Subgroups — #34178055

Order 20224.

584 conjugacy classes of subgroups.

The subgroup lattice has 456 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	#431×D₇₉	C₂	1	1	yes	maximal, characteristic
3	#23765793	C₂	1	1	yes	maximal, characteristic
4	#23761260	C₂	1	1	yes	maximal, characteristic, complemented
5	#23761259	C₂	1	1	yes	maximal, characteristic, complemented
6	#23761258	C₂	1	1	yes	maximal, characteristic, complemented
7	C₇₉×#1286	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₄²×D₇₉	C₂²	1	1	yes	characteristic
9	#19098619	—	2	1	no	—
10	#19098619	C₄	1	2	yes	complemented
11	#19098616	C₂²	1	1	yes	characteristic
12	#19098615	—	2	1	no	—
13	#19098615	—	2	1	no	—
14	#19098615	C₄	1	2	yes	complemented
15	#19098614	C₄	1	2	yes	complemented
16	#19098613	—	2	1	no	—
17	#19098587	C₂²	1	1	yes	characteristic
18	C₄⋊C₈×D₇₉	—	2	1	no	—
19	#19098526	—	2	1	no	—
20	C₂²⋊C₈×D₇₉	—	2	1	no	—
21	M₁₆×Dic₇₉	—	2	1	no	—
22	C₄×C₈×D₇₉	C₄	1	2	yes	complemented
23	#19098430	C₄	1	2	yes	—
24	#19098429	C₂²	1	1	yes	characteristic
25	#19098425	—	2	1	no	—
26	#19098420	—	2	1	no	—
27	C₄⋊C₄×Dic₇₉	—	2	1	no	—
28	#19098410	C₄	1	2	yes	—
29	#19098408	—	2	1	no	—
30	#431×C₇₉	C₂²	1	1	yes	characteristic
31	#423×C₇₉	C₂²	1	1	yes	characteristic
32	#382×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	D₄	1	1	yes	characteristic
36	C₂×#11929608	—	2	1	no	—
37	C₂×C₈×D₇₉	—	2	2	no	—
38	C₂×C₄⋊Dic₇₉	—	2	1	no	—
39	C₂×(C₂×D₇₉)⋊C₄	—	2	2	no	—
40	C₂×C₄×Dic₇₉	—	2	2	no	—
41	C₂×C₄×Dic₇₉	C₂×C₄	1	1	yes	characteristic
42	C₂×C₄×Dic₇₉	D₄	1	1	yes	characteristic
43	C₂×C₄×Dic₇₉	D₄	1	1	yes	characteristic
44	C₄²×D₇₉	C₂×C₄	1	1	yes	characteristic
45	C₄²×D₇₉	C₂×C₄	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	D₄	1	1	yes	characteristic
49	C₄²×D₇₉	D₄	1	1	yes	characteristic
50	C₄²×D₇₉	Q₈	1	1	yes	characteristic
51	C₄²×D₇₉	Q₈	1	1	yes	characteristic
52	C₄⋊(C₇₉⋊C₈)	—	2	1	no	—
53	C₄⋊(C₇₉⋊C₈)	—	2	1	no	—
54	C₄⋊(C₇₉⋊C₈)	C₂×C₄	1	2	yes	—
55	Dic₇₉⋊C₈	—	2	2	no	—
56	C₂²⋊(C₇₉⋊C₈)	—	2	1	no	—
57	(C₂×D₇₉)⋊C₈	—	2	2	no	—
58	(C₂×D₇₉)⋊C₈	—	2	2	no	—
59	(C₂×D₇₉)⋊C₈	—	2	2	no	—
60	#14579071	—	2	2	no	—
61	C₄×C₇₉⋊C₈	C₂×C₄	1	2	yes	—
62	C₈×Dic₇₉	—	2	2	no	—
63	C₈×Dic₇₉	—	2	2	no	—
