Subgroups — #34179265

Order 20224.

522 conjugacy classes of subgroups.

The subgroup lattice has 418 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#23763176	C₂	1	1	yes	maximal, characteristic, complemented
2	C₈×C₂²⋊Dic₇₉	C₂	1	1	yes	maximal, characteristic, complemented
3	#23761891	C₂	1	1	yes	maximal, characteristic
4	#23761891	C₂	1	1	yes	maximal, characteristic
5	#23761287	C₂	1	1	yes	maximal, characteristic, complemented
6	#23761285	C₂	1	1	yes	maximal, characteristic, complemented
7	C₇₉×#2929	C₂	1	1	yes	maximal, characteristic
8	C₂×C₂²⋊(C₇₉⋊C₈)	C₂²	1	1	yes	characteristic
9	C₂×C₂²⋊(C₇₉⋊C₈)	C₂²	1	1	yes	characteristic
10	C₂×#14579071	—	2	1	no	—
11	C₂×C₈×Dic₇₉	—	2	1	no	—
12	C₄×C₂²⋊Dic₇₉	C₂²	1	1	yes	characteristic
13	C₄×C₂²⋊Dic₇₉	C₂²	1	1	yes	characteristic
14	#19098317	—	2	1	no	—
15	#19098317	—	2	1	no	—
16	#19098300	C₄	1	2	yes	complemented
17	#19098300	C₄	1	2	yes	complemented
18	#19098297	C₄	1	2	yes	complemented
19	#19098297	C₄	1	2	yes	complemented
20	C₂×#131×C₇₉	C₄	1	1	yes	characteristic, complemented
21	C₂³×C₈×C₇₉	C₂²	1	1	yes	characteristic
22	#525×C₇₉	C₂²	1	1	yes	characteristic
23	#435×C₇₉	—	2	1	no	—
24	#435×C₇₉	—	2	1	no	—
25	C₈×D₄×C₇₉	—	2	1	no	—
26	C₈×D₄×C₇₉	—	2	1	no	—
27	#424×C₇₉	C₄	1	1	yes	characteristic, complemented
28	#408×C₇₉	C₄	1	1	yes	characteristic, complemented
29	#407×C₇₉	C₂²	1	1	yes	characteristic
30	#405×C₇₉	C₄	1	1	yes	characteristic, complemented
31	C₂²×C₇₉⋊C₈	—	2	1	no	—
32	C₂²×C₇₉⋊C₈	—	2	1	no	—
33	C₂×C₂²⋊Dic₇₉	—	2	1	no	—
34	C₂×C₂²⋊Dic₇₉	—	2	1	no	—
35	C₂×C₄×Dic₇₉	—	2	1	no	—
36	C₂×C₄×Dic₇₉	—	2	1	no	—
37	C₂²⋊(C₇₉⋊C₈)	—	2	1	no	—
38	C₂²⋊(C₇₉⋊C₈)	—	2	1	no	—
39	C₂²⋊(C₇₉⋊C₈)	C₂×C₄	1	2	yes	—
40	C₂²⋊(C₇₉⋊C₈)	C₂×C₄	1	2	yes	—
41	#14579071	—	4	2	no	—
42	C₈×Dic₇₉	—	4	2	no	—
43	C₇₉⋊#95	C₂×C₄	1	2	yes	—
44	C₇₉⋊#95	C₂×C₄	1	2	yes	—
45	C₂×#41×C₇₉	C₂×C₄	1	1	yes	characteristic
46	C₂³×C₄×C₇₉	C₂³	1	1	yes	characteristic
47	#131×C₇₉	—	4	2	no	—
48	C₂×M₁₆×C₇₉	—	2	1	no	—
