Subgroups — D₄×#14579096 #34306517

Order 20224.

894 conjugacy classes of subgroups.

The subgroup lattice has 472 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₄×#11929608	C₂	1	1	yes	maximal, characteristic
2	C₂×D₄×C₇₉⋊C₈	C₂	1	1	yes	maximal, characteristic
3	C₂²×#14579096	C₂	1	2	yes	maximal, complemented
4	#23764175	C₂	1	1	yes	maximal, characteristic, complemented
5	#23764173	C₂	1	1	yes	maximal, characteristic, complemented
6	#23763605	C₂	1	2	yes	maximal, complemented
7	#23763604	C₂	1	2	yes	maximal, complemented
8	#23763571	C₂	1	1	yes	maximal, characteristic, complemented
9	#23763436	C₂	1	2	yes	maximal, complemented
10	C₄×#14579096	C₂	1	1	yes	maximal, characteristic, complemented
11	D₄×M₁₆×C₇₉	C₂	1	1	yes	maximal, characteristic
12	C₂²×#11929608	C₂²	1	2	yes	—
13	C₂³×C₇₉⋊C₈	C₂²	1	2	yes	—
14	#19098641	—	2	1	no	—
15	#19098635	—	2	2	no	—
16	D₄×C₇₉⋊C₈	—	2	1	no	—
17	D₄×C₇₉⋊C₈	C₄	1	4	yes	—
18	D₄×C₇₉⋊C₈	C₄	1	2	yes	—
19	D₄×C₇₉⋊C₈	C₄	1	2	yes	—
20	C₂×#14579096	—	2	8	no	—
21	C₂×#14579096	C₂²	1	2	yes	—
22	C₂×#14579096	C₂²	1	2	yes	—
23	C₂×#14579096	C₂²	1	2	yes	—
24	C₂×#14579096	C₂²	1	1	yes	characteristic
25	C₂×#14579096	C₂²	1	2	yes	—
26	C₂×#14579096	C₂²	1	1	yes	characteristic
27	#19098587	C₂²	1	1	yes	characteristic
28	C₂×C₄⋊(C₇₉⋊C₈)	C₂²	1	1	yes	characteristic
29	#19098527	C₂²	1	2	yes	—
30	C₂×C₂²⋊(C₇₉⋊C₈)	C₂²	1	2	yes	—
31	C₄×#11929608	C₂²	1	1	yes	characteristic
32	C₂×C₄×C₇₉⋊C₈	C₂²	1	1	yes	characteristic
33	#19098327	C₂²	1	1	yes	characteristic
34	#19098327	C₂²	1	1	yes	characteristic
35	#19098327	C₂²	1	2	yes	—
36	#19098327	C₂²	1	2	yes	—
37	C₂²×M₁₆×C₇₉	C₂²	1	2	yes	—
38	C₂×C₄×D₄×C₇₉	C₂²	1	1	yes	characteristic
39	#436×C₇₉	—	2	1	no	—
40	#435×C₇₉	—	2	2	no	—
41	C₈×D₄×C₇₉	—	2	1	no	—
42	#423×C₇₉	C₂²	1	1	yes	characteristic
43	#407×C₇₉	C₂²	1	2	yes	—
44	C₄×M₁₆×C₇₉	C₂²	1	1	yes	characteristic
45	C₂×#11929608	—	2	2	no	—
46	C₂×#11929608	—	2	4	no	—
47	C₂×#11929608	—	4	2	no	—