64	C₇₉⋊#95	—	2	1	no	—
65	C₇₉⋊#95	—	2	2	no	—
66	C₇₉⋊#95	—	2	2	no	—
67	C₇₉⋊#95	C₂×C₄	1	2	yes	—
68	C₂×M₁₆×C₇₉	—	2	1	no	—
69	C₂×C₄⋊C₄×C₇₉	—	2	1	no	—
70	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
71	C₄⋊C₈×C₇₉	—	2	1	no	—
72	C₄⋊C₈×C₇₉	—	2	1	no	—
73	C₄⋊C₈×C₇₉	C₂×C₄	1	2	yes	—
74	C₂²⋊C₈×C₇₉	—	2	1	no	—
75	C₄×C₈×C₇₉	C₂×C₄	1	2	yes	—
76	#95×C₇₉	—	2	1	no	—
77	#95×C₇₉	C₂×C₄	1	2	yes	—
78	C₂³×D₇₉	C₂²⋊C₄	1	1	yes	characteristic
79	C₂²×Dic₇₉	—	2	2	no	—
80	C₂²×Dic₇₉	C₂²⋊C₄	1	1	yes	characteristic
81	C₂²×Dic₇₉	C₂²⋊C₄	1	1	yes	characteristic
82	C₂²×Dic₇₉	C₂²⋊C₄	1	1	yes	characteristic
83	C₂×C₄×D₇₉	—	2	1	no	—
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	—	4	2	no	—
88	C₂×C₄×D₇₉	—	4	2	no	—
89	C₂×C₄×D₇₉	C₄²	1	1	yes	characteristic
90	C₂×C₄×D₇₉	C₄²	1	1	yes	characteristic
91	C₂×C₄×D₇₉	C₂²⋊C₄	1	1	yes	characteristic
92	C₂×C₄×D₇₉	C₂²⋊C₄	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	C₄⋊C₄	1	1	yes	characteristic
96	C₂×C₄×D₇₉	C₄⋊C₄	1	1	yes	characteristic
97	C₂×C₄×D₇₉	C₄⋊C₄	1	1	yes	characteristic
98	C₂×C₄×D₇₉	C₄⋊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	#11929608	—	4	1	no	—
102	#11929608	—	4	1	no	—
103	C₂×C₇₉⋊C₈	—	2	2	no	—
104	C₂×C₇₉⋊C₈	—	2	2	no	—
105	C₈×D₇₉	—	4	4	no	—
106	C₄⋊Dic₇₉	—	4	1	no	—
107	C₄⋊Dic₇₉	—	4	1	no	—
108	(C₂×D₇₉)⋊C₄	—	4	4	no	—
109	C₄×Dic₇₉	—	4	4	no	—
110	C₄×Dic₇₉	C₄²	1	1	yes	characteristic
111	C₄×Dic₇₉	C₄²	1	1	yes	characteristic
112	C₄×Dic₇₉	C₂²⋊C₄	1	1	yes	characteristic
113	C₄×Dic₇₉	C₂²⋊C₄	1	1	yes	characteristic
114	C₄×Dic₇₉	C₂²⋊C₄	1	1	yes	characteristic
115	C₄×Dic₇₉	C₂²⋊C₄	1	1	yes	characteristic
116	C₄×Dic₇₉	C₄⋊C₄	1	1	yes	characteristic
117	C₄×Dic₇₉	C₄⋊C₄	1	1	yes	characteristic
118	C₄×Dic₇₉	C₄⋊C₄	1	1	yes	characteristic
119	C₄×Dic₇₉	C₄⋊C₄	1	1	yes	characteristic
120	C₄×Dic₇₉	C₄⋊C₄	1	1	yes	characteristic
121	C₄×Dic₇₉	C₄⋊C₄	1	1	yes	characteristic
122	C₂²×C₄×C₇₉	—	2	2	no	—
123	C₂²×C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
124	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
125	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
126	M₁₆×C₇₉	—	4	1	no	—
127	M₁₆×C₇₉	—	4	1	no	—
128	C₂×C₈×C₇₉	—	2	2	no	—
129	C₂×C₈×C₇₉	—	2	2	no	—
130	C₄⋊C₄×C₇₉	—	4	1	no	—
