Subgroups — #34306712

Order 20224.

858 conjugacy classes of subgroups.

The subgroup lattice has 474 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#19098685	C₂	1	1	yes	maximal, characteristic
2	#135×Dic₇₉	C₂	1	1	yes	maximal, characteristic
3	#23771966	C₂	1	2	yes	maximal, complemented
4	#23764153	C₂	1	1	yes	maximal, characteristic, complemented
5	#23764151	C₂	1	1	yes	maximal, characteristic, complemented
6	#23763675	C₂	1	2	yes	maximal, complemented
7	#23763673	C₂	1	2	yes	maximal, complemented
8	#23763570	C₂	1	1	yes	maximal, characteristic, complemented
9	#23763418	C₂	1	2	yes	maximal, complemented
10	#23763268	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×#444×C₇₉	C₂	1	1	yes	maximal, characteristic
12	C₂×#14579168	C₂²	1	2	yes	—
13	#41×Dic₇₉	C₂²	1	2	yes	—
14	#19098685	—	2	4	no	—
15	Q₁₆×Dic₇₉	C₄	1	1	yes	characteristic, complemented
16	Q₁₆×Dic₇₉	C₄	1	1	yes	characteristic, complemented
17	SD₁₆×Dic₇₉	C₄	1	2	yes	complemented
18	SD₁₆×Dic₇₉	C₄	1	2	yes	complemented
19	D₈×Dic₇₉	C₄	1	1	yes	characteristic, complemented
20	D₈×Dic₇₉	C₄	1	1	yes	characteristic, complemented
21	C₂×#14579097	C₂²	1	1	yes	characteristic
22	C₂×#14579096	C₂²	1	2	yes	—
23	#19098601	C₂²	1	1	yes	characteristic
24	#19098591	—	2	2	no	—
25	#19098591	C₂²	1	2	yes	—
26	#19098589	—	2	2	no	—
27	#19098589	C₂²	1	2	yes	—
28	#19098586	—	2	2	no	—
29	#19098586	C₂²	1	2	yes	—
30	C₂×Dic₇₉⋊C₈	—	2	2	no	—
31	C₂×Dic₇₉⋊C₈	C₂²	1	1	yes	characteristic
32	C₂×#14579088	C₂²	1	2	yes	—
33	#19098559	C₂²	1	2	yes	—
34	C₂×#14579071	C₂²	1	1	yes	characteristic
35	C₂×C₈×Dic₇₉	C₂²	1	1	yes	characteristic
36	C₄×Dic₇₉⋊C₄	C₂²	1	1	yes	characteristic
37	#19098324	C₂²	1	2	yes	—
38	#19098323	C₂²	1	2	yes	—
39	#19098318	C₂²	1	1	yes	characteristic
40	#19098317	C₂²	1	1	yes	characteristic
41	C₂×#135×C₇₉	C₂²	1	1	yes	characteristic
42	C₂×#131×C₇₉	C₂²	1	2	yes	—
43	#444×C₇₉	—	2	4	no	—
44	C₂×#108×C₇₉	C₂²	1	1	yes	characteristic
45	C₂×#104×C₇₉	C₂²	1	2	yes	—
46	C₂×#97×C₇₉	C₂²	1	1	yes	characteristic
47	#14579168	—	2	4	no	—
48	#14579168	—	4	2	no	—
49	C₂×#11929608	—	2	2	no	—
50	C₂×#11929608	C₂³	1	2	yes	—
51	C₂²×C₇₉⋊C₈	—	2	2	no	—
52	C₂²×C₇₉⋊C₈	C₂³	1	1	yes	characteristic