49	C₂×M₁₆×C₇₉	C₂×C₄	1	1	yes	characteristic
50	C₂×M₁₆×C₇₉	C₂×C₄	1	1	yes	characteristic
51	C₂²×C₈×C₇₉	—	2	1	no	—
52	C₂²×C₈×C₇₉	—	4	2	no	—
53	C₂²×C₈×C₇₉	C₂×C₄	1	1	yes	characteristic
54	C₂²×C₈×C₇₉	C₂×C₄	1	1	yes	characteristic
55	C₂²×C₈×C₇₉	D₄	1	1	yes	characteristic
56	C₂²×C₈×C₇₉	D₄	1	1	yes	characteristic
57	C₂²×C₈×C₇₉	D₄	1	1	yes	characteristic
58	C₂²×C₈×C₇₉	D₄	1	1	yes	characteristic
59	#123×C₇₉	—	2	1	no	—
60	C₂²⋊Q₈×C₇₉	C₂×C₄	1	1	yes	characteristic
61	C₂²⋊Q₈×C₇₉	C₂×C₄	1	1	yes	characteristic
62	#121×C₇₉	C₂×C₄	1	1	yes	characteristic
63	#121×C₇₉	C₂×C₄	1	1	yes	characteristic
64	#120×C₇₉	—	2	1	no	—
65	C₄×D₄×C₇₉	—	2	1	no	—
66	C₄×D₄×C₇₉	—	2	1	no	—
67	#117×C₇₉	C₂×C₄	1	1	yes	characteristic
68	C₄⋊C₈×C₇₉	—	2	1	no	—
69	C₄⋊C₈×C₇₉	—	2	1	no	—
70	C₂²⋊C₈×C₇₉	—	2	1	no	—
71	C₂²⋊C₈×C₇₉	—	2	1	no	—
72	C₂²⋊C₈×C₇₉	—	2	1	no	—
73	C₂²⋊C₈×C₇₉	—	2	1	no	—
74	#97×C₇₉	—	2	1	no	—
75	C₄×C₈×C₇₉	—	2	1	no	—
76	C₂²×Dic₇₉	—	2	2	no	—
77	C₂²×Dic₇₉	—	2	2	no	—
78	C₂×C₇₉⋊C₈	—	2	2	no	—
79	C₂×C₇₉⋊C₈	—	2	2	no	—
80	C₂×C₇₉⋊C₈	—	4	1	no	—
81	C₂×C₇₉⋊C₈	—	4	1	no	—
82	C₂×C₇₉⋊C₈	—	4	1	no	—
83	C₂×C₇₉⋊C₈	—	4	1	no	—
84	C₂²⋊Dic₇₉	—	2	4	no	—
85	C₂²⋊Dic₇₉	—	4	2	no	—
86	C₄×Dic₇₉	—	4	1	no	—
87	C₄×Dic₇₉	—	4	1	no	—
88	C₄×Dic₇₉	—	4	1	no	—
89	C₄×Dic₇₉	—	4	1	no	—
90	C₂⁴×C₇₉	#41	1	1	yes	characteristic
91	#41×C₇₉	—	4	1	no	—
92	#41×C₇₉	—	4	1	no	—
93	C₂×Q₈×C₇₉	C₄²	1	1	yes	characteristic
94	C₂×D₄×C₇₉	—	2	1	no	—
95	C₂×D₄×C₇₉	—	2	1	no	—
96	C₂×D₄×C₇₉	—	2	1	no	—
97	C₂×D₄×C₇₉	C₄²	1	1	yes	characteristic
98	C₂²×C₄×C₇₉	—	2	1	no	—
99	C₂²×C₄×C₇₉	—	4	1	no	—
100	C₂²×C₄×C₇₉	—	4	1	no	—
101	C₂²×C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
102	C₂²×C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
103	C₂²×C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
104	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
105	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
106	C₂²×C₄×C₇₉	#41	1	1	yes	characteristic
