Subgroups — #34178223

Order 20224.

568 conjugacy classes of subgroups.

The subgroup lattice has 460 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#23772032	C₂	1	1	yes	maximal, characteristic
2	C₂×#19098619	C₂	1	1	yes	maximal, characteristic
3	#423×D₇₉	C₂	1	1	yes	maximal, characteristic
4	#23761275	C₂	1	1	yes	maximal, characteristic, complemented
5	#23761274	C₂	1	1	yes	maximal, characteristic, complemented
6	#23761274	C₂	1	1	yes	maximal, characteristic, complemented
7	C₇₉×#1292	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×M₁₆×D₇₉	—	2	1	no	—
9	C₂×C₄²×D₇₉	C₂²	1	1	yes	characteristic
10	#19098619	—	2	1	no	—
11	#19098619	—	2	1	no	—
12	#19098619	—	2	1	no	—
13	#19098619	—	2	1	no	—
14	#19098619	—	2	1	no	—
15	#19098619	C₄	1	2	yes	—
16	#19098615	—	2	1	no	—
17	#19098615	C₄	1	2	yes	—
18	#19098587	C₂²	1	1	yes	characteristic
19	#19098587	C₂²	1	1	yes	characteristic
20	#19098586	—	2	1	no	—
21	#19098585	—	2	1	no	—
22	#19098585	C₄	1	2	yes	—
23	C₂×C₄⋊(C₇₉⋊C₈)	C₂²	1	1	yes	characteristic
24	C₄⋊C₈×D₇₉	—	2	1	no	—
25	C₄⋊C₈×D₇₉	C₄	1	2	yes	—
26	#19098526	—	2	1	no	—
27	C₂×(C₂×D₇₉)⋊C₈	C₄	1	2	yes	—
28	M₁₆×Dic₇₉	—	2	1	no	—
29	C₂×#14579071	C₄	1	2	yes	—
30	#423×C₇₉	C₂²	1	1	yes	characteristic
31	#423×C₇₉	C₂²	1	1	yes	characteristic
32	C₂×C₄⋊C₈×C₇₉	C₂²	1	1	yes	characteristic
33	C₂²×C₄×D₇₉	C₂×C₄	1	1	yes	characteristic
34	C₂²×C₄×D₇₉	D₄	1	1	yes	characteristic
35	C₂²×C₄×D₇₉	Q₈	1	1	yes	characteristic
36	C₂×#11929608	—	2	1	no	—
37	C₂×#11929608	—	2	1	no	—
38	C₂×#11929607	—	2	2	no	—
39	M₁₆×D₇₉	—	4	2	no	—
40	M₁₆×D₇₉	—	4	2	no	—
41	C₂²×C₇₉⋊C₈	C₂×C₄	1	2	yes	—
42	C₂×C₈×D₇₉	—	2	2	no	—
43	C₂×C₄×Dic₇₉	C₂×C₄	1	1	yes	characteristic
44	C₂×C₄×Dic₇₉	D₄	1	1	yes	characteristic
45	C₂×C₄×Dic₇₉	Q₈	1	1	yes	characteristic
46	C₄²×D₇₉	C₂×C₄	1	1	yes	characteristic
47	C₄²×D₇₉	C₂×C₄	1	1	yes	characteristic
48	C₄²×D₇₉	C₂×C₄	1	1	yes	characteristic
49	C₄²×D₇₉	C₂×C₄	1	1	yes	characteristic
50	C₄²×D₇₉	D₄	1	1	yes	characteristic
51	C₄²×D₇₉	D₄	1	1	yes	characteristic
52	C₄²×D₇₉	D₄	1	1	yes	characteristic
