Subgroups — #34286285

Order 20224.

1018 conjugacy classes of subgroups.

The subgroup lattice has 412 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#19098610	C₂	1	1	yes	maximal, characteristic
2	#23771988	C₂	1	1	yes	maximal, characteristic
3	C₂×#19098517	C₂	1	1	yes	maximal, characteristic
4	#405×D₇₉	C₂	1	2	yes	maximal
5	#23763287	C₂	1	1	yes	maximal, characteristic, complemented
6	#23763286	C₂	1	1	yes	maximal, characteristic, complemented
7	#23763283	C₂	1	2	yes	maximal, complemented
8	#23763280	C₂	1	2	yes	maximal, complemented
9	#23763279	C₂	1	1	yes	maximal, characteristic, complemented
10	#23763108	C₂	1	2	yes	maximal
11	C₇₉×#1772	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×#11929607	C₂²	1	1	yes	characteristic
13	C₂×M₁₆×D₇₉	C₂²	1	2	yes	—
14	C₂²×C₈×D₇₉	C₂²	1	1	yes	characteristic
15	C₂×#14579118	C₂²	1	1	yes	characteristic
16	#117×D₇₉	C₂²	1	2	yes	—
17	#19098610	C₄	1	8	yes	complemented
18	C₂×#14579097	C₂²	1	1	yes	characteristic
19	C₂×#14579096	C₂²	1	2	yes	—
20	#19098604	C₄	1	4	yes	complemented
21	#19098602	C₄	1	4	yes	complemented
22	#19098601	C₂²	1	1	yes	characteristic
23	#19098599	C₂²	1	2	yes	—
24	#19098521	C₂²	1	2	yes	—
25	#19098520	—	2	2	no	—
26	#19098519	C₂²	1	2	yes	—
27	#19098518	C₂²	1	2	yes	—
28	#19098517	—	2	2	no	—
29	#19098517	C₄	1	8	yes	complemented
30	C₂×#14579072	C₂²	1	1	yes	characteristic
31	C₂×#14579071	C₂²	1	1	yes	characteristic
32	#97×D₇₉	—	2	2	no	—
33	C₂×C₈×Dic₇₉	C₂²	1	1	yes	characteristic
34	C₄×C₈×D₇₉	—	2	2	no	—
35	#19098324	C₂²	1	2	yes	—
36	#19098323	C₂²	1	2	yes	—
37	#19098322	C₂²	1	2	yes	—
38	C₂×#108×C₇₉	C₂²	1	1	yes	characteristic
39	#427×C₇₉	C₂²	1	1	yes	characteristic
40	#405×C₇₉	C₂²	1	2	yes	—
41	C₂×C₄×C₈×C₇₉	C₂²	1	1	yes	characteristic
42	#339×C₇₉	C₂²	1	2	yes	—
43	C₂²×C₄×D₇₉	C₂³	1	1	yes	characteristic
44	C₂×#11929608	C₂³	1	2	yes	—
45	C₂×#11929607	—	2	2	no	—
46	C₂×#11929607	C₂×C₄	1	4	yes	—
