Subgroups — #34295176

Order 20224.

874 conjugacy classes of subgroups.

The subgroup lattice has 470 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#19098835	C₂	1	1	yes	maximal, characteristic
2	C₄×#14579192	C₂	1	2	yes	maximal
3	#23771825	C₂	1	1	yes	maximal, characteristic
4	#23764316	C₂	1	1	yes	maximal, characteristic, complemented
5	#23764178	C₂	1	1	yes	maximal, characteristic, complemented
6	#23764052	C₂	1	2	yes	maximal, complemented
7	#23763918	C₂	1	2	yes	maximal
8	#23763460	C₂	1	1	yes	maximal, characteristic
9	#23763306	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄×#14579080	C₂	1	2	yes	maximal, complemented
11	C₂×#441×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#14579192	C₂²	1	2	yes	—
13	C₂×#14579167	C₂²	1	1	yes	characteristic
14	C₂×#14579167	C₂²	1	1	yes	characteristic
15	C₄×#11929624	C₂²	1	1	yes	characteristic
16	#19098835	C₄	1	8	yes	complemented
17	#19098668	—	2	2	no	—
18	#19098661	—	2	2	no	—
19	C₄×#11929614	—	2	2	no	—
20	C₄×#11929611	—	2	2	no	—
21	C₂×#14579097	C₂²	1	1	yes	characteristic
22	C₂×#14579097	C₂²	1	1	yes	characteristic
23	#19098603	C₂²	1	2	yes	—
24	#19098572	C₂²	1	2	yes	—
25	#19098562	C₂²	1	2	yes	—
26	C₂×#14579080	C₂²	1	2	yes	—
27	C₂×#14579080	C₂²	1	2	yes	—
28	#19098520	—	2	1	no	—
29	#19098520	—	2	1	no	—
30	#19098518	C₂²	1	1	yes	characteristic
31	#19098518	C₂²	1	1	yes	characteristic
32	C₄×#11929608	C₂²	1	2	yes	—
33	C₄×#11929608	C₂²	1	1	yes	characteristic
34	#19098515	—	2	1	no	—
35	#97×D₇₉	—	2	1	no	—
36	#19098332	C₂²	1	2	yes	—
37	#19098332	C₂²	1	2	yes	—
38	#19098328	C₂²	1	2	yes	—
39	C₂²×Q₁₆×C₇₉	C₂²	1	1	yes	characteristic
40	C₂×C₄×Q₈×C₇₉	C₂²	1	2	yes	—
41	#441×C₇₉	—	2	1	no	—
42	#441×C₇₉	—	2	1	no	—
43	#441×C₇₉	—	2	1	no	—
44	#441×C₇₉	—	2	1	no	—
45	C₂×#106×C₇₉	C₂²	1	1	yes	characteristic
46	C₂×#103×C₇₉	C₂²	1	2	yes	—
47	C₂×#97×C₇₉	C₂²	1	1	yes	characteristic
48	C₂×#11929624	C₂³	1	1	yes	characteristic
49	#14579192	—	2	4	no	—
50	#14579192	C₂×C₄	1	8	yes	—
51	C₂×#11929614	—	2	2	no	—
52	C₂×#11929611	—	2	2	no	—
53	#14579167	—	2	2	no	—
54	#14579167	—	2	2	no	—