53	C₄²×D₇₉	D₄	1	1	yes	characteristic
54	C₄⋊(C₇₉⋊C₈)	—	2	1	no	—
55	C₄⋊(C₇₉⋊C₈)	—	2	1	no	—
56	C₄⋊(C₇₉⋊C₈)	—	2	1	no	—
57	C₄⋊(C₇₉⋊C₈)	—	2	1	no	—
58	C₄⋊(C₇₉⋊C₈)	C₂×C₄	1	2	yes	—
59	C₄⋊(C₇₉⋊C₈)	C₂×C₄	1	2	yes	—
60	Dic₇₉⋊C₈	—	2	2	no	—
61	Dic₇₉⋊C₈	—	2	2	no	—
62	(C₂×D₇₉)⋊C₈	—	2	2	no	—
63	(C₂×D₇₉)⋊C₈	—	2	2	no	—
64	(C₂×D₇₉)⋊C₈	—	2	2	no	—
65	(C₂×D₇₉)⋊C₈	—	2	2	no	—
66	#14579071	—	2	2	no	—
67	#14579071	—	2	2	no	—
68	#14579071	—	2	2	no	—
69	C₈×Dic₇₉	—	2	2	no	—
70	C₂×M₁₆×C₇₉	—	2	1	no	—
71	C₂×M₁₆×C₇₉	—	2	1	no	—
72	C₂²×C₈×C₇₉	C₂×C₄	1	2	yes	—
73	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
74	C₄⋊C₈×C₇₉	—	2	1	no	—
75	C₄⋊C₈×C₇₉	—	2	1	no	—
76	C₄⋊C₈×C₇₉	—	2	1	no	—
77	C₄⋊C₈×C₇₉	—	2	1	no	—
78	C₄⋊C₈×C₇₉	C₂×C₄	1	2	yes	—
79	C₄⋊C₈×C₇₉	C₂×C₄	1	2	yes	—
80	C₂³×D₇₉	C₄⋊C₄	1	1	yes	characteristic
81	C₂²×Dic₇₉	C₄⋊C₄	1	1	yes	characteristic
82	C₂²×Dic₇₉	C₄⋊C₄	1	1	yes	characteristic
83	C₂²×Dic₇₉	C₄⋊C₄	1	1	yes	characteristic
84	C₂×C₄×D₇₉	—	2	1	no	—
85	C₂×C₄×D₇₉	—	2	1	no	—
86	C₂×C₄×D₇₉	—	2	1	no	—
87	C₂×C₄×D₇₉	—	2	1	no	—
88	C₂×C₄×D₇₉	—	4	1	no	—
89	C₂×C₄×D₇₉	—	4	1	no	—
90	C₂×C₄×D₇₉	—	4	2	no	—
91	C₂×C₄×D₇₉	C₄²	1	1	yes	characteristic
92	C₂×C₄×D₇₉	C₄²	1	1	yes	characteristic
93	C₂×C₄×D₇₉	C₂²⋊C₄	1	1	yes	characteristic
94	C₂×C₄×D₇₉	C₂²⋊C₄	1	1	yes	characteristic
95	C₂×C₄×D₇₉	C₂²⋊C₄	1	1	yes	characteristic
96	C₂×C₄×D₇₉	C₂²⋊C₄	1	1	yes	characteristic
97	C₂×C₄×D₇₉	C₂²⋊C₄	1	1	yes	characteristic
98	C₂×C₄×D₇₉	C₂²⋊C₄	1	1	yes	characteristic
99	C₂×C₄×D₇₉	C₄⋊C₄	1	1	yes	characteristic
100	C₂×C₄×D₇₉	C₄⋊C₄	1	1	yes	characteristic
101	C₂×C₄×D₇₉	C₄⋊C₄	1	1	yes	characteristic
102	C₂×C₄×D₇₉	C₄⋊C₄	1	1	yes	characteristic
103	#11929608	—	4	1	no	—
104	#11929608	—	4	1	no	—
105	#11929608	—	4	1	no	—
106	#11929608	—	4	1	no	—
107	#11929607	—	4	4	no	—
108	C₂×C₇₉⋊C₈	—	2	2	no	—
109	C₂×C₇₉⋊C₈	—	2	2	no	—
110	C₂×C₇₉⋊C₈	—	2	2	no	—
111	C₂×C₇₉⋊C₈	—	4	2	no	—
112	C₈×D₇₉	—	4	4	no	—
113	C₄×Dic₇₉	C₄²	1	1	yes	characteristic
114	C₄×Dic₇₉	C₄²	1	1	yes	characteristic
115	C₄×Dic₇₉	C₂²⋊C₄	1	1	yes	characteristic
116	C₄×Dic₇₉	C₂²⋊C₄	1	1	yes	characteristic
