Subgroups — #34307982

Order 20224.

710 conjugacy classes of subgroups.

The subgroup lattice has 434 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#23772066	C₂	1	2	yes	maximal, complemented
2	#23764294	C₂	1	1	yes	maximal, characteristic
3	#23764289	C₂	1	1	yes	maximal, characteristic
4	#23764050	C₂	1	2	yes	maximal, complemented
5	#23764050	C₂	1	2	yes	maximal, complemented
6	#23763575	C₂	1	1	yes	maximal, characteristic, complemented
7	#23763420	C₂	1	2	yes	maximal, complemented
8	#23763286	C₂	1	1	yes	maximal, characteristic, complemented
9	#23763281	C₂	1	1	yes	maximal, characteristic, complemented
10	#23763272	C₂	1	1	yes	maximal, characteristic, complemented
11	C₇₉×#2943	C₂	1	1	yes	maximal, characteristic
12	#19098624	—	2	2	no	—
13	#19098624	—	2	2	no	—
14	#19098620	—	2	2	no	—
15	#19098616	—	2	2	no	—
16	C₂×#14579097	C₂²	1	1	yes	characteristic
17	C₂×#14579097	C₂²	1	1	yes	characteristic
18	C₂×#14579097	C₂²	1	2	yes	—
19	#19098587	C₂²	1	2	yes	—
20	C₂×C₄⋊(C₇₉⋊C₈)	C₂²	1	1	yes	characteristic
21	C₂×#14579088	C₂²	1	2	yes	—
22	C₂×#14579088	C₂²	1	2	yes	—
23	#19098530	C₂²	1	2	yes	—
24	#19098530	C₂²	1	2	yes	—
25	#19098519	C₂²	1	2	yes	—
26	#19098519	C₂²	1	2	yes	—
27	C₂×#14579071	C₂²	1	1	yes	characteristic
28	C₂×C₈×Dic₇₉	C₂²	1	1	yes	characteristic
29	C₄×C₄⋊Dic₇₉	C₂²	1	1	yes	characteristic
30	#19098322	C₂²	1	2	yes	—
31	#19098322	C₂²	1	2	yes	—
32	#19098317	C₂²	1	1	yes	characteristic
33	#19098317	C₂²	1	1	yes	characteristic
34	C₂×#135×C₇₉	C₂²	1	1	yes	characteristic
35	C₄×#41×C₇₉	C₂²	1	2	yes	—
36	#442×C₇₉	C₄	1	2	yes	complemented
37	#441×C₇₉	C₄	1	2	yes	complemented
38	#440×C₇₉	C₄	1	2	yes	complemented
39	#440×C₇₉	C₄	1	2	yes	complemented
40	#427×C₇₉	C₂²	1	1	yes	characteristic
41	#416×C₇₉	C₂²	1	2	yes	—
42	C₂×#97×C₇₉	C₂²	1	1	yes	characteristic
43	C₂×#11929608	C₂³	1	2	yes	—
44	C₂×#11929608	C₂³	1	2	yes	—
45	C₂²×C₇₉⋊C₈	C₂³	1	1	yes	characteristic
46	C₂²×C₇₉⋊C₈	C₂³	1	1	yes	characteristic