107	M₁₆×C₇₉	—	4	1	no	—
108	M₁₆×C₇₉	—	4	1	no	—
109	M₁₆×C₇₉	—	4	2	no	—
110	C₂×C₈×C₇₉	—	2	2	no	—
111	C₂×C₈×C₇₉	—	2	2	no	—
112	C₂×C₈×C₇₉	—	2	2	no	—
113	C₂×C₈×C₇₉	—	2	1	no	—
114	C₂×C₈×C₇₉	—	2	1	no	—
115	C₂×C₈×C₇₉	—	4	1	no	—
116	C₂×C₈×C₇₉	—	4	1	no	—
117	C₂×C₈×C₇₉	—	4	1	no	—
118	C₂×C₈×C₇₉	—	4	2	no	—
119	C₂×C₈×C₇₉	C₂²⋊C₄	1	1	yes	characteristic
120	C₂×C₈×C₇₉	C₂²⋊C₄	1	1	yes	characteristic
121	C₂×C₈×C₇₉	C₂²⋊C₄	1	1	yes	characteristic
122	C₂×C₈×C₇₉	C₂²⋊C₄	1	1	yes	characteristic
123	C₄⋊C₄×C₇₉	—	2	1	no	—
124	C₄⋊C₄×C₇₉	—	2	1	no	—
125	C₄⋊C₄×C₇₉	C₄²	1	1	yes	characteristic
126	C₄⋊C₄×C₇₉	C₄²	1	1	yes	characteristic
127	C₂²⋊C₄×C₇₉	—	2	1	no	—
128	C₂²⋊C₄×C₇₉	—	2	1	no	—
129	C₂²⋊C₄×C₇₉	—	2	1	no	—
130	C₂²⋊C₄×C₇₉	—	2	1	no	—
131	C₂²⋊C₄×C₇₉	—	2	1	no	—
132	C₄²×C₇₉	—	2	1	no	—
133	C₂³×C₇₉	—	2	2	no	—
134	C₂³×C₇₉	—	2	2	no	—
135	C₂³×C₇₉	—	2	1	no	—
136	C₂³×C₇₉	—	4	1	no	—
137	C₂³×C₇₉	#117	1	1	yes	characteristic
138	C₂³×C₇₉	C₄×D₄	1	1	yes	characteristic
139	C₂³×C₇₉	C₄×D₄	1	1	yes	characteristic
140	Q₈×C₇₉	—	4	1	no	—
141	D₄×C₇₉	—	4	1	no	—
142	D₄×C₇₉	—	4	2	no	—
143	D₄×C₇₉	—	4	2	no	—
144	D₄×C₇₉	—	4	2	no	—
145	C₂×C₄×C₇₉	—	2	1	no	—
146	C₂×C₄×C₇₉	—	2	1	no	—
147	C₂×C₄×C₇₉	—	2	1	no	—
148	C₂×C₄×C₇₉	—	2	1	no	—
149	C₂×C₄×C₇₉	—	2	1	no	—
150	C₂×C₄×C₇₉	—	2	1	no	—
151	C₂×C₄×C₇₉	—	2	1	no	—
152	C₂×C₄×C₇₉	—	2	1	no	—
153	C₂×C₄×C₇₉	—	2	1	no	—
154	C₂×C₄×C₇₉	—	4	1	no	—
155	C₂×C₄×C₇₉	—	4	1	no	—
156	C₂×C₄×C₇₉	—	4	1	no	—
157	C₂×C₄×C₇₉	—	4	1	no	—
158	C₂×C₄×C₇₉	—	4	1	no	—
159	C₂×C₄×C₇₉	C₂×C₄²	1	1	yes	characteristic
160	C₂×C₄×C₇₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
161	C₂×C₄×C₇₉	C₄×D₄	1	1	yes	characteristic
162	C₂×C₄×C₇₉	C₄×D₄	1	1	yes	characteristic
163	C₂×Dic₇₉	—	2	4	no	—
164	C₂×Dic₇₉	—	4	2	no	—
165	C₂×Dic₇₉	—	4	2	no	—
166	C₂×Dic₇₉	—	4	2	no	—
167	C₂×Dic₇₉	—	4	2	no	—
168	C₂×Dic₇₉	—	4	2	no	—
169	C₈×C₇₉	—	2	1	no	—
170	C₈×C₇₉	—	2	1	no	—
171	C₈×C₇₉	—	2	1	no	—
172	C₈×C₇₉	—	4	1	no	—
173	C₈×C₇₉	—	4	1	no	—
174	C₈×C₇₉	#99	1	2	yes	—
