Subgroups — #23777667

Order 10112.

1058 conjugacy classes of subgroups.

The subgroup lattice has 592 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19099306	C₂	1	2	yes	maximal, complemented
2	#19099302	C₂	1	1	yes	maximal, characteristic, complemented
3	#19099299	C₂	1	1	yes	maximal, characteristic, complemented
4	#19099297	C₂	1	1	yes	maximal, characteristic, complemented
5	#19099280	C₂	1	2	yes	maximal, complemented
6	#19099277	C₂	1	2	yes	maximal, complemented
7	#19099236	C₂	1	2	yes	maximal, complemented
8	#19099219	C₂	1	2	yes	maximal, complemented
9	#19099202	C₂	1	2	yes	maximal, complemented
10	#19099181	C₂	1	2	yes	maximal, complemented
11	#19099180	C₂	1	2	yes	maximal, complemented
12	#19099179	C₂	1	2	yes	maximal, complemented
13	#19099150	C₂	1	2	yes	maximal, complemented
14	#19099145	C₂	1	2	yes	maximal, complemented
15	#19099135	C₂	1	1	yes	maximal, characteristic, complemented
16	#19099126	C₂	1	1	yes	maximal, characteristic, complemented
17	#19099069	C₂	1	1	yes	maximal, characteristic, complemented
18	#19099069	C₂	1	2	yes	maximal, complemented
19	#560×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×#11929623	C₂²	1	2	yes	—
21	C₂×#11929623	C₂²	1	1	yes	characteristic
22	C₂²×Dic₁₅₈	C₂²	1	1	yes	characteristic, complemented
23	C₂×D₄×D₇₉	C₂²	1	1	yes	characteristic, complemented
24	C₂³×Dic₇₉	C₂²	1	1	yes	characteristic, complemented
25	#14579160	C₂²	1	2	yes	complemented
26	#14579160	C₂²	1	2	yes	complemented
27	#14579157	C₂²	1	1	yes	characteristic
28	#14579156	C₂²	1	2	yes	complemented
29	#14579156	C₂²	1	2	yes	complemented
30	#14579156	C₂²	1	2	yes	complemented
31	#14579154	C₂²	1	2	yes	complemented
32	#14579154	C₂²	1	2	yes	complemented
33	#14579149	C₂²	1	1	yes	characteristic, complemented
34	#14579148	C₂²	1	2	yes	complemented
35	#14579148	C₂²	1	1	yes	characteristic, complemented
36	#14579148	C₂²	1	2	yes	complemented
37	#14579148	C₂²	1	2	yes	complemented
38	#14579148	C₂²	1	2	yes	complemented
39	#14579147	C₂²	1	2	yes	—
40	#14579147	C₂²	1	2	yes	—
41	#14579147	C₂²	1	2	yes	—
42	#14579147	C₂²	1	2	yes	complemented
43	#14579147	C₂²	1	2	yes	complemented
44	#14579147	C₂²	1	2	yes	complemented
45	#14579147	C₂²	1	2	yes	complemented
46	#14579147	C₂²	1	2	yes	complemented
47	#14579146	C₂²	1	2	yes	complemented
48	#14579145	C₂²	1	1	yes	characteristic
49	#14579145	C₂²	1	1	yes	characteristic, complemented
50	#14579145	C₂²	1	2	yes	complemented
51	#14579144	C₂²	1	1	yes	characteristic, complemented
52	#14579143	C₂²	1	2	yes	complemented
