Subgroups — #34178583

Order 20224.

742 conjugacy classes of subgroups.

The subgroup lattice has 474 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	#23772028	C₂	1	1	yes	maximal, characteristic
3	C₄×C₄⋊C₄×D₇₉	C₂	1	1	yes	maximal, characteristic
4	#23761303	C₂	1	1	yes	maximal, characteristic, complemented
5	#23761302	C₂	1	1	yes	maximal, characteristic, complemented
6	#23761301	C₂	1	1	yes	maximal, characteristic, complemented
7	C₇₉×#1303	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₄⋊C₄×D₇₉	—	2	1	no	—
9	C₂×C₄²×D₇₉	—	2	1	no	—
10	C₂×C₄²×D₇₉	C₂²	1	1	yes	characteristic
11	#19098619	—	2	1	no	—
12	#19098619	C₄	1	2	yes	complemented
13	#19098619	C₄	1	2	yes	complemented
14	#19098617	—	2	1	no	—
15	#19098616	C₂²	1	1	yes	characteristic
16	#19098615	—	2	1	no	—
17	#19098615	C₄	1	2	yes	complemented
18	#19098614	—	2	1	no	—
19	#19098587	C₂²	1	1	yes	characteristic
20	#19098585	C₄	1	2	yes	complemented
21	#19098526	—	2	1	no	—
22	#19098525	—	2	1	no	—
23	M₁₆×Dic₇₉	—	2	1	no	—
24	C₄×#11929607	—	2	1	no	—
25	C₄⋊C₄×Dic₇₉	—	2	1	no	—
26	C₄×Dic₇₉⋊C₄	—	2	1	no	—
27	C₄×C₄⋊Dic₇₉	C₂²	1	1	yes	characteristic
28	#19098414	C₄	1	2	yes	—
29	#95×D₇₉	C₄	1	2	yes	—
30	#431×C₇₉	C₂²	1	1	yes	characteristic
31	#423×C₇₉	C₂²	1	1	yes	characteristic
32	C₄×C₄⋊C₄×C₇₉	C₂²	1	1	yes	characteristic
33	C₂²×C₄×D₇₉	—	2	2	no	—
34	C₂²×C₄×D₇₉	C₂×C₄	1	1	yes	characteristic
35	C₂²×C₄×D₇₉	D₄	1	1	yes	characteristic
36	C₂²×C₄×D₇₉	D₄	1	1	yes	characteristic
37	C₂×#11929608	—	2	1	no	—
38	C₂×#11929607	—	2	2	no	—
39	C₂×C₄⋊Dic₇₉	—	2	1	no	—
40	C₂×Dic₇₉⋊C₄	—	2	2	no	—
41	C₄⋊C₄×D₇₉	—	2	8	no	—
42	C₂×C₄×Dic₇₉	—	2	1	no	—
43	C₂×C₄×Dic₇₉	—	2	2	no	—
44	C₂×C₄×Dic₇₉	C₂×C₄	1	1	yes	characteristic
45	C₂×C₄×Dic₇₉	D₄	1	1	yes	characteristic
46	C₂×C₄×Dic₇₉	D₄	1	1	yes	characteristic
47	C₄²×D₇₉	—	4	2	no	—
48	C₄²×D₇₉	—	4	2	no	—
49	C₄²×D₇₉	C₂×C₄	1	1	yes	characteristic
50	C₄²×D₇₉	C₂×C₄	1	1	yes	characteristic
51	C₄²×D₇₉	C₂×C₄	1	1	yes	characteristic
52	C₄²×D₇₉	C₂×C₄	1	1	yes	characteristic
53	C₄²×D₇₉	D₄	1	1	yes	characteristic
54	C₄²×D₇₉	D₄	1	1	yes	characteristic
55	C₄²×D₇₉	Q₈	1	1	yes	characteristic
