Dic₇₉⋊C₄	—	4	1	no	—
130	Dic₇₉⋊C₄	—	4	2	no	—
131	Dic₇₉⋊C₄	—	4	2	no	—
132	Dic₇₉⋊C₄	—	4	1	no	—
133	C₄×Dic₇₉	—	4	1	no	—
134	C₄×Dic₇₉	—	4	1	no	—
135	C₄×Dic₇₉	—	4	1	no	—
136	C₄×Dic₇₉	D₈	1	1	yes	characteristic
137	C₄×Dic₇₉	D₈	1	1	yes	characteristic
138	C₄×Dic₇₉	C₂×D₄	1	1	yes	characteristic
139	C₇₉⋊C₁₆	—	2	2	no	—
140	C₂×Q₈×C₇₉	—	2	1	no	—
141	C₂×Q₈×C₇₉	—	2	2	no	—
142	Q₁₆×C₇₉	—	2	1	no	—
143	Q₁₆×C₇₉	—	2	2	no	—
144	Q₁₆×C₇₉	—	2	2	no	—
145	Q₁₆×C₇₉	—	4	2	no	—
146	Q₁₆×C₇₉	C₂×D₄	1	2	yes	—
147	C₂×C₈×C₇₉	C₂×D₄	1	1	yes	characteristic
148	C₂×C₈×C₇₉	C₂⁴	1	1	yes	characteristic
149	C₄⋊C₄×C₇₉	—	2	1	no	—
150	C₄⋊C₄×C₇₉	—	4	1	no	—
151	C₄⋊C₄×C₇₉	—	4	1	no	—
152	C₄⋊C₄×C₇₉	—	4	1	no	—
153	C₄²×C₇₉	—	4	1	no	—
154	C₄²×C₇₉	C₂×D₄	1	1	yes	characteristic
155	C₁₆×C₇₉	—	2	2	no	—
156	C₂²×D₇₉	C₂×D₈	1	1	yes	characteristic
157	Q₈×C₇₉	—	2	2	no	—
158	Q₈×C₇₉	—	4	1	no	—
159	Q₈×C₇₉	—	4	2	no	—
160	Q₈×C₇₉	—	4	2	no	—
161	C₂×C₄×C₇₉	—	4	1	no	—
162	C₂×C₄×C₇₉	—	4	1	no	—
163	C₂×C₄×C₇₉	—	4	2	no	—
164	C₂×C₄×C₇₉	C₂×D₈	1	1	yes	characteristic
165	C₂×C₄×C₇₉	C₂×D₈	1	1	yes	characteristic
166	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
167	C₂×Dic₇₉	—	4	1	no	—
168	C₂×Dic₇₉	—	4	1	no	—
169	C₂×Dic₇₉	—	4	2	no	—
170	C₂×Dic₇₉	C₂×D₈	1	1	yes	characteristic
171	C₂×Dic₇₉	C₂×D₈	1	1	yes	characteristic
172	C₂×Dic₇₉	C₂×D₈	1	1	yes	characteristic
173	C₄×D₇₉	—	2	2	no	—
174	C₄×D₇₉	—	4	4	no	—
175	C₄×D₇₉	—	8	4	no	—
176	C₄×D₇₉	—	8	2	no	—
177	C₄×D₇₉	Q₃₂	1	4	yes	complemented
178	C₄×D₇₉	#121	1	2	yes	—
179	C₄×D₇₉	AGL(1,ℤ/8)	1	2	yes	—
180	Dic₁₅₈	—	2	2	no	—
181	Dic₁₅₈	—	4	1	no	—
182	Dic₁₅₈	—	4	4	no	—
183	Dic₁₅₈	—	4	2	no	—
184	Dic₁₅₈	—	4	2	no	—
185	Dic₁₅₈	—	8	4	no	—
186	C₈×C₇₉	—	2	1	no	—
187	C₈×C₇₉	C₂²×D₄	1	1	yes	characteristic
188	C₈×C₇₉	C₂×#41	1	1	yes	characteristic
189	C₇₉⋊C₈	—	2	1	no	—
190	C₇₉⋊C₈	#121	1	2	yes	—
191	C₂²×C₇₉	C₂²×D₈	1	1	yes	characteristic
192	C₂×D₇₉	#459	1	2	yes	—
193	C₂×D₇₉	C₂×Q₃₂	1	2	yes	—
194	C₂×D₇₉	#510	1	2	yes	—
195	C₄×C₇₉	—	2	1	no	—
196	C₄×C₇₉	—	4	2	no	—
197	C₄×C₇₉	—	8	1	no	—
198	C₄×C₇₉	—	8	2	no	—
199	C₄×C₇₉	C₂×Q₃₂	1	2	yes	complemented
200	C₄×C₇₉	C₂×#121	1	1	yes	characteristic
201	C₄×C₇₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
202	Dic₇₉	—	2	1	no	—
203	Dic₇₉	—	4	2	no	—
