Subgroups — #35152445

Order 20224.

2706 conjugacy classes of subgroups.

The subgroup lattice has 530 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#23776603	C₂	1	2	yes	maximal, complemented
2	#23772284	C₂	1	4	yes	maximal, complemented
3	#23772276	C₂	1	4	yes	maximal, complemented
4	#23772268	C₂	1	2	yes	maximal, complemented
5	#23772260	C₂	1	4	yes	maximal, complemented
6	#23772252	C₂	1	2	yes	maximal, complemented
7	#23772201	C₂	1	4	yes	maximal, complemented
8	#135×Dic₇₉	C₂	1	4	yes	maximal, complemented
9	C₂×#19098601	C₂	1	1	yes	maximal, characteristic, complemented
10	#23771919	C₂	1	2	yes	maximal, complemented
11	C₂×#19098518	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×#135×C₇₉	C₂	1	1	yes	maximal, characteristic
13	C₂²×#11929608	C₂²	1	1	yes	characteristic
14	#19099046	—	2	4	no	—
15	#19099046	C₂²	1	8	yes	complemented
16	#19099041	C₂²	1	4	yes	—
17	#19099038	—	2	4	no	—
18	#19099038	C₂²	1	4	yes	—
19	#41×Dic₇₉	—	2	4	no	—
20	#41×Dic₇₉	C₂²	1	8	yes	complemented
21	C₂×#14579120	—	2	4	no	—
22	C₂×#14579120	C₂²	1	2	yes	—
23	C₂×#14579120	C₂²	1	1	yes	characteristic
24	#19098675	C₂²	1	8	yes	complemented
25	#19098670	C₂²	1	8	yes	complemented
26	#19098664	C₂²	1	16	yes	complemented
27	Q₁₆×Dic₇₉	C₂²	1	8	yes	complemented
28	SD₁₆×Dic₇₉	C₂²	1	16	yes	complemented
29	D₈×Dic₇₉	C₂²	1	8	yes	complemented
30	#19098601	C₂²	1	2	yes	—
31	#19098601	C₂²	1	2	yes	—
32	#19098601	C₂²	1	2	yes	complemented
33	#19098601	C₂²	1	2	yes	complemented
34	C₂×#14579095	C₂²	1	2	yes	complemented
35	C₂×#14579093	C₂²	1	2	yes	complemented
36	#19098572	C₂²	1	4	yes	—
37	#19098568	C₂²	1	4	yes	—
38	#19098564	C₂²	1	8	yes	complemented
39	#19098559	C₂²	1	8	yes	complemented
40	#19098518	C₂²	1	2	yes	—
41	#19098518	C₂²	1	2	yes	—
42	#19098518	C₂²	1	2	yes	complemented
43	#19098518	C₂²	1	2	yes	complemented
44	C₂×#14579071	C₂²	1	2	yes	complemented
45	C₂×C₈×Dic₇₉	C₂²	1	2	yes	complemented
46	C₂²×#41×C₇₉	C₂²	1	2	yes	—
47	C₂×#135×C₇₉	C₄	1	16	yes	complemented
48	C₂×#135×C₇₉	C₂²	1	2	yes	—
49	C₂×#135×C₇₉	C₂²	1	2	yes	—
50	C₂×#135×C₇₉	C₂²	1	2	yes	—
51	C₂×#135×C₇₉	C₂²	1	2	yes	—
52	C₂²×Q₁₆×C₇₉	C₂²	1	1	yes	characteristic
53	C₂²×SD₁₆×C₇₉	C₂²	1	2	yes	—
54	C₂²×D₈×C₇₉	C₂²	1	1	yes	characteristic
55	C₂³×C₈×C₇₉	C₂²	1	1	yes	characteristic