56	C₄²×D₇₉	Q₈	1	1	yes	characteristic
57	C₄⋊(C₇₉⋊C₈)	—	2	1	no	—
58	C₄⋊(C₇₉⋊C₈)	C₂×C₄	1	2	yes	complemented
59	C₄⋊(C₇₉⋊C₈)	C₂×C₄	1	2	yes	complemented
60	Dic₇₉⋊C₈	—	2	2	no	—
61	C₂²⋊(C₇₉⋊C₈)	—	2	1	no	—
62	(C₂×D₇₉)⋊C₈	—	2	2	no	—
63	(C₂×D₇₉)⋊C₈	—	2	2	no	—
64	(C₂×D₇₉)⋊C₈	—	2	2	no	—
65	#14579071	—	2	2	no	—
66	#14579071	—	2	2	no	—
67	C₄×C₇₉⋊C₈	—	2	1	no	—
68	C₈×Dic₇₉	—	2	2	no	—
69	C₇₉⋊#95	—	2	2	no	—
70	C₇₉⋊#95	C₂×C₄	1	2	yes	—
71	C₂×M₁₆×C₇₉	—	2	1	no	—
72	C₂×C₄⋊C₄×C₇₉	—	2	1	no	—
73	C₂×C₄²×C₇₉	—	2	1	no	—
74	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
75	C₄⋊C₈×C₇₉	—	2	1	no	—
76	C₄⋊C₈×C₇₉	C₂×C₄	1	2	yes	complemented
77	C₄⋊C₈×C₇₉	C₂×C₄	1	2	yes	complemented
78	C₂²⋊C₈×C₇₉	—	2	1	no	—
79	C₄×C₈×C₇₉	—	2	1	no	—
80	#95×C₇₉	C₂×C₄	1	2	yes	—
81	C₂³×D₇₉	C₂²⋊C₄	1	1	yes	characteristic
82	C₂²×Dic₇₉	—	2	2	no	—
83	C₂²×Dic₇₉	C₂²⋊C₄	1	1	yes	characteristic
84	C₂²×Dic₇₉	C₂²⋊C₄	1	1	yes	characteristic
85	C₂²×Dic₇₉	C₂²⋊C₄	1	1	yes	characteristic
86	C₂×C₄×D₇₉	—	2	4	no	—
87	C₂×C₄×D₇₉	—	2	8	no	—
88	C₂×C₄×D₇₉	—	2	1	no	—
89	C₂×C₄×D₇₉	—	2	1	no	—
90	C₂×C₄×D₇₉	—	2	1	no	—
91	C₂×C₄×D₇₉	—	2	1	no	—
92	C₂×C₄×D₇₉	—	4	2	no	—
93	C₂×C₄×D₇₉	—	4	4	no	—
94	C₂×C₄×D₇₉	—	4	4	no	—
95	C₂×C₄×D₇₉	C₄²	1	1	yes	characteristic
96	C₂×C₄×D₇₉	C₄²	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	C₂²⋊C₄	1	1	yes	characteristic
100	C₂×C₄×D₇₉	C₂²⋊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	C₂×C₄×D₇₉	C₄⋊C₄	1	1	yes	characteristic
104	C₂×C₄×D₇₉	C₄⋊C₄	1	1	yes	characteristic
105	C₂×C₄×D₇₉	C₄⋊C₄	1	1	yes	characteristic
106	C₂×C₄×D₇₉	C₄⋊C₄	1	1	yes	characteristic
107	#11929608	—	4	1	no	—
108	#11929608	—	4	1	no	—
109	#11929607	—	4	4	no	—
110	C₂×C₇₉⋊C₈	—	2	2	no	—
111	C₂×C₇₉⋊C₈	—	2	2	no	—
112	C₄⋊Dic₇₉	—	2	4	no	—
113	Dic₇₉⋊C₄	—	2	8	no	—
114	C₄×Dic₇₉	—	4	4	no	—
115	C₄×Dic₇₉	—	4	1	no	—
116	C₄×Dic₇₉	—	4	1	no	—
117	C₄×Dic₇₉	C₄²	1	1	yes	characteristic
118	C₄×Dic₇₉	C₄²	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	C₂²⋊C₄	1	1	yes	characteristic
122	C₄×Dic₇₉	C₂²⋊C₄	1	1	yes	characteristic
123	C₄×Dic₇₉	C₄⋊C₄	1	1	yes	characteristic
124	C₄×Dic₇₉	C₄⋊C₄	1	1	yes	characteristic
125	C₄×Dic₇₉	C₄⋊C₄	1	1	yes	characteristic