53	C₂²×C₇₉⋊C₈	C₂³	1	1	yes	characteristic
54	Q₈×Dic₇₉	C₂×C₄	1	2	yes	—
55	Q₈×Dic₇₉	C₂×C₄	1	2	yes	—
56	D₄×Dic₇₉	—	2	2	no	—
57	D₄×Dic₇₉	—	2	2	no	—
58	D₄×Dic₇₉	C₂×C₄	1	2	yes	—
59	D₄×Dic₇₉	C₂×C₄	1	2	yes	—
60	#14579120	—	2	2	no	—
61	#14579120	C₂³	1	2	yes	—
62	C₂×Dic₇₉⋊C₄	—	2	1	no	—
63	C₂×C₄×Dic₇₉	—	2	2	no	—
64	C₂×C₄×Dic₇₉	C₂³	1	1	yes	characteristic
65	C₂×C₄×Dic₇₉	C₂³	1	1	yes	characteristic
66	#14579097	—	2	2	no	—
67	#14579096	—	4	2	no	—
68	#14579095	C₂×C₄	1	1	yes	characteristic
69	#14579095	C₂×C₄	1	1	yes	characteristic
70	#14579093	C₂×C₄	1	2	yes	—
71	Dic₇₉⋊C₈	—	2	2	no	—
72	Dic₇₉⋊C₈	—	2	2	no	—
73	Dic₇₉⋊C₈	—	2	2	no	—
74	Dic₇₉⋊C₈	—	2	2	no	—
75	Dic₇₉⋊C₈	—	2	2	no	—
76	Dic₇₉⋊C₈	—	2	2	no	—
77	Dic₇₉⋊C₈	D₄	1	2	yes	—
78	Dic₇₉⋊C₈	D₄	1	2	yes	—
79	#14579088	—	2	4	no	—
80	#14579085	C₂×C₄	1	2	yes	—
81	#14579085	C₂×C₄	1	2	yes	—
82	#14579082	C₂×C₄	1	2	yes	—
83	#14579082	C₂×C₄	1	2	yes	—
84	#14579071	—	2	2	no	—
85	C₈×Dic₇₉	C₂×C₄	1	1	yes	characteristic
86	C₈×Dic₇₉	C₂×C₄	1	1	yes	characteristic
87	C₈×Dic₇₉	C₂×C₄	1	1	yes	characteristic
88	C₈×Dic₇₉	C₂×C₄	1	1	yes	characteristic
89	C₇₉⋊#95	—	2	1	no	—
90	C₂×#41×C₇₉	C₂³	1	2	yes	—
91	#135×C₇₉	D₄	1	4	yes	—
92	#135×C₇₉	Q₈	1	4	yes	—
93	C₂×Q₁₆×C₇₉	C₂×C₄	1	1	yes	characteristic
94	C₂×SD₁₆×C₇₉	C₂×C₄	1	2	yes	—
95	C₂×D₈×C₇₉	C₂×C₄	1	1	yes	characteristic
96	#131×C₇₉	—	2	4	no	—
97	#131×C₇₉	—	4	2	no	—
98	C₂×M₁₆×C₇₉	—	2	2	no	—
99	C₂×M₁₆×C₇₉	C₂³	1	2	yes	—
100	C₂²×C₈×C₇₉	—	2	2	no	—
101	C₂²×C₈×C₇₉	C₂³	1	1	yes	characteristic
102	C₂²×C₈×C₇₉	C₂³	1	1	yes	characteristic
103	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
104	#108×C₇₉	—	2	2	no	—
105	#104×C₇₉	—	2	4	no	—
106	#97×C₇₉	—	2	2	no	—
107	C₂²×Dic₇₉	—	2	2	no	—
108	C₂²×Dic₇₉	—	2	2	no	—
109	C₂²×Dic₇₉	—	2	1	no	—
110	C₂²×Dic₇₉	#41	1	1	yes	characteristic
111	C₂²×Dic₇₉	#41	1	1	yes	characteristic
112	#11929608	—	2	2	no	—
113	#11929608	—	2	2	no	—
114	#11929608	—	4	4	no	—
115	C₂×C₇₉⋊C₈	—	2	1	no	—
116	C₂×C₇₉⋊C₈	—	2	2	no	—
117	C₂×C₇₉⋊C₈	—	2	1	no	—
118	C₂×C₇₉⋊C₈	—	2	1	no	—
119	C₂×C₇₉⋊C₈	—	2	1	no	—
120	C₂×C₇₉⋊C₈	—	4	4	no	—
121	C₂×C₇₉⋊C₈	C₂²×C₄	1	1	yes	characteristic
122	C₂×C₇₉⋊C₈	C₂²×C₄	1	1	yes	characteristic
