Subgroups — #34260040

Order 20224.

654 conjugacy classes of subgroups.

The subgroup lattice has 428 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#23773955	C₂	1	1	yes	maximal, characteristic
2	#23772343	C₂	1	1	yes	maximal, characteristic, complemented
3	#23772144	C₂	1	1	yes	maximal, characteristic
4	#23762293	C₂	1	2	yes	maximal, complemented
5	#23762246	C₂	1	2	yes	maximal, complemented
6	#23762233	C₂	1	2	yes	maximal, complemented
7	#23762203	C₂	1	2	yes	maximal, complemented
8	C₂×#19098313	C₂	1	1	yes	maximal, characteristic, complemented
9	#23761804	C₂	1	1	yes	maximal, characteristic, complemented
10	#23761681	C₂	1	1	yes	maximal, characteristic, complemented
11	C₇₉×#1480	C₂	1	1	yes	maximal, characteristic
12	C₂×#14579168	—	2	1	no	—
13	#19099120	C₂²	1	1	yes	characteristic
14	#19098959	C₄	1	1	yes	characteristic
15	#19098935	C₄	1	1	yes	characteristic
16	#19098915	C₄	1	1	yes	characteristic
17	#19098909	C₄	1	1	yes	characteristic
18	#19098790	C₄	1	2	yes	—
19	#19098790	C₄	1	2	yes	—
20	#19098692	—	2	2	no	—
21	#19098690	C₂²	1	2	yes	—
22	#19098687	C₂²	1	2	yes	—
23	C₄×#11929612	C₂²	1	2	yes	—
24	C₄×#11929612	C₂²	1	2	yes	—
25	#19098641	C₂²	1	2	yes	—
26	#19098635	—	2	2	no	—
27	D₄×C₇₉⋊C₈	C₂²	1	2	yes	—
28	#19098589	—	2	1	no	—
29	C₂×C₄⋊(C₇₉⋊C₈)	C₂²	1	1	yes	characteristic
30	#19098530	—	2	1	no	—
31	#19098518	—	2	1	no	—
32	C₄×#11929608	C₂²	1	1	yes	characteristic
33	C₂×C₄×C₇₉⋊C₈	C₂²	1	1	yes	characteristic
34	#19098313	C₂²	1	1	yes	characteristic
35	#19098313	C₂²	1	1	yes	characteristic
36	#19098313	C₂²	1	1	yes	characteristic
37	#19098313	C₂²	1	1	yes	characteristic
38	#19098295	C₂²	1	2	yes	—
39	#19098295	C₂²	1	2	yes	—
40	#19098285	C₂²	1	2	yes	—
41	C₈×C₇₉⋊C₈	C₂²	1	2	yes	—
42	#532×C₇₉	C₂²	1	1	yes	characteristic
43	#431×C₇₉	C₂²	1	1	yes	characteristic
44	C₂×C₄⋊C₈×C₇₉	C₂²	1	1	yes	characteristic
45	D₄⋊C₈×C₇₉	C₂²	1	2	yes	—
46	D₄⋊C₈×C₇₉	C₂²	1	2	yes	—
47	C₂×#11929612	C₂×C₄	1	2	yes	—
48	C₂×#11929612	C₂×C₄	1	2	yes	—
49	#14579168	—	4	4	no	—
50	C₂×#11929608	—	2	2	no	—
51	C₂×#11929608	D₄	1	1	yes	characteristic
52	C₂×#11929608	D₄	1	1	yes	characteristic
53	C₂²×C₇₉⋊C₈	—	2	1	no	—
54	C₂²×C₇₉⋊C₈	—	2	2	no	—