126	C₄×Dic₇₉	C₄⋊C₄	1	1	yes	characteristic
127	C₄×Dic₇₉	C₄⋊C₄	1	1	yes	characteristic
128	C₄×Dic₇₉	C₄⋊C₄	1	1	yes	characteristic
129	C₂²×C₄×C₇₉	—	2	2	no	—
130	C₂²×C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
131	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
132	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
133	M₁₆×C₇₉	—	4	1	no	—
134	M₁₆×C₇₉	—	4	1	no	—
135	C₂×C₈×C₇₉	—	2	2	no	—
136	C₂×C₈×C₇₉	—	2	2	no	—
137	C₄⋊C₄×C₇₉	—	2	4	no	—
138	C₄²×C₇₉	—	4	1	no	—
139	C₄²×C₇₉	—	4	1	no	—
140	C₄²×C₇₉	C₂²×C₄	1	1	yes	characteristic
141	C₄²×C₇₉	C₂²×C₄	1	1	yes	characteristic
142	C₄²×C₇₉	C₂×D₄	1	1	yes	characteristic
143	C₄²×C₇₉	C₂×Q₈	1	1	yes	characteristic
144	C₂³×C₇₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
145	C₂²×D₇₉	—	2	1	no	—
146	C₂²×D₇₉	—	2	1	no	—
147	C₂²×D₇₉	—	2	2	no	—
148	C₂²×D₇₉	—	2	2	no	—
149	C₂²×D₇₉	#95	1	1	yes	characteristic
150	C₂²×D₇₉	#95	1	1	yes	characteristic
151	C₂×C₄×C₇₉	—	2	2	no	—
152	C₂×C₄×C₇₉	—	2	4	no	—
153	C₂×C₄×C₇₉	—	4	1	no	—
154	C₂×C₄×C₇₉	—	4	2	no	—
155	C₂×C₄×C₇₉	—	4	2	no	—
156	C₂×C₄×C₇₉	C₂×C₄²	1	1	yes	characteristic
157	C₂×C₄×C₇₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
158	C₂×C₄×C₇₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
159	C₂×C₄×C₇₉	C₂×C₄⋊C₄	1	1	yes	characteristic
160	C₂×C₄×C₇₉	C₂×C₄⋊C₄	1	1	yes	characteristic
161	C₂×C₄×C₇₉	C₂×C₄⋊C₄	1	1	yes	characteristic
162	C₂×C₄×C₇₉	AGL(1,ℤ/8)	1	1	yes	characteristic
163	C₂×C₄×C₇₉	AGL(1,ℤ/8)	1	1	yes	characteristic
164	C₂×C₄×C₇₉	#137	1	1	yes	characteristic
165	C₂×C₄×C₇₉	#137	1	1	yes	characteristic
166	C₂×Dic₇₉	—	2	1	no	—
167	C₂×Dic₇₉	—	2	1	no	—
168	C₂×Dic₇₉	—	2	2	no	—
169	C₂×Dic₇₉	—	2	4	no	—
170	C₂×Dic₇₉	—	4	1	no	—
171	C₂×Dic₇₉	—	4	2	no	—
172	C₂×Dic₇₉	—	4	2	no	—
173	C₂×Dic₇₉	#95	1	1	yes	characteristic
174	C₂×Dic₇₉	#95	1	1	yes	characteristic
175	C₂×Dic₇₉	#95	1	1	yes	characteristic
176	C₂×Dic₇₉	#95	1	1	yes	characteristic
177	C₂×Dic₇₉	#95	1	1	yes	characteristic
178	C₂×Dic₇₉	#95	1	1	yes	characteristic
179	C₄×D₇₉	—	2	2	no	—
180	C₄×D₇₉	—	2	2	no	—
181	C₄×D₇₉	—	2	2	no	—
182	C₄×D₇₉	—	2	1	no	—
183	C₄×D₇₉	—	2	1	no	—
