Subgroups — #23777112

Order 10112.

1040 conjugacy classes of subgroups.

The subgroup lattice has 566 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19099285	C₂	1	2	yes	maximal, complemented
2	#19099280	C₂	1	2	yes	maximal, complemented
3	#19099276	C₂	1	2	yes	maximal, complemented
4	#19099275	C₂	1	2	yes	maximal, complemented
5	#19099264	C₂	1	2	yes	maximal, complemented
6	#19099262	C₂	1	2	yes	maximal, complemented
7	#19099246	C₂	1	2	yes	maximal, complemented
8	#19099245	C₂	1	2	yes	maximal, complemented
9	#19099192	C₂	1	1	yes	maximal, characteristic, complemented
10	#19099153	C₂	1	1	yes	maximal, characteristic, complemented
11	#19099150	C₂	1	1	yes	maximal, characteristic, complemented
12	#19099146	C₂	1	2	yes	maximal, complemented
13	#19099140	C₂	1	1	yes	maximal, characteristic, complemented
14	#19099097	C₂	1	1	yes	maximal, characteristic, complemented
15	#19099090	C₂	1	2	yes	maximal, complemented
16	#19099071	C₂	1	2	yes	maximal, complemented
17	#19099042	C₂	1	2	yes	maximal, complemented
18	C₂×#14579118	C₂	1	1	yes	maximal, characteristic, complemented
19	#529×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×#11929623	C₂²	1	2	yes	—
21	C₂²×C₄×D₇₉	C₂²	1	1	yes	characteristic
22	#14579160	C₂²	1	2	yes	complemented
23	#14579159	C₂²	1	2	yes	complemented
24	#14579156	C₂²	1	2	yes	—
25	#14579156	C₂²	1	2	yes	—
26	#14579156	C₂²	1	2	yes	—
27	#14579156	C₂²	1	2	yes	complemented
28	#14579155	C₂²	1	2	yes	—
29	#14579155	C₂²	1	2	yes	complemented
30	#14579154	C₂²	1	2	yes	complemented
31	#14579153	C₂²	1	1	yes	characteristic, complemented
32	#14579151	C₂²	1	2	yes	complemented
33	#14579151	C₂²	1	2	yes	complemented
34	#14579151	C₂²	1	2	yes	complemented
35	#14579150	C₂²	1	2	yes	—
36	#14579149	C₂²	1	2	yes	—
37	#14579149	C₂²	1	1	yes	characteristic, complemented
38	#14579147	C₂²	1	2	yes	—
39	#14579147	C₂²	1	2	yes	—
40	#14579147	C₂²	1	2	yes	complemented
41	#14579146	C₂²	1	2	yes	—
42	#14579146	C₂²	1	2	yes	—
43	#14579145	C₂²	1	2	yes	—
44	#14579144	C₂²	1	2	yes	—
45	#14579144	C₂²	1	2	yes	—
46	#14579140	C₂²	1	1	yes	characteristic
47	#14579139	C₂²	1	2	yes	—
48	#14579139	C₂²	1	2	yes	—
49	#14579139	C₂²	1	2	yes	complemented
50	#14579138	C₂²	1	2	yes	—
51	#14579138	C₂²	1	2	yes	complemented
52	#14579136	C₂²	1	2	yes	—
