Subgroups — Q₁₆×Dic₇₉⋊C₄ #34306696

Order 20224.

926 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	C₂×Q₁₆×Dic₇₉	C₂	1	1	yes	maximal, characteristic
2	C₂×Q₁₆×Dic₇₉	C₂	1	1	yes	maximal, characteristic
3	Q₈×Dic₇₉⋊C₄	C₂	1	2	yes	maximal
4	#23764133	C₂	1	1	yes	maximal, characteristic
5	#23764131	C₂	1	1	yes	maximal, characteristic
6	#23763654	C₂	1	2	yes	maximal
7	#23763652	C₂	1	2	yes	maximal
8	#23763558	C₂	1	1	yes	maximal, characteristic
9	#23763403	C₂	1	2	yes	maximal
10	C₈×Dic₇₉⋊C₄	C₂	1	1	yes	maximal, characteristic
11	C₂×C₄×Q₁₆×C₇₉	C₂	1	1	yes	maximal, characteristic
12	C₂×Q₈×Dic₇₉	C₂²	1	2	yes	—
13	C₂×Q₈×Dic₇₉	C₂²	1	2	yes	—
14	Q₁₆×Dic₇₉	—	2	4	no	—
15	Q₁₆×Dic₇₉	C₄	1	8	yes	complemented
16	C₂×#14579095	C₂²	1	1	yes	characteristic
17	C₂×#14579095	C₂²	1	1	yes	characteristic
18	C₂×#14579094	C₂²	1	2	yes	—
19	C₂×Dic₇₉⋊C₈	C₂²	1	1	yes	characteristic
20	C₂×#14579085	C₂²	1	2	yes	—
21	C₂×#14579085	C₂²	1	2	yes	—
22	C₂×C₈×Dic₇₉	C₂²	1	1	yes	characteristic
23	C₂×C₈×Dic₇₉	C₂²	1	1	yes	characteristic
24	#19098461	—	2	2	no	—
25	#19098461	C₂²	1	2	yes	—
26	#19098459	—	2	2	no	—
27	#19098459	C₂²	1	2	yes	—
28	#19098432	—	2	2	no	—
29	#19098432	C₂²	1	2	yes	—
30	C₄×Dic₇₉⋊C₄	—	2	2	no	—
31	C₄×Dic₇₉⋊C₄	C₂²	1	1	yes	characteristic
32	#19098326	C₂²	1	2	yes	—
33	#19098325	C₂²	1	2	yes	—
34	#19098318	C₂²	1	1	yes	characteristic
35	#19098317	C₂²	1	1	yes	characteristic
36	C₂²×Q₁₆×C₇₉	C₂²	1	1	yes	characteristic
37	C₂×C₄×Q₈×C₇₉	C₂²	1	2	yes	—
38	C₄×Q₁₆×C₇₉	—	2	4	no	—
39	C₂×#107×C₇₉	C₂²	1	1	yes	characteristic
40	C₂×#103×C₇₉	C₂²	1	2	yes	—
41	C₂×C₄×C₈×C₇₉	C₂²	1	1	yes	characteristic
42	C₂²×C₇₉⋊C₈	C₂³	1	1	yes	characteristic
43	C₂²×C₇₉⋊C₈	C₂³	1	1	yes	characteristic
44	Q₈×Dic₇₉	—	2	4	no	—
45	Q₈×Dic₇₉	—	2	4	no	—
46	Q₈×Dic₇₉	—	4	2	no	—
47	Q₈×Dic₇₉	C₂×C₄	1	8	yes	—
48	C₂×C₄⋊Dic₇₉	—	2	2	no	—
49	C₂×C₄⋊Dic₇₉	—	2	2	no	—
50	C₂×C₄⋊Dic₇₉	C₂³	1	2	yes	—
51	C₂×C₄⋊Dic₇₉	C₂³	1	2	yes	—
52	C₂×Dic₇₉⋊C₄	—	2	2	no	—
53	C₂×Dic₇₉⋊C₄	—	2	2	no	—
