Subgroups — #23777673

Order 10112.

1058 conjugacy classes of subgroups.

The subgroup lattice has 594 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19099306	C₂	1	1	yes	maximal, characteristic, complemented
2	#19099302	C₂	1	2	yes	maximal, complemented
3	#19099295	C₂	1	2	yes	maximal, complemented
4	#19099282	C₂	1	2	yes	maximal, complemented
5	#19099275	C₂	1	2	yes	maximal, complemented
6	#19099244	C₂	1	1	yes	maximal, characteristic, complemented
7	#19099243	C₂	1	1	yes	maximal, characteristic, complemented
8	#19099221	C₂	1	2	yes	maximal, complemented
9	#19099200	C₂	1	2	yes	maximal, complemented
10	#19099182	C₂	1	2	yes	maximal, complemented
11	#19099177	C₂	1	2	yes	maximal, complemented
12	#19099177	C₂	1	2	yes	maximal, complemented
13	#19099148	C₂	1	2	yes	maximal, complemented
14	#19099147	C₂	1	2	yes	maximal, complemented
15	#19099133	C₂	1	1	yes	maximal, characteristic, complemented
16	#19099128	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	H(3,𝔽₄)×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×#11929623	C₂²	1	2	yes	—
21	C₂×#11929623	C₂²	1	1	yes	characteristic
22	C₂×Q₈×D₇₉	C₂²	1	1	yes	characteristic, complemented
23	C₂²×C₂²⋊D₇₉	C₂²	1	1	yes	characteristic, complemented
24	C₂³×Dic₇₉	C₂²	1	1	yes	characteristic, complemented
25	#14579161	C₂²	1	1	yes	characteristic, complemented
26	#14579159	C₂²	1	1	yes	characteristic, complemented
27	#14579159	C₂²	1	2	yes	complemented
28	#14579157	C₂²	1	2	yes	—
29	#14579155	C₂²	1	2	yes	complemented
30	#14579154	C₂²	1	2	yes	complemented
31	#14579154	C₂²	1	2	yes	complemented
32	#14579154	C₂²	1	2	yes	complemented
33	#14579154	C₂²	1	2	yes	complemented
34	#14579154	C₂²	1	2	yes	complemented
35	#14579150	C₂²	1	2	yes	complemented
36	#14579148	C₂²	1	2	yes	—
37	#14579148	C₂²	1	1	yes	characteristic
38	#14579147	C₂²	1	2	yes	complemented
39	#14579147	C₂²	1	2	yes	complemented
40	#14579147	C₂²	1	2	yes	complemented
41	#14579147	C₂²	1	2	yes	complemented
42	#14579147	C₂²	1	2	yes	complemented
43	#14579147	C₂²	1	2	yes	complemented
44	#14579145	C₂²	1	2	yes	complemented
45	#14579145	C₂²	1	2	yes	complemented
46	#14579145	C₂²	1	1	yes	characteristic, complemented
47	#14579143	C₂²	1	2	yes	complemented
48	#14579143	C₂²	1	2	yes	complemented
