Subgroups — #34260033

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	#23772347	C₂	1	1	yes	maximal, characteristic, complemented
3	#23762288	C₂	1	2	yes	maximal, complemented
4	#23762241	C₂	1	2	yes	maximal, complemented
5	#23762236	C₂	1	2	yes	maximal, complemented
6	C₈×#11929612	C₂	1	2	yes	maximal, complemented
7	C₂×#19098313	C₂	1	1	yes	maximal, characteristic, complemented
8	#23761802	C₂	1	1	yes	maximal, characteristic, complemented
9	#23761799	C₂	1	1	yes	maximal, characteristic
10	M₁₆×C₇₉⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
11	C₇₉×#2935	C₂	1	1	yes	maximal, characteristic
12	#19099120	C₂²	1	1	yes	characteristic
13	#19098959	C₄	1	1	yes	characteristic
14	#19098935	C₄	1	1	yes	characteristic
15	#19098915	C₄	1	1	yes	characteristic
16	#19098909	C₄	1	1	yes	characteristic
17	#19098790	C₄	1	2	yes	—
18	#19098790	C₄	1	2	yes	—
19	#19098693	C₂²	1	2	yes	—
20	#19098691	—	2	2	no	—
21	C₈×Dic₁₅₈	C₂²	1	2	yes	—
22	C₄×#11929612	C₂²	1	2	yes	—
23	C₄×#11929612	C₂²	1	2	yes	—
24	#19098616	C₂²	1	1	yes	characteristic
25	#19098591	—	2	1	no	—
26	C₂×C₄⋊(C₇₉⋊C₈)	C₂²	1	1	yes	characteristic
27	#19098521	—	2	1	no	—
28	C₂×C₄×C₇₉⋊C₈	C₂²	1	1	yes	characteristic
29	#19098313	C₂²	1	1	yes	characteristic
30	#19098313	C₂²	1	1	yes	characteristic
31	#19098313	C₂²	1	1	yes	characteristic
32	#19098313	C₂²	1	1	yes	characteristic
33	#19098293	C₂²	1	2	yes	—
34	#19098293	C₂²	1	2	yes	—
35	D₄⋊(C₇₉⋊C₈)	C₂²	1	2	yes	—
36	D₄⋊(C₇₉⋊C₈)	C₂²	1	2	yes	—
37	#19098284	C₂²	1	2	yes	—
38	C₈×C₇₉⋊C₈	C₂²	1	2	yes	—
39	C₂×#131×C₇₉	—	2	1	no	—
40	#532×C₇₉	C₂²	1	1	yes	characteristic
41	#436×C₇₉	C₂²	1	2	yes	—
42	#435×C₇₉	—	2	2	no	—
43	C₈×D₄×C₇₉	C₂²	1	2	yes	—
44	C₂×C₄⋊C₈×C₇₉	C₂²	1	1	yes	characteristic
45	#408×C₇₉	—	2	1	no	—
46	C₄×M₁₆×C₇₉	C₂²	1	1	yes	characteristic
47	C₂×#11929612	C₂×C₄	1	2	yes	—
48	C₂×#11929612	C₂×C₄	1	2	yes	—
49	C₂²×C₇₉⋊C₈	—	2	1	no	—
50	C₂²×C₇₉⋊C₈	C₂×C₄	1	1	yes	characteristic
51	C₂²×C₇₉⋊C₈	C₂×C₄	1	1	yes	characteristic
52	#14579161	C₂×C₄	1	1	yes	characteristic
53	#14579161	C₂×C₄	1	1	yes	characteristic
54	#14579153	—	2	1	no	—
55	#14579140	—	2	1	no	—
56	#14579140	C₂×C₄	1	2	yes	—
57	C₄×Dic₁₅₈	—	2	1	no	—
58	C₄×Dic₁₅₈	C₂³	1	2	yes	—
59	#14579120	—	2	1	no	—
60	#14579092	C₂×C₄	1	2	yes	—
61	#14579092	C₂×C₄	1	2	yes	—
62	C₄⋊(C₇₉⋊C₈)	—	2	1	no	—
63	C₄⋊(C₇₉⋊C₈)	—	2	1	no	—
64	C₄⋊(C₇₉⋊C₈)	C₂³	1	1	yes	characteristic
