Subgroups — #34258246

Order 20224.

632 conjugacy classes of subgroups.

The subgroup lattice has 444 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#23773480	C₂	1	1	yes	maximal, characteristic
2	#23772369	C₂	1	1	yes	maximal, characteristic
3	C₂×Q₈×C₇₉⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
4	#23762275	C₂	1	2	yes	maximal, complemented
5	#23762268	C₂	1	2	yes	maximal, complemented
6	#23762204	C₂	1	2	yes	maximal, complemented
7	#23762197	C₂	1	2	yes	maximal, complemented
8	#23762186	C₂	1	1	yes	maximal, characteristic, complemented
9	#23761814	C₂	1	1	yes	maximal, characteristic
10	M₁₆×C₇₉⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
11	C₇₉×#1491	C₂	1	1	yes	maximal, characteristic, complemented
12	#19099097	C₂²	1	1	yes	characteristic
13	#19098893	C₄	1	1	yes	characteristic
14	#19098876	C₄	1	1	yes	characteristic
15	#19098870	C₄	1	2	yes	—
16	#19098785	C₄	1	2	yes	—
17	#19098719	C₄	1	1	yes	characteristic
18	#19098702	C₄	1	1	yes	characteristic
19	#19098690	C₂²	1	1	yes	characteristic
20	Q₈×C₇₉⋊C₈	—	2	1	no	—
21	Q₈×C₇₉⋊C₈	—	2	1	no	—
22	Q₈×C₇₉⋊C₈	C₂²	1	2	yes	—
23	Q₈×C₇₉⋊C₈	C₂²	1	2	yes	—
24	#19098687	C₂²	1	1	yes	characteristic
25	C₄×#11929614	C₂²	1	2	yes	—
26	C₄×#11929611	C₂²	1	2	yes	—
27	#19098640	C₂²	1	1	yes	characteristic
28	#19098631	—	2	1	no	—
29	#19098628	C₂²	1	1	yes	characteristic
30	(C₂²⋊D₇₉)⋊C₈	—	2	1	no	—
31	#19098625	—	2	1	no	—
32	#19098616	C₂²	1	1	yes	characteristic
33	C₂×C₄⋊(C₇₉⋊C₈)	—	2	1	no	—
34	C₂×C₄⋊(C₇₉⋊C₈)	C₂²	1	1	yes	characteristic
35	#19098520	—	2	1	no	—
36	C₂×C₄×C₇₉⋊C₈	—	2	1	no	—
37	C₂×C₄×C₇₉⋊C₈	C₂²	1	1	yes	characteristic
38	#19098315	C₂²	1	2	yes	—
39	#19098313	C₂²	1	2	yes	—
40	#19098295	C₂²	1	2	yes	—
41	#19098292	C₂²	1	2	yes	—
42	#19098284	C₂²	1	2	yes	—
43	C₈×C₇₉⋊C₈	C₂²	1	2	yes	—
44	C₂×C₄×Q₈×C₇₉	C₂²	1	1	yes	characteristic
45	#432×C₇₉	C₂²	1	1	yes	characteristic
46	C₄×M₁₆×C₇₉	C₂²	1	1	yes	characteristic
47	Q₈⋊C₈×C₇₉	C₂²	1	2	yes	—