53	#14579135	C₂²	1	1	yes	characteristic
54	#14579135	C₂²	1	2	yes	—
55	#14579134	C₂²	1	2	yes	—
56	#14579134	C₂²	1	2	yes	—
57	#14579134	C₂²	1	2	yes	—
58	#14579134	C₂²	1	2	yes	complemented
59	#14579133	C₂²	1	2	yes	—
60	#14579133	C₂²	1	2	yes	—
61	#14579133	C₂²	1	2	yes	complemented
62	#14579131	C₂²	1	2	yes	—
63	#14579129	C₂²	1	2	yes	—
64	C₄×Dic₁₅₈	C₂²	1	2	yes	complemented
65	C₄×Dic₁₅₈	C₂²	1	1	yes	characteristic, complemented
66	#14579126	C₂²	1	2	yes	complemented
67	#14579126	C₂²	1	2	yes	complemented
68	C₄×D₃₁₆	C₂²	1	1	yes	characteristic, complemented
69	D₄×Dic₇₉	C₂²	1	2	yes	—
70	#14579123	C₂²	1	2	yes	—
71	#14579123	C₂²	1	2	yes	—
72	C₄×C₂²⋊D₇₉	C₂²	1	2	yes	—
73	C₄×C₂²⋊D₇₉	C₂²	1	2	yes	complemented
74	(C₂²⋊D₇₉)⋊C₄	C₂²	1	2	yes	—
75	(C₂²⋊D₇₉)⋊C₄	C₂²	1	2	yes	—
76	(C₂²⋊D₇₉)⋊C₄	C₂²	1	2	yes	—
77	(C₂²⋊D₇₉)⋊C₄	C₂²	1	2	yes	complemented
78	(C₂²⋊D₇₉)⋊C₄	C₂²	1	2	yes	complemented
79	#14579119	C₂²	1	2	yes	complemented
80	#14579118	C₂²	1	2	yes	—
81	#14579118	C₂²	1	2	yes	—
82	#14579118	C₂²	1	2	yes	—
83	#14579118	C₂²	1	2	yes	—
84	#14579118	C₂²	1	2	yes	complemented
85	#14579118	C₂²	1	2	yes	complemented
86	#14579117	C₂²	1	2	yes	—
87	#14579117	C₂²	1	2	yes	complemented
88	#14579117	C₂²	1	2	yes	complemented
89	C₂×Dic₇₉⋊C₄	C₂²	1	1	yes	characteristic
90	C₂×Dic₇₉⋊C₄	C₂²	1	1	yes	characteristic
91	C₂×Dic₇₉⋊C₄	C₂²	1	2	yes	complemented
92	C₄⋊C₄×D₇₉	C₂²	1	2	yes	complemented
93	C₂×(C₂×D₇₉)⋊C₄	C₂²	1	1	yes	characteristic
94	C₂×(C₂×D₇₉)⋊C₄	C₂²	1	1	yes	characteristic
95	C₂×C₄×Dic₇₉	C₂²	1	1	yes	characteristic
96	#126×C₇₉	C₂²	1	2	yes	complemented
97	#125×C₇₉	C₂²	1	1	yes	characteristic, complemented
98	#124×C₇₉	C₂²	1	1	yes	characteristic, complemented
99	#123×C₇₉	C₂²	1	2	yes	—
100	C₂²⋊Q₈×C₇₉	C₂²	1	1	yes	characteristic
101	#121×C₇₉	C₂²	1	1	yes	characteristic
102	C₄×Q₈×C₇₉	C₂²	1	1	yes	characteristic, complemented
103	C₄×D₄×C₇₉	C₂²	1	2	yes	—
104	C₄×D₄×C₇₉	C₂²	1	1	yes	characteristic, complemented
105	#117×C₇₉	C₂²	1	2	yes	complemented
106	C₂×C₄²×C₇₉	C₂²	1	1	yes	characteristic
107	C₂³×D₇₉	C₂³	1	1	yes	characteristic
108	#11929623	—	2	8	no	—
109	C₂×Dic₁₅₈	C₂³	1	2	yes	—
110	C₂×Dic₁₅₈	C₂³	1	2	yes	—
111	C₂×Dic₁₅₈	C₂³	1	1	yes	characteristic
112	C₂×D₃₁₆	C₂³	1	2	yes	—
113	C₂×D₃₁₆	C₂³	1	2	yes	—
114	C₂×D₃₁₆	C₂³	1	1	yes	characteristic
115	C₂×C₂²⋊D₇₉	C₂³	1	2	yes	—