184	C₄×D₇₉	—	2	1	no	—
185	C₄×D₇₉	—	2	1	no	—
186	C₄×D₇₉	—	2	2	no	—
187	C₄×D₇₉	—	2	1	no	—
188	C₄×D₇₉	—	2	1	no	—
189	C₄×D₇₉	—	2	1	no	—
190	C₄×D₇₉	—	2	1	no	—
191	C₄×D₇₉	—	2	2	no	—
192	C₄×D₇₉	—	4	1	no	—
193	C₄×D₇₉	—	4	1	no	—
194	C₄×D₇₉	—	4	16	no	—
195	C₄×D₇₉	#104	1	4	yes	—
196	C₈×C₇₉	—	4	2	no	—
197	C₈×C₇₉	—	4	2	no	—
198	C₇₉⋊C₈	—	4	2	no	—
199	C₇₉⋊C₈	—	4	2	no	—
200	C₂²×C₇₉	—	2	1	no	—
201	C₂²×C₇₉	—	2	1	no	—
202	C₂²×C₇₉	C₂×#95	1	1	yes	characteristic
203	C₂²×C₇₉	#418	1	1	yes	characteristic
204	C₂²×C₇₉	#419	1	1	yes	characteristic
205	C₂×D₇₉	—	2	4	no	—
206	C₂×D₇₉	—	2	4	no	—
207	C₂×D₇₉	—	2	1	no	—
208	C₂×D₇₉	—	2	1	no	—
209	C₂×D₇₉	—	2	1	no	—
210	C₂×D₇₉	—	2	1	no	—
211	C₂×D₇₉	#339	1	2	yes	—
212	C₂×D₇₉	#344	1	2	yes	—
213	C₄×C₇₉	—	2	1	no	—
214	C₄×C₇₉	—	2	1	no	—
215	C₄×C₇₉	—	2	1	no	—
216	C₄×C₇₉	—	4	4	no	—
217	C₄×C₇₉	#417	1	1	yes	characteristic
218	C₄×C₇₉	#417	1	1	yes	characteristic
219	C₄×C₇₉	C₂×#104	1	2	yes	—
220	C₄×C₇₉	#428	1	1	yes	characteristic
221	C₄×C₇₉	#428	1	1	yes	characteristic
222	Dic₇₉	—	2	1	no	—
223	Dic₇₉	—	2	1	no	—
224	Dic₇₉	—	2	1	no	—
225	Dic₇₉	—	2	1	no	—
226	Dic₇₉	—	2	1	no	—
227	Dic₇₉	—	4	4	no	—
228	Dic₇₉	#339	1	2	yes	—
229	#8098	—	79	1	no	maximal, Sylow
230	C₂×C₇₉	—	2	1	no	—
231	C₂×C₇₉	—	2	1	no	—
232	C₂×C₇₉	C₂×#339	1	1	yes	characteristic
233	C₂×C₇₉	#1736	1	1	yes	characteristic
234	C₂×C₇₉	C₂×#344	1	1	yes	characteristic
235	D₇₉	—	2	2	no	—
236	D₇₉	—	2	2	no	—
237	#2920	—	79	1	no	—
238	#2920	—	79	1	no	—
239	C₂×C₄×C₄⋊C₄	—	79	1	no	—
240	#1303	—	79	1	no	—
241	#1303	—	79	1	no	—
242	#1303	—	79	1	no	—
243	#1303	D₇₉	1	1	yes	characteristic, complemented
244	C₇₉	#8098	1	1	yes	characteristic, complemented, Sylow
245	C₂²×C₄⋊C₄	—	158	1	no	—
246	C₂²×C₄²	—	79	1	no	—
247	C₂²×C₄²	—	158	1	no	—
248	#432	—	79	2	no	—
249	#432	—	79	2	no	—
250	#432	—	158	1	no	—
251	#432	—	158	1	no	—
252	#431	—	79	1	no	—
253	#431	—	79	2	no	—
254	#431	—	158	1	no	—
255	#431	—	158	1	no	—
256	#431	C₂×D₇₉	1	1	yes	characteristic
257	#423	—	79	1	no	—
258	#423	—	79	2	no	—
259	#423	C₂×D₇₉	1	1	yes	characteristic
260	#407	—	158	1	no	—
261	#407	—	158	1	no	—
262	C₄×M₁₆	—	158	1	no	—
