Subgroups — #34258272

Order 20224.

632 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	#23773472	C₂	1	1	yes	maximal, characteristic
2	#23772356	C₂	1	1	yes	maximal, characteristic
3	#23772330	C₂	1	1	yes	maximal, characteristic, complemented
4	#23762270	C₂	1	2	yes	maximal, complemented
5	#23762256	C₂	1	2	yes	maximal, complemented
6	#23762206	C₂	1	2	yes	maximal, complemented
7	#23762199	C₂	1	2	yes	maximal, complemented
8	#23761837	C₂	1	1	yes	maximal, characteristic
9	#23761820	C₂	1	1	yes	maximal, characteristic, complemented
10	#23761681	C₂	1	1	yes	maximal, characteristic, complemented
11	C₇₉×#1574	C₂	1	1	yes	maximal, characteristic, complemented
12	#19099120	C₂²	1	1	yes	characteristic
13	C₄×#11929624	C₂²	1	1	yes	characteristic
14	#19098905	C₄	1	2	yes	—
15	#19098849	C₄	1	1	yes	characteristic
16	#19098844	C₄	1	1	yes	characteristic
17	#19098774	C₄	1	1	yes	characteristic
18	#19098769	C₄	1	1	yes	characteristic
19	#19098727	C₄	1	2	yes	—
20	#19098690	—	2	1	no	—
21	#19098690	C₂²	1	2	yes	—
22	#19098687	—	2	1	no	—
23	#19098687	C₂²	1	2	yes	—
24	#19098687	C₂²	1	1	yes	characteristic
25	#19098687	C₂²	1	1	yes	characteristic
26	C₄×Dic₃₁₆	C₂²	1	2	yes	—
27	C₄×#11929613	C₂²	1	2	yes	—
28	#19098628	C₂²	1	1	yes	characteristic
29	#19098628	C₂²	1	1	yes	characteristic
30	(C₂²⋊D₇₉)⋊C₈	—	2	1	no	—
31	(C₂²⋊D₇₉)⋊C₈	—	2	1	no	—
32	#19098614	—	2	1	no	—
33	#19098591	—	2	1	no	—
34	#19098521	—	2	1	no	—
35	C₄×#11929608	C₂²	1	1	yes	characteristic
36	C₂×C₄×C₇₉⋊C₈	C₂²	1	1	yes	characteristic
37	C₄×C₈×D₇₉	—	2	1	no	—
38	#19098293	C₂²	1	2	yes	—
39	#19098293	C₂²	1	2	yes	—
40	#19098293	C₂²	1	2	yes	—
41	#19098290	C₂²	1	2	yes	—
42	#19098285	C₂²	1	2	yes	—
43	C₈×C₇₉⋊C₈	C₂²	1	2	yes	—
44	#431×C₇₉	C₂²	1	1	yes	characteristic
45	#431×C₇₉	C₂²	1	1	yes	characteristic
46	#423×C₇₉	C₂²	1	1	yes	characteristic
47	#335×C₇₉	C₂²	1	2	yes	—
48	#334×C₇₉	C₂²	1	2	yes	—
49	C₂×#11929624	C₂×C₄	1	1	yes	characteristic
50	C₂×Dic₃₁₆	C₂×C₄	1	2	yes	—
51	C₂×#11929613	C₂×C₄	1	2	yes	—
