Subgroups — #34307961

Order 20224.

722 conjugacy classes of subgroups.

The subgroup lattice has 558 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×#14579181	C₂	1	1	yes	maximal, characteristic
2	#23772068	C₂	1	1	yes	maximal, characteristic, complemented
3	#23772066	C₂	1	1	yes	maximal, characteristic, complemented
4	#23764285	C₂	1	2	yes	maximal
5	#23764051	C₂	1	2	yes	maximal, complemented
6	#23764046	C₂	1	2	yes	maximal, complemented
7	#23763571	C₂	1	1	yes	maximal, characteristic, complemented
8	#23763421	C₂	1	1	yes	maximal, characteristic, complemented
9	#23763278	C₂	1	2	yes	maximal, complemented
10	C₄⋊C₄×C₇₉⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
11	C₇₉×#1806	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#14579181	C₂²	1	1	yes	characteristic
13	C₄×#11929624	C₂²	1	1	yes	characteristic
14	C₄×#11929614	C₄	1	1	yes	characteristic, complemented
15	C₄×#11929614	C₄	1	1	yes	characteristic, complemented
16	C₄×#11929611	C₄	1	1	yes	characteristic, complemented
17	C₄×#11929611	C₄	1	1	yes	characteristic, complemented
18	C₄×#11929612	C₄	1	1	yes	characteristic, complemented
19	C₄×#11929612	C₄	1	1	yes	characteristic, complemented
20	C₄×#11929609	C₄	1	1	yes	characteristic, complemented
21	C₄×#11929609	C₄	1	1	yes	characteristic, complemented
22	#19098624	—	2	2	no	—
23	#19098623	—	2	2	no	—
24	#19098620	—	2	1	no	—
25	#19098619	—	2	1	no	—
26	#19098616	—	2	1	no	—
27	#19098615	—	2	1	no	—
28	C₂×#14579096	C₂²	1	2	yes	—
29	C₂×#14579096	C₂²	1	2	yes	—
30	#19098599	C₂²	1	1	yes	characteristic
31	#19098587	C₂²	1	1	yes	characteristic
32	C₂×C₄⋊(C₇₉⋊C₈)	C₂²	1	1	yes	characteristic
33	C₂×#14579089	C₂²	1	2	yes	—
34	#19098559	C₂²	1	1	yes	characteristic
35	#19098557	C₂²	1	1	yes	characteristic
36	#19098531	C₂²	1	2	yes	—
37	#19098530	C₂²	1	2	yes	—
38	#19098521	C₂²	1	2	yes	—
39	#19098519	C₂²	1	2	yes	—
40	C₂×C₄×C₇₉⋊C₈	C₂²	1	2	yes	—
41	C₂×C₄×C₇₉⋊C₈	C₂²	1	1	yes	characteristic
42	#19098323	C₂²	1	2	yes	—
43	#19098318	C₂²	1	2	yes	—
44	C₄×#41×C₇₉	C₂²	1	1	yes	characteristic
45	#423×C₇₉	C₂²	1	1	yes	characteristic
46	C₂×#104×C₇₉	C₂²	1	2	yes	—
47	C₄×C₄⋊C₄×C₇₉	C₂²	1	1	yes	characteristic
48	#339×C₇₉	C₂²	1	2	yes	—
49	C₂×#11929624	C₂³	1	1	yes	characteristic