131	C₄⋊C₄×C₇₉	—	4	1	no	—
132	C₄²×C₇₉	C₂²×C₄	1	1	yes	characteristic
133	C₄²×C₇₉	C₂²×C₄	1	1	yes	characteristic
134	C₄²×C₇₉	C₂×D₄	1	1	yes	characteristic
135	C₄²×C₇₉	C₂×Q₈	1	1	yes	characteristic
136	C₂³×C₇₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
137	C₂²×D₇₉	—	2	1	no	—
138	C₂²×D₇₉	—	2	1	no	—
139	C₂²×D₇₉	—	2	2	no	—
140	C₂²×D₇₉	—	4	1	no	—
141	C₂²×D₇₉	#95	1	1	yes	characteristic
142	C₂²×D₇₉	#95	1	1	yes	characteristic
143	C₂×C₄×C₇₉	—	4	1	no	—
144	C₂×C₄×C₇₉	—	4	1	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	C₂×C₄²	1	1	yes	characteristic
149	C₂×C₄×C₇₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
150	C₂×C₄×C₇₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
151	C₂×C₄×C₇₉	C₂×C₄⋊C₄	1	1	yes	characteristic
152	C₂×C₄×C₇₉	C₂×C₄⋊C₄	1	1	yes	characteristic
153	C₂×C₄×C₇₉	C₂×C₄⋊C₄	1	1	yes	characteristic
154	C₂×C₄×C₇₉	#135	1	1	yes	characteristic
155	C₂×C₄×C₇₉	#135	1	1	yes	characteristic
156	C₂×C₄×C₇₉	#135	1	1	yes	characteristic
157	C₂×C₄×C₇₉	#135	1	1	yes	characteristic
158	C₂×Dic₇₉	—	2	1	no	—
159	C₂×Dic₇₉	—	2	1	no	—
160	C₂×Dic₇₉	—	2	2	no	—
161	C₂×Dic₇₉	—	4	1	no	—
162	C₂×Dic₇₉	—	4	2	no	—
163	C₂×Dic₇₉	—	4	2	no	—
164	C₂×Dic₇₉	—	4	2	no	—
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	C₂×Dic₇₉	#95	1	1	yes	characteristic
171	C₄×D₇₉	—	2	2	no	—
172	C₄×D₇₉	—	2	2	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	2	no	—
182	C₄×D₇₉	—	2	2	no	—
183	C₄×D₇₉	—	4	1	no	—
184	C₄×D₇₉	—	4	1	no	—
185	C₄×D₇₉	—	4	1	no	—
186	C₄×D₇₉	—	4	1	no	—
187	C₈×C₇₉	—	4	2	no	—
188	C₈×C₇₉	—	4	2	no	—
189	C₇₉⋊C₈	—	4	2	no	—
190	C₇₉⋊C₈	—	4	2	no	—
191	C₂²×C₇₉	—	2	1	no	—
192	C₂²×C₇₉	—	2	1	no	—
193	C₂²×C₇₉	C₂×#95	1	1	yes	characteristic
194	C₂²×C₇₉	#416	1	1	yes	characteristic
195	C₂²×C₇₉	#416	1	1	yes	characteristic
196	C₂×D₇₉	—	2	1	no	—
197	C₂×D₇₉	—	2	1	no	—
198	C₂×D₇₉	—	2	1	no	—
199	C₂×D₇₉	—	2	1	no	—
200	C₂×D₇₉	—	2	1	no	—
201	C₂×D₇₉	—	4	2	no	—
202	C₂×D₇₉	—	4	2	no	—
203	C₂×D₇₉	H(3,ℤ/4)	1	2	yes	—
204	C₄×C₇₉	—	2	1	no	—
205	C₄×C₇₉	—	2	1	no	—
206	C₄×C₇₉	—	2	1	no	—
207	C₄×C₇₉	—	2	1	no	—
208	C₄×C₇₉	—	8	2	no	—
209	C₄×C₇₉	#416	1	1	yes	characteristic
210	C₄×C₇₉	#416	1	1	yes	characteristic
211	C₄×C₇₉	#427	1	1	yes	characteristic