49	#14579143	C₂²	1	2	yes	complemented
50	#14579143	C₂²	1	2	yes	complemented
51	#14579142	C₂²	1	1	yes	characteristic
52	#14579142	C₂²	1	2	yes	complemented
53	#14579142	C₂²	1	2	yes	complemented
54	#14579138	C₂²	1	2	yes	complemented
55	#14579138	C₂²	1	2	yes	complemented
56	#14579138	C₂²	1	2	yes	complemented
57	#14579138	C₂²	1	2	yes	complemented
58	#14579138	C₂²	1	2	yes	complemented
59	#14579138	C₂²	1	2	yes	complemented
60	#14579137	C₂²	1	2	yes	complemented
61	#14579137	C₂²	1	2	yes	complemented
62	#14579134	C₂²	1	2	yes	complemented
63	#14579134	C₂²	1	2	yes	complemented
64	#14579134	C₂²	1	2	yes	complemented
65	#14579133	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	#14579132	C₂²	1	2	yes	—
71	#14579132	C₂²	1	2	yes	complemented
72	#14579131	C₂²	1	1	yes	characteristic, complemented
73	#14579130	C₂²	1	1	yes	characteristic, complemented
74	#14579130	C₂²	1	1	yes	characteristic, complemented
75	#14579130	C₂²	1	2	yes	complemented
76	#14579129	C₂²	1	2	yes	—
77	#14579129	C₂²	1	1	yes	characteristic
78	Q₈×Dic₇₉	C₂²	1	2	yes	complemented
79	C₄×Dic₁₅₈	C₂²	1	2	yes	complemented
80	C₄×Dic₁₅₈	C₂²	1	2	yes	complemented
81	C₄×D₃₁₆	C₂²	1	2	yes	complemented
82	D₄×Dic₇₉	C₂²	1	2	yes	—
83	D₄×Dic₇₉	C₂²	1	2	yes	complemented
84	D₄×Dic₇₉	C₂²	1	2	yes	complemented
85	(C₂²⋊D₇₉)⋊C₄	C₂²	1	2	yes	complemented
86	(C₂²⋊D₇₉)⋊C₄	C₂²	1	2	yes	complemented
87	(C₂²⋊D₇₉)⋊C₄	C₂²	1	2	yes	complemented
88	(C₂²⋊D₇₉)⋊C₄	C₂²	1	2	yes	complemented
89	(C₂²⋊D₇₉)⋊C₄	C₂²	1	2	yes	complemented
90	#14579118	C₂²	1	2	yes	complemented
91	#14579118	C₂²	1	1	yes	characteristic, complemented
92	#14579117	C₂²	1	1	yes	characteristic, complemented
93	#14579117	C₂²	1	2	yes	complemented
94	#14579117	C₂²	1	2	yes	complemented
95	#14579117	C₂²	1	1	yes	characteristic, complemented
96	C₂×C₂²⋊Dic₇₉	C₂²	1	2	yes	complemented
97	C₂²⋊C₄×D₇₉	C₂²	1	2	yes	complemented
98	#124×C₇₉	C₂²	1	2	yes	—
99	#124×C₇₉	C₂²	1	1	yes	characteristic
100	#124×C₇₉	C₂²	1	2	yes	complemented
101	#124×C₇₉	C₂²	1	2	yes	complemented
102	#124×C₇₉	C₂²	1	2	yes	complemented
103	#120×C₇₉	C₂²	1	2	yes	—
104	#120×C₇₉	C₂²	1	1	yes	characteristic
105	#120×C₇₉	C₂²	1	1	yes	characteristic
106	#120×C₇₉	C₂²	1	2	yes	complemented
107	C₂³×D₇₉	C₂³	1	1	yes	characteristic
