Subgroups — #34292494

Order 20224.

822 conjugacy classes of subgroups.

The subgroup lattice has 418 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Q₁₆×Dic₇₉	C₂	1	1	yes	maximal, characteristic
2	#23765875	C₂	1	2	yes	maximal
3	#23764262	C₂	1	1	yes	maximal, characteristic
4	#23764133	C₂	1	1	yes	maximal, characteristic
5	#23764131	C₂	1	1	yes	maximal, characteristic
6	#23764079	C₂	1	2	yes	maximal
7	#23764073	C₂	1	2	yes	maximal
8	#107×Dic₇₉	C₂	1	1	yes	maximal, characteristic
9	#103×Dic₇₉	C₂	1	2	yes	maximal
10	C₄×C₈×Dic₇₉	C₂	1	1	yes	maximal, characteristic
11	C₇₉×#1969	C₂	1	1	yes	maximal, characteristic
12	C₂×Q₈×Dic₇₉	C₂²	1	2	yes	—
13	Q₁₆×Dic₇₉	C₄	1	8	yes	complemented
14	C₂×#14579095	C₂²	1	1	yes	characteristic
15	C₂×#14579095	C₂²	1	1	yes	characteristic
16	C₂×#14579085	C₂²	1	2	yes	—
17	C₂×#14579085	C₂²	1	2	yes	—
18	C₂×C₄×C₇₉⋊C₈	C₂²	1	1	yes	characteristic
19	C₂×C₈×Dic₇₉	C₂²	1	1	yes	characteristic
20	C₂×C₈×Dic₇₉	C₂²	1	1	yes	characteristic
21	C₂×C₈×Dic₇₉	C₂²	1	1	yes	characteristic
22	C₂×C₈×Dic₇₉	C₂²	1	1	yes	characteristic
23	#19098470	C₂²	1	2	yes	—
24	#19098461	C₂²	1	2	yes	—
25	#19098459	C₂²	1	2	yes	—
26	#19098448	—	2	2	no	—
27	#19098446	—	2	2	no	—
28	C₄⋊C₄×Dic₇₉	C₂²	1	2	yes	—
29	#19098414	—	2	2	no	—
30	#19098408	—	2	2	no	—
31	C₄²×Dic₇₉	C₂²	1	1	yes	characteristic
32	#19098326	C₂²	1	2	yes	—
33	#19098325	C₂²	1	2	yes	—
34	#19098325	C₂²	1	2	yes	—
35	C₂²×Q₁₆×C₇₉	C₂²	1	1	yes	characteristic
36	C₂×#107×C₇₉	C₂²	1	1	yes	characteristic
37	C₂×#103×C₇₉	C₂²	1	2	yes	—
38	C₂×C₄×C₈×C₇₉	C₂²	1	1	yes	characteristic
39	#391×C₇₉	C₂²	1	2	yes	—
40	C₂²×C₇₉⋊C₈	C₂³	1	1	yes	characteristic
41	C₂²×C₇₉⋊C₈	C₂³	1	1	yes	characteristic
42	Q₈×Dic₇₉	—	2	4	no	—
43	Q₈×Dic₇₉	C₂×C₄	1	8	yes	—
44	C₂×C₄⋊Dic₇₉	—	2	2	no	—
45	C₂×C₄⋊Dic₇₉	C₂³	1	2	yes	—
46	C₂×C₄⋊Dic₇₉	C₂³	1	2	yes	—
47	C₂×Dic₇₉⋊C₄	—	2	2	no	—
48	C₂×Dic₇₉⋊C₄	—	2	2	no	—
49	C₂×C₄×Dic₇₉	—	2	2	no	—
50	C₂×C₄×Dic₇₉	—	2	2	no	—
51	C₂×C₄×Dic₇₉	D₄	1	1	yes	characteristic
52	C₂×C₄×Dic₇₉	D₄	1	1	yes	characteristic
53	C₂×C₄×Dic₇₉	D₄	1	1	yes	characteristic
54	C₂×C₄×Dic₇₉	D₄	1	1	yes	characteristic
55	C₂×C₄×Dic₇₉	C₂³	1	1	yes	characteristic
56	C₂×C₄×Dic₇₉	C₂³	1	1	yes	characteristic