55	C₂²×C₇₉⋊C₈	C₂×C₄	1	1	yes	characteristic
56	C₂²×C₇₉⋊C₈	C₂×C₄	1	1	yes	characteristic
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	C₂³	1	2	yes	—
64	#14579120	—	2	1	no	—
65	#14579092	C₂×C₄	1	2	yes	—
66	#14579092	C₂×C₄	1	2	yes	—
67	C₄⋊(C₇₉⋊C₈)	—	2	1	no	—
68	C₄⋊(C₇₉⋊C₈)	C₂³	1	1	yes	characteristic
69	C₄⋊(C₇₉⋊C₈)	C₂³	1	1	yes	characteristic
70	Dic₇₉⋊C₈	—	2	2	no	—
71	Dic₇₉⋊C₈	—	2	2	no	—
72	#14579084	C₂×C₄	1	2	yes	—
73	#14579084	C₂×C₄	1	2	yes	—
74	#14579082	C₂×C₄	1	2	yes	—
75	#14579082	C₂×C₄	1	2	yes	—
76	C₂²⋊(C₇₉⋊C₈)	—	2	2	no	—
77	C₂²⋊(C₇₉⋊C₈)	—	2	2	no	—
78	#14579072	D₄	1	2	yes	—
79	#14579071	—	2	2	no	—
80	C₄×C₇₉⋊C₈	C₂×C₄	1	1	yes	characteristic
81	C₄×C₇₉⋊C₈	C₂×C₄	1	1	yes	characteristic
82	C₄×C₇₉⋊C₈	C₂³	1	1	yes	characteristic
83	C₄×C₇₉⋊C₈	C₂³	1	1	yes	characteristic
84	C₄×C₇₉⋊C₈	C₂³	1	2	yes	—
85	C₈×Dic₇₉	—	2	2	no	—
86	C₂×#41×C₇₉	—	2	1	no	—
87	C₂²×C₈×C₇₉	—	2	1	no	—
88	C₄⋊Q₈×C₇₉	C₂×C₄	1	1	yes	characteristic
89	#127×C₇₉	C₂×C₄	1	1	yes	characteristic
90	#124×C₇₉	—	2	1	no	—
91	#121×C₇₉	—	2	1	no	—
92	#121×C₇₉	C₂×C₄	1	2	yes	—
93	C₄×D₄×C₇₉	—	2	1	no	—
94	C₄×D₄×C₇₉	C₂³	1	2	yes	—
95	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
96	C₄⋊C₈×C₇₉	—	2	1	no	—
97	C₄⋊C₈×C₇₉	—	2	1	no	—
98	C₄⋊C₈×C₇₉	C₂³	1	1	yes	characteristic
99	C₄⋊C₈×C₇₉	C₂³	1	1	yes	characteristic
100	C₂²⋊C₈×C₇₉	—	2	1	no	—
101	C₄×C₈×C₇₉	C₂³	1	2	yes	—
102	C₂×Dic₁₅₈	—	2	1	no	—
103	C₂×Dic₁₅₈	C₂²×C₄	1	2	yes	—
104	#11929612	—	2	4	no	—
105	#11929612	—	4	2	no	—
106	#11929608	—	2	2	no	—
107	#11929608	—	4	4	no	—
108	#11929608	SD₁₆	1	4	yes	complemented
109	C₂×C₇₉⋊C₈	—	2	2	no	—
110	C₂×C₇₉⋊C₈	—	2	1	no	—
111	C₂×C₇₉⋊C₈	—	2	1	no	—
112	C₂×C₇₉⋊C₈	—	4	1	no	—
113	C₂×C₇₉⋊C₈	—	4	4	no	—
114	C₂×C₇₉⋊C₈	—	4	2	no	—
115	C₂×C₇₉⋊C₈	C₂²×C₄	1	1	yes	characteristic
116	C₂×C₇₉⋊C₈	C₂²×C₄	1	1	yes	characteristic
117	C₂×C₇₉⋊C₈	C₂²×C₄	1	1	yes	characteristic
118	C₂×C₇₉⋊C₈	C₂²×C₄	1	1	yes	characteristic
119	C₂×C₇₉⋊C₈	C₂×D₄	1	2	yes	—
120	C₂×C₇₉⋊C₈	C₂×D₄	1	2	yes	—
121	C₄⋊Dic₇₉	—	2	1	no	—
122	C₄⋊Dic₇₉	—	2	1	no	—
123	C₄⋊Dic₇₉	—	2	1	no	—
124	C₄⋊Dic₇₉	C₂²×C₄	1	2	yes	—
125	Dic₇₉⋊C₄	—	2	2	no	—
126	Dic₇₉⋊C₄	—	2	2	no	—
127	C₂²⋊Dic₇₉	—	2	2	no	—
128	C₄×Dic₇₉	—	2	2	no	—
129	#41×C₇₉	—	4	2	no	—
130	#41×C₇₉	—	4	2	no	—