55	#14579167	—	2	2	no	—
56	#14579167	C₂×C₄	1	4	yes	—
57	C₂×#11929608	C₂³	1	2	yes	—
58	C₂×#11929608	C₂³	1	1	yes	characteristic
59	C₂×#11929608	C₂³	1	2	yes	—
60	C₂×#11929608	C₂³	1	1	yes	characteristic
61	C₂×#11929607	—	2	1	no	—
62	C₂×#11929607	—	2	1	no	—
63	C₂×C₈×D₇₉	—	2	1	no	—
64	C₂×C₈×D₇₉	—	2	1	no	—
65	C₄×Dic₁₅₈	D₄	1	2	yes	—
66	C₄×D₃₁₆	D₄	1	2	yes	—
67	C₄×C₂²⋊D₇₉	—	2	2	no	—
68	#14579120	C₂³	1	1	yes	characteristic
69	#14579118	—	2	1	no	—
70	C₄²×D₇₉	—	2	1	no	—
71	#14579097	—	2	2	no	—
72	#14579097	C₂×C₄	1	4	yes	complemented
73	#14579094	—	2	2	no	—
74	#14579092	—	2	2	no	—
75	#14579085	—	2	2	no	—
76	#14579085	—	2	2	no	—
77	#14579084	—	2	2	no	—
78	#14579081	—	2	2	no	—
79	#14579080	—	2	4	no	—
80	#14579080	C₂×C₄	1	8	yes	complemented
81	#14579072	—	2	2	no	—
82	#14579072	—	2	1	no	—
83	#14579071	—	2	1	no	—
84	#14579071	—	2	1	no	—
85	C₄×C₇₉⋊C₈	—	2	2	no	—
86	C₄×C₇₉⋊C₈	—	2	1	no	—
87	C₈×Dic₇₉	—	2	1	no	—
88	C₈×Dic₇₉	—	2	1	no	—
89	C₂²×Q₈×C₇₉	C₂³	1	2	yes	—
90	C₂×Q₁₆×C₇₉	—	2	1	no	—
91	C₂×Q₁₆×C₇₉	—	2	1	no	—
92	C₂×Q₁₆×C₇₉	—	2	2	no	—
93	C₂×Q₁₆×C₇₉	C₂×C₄	1	4	yes	complemented
94	C₂²×C₈×C₇₉	C₂³	1	1	yes	characteristic
95	C₂²×C₈×C₇₉	C₂³	1	1	yes	characteristic
96	C₄×Q₈×C₇₉	—	2	2	no	—
97	C₄×Q₈×C₇₉	—	2	2	no	—
98	C₄×Q₈×C₇₉	—	2	2	no	—
99	C₄×Q₈×C₇₉	—	2	2	no	—
100	C₂×C₄⋊C₄×C₇₉	—	2	2	no	—
101	C₂×C₄⋊C₄×C₇₉	C₂³	1	2	yes	—
102	C₂×C₄²×C₇₉	—	2	2	no	—
103	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
104	#106×C₇₉	—	2	1	no	—
105	#106×C₇₉	—	2	1	no	—
106	#103×C₇₉	—	2	2	no	—
107	#103×C₇₉	—	2	2	no	—
108	#97×C₇₉	D₄	1	1	yes	characteristic
109	#97×C₇₉	D₄	1	1	yes	characteristic
110	#97×C₇₉	D₄	1	1	yes	characteristic
111	#97×C₇₉	D₄	1	1	yes	characteristic
112	#11929624	—	2	1	no	—
113	#11929624	—	2	1	no	—
114	#11929624	C₂²×C₄	1	2	yes	—
115	#11929624	#41	1	2	yes	—
116	C₂×Dic₁₅₈	C₂×D₄	1	1	yes	characteristic
117	C₂×D₃₁₆	C₂×D₄	1	1	yes	characteristic
118	C₂×C₂²⋊D₇₉	—	2	1	no	—
119	C₂×C₄×D₇₉	—	2	2	no	—
120	C₂×C₄×D₇₉	—	2	1	no	—
121	#11929614	—	2	8	no	—
122	#11929611	—	2	8	no	—
123	#11929608	—	2	1	no	—
124	#11929608	—	2	1	no	—
125	#11929608	—	2	2	no	—