65	C₄⋊(C₇₉⋊C₈)	C₂³	1	1	yes	characteristic
66	Dic₇₉⋊C₈	—	2	2	no	—
67	Dic₇₉⋊C₈	—	2	2	no	—
68	#14579084	C₂×C₄	1	2	yes	—
69	#14579084	C₂×C₄	1	2	yes	—
70	#14579082	C₂×C₄	1	2	yes	—
71	#14579082	C₂×C₄	1	2	yes	—
72	C₂²⋊(C₇₉⋊C₈)	—	2	1	no	—
73	#14579071	—	2	2	no	—
74	C₄×C₇₉⋊C₈	C₂×C₄	1	1	yes	characteristic
75	C₄×C₇₉⋊C₈	C₂×C₄	1	1	yes	characteristic
76	C₄×C₇₉⋊C₈	C₂³	1	2	yes	—
77	C₄×C₇₉⋊C₈	C₂³	1	1	yes	characteristic
78	C₄×C₇₉⋊C₈	C₂³	1	1	yes	characteristic
79	C₈×Dic₇₉	—	2	2	no	—
80	C₂×#41×C₇₉	—	2	1	no	—
81	#131×C₇₉	—	4	4	no	—
82	C₂×M₁₆×C₇₉	—	2	2	no	—
83	C₂×M₁₆×C₇₉	D₄	1	1	yes	characteristic
84	C₂×M₁₆×C₇₉	D₄	1	1	yes	characteristic
85	C₂²×C₈×C₇₉	—	2	1	no	—
86	C₂²×C₈×C₇₉	—	2	2	no	—
87	C₄⋊Q₈×C₇₉	C₂×C₄	1	1	yes	characteristic
88	#127×C₇₉	C₂×C₄	1	1	yes	characteristic
89	#124×C₇₉	—	2	1	no	—
90	#121×C₇₉	—	2	1	no	—
91	#121×C₇₉	C₂×C₄	1	2	yes	—
92	C₄×D₄×C₇₉	—	2	1	no	—
93	C₄×D₄×C₇₉	C₂³	1	2	yes	—
94	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
95	C₄⋊C₈×C₇₉	—	2	1	no	—
96	C₄⋊C₈×C₇₉	C₂³	1	1	yes	characteristic
97	C₄⋊C₈×C₇₉	C₂³	1	1	yes	characteristic
98	C₂²⋊C₈×C₇₉	—	2	2	no	—
99	C₂²⋊C₈×C₇₉	—	2	2	no	—
100	#97×C₇₉	D₄	1	2	yes	—
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	C₂×C₇₉⋊C₈	—	2	2	no	—
107	C₂×C₇₉⋊C₈	—	2	1	no	—
108	C₂×C₇₉⋊C₈	—	2	1	no	—
109	C₂×C₇₉⋊C₈	—	2	2	no	—
110	C₂×C₇₉⋊C₈	—	4	1	no	—
111	C₂×C₇₉⋊C₈	—	4	2	no	—
112	C₂×C₇₉⋊C₈	C₂²×C₄	1	1	yes	characteristic
113	C₂×C₇₉⋊C₈	C₂²×C₄	1	1	yes	characteristic
114	C₂×C₇₉⋊C₈	C₂²×C₄	1	1	yes	characteristic
115	C₂×C₇₉⋊C₈	C₂²×C₄	1	1	yes	characteristic
116	C₄⋊Dic₇₉	—	2	1	no	—
117	C₄⋊Dic₇₉	—	2	1	no	—
118	C₄⋊Dic₇₉	—	2	1	no	—
119	C₄⋊Dic₇₉	C₂²×C₄	1	2	yes	—
120	Dic₇₉⋊C₄	—	2	2	no	—
121	Dic₇₉⋊C₄	—	2	2	no	—
122	C₂²⋊Dic₇₉	—	2	2	no	—
123	C₄×Dic₇₉	—	2	2	no	—
124	#41×C₇₉	—	4	2	no	—
125	#41×C₇₉	—	4	2	no	—
126	C₂×Q₈×C₇₉	—	2	1	no	—
127	C₂×D₄×C₇₉	—	2	2	no	—
128	C₂×D₄×C₇₉	—	2	1	no	—
129	C₂×D₄×C₇₉	—	2	1	no	—
130	C₂×D₄×C₇₉	C₂²×C₄	1	2	yes	—
131	C₂²×C₄×C₇₉	—	2	2	no	—
132	C₂²×C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
133	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
134	C₂²×C₄×C₇₉	#41	1	1	yes	characteristic
135	M₁₆×C₇₉	—	2	2	no	—
136	M₁₆×C₇₉	—	4	4	no	—
137	M₁₆×C₇₉	SD₁₆	1	4	yes	complemented
138	C₂×C₈×C₇₉	—	2	1	no	—
139	C₂×C₈×C₇₉	—	2	1	no	—
140	C₂×C₈×C₇₉	—	4	4	no	—
141	C₂×C₈×C₇₉	—	4	2	no	—
142	C₂×C₈×C₇₉	C₂×D₄	1	2	yes	—