54	C₂×Dic₇₉⋊C₄	—	2	2	no	—
55	C₂×Dic₇₉⋊C₄	—	2	2	no	—
56	C₂×Dic₇₉⋊C₄	D₄	1	1	yes	characteristic
57	C₂×Dic₇₉⋊C₄	D₄	1	1	yes	characteristic
58	C₂×C₄×Dic₇₉	—	2	2	no	—
59	C₂×C₄×Dic₇₉	—	2	2	no	—
60	C₂×C₄×Dic₇₉	C₂³	1	1	yes	characteristic
61	C₂×C₄×Dic₇₉	C₂³	1	1	yes	characteristic
62	#14579095	—	2	2	no	—
63	#14579095	C₂×C₄	1	4	yes	—
64	#14579094	—	4	2	no	—
65	Dic₇₉⋊C₈	—	2	2	no	—
66	#14579085	—	2	4	no	—
67	#14579085	C₂×C₄	1	8	yes	—
68	C₈×Dic₇₉	—	2	2	no	—
69	C₈×Dic₇₉	C₂×C₄	1	4	yes	—
70	C₇₉⋊#95	—	2	2	no	—
71	C₇₉⋊#95	—	2	2	no	—
72	C₇₉⋊#95	D₄	1	1	yes	characteristic
73	C₇₉⋊#95	D₄	1	1	yes	characteristic
74	C₂²×Q₈×C₇₉	C₂³	1	2	yes	—
75	C₂×Q₁₆×C₇₉	C₂×C₄	1	4	yes	—
76	C₂×Q₁₆×C₇₉	D₄	1	4	yes	—
77	C₂×Q₁₆×C₇₉	Q₈	1	4	yes	—
78	C₂²×C₈×C₇₉	C₂³	1	1	yes	characteristic
79	C₂²×C₈×C₇₉	C₂³	1	1	yes	characteristic
80	C₄×Q₈×C₇₉	—	2	4	no	—
81	C₄×Q₈×C₇₉	—	4	2	no	—
82	C₂×C₄⋊C₄×C₇₉	—	2	2	no	—
83	C₂×C₄⋊C₄×C₇₉	C₂³	1	2	yes	—
84	C₂×C₄²×C₇₉	—	2	2	no	—
85	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
86	#107×C₇₉	—	2	2	no	—
87	#103×C₇₉	—	2	4	no	—
88	C₄×C₈×C₇₉	—	2	2	no	—
89	C₂²×Dic₇₉	—	2	2	no	—
90	C₂²×Dic₇₉	—	2	2	no	—
91	C₂²×Dic₇₉	C₂×D₄	1	1	yes	characteristic
92	C₂²×Dic₇₉	C₂×D₄	1	1	yes	characteristic
93	C₂²×Dic₇₉	C₂×D₄	1	1	yes	characteristic
94	C₂²×Dic₇₉	C₂×D₄	1	1	yes	characteristic
95	C₂×C₇₉⋊C₈	—	2	1	no	—
96	C₂×C₇₉⋊C₈	—	2	1	no	—
97	C₂×C₇₉⋊C₈	—	2	1	no	—
98	C₂×C₇₉⋊C₈	—	2	1	no	—
99	C₂×C₇₉⋊C₈	—	2	1	no	—
100	C₂×C₇₉⋊C₈	C₂²×C₄	1	2	yes	—
101	C₄⋊Dic₇₉	—	2	8	no	—
102	C₄⋊Dic₇₉	—	2	2	no	—
103	C₄⋊Dic₇₉	—	2	2	no	—
104	C₄⋊Dic₇₉	—	2	2	no	—
105	C₄⋊Dic₇₉	—	4	4	no	—
106	C₄⋊Dic₇₉	C₂²×C₄	1	4	yes	—
107	Dic₇₉⋊C₄	—	2	2	no	—
108	Dic₇₉⋊C₄	—	4	4	no	—
109	Dic₇₉⋊C₄	—	8	2	no	—
110	Dic₇₉⋊C₄	—	8	2	no	—
111	Dic₇₉⋊C₄	—	8	2	no	—
112	Dic₇₉⋊C₄	Q₁₆	1	4	yes	direct product factor
113	C₄×Dic₇₉	—	2	8	no	—
114	C₄×Dic₇₉	—	2	1	no	—
115	C₄×Dic₇₉	—	2	1	no	—
116	C₄×Dic₇₉	—	4	4	no	—
117	C₄×Dic₇₉	C₂²×C₄	1	2	yes	—
118	C₄×Dic₇₉	#41	1	2	yes	—