47	C₂×#11929607	C₂×C₄	1	2	yes	—
48	C₂×#11929607	C₂×C₄	1	2	yes	—
49	C₂×#11929607	C₂×C₄	1	4	yes	—
50	M₁₆×D₇₉	—	2	4	no	—
51	M₁₆×D₇₉	C₂×C₄	1	8	yes	—
52	C₂²×C₇₉⋊C₈	C₂³	1	1	yes	characteristic
53	C₂²×C₇₉⋊C₈	C₂³	1	1	yes	characteristic
54	C₂×C₈×D₇₉	—	2	2	no	—
55	C₂×C₈×D₇₉	C₂×C₄	1	4	yes	—
56	C₂×C₈×D₇₉	D₄	1	2	yes	—
57	C₂×C₈×D₇₉	D₄	1	2	yes	—
58	C₂×C₈×D₇₉	Q₈	1	4	yes	—
59	#14579120	C₂³	1	2	yes	—
60	#14579119	C₂×C₄	1	4	yes	—
61	#14579118	—	2	2	no	—
62	#14579118	—	2	2	no	—
63	#14579118	C₂×C₄	1	4	yes	—
64	#14579117	—	2	2	no	—
65	C₂×Dic₇₉⋊C₄	—	2	1	no	—
66	C₄⋊C₄×D₇₉	C₂×C₄	1	4	yes	—
67	C₂×(C₂×D₇₉)⋊C₄	—	2	1	no	—
68	C₂²⋊C₄×D₇₉	—	2	2	no	—
69	C₂×C₄×Dic₇₉	C₂³	1	1	yes	characteristic
70	C₄²×D₇₉	—	2	2	no	—
71	#14579097	C₂×C₄	1	4	yes	complemented
72	#14579096	C₂×C₄	1	8	yes	complemented
73	#14579095	C₂×C₄	1	2	yes	—
74	#14579094	C₂×C₄	1	4	yes	—
75	#14579093	C₂×C₄	1	2	yes	—
76	#14579092	C₂×C₄	1	4	yes	—
77	#14579072	—	2	2	no	—
78	#14579072	C₂×C₄	1	4	yes	complemented
79	#14579071	—	2	2	no	—
80	#14579071	—	2	2	no	—
81	#14579071	C₂×C₄	1	4	yes	complemented
82	C₄×C₇₉⋊C₈	—	2	2	no	—
83	C₈×Dic₇₉	—	2	2	no	—
84	C₈×Dic₇₉	—	2	2	no	—
85	C₈×Dic₇₉	C₂×C₄	1	4	yes	complemented
86	C₂×M₁₆×C₇₉	C₂³	1	2	yes	—
87	C₂²×C₈×C₇₉	C₂³	1	1	yes	characteristic
88	C₂²×C₈×C₇₉	C₂³	1	1	yes	characteristic
89	#117×C₇₉	C₂³	1	2	yes	—
90	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
91	#108×C₇₉	C₂×C₄	1	4	yes	complemented
92	#107×C₇₉	C₂×C₄	1	2	yes	—
93	#106×C₇₉	C₂×C₄	1	2	yes	—
94	#97×C₇₉	—	2	2	no	—
95	C₄×C₈×C₇₉	—	2	2	no	—
96	C₄×C₈×C₇₉	C₂×C₄	1	4	yes	complemented
97	C₂³×D₇₉	#41	1	1	yes	characteristic
98	C₂²×Dic₇₉	—	2	1	no	—
99	C₂²×Dic₇₉	#41	1	1	yes	characteristic
100	C₂×C₄×D₇₉	—	2	4	no	—
101	C₂×C₄×D₇₉	C₂²×C₄	1	2	yes	—
102	C₂×C₄×D₇₉	C₂²×C₄	1	2	yes	—
103	C₂×C₄×D₇₉	C₂²×C₄	1	2	yes	—
104	C₂×C₄×D₇₉	C₂×D₄	1	2	yes	—
105	C₂×C₄×D₇₉	C₂×Q₈	1	2	yes	—
106	C₂×C₄×D₇₉	#41	1	2	yes	—
107	#11929608	—	2	2	no	—
108	#11929608	C₂²×C₄	1	4	yes	—