117	C₄×Dic₇₉	C₂²⋊C₄	1	1	yes	characteristic
118	C₄×Dic₇₉	C₂²⋊C₄	1	1	yes	characteristic
119	C₄×Dic₇₉	C₂²⋊C₄	1	1	yes	characteristic
120	C₄×Dic₇₉	C₂²⋊C₄	1	1	yes	characteristic
121	C₄×Dic₇₉	C₄⋊C₄	1	1	yes	characteristic
122	C₄×Dic₇₉	C₄⋊C₄	1	1	yes	characteristic
123	C₄×Dic₇₉	C₄⋊C₄	1	1	yes	characteristic
124	C₄×Dic₇₉	C₄⋊C₄	1	1	yes	characteristic
125	C₂²×C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
126	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
127	C₂²×C₄×C₇₉	C₂×Q₈	1	1	yes	characteristic
128	M₁₆×C₇₉	—	4	1	no	—
129	M₁₆×C₇₉	—	4	1	no	—
130	M₁₆×C₇₉	—	4	1	no	—
131	M₁₆×C₇₉	—	4	1	no	—
132	C₂×C₈×C₇₉	—	2	2	no	—
133	C₂×C₈×C₇₉	—	2	2	no	—
134	C₂×C₈×C₇₉	—	2	2	no	—
135	C₂×C₈×C₇₉	—	4	2	no	—
136	C₄²×C₇₉	C₂²×C₄	1	1	yes	characteristic
137	C₄²×C₇₉	C₂²×C₄	1	1	yes	characteristic
138	C₄²×C₇₉	C₂×D₄	1	1	yes	characteristic
139	C₄²×C₇₉	C₂×D₄	1	1	yes	characteristic
140	C₂³×C₇₉	C₂×C₄⋊C₄	1	1	yes	characteristic
141	C₂²×D₇₉	—	2	1	no	—
142	C₂²×D₇₉	—	2	1	no	—
143	C₂²×D₇₉	—	2	2	no	—
144	C₂²×D₇₉	—	4	1	no	—
145	C₂²×D₇₉	#95	1	1	yes	characteristic
146	C₂²×D₇₉	#95	1	1	yes	characteristic
147	C₂×C₄×C₇₉	—	2	1	no	—
148	C₂×C₄×C₇₉	—	2	1	no	—
149	C₂×C₄×C₇₉	—	4	1	no	—
150	C₂×C₄×C₇₉	C₂×C₄²	1	1	yes	characteristic
151	C₂×C₄×C₇₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
152	C₂×C₄×C₇₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
153	C₂×C₄×C₇₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
154	C₂×C₄×C₇₉	C₂×C₄⋊C₄	1	1	yes	characteristic
155	C₂×C₄×C₇₉	C₂×C₄⋊C₄	1	1	yes	characteristic
156	C₂×C₄×C₇₉	AGL(1,ℤ/8)	1	1	yes	characteristic
157	C₂×C₄×C₇₉	AGL(1,ℤ/8)	1	1	yes	characteristic
158	C₂×C₄×C₇₉	#137	1	1	yes	characteristic
159	C₂×C₄×C₇₉	#137	1	1	yes	characteristic
160	C₂×Dic₇₉	—	2	1	no	—
161	C₂×Dic₇₉	—	2	1	no	—
162	C₂×Dic₇₉	—	4	1	no	—
163	C₂×Dic₇₉	—	4	1	no	—
164	C₂×Dic₇₉	#95	1	1	yes	characteristic
165	C₂×Dic₇₉	#95	1	1	yes	characteristic
166	C₂×Dic₇₉	#95	1	1	yes	characteristic
167	C₂×Dic₇₉	#95	1	1	yes	characteristic
168	C₂×Dic₇₉	#95	1	1	yes	characteristic
169	C₂×Dic₇₉	#95	1	1	yes	characteristic