123	C₂×C₇₉⋊C₈	C₂×D₄	1	2	yes	—
124	C₄⋊Dic₇₉	—	2	2	no	—
125	C₄⋊Dic₇₉	—	2	2	no	—
126	C₄⋊Dic₇₉	C₂²×C₄	1	2	yes	—
127	C₄⋊Dic₇₉	C₂²×C₄	1	2	yes	—
128	Dic₇₉⋊C₄	—	4	2	no	—
129	C₂²⋊Dic₇₉	—	2	2	no	—
130	C₂²⋊Dic₇₉	—	2	2	no	—
131	C₂²⋊Dic₇₉	—	2	2	no	—
132	C₄×Dic₇₉	—	2	2	no	—
133	C₄×Dic₇₉	—	2	2	no	—
134	C₄×Dic₇₉	—	2	2	no	—
135	C₄×Dic₇₉	—	2	1	no	—
136	C₄×Dic₇₉	—	2	1	no	—
137	C₄×Dic₇₉	C₂²×C₄	1	1	yes	characteristic
138	C₄×Dic₇₉	C₂²×C₄	1	1	yes	characteristic
139	C₄×Dic₇₉	C₂×D₄	1	1	yes	characteristic
140	C₄×Dic₇₉	C₂×D₄	1	1	yes	characteristic
141	#41×C₇₉	—	2	2	no	—
142	#41×C₇₉	—	2	2	no	—
143	#41×C₇₉	C₂×D₄	1	4	yes	—
144	#41×C₇₉	C₂×Q₈	1	4	yes	—
145	C₂×Q₈×C₇₉	C₂²×C₄	1	2	yes	—
146	C₂×D₄×C₇₉	—	2	2	no	—
147	C₂×D₄×C₇₉	C₂²×C₄	1	2	yes	—
148	C₂²×C₄×C₇₉	—	2	2	no	—
149	C₂²×C₄×C₇₉	—	2	1	no	—
150	C₂²×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
151	Q₁₆×C₇₉	C₄⋊C₄	1	4	yes	complemented
152	SD₁₆×C₇₉	C₄⋊C₄	1	8	yes	complemented
153	D₈×C₇₉	C₄⋊C₄	1	4	yes	complemented
154	M₁₆×C₇₉	—	2	2	no	—
155	M₁₆×C₇₉	—	2	2	no	—
156	M₁₆×C₇₉	—	4	4	no	—
157	C₂×C₈×C₇₉	—	2	1	no	—
158	C₂×C₈×C₇₉	—	2	2	no	—
159	C₂×C₈×C₇₉	—	2	1	no	—
160	C₂×C₈×C₇₉	—	4	4	no	—
161	C₂×C₈×C₇₉	C₂²×C₄	1	1	yes	characteristic
162	C₂×C₈×C₇₉	C₂²×C₄	1	1	yes	characteristic
163	C₂×C₈×C₇₉	C₂×D₄	1	2	yes	—
164	C₂×C₈×C₇₉	C₂×D₄	1	2	yes	—
165	C₂×C₈×C₇₉	C₂×Q₈	1	2	yes	—
166	C₄²×C₇₉	—	2	1	no	—
167	C₄²×C₇₉	—	2	1	no	—
168	C₂³×C₇₉	—	2	2	no	—
169	C₂³×C₇₉	C₂×#41	1	1	yes	characteristic
170	Q₈×C₇₉	—	2	2	no	—
171	Q₈×C₇₉	C₂×C₄⋊C₄	1	4	yes	—
172	D₄×C₇₉	—	2	4	no	—
173	D₄×C₇₉	—	2	4	no	—
174	D₄×C₇₉	—	2	2	no	—
175	D₄×C₇₉	C₂×C₄⋊C₄	1	4	yes	—
176	C₂×C₄×C₇₉	—	2	2	no	—
177	C₂×C₄×C₇₉	—	2	4	no	—
178	C₂×C₄×C₇₉	—	2	4	no	—
179	C₂×C₄×C₇₉	—	4	1	no	—
180	C₂×C₄×C₇₉	—	4	1	no	—
181	C₂×C₄×C₇₉	—	4	1	no	—
182	C₂×C₄×C₇₉	C₂³×C₄	1	1	yes	characteristic
183	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
184	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
185	C₂×C₄×C₇₉	C₂²×Q₈	1	1	yes	characteristic
186	C₂×C₄×C₇₉	H(5,𝔽₂)	1	1	yes	characteristic
187	C₂×C₄×C₇₉	2₋¹⁺⁴	1	1	yes	characteristic
188	C₂×Dic₇₉	—	2	2	no	—
189	C₂×Dic₇₉	—	2	2	no	—
190	C₂×Dic₇₉	—	2	2	no	—
191	C₂×Dic₇₉	—	4	1	no	—
