Subgroups — #34306720

Order 20224.

858 conjugacy classes of subgroups.

The subgroup lattice has 454 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#19098680	C₂	1	1	yes	maximal, characteristic
2	#23772201	C₂	1	1	yes	maximal, characteristic
3	#23771966	C₂	1	2	yes	maximal, complemented
4	#23764153	C₂	1	1	yes	maximal, characteristic, complemented
5	#23764146	C₂	1	1	yes	maximal, characteristic, complemented
6	#23763675	C₂	1	2	yes	maximal, complemented
7	#23763673	C₂	1	2	yes	maximal, complemented
8	#23763573	C₂	1	1	yes	maximal, characteristic, complemented
9	#23763418	C₂	1	2	yes	maximal, complemented
10	#23763276	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	#19098680	—	2	4	no	—
15	#19098675	C₄	1	2	yes	complemented
16	#19098670	C₄	1	2	yes	complemented
17	#19098664	C₄	1	2	yes	complemented
18	#19098664	C₄	1	2	yes	complemented
19	C₂×#14579097	C₂²	1	1	yes	characteristic
20	C₂×#14579096	C₂²	1	2	yes	—
21	#19098601	C₂²	1	1	yes	characteristic
22	#19098591	—	2	2	no	—
23	#19098591	C₂²	1	2	yes	—
24	#19098589	—	2	2	no	—
25	#19098589	C₂²	1	2	yes	—
26	#19098586	—	2	2	no	—
27	#19098586	C₂²	1	2	yes	—
28	C₂×Dic₇₉⋊C₈	—	2	2	no	—
29	C₂×Dic₇₉⋊C₈	C₂²	1	1	yes	characteristic
30	C₂×#14579088	C₂²	1	2	yes	—
31	#19098559	C₂²	1	2	yes	—
32	C₂×#14579071	C₂²	1	1	yes	characteristic
33	C₂×C₈×Dic₇₉	C₂²	1	1	yes	characteristic
34	C₄×Dic₇₉⋊C₄	C₂²	1	1	yes	characteristic
35	#19098324	C₂²	1	2	yes	—
36	#19098323	C₂²	1	2	yes	—
37	#19098318	C₂²	1	1	yes	characteristic
38	#19098317	C₂²	1	1	yes	characteristic
39	C₂×#135×C₇₉	C₂²	1	1	yes	characteristic
40	C₂×#131×C₇₉	C₂²	1	2	yes	—
41	#444×C₇₉	—	2	4	no	—
42	C₂×#108×C₇₉	C₂²	1	1	yes	characteristic
43	C₂×#104×C₇₉	C₂²	1	2	yes	—
44	C₂×#97×C₇₉	C₂²	1	1	yes	characteristic
45	#14579168	—	2	4	no	—
46	#14579168	—	4	2	no	—
47	C₂×#11929608	—	2	2	no	—
48	C₂×#11929608	C₂³	1	2	yes	—
49	C₂²×C₇₉⋊C₈	—	2	2	no	—
50	C₂²×C₇₉⋊C₈	C₂³	1	1	yes	characteristic
51	C₂²×C₇₉⋊C₈	C₂³	1	1	yes	characteristic