52	C₂×#11929608	—	2	1	no	—
53	C₂²×C₇₉⋊C₈	D₄	1	1	yes	characteristic
54	C₂²×C₇₉⋊C₈	D₄	1	1	yes	characteristic
55	C₂×C₈×D₇₉	—	2	1	no	—
56	C₂×C₈×D₇₉	—	2	1	no	—
57	#14579161	C₂×C₄	1	1	yes	characteristic
58	#14579161	C₂×C₄	1	1	yes	characteristic
59	#14579153	—	2	1	no	—
60	#14579140	—	2	1	no	—
61	#14579140	C₂×C₄	1	2	yes	—
62	C₄×Dic₁₅₈	—	2	1	no	—
63	C₄×Dic₁₅₈	C₂×C₄	1	1	yes	characteristic
64	C₄×Dic₁₅₈	C₂³	1	2	yes	—
65	C₄×Dic₁₅₈	C₂³	1	1	yes	characteristic
66	C₄×D₃₁₆	C₂×C₄	1	1	yes	characteristic
67	C₄×D₃₁₆	C₂³	1	1	yes	characteristic
68	C₄×C₂²⋊D₇₉	—	2	1	no	—
69	C₄×C₂²⋊D₇₉	—	2	1	no	—
70	#14579120	—	2	1	no	—
71	#14579120	C₂×C₄	1	1	yes	characteristic
72	#14579118	—	2	1	no	—
73	C₄²×D₇₉	—	2	1	no	—
74	#14579095	C₂×C₄	1	2	yes	—
75	#14579093	C₂×C₄	1	2	yes	—
76	Dic₇₉⋊C₈	—	2	1	no	—
77	Dic₇₉⋊C₈	—	2	1	no	—
78	Dic₇₉⋊C₈	—	2	2	no	—
79	Dic₇₉⋊C₈	—	2	2	no	—
80	#14579086	C₂×C₄	1	2	yes	—
81	#14579086	C₂×C₄	1	2	yes	—
82	#14579086	C₂×C₄	1	2	yes	—
83	#14579083	C₂×C₄	1	2	yes	—
84	(C₂×D₇₉)⋊C₈	—	2	1	no	—
85	(C₂×D₇₉)⋊C₈	—	2	1	no	—
86	#14579072	—	2	1	no	—
87	#14579071	—	2	2	no	—
88	C₄×C₇₉⋊C₈	D₄	1	1	yes	characteristic
89	C₄×C₇₉⋊C₈	D₄	1	1	yes	characteristic
90	C₄×C₇₉⋊C₈	C₂³	1	2	yes	—
91	C₄×C₇₉⋊C₈	C₂³	1	1	yes	characteristic
92	C₄×C₇₉⋊C₈	C₂³	1	1	yes	characteristic
93	C₈×Dic₇₉	—	2	1	no	—
94	C₈×Dic₇₉	—	2	1	no	—
95	C₈×Dic₇₉	—	2	2	no	—
96	C₂×M₁₆×C₇₉	—	2	1	no	—
97	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
98	C₄⋊C₈×C₇₉	—	2	1	no	—
99	C₄⋊C₈×C₇₉	C₂×C₄	1	1	yes	characteristic
100	C₄⋊C₈×C₇₉	C₂×C₄	1	1	yes	characteristic
101	C₄⋊C₈×C₇₉	C₂³	1	1	yes	characteristic
102	C₄⋊C₈×C₇₉	C₂³	1	1	yes	characteristic
103	C₄⋊C₈×C₇₉	C₂³	1	2	yes	—
104	C₂²⋊C₈×C₇₉	—	2	1	no	—
105	C₂²⋊C₈×C₇₉	C₂×C₄	1	2	yes	—
106	C₄×C₈×C₇₉	—	2	1	no	—
107	C₄×C₈×C₇₉	C₂³	1	2	yes	—
108	#11929624	—	2	2	no	—
109	#11929624	—	2	2	no	—
110	C₂×Dic₁₅₈	—	2	1	no	—
111	C₂×Dic₁₅₈	C₂²×C₄	1	2	yes	—
112	C₂×Dic₁₅₈	C₂²×C₄	1	1	yes	characteristic
113	C₂×D₃₁₆	C₂²×C₄	1	1	yes	characteristic