192	C₂×Dic₇₉	—	4	4	no	—
193	C₂×Dic₇₉	—	4	1	no	—
194	C₂×Dic₇₉	—	4	1	no	—
195	C₂×Dic₇₉	—	4	1	no	—
196	C₂×Dic₇₉	—	8	2	no	—
197	C₂×Dic₇₉	C₄×D₄	1	1	yes	characteristic
198	C₂×Dic₇₉	C₄×D₄	1	1	yes	characteristic
199	C₂×Dic₇₉	C₄×D₄	1	1	yes	characteristic
200	C₂×Dic₇₉	C₄×D₄	1	1	yes	characteristic
201	C₈×C₇₉	—	2	2	no	—
202	C₈×C₇₉	—	4	2	no	—
203	C₈×C₇₉	C₂×C₄⋊C₄	1	2	yes	—
204	C₈×C₇₉	C₂×C₄⋊C₄	1	2	yes	—
205	C₇₉⋊C₈	—	2	1	no	—
206	C₇₉⋊C₈	—	2	1	no	—
207	C₇₉⋊C₈	—	2	2	no	—
208	C₇₉⋊C₈	—	4	2	no	—
209	C₂²×C₇₉	—	2	1	no	—
210	C₂²×C₇₉	—	2	1	no	—
211	C₂²×C₇₉	—	2	4	no	—
212	C₂²×C₇₉	—	4	2	no	—
213	C₂²×C₇₉	—	4	2	no	—
214	C₂²×C₇₉	C₂×C₄×D₄	1	1	yes	characteristic
215	C₂²×C₇₉	#547	1	1	yes	characteristic
216	C₂²×C₇₉	#554	1	1	yes	characteristic
217	C₄×C₇₉	—	2	4	no	—
218	C₄×C₇₉	—	8	1	no	—
219	C₄×C₇₉	C₂²×C₄⋊C₄	1	1	yes	characteristic
220	C₄×C₇₉	#520	1	1	yes	characteristic
221	C₄×C₇₉	D₄²	1	1	yes	characteristic
222	C₄×C₇₉	D₄×Q₈	1	1	yes	characteristic
223	Dic₇₉	—	2	1	no	—
224	Dic₇₉	—	2	1	no	—
225	Dic₇₉	—	2	1	no	—
226	Dic₇₉	—	4	2	no	—
227	Dic₇₉	—	4	2	no	—
228	Dic₇₉	—	8	1	no	—
229	Dic₇₉	#444	1	2	yes	complemented
230	#22686	—	79	1	no	maximal, Sylow
231	C₂×C₇₉	—	2	1	no	—
232	C₂×C₇₉	—	2	1	no	—
233	C₂×C₇₉	—	4	4	no	—
234	C₂×C₇₉	D₄×C₄⋊C₄	1	1	yes	characteristic
235	C₂×C₇₉	C₂×#444	1	1	yes	characteristic
236	C₂×C₇₉	#2957	1	1	yes	characteristic
237	C₂×#444	—	79	1	no	—
238	C₂×#444	D₇₉	1	1	yes	characteristic
239	C₄×#135	—	79	1	no	—
240	#2906	—	79	2	no	—
241	#1946	—	79	1	no	—
242	#1946	—	79	1	no	—
243	#1866	—	79	2	no	—
244	#1866	—	79	2	no	—
245	#1848	—	79	1	no	—
246	#1806	—	79	2	no	—
247	#1770	—	79	1	no	—
248	C₇₉	#22686	1	1	yes	characteristic, complemented, Sylow
249	C₂×#135	C₂×D₇₉	1	1	yes	characteristic
250	C₂×#131	—	79	2	no	—
251	C₂×#131	C₂×D₇₉	1	2	yes	—
252	C₄×#41	—	79	2	no	—
253	#444	—	2	4	no	—
254	#444	—	158	4	no	—
255	C₄×Q₁₆	—	79	1	no	—
256	C₄×Q₁₆	—	79	1	no	—
257	C₄×SD₁₆	—	79	2	no	—
258	C₄×SD₁₆	—	79	2	no	—
259	C₄×D₈	—	79	1	no	—
260	C₄×D₈	—	79	1	no	—
261	C₂×#108	—	79	2	no	—
262	C₂×#108	—	79	1	no	—
263	C₂×#108	C₂×D₇₉	1	1	yes	characteristic
264	#427	—	79	1	no	—
265	#424	—	79	2	no	—
266	#424	—	79	2	no	—
267	#424	—	158	2	no	—
