Subgroups — #34306483

Order 20224.

1022 conjugacy classes of subgroups.

The subgroup lattice has 476 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#19098605	C₂	1	2	yes	maximal, complemented
2	#23766349	C₂	1	1	yes	maximal, characteristic
3	D₄×C₄⋊Dic₇₉	C₂	1	1	yes	maximal, characteristic
4	#23764164	C₂	1	1	yes	maximal, characteristic, complemented
5	#23764159	C₂	1	1	yes	maximal, characteristic, complemented
6	#23763601	C₂	1	2	yes	maximal, complemented
7	#23763595	C₂	1	2	yes	maximal, complemented
8	#23763557	C₂	1	1	yes	maximal, characteristic, complemented
9	#23763433	C₂	1	2	yes	maximal, complemented
10	C₄×#14579095	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×#436×C₇₉	C₂	1	1	yes	maximal, characteristic
12	C₂×D₄×Dic₇₉	—	2	1	no	—
13	C₂×#14579120	C₂²	1	2	yes	—
14	C₂²×C₄⋊Dic₇₉	C₂²	1	2	yes	—
15	#19098605	—	2	8	no	—
16	C₂×#14579095	C₂²	1	2	yes	—
17	C₂×#14579095	C₂²	1	1	yes	characteristic
18	C₂×#14579095	C₂²	1	1	yes	characteristic
19	C₂×#14579093	C₂²	1	2	yes	—
20	C₂×#14579093	C₂²	1	2	yes	—
21	C₂×#14579093	C₂²	1	2	yes	—
22	#19098466	—	2	1	no	—
23	#19098462	—	2	1	no	—
24	#19098456	—	2	2	no	—
25	#19098438	—	2	2	no	—
26	#19098433	C₂²	1	1	yes	characteristic
27	#19098433	C₂²	1	1	yes	characteristic
28	#19098423	C₂²	1	2	yes	—
29	#19098423	C₂²	1	2	yes	—
30	C₄⋊C₄×Dic₇₉	—	2	1	no	—
31	C₄×C₄⋊Dic₇₉	C₂²	1	1	yes	characteristic
32	C₄×C₄⋊Dic₇₉	C₂²	1	1	yes	characteristic
33	#19098326	C₂²	1	1	yes	characteristic
34	#19098326	C₂²	1	1	yes	characteristic
35	#19098326	C₂²	1	2	yes	—
36	#19098326	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	C₄	1	8	yes	complemented
40	C₂×C₄⋊C₈×C₇₉	C₂²	1	1	yes	characteristic
41	C₂×C₂²⋊C₈×C₇₉	C₂²	1	2	yes	—
42	C₂×C₄×C₈×C₇₉	C₂²	1	1	yes	characteristic
43	C₂³×Dic₇₉	—	2	2	no	—
44	D₄×Dic₇₉	—	4	4	no	—
45	#14579120	—	2	4	no	—
46	#14579120	—	4	2	no	—
47	C₂×C₄⋊Dic₇₉	—	2	4	no	—
48	C₂×C₄⋊Dic₇₉	—	2	1	no	—
49	C₂×C₄⋊Dic₇₉	—	2	1	no	—
50	C₂×C₄⋊Dic₇₉	—	2	2	no	—