119	C₂×Q₈×C₇₉	—	2	2	no	—
120	C₂×Q₈×C₇₉	—	2	2	no	—
121	C₂×Q₈×C₇₉	—	2	2	no	—
122	C₂×Q₈×C₇₉	C₂²×C₄	1	4	yes	—
123	C₂×Q₈×C₇₉	C₂×D₄	1	4	yes	—
124	C₂×Q₈×C₇₉	C₂×Q₈	1	4	yes	—
125	C₂²×C₄×C₇₉	—	2	2	no	—
126	C₂²×C₄×C₇₉	—	2	2	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	C₂⁴	1	1	yes	characteristic
130	Q₁₆×C₇₉	C₄⋊C₄	1	16	yes	complemented
131	C₂×C₈×C₇₉	—	2	1	no	—
132	C₂×C₈×C₇₉	—	2	1	no	—
133	C₂×C₈×C₇₉	—	2	1	no	—
134	C₂×C₈×C₇₉	C₂²×C₄	1	2	yes	—
135	C₂×C₈×C₇₉	C₂×D₄	1	2	yes	—
136	C₂×C₈×C₇₉	C₂×Q₈	1	2	yes	—
137	C₄⋊C₄×C₇₉	—	2	2	no	—
138	C₄⋊C₄×C₇₉	—	2	2	no	—
139	C₄⋊C₄×C₇₉	—	4	4	no	—
140	C₄²×C₇₉	—	2	1	no	—
141	C₄²×C₇₉	—	2	1	no	—
142	C₄²×C₇₉	—	4	4	no	—
143	C₂³×C₇₉	C₂²×D₄	1	1	yes	characteristic
144	Q₈×C₇₉	—	2	4	no	—
145	Q₈×C₇₉	—	2	4	no	—
146	Q₈×C₇₉	—	2	4	no	—
147	Q₈×C₇₉	C₂×C₄⋊C₄	1	8	yes	—
148	C₂×C₄×C₇₉	—	2	4	no	—
149	C₂×C₄×C₇₉	—	2	4	no	—
150	C₂×C₄×C₇₉	—	2	1	no	—
151	C₂×C₄×C₇₉	—	2	4	no	—
152	C₂×C₄×C₇₉	—	2	1	no	—
153	C₂×C₄×C₇₉	—	2	1	no	—
154	C₂×C₄×C₇₉	—	2	1	no	—
155	C₂×C₄×C₇₉	—	2	1	no	—
156	C₂×C₄×C₇₉	—	4	2	no	—
157	C₂×C₄×C₇₉	—	4	2	no	—
158	C₂×C₄×C₇₉	—	4	2	no	—
159	C₂×C₄×C₇₉	C₂×Q₁₆	1	2	yes	—
160	C₂×C₄×C₇₉	C₂³×C₄	1	1	yes	characteristic
161	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
162	C₂×C₄×C₇₉	C₂²×Q₈	1	1	yes	characteristic
163	C₂×C₄×C₇₉	C₂×#41	1	1	yes	characteristic
164	C₂×C₄×C₇₉	H(5,𝔽₂)	1	1	yes	characteristic
165	C₂×C₄×C₇₉	2₋¹⁺⁴	1	1	yes	characteristic
166	C₂×Dic₇₉	—	2	1	no	—
167	C₂×Dic₇₉	—	2	1	no	—
168	C₂×Dic₇₉	—	2	1	no	—
169	C₂×Dic₇₉	—	2	1	no	—
170	C₂×Dic₇₉	—	2	4	no	—
171	C₂×Dic₇₉	—	2	1	no	—
172	C₂×Dic₇₉	—	2	1	no	—
173	C₂×Dic₇₉	—	2	1	no	—
174	C₂×Dic₇₉	—	4	2	no	—
175	C₂×Dic₇₉	—	4	2	no	—
176	C₂×Dic₇₉	—	4	2	no	—
177	C₂×Dic₇₉	—	4	2	no	—
178	C₂×Dic₇₉	—	4	2	no	—
179	C₂×Dic₇₉	C₄×D₄	1	2	yes	—
180	C₂×Dic₇₉	C₄×D₄	1	2	yes	—
181	C₂×Dic₇₉	C₂×Q₁₆	1	2	yes	—
182	C₂×Dic₇₉	C₂×Q₁₆	1	2	yes	—
183	C₂×Dic₇₉	#135	1	2	yes	—
184	C₈×C₇₉	—	4	1	no	—
185	C₈×C₇₉	C₂×C₄⋊C₄	1	4	yes	—
186	C₇₉⋊C₈	—	2	2	no	—