50	#14579181	—	2	2	no	—
51	#14579181	—	2	2	no	—
52	C₂×#11929614	C₂×C₄	1	1	yes	characteristic
53	C₂×#11929612	C₂×C₄	1	1	yes	characteristic
54	C₂×#11929611	C₂×C₄	1	1	yes	characteristic
55	C₂×#11929609	C₂×C₄	1	1	yes	characteristic
56	C₂×#11929608	C₂³	1	2	yes	—
57	C₂²×C₇₉⋊C₈	C₂³	1	1	yes	characteristic
58	C₂²×C₇₉⋊C₈	C₂³	1	2	yes	—
59	C₂²×C₇₉⋊C₈	C₂³	1	1	yes	characteristic
60	C₄×Dic₁₅₈	C₂×C₄	1	1	yes	characteristic
61	C₄×Dic₁₅₈	C₂×C₄	1	1	yes	characteristic
62	C₄×D₃₁₆	C₂×C₄	1	1	yes	characteristic
63	C₄×D₃₁₆	C₂×C₄	1	1	yes	characteristic
64	C₄×C₂²⋊D₇₉	—	2	1	no	—
65	C₄×C₂²⋊D₇₉	—	2	1	no	—
66	#14579120	C₂³	1	1	yes	characteristic
67	#14579118	—	2	1	no	—
68	C₄²×D₇₉	—	2	1	no	—
69	#14579096	—	2	4	no	—
70	#14579096	—	4	2	no	—
71	#14579094	C₂×C₄	1	1	yes	characteristic
72	#14579094	C₂×C₄	1	1	yes	characteristic
73	#14579092	C₂×C₄	1	1	yes	characteristic
74	#14579092	C₂×C₄	1	1	yes	characteristic
75	C₄⋊(C₇₉⋊C₈)	—	2	1	no	—
76	C₄⋊(C₇₉⋊C₈)	—	2	1	no	—
77	C₄⋊(C₇₉⋊C₈)	D₄	1	2	yes	—
78	C₄⋊(C₇₉⋊C₈)	D₄	1	1	yes	characteristic
79	C₄⋊(C₇₉⋊C₈)	D₄	1	1	yes	characteristic
80	#14579089	—	4	2	no	—
81	#14579085	C₂×C₄	1	1	yes	characteristic
82	#14579085	C₂×C₄	1	1	yes	characteristic
83	#14579084	C₂×C₄	1	1	yes	characteristic
84	#14579084	C₂×C₄	1	1	yes	characteristic
85	#14579082	C₂×C₄	1	1	yes	characteristic
86	#14579082	C₂×C₄	1	1	yes	characteristic
87	#14579081	C₂×C₄	1	1	yes	characteristic
88	#14579081	C₂×C₄	1	1	yes	characteristic
89	C₂²⋊(C₇₉⋊C₈)	—	2	2	no	—
90	C₂²⋊(C₇₉⋊C₈)	—	2	2	no	—
91	(C₂×D₇₉)⋊C₈	—	2	2	no	—
92	(C₂×D₇₉)⋊C₈	—	2	2	no	—
93	#14579072	—	2	2	no	—
94	#14579071	—	2	2	no	—
95	C₄×C₇₉⋊C₈	—	2	2	no	—
96	C₄×C₇₉⋊C₈	—	2	4	no	—
97	C₄×C₇₉⋊C₈	C₂×C₄	1	1	yes	characteristic
98	C₄×C₇₉⋊C₈	C₂×C₄	1	1	yes	characteristic
99	C₄×C₇₉⋊C₈	C₂×C₄	1	1	yes	characteristic
100	C₄×C₇₉⋊C₈	C₂×C₄	1	1	yes	characteristic
101	C₈×Dic₇₉	—	2	2	no	—
102	C₂×#41×C₇₉	C₂³	1	1	yes	characteristic
103	C₂×M₁₆×C₇₉	C₂³	1	2	yes	—
104	C₄×Q₈×C₇₉	C₂×C₄	1	1	yes	characteristic
105	C₄×Q₈×C₇₉	C₂×C₄	1	1	yes	characteristic
106	C₄×D₄×C₇₉	—	2	1	no	—
107	C₄×D₄×C₇₉	—	2	1	no	—
108	C₄×D₄×C₇₉	C₂×C₄	1	1	yes	characteristic
109	C₄×D₄×C₇₉	C₂×C₄	1	1	yes	characteristic
110	#117×C₇₉	—	2	1	no	—
111	#117×C₇₉	C₂³	1	1	yes	characteristic