131	C₂×Q₈×C₇₉	—	2	1	no	—
132	C₂×D₄×C₇₉	—	2	2	no	—
133	C₂×D₄×C₇₉	—	2	1	no	—
134	C₂×D₄×C₇₉	—	2	1	no	—
135	C₂×D₄×C₇₉	C₂²×C₄	1	2	yes	—
136	C₂²×C₄×C₇₉	—	2	2	no	—
137	C₂²×C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
138	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
139	C₂²×C₄×C₇₉	#41	1	1	yes	characteristic
140	C₂×C₈×C₇₉	—	2	1	no	—
141	C₂×C₈×C₇₉	—	2	1	no	—
142	C₂×C₈×C₇₉	—	2	2	no	—
143	C₂×C₈×C₇₉	—	4	2	no	—
144	C₄⋊C₄×C₇₉	—	2	1	no	—
145	C₄⋊C₄×C₇₉	C₂²×C₄	1	2	yes	—
146	C₂²⋊C₄×C₇₉	—	2	2	no	—
147	C₂²⋊C₄×C₇₉	—	2	2	no	—
148	C₄²×C₇₉	C₂²×C₄	1	1	yes	characteristic
149	C₄²×C₇₉	C₂×D₄	1	1	yes	characteristic
150	C₄²×C₇₉	#41	1	1	yes	characteristic
151	C₄²×C₇₉	C₂⁴	1	1	yes	characteristic
152	C₂³×C₇₉	—	2	2	no	—
153	C₂³×C₇₉	C₄×D₄	1	1	yes	characteristic
154	Q₈×C₇₉	—	4	2	no	—
155	D₄×C₇₉	—	2	2	no	—
156	D₄×C₇₉	—	2	2	no	—
157	D₄×C₇₉	—	4	4	no	—
158	D₄×C₇₉	—	4	2	no	—
159	D₄×C₇₉	—	8	1	no	—
160	C₂×C₄×C₇₉	—	2	1	no	—
161	C₂×C₄×C₇₉	—	2	1	no	—
162	C₂×C₄×C₇₉	—	2	2	no	—
163	C₂×C₄×C₇₉	—	4	1	no	—
164	C₂×C₄×C₇₉	—	4	2	no	—
165	C₂×C₄×C₇₉	—	4	2	no	—
166	C₂×C₄×C₇₉	C₄×D₄	1	1	yes	characteristic
167	C₂×C₄×C₇₉	C₄×D₄	1	1	yes	characteristic
168	C₂×C₄×C₇₉	C₄×D₄	1	1	yes	characteristic
169	C₂×C₄×C₇₉	C₂×SD₁₆	1	2	yes	—
170	C₂×C₄×C₇₉	#135	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×Dic₇₉	—	2	2	no	—
175	C₂×Dic₇₉	—	2	2	no	—
176	Dic₁₅₈	—	2	2	no	—
177	Dic₁₅₈	—	2	2	no	—
178	Dic₁₅₈	—	8	1	no	—
179	C₈×C₇₉	—	4	2	no	—
180	C₈×C₇₉	—	4	1	no	—
181	C₈×C₇₉	—	4	1	no	—
182	C₇₉⋊C₈	—	2	1	no	—
183	C₇₉⋊C₈	—	2	1	no	—
184	C₇₉⋊C₈	—	2	1	no	—
185	C₇₉⋊C₈	—	2	2	no	—
186	C₇₉⋊C₈	—	4	1	no	—
187	C₇₉⋊C₈	—	4	1	no	—
188	C₇₉⋊C₈	#131	1	2	yes	complemented
189	C₇₉⋊C₈	C₂×SD₁₆	1	4	yes	—
190	C₂²×C₇₉	—	2	1	no	—
191	C₂²×C₇₉	—	2	1	no	—
192	C₂²×C₇₉	—	4	2	no	—
193	C₂²×C₇₉	—	4	2	no	—
194	C₂²×C₇₉	—	4	2	no	—
195	C₂²×C₇₉	C₄×SD₁₆	1	2	yes	—
196	C₂²×C₇₉	C₂×C₄×D₄	1	1	yes	characteristic
197	C₄×C₇₉	—	2	1	no	—
198	C₄×C₇₉	—	2	1	no	—
199	C₄×C₇₉	—	2	1	no	—
200	C₄×C₇₉	—	4	2	no	—
201	C₄×C₇₉	C₄×SD₁₆	1	2	yes	—
202	C₄×C₇₉	C₂×#131	1	1	yes	characteristic
203	C₄×C₇₉	#568	1	1	yes	characteristic
204	C₄×C₇₉	C₂²×SD₁₆	1	1	yes	characteristic
205	C₄×C₇₉	C₂×#135	1	1	yes	characteristic
206	Dic₇₉	—	4	2	no	—