57	#14579095	—	2	2	no	—
58	#14579095	C₂×C₄	1	4	yes	—
59	#14579085	—	2	4	no	—
60	#14579085	C₂×C₄	1	8	yes	—
61	C₄×C₇₉⋊C₈	—	2	2	no	—
62	C₈×Dic₇₉	—	2	2	no	—
63	C₈×Dic₇₉	—	2	2	no	—
64	C₈×Dic₇₉	—	2	2	no	—
65	C₈×Dic₇₉	C₂×C₄	1	4	yes	—
66	C₇₉⋊#95	—	2	2	no	—
67	C₇₉⋊#95	—	2	2	no	—
68	C₇₉⋊#95	—	2	2	no	—
69	C₇₉⋊#95	—	2	2	no	—
70	C₇₉⋊#95	—	2	2	no	—
71	C₂²×Q₈×C₇₉	C₂³	1	2	yes	—
72	C₂×Q₁₆×C₇₉	—	2	2	no	—
73	C₂×Q₁₆×C₇₉	—	2	2	no	—
74	C₂×Q₁₆×C₇₉	C₂×C₄	1	4	yes	—
75	C₂²×C₈×C₇₉	C₂³	1	1	yes	characteristic
76	C₂²×C₈×C₇₉	C₂³	1	1	yes	characteristic
77	C₂×C₄⋊C₄×C₇₉	C₂³	1	2	yes	—
78	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
79	#107×C₇₉	—	2	2	no	—
80	#103×C₇₉	—	2	4	no	—
81	C₄×C₈×C₇₉	—	2	2	no	—
82	#95×C₇₉	—	2	2	no	—
83	#95×C₇₉	—	2	2	no	—
84	C₂²×Dic₇₉	—	2	2	no	—
85	C₂²×Dic₇₉	—	2	2	no	—
86	C₂²×Dic₇₉	C₂×D₄	1	1	yes	characteristic
87	C₂²×Dic₇₉	C₂×D₄	1	1	yes	characteristic
88	C₂²×Dic₇₉	C₂×D₄	1	1	yes	characteristic
89	C₂²×Dic₇₉	C₂×D₄	1	1	yes	characteristic
90	C₂×C₇₉⋊C₈	—	2	1	no	—
91	C₂×C₇₉⋊C₈	—	2	1	no	—
92	C₂×C₇₉⋊C₈	—	2	1	no	—
93	C₂×C₇₉⋊C₈	—	2	1	no	—
94	C₂×C₇₉⋊C₈	C₂²×C₄	1	2	yes	—
95	C₂×C₇₉⋊C₈	#41	1	2	yes	—
96	C₄⋊Dic₇₉	—	2	8	no	—
97	C₄⋊Dic₇₉	—	2	2	no	—
98	C₄⋊Dic₇₉	—	2	2	no	—
99	C₄⋊Dic₇₉	—	2	2	no	—
100	C₄⋊Dic₇₉	C₂²×C₄	1	4	yes	—
101	Dic₇₉⋊C₄	—	4	4	no	—
102	Dic₇₉⋊C₄	—	4	4	no	—
103	C₄×Dic₇₉	—	2	8	no	—
104	C₄×Dic₇₉	—	2	2	no	—
105	C₄×Dic₇₉	—	2	2	no	—
106	C₄×Dic₇₉	—	2	2	no	—
107	C₄×Dic₇₉	—	2	1	no	—
108	C₄×Dic₇₉	—	2	1	no	—
109	C₄×Dic₇₉	—	4	4	no	—
110	C₄×Dic₇₉	Q₁₆	1	4	yes	complemented
111	C₄×Dic₇₉	C₂²×C₄	1	2	yes	—
112	C₄×Dic₇₉	#41	1	2	yes	—
113	C₂×Q₈×C₇₉	—	2	2	no	—
114	C₂×Q₈×C₇₉	—	2	2	no	—
115	C₂×Q₈×C₇₉	—	2	2	no	—
116	C₂×Q₈×C₇₉	—	2	2	no	—
117	C₂×Q₈×C₇₉	—	2	2	no	—
118	C₂×Q₈×C₇₉	C₂²×C₄	1	4	yes	—
119	C₂²×C₄×C₇₉	—	2	2	no	—
120	C₂²×C₄×C₇₉	—	2	2	no	—
121	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
122	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
123	C₂²×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
124	Q₁₆×C₇₉	—	2	8	no	—
125	C₂×C₈×C₇₉	—	2	1	no	—
126	C₂×C₈×C₇₉	—	2	1	no	—
127	C₂×C₈×C₇₉	C₂²×C₄	1	2	yes	—
128	C₂×C₈×C₇₉	#41	1	2	yes	—
129	C₂×C₈×C₇₉	#41	1	2	yes	—
130	C₂×C₈×C₇₉	#41	1	2	yes	—