116	C₂×C₂²⋊D₇₉	C₂³	1	2	yes	—
117	C₂×C₂²⋊D₇₉	C₂³	1	2	yes	—
118	C₂×C₂²⋊D₇₉	C₂³	1	2	yes	—
119	C₂×C₂²⋊D₇₉	C₂³	1	2	yes	—
120	C₂²×Dic₇₉	C₂³	1	2	yes	—
121	C₂²×Dic₇₉	C₂³	1	1	yes	characteristic
122	C₂²×Dic₇₉	C₂³	1	1	yes	characteristic
123	C₂²×Dic₇₉	C₂³	1	2	yes	—
124	C₂²×Dic₇₉	C₂³	1	1	yes	characteristic
125	C₂×C₄×D₇₉	—	2	4	no	—
126	C₂×C₄×D₇₉	C₂³	1	2	yes	—
127	C₂×C₄×D₇₉	C₂³	1	2	yes	—
128	C₂×C₄×D₇₉	C₂³	1	2	yes	—
129	C₂×C₄×D₇₉	C₂³	1	2	yes	—
130	C₂×C₄×D₇₉	C₂³	1	2	yes	—
131	C₄⋊Dic₇₉	C₂³	1	2	yes	—
132	C₄⋊Dic₇₉	C₂³	1	2	yes	—
133	C₄⋊Dic₇₉	C₂³	1	1	yes	characteristic
134	C₄⋊Dic₇₉	C₂³	1	1	yes	characteristic
135	Dic₇₉⋊C₄	C₂³	1	2	yes	—
136	Dic₇₉⋊C₄	C₂³	1	2	yes	—
137	Dic₇₉⋊C₄	C₂³	1	2	yes	—
138	Dic₇₉⋊C₄	C₂³	1	2	yes	—
139	Dic₇₉⋊C₄	C₂³	1	2	yes	—
140	Dic₇₉⋊C₄	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	2	yes	—
151	C₂²⋊Dic₇₉	C₂³	1	2	yes	—
152	(C₂×D₇₉)⋊C₄	C₂³	1	2	yes	—
153	(C₂×D₇₉)⋊C₄	C₂³	1	2	yes	—
154	(C₂×D₇₉)⋊C₄	C₂³	1	2	yes	—
155	(C₂×D₇₉)⋊C₄	C₂³	1	2	yes	—
156	(C₂×D₇₉)⋊C₄	C₂³	1	2	yes	—
157	(C₂×D₇₉)⋊C₄	C₂³	1	2	yes	—
158	(C₂×D₇₉)⋊C₄	C₂³	1	2	yes	—
159	(C₂×D₇₉)⋊C₄	C₂³	1	2	yes	—
160	(C₂×D₇₉)⋊C₄	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	C₄×Dic₇₉	C₂³	1	2	yes	—
167	C₄×Dic₇₉	C₂³	1	2	yes	—
168	C₄×Dic₇₉	C₂³	1	2	yes	—
169	C₄×Dic₇₉	C₂³	1	2	yes	—
170	C₄×Dic₇₉	C₂³	1	2	yes	—
171	C₄×Dic₇₉	C₂³	1	2	yes	—
172	C₄×Dic₇₉	C₂³	1	2	yes	—
173	C₂×Q₈×C₇₉	C₂³	1	1	yes	characteristic
174	C₂×D₄×C₇₉	C₂³	1	2	yes	—
175	C₂×D₄×C₇₉	C₂³	1	1	yes	characteristic
176	C₂²×C₄×C₇₉	C₂³	1	1	yes	characteristic
177	C₂²×C₄×C₇₉	C₂³	1	1	yes	characteristic
178	C₂²×C₄×C₇₉	C₂³	1	1	yes	characteristic
179	C₂²×C₄×C₇₉	C₂³	1	2	yes	—
180	C₄⋊C₄×C₇₉	C₂³	1	2	yes	—
181	C₄⋊C₄×C₇₉	C₂³	1	2	yes	—
182	C₄⋊C₄×C₇₉	C₂³	1	2	yes	—
183	C₄⋊C₄×C₇₉	C₂³	1	1	yes	characteristic
184	C₄⋊C₄×C₇₉	C₂³	1	1	yes	characteristic
185	C₄⋊C₄×C₇₉	C₂³	1	2	yes	—
186	C₂²⋊C₄×C₇₉	C₂³	1	2	yes	—
187	C₂²⋊C₄×C₇₉	C₂³	1	2	yes	—
188	C₂²⋊C₄×C₇₉	C₂³	1	2	yes	—
189	C₂²⋊C₄×C₇₉	C₂³	1	2	yes	—
190	C₂²⋊C₄×C₇₉	C₂³	1	2	yes	—
191	C₄²×C₇₉	C₂³	1	1	yes	characteristic
192	C₄²×C₇₉	C₂³	1	1	yes	characteristic
193	C₄²×C₇₉	C₂³	1	1	yes	characteristic
194	C₄²×C₇₉	C₂³	1	1	yes	characteristic
195	C₄²×C₇₉	C₂³	1	2	yes	—
196	C₂³×C₇₉	C₂⁴	1	2	yes	—
197	C₂³×C₇₉	C₂⁴	1	1	yes	characteristic
198	C₂²×D₇₉	—	2	2	no	—
199	C₂²×D₇₉	—	4	1	no	—
200	C₂²×D₇₉	—	4	1	no	—