108	#11929623	—	4	4	no	—
109	#11929623	—	4	2	no	—
110	C₂×Dic₁₅₈	C₂³	1	2	yes	—
111	C₂×Dic₁₅₈	C₂³	1	1	yes	characteristic
112	C₂×Dic₁₅₈	C₂³	1	1	yes	characteristic
113	C₂×Dic₁₅₈	C₂³	1	2	yes	—
114	Q₈×D₇₉	—	4	2	no	—
115	C₂×D₃₁₆	C₂³	1	2	yes	—
116	C₂×C₂²⋊D₇₉	—	4	2	no	—
117	C₂×C₂²⋊D₇₉	C₂³	1	2	yes	—
118	C₂×C₂²⋊D₇₉	C₂³	1	2	yes	—
119	C₂×C₂²⋊D₇₉	C₂³	1	1	yes	characteristic
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	C₂×C₂²⋊D₇₉	C₂³	1	2	yes	—
126	C₂²×Dic₇₉	—	4	2	no	—
127	C₂²×Dic₇₉	C₂³	1	2	yes	—
128	C₂²×Dic₇₉	C₂³	1	1	yes	characteristic
129	C₂²×Dic₇₉	C₂³	1	1	yes	characteristic
130	C₂²×Dic₇₉	C₂³	1	2	yes	—
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	C₂×C₄×D₇₉	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	C₄⋊Dic₇₉	C₂³	1	2	yes	—
142	C₄⋊Dic₇₉	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	Dic₇₉⋊C₄	C₂³	1	2	yes	—
150	Dic₇₉⋊C₄	C₂³	1	2	yes	—
151	Dic₇₉⋊C₄	C₂³	1	2	yes	—
152	Dic₇₉⋊C₄	C₂³	1	2	yes	—
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	1	yes	characteristic
158	C₂²⋊Dic₇₉	C₂³	1	2	yes	—
159	C₂²⋊Dic₇₉	C₂³	1	1	yes	characteristic
160	C₂²⋊Dic₇₉	C₂³	1	2	yes	—
161	C₂²⋊Dic₇₉	C₂³	1	2	yes	—
162	C₂²⋊Dic₇₉	C₂³	1	2	yes	—
163	C₂²⋊Dic₇₉	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	(C₂×D₇₉)⋊C₄	C₂³	1	2	yes	—
172	C₄×Dic₇₉	C₂³	1	1	yes	characteristic
173	C₄×Dic₇₉	C₂³	1	2	yes	—
174	C₄×Dic₇₉	C₂³	1	2	yes	—
175	C₄×Dic₇₉	C₂³	1	2	yes	—
176	C₄×Dic₇₉	C₂³	1	2	yes	—
177	C₄×Dic₇₉	C₂³	1	2	yes	—
178	C₂⁴×C₇₉	C₂³	1	1	yes	characteristic
179	C₂⁴×C₇₉	C₂³	1	1	yes	characteristic
180	C₂×Q₈×C₇₉	C₂³	1	1	yes	characteristic
181	C₂×Q₈×C₇₉	C₂³	1	2	yes	—
182	C₂×D₄×C₇₉	C₂³	1	1	yes	characteristic
183	C₂×D₄×C₇₉	C₂³	1	2	yes	—
184	C₂×D₄×C₇₉	C₂³	1	2	yes	—
185	C₂×D₄×C₇₉	C₂³	1	2	yes	—
186	C₂×D₄×C₇₉	C₂³	1	2	yes	—
187	C₂²⋊C₄×C₇₉	C₂³	1	2	yes	—
188	C₂²⋊C₄×C₇₉	C₂³	1	1	yes	characteristic
189	C₂²⋊C₄×C₇₉	C₂³	1	2	yes	—
190	C₂²⋊C₄×C₇₉	C₂³	1	1	yes	characteristic
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	2	yes	—
195	C₂²⋊C₄×C₇₉	C₂³	1	2	yes	—
196	C₂²⋊C₄×C₇₉	C₂³	1	2	yes	—
197	C₄²×C₇₉	C₂³	1	1	yes	characteristic
198	C₄²×C₇₉	C₂³	1	2	yes	—
199	C₂³×C₇₉	—	4	1	no	—
200	C₂³×C₇₉	—	4	2	no	—
201	C₂³×C₇₉	—	4	1	no	—
202	C₂³×C₇₉	—	4	2	no	—
203	C₂³×C₇₉	C₂⁴	1	1	yes	characteristic
204	C₂³×C₇₉	C₂⁴	1	2	yes	—