131	C₄⋊C₄×C₇₉	—	2	2	no	—
132	C₄⋊C₄×C₇₉	—	2	2	no	—
133	C₄²×C₇₉	—	2	1	no	—
134	C₄²×C₇₉	—	2	1	no	—
135	C₂³×C₇₉	C₂²×D₄	1	1	yes	characteristic
136	Q₈×C₇₉	—	2	4	no	—
137	Q₈×C₇₉	—	2	4	no	—
138	Q₈×C₇₉	—	4	2	no	—
139	Q₈×C₇₉	—	4	2	no	—
140	C₂×C₄×C₇₉	—	2	1	no	—
141	C₂×C₄×C₇₉	—	2	1	no	—
142	C₂×C₄×C₇₉	—	2	1	no	—
143	C₂×C₄×C₇₉	—	2	1	no	—
144	C₂×C₄×C₇₉	—	2	4	no	—
145	C₂×C₄×C₇₉	—	4	2	no	—
146	C₂×C₄×C₇₉	—	4	2	no	—
147	C₂×C₄×C₇₉	—	4	2	no	—
148	C₂×C₄×C₇₉	—	4	2	no	—
149	C₂×C₄×C₇₉	—	4	2	no	—
150	C₂×C₄×C₇₉	C₂×Q₁₆	1	2	yes	—
151	C₂×C₄×C₇₉	#135	1	2	yes	—
152	C₂×C₄×C₇₉	C₂³×C₄	1	1	yes	characteristic
153	C₂×C₄×C₇₉	C₂×#41	1	1	yes	characteristic
154	C₂×C₄×C₇₉	C₂×#41	1	1	yes	characteristic
155	C₂×C₄×C₇₉	C₂×#41	1	1	yes	characteristic
156	C₂×C₄×C₇₉	C₂×#41	1	1	yes	characteristic
157	C₂×C₄×C₇₉	C₂×#41	1	1	yes	characteristic
158	C₂×Dic₇₉	—	2	1	no	—
159	C₂×Dic₇₉	—	2	1	no	—
160	C₂×Dic₇₉	—	2	1	no	—
161	C₂×Dic₇₉	—	2	1	no	—
162	C₂×Dic₇₉	—	2	1	no	—
163	C₂×Dic₇₉	—	2	1	no	—
164	C₂×Dic₇₉	—	2	4	no	—
165	C₂×Dic₇₉	—	4	2	no	—
166	C₂×Dic₇₉	—	4	2	no	—
167	C₂×Dic₇₉	—	4	2	no	—
168	C₂×Dic₇₉	—	4	2	no	—
169	C₂×Dic₇₉	—	4	2	no	—
170	C₂×Dic₇₉	C₄×D₄	1	2	yes	—
171	C₂×Dic₇₉	C₄×D₄	1	2	yes	—
172	C₂×Dic₇₉	C₂×Q₁₆	1	2	yes	—
173	C₂×Dic₇₉	C₂×Q₁₆	1	2	yes	—
174	C₂×Dic₇₉	#135	1	2	yes	—
175	C₂×Dic₇₉	#135	1	2	yes	—
176	C₈×C₇₉	—	2	2	no	—
177	C₈×C₇₉	#117	1	4	yes	—
178	C₇₉⋊C₈	—	2	2	no	—
179	C₇₉⋊C₈	—	2	2	no	—
180	C₂²×C₇₉	C₂×C₄×D₄	1	1	yes	characteristic
181	C₂²×C₇₉	#532	1	1	yes	characteristic
182	C₂²×C₇₉	#532	1	1	yes	characteristic
183	C₂²×C₇₉	C₂²×Q₁₆	1	1	yes	characteristic
184	C₂²×C₇₉	C₂×#135	1	1	yes	characteristic
185	C₂²×C₇₉	C₂×#135	1	1	yes	characteristic
186	C₂²×C₇₉	C₂×#135	1	1	yes	characteristic
187	C₄×C₇₉	—	2	2	no	—
188	C₄×C₇₉	—	2	2	no	—
189	C₄×C₇₉	—	4	4	no	—
190	C₄×C₇₉	—	8	2	no	—
191	C₄×C₇₉	C₂×#117	1	1	yes	characteristic
192	C₄×C₇₉	C₄×#41	1	1	yes	characteristic
193	C₄×C₇₉	#529	1	1	yes	characteristic
194	C₄×C₇₉	#529	1	1	yes	characteristic
195	Dic₇₉	—	2	2	no	—
196	Dic₇₉	—	2	2	no	—
197	Dic₇₉	—	2	2	no	—
198	Dic₇₉	—	4	4	no	—
199	Dic₇₉	—	8	2	no	—
200	Dic₇₉	C₄×Q₁₆	1	4	yes	—
201	#21276	—	79	1	no	maximal, Sylow
202	C₂×C₇₉	#2293	1	1	yes	characteristic