175	C₇₉⋊C₈	—	4	2	no	—
176	C₇₉⋊C₈	—	4	2	no	—
177	C₂²×C₇₉	—	2	1	no	—
178	C₂²×C₇₉	—	2	1	no	—
179	C₂²×C₇₉	—	2	1	no	—
180	C₂²×C₇₉	—	2	1	no	—
181	C₂²×C₇₉	—	2	1	no	—
182	C₂²×C₇₉	—	2	1	no	—
183	C₂²×C₇₉	—	2	1	no	—
184	C₂²×C₇₉	—	4	4	no	—
185	C₂²×C₇₉	—	4	1	no	—
186	C₂²×C₇₉	—	4	1	no	—
187	C₂²×C₇₉	—	4	1	no	—
188	C₂²×C₇₉	C₄×C₂²⋊C₄	1	1	yes	characteristic
189	C₂²×C₇₉	#443	1	2	yes	—
190	C₂²×C₇₉	#444	1	2	yes	—
191	C₄×C₇₉	—	2	1	no	—
192	C₄×C₇₉	—	2	1	no	—
193	C₄×C₇₉	—	2	1	no	—
194	C₄×C₇₉	—	4	1	no	—
195	C₄×C₇₉	—	4	1	no	—
196	C₄×C₇₉	—	4	1	no	—
197	C₄×C₇₉	C₂×#99	1	1	yes	characteristic
198	C₄×C₇₉	#410	1	1	yes	characteristic
199	Dic₇₉	—	4	4	no	—
200	Dic₇₉	—	8	2	no	—
201	#8240	—	79	1	no	maximal, Sylow
202	C₂×C₇₉	—	2	2	no	—
203	C₂×C₇₉	—	2	2	no	—
204	C₂×C₇₉	—	4	1	no	—
205	C₂×C₇₉	—	8	1	no	—
206	C₂×C₇₉	C₄×#99	1	1	yes	characteristic
207	C₂×C₇₉	#1764	1	1	yes	characteristic
208	C₂×C₇₉	#1765	1	1	yes	characteristic
209	#2929	D₇₉	1	1	yes	characteristic
210	#1752	—	79	1	no	—
211	C₈×C₂²⋊C₄	—	79	1	no	—
212	#1501	—	79	1	no	—
213	#1501	—	79	1	no	—
214	#1298	—	79	1	no	—
215	#1297	—	79	1	no	—
216	C₇₉	#8240	1	1	yes	characteristic, complemented, Sylow
217	C₂×#131	Dic₇₉	1	1	yes	characteristic, complemented
218	C₂³×C₈	C₂×D₇₉	1	1	yes	characteristic
219	#525	C₂×D₇₉	1	1	yes	characteristic
220	#435	—	2	1	no	—
221	#435	—	2	1	no	—
222	C₈×D₄	—	2	1	no	—
223	C₈×D₄	—	2	1	no	—
224	#424	Dic₇₉	1	1	yes	characteristic, complemented
225	#408	Dic₇₉	1	1	yes	characteristic, complemented
226	#407	C₂×D₇₉	1	1	yes	characteristic
227	C₂×C₂²⋊C₈	—	79	1	no	—
228	C₂×C₂²⋊C₈	—	79	1	no	—
229	#405	Dic₇₉	1	1	yes	characteristic, complemented
230	C₂×#97	—	158	1	no	—
231	C₂×C₄×C₈	—	158	1	no	—
232	C₄×C₂²⋊C₄	—	79	1	no	—
233	C₄×C₂²⋊C₄	—	79	1	no	—
234	#336	—	158	1	no	—
235	#336	—	158	1	no	—
236	#328	—	79	2	no	—
237	#328	—	79	2	no	—
238	#327	—	79	2	no	—
239	#327	—	79	2	no	—
240	C₂×#41	C₂×Dic₇₉	1	1	yes	characteristic