204	Dic₇₉	—	8	1	no	—
205	Dic₇₉	—	8	2	no	—
206	Dic₇₉	#459	1	2	yes	—
207	Dic₇₉	C₂×Q₃₂	1	2	yes	complemented
208	C₂×#2209	—	79	1	no	maximal, Sylow
209	C₂×C₇₉	C₂×#459	1	1	yes	characteristic
210	C₂×C₇₉	C₂²×Q₃₂	1	1	yes	characteristic
211	C₂×C₇₉	C₂×#510	1	1	yes	characteristic
212	D₇₉	#2209	1	4	yes	direct product factor
213	C₂²×Q₃₂	—	79	2	no	—
214	C₂×#494	—	79	1	no	—
215	C₂×C₄×Q₁₆	—	79	1	no	—
216	#2209	—	79	2	no	—
217	#2209	—	79	1	no	—
218	#2209	—	79	1	no	—
219	#2209	—	79	1	no	—
220	#2209	—	79	2	no	—
221	#2209	D₇₉	1	1	yes	characteristic, direct product factor
222	C₂×C₄⋊C₁₆	—	79	1	no	—
223	C₂×#358	—	79	2	no	—
224	C₇₉	C₂×#2209	1	1	yes	characteristic, complemented, Sylow
225	C₂²×Q₁₆	—	79	1	no	—
226	C₂²×Q₁₆	—	79	2	no	—
227	C₂²×Q₁₆	—	158	1	no	—
228	C₂×C₄⋊Q₈	—	158	1	no	—
229	C₂×C₄×Q₈	—	158	1	no	—
230	C₂×Q₃₂	—	79	2	no	—
231	C₂×Q₃₂	—	79	2	no	—
232	C₂×Q₃₂	—	79	2	no	—
233	C₂×Q₃₂	—	158	8	no	—
234	C₂×Q₃₂	C₂×D₇₉	1	2	yes	—
235	C₂²×C₁₆	—	79	2	no	—
236	#494	—	79	2	no	—
237	#494	—	79	1	no	—
238	#494	—	158	1	no	—
239	#494	—	158	1	no	—
240	#494	C₂×D₇₉	1	1	yes	characteristic
241	C₄×Q₁₆	—	79	1	no	—
242	C₄×Q₁₆	—	79	1	no	—
243	C₄×Q₁₆	—	79	1	no	—
244	C₄×Q₁₆	—	158	1	no	—
245	C₄×Q₁₆	—	158	1	no	—
246	C₄×Q₁₆	C₂×D₇₉	1	1	yes	characteristic
247	C₂×#107	—	79	1	no	—
248	C₂×#103	—	158	1	no	—
249	C₂×C₄×C₈	—	79	1	no	—
250	C₄⋊C₁₆	—	79	2	no	—
251	C₄⋊C₁₆	—	79	1	no	—
252	C₄⋊C₁₆	C₂×D₇₉	1	1	yes	characteristic
253	#358	—	79	2	no	—
254	#358	—	79	2	no	—
255	#358	—	79	2	no	—
256	#358	C₂×D₇₉	1	2	yes	—
257	C₂²×Q₈	—	158	2	no	—
258	C₂²×Q₈	—	158	1	no	—
259	C₂×Q₁₆	—	2	1	no	—
260	C₂×Q₁₆	—	316	4	no	—
261	C₂×Q₁₆	—	79	4	no	—
262	C₂×Q₁₆	—	79	1	no	—
263	C₂×Q₁₆	—	79	2	no	—
264	C₂×Q₁₆	—	158	4	no	—
265	C₂×Q₁₆	—	158	4	no	—
266	C₂×Q₁₆	—	158	2	no	—
267	C₂×Q₁₆	—	158	2	no	—
268	C₂×Q₁₆	—	158	2	no	—
269	C₂×Q₁₆	—	158	1	no	—
270	C₂×Q₁₆	—	158	1	no	—
271	C₂×Q₁₆	C₂²×D₇₉	1	2	yes	—
272	C₂×Q₁₆	C₂²×D₇₉	1	1	yes	characteristic
273	C₂²×C₈	—	79	1	no	—
274	C₂²×C₈	—	79	1	no	—
275	C₄⋊Q₈	—	2	1	no	—
276	C₄⋊Q₈	—	316	1	no	—
277	C₄⋊Q₈	—	316	1	no	—
278	C₄⋊Q₈	—	158	2	no	—
279	C₄⋊Q₈	—	158	1	no	—
280	C₄×Q₈	—	2	1	no	—
281	C₄×Q₈	—	316	1	no	—
282	C₄×Q₈	—	316	1	no	—
283	C₄×Q₈	—	158	1	no	—
284	C₄×Q₈	—	158	1	no	—
285	C₄×Q₈	—	158	1	no	—