53	#14579142	C₂²	1	2	yes	complemented
54	#14579142	C₂²	1	2	yes	complemented
55	#14579142	C₂²	1	1	yes	characteristic, complemented
56	#14579142	C₂²	1	1	yes	characteristic, complemented
57	#14579141	C₂²	1	2	yes	complemented
58	#14579140	C₂²	1	2	yes	complemented
59	#14579139	C₂²	1	2	yes	complemented
60	#14579139	C₂²	1	2	yes	complemented
61	#14579138	C₂²	1	2	yes	complemented
62	#14579138	C₂²	1	2	yes	complemented
63	#14579138	C₂²	1	2	yes	complemented
64	#14579138	C₂²	1	2	yes	complemented
65	#14579134	C₂²	1	2	yes	—
66	#14579133	C₂²	1	2	yes	—
67	#14579133	C₂²	1	2	yes	—
68	#14579133	C₂²	1	2	yes	—
69	#14579133	C₂²	1	2	yes	complemented
70	#14579133	C₂²	1	2	yes	complemented
71	#14579132	C₂²	1	2	yes	complemented
72	#14579130	C₂²	1	1	yes	characteristic
73	#14579130	C₂²	1	2	yes	complemented
74	#14579129	C₂²	1	2	yes	—
75	#14579129	C₂²	1	2	yes	—
76	#14579129	C₂²	1	2	yes	—
77	#14579129	C₂²	1	2	yes	complemented
78	C₄×Dic₁₅₈	C₂²	1	2	yes	complemented
79	#14579126	C₂²	1	2	yes	complemented
80	#14579126	C₂²	1	2	yes	complemented
81	D₄×Dic₇₉	C₂²	1	2	yes	complemented
82	D₄×Dic₇₉	C₂²	1	2	yes	complemented
83	D₄×Dic₇₉	C₂²	1	2	yes	complemented
84	D₄×Dic₇₉	C₂²	1	2	yes	complemented
85	C₄×C₂²⋊D₇₉	C₂²	1	2	yes	complemented
86	C₄×C₂²⋊D₇₉	C₂²	1	2	yes	complemented
87	(C₂²⋊D₇₉)⋊C₄	C₂²	1	2	yes	—
88	(C₂²⋊D₇₉)⋊C₄	C₂²	1	2	yes	complemented
89	(C₂²⋊D₇₉)⋊C₄	C₂²	1	2	yes	complemented
90	#14579120	C₂²	1	2	yes	complemented
91	#14579119	C₂²	1	2	yes	complemented
92	#14579118	C₂²	1	1	yes	characteristic, complemented
93	#14579117	C₂²	1	1	yes	characteristic, complemented
94	#14579117	C₂²	1	1	yes	characteristic, complemented
95	#14579117	C₂²	1	2	yes	complemented
96	C₂×(C₂×D₇₉)⋊C₄	C₂²	1	2	yes	complemented
97	C₂²⋊C₄×D₇₉	C₂²	1	2	yes	complemented
98	#127×C₇₉	C₂²	1	1	yes	characteristic
99	#126×C₇₉	C₂²	1	2	yes	complemented
100	#123×C₇₉	C₂²	1	2	yes	complemented
101	#123×C₇₉	C₂²	1	1	yes	characteristic, complemented
102	#121×C₇₉	C₂²	1	2	yes	—
103	#121×C₇₉	C₂²	1	2	yes	complemented
104	#121×C₇₉	C₂²	1	2	yes	complemented
105	#120×C₇₉	C₂²	1	1	yes	characteristic, complemented
106	#120×C₇₉	C₂²	1	2	yes	complemented
107	C₂³×D₇₉	C₂³	1	2	yes	—
108	#11929623	—	4	4	no	—
109	#11929623	—	4	2	no	—
110	C₂×Dic₁₅₈	—	4	2	no	—
111	C₂×Dic₁₅₈	C₂³	1	2	yes	—
112	C₂×Dic₁₅₈	C₂³	1	2	yes	—
113	C₂×Dic₁₅₈	C₂³	1	1	yes	characteristic
114	C₂×Dic₁₅₈	C₂³	1	2	yes	—
115	C₂×Dic₁₅₈	C₂³	1	2	yes	—
116	C₂×D₃₁₆	C₂³	1	1	yes	characteristic
117	C₂×C₂²⋊D₇₉	C₂³	1	2	yes	—
118	C₂×C₂²⋊D₇₉	C₂³	1	1	yes	characteristic
119	C₂×C₂²⋊D₇₉	C₂³	1	2	yes	—