52	Q₈×Dic₇₉	C₂×C₄	1	2	yes	—
53	Q₈×Dic₇₉	C₂×C₄	1	2	yes	—
54	D₄×Dic₇₉	—	2	2	no	—
55	D₄×Dic₇₉	—	2	2	no	—
56	D₄×Dic₇₉	C₂×C₄	1	2	yes	—
57	D₄×Dic₇₉	C₂×C₄	1	2	yes	—
58	#14579120	—	2	2	no	—
59	#14579120	C₂³	1	2	yes	—
60	C₂×Dic₇₉⋊C₄	—	2	1	no	—
61	C₂×C₄×Dic₇₉	—	2	2	no	—
62	C₂×C₄×Dic₇₉	C₂³	1	1	yes	characteristic
63	C₂×C₄×Dic₇₉	C₂³	1	1	yes	characteristic
64	#14579097	—	2	2	no	—
65	#14579096	—	4	2	no	—
66	#14579095	C₂×C₄	1	1	yes	characteristic
67	#14579095	C₂×C₄	1	1	yes	characteristic
68	#14579093	C₂×C₄	1	2	yes	—
69	Dic₇₉⋊C₈	—	2	2	no	—
70	Dic₇₉⋊C₈	—	2	2	no	—
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	D₄	1	2	yes	—
76	Dic₇₉⋊C₈	D₄	1	2	yes	—
77	#14579088	—	2	4	no	—
78	#14579085	C₂×C₄	1	2	yes	—
79	#14579085	C₂×C₄	1	2	yes	—
80	#14579082	C₂×C₄	1	2	yes	—
81	#14579082	C₂×C₄	1	2	yes	—
82	#14579071	C₂×C₄	1	2	yes	—
83	#14579071	C₂×C₄	1	2	yes	—
84	C₈×Dic₇₉	—	2	2	no	—
85	C₇₉⋊#95	—	2	1	no	—
86	C₂×#41×C₇₉	C₂³	1	2	yes	—
87	#135×C₇₉	D₄	1	4	yes	—
88	#135×C₇₉	Q₈	1	4	yes	—
89	C₂×Q₁₆×C₇₉	C₂×C₄	1	1	yes	characteristic
90	C₂×SD₁₆×C₇₉	C₂×C₄	1	2	yes	—
91	C₂×D₈×C₇₉	C₂×C₄	1	1	yes	characteristic
92	#131×C₇₉	—	2	4	no	—
93	#131×C₇₉	—	4	2	no	—
94	C₂×M₁₆×C₇₉	—	2	2	no	—
95	C₂×M₁₆×C₇₉	C₂³	1	2	yes	—
96	C₂²×C₈×C₇₉	—	2	2	no	—
97	C₂²×C₈×C₇₉	C₂³	1	1	yes	characteristic
98	C₂²×C₈×C₇₉	C₂³	1	1	yes	characteristic
99	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
100	#108×C₇₉	—	2	2	no	—
101	#104×C₇₉	—	2	4	no	—
102	#97×C₇₉	—	2	2	no	—
103	C₂²×Dic₇₉	—	2	2	no	—
104	C₂²×Dic₇₉	—	2	2	no	—
105	C₂²×Dic₇₉	—	2	1	no	—
106	C₂²×Dic₇₉	#41	1	1	yes	characteristic
107	C₂²×Dic₇₉	#41	1	1	yes	characteristic
108	#11929608	—	2	2	no	—
109	#11929608	—	2	2	no	—
110	#11929608	—	4	4	no	—
111	C₂×C₇₉⋊C₈	—	2	1	no	—
112	C₂×C₇₉⋊C₈	—	2	2	no	—
113	C₂×C₇₉⋊C₈	—	2	1	no	—
114	C₂×C₇₉⋊C₈	—	2	1	no	—
115	C₂×C₇₉⋊C₈	—	2	1	no	—
116	C₂×C₇₉⋊C₈	—	4	4	no	—
117	C₂×C₇₉⋊C₈	C₂²×C₄	1	2	yes	—
118	C₂×C₇₉⋊C₈	C₂×D₄	1	1	yes	characteristic
119	C₂×C₇₉⋊C₈	C₂×D₄	1	1	yes	characteristic