48	C₂×#11929608	C₂³	1	1	yes	characteristic
49	C₂×#11929608	C₂³	1	2	yes	—
50	C₂×#11929608	C₂³	1	1	yes	characteristic
51	C₂²×C₇₉⋊C₈	—	2	4	no	—
52	C₂²×C₇₉⋊C₈	—	2	4	no	—
53	C₂²×C₇₉⋊C₈	—	2	2	no	—
54	C₂²×C₇₉⋊C₈	C₂×C₄	1	4	yes	—
55	C₂²×C₇₉⋊C₈	C₂×C₄	1	4	yes	—
56	C₂²×C₇₉⋊C₈	C₂³	1	1	yes	characteristic
57	C₂²×C₇₉⋊C₈	C₂³	1	2	yes	—
58	C₂²×C₇₉⋊C₈	C₂³	1	1	yes	characteristic
59	#14579096	—	2	4	no	—
60	#14579096	—	2	4	no	—
61	#14579096	—	2	4	no	—
62	#14579096	—	2	2	no	—
63	#14579096	—	4	2	no	—
64	#14579096	D₄	1	4	yes	direct product factor
65	C₄⋊(C₇₉⋊C₈)	—	2	1	no	—
66	C₄⋊(C₇₉⋊C₈)	—	2	1	no	—
67	C₄⋊(C₇₉⋊C₈)	C₂×C₄	1	2	yes	—
68	C₄⋊(C₇₉⋊C₈)	C₂×C₄	1	2	yes	—
69	C₂²⋊(C₇₉⋊C₈)	—	2	2	no	—
70	C₂²⋊(C₇₉⋊C₈)	—	2	2	no	—
71	C₂²⋊(C₇₉⋊C₈)	C₂×C₄	1	4	yes	—
72	C₂²⋊(C₇₉⋊C₈)	C₂×C₄	1	4	yes	—
73	#14579072	—	2	1	no	—
74	C₄×C₇₉⋊C₈	—	2	1	no	—
75	C₄×C₇₉⋊C₈	C₂×C₄	1	2	yes	—
76	C₄×C₇₉⋊C₈	C₂×C₄	1	2	yes	—
77	C₂²×D₄×C₇₉	Q₈	1	1	yes	characteristic
78	C₂³×C₄×C₇₉	C₂³	1	2	yes	—
79	C₂×M₁₆×C₇₉	—	2	2	no	—
80	C₂×M₁₆×C₇₉	—	2	4	no	—
81	C₂×M₁₆×C₇₉	—	4	2	no	—
82	C₂×M₁₆×C₇₉	C₂³	1	2	yes	—
83	C₂×M₁₆×C₇₉	C₂³	1	1	yes	characteristic
84	C₂×M₁₆×C₇₉	C₂³	1	1	yes	characteristic
85	C₂²×C₈×C₇₉	—	2	2	no	—
86	C₄×D₄×C₇₉	C₂×C₄	1	2	yes	—
87	C₄×D₄×C₇₉	C₂×C₄	1	1	yes	characteristic
88	C₄×D₄×C₇₉	C₂×C₄	1	1	yes	characteristic
89	C₄×D₄×C₇₉	D₄	1	1	yes	characteristic
90	C₄×D₄×C₇₉	D₄	1	2	yes	—
91	C₄×D₄×C₇₉	D₄	1	1	yes	characteristic
92	C₂×C₄⋊C₄×C₇₉	Q₈	1	1	yes	characteristic
93	C₂×C₂²⋊C₄×C₇₉	Q₈	1	2	yes	—
94	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
95	C₄⋊C₈×C₇₉	—	2	1	no	—
96	C₄⋊C₈×C₇₉	—	2	1	no	—
97	C₂²⋊C₈×C₇₉	—	2	2	no	—
98	C₂²⋊C₈×C₇₉	—	2	2	no	—
99	#97×C₇₉	—	2	1	no	—
100	C₄×C₈×C₇₉	—	2	1	no	—
101	#11929608	—	2	2	no	—
102	#11929608	—	2	1	no	—
103	#11929608	—	2	1	no	—
104	#11929608	—	2	2	no	—
105	#11929608	—	2	1	no	—
106	#11929608	—	4	4	no	—
107	#11929608	C₂×D₄	1	2	yes	—
108	C₂×C₇₉⋊C₈	—	2	8	no	—
109	C₂×C₇₉⋊C₈	—	2	8	no	—
110	C₂×C₇₉⋊C₈	—	2	1	no	—
111	C₂×C₇₉⋊C₈	—	2	2	no	—