201	C₂²×D₇₉	C₂⁴	1	2	yes	—
202	C₂²×D₇₉	C₂⁴	1	2	yes	—
203	Q₈×C₇₉	—	4	1	no	—
204	D₄×C₇₉	—	2	4	no	—
205	D₄×C₇₉	—	4	1	no	—
206	C₂×C₄×C₇₉	—	2	2	no	—
207	C₂×C₄×C₇₉	—	4	1	no	—
208	C₂×C₄×C₇₉	—	4	2	no	—
209	C₂×C₄×C₇₉	—	4	1	no	—
210	C₂×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
211	C₂×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
212	C₂×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
213	C₂×C₄×C₇₉	C₂⁴	1	2	yes	—
214	C₂×C₄×C₇₉	C₂⁴	1	2	yes	—
215	C₂×C₄×C₇₉	C₂⁴	1	2	yes	—
216	C₂×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
217	C₂×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
218	C₂×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
219	C₂²⋊D₇₉	—	2	4	no	—
220	C₂²⋊D₇₉	—	2	4	no	—
221	C₂²⋊D₇₉	—	4	2	no	—
222	C₂²⋊D₇₉	—	4	2	no	—
223	C₂²⋊D₇₉	—	4	2	no	—
224	C₂×Dic₇₉	—	2	4	no	—
225	C₂×Dic₇₉	—	4	1	no	—
226	C₂×Dic₇₉	—	4	2	no	—
227	C₂×Dic₇₉	—	4	1	no	—
228	C₂×Dic₇₉	#41	1	4	yes	—
229	C₂×Dic₇₉	C₂⁴	1	2	yes	—
230	C₂×Dic₇₉	C₂⁴	1	2	yes	—
231	C₂×Dic₇₉	C₂⁴	1	2	yes	—
232	C₂×Dic₇₉	C₂⁴	1	2	yes	—
233	C₂×Dic₇₉	C₂⁴	1	2	yes	—
234	C₂×Dic₇₉	C₂⁴	1	2	yes	—
235	D₃₁₆	—	4	1	no	—
236	D₃₁₆	—	4	2	no	—
237	D₃₁₆	—	4	2	no	—
238	C₄×D₇₉	—	2	4	no	—
239	C₄×D₇₉	—	2	4	no	—
240	C₄×D₇₉	—	2	4	no	—
241	C₄×D₇₉	—	4	2	no	—
242	C₄×D₇₉	—	4	2	no	—
243	Dic₁₅₈	—	2	4	no	—
244	Dic₁₅₈	—	4	1	no	—
245	Dic₁₅₈	—	4	2	no	—
246	C₂²×C₇₉	—	2	1	no	—
247	C₂²×C₇₉	—	2	1	no	—
248	C₂²×C₇₉	—	2	2	no	—
249	C₂²×C₇₉	—	2	2	no	—
250	C₂²×C₇₉	—	2	2	no	—
251	C₂²×C₇₉	C₂×#41	1	2	yes	—
252	C₂²×C₇₉	C₂⁵	1	1	yes	characteristic
253	C₂×D₇₉	—	2	2	no	—
254	C₂×D₇₉	—	2	2	no	—
255	C₂×D₇₉	—	2	2	no	—
256	C₂×D₇₉	—	2	2	no	—
257	C₂×D₇₉	—	2	2	no	—
258	C₂×D₇₉	—	2	2	no	—
259	C₂×D₇₉	—	4	4	no	—
260	C₄×C₇₉	—	2	1	no	—
261	C₄×C₇₉	—	2	1	no	—
262	C₄×C₇₉	—	2	2	no	—
263	C₄×C₇₉	—	2	1	no	—
264	C₄×C₇₉	—	2	1	no	—
265	C₄×C₇₉	—	2	1	no	—
266	C₄×C₇₉	—	2	1	no	—
267	C₄×C₇₉	—	2	2	no	—
268	C₄×C₇₉	—	2	2	no	—
269	Dic₇₉	—	2	2	no	—
270	Dic₇₉	—	2	2	no	—
271	Dic₇₉	—	2	2	no	—
272	Dic₇₉	—	2	2	no	—
273	Dic₇₉	—	2	2	no	—
274	Dic₇₉	C₂×#41	1	4	yes	—
275	C₂×C₇₉	—	2	2	no	—
276	C₂×C₇₉	—	4	2	no	—
277	C₂×C₇₉	C₂²×#41	1	1	yes	characteristic
278	C₂×C₇₉	#585	1	1	yes	characteristic
279	C₂×C₇₉	#585	1	1	yes	characteristic
280	D₇₉	—	4	2	no	—
281	D₇₉	—	4	2	no	—
282	#3493	—	79	1	no	maximal, Sylow