120	C₂×C₂²⋊D₇₉	C₂³	1	1	yes	characteristic
121	C₂×C₂²⋊D₇₉	C₂³	1	2	yes	—
122	C₂×C₂²⋊D₇₉	C₂³	1	2	yes	—
123	C₂×C₂²⋊D₇₉	C₂³	1	2	yes	—
124	C₂×C₂²⋊D₇₉	C₂³	1	2	yes	—
125	D₄×D₇₉	—	4	2	no	—
126	C₂²×Dic₇₉	—	4	2	no	—
127	C₂²×Dic₇₉	C₂³	1	1	yes	characteristic
128	C₂²×Dic₇₉	C₂³	1	2	yes	—
129	C₂²×Dic₇₉	C₂³	1	1	yes	characteristic
130	C₂²×Dic₇₉	C₂³	1	1	yes	characteristic
131	C₂²×Dic₇₉	C₂³	1	2	yes	—
132	C₂²×Dic₇₉	C₂³	1	1	yes	characteristic
133	C₂²×Dic₇₉	C₂³	1	2	yes	—
134	C₂×C₄×D₇₉	C₂³	1	1	yes	characteristic
135	C₂×C₄×D₇₉	C₂³	1	2	yes	—
136	C₂×C₄×D₇₉	C₂³	1	2	yes	—
137	C₄⋊Dic₇₉	C₂³	1	2	yes	—
138	C₄⋊Dic₇₉	C₂³	1	2	yes	—
139	C₄⋊Dic₇₉	C₂³	1	2	yes	—
140	C₄⋊Dic₇₉	C₂³	1	2	yes	—
141	Dic₇₉⋊C₄	C₂³	1	2	yes	—
142	Dic₇₉⋊C₄	C₂³	1	2	yes	—
143	Dic₇₉⋊C₄	C₂³	1	2	yes	—
144	Dic₇₉⋊C₄	C₂³	1	2	yes	—
145	Dic₇₉⋊C₄	C₂³	1	2	yes	—
146	Dic₇₉⋊C₄	C₂³	1	2	yes	—
147	Dic₇₉⋊C₄	C₂³	1	2	yes	—
148	Dic₇₉⋊C₄	C₂³	1	2	yes	—
149	C₂²⋊Dic₇₉	C₂³	1	2	yes	—
150	C₂²⋊Dic₇₉	C₂³	1	1	yes	characteristic
151	C₂²⋊Dic₇₉	C₂³	1	2	yes	—
152	C₂²⋊Dic₇₉	C₂³	1	1	yes	characteristic
153	C₂²⋊Dic₇₉	C₂³	1	2	yes	—
154	C₂²⋊Dic₇₉	C₂³	1	2	yes	—
155	C₂²⋊Dic₇₉	C₂³	1	2	yes	—
156	C₂²⋊Dic₇₉	C₂³	1	2	yes	—
157	C₂²⋊Dic₇₉	C₂³	1	2	yes	—
158	C₂²⋊Dic₇₉	C₂³	1	2	yes	—
159	C₂²⋊Dic₇₉	C₂³	1	2	yes	—
160	C₂²⋊Dic₇₉	C₂³	1	2	yes	—
161	(C₂×D₇₉)⋊C₄	C₂³	1	2	yes	—
162	(C₂×D₇₉)⋊C₄	C₂³	1	2	yes	—
163	(C₂×D₇₉)⋊C₄	C₂³	1	2	yes	—
164	(C₂×D₇₉)⋊C₄	C₂³	1	2	yes	—
165	(C₂×D₇₉)⋊C₄	C₂³	1	2	yes	—
166	(C₂×D₇₉)⋊C₄	C₂³	1	2	yes	—
167	(C₂×D₇₉)⋊C₄	C₂³	1	2	yes	—
168	(C₂×D₇₉)⋊C₄	C₂³	1	2	yes	—
169	(C₂×D₇₉)⋊C₄	C₂³	1	2	yes	—
170	(C₂×D₇₉)⋊C₄	C₂³	1	2	yes	—
171	C₄×Dic₇₉	C₂³	1	2	yes	—
172	C₄×Dic₇₉	C₂³	1	2	yes	—
173	C₄×Dic₇₉	C₂³	1	2	yes	—
174	C₄×Dic₇₉	C₂³	1	2	yes	—
175	C₄×Dic₇₉	C₂³	1	1	yes	characteristic
176	C₄×Dic₇₉	C₂³	1	2	yes	—
177	C₄×Dic₇₉	C₂³	1	2	yes	—
178	C₂⁴×C₇₉	C₂³	1	1	yes	characteristic
179	C₂×D₄×C₇₉	C₂³	1	2	yes	—
180	C₂×D₄×C₇₉	C₂³	1	1	yes	characteristic
181	C₂×D₄×C₇₉	C₂³	1	2	yes	—
182	C₂×D₄×C₇₉	C₂³	1	2	yes	—
183	C₂×D₄×C₇₉	C₂³	1	2	yes	—
184	C₂×D₄×C₇₉	C₂³	1	1	yes	characteristic
185	C₂×D₄×C₇₉	C₂³	1	2	yes	—
186	C₂²×C₄×C₇₉	C₂³	1	1	yes	characteristic
187	C₂²×C₄×C₇₉	C₂³	1	2	yes	—
188	C₄⋊C₄×C₇₉	C₂³	1	2	yes	—
189	C₄⋊C₄×C₇₉	C₂³	1	2	yes	—
190	C₄⋊C₄×C₇₉	C₂³	1	2	yes	—
191	C₂²⋊C₄×C₇₉	C₂³	1	2	yes	—
192	C₂²⋊C₄×C₇₉	C₂³	1	2	yes	—
193	C₂²⋊C₄×C₇₉	C₂³	1	2	yes	—
194	C₂²⋊C₄×C₇₉	C₂³	1	1	yes	characteristic
195	C₂²⋊C₄×C₇₉	C₂³	1	2	yes	—
196	C₂²⋊C₄×C₇₉	C₂³	1	2	yes	—
197	C₂²⋊C₄×C₇₉	C₂³	1	1	yes	characteristic
198	C₄²×C₇₉	C₂³	1	1	yes	characteristic
199	C₂³×C₇₉	—	4	1	no	—
200	C₂³×C₇₉	—	4	2	no	—