187	C₇₉⋊C₈	—	4	1	no	—
188	C₂²×C₇₉	C₂×C₄×D₄	1	1	yes	characteristic
189	C₂²×C₇₉	D₄²	1	1	yes	characteristic
190	C₂²×C₇₉	D₄×Q₈	1	1	yes	characteristic
191	C₂²×C₇₉	C₂²×Q₁₆	1	1	yes	characteristic
192	C₂²×C₇₉	C₂×#135	1	1	yes	characteristic
193	C₂²×C₇₉	#576	1	1	yes	characteristic
194	C₂²×C₇₉	#578	1	1	yes	characteristic
195	C₄×C₇₉	—	2	8	no	—
196	C₄×C₇₉	—	2	2	no	—
197	C₄×C₇₉	—	4	1	no	—
198	C₄×C₇₉	—	8	2	no	—
199	C₄×C₇₉	C₂²×C₄⋊C₄	1	1	yes	characteristic
200	C₄×C₇₉	#520	1	1	yes	characteristic
201	C₄×C₇₉	#547	1	1	yes	characteristic
202	C₄×C₇₉	#554	1	1	yes	characteristic
203	Dic₇₉	—	2	2	no	—
204	Dic₇₉	—	2	2	no	—
205	Dic₇₉	—	4	4	no	—
206	Dic₇₉	—	4	1	no	—
207	Dic₇₉	—	8	2	no	—
208	Dic₇₉	C₄×Q₁₆	1	4	yes	complemented
209	C₄⋊C₄×Q₁₆	—	79	1	no	maximal, Sylow
210	C₂×C₇₉	D₄×C₄⋊C₄	1	1	yes	characteristic
211	C₂×C₇₉	C₂×C₄×Q₁₆	1	1	yes	characteristic
212	C₂×C₇₉	#2951	1	1	yes	characteristic
213	C₂×C₇₉	D₄×Q₁₆	1	1	yes	characteristic
214	C₂×C₇₉	#3287	1	1	yes	characteristic
215	C₂×C₇₉	Q₈×Q₁₆	1	1	yes	characteristic
216	C₂×C₇₉	#3383	1	1	yes	characteristic
217	C₂×C₄×Q₁₆	—	79	1	no	—
218	C₂×C₄×Q₁₆	—	79	1	no	—
219	C₂×C₄×Q₁₆	D₇₉	1	1	yes	characteristic
220	Q₈×C₄⋊C₄	—	79	2	no	—
221	#1942	—	79	1	no	—
222	#1942	—	79	1	no	—
223	#1863	—	79	2	no	—
224	#1863	—	79	2	no	—
225	#1845	—	79	1	no	—
226	#1803	—	79	2	no	—
227	C₈×C₄⋊C₄	—	79	1	no	—
228	C₇₉	C₄⋊C₄×Q₁₆	1	1	yes	characteristic, complemented, Sylow
229	C₂²×Q₁₆	C₂×D₇₉	1	1	yes	characteristic
230	C₂×C₄×Q₈	—	79	2	no	—
231	C₂×C₄×Q₈	—	79	2	no	—
232	C₂×C₄×Q₈	C₂×D₇₉	1	2	yes	—
233	C₄×Q₁₆	—	2	4	no	—
234	C₄×Q₁₆	—	79	8	no	—
235	C₄×Q₁₆	—	158	4	no	—
236	C₂×#107	—	79	2	no	—
237	C₂×#107	—	79	1	no	—
238	C₂×#107	—	79	1	no	—
239	C₂×#107	C₂×D₇₉	1	1	yes	characteristic
240	C₂×C₄⋊C₈	—	79	1	no	—
241	C₂×#103	—	79	2	no	—
242	C₂×#103	—	79	2	no	—
243	C₂×#103	C₂×D₇₉	1	2	yes	—
244	C₂×C₄×C₈	—	79	1	no	—
245	C₂×C₄×C₈	—	79	1	no	—
246	C₂×C₄×C₈	C₂×D₇₉	1	1	yes	characteristic
247	#389	—	79	2	no	—