56	C₂×#11929608	—	2	4	no	—
57	C₂×#11929608	C₂³	1	2	yes	—
58	C₂×#11929608	C₂³	1	2	yes	—
59	C₂²×C₇₉⋊C₈	C₂³	1	2	yes	—
60	Q₈×Dic₇₉	—	2	8	no	—
61	Q₈×Dic₇₉	C₂³	1	16	yes	—
62	D₄×Dic₇₉	—	2	16	no	—
63	D₄×Dic₇₉	—	2	8	no	—
64	D₄×Dic₇₉	—	2	16	no	—
65	D₄×Dic₇₉	C₂³	1	16	yes	—
66	#14579120	—	2	2	no	—
67	#14579120	—	2	2	no	—
68	#14579120	—	2	8	no	—
69	#14579120	—	2	8	no	—
70	#14579120	—	2	8	no	—
71	#14579120	D₄	1	2	yes	—
72	#14579120	D₄	1	2	yes	—
73	#14579120	C₂³	1	4	yes	—
74	#14579120	C₂³	1	4	yes	—
75	#14579120	C₂³	1	2	yes	—
76	#14579120	C₂³	1	2	yes	—
77	C₂×C₄⋊Dic₇₉	—	2	8	no	—
78	C₂×C₄⋊Dic₇₉	D₄	1	2	yes	—
79	C₂×C₄⋊Dic₇₉	C₂³	1	4	yes	—
80	C₂×C₂²⋊Dic₇₉	—	2	2	no	—
81	C₂×C₂²⋊Dic₇₉	—	2	8	no	—
82	C₂×C₂²⋊Dic₇₉	D₄	1	2	yes	—
83	C₂×C₄×Dic₇₉	—	2	2	no	—
84	C₂×C₄×Dic₇₉	—	2	8	no	—
85	C₂×C₄×Dic₇₉	C₂³	1	2	yes	—
86	#14579095	C₂³	1	4	yes	—
87	#14579095	C₂³	1	4	yes	—
88	#14579093	C₂³	1	4	yes	—
89	#14579093	C₂³	1	4	yes	—
90	#14579085	C₂³	1	16	yes	—
91	#14579082	C₂³	1	16	yes	—
92	#14579071	C₂³	1	4	yes	—
93	#14579071	C₂³	1	4	yes	—
94	C₈×Dic₇₉	C₂³	1	4	yes	—
95	C₈×Dic₇₉	C₂³	1	4	yes	—
96	C₂×#41×C₇₉	—	2	2	no	—
97	C₂×#41×C₇₉	—	2	2	no	—
98	C₂×#41×C₇₉	—	2	8	no	—
99	C₂×#41×C₇₉	C₂×C₄	1	16	yes	complemented
100	C₂×#41×C₇₉	C₂³	1	4	yes	—
101	C₂×#41×C₇₉	C₂³	1	4	yes	—
102	C₂²×Q₈×C₇₉	C₂³	1	2	yes	—
103	C₂²×D₄×C₇₉	—	2	2	no	—
104	C₂²×D₄×C₇₉	C₂³	1	2	yes	—
105	C₂³×C₄×C₇₉	—	2	2	no	—
106	C₂³×C₄×C₇₉	C₂³	1	1	yes	characteristic
107	#135×C₇₉	C₂×C₄	1	16	yes	complemented
108	#135×C₇₉	C₂×C₄	1	16	yes	complemented
109	#135×C₇₉	C₂×C₄	1	16	yes	complemented
110	#135×C₇₉	C₂×C₄	1	16	yes	complemented
111	C₂×Q₁₆×C₇₉	C₂×C₄	1	8	yes	complemented
112	C₂×Q₁₆×C₇₉	C₂³	1	2	yes	—
113	C₂×Q₁₆×C₇₉	C₂³	1	2	yes	—
114	C₂×SD₁₆×C₇₉	C₂×C₄	1	16	yes	complemented
115	C₂×SD₁₆×C₇₉	C₂³	1	4	yes	—
116	C₂×SD₁₆×C₇₉	C₂³	1	4	yes	—
117	C₂×D₈×C₇₉	C₂×C₄	1	8	yes	complemented
118	C₂×D₈×C₇₉	C₂³	1	2	yes	—
119	C₂×D₈×C₇₉	C₂³	1	2	yes	—
120	C₂²×C₈×C₇₉	C₂×C₄	1	8	yes	complemented
121	C₂²×C₈×C₇₉	C₂³	1	1	yes	characteristic
122	C₂²×C₈×C₇₉	C₂³	1	1	yes	characteristic
123	C₂²×C₈×C₇₉	C₂³	1	1	yes	characteristic
124	C₂²×C₈×C₇₉	C₂³	1	1	yes	characteristic
125	C₂²×C₈×C₇₉	C₂³	1	1	yes	characteristic
126	C₂²×C₈×C₇₉	C₂³	1	1	yes	characteristic
127	C₂²×Dic₇₉	—	2	16	no	—
128	C₂²×Dic₇₉	—	2	4	no	—
129	C₂²×Dic₇₉	C₂×D₄	1	4	yes	—