207	Dic₇₉	—	4	2	no	—
208	#18067	—	79	1	no	maximal, Sylow
209	C₂×C₇₉	—	2	2	no	—
210	C₂×C₇₉	—	8	2	no	—
211	C₂×C₇₉	#2935	1	1	yes	characteristic
212	C₂×C₇₉	C₂×C₄×SD₁₆	1	1	yes	characteristic
213	C₂×C₇₉	#2957	1	1	yes	characteristic
214	#3167	—	79	1	no	—
215	#2962	—	79	1	no	—
216	#2935	—	79	1	no	—
217	#1590	—	79	2	no	—
218	#1583	—	79	2	no	—
219	#1582	—	79	2	no	—
220	C₈×SD₁₆	—	79	2	no	—
221	C₂×#334	—	79	1	no	—
222	#1481	—	79	1	no	—
223	#1480	D₇₉	1	1	yes	characteristic
224	C₈×M₁₆	—	79	1	no	—
225	C₇₉	#18067	1	1	yes	characteristic, complemented, Sylow
226	C₂×#131	—	158	1	no	—
227	#533	—	79	1	no	—
228	#532	C₂×D₇₉	1	1	yes	characteristic
229	#498	—	79	1	no	—
230	#492	—	79	1	no	—
231	#487	—	79	1	no	—
232	#486	—	79	1	no	—
233	#465	—	79	2	no	—
234	#465	—	79	2	no	—
235	#446	—	79	2	no	—
236	#446	—	158	2	no	—
237	C₈×Q₈	—	79	2	no	—
238	C₄×SD₁₆	—	79	2	no	—
239	C₄×SD₁₆	—	79	2	no	—
240	#436	—	79	2	no	—
241	#435	—	158	2	no	—
242	C₈×D₄	—	79	2	no	—
243	#431	C₂×D₇₉	1	1	yes	characteristic
244	#424	—	158	1	no	—
245	C₂×C₄⋊C₈	—	79	1	no	—
246	C₂×C₄⋊C₈	C₂×D₇₉	1	1	yes	characteristic
247	#408	—	158	1	no	—
248	#405	—	158	1	no	—
249	C₄×M₁₆	—	79	1	no	—
250	C₂×C₄×C₈	—	79	1	no	—
251	#334	—	79	1	no	—
252	#334	—	79	1	no	—
253	#334	—	79	1	no	—
254	#334	—	79	1	no	—
255	Q₈⋊C₈	—	79	2	no	—
256	Q₈⋊C₈	—	79	2	no	—
257	D₄⋊C₈	C₂×D₇₉	1	2	yes	—
258	D₄⋊C₈	C₂×D₇₉	1	2	yes	—
259	#322	—	79	2	no	—
260	C₈²	—	79	2	no	—
261	C₂×#41	—	2	1	no	—
262	C₂×SD₁₆	—	79	2	no	—
263	C₂×SD₁₆	—	79	2	no	—
264	#131	—	316	4	no	—
265	C₂×M₁₆	—	79	1	no	—
266	C₂×M₁₆	—	79	1	no	—
267	C₂×M₁₆	—	158	2	no	—
268	C₂²×C₈	—	2	1	no	—
269	C₂²×C₈	—	79	1	no	—
270	C₂²×C₈	—	79	1	no	—
271	C₂²×C₈	—	158	2	no	—
272	C₂²×C₈	—	158	1	no	—
273	C₄⋊Q₈	—	79	1	no	—
274	C₄⋊Q₈	—	79	1	no	—
275	C₄⋊Q₈	C₄×D₇₉	1	1	yes	characteristic
276	#127	C₄×D₇₉	1	1	yes	characteristic
277	#125	—	158	1	no	—
278	#124	—	2	1	no	—
279	C₂²⋊Q₈	—	79	2	no	—
280	C₂²⋊Q₈	—	158	1	no	—
281	#121	—	2	1	no	—
282	#121	C₄×D₇₉	1	2	yes	—
283	C₄×Q₈	—	79	2	no	—
284	C₄×Q₈	—	158	1	no	—
285	C₄×D₄	—	2	1	no	—
286	C₄×D₄	C₂²×D₇₉	1	2	yes	—
287	#117	—	158	1	no	—
288	C₂×C₄²	C₂²×D₇₉	1	1	yes	characteristic
289	#106	—	79	2	no	—
290	#106	—	79	2	no	—