203	C₂×C₇₉	C₂×C₄×Q₁₆	1	1	yes	characteristic
204	C₂×C₇₉	C₄×#135	1	1	yes	characteristic
205	C₂×C₇₉	#3168	1	1	yes	characteristic
206	C₂×C₇₉	#3168	1	1	yes	characteristic
207	C₂×C₇₉	#3170	1	1	yes	characteristic
208	C₂×C₇₉	#3170	1	1	yes	characteristic
209	C₂×C₄×Q₁₆	—	79	1	no	—
210	#2295	—	79	2	no	—
211	#1969	—	79	1	no	—
212	#1969	D₇₉	1	1	yes	characteristic
213	#1942	—	79	1	no	—
214	#1942	—	79	1	no	—
215	#1933	—	79	2	no	—
216	#1933	—	79	2	no	—
217	C₄×#107	—	79	1	no	—
218	C₄×#103	—	79	2	no	—
219	C₄²×C₈	—	79	1	no	—
220	C₇₉	#21276	1	1	yes	characteristic, complemented, Sylow
221	C₂²×Q₁₆	C₂×D₇₉	1	1	yes	characteristic
222	C₂×C₄×Q₈	—	79	2	no	—
223	C₄×Q₁₆	—	79	8	no	—
224	C₂×#107	—	79	1	no	—
225	C₂×#107	—	79	1	no	—
226	C₂×#107	C₂×D₇₉	1	1	yes	characteristic
227	C₂×#103	—	79	2	no	—
228	C₂×#103	—	79	2	no	—
229	C₂×#103	C₂×D₇₉	1	2	yes	—
230	C₂×C₄×C₈	—	79	1	no	—
231	C₂×C₄×C₈	—	79	1	no	—
232	C₂×C₄×C₈	—	79	1	no	—
233	C₂×C₄×C₈	—	79	1	no	—
234	C₂×C₄×C₈	—	79	1	no	—
235	C₂×C₄×C₈	C₂×D₇₉	1	1	yes	characteristic
236	#391	—	79	2	no	—
237	#391	C₂×D₇₉	1	2	yes	—
238	#389	—	79	2	no	—
239	#389	—	79	2	no	—
240	#387	—	158	2	no	—
241	#387	—	158	2	no	—
242	C₄×C₄⋊C₄	—	79	2	no	—
243	C₄×C₄⋊C₄	—	158	2	no	—
244	#376	—	158	2	no	—
245	C₄³	—	79	1	no	—
246	#340	—	79	2	no	—
247	#340	—	79	2	no	—
248	#340	—	79	2	no	—
249	C₂²×Q₈	C₂²×D₇₉	1	2	yes	—
250	C₂×Q₁₆	—	2	2	no	—
251	C₂×Q₁₆	—	2	2	no	—
252	C₂×Q₁₆	C₄×D₇₉	1	4	yes	—
253	C₂²×C₈	—	79	1	no	—
254	C₂²×C₈	—	79	1	no	—
255	C₂²×C₈	C₂²×D₇₉	1	1	yes	characteristic
256	C₂²×C₈	C₂²×D₇₉	1	1	yes	characteristic
257	C₄×Q₈	—	79	8	no	—
258	C₄×Q₈	—	158	4	no	—
259	C₂×C₄⋊C₄	—	79	2	no	—
260	C₂×C₄⋊C₄	—	79	2	no	—
261	C₂×C₄⋊C₄	—	158	2	no	—
262	C₂×C₄⋊C₄	—	158	2	no	—
263	C₂×C₄⋊C₄	—	158	2	no	—
264	C₂×C₄⋊C₄	C₂²×D₇₉	1	2	yes	—
265	C₂×C₄²	—	79	1	no	—
266	C₂×C₄²	—	79	1	no	—
267	C₂×C₄²	—	79	1	no	—
268	C₂×C₄²	—	79	1	no	—
269	C₂×C₄²	—	79	1	no	—
270	C₂×C₄²	—	79	1	no	—
271	C₂×C₄²	—	158	2	no	—
272	C₂×C₄²	—	158	2	no	—
273	C₂×C₄²	C₂²×D₇₉	1	1	yes	characteristic
274	#107	—	2	2	no	—
275	#107	—	79	4	no	—
276	#107	—	158	2	no	—
277	#103	—	2	4	no	—
278	#103	—	79	8	no	—
279	#103	—	158	4	no	—
280	C₄×C₈	—	2	2	no	—
281	C₄×C₈	—	79	4	no	—