130	#11929608	—	2	4	no	—
131	#11929608	—	2	4	no	—
132	C₂×C₇₉⋊C₈	—	2	4	no	—
133	C₂×C₇₉⋊C₈	C₂⁴	1	4	yes	—
134	C₄⋊Dic₇₉	—	2	16	no	—
135	C₄⋊Dic₇₉	—	2	4	no	—
136	C₄⋊Dic₇₉	C₂×D₄	1	4	yes	—
137	C₄⋊Dic₇₉	C₂×D₄	1	4	yes	—
138	C₄⋊Dic₇₉	C₂⁴	1	8	yes	—
139	C₂²⋊Dic₇₉	—	2	16	no	—
140	C₂²⋊Dic₇₉	—	2	4	no	—
141	C₂²⋊Dic₇₉	—	2	4	no	—
142	C₂²⋊Dic₇₉	C₂×D₄	1	4	yes	—
143	C₂²⋊Dic₇₉	C₂×D₄	1	4	yes	—
144	C₄×Dic₇₉	—	2	16	no	—
145	C₄×Dic₇₉	—	2	4	no	—
146	C₄×Dic₇₉	—	2	4	no	—
147	C₄×Dic₇₉	C₂×D₄	1	4	yes	—
148	C₄×Dic₇₉	C₂⁴	1	4	yes	—
149	C₂⁴×C₇₉	—	2	2	no	—
150	C₂⁴×C₇₉	C₂×D₄	1	1	yes	characteristic
151	#41×C₇₉	—	2	16	no	—
152	#41×C₇₉	—	2	16	no	—
153	#41×C₇₉	—	2	8	no	—
154	#41×C₇₉	—	2	8	no	—
155	#41×C₇₉	C₂²×C₄	1	16	yes	—
156	#41×C₇₉	C₂²×C₄	1	16	yes	—
157	C₂×Q₈×C₇₉	—	2	2	no	—
158	C₂×Q₈×C₇₉	—	2	4	no	—
159	C₂×Q₈×C₇₉	C₂²×C₄	1	8	yes	—
160	C₂×Q₈×C₇₉	C₂⁴	1	4	yes	—
161	C₂×D₄×C₇₉	—	2	16	no	—
162	C₂×D₄×C₇₉	—	2	4	no	—
163	C₂×D₄×C₇₉	—	2	4	no	—
164	C₂×D₄×C₇₉	—	2	2	no	—
165	C₂×D₄×C₇₉	—	2	4	no	—
166	C₂×D₄×C₇₉	C₂²×C₄	1	8	yes	—
167	C₂×D₄×C₇₉	C₂⁴	1	4	yes	—
168	C₂²×C₄×C₇₉	—	2	2	no	—
169	C₂²×C₄×C₇₉	—	2	16	no	—
170	C₂²×C₄×C₇₉	—	2	4	no	—
171	C₂²×C₄×C₇₉	—	2	4	no	—
172	C₂²×C₄×C₇₉	C₂²×C₄	1	4	yes	—
173	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
174	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
175	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
176	C₂²×C₄×C₇₉	#41	1	4	yes	—
177	C₂²×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
178	C₂²×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
179	C₂²×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
180	Q₁₆×C₇₉	C₂²×C₄	1	8	yes	—
181	Q₁₆×C₇₉	C₂²×C₄	1	8	yes	—
182	SD₁₆×C₇₉	C₂²×C₄	1	16	yes	—
183	SD₁₆×C₇₉	C₂²×C₄	1	16	yes	—
184	D₈×C₇₉	C₂²×C₄	1	8	yes	—
185	D₈×C₇₉	C₂²×C₄	1	8	yes	—
186	C₂×C₈×C₇₉	C₂²×C₄	1	4	yes	—
187	C₂×C₈×C₇₉	C₂²×C₄	1	4	yes	—
188	C₂×C₈×C₇₉	C₂²×C₄	1	4	yes	—
189	C₂×C₈×C₇₉	C₂²×C₄	1	4	yes	—
190	C₂×C₈×C₇₉	C₂²×C₄	1	4	yes	—
191	C₂×C₈×C₇₉	C₂²×C₄	1	4	yes	—
192	C₂×C₈×C₇₉	C₂⁴	1	1	yes	characteristic
193	C₂×C₈×C₇₉	C₂⁴	1	1	yes	characteristic
194	C₂×C₈×C₇₉	C₂⁴	1	1	yes	characteristic
195	C₂×C₈×C₇₉	C₂⁴	1	1	yes	characteristic
196	C₂³×C₇₉	—	2	4	no	—
197	C₂³×C₇₉	—	2	8	no	—
198	C₂³×C₇₉	—	4	2	no	—
199	C₂³×C₇₉	—	8	4	no	—
200	C₂³×C₇₉	C₄×D₄	1	4	yes	—