112	C₂×C₄⋊C₄×C₇₉	—	2	1	no	—
113	C₂×C₄²×C₇₉	—	2	1	no	—
114	C₂×C₄²×C₇₉	C₂³	1	2	yes	—
115	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
116	C₄⋊C₈×C₇₉	—	2	1	no	—
117	C₄⋊C₈×C₇₉	—	2	1	no	—
118	#104×C₇₉	—	4	2	no	—
119	#95×C₇₉	—	2	1	no	—
120	#11929624	—	2	1	no	—
121	#11929624	—	2	1	no	—
122	#11929624	—	2	1	no	—
123	#11929624	—	2	1	no	—
124	C₂×Dic₁₅₈	C₂²×C₄	1	1	yes	characteristic
125	C₂×D₃₁₆	C₂²×C₄	1	1	yes	characteristic
126	C₂×C₂²⋊D₇₉	—	2	1	no	—
127	C₂×C₄×D₇₉	—	2	1	no	—
128	C₂×C₄×D₇₉	—	2	1	no	—
129	C₂×C₄×D₇₉	—	2	1	no	—
130	#11929614	—	2	2	no	—
131	#11929612	—	2	2	no	—
132	#11929611	—	2	2	no	—
133	#11929609	—	2	2	no	—
134	#11929608	—	2	2	no	—
135	#11929608	—	2	2	no	—
136	C₂×C₇₉⋊C₈	—	2	2	no	—
137	C₂×C₇₉⋊C₈	—	2	2	no	—
138	C₂×C₇₉⋊C₈	—	2	1	no	—
139	C₂×C₇₉⋊C₈	—	2	1	no	—
140	C₂×C₇₉⋊C₈	—	2	2	no	—
141	C₂×C₇₉⋊C₈	C₂²×C₄	1	1	yes	characteristic
142	C₂×C₇₉⋊C₈	C₂²×C₄	1	1	yes	characteristic
143	C₂×C₇₉⋊C₈	C₂²×C₄	1	1	yes	characteristic
144	C₂×C₇₉⋊C₈	C₂²×C₄	1	1	yes	characteristic
145	C₂×C₇₉⋊C₈	C₂×D₄	1	2	yes	—
146	C₂×C₇₉⋊C₈	C₂×D₄	1	2	yes	—
147	C₂×C₇₉⋊C₈	#41	1	2	yes	—
148	C₂×C₇₉⋊C₈	#41	1	2	yes	—
149	C₄⋊Dic₇₉	C₂²×C₄	1	1	yes	characteristic
150	C₄⋊Dic₇₉	C₂²×C₄	1	1	yes	characteristic
151	Dic₇₉⋊C₄	—	2	1	no	—
152	Dic₇₉⋊C₄	—	2	1	no	—
153	C₂²⋊Dic₇₉	—	2	1	no	—
154	(C₂×D₇₉)⋊C₄	—	2	1	no	—
155	(C₂×D₇₉)⋊C₄	—	2	1	no	—
156	C₄×Dic₇₉	—	2	1	no	—
157	C₄×Dic₇₉	—	2	1	no	—
158	C₄×Dic₇₉	—	2	1	no	—
159	#41×C₇₉	—	2	1	no	—
160	#41×C₇₉	—	2	1	no	—
161	#41×C₇₉	—	2	1	no	—
162	#41×C₇₉	—	2	1	no	—
163	C₂×Q₈×C₇₉	C₂²×C₄	1	1	yes	characteristic
164	C₂×D₄×C₇₉	—	2	1	no	—
165	C₂×D₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
166	C₂²×C₄×C₇₉	—	2	2	no	—
167	C₂²×C₄×C₇₉	—	2	1	no	—
168	C₂²×C₄×C₇₉	—	2	1	no	—
169	C₂²×C₄×C₇₉	—	2	1	no	—
170	C₂²×C₄×C₇₉	#41	1	1	yes	characteristic
171	C₂²×C₄×C₇₉	#41	1	1	yes	characteristic
172	C₂²×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
173	M₁₆×C₇₉	—	2	2	no	—
174	M₁₆×C₇₉	—	2	2	no	—
175	C₂×C₈×C₇₉	—	2	2	no	—
176	C₄⋊C₄×C₇₉	—	2	4	no	—
177	C₄⋊C₄×C₇₉	—	2	1	no	—
178	C₄⋊C₄×C₇₉	—	2	1	no	—
179	C₄⋊C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
180	C₄⋊C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
181	C₂²⋊C₄×C₇₉	—	2	1	no	—
182	C₂²⋊C₄×C₇₉	—	2	1	no	—