263	C₄×M₁₆	—	158	1	no	—
264	C₄×C₄⋊C₄	—	79	1	no	—
265	C₄×C₄⋊C₄	—	79	2	no	—
266	C₄×C₄⋊C₄	—	158	1	no	—
267	C₄×C₄⋊C₄	—	158	1	no	—
268	C₄×C₄⋊C₄	C₂×D₇₉	1	1	yes	characteristic
269	C₂×#95	—	79	2	no	—
270	C₂³×C₄	—	79	1	no	—
271	C₂³×C₄	—	79	1	no	—
272	C₂³×C₄	—	79	1	no	—
273	C₂³×C₄	—	158	2	no	—
274	C₂×M₁₆	—	2	1	no	—
275	C₂×M₁₆	—	158	2	no	—
276	C₂×M₁₆	—	158	1	no	—
277	C₂×C₄⋊C₄	—	2	1	no	—
278	C₂×C₄⋊C₄	—	158	8	no	—
279	C₂×C₄⋊C₄	—	158	2	no	—
280	C₂×C₄⋊C₄	—	158	1	no	—
281	C₂×C₄²	—	2	1	no	—
282	C₂×C₄²	—	316	2	no	—
283	C₂×C₄²	—	316	2	no	—
284	C₂×C₄²	—	79	1	no	—
285	C₂×C₄²	—	79	1	no	—
286	C₂×C₄²	—	79	1	no	—
287	C₂×C₄²	—	79	1	no	—
288	C₂×C₄²	—	79	1	no	—
289	C₂×C₄²	—	79	1	no	—
290	C₂×C₄²	—	79	1	no	—
291	C₂×C₄²	—	79	1	no	—
292	C₂×C₄²	—	79	1	no	—
293	C₂×C₄²	—	79	1	no	—
294	C₂×C₄²	—	79	1	no	—
295	C₂×C₄²	—	158	2	no	—
296	C₂×C₄²	—	158	1	no	—
297	C₂×C₄²	C₂²×D₇₉	1	1	yes	characteristic
298	C₄⋊C₈	—	2	1	no	—
299	C₄⋊C₈	—	79	2	no	—
300	C₄⋊C₈	—	79	2	no	—
301	C₄⋊C₈	—	158	2	no	—
302	C₄⋊C₈	—	158	1	no	—
303	C₄⋊C₈	C₄×D₇₉	1	2	yes	complemented
304	C₄⋊C₈	C₄×D₇₉	1	2	yes	complemented
305	C₂²⋊C₈	—	2	1	no	—
306	C₂²⋊C₈	—	158	2	no	—
307	C₂²⋊C₈	—	158	2	no	—
308	C₂²⋊C₈	—	158	2	no	—
309	C₂²⋊C₈	—	158	1	no	—
310	#97	—	158	2	no	—
311	#97	—	158	2	no	—
312	C₄×C₈	—	2	1	no	—
313	C₄×C₈	—	158	2	no	—
314	C₄×C₈	—	158	1	no	—
315	#95	—	79	2	no	—
316	#95	—	158	2	no	—
317	#95	C₄×D₇₉	1	2	yes	—
318	C₂⁴	—	79	1	no	—
319	C₂²×C₄	—	2	2	no	—
320	C₂²×C₄	—	316	4	no	—
321	C₂²×C₄	—	316	4	no	—
322	C₂²×C₄	—	316	2	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	—	79	1	no	—
330	C₂²×C₄	—	79	1	no	—
331	C₂²×C₄	—	79	1	no	—
332	C₂²×C₄	—	79	1	no	—
333	C₂²×C₄	—	79	1	no	—
334	C₂²×C₄	—	79	1	no	—
335	C₂²×C₄	—	79	1	no	—
336	C₂²×C₄	—	79	1	no	—
337	C₂²×C₄	—	79	1	no	—
338	C₂²×C₄	—	158	8	no	—
339	C₂²×C₄	—	158	4	no	—
340	C₂²×C₄	—	158	2	no	—
341	C₂²×C₄	—	158	1	no	—
342	C₂²×C₄	—	158	1	no	—
343	C₂²×C₄	—	158	1	no	—
344	C₂²×C₄	—	158	1	no	—
345	C₂²×C₄	C₂×C₄×D₇₉	1	1	yes	characteristic
346	C₂²×C₄	D₄×D₇₉	1	1	yes	characteristic
347	C₂²×C₄	D₄×D₇₉	1	1	yes	characteristic
348	M₁₆	—	4	1	no	—
349	M₁₆	—	4	1	no	—
350	M₁₆	—	316	4	no	—