170	C₄×D₇₉	—	2	2	no	—
171	C₄×D₇₉	—	2	2	no	—
172	C₄×D₇₉	—	2	1	no	—
173	C₄×D₇₉	—	2	1	no	—
174	C₄×D₇₉	—	2	1	no	—
175	C₄×D₇₉	—	2	1	no	—
176	C₄×D₇₉	—	2	1	no	—
177	C₄×D₇₉	—	2	1	no	—
178	C₄×D₇₉	—	2	1	no	—
179	C₄×D₇₉	—	2	1	no	—
180	C₄×D₇₉	—	2	1	no	—
181	C₄×D₇₉	—	2	1	no	—
182	C₄×D₇₉	—	2	1	no	—
183	C₄×D₇₉	—	2	1	no	—
184	C₄×D₇₉	—	4	1	no	—
185	C₄×D₇₉	—	4	1	no	—
186	C₄×D₇₉	—	4	1	no	—
187	C₄×D₇₉	—	4	1	no	—
188	C₈×C₇₉	—	4	2	no	—
189	C₈×C₇₉	—	4	2	no	—
190	C₈×C₇₉	—	4	2	no	—
191	C₇₉⋊C₈	—	4	2	no	—
192	C₇₉⋊C₈	—	4	2	no	—
193	C₇₉⋊C₈	—	4	2	no	—
194	C₂²×C₇₉	—	2	1	no	—
195	C₂²×C₇₉	—	2	1	no	—
196	C₂²×C₇₉	C₂×#95	1	1	yes	characteristic
197	C₂²×C₇₉	#428	1	1	yes	characteristic
198	C₂²×C₇₉	#428	1	1	yes	characteristic
199	C₂×D₇₉	—	2	1	no	—
200	C₂×D₇₉	—	2	1	no	—
201	C₂×D₇₉	—	2	1	no	—
202	C₂×D₇₉	—	2	1	no	—
203	C₂×D₇₉	—	2	1	no	—
204	C₂×D₇₉	—	4	2	no	—
205	C₂×D₇₉	—	4	2	no	—
206	C₂×D₇₉	#338	1	2	yes	—
207	C₄×C₇₉	—	2	1	no	—
208	C₄×C₇₉	—	2	1	no	—
209	C₄×C₇₉	—	2	1	no	—
210	C₄×C₇₉	#413	1	1	yes	characteristic
211	C₄×C₇₉	#413	1	1	yes	characteristic
212	C₄×C₇₉	#417	1	1	yes	characteristic
213	C₄×C₇₉	#417	1	1	yes	characteristic
214	C₄×C₇₉	#418	1	1	yes	characteristic
215	C₄×C₇₉	#419	1	1	yes	characteristic
216	Dic₇₉	—	2	1	no	—
217	Dic₇₉	—	2	1	no	—
218	Dic₇₉	—	2	1	no	—
219	Dic₇₉	—	2	1	no	—
220	Dic₇₉	—	2	1	no	—
221	Dic₇₉	—	2	1	no	—
222	#8003	—	79	1	no	maximal, Sylow
223	C₂×C₇₉	—	2	1	no	—
224	C₂×C₇₉	—	2	1	no	—
225	C₂×C₇₉	C₂×#338	1	1	yes	characteristic
226	C₂×C₇₉	#1736	1	1	yes	characteristic
227	C₂×C₇₉	#1742	1	1	yes	characteristic
228	D₇₉	—	2	2	no	—
229	D₇₉	—	4	1	no	—
230	#2920	—	79	1	no	—
231	C₂×#432	—	79	1	no	—
232	C₂×#423	—	79	1	no	—
233	#1292	—	79	1	no	—
234	#1292	—	79	1	no	—
235	#1292	—	79	1	no	—
236	#1292	D₇₉	1	1	yes	characteristic, complemented
237	C₇₉	#8003	1	1	yes	characteristic, complemented, Sylow
238	C₂²×M₁₆	—	158	1	no	—
239	C₂²×C₄²	—	79	1	no	—
240	#432	—	79	2	no	—
241	#432	—	158	1	no	—
242	#432	—	158	1	no	—
243	#432	—	158	1	no	—
244	#432	—	158	1	no	—
245	#432	—	158	1	no	—
246	#431	—	79	2	no	—