241	C₂³×C₄	C₂²×D₇₉	1	1	yes	characteristic
242	#131	—	4	2	no	—
243	C₂×M₁₆	—	2	1	no	—
244	C₂×M₁₆	C₂×Dic₇₉	1	1	yes	characteristic
245	C₂×M₁₆	C₂×Dic₇₉	1	1	yes	characteristic
246	C₂²×C₈	—	2	1	no	—
247	C₂²×C₈	—	4	2	no	—
248	C₂²×C₈	—	158	1	no	—
249	C₂²×C₈	—	158	1	no	—
250	C₂²×C₈	C₂×Dic₇₉	1	1	yes	characteristic
251	C₂²×C₈	C₂×Dic₇₉	1	1	yes	characteristic
252	C₂²×C₈	C₂²⋊D₇₉	1	1	yes	characteristic
253	C₂²×C₈	C₂²⋊D₇₉	1	1	yes	characteristic
254	C₂²×C₈	C₂²⋊D₇₉	1	1	yes	characteristic
255	C₂²×C₈	C₂²⋊D₇₉	1	1	yes	characteristic
256	#123	—	2	1	no	—
257	C₂²⋊Q₈	C₄×D₇₉	1	1	yes	characteristic
258	C₂²⋊Q₈	C₄×D₇₉	1	1	yes	characteristic
259	#121	C₄×D₇₉	1	1	yes	characteristic
260	#121	C₄×D₇₉	1	1	yes	characteristic
261	#120	—	2	1	no	—
262	C₄×D₄	—	2	1	no	—
263	C₄×D₄	—	2	1	no	—
264	#117	C₂×Dic₇₉	1	1	yes	characteristic
265	C₂×C₂²⋊C₄	—	158	1	no	—
266	C₂×C₂²⋊C₄	—	158	1	no	—
267	C₂×C₄²	—	158	1	no	—
268	C₂×C₄²	—	158	1	no	—
269	C₄⋊C₈	—	2	1	no	—
270	C₄⋊C₈	—	2	1	no	—
271	C₂²⋊C₈	—	2	1	no	—
272	C₂²⋊C₈	—	2	1	no	—
273	C₂²⋊C₈	—	2	1	no	—
274	C₂²⋊C₈	—	2	1	no	—
275	C₂²⋊C₈	—	79	2	no	—
276	C₂²⋊C₈	—	79	2	no	—
277	C₂²⋊C₈	—	158	1	no	—
278	C₂²⋊C₈	—	158	1	no	—
279	#97	—	2	1	no	—
280	#97	—	316	2	no	—
281	C₄×C₈	—	2	1	no	—
282	C₄×C₈	—	316	2	no	—
283	#95	—	79	2	no	—
284	#95	—	79	2	no	—
285	C₂⁴	#11929624	1	1	yes	characteristic
286	#41	—	4	1	no	—
287	#41	—	4	1	no	—
288	C₂×Q₈	C₄×Dic₇₉	1	1	yes	characteristic
289	C₂×D₄	—	2	1	no	—
290	C₂×D₄	—	2	1	no	—
291	C₂×D₄	—	2	1	no	—
292	C₂×D₄	C₄×Dic₇₉	1	1	yes	characteristic
293	C₂²×C₄	—	2	1	no	—
294	C₂²×C₄	—	4	1	no	—
295	C₂²×C₄	—	4	1	no	—
296	C₂²×C₄	—	158	2	no	—
297	C₂²×C₄	—	158	2	no	—
298	C₂²×C₄	C₂×C₄×D₇₉	1	1	yes	characteristic
299	C₂²×C₄	C₂×C₄×D₇₉	1	1	yes	characteristic
300	C₂²×C₄	C₂²×Dic₇₉	1	1	yes	characteristic
301	C₂²×C₄	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
302	C₂²×C₄	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
303	C₂²×C₄	#11929624	1	1	yes	characteristic
304	M₁₆	—	4	2	no	—