114	C₂×C₂²⋊D₇₉	—	2	1	no	—
115	C₂×C₄×D₇₉	—	2	1	no	—
116	C₂×C₄×D₇₉	—	2	1	no	—
117	C₂×C₄×D₇₉	—	2	1	no	—
118	Dic₃₁₆	—	2	4	no	—
119	#11929613	—	2	4	no	—
120	#11929608	—	2	4	no	—
121	C₂×C₇₉⋊C₈	—	2	2	no	—
122	C₂×C₇₉⋊C₈	—	2	2	no	—
123	C₂×C₇₉⋊C₈	—	4	1	no	—
124	C₂×C₇₉⋊C₈	C₂×D₄	1	1	yes	characteristic
125	C₂×C₇₉⋊C₈	C₂×D₄	1	1	yes	characteristic
126	C₂×C₇₉⋊C₈	C₂×D₄	1	1	yes	characteristic
127	C₂×C₇₉⋊C₈	C₂×D₄	1	1	yes	characteristic
128	C₈×D₇₉	—	4	2	no	—
129	C₈×D₇₉	—	4	2	no	—
130	C₄⋊Dic₇₉	—	2	1	no	—
131	C₄⋊Dic₇₉	—	2	1	no	—
132	C₄⋊Dic₇₉	—	2	1	no	—
133	C₄⋊Dic₇₉	C₂²×C₄	1	2	yes	—
134	C₄⋊Dic₇₉	C₂²×C₄	1	1	yes	characteristic
135	C₄⋊Dic₇₉	C₂²×C₄	1	1	yes	characteristic
136	Dic₇₉⋊C₄	—	2	1	no	—
137	Dic₇₉⋊C₄	—	2	2	no	—
138	Dic₇₉⋊C₄	—	2	1	no	—
139	Dic₇₉⋊C₄	—	2	2	no	—
140	C₂²⋊Dic₇₉	—	2	2	no	—
141	C₂²⋊Dic₇₉	—	2	1	no	—
142	(C₂×D₇₉)⋊C₄	—	2	1	no	—
143	(C₂×D₇₉)⋊C₄	—	2	1	no	—
144	C₄×Dic₇₉	—	2	1	no	—
145	C₄×Dic₇₉	—	2	1	no	—
146	C₄×Dic₇₉	—	2	1	no	—
147	C₄×Dic₇₉	—	2	2	no	—
148	C₂²×C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
149	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
150	C₂²×C₄×C₇₉	#41	1	1	yes	characteristic
151	M₁₆×C₇₉	—	4	2	no	—
152	C₂×C₈×C₇₉	—	2	1	no	—
153	C₂×C₈×C₇₉	—	2	1	no	—
154	C₂×C₈×C₇₉	—	2	2	no	—
155	C₂×C₈×C₇₉	C₂²×C₄	1	2	yes	—
156	C₂×C₈×C₇₉	C₂²×C₄	1	2	yes	—
157	C₄²×C₇₉	C₂²×C₄	1	1	yes	characteristic
158	C₄²×C₇₉	C₂×D₄	1	1	yes	characteristic
159	C₄²×C₇₉	#41	1	1	yes	characteristic
160	C₄²×C₇₉	C₂⁴	1	1	yes	characteristic
161	C₂³×C₇₉	C₄×D₄	1	1	yes	characteristic
162	C₂²×D₇₉	—	2	1	no	—
163	C₂×C₄×C₇₉	—	2	1	no	—
164	C₂×C₄×C₇₉	—	2	1	no	—
165	C₂×C₄×C₇₉	—	2	1	no	—
166	C₂×C₄×C₇₉	—	2	1	no	—
167	C₂×C₄×C₇₉	—	2	2	no	—
168	C₂×C₄×C₇₉	C₄×D₄	1	1	yes	characteristic
169	C₂×C₄×C₇₉	C₄×D₄	1	1	yes	characteristic
170	C₂×C₄×C₇₉	C₄×D₄	1	1	yes	characteristic
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	C₂²⋊D₇₉	—	2	4	no	—
175	C₂×Dic₇₉	—	2	1	no	—
176	C₂×Dic₇₉	—	2	1	no	—
177	C₂×Dic₇₉	—	2	1	no	—
178	C₂×Dic₇₉	—	2	2	no	—
179	C₂×Dic₇₉	—	2	2	no	—