283	C₇₉	#3493	1	1	yes	characteristic, complemented, Sylow
284	#556	—	79	2	no	—
285	#556	—	79	2	no	—
286	#555	—	79	2	no	—
287	#555	—	79	2	no	—
288	#553	—	79	2	no	—
289	#553	—	79	2	no	—
290	#552	—	79	2	no	—
291	#552	—	79	2	no	—
292	#544	—	79	1	no	—
293	#538	—	79	1	no	—
294	#538	—	79	1	no	—
295	#538	—	79	2	no	—
296	#537	—	79	1	no	—
297	#529	—	79	2	no	—
298	#529	—	79	1	no	—
299	#529	D₇₉	1	1	yes	characteristic, complemented
300	#525	—	79	2	no	—
301	#520	—	79	2	no	—
302	C₂×#117	—	79	1	no	—
303	C₂×#41	—	79	2	no	—
304	C₂³×C₄	—	79	1	no	—
305	C₄⋊Q₈	—	79	2	no	—
306	C₄⋊Q₈	—	79	2	no	—
307	#126	—	79	2	no	—
308	#126	—	79	2	no	—
309	#126	—	79	2	no	—
310	#126	—	79	2	no	—
311	#126	—	79	2	no	—
312	#126	—	79	2	no	—
313	#126	—	79	2	no	—
314	#126	C₂×D₇₉	1	2	yes	complemented
315	#125	—	79	2	no	—
316	#125	—	79	2	no	—
317	#125	—	79	2	no	—
318	#125	—	79	1	no	—
319	#125	C₂×D₇₉	1	1	yes	characteristic, complemented
320	#124	—	79	2	no	—
321	#124	—	79	2	no	—
322	#124	—	79	2	no	—
323	#124	—	79	2	no	—
324	#124	—	79	1	no	—
325	#124	—	79	2	no	—
326	#124	C₂×D₇₉	1	1	yes	characteristic, complemented
327	#123	—	79	2	no	—
328	#123	—	79	2	no	—
329	#123	—	79	2	no	—
330	#123	—	79	2	no	—
331	#123	—	79	2	no	—
332	#123	C₂×D₇₉	1	2	yes	—
333	C₂²⋊Q₈	—	79	1	no	—
334	C₂²⋊Q₈	—	79	2	no	—
335	C₂²⋊Q₈	—	79	2	no	—
336	C₂²⋊Q₈	—	79	2	no	—
337	C₂²⋊Q₈	—	79	2	no	—
338	C₂²⋊Q₈	—	79	2	no	—
339	C₂²⋊Q₈	C₂×D₇₉	1	1	yes	characteristic
340	#121	—	79	2	no	—
341	#121	—	79	2	no	—
342	#121	—	79	2	no	—
343	#121	—	79	1	no	—
344	#121	—	79	2	no	—
345	#121	—	79	2	no	—
346	#121	—	79	2	no	—
347	#121	—	79	2	no	—
348	#121	—	79	2	no	—
349	#121	—	79	2	no	—
350	#121	C₂×D₇₉	1	1	yes	characteristic
351	#120	—	79	2	no	—
352	#120	—	79	2	no	—
353	C₄×Q₈	—	79	2	no	—
354	C₄×Q₈	—	79	2	no	—
355	C₄×Q₈	—	79	2	no	—
356	C₄×Q₈	—	79	1	no	—
357	C₄×Q₈	C₂×D₇₉	1	1	yes	characteristic, complemented
358	C₄×D₄	—	79	2	no	—
359	C₄×D₄	—	79	2	no	—
360	C₄×D₄	—	79	2	no	—
361	C₄×D₄	—	79	2	no	—
362	C₄×D₄	—	79	2	no	—
363	C₄×D₄	—	79	2	no	—
364	C₄×D₄	—	79	2	no	—
365	C₄×D₄	—	79	2	no	—
366	C₄×D₄	—	79	2	no	—
367	C₄×D₄	—	79	2	no	—
368	C₄×D₄	—	79	1	no	—
369	C₄×D₄	C₂×D₇₉	1	2	yes	—
370	C₄×D₄	C₂×D₇₉	1	1	yes	characteristic, complemented
371	#117	—	79	2	no	—
372	#117	—	79	2	no	—
373	#117	—	79	2	no	—
374	#117	—	79	2	no	—
375	#117	—	79	2	no	—