47	C₂×C₄⋊Dic₇₉	—	2	1	no	—
48	C₂×C₄×Dic₇₉	C₂³	1	1	yes	characteristic
49	C₂×C₄×Dic₇₉	C₂³	1	1	yes	characteristic
50	#14579097	—	2	2	no	—
51	#14579097	—	2	2	no	—
52	#14579097	—	4	2	no	—
53	C₄⋊(C₇₉⋊C₈)	—	2	2	no	—
54	C₄⋊(C₇₉⋊C₈)	—	2	2	no	—
55	C₄⋊(C₇₉⋊C₈)	D₄	1	2	yes	—
56	C₄⋊(C₇₉⋊C₈)	D₄	1	2	yes	—
57	#14579088	—	4	2	no	—
58	#14579088	—	4	2	no	—
59	C₂²⋊(C₇₉⋊C₈)	—	2	2	no	—
60	C₂²⋊(C₇₉⋊C₈)	—	2	2	no	—
61	C₂²⋊(C₇₉⋊C₈)	—	2	2	no	—
62	C₂²⋊(C₇₉⋊C₈)	—	2	2	no	—
63	#14579072	—	2	2	no	—
64	#14579072	—	2	2	no	—
65	#14579071	—	2	2	no	—
66	C₄×C₇₉⋊C₈	—	2	2	no	—
67	C₄×C₇₉⋊C₈	—	2	2	no	—
68	C₈×Dic₇₉	—	2	2	no	—
69	C₇₉⋊#95	—	2	1	no	—
70	C₂×#41×C₇₉	C₂³	1	2	yes	—
71	#135×C₇₉	—	2	2	no	—
72	#135×C₇₉	—	2	2	no	—
73	C₂×Q₁₆×C₇₉	C₂×C₄	1	1	yes	characteristic
74	C₂×SD₁₆×C₇₉	C₂×C₄	1	2	yes	—
75	C₂×D₈×C₇₉	C₂×C₄	1	1	yes	characteristic
76	C₂²×C₈×C₇₉	C₂³	1	1	yes	characteristic
77	C₂²×C₈×C₇₉	C₂³	1	1	yes	characteristic
78	C₄×Q₈×C₇₉	C₂×C₄	1	2	yes	—
79	C₄×Q₈×C₇₉	C₂×C₄	1	2	yes	—
80	C₄×D₄×C₇₉	—	2	2	no	—
81	C₄×D₄×C₇₉	—	2	2	no	—
82	C₄×D₄×C₇₉	C₂×C₄	1	2	yes	—
83	C₄×D₄×C₇₉	C₂×C₄	1	2	yes	—
84	#117×C₇₉	—	2	2	no	—
85	#117×C₇₉	C₂³	1	2	yes	—
86	C₂×C₄²×C₇₉	—	2	2	no	—
87	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
88	#107×C₇₉	C₂×C₄	1	1	yes	characteristic
89	#107×C₇₉	C₂×C₄	1	1	yes	characteristic
90	#106×C₇₉	C₂×C₄	1	2	yes	—
91	#103×C₇₉	C₂×C₄	1	2	yes	—
92	#103×C₇₉	C₂×C₄	1	2	yes	—
93	#102×C₇₉	C₂×C₄	1	2	yes	—
94	#102×C₇₉	C₂×C₄	1	2	yes	—
95	#97×C₇₉	C₂×C₄	1	2	yes	—
96	#97×C₇₉	C₂×C₄	1	2	yes	—
97	C₂²×Dic₇₉	—	2	1	no	—
98	C₂²×Dic₇₉	—	2	1	no	—
99	#11929608	—	2	2	no	—
100	#11929608	—	2	2	no	—
101	#11929608	—	2	2	no	—
102	#11929608	—	2	2	no	—
103	C₂×C₇₉⋊C₈	—	2	2	no	—
104	C₂×C₇₉⋊C₈	—	2	2	no	—
105	C₂×C₇₉⋊C₈	—	2	1	no	—
106	C₂×C₇₉⋊C₈	—	2	1	no	—
107	C₂×C₇₉⋊C₈	—	2	1	no	—
108	C₂×C₇₉⋊C₈	—	2	1	no	—
109	C₂×C₇₉⋊C₈	C₂×D₄	1	1	yes	characteristic
110	C₂×C₇₉⋊C₈	C₂×D₄	1	2	yes	—
111	C₂×C₇₉⋊C₈	C₂×D₄	1	1	yes	characteristic
112	C₄⋊Dic₇₉	—	4	2	no	—
113	C₄×Dic₇₉	—	2	1	no	—