48	Q₈⋊C₈×C₇₉	C₂²	1	2	yes	—
49	C₂×#11929614	C₂×C₄	1	2	yes	—
50	C₂×#11929611	C₂×C₄	1	2	yes	—
51	C₂×#11929607	—	2	1	no	—
52	C₂²×C₇₉⋊C₈	—	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	#14579155	—	2	1	no	—
57	#14579153	C₂×C₄	1	1	yes	characteristic
58	#14579149	C₂×C₄	1	1	yes	characteristic
59	#14579144	—	2	1	no	—
60	#14579140	C₂×C₄	1	1	yes	characteristic
61	#14579135	C₂×C₄	1	1	yes	characteristic
62	C₄×Dic₁₅₈	C₂³	1	1	yes	characteristic
63	C₄×D₃₁₆	C₂³	1	1	yes	characteristic
64	C₄×C₂²⋊D₇₉	—	2	1	no	—
65	#14579118	—	2	1	no	—
66	#14579094	C₂×C₄	1	2	yes	—
67	#14579092	C₂×C₄	1	2	yes	—
68	C₄⋊(C₇₉⋊C₈)	—	2	1	no	—
69	C₄⋊(C₇₉⋊C₈)	—	2	2	no	—
70	C₄⋊(C₇₉⋊C₈)	—	2	2	no	—
71	C₄⋊(C₇₉⋊C₈)	C₂×C₄	1	2	yes	—
72	C₄⋊(C₇₉⋊C₈)	C₂³	1	2	yes	—
73	Dic₇₉⋊C₈	—	2	1	no	—
74	Dic₇₉⋊C₈	—	2	1	no	—
75	#14579085	C₂×C₄	1	2	yes	—
76	#14579085	C₂×C₄	1	2	yes	—
77	#14579084	C₂×C₄	1	2	yes	—
78	#14579081	C₂×C₄	1	2	yes	—
79	C₂²⋊(C₇₉⋊C₈)	C₂×C₄	1	1	yes	characteristic
80	C₂²⋊(C₇₉⋊C₈)	C₂×C₄	1	1	yes	characteristic
81	(C₂×D₇₉)⋊C₈	—	2	1	no	—
82	(C₂×D₇₉)⋊C₈	—	2	1	no	—
83	#14579071	—	2	1	no	—
84	C₄×C₇₉⋊C₈	—	2	2	no	—
85	C₄×C₇₉⋊C₈	—	2	2	no	—
86	C₄×C₇₉⋊C₈	D₄	1	1	yes	characteristic
87	C₄×C₇₉⋊C₈	D₄	1	1	yes	characteristic
88	C₄×C₇₉⋊C₈	C₂³	1	2	yes	—
89	C₄×C₇₉⋊C₈	C₂³	1	1	yes	characteristic
90	C₄×C₇₉⋊C₈	C₂³	1	1	yes	characteristic
91	C₈×Dic₇₉	—	2	1	no	—
92	C₂²×Q₈×C₇₉	C₂×C₄	1	1	yes	characteristic
93	C₂×M₁₆×C₇₉	—	2	1	no	—
94	C₄×Q₈×C₇₉	—	2	1	no	—
95	C₄×Q₈×C₇₉	—	2	1	no	—
96	C₄×Q₈×C₇₉	C₂×C₄	1	2	yes	—
97	C₄×Q₈×C₇₉	C₂³	1	2	yes	—
98	C₂×C₄⋊C₄×C₇₉	—	2	1	no	—
99	C₂×C₄⋊C₄×C₇₉	C₂×C₄	1	1	yes	characteristic
100	C₂×C₄²×C₇₉	—	2	1	no	—
101	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
102	C₄⋊C₈×C₇₉	C₂³	1	1	yes	characteristic
103	C₄⋊C₈×C₇₉	C₂³	1	1	yes	characteristic
104	C₂²⋊C₈×C₇₉	—	2	1	no	—
105	#97×C₇₉	—	2	1	no	—
106	#97×C₇₉	—	2	1	no	—
107	C₄×C₈×C₇₉	C₂³	1	2	yes	—
108	C₂×Dic₁₅₈	C₂²×C₄	1	1	yes	characteristic
109	C₂×D₃₁₆	C₂²×C₄	1	1	yes	characteristic
110	C₂×C₂²⋊D₇₉	—	2	1	no	—