376	#117	—	79	2	no	—
377	#117	—	79	2	no	—
378	#117	—	79	2	no	—
379	#117	—	79	2	no	—
380	#117	—	79	2	no	—
381	#117	C₂×D₇₉	1	2	yes	complemented
382	C₂×C₄⋊C₄	—	79	1	no	—
383	C₂×C₄⋊C₄	—	79	1	no	—
384	C₂×C₄⋊C₄	—	79	2	no	—
385	C₂×C₄⋊C₄	—	79	2	no	—
386	C₂×C₂²⋊C₄	—	79	1	no	—
387	C₂×C₂²⋊C₄	—	79	1	no	—
388	C₂×C₄²	—	79	1	no	—
389	C₂×C₄²	C₂×D₇₉	1	1	yes	characteristic
390	C₂⁴	—	79	1	no	—
391	#41	—	158	8	no	—
392	C₂×Q₈	—	79	1	no	—
393	C₂×Q₈	—	79	2	no	—
394	C₂×Q₈	—	79	2	no	—
395	C₂×Q₈	C₂²×D₇₉	1	1	yes	characteristic
396	C₂×D₄	—	79	2	no	—
397	C₂×D₄	—	79	2	no	—
398	C₂×D₄	—	79	2	no	—
399	C₂×D₄	—	79	2	no	—
400	C₂×D₄	—	79	2	no	—
401	C₂×D₄	—	79	2	no	—
402	C₂×D₄	—	79	2	no	—
403	C₂×D₄	—	79	1	no	—
404	C₂×D₄	C₂²×D₇₉	1	2	yes	—
405	C₂×D₄	C₂²×D₇₉	1	1	yes	characteristic
406	C₂²×C₄	—	79	1	no	—
407	C₂²×C₄	—	79	1	no	—
408	C₂²×C₄	—	79	2	no	—
409	C₂²×C₄	—	79	2	no	—
410	C₂²×C₄	—	79	2	no	—
411	C₂²×C₄	—	79	1	no	—
412	C₂²×C₄	—	79	2	no	—
413	C₂²×C₄	—	79	2	no	—
414	C₂²×C₄	—	79	2	no	—
415	C₂²×C₄	—	79	2	no	—
416	C₂²×C₄	—	158	4	no	—
417	C₂²×C₄	C₂²×D₇₉	1	1	yes	characteristic
418	C₂²×C₄	C₂²×D₇₉	1	1	yes	characteristic
419	C₂²×C₄	C₂²×D₇₉	1	1	yes	characteristic
420	C₂²×C₄	C₂²×D₇₉	1	2	yes	—
421	C₄⋊C₄	—	79	2	no	—
422	C₄⋊C₄	—	79	2	no	—
423	C₄⋊C₄	—	79	2	no	—
424	C₄⋊C₄	—	79	2	no	—
425	C₄⋊C₄	—	79	2	no	—
426	C₄⋊C₄	—	79	2	no	—
427	C₄⋊C₄	—	79	2	no	—
428	C₄⋊C₄	—	79	2	no	—
429	C₄⋊C₄	—	79	2	no	—
430	C₄⋊C₄	—	79	2	no	—
431	C₄⋊C₄	—	79	2	no	—
432	C₄⋊C₄	—	79	2	no	—
433	C₄⋊C₄	—	79	2	no	—
434	C₄⋊C₄	—	79	2	no	—
435	C₄⋊C₄	—	79	2	no	—
436	C₄⋊C₄	—	79	2	no	—
437	C₄⋊C₄	—	79	1	no	—
438	C₄⋊C₄	—	79	1	no	—
439	C₄⋊C₄	C₂²×D₇₉	1	2	yes	—
440	C₄⋊C₄	C₂²×D₇₉	1	2	yes	—
441	C₄⋊C₄	C₂²×D₇₉	1	2	yes	—
442	C₄⋊C₄	C₂²×D₇₉	1	2	yes	—
443	C₄⋊C₄	C₂²×D₇₉	1	1	yes	characteristic
444	C₄⋊C₄	C₂²×D₇₉	1	1	yes	characteristic
445	C₂²⋊C₄	—	79	2	no	—
446	C₂²⋊C₄	—	79	2	no	—
447	C₂²⋊C₄	—	79	2	no	—
448	C₂²⋊C₄	—	79	2	no	—
449	C₂²⋊C₄	—	79	2	no	—
450	C₂²⋊C₄	—	79	2	no	—
451	C₂²⋊C₄	—	79	2	no	—
452	C₂²⋊C₄	—	79	2	no	—
453	C₂²⋊C₄	—	79	2	no	—
454	C₂²⋊C₄	—	79	2	no	—
455	C₂²⋊C₄	—	79	2	no	—
456	C₂²⋊C₄	—	79	2	no	—
457	C₂²⋊C₄	—	79	2	no	—
458	C₂²⋊C₄	—	79	2	no	—
459	C₂²⋊C₄	—	79	2	no	—
460	C₂²⋊C₄	—	79	2	no	—
461	C₂²⋊C₄	—	79	2	no	—
462	C₂²⋊C₄	C₂²×D₇₉	1	2	yes	—
463	C₂²⋊C₄	C₂²×D₇₉	1	2	yes	—
464	C₂²⋊C₄	C₂²×D₇₉	1	2	yes	—