109	#11929607	—	2	8	no	—
110	#11929607	C₄²	1	8	yes	—
111	#11929607	C₄²	1	8	yes	—
112	C₂×C₇₉⋊C₈	—	2	2	no	—
113	C₂×C₇₉⋊C₈	C₂²×C₄	1	2	yes	—
114	C₂×C₇₉⋊C₈	C₂²×C₄	1	2	yes	—
115	C₂×C₇₉⋊C₈	C₂²×C₄	1	2	yes	—
116	C₂×C₇₉⋊C₈	C₂²×C₄	1	2	yes	—
117	C₂×C₇₉⋊C₈	C₂×D₄	1	2	yes	—
118	C₂×C₇₉⋊C₈	C₂×Q₈	1	2	yes	—
119	C₈×D₇₉	—	2	8	no	—
120	C₈×D₇₉	C₄⋊C₄	1	8	yes	—
121	C₈×D₇₉	C₄⋊C₄	1	8	yes	—
122	C₄⋊Dic₇₉	C₂²×C₄	1	4	yes	—
123	Dic₇₉⋊C₄	—	2	4	no	—
124	Dic₇₉⋊C₄	—	2	4	no	—
125	C₂²⋊Dic₇₉	—	2	2	no	—
126	(C₂×D₇₉)⋊C₄	—	2	4	no	—
127	(C₂×D₇₉)⋊C₄	—	2	4	no	—
128	C₄×Dic₇₉	—	2	4	no	—
129	C₄×Dic₇₉	—	2	2	no	—
130	C₄×Dic₇₉	—	2	1	no	—
131	C₄×Dic₇₉	C₂²×C₄	1	2	yes	—
132	C₂²×C₄×C₇₉	—	2	1	no	—
133	C₂²×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
134	M₁₆×C₇₉	—	2	2	no	—
135	M₁₆×C₇₉	C₂²×C₄	1	4	yes	—
136	C₂×C₈×C₇₉	—	2	2	no	—
137	C₂×C₈×C₇₉	C₂²×C₄	1	2	yes	—
138	C₂×C₈×C₇₉	C₂²×C₄	1	1	yes	characteristic
139	C₂×C₈×C₇₉	C₂²×C₄	1	1	yes	characteristic
140	C₂×C₈×C₇₉	C₂²×C₄	1	2	yes	—
141	C₂×C₈×C₇₉	C₂²×C₄	1	2	yes	—
142	C₂×C₈×C₇₉	C₂×D₄	1	1	yes	characteristic
143	C₂×C₈×C₇₉	C₂×D₄	1	1	yes	characteristic
144	C₂×C₈×C₇₉	C₂×Q₈	1	2	yes	—
145	C₄⋊C₄×C₇₉	C₂²×C₄	1	4	yes	—
146	C₂²⋊C₄×C₇₉	—	2	2	no	—
147	C₄²×C₇₉	—	2	2	no	—
148	C₄²×C₇₉	—	2	1	no	—
149	C₄²×C₇₉	C₂²×C₄	1	2	yes	—
150	C₂³×C₇₉	C₂×#41	1	1	yes	characteristic
151	C₂²×D₇₉	—	4	2	no	—
152	C₂²×D₇₉	#117	1	2	yes	—
153	C₂²×D₇₉	C₄×D₄	1	2	yes	—
154	C₂²×D₇₉	C₄×Q₈	1	2	yes	—
155	C₂×C₄×C₇₉	—	2	2	no	—
156	C₂×C₄×C₇₉	—	2	4	no	—
157	C₂×C₄×C₇₉	—	4	2	no	—
158	C₂×C₄×C₇₉	C₂³×C₄	1	1	yes	characteristic
159	C₂×C₄×C₇₉	C₂³×C₄	1	1	yes	characteristic
160	C₂×C₄×C₇₉	C₂³×C₄	1	1	yes	characteristic
161	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
162	C₂×C₄×C₇₉	C₂²×Q₈	1	1	yes	characteristic
163	C₂×C₄×C₇₉	C₂×#41	1	1	yes	characteristic
164	C₂×Dic₇₉	—	2	2	no	—
165	C₂×Dic₇₉	—	2	4	no	—
166	C₂×Dic₇₉	—	4	2	no	—
167	C₂×Dic₇₉	#117	1	2	yes	—
168	C₂×Dic₇₉	C₄×D₄	1	2	yes	—