205	C₂³×C₇₉	C₂⁴	1	2	yes	—
206	C₂³×C₇₉	C₂⁴	1	1	yes	characteristic
207	C₂²×D₇₉	—	4	1	no	—
208	C₂²×D₇₉	—	4	2	no	—
209	C₂²×D₇₉	C₂⁴	1	2	yes	—
210	C₂²×D₇₉	C₂⁴	1	1	yes	characteristic
211	Q₈×C₇₉	—	4	1	no	—
212	Q₈×C₇₉	—	4	2	no	—
213	D₄×C₇₉	—	4	2	no	—
214	D₄×C₇₉	—	4	1	no	—
215	D₄×C₇₉	—	4	2	no	—
216	D₄×C₇₉	—	4	2	no	—
217	D₄×C₇₉	—	4	2	no	—
218	C₂×C₄×C₇₉	C₂⁴	1	2	yes	—
219	C₂×C₄×C₇₉	C₂⁴	1	2	yes	—
220	C₂×C₄×C₇₉	C₂⁴	1	2	yes	—
221	C₂×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
222	C₂×C₄×C₇₉	C₂⁴	1	2	yes	—
223	C₂²⋊D₇₉	—	2	4	no	—
224	C₂²⋊D₇₉	—	4	2	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	1	no	—
230	C₂²⋊D₇₉	—	4	2	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	2	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	2	yes	—
242	C₂×Dic₇₉	C₂⁴	1	1	yes	characteristic
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	2	no	—
248	C₄×D₇₉	—	2	2	no	—
249	C₄×D₇₉	—	4	2	no	—
250	C₄×D₇₉	—	4	2	no	—
251	C₄×D₇₉	—	4	2	no	—
252	Dic₁₅₈	—	2	4	no	—
253	Dic₁₅₈	—	4	1	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	1	no	—
259	C₂²×C₇₉	—	2	2	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	—	8	2	no	—
268	C₂²×C₇₉	C₂⁵	1	1	yes	characteristic
269	C₂×D₇₉	—	2	2	no	—
270	C₂×D₇₉	—	2	1	no	—
271	C₂×D₇₉	—	2	2	no	—
272	C₂×D₇₉	—	2	2	no	—
273	C₂×D₇₉	—	2	2	no	—
274	C₂×D₇₉	—	8	2	no	—
275	C₄×C₇₉	—	2	2	no	—
276	C₄×C₇₉	—	2	1	no	—
277	C₄×C₇₉	—	2	2	no	—
278	C₄×C₇₉	—	2	2	no	—
279	C₄×C₇₉	—	2	2	no	—
280	Dic₇₉	—	2	1	no	—
281	Dic₇₉	—	2	2	no	—
282	Dic₇₉	—	2	1	no	—
283	Dic₇₉	—	2	2	no	—
284	Dic₇₉	—	2	2	no	—
285	Dic₇₉	—	2	2	no	—
286	Dic₇₉	—	2	2	no	—
287	Dic₇₉	H(5,𝔽₂)	1	2	yes	—
288	C₂×C₇₉	—	4	1	no	—
289	C₂×C₇₉	—	4	1	no	—
290	C₂×C₇₉	—	4	2	no	—
291	C₂×C₇₉	—	4	2	no	—
292	C₂×C₇₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
293	C₂×C₇₉	#585	1	2	yes	—
294	D₇₉	—	4	1	no	—
295	D₇₉	—	4	2	no	—
296	#3540	—	79	1	no	maximal, Sylow
297	C₇₉	#3540	1	1	yes	characteristic, complemented, Sylow
298	H(3,𝔽₄)	—	79	1	no	—
299	H(3,𝔽₄)	D₇₉	1	1	yes	characteristic, complemented
300	#560	—	79	2	no	—
301	#559	—	79	2	no	—
302	#556	—	79	2	no	—
303	#555	—	79	2	no	—
304	#551	—	79	1	no	—
305	#551	—	79	1	no	—
306	#548	—	79	2	no	—
307	#546	—	79	2	no	—
308	#542	—	79	2	no	—
309	#542	—	79	2	no	—
310	#542	—	79	2	no	—