465	C₂²⋊C₄	C₂²×D₇₉	1	2	yes	—
466	C₂²⋊C₄	C₂²×D₇₉	1	2	yes	—
467	C₄²	—	79	2	no	—
468	C₄²	—	79	2	no	—
469	C₄²	—	79	2	no	—
470	C₄²	—	79	2	no	—
471	C₄²	—	79	2	no	—
472	C₄²	—	79	2	no	—
473	C₄²	—	79	2	no	—
474	C₄²	C₂²×D₇₉	1	1	yes	characteristic
475	C₄²	C₂²×D₇₉	1	1	yes	characteristic
476	C₄²	C₂²×D₇₉	1	1	yes	characteristic
477	C₄²	C₂²×D₇₉	1	1	yes	characteristic
478	C₄²	C₂²×D₇₉	1	2	yes	—
479	C₂³	—	316	1	no	—
480	C₂³	—	316	1	no	—
481	C₂³	—	79	2	no	—
482	C₂³	—	79	2	no	—
483	C₂³	—	158	2	no	—
484	C₂³	C₂³×D₇₉	1	2	yes	—
485	C₂³	C₂³×D₇₉	1	1	yes	characteristic
486	Q₈	—	4	1	no	—
487	Q₈	—	316	1	no	—
488	Q₈	—	316	2	no	—
489	Q₈	—	158	4	no	—
490	D₄	—	2	4	no	—
491	D₄	—	4	1	no	—
492	D₄	—	316	2	no	—
493	D₄	—	316	1	no	—
494	D₄	—	316	2	no	—
495	D₄	—	316	2	no	—
496	D₄	—	316	2	no	—
497	D₄	—	316	2	no	—
498	D₄	—	158	4	no	—
499	D₄	—	158	4	no	—
500	C₂×C₄	—	2	2	no	—
501	C₂×C₄	—	4	1	no	—
502	C₂×C₄	—	4	2	no	—
503	C₂×C₄	—	4	1	no	—
504	C₂×C₄	—	316	2	no	—
505	C₂×C₄	—	316	2	no	—
506	C₂×C₄	—	316	1	no	—
507	C₂×C₄	—	316	2	no	—
508	C₂×C₄	—	316	1	no	—
509	C₂×C₄	—	79	4	no	—
510	C₂×C₄	—	79	2	no	—
511	C₂×C₄	—	79	2	no	—
512	C₂×C₄	—	79	2	no	—
513	C₂×C₄	—	79	2	no	—
514	C₂×C₄	—	79	2	no	—
515	C₂×C₄	—	79	2	no	—
516	C₂×C₄	—	158	4	no	—
517	C₂×C₄	—	158	4	no	—
518	C₂×C₄	—	158	4	no	—
519	C₂×C₄	—	158	4	no	—
520	C₂×C₄	C₂³×D₇₉	1	1	yes	characteristic
521	C₂×C₄	C₂³×D₇₉	1	1	yes	characteristic
522	C₂×C₄	C₂³×D₇₉	1	1	yes	characteristic
523	C₂×C₄	C₂³×D₇₉	1	2	yes	—
524	C₂×C₄	C₂³×D₇₉	1	2	yes	—
525	C₂×C₄	C₂³×D₇₉	1	2	yes	—
526	C₂×C₄	C₂³×D₇₉	1	1	yes	characteristic
527	C₂×C₄	C₂³×D₇₉	1	1	yes	characteristic
528	C₂×C₄	C₂³×D₇₉	1	1	yes	characteristic
529	C₂²	—	2	1	no	—
530	C₂²	—	2	1	no	—
531	C₂²	—	2	2	no	—
532	C₂²	—	2	2	no	—
533	C₂²	—	2	2	no	—
534	C₂²	—	316	4	no	—
535	C₂²	—	158	2	no	—
536	C₂²	—	158	2	no	—
537	C₂²	—	158	2	no	—
538	C₂²	—	158	2	no	—
539	C₂²	—	158	2	no	—
540	C₂²	—	158	2	no	—
541	C₂²	#41×D₇₉	1	2	yes	—
542	C₂²	C₂⁴×D₇₉	1	1	yes	characteristic
543	C₄	—	2	1	no	—
544	C₄	—	2	1	no	—
545	C₄	—	2	2	no	—
546	C₄	—	2	1	no	—
547	C₄	—	2	1	no	—
548	C₄	—	2	2	no	—
549	C₄	—	2	1	no	—
550	C₄	—	2	1	no	—
551	C₄	—	2	2	no	—
552	C₄	—	79	4	no	—
553	C₄	—	158	2	no	—
554	C₄	—	158	2	no	—
555	C₄	—	158	2	no	—
556	C₄	—	158	2	no	—
557	C₄	—	158	2	no	—
558	C₂	—	2	2	no	—
559	C₂	—	4	2	no	—
560	C₂	—	316	2	no	—