183	C₂²⋊C₄×C₇₉	—	2	1	no	—
184	C₄²×C₇₉	—	2	1	no	—
185	C₄²×C₇₉	—	2	1	no	—
186	C₄²×C₇₉	—	2	1	no	—
187	C₄²×C₇₉	—	2	2	no	—
188	C₄²×C₇₉	—	2	2	no	—
189	C₄²×C₇₉	C₂²×C₄	1	1	yes	characteristic
190	C₄²×C₇₉	C₂²×C₄	1	1	yes	characteristic
191	C₄²×C₇₉	C₂×D₄	1	1	yes	characteristic
192	C₄²×C₇₉	C₂×D₄	1	1	yes	characteristic
193	C₂³×C₇₉	—	2	1	no	—
194	C₂³×C₇₉	C₂×#41	1	1	yes	characteristic
195	C₂²×D₇₉	—	2	1	no	—
196	Q₈×C₇₉	—	2	1	no	—
197	Q₈×C₇₉	—	2	1	no	—
198	D₄×C₇₉	—	2	1	no	—
199	D₄×C₇₉	—	2	1	no	—
200	D₄×C₇₉	—	4	1	no	—
201	D₄×C₇₉	—	4	1	no	—
202	C₂×C₄×C₇₉	—	2	2	no	—
203	C₂×C₄×C₇₉	—	2	4	no	—
204	C₂×C₄×C₇₉	—	2	1	no	—
205	C₂×C₄×C₇₉	—	2	1	no	—
206	C₂×C₄×C₇₉	—	2	1	no	—
207	C₂×C₄×C₇₉	—	4	1	no	—
208	C₂×C₄×C₇₉	—	4	2	no	—
209	C₂×C₄×C₇₉	—	4	2	no	—
210	C₂×C₄×C₇₉	—	4	1	no	—
211	C₂×C₄×C₇₉	—	4	1	no	—
212	C₂×C₄×C₇₉	—	4	2	no	—
213	C₂×C₄×C₇₉	—	8	1	no	—
214	C₂×C₄×C₇₉	C₄×D₄	1	1	yes	characteristic
215	C₂×C₄×C₇₉	C₄×D₄	1	1	yes	characteristic
216	C₂×C₄×C₇₉	C₄×D₄	1	1	yes	characteristic
217	C₂×C₄×C₇₉	C₄×D₄	1	1	yes	characteristic
218	C₂×C₄×C₇₉	C₂³×C₄	1	1	yes	characteristic
219	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
220	C₂×C₄×C₇₉	C₂×#41	1	1	yes	characteristic
221	C₂×C₄×C₇₉	C₂×#41	1	1	yes	characteristic
222	C₂×C₄×C₇₉	H(5,𝔽₂)	1	1	yes	characteristic
223	C₂×C₄×C₇₉	2₋¹⁺⁴	1	1	yes	characteristic
224	C₂²⋊D₇₉	—	4	1	no	—
225	C₂²⋊D₇₉	—	4	1	no	—
226	C₂×Dic₇₉	—	2	1	no	—
227	C₂×Dic₇₉	—	2	1	no	—
228	C₂×Dic₇₉	—	2	1	no	—
229	D₃₁₆	—	2	1	no	—
230	D₃₁₆	—	2	1	no	—
231	C₄×D₇₉	—	4	1	no	—
232	C₄×D₇₉	—	4	1	no	—
233	C₄×D₇₉	—	4	2	no	—
234	C₄×D₇₉	—	8	1	no	—
235	Dic₁₅₈	—	2	1	no	—
236	Dic₁₅₈	—	2	1	no	—
237	C₈×C₇₉	—	4	2	no	—
238	C₇₉⋊C₈	—	2	1	no	—
239	C₇₉⋊C₈	—	2	1	no	—
240	C₇₉⋊C₈	—	2	2	no	—
241	C₇₉⋊C₈	—	2	2	no	—
242	C₇₉⋊C₈	—	4	2	no	—
243	C₇₉⋊C₈	#117	1	2	yes	—
244	C₇₉⋊C₈	#117	1	2	yes	—
245	C₂²×C₇₉	—	2	1	no	—
246	C₂²×C₇₉	—	2	1	no	—
247	C₂²×C₇₉	—	4	1	no	—
248	C₂²×C₇₉	—	4	1	no	—
249	C₂²×C₇₉	—	4	1	no	—
250	C₂²×C₇₉	C₂×C₄×D₄	1	1	yes	characteristic
251	C₂²×C₇₉	#555	1	1	yes	characteristic
252	C₂²×C₇₉	#556	1	1	yes	characteristic
253	C₂×D₇₉	—	4	1	no	—
254	C₂×D₇₉	—	4	1	no	—
255	C₂×D₇₉	—	4	1	no	—
256	C₄×C₇₉	—	2	1	no	—
257	C₄×C₇₉	—	2	1	no	—
258	C₄×C₇₉	—	2	1	no	—
259	C₄×C₇₉	—	4	4	no	—