212	C₄×C₇₉	#427	1	1	yes	characteristic
213	Dic₇₉	—	2	1	no	—
214	Dic₇₉	—	2	1	no	—
215	Dic₇₉	—	2	1	no	—
216	Dic₇₉	—	2	1	no	—
217	Dic₇₉	—	2	1	no	—
218	Dic₇₉	—	8	2	no	—
219	Dic₇₉	#344	1	2	yes	—
220	#7958	—	79	1	no	maximal, Sylow
221	C₂×C₇₉	—	2	1	no	—
222	C₂×C₇₉	—	2	1	no	—
223	C₂×C₇₉	C₂×H(3,ℤ/4)	1	1	yes	characteristic
224	C₂×C₇₉	#1735	1	1	yes	characteristic
225	C₂×C₇₉	C₂×#344	1	1	yes	characteristic
226	D₇₉	—	2	2	no	—
227	D₇₉	—	4	1	no	—
228	#2920	—	79	1	no	—
229	C₂×#431	—	79	1	no	—
230	#2283	—	79	1	no	—
231	#1286	—	79	1	no	—
232	#1286	—	79	1	no	—
233	#1286	—	79	1	no	—
234	#1286	D₇₉	1	1	yes	characteristic, complemented
235	C₇₉	#7958	1	1	yes	characteristic, complemented, Sylow
236	C₂²×C₄²	—	79	1	no	—
237	#432	—	79	2	no	—
238	#432	—	158	1	no	—
239	#431	—	79	1	no	—
240	#431	—	79	2	no	—
241	#431	—	79	2	no	—
242	#431	—	158	1	no	—
243	#431	—	158	1	no	—
244	#431	—	158	1	no	—
245	#431	C₂×D₇₉	1	1	yes	characteristic
246	#423	—	79	1	no	—
247	#423	C₂×D₇₉	1	1	yes	characteristic
248	C₂×C₄⋊C₈	—	158	1	no	—
249	#407	—	158	1	no	—
250	C₂×C₂²⋊C₈	—	158	1	no	—
251	C₄×M₁₆	—	158	1	no	—
252	C₂×C₄×C₈	—	79	2	no	—
253	#383	—	79	2	no	—
254	#382	—	79	1	no	—
255	#382	C₂×D₇₉	1	1	yes	characteristic
256	#381	—	158	1	no	—
257	#380	—	158	1	no	—
258	C₄×C₄⋊C₄	—	158	1	no	—
259	C₄×C₂²⋊C₄	—	79	2	no	—
260	#376	—	158	1	no	—
261	C₂³×C₄	—	79	1	no	—
262	C₂³×C₄	—	79	1	no	—
263	C₂³×C₄	—	79	1	no	—
264	C₂×M₁₆	—	2	1	no	—
265	C₂×M₁₆	—	158	1	no	—
266	C₂²×C₈	—	158	2	no	—
267	C₂×C₄⋊C₄	—	2	1	no	—
268	C₂×C₄⋊C₄	—	158	1	no	—
269	C₂×C₂²⋊C₄	—	158	2	no	—
270	C₂×C₄²	—	79	1	no	—
271	C₂×C₄²	—	79	1	no	—
272	C₂×C₄²	—	79	1	no	—
273	C₂×C₄²	—	79	1	no	—
274	C₂×C₄²	—	79	1	no	—
275	C₂×C₄²	—	79	1	no	—
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	—	158	2	no	—
282	C₂×C₄²	C₂²×D₇₉	1	1	yes	characteristic
283	C₄⋊C₈	—	2	1	no	—
284	C₄⋊C₈	—	2	1	no	—
285	C₄⋊C₈	—	79	2	no	—
286	C₄⋊C₈	—	158	2	no	—
287	C₄⋊C₈	—	158	1	no	—
288	C₄⋊C₈	—	158	1	no	—
289	C₄⋊C₈	C₄×D₇₉	1	2	yes	—
290	C₂²⋊C₈	—	2	1	no	—
291	C₂²⋊C₈	—	158	2	no	—
292	C₂²⋊C₈	—	158	2	no	—
293	C₂²⋊C₈	—	158	2	no	—
294	C₂²⋊C₈	—	158	1	no	—
295	#97	—	158	2	no	—
296	C₄×C₈	—	79	2	no	—
297	C₄×C₈	—	158	2	no	—