112	C₂×C₇₉⋊C₈	—	2	1	no	—
113	C₂×C₇₉⋊C₈	—	2	2	no	—
114	C₂×C₇₉⋊C₈	—	2	2	no	—
115	C₂×C₇₉⋊C₈	—	2	1	no	—
116	C₂×C₇₉⋊C₈	—	2	1	no	—
117	C₂×C₇₉⋊C₈	—	4	4	no	—
118	C₂×C₇₉⋊C₈	C₂²×C₄	1	2	yes	—
119	C₂×C₇₉⋊C₈	C₂²×C₄	1	4	yes	—
120	C₂×C₇₉⋊C₈	C₂²×C₄	1	2	yes	—
121	C₂×C₇₉⋊C₈	C₂×D₄	1	2	yes	—
122	C₂×C₇₉⋊C₈	#41	1	2	yes	—
123	C₂⁴×C₇₉	C₂×Q₈	1	2	yes	—
124	C₂×D₄×C₇₉	—	2	4	no	—
125	C₂×D₄×C₇₉	C₄⋊C₄	1	2	yes	—
126	C₂×D₄×C₇₉	C₄⋊C₄	1	1	yes	characteristic
127	C₂×D₄×C₇₉	C₄⋊C₄	1	1	yes	characteristic
128	C₂²×C₄×C₇₉	—	2	2	no	—
129	C₂²×C₄×C₇₉	—	2	2	no	—
130	C₂²×C₄×C₇₉	—	2	2	no	—
131	C₂²×C₄×C₇₉	—	2	2	no	—
132	C₂²×C₄×C₇₉	C₂²×C₄	1	2	yes	—
133	C₂²×C₄×C₇₉	C₂²×C₄	1	2	yes	—
134	C₂²×C₄×C₇₉	C₂×D₄	1	2	yes	—
135	C₂²×C₄×C₇₉	C₂×D₄	1	2	yes	—
136	C₂²×C₄×C₇₉	C₂×Q₈	1	1	yes	characteristic
137	C₂²×C₄×C₇₉	C₂×Q₈	1	2	yes	—
138	C₂²×C₄×C₇₉	C₂×Q₈	1	1	yes	characteristic
139	C₂²×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
140	M₁₆×C₇₉	—	2	2	no	—
141	M₁₆×C₇₉	—	2	1	no	—
142	M₁₆×C₇₉	—	2	1	no	—
143	M₁₆×C₇₉	—	2	2	no	—
144	M₁₆×C₇₉	—	2	1	no	—
145	M₁₆×C₇₉	—	4	4	no	—
146	M₁₆×C₇₉	C₂×D₄	1	2	yes	—
147	C₂×C₈×C₇₉	—	2	1	no	—
148	C₂×C₈×C₇₉	—	2	1	no	—
149	C₂×C₈×C₇₉	—	2	2	no	—
150	C₂×C₈×C₇₉	—	4	4	no	—
151	C₄⋊C₄×C₇₉	C₄⋊C₄	1	2	yes	—
152	C₄⋊C₄×C₇₉	C₄⋊C₄	1	1	yes	characteristic
153	C₄⋊C₄×C₇₉	C₄⋊C₄	1	1	yes	characteristic
154	C₂²⋊C₄×C₇₉	C₄⋊C₄	1	2	yes	—
155	C₂²⋊C₄×C₇₉	C₄⋊C₄	1	2	yes	—
156	C₂²⋊C₄×C₇₉	C₄⋊C₄	1	2	yes	—
157	C₂²⋊C₄×C₇₉	C₄⋊C₄	1	2	yes	—
158	C₄²×C₇₉	C₂²×C₄	1	1	yes	characteristic
159	C₄²×C₇₉	C₂²×C₄	1	1	yes	characteristic
160	C₄²×C₇₉	C₂×D₄	1	1	yes	characteristic
161	C₄²×C₇₉	C₂×D₄	1	1	yes	characteristic
162	C₂³×C₇₉	—	2	2	no	—
163	C₂³×C₇₉	—	2	2	no	—
164	C₂³×C₇₉	—	2	4	no	—
165	C₂³×C₇₉	—	4	2	no	—
166	C₂³×C₇₉	C₂×C₄⋊C₄	1	2	yes	—
167	C₂³×C₇₉	C₂×C₄⋊C₄	1	2	yes	—
168	C₂³×C₇₉	C₂²×Q₈	1	1	yes	characteristic
169	D₄×C₇₉	—	2	4	no	—
170	D₄×C₇₉	—	2	2	no	—
171	D₄×C₇₉	#108	1	4	yes	complemented
172	C₂×C₄×C₇₉	—	2	2	no	—
173	C₂×C₄×C₇₉	—	2	2	no	—