51	C₂×C₄⋊Dic₇₉	—	2	1	no	—
52	C₂×C₄⋊Dic₇₉	—	2	1	no	—
53	C₂×C₄⋊Dic₇₉	—	4	2	no	—
54	C₂×C₄⋊Dic₇₉	C₂³	1	1	yes	characteristic
55	C₂×C₄⋊Dic₇₉	C₂³	1	1	yes	characteristic
56	C₂×C₄⋊Dic₇₉	C₂³	1	2	yes	—
57	C₂×C₄⋊Dic₇₉	C₂³	1	2	yes	—
58	C₂×C₄⋊Dic₇₉	C₂³	1	1	yes	characteristic
59	C₂×C₄⋊Dic₇₉	C₂³	1	1	yes	characteristic
60	C₂×C₂²⋊Dic₇₉	—	2	2	no	—
61	C₂×C₂²⋊Dic₇₉	—	2	2	no	—
62	C₂×C₂²⋊Dic₇₉	—	2	2	no	—
63	C₂×C₄×Dic₇₉	—	2	1	no	—
64	C₂×C₄×Dic₇₉	—	2	1	no	—
65	C₂×C₄×Dic₇₉	—	2	2	no	—
66	#14579095	—	2	2	no	—
67	#14579095	—	2	4	no	—
68	#14579095	D₄	1	4	yes	complemented
69	#14579093	—	2	4	no	—
70	#14579093	—	2	4	no	—
71	#14579093	—	4	2	no	—
72	C₇₉⋊#95	—	2	1	no	—
73	C₇₉⋊#95	—	2	1	no	—
74	C₇₉⋊#95	—	2	2	no	—
75	C₇₉⋊#95	—	2	2	no	—
76	C₂²×D₄×C₇₉	D₄	1	1	yes	characteristic
77	C₂³×C₄×C₇₉	C₂³	1	2	yes	—
78	C₂×M₁₆×C₇₉	—	2	4	no	—
79	C₂×M₁₆×C₇₉	—	2	4	no	—
80	C₂×M₁₆×C₇₉	C₂×C₄	1	8	yes	complemented
81	C₂²×C₈×C₇₉	C₂³	1	2	yes	—
82	C₂²×C₈×C₇₉	C₂³	1	1	yes	characteristic
83	C₂²×C₈×C₇₉	C₂³	1	1	yes	characteristic
84	C₄×D₄×C₇₉	C₂×C₄	1	4	yes	—
85	C₄×D₄×C₇₉	Q₈	1	4	yes	—
86	C₂×C₄⋊C₄×C₇₉	D₄	1	1	yes	characteristic
87	C₂×C₂²⋊C₄×C₇₉	D₄	1	2	yes	—
88	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
89	C₄⋊C₈×C₇₉	C₂×C₄	1	4	yes	complemented
90	C₂²⋊C₈×C₇₉	C₂×C₄	1	8	yes	complemented
91	C₄×C₈×C₇₉	C₂×C₄	1	4	yes	complemented
92	C₂²×Dic₇₉	—	2	1	no	—
93	C₂²×Dic₇₉	—	2	1	no	—
94	C₂²×Dic₇₉	—	2	1	no	—
95	C₂²×Dic₇₉	—	2	1	no	—
96	C₂²×Dic₇₉	—	2	2	no	—
97	C₂²×Dic₇₉	—	2	2	no	—
98	C₂²×Dic₇₉	—	4	4	no	—
99	C₂²×Dic₇₉	—	4	4	no	—
100	C₂²×Dic₇₉	—	8	2	no	—
101	C₄⋊Dic₇₉	—	2	2	no	—
102	C₄⋊Dic₇₉	—	2	2	no	—
103	C₄⋊Dic₇₉	—	2	1	no	—
104	C₄⋊Dic₇₉	—	2	1	no	—
105	C₄⋊Dic₇₉	—	2	1	no	—
106	C₄⋊Dic₇₉	—	2	1	no	—
107	C₄⋊Dic₇₉	—	2	2	no	—
108	C₄⋊Dic₇₉	—	2	2	no	—
109	C₄⋊Dic₇₉	—	2	1	no	—
110	C₄⋊Dic₇₉	—	2	1	no	—
111	C₄⋊Dic₇₉	—	4	4	no	—
112	C₄⋊Dic₇₉	—	4	2	no	—
113	C₄⋊Dic₇₉	—	4	2	no	—
114	C₄⋊Dic₇₉	—	8	1	no	—
115	C₄⋊Dic₇₉	—	8	1	no	—
116	C₄⋊Dic₇₉	C₂×D₄	1	2	yes	—