180	D₃₁₆	—	2	1	no	—
181	D₃₁₆	#131	1	2	yes	—
182	C₄×D₇₉	—	2	4	no	—
183	C₄×D₇₉	—	4	1	no	—
184	C₄×D₇₉	—	4	1	no	—
185	C₄×D₇₉	—	4	2	no	—
186	Dic₁₅₈	—	2	1	no	—
187	Dic₁₅₈	—	2	2	no	—
188	Dic₁₅₈	—	2	2	no	—
189	Dic₁₅₈	—	4	2	no	—
190	Dic₁₅₈	#131	1	2	yes	—
191	C₈×C₇₉	—	2	2	no	—
192	C₈×C₇₉	—	2	2	no	—
193	C₈×C₇₉	—	4	1	no	—
194	C₈×C₇₉	—	4	1	no	—
195	C₈×C₇₉	—	4	2	no	—
196	C₇₉⋊C₈	—	2	4	no	—
197	C₇₉⋊C₈	—	2	1	no	—
198	C₇₉⋊C₈	—	2	1	no	—
199	C₇₉⋊C₈	—	2	1	no	—
200	C₇₉⋊C₈	#137	1	2	yes	—
201	C₂²×C₇₉	—	2	1	no	—
202	C₂²×C₇₉	—	2	1	no	—
203	C₂²×C₇₉	—	2	1	no	—
204	C₂²×C₇₉	C₂×C₄×D₄	1	1	yes	characteristic
205	C₂×D₇₉	—	2	2	no	—
206	C₂×D₇₉	—	4	1	no	—
207	C₂×D₇₉	—	4	1	no	—
208	C₄×C₇₉	—	2	1	no	—
209	C₄×C₇₉	—	2	1	no	—
210	C₄×C₇₉	—	2	1	no	—
211	C₄×C₇₉	#443	1	2	yes	—
212	C₄×C₇₉	C₂×#131	1	1	yes	characteristic
213	C₄×C₇₉	C₂×#131	1	1	yes	characteristic
214	C₄×C₇₉	C₂×#137	1	1	yes	characteristic
215	C₄×C₇₉	#575	1	1	yes	characteristic
216	Dic₇₉	—	2	2	no	—
217	Dic₇₉	—	4	2	no	—
218	Dic₇₉	—	4	1	no	—
219	Dic₇₉	—	4	2	no	—
220	Dic₇₉	—	4	1	no	—
221	#17913	—	79	1	no	maximal, Sylow
222	C₂×C₇₉	—	4	1	no	—
223	C₂×C₇₉	#2929	1	1	yes	characteristic
224	C₂×C₇₉	C₄×#137	1	1	yes	characteristic
225	C₂×C₇₉	C₂×#443	1	1	yes	characteristic
226	D₇₉	—	4	2	no	—
227	#3107	—	79	1	no	—
228	C₈×#41	—	79	1	no	—
229	#2960	—	79	1	no	—
230	#1587	—	79	2	no	—
231	#1585	—	79	2	no	—
232	C₈×Q₁₆	—	79	2	no	—
233	C₈×SD₁₆	—	79	2	no	—
234	#1574	D₇₉	1	1	yes	characteristic, complemented
235	#1489	—	79	1	no	—
236	#1485	—	79	1	no	—
237	C₈×M₁₆	—	79	1	no	—
238	C₇₉	#17913	1	1	yes	characteristic, complemented, Sylow
239	#533	—	79	1	no	—
240	C₄×#41	—	79	1	no	—
241	#485	—	79	2	no	—
242	#475	—	79	1	no	—
243	#474	—	79	1	no	—
244	#462	—	79	1	no	—
245	#461	—	79	1	no	—
246	#452	—	79	2	no	—
247	#446	—	79	2	no	—
248	#446	—	158	1	no	—
249	C₈×Q₈	—	79	2	no	—
250	C₈×Q₈	—	79	1	no	—
251	C₈×Q₈	—	79	1	no	—
252	C₈×Q₈	—	158	1	no	—
253	C₄×Q₁₆	—	79	2	no	—
254	C₄×SD₁₆	—	79	2	no	—
255	C₈×D₄	—	79	1	no	—