305	M₁₆	—	4	1	no	—
306	M₁₆	—	4	1	no	—
307	C₂×C₈	—	2	2	no	—
308	C₂×C₈	—	2	2	no	—
309	C₂×C₈	—	2	2	no	—
310	C₂×C₈	—	2	1	no	—
311	C₂×C₈	—	2	1	no	—
312	C₂×C₈	—	4	1	no	—
313	C₂×C₈	—	4	1	no	—
314	C₂×C₈	—	4	1	no	—
315	C₂×C₈	—	4	2	no	—
316	C₂×C₈	—	316	1	no	—
317	C₂×C₈	—	316	1	no	—
318	C₂×C₈	—	316	1	no	—
319	C₂×C₈	—	316	1	no	—
320	C₂×C₈	—	158	2	no	—
321	C₂×C₈	—	158	2	no	—
322	C₂×C₈	C₂²⋊Dic₇₉	1	1	yes	characteristic
323	C₂×C₈	C₂²⋊Dic₇₉	1	1	yes	characteristic
324	C₂×C₈	C₂²⋊Dic₇₉	1	1	yes	characteristic
325	C₂×C₈	C₂²⋊Dic₇₉	1	1	yes	characteristic
326	C₄⋊C₄	—	2	1	no	—
327	C₄⋊C₄	—	2	1	no	—
328	C₄⋊C₄	C₄×Dic₇₉	1	1	yes	characteristic
329	C₄⋊C₄	C₄×Dic₇₉	1	1	yes	characteristic
330	C₂²⋊C₄	—	2	1	no	—
331	C₂²⋊C₄	—	2	1	no	—
332	C₂²⋊C₄	—	2	1	no	—
333	C₂²⋊C₄	—	2	1	no	—
334	C₂²⋊C₄	—	2	1	no	—
335	C₂²⋊C₄	—	316	2	no	—
336	C₂²⋊C₄	—	158	4	no	—
337	C₄²	—	2	1	no	—
338	C₄²	—	316	1	no	—
339	C₄²	—	316	1	no	—
340	C₄²	—	316	1	no	—
341	C₄²	—	316	1	no	—
342	C₂³	—	2	2	no	—
343	C₂³	—	2	2	no	—
344	C₂³	—	2	1	no	—
345	C₂³	—	4	1	no	—
346	C₂³	#14579120	1	1	yes	characteristic
347	C₂³	C₄×C₂²⋊D₇₉	1	1	yes	characteristic
348	C₂³	C₄×C₂²⋊D₇₉	1	1	yes	characteristic
349	Q₈	—	4	1	no	—
350	D₄	—	4	1	no	—
351	D₄	—	4	2	no	—
352	D₄	—	4	2	no	—
353	D₄	—	4	2	no	—
354	C₂×C₄	—	2	1	no	—
355	C₂×C₄	—	2	1	no	—
356	C₂×C₄	—	2	1	no	—
357	C₂×C₄	—	2	1	no	—
358	C₂×C₄	—	2	1	no	—
359	C₂×C₄	—	2	1	no	—
360	C₂×C₄	—	2	1	no	—
361	C₂×C₄	—	2	1	no	—
362	C₂×C₄	—	2	1	no	—
363	C₂×C₄	—	4	1	no	—
364	C₂×C₄	—	4	1	no	—
365	C₂×C₄	—	4	1	no	—
366	C₂×C₄	—	4	1	no	—
367	C₂×C₄	—	4	1	no	—
368	C₂×C₄	—	316	2	no	—
369	C₂×C₄	—	316	2	no	—
370	C₂×C₄	—	316	2	no	—
371	C₂×C₄	—	316	2	no	—
372	C₂×C₄	—	316	2	no	—
373	C₂×C₄	—	158	4	no	—
374	C₂×C₄	C₂×C₄×Dic₇₉	1	1	yes	characteristic
375	C₂×C₄	C₂×C₂²⋊Dic₇₉	1	1	yes	characteristic
376	C₂×C₄	C₄×C₂²⋊D₇₉	1	1	yes	characteristic
377	C₂×C₄	C₄×C₂²⋊D₇₉	1	1	yes	characteristic
378	C₈	—	2	1	no	—
379	C₈	—	2	1	no	—
380	C₈	—	2	1	no	—