120	C₄⋊Dic₇₉	—	2	2	no	—
121	C₄⋊Dic₇₉	—	2	2	no	—
122	C₄⋊Dic₇₉	C₂²×C₄	1	2	yes	—
123	C₄⋊Dic₇₉	C₂²×C₄	1	2	yes	—
124	Dic₇₉⋊C₄	—	4	2	no	—
125	C₂²⋊Dic₇₉	—	2	2	no	—
126	C₂²⋊Dic₇₉	—	2	2	no	—
127	C₂²⋊Dic₇₉	—	2	2	no	—
128	C₄×Dic₇₉	—	2	2	no	—
129	C₄×Dic₇₉	—	2	2	no	—
130	C₄×Dic₇₉	—	2	2	no	—
131	C₄×Dic₇₉	—	2	1	no	—
132	C₄×Dic₇₉	—	2	1	no	—
133	C₄×Dic₇₉	C₂²×C₄	1	2	yes	—
134	C₄×Dic₇₉	C₂×D₄	1	2	yes	—
135	#41×C₇₉	—	2	2	no	—
136	#41×C₇₉	—	2	2	no	—
137	#41×C₇₉	C₂×D₄	1	4	yes	—
138	#41×C₇₉	C₂×Q₈	1	4	yes	—
139	C₂×Q₈×C₇₉	C₂²×C₄	1	2	yes	—
140	C₂×D₄×C₇₉	—	2	2	no	—
141	C₂×D₄×C₇₉	C₂²×C₄	1	2	yes	—
142	C₂²×C₄×C₇₉	—	2	2	no	—
143	C₂²×C₄×C₇₉	—	2	1	no	—
144	C₂²×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
145	Q₁₆×C₇₉	C₄⋊C₄	1	4	yes	complemented
146	SD₁₆×C₇₉	C₄⋊C₄	1	8	yes	complemented
147	D₈×C₇₉	C₄⋊C₄	1	4	yes	complemented
148	M₁₆×C₇₉	—	2	2	no	—
149	M₁₆×C₇₉	—	2	2	no	—
150	M₁₆×C₇₉	—	4	4	no	—
151	C₂×C₈×C₇₉	—	2	1	no	—
152	C₂×C₈×C₇₉	—	2	2	no	—
153	C₂×C₈×C₇₉	—	2	1	no	—
154	C₂×C₈×C₇₉	—	4	4	no	—
155	C₂×C₈×C₇₉	C₂²×C₄	1	1	yes	characteristic
156	C₂×C₈×C₇₉	C₂²×C₄	1	1	yes	characteristic
157	C₂×C₈×C₇₉	C₂×D₄	1	2	yes	—
158	C₂×C₈×C₇₉	C₂×D₄	1	2	yes	—
159	C₂×C₈×C₇₉	C₂×Q₈	1	2	yes	—
160	C₄²×C₇₉	—	2	1	no	—
161	C₄²×C₇₉	—	2	1	no	—
162	C₂³×C₇₉	—	2	2	no	—
163	C₂³×C₇₉	C₂×#41	1	1	yes	characteristic
164	Q₈×C₇₉	—	2	2	no	—
165	Q₈×C₇₉	C₂×C₄⋊C₄	1	4	yes	—
166	D₄×C₇₉	—	2	4	no	—
167	D₄×C₇₉	—	2	4	no	—
168	D₄×C₇₉	—	2	2	no	—
169	D₄×C₇₉	C₂×C₄⋊C₄	1	4	yes	—
170	C₂×C₄×C₇₉	—	2	2	no	—
171	C₂×C₄×C₇₉	—	2	4	no	—
172	C₂×C₄×C₇₉	—	2	4	no	—
173	C₂×C₄×C₇₉	—	4	1	no	—
174	C₂×C₄×C₇₉	—	4	1	no	—
175	C₂×C₄×C₇₉	—	4	1	no	—
176	C₂×C₄×C₇₉	C₂³×C₄	1	1	yes	characteristic
177	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
178	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
179	C₂×C₄×C₇₉	C₂²×Q₈	1	1	yes	characteristic
180	C₂×C₄×C₇₉	H(5,𝔽₂)	1	1	yes	characteristic
181	C₂×C₄×C₇₉	2₋¹⁺⁴	1	1	yes	characteristic
182	C₂×Dic₇₉	—	2	2	no	—