247	#431	—	158	1	no	—
248	#423	—	79	1	no	—
249	#423	—	79	1	no	—
250	#423	—	79	2	no	—
251	#423	—	158	1	no	—
252	#423	—	158	1	no	—
253	#423	C₂×D₇₉	1	1	yes	characteristic
254	#423	C₂×D₇₉	1	1	yes	characteristic
255	C₂×C₄⋊C₈	—	79	2	no	—
256	C₂×C₄⋊C₈	—	79	1	no	—
257	C₂×C₄⋊C₈	—	158	1	no	—
258	C₂×C₄⋊C₈	C₂×D₇₉	1	1	yes	characteristic
259	#407	—	158	1	no	—
260	C₂×C₂²⋊C₈	—	79	2	no	—
261	C₄×M₁₆	—	158	1	no	—
262	C₂×#97	—	79	2	no	—
263	C₂³×C₄	—	79	1	no	—
264	C₂³×C₄	—	79	1	no	—
265	C₂³×C₄	—	79	1	no	—
266	C₂×M₁₆	—	2	1	no	—
267	C₂×M₁₆	—	2	1	no	—
268	C₂×M₁₆	—	316	2	no	—
269	C₂×M₁₆	—	316	2	no	—
270	C₂×M₁₆	—	158	2	no	—
271	C₂×M₁₆	—	158	1	no	—
272	C₂×M₁₆	—	158	1	no	—
273	C₂²×C₈	—	79	2	no	—
274	C₂²×C₈	—	158	2	no	—
275	C₂²×C₈	C₄×D₇₉	1	2	yes	—
276	C₂×C₄²	—	79	1	no	—
277	C₂×C₄²	—	79	1	no	—
278	C₂×C₄²	—	79	1	no	—
279	C₂×C₄²	—	79	1	no	—
280	C₂×C₄²	—	79	1	no	—
281	C₂×C₄²	—	79	1	no	—
282	C₂×C₄²	—	79	1	no	—
283	C₂×C₄²	—	79	1	no	—
284	C₂×C₄²	—	79	1	no	—
285	C₂×C₄²	—	79	1	no	—
286	C₂×C₄²	—	79	1	no	—
287	C₂×C₄²	C₂²×D₇₉	1	1	yes	characteristic
288	C₄⋊C₈	—	2	1	no	—
289	C₄⋊C₈	—	2	1	no	—
290	C₄⋊C₈	—	2	1	no	—
291	C₄⋊C₈	—	2	1	no	—
292	C₄⋊C₈	—	79	2	no	—
293	C₄⋊C₈	—	79	2	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	—	158	1	no	—
299	C₄⋊C₈	—	158	1	no	—
300	C₄⋊C₈	C₄×D₇₉	1	2	yes	—
301	C₄⋊C₈	C₄×D₇₉	1	2	yes	—
302	C₂²⋊C₈	—	158	2	no	—
303	C₂²⋊C₈	—	158	2	no	—
304	C₂²⋊C₈	—	158	2	no	—
305	C₂²⋊C₈	—	158	2	no	—
306	#97	—	158	2	no	—
307	#97	—	158	2	no	—
308	#97	—	158	2	no	—
309	C₄×C₈	—	158	2	no	—
310	C₂⁴	—	79	1	no	—
311	C₂²×C₄	—	316	1	no	—
312	C₂²×C₄	—	316	1	no	—
313	C₂²×C₄	—	316	2	no	—
314	C₂²×C₄	—	79	1	no	—
315	C₂²×C₄	—	79	1	no	—
316	C₂²×C₄	—	79	1	no	—
317	C₂²×C₄	—	79	1	no	—
318	C₂²×C₄	—	79	1	no	—
319	C₂²×C₄	—	79	1	no	—
320	C₂²×C₄	—	79	1	no	—
321	C₂²×C₄	—	79	1	no	—
322	C₂²×C₄	—	79	1	no	—
323	C₂²×C₄	—	79	1	no	—
324	C₂²×C₄	—	79	1	no	—
325	C₂²×C₄	—	79	1	no	—
326	C₂²×C₄	—	79	1	no	—
327	C₂²×C₄	—	79	1	no	—
328	C₂²×C₄	—	79	1	no	—
329	C₂²×C₄	—	158	1	no	—
330	C₂²×C₄	—	158	1	no	—
331	C₂²×C₄	—	158	1	no	—