201	C₂³×C₇₉	C₂⁴	1	2	yes	—
202	C₂³×C₇₉	C₂⁴	1	1	yes	characteristic
203	C₂³×C₇₉	C₂⁴	1	2	yes	—
204	C₂³×C₇₉	C₂⁴	1	1	yes	characteristic
205	C₂²×D₇₉	—	4	2	no	—
206	C₂²×D₇₉	—	4	2	no	—
207	C₂²×D₇₉	—	4	2	no	—
208	C₂²×D₇₉	C₂⁴	1	1	yes	characteristic
209	C₂²×D₇₉	C₂⁴	1	2	yes	—
210	D₄×C₇₉	—	4	1	no	—
211	D₄×C₇₉	—	4	2	no	—
212	D₄×C₇₉	—	4	1	no	—
213	D₄×C₇₉	—	4	2	no	—
214	D₄×C₇₉	—	4	2	no	—
215	D₄×C₇₉	—	4	2	no	—
216	D₄×C₇₉	—	4	2	no	—
217	C₂×C₄×C₇₉	—	4	1	no	—
218	C₂×C₄×C₇₉	—	4	2	no	—
219	C₂×C₄×C₇₉	C₂⁴	1	2	yes	—
220	C₂×C₄×C₇₉	C₂⁴	1	2	yes	—
221	C₂×C₄×C₇₉	C₂⁴	1	2	yes	—
222	C₂×C₄×C₇₉	C₂⁴	1	2	yes	—
223	C₂×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
224	C₂²⋊D₇₉	—	2	4	no	—
225	C₂²⋊D₇₉	—	4	2	no	—
226	C₂²⋊D₇₉	—	4	2	no	—
227	C₂²⋊D₇₉	—	4	2	no	—
228	C₂²⋊D₇₉	—	4	2	no	—
229	C₂²⋊D₇₉	—	4	2	no	—
230	C₂²⋊D₇₉	—	4	1	no	—
231	C₂²⋊D₇₉	—	4	1	no	—
232	C₂×Dic₇₉	—	2	2	no	—
233	C₂×Dic₇₉	—	2	4	no	—
234	C₂×Dic₇₉	—	2	2	no	—
235	C₂×Dic₇₉	—	4	2	no	—
236	C₂×Dic₇₉	—	4	1	no	—
237	C₂×Dic₇₉	—	4	1	no	—
238	C₂×Dic₇₉	—	4	2	no	—
239	C₂×Dic₇₉	C₂⁴	1	2	yes	—
240	C₂×Dic₇₉	C₂⁴	1	2	yes	—
241	C₂×Dic₇₉	C₂⁴	1	1	yes	characteristic
242	C₂×Dic₇₉	C₂⁴	1	2	yes	—
243	C₂×Dic₇₉	C₂⁴	1	2	yes	—
244	C₂×Dic₇₉	C₂⁴	1	2	yes	—
245	C₂×Dic₇₉	C₂⁴	1	1	yes	characteristic
246	C₂×Dic₇₉	C₂⁴	1	1	yes	characteristic
247	D₃₁₆	—	4	1	no	—
248	C₄×D₇₉	—	2	2	no	—
249	C₄×D₇₉	—	4	2	no	—
250	C₄×D₇₉	—	4	2	no	—
251	Dic₁₅₈	—	2	4	no	—
252	Dic₁₅₈	—	4	2	no	—
253	Dic₁₅₈	—	4	2	no	—
254	Dic₁₅₈	—	4	2	no	—
255	Dic₁₅₈	—	4	1	no	—
256	C₂²×C₇₉	—	2	2	no	—
257	C₂²×C₇₉	—	2	1	no	—
258	C₂²×C₇₉	—	2	2	no	—
259	C₂²×C₇₉	—	2	1	no	—
260	C₂²×C₇₉	—	2	2	no	—
261	C₂²×C₇₉	—	2	2	no	—
262	C₂²×C₇₉	—	2	2	no	—
263	C₂²×C₇₉	—	2	2	no	—
264	C₂²×C₇₉	—	2	2	no	—
265	C₂²×C₇₉	—	2	2	no	—
266	C₂²×C₇₉	—	4	4	no	—
267	C₂²×C₇₉	C₂⁵	1	1	yes	characteristic
268	C₂×D₇₉	—	2	2	no	—
269	C₂×D₇₉	—	2	1	no	—
270	C₂×D₇₉	—	2	2	no	—
271	C₂×D₇₉	—	2	2	no	—
272	C₂×D₇₉	—	2	2	no	—
273	C₂×D₇₉	—	8	4	no	—
274	C₄×C₇₉	—	2	2	no	—
275	C₄×C₇₉	—	2	1	no	—
276	C₄×C₇₉	—	2	2	no	—
277	C₄×C₇₉	—	2	2	no	—
278	C₄×C₇₉	—	2	2	no	—
279	Dic₇₉	—	2	2	no	—
280	Dic₇₉	—	2	1	no	—
281	Dic₇₉	—	2	1	no	—
282	Dic₇₉	—	2	2	no	—
283	Dic₇₉	—	2	2	no	—
284	Dic₇₉	—	2	2	no	—
285	Dic₇₉	—	2	2	no	—
286	Dic₇₉	H(5,𝔽₂)	1	2	yes	—
287	C₂×C₇₉	—	4	2	no	—
288	C₂×C₇₉	—	4	1	no	—
289	C₂×C₇₉	—	4	2	no	—
290	C₂×C₇₉	—	4	1	no	—
291	C₂×C₇₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
292	C₂×C₇₉	#585	1	2	yes	—
293	D₇₉	—	4	2	no	—
294	D₇₉	—	4	1	no	—
295	#3540	—	79	1	no	maximal, Sylow
296	C₇₉	#3540	1	1	yes	characteristic, complemented, Sylow
297	H(3,𝔽₄)	—	79	2	no	—