183	C₂×Dic₇₉	—	2	2	no	—
184	C₂×Dic₇₉	—	2	2	no	—
185	C₂×Dic₇₉	—	4	1	no	—
186	C₂×Dic₇₉	—	4	1	no	—
187	C₂×Dic₇₉	—	4	4	no	—
188	C₂×Dic₇₉	—	4	1	no	—
189	C₂×Dic₇₉	—	4	1	no	—
190	C₂×Dic₇₉	—	8	2	no	—
191	C₂×Dic₇₉	C₄×D₄	1	2	yes	—
192	C₂×Dic₇₉	C₄×D₄	1	2	yes	—
193	C₈×C₇₉	—	2	2	no	—
194	C₈×C₇₉	—	4	2	no	—
195	C₈×C₇₉	C₂×C₄⋊C₄	1	2	yes	—
196	C₈×C₇₉	C₂×C₄⋊C₄	1	2	yes	—
197	C₇₉⋊C₈	—	2	2	no	—
198	C₇₉⋊C₈	—	2	1	no	—
199	C₇₉⋊C₈	—	2	1	no	—
200	C₇₉⋊C₈	—	4	2	no	—
201	C₂²×C₇₉	—	2	1	no	—
202	C₂²×C₇₉	—	2	1	no	—
203	C₂²×C₇₉	—	2	4	no	—
204	C₂²×C₇₉	—	4	2	no	—
205	C₂²×C₇₉	—	4	2	no	—
206	C₂²×C₇₉	C₂×C₄×D₄	1	1	yes	characteristic
207	C₂²×C₇₉	#547	1	1	yes	characteristic
208	C₂²×C₇₉	#554	1	1	yes	characteristic
209	C₄×C₇₉	—	2	4	no	—
210	C₄×C₇₉	—	8	1	no	—
211	C₄×C₇₉	C₂²×C₄⋊C₄	1	1	yes	characteristic
212	C₄×C₇₉	#520	1	1	yes	characteristic
213	C₄×C₇₉	D₄²	1	1	yes	characteristic
214	C₄×C₇₉	D₄×Q₈	1	1	yes	characteristic
215	Dic₇₉	—	2	2	no	—
216	Dic₇₉	—	2	2	no	—
217	Dic₇₉	—	4	2	no	—
218	Dic₇₉	—	4	2	no	—
219	Dic₇₉	—	4	2	no	—
220	#22687	—	79	1	no	maximal, Sylow
221	C₂×C₇₉	—	2	1	no	—
222	C₂×C₇₉	—	2	1	no	—
223	C₂×C₇₉	—	4	4	no	—
224	C₂×C₇₉	D₄×C₄⋊C₄	1	1	yes	characteristic
225	C₂×C₇₉	#2955	1	1	yes	characteristic
226	C₂×C₇₉	#2956	1	1	yes	characteristic
227	C₂×#444	D₇₉	1	1	yes	characteristic
228	C₂×#443	—	79	1	no	—
229	#2943	—	79	1	no	—
230	#2906	—	79	2	no	—
231	#1946	—	79	1	no	—
232	#1945	—	79	1	no	—
233	#1866	—	79	2	no	—
234	#1866	—	79	2	no	—
235	#1849	—	79	1	no	—
236	#1806	—	79	2	no	—
237	#1771	—	79	1	no	—
238	C₇₉	#22687	1	1	yes	characteristic, complemented, Sylow
239	C₂×#135	C₂×D₇₉	1	1	yes	characteristic
240	C₂×#131	—	79	2	no	—
241	C₂×#131	C₂×D₇₉	1	2	yes	—
242	C₄×#41	—	79	2	no	—
243	#444	—	2	4	no	—
244	#443	—	158	4	no	—
245	#442	—	79	2	no	—
246	#441	—	79	2	no	—
247	#440	—	79	2	no	—
248	#440	—	79	2	no	—
249	C₂×#108	—	79	2	no	—
250	C₂×#108	—	79	1	no	—
251	C₂×#108	C₂×D₇₉	1	1	yes	characteristic
252	#427	—	79	1	no	—
253	#424	—	79	2	no	—