332	C₂²×C₄	—	158	1	no	—
333	C₂²×C₄	C₂×C₄×D₇₉	1	1	yes	characteristic
334	C₂²×C₄	D₄×D₇₉	1	1	yes	characteristic
335	C₂²×C₄	Q₈×D₇₉	1	1	yes	characteristic
336	M₁₆	—	4	1	no	—
337	M₁₆	—	4	1	no	—
338	M₁₆	—	4	1	no	—
339	M₁₆	—	4	1	no	—
340	M₁₆	—	316	4	no	—
341	M₁₆	—	316	1	no	—
342	M₁₆	—	316	1	no	—
343	M₁₆	—	316	1	no	—
344	M₁₆	—	316	1	no	—
345	C₂×C₈	—	2	2	no	—
346	C₂×C₈	—	2	2	no	—
347	C₂×C₈	—	2	2	no	—
348	C₂×C₈	—	4	2	no	—
349	C₂×C₈	—	316	4	no	—
350	C₂×C₈	—	316	2	no	—
351	C₂×C₈	—	158	2	no	—
352	C₂×C₈	—	158	2	no	—
353	C₂×C₈	—	158	2	no	—
354	C₄²	—	79	1	no	—
355	C₄²	—	79	1	no	—
356	C₄²	—	79	1	no	—
357	C₄²	—	79	1	no	—
358	C₄²	—	79	1	no	—
359	C₄²	—	79	1	no	—
360	C₄²	—	79	1	no	—
361	C₄²	—	79	1	no	—
362	C₄²	—	79	1	no	—
363	C₄²	—	79	1	no	—
364	C₄²	—	79	1	no	—
365	C₄²	—	79	1	no	—
366	C₄²	C₂×C₄×D₇₉	1	1	yes	characteristic
367	C₄²	C₂×C₄×D₇₉	1	1	yes	characteristic
368	C₄²	D₄×D₇₉	1	1	yes	characteristic
369	C₄²	D₄×D₇₉	1	1	yes	characteristic
370	C₂³	—	316	1	no	—
371	C₂³	—	79	1	no	—
372	C₂³	—	79	1	no	—
373	C₂³	—	158	2	no	—
374	C₂³	—	158	1	no	—
375	C₂³	—	158	1	no	—
376	C₂³	C₄⋊C₄×D₇₉	1	1	yes	characteristic
377	C₂×C₄	—	2	1	no	—
378	C₂×C₄	—	2	1	no	—
379	C₂×C₄	—	4	1	no	—
380	C₂×C₄	—	316	1	no	—
381	C₂×C₄	—	316	1	no	—
382	C₂×C₄	—	316	1	no	—
383	C₂×C₄	—	316	1	no	—
384	C₂×C₄	—	316	1	no	—
385	C₂×C₄	—	316	1	no	—
386	C₂×C₄	—	79	1	no	—
387	C₂×C₄	—	79	1	no	—
388	C₂×C₄	—	79	1	no	—
389	C₂×C₄	—	79	1	no	—
390	C₂×C₄	—	79	1	no	—
391	C₂×C₄	—	79	1	no	—
392	C₂×C₄	—	158	2	no	—
393	C₂×C₄	—	158	2	no	—
394	C₂×C₄	—	158	1	no	—
395	C₂×C₄	—	158	1	no	—
396	C₂×C₄	—	158	1	no	—
397	C₂×C₄	—	158	1	no	—
398	C₂×C₄	—	158	1	no	—
399	C₂×C₄	—	158	1	no	—
400	C₂×C₄	—	158	1	no	—
401	C₂×C₄	—	158	1	no	—
402	C₂×C₄	—	158	1	no	—
403	C₂×C₄	—	158	1	no	—
404	C₂×C₄	—	158	1	no	—
405	C₂×C₄	—	158	1	no	—
406	C₂×C₄	—	158	1	no	—
407	C₂×C₄	—	158	1	no	—
408	C₂×C₄	C₄²×D₇₉	1	1	yes	characteristic
409	C₂×C₄	C₂²⋊C₄×D₇₉	1	1	yes	characteristic
410	C₂×C₄	C₂²⋊C₄×D₇₉	1	1	yes	characteristic
411	C₂×C₄	C₂²⋊C₄×D₇₉	1	1	yes	characteristic
412	C₂×C₄	C₄⋊C₄×D₇₉	1	1	yes	characteristic