298	#560	—	79	1	no	—
299	#560	D₇₉	1	1	yes	characteristic, complemented
300	#559	—	79	1	no	—
301	#559	—	79	1	no	—
302	#556	—	79	2	no	—
303	#555	—	79	2	no	—
304	#551	—	79	2	no	—
305	#548	—	79	2	no	—
306	#546	—	79	2	no	—
307	#542	—	79	2	no	—
308	#542	—	79	2	no	—
309	#542	—	79	2	no	—
310	#538	—	79	2	no	—
311	#538	—	79	2	no	—
312	#536	—	79	1	no	—
313	#535	—	79	1	no	—
314	#525	—	79	1	no	—
315	#525	—	79	2	no	—
316	C₂×#41	—	79	1	no	—
317	C₂×#41	—	79	2	no	—
318	C₂²×Q₈	—	79	1	no	—
319	C₂²×D₄	—	79	1	no	—
320	C₂³×C₄	—	79	1	no	—
321	C₄⋊Q₈	—	79	2	no	—
322	C₄⋊Q₈	—	79	2	no	—
323	#127	—	79	1	no	—
324	#127	C₂×D₇₉	1	1	yes	characteristic
325	#126	—	79	2	no	—
326	#126	—	79	2	no	—
327	#126	—	79	2	no	—
328	#126	—	79	2	no	—
329	#126	—	79	2	no	—
330	#126	C₂×D₇₉	1	2	yes	complemented
331	#124	—	79	1	no	—
332	#124	—	79	2	no	—
333	#124	—	79	2	no	—
334	#124	—	79	2	no	—
335	#124	—	79	2	no	—
336	#124	—	79	2	no	—
337	#124	—	79	2	no	—
338	#124	—	79	2	no	—
339	#124	—	79	2	no	—
340	#124	—	79	2	no	—
341	#124	—	79	2	no	—
342	#124	—	79	2	no	—
343	#124	—	79	2	no	—
344	#124	—	79	1	no	—
345	#123	—	79	2	no	—
346	#123	—	79	1	no	—
347	#123	—	79	1	no	—
348	#123	—	79	2	no	—
349	#123	—	79	1	no	—
350	#123	—	79	2	no	—
351	#123	—	79	2	no	—
352	#123	—	79	1	no	—
353	#123	—	79	1	no	—
354	#123	—	79	2	no	—
355	#123	C₂×D₇₉	1	1	yes	characteristic, complemented
356	#123	C₂×D₇₉	1	2	yes	complemented
357	C₂²⋊Q₈	—	79	2	no	—
358	C₂²⋊Q₈	—	79	2	no	—
359	C₂²⋊Q₈	—	79	2	no	—
360	C₂²⋊Q₈	—	79	2	no	—
361	C₂²⋊Q₈	—	79	2	no	—
362	C₂²⋊Q₈	—	79	2	no	—
363	C₂²⋊Q₈	—	79	2	no	—
364	C₂²⋊Q₈	—	79	2	no	—
365	#121	—	79	2	no	—
366	#121	—	79	2	no	—
367	#121	—	79	2	no	—
368	#121	—	79	2	no	—
369	#121	—	79	2	no	—
370	#121	—	79	2	no	—
371	#121	—	79	2	no	—
372	#121	C₂×D₇₉	1	2	yes	—
373	#121	C₂×D₇₉	1	2	yes	complemented
374	#121	C₂×D₇₉	1	2	yes	complemented
375	#120	—	79	2	no	—
376	#120	—	79	1	no	—
377	#120	—	79	2	no	—
378	#120	—	79	2	no	—
379	#120	—	79	2	no	—
380	#120	—	79	2	no	—
381	#120	C₂×D₇₉	1	1	yes	characteristic, complemented
382	#120	C₂×D₇₉	1	2	yes	complemented
383	C₄×Q₈	—	79	2	no	—
384	C₄×Q₈	—	79	2	no	—
385	C₄×Q₈	—	79	2	no	—
386	C₄×D₄	—	79	2	no	—
387	C₄×D₄	—	79	2	no	—
388	C₄×D₄	—	79	2	no	—
389	C₄×D₄	—	79	2	no	—
390	C₄×D₄	—	79	2	no	—
391	C₄×D₄	—	79	2	no	—
392	C₄×D₄	—	79	2	no	—
393	C₄×D₄	—	79	2	no	—
394	C₄×D₄	—	79	2	no	—
395	#117	—	79	2	no	—
396	#117	—	79	2	no	—
397	#117	—	79	1	no	—
398	#117	—	79	2	no	—
399	#117	—	79	1	no	—
400	#117	—	79	1	no	—
401	C₂×C₂²⋊C₄	—	79	2	no	—
402	C₂×C₂²⋊C₄	—	79	2	no	—
403	C₂⁴	—	79	2	no	—