561	C₂	—	316	2	no	—
562	C₂	C₂×#41×D₇₉	1	1	yes	characteristic
563	C₂	#19099399	1	1	yes	characteristic
564	C₂	#19099399	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₇₉
commutator, socle, cosocle	C₂²×C₇₉	C₂⁵
Fitting	#529×C₇₉	C₂
hypercenter	#529	D₇₉
hypocenter	C₇₉	#3493
LCS	G ▷ C₂²×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂² ◁ #529

Complements

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

N	H ≅ G/N	type
1. #19099285	C₂	semidirect
2. #19099280	C₂	semidirect
3. #19099276	C₂	semidirect
4. #19099275	C₂	semidirect
5. #19099264	C₂	semidirect
6. #19099262	C₂	semidirect
7. #19099246	C₂	semidirect
8. #19099245	C₂	semidirect
9. #19099192	C₂	semidirect
10. #19099153	C₂	semidirect
11. #19099150	C₂	semidirect
12. #19099146	C₂	semidirect
13. #19099140	C₂	semidirect
14. #19099097	C₂	semidirect
15. #19099090	C₂	semidirect
16. #19099071	C₂	semidirect
17. #19099042	C₂	semidirect
18. C₂×#14579118	C₂	semidirect
19. #529×C₇₉	C₂	semidirect
22. #14579160	C₂²	semidirect
23. #14579159	C₂²	semidirect
27. #14579156	C₂²	semidirect
29. #14579155	C₂²	semidirect
30. #14579154	C₂²	semidirect
31. #14579153	C₂²	semidirect
32. #14579151	C₂²	semidirect
33. #14579151	C₂²	semidirect
34. #14579151	C₂²	semidirect
37. #14579149	C₂²	semidirect
40. #14579147	C₂²	semidirect
49. #14579139	C₂²	semidirect
51. #14579138	C₂²	semidirect
58. #14579134	C₂²	semidirect
61. #14579133	C₂²	semidirect
64. C₄×Dic₁₅₈	C₂²	semidirect
65. C₄×Dic₁₅₈	C₂²	semidirect
66. #14579126	C₂²	semidirect
67. #14579126	C₂²	semidirect
68. C₄×D₃₁₆	C₂²	semidirect
73. C₄×C₂²⋊D₇₉	C₂²	semidirect
77. (C₂²⋊D₇₉)⋊C₄	C₂²	semidirect
78. (C₂²⋊D₇₉)⋊C₄	C₂²	semidirect
79. #14579119	C₂²	semidirect
84. #14579118	C₂²	semidirect
85. #14579118	C₂²	semidirect
87. #14579117	C₂²	semidirect
88. #14579117	C₂²	semidirect
91. C₂×Dic₇₉⋊C₄	C₂²	semidirect
92. C₄⋊C₄×D₇₉	C₂²	semidirect
96. #126×C₇₉	C₂²	semidirect
97. #125×C₇₉	C₂²	semidirect
98. #124×C₇₉	C₂²	semidirect
102. C₄×Q₈×C₇₉	C₂²	semidirect
104. C₄×D₄×C₇₉	C₂²	semidirect
105. #117×C₇₉	C₂²	semidirect
283. C₇₉	#3493	semidirect
299. #529	D₇₉	semidirect
314. #126	C₂×D₇₉	semidirect
319. #125	C₂×D₇₉	semidirect
326. #124	C₂×D₇₉	semidirect
357. C₄×Q₈	C₂×D₇₉	semidirect
370. C₄×D₄	C₂×D₇₉	semidirect
381. #117	C₂×D₇₉	semidirect