256	C₈×D₄	—	79	1	no	—
257	C₈×D₄	—	158	1	no	—
258	C₈×D₄	—	158	1	no	—
259	#431	—	158	1	no	—
260	#431	C₂×D₇₉	1	1	yes	characteristic
261	#431	C₂×D₇₉	1	1	yes	characteristic
262	#424	—	158	1	no	—
263	#423	C₂×D₇₉	1	1	yes	characteristic
264	#405	—	158	1	no	—
265	C₄×M₁₆	—	79	1	no	—
266	C₂×C₄×C₈	—	79	1	no	—
267	C₂×C₄×C₈	—	158	1	no	—
268	#335	C₂×D₇₉	1	2	yes	—
269	#334	C₂×D₇₉	1	2	yes	—
270	Q₈⋊C₈	—	79	2	no	—
271	Q₈⋊C₈	—	79	2	no	—
272	Q₈⋊C₈	—	79	2	no	—
273	D₄⋊C₈	—	79	2	no	—
274	#322	—	79	2	no	—
275	C₈²	—	79	2	no	—
276	C₂×#41	—	79	1	no	—
277	C₂×Q₁₆	—	79	2	no	—
278	C₂×SD₁₆	—	79	2	no	—
279	C₂×M₁₆	—	2	1	no	—
280	C₂×M₁₆	—	158	1	no	—
281	C₂²×C₈	—	79	1	no	—
282	C₂²×C₈	—	79	1	no	—
283	C₂²×C₈	—	158	1	no	—
284	C₂²×C₈	—	158	1	no	—
285	C₄⋊Q₈	—	79	1	no	—
286	C₄⋊Q₈	—	79	1	no	—
287	#125	—	158	1	no	—
288	C₂²⋊Q₈	—	79	2	no	—
289	C₂²⋊Q₈	—	158	1	no	—
290	C₄×Q₈	—	79	1	no	—
291	C₄×Q₈	—	79	1	no	—
292	C₄×Q₈	—	79	2	no	—
293	C₄×Q₈	—	158	1	no	—
294	C₄×D₄	—	79	1	no	—
295	C₄×D₄	—	79	1	no	—
296	C₄×D₄	—	158	1	no	—
297	C₄×D₄	—	158	1	no	—
298	#117	—	79	1	no	—
299	#117	—	158	1	no	—
300	#117	—	158	1	no	—
301	C₂×C₄²	—	158	1	no	—
302	C₂×C₄²	C₂²×D₇₉	1	1	yes	characteristic
303	#107	—	79	2	no	—
304	#106	—	79	2	no	—
305	C₄⋊C₈	—	2	1	no	—
306	C₄⋊C₈	—	158	2	no	—
307	C₄⋊C₈	—	158	2	no	—
308	C₄⋊C₈	—	158	1	no	—
309	C₄⋊C₈	—	158	1	no	—
310	C₄⋊C₈	C₄×D₇₉	1	1	yes	characteristic
311	C₄⋊C₈	C₄×D₇₉	1	1	yes	characteristic
312	C₄⋊C₈	C₂²×D₇₉	1	2	yes	—
313	C₄⋊C₈	C₂²×D₇₉	1	1	yes	characteristic
314	C₄⋊C₈	C₂²×D₇₉	1	1	yes	characteristic
315	#103	—	79	2	no	—
316	#103	—	79	2	no	—
317	#103	—	79	2	no	—
318	#102	—	79	2	no	—
319	C₂²⋊C₈	—	2	1	no	—
320	C₂²⋊C₈	—	158	1	no	—
321	C₂²⋊C₈	—	158	1	no	—
322	C₂²⋊C₈	C₄×D₇₉	1	2	yes	—
323	#97	—	158	2	no	—
324	#97	—	158	1	no	—
325	C₄×C₈	—	2	1	no	—
326	C₄×C₈	—	79	1	no	—
327	C₄×C₈	—	79	1	no	—
328	C₄×C₈	—	79	1	no	—
329	C₄×C₈	—	79	1	no	—
330	C₄×C₈	—	79	2	no	—
331	C₄×C₈	—	158	1	no	—
332	C₄×C₈	—	158	1	no	—
333	C₄×C₈	—	158	2	no	—
334	C₄×C₈	C₂²×D₇₉	1	2	yes	—