174	C₂×C₄×C₇₉	—	2	2	no	—
175	C₂×C₄×C₇₉	—	2	2	no	—
176	C₂×C₄×C₇₉	—	2	2	no	—
177	C₂×C₄×C₇₉	—	2	2	no	—
178	C₂×C₄×C₇₉	—	2	2	no	—
179	C₂×C₄×C₇₉	—	2	2	no	—
180	C₂×C₄×C₇₉	—	2	2	no	—
181	C₂×C₄×C₇₉	—	2	2	no	—
182	C₂×C₄×C₇₉	—	2	2	no	—
183	C₂×C₄×C₇₉	—	4	1	no	—
184	C₂×C₄×C₇₉	C₂×C₄⋊C₄	1	1	yes	characteristic
185	C₂×C₄×C₇₉	C₂×C₄⋊C₄	1	1	yes	characteristic
186	C₂×C₄×C₇₉	C₂×C₄⋊C₄	1	1	yes	characteristic
187	C₂×C₄×C₇₉	C₂×C₄⋊C₄	1	2	yes	—
188	C₂×C₄×C₇₉	C₂×C₄⋊C₄	1	2	yes	—
189	C₂×C₄×C₇₉	C₂×C₄⋊C₄	1	1	yes	characteristic
190	C₂×C₄×C₇₉	C₂³×C₄	1	1	yes	characteristic
191	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
192	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
193	C₂×C₄×C₇₉	C₂×#41	1	1	yes	characteristic
194	C₂×C₄×C₇₉	H(5,𝔽₂)	1	1	yes	characteristic
195	C₂×C₄×C₇₉	2₋¹⁺⁴	1	1	yes	characteristic
196	C₈×C₇₉	—	2	2	no	—
197	C₈×C₇₉	—	4	2	no	—
198	C₈×C₇₉	—	4	1	no	—
199	C₇₉⋊C₈	—	2	4	no	—
200	C₇₉⋊C₈	—	2	2	no	—
201	C₇₉⋊C₈	—	2	2	no	—
202	C₇₉⋊C₈	—	4	2	no	—
203	C₇₉⋊C₈	—	4	1	no	—
204	C₇₉⋊C₈	C₄×D₄	1	4	yes	—
205	C₂²×C₇₉	—	2	2	no	—
206	C₂²×C₇₉	—	2	1	no	—
207	C₂²×C₇₉	—	2	1	no	—
208	C₂²×C₇₉	—	2	2	no	—
209	C₂²×C₇₉	—	2	2	no	—
210	C₂²×C₇₉	—	2	2	no	—
211	C₂²×C₇₉	—	2	2	no	—
212	C₂²×C₇₉	—	4	4	no	—
213	C₂²×C₇₉	—	4	4	no	—
214	C₂²×C₇₉	C₂×#108	1	4	yes	complemented
215	C₂²×C₇₉	C₂²×C₄⋊C₄	1	1	yes	characteristic
216	C₂²×C₇₉	D₄×Q₈	1	1	yes	characteristic
217	C₂²×C₇₉	#554	1	1	yes	characteristic
218	C₄×C₇₉	—	2	2	no	—
219	C₄×C₇₉	—	2	2	no	—
220	C₄×C₇₉	—	2	1	no	—
221	C₄×C₇₉	—	2	1	no	—
222	C₄×C₇₉	—	2	1	no	—
223	C₄×C₇₉	C₂×#108	1	2	yes	complemented
224	C₄×C₇₉	C₂×C₄×D₄	1	1	yes	characteristic
225	C₄×C₇₉	#520	1	1	yes	characteristic
226	C₄×C₇₉	D₄²	1	1	yes	characteristic
227	C₄×C₇₉	#547	1	1	yes	characteristic
228	D₄×#108	—	79	1	no	maximal, Sylow
229	C₂×C₇₉	—	2	1	no	—
230	C₂×C₇₉	—	2	1	no	—
231	C₂×C₇₉	—	2	4	no	—
232	C₂×C₇₉	—	4	2	no	—
233	C₂×C₇₉	D₄×C₄⋊C₄	1	1	yes	characteristic
234	C₂×C₇₉	C₂²×#108	1	1	yes	characteristic