286	C₂×C₄⋊C₄	—	316	1	no	—
287	C₂×C₄⋊C₄	—	316	1	no	—
288	C₂×C₄⋊C₄	—	316	1	no	—
289	C₂×C₄⋊C₄	—	158	1	no	—
290	C₂×C₄²	—	316	1	no	—
291	C₂×C₄²	—	79	1	no	—
292	Q₃₂	—	2	4	no	—
293	Q₃₂	—	158	4	no	—
294	Q₃₂	—	158	4	no	—
295	Q₃₂	—	158	4	no	—
296	C₂×C₁₆	—	79	2	no	—
297	C₂×C₁₆	—	158	4	no	—
298	C₂×C₁₆	C₂²×D₇₉	1	2	yes	—
299	#107	—	79	1	no	—
300	#107	—	158	1	no	—
301	#107	C₂²×D₇₉	1	1	yes	characteristic
302	#103	—	2	1	no	—
303	#103	—	158	1	no	—
304	#103	—	158	1	no	—
305	#103	—	158	1	no	—
306	C₄×C₈	—	79	1	no	—
307	C₄×C₈	—	79	1	no	—
308	C₄×C₈	—	79	1	no	—
309	C₄×C₈	C₂²×D₇₉	1	1	yes	characteristic
310	C₂×Q₈	—	2	1	no	—
311	C₂×Q₈	—	2	2	no	—
312	C₂×Q₈	—	316	1	no	—
313	C₂×Q₈	—	316	2	no	—
314	C₂×Q₈	—	316	2	no	—
315	C₂×Q₈	—	316	4	no	—
316	C₂×Q₈	—	316	4	no	—
317	C₂×Q₈	—	158	4	no	—
318	C₂×Q₈	—	158	2	no	—
319	C₂×Q₈	—	158	1	no	—
320	C₂²×C₄	—	316	1	no	—
321	C₂²×C₄	—	316	1	no	—
322	C₂²×C₄	—	316	2	no	—
323	C₂²×C₄	—	79	1	no	—
324	C₂²×C₄	—	79	1	no	—
325	C₂²×C₄	—	79	1	no	—
326	Q₁₆	—	2	1	no	—
327	Q₁₆	—	2	2	no	—
328	Q₁₆	—	2	2	no	—
329	Q₁₆	—	4	2	no	—
330	Q₁₆	—	316	2	no	—
331	Q₁₆	—	316	4	no	—
332	Q₁₆	—	316	4	no	—
333	Q₁₆	—	79	2	no	—
334	Q₁₆	—	158	4	no	—
335	Q₁₆	—	158	2	no	—
336	Q₁₆	—	158	1	no	—
337	Q₁₆	—	158	2	no	—
338	Q₁₆	D₄×D₇₉	1	2	yes	—
339	C₂×C₈	—	79	1	no	—
340	C₂×C₈	—	79	2	no	—
341	C₂×C₈	—	79	2	no	—
342	C₂×C₈	—	79	1	no	—
343	C₂×C₈	—	158	2	no	—
344	C₂×C₈	D₄×D₇₉	1	1	yes	characteristic
345	C₂×C₈	C₂³×D₇₉	1	1	yes	characteristic
346	C₄⋊C₄	—	2	1	no	—
347	C₄⋊C₄	—	4	1	no	—
348	C₄⋊C₄	—	4	1	no	—
349	C₄⋊C₄	—	4	1	no	—
350	C₄⋊C₄	—	316	1	no	—
351	C₄⋊C₄	—	316	2	no	—
352	C₄⋊C₄	—	316	2	no	—
353	C₄⋊C₄	—	316	1	no	—
354	C₄⋊C₄	—	316	1	no	—
355	C₄⋊C₄	—	316	1	no	—
356	C₄⋊C₄	—	316	1	no	—
357	C₄⋊C₄	—	316	1	no	—
358	C₄⋊C₄	—	158	1	no	—
359	C₄²	—	4	1	no	—
360	C₄²	—	316	1	no	—
361	C₄²	—	316	1	no	—
362	C₄²	—	316	1	no	—
363	C₄²	—	79	1	no	—
364	C₄²	—	79	1	no	—
365	C₄²	—	79	1	no	—
366	C₄²	D₄×D₇₉	1	1	yes	characteristic
367	C₁₆	—	2	2	no	—
368	C₁₆	—	158	2	no	—
369	C₂³	—	79	1	no	—
370	Q₈	—	2	2	no	—
371	Q₈	—	4	1	no	—
372	Q₈	—	4	2	no	—
373	Q₈	—	4	2	no	—
374	Q₈	—	316	4	no	—
375	Q₈	—	316	1	no	—
376	Q₈	—	316	2	no	—
377	Q₈	—	316	2	no	—
378	Q₈	—	632	4	no	—
379	Q₈	—	158	2	no	—
380	C₂×C₄	—	4	1	no	—