143	C₂×C₈×C₇₉	C₂×D₄	1	2	yes	—
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	—	2	2	no	—
180	C₈×C₇₉	—	4	1	no	—
181	C₈×C₇₉	—	4	1	no	—
182	C₈×C₇₉	C₂×SD₁₆	1	4	yes	—
183	C₇₉⋊C₈	—	2	1	no	—
184	C₇₉⋊C₈	—	2	1	no	—
185	C₇₉⋊C₈	—	2	1	no	—
186	C₇₉⋊C₈	—	4	2	no	—
187	C₇₉⋊C₈	—	4	1	no	—
188	C₇₉⋊C₈	—	4	1	no	—
189	C₇₉⋊C₈	#131	1	2	yes	complemented
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	D₇₉	1	1	yes	characteristic
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	—	79	1	no	—
224	C₈×M₁₆	—	79	1	no	—
225	C₇₉	#18067	1	1	yes	characteristic, complemented, Sylow
226	C₂×#131	—	2	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	C₂×D₇₉	1	2	yes	—
241	#435	—	2	2	no	—
242	C₈×D₄	C₂×D₇₉	1	2	yes	—
243	#431	—	79	1	no	—
244	#424	—	158	1	no	—
245	C₂×C₄⋊C₈	—	79	1	no	—
246	C₂×C₄⋊C₈	C₂×D₇₉	1	1	yes	characteristic
247	#408	—	2	1	no	—
248	#405	—	158	1	no	—
249	C₄×M₁₆	C₂×D₇₉	1	1	yes	characteristic
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	—	79	2	no	—
258	D₄⋊C₈	—	79	2	no	—
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	—	4	4	no	—
265	C₂×M₁₆	—	2	2	no	—
266	C₂×M₁₆	C₂²⋊D₇₉	1	1	yes	characteristic
267	C₂×M₁₆	C₂²⋊D₇₉	1	1	yes	characteristic
268	C₂²×C₈	—	2	1	no	—
269	C₂²×C₈	—	2	2	no	—
270	C₂²×C₈	—	79	1	no	—
271	C₂²×C₈	—	79	1	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	—	79	1	no	—
293	C₄⋊C₈	—	79	1	no	—
294	C₄⋊C₈	—	158	2	no	—
295	C₄⋊C₈	—	158	2	no	—
296	C₄⋊C₈	—	158	1	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	2	no	—
305	C₂²⋊C₈	—	2	2	no	—
306	C₂²⋊C₈	—	158	1	no	—
307	#97	—	158	2	no	—
308	#97	C₂²⋊D₇₉	1	2	yes	—
309	C₄×C₈	—	79	1	no	—
310	C₄×C₈	—	79	1	no	—
311	C₄×C₈	—	79	1	no	—
312	C₄×C₈	—	79	1	no	—
313	C₄×C₈	—	79	2	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	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
328	C₂²×C₄	#11929624	1	1	yes	characteristic
329	SD₁₆	—	316	2	no	—
330	SD₁₆	—	158	4	no	—
331	M₁₆	—	2	2	no	—
332	M₁₆	—	4	4	no	—
333	M₁₆	#11929612	1	4	yes	complemented
334	C₂×C₈	—	2	1	no	—
335	C₂×C₈	—	2	1	no	—
336	C₂×C₈	—	4	2	no	—
337	C₂×C₈	—	4	4	no	—
338	C₂×C₈	—	316	2	no	—
339	C₂×C₈	—	316	1	no	—
340	C₂×C₈	—	79	1	no	—
341	C₂×C₈	—	79	1	no	—
342	C₂×C₈	—	79	1	no	—
343	C₂×C₈	—	79	1	no	—
344	C₂×C₈	—	158	2	no	—
345	C₂×C₈	—	158	1	no	—
346	C₂×C₈	—	158	1	no	—
347	C₂×C₈	—	158	2	no	—
348	C₂×C₈	C₂×C₂²⋊D₇₉	1	2	yes	—
349	C₂×C₈	C₂×C₂²⋊D₇₉	1	2	yes	—