235	C₂×C₇₉	#2916	1	1	yes	characteristic
236	D₄×M₁₆	—	79	1	no	—
237	D₄×M₁₆	D₇₉	1	1	yes	characteristic
238	C₂×C₈×D₄	—	79	1	no	—
239	C₂²×#108	—	79	2	no	—
240	#1950	—	79	1	no	—
241	#1950	—	79	1	no	—
242	#1855	—	79	2	no	—
243	#1855	—	79	2	no	—
244	#1848	—	79	1	no	—
245	#1810	—	79	2	no	—
246	C₄×#108	—	79	1	no	—
247	C₇₉	D₄×#108	1	1	yes	characteristic, complemented, Sylow
248	C₂²×M₁₆	—	79	2	no	—
249	C₂²×M₁₆	C₂×D₇₉	1	2	yes	—
250	C₂³×C₈	—	79	2	no	—
251	C₂×C₄×D₄	C₂×D₇₉	1	1	yes	characteristic
252	#436	—	2	1	no	—
253	#436	—	158	1	no	—
254	#435	—	2	2	no	—
255	#435	—	158	2	no	—
256	C₈×D₄	—	2	1	no	—
257	C₈×D₄	—	79	4	no	—
258	C₈×D₄	—	79	2	no	—
259	C₈×D₄	—	79	2	no	—
260	C₈×D₄	—	158	1	no	—
261	C₂×#108	—	79	2	no	—
262	C₂×#108	—	79	1	no	—
263	C₂×#108	—	79	1	no	—
264	C₂×#108	—	79	2	no	—
265	C₂×#108	—	79	2	no	—
266	C₂×#108	—	79	2	no	—
267	C₂×#108	—	158	8	no	—
268	#423	—	79	1	no	—
269	#423	C₂×D₇₉	1	1	yes	characteristic
270	C₂×C₄⋊C₈	—	79	1	no	—
271	#407	—	79	2	no	—
272	#407	C₂×D₇₉	1	2	yes	—
273	C₂×C₂²⋊C₈	—	79	2	no	—
274	C₄×M₁₆	—	79	1	no	—
275	C₄×M₁₆	C₂×D₇₉	1	1	yes	characteristic
276	C₂×C₄×C₈	—	79	1	no	—
277	#341	—	79	2	no	—
278	#341	—	79	2	no	—
279	#341	—	79	1	no	—
280	#341	—	79	1	no	—
281	C₂²×D₄	Dic₁₅₈	1	1	yes	characteristic
282	C₂³×C₄	C₂²×D₇₉	1	2	yes	—
283	C₂×M₁₆	—	2	2	no	—
284	C₂×M₁₆	—	2	4	no	—
285	C₂×M₁₆	—	4	2	no	—
286	C₂×M₁₆	—	316	2	no	—
287	C₂×M₁₆	—	79	1	no	—
288	C₂×M₁₆	—	79	2	no	—
289	C₂×M₁₆	—	79	1	no	—
290	C₂×M₁₆	—	158	4	no	—
291	C₂×M₁₆	—	158	2	no	—
292	C₂×M₁₆	C₂²×D₇₉	1	2	yes	—
293	C₂×M₁₆	C₂²×D₇₉	1	1	yes	characteristic
294	C₂×M₁₆	C₂²×D₇₉	1	1	yes	characteristic
295	C₂²×C₈	—	2	2	no	—
296	C₂²×C₈	—	79	1	no	—
297	C₂²×C₈	—	79	4	no	—
298	C₂²×C₈	—	79	4	no	—
299	C₂²×C₈	—	79	2	no	—
300	C₂²×C₈	—	79	1	no	—
301	C₂²×C₈	—	158	2	no	—
302	C₂²×C₈	—	158	4	no	—
303	C₂²×C₈	—	158	4	no	—
304	C₄×D₄	C₄×D₇₉	1	2	yes	—
305	C₄×D₄	C₄×D₇₉	1	1	yes	characteristic
306	C₄×D₄	C₄×D₇₉	1	1	yes	characteristic
307	C₄×D₄	C₂²⋊D₇₉	1	1	yes	characteristic