381	C₂×C₄	—	4	1	no	—
382	C₂×C₄	—	4	2	no	—
383	C₂×C₄	—	316	4	no	—
384	C₂×C₄	—	316	1	no	—
385	C₂×C₄	—	316	1	no	—
386	C₂×C₄	—	316	2	no	—
387	C₂×C₄	—	79	1	no	—
388	C₂×C₄	—	79	1	no	—
389	C₂×C₄	—	79	4	no	—
390	C₂×C₄	—	79	2	no	—
391	C₂×C₄	—	79	2	no	—
392	C₂×C₄	—	79	1	no	—
393	C₂×C₄	—	632	4	no	—
394	C₂×C₄	—	632	2	no	—
395	C₂×C₄	—	158	2	no	—
396	C₂×C₄	D₈×D₇₉	1	1	yes	characteristic
397	C₂×C₄	D₈×D₇₉	1	1	yes	characteristic
398	C₂×C₄	C₂×D₄×D₇₉	1	1	yes	characteristic
399	C₈	—	2	1	no	—
400	C₈	—	79	2	no	—
401	C₈	—	158	1	no	—
402	C₈	C₂×D₄×D₇₉	1	1	yes	characteristic
403	C₈	#41×D₇₉	1	1	yes	characteristic
404	C₂²	—	79	2	no	—
405	C₂²	—	79	2	no	—
406	C₂²	—	79	2	no	—
407	C₂²	C₂×D₈×D₇₉	1	1	yes	characteristic
408	C₄	—	2	1	no	—
409	C₄	—	4	2	no	—
410	C₄	—	8	1	no	—
411	C₄	—	8	2	no	—
412	C₄	—	316	2	no	—
413	C₄	—	79	2	no	—
414	C₄	—	79	2	no	—
415	C₄	—	632	1	no	—
416	C₄	—	632	2	no	—
417	C₄	—	158	1	no	—
418	C₄	Q₃₂×D₇₉	1	2	yes	complemented
419	C₄	#121×D₇₉	1	1	yes	characteristic
420	C₄	AGL(1,ℤ/8)×D₇₉	1	1	yes	characteristic
421	C₂	—	79	4	no	—
422	C₂	#459×D₇₉	1	1	yes	characteristic
423	C₂	C₂×Q₃₂×D₇₉	1	1	yes	characteristic
424	C₂	#510×D₇₉	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×D₈×D₇₉
commutator, cosocle	C₂×C₈×C₇₉	C₂⁴
Frattini	C₂×C₈	C₂³×D₇₉
Fitting	C₇₉×#2209	C₂
socle	C₂²×C₇₉	C₂²×D₈
prime radical	C₂²×D₇₉	C₂×D₈
hypercenter	#2209	D₇₉
hypocenter	C₇₉	C₂×#2209
LCS	G ▷ C₂×C₈×C₇₉ ▷ C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ #2209

Complements

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

N	H ≅ G/N	type
4. #23765451	C₂	semidirect
5. #23765450	C₂	semidirect
6. #23765449	C₂	semidirect
7. #23765448	C₂	semidirect
8. #23765447	C₂	semidirect
11. C₇₉×#2209	C₂	semidirect
177. C₄×D₇₉	Q₃₂	semidirect
199. C₄×C₇₉	C₂×Q₃₂	semidirect
207. Dic₇₉	C₂×Q₃₂	semidirect
212. D₇₉	#2209	direct (N × H)
221. #2209	D₇₉	direct (N × H)
224. C₇₉	C₂×#2209	semidirect
418. C₄	Q₃₂×D₇₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×Q₃₂×D₇₉	2
#494×D₇₉	2
C₄×Q₁₆×D₇₉	2
#23765451	2
#23765450	2
#23765449	2
#23765448	2
#23765447	2
C₄⋊C₁₆×D₇₉	2
#358×D₇₉	2
C₇₉×#2209	2
C₂×#2209	79

Subgroups — #2209×D79 #34442515

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #2209×D₇₉ #34442515