126	#11929608	—	2	2	no	—
127	#11929608	—	2	2	no	—
128	#11929608	C₂²×C₄	1	2	yes	—
129	#11929608	C₂²×C₄	1	4	yes	—
130	#11929608	#41	1	2	yes	—
131	#11929607	—	2	4	no	—
132	#11929607	—	2	4	no	—
133	C₂×C₇₉⋊C₈	—	2	1	no	—
134	C₂×C₇₉⋊C₈	—	2	1	no	—
135	C₂×C₇₉⋊C₈	—	2	2	no	—
136	C₂×C₇₉⋊C₈	—	2	2	no	—
137	C₈×D₇₉	—	2	4	no	—
138	C₈×D₇₉	—	2	4	no	—
139	C₄⋊Dic₇₉	C₂×D₄	1	2	yes	—
140	Dic₇₉⋊C₄	—	2	2	no	—
141	C₂²⋊Dic₇₉	—	2	1	no	—
142	(C₂×D₇₉)⋊C₄	—	2	2	no	—
143	C₄×Dic₇₉	—	2	2	no	—
144	C₄×Dic₇₉	—	2	1	no	—
145	C₂×Q₈×C₇₉	—	2	2	no	—
146	C₂×Q₈×C₇₉	—	2	2	no	—
147	C₂×Q₈×C₇₉	—	2	2	no	—
148	C₂×Q₈×C₇₉	—	2	2	no	—
149	C₂×Q₈×C₇₉	—	2	2	no	—
150	C₂×Q₈×C₇₉	C₂²×C₄	1	4	yes	—
151	C₂²×C₄×C₇₉	—	2	2	no	—
152	C₂²×C₄×C₇₉	—	2	2	no	—
153	C₂²×C₄×C₇₉	#41	1	2	yes	—
154	C₂²×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
155	Q₁₆×C₇₉	—	2	4	no	—
156	Q₁₆×C₇₉	—	2	4	no	—
157	C₂×C₈×C₇₉	—	2	1	no	—
158	C₂×C₈×C₇₉	—	2	1	no	—
159	C₂×C₈×C₇₉	C₂²×C₄	1	2	yes	—
160	C₂×C₈×C₇₉	C₂×D₄	1	1	yes	characteristic
161	C₂×C₈×C₇₉	C₂×D₄	1	1	yes	characteristic
162	C₂×C₈×C₇₉	C₂×D₄	1	1	yes	characteristic
163	C₂×C₈×C₇₉	C₂×D₄	1	1	yes	characteristic
164	C₂×C₈×C₇₉	#41	1	2	yes	—
165	C₄⋊C₄×C₇₉	—	2	2	no	—
166	C₄⋊C₄×C₇₉	—	2	2	no	—
167	C₄⋊C₄×C₇₉	—	4	2	no	—
168	C₄⋊C₄×C₇₉	—	4	2	no	—
169	C₄²×C₇₉	—	4	2	no	—
170	C₄²×C₇₉	—	4	2	no	—
171	C₄²×C₇₉	C₂×D₄	1	2	yes	—
172	C₄²×C₇₉	C₂×D₄	1	1	yes	characteristic
173	C₄²×C₇₉	C₂×D₄	1	1	yes	characteristic
174	C₂³×C₇₉	C₂×#41	1	1	yes	characteristic
175	C₂²×D₇₉	—	2	1	no	—
176	Q₈×C₇₉	—	2	4	no	—
177	Q₈×C₇₉	—	2	4	no	—
178	Q₈×C₇₉	—	4	2	no	—
179	Q₈×C₇₉	—	4	2	no	—
180	C₂×C₄×C₇₉	—	2	4	no	—
181	C₂×C₄×C₇₉	—	4	2	no	—
182	C₂×C₄×C₇₉	—	4	2	no	—
183	C₂×C₄×C₇₉	—	4	2	no	—
184	C₂×C₄×C₇₉	—	4	2	no	—
185	C₂×C₄×C₇₉	—	8	2	no	—
186	C₂×C₄×C₇₉	#121	1	2	yes	—
187	C₂×C₄×C₇₉	#121	1	2	yes	—
188	C₂×C₄×C₇₉	C₂³×C₄	1	1	yes	characteristic
189	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
190	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
191	C₂×C₄×C₇₉	C₂×#41	1	1	yes	characteristic
192	C₂×C₄×C₇₉	C₂×#41	1	1	yes	characteristic
193	C₂×C₄×C₇₉	C₂×#41	1	1	yes	characteristic