201	C₂³×C₇₉	C₂²×D₄	1	1	yes	characteristic
202	C₂³×C₇₉	C₂²×D₄	1	1	yes	characteristic
203	C₂³×C₇₉	C₂²×D₄	1	1	yes	characteristic
204	Q₈×C₇₉	—	2	8	no	—
205	Q₈×C₇₉	—	2	4	no	—
206	Q₈×C₇₉	C₂³×C₄	1	8	yes	—
207	D₄×C₇₉	—	2	16	no	—
208	D₄×C₇₉	—	2	16	no	—
209	D₄×C₇₉	—	2	8	no	—
210	D₄×C₇₉	—	2	4	no	—
211	D₄×C₇₉	C₂³×C₄	1	8	yes	—
212	C₂×C₄×C₇₉	—	2	8	no	—
213	C₂×C₄×C₇₉	—	2	4	no	—
214	C₂×C₄×C₇₉	—	2	16	no	—
215	C₂×C₄×C₇₉	—	2	16	no	—
216	C₂×C₄×C₇₉	C₄×D₄	1	4	yes	—
217	C₂×C₄×C₇₉	C₄×D₄	1	4	yes	—
218	C₂×C₄×C₇₉	C₄×D₄	1	4	yes	—
219	C₂×C₄×C₇₉	C₂³×C₄	1	2	yes	—
220	C₂×C₄×C₇₉	C₂³×C₄	1	2	yes	—
221	C₂×C₄×C₇₉	C₂³×C₄	1	2	yes	—
222	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
223	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
224	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
225	C₂×C₄×C₇₉	C₂×#41	1	2	yes	—
226	C₂×C₄×C₇₉	C₂×#41	1	2	yes	—
227	C₂×C₄×C₇₉	C₂×#41	1	2	yes	—
228	C₂×C₄×C₇₉	C₂⁵	1	1	yes	characteristic
229	C₂×Dic₇₉	—	2	8	no	—
230	C₂×Dic₇₉	—	4	4	no	—
231	C₂×Dic₇₉	—	8	16	no	—
232	C₂×Dic₇₉	—	8	4	no	—
233	C₂×Dic₇₉	C₂²×D₄	1	8	yes	—
234	C₈×C₇₉	C₂³×C₄	1	2	yes	—
235	C₈×C₇₉	C₂³×C₄	1	2	yes	—
236	C₈×C₇₉	C₂³×C₄	1	2	yes	—
237	C₈×C₇₉	C₂³×C₄	1	2	yes	—
238	C₇₉⋊C₈	—	2	4	no	—
239	C₂²×C₇₉	—	2	2	no	—
240	C₂²×C₇₉	—	2	2	no	—
241	C₂²×C₇₉	—	2	2	no	—
242	C₂²×C₇₉	—	2	8	no	—
243	C₂²×C₇₉	—	4	4	no	—
244	C₂²×C₇₉	—	4	8	no	—
245	C₂²×C₇₉	—	8	8	no	—
246	C₂²×C₇₉	C₂×C₄×D₄	1	2	yes	—
247	C₂²×C₇₉	C₂×C₄×D₄	1	2	yes	—
248	C₂²×C₇₉	C₂×C₄×D₄	1	2	yes	—
249	C₂²×C₇₉	C₂³×D₄	1	1	yes	characteristic
250	C₄×C₇₉	—	2	8	no	—
251	C₄×C₇₉	C₂×C₄×D₄	1	2	yes	—
252	C₄×C₇₉	C₂×C₄×D₄	1	2	yes	—
253	C₄×C₇₉	C₂×C₄×D₄	1	2	yes	—
254	C₄×C₇₉	C₂⁴×C₄	1	1	yes	characteristic
255	C₄×C₇₉	C₂²×#41	1	1	yes	characteristic
256	Dic₇₉	—	2	8	no	—
257	Dic₇₉	—	4	8	no	—
258	#60167	—	79	1	no	maximal, Sylow
259	C₂×C₇₉	—	2	2	no	—
260	C₂×C₇₉	—	2	2	no	—
261	C₂×C₇₉	—	2	2	no	—
262	C₂×C₇₉	—	4	8	no	—
263	C₂×C₇₉	C₂²×C₄×D₄	1	1	yes	characteristic
264	C₂×C₇₉	#3584	1	2	yes	—
265	C₂²×#135	D₇₉	1	1	yes	characteristic
266	#3428	—	79	2	no	—
267	#2952	—	79	4	no	—
268	#2951	—	79	4	no	—
269	#2950	—	79	2	no	—
270	#2949	—	79	4	no	—
271	#2948	—	79	2	no	—
272	#2943	—	79	4	no	—
273	C₄×#135	—	79	4	no	—
274	C₂×#427	—	79	1	no	—
275	#2896	—	79	2	no	—
276	C₂×#405	—	79	1	no	—
277	C₇₉	#60167	1	1	yes	characteristic, complemented, Sylow