169	C₂×Dic₇₉	C₄×Q₈	1	2	yes	—
170	C₄×D₇₉	—	4	8	no	—
171	C₄×D₇₉	C₂×C₄²	1	4	yes	—
172	C₄×D₇₉	C₂×C₄⋊C₄	1	4	yes	—
173	C₄×D₇₉	C₄×D₄	1	4	yes	—
174	C₄×D₇₉	C₄×Q₈	1	4	yes	—
175	C₈×C₇₉	—	2	4	no	—
176	C₈×C₇₉	C₂×C₄²	1	2	yes	—
177	C₈×C₇₉	C₂×C₄²	1	2	yes	—
178	C₈×C₇₉	C₂×C₄⋊C₄	1	2	yes	—
179	C₈×C₇₉	C₂×C₄⋊C₄	1	2	yes	—
180	C₇₉⋊C₈	—	2	4	no	—
181	C₇₉⋊C₈	C₂×C₄²	1	4	yes	—
182	C₇₉⋊C₈	C₂×C₄⋊C₄	1	4	yes	—
183	C₂²×C₇₉	—	2	2	no	—
184	C₂²×C₇₉	C₂×#117	1	1	yes	characteristic
185	C₂²×C₇₉	C₂×C₄×D₄	1	1	yes	characteristic
186	C₂²×C₇₉	C₂×C₄×Q₈	1	1	yes	characteristic
187	C₂×D₇₉	—	2	4	no	—
188	C₂×D₇₉	—	4	2	no	—
189	C₂×D₇₉	—	4	2	no	—
190	C₂×D₇₉	C₄×C₄⋊C₄	1	4	yes	—
191	C₄×C₇₉	—	4	2	no	—
192	C₄×C₇₉	—	4	4	no	—
193	C₄×C₇₉	C₂²×C₄²	1	1	yes	characteristic
194	C₄×C₇₉	C₂²×C₄⋊C₄	1	1	yes	characteristic
195	C₄×C₇₉	C₂×C₄×D₄	1	1	yes	characteristic
196	C₄×C₇₉	C₂×C₄×Q₈	1	1	yes	characteristic
197	Dic₇₉	—	4	2	no	—
198	Dic₇₉	—	4	4	no	—
199	Dic₇₉	C₄×C₄⋊C₄	1	4	yes	—
200	#20444	—	79	1	no	maximal, Sylow
201	C₂×C₇₉	—	2	1	no	—
202	C₂×C₇₉	—	2	1	no	—
203	C₂×C₇₉	C₂×C₄×C₄⋊C₄	1	1	yes	characteristic
204	C₂×C₇₉	#2955	1	2	yes	—
205	D₇₉	—	2	4	no	—
206	C₂×#430	—	79	1	no	—
207	#2911	—	79	1	no	—
208	C₂×#405	—	79	1	no	—
209	C₂×#405	—	79	2	no	—
210	#1773	—	79	1	no	—
211	#1773	—	79	1	no	—
212	#1773	—	79	2	no	—
213	#1772	—	79	2	no	—
214	#1772	—	79	1	no	—
215	#1772	D₇₉	1	1	yes	characteristic, complemented
216	#1733	—	79	2	no	—
217	C₇₉	#20444	1	1	yes	characteristic, complemented, Sylow
218	C₂²×M₁₆	—	79	1	no	—
219	C₂²×M₁₆	—	79	2	no	—
220	C₂³×C₈	—	79	1	no	—
221	C₂×#117	—	79	1	no	—
222	C₂×#117	—	79	2	no	—
223	#430	—	79	8	no	—
224	C₂×#108	—	79	2	no	—
225	C₂×#108	—	79	1	no	—
226	C₂×#108	C₂×D₇₉	1	1	yes	characteristic
227	#428	—	79	4	no	—
228	#428	—	79	4	no	—
229	#427	—	79	1	no	—
230	#427	—	79	2	no	—
231	#427	C₂×D₇₉	1	1	yes	characteristic
232	#405	—	79	8	no	—
233	#405	—	79	2	no	—
234	#405	—	79	2	no	—
235	#405	—	79	2	no	—