268	#424	—	158	2	no	—
269	#423	—	79	2	no	—
270	#423	—	158	2	no	—
271	C₂×C₄⋊C₈	—	79	1	no	—
272	C₂×C₄⋊C₈	—	158	2	no	—
273	C₂×#104	—	79	2	no	—
274	C₂×#104	C₂×D₇₉	1	2	yes	—
275	#416	—	79	2	no	—
276	C₂×#97	—	79	1	no	—
277	C₂×#97	C₂×D₇₉	1	1	yes	characteristic
278	C₂×C₄×C₈	—	79	1	no	—
279	C₄×C₄⋊C₄	—	79	1	no	—
280	#339	—	79	2	no	—
281	#339	—	79	2	no	—
282	#336	—	79	1	no	—
283	#336	—	79	1	no	—
284	C₂×#41	C₂²×D₇₉	1	2	yes	—
285	#135	Dic₁₅₈	1	4	yes	—
286	#135	C₂²⋊D₇₉	1	4	yes	—
287	C₂×Q₁₆	C₄×D₇₉	1	1	yes	characteristic
288	C₂×SD₁₆	C₄×D₇₉	1	2	yes	—
289	C₂×D₈	C₄×D₇₉	1	1	yes	characteristic
290	#131	—	2	4	no	—
291	#131	—	4	2	no	—
292	#131	—	316	2	no	—
293	#131	—	158	4	no	—
294	C₂×M₁₆	—	2	2	no	—
295	C₂×M₁₆	—	79	2	no	—
296	C₂×M₁₆	—	158	2	no	—
297	C₂×M₁₆	C₂²×D₇₉	1	2	yes	—
298	C₂²×C₈	—	2	2	no	—
299	C₂²×C₈	—	79	1	no	—
300	C₂²×C₈	—	79	1	no	—
301	C₂²×C₈	—	158	2	no	—
302	C₂²×C₈	C₂²×D₇₉	1	1	yes	characteristic
303	C₂²×C₈	C₂²×D₇₉	1	1	yes	characteristic
304	C₄×Q₈	—	79	2	no	—
305	C₄×Q₈	—	79	2	no	—
306	C₄×D₄	—	79	2	no	—
307	C₄×D₄	—	79	2	no	—
308	C₄×D₄	—	158	2	no	—
309	C₄×D₄	—	158	2	no	—
310	#117	—	79	2	no	—
311	#117	—	158	2	no	—
312	C₂×C₄⋊C₄	—	158	1	no	—
313	C₂×C₄²	—	79	1	no	—
314	C₂×C₄²	—	79	1	no	—
315	C₂×C₄²	—	158	2	no	—
316	C₂×C₄²	C₂²×D₇₉	1	1	yes	characteristic
317	#108	—	2	2	no	—
318	#108	—	316	2	no	—
319	#108	—	158	2	no	—
320	#107	—	79	1	no	—
321	#107	—	79	1	no	—
322	#106	—	79	2	no	—
323	C₄⋊C₈	—	79	2	no	—
324	C₄⋊C₈	—	79	2	no	—
325	C₄⋊C₈	—	158	2	no	—
326	C₄⋊C₈	—	158	2	no	—
327	C₄⋊C₈	—	158	2	no	—
328	C₄⋊C₈	—	158	2	no	—
329	C₄⋊C₈	—	158	2	no	—
330	C₄⋊C₈	—	158	2	no	—
331	#104	—	2	4	no	—
332	#104	—	158	4	no	—
333	#103	—	79	2	no	—
334	#103	—	79	2	no	—
335	#102	—	79	2	no	—
336	#102	—	79	2	no	—
337	#97	—	2	2	no	—
338	#97	—	158	2	no	—
339	C₄×C₈	—	79	1	no	—
340	C₄×C₈	—	79	1	no	—
341	C₄×C₈	—	79	1	no	—
342	C₄×C₈	—	79	1	no	—
343	#95	—	158	1	no	—
344	#41	—	2	2	no	—
345	#41	—	2	2	no	—
346	#41	C₂×C₂²⋊D₇₉	1	4	yes	—
347	#41	C₂×Dic₁₅₈	1	4	yes	—
348	C₂×Q₈	C₂×C₄×D₇₉	1	2	yes	—
349	C₂×D₄	—	2	2	no	—
350	C₂×D₄	C₂×C₄×D₇₉	1	2	yes	—
351	C₂²×C₄	—	2	2	no	—
352	C₂²×C₄	—	2	1	no	—
353	C₂²×C₄	—	79	1	no	—
354	C₂²×C₄	—	79	1	no	—