278	C₂²×#41	C₂×D₇₉	1	2	yes	—
279	C₂×#135	Dic₇₉	1	16	yes	complemented
280	C₂×#135	C₂×D₇₉	1	2	yes	—
281	C₂×#135	C₂×D₇₉	1	2	yes	—
282	C₂×#135	C₂×D₇₉	1	2	yes	—
283	C₂×#135	C₂×D₇₉	1	2	yes	—
284	C₂²×Q₁₆	C₂×D₇₉	1	1	yes	characteristic
285	C₂²×SD₁₆	C₂×D₇₉	1	2	yes	—
286	C₂²×D₈	C₂×D₇₉	1	1	yes	characteristic
287	C₂²×M₁₆	—	79	1	no	—
288	C₂³×C₈	C₂×D₇₉	1	1	yes	characteristic
289	#520	—	79	8	no	—
290	#520	—	158	4	no	—
291	#519	—	79	4	no	—
292	#518	—	79	4	no	—
293	#518	—	158	4	no	—
294	C₄×#41	—	79	8	no	—
295	C₄×#41	—	158	4	no	—
296	C₂×#117	—	79	1	no	—
297	C₂×#117	—	79	2	no	—
298	C₂×#117	—	158	4	no	—
299	#442	—	79	8	no	—
300	#441	—	79	8	no	—
301	#440	—	79	16	no	—
302	C₄×Q₁₆	—	79	8	no	—
303	C₄×SD₁₆	—	79	16	no	—
304	C₄×D₈	—	79	8	no	—
305	#427	—	79	2	no	—
306	#427	—	79	2	no	—
307	#427	—	79	2	no	—
308	#427	—	79	2	no	—
309	C₂×#107	—	79	2	no	—
310	C₂×#106	—	79	2	no	—
311	#419	—	79	4	no	—
312	#418	—	79	4	no	—
313	#417	—	79	8	no	—
314	#416	—	79	8	no	—
315	#405	—	79	2	no	—
316	#405	—	79	2	no	—
317	#405	—	79	2	no	—
318	#405	—	79	2	no	—
319	C₂×#97	—	79	2	no	—
320	C₂×C₄×C₈	—	79	2	no	—
321	C₂×#41	—	2	2	no	—
322	C₂×#41	—	2	2	no	—
323	C₂×#41	—	2	8	no	—
324	C₂×#41	C₂×Dic₇₉	1	16	yes	complemented
325	C₂×#41	C₂²×D₇₉	1	4	yes	—
326	C₂×#41	C₂²×D₇₉	1	4	yes	—
327	C₂²×Q₈	C₂²×D₇₉	1	2	yes	—
328	C₂²×D₄	—	2	2	no	—
329	C₂²×D₄	C₂²×D₇₉	1	2	yes	—
330	C₂³×C₄	—	2	2	no	—
331	C₂³×C₄	C₂²×D₇₉	1	1	yes	characteristic
332	#135	C₂×Dic₇₉	1	16	yes	complemented
333	#135	C₂×Dic₇₉	1	16	yes	complemented
334	#135	C₂×Dic₇₉	1	16	yes	complemented
335	#135	C₂×Dic₇₉	1	16	yes	complemented
336	C₂×Q₁₆	C₂×Dic₇₉	1	8	yes	complemented
337	C₂×Q₁₆	C₂²×D₇₉	1	2	yes	—
338	C₂×Q₁₆	C₂²×D₇₉	1	2	yes	—
339	C₂×SD₁₆	C₂×Dic₇₉	1	16	yes	complemented
340	C₂×SD₁₆	C₂²×D₇₉	1	4	yes	—
341	C₂×SD₁₆	C₂²×D₇₉	1	4	yes	—
342	C₂×D₈	C₂×Dic₇₉	1	8	yes	complemented
343	C₂×D₈	C₂²×D₇₉	1	2	yes	—
344	C₂×D₈	C₂²×D₇₉	1	2	yes	—
345	C₂×M₁₆	—	79	2	no	—
346	C₂×M₁₆	—	79	2	no	—
347	C₂×M₁₆	—	158	4	no	—
348	C₂²×C₈	—	79	2	no	—
349	C₂²×C₈	C₂×Dic₇₉	1	8	yes	complemented
350	C₂²×C₈	C₂²×D₇₉	1	1	yes	characteristic
351	C₂²×C₈	C₂²×D₇₉	1	1	yes	characteristic
352	C₂²×C₈	C₂²×D₇₉	1	1	yes	characteristic
353	C₂²×C₈	C₂²×D₇₉	1	1	yes	characteristic
354	C₂²×C₈	C₂²×D₇₉	1	1	yes	characteristic