114	C₄×Dic₇₉	—	2	1	no	—
115	C₄×Dic₇₉	—	2	1	no	—
116	C₄×Dic₇₉	—	2	1	no	—
117	#41×C₇₉	—	2	2	no	—
118	#41×C₇₉	—	2	2	no	—
119	#41×C₇₉	—	2	2	no	—
120	#41×C₇₉	—	2	2	no	—
121	C₂×Q₈×C₇₉	C₂²×C₄	1	2	yes	—
122	C₂×D₄×C₇₉	—	2	2	no	—
123	C₂×D₄×C₇₉	C₂²×C₄	1	2	yes	—
124	C₂²×C₄×C₇₉	—	2	2	no	—
125	C₂²×C₄×C₇₉	—	2	2	no	—
126	C₂²×C₄×C₇₉	—	2	2	no	—
127	C₂²×C₄×C₇₉	#41	1	1	yes	characteristic
128	C₂²×C₄×C₇₉	#41	1	1	yes	characteristic
129	C₂²×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
130	Q₁₆×C₇₉	—	2	2	no	—
131	SD₁₆×C₇₉	—	2	4	no	—
132	D₈×C₇₉	—	2	2	no	—
133	C₂×C₈×C₇₉	—	2	1	no	—
134	C₂×C₈×C₇₉	—	2	1	no	—
135	C₂×C₈×C₇₉	C₂²×C₄	1	2	yes	—
136	C₂×C₈×C₇₉	C₂²×C₄	1	1	yes	characteristic
137	C₂×C₈×C₇₉	C₂²×C₄	1	1	yes	characteristic
138	C₂×C₈×C₇₉	#41	1	2	yes	—
139	C₂×C₈×C₇₉	#41	1	2	yes	—
140	C₄⋊C₄×C₇₉	—	2	2	no	—
141	C₄⋊C₄×C₇₉	—	2	2	no	—
142	C₄⋊C₄×C₇₉	C₂²×C₄	1	2	yes	—
143	C₄⋊C₄×C₇₉	C₂²×C₄	1	2	yes	—
144	C₂²⋊C₄×C₇₉	—	2	2	no	—
145	C₂²⋊C₄×C₇₉	—	2	2	no	—
146	C₂²⋊C₄×C₇₉	—	2	2	no	—
147	C₄²×C₇₉	—	2	2	no	—
148	C₄²×C₇₉	—	2	2	no	—
149	C₄²×C₇₉	—	2	2	no	—
150	C₄²×C₇₉	C₂²×C₄	1	2	yes	—
151	C₄²×C₇₉	C₂×D₄	1	2	yes	—
152	C₂³×C₇₉	—	2	2	no	—
153	C₂³×C₇₉	C₂×#41	1	1	yes	characteristic
154	Q₈×C₇₉	—	2	2	no	—
155	Q₈×C₇₉	—	2	2	no	—
156	D₄×C₇₉	—	2	2	no	—
157	D₄×C₇₉	—	2	2	no	—
158	D₄×C₇₉	—	4	2	no	—
159	D₄×C₇₉	—	4	2	no	—
160	C₂×C₄×C₇₉	—	2	2	no	—
161	C₂×C₄×C₇₉	—	2	2	no	—
162	C₂×C₄×C₇₉	—	2	2	no	—
163	C₂×C₄×C₇₉	—	4	1	no	—
164	C₂×C₄×C₇₉	—	4	1	no	—
165	C₂×C₄×C₇₉	—	4	4	no	—
166	C₂×C₄×C₇₉	—	4	2	no	—
167	C₂×C₄×C₇₉	—	4	2	no	—
168	C₂×C₄×C₇₉	—	8	2	no	—
169	C₂×C₄×C₇₉	C₄×D₄	1	2	yes	—
170	C₂×C₄×C₇₉	C₄×D₄	1	2	yes	—
171	C₂×C₄×C₇₉	C₂³×C₄	1	1	yes	characteristic
172	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
173	C₂×C₄×C₇₉	C₂×#41	1	1	yes	characteristic
174	C₂×C₄×C₇₉	C₂×#41	1	1	yes	characteristic
175	C₂×C₄×C₇₉	H(5,𝔽₂)	1	1	yes	characteristic
176	C₂×C₄×C₇₉	2₋¹⁺⁴	1	1	yes	characteristic
177	C₂×Dic₇₉	—	2	2	no	—
178	C₂×Dic₇₉	—	4	1	no	—
179	C₂×Dic₇₉	—	4	1	no	—