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	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
364	C₄²	#11929624	1	1	yes	characteristic
365	C₄²	C₂³×D₇₉	1	1	yes	characteristic
366	C₂³	—	2	2	no	—
367	C₂³	C₄×C₂²⋊D₇₉	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	C₄×C₂²⋊D₇₉	1	1	yes	characteristic
386	C₂×C₄	C₄×C₂²⋊D₇₉	1	1	yes	characteristic
387	C₂×C₄	C₄×C₂²⋊D₇₉	1	1	yes	characteristic
388	C₂×C₄	C₂×#11929612	1	2	yes	—
389	C₂×C₄	#14579181	1	2	yes	—
390	C₂×C₄	C₂²×C₄×D₇₉	1	1	yes	characteristic
391	C₂×C₄	C₂²×C₂²⋊D₇₉	1	1	yes	characteristic
392	C₂×C₄	C₂×#11929624	1	1	yes	characteristic
393	C₈	—	2	2	no	—
394	C₈	—	4	1	no	—
395	C₈	—	4	1	no	—
396	C₈	—	316	2	no	—
397	C₈	—	316	1	no	—
398	C₈	—	316	1	no	—
399	C₈	—	79	2	no	—
400	C₈	—	158	1	no	—
401	C₈	—	158	1	no	—
402	C₈	—	158	1	no	—
403	C₈	C₂×#11929612	1	4	yes	—
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	C₄×#11929612	1	2	yes	—
410	C₂²	C₂×C₄×C₂²⋊D₇₉	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	C₄×#11929612	1	2	yes	—
418	C₄	#131×D₇₉	1	1	yes	characteristic
419	C₄	#19099328	1	1	yes	characteristic
420	C₄	C₂²×#11929612	1	1	yes	characteristic
421	C₄	C₂×#14579181	1	1	yes	characteristic
422	C₂	—	2	2	no	—
423	C₂	—	8	2	no	—
424	C₂	#23772142	1	1	yes	characteristic
425	C₂	C₂×C₄×#11929612	1	1	yes	characteristic
426	C₂	#23772315	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²×C₂²⋊D₇₉
commutator	C₂×C₄×C₇₉	C₂³×C₄
Frattini	C₄²	C₂³×D₇₉
Fitting	C₇₉×#2935	C₂
socle	C₂²×C₇₉	C₂×C₄×D₄
prime radical	#532×C₇₉	C₂²
cosocle	C₄²×C₇₉	C₂⁴
hypercenter	#2935	D₇₉
hypocenter	C₇₉	#18067
LCS	G ▷ C₂×C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂×C₄ ◁ C₄×M₁₆ ◁ #2935

Complements

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

N	H ≅ G/N	type
2. #23772347	C₂	semidirect
3. #23762288	C₂	semidirect
4. #23762241	C₂	semidirect
5. #23762236	C₂	semidirect
6. C₈×#11929612	C₂	semidirect
7. C₂×#19098313	C₂	semidirect
8. #23761802	C₂	semidirect
10. M₁₆×C₇₉⋊C₈	C₂	semidirect
137. M₁₆×C₇₉	SD₁₆	semidirect
189. C₇₉⋊C₈	#131	semidirect
225. C₇₉	#18067	semidirect
333. M₁₆	#11929612	semidirect

Maximal subgroups

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

subgroup	index
#23773955	2
#23772347	2
#23762288	2
#23762241	2
#23762236	2
C₈×#11929612	2
C₂×#19098313	2
#23761802	2
#23761799	2
M₁₆×C₇₉⋊C₈	2
C₇₉×#2935	2
#18067	79