117	C₄⋊Dic₇₉	C₂×D₄	1	2	yes	—
118	C₂²⋊Dic₇₉	—	4	4	no	—
119	C₂²⋊Dic₇₉	—	4	4	no	—
120	C₂²⋊Dic₇₉	—	8	2	no	—
121	C₄×Dic₇₉	—	4	4	no	—
122	C₄×Dic₇₉	—	4	2	no	—
123	C₄×Dic₇₉	—	4	2	no	—
124	C₂⁴×C₇₉	C₂×D₄	1	2	yes	—
125	C₂×D₄×C₇₉	—	2	2	no	—
126	C₂×D₄×C₇₉	—	2	2	no	—
127	C₂×D₄×C₇₉	C₄⋊C₄	1	4	yes	—
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	4	yes	—
133	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
134	C₂²×C₄×C₇₉	C₂×D₄	1	2	yes	—
135	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
136	C₂²×C₄×C₇₉	C₂×Q₈	1	4	yes	—
137	C₂²×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
138	M₁₆×C₇₉	—	2	16	no	—
139	C₂×C₈×C₇₉	—	2	2	no	—
140	C₂×C₈×C₇₉	—	2	2	no	—
141	C₂×C₈×C₇₉	—	2	1	no	—
142	C₂×C₈×C₇₉	—	2	1	no	—
143	C₂×C₈×C₇₉	C₂²×C₄	1	2	yes	—
144	C₂×C₈×C₇₉	C₂²×C₄	1	4	yes	—
145	C₂×C₈×C₇₉	C₂²×C₄	1	2	yes	—
146	C₂×C₈×C₇₉	C₂×D₄	1	2	yes	—
147	C₂×C₈×C₇₉	#41	1	2	yes	—
148	C₄⋊C₄×C₇₉	C₄⋊C₄	1	4	yes	—
149	C₂²⋊C₄×C₇₉	C₄⋊C₄	1	8	yes	—
150	C₄²×C₇₉	C₂²×C₄	1	2	yes	—
151	C₄²×C₇₉	C₂×Q₈	1	2	yes	—
152	C₂³×C₇₉	—	2	2	no	—
153	C₂³×C₇₉	—	2	2	no	—
154	C₂³×C₇₉	—	2	2	no	—
155	C₂³×C₇₉	—	2	2	no	—
156	C₂³×C₇₉	—	2	2	no	—
157	C₂³×C₇₉	—	2	2	no	—
158	C₂³×C₇₉	C₂×C₄⋊C₄	1	4	yes	—
159	C₂³×C₇₉	C₂²×D₄	1	1	yes	characteristic
160	D₄×C₇₉	—	2	8	no	—
161	C₂×C₄×C₇₉	—	2	2	no	—
162	C₂×C₄×C₇₉	—	2	2	no	—
163	C₂×C₄×C₇₉	—	2	1	no	—
164	C₂×C₄×C₇₉	—	2	1	no	—
165	C₂×C₄×C₇₉	—	2	4	no	—
166	C₂×C₄×C₇₉	—	2	4	no	—
167	C₂×C₄×C₇₉	—	2	4	no	—
168	C₂×C₄×C₇₉	—	2	4	no	—
169	C₂×C₄×C₇₉	C₂×C₄⋊C₄	1	2	yes	—
170	C₂×C₄×C₇₉	C₂×C₄⋊C₄	1	4	yes	—
171	C₂×C₄×C₇₉	C₂×C₄⋊C₄	1	2	yes	—
172	C₂×C₄×C₇₉	AGL(1,ℤ/8)	1	2	yes	—
173	C₂×C₄×C₇₉	#137	1	2	yes	—
174	C₂×C₄×C₇₉	C₂³×C₄	1	1	yes	characteristic
175	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
176	C₂×C₄×C₇₉	C₂²×Q₈	1	1	yes	characteristic
177	C₂×C₄×C₇₉	C₂×#41	1	1	yes	characteristic
178	C₂×C₄×C₇₉	H(5,𝔽₂)	1	1	yes	characteristic
179	C₂×C₄×C₇₉	2₋¹⁺⁴	1	1	yes	characteristic
180	C₂×Dic₇₉	—	2	2	no	—