111	C₂×C₄×D₇₉	—	2	1	no	—
112	#11929614	—	2	4	no	—
113	#11929611	—	2	4	no	—
114	#11929607	—	4	2	no	—
115	C₂×C₇₉⋊C₈	—	2	2	no	—
116	C₂×C₇₉⋊C₈	—	2	2	no	—
117	C₂×C₇₉⋊C₈	—	4	1	no	—
118	C₂×C₇₉⋊C₈	—	4	2	no	—
119	C₂×C₇₉⋊C₈	C₂²×C₄	1	2	yes	—
120	C₂×C₇₉⋊C₈	C₂²×C₄	1	2	yes	—
121	C₂×C₇₉⋊C₈	C₂×D₄	1	1	yes	characteristic
122	C₂×C₇₉⋊C₈	C₂×D₄	1	1	yes	characteristic
123	C₂×C₇₉⋊C₈	C₂×D₄	1	1	yes	characteristic
124	C₂×C₇₉⋊C₈	C₂×D₄	1	1	yes	characteristic
125	C₈×D₇₉	—	4	2	no	—
126	C₄⋊Dic₇₉	C₂²×C₄	1	1	yes	characteristic
127	C₄⋊Dic₇₉	C₂²×C₄	1	1	yes	characteristic
128	Dic₇₉⋊C₄	—	2	1	no	—
129	Dic₇₉⋊C₄	—	2	1	no	—
130	Dic₇₉⋊C₄	—	2	1	no	—
131	Dic₇₉⋊C₄	—	2	1	no	—
132	C₂²⋊Dic₇₉	—	2	1	no	—
133	(C₂×D₇₉)⋊C₄	—	2	1	no	—
134	(C₂×D₇₉)⋊C₄	—	2	1	no	—
135	(C₂×D₇₉)⋊C₄	—	2	1	no	—
136	(C₂×D₇₉)⋊C₄	—	2	1	no	—
137	C₄×Dic₇₉	—	2	1	no	—
138	C₂×Q₈×C₇₉	—	2	4	no	—
139	C₂×Q₈×C₇₉	—	2	1	no	—
140	C₂×Q₈×C₇₉	C₂²×C₄	1	2	yes	—
141	C₂²×C₄×C₇₉	—	2	1	no	—
142	C₂²×C₄×C₇₉	—	2	1	no	—
143	C₂²×C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
144	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
145	C₂²×C₄×C₇₉	#41	1	1	yes	characteristic
146	M₁₆×C₇₉	—	2	4	no	—
147	C₂×C₈×C₇₉	—	2	1	no	—
148	C₂×C₈×C₇₉	—	2	1	no	—
149	C₂×C₈×C₇₉	—	2	2	no	—
150	C₄⋊C₄×C₇₉	—	2	2	no	—
151	C₄⋊C₄×C₇₉	—	2	1	no	—
152	C₄⋊C₄×C₇₉	—	2	2	no	—
153	C₄⋊C₄×C₇₉	C₂²×C₄	1	2	yes	—
154	C₄²×C₇₉	—	2	2	no	—
155	C₄²×C₇₉	—	2	2	no	—
156	C₄²×C₇₉	C₂²×C₄	1	1	yes	characteristic
157	C₄²×C₇₉	C₂×D₄	1	1	yes	characteristic
158	C₄²×C₇₉	#41	1	1	yes	characteristic
159	C₄²×C₇₉	C₂⁴	1	1	yes	characteristic
160	C₂³×C₇₉	C₄×D₄	1	1	yes	characteristic
161	C₂²×D₇₉	—	2	1	no	—
162	Q₈×C₇₉	—	2	4	no	—
163	Q₈×C₇₉	—	2	2	no	—
164	Q₈×C₇₉	#131	1	4	yes	—
165	C₂×C₄×C₇₉	—	2	4	no	—
166	C₂×C₄×C₇₉	—	2	2	no	—
167	C₂×C₄×C₇₉	—	2	2	no	—
168	C₂×C₄×C₇₉	—	2	2	no	—
169	C₂×C₄×C₇₉	—	2	1	no	—
170	C₂×C₄×C₇₉	—	2	1	no	—
171	C₂×C₄×C₇₉	—	2	2	no	—
172	C₂×C₄×C₇₉	—	4	2	no	—
173	C₂×C₄×C₇₉	C₄×D₄	1	1	yes	characteristic