351	M₁₆	—	316	1	no	—
352	M₁₆	—	316	1	no	—
353	C₂×C₈	—	2	2	no	—
354	C₂×C₈	—	2	2	no	—
355	C₂×C₈	—	158	2	no	—
356	C₂×C₈	—	158	2	no	—
357	C₄⋊C₄	—	2	4	no	—
358	C₄⋊C₄	—	158	8	no	—
359	C₄⋊C₄	—	158	4	no	—
360	C₄²	—	4	1	no	—
361	C₄²	—	4	1	no	—
362	C₄²	—	316	4	no	—
363	C₄²	—	316	1	no	—
364	C₄²	—	316	1	no	—
365	C₄²	—	79	1	no	—
366	C₄²	—	79	1	no	—
367	C₄²	—	79	1	no	—
368	C₄²	—	79	1	no	—
369	C₄²	—	79	1	no	—
370	C₄²	—	79	1	no	—
371	C₄²	—	79	1	no	—
372	C₄²	—	79	1	no	—
373	C₄²	—	79	1	no	—
374	C₄²	—	79	1	no	—
375	C₄²	—	79	1	no	—
376	C₄²	—	79	1	no	—
377	C₄²	C₂×C₄×D₇₉	1	1	yes	characteristic
378	C₄²	C₂×C₄×D₇₉	1	1	yes	characteristic
379	C₄²	D₄×D₇₉	1	1	yes	characteristic
380	C₄²	Q₈×D₇₉	1	1	yes	characteristic
381	C₂³	—	79	1	no	—
382	C₂³	—	79	1	no	—
383	C₂³	—	158	2	no	—
384	C₂³	—	158	2	no	—
385	C₂³	—	158	1	no	—
386	C₂³	—	158	1	no	—
387	C₂³	C₂²⋊C₄×D₇₉	1	1	yes	characteristic
388	C₂×C₄	—	2	2	no	—
389	C₂×C₄	—	2	4	no	—
390	C₂×C₄	—	4	1	no	—
391	C₂×C₄	—	4	2	no	—
392	C₂×C₄	—	4	2	no	—
393	C₂×C₄	—	316	1	no	—
394	C₂×C₄	—	316	1	no	—
395	C₂×C₄	—	316	16	no	—
396	C₂×C₄	—	316	2	no	—
397	C₂×C₄	—	316	2	no	—
398	C₂×C₄	—	316	1	no	—
399	C₂×C₄	—	79	1	no	—
400	C₂×C₄	—	79	4	no	—
401	C₂×C₄	—	79	1	no	—
402	C₂×C₄	—	79	1	no	—
403	C₂×C₄	—	79	1	no	—
404	C₂×C₄	—	79	1	no	—
405	C₂×C₄	—	79	1	no	—
406	C₂×C₄	—	158	2	no	—
407	C₂×C₄	—	158	2	no	—
408	C₂×C₄	—	158	2	no	—
409	C₂×C₄	—	158	2	no	—
410	C₂×C₄	—	158	4	no	—
411	C₂×C₄	—	158	2	no	—
412	C₂×C₄	—	158	1	no	—
413	C₂×C₄	—	158	1	no	—
414	C₂×C₄	—	158	1	no	—
415	C₂×C₄	—	158	1	no	—
416	C₂×C₄	—	158	1	no	—
417	C₂×C₄	—	158	1	no	—
418	C₂×C₄	—	158	2	no	—
419	C₂×C₄	—	158	1	no	—
420	C₂×C₄	—	158	1	no	—
421	C₂×C₄	—	158	1	no	—
422	C₂×C₄	—	158	1	no	—
423	C₂×C₄	C₄²×D₇₉	1	1	yes	characteristic
424	C₂×C₄	C₂²⋊C₄×D₇₉	1	1	yes	characteristic
425	C₂×C₄	C₂²⋊C₄×D₇₉	1	1	yes	characteristic
426	C₂×C₄	C₄⋊C₄×D₇₉	1	1	yes	characteristic
427	C₂×C₄	C₄⋊C₄×D₇₉	1	1	yes	characteristic
428	C₂×C₄	C₄⋊C₄×D₇₉	1	1	yes	characteristic
429	C₂×C₄	#14579185	1	1	yes	characteristic
430	C₂×C₄	#14579188	1	1	yes	characteristic
431	C₂×C₄	#14579190	1	1	yes	characteristic