236	#405	—	158	2	no	—
237	#405	—	158	2	no	—
238	#405	C₂×D₇₉	1	2	yes	—
239	C₂×#97	—	79	1	no	—
240	C₂×#97	—	79	1	no	—
241	C₂×#97	—	158	2	no	—
242	C₂×C₄×C₈	—	79	1	no	—
243	C₂×C₄×C₈	—	158	2	no	—
244	C₂×C₄×C₈	C₂×D₇₉	1	1	yes	characteristic
245	#339	—	79	2	no	—
246	#339	—	79	2	no	—
247	#339	—	79	2	no	—
248	#339	C₂×D₇₉	1	2	yes	—
249	C₂³×C₄	—	79	1	no	—
250	C₂×M₁₆	—	79	4	no	—
251	C₂×M₁₆	—	79	2	no	—
252	C₂×M₁₆	—	79	2	no	—
253	C₂×M₁₆	—	79	4	no	—
254	C₂×M₁₆	—	79	2	no	—
255	C₂×M₁₆	—	79	8	no	—
256	C₂×M₁₆	—	158	2	no	—
257	C₂×M₁₆	—	158	4	no	—
258	C₂×M₁₆	C₂²×D₇₉	1	2	yes	—
259	C₂²×C₈	—	79	1	no	—
260	C₂²×C₈	—	79	1	no	—
261	C₂²×C₈	—	79	4	no	—
262	C₂²×C₈	—	79	2	no	—
263	C₂²×C₈	—	79	2	no	—
264	C₂²×C₈	—	79	4	no	—
265	C₂²×C₈	—	158	2	no	—
266	C₂²×C₈	C₂²×D₇₉	1	1	yes	characteristic
267	C₂²×C₈	C₂²×D₇₉	1	1	yes	characteristic
268	#117	—	79	4	no	—
269	#117	—	79	2	no	—
270	#117	—	79	4	no	—
271	#117	—	158	2	no	—
272	#117	—	158	2	no	—
273	#117	—	158	2	no	—
274	#117	C₂²×D₇₉	1	2	yes	—
275	C₂×C₄⋊C₄	—	79	4	no	—
276	C₂×C₄⋊C₄	—	158	1	no	—
277	C₂×C₂²⋊C₄	—	158	2	no	—
278	C₂×C₂²⋊C₄	—	158	1	no	—
279	C₂×C₄²	—	79	1	no	—
280	C₂×C₄²	—	158	2	no	—
281	C₂×C₄²	C₂²×D₇₉	1	1	yes	characteristic
282	#108	—	79	8	no	—
283	#108	—	79	4	no	—
284	#108	C₄×D₇₉	1	4	yes	complemented
285	#107	—	79	2	no	—
286	#107	—	79	4	no	—
287	#107	C₄×D₇₉	1	2	yes	—
288	#106	—	79	2	no	—
289	#106	—	79	4	no	—
290	#106	C₄×D₇₉	1	2	yes	—
291	#97	—	2	2	no	—
292	#97	—	79	4	no	—
293	#97	—	79	4	no	—
294	#97	—	158	2	no	—
295	#97	—	158	2	no	—
296	#97	—	158	2	no	—
297	C₄×C₈	—	2	2	no	—
298	C₄×C₈	—	79	4	no	—
299	C₄×C₈	—	158	2	no	—
300	C₄×C₈	—	158	2	no	—
301	C₄×C₈	—	158	2	no	—
302	C₄×C₈	C₄×D₇₉	1	4	yes	complemented
303	C₂⁴	—	79	1	no	—
304	C₂²×C₄	—	2	1	no	—
305	C₂²×C₄	—	79	1	no	—
306	C₂²×C₄	—	79	2	no	—
307	C₂²×C₄	—	79	2	no	—
308	C₂²×C₄	—	79	2	no	—
309	C₂²×C₄	—	79	2	no	—
310	C₂²×C₄	—	79	2	no	—
311	C₂²×C₄	—	79	2	no	—
312	C₂²×C₄	—	158	4	no	—