174	C₂×C₄×C₇₉	C₄×D₄	1	1	yes	characteristic
175	C₂×C₄×C₇₉	C₄×D₄	1	1	yes	characteristic
176	C₂×C₄×C₇₉	C₂³×C₄	1	1	yes	characteristic
177	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
178	C₂×C₄×C₇₉	C₂×#41	1	1	yes	characteristic
179	C₂²⋊D₇₉	—	4	2	no	—
180	C₂×Dic₇₉	—	2	1	no	—
181	C₂×Dic₇₉	—	2	1	no	—
182	C₂×Dic₇₉	—	2	1	no	—
183	D₃₁₆	—	2	2	no	—
184	C₄×D₇₉	—	4	1	no	—
185	C₄×D₇₉	—	4	1	no	—
186	Dic₁₅₈	—	2	2	no	—
187	C₈×C₇₉	—	2	4	no	—
188	C₈×C₇₉	—	4	1	no	—
189	C₈×C₇₉	—	4	1	no	—
190	C₇₉⋊C₈	—	2	2	no	—
191	C₇₉⋊C₈	—	2	2	no	—
192	C₇₉⋊C₈	—	2	1	no	—
193	C₇₉⋊C₈	—	2	1	no	—
194	C₇₉⋊C₈	—	2	1	no	—
195	C₇₉⋊C₈	—	4	2	no	—
196	C₇₉⋊C₈	#137	1	2	yes	—
197	C₂²×C₇₉	—	2	1	no	—
198	C₂²×C₇₉	—	2	1	no	—
199	C₂²×C₇₉	#443	1	2	yes	—
200	C₂²×C₇₉	C₂×C₄×D₄	1	1	yes	characteristic
201	C₂×D₇₉	—	4	1	no	—
202	C₂×D₇₉	—	4	1	no	—
203	C₂×D₇₉	—	4	1	no	—
204	C₄×C₇₉	—	2	4	no	—
205	C₄×C₇₉	—	2	1	no	—
206	C₄×C₇₉	—	2	1	no	—
207	C₄×C₇₉	—	2	1	no	—
208	C₄×C₇₉	—	2	1	no	—
209	C₄×C₇₉	—	4	2	no	—
210	C₄×C₇₉	C₂×#131	1	2	yes	—
211	C₄×C₇₉	C₂×#137	1	1	yes	characteristic
212	C₄×C₇₉	#575	1	1	yes	characteristic
213	Dic₇₉	—	4	1	no	—
214	Dic₇₉	—	4	1	no	—
215	Dic₇₉	—	4	1	no	—
216	#17911	—	79	1	no	maximal, Sylow
217	C₂×C₇₉	—	2	2	no	—
218	C₂×C₇₉	#2929	1	1	yes	characteristic
219	C₂×C₇₉	C₄×#137	1	1	yes	characteristic
220	C₂×C₇₉	C₂×#443	1	1	yes	characteristic
221	D₇₉	—	8	1	no	—
222	#3108	—	79	1	no	—
223	#2966	—	79	1	no	—
224	C₂×C₈×Q₈	—	79	1	no	—
225	#1588	—	79	2	no	—
226	#1587	—	79	2	no	—
227	C₈×Q₁₆	—	79	2	no	—
228	C₈×SD₁₆	—	79	2	no	—
229	#1573	—	79	1	no	—
230	#1491	D₇₉	1	1	yes	characteristic, complemented
231	#1483	—	79	1	no	—
232	C₈×M₁₆	—	79	1	no	—
233	C₇₉	#17911	1	1	yes	characteristic, complemented, Sylow
234	#529	—	79	1	no	—
235	C₂×C₄×Q₈	C₂×D₇₉	1	1	yes	characteristic
236	#483	—	79	1	no	—
237	#480	—	79	1	no	—
238	#479	—	79	2	no	—
239	#464	—	79	2	no	—
240	#451	—	79	1	no	—
241	#448	—	79	1	no	—
242	#446	—	79	1	no	—
243	C₈×Q₈	—	79	2	no	—
244	C₈×Q₈	—	79	2	no	—