308	C₄×D₄	C₂²⋊D₇₉	1	2	yes	—
309	C₄×D₄	C₂²⋊D₇₉	1	1	yes	characteristic
310	C₂×C₄⋊C₄	Dic₁₅₈	1	1	yes	characteristic
311	C₂×C₂²⋊C₄	Dic₁₅₈	1	2	yes	—
312	C₂×C₄²	C₂²×D₇₉	1	1	yes	characteristic
313	#108	—	316	2	no	—
314	#108	—	79	4	no	—
315	#108	—	158	2	no	—
316	#108	—	158	4	no	—
317	#108	—	158	4	no	—
318	#108	—	158	4	no	—
319	C₄⋊C₈	—	2	1	no	—
320	C₄⋊C₈	—	2	1	no	—
321	C₄⋊C₈	—	79	2	no	—
322	C₄⋊C₈	—	79	2	no	—
323	C₄⋊C₈	—	158	1	no	—
324	C₄⋊C₈	—	158	1	no	—
325	C₂²⋊C₈	—	2	2	no	—
326	C₂²⋊C₈	—	2	2	no	—
327	C₂²⋊C₈	—	79	4	no	—
328	C₂²⋊C₈	—	79	4	no	—
329	C₂²⋊C₈	—	158	2	no	—
330	C₂²⋊C₈	—	158	2	no	—
331	#97	—	2	1	no	—
332	#97	—	158	1	no	—
333	C₄×C₈	—	2	1	no	—
334	C₄×C₈	—	79	2	no	—
335	C₄×C₈	—	79	2	no	—
336	C₄×C₈	—	158	1	no	—
337	C₂⁴	C₂×Dic₁₅₈	1	2	yes	—
338	C₂×D₄	—	2	4	no	—
339	C₂×D₄	Dic₇₉⋊C₄	1	2	yes	—
340	C₂×D₄	Dic₇₉⋊C₄	1	1	yes	characteristic
341	C₂×D₄	Dic₇₉⋊C₄	1	1	yes	characteristic
342	C₂²×C₄	—	2	2	no	—
343	C₂²×C₄	—	2	2	no	—
344	C₂²×C₄	—	2	2	no	—
345	C₂²×C₄	—	2	2	no	—
346	C₂²×C₄	C₂×C₄×D₇₉	1	2	yes	—
347	C₂²×C₄	C₂×C₄×D₇₉	1	2	yes	—
348	C₂²×C₄	C₂×C₂²⋊D₇₉	1	2	yes	—
349	C₂²×C₄	C₂×C₂²⋊D₇₉	1	2	yes	—
350	C₂²×C₄	C₂×Dic₁₅₈	1	1	yes	characteristic
351	C₂²×C₄	C₂×Dic₁₅₈	1	2	yes	—
352	C₂²×C₄	C₂×Dic₁₅₈	1	1	yes	characteristic
353	C₂²×C₄	C₂³×D₇₉	1	1	yes	characteristic
354	M₁₆	—	2	1	no	—
355	M₁₆	—	2	1	no	—
356	M₁₆	—	2	2	no	—
357	M₁₆	—	2	1	no	—
358	M₁₆	—	2	2	no	—
359	M₁₆	—	4	4	no	—
360	M₁₆	—	316	4	no	—
361	M₁₆	—	79	2	no	—
362	M₁₆	—	158	1	no	—
363	M₁₆	—	158	2	no	—
364	M₁₆	—	158	1	no	—
365	M₁₆	—	158	2	no	—
366	M₁₆	—	158	1	no	—
367	M₁₆	D₄×D₇₉	1	2	yes	—
368	C₂×C₈	—	2	1	no	—
369	C₂×C₈	—	2	1	no	—
370	C₂×C₈	—	2	2	no	—
371	C₂×C₈	—	4	4	no	—
372	C₂×C₈	—	316	4	no	—
373	C₂×C₈	—	79	2	no	—
374	C₂×C₈	—	79	2	no	—
375	C₂×C₈	—	79	2	no	—
376	C₂×C₈	—	79	2	no	—
377	C₂×C₈	—	79	4	no	—
378	C₂×C₈	—	158	1	no	—
379	C₂×C₈	—	158	2	no	—
380	C₂×C₈	—	158	8	no	—
381	C₂×C₈	—	158	8	no	—
382	C₂×C₈	—	158	2	no	—
383	C₂×C₈	—	158	1	no	—