291	C₄⋊C₈	—	2	1	no	—
292	C₄⋊C₈	—	2	1	no	—
293	C₄⋊C₈	—	79	1	no	—
294	C₄⋊C₈	—	79	1	no	—
295	C₄⋊C₈	—	158	2	no	—
296	C₄⋊C₈	—	158	2	no	—
297	C₄⋊C₈	—	158	1	no	—
298	C₄⋊C₈	C₂²×D₇₉	1	1	yes	characteristic
299	C₄⋊C₈	C₂²×D₇₉	1	1	yes	characteristic
300	#103	—	79	2	no	—
301	#103	—	79	2	no	—
302	#102	—	79	2	no	—
303	#102	—	79	2	no	—
304	C₂²⋊C₈	—	2	1	no	—
305	C₂²⋊C₈	—	158	2	no	—
306	C₂²⋊C₈	—	158	2	no	—
307	#97	—	79	2	no	—
308	#97	—	158	2	no	—
309	C₄×C₈	—	79	1	no	—
310	C₄×C₈	—	79	1	no	—
311	C₄×C₈	—	79	1	no	—
312	C₄×C₈	—	79	2	no	—
313	C₄×C₈	—	79	1	no	—
314	C₄×C₈	—	158	2	no	—
315	C₄×C₈	C₂²×D₇₉	1	2	yes	—
316	#41	—	4	2	no	—
317	#41	—	4	2	no	—
318	C₂×Q₈	—	2	1	no	—
319	C₂×Q₈	—	79	2	no	—
320	C₂×Q₈	—	158	1	no	—
321	C₂×D₄	—	2	2	no	—
322	C₂×D₄	—	2	1	no	—
323	C₂×D₄	—	2	1	no	—
324	C₂×D₄	C₂×C₄×D₇₉	1	2	yes	—
325	C₂²×C₄	—	2	2	no	—
326	C₂²×C₄	C₂×C₄×D₇₉	1	1	yes	characteristic
327	C₂²×C₄	D₄×D₇₉	1	1	yes	characteristic
328	C₂²×C₄	#11929623	1	1	yes	characteristic
329	SD₁₆	—	316	2	no	—
330	SD₁₆	—	158	4	no	—
331	M₁₆	—	316	4	no	—
332	M₁₆	—	79	4	no	—
333	M₁₆	—	158	2	no	—
334	C₂×C₈	—	2	2	no	—
335	C₂×C₈	—	2	1	no	—
336	C₂×C₈	—	2	1	no	—
337	C₂×C₈	—	4	2	no	—
338	C₂×C₈	—	316	2	no	—
339	C₂×C₈	—	316	4	no	—
340	C₂×C₈	—	316	1	no	—
341	C₂×C₈	—	79	1	no	—
342	C₂×C₈	—	79	2	no	—
343	C₂×C₈	—	79	1	no	—
344	C₂×C₈	—	79	1	no	—
345	C₂×C₈	—	79	1	no	—
346	C₂×C₈	—	79	2	no	—
347	C₂×C₈	—	158	1	no	—
348	C₂×C₈	—	158	1	no	—
349	C₂×C₈	—	158	2	no	—
350	C₄⋊C₄	—	2	1	no	—
351	C₄⋊C₄	—	79	2	no	—
352	C₄⋊C₄	—	158	2	no	—
353	C₄⋊C₄	—	158	2	no	—
354	C₄⋊C₄	—	158	1	no	—
355	C₄⋊C₄	—	158	1	no	—
356	C₄⋊C₄	—	158	1	no	—
357	C₄⋊C₄	C₂×C₄×D₇₉	1	2	yes	—
358	C₂²⋊C₄	—	2	2	no	—
359	C₂²⋊C₄	—	2	2	no	—
360	C₂²⋊C₄	—	158	2	no	—
361	C₄²	—	158	2	no	—
362	C₄²	C₂×C₄×D₇₉	1	1	yes	characteristic
363	C₄²	D₄×D₇₉	1	1	yes	characteristic
364	C₄²	#11929623	1	1	yes	characteristic
365	C₄²	C₂³×D₇₉	1	1	yes	characteristic
366	C₂³	—	2	2	no	—
367	C₂³	(C₂²⋊D₇₉)⋊C₄	1	1	yes	characteristic
368	Q₈	—	4	2	no	—
369	Q₈	—	632	1	no	—
370	Q₈	—	158	2	no	—
371	Q₈	—	158	2	no	—
372	D₄	—	2	2	no	—
373	D₄	—	2	2	no	—
374	D₄	—	4	4	no	—
375	D₄	—	4	2	no	—
376	D₄	—	8	1	no	—
377	C₂×C₄	—	2	1	no	—
378	C₂×C₄	—	2	1	no	—
379	C₂×C₄	—	2	2	no	—