311	#538	—	79	2	no	—
312	#538	—	79	2	no	—
313	#536	—	79	1	no	—
314	#535	—	79	1	no	—
315	#525	—	79	1	no	—
316	#525	—	79	2	no	—
317	C₂×#41	—	79	1	no	—
318	C₂×#41	—	79	2	no	—
319	C₂²×Q₈	—	79	1	no	—
320	C₂²×D₄	—	79	1	no	—
321	C₂³×C₄	—	79	1	no	—
322	C₄⋊Q₈	—	79	1	no	—
323	C₄⋊Q₈	—	79	2	no	—
324	C₄⋊Q₈	—	79	1	no	—
325	#127	—	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	—	79	2	no	—
331	#126	—	79	2	no	—
332	#124	—	79	2	no	—
333	#124	—	79	1	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	C₂×D₇₉	1	1	yes	characteristic
342	#124	C₂×D₇₉	1	2	yes	—
343	#124	C₂×D₇₉	1	2	yes	complemented
344	#124	C₂×D₇₉	1	2	yes	complemented
345	#124	C₂×D₇₉	1	2	yes	complemented
346	#123	—	79	2	no	—
347	#123	—	79	1	no	—
348	#123	—	79	2	no	—
349	#123	—	79	2	no	—
350	#123	—	79	1	no	—
351	#123	—	79	2	no	—
352	#123	—	79	2	no	—
353	#123	—	79	2	no	—
354	#123	—	79	2	no	—
355	#123	—	79	2	no	—
356	C₂²⋊Q₈	—	79	2	no	—
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	#121	—	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	—	79	2	no	—
373	#121	—	79	2	no	—
374	#120	—	79	1	no	—
375	#120	—	79	2	no	—
376	#120	—	79	1	no	—
377	#120	—	79	1	no	—
378	#120	—	79	2	no	—
379	#120	—	79	1	no	—
380	#120	C₂×D₇₉	1	1	yes	characteristic
381	#120	C₂×D₇₉	1	1	yes	characteristic
382	#120	C₂×D₇₉	1	2	yes	—
383	#120	C₂×D₇₉	1	2	yes	complemented
384	C₄×Q₈	—	79	2	no	—
385	C₄×Q₈	—	79	2	no	—
386	C₄×Q₈	—	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	C₄×D₄	—	79	2	no	—
396	#117	—	79	1	no	—
397	#117	—	79	2	no	—
398	#117	—	79	1	no	—
399	#117	—	79	2	no	—
400	#117	—	79	1	no	—
401	#117	—	79	2	no	—
402	C₂×C₂²⋊C₄	—	79	2	no	—
403	C₂×C₂²⋊C₄	—	79	2	no	—
404	C₂⁴	—	79	1	no	—
405	C₂⁴	C₂²×D₇₉	1	1	yes	characteristic
406	C₂⁴	C₂²×D₇₉	1	1	yes	characteristic
407	#41	—	316	4	no	—
408	#41	—	316	2	no	—
409	C₂×Q₈	—	316	2	no	—
410	C₂×Q₈	—	79	2	no	—
411	C₂×Q₈	—	79	1	no	—
412	C₂×Q₈	—	79	1	no	—
413	C₂×Q₈	—	79	2	no	—
414	C₂×Q₈	C₂²×D₇₉	1	2	yes	—
415	C₂×Q₈	C₂²×D₇₉	1	1	yes	characteristic
416	C₂×D₄	—	316	2	no	—
417	C₂×D₄	—	79	2	no	—
418	C₂×D₄	—	79	2	no	—
419	C₂×D₄	—	79	2	no	—
420	C₂×D₄	—	79	2	no	—
421	C₂×D₄	—	79	1	no	—
422	C₂×D₄	—	79	2	no	—
423	C₂×D₄	—	79	1	no	—
424	C₂×D₄	—	79	2	no	—
425	C₂×D₄	—	79	2	no	—
426	C₂×D₄	—	79	2	no	—