355	C₂²×C₄	—	158	1	no	—
356	C₂²×C₄	—	158	2	no	—
357	C₂²×C₄	—	158	2	no	—
358	C₂²×C₄	C₂³×D₇₉	1	1	yes	characteristic
359	Q₁₆	Dic₇₉⋊C₄	1	4	yes	complemented
360	SD₁₆	Dic₇₉⋊C₄	1	8	yes	complemented
361	D₈	Dic₇₉⋊C₄	1	4	yes	complemented
362	M₁₆	—	2	2	no	—
363	M₁₆	—	2	2	no	—
364	M₁₆	—	4	4	no	—
365	M₁₆	—	316	4	no	—
366	M₁₆	—	158	2	no	—
367	M₁₆	—	158	2	no	—
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	1	no	—
374	C₂×C₈	—	79	1	no	—
375	C₂×C₈	—	79	2	no	—
376	C₂×C₈	—	158	2	no	—
377	C₂×C₈	—	158	1	no	—
378	C₂×C₈	—	158	1	no	—
379	C₂×C₈	—	158	1	no	—
380	C₂×C₈	—	158	1	no	—
381	C₂×C₈	C₂×C₄×D₇₉	1	1	yes	characteristic
382	C₂×C₈	C₂×C₄×D₇₉	1	1	yes	characteristic
383	C₂×C₈	D₄×D₇₉	1	2	yes	—
384	C₂×C₈	C₂×C₂²⋊D₇₉	1	2	yes	—
385	C₂×C₈	C₂×Dic₁₅₈	1	2	yes	—
386	C₄⋊C₄	—	316	2	no	—
387	C₄⋊C₄	—	79	2	no	—
388	C₄⋊C₄	—	79	2	no	—
389	C₄⋊C₄	—	158	2	no	—
390	C₄⋊C₄	—	158	2	no	—
391	C₂²⋊C₄	—	158	2	no	—
392	C₂²⋊C₄	—	158	2	no	—
393	C₂²⋊C₄	—	158	2	no	—
394	C₄²	—	2	1	no	—
395	C₄²	—	2	1	no	—
396	C₄²	—	79	1	no	—
397	C₄²	—	79	1	no	—
398	C₄²	—	79	1	no	—
399	C₄²	—	79	1	no	—
400	C₄²	—	158	2	no	—
401	C₄²	—	158	2	no	—
402	C₄²	—	158	1	no	—
403	C₄²	—	158	1	no	—
404	C₄²	—	158	2	no	—
405	C₂³	—	2	2	no	—
406	C₂³	#41×D₇₉	1	1	yes	characteristic
407	Q₈	—	2	2	no	—
408	Q₈	C₂×Dic₇₉⋊C₄	1	4	yes	—
409	D₄	—	2	4	no	—
410	D₄	—	2	4	no	—
411	D₄	—	2	2	no	—
412	D₄	C₂×Dic₇₉⋊C₄	1	4	yes	—
413	C₂×C₄	—	2	2	no	—
414	C₂×C₄	—	2	4	no	—
415	C₂×C₄	—	2	4	no	—
416	C₂×C₄	—	4	1	no	—
417	C₂×C₄	—	4	1	no	—
418	C₂×C₄	—	4	1	no	—
419	C₂×C₄	—	316	4	no	—
420	C₂×C₄	—	316	1	no	—
421	C₂×C₄	—	316	1	no	—
422	C₂×C₄	—	316	1	no	—
423	C₂×C₄	—	316	1	no	—
424	C₂×C₄	—	79	1	no	—
425	C₂×C₄	—	79	1	no	—
426	C₂×C₄	—	79	1	no	—
427	C₂×C₄	—	79	1	no	—
428	C₂×C₄	—	632	2	no	—
429	C₂×C₄	—	158	2	no	—
430	C₂×C₄	—	158	2	no	—
431	C₂×C₄	—	158	2	no	—
432	C₂×C₄	C₂²×C₄×D₇₉	1	1	yes	characteristic
433	C₂×C₄	C₂×D₄×D₇₉	1	1	yes	characteristic
434	C₂×C₄	C₂²×C₂²⋊D₇₉	1	1	yes	characteristic
435	C₂×C₄	C₂²×Dic₁₅₈	1	1	yes	characteristic
436	C₂×C₄	#14579206	1	1	yes	characteristic
437	C₂×C₄	#14579208	1	1	yes	characteristic
438	C₈	—	2	2	no	—
439	C₈	—	4	2	no	—
440	C₈	—	316	2	no	—
441	C₈	—	158	2	no	—