254	#424	—	79	2	no	—
255	#424	—	158	2	no	—
256	#424	—	158	2	no	—
257	#423	—	79	2	no	—
258	#423	—	158	2	no	—
259	C₂×C₄⋊C₈	—	79	1	no	—
260	C₂×C₄⋊C₈	—	158	2	no	—
261	C₂×#104	—	79	2	no	—
262	C₂×#104	C₂×D₇₉	1	2	yes	—
263	#416	—	79	2	no	—
264	C₂×#97	—	79	1	no	—
265	C₂×#97	C₂×D₇₉	1	1	yes	characteristic
266	C₂×C₄×C₈	—	79	1	no	—
267	C₄×C₄⋊C₄	—	79	1	no	—
268	#339	—	79	2	no	—
269	#339	—	79	2	no	—
270	#336	—	79	1	no	—
271	#336	—	79	1	no	—
272	C₂×#41	C₂²×D₇₉	1	2	yes	—
273	#135	Dic₁₅₈	1	4	yes	—
274	#135	C₂²⋊D₇₉	1	4	yes	—
275	C₂×Q₁₆	C₄×D₇₉	1	1	yes	characteristic
276	C₂×SD₁₆	C₄×D₇₉	1	2	yes	—
277	C₂×D₈	C₄×D₇₉	1	1	yes	characteristic
278	#131	—	2	4	no	—
279	#131	—	4	2	no	—
280	#131	—	316	2	no	—
281	#131	—	158	4	no	—
282	C₂×M₁₆	—	2	2	no	—
283	C₂×M₁₆	—	79	2	no	—
284	C₂×M₁₆	—	158	2	no	—
285	C₂×M₁₆	C₂²×D₇₉	1	2	yes	—
286	C₂²×C₈	—	2	2	no	—
287	C₂²×C₈	—	79	1	no	—
288	C₂²×C₈	—	79	1	no	—
289	C₂²×C₈	—	158	2	no	—
290	C₂²×C₈	C₂²×D₇₉	1	1	yes	characteristic
291	C₂²×C₈	C₂²×D₇₉	1	1	yes	characteristic
292	C₄×Q₈	—	79	2	no	—
293	C₄×Q₈	—	79	2	no	—
294	C₄×D₄	—	79	2	no	—
295	C₄×D₄	—	79	2	no	—
296	C₄×D₄	—	158	2	no	—
297	C₄×D₄	—	158	2	no	—
298	#117	—	79	2	no	—
299	#117	—	158	2	no	—
300	C₂×C₄⋊C₄	—	158	1	no	—
301	C₂×C₄²	—	79	1	no	—
302	C₂×C₄²	—	79	1	no	—
303	C₂×C₄²	—	158	2	no	—
304	C₂×C₄²	C₂²×D₇₉	1	1	yes	characteristic
305	#108	—	2	2	no	—
306	#108	—	316	2	no	—
307	#108	—	158	2	no	—
308	#107	—	79	1	no	—
309	#107	—	79	1	no	—
310	#106	—	79	2	no	—
311	C₄⋊C₈	—	79	2	no	—
312	C₄⋊C₈	—	79	2	no	—
313	C₄⋊C₈	—	158	2	no	—
314	C₄⋊C₈	—	158	2	no	—
315	C₄⋊C₈	—	158	2	no	—
316	C₄⋊C₈	—	158	2	no	—
317	C₄⋊C₈	—	158	2	no	—
318	C₄⋊C₈	—	158	2	no	—
319	#104	—	2	4	no	—
320	#104	—	158	4	no	—
321	#103	—	79	2	no	—
322	#103	—	79	2	no	—
323	#102	—	79	2	no	—
324	#102	—	79	2	no	—
325	#97	—	2	2	no	—
326	#97	—	79	2	no	—
327	#97	—	79	2	no	—
328	C₄×C₈	—	158	2	no	—
329	#95	—	158	1	no	—
330	#41	—	2	2	no	—
331	#41	—	2	2	no	—
332	#41	C₂×C₂²⋊D₇₉	1	4	yes	—