260	C₄×C₇₉	—	4	1	no	—
261	C₄×C₇₉	—	4	1	no	—
262	C₄×C₇₉	—	4	1	no	—
263	C₄×C₇₉	#443	1	2	yes	—
264	C₄×C₇₉	C₂×#117	1	1	yes	characteristic
265	C₄×C₇₉	#520	1	1	yes	characteristic
266	C₄×C₇₉	#547	1	1	yes	characteristic
267	C₄×C₇₉	#550	1	1	yes	characteristic
268	Dic₇₉	—	4	1	no	—
269	Dic₇₉	—	4	1	no	—
270	Dic₇₉	—	4	1	no	—
271	#22802	—	79	1	no	maximal, Sylow
272	C₂×C₇₉	—	2	1	no	—
273	C₂×C₇₉	—	2	1	no	—
274	C₂×C₇₉	—	8	1	no	—
275	C₂×C₇₉	#2354	1	1	yes	characteristic
276	C₂×C₇₉	C₂×#443	1	1	yes	characteristic
277	C₂×C₇₉	#2957	1	1	yes	characteristic
278	D₇₉	—	8	1	no	—
279	C₄×#135	—	79	1	no	—
280	#2925	—	79	1	no	—
281	#2925	—	79	1	no	—
282	#1974	—	79	2	no	—
283	#1929	—	79	2	no	—
284	#1929	—	79	2	no	—
285	#1848	—	79	1	no	—
286	#1806	—	79	1	no	—
287	#1806	D₇₉	1	1	yes	characteristic, complemented
288	#1772	—	79	2	no	—
289	C₈×C₄⋊C₄	—	79	1	no	—
290	C₇₉	#22802	1	1	yes	characteristic, complemented, Sylow
291	C₂×#135	—	79	1	no	—
292	C₄×#41	—	79	1	no	—
293	C₄×#41	C₂×D₇₉	1	1	yes	characteristic
294	C₄×Q₁₆	—	79	1	no	—
295	C₄×Q₁₆	—	79	1	no	—
296	C₄×SD₁₆	—	79	1	no	—
297	C₄×SD₁₆	—	79	1	no	—
298	C₄×SD₁₆	—	79	1	no	—
299	C₄×SD₁₆	—	79	1	no	—
300	C₄×D₈	—	79	1	no	—
301	C₄×D₈	—	79	1	no	—
302	#433	—	158	2	no	—
303	#433	—	158	2	no	—
304	#432	—	158	1	no	—
305	#432	—	158	1	no	—
306	#431	—	158	1	no	—
307	#431	—	158	1	no	—
308	C₂×#108	—	79	2	no	—
309	C₂×#108	—	79	2	no	—
310	#427	—	79	1	no	—
311	#423	—	79	1	no	—
312	#423	C₂×D₇₉	1	1	yes	characteristic
313	C₂×C₄⋊C₈	—	79	1	no	—
314	C₂×#104	—	79	2	no	—
315	C₂×#104	C₂×D₇₉	1	2	yes	—
316	#416	—	79	1	no	—
317	#416	—	79	1	no	—
318	#408	—	79	2	no	—
319	#408	—	79	2	no	—
320	#405	—	79	2	no	—
321	#405	—	79	2	no	—
322	C₂×C₄×C₈	—	79	1	no	—
323	C₂×C₄×C₈	—	79	2	no	—
324	C₄×C₄⋊C₄	C₂×D₇₉	1	1	yes	characteristic
325	#339	—	79	2	no	—
326	#339	C₂×D₇₉	1	2	yes	—
327	#336	—	79	2	no	—
328	C₂×#41	—	79	1	no	—
329	C₂×#41	C₂²×D₇₉	1	1	yes	characteristic
330	#135	—	158	2	no	—
331	#135	—	158	2	no	—
332	C₂×Q₁₆	—	79	1	no	—
333	C₂×SD₁₆	—	79	1	no	—
334	C₂×SD₁₆	—	79	1	no	—
335	C₂×D₈	—	79	1	no	—
336	C₂×M₁₆	—	79	2	no	—
337	C₂×M₁₆	C₂²×D₇₉	1	2	yes	—
338	C₂²×C₈	—	79	1	no	—
339	C₂²×C₈	—	79	1	no	—
340	C₂²×C₈	—	79	2	no	—
341	C₄×Q₈	—	79	1	no	—
342	C₄×Q₈	—	79	1	no	—