384	C₂×C₈	—	158	1	no	—
385	C₂×C₈	—	158	2	no	—
386	C₂×C₈	—	158	1	no	—
387	C₄⋊C₄	Dic₇₉⋊C₄	1	2	yes	—
388	C₄⋊C₄	Dic₇₉⋊C₄	1	1	yes	characteristic
389	C₄⋊C₄	Dic₇₉⋊C₄	1	1	yes	characteristic
390	C₂²⋊C₄	Dic₇₉⋊C₄	1	2	yes	—
391	C₂²⋊C₄	Dic₇₉⋊C₄	1	2	yes	—
392	C₂²⋊C₄	Dic₇₉⋊C₄	1	2	yes	—
393	C₂²⋊C₄	Dic₇₉⋊C₄	1	2	yes	—
394	C₄²	C₂×C₄×D₇₉	1	1	yes	characteristic
395	C₄²	C₂×C₄×D₇₉	1	1	yes	characteristic
396	C₄²	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
397	C₄²	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
398	C₂³	—	2	2	no	—
399	C₂³	—	2	2	no	—
400	C₂³	—	2	4	no	—
401	C₂³	—	4	2	no	—
402	C₂³	C₂×Dic₇₉⋊C₄	1	2	yes	—
403	C₂³	C₂×Dic₇₉⋊C₄	1	2	yes	—
404	C₂³	C₂²×Dic₁₅₈	1	1	yes	characteristic
405	D₄	—	2	4	no	—
406	D₄	—	2	2	no	—
407	D₄	#14579096	1	4	yes	direct product factor
408	C₂×C₄	—	2	2	no	—
409	C₂×C₄	—	2	2	no	—
410	C₂×C₄	—	2	2	no	—
411	C₂×C₄	—	2	2	no	—
412	C₂×C₄	—	2	2	no	—
413	C₂×C₄	—	2	2	no	—
414	C₂×C₄	—	2	2	no	—
415	C₂×C₄	—	2	2	no	—
416	C₂×C₄	—	2	2	no	—
417	C₂×C₄	—	2	2	no	—
418	C₂×C₄	—	2	2	no	—
419	C₂×C₄	—	4	1	no	—
420	C₂×C₄	C₂×Dic₇₉⋊C₄	1	1	yes	characteristic
421	C₂×C₄	C₂×Dic₇₉⋊C₄	1	1	yes	characteristic
422	C₂×C₄	C₂×Dic₇₉⋊C₄	1	1	yes	characteristic
423	C₂×C₄	C₂×Dic₇₉⋊C₄	1	2	yes	—
424	C₂×C₄	C₂×Dic₇₉⋊C₄	1	2	yes	—
425	C₂×C₄	C₂×Dic₇₉⋊C₄	1	1	yes	characteristic
426	C₂×C₄	C₂²×C₄×D₇₉	1	1	yes	characteristic
427	C₂×C₄	C₂×D₄×D₇₉	1	1	yes	characteristic
428	C₂×C₄	C₂²×C₂²⋊D₇₉	1	1	yes	characteristic
429	C₂×C₄	#41×D₇₉	1	1	yes	characteristic
430	C₂×C₄	#14579206	1	1	yes	characteristic
431	C₂×C₄	#14579208	1	1	yes	characteristic
432	C₈	—	2	2	no	—
433	C₈	—	4	2	no	—
434	C₈	—	4	1	no	—
435	C₈	—	316	2	no	—
436	C₈	—	316	1	no	—
437	C₈	—	79	4	no	—
438	C₈	—	158	2	no	—
439	C₈	—	158	4	no	—
440	C₈	—	158	2	no	—
441	C₂²	—	2	2	no	—
442	C₂²	—	2	1	no	—
443	C₂²	—	2	1	no	—
444	C₂²	—	2	2	no	—
445	C₂²	—	2	2	no	—
446	C₂²	—	2	2	no	—
447	C₂²	—	2	2	no	—
448	C₂²	—	4	4	no	—
449	C₂²	—	4	4	no	—