245	C₈×Q₈	—	79	1	no	—
246	C₈×Q₈	—	158	1	no	—
247	C₈×Q₈	—	158	1	no	—
248	C₄×Q₁₆	—	79	2	no	—
249	C₄×SD₁₆	—	79	2	no	—
250	#436	—	79	1	no	—
251	#435	—	158	1	no	—
252	C₈×D₄	—	79	1	no	—
253	C₈×D₄	—	158	1	no	—
254	#433	—	158	1	no	—
255	#432	C₂×D₇₉	1	1	yes	characteristic
256	#431	—	79	1	no	—
257	C₂×C₄⋊C₈	—	79	1	no	—
258	C₂×C₄⋊C₈	—	158	1	no	—
259	#405	—	158	1	no	—
260	C₄×M₁₆	C₂×D₇₉	1	1	yes	characteristic
261	C₂×C₄×C₈	—	79	1	no	—
262	C₂×C₄×C₈	—	158	1	no	—
263	#335	—	79	2	no	—
264	#334	—	79	2	no	—
265	Q₈⋊C₈	—	79	2	no	—
266	Q₈⋊C₈	C₂×D₇₉	1	2	yes	—
267	Q₈⋊C₈	C₂×D₇₉	1	2	yes	—
268	D₄⋊C₈	—	79	2	no	—
269	#322	—	79	2	no	—
270	C₈²	—	79	2	no	—
271	C₂²×Q₈	C₄×D₇₉	1	1	yes	characteristic
272	C₂×Q₁₆	—	79	2	no	—
273	C₂×SD₁₆	—	79	2	no	—
274	C₂×M₁₆	—	2	1	no	—
275	C₂×M₁₆	—	158	1	no	—
276	C₂²×C₈	—	79	1	no	—
277	C₂²×C₈	—	79	1	no	—
278	C₂²×C₈	—	158	1	no	—
279	C₂²×C₈	—	158	1	no	—
280	#126	—	158	1	no	—
281	#125	—	79	1	no	—
282	#124	—	79	1	no	—
283	#123	—	158	1	no	—
284	C₂²⋊Q₈	—	79	1	no	—
285	#121	—	79	1	no	—
286	C₄×Q₈	—	2	1	no	—
287	C₄×Q₈	—	2	1	no	—
288	C₄×Q₈	—	79	1	no	—
289	C₄×Q₈	C₄×D₇₉	1	2	yes	—
290	C₄×Q₈	C₂²×D₇₉	1	2	yes	—
291	C₄×D₄	—	79	1	no	—
292	C₄×D₄	—	158	1	no	—
293	#117	—	158	1	no	—
294	C₂×C₄⋊C₄	—	2	1	no	—
295	C₂×C₄⋊C₄	C₄×D₇₉	1	1	yes	characteristic
296	C₂×C₄²	—	2	1	no	—
297	C₂×C₄²	C₂²×D₇₉	1	1	yes	characteristic
298	#107	—	79	2	no	—
299	#106	—	79	2	no	—
300	C₄⋊C₈	—	79	2	no	—
301	C₄⋊C₈	—	79	2	no	—
302	C₄⋊C₈	—	158	2	no	—
303	C₄⋊C₈	—	158	2	no	—
304	C₄⋊C₈	—	158	1	no	—
305	C₄⋊C₈	—	158	1	no	—
306	C₄⋊C₈	—	158	1	no	—
307	C₄⋊C₈	C₂²×D₇₉	1	1	yes	characteristic
308	C₄⋊C₈	C₂²×D₇₉	1	1	yes	characteristic
309	#103	—	79	2	no	—
310	#103	—	79	2	no	—
311	#103	—	79	2	no	—
312	#102	—	79	2	no	—
313	C₂²⋊C₈	—	2	1	no	—
314	C₂²⋊C₈	—	79	1	no	—
315	C₂²⋊C₈	—	79	1	no	—
316	C₂²⋊C₈	—	158	1	no	—
317	C₂²⋊C₈	—	158	1	no	—
318	#97	—	2	1	no	—
319	#97	—	2	1	no	—
320	#97	—	158	1	no	—
321	C₄×C₈	—	79	1	no	—
322	C₄×C₈	—	79	1	no	—
323	C₄×C₈	—	79	1	no	—