343	C₄×Q₈	C₄×D₇₉	1	1	yes	characteristic
344	C₄×Q₈	C₄×D₇₉	1	1	yes	characteristic
345	C₄×D₄	—	2	1	no	—
346	C₄×D₄	—	2	1	no	—
347	C₄×D₄	—	79	1	no	—
348	C₄×D₄	—	79	1	no	—
349	C₄×D₄	—	158	1	no	—
350	C₄×D₄	—	158	1	no	—
351	C₄×D₄	C₄×D₇₉	1	1	yes	characteristic
352	C₄×D₄	C₄×D₇₉	1	1	yes	characteristic
353	#117	—	2	1	no	—
354	#117	—	79	1	no	—
355	#117	—	158	1	no	—
356	#117	C₂²×D₇₉	1	1	yes	characteristic
357	C₂×C₄⋊C₄	—	2	1	no	—
358	C₂×C₄²	—	2	1	no	—
359	C₂×C₄²	—	158	1	no	—
360	C₂×C₄²	C₂²×D₇₉	1	2	yes	—
361	C₂×C₄²	C₂²×D₇₉	1	1	yes	characteristic
362	#108	—	316	2	no	—
363	#108	—	158	4	no	—
364	#107	—	79	1	no	—
365	#107	—	79	1	no	—
366	#106	—	79	1	no	—
367	#106	—	79	1	no	—
368	C₄⋊C₈	—	2	1	no	—
369	C₄⋊C₈	—	2	1	no	—
370	C₄⋊C₈	—	79	1	no	—
371	C₄⋊C₈	—	79	1	no	—
372	C₄⋊C₈	—	79	2	no	—
373	C₄⋊C₈	—	158	1	no	—
374	C₄⋊C₈	—	158	1	no	—
375	#104	—	4	2	no	—
376	#104	—	316	2	no	—
377	#103	—	79	1	no	—
378	#103	—	79	1	no	—
379	#103	—	79	1	no	—
380	#103	—	79	1	no	—
381	#102	—	79	1	no	—
382	#102	—	79	1	no	—
383	#102	—	79	1	no	—
384	#102	—	79	1	no	—
385	C₂²⋊C₈	—	158	2	no	—
386	C₂²⋊C₈	—	158	2	no	—
387	C₂²⋊C₈	—	158	2	no	—
388	C₂²⋊C₈	—	158	2	no	—
389	#97	—	158	2	no	—
390	#97	—	158	2	no	—
391	C₄×C₈	—	79	1	no	—
392	C₄×C₈	—	79	1	no	—
393	C₄×C₈	—	79	1	no	—
394	C₄×C₈	—	79	1	no	—
395	C₄×C₈	—	158	4	no	—
396	C₄×C₈	—	158	2	no	—
397	C₄×C₈	—	158	2	no	—
398	#95	—	2	1	no	—
399	#41	—	2	1	no	—
400	#41	—	2	1	no	—
401	#41	—	2	1	no	—
402	#41	—	2	1	no	—
403	#41	—	158	1	no	—
404	#41	—	158	1	no	—
405	#41	—	158	1	no	—
406	#41	—	158	1	no	—
407	C₂×Q₈	—	79	1	no	—
408	C₂×Q₈	C₂×C₄×D₇₉	1	1	yes	characteristic
409	C₂×D₄	—	2	1	no	—
410	C₂×D₄	—	79	1	no	—
411	C₂×D₄	—	158	1	no	—
412	C₂×D₄	C₂×C₄×D₇₉	1	1	yes	characteristic
413	C₂²×C₄	—	2	2	no	—
414	C₂²×C₄	—	2	1	no	—
415	C₂²×C₄	—	2	1	no	—
416	C₂²×C₄	—	2	1	no	—
417	C₂²×C₄	—	158	1	no	—
418	C₂²×C₄	—	158	1	no	—
419	C₂²×C₄	—	158	1	no	—
420	C₂²×C₄	#11929623	1	1	yes	characteristic
421	C₂²×C₄	#11929623	1	1	yes	characteristic
422	C₂²×C₄	C₂³×D₇₉	1	1	yes	characteristic
423	Q₁₆	—	158	2	no	—
424	SD₁₆	—	158	2	no	—
425	SD₁₆	—	158	2	no	—
426	D₈	—	158	2	no	—
427	M₁₆	—	2	2	no	—
428	M₁₆	—	2	2	no	—
429	M₁₆	—	158	2	no	—
430	M₁₆	—	158	2	no	—
431	C₂×C₈	—	2	2	no	—
432	C₂×C₈	—	79	2	no	—