335	#41	—	158	2	no	—
336	#41	—	158	2	no	—
337	C₂×Q₈	—	79	1	no	—
338	C₂×Q₈	—	79	2	no	—
339	C₂×Q₈	—	158	1	no	—
340	C₂×D₄	—	79	1	no	—
341	C₂×D₄	—	158	1	no	—
342	C₂²×C₄	—	158	1	no	—
343	C₂²×C₄	—	158	1	no	—
344	C₂²×C₄	—	158	1	no	—
345	C₂²×C₄	C₂×C₄×D₇₉	1	1	yes	characteristic
346	C₂²×C₄	D₄×D₇₉	1	1	yes	characteristic
347	C₂²×C₄	#11929625	1	1	yes	characteristic
348	Q₁₆	—	158	4	no	—
349	SD₁₆	—	158	4	no	—
350	M₁₆	—	4	2	no	—
351	M₁₆	—	158	4	no	—
352	C₂×C₈	—	2	1	no	—
353	C₂×C₈	—	2	1	no	—
354	C₂×C₈	—	2	2	no	—
355	C₂×C₈	—	316	2	no	—
356	C₂×C₈	—	316	2	no	—
357	C₂×C₈	—	316	1	no	—
358	C₂×C₈	—	79	1	no	—
359	C₂×C₈	—	79	1	no	—
360	C₂×C₈	—	79	1	no	—
361	C₂×C₈	—	79	1	no	—
362	C₂×C₈	—	158	2	no	—
363	C₂×C₈	—	158	2	no	—
364	C₂×C₈	C₂×C₄×D₇₉	1	2	yes	—
365	C₂×C₈	C₂×C₄×D₇₉	1	2	yes	—
366	C₄⋊C₄	—	79	2	no	—
367	C₄⋊C₄	—	79	1	no	—
368	C₄⋊C₄	—	79	1	no	—
369	C₄⋊C₄	—	158	1	no	—
370	C₄⋊C₄	—	158	2	no	—
371	C₄⋊C₄	—	158	1	no	—
372	C₄⋊C₄	—	158	2	no	—
373	C₄⋊C₄	—	158	1	no	—
374	C₄⋊C₄	—	158	1	no	—
375	C₄⋊C₄	—	158	1	no	—
376	C₂²⋊C₄	—	158	1	no	—
377	C₂²⋊C₄	—	158	2	no	—
378	C₂²⋊C₄	—	158	1	no	—
379	C₂²⋊C₄	—	158	1	no	—
380	C₄²	—	158	1	no	—
381	C₄²	—	158	1	no	—
382	C₄²	—	158	1	no	—
383	C₄²	—	158	2	no	—
384	C₄²	C₂×C₄×D₇₉	1	1	yes	characteristic
385	C₄²	D₄×D₇₉	1	1	yes	characteristic
386	C₄²	#11929625	1	1	yes	characteristic
387	C₄²	C₂³×D₇₉	1	1	yes	characteristic
388	C₂³	—	158	1	no	—
389	C₂³	#14579123	1	1	yes	characteristic
390	Q₈	—	316	2	no	—
391	Q₈	—	79	2	no	—
392	Q₈	—	158	2	no	—
393	Q₈	—	158	2	no	—
394	Q₈	—	158	1	no	—
395	D₄	—	79	2	no	—
396	D₄	—	158	4	no	—
397	D₄	—	158	1	no	—
398	C₂×C₄	—	2	2	no	—
399	C₂×C₄	—	2	1	no	—
400	C₂×C₄	—	2	1	no	—
401	C₂×C₄	—	2	1	no	—
402	C₂×C₄	—	2	1	no	—
403	C₂×C₄	—	316	2	no	—
404	C₂×C₄	—	316	1	no	—
405	C₂×C₄	—	316	1	no	—
406	C₂×C₄	—	158	4	no	—
407	C₂×C₄	—	158	1	no	—
408	C₂×C₄	—	158	1	no	—
409	C₂×C₄	—	158	2	no	—
410	C₂×C₄	—	158	2	no	—
411	C₂×C₄	—	158	1	no	—
412	C₂×C₄	#14579123	1	1	yes	characteristic