324	C₄×C₈	—	79	2	no	—
325	C₄×C₈	—	79	1	no	—
326	C₄×C₈	—	158	2	no	—
327	C₄×C₈	—	158	2	no	—
328	C₄×C₈	—	158	1	no	—
329	C₄×C₈	C₂²×D₇₉	1	2	yes	—
330	C₂×Q₈	—	2	4	no	—
331	C₂×Q₈	—	2	1	no	—
332	C₂×Q₈	—	79	1	no	—
333	C₂×Q₈	C₂×C₄×D₇₉	1	2	yes	—
334	C₂×D₄	—	79	1	no	—
335	C₂×D₄	—	158	1	no	—
336	C₂²×C₄	—	2	1	no	—
337	C₂²×C₄	—	2	1	no	—
338	C₂²×C₄	—	158	1	no	—
339	C₂²×C₄	C₂×C₄×D₇₉	1	1	yes	characteristic
340	C₂²×C₄	D₄×D₇₉	1	1	yes	characteristic
341	C₂²×C₄	#11929623	1	1	yes	characteristic
342	Q₁₆	—	158	4	no	—
343	SD₁₆	—	158	4	no	—
344	M₁₆	—	2	4	no	—
345	M₁₆	—	316	2	no	—
346	C₂×C₈	—	2	2	no	—
347	C₂×C₈	—	2	1	no	—
348	C₂×C₈	—	2	1	no	—
349	C₂×C₈	—	316	2	no	—
350	C₂×C₈	—	316	2	no	—
351	C₂×C₈	—	316	1	no	—
352	C₂×C₈	—	79	1	no	—
353	C₂×C₈	—	79	2	no	—
354	C₂×C₈	—	79	2	no	—
355	C₂×C₈	—	79	1	no	—
356	C₂×C₈	—	79	1	no	—
357	C₂×C₈	—	79	1	no	—
358	C₂×C₈	—	158	2	no	—
359	C₂×C₈	—	158	2	no	—
360	C₄⋊C₄	—	2	2	no	—
361	C₄⋊C₄	—	2	2	no	—
362	C₄⋊C₄	—	2	1	no	—
363	C₄⋊C₄	—	79	1	no	—
364	C₄⋊C₄	—	79	1	no	—
365	C₄⋊C₄	—	158	1	no	—
366	C₄⋊C₄	—	158	1	no	—
367	C₄⋊C₄	—	158	1	no	—
368	C₄⋊C₄	—	158	1	no	—
369	C₄⋊C₄	C₂×C₄×D₇₉	1	2	yes	—
370	C₂²⋊C₄	—	158	1	no	—
371	C₂²⋊C₄	—	158	1	no	—
372	C₂²⋊C₄	—	158	1	no	—
373	C₂²⋊C₄	—	158	1	no	—
374	C₂²⋊C₄	—	158	1	no	—
375	C₄²	—	2	2	no	—
376	C₄²	—	2	2	no	—
377	C₄²	—	158	1	no	—
378	C₄²	C₂×C₄×D₇₉	1	1	yes	characteristic
379	C₄²	D₄×D₇₉	1	1	yes	characteristic
380	C₄²	#11929623	1	1	yes	characteristic
381	C₄²	C₂³×D₇₉	1	1	yes	characteristic
382	C₂³	—	158	1	no	—
383	C₂³	(C₂²⋊D₇₉)⋊C₄	1	1	yes	characteristic
384	Q₈	—	2	4	no	—
385	Q₈	—	2	2	no	—
386	Q₈	—	158	2	no	—
387	Q₈	#14579169	1	4	yes	—
388	D₄	—	316	2	no	—
389	D₄	—	158	2	no	—
390	C₂×C₄	—	2	4	no	—
391	C₂×C₄	—	2	2	no	—
392	C₂×C₄	—	2	2	no	—
393	C₂×C₄	—	2	2	no	—
394	C₂×C₄	—	2	1	no	—
395	C₂×C₄	—	2	1	no	—
396	C₂×C₄	—	2	2	no	—
397	C₂×C₄	—	4	2	no	—
398	C₂×C₄	—	316	1	no	—
399	C₂×C₄	—	316	1	no	—
400	C₂×C₄	—	158	1	no	—
401	C₂×C₄	—	158	1	no	—
402	C₂×C₄	—	158	1	no	—