432	C₂×C₄	#14579193	1	1	yes	characteristic
433	C₈	—	4	2	no	—
434	C₈	—	4	2	no	—
435	C₈	—	316	2	no	—
436	C₈	—	316	2	no	—
437	C₂²	—	2	1	no	—
438	C₂²	—	2	1	no	—
439	C₂²	—	79	2	no	—
440	C₂²	—	79	2	no	—
441	C₂²	—	158	4	no	—
442	C₂²	—	158	4	no	—
443	C₂²	—	158	1	no	—
444	C₂²	—	158	1	no	—
445	C₂²	—	158	1	no	—
446	C₂²	—	158	1	no	—
447	C₂²	#95×D₇₉	1	1	yes	characteristic
448	C₂²	#19098566	1	1	yes	characteristic
449	C₂²	#19098570	1	1	yes	characteristic
450	C₄	—	2	1	no	—
451	C₄	—	2	1	no	—
452	C₄	—	2	1	no	—
453	C₄	—	4	4	no	—
454	C₄	—	316	4	no	—
455	C₄	—	79	2	no	—
456	C₄	—	158	1	no	—
457	C₄	—	158	1	no	—
458	C₄	—	158	1	no	—
459	C₄	—	158	1	no	—
460	C₄	—	158	1	no	—
461	C₄	#19098561	1	1	yes	characteristic
462	C₄	#19098563	1	1	yes	characteristic
463	C₄	#104×D₇₉	1	2	yes	—
464	C₄	#19098602	1	1	yes	characteristic
465	C₄	#19098604	1	1	yes	characteristic
466	C₂	—	2	1	no	—
467	C₂	—	2	1	no	—
468	C₂	—	158	2	no	—
469	C₂	—	158	2	no	—
470	C₂	#339×D₇₉	1	1	yes	characteristic
471	C₂	#23763118	1	1	yes	characteristic
472	C₂	#344×D₇₉	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²⋊C₄×D₇₉
commutator	C₂×C₄×C₇₉	C₂×C₄²
Frattini	C₂×C₄²	C₂²×D₇₉
Fitting	C₇₉×#1303	C₂
socle	C₂²×C₇₉	C₂×#95
prime radical	C₂³×D₇₉	C₂²⋊C₄
cosocle	C₂×C₄²×C₇₉	C₂³
hypercenter	#1303	D₇₉
hypocenter	C₇₉	#8098
LCS	G ▷ C₂×C₄×C₇₉ ▷ C₂²×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1303

Complements

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

N	H ≅ G/N	type
4. #23761303	C₂	semidirect
5. #23761302	C₂	semidirect
6. #23761301	C₂	semidirect
7. C₇₉×#1303	C₂	semidirect
12. #19098619	C₄	semidirect
13. #19098619	C₄	semidirect
17. #19098615	C₄	semidirect
20. #19098585	C₄	semidirect
58. C₄⋊(C₇₉⋊C₈)	C₂×C₄	semidirect
59. C₄⋊(C₇₉⋊C₈)	C₂×C₄	semidirect
76. C₄⋊C₈×C₇₉	C₂×C₄	semidirect
77. C₄⋊C₈×C₇₉	C₂×C₄	semidirect
243. #1303	D₇₉	semidirect
244. C₇₉	#8098	semidirect
303. C₄⋊C₈	C₄×D₇₉	semidirect
304. C₄⋊C₈	C₄×D₇₉	semidirect

Maximal subgroups

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

subgroup	index
#23772032	2
#23772028	2
C₄×C₄⋊C₄×D₇₉	2
#23761303	2
#23761302	2
#23761301	2
C₇₉×#1303	2
#8098	79