194	C₂²⋊D₇₉	—	2	2	no	—
195	C₂²⋊D₇₉	—	2	2	no	—
196	C₂×Dic₇₉	—	2	1	no	—
197	C₂×Dic₇₉	—	2	2	no	—
198	D₃₁₆	—	2	1	no	—
199	D₃₁₆	C₄×D₄	1	2	yes	—
200	C₄×D₇₉	—	2	2	no	—
201	C₄×D₇₉	—	2	2	no	—
202	C₄×D₇₉	—	8	2	no	—
203	Dic₁₅₈	—	2	1	no	—
204	Dic₁₅₈	C₄×D₄	1	2	yes	—
205	C₈×C₇₉	—	2	1	no	—
206	C₈×C₇₉	—	2	1	no	—
207	C₈×C₇₉	C₄×D₄	1	2	yes	—
208	C₈×C₇₉	C₄×D₄	1	2	yes	—
209	C₇₉⋊C₈	—	2	2	no	—
210	C₇₉⋊C₈	—	2	4	no	—
211	C₇₉⋊C₈	—	2	2	no	—
212	C₇₉⋊C₈	—	4	2	no	—
213	C₂²×C₇₉	—	2	2	no	—
214	C₂²×C₇₉	C₄×#41	1	1	yes	characteristic
215	C₂²×C₇₉	C₂×#121	1	1	yes	characteristic
216	C₂²×C₇₉	#529	1	1	yes	characteristic
217	C₂×D₇₉	—	2	2	no	—
218	C₂×D₇₉	—	4	2	no	—
219	C₄×C₇₉	—	2	2	no	—
220	C₄×C₇₉	—	2	2	no	—
221	C₄×C₇₉	—	4	4	no	—
222	C₄×C₇₉	—	8	2	no	—
223	C₄×C₇₉	C₂×C₄×D₄	1	1	yes	characteristic
224	C₄×C₇₉	C₂×C₄×D₄	1	1	yes	characteristic
225	C₄×C₇₉	#525	1	1	yes	characteristic
226	C₄×C₇₉	#532	1	1	yes	characteristic
227	Dic₇₉	—	2	2	no	—
228	Dic₇₉	—	4	2	no	—
229	#21556	—	79	1	no	maximal, Sylow
230	C₂×C₇₉	—	2	1	no	—
231	C₂×C₇₉	—	2	1	no	—
232	C₂×C₇₉	C₄×#121	1	1	yes	characteristic
233	C₂×C₇₉	#3069	1	2	yes	—
234	D₇₉	—	4	2	no	—
235	C₂×#473	—	79	1	no	—
236	C₄×#137	—	79	2	no	—
237	C₂×#441	D₇₉	1	1	yes	characteristic, complemented
238	#2875	—	79	1	no	—
239	#1979	—	79	1	no	—
240	#1951	—	79	1	no	—
241	#1930	—	79	2	no	—
242	#1908	—	79	2	no	—
243	#1815	—	79	1	no	—
244	#1778	—	79	1	no	—
245	C₄×#101	—	79	2	no	—
246	C₇₉	#21556	1	1	yes	characteristic, complemented, Sylow
247	C₂×#137	—	79	2	no	—
248	C₂²×Q₁₆	C₂×D₇₉	1	1	yes	characteristic
249	C₂×#131	—	79	1	no	—
250	C₂×#131	—	79	1	no	—
251	C₄×#41	—	79	1	no	—
252	C₂×C₄×Q₈	C₂×D₇₉	1	2	yes	—
253	#473	—	79	8	no	—
254	#441	—	2	1	no	—
255	#441	—	2	1	no	—
256	#441	—	2	1	no	—
257	#441	—	2	1	no	—
258	#441	—	158	2	no	—
259	#440	—	158	2	no	—
260	C₄×Q₁₆	—	158	2	no	—
261	C₄×SD₁₆	—	158	2	no	—
262	C₂×#108	—	79	1	no	—
263	C₂×#108	—	79	1	no	—
264	#428	—	79	2	no	—
265	C₂×#106	C₂×D₇₉	1	1	yes	characteristic
266	#419	—	79	2	no	—
267	#417	—	79	2	no	—
268	C₂×#103	C₂×D₇₉	1	2	yes	—
269	C₂×#101	—	79	2	no	—
270	C₂×#101	—	79	2	no	—