248	#389	—	79	2	no	—
249	#389	—	158	2	no	—
250	#389	—	158	2	no	—
251	#384	—	79	2	no	—
252	#384	—	158	2	no	—
253	C₄×C₄⋊C₄	—	79	1	no	—
254	C₄×C₄⋊C₄	—	158	2	no	—
255	#340	—	79	2	no	—
256	#340	—	79	2	no	—
257	#336	—	79	1	no	—
258	#336	—	79	1	no	—
259	C₂²×Q₈	C₂²×D₇₉	1	2	yes	—
260	C₂×Q₁₆	Dic₁₅₈	1	4	yes	—
261	C₂×Q₁₆	C₄×D₇₉	1	4	yes	—
262	C₂×Q₁₆	C₂²⋊D₇₉	1	4	yes	—
263	C₂²×C₈	—	79	1	no	—
264	C₂²×C₈	—	79	1	no	—
265	C₂²×C₈	C₂²×D₇₉	1	1	yes	characteristic
266	C₂²×C₈	C₂²×D₇₉	1	1	yes	characteristic
267	C₄×Q₈	—	2	4	no	—
268	C₄×Q₈	—	4	2	no	—
269	C₄×Q₈	—	316	2	no	—
270	C₄×Q₈	—	79	8	no	—
271	C₄×Q₈	—	158	4	no	—
272	C₄×Q₈	—	158	4	no	—
273	C₂×C₄⋊C₄	—	2	2	no	—
274	C₂×C₄⋊C₄	—	79	1	no	—
275	C₂×C₄⋊C₄	—	79	2	no	—
276	C₂×C₄⋊C₄	—	79	1	no	—
277	C₂×C₄⋊C₄	—	79	2	no	—
278	C₂×C₄⋊C₄	—	158	2	no	—
279	C₂×C₄⋊C₄	—	158	2	no	—
280	C₂×C₄⋊C₄	—	158	2	no	—
281	C₂×C₄⋊C₄	—	158	2	no	—
282	C₂×C₄⋊C₄	—	158	2	no	—
283	C₂×C₄⋊C₄	—	158	2	no	—
284	C₂×C₄⋊C₄	C₂²×D₇₉	1	2	yes	—
285	C₂×C₄²	—	2	2	no	—
286	C₂×C₄²	—	79	1	no	—
287	C₂×C₄²	—	79	1	no	—
288	C₂×C₄²	—	158	2	no	—
289	C₂×C₄²	—	158	2	no	—
290	C₂×C₄²	C₂²×D₇₉	1	1	yes	characteristic
291	#107	—	2	2	no	—
292	#107	—	316	2	no	—
293	#107	—	79	4	no	—
294	#107	—	158	2	no	—
295	C₄⋊C₈	—	158	2	no	—
296	#103	—	2	4	no	—
297	#103	—	79	8	no	—
298	#103	—	158	4	no	—
299	C₄×C₈	—	2	2	no	—
300	C₄×C₈	—	79	4	no	—
301	C₄×C₈	—	158	2	no	—
302	#95	—	79	1	no	—
303	#95	—	79	1	no	—
304	#95	—	158	2	no	—
305	#95	—	158	2	no	—
306	C₂×Q₈	—	2	2	no	—
307	C₂×Q₈	—	2	2	no	—
308	C₂×Q₈	—	2	2	no	—
309	C₂×Q₈	C₂×C₄×D₇₉	1	4	yes	—
310	C₂×Q₈	C₂×C₂²⋊D₇₉	1	4	yes	—
311	C₂×Q₈	C₂×Dic₁₅₈	1	4	yes	—
312	C₂²×C₄	—	2	2	no	—
313	C₂²×C₄	—	2	2	no	—
314	C₂²×C₄	—	79	1	no	—
315	C₂²×C₄	—	79	1	no	—
316	C₂²×C₄	—	79	1	no	—
317	C₂²×C₄	—	79	1	no	—
318	C₂²×C₄	—	158	2	no	—
319	C₂²×C₄	—	158	2	no	—
320	C₂²×C₄	D₄×D₇₉	1	1	yes	characteristic
321	C₂²×C₄	D₄×D₇₉	1	1	yes	characteristic
322	C₂²×C₄	C₂³×D₇₉	1	1	yes	characteristic