442	C₈	—	158	1	no	—
443	C₈	—	158	1	no	—
444	C₈	C₂×Dic₇₉⋊C₄	1	2	yes	—
445	C₈	C₂×Dic₇₉⋊C₄	1	2	yes	—
446	C₂²	—	2	1	no	—
447	C₂²	—	2	1	no	—
448	C₂²	—	2	4	no	—
449	C₂²	—	4	2	no	—
450	C₂²	—	4	2	no	—
451	C₂²	C₄×D₄×D₇₉	1	1	yes	characteristic
452	C₂²	#19099212	1	1	yes	characteristic
453	C₂²	#19099272	1	1	yes	characteristic
454	C₄	—	2	4	no	—
455	C₄	—	8	1	no	—
456	C₄	—	316	2	no	—
457	C₄	—	316	2	no	—
458	C₄	—	79	2	no	—
459	C₄	—	632	1	no	—
460	C₄	—	158	1	no	—
461	C₄	—	158	1	no	—
462	C₄	—	158	1	no	—
463	C₄	C₂²×Dic₇₉⋊C₄	1	1	yes	characteristic
464	C₄	#19099042	1	1	yes	characteristic
465	C₄	D₄×C₂²⋊D₇₉	1	1	yes	characteristic
466	C₄	D₄×Dic₁₅₈	1	1	yes	characteristic
467	C₂	—	2	1	no	—
468	C₂	—	2	1	no	—
469	C₂	—	4	4	no	—
470	C₂	D₄×Dic₇₉⋊C₄	1	1	yes	characteristic
471	C₂	#444×D₇₉	1	1	yes	characteristic
472	C₂	#23772314	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₇₉
commutator	C₂×C₄×C₇₉	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₇₉
Fitting	C₂×#444×C₇₉	C₂
socle	C₂²×C₇₉	C₂×C₄×D₄
prime radical	C₂×#135×C₇₉	C₂²
cosocle	C₂²×C₄×C₇₉	C₂⁴
hypercenter	C₂×#444	D₇₉
hypocenter	C₇₉	#22686
LCS	G ▷ C₂×C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₈ ◁ C₂×#444

Complements

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

N	H ≅ G/N	type
3. #23771966	C₂	semidirect
4. #23764153	C₂	semidirect
5. #23764151	C₂	semidirect
6. #23763675	C₂	semidirect
7. #23763673	C₂	semidirect
8. #23763570	C₂	semidirect
9. #23763418	C₂	semidirect
10. #23763268	C₂	semidirect
15. Q₁₆×Dic₇₉	C₄	semidirect
16. Q₁₆×Dic₇₉	C₄	semidirect
17. SD₁₆×Dic₇₉	C₄	semidirect
18. SD₁₆×Dic₇₉	C₄	semidirect
19. D₈×Dic₇₉	C₄	semidirect
20. D₈×Dic₇₉	C₄	semidirect
151. Q₁₆×C₇₉	C₄⋊C₄	semidirect
152. SD₁₆×C₇₉	C₄⋊C₄	semidirect
153. D₈×C₇₉	C₄⋊C₄	semidirect
229. Dic₇₉	#444	semidirect
248. C₇₉	#22686	semidirect
359. Q₁₆	Dic₇₉⋊C₄	semidirect
360. SD₁₆	Dic₇₉⋊C₄	semidirect
361. D₈	Dic₇₉⋊C₄	semidirect

Maximal subgroups

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

subgroup	index
C₂×#19098685	2
#135×Dic₇₉	2
#23771966	2
#23764153	2
#23764151	2
#23763675	2
#23763673	2
#23763570	2
#23763418	2
#23763268	2
C₂×#444×C₇₉	2
#22686	79