355	C₂²×C₈	C₂²×D₇₉	1	1	yes	characteristic
356	C₄×Q₈	—	79	16	no	—
357	C₄×Q₈	—	158	8	no	—
358	C₄×D₄	—	79	16	no	—
359	C₄×D₄	—	158	16	no	—
360	C₄×D₄	—	158	8	no	—
361	C₄×D₄	—	158	16	no	—
362	#117	—	79	2	no	—
363	#117	—	79	2	no	—
364	#117	—	79	2	no	—
365	#117	—	79	2	no	—
366	#117	—	79	4	no	—
367	#117	—	79	4	no	—
368	#117	—	158	8	no	—
369	#117	—	158	8	no	—
370	#117	—	158	8	no	—
371	#117	—	158	2	no	—
372	#117	—	158	2	no	—
373	C₂×C₄⋊C₄	—	79	2	no	—
374	C₂×C₄⋊C₄	—	79	4	no	—
375	C₂×C₄⋊C₄	—	158	8	no	—
376	C₂×C₂²⋊C₄	—	79	2	no	—
377	C₂×C₂²⋊C₄	—	158	8	no	—
378	C₂×C₂²⋊C₄	—	158	2	no	—
379	C₂×C₄²	—	79	2	no	—
380	C₂×C₄²	—	158	8	no	—
381	C₂×C₄²	—	158	2	no	—
382	#107	—	79	4	no	—
383	#107	—	79	4	no	—
384	#106	—	79	4	no	—
385	#106	—	79	4	no	—
386	#103	—	79	16	no	—
387	#102	—	79	16	no	—
388	#97	—	79	4	no	—
389	#97	—	79	4	no	—
390	C₄×C₈	—	79	4	no	—
391	C₄×C₈	—	79	4	no	—
392	C₂⁴	—	2	2	no	—
393	C₂⁴	D₄×D₇₉	1	1	yes	characteristic
394	#41	—	2	8	no	—
395	#41	—	2	8	no	—
396	#41	—	2	16	no	—
397	#41	—	2	16	no	—
398	#41	C₂²×Dic₇₉	1	16	yes	—
399	#41	C₂²×Dic₇₉	1	16	yes	—
400	C₂×Q₈	—	2	4	no	—
401	C₂×Q₈	—	2	2	no	—
402	C₂×Q₈	C₂²×Dic₇₉	1	8	yes	—
403	C₂×Q₈	C₂³×D₇₉	1	4	yes	—
404	C₂×D₄	—	2	16	no	—
405	C₂×D₄	—	2	4	no	—
406	C₂×D₄	—	2	4	no	—
407	C₂×D₄	—	2	4	no	—
408	C₂×D₄	—	2	2	no	—
409	C₂×D₄	C₂²×Dic₇₉	1	8	yes	—
410	C₂×D₄	C₂³×D₇₉	1	4	yes	—
411	C₂²×C₄	—	2	2	no	—
412	C₂²×C₄	—	2	16	no	—
413	C₂²×C₄	—	2	4	no	—
414	C₂²×C₄	—	2	4	no	—
415	C₂²×C₄	—	79	4	no	—
416	C₂²×C₄	—	158	16	no	—
417	C₂²×C₄	—	158	4	no	—
418	C₂²×C₄	C₂²×Dic₇₉	1	4	yes	—
419	C₂²×C₄	D₄×D₇₉	1	1	yes	characteristic
420	C₂²×C₄	D₄×D₇₉	1	1	yes	characteristic
421	C₂²×C₄	D₄×D₇₉	1	1	yes	characteristic
422	C₂²×C₄	#11929623	1	4	yes	—
423	C₂²×C₄	C₂³×D₇₉	1	1	yes	characteristic
424	C₂²×C₄	C₂³×D₇₉	1	1	yes	characteristic
425	C₂²×C₄	C₂³×D₇₉	1	1	yes	characteristic
426	Q₁₆	C₂²×Dic₇₉	1	8	yes	—
427	Q₁₆	C₂²×Dic₇₉	1	8	yes	—
428	SD₁₆	C₂²×Dic₇₉	1	16	yes	—
429	SD₁₆	C₂²×Dic₇₉	1	16	yes	—
430	D₈	C₂²×Dic₇₉	1	8	yes	—
431	D₈	C₂²×Dic₇₉	1	8	yes	—
432	M₁₆	—	158	4	no	—
433	M₁₆	—	158	4	no	—
434	C₂×C₈	—	79	4	no	—
435	C₂×C₈	—	158	4	no	—
436	C₂×C₈	C₂²×Dic₇₉	1	4	yes	—
437	C₂×C₈	C₂²×Dic₇₉	1	4	yes	—
438	C₂×C₈	C₂²×Dic₇₉	1	4	yes	—
439	C₂×C₈	C₂²×Dic₇₉	1	4	yes	—
440	C₂×C₈	C₂²×Dic₇₉	1	4	yes	—
441	C₂×C₈	C₂²×Dic₇₉	1	4	yes	—