282	C₄×C₈	—	158	2	no	—
283	C₄×C₈	—	158	2	no	—
284	C₄×C₈	—	158	2	no	—
285	C₄×C₈	—	158	2	no	—
286	#95	—	2	2	no	—
287	#95	—	2	2	no	—
288	#95	—	158	2	no	—
289	#95	—	158	2	no	—
290	#95	—	158	2	no	—
291	#95	—	158	2	no	—
292	#95	—	158	2	no	—
293	C₂×Q₈	—	2	2	no	—
294	C₂×Q₈	—	2	2	no	—
295	C₂×Q₈	—	2	2	no	—
296	C₂×Q₈	—	2	2	no	—
297	C₂×Q₈	—	2	2	no	—
298	C₂×Q₈	C₂×C₄×D₇₉	1	4	yes	—
299	C₂²×C₄	—	2	2	no	—
300	C₂²×C₄	—	2	2	no	—
301	C₂²×C₄	—	79	1	no	—
302	C₂²×C₄	—	79	1	no	—
303	C₂²×C₄	—	79	1	no	—
304	C₂²×C₄	—	79	1	no	—
305	C₂²×C₄	—	158	2	no	—
306	C₂²×C₄	—	158	2	no	—
307	C₂²×C₄	D₄×D₇₉	1	1	yes	characteristic
308	C₂²×C₄	D₄×D₇₉	1	1	yes	characteristic
309	C₂²×C₄	C₂³×D₇₉	1	1	yes	characteristic
310	Q₁₆	—	2	8	no	—
311	C₂×C₈	—	2	1	no	—
312	C₂×C₈	—	2	1	no	—
313	C₂×C₈	—	79	2	no	—
314	C₂×C₈	—	79	2	no	—
315	C₂×C₈	—	158	1	no	—
316	C₂×C₈	—	158	1	no	—
317	C₂×C₈	—	158	1	no	—
318	C₂×C₈	—	158	1	no	—
319	C₂×C₈	C₂×C₄×D₇₉	1	2	yes	—
320	C₂×C₈	#11929623	1	2	yes	—
321	C₂×C₈	#11929623	1	2	yes	—
322	C₂×C₈	#11929623	1	2	yes	—
323	C₄⋊C₄	—	2	2	no	—
324	C₄⋊C₄	—	2	2	no	—
325	C₄⋊C₄	—	316	4	no	—
326	C₄⋊C₄	—	316	4	no	—
327	C₄⋊C₄	—	79	4	no	—
328	C₄⋊C₄	—	158	8	no	—
329	C₄⋊C₄	—	158	2	no	—
330	C₄⋊C₄	—	158	2	no	—
331	C₄⋊C₄	—	158	2	no	—
332	C₄²	—	2	1	no	—
333	C₄²	—	2	1	no	—
334	C₄²	—	316	4	no	—
335	C₄²	—	79	2	no	—
336	C₄²	—	79	4	no	—
337	C₄²	—	79	2	no	—
338	C₄²	—	158	2	no	—
339	C₄²	—	158	2	no	—
340	C₄²	—	158	8	no	—
341	C₄²	—	158	1	no	—
342	C₄²	—	158	1	no	—
343	C₄²	—	158	2	no	—
344	C₂³	C₂×D₄×D₇₉	1	1	yes	characteristic
345	Q₈	—	2	4	no	—
346	Q₈	—	2	4	no	—
347	Q₈	—	4	2	no	—
348	Q₈	—	4	2	no	—
349	C₂×C₄	—	2	1	no	—
350	C₂×C₄	—	2	1	no	—
351	C₂×C₄	—	2	1	no	—
352	C₂×C₄	—	2	1	no	—
353	C₂×C₄	—	2	4	no	—
354	C₂×C₄	—	4	2	no	—
355	C₂×C₄	—	4	2	no	—
356	C₂×C₄	—	4	2	no	—
357	C₂×C₄	—	4	2	no	—
358	C₂×C₄	—	4	2	no	—
359	C₂×C₄	—	316	2	no	—
360	C₂×C₄	—	316	2	no	—
361	C₂×C₄	—	316	2	no	—
362	C₂×C₄	—	316	2	no	—
363	C₂×C₄	—	316	2	no	—
364	C₂×C₄	—	79	2	no	—
365	C₂×C₄	—	79	2	no	—
366	C₂×C₄	—	79	2	no	—
367	C₂×C₄	—	79	2	no	—
368	C₂×C₄	—	79	2	no	—
369	C₂×C₄	—	79	2	no	—
370	C₂×C₄	—	158	4	no	—
371	C₂×C₄	—	158	1	no	—
372	C₂×C₄	—	158	1	no	—
373	C₂×C₄	—	158	1	no	—