180	C₂×Dic₇₉	—	4	1	no	—
181	C₂×Dic₇₉	—	4	1	no	—
182	C₂×Dic₇₉	—	4	1	no	—
183	C₈×C₇₉	—	2	2	no	—
184	C₈×C₇₉	#117	1	2	yes	—
185	C₈×C₇₉	#117	1	2	yes	—
186	C₇₉⋊C₈	—	2	1	no	—
187	C₇₉⋊C₈	—	2	1	no	—
188	C₇₉⋊C₈	—	2	2	no	—
189	C₇₉⋊C₈	—	4	2	no	—
190	C₇₉⋊C₈	—	4	2	no	—
191	C₂²×C₇₉	—	2	1	no	—
192	C₂²×C₇₉	—	2	1	no	—
193	C₂²×C₇₉	—	4	2	no	—
194	C₂²×C₇₉	—	4	2	no	—
195	C₂²×C₇₉	—	4	2	no	—
196	C₂²×C₇₉	C₂×C₄×D₄	1	1	yes	characteristic
197	C₂²×C₇₉	#555	1	1	yes	characteristic
198	C₂²×C₇₉	#556	1	1	yes	characteristic
199	C₄×C₇₉	—	2	2	no	—
200	C₄×C₇₉	—	2	2	no	—
201	C₄×C₇₉	—	4	2	no	—
202	C₄×C₇₉	—	4	2	no	—
203	C₄×C₇₉	—	4	2	no	—
204	C₄×C₇₉	C₂×#117	1	1	yes	characteristic
205	C₄×C₇₉	#520	1	1	yes	characteristic
206	C₄×C₇₉	#547	1	1	yes	characteristic
207	C₄×C₇₉	#550	1	1	yes	characteristic
208	Dic₇₉	—	4	2	no	—
209	Dic₇₉	—	8	1	no	—
210	#22804	—	79	1	no	maximal, Sylow
211	C₂×C₇₉	—	2	1	no	—
212	C₂×C₇₉	—	2	1	no	—
213	C₂×C₇₉	—	8	2	no	—
214	C₂×C₇₉	#2354	1	1	yes	characteristic
215	C₂×C₇₉	#2955	1	1	yes	characteristic
216	C₂×C₇₉	#2956	1	1	yes	characteristic
217	#2943	D₇₉	1	1	yes	characteristic
218	#2925	—	79	2	no	—
219	#1975	—	79	1	no	—
220	#1974	—	79	1	no	—
221	#1929	—	79	2	no	—
222	#1929	—	79	2	no	—
223	#1849	—	79	1	no	—
224	#1806	—	79	2	no	—
225	#1773	—	79	1	no	—
226	#1772	—	79	1	no	—
227	#1771	—	79	1	no	—
228	C₇₉	#22804	1	1	yes	characteristic, complemented, Sylow
229	C₂×#135	C₂×D₇₉	1	1	yes	characteristic
230	C₄×#41	C₂×D₇₉	1	2	yes	—
231	#442	Dic₇₉	1	2	yes	complemented
232	#441	Dic₇₉	1	2	yes	complemented
233	#440	Dic₇₉	1	2	yes	complemented
234	#440	Dic₇₉	1	2	yes	complemented
235	#433	—	158	2	no	—
236	#433	—	158	2	no	—
237	#432	—	158	2	no	—
238	#431	—	158	2	no	—
239	C₂×#108	—	79	2	no	—
240	C₂×#108	—	79	1	no	—
241	C₂×#108	—	79	1	no	—
242	#427	C₂×D₇₉	1	1	yes	characteristic
243	#423	—	79	2	no	—
244	C₂×C₄⋊C₈	—	79	1	no	—
245	C₂×#104	—	79	2	no	—
246	C₂×#104	—	79	2	no	—
247	#416	C₂×D₇₉	1	2	yes	—
248	#408	—	79	2	no	—