442	C₂×C₈	C₂³×D₇₉	1	1	yes	characteristic
443	C₂×C₈	C₂³×D₇₉	1	1	yes	characteristic
444	C₂×C₈	C₂³×D₇₉	1	1	yes	characteristic
445	C₂×C₈	C₂³×D₇₉	1	1	yes	characteristic
446	C₄⋊C₄	—	79	4	no	—
447	C₄⋊C₄	—	79	4	no	—
448	C₄⋊C₄	—	79	8	no	—
449	C₄⋊C₄	—	158	16	no	—
450	C₄⋊C₄	—	158	4	no	—
451	C₂²⋊C₄	—	79	4	no	—
452	C₂²⋊C₄	—	79	4	no	—
453	C₂²⋊C₄	—	158	16	no	—
454	C₂²⋊C₄	—	158	4	no	—
455	C₂²⋊C₄	—	158	4	no	—
456	C₄²	—	79	4	no	—
457	C₄²	—	79	4	no	—
458	C₄²	—	158	16	no	—
459	C₄²	—	158	4	no	—
460	C₄²	—	158	4	no	—
461	C₂³	—	2	4	no	—
462	C₂³	—	2	8	no	—
463	C₂³	—	4	2	no	—
464	C₂³	—	8	4	no	—
465	C₂³	D₄×Dic₇₉	1	4	yes	—
466	C₂³	C₂×D₄×D₇₉	1	1	yes	characteristic
467	C₂³	C₂×D₄×D₇₉	1	1	yes	characteristic
468	C₂³	C₂×D₄×D₇₉	1	1	yes	characteristic
469	Q₈	—	2	8	no	—
470	Q₈	—	2	4	no	—
471	Q₈	C₂³×Dic₇₉	1	8	yes	—
472	D₄	—	2	16	no	—
473	D₄	—	2	16	no	—
474	D₄	—	2	8	no	—
475	D₄	—	2	4	no	—
476	D₄	C₂³×Dic₇₉	1	8	yes	—
477	C₂×C₄	—	2	8	no	—
478	C₂×C₄	—	2	4	no	—
479	C₂×C₄	—	2	16	no	—
480	C₂×C₄	—	2	16	no	—
481	C₂×C₄	—	316	4	no	—
482	C₂×C₄	—	79	8	no	—
483	C₂×C₄	—	632	4	no	—
484	C₂×C₄	—	632	16	no	—
485	C₂×C₄	—	158	8	no	—
486	C₂×C₄	D₄×Dic₇₉	1	4	yes	—
487	C₂×C₄	D₄×Dic₇₉	1	4	yes	—
488	C₂×C₄	D₄×Dic₇₉	1	4	yes	—
489	C₂×C₄	C₂³×Dic₇₉	1	2	yes	—
490	C₂×C₄	C₂³×Dic₇₉	1	2	yes	—
491	C₂×C₄	C₂³×Dic₇₉	1	2	yes	—
492	C₂×C₄	C₂×D₄×D₇₉	1	1	yes	characteristic
493	C₂×C₄	C₂×D₄×D₇₉	1	1	yes	characteristic
494	C₂×C₄	C₂×D₄×D₇₉	1	1	yes	characteristic
495	C₂×C₄	C₂×#11929623	1	2	yes	—
496	C₂×C₄	C₂×#11929623	1	2	yes	—
497	C₂×C₄	C₂×#11929623	1	2	yes	—
498	C₂×C₄	C₂⁴×D₇₉	1	1	yes	characteristic
499	C₈	—	158	4	no	—
500	C₈	C₂³×Dic₇₉	1	2	yes	—
501	C₈	C₂³×Dic₇₉	1	2	yes	—
502	C₈	C₂³×Dic₇₉	1	2	yes	—
503	C₈	C₂³×Dic₇₉	1	2	yes	—
504	C₂²	—	2	2	no	—
505	C₂²	—	2	2	no	—
506	C₂²	—	2	2	no	—
507	C₂²	—	2	8	no	—
508	C₂²	—	4	4	no	—
509	C₂²	—	4	8	no	—
510	C₂²	—	8	8	no	—
511	C₂²	C₂×D₄×Dic₇₉	1	2	yes	—
512	C₂²	C₂×D₄×Dic₇₉	1	2	yes	—
513	C₂²	C₂×D₄×Dic₇₉	1	2	yes	—
514	C₂²	C₂²×D₄×D₇₉	1	1	yes	characteristic
515	C₄	—	2	8	no	—
516	C₄	—	316	8	no	—
517	C₄	—	158	8	no	—
518	C₄	C₂×D₄×Dic₇₉	1	2	yes	—
519	C₄	C₂×D₄×Dic₇₉	1	2	yes	—
520	C₄	C₂×D₄×Dic₇₉	1	2	yes	—
521	C₄	C₂⁴×Dic₇₉	1	1	yes	characteristic
522	C₄	C₂²×#11929623	1	1	yes	characteristic
523	C₂	—	2	2	no	—
524	C₂	—	2	2	no	—
525	C₂	—	2	2	no	—