333	#41	C₂×Dic₁₅₈	1	4	yes	—
334	C₂×Q₈	C₂×C₄×D₇₉	1	2	yes	—
335	C₂×D₄	—	2	2	no	—
336	C₂×D₄	C₂×C₄×D₇₉	1	2	yes	—
337	C₂²×C₄	—	2	2	no	—
338	C₂²×C₄	—	2	1	no	—
339	C₂²×C₄	—	79	1	no	—
340	C₂²×C₄	—	79	1	no	—
341	C₂²×C₄	—	158	2	no	—
342	C₂²×C₄	—	158	1	no	—
343	C₂²×C₄	—	158	2	no	—
344	C₂²×C₄	C₂³×D₇₉	1	1	yes	characteristic
345	Q₁₆	Dic₇₉⋊C₄	1	4	yes	complemented
346	SD₁₆	Dic₇₉⋊C₄	1	8	yes	complemented
347	D₈	Dic₇₉⋊C₄	1	4	yes	complemented
348	M₁₆	—	2	2	no	—
349	M₁₆	—	2	2	no	—
350	M₁₆	—	4	4	no	—
351	M₁₆	—	316	4	no	—
352	M₁₆	—	158	2	no	—
353	M₁₆	—	158	2	no	—
354	C₂×C₈	—	2	1	no	—
355	C₂×C₈	—	2	1	no	—
356	C₂×C₈	—	2	2	no	—
357	C₂×C₈	—	4	4	no	—
358	C₂×C₈	—	316	4	no	—
359	C₂×C₈	—	79	2	no	—
360	C₂×C₈	—	79	1	no	—
361	C₂×C₈	—	79	1	no	—
362	C₂×C₈	—	158	2	no	—
363	C₂×C₈	—	158	1	no	—
364	C₂×C₈	—	158	1	no	—
365	C₂×C₈	—	158	1	no	—
366	C₂×C₈	—	158	1	no	—
367	C₂×C₈	C₂×C₄×D₇₉	1	1	yes	characteristic
368	C₂×C₈	C₂×C₄×D₇₉	1	1	yes	characteristic
369	C₂×C₈	D₄×D₇₉	1	2	yes	—
370	C₂×C₈	C₂×C₂²⋊D₇₉	1	2	yes	—
371	C₂×C₈	C₂×Dic₁₅₈	1	2	yes	—
372	C₄⋊C₄	—	316	2	no	—
373	C₄⋊C₄	—	79	2	no	—
374	C₄⋊C₄	—	79	2	no	—
375	C₄⋊C₄	—	158	2	no	—
376	C₄⋊C₄	—	158	2	no	—
377	C₂²⋊C₄	—	158	2	no	—
378	C₂²⋊C₄	—	158	2	no	—
379	C₂²⋊C₄	—	158	2	no	—
380	C₄²	—	2	1	no	—
381	C₄²	—	2	1	no	—
382	C₄²	—	79	2	no	—
383	C₄²	—	79	2	no	—
384	C₄²	—	158	2	no	—
385	C₄²	—	158	2	no	—
386	C₄²	—	158	1	no	—
387	C₄²	—	158	1	no	—
388	C₄²	—	158	2	no	—
389	C₂³	—	2	2	no	—
390	C₂³	#41×D₇₉	1	1	yes	characteristic
391	Q₈	—	2	2	no	—
392	Q₈	C₂×Dic₇₉⋊C₄	1	4	yes	—
393	D₄	—	2	4	no	—
394	D₄	—	2	4	no	—
395	D₄	—	2	2	no	—
396	D₄	C₂×Dic₇₉⋊C₄	1	4	yes	—
397	C₂×C₄	—	2	2	no	—
398	C₂×C₄	—	2	4	no	—
399	C₂×C₄	—	2	4	no	—
400	C₂×C₄	—	4	1	no	—
401	C₂×C₄	—	4	1	no	—
402	C₂×C₄	—	4	1	no	—
403	C₂×C₄	—	316	1	no	—
404	C₂×C₄	—	316	1	no	—
405	C₂×C₄	—	316	4	no	—
406	C₂×C₄	—	316	1	no	—
407	C₂×C₄	—	316	1	no	—
408	C₂×C₄	—	79	2	no	—
409	C₂×C₄	—	79	2	no	—
410	C₂×C₄	—	632	2	no	—
411	C₂×C₄	—	158	2	no	—
412	C₂×C₄	—	158	2	no	—