271	#405	—	79	1	no	—
272	#405	—	79	1	no	—
273	#405	—	158	1	no	—
274	#405	—	158	1	no	—
275	C₄×M₁₆	—	79	1	no	—
276	C₄×M₁₆	—	79	2	no	—
277	C₄×M₁₆	—	158	1	no	—
278	C₂×#97	—	158	1	no	—
279	C₂×#97	C₂×D₇₉	1	1	yes	characteristic
280	#343	—	79	2	no	—
281	#343	—	79	2	no	—
282	#341	—	79	2	no	—
283	C₂×#41	—	79	1	no	—
284	C₂²×Q₈	C₂²×D₇₉	1	2	yes	—
285	#137	—	79	8	no	—
286	#137	—	158	4	no	—
287	C₂×Q₁₆	—	2	1	no	—
288	C₂×Q₁₆	—	2	1	no	—
289	C₂×Q₁₆	—	2	2	no	—
290	C₂×Q₁₆	—	158	2	no	—
291	C₂×Q₁₆	C₄×D₇₉	1	4	yes	complemented
292	C₂×SD₁₆	—	158	2	no	—
293	#131	—	79	4	no	—
294	#131	—	158	2	no	—
295	#131	—	158	2	no	—
296	#131	—	158	2	no	—
297	C₂×M₁₆	—	79	1	no	—
298	C₂×M₁₆	—	79	1	no	—
299	C₂×M₁₆	—	79	2	no	—
300	C₂×M₁₆	—	79	2	no	—
301	C₂×M₁₆	—	158	1	no	—
302	C₂×M₁₆	—	158	1	no	—
303	C₂²×C₈	—	158	1	no	—
304	C₂²×C₈	—	158	1	no	—
305	C₂²×C₈	C₂²×D₇₉	1	1	yes	characteristic
306	C₂²×C₈	C₂²×D₇₉	1	1	yes	characteristic
307	C₄×Q₈	—	2	2	no	—
308	C₄×Q₈	—	2	2	no	—
309	C₄×Q₈	—	2	2	no	—
310	C₄×Q₈	—	2	2	no	—
311	C₄×Q₈	—	79	2	no	—
312	C₄×D₄	—	79	2	no	—
313	C₄×D₄	—	158	2	no	—
314	#117	—	79	1	no	—
315	#117	—	158	1	no	—
316	C₂×C₄⋊C₄	—	2	2	no	—
317	C₂×C₄⋊C₄	C₂²×D₇₉	1	2	yes	—
318	C₂×C₄²	—	2	2	no	—
319	C₂×C₄²	—	158	1	no	—
320	C₂×C₄²	C₂²×D₇₉	1	1	yes	characteristic
321	#108	—	79	4	no	—
322	#108	—	158	2	no	—
323	#107	—	158	2	no	—
324	#106	—	2	1	no	—
325	#106	—	2	1	no	—
326	#106	—	158	2	no	—
327	#103	—	2	2	no	—
328	#103	—	2	2	no	—
329	#103	—	158	2	no	—
330	#103	—	158	2	no	—
331	#103	—	158	2	no	—
332	#102	—	158	2	no	—
333	#101	—	79	8	no	—
334	#101	—	158	4	no	—
335	#97	—	158	1	no	—
336	#97	—	158	1	no	—
337	#97	—	158	2	no	—
338	#97	—	158	1	no	—
339	#97	C₂²⋊D₇₉	1	1	yes	characteristic
340	#97	C₂²⋊D₇₉	1	1	yes	characteristic
341	#97	C₂²⋊D₇₉	1	1	yes	characteristic
342	#97	C₂²⋊D₇₉	1	1	yes	characteristic
343	C₄×C₈	—	158	1	no	—
344	C₄×C₈	—	158	1	no	—
345	C₄×C₈	—	158	2	no	—
346	C₄×C₈	—	158	1	no	—
347	#41	—	79	2	no	—
348	#41	—	79	2	no	—
349	#41	—	158	1	no	—
350	#41	—	158	1	no	—
351	C₂×Q₈	—	2	2	no	—
352	C₂×Q₈	—	2	2	no	—
353	C₂×Q₈	—	2	2	no	—
354	C₂×Q₈	—	2	2	no	—