181	C₂×Dic₇₉	—	2	2	no	—
182	C₂×Dic₇₉	—	4	1	no	—
183	C₂×Dic₇₉	—	4	1	no	—
184	C₂×Dic₇₉	—	4	1	no	—
185	C₂×Dic₇₉	—	4	1	no	—
186	C₂×Dic₇₉	—	4	2	no	—
187	C₂×Dic₇₉	—	4	2	no	—
188	C₂×Dic₇₉	—	4	1	no	—
189	C₂×Dic₇₉	—	4	1	no	—
190	C₂×Dic₇₉	—	4	1	no	—
191	C₂×Dic₇₉	—	4	1	no	—
192	C₂×Dic₇₉	—	4	2	no	—
193	C₂×Dic₇₉	—	4	2	no	—
194	C₂×Dic₇₉	—	4	1	no	—
195	C₂×Dic₇₉	—	4	2	no	—
196	C₂×Dic₇₉	—	4	2	no	—
197	C₂×Dic₇₉	—	4	1	no	—
198	C₂×Dic₇₉	—	8	8	no	—
199	C₈×C₇₉	—	2	4	no	—
200	C₈×C₇₉	—	2	2	no	—
201	C₈×C₇₉	C₄×D₄	1	4	yes	complemented
202	C₂²×C₇₉	—	2	4	no	—
203	C₂²×C₇₉	—	2	4	no	—
204	C₂²×C₇₉	—	2	4	no	—
205	C₂²×C₇₉	—	4	2	no	—
206	C₂²×C₇₉	—	4	2	no	—
207	C₂²×C₇₉	—	4	2	no	—
208	C₂²×C₇₉	—	4	2	no	—
209	C₂²×C₇₉	C₂²×C₄⋊C₄	1	1	yes	characteristic
210	C₂²×C₇₉	D₄²	1	1	yes	characteristic
211	C₂²×C₇₉	#547	1	1	yes	characteristic
212	C₂²×C₇₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
213	C₂²×C₇₉	C₂×#137	1	1	yes	characteristic
214	C₂²×C₇₉	#577	1	1	yes	characteristic
215	C₂²×C₇₉	#577	1	1	yes	characteristic
216	C₄×C₇₉	—	2	4	no	—
217	C₄×C₇₉	—	2	2	no	—
218	C₄×C₇₉	#428	1	4	yes	complemented
219	C₄×C₇₉	C₂×C₄×D₄	1	1	yes	characteristic
220	C₄×C₇₉	#520	1	1	yes	characteristic
221	C₄×C₇₉	D₄×Q₈	1	1	yes	characteristic
222	C₄×C₇₉	#554	1	1	yes	characteristic
223	Dic₇₉	—	4	2	no	—
224	Dic₇₉	—	4	2	no	—
225	Dic₇₉	—	8	1	no	—
226	Dic₇₉	—	8	1	no	—
227	Dic₇₉	—	8	2	no	—
228	Dic₇₉	—	8	2	no	—
229	#22663	—	79	1	no	maximal, Sylow
230	C₂×C₇₉	—	4	4	no	—
231	C₂×C₇₉	D₄×C₄⋊C₄	1	1	yes	characteristic
232	C₂×C₇₉	C₂×#428	1	1	yes	characteristic
233	C₂×C₇₉	#2912	1	1	yes	characteristic
234	C₂×C₇₉	#3272	1	1	yes	characteristic
235	C₂×C₇₉	#3278	1	1	yes	characteristic
236	C₂×C₇₉	#3354	1	1	yes	characteristic
237	C₂×C₇₉	#3356	1	1	yes	characteristic
238	C₂×#436	D₇₉	1	1	yes	characteristic
239	C₂×#428	—	79	2	no	—
240	#2354	—	79	1	no	—
241	D₄×C₄⋊C₄	—	79	1	no	—
242	#1948	—	79	1	no	—
243	#1947	—	79	1	no	—
244	#1854	—	79	2	no	—