413	C₂×C₄	#14579123	1	1	yes	characteristic
414	C₂×C₄	#14579123	1	1	yes	characteristic
415	C₂×C₄	C₂²×C₄×D₇₉	1	1	yes	characteristic
416	C₂×C₄	C₂×D₄×D₇₉	1	1	yes	characteristic
417	C₂×C₄	C₂×#11929625	1	1	yes	characteristic
418	C₈	—	2	2	no	—
419	C₈	—	2	2	no	—
420	C₈	—	4	1	no	—
421	C₈	—	4	1	no	—
422	C₈	—	4	2	no	—
423	C₈	—	79	2	no	—
424	C₈	—	158	4	no	—
425	C₈	—	158	1	no	—
426	C₈	—	158	1	no	—
427	C₈	—	158	1	no	—
428	C₂²	—	2	1	no	—
429	C₂²	—	2	1	no	—
430	C₂²	—	2	1	no	—
431	C₂²	—	316	1	no	—
432	C₂²	—	316	1	no	—
433	C₂²	—	158	2	no	—
434	C₂²	C₂×#14579123	1	1	yes	characteristic
435	C₄	—	2	1	no	—
436	C₄	—	2	1	no	—
437	C₄	—	2	1	no	—
438	C₄	—	316	1	no	—
439	C₄	—	316	1	no	—
440	C₄	—	316	2	no	—
441	C₄	—	316	2	no	—
442	C₄	—	158	2	no	—
443	C₄	#19098679	1	2	yes	—
444	C₄	#131×D₇₉	1	1	yes	characteristic
445	C₄	#131×D₇₉	1	1	yes	characteristic
446	C₄	#137×D₇₉	1	1	yes	characteristic
447	C₄	#19099359	1	1	yes	characteristic
448	C₂	—	4	1	no	—
449	C₂	—	316	2	no	—
450	C₂	#23772093	1	1	yes	characteristic
451	C₂	#23772218	1	1	yes	characteristic
452	C₂	C₂×#19098679	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₇₉
commutator	C₂×C₄×C₇₉	C₂³×C₄
Frattini	C₄²	C₂³×D₇₉
Fitting	C₇₉×#1574	C₂
socle	C₂²×C₇₉	C₂×C₄×D₄
prime radical	C₂×#11929624	C₂×C₄
cosocle	C₄²×C₇₉	C₂⁴
hypercenter	#1574	D₇₉
hypocenter	C₇₉	#17913
LCS	G ▷ C₂×C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1574

Complements

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

N	H ≅ G/N	type
3. #23772330	C₂	semidirect
4. #23762270	C₂	semidirect
5. #23762256	C₂	semidirect
6. #23762206	C₂	semidirect
7. #23762199	C₂	semidirect
9. #23761820	C₂	semidirect
10. #23761681	C₂	semidirect
11. C₇₉×#1574	C₂	semidirect
234. #1574	D₇₉	semidirect
238. C₇₉	#17913	semidirect

Maximal subgroups

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

subgroup	index
#23773472	2
#23772356	2
#23772330	2
#23762270	2
#23762256	2
#23762206	2
#23762199	2
#23761837	2
#23761820	2
#23761681	2
C₇₉×#1574	2
#17913	79