404	C₂⁴	C₂²×D₇₉	1	1	yes	characteristic
405	#41	—	316	4	no	—
406	#41	—	316	2	no	—
407	C₂×Q₈	—	316	2	no	—
408	C₂×Q₈	—	79	2	no	—
409	C₂×Q₈	—	79	2	no	—
410	C₂×Q₈	—	79	2	no	—
411	C₂×Q₈	—	79	1	no	—
412	C₂×Q₈	—	79	2	no	—
413	C₂×D₄	—	316	2	no	—
414	C₂×D₄	—	79	2	no	—
415	C₂×D₄	—	79	2	no	—
416	C₂×D₄	—	79	2	no	—
417	C₂×D₄	—	79	2	no	—
418	C₂×D₄	—	79	1	no	—
419	C₂×D₄	—	79	1	no	—
420	C₂×D₄	—	79	2	no	—
421	C₂×D₄	—	79	2	no	—
422	C₂×D₄	—	79	1	no	—
423	C₂×D₄	C₂²×D₇₉	1	2	yes	—
424	C₂×D₄	C₂²×D₇₉	1	2	yes	—
425	C₂×D₄	C₂²×D₇₉	1	2	yes	—
426	C₂×D₄	C₂²×D₇₉	1	2	yes	—
427	C₂×D₄	C₂²×D₇₉	1	2	yes	—
428	C₂×D₄	C₂²×D₇₉	1	1	yes	characteristic
429	C₂×D₄	C₂²×D₇₉	1	1	yes	characteristic
430	C₂²×C₄	—	316	2	no	—
431	C₂²×C₄	—	79	2	no	—
432	C₂²×C₄	—	79	1	no	—
433	C₂²×C₄	—	79	1	no	—
434	C₂²×C₄	—	79	2	no	—
435	C₂²×C₄	—	79	2	no	—
436	C₂²×C₄	—	79	2	no	—
437	C₂²×C₄	—	79	1	no	—
438	C₂²×C₄	—	79	2	no	—
439	C₂²×C₄	—	79	1	no	—
440	C₂²×C₄	—	79	1	no	—
441	C₂²×C₄	C₂²×D₇₉	1	2	yes	—
442	C₂²×C₄	C₂²×D₇₉	1	1	yes	characteristic
443	C₄⋊C₄	—	79	2	no	—
444	C₄⋊C₄	—	79	2	no	—
445	C₄⋊C₄	—	79	2	no	—
446	C₄⋊C₄	—	79	2	no	—
447	C₄⋊C₄	—	79	2	no	—
448	C₄⋊C₄	—	79	2	no	—
449	C₄⋊C₄	—	79	2	no	—
450	C₄⋊C₄	—	79	2	no	—
451	C₄⋊C₄	—	79	2	no	—
452	C₄⋊C₄	—	79	2	no	—
453	C₄⋊C₄	—	79	2	no	—
454	C₄⋊C₄	—	79	2	no	—
455	C₄⋊C₄	C₂²×D₇₉	1	2	yes	—
456	C₄⋊C₄	C₂²×D₇₉	1	2	yes	—
457	C₄⋊C₄	C₂²×D₇₉	1	2	yes	—
458	C₂²⋊C₄	—	79	2	no	—
459	C₂²⋊C₄	—	79	2	no	—
460	C₂²⋊C₄	—	79	2	no	—
461	C₂²⋊C₄	—	79	1	no	—
462	C₂²⋊C₄	—	79	1	no	—
463	C₂²⋊C₄	—	79	2	no	—
464	C₂²⋊C₄	—	79	2	no	—
465	C₂²⋊C₄	—	79	2	no	—
466	C₂²⋊C₄	—	79	2	no	—
467	C₂²⋊C₄	—	79	2	no	—
468	C₂²⋊C₄	—	79	2	no	—
469	C₂²⋊C₄	—	79	2	no	—
470	C₂²⋊C₄	—	79	2	no	—
471	C₂²⋊C₄	—	79	2	no	—
472	C₂²⋊C₄	—	79	2	no	—
473	C₂²⋊C₄	—	79	2	no	—
474	C₂²⋊C₄	—	79	2	no	—
475	C₂²⋊C₄	—	79	2	no	—
476	C₂²⋊C₄	—	79	2	no	—
477	C₂²⋊C₄	—	79	2	no	—
478	C₂²⋊C₄	—	79	2	no	—
479	C₂²⋊C₄	—	79	2	no	—
480	C₂²⋊C₄	C₂²×D₇₉	1	2	yes	—
481	C₂²⋊C₄	C₂²×D₇₉	1	2	yes	—
482	C₂²⋊C₄	C₂²×D₇₉	1	1	yes	characteristic
483	C₂²⋊C₄	C₂²×D₇₉	1	1	yes	characteristic
484	C₂²⋊C₄	C₂²×D₇₉	1	2	yes	—
485	C₂²⋊C₄	C₂²×D₇₉	1	2	yes	—
486	C₂²⋊C₄	C₂²×D₇₉	1	2	yes	—
487	C₄²	—	79	2	no	—
488	C₄²	—	79	2	no	—
489	C₄²	—	79	2	no	—
490	C₄²	—	79	2	no	—
491	C₄²	—	79	1	no	—
492	C₄²	—	79	2	no	—
493	C₄²	—	79	2	no	—
494	C₄²	C₂²×D₇₉	1	1	yes	characteristic
495	C₂³	—	4	1	no	—
496	C₂³	—	4	2	no	—
497	C₂³	—	316	2	no	—
498	C₂³	—	316	2	no	—
499	C₂³	—	316	2	no	—
500	C₂³	—	79	1	no	—
501	C₂³	—	79	2	no	—
502	C₂³	C₂³×D₇₉	1	2	yes	—
503	C₂³	C₂³×D₇₉	1	2	yes	—
504	C₂³	C₂³×D₇₉	1	1	yes	characteristic