249	#408	—	79	2	no	—
250	#405	—	79	2	no	—
251	#405	—	79	2	no	—
252	C₂×#97	—	79	1	no	—
253	C₂×#97	C₂×D₇₉	1	1	yes	characteristic
254	C₂×C₄×C₈	—	79	1	no	—
255	C₄×C₄⋊C₄	—	79	1	no	—
256	#339	—	79	2	no	—
257	#339	—	79	2	no	—
258	#336	—	79	1	no	—
259	#336	—	79	1	no	—
260	C₂×#41	C₂²×D₇₉	1	2	yes	—
261	#135	—	2	2	no	—
262	#135	—	2	2	no	—
263	C₂×Q₁₆	C₂×Dic₇₉	1	1	yes	characteristic
264	C₂×SD₁₆	C₂×Dic₇₉	1	2	yes	—
265	C₂×D₈	C₂×Dic₇₉	1	1	yes	characteristic
266	C₂×M₁₆	—	79	2	no	—
267	C₂×M₁₆	—	79	2	no	—
268	C₂²×C₈	—	79	1	no	—
269	C₂²×C₈	—	79	1	no	—
270	C₂²×C₈	C₂²×D₇₉	1	1	yes	characteristic
271	C₂²×C₈	C₂²×D₇₉	1	1	yes	characteristic
272	C₄×Q₈	C₂×Dic₇₉	1	2	yes	—
273	C₄×Q₈	C₂×Dic₇₉	1	2	yes	—
274	C₄×D₄	—	2	2	no	—
275	C₄×D₄	—	2	2	no	—
276	C₄×D₄	C₂×Dic₇₉	1	2	yes	—
277	C₄×D₄	C₂×Dic₇₉	1	2	yes	—
278	#117	—	2	2	no	—
279	#117	C₂²×D₇₉	1	2	yes	—
280	C₂×C₄⋊C₄	—	158	1	no	—
281	C₂×C₄²	—	2	2	no	—
282	C₂×C₄²	—	79	1	no	—
283	C₂×C₄²	—	79	1	no	—
284	C₂×C₄²	C₂²×D₇₉	1	1	yes	characteristic
285	#108	—	316	2	no	—
286	#108	—	158	2	no	—
287	#108	—	158	2	no	—
288	#107	C₂×Dic₇₉	1	1	yes	characteristic
289	#107	C₂×Dic₇₉	1	1	yes	characteristic
290	#106	C₂×Dic₇₉	1	2	yes	—
291	C₄⋊C₈	—	79	2	no	—
292	C₄⋊C₈	—	79	2	no	—
293	C₄⋊C₈	—	158	2	no	—
294	C₄⋊C₈	—	158	2	no	—
295	#104	—	316	2	no	—
296	#104	—	316	2	no	—
297	#103	C₂×Dic₇₉	1	2	yes	—
298	#103	C₂×Dic₇₉	1	2	yes	—
299	#102	C₂×Dic₇₉	1	2	yes	—
300	#102	C₂×Dic₇₉	1	2	yes	—
301	C₂²⋊C₈	—	158	2	no	—
302	C₂²⋊C₈	—	158	2	no	—
303	C₂²⋊C₈	—	158	2	no	—
304	C₂²⋊C₈	—	158	2	no	—
305	#97	—	158	2	no	—
306	#97	—	158	2	no	—
307	#97	—	158	2	no	—
308	#97	C₂×Dic₇₉	1	2	yes	—
309	#97	C₂×Dic₇₉	1	2	yes	—
310	C₄×C₈	—	158	2	no	—
311	C₄×C₈	—	158	2	no	—
312	C₄×C₈	—	158	2	no	—
313	#95	—	158	1	no	—
314	#41	—	2	2	no	—
315	#41	—	2	2	no	—
316	#41	—	2	2	no	—
317	#41	—	2	2	no	—
318	C₂×Q₈	C₂²×Dic₇₉	1	2	yes	—
319	C₂×D₄	—	2	2	no	—
320	C₂×D₄	C₂²×Dic₇₉	1	2	yes	—
321	C₂²×C₄	—	2	2	no	—
322	C₂²×C₄	—	2	2	no	—
323	C₂²×C₄	—	2	2	no	—