245	#1853	—	79	2	no	—
246	#1844	—	79	1	no	—
247	#1809	—	79	2	no	—
248	C₄×#107	—	79	1	no	—
249	C₇₉	#22663	1	1	yes	characteristic, complemented, Sylow
250	C₂²×M₁₆	C₂×D₇₉	1	2	yes	—
251	C₂×C₄×D₄	—	158	1	no	—
252	C₂×C₄×D₄	C₂×D₇₉	1	1	yes	characteristic
253	C₂×#117	—	79	2	no	—
254	C₂²×C₄⋊C₄	—	79	2	no	—
255	#436	Dic₇₉	1	8	yes	complemented
256	#428	—	158	8	no	—
257	C₂×#107	—	79	1	no	—
258	C₂×#107	—	79	1	no	—
259	C₂×#107	—	79	2	no	—
260	C₂×#106	—	79	2	no	—
261	C₂×#106	—	79	2	no	—
262	C₂×#106	—	79	2	no	—
263	C₂×C₄⋊C₈	C₂×D₇₉	1	1	yes	characteristic
264	C₂×C₂²⋊C₈	C₂×D₇₉	1	2	yes	—
265	C₂×C₄×C₈	C₂×D₇₉	1	1	yes	characteristic
266	#390	—	158	1	no	—
267	#389	—	158	1	no	—
268	#388	—	158	2	no	—
269	#385	—	158	2	no	—
270	#384	—	79	1	no	—
271	#384	—	79	1	no	—
272	#380	—	79	2	no	—
273	#380	—	79	2	no	—
274	C₄×C₄⋊C₄	—	79	1	no	—
275	C₄×C₄⋊C₄	—	79	1	no	—
276	C₄×C₄⋊C₄	—	158	1	no	—
277	#340	—	79	2	no	—
278	#340	—	79	2	no	—
279	#340	—	79	1	no	—
280	#340	—	79	1	no	—
281	C₂²×D₄	D₃₁₆	1	1	yes	characteristic
282	C₂³×C₄	—	158	2	no	—
283	C₂³×C₄	C₂²×D₇₉	1	2	yes	—
284	C₂×M₁₆	—	2	4	no	—
285	C₂×M₁₆	—	2	4	no	—
286	C₂×M₁₆	C₂×Dic₇₉	1	8	yes	complemented
287	C₂²×C₈	C₂²×D₇₉	1	2	yes	—
288	C₂²×C₈	C₂²×D₇₉	1	1	yes	characteristic
289	C₂²×C₈	C₂²×D₇₉	1	1	yes	characteristic
290	C₄×D₄	—	316	4	no	—
291	C₄×D₄	Dic₁₅₈	1	4	yes	—
292	C₄×D₄	C₂×Dic₇₉	1	4	yes	—
293	#117	—	316	2	no	—
294	#117	—	158	4	no	—
295	C₂×C₄⋊C₄	—	316	2	no	—
296	C₂×C₄⋊C₄	—	79	1	no	—
297	C₂×C₄⋊C₄	—	79	1	no	—
298	C₂×C₄⋊C₄	—	79	2	no	—
299	C₂×C₄⋊C₄	—	79	2	no	—
300	C₂×C₄⋊C₄	—	79	1	no	—
301	C₂×C₄⋊C₄	—	79	1	no	—
302	C₂×C₄⋊C₄	—	158	2	no	—
303	C₂×C₄⋊C₄	—	158	1	no	—
304	C₂×C₄⋊C₄	—	158	1	no	—
305	C₂×C₄⋊C₄	—	158	4	no	—
306	C₂×C₄⋊C₄	—	158	1	no	—
307	C₂×C₄⋊C₄	—	158	1	no	—
308	C₂×C₄⋊C₄	D₃₁₆	1	1	yes	characteristic
309	C₂×C₂²⋊C₄	—	158	2	no	—
310	C₂×C₂²⋊C₄	—	158	2	no	—
311	C₂×C₂²⋊C₄	—	158	2	no	—
312	C₂×C₂²⋊C₄	D₃₁₆	1	2	yes	—
313	C₂×C₄²	—	158	2	no	—
314	C₂×C₄²	—	158	1	no	—