505	C₂³	C₂³×D₇₉	1	1	yes	characteristic
506	Q₈	—	316	2	no	—
507	Q₈	—	316	1	no	—
508	Q₈	—	316	2	no	—
509	Q₈	—	316	2	no	—
510	Q₈	—	158	4	no	—
511	D₄	—	4	1	no	—
512	D₄	—	4	2	no	—
513	D₄	—	4	2	no	—
514	D₄	—	4	2	no	—
515	D₄	—	4	2	no	—
516	D₄	—	4	2	no	—
517	D₄	—	4	1	no	—
518	D₄	—	316	1	no	—
519	D₄	—	316	2	no	—
520	D₄	—	316	2	no	—
521	D₄	—	316	2	no	—
522	D₄	—	316	2	no	—
523	D₄	—	316	1	no	—
524	D₄	—	316	2	no	—
525	D₄	—	316	1	no	—
526	D₄	—	158	4	no	—
527	C₂×C₄	—	4	2	no	—
528	C₂×C₄	—	4	1	no	—
529	C₂×C₄	—	316	2	no	—
530	C₂×C₄	—	316	2	no	—
531	C₂×C₄	—	316	1	no	—
532	C₂×C₄	—	316	2	no	—
533	C₂×C₄	—	316	1	no	—
534	C₂×C₄	—	316	2	no	—
535	C₂×C₄	—	79	1	no	—
536	C₂×C₄	—	79	2	no	—
537	C₂×C₄	—	79	2	no	—
538	C₂×C₄	—	79	2	no	—
539	C₂×C₄	—	79	1	no	—
540	C₂×C₄	—	79	2	no	—
541	C₂×C₄	—	79	2	no	—
542	C₂×C₄	—	79	1	no	—
543	C₂×C₄	—	158	2	no	—
544	C₂×C₄	—	158	4	no	—
545	C₂×C₄	—	158	2	no	—
546	C₂×C₄	—	158	2	no	—
547	C₂×C₄	C₂³×D₇₉	1	2	yes	—
548	C₂×C₄	C₂³×D₇₉	1	2	yes	—
549	C₂×C₄	C₂³×D₇₉	1	1	yes	characteristic
550	C₂×C₄	C₂³×D₇₉	1	2	yes	—
551	C₂×C₄	C₂³×D₇₉	1	2	yes	—
552	C₂²	—	2	1	no	—
553	C₂²	—	2	1	no	—
554	C₂²	—	2	2	no	—
555	C₂²	—	2	2	no	—
556	C₂²	—	2	2	no	—
557	C₂²	—	2	2	no	—
558	C₂²	—	2	2	no	—
559	C₂²	—	2	2	no	—
560	C₂²	—	2	2	no	—
561	C₂²	—	2	2	no	—
562	C₂²	—	4	4	no	—
563	C₂²	—	632	4	no	—
564	C₂²	—	158	2	no	—
565	C₂²	—	158	1	no	—
566	C₂²	—	158	2	no	—
567	C₂²	—	158	2	no	—
568	C₂²	—	158	2	no	—
569	C₂²	C₂⁴×D₇₉	1	1	yes	characteristic
570	C₄	—	2	2	no	—
571	C₄	—	2	1	no	—
572	C₄	—	2	2	no	—
573	C₄	—	2	2	no	—
574	C₄	—	2	2	no	—
575	C₄	—	79	2	no	—
576	C₄	—	158	2	no	—
577	C₄	—	158	1	no	—
578	C₄	—	158	2	no	—
579	C₄	—	158	1	no	—
580	C₄	—	158	2	no	—
581	C₄	—	158	2	no	—
582	C₄	—	158	2	no	—
583	C₂	—	4	1	no	—
584	C₂	—	4	2	no	—
585	C₂	—	4	2	no	—
586	C₂	—	4	1	no	—
587	C₂	—	316	1	no	—
588	C₂	—	316	2	no	—
589	C₂	H(5,𝔽₂)×D₇₉	1	1	yes	characteristic
590	C₂	#19099398	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₇₉
commutator, socle, cosocle	C₂²×C₇₉	C₂⁵
Fitting	#560×C₇₉	C₂
hypercenter	#560	D₇₉
hypocenter	C₇₉	#3540
LCS	G ▷ C₂²×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂² ◁ #560

Complements

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

N	H ≅ G/N	type
1. #19099306	C₂	semidirect
2. #19099302	C₂	semidirect
3. #19099299	C₂	semidirect
4. #19099297	C₂	semidirect
5. #19099280	C₂	semidirect
6. #19099277	C₂	semidirect
7. #19099236	C₂	semidirect
8. #19099219	C₂	semidirect
9. #19099202	C₂	semidirect
10. #19099181	C₂	semidirect
11. #19099180	C₂	semidirect