450	C₂²	C₂×#14579096	1	4	yes	complemented
451	C₂²	C₂²×Dic₇₉⋊C₄	1	1	yes	characteristic
452	C₂²	D₄×Dic₁₅₈	1	1	yes	characteristic
453	C₂²	#19099272	1	1	yes	characteristic
454	C₄	—	2	2	no	—
455	C₄	—	2	2	no	—
456	C₄	—	2	1	no	—
457	C₄	—	2	1	no	—
458	C₄	—	2	1	no	—
459	C₄	C₂×#14579096	1	2	yes	complemented
460	C₄	C₄×D₄×D₇₉	1	1	yes	characteristic
461	C₄	#19099042	1	1	yes	characteristic
462	C₄	D₄×C₂²⋊D₇₉	1	1	yes	characteristic
463	C₄	#19099212	1	1	yes	characteristic
464	C₂	—	2	1	no	—
465	C₂	—	2	1	no	—
466	C₂	—	2	4	no	—
467	C₂	—	4	2	no	—
468	C₂	D₄×Dic₇₉⋊C₄	1	1	yes	characteristic
469	C₂	C₂²×#14579096	1	1	yes	characteristic
470	C₂	#23772009	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²×C₂²⋊D₇₉
commutator	C₂×C₄×C₇₉	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₇₉
Fitting	D₄×M₁₆×C₇₉	C₂
socle	C₂²×C₇₉	C₂²×C₄⋊C₄
prime radical	C₂²×D₄×C₇₉	Q₈
cosocle	C₂²×C₄×C₇₉	C₂⁴
hypercenter	D₄×M₁₆	D₇₉
hypocenter	C₇₉	D₄×#108
LCS	G ▷ C₂×C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄×D₄ ◁ D₄×M₁₆

Complements

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

N	H ≅ G/N	type
3. C₂²×#14579096	C₂	semidirect
4. #23764175	C₂	semidirect
5. #23764173	C₂	semidirect
6. #23763605	C₂	semidirect
7. #23763604	C₂	semidirect
8. #23763571	C₂	semidirect
9. #23763436	C₂	semidirect
10. C₄×#14579096	C₂	semidirect
64. #14579096	D₄	direct (N × H)
171. D₄×C₇₉	#108	semidirect
214. C₂²×C₇₉	C₂×#108	semidirect
223. C₄×C₇₉	C₂×#108	semidirect
247. C₇₉	D₄×#108	semidirect
407. D₄	#14579096	direct (N × H)
450. C₂²	C₂×#14579096	semidirect
459. C₄	C₂×#14579096	semidirect

Maximal subgroups

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

subgroup	index
D₄×#11929608	2
C₂×D₄×C₇₉⋊C₈	2
C₂²×#14579096	2
#23764175	2
#23764173	2
#23763605	2
#23763604	2
#23763571	2
#23763436	2
C₄×#14579096	2
D₄×M₁₆×C₇₉	2
D₄×#108	79

Subgroups — D4×#14579096 #34306517

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₄×#14579096 #34306517