315	C₂×C₄²	—	158	1	no	—
316	C₂×C₄²	C₂²×D₇₉	1	1	yes	characteristic
317	#107	—	79	4	no	—
318	#107	—	158	4	no	—
319	#107	—	158	2	no	—
320	#106	—	316	2	no	—
321	#106	—	158	4	no	—
322	#106	—	158	4	no	—
323	C₄⋊C₈	C₂×Dic₇₉	1	4	yes	complemented
324	C₂²⋊C₈	C₂×Dic₇₉	1	8	yes	complemented
325	C₄×C₈	C₂×Dic₇₉	1	4	yes	complemented
326	#95	—	158	1	no	—
327	#95	—	158	1	no	—
328	#95	—	158	2	no	—
329	#95	—	158	2	no	—
330	C₂⁴	C₂×D₃₁₆	1	2	yes	—
331	C₂×D₄	—	2	2	no	—
332	C₂×D₄	—	2	2	no	—
333	C₂×D₄	C₄⋊Dic₇₉	1	4	yes	—
334	C₂²×C₄	—	2	2	no	—
335	C₂²×C₄	—	2	2	no	—
336	C₂²×C₄	—	2	2	no	—
337	C₂²×C₄	—	2	2	no	—
338	C₂²×C₄	—	316	4	no	—
339	C₂²×C₄	—	316	4	no	—
340	C₂²×C₄	—	632	2	no	—
341	C₂²×C₄	—	158	1	no	—
342	C₂²×C₄	—	158	1	no	—
343	C₂²×C₄	—	158	2	no	—
344	C₂²×C₄	—	158	2	no	—
345	C₂²×C₄	—	158	1	no	—
346	C₂²×C₄	—	158	1	no	—
347	C₂²×C₄	C₂²×Dic₇₉	1	4	yes	—
348	C₂²×C₄	C₂×D₃₁₆	1	2	yes	—
349	C₂²×C₄	C₂×D₃₁₆	1	1	yes	characteristic
350	C₂²×C₄	C₂×D₃₁₆	1	1	yes	characteristic
351	C₂²×C₄	C₂×Dic₁₅₈	1	4	yes	—
352	C₂²×C₄	C₂³×D₇₉	1	1	yes	characteristic
353	M₁₆	—	2	16	no	—
354	C₂×C₈	—	2	2	no	—
355	C₂×C₈	—	2	1	no	—
356	C₂×C₈	—	2	1	no	—
357	C₂×C₈	—	2	2	no	—
358	C₂×C₈	C₂²×Dic₇₉	1	2	yes	—
359	C₂×C₈	C₂²×Dic₇₉	1	4	yes	—
360	C₂×C₈	C₂²×Dic₇₉	1	2	yes	—
361	C₂×C₈	D₄×D₇₉	1	2	yes	—
362	C₂×C₈	#11929623	1	2	yes	—
363	C₄⋊C₄	—	316	4	no	—
364	C₄⋊C₄	—	316	2	no	—
365	C₄⋊C₄	—	316	2	no	—
366	C₄⋊C₄	—	79	2	no	—
367	C₄⋊C₄	—	79	2	no	—
368	C₄⋊C₄	—	632	1	no	—
369	C₄⋊C₄	—	632	1	no	—
370	C₄⋊C₄	—	158	1	no	—
371	C₄⋊C₄	—	158	1	no	—
372	C₄⋊C₄	—	158	2	no	—
373	C₄⋊C₄	—	158	2	no	—
374	C₄⋊C₄	—	158	1	no	—
375	C₄⋊C₄	—	158	1	no	—
376	C₄⋊C₄	—	158	2	no	—
377	C₄⋊C₄	—	158	2	no	—
378	C₄⋊C₄	—	158	1	no	—
379	C₄⋊C₄	—	158	1	no	—
380	C₄⋊C₄	C₄⋊Dic₇₉	1	4	yes	—
381	C₂²⋊C₄	—	316	4	no	—
382	C₂²⋊C₄	—	316	4	no	—
383	C₂²⋊C₄	—	632	2	no	—
384	C₂²⋊C₄	C₄⋊Dic₇₉	1	8	yes	—
385	C₄²	—	316	4	no	—
386	C₄²	—	316	2	no	—
387	C₄²	—	316	2	no	—
388	C₄²	C₂²×Dic₇₉	1	2	yes	—