298	C₄×C₈	—	158	2	no	—
299	C₄×C₈	C₄×D₇₉	1	2	yes	—
300	#95	—	2	1	no	—
301	#95	—	79	2	no	—
302	#95	—	158	2	no	—
303	#95	—	158	2	no	—
304	#95	—	158	1	no	—
305	#95	C₄×D₇₉	1	2	yes	—
306	C₂⁴	—	79	1	no	—
307	C₂²×C₄	—	2	2	no	—
308	C₂²×C₄	—	316	2	no	—
309	C₂²×C₄	—	316	2	no	—
310	C₂²×C₄	—	79	1	no	—
311	C₂²×C₄	—	79	1	no	—
312	C₂²×C₄	—	79	1	no	—
313	C₂²×C₄	—	79	1	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	—	158	2	no	—
326	C₂²×C₄	—	158	1	no	—
327	C₂²×C₄	—	158	1	no	—
328	C₂²×C₄	—	158	1	no	—
329	C₂²×C₄	—	158	1	no	—
330	C₂²×C₄	C₂×C₄×D₇₉	1	1	yes	characteristic
331	C₂²×C₄	D₄×D₇₉	1	1	yes	characteristic
332	C₂²×C₄	D₄×D₇₉	1	1	yes	characteristic
333	M₁₆	—	4	1	no	—
334	M₁₆	—	4	1	no	—
335	M₁₆	—	316	1	no	—
336	M₁₆	—	316	1	no	—
337	C₂×C₈	—	2	2	no	—
338	C₂×C₈	—	2	2	no	—
339	C₂×C₈	—	316	4	no	—
340	C₂×C₈	—	158	2	no	—
341	C₂×C₈	—	158	2	no	—
342	C₄⋊C₄	—	4	1	no	—
343	C₄⋊C₄	—	4	1	no	—
344	C₄⋊C₄	—	316	1	no	—
345	C₄⋊C₄	—	316	1	no	—
346	C₂²⋊C₄	—	316	4	no	—
347	C₄²	—	316	4	no	—
348	C₄²	—	79	1	no	—
349	C₄²	—	79	1	no	—
350	C₄²	—	79	1	no	—
351	C₄²	—	79	1	no	—
352	C₄²	—	79	1	no	—
353	C₄²	—	79	1	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	C₂×C₄×D₇₉	1	1	yes	characteristic
361	C₄²	C₂×C₄×D₇₉	1	1	yes	characteristic
362	C₄²	D₄×D₇₉	1	1	yes	characteristic
363	C₄²	Q₈×D₇₉	1	1	yes	characteristic
364	C₂³	—	316	1	no	—
365	C₂³	—	79	1	no	—
366	C₂³	—	79	1	no	—
367	C₂³	—	158	2	no	—
368	C₂³	—	158	1	no	—
369	C₂³	—	158	1	no	—
370	C₂³	C₂²⋊C₄×D₇₉	1	1	yes	characteristic
371	C₂×C₄	—	4	1	no	—
372	C₂×C₄	—	4	1	no	—
373	C₂×C₄	—	4	2	no	—
374	C₂×C₄	—	4	2	no	—
375	C₂×C₄	—	4	2	no	—
376	C₂×C₄	—	316	1	no	—
377	C₂×C₄	—	316	1	no	—
378	C₂×C₄	—	316	1	no	—
379	C₂×C₄	—	316	1	no	—
380	C₂×C₄	—	316	2	no	—
381	C₂×C₄	—	316	2	no	—
382	C₂×C₄	—	316	2	no	—
383	C₂×C₄	—	316	1	no	—
384	C₂×C₄	—	79	1	no	—
385	C₂×C₄	—	79	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	—	158	2	no	—
391	C₂×C₄	—	158	2	no	—
392	C₂×C₄	—	158	2	no	—
393	C₂×C₄	—	158	2	no	—
394	C₂×C₄	—	158	2	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	C₄²×D₇₉	1	1	yes	characteristic
406	C₂×C₄	C₂²⋊C₄×D₇₉	1	1	yes	characteristic
407	C₂×C₄	C₂²⋊C₄×D₇₉	1	1	yes	characteristic