433	C₂×C₈	—	79	2	no	—
434	C₂×C₈	—	79	1	no	—
435	C₂×C₈	—	79	1	no	—
436	C₂×C₈	—	79	1	no	—
437	C₂×C₈	—	79	1	no	—
438	C₂×C₈	—	79	2	no	—
439	C₂×C₈	—	79	2	no	—
440	C₂×C₈	—	158	2	no	—
441	C₂×C₈	—	158	2	no	—
442	C₂×C₈	—	158	1	no	—
443	C₂×C₈	—	158	2	no	—
444	C₂×C₈	—	158	1	no	—
445	C₄⋊C₄	—	2	4	no	—
446	C₄⋊C₄	—	2	1	no	—
447	C₄⋊C₄	—	2	1	no	—
448	C₄⋊C₄	—	79	1	no	—
449	C₄⋊C₄	—	79	1	no	—
450	C₄⋊C₄	—	158	1	no	—
451	C₄⋊C₄	—	158	1	no	—
452	C₄⋊C₄	C₂×C₄×D₇₉	1	1	yes	characteristic
453	C₄⋊C₄	C₂×C₄×D₇₉	1	1	yes	characteristic
454	C₂²⋊C₄	—	2	1	no	—
455	C₂²⋊C₄	—	2	1	no	—
456	C₂²⋊C₄	—	2	1	no	—
457	C₂²⋊C₄	—	158	1	no	—
458	C₂²⋊C₄	—	158	1	no	—
459	C₂²⋊C₄	—	158	1	no	—
460	C₄²	—	2	1	no	—
461	C₄²	—	2	1	no	—
462	C₄²	—	2	1	no	—
463	C₄²	—	2	2	no	—
464	C₄²	—	2	2	no	—
465	C₄²	—	158	1	no	—
466	C₄²	—	158	1	no	—
467	C₄²	—	158	1	no	—
468	C₄²	C₂×C₄×D₇₉	1	1	yes	characteristic
469	C₄²	C₂×C₄×D₇₉	1	1	yes	characteristic
470	C₄²	D₄×D₇₉	1	1	yes	characteristic
471	C₄²	D₄×D₇₉	1	1	yes	characteristic
472	C₂³	—	2	1	no	—
473	C₂³	—	158	1	no	—
474	C₂³	C₂×#11929623	1	1	yes	characteristic
475	Q₈	—	2	1	no	—
476	Q₈	—	2	1	no	—
477	Q₈	—	158	1	no	—
478	Q₈	—	158	1	no	—
479	D₄	—	2	1	no	—
480	D₄	—	2	1	no	—
481	D₄	—	4	1	no	—
482	D₄	—	4	1	no	—
483	D₄	—	316	1	no	—
484	D₄	—	316	1	no	—
485	D₄	—	158	1	no	—
486	D₄	—	158	1	no	—
487	C₂×C₄	—	2	2	no	—
488	C₂×C₄	—	2	4	no	—
489	C₂×C₄	—	2	1	no	—
490	C₂×C₄	—	2	1	no	—
491	C₂×C₄	—	2	1	no	—
492	C₂×C₄	—	4	1	no	—
493	C₂×C₄	—	4	2	no	—
494	C₂×C₄	—	4	2	no	—
495	C₂×C₄	—	4	2	no	—
496	C₂×C₄	—	4	1	no	—
497	C₂×C₄	—	4	1	no	—
498	C₂×C₄	—	8	1	no	—
499	C₂×C₄	—	316	2	no	—
500	C₂×C₄	—	316	1	no	—
501	C₂×C₄	—	316	1	no	—
502	C₂×C₄	—	632	1	no	—
503	C₂×C₄	—	158	1	no	—
504	C₂×C₄	—	158	1	no	—
505	C₂×C₄	—	158	1	no	—
506	C₂×C₄	(C₂²⋊D₇₉)⋊C₄	1	1	yes	characteristic
507	C₂×C₄	(C₂²⋊D₇₉)⋊C₄	1	1	yes	characteristic
508	C₂×C₄	(C₂²⋊D₇₉)⋊C₄	1	1	yes	characteristic
509	C₂×C₄	(C₂²⋊D₇₉)⋊C₄	1	1	yes	characteristic
510	C₂×C₄	C₂²×C₄×D₇₉	1	1	yes	characteristic
511	C₂×C₄	C₂×D₄×D₇₉	1	1	yes	characteristic
512	C₂×C₄	#41×D₇₉	1	1	yes	characteristic
513	C₂×C₄	#41×D₇₉	1	1	yes	characteristic
514	C₂×C₄	#14579206	1	1	yes	characteristic
515	C₂×C₄	#14579209	1	1	yes	characteristic
516	C₈	—	4	2	no	—
517	C₈	—	316	2	no	—