324	C₂²×C₄	—	158	1	no	—
325	C₂²×C₄	—	158	1	no	—
326	C₂²×C₄	#11929623	1	1	yes	characteristic
327	C₂²×C₄	#11929623	1	1	yes	characteristic
328	C₂²×C₄	C₂³×D₇₉	1	1	yes	characteristic
329	Q₁₆	—	2	2	no	—
330	SD₁₆	—	2	4	no	—
331	D₈	—	2	2	no	—
332	M₁₆	—	158	2	no	—
333	M₁₆	—	158	2	no	—
334	M₁₆	—	158	2	no	—
335	M₁₆	—	158	2	no	—
336	C₂×C₈	—	2	1	no	—
337	C₂×C₈	—	2	1	no	—
338	C₂×C₈	—	79	1	no	—
339	C₂×C₈	—	79	2	no	—
340	C₂×C₈	—	79	1	no	—
341	C₂×C₈	—	158	2	no	—
342	C₂×C₈	—	158	2	no	—
343	C₂×C₈	—	158	1	no	—
344	C₂×C₈	—	158	1	no	—
345	C₂×C₈	—	158	1	no	—
346	C₂×C₈	—	158	1	no	—
347	C₂×C₈	C₂²×Dic₇₉	1	2	yes	—
348	C₂×C₈	C₂²×Dic₇₉	1	1	yes	characteristic
349	C₂×C₈	C₂²×Dic₇₉	1	1	yes	characteristic
350	C₂×C₈	#11929624	1	2	yes	—
351	C₂×C₈	#11929624	1	2	yes	—
352	C₄⋊C₄	—	2	2	no	—
353	C₄⋊C₄	—	2	2	no	—
354	C₄⋊C₄	—	316	2	no	—
355	C₄⋊C₄	C₂²×Dic₇₉	1	2	yes	—
356	C₄⋊C₄	C₂²×Dic₇₉	1	2	yes	—
357	C₂²⋊C₄	—	2	2	no	—
358	C₂²⋊C₄	—	2	2	no	—
359	C₂²⋊C₄	—	2	2	no	—
360	C₄²	—	2	2	no	—
361	C₄²	—	2	2	no	—
362	C₄²	—	2	2	no	—
363	C₄²	—	158	1	no	—
364	C₄²	—	158	1	no	—
365	C₄²	—	158	1	no	—
366	C₄²	—	158	1	no	—
367	C₄²	C₂²×Dic₇₉	1	2	yes	—
368	C₄²	D₄×D₇₉	1	2	yes	—
369	C₂³	—	2	2	no	—
370	C₂³	C₂×#11929623	1	1	yes	characteristic
371	Q₈	—	2	2	no	—
372	Q₈	—	2	2	no	—
373	D₄	—	2	2	no	—
374	D₄	—	2	2	no	—
375	D₄	—	4	2	no	—
376	D₄	—	4	2	no	—
377	C₂×C₄	—	2	2	no	—
378	C₂×C₄	—	2	2	no	—
379	C₂×C₄	—	2	2	no	—
380	C₂×C₄	—	4	1	no	—
381	C₂×C₄	—	4	1	no	—
382	C₂×C₄	—	4	4	no	—
383	C₂×C₄	—	4	2	no	—
384	C₂×C₄	—	4	2	no	—
385	C₂×C₄	—	8	2	no	—
386	C₂×C₄	—	316	1	no	—
387	C₂×C₄	—	316	1	no	—
388	C₂×C₄	—	316	1	no	—
389	C₂×C₄	—	316	1	no	—
390	C₂×C₄	—	316	1	no	—
391	C₂×C₄	—	158	2	no	—
392	C₂×C₄	D₄×Dic₇₉	1	2	yes	—
393	C₂×C₄	D₄×Dic₇₉	1	2	yes	—
394	C₂×C₄	C₂³×Dic₇₉	1	1	yes	characteristic
395	C₂×C₄	C₂×D₄×D₇₉	1	1	yes	characteristic
396	C₂×C₄	C₂×#11929624	1	1	yes	characteristic
397	C₂×C₄	C₂×#11929624	1	1	yes	characteristic
398	C₂×C₄	#14579207	1	1	yes	characteristic