381	C₈	—	4	1	no	—
382	C₈	—	4	1	no	—
383	C₈	—	316	2	no	—
384	C₈	—	316	2	no	—
385	C₈	#14579076	1	2	yes	—
386	C₂²	—	2	1	no	—
387	C₂²	—	2	1	no	—
388	C₂²	—	2	1	no	—
389	C₂²	—	2	1	no	—
390	C₂²	—	2	1	no	—
391	C₂²	—	2	1	no	—
392	C₂²	—	2	1	no	—
393	C₂²	—	4	4	no	—
394	C₂²	—	4	1	no	—
395	C₂²	—	4	1	no	—
396	C₂²	—	4	1	no	—
397	C₂²	C₄×C₂²⋊Dic₇₉	1	1	yes	characteristic
398	C₂²	#19098678	1	2	yes	—
399	C₂²	#19098683	1	2	yes	—
400	C₄	—	2	1	no	—
401	C₄	—	2	1	no	—
402	C₄	—	2	1	no	—
403	C₄	—	4	1	no	—
404	C₄	—	4	1	no	—
405	C₄	—	4	1	no	—
406	C₄	—	316	4	no	—
407	C₄	—	632	2	no	—
408	C₄	C₂×#14579076	1	1	yes	characteristic
409	C₄	#19098537	1	1	yes	characteristic
410	C₂	—	2	2	no	—
411	C₂	—	2	2	no	—
412	C₂	—	4	1	no	—
413	C₂	—	8	1	no	—
414	C₂	C₄×#14579076	1	1	yes	characteristic
415	C₂	#23763235	1	1	yes	characteristic
416	C₂	#23763242	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×C₂²⋊Dic₇₉
commutator	C₂×C₄×C₇₉	C₂×C₄²
Frattini	C₂³×C₄	C₂²×D₇₉
Fitting	C₇₉×#2929	C₂
socle	C₂²×C₇₉	C₄×C₂²⋊C₄
prime radical	#525×C₇₉	C₂²
cosocle	C₂³×C₄×C₇₉	C₂³
hypercenter	#2929	D₇₉
hypocenter	C₇₉	#8240
LCS	G ▷ C₂×C₄×C₇₉ ▷ C₂²×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂³×C₈ ◁ #2929

Complements

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

N	H ≅ G/N	type
1. #23763176	C₂	semidirect
2. C₈×C₂²⋊Dic₇₉	C₂	semidirect
5. #23761287	C₂	semidirect
6. #23761285	C₂	semidirect
16. #19098300	C₄	semidirect
17. #19098300	C₄	semidirect
18. #19098297	C₄	semidirect
19. #19098297	C₄	semidirect
20. C₂×#131×C₇₉	C₄	semidirect
27. #424×C₇₉	C₄	semidirect
28. #408×C₇₉	C₄	semidirect
30. #405×C₇₉	C₄	semidirect
216. C₇₉	#8240	semidirect
217. C₂×#131	Dic₇₉	semidirect
224. #424	Dic₇₉	semidirect
225. #408	Dic₇₉	semidirect
229. #405	Dic₇₉	semidirect

Maximal subgroups

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

subgroup	index
#23763176	2
C₈×C₂²⋊Dic₇₉	2
#23761891	2
#23761287	2
#23761285	2
C₇₉×#2929	2
#8240	79