12. #19099179	C₂	semidirect
13. #19099150	C₂	semidirect
14. #19099145	C₂	semidirect
15. #19099135	C₂	semidirect
16. #19099126	C₂	semidirect
17. #19099069	C₂	semidirect
18. #19099069	C₂	semidirect
19. #560×C₇₉	C₂	semidirect
22. C₂²×Dic₁₅₈	C₂²	semidirect
23. C₂×D₄×D₇₉	C₂²	semidirect
24. C₂³×Dic₇₉	C₂²	semidirect
25. #14579160	C₂²	semidirect
26. #14579160	C₂²	semidirect
28. #14579156	C₂²	semidirect
29. #14579156	C₂²	semidirect
30. #14579156	C₂²	semidirect
31. #14579154	C₂²	semidirect
32. #14579154	C₂²	semidirect
33. #14579149	C₂²	semidirect
34. #14579148	C₂²	semidirect
35. #14579148	C₂²	semidirect
36. #14579148	C₂²	semidirect
37. #14579148	C₂²	semidirect
38. #14579148	C₂²	semidirect
42. #14579147	C₂²	semidirect
43. #14579147	C₂²	semidirect
44. #14579147	C₂²	semidirect
45. #14579147	C₂²	semidirect
46. #14579147	C₂²	semidirect
47. #14579146	C₂²	semidirect
49. #14579145	C₂²	semidirect
50. #14579145	C₂²	semidirect
51. #14579144	C₂²	semidirect
52. #14579143	C₂²	semidirect
53. #14579142	C₂²	semidirect
54. #14579142	C₂²	semidirect
55. #14579142	C₂²	semidirect
56. #14579142	C₂²	semidirect
57. #14579141	C₂²	semidirect
58. #14579140	C₂²	semidirect
59. #14579139	C₂²	semidirect
60. #14579139	C₂²	semidirect
61. #14579138	C₂²	semidirect
62. #14579138	C₂²	semidirect
63. #14579138	C₂²	semidirect
64. #14579138	C₂²	semidirect
69. #14579133	C₂²	semidirect
70. #14579133	C₂²	semidirect
71. #14579132	C₂²	semidirect
73. #14579130	C₂²	semidirect
77. #14579129	C₂²	semidirect
78. C₄×Dic₁₅₈	C₂²	semidirect
79. #14579126	C₂²	semidirect
80. #14579126	C₂²	semidirect
81. D₄×Dic₇₉	C₂²	semidirect
82. D₄×Dic₇₉	C₂²	semidirect
83. D₄×Dic₇₉	C₂²	semidirect
84. D₄×Dic₇₉	C₂²	semidirect
85. C₄×C₂²⋊D₇₉	C₂²	semidirect
86. C₄×C₂²⋊D₇₉	C₂²	semidirect
88. (C₂²⋊D₇₉)⋊C₄	C₂²	semidirect
89. (C₂²⋊D₇₉)⋊C₄	C₂²	semidirect
90. #14579120	C₂²	semidirect
91. #14579119	C₂²	semidirect
92. #14579118	C₂²	semidirect
93. #14579117	C₂²	semidirect
94. #14579117	C₂²	semidirect
95. #14579117	C₂²	semidirect
96. C₂×(C₂×D₇₉)⋊C₄	C₂²	semidirect
97. C₂²⋊C₄×D₇₉	C₂²	semidirect
99. #126×C₇₉	C₂²	semidirect
100. #123×C₇₉	C₂²	semidirect
101. #123×C₇₉	C₂²	semidirect
103. #121×C₇₉	C₂²	semidirect
104. #121×C₇₉	C₂²	semidirect
105. #120×C₇₉	C₂²	semidirect
106. #120×C₇₉	C₂²	semidirect
296. C₇₉	#3540	semidirect
299. #560	D₇₉	semidirect
330. #126	C₂×D₇₉	semidirect
355. #123	C₂×D₇₉	semidirect
356. #123	C₂×D₇₉	semidirect
373. #121	C₂×D₇₉	semidirect
374. #121	C₂×D₇₉	semidirect
381. #120	C₂×D₇₉	semidirect
382. #120	C₂×D₇₉	semidirect