526	C₂	—	4	8	no	—
527	C₂	C₂²×D₄×Dic₇₉	1	1	yes	characteristic
528	C₂	#23778169	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₇₉
commutator	C₄×C₇₉	C₂⁴×C₄
Frattini	C₂×C₄	C₂⁴×D₇₉
Fitting, prime radical	C₂²×#135×C₇₉	C₂
socle	C₂²×C₇₉	C₂³×D₄
cosocle	C₂×C₄×C₇₉	C₂⁵
hypercenter	C₂²×#135	D₇₉
hypocenter	C₇₉	#60167
LCS	G ▷ C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂³×C₄ ◁ C₂²×#135

Complements

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

N	H ≅ G/N	type
1. #23776603	C₂	semidirect
2. #23772284	C₂	semidirect
3. #23772276	C₂	semidirect
4. #23772268	C₂	semidirect
5. #23772260	C₂	semidirect
6. #23772252	C₂	semidirect
7. #23772201	C₂	semidirect
8. #135×Dic₇₉	C₂	semidirect
9. C₂×#19098601	C₂	semidirect
10. #23771919	C₂	semidirect
11. C₂×#19098518	C₂	semidirect
15. #19099046	C₂²	semidirect
20. #41×Dic₇₉	C₂²	semidirect
24. #19098675	C₂²	semidirect
25. #19098670	C₂²	semidirect
26. #19098664	C₂²	semidirect
27. Q₁₆×Dic₇₉	C₂²	semidirect
28. SD₁₆×Dic₇₉	C₂²	semidirect
29. D₈×Dic₇₉	C₂²	semidirect
32. #19098601	C₂²	semidirect
33. #19098601	C₂²	semidirect
34. C₂×#14579095	C₂²	semidirect
35. C₂×#14579093	C₂²	semidirect
38. #19098564	C₂²	semidirect
39. #19098559	C₂²	semidirect
42. #19098518	C₂²	semidirect
43. #19098518	C₂²	semidirect
44. C₂×#14579071	C₂²	semidirect
45. C₂×C₈×Dic₇₉	C₂²	semidirect
47. C₂×#135×C₇₉	C₄	semidirect
99. C₂×#41×C₇₉	C₂×C₄	semidirect
107. #135×C₇₉	C₂×C₄	semidirect
108. #135×C₇₉	C₂×C₄	semidirect
109. #135×C₇₉	C₂×C₄	semidirect
110. #135×C₇₉	C₂×C₄	semidirect
111. C₂×Q₁₆×C₇₉	C₂×C₄	semidirect
114. C₂×SD₁₆×C₇₉	C₂×C₄	semidirect
117. C₂×D₈×C₇₉	C₂×C₄	semidirect
120. C₂²×C₈×C₇₉	C₂×C₄	semidirect
277. C₇₉	#60167	semidirect
279. C₂×#135	Dic₇₉	semidirect
324. C₂×#41	C₂×Dic₇₉	semidirect
332. #135	C₂×Dic₇₉	semidirect
333. #135	C₂×Dic₇₉	semidirect
334. #135	C₂×Dic₇₉	semidirect
335. #135	C₂×Dic₇₉	semidirect
336. C₂×Q₁₆	C₂×Dic₇₉	semidirect
339. C₂×SD₁₆	C₂×Dic₇₉	semidirect
342. C₂×D₈	C₂×Dic₇₉	semidirect
349. C₂²×C₈	C₂×Dic₇₉	semidirect

Maximal subgroups

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

subgroup	index
#23776603	2
#23772284	2
#23772276	2
#23772268	2
#23772260	2
#23772252	2
#23772201	2
#135×Dic₇₉	2
C₂×#19098601	2
#23771919	2
C₂×#19098518	2
C₂²×#135×C₇₉	2
#60167	79