323	Q₁₆	Dic₇₉⋊C₄	1	16	yes	direct product factor
324	C₂×C₈	—	2	1	no	—
325	C₂×C₈	—	2	1	no	—
326	C₂×C₈	—	2	1	no	—
327	C₂×C₈	—	79	2	no	—
328	C₂×C₈	—	158	1	no	—
329	C₂×C₈	—	158	1	no	—
330	C₂×C₈	—	158	1	no	—
331	C₂×C₈	—	158	1	no	—
332	C₂×C₈	—	158	1	no	—
333	C₂×C₈	C₂×C₄×D₇₉	1	2	yes	—
334	C₂×C₈	C₂×C₂²⋊D₇₉	1	2	yes	—
335	C₂×C₈	C₂×Dic₁₅₈	1	2	yes	—
336	C₄⋊C₄	—	2	2	no	—
337	C₄⋊C₄	—	2	2	no	—
338	C₄⋊C₄	—	4	4	no	—
339	C₄⋊C₄	—	316	4	no	—
340	C₄⋊C₄	—	316	4	no	—
341	C₄⋊C₄	—	79	4	no	—
342	C₄⋊C₄	—	79	4	no	—
343	C₄⋊C₄	—	632	2	no	—
344	C₄⋊C₄	—	632	2	no	—
345	C₄⋊C₄	—	632	2	no	—
346	C₄⋊C₄	—	158	2	no	—
347	C₄⋊C₄	—	158	8	no	—
348	C₄⋊C₄	—	158	2	no	—
349	C₄⋊C₄	—	158	2	no	—
350	C₄⋊C₄	—	158	2	no	—
351	C₄²	—	2	1	no	—
352	C₄²	—	2	1	no	—
353	C₄²	—	4	4	no	—
354	C₄²	—	316	4	no	—
355	C₄²	—	79	2	no	—
356	C₄²	—	79	2	no	—
357	C₄²	—	158	8	no	—
358	C₄²	—	158	1	no	—
359	C₄²	—	158	1	no	—
360	C₂³	C₂×D₄×D₇₉	1	1	yes	characteristic
361	Q₈	—	2	4	no	—
362	Q₈	—	2	4	no	—
363	Q₈	—	2	4	no	—
364	Q₈	C₂×Dic₇₉⋊C₄	1	8	yes	—
365	C₂×C₄	—	2	1	no	—
366	C₂×C₄	—	2	4	no	—
367	C₂×C₄	—	2	4	no	—
368	C₂×C₄	—	2	4	no	—
369	C₂×C₄	—	2	1	no	—
370	C₂×C₄	—	2	1	no	—
371	C₂×C₄	—	2	1	no	—
372	C₂×C₄	—	2	1	no	—
373	C₂×C₄	—	4	2	no	—
374	C₂×C₄	—	4	2	no	—
375	C₂×C₄	—	4	2	no	—
376	C₂×C₄	—	316	2	no	—
377	C₂×C₄	—	316	2	no	—
378	C₂×C₄	—	316	2	no	—
379	C₂×C₄	—	316	2	no	—
380	C₂×C₄	—	316	2	no	—
381	C₂×C₄	—	79	2	no	—
382	C₂×C₄	—	79	2	no	—
383	C₂×C₄	—	79	2	no	—
384	C₂×C₄	—	79	2	no	—
385	C₂×C₄	—	79	2	no	—
386	C₂×C₄	—	158	1	no	—
387	C₂×C₄	—	158	4	no	—
388	C₂×C₄	—	158	1	no	—
389	C₂×C₄	—	158	1	no	—
390	C₂×C₄	—	158	1	no	—
391	C₂×C₄	—	158	1	no	—
392	C₂×C₄	—	158	1	no	—
393	C₂×C₄	—	158	1	no	—
394	C₂×C₄	Q₁₆×D₇₉	1	2	yes	—
395	C₂×C₄	C₂²×C₄×D₇₉	1	1	yes	characteristic
396	C₂×C₄	C₂²×C₂²⋊D₇₉	1	1	yes	characteristic
397	C₂×C₄	C₂²×Dic₁₅₈	1	1	yes	characteristic
398	C₂×C₄	#41×D₇₉	1	1	yes	characteristic
399	C₂×C₄	#14579206	1	1	yes	characteristic
400	C₂×C₄	#14579208	1	1	yes	characteristic