313	C₂²×C₄	—	158	1	no	—
314	C₂²×C₄	C₂³×D₇₉	1	1	yes	characteristic
315	M₁₆	—	2	2	no	—
316	M₁₆	—	79	8	no	—
317	M₁₆	—	79	8	no	—
318	M₁₆	—	79	4	no	—
319	M₁₆	—	158	8	no	—
320	M₁₆	—	158	2	no	—
321	M₁₆	C₂×C₄×D₇₉	1	4	yes	—
322	C₂×C₈	—	2	2	no	—
323	C₂×C₈	—	79	2	no	—
324	C₂×C₈	—	79	2	no	—
325	C₂×C₈	—	79	2	no	—
326	C₂×C₈	—	79	2	no	—
327	C₂×C₈	—	79	2	no	—
328	C₂×C₈	—	79	2	no	—
329	C₂×C₈	—	79	8	no	—
330	C₂×C₈	—	79	8	no	—
331	C₂×C₈	—	158	8	no	—
332	C₂×C₈	—	158	2	no	—
333	C₂×C₈	C₂×C₄×D₇₉	1	2	yes	—
334	C₂×C₈	C₂×C₄×D₇₉	1	1	yes	characteristic
335	C₂×C₈	C₂×C₄×D₇₉	1	1	yes	characteristic
336	C₂×C₈	C₂×C₄×D₇₉	1	2	yes	—
337	C₂×C₈	C₂×C₄×D₇₉	1	2	yes	—
338	C₂×C₈	D₄×D₇₉	1	1	yes	characteristic
339	C₂×C₈	D₄×D₇₉	1	1	yes	characteristic
340	C₂×C₈	Q₈×D₇₉	1	2	yes	—
341	C₄⋊C₄	—	79	4	no	—
342	C₄⋊C₄	—	158	4	no	—
343	C₄⋊C₄	—	158	4	no	—
344	C₄⋊C₄	C₂×C₄×D₇₉	1	4	yes	—
345	C₂²⋊C₄	—	2	2	no	—
346	C₂²⋊C₄	—	158	4	no	—
347	C₂²⋊C₄	—	158	4	no	—
348	C₂²⋊C₄	—	158	2	no	—
349	C₄²	—	2	1	no	—
350	C₄²	—	2	2	no	—
351	C₄²	—	79	2	no	—
352	C₄²	—	158	4	no	—
353	C₄²	—	158	1	no	—
354	C₄²	—	158	2	no	—
355	C₄²	C₂×C₄×D₇₉	1	2	yes	—
356	C₂³	—	316	2	no	—
357	C₂³	—	79	2	no	—
358	C₂³	—	79	2	no	—
359	C₂³	—	79	2	no	—
360	C₂³	#41×D₇₉	1	1	yes	characteristic
361	C₂×C₄	—	2	2	no	—
362	C₂×C₄	—	2	4	no	—
363	C₂×C₄	—	4	2	no	—
364	C₂×C₄	—	316	8	no	—
365	C₂×C₄	—	316	2	no	—
366	C₂×C₄	—	79	2	no	—
367	C₂×C₄	—	79	2	no	—
368	C₂×C₄	—	79	2	no	—
369	C₂×C₄	—	79	4	no	—
370	C₂×C₄	—	79	4	no	—
371	C₂×C₄	—	79	4	no	—
372	C₂×C₄	—	79	4	no	—
373	C₂×C₄	—	158	2	no	—
374	C₂×C₄	—	158	4	no	—
375	C₂×C₄	C₂²×C₄×D₇₉	1	1	yes	characteristic
376	C₂×C₄	C₂²×C₄×D₇₉	1	1	yes	characteristic
377	C₂×C₄	C₂²×C₄×D₇₉	1	1	yes	characteristic
378	C₂×C₄	C₂×D₄×D₇₉	1	1	yes	characteristic
379	C₂×C₄	C₂×Q₈×D₇₉	1	1	yes	characteristic
380	C₂×C₄	#41×D₇₉	1	1	yes	characteristic
381	C₈	—	2	4	no	—
382	C₈	—	79	4	no	—
383	C₈	—	79	4	no	—
384	C₈	—	158	4	no	—
385	C₈	C₄²×D₇₉	1	2	yes	—