355	C₂×Q₈	—	2	2	no	—
356	C₂×Q₈	—	79	1	no	—
357	C₂×Q₈	C₂×C₄×D₇₉	1	4	yes	—
358	C₂×D₄	—	79	1	no	—
359	C₂×D₄	—	158	1	no	—
360	C₂²×C₄	—	2	2	no	—
361	C₂²×C₄	—	2	2	no	—
362	C₂²×C₄	—	158	2	no	—
363	C₂²×C₄	—	158	1	no	—
364	C₂²×C₄	#11929623	1	2	yes	—
365	C₂²×C₄	C₂³×D₇₉	1	1	yes	characteristic
366	Q₁₆	—	2	4	no	—
367	Q₁₆	—	2	4	no	—
368	Q₁₆	—	158	8	no	—
369	SD₁₆	—	158	8	no	—
370	M₁₆	—	79	2	no	—
371	M₁₆	—	79	2	no	—
372	M₁₆	—	79	4	no	—
373	M₁₆	—	158	4	no	—
374	M₁₆	—	158	2	no	—
375	M₁₆	—	158	2	no	—
376	M₁₆	—	158	1	no	—
377	M₁₆	—	158	2	no	—
378	M₁₆	—	158	1	no	—
379	M₁₆	—	158	4	no	—
380	C₂×C₈	—	2	1	no	—
381	C₂×C₈	—	2	1	no	—
382	C₂×C₈	—	158	4	no	—
383	C₂×C₈	—	158	2	no	—
384	C₂×C₈	—	158	2	no	—
385	C₂×C₈	—	158	1	no	—
386	C₂×C₈	—	158	1	no	—
387	C₂×C₈	—	158	4	no	—
388	C₂×C₈	C₂×C₄×D₇₉	1	2	yes	—
389	C₂×C₈	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
390	C₂×C₈	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
391	C₂×C₈	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
392	C₂×C₈	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
393	C₂×C₈	#11929624	1	2	yes	—
394	C₄⋊C₄	—	2	2	no	—
395	C₄⋊C₄	—	2	2	no	—
396	C₄⋊C₄	—	4	2	no	—
397	C₄⋊C₄	—	4	2	no	—
398	C₄⋊C₄	—	79	2	no	—
399	C₄⋊C₄	—	158	2	no	—
400	C₂²⋊C₄	—	158	1	no	—
401	C₂²⋊C₄	—	158	2	no	—
402	C₄²	—	4	2	no	—
403	C₄²	—	4	2	no	—
404	C₄²	—	158	2	no	—
405	C₄²	—	158	1	no	—
406	C₄²	D₄×D₇₉	1	2	yes	—
407	C₄²	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
408	C₄²	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
409	C₂³	—	158	1	no	—
410	C₂³	C₂×#11929623	1	1	yes	characteristic
411	Q₈	—	2	4	no	—
412	Q₈	—	2	4	no	—
413	Q₈	—	4	2	no	—
414	Q₈	—	4	2	no	—
415	Q₈	—	79	2	no	—
416	Q₈	—	158	1	no	—
417	D₄	—	79	2	no	—
418	D₄	—	158	2	no	—
419	D₄	—	158	2	no	—
420	D₄	—	158	1	no	—
421	C₂×C₄	—	2	4	no	—
422	C₂×C₄	—	4	2	no	—
423	C₂×C₄	—	4	2	no	—
424	C₂×C₄	—	4	2	no	—
425	C₂×C₄	—	4	2	no	—
426	C₂×C₄	—	8	2	no	—
427	C₂×C₄	—	632	2	no	—
428	C₂×C₄	—	158	2	no	—
429	C₂×C₄	—	158	1	no	—
430	C₂×C₄	—	158	2	no	—
431	C₂×C₄	—	158	2	no	—
432	C₂×C₄	#14579132	1	2	yes	—
433	C₂×C₄	#14579132	1	2	yes	—