408	C₂×C₄	C₄⋊C₄×D₇₉	1	1	yes	characteristic
409	C₂×C₄	C₄⋊C₄×D₇₉	1	1	yes	characteristic
410	C₂×C₄	C₄⋊C₄×D₇₉	1	1	yes	characteristic
411	C₂×C₄	#14579180	1	1	yes	characteristic
412	C₂×C₄	#14579182	1	1	yes	characteristic
413	C₂×C₄	#14579182	1	1	yes	characteristic
414	C₂×C₄	#14579184	1	1	yes	characteristic
415	C₈	—	4	2	no	—
416	C₈	—	4	2	no	—
417	C₈	—	316	2	no	—
418	C₈	—	316	2	no	—
419	C₂²	—	2	1	no	—
420	C₂²	—	2	1	no	—
421	C₂²	—	316	2	no	—
422	C₂²	—	316	2	no	—
423	C₂²	—	79	2	no	—
424	C₂²	—	158	1	no	—
425	C₂²	—	158	1	no	—
426	C₂²	—	158	1	no	—
427	C₂²	—	158	1	no	—
428	C₂²	—	158	1	no	—
429	C₂²	#95×D₇₉	1	1	yes	characteristic
430	C₂²	#19098556	1	1	yes	characteristic
431	C₂²	#19098558	1	1	yes	characteristic
432	C₄	—	2	1	no	—
433	C₄	—	2	1	no	—
434	C₄	—	2	1	no	—
435	C₄	—	2	1	no	—
436	C₄	—	8	2	no	—
437	C₄	—	79	2	no	—
438	C₄	—	632	2	no	—
439	C₄	—	158	1	no	—
440	C₄	—	158	1	no	—
441	C₄	—	158	1	no	—
442	C₄	—	158	1	no	—
443	C₄	—	158	1	no	—
444	C₄	#19098556	1	1	yes	characteristic
445	C₄	#19098558	1	1	yes	characteristic
446	C₄	#19098598	1	1	yes	characteristic
447	C₄	#19098600	1	1	yes	characteristic
448	C₂	—	2	1	no	—
449	C₂	—	2	1	no	—
450	C₂	—	316	1	no	—
451	C₂	—	158	2	no	—
452	C₂	H(3,ℤ/4)×D₇₉	1	1	yes	characteristic
453	C₂	#23763115	1	1	yes	characteristic
454	C₂	#344×D₇₉	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#95×D₇₉
commutator	C₂×C₄×C₇₉	C₂×C₄²
Frattini	C₂×C₄²	C₂²×D₇₉
Fitting	C₇₉×#1286	C₂
socle	C₂²×C₇₉	C₂×#95
prime radical	C₂³×D₇₉	C₂²⋊C₄
cosocle	C₂×C₄²×C₇₉	C₂³
hypercenter	#1286	D₇₉
hypocenter	C₇₉	#7958
LCS	G ▷ C₂×C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #1286

Complements

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

N	H ≅ G/N	type
4. #23761260	C₂	semidirect
5. #23761259	C₂	semidirect
6. #23761258	C₂	semidirect
7. C₇₉×#1286	C₂	semidirect
10. #19098619	C₄	semidirect
14. #19098615	C₄	semidirect
15. #19098614	C₄	semidirect
22. C₄×C₈×D₇₉	C₄	semidirect
234. #1286	D₇₉	semidirect
235. C₇₉	#7958	semidirect

Maximal subgroups

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

subgroup	index
#23772032	2
#431×D₇₉	2
#23765793	2
#23761260	2
#23761259	2
#23761258	2
C₇₉×#1286	2
#7958	79