403	C₂×C₄	(C₂²⋊D₇₉)⋊C₄	1	1	yes	characteristic
404	C₂×C₄	(C₂²⋊D₇₉)⋊C₄	1	1	yes	characteristic
405	C₂×C₄	(C₂²⋊D₇₉)⋊C₄	1	1	yes	characteristic
406	C₂×C₄	C₂²×C₄×D₇₉	1	1	yes	characteristic
407	C₂×C₄	C₂×D₄×D₇₉	1	1	yes	characteristic
408	C₂×C₄	C₂×#11929623	1	1	yes	characteristic
409	C₈	—	2	4	no	—
410	C₈	—	4	1	no	—
411	C₈	—	4	1	no	—
412	C₈	—	316	2	no	—
413	C₈	—	79	2	no	—
414	C₈	—	158	2	no	—
415	C₈	—	158	2	no	—
416	C₈	—	158	1	no	—
417	C₈	—	158	1	no	—
418	C₈	—	158	1	no	—
419	C₂²	—	2	1	no	—
420	C₂²	—	2	1	no	—
421	C₂²	—	316	1	no	—
422	C₂²	—	316	1	no	—
423	C₂²	—	316	1	no	—
424	C₂²	#19098677	1	2	yes	—
425	C₂²	C₂×(C₂²⋊D₇₉)⋊C₄	1	1	yes	characteristic
426	C₄	—	2	1	no	—
427	C₄	—	2	1	no	—
428	C₄	—	2	1	no	—
429	C₄	—	2	4	no	—
430	C₄	—	2	1	no	—
431	C₄	—	4	2	no	—
432	C₄	—	316	1	no	—
433	C₄	—	316	1	no	—
434	C₄	—	316	1	no	—
435	C₄	C₂×#14579169	1	2	yes	—
436	C₄	#137×D₇₉	1	1	yes	characteristic
437	C₄	#19099362	1	1	yes	characteristic
438	C₂	—	2	2	no	—
439	C₂	—	632	1	no	—
440	C₂	#23772090	1	1	yes	characteristic
441	C₂	#23772215	1	1	yes	characteristic
442	C₂	C₂×#19098677	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×#1491	C₂
socle	C₂²×C₇₉	C₂×C₄×D₄
prime radical	#14579135	C₂×C₄
cosocle	C₄²×C₇₉	C₂⁴
hypercenter	#1491	D₇₉
hypocenter	C₇₉	#17911
LCS	G ▷ C₂×C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1491

Complements

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

N	H ≅ G/N	type
3. C₂×Q₈×C₇₉⋊C₈	C₂	semidirect
4. #23762275	C₂	semidirect
5. #23762268	C₂	semidirect
6. #23762204	C₂	semidirect
7. #23762197	C₂	semidirect
8. #23762186	C₂	semidirect
10. M₁₆×C₇₉⋊C₈	C₂	semidirect
11. C₇₉×#1491	C₂	semidirect
230. #1491	D₇₉	semidirect
233. C₇₉	#17911	semidirect

Maximal subgroups

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

subgroup	index
#23773480	2
#23772369	2
C₂×Q₈×C₇₉⋊C₈	2
#23762275	2
#23762268	2
#23762204	2
#23762197	2
#23762186	2
#23761814	2
M₁₆×C₇₉⋊C₈	2
C₇₉×#1491	2
#17911	79