374	C₂×C₄	—	158	1	no	—
375	C₂×C₄	—	158	1	no	—
376	C₂×C₄	—	158	1	no	—
377	C₂×C₄	Q₁₆×D₇₉	1	2	yes	—
378	C₂×C₄	#14579184	1	2	yes	—
379	C₂×C₄	C₂²×C₄×D₇₉	1	1	yes	characteristic
380	C₂×C₄	#41×D₇₉	1	1	yes	characteristic
381	C₂×C₄	#41×D₇₉	1	1	yes	characteristic
382	C₂×C₄	C₂×#11929623	1	1	yes	characteristic
383	C₂×C₄	C₂×#11929623	1	1	yes	characteristic
384	C₂×C₄	C₂×#11929623	1	1	yes	characteristic
385	C₈	—	2	2	no	—
386	C₈	—	158	2	no	—
387	C₈	—	158	2	no	—
388	C₈	#14579117	1	4	yes	—
389	C₂²	C₄×D₄×D₇₉	1	1	yes	characteristic
390	C₂²	#19099108	1	1	yes	characteristic
391	C₂²	#19099111	1	1	yes	characteristic
392	C₂²	C₂×Q₁₆×D₇₉	1	1	yes	characteristic
393	C₂²	#135×D₇₉	1	1	yes	characteristic
394	C₂²	#135×D₇₉	1	1	yes	characteristic
395	C₂²	C₂×#14579184	1	1	yes	characteristic
396	C₄	—	2	2	no	—
397	C₄	—	2	2	no	—
398	C₄	—	4	4	no	—
399	C₄	—	8	2	no	—
400	C₄	—	316	4	no	—
401	C₄	—	79	4	no	—
402	C₄	—	632	2	no	—
403	C₄	—	158	2	no	—
404	C₄	—	158	2	no	—
405	C₄	—	158	2	no	—
406	C₄	C₂×#14579117	1	1	yes	characteristic
407	C₄	C₄×#11929623	1	1	yes	characteristic
408	C₄	#19099092	1	1	yes	characteristic
409	C₄	#19099094	1	1	yes	characteristic
410	C₂	#23765862	1	1	yes	characteristic
411	C₂	C₄×Q₁₆×D₇₉	1	1	yes	characteristic
412	C₂	C₄×#14579184	1	1	yes	characteristic
413	C₂	#23773967	1	1	yes	characteristic
414	C₂	#23773971	1	1	yes	characteristic
415	C₂	#23773981	1	1	yes	characteristic
416	C₂	#23773984	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂×D₄×D₇₉
commutator	C₂×C₄×C₇₉	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₇₉
Fitting	C₇₉×#1969	C₂
socle, prime radical	C₂³×C₇₉	C₂²×D₄
cosocle	C₂²×C₄×C₇₉	C₂⁴
hypercenter	#1969	D₇₉
hypocenter	C₇₉	#21276
LCS	G ▷ C₂×C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #1969

Complements

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

N	H ≅ G/N	type
13. Q₁₆×Dic₇₉	C₄	semidirect
110. C₄×Dic₇₉	Q₁₆	semidirect
220. C₇₉	#21276	semidirect

Maximal subgroups

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

subgroup	index
C₂×Q₁₆×Dic₇₉	2
#23765875	2
#23764262	2
#23764133	2
#23764131	2
#23764079	2
#23764073	2
#107×Dic₇₉	2
#103×Dic₇₉	2
C₄×C₈×Dic₇₉	2
C₇₉×#1969	2
#21276	79