389	C₄²	C₂×Dic₁₅₈	1	2	yes	—
390	C₂³	—	2	2	no	—
391	C₂³	—	2	2	no	—
392	C₂³	—	2	2	no	—
393	C₂³	—	2	2	no	—
394	C₂³	—	2	2	no	—
395	C₂³	—	2	2	no	—
396	C₂³	C₂×C₄⋊Dic₇₉	1	4	yes	—
397	C₂³	C₂²×D₃₁₆	1	1	yes	characteristic
398	D₄	—	2	8	no	—
399	C₂×C₄	—	2	2	no	—
400	C₂×C₄	—	2	2	no	—
401	C₂×C₄	—	2	1	no	—
402	C₂×C₄	—	2	1	no	—
403	C₂×C₄	—	2	4	no	—
404	C₂×C₄	—	2	4	no	—
405	C₂×C₄	—	2	4	no	—
406	C₂×C₄	—	2	4	no	—
407	C₂×C₄	—	316	1	no	—
408	C₂×C₄	—	316	1	no	—
409	C₂×C₄	—	316	1	no	—
410	C₂×C₄	—	316	1	no	—
411	C₂×C₄	—	316	2	no	—
412	C₂×C₄	—	316	2	no	—
413	C₂×C₄	—	316	1	no	—
414	C₂×C₄	—	316	1	no	—
415	C₂×C₄	—	316	1	no	—
416	C₂×C₄	—	316	1	no	—
417	C₂×C₄	—	316	2	no	—
418	C₂×C₄	—	316	2	no	—
419	C₂×C₄	—	316	1	no	—
420	C₂×C₄	—	316	2	no	—
421	C₂×C₄	—	316	2	no	—
422	C₂×C₄	—	316	1	no	—
423	C₂×C₄	—	632	8	no	—
424	C₂×C₄	—	158	2	no	—
425	C₂×C₄	—	158	2	no	—
426	C₂×C₄	C₂×C₄⋊Dic₇₉	1	2	yes	—
427	C₂×C₄	C₂×C₄⋊Dic₇₉	1	4	yes	—
428	C₂×C₄	C₂×C₄⋊Dic₇₉	1	2	yes	—
429	C₂×C₄	#14579189	1	2	yes	—
430	C₂×C₄	#14579194	1	2	yes	—
431	C₂×C₄	C₂³×Dic₇₉	1	1	yes	characteristic
432	C₂×C₄	C₂×D₄×D₇₉	1	1	yes	characteristic
433	C₂×C₄	C₂²×Dic₁₅₈	1	1	yes	characteristic
434	C₂×C₄	C₂×#11929623	1	1	yes	characteristic
435	C₂×C₄	#14579207	1	1	yes	characteristic
436	C₂×C₄	#14579208	1	1	yes	characteristic
437	C₈	—	2	4	no	—
438	C₈	—	2	2	no	—
439	C₈	D₄×Dic₇₉	1	4	yes	complemented
440	C₂²	—	2	4	no	—
441	C₂²	—	2	4	no	—
442	C₂²	—	2	4	no	—
443	C₂²	—	4	2	no	—
444	C₂²	—	4	2	no	—
445	C₂²	—	4	2	no	—
446	C₂²	—	4	2	no	—
447	C₂²	C₂²×C₄⋊Dic₇₉	1	1	yes	characteristic
448	C₂²	D₄×D₃₁₆	1	1	yes	characteristic
449	C₂²	#19099217	1	1	yes	characteristic
450	C₂²	C₂×#14579189	1	1	yes	characteristic
451	C₂²	C₂×#14579194	1	1	yes	characteristic
452	C₂²	#19099375	1	1	yes	characteristic
453	C₂²	#19099375	1	1	yes	characteristic
454	C₄	—	2	4	no	—
455	C₄	—	2	2	no	—
456	C₄	—	316	2	no	—
457	C₄	—	316	2	no	—
458	C₄	—	632	2	no	—
459	C₄	—	632	2	no	—
460	C₄	—	632	1	no	—