380	C₂×C₄	—	4	1	no	—
381	C₂×C₄	—	4	2	no	—
382	C₂×C₄	—	4	2	no	—
383	C₂×C₄	—	158	2	no	—
384	C₂×C₄	—	158	2	no	—
385	C₂×C₄	(C₂²⋊D₇₉)⋊C₄	1	1	yes	characteristic
386	C₂×C₄	(C₂²⋊D₇₉)⋊C₄	1	1	yes	characteristic
387	C₂×C₄	(C₂²⋊D₇₉)⋊C₄	1	1	yes	characteristic
388	C₂×C₄	SD₁₆×D₇₉	1	2	yes	—
389	C₂×C₄	#14579180	1	2	yes	—
390	C₂×C₄	C₂²×C₄×D₇₉	1	1	yes	characteristic
391	C₂×C₄	C₂×D₄×D₇₉	1	1	yes	characteristic
392	C₂×C₄	C₂×#11929623	1	1	yes	characteristic
393	C₈	—	4	2	no	—
394	C₈	—	4	1	no	—
395	C₈	—	4	1	no	—
396	C₈	—	316	1	no	—
397	C₈	—	316	1	no	—
398	C₈	—	79	2	no	—
399	C₈	—	79	4	no	—
400	C₈	—	158	1	no	—
401	C₈	—	158	1	no	—
402	C₈	—	158	1	no	—
403	C₈	—	158	2	no	—
404	C₂²	—	2	1	no	—
405	C₂²	—	2	1	no	—
406	C₂²	—	4	2	no	—
407	C₂²	—	4	2	no	—
408	C₂²	—	4	2	no	—
409	C₂²	#19098654	1	2	yes	—
410	C₂²	C₂×(C₂²⋊D₇₉)⋊C₄	1	1	yes	characteristic
411	C₄	—	2	1	no	—
412	C₄	—	2	1	no	—
413	C₄	—	2	1	no	—
414	C₄	—	4	2	no	—
415	C₄	—	316	2	no	—
416	C₄	—	316	2	no	—
417	C₄	#19098654	1	2	yes	—
418	C₄	#131×D₇₉	1	1	yes	characteristic
419	C₄	#19099328	1	1	yes	characteristic
420	C₄	C₂×SD₁₆×D₇₉	1	1	yes	characteristic
421	C₄	C₂×#14579180	1	1	yes	characteristic
422	C₂	—	2	2	no	—
423	C₂	—	8	2	no	—
424	C₂	#23772140	1	1	yes	characteristic
425	C₂	C₂×#19098654	1	1	yes	characteristic
426	C₂	#23772313	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×#1480	C₂
socle	C₂²×C₇₉	C₂×C₄×D₄
prime radical	#532×C₇₉	C₂²
cosocle	C₄²×C₇₉	C₂⁴
hypercenter	#1480	D₇₉
hypocenter	C₇₉	#18067
LCS	G ▷ C₂×C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1480

Complements

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

N	H ≅ G/N	type
2. #23772343	C₂	semidirect
4. #23762293	C₂	semidirect
5. #23762246	C₂	semidirect
6. #23762233	C₂	semidirect
7. #23762203	C₂	semidirect
8. C₂×#19098313	C₂	semidirect
9. #23761804	C₂	semidirect
10. #23761681	C₂	semidirect
108. #11929608	SD₁₆	semidirect
188. C₇₉⋊C₈	#131	semidirect
225. C₇₉	#18067	semidirect

Maximal subgroups

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

subgroup	index
#23773955	2
#23772343	2
#23772144	2
#23762293	2
#23762246	2
#23762233	2
#23762203	2
C₂×#19098313	2
#23761804	2
#23761681	2
C₇₉×#1480	2
#18067	79