401	C₈	—	4	1	no	—
402	C₈	—	316	1	no	—
403	C₈	—	158	2	no	—
404	C₈	C₂×Dic₇₉⋊C₄	1	4	yes	—
405	C₂²	C₄×D₄×D₇₉	1	1	yes	characteristic
406	C₂²	D₄×C₂²⋊D₇₉	1	1	yes	characteristic
407	C₂²	D₄×Dic₁₅₈	1	1	yes	characteristic
408	C₂²	C₂×Q₁₆×D₇₉	1	1	yes	characteristic
409	C₂²	#135×D₇₉	1	1	yes	characteristic
410	C₂²	#19099365	1	1	yes	characteristic
411	C₂²	#19099376	1	1	yes	characteristic
412	C₄	—	2	8	no	—
413	C₄	—	2	2	no	—
414	C₄	—	4	1	no	—
415	C₄	—	8	2	no	—
416	C₄	—	316	4	no	—
417	C₄	—	316	1	no	—
418	C₄	—	79	4	no	—
419	C₄	—	632	2	no	—
420	C₄	—	158	2	no	—
421	C₄	—	158	2	no	—
422	C₄	C₂²×Dic₇₉⋊C₄	1	1	yes	characteristic
423	C₄	#19099042	1	1	yes	characteristic
424	C₄	#19099212	1	1	yes	characteristic
425	C₄	#19099272	1	1	yes	characteristic
426	C₂	D₄×Dic₇₉⋊C₄	1	1	yes	characteristic
427	C₂	C₄×Q₁₆×D₇₉	1	1	yes	characteristic
428	C₂	#23772275	1	1	yes	characteristic
429	C₂	Q₁₆×C₂²⋊D₇₉	1	1	yes	characteristic
430	C₂	#23775154	1	1	yes	characteristic
431	C₂	Q₁₆×Dic₁₅₈	1	1	yes	characteristic
432	C₂	#23776291	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂×D₄×D₇₉
commutator	C₂×C₄×C₇₉	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₇₉
Fitting	C₂×C₄×Q₁₆×C₇₉	C₂
socle, prime radical	C₂³×C₇₉	C₂²×D₄
cosocle	C₂²×C₄×C₇₉	C₂⁴
hypercenter	C₂×C₄×Q₁₆	D₇₉
hypocenter	C₇₉	C₄⋊C₄×Q₁₆
LCS	G ▷ C₂×C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×C₄×Q₁₆

Complements

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

N	H ≅ G/N	type
15. Q₁₆×Dic₇₉	C₄	semidirect
112. Dic₇₉⋊C₄	Q₁₆	direct (N × H)
130. Q₁₆×C₇₉	C₄⋊C₄	semidirect
208. Dic₇₉	C₄×Q₁₆	semidirect
228. C₇₉	C₄⋊C₄×Q₁₆	semidirect
323. Q₁₆	Dic₇₉⋊C₄	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×Q₁₆×Dic₇₉	2
Q₈×Dic₇₉⋊C₄	2
#23764133	2
#23764131	2
#23763654	2
#23763652	2
#23763558	2
#23763403	2
C₈×Dic₇₉⋊C₄	2
C₂×C₄×Q₁₆×C₇₉	2
C₄⋊C₄×Q₁₆	79

Subgroups — Q16×Dic79⋊C4 #34306696

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — Q₁₆×Dic₇₉⋊C₄ #34306696