413	C₂×C₄	C₄⋊C₄×D₇₉	1	1	yes	characteristic
414	C₂×C₄	#14579185	1	1	yes	characteristic
415	C₂×C₄	#14579188	1	1	yes	characteristic
416	C₂×C₄	#14579190	1	1	yes	characteristic
417	C₂×C₄	#14579193	1	1	yes	characteristic
418	C₈	—	4	2	no	—
419	C₈	—	4	2	no	—
420	C₈	—	4	2	no	—
421	C₈	—	316	2	no	—
422	C₈	—	316	2	no	—
423	C₈	—	316	2	no	—
424	C₂²	—	2	1	no	—
425	C₂²	—	2	1	no	—
426	C₂²	—	316	2	no	—
427	C₂²	—	316	2	no	—
428	C₂²	—	79	2	no	—
429	C₂²	—	158	1	no	—
430	C₂²	—	158	1	no	—
431	C₂²	—	158	1	no	—
432	C₂²	—	158	1	no	—
433	C₂²	—	158	1	no	—
434	C₂²	#95×D₇₉	1	1	yes	characteristic
435	C₂²	#19098602	1	1	yes	characteristic
436	C₂²	#19098604	1	1	yes	characteristic
437	C₄	—	2	1	no	—
438	C₄	—	2	1	no	—
439	C₄	—	2	1	no	—
440	C₄	—	158	1	no	—
441	C₄	—	158	1	no	—
442	C₄	—	158	1	no	—
443	C₄	—	158	1	no	—
444	C₄	—	158	1	no	—
445	C₄	—	158	1	no	—
446	C₄	#19098544	1	1	yes	characteristic
447	C₄	#19098546	1	1	yes	characteristic
448	C₄	#19098561	1	1	yes	characteristic
449	C₄	#19098563	1	1	yes	characteristic
450	C₄	#19098566	1	1	yes	characteristic
451	C₄	#19098570	1	1	yes	characteristic
452	C₂	—	2	1	no	—
453	C₂	—	2	1	no	—
454	C₂	—	316	1	no	—
455	C₂	—	158	2	no	—
456	C₂	#338×D₇₉	1	1	yes	characteristic
457	C₂	#23763118	1	1	yes	characteristic
458	C₂	#23763137	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#95×D₇₉
commutator	C₂×C₄×C₇₉	C₂×C₄²
Frattini	C₂×C₄²	C₂²×D₇₉
Fitting	C₇₉×#1292	C₂
socle	C₂²×C₇₉	C₂×#95
prime radical	C₂³×D₇₉	C₄⋊C₄
cosocle	C₂×C₄²×C₇₉	C₂³
hypercenter	#1292	D₇₉
hypocenter	C₇₉	#8003
LCS	G ▷ C₂×C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #1292

Complements

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

N	H ≅ G/N	type
4. #23761275	C₂	semidirect
5. #23761274	C₂	semidirect
6. #23761274	C₂	semidirect
7. C₇₉×#1292	C₂	semidirect
236. #1292	D₇₉	semidirect
237. C₇₉	#8003	semidirect

Maximal subgroups

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

subgroup	index
#23772032	2
C₂×#19098619	2
#423×D₇₉	2
#23761275	2
#23761274	2
C₇₉×#1292	2
#8003	79