413	C₂×C₄	—	158	2	no	—
414	C₂×C₄	C₂²×C₄×D₇₉	1	1	yes	characteristic
415	C₂×C₄	C₂×D₄×D₇₉	1	1	yes	characteristic
416	C₂×C₄	C₂²×C₂²⋊D₇₉	1	1	yes	characteristic
417	C₂×C₄	C₂²×Dic₁₅₈	1	1	yes	characteristic
418	C₂×C₄	#14579206	1	1	yes	characteristic
419	C₂×C₄	#14579208	1	1	yes	characteristic
420	C₈	—	2	2	no	—
421	C₈	—	4	2	no	—
422	C₈	—	316	2	no	—
423	C₈	—	158	1	no	—
424	C₈	—	158	1	no	—
425	C₈	—	158	2	no	—
426	C₈	C₂×Dic₇₉⋊C₄	1	2	yes	—
427	C₈	C₂×Dic₇₉⋊C₄	1	2	yes	—
428	C₂²	—	2	1	no	—
429	C₂²	—	2	1	no	—
430	C₂²	—	2	4	no	—
431	C₂²	—	4	2	no	—
432	C₂²	—	4	2	no	—
433	C₂²	C₄×D₄×D₇₉	1	1	yes	characteristic
434	C₂²	#19099212	1	1	yes	characteristic
435	C₂²	#19099272	1	1	yes	characteristic
436	C₄	—	2	4	no	—
437	C₄	—	8	1	no	—
438	C₄	—	316	2	no	—
439	C₄	—	316	2	no	—
440	C₄	—	316	2	no	—
441	C₄	—	158	2	no	—
442	C₄	—	158	2	no	—
443	C₄	C₂²×Dic₇₉⋊C₄	1	1	yes	characteristic
444	C₄	#19099042	1	1	yes	characteristic
445	C₄	D₄×C₂²⋊D₇₉	1	1	yes	characteristic
446	C₄	D₄×Dic₁₅₈	1	1	yes	characteristic
447	C₂	—	2	1	no	—
448	C₂	—	2	1	no	—
449	C₂	—	4	4	no	—
450	C₂	D₄×Dic₇₉⋊C₄	1	1	yes	characteristic
451	C₂	#23772300	1	1	yes	characteristic
452	C₂	#23772308	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	#22687
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. #23764146	C₂	semidirect
6. #23763675	C₂	semidirect
7. #23763673	C₂	semidirect
8. #23763573	C₂	semidirect
9. #23763418	C₂	semidirect
10. #23763276	C₂	semidirect
15. #19098675	C₄	semidirect
16. #19098670	C₄	semidirect
17. #19098664	C₄	semidirect
18. #19098664	C₄	semidirect
145. Q₁₆×C₇₉	C₄⋊C₄	semidirect
146. SD₁₆×C₇₉	C₄⋊C₄	semidirect
147. D₈×C₇₉	C₄⋊C₄	semidirect
238. C₇₉	#22687	semidirect
345. Q₁₆	Dic₇₉⋊C₄	semidirect
346. SD₁₆	Dic₇₉⋊C₄	semidirect
347. 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×#19098680	2
#23772201	2
#23771966	2
#23764153	2
#23764146	2
#23763675	2
#23763673	2
#23763573	2
#23763418	2
#23763276	2
C₂×#444×C₇₉	2
#22687	79