386	C₈	C₄²×D₇₉	1	2	yes	—
387	C₈	C₄⋊C₄×D₇₉	1	2	yes	—
388	C₈	C₄⋊C₄×D₇₉	1	2	yes	—
389	C₂²	—	2	2	no	—
390	C₂²	—	316	2	no	—
391	C₂²	—	316	2	no	—
392	C₂²	—	79	4	no	—
393	C₂²	—	158	4	no	—
394	C₂²	#117×D₇₉	1	1	yes	characteristic
395	C₂²	C₄×D₄×D₇₉	1	1	yes	characteristic
396	C₂²	C₄×Q₈×D₇₉	1	1	yes	characteristic
397	C₄	—	4	2	no	—
398	C₄	—	4	4	no	—
399	C₄	—	316	2	no	—
400	C₄	—	316	4	no	—
401	C₄	—	79	4	no	—
402	C₄	C₂×C₄²×D₇₉	1	1	yes	characteristic
403	C₄	C₂×C₄⋊C₄×D₇₉	1	1	yes	characteristic
404	C₄	C₄×D₄×D₇₉	1	1	yes	characteristic
405	C₄	C₄×Q₈×D₇₉	1	1	yes	characteristic
406	C₂	—	2	1	no	—
407	C₂	—	2	1	no	—
408	C₂	—	158	4	no	—
409	C₂	C₄×C₄⋊C₄×D₇₉	1	1	yes	characteristic
410	C₂	#23772298	1	2	yes	—

	subgroup	G/H
center	C₂×C₈	D₄×D₇₉
commutator	C₄×C₇₉	C₂²×C₄²
Frattini	C₂²×C₄	C₂³×D₇₉
Fitting	C₇₉×#1772	C₂
socle	C₂²×C₇₉	C₂×C₄×D₄
prime radical	C₂³×D₇₉	#41
cosocle	C₂²×C₄×C₇₉	C₂⁴
hypercenter	#1772	D₇₉
hypocenter	C₇₉	#20444
LCS	G ▷ C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂×C₈ ◁ C₂²×C₈ ◁ #1772

Complements

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

N	H ≅ G/N	type
5. #23763287	C₂	semidirect
6. #23763286	C₂	semidirect
7. #23763283	C₂	semidirect
8. #23763280	C₂	semidirect
9. #23763279	C₂	semidirect
11. C₇₉×#1772	C₂	semidirect
17. #19098610	C₄	semidirect
20. #19098604	C₄	semidirect
21. #19098602	C₄	semidirect
29. #19098517	C₄	semidirect
71. #14579097	C₂×C₄	semidirect
72. #14579096	C₂×C₄	semidirect
78. #14579072	C₂×C₄	semidirect
81. #14579071	C₂×C₄	semidirect
85. C₈×Dic₇₉	C₂×C₄	semidirect
91. #108×C₇₉	C₂×C₄	semidirect
96. C₄×C₈×C₇₉	C₂×C₄	semidirect
215. #1772	D₇₉	semidirect
217. C₇₉	#20444	semidirect
284. #108	C₄×D₇₉	semidirect
302. 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
C₂×#19098610	2
#23771988	2
C₂×#19098517	2
#405×D₇₉	2
#23763287	2
#23763286	2
#23763283	2
#23763280	2
#23763279	2
#23763108	2
C₇₉×#1772	2
#20444	79