434	C₂×C₄	C₂²×C₄×D₇₉	1	1	yes	characteristic
435	C₂×C₄	C₂×D₄×D₇₉	1	1	yes	characteristic
436	C₂×C₄	C₂²×C₂²⋊D₇₉	1	1	yes	characteristic
437	C₂×C₄	#41×D₇₉	1	1	yes	characteristic
438	C₂×C₄	#41×D₇₉	1	1	yes	characteristic
439	C₂×C₄	C₂×#11929624	1	1	yes	characteristic
440	C₈	—	2	1	no	—
441	C₈	—	2	1	no	—
442	C₈	—	316	2	no	—
443	C₈	—	158	4	no	—
444	C₈	—	158	2	no	—
445	C₈	—	158	2	no	—
446	C₈	C₄×C₂²⋊D₇₉	1	2	yes	—
447	C₈	C₄×C₂²⋊D₇₉	1	2	yes	—
448	C₂²	—	2	2	no	—
449	C₂²	—	316	2	no	—
450	C₂²	—	158	2	no	—
451	C₂²	C₄×#11929623	1	1	yes	characteristic
452	C₂²	C₂×#14579132	1	1	yes	characteristic
453	C₂²	#19099095	1	1	yes	characteristic
454	C₄	—	2	2	no	—
455	C₄	—	2	2	no	—
456	C₄	—	4	4	no	—
457	C₄	—	8	2	no	—
458	C₄	—	316	2	no	—
459	C₄	—	158	2	no	—
460	C₄	C₄×D₄×D₇₉	1	1	yes	characteristic
461	C₄	C₂×C₄×C₂²⋊D₇₉	1	1	yes	characteristic
462	C₄	#19099070	1	1	yes	characteristic
463	C₄	#19099110	1	1	yes	characteristic
464	C₂	—	2	1	no	—
465	C₂	—	2	1	no	—
466	C₂	—	316	2	no	—
467	C₂	C₄×#14579132	1	1	yes	characteristic
468	C₂	#23773133	1	2	yes	—

	subgroup	G/H
center	C₂²	C₂×#14579132
commutator	C₂×C₄×C₇₉	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₇₉
Fitting	C₂×#441×C₇₉	C₂
socle	C₂²×C₇₉	C₂×#121
prime radical	C₂×#11929624	C₂³
cosocle	C₂²×C₄×C₇₉	C₂⁴
hypercenter	C₂×#441	D₇₉
hypocenter	C₇₉	#21556
LCS	G ▷ C₂×C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ C₂×#441

Complements

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

N	H ≅ G/N	type
4. #23764316	C₂	semidirect
5. #23764178	C₂	semidirect
6. #23764052	C₂	semidirect
9. #23763306	C₂	semidirect
10. C₄×#14579080	C₂	semidirect
11. C₂×#441×C₇₉	C₂	semidirect
16. #19098835	C₄	semidirect
72. #14579097	C₂×C₄	semidirect
80. #14579080	C₂×C₄	semidirect
93. C₂×Q₁₆×C₇₉	C₂×C₄	semidirect
237. C₂×#441	D₇₉	semidirect
246. C₇₉	#21556	semidirect
291. C₂×Q₁₆	C₄×D₇₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×#19098835	2
C₄×#14579192	2
#23771825	2
#23764316	2
#23764178	2
#23764052	2
#23763918	2
#23763460	2
#23763306	2
C₄×#14579080	2
C₂×#441×C₇₉	2
#21556	79