518	C₈	—	79	2	no	—
519	C₈	—	79	2	no	—
520	C₈	—	158	2	no	—
521	C₈	—	158	2	no	—
522	C₈	—	158	1	no	—
523	C₈	—	158	1	no	—
524	C₂²	—	2	1	no	—
525	C₂²	—	2	1	no	—
526	C₂²	—	4	1	no	—
527	C₂²	—	4	1	no	—
528	C₂²	—	4	1	no	—
529	C₂²	—	316	1	no	—
530	C₂²	—	316	1	no	—
531	C₂²	—	316	1	no	—
532	C₂²	C₂×(C₂²⋊D₇₉)⋊C₄	1	1	yes	characteristic
533	C₂²	#19099277	1	1	yes	characteristic
534	C₂²	#19099284	1	1	yes	characteristic
535	C₄	—	2	1	no	—
536	C₄	—	2	1	no	—
537	C₄	—	2	1	no	—
538	C₄	—	4	4	no	—
539	C₄	—	4	1	no	—
540	C₄	—	4	1	no	—
541	C₄	—	4	1	no	—
542	C₄	—	316	1	no	—
543	C₄	—	316	1	no	—
544	C₄	—	316	1	no	—
545	C₄	#19098677	1	2	yes	—
546	C₄	#117×D₇₉	1	1	yes	characteristic
547	C₄	#19099044	1	1	yes	characteristic
548	C₄	#19099215	1	1	yes	characteristic
549	C₄	#19099231	1	1	yes	characteristic
550	C₂	—	2	1	no	—
551	C₂	—	2	1	no	—
552	C₂	—	8	1	no	—
553	C₂	—	632	1	no	—
554	C₂	#23766344	1	1	yes	characteristic
555	C₂	C₂×#19098677	1	1	yes	characteristic
556	C₂	#23772313	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₇₉
commutator	C₂×C₄×C₇₉	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₇₉
Fitting	C₇₉×#1806	C₂
socle	C₂²×C₇₉	C₂×C₄×D₄
prime radical	C₂×#14579181	C₂²
cosocle	C₂²×C₄×C₇₉	C₂⁴
hypercenter	#1806	D₇₉
hypocenter	C₇₉	#22802
LCS	G ▷ C₂×C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1806

Complements

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

N	H ≅ G/N	type
2. #23772068	C₂	semidirect
3. #23772066	C₂	semidirect
5. #23764051	C₂	semidirect
6. #23764046	C₂	semidirect
7. #23763571	C₂	semidirect
8. #23763421	C₂	semidirect
9. #23763278	C₂	semidirect
10. C₄⋊C₄×C₇₉⋊C₈	C₂	semidirect
11. C₇₉×#1806	C₂	semidirect
14. C₄×#11929614	C₄	semidirect
15. C₄×#11929614	C₄	semidirect
16. C₄×#11929611	C₄	semidirect
17. C₄×#11929611	C₄	semidirect
18. C₄×#11929612	C₄	semidirect
19. C₄×#11929612	C₄	semidirect
20. C₄×#11929609	C₄	semidirect
21. C₄×#11929609	C₄	semidirect
287. #1806	D₇₉	semidirect
290. C₇₉	#22802	semidirect

Maximal subgroups

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

subgroup	index
C₄×#14579181	2
#23772068	2
#23772066	2
#23764285	2
#23764051	2
#23764046	2
#23763571	2
#23763421	2
#23763278	2
C₄⋊C₄×C₇₉⋊C₈	2
C₇₉×#1806	2
#22802	79