399	C₂×C₄	#14579208	1	1	yes	characteristic
400	C₈	—	2	2	no	—
401	C₈	—	316	2	no	—
402	C₈	—	316	2	no	—
403	C₈	—	158	1	no	—
404	C₈	—	158	2	no	—
405	C₈	—	158	1	no	—
406	C₈	#14579120	1	2	yes	—
407	C₈	#14579120	1	2	yes	—
408	C₂²	—	2	1	no	—
409	C₂²	—	2	1	no	—
410	C₂²	—	4	2	no	—
411	C₂²	—	4	2	no	—
412	C₂²	—	4	2	no	—
413	C₂²	C₂×D₄×Dic₇₉	1	1	yes	characteristic
414	C₂²	#19099278	1	1	yes	characteristic
415	C₂²	#19099283	1	1	yes	characteristic
416	C₄	—	2	2	no	—
417	C₄	—	2	2	no	—
418	C₄	—	4	2	no	—
419	C₄	—	4	2	no	—
420	C₄	—	4	2	no	—
421	C₄	—	316	2	no	—
422	C₄	—	632	1	no	—
423	C₄	C₂×#14579120	1	1	yes	characteristic
424	C₄	#19099046	1	1	yes	characteristic
425	C₄	#19099218	1	1	yes	characteristic
426	C₄	#19099234	1	1	yes	characteristic
427	C₂	—	2	1	no	—
428	C₂	—	2	1	no	—
429	C₂	—	8	2	no	—
430	C₂	#23766349	1	1	yes	characteristic
431	C₂	#23772303	1	1	yes	characteristic
432	C₂	#23772310	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	C₇₉×#2943	C₂
socle	C₂²×C₇₉	C₂×C₄×D₄
prime radical	C₂×#135×C₇₉	C₂²
cosocle	C₂²×C₄×C₇₉	C₂⁴
hypercenter	#2943	D₇₉
hypocenter	C₇₉	#22804
LCS	G ▷ C₂×C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #2943

Complements

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

N	H ≅ G/N	type
1. #23772066	C₂	semidirect
4. #23764050	C₂	semidirect
5. #23764050	C₂	semidirect
6. #23763575	C₂	semidirect
7. #23763420	C₂	semidirect
8. #23763286	C₂	semidirect
9. #23763281	C₂	semidirect
10. #23763272	C₂	semidirect
36. #442×C₇₉	C₄	semidirect
37. #441×C₇₉	C₄	semidirect
38. #440×C₇₉	C₄	semidirect
39. #440×C₇₉	C₄	semidirect
228. C₇₉	#22804	semidirect
231. #442	Dic₇₉	semidirect
232. #441	Dic₇₉	semidirect
233. #440	Dic₇₉	semidirect
234. #440	Dic₇₉	semidirect

Maximal subgroups

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

subgroup	index
#23772066	2
#23764294	2
#23764289	2
#23764050	2
#23763575	2
#23763420	2
#23763286	2
#23763281	2
#23763272	2
C₇₉×#2943	2
#22804	79