461	C₄	—	632	1	no	—
462	C₄	#19098605	1	4	yes	complemented
463	C₄	C₂×D₄×Dic₇₉	1	1	yes	characteristic
464	C₄	#19099046	1	1	yes	characteristic
465	C₄	D₄×Dic₁₅₈	1	1	yes	characteristic
466	C₄	#19099270	1	1	yes	characteristic
467	C₂	—	4	4	no	—
468	C₂	D₄×C₄⋊Dic₇₉	1	1	yes	characteristic
469	C₂	C₂×#19098605	1	1	yes	characteristic
470	C₂	#23771995	1	1	yes	characteristic
471	C₂	#23775002	1	1	yes	characteristic
472	C₂	#23775068	1	1	yes	characteristic
473	C₂	#23775996	1	1	yes	characteristic
474	C₂	#23776016	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂²×D₃₁₆
commutator	C₂×C₄×C₇₉	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₇₉
Fitting	C₂×#436×C₇₉	C₂
socle	C₂³×C₇₉	C₂²×D₄
prime radical	C₂²×D₄×C₇₉	D₄
cosocle	C₂²×C₄×C₇₉	C₂⁴
hypercenter	C₂×#436	D₇₉
hypocenter	C₇₉	#22663
LCS	G ▷ C₂×C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂³ ◁ C₂×C₄×D₄ ◁ C₂×#436

Complements

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

N	H ≅ G/N	type
1. C₂×#19098605	C₂	semidirect
4. #23764164	C₂	semidirect
5. #23764159	C₂	semidirect
6. #23763601	C₂	semidirect
7. #23763595	C₂	semidirect
8. #23763557	C₂	semidirect
9. #23763433	C₂	semidirect
10. C₄×#14579095	C₂	semidirect
39. #436×C₇₉	C₄	semidirect
68. #14579095	D₄	semidirect
80. C₂×M₁₆×C₇₉	C₂×C₄	semidirect
89. C₄⋊C₈×C₇₉	C₂×C₄	semidirect
90. C₂²⋊C₈×C₇₉	C₂×C₄	semidirect
91. C₄×C₈×C₇₉	C₂×C₄	semidirect
201. C₈×C₇₉	C₄×D₄	semidirect
218. C₄×C₇₉	#428	semidirect
249. C₇₉	#22663	semidirect
255. #436	Dic₇₉	semidirect
286. C₂×M₁₆	C₂×Dic₇₉	semidirect
323. C₄⋊C₈	C₂×Dic₇₉	semidirect
324. C₂²⋊C₈	C₂×Dic₇₉	semidirect
325. C₄×C₈	C₂×Dic₇₉	semidirect
439. C₈	D₄×Dic₇₉	semidirect
462. C₄	#19098605	semidirect

Maximal subgroups

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

subgroup	index
C₂×#19098605	2
#23766349	2
D₄×C₄⋊Dic₇₉	2
#23764164	2
#23764159	2
#23763601	2
#23763595	2
#23763557	2
#23763433	2
C₄×#14579095	2
C₂×#436×C₇₉	2
#22663	79