427	C₂×D₄	C₂²×D₇₉	1	2	yes	—
428	C₂×D₄	C₂²×D₇₉	1	2	yes	—
429	C₂×D₄	C₂²×D₇₉	1	2	yes	—
430	C₂×D₄	C₂²×D₇₉	1	1	yes	characteristic
431	C₂×D₄	C₂²×D₇₉	1	2	yes	—
432	C₂²×C₄	—	316	2	no	—
433	C₂²×C₄	—	79	2	no	—
434	C₂²×C₄	—	79	2	no	—
435	C₂²×C₄	—	79	1	no	—
436	C₂²×C₄	—	79	2	no	—
437	C₂²×C₄	—	79	2	no	—
438	C₂²×C₄	—	79	2	no	—
439	C₂²×C₄	—	79	2	no	—
440	C₂²×C₄	—	79	2	no	—
441	C₂²×C₄	—	79	1	no	—
442	C₂²×C₄	—	79	1	no	—
443	C₂²×C₄	—	79	1	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	—	79	2	no	—
456	C₄⋊C₄	—	79	2	no	—
457	C₄⋊C₄	—	79	2	no	—
458	C₄⋊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	—	79	2	no	—
463	C₂²⋊C₄	—	79	1	no	—
464	C₂²⋊C₄	—	79	2	no	—
465	C₂²⋊C₄	—	79	1	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	C₂²×D₇₉	1	2	yes	—
479	C₂²⋊C₄	C₂²×D₇₉	1	1	yes	characteristic
480	C₂²⋊C₄	C₂²×D₇₉	1	2	yes	—
481	C₂²⋊C₄	C₂²×D₇₉	1	1	yes	characteristic
482	C₂²⋊C₄	C₂²×D₇₉	1	2	yes	—
483	C₂²⋊C₄	C₂²×D₇₉	1	2	yes	—
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	C₂²⋊C₄	C₂²×D₇₉	1	2	yes	—
488	C₄²	—	79	1	no	—
489	C₄²	—	79	2	no	—
490	C₄²	—	79	2	no	—
491	C₄²	—	79	2	no	—
492	C₄²	—	79	2	no	—
493	C₄²	—	79	2	no	—
494	C₄²	C₂²×D₇₉	1	1	yes	characteristic
495	C₄²	C₂²×D₇₉	1	2	yes	—
496	C₂³	—	4	1	no	—
497	C₂³	—	4	2	no	—
498	C₂³	—	4	1	no	—
499	C₂³	—	4	2	no	—
500	C₂³	—	316	1	no	—
501	C₂³	—	316	2	no	—
502	C₂³	—	79	2	no	—
503	C₂³	—	79	1	no	—
504	C₂³	C₂³×D₇₉	1	1	yes	characteristic
505	C₂³	C₂³×D₇₉	1	2	yes	—
506	C₂³	C₂³×D₇₉	1	1	yes	characteristic
507	C₂³	C₂³×D₇₉	1	2	yes	—
508	Q₈	—	4	1	no	—
509	Q₈	—	4	2	no	—
510	Q₈	—	316	1	no	—
511	Q₈	—	316	1	no	—
512	Q₈	—	316	2	no	—
513	Q₈	—	158	4	no	—
514	D₄	—	4	2	no	—
515	D₄	—	4	2	no	—
516	D₄	—	4	2	no	—
517	D₄	—	4	2	no	—
518	D₄	—	4	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	2	no	—
524	D₄	—	316	2	no	—
525	D₄	—	316	1	no	—
526	D₄	—	316	2	no	—
527	D₄	—	316	1	no	—
528	D₄	—	158	4	no	—
529	C₂×C₄	—	316	2	no	—
530	C₂×C₄	—	316	2	no	—
531	C₂×C₄	—	316	2	no	—
532	C₂×C₄	—	316	1	no	—
533	C₂×C₄	—	316	2	no	—
534	C₂×C₄	—	316	2	no	—
535	C₂×C₄	—	316	2	no	—
536	C₂×C₄	—	79	1	no	—
537	C₂×C₄	—	79	2	no	—
538	C₂×C₄	—	79	2	no	—
539	C₂×C₄	—	79	2	no	—
540	C₂×C₄	—	79	1	no	—
541	C₂×C₄	—	79	2	no	—
542	C₂×C₄	—	79	2	no	—
543	C₂×C₄	—	79	1	no	—
544	C₂×C₄	—	158	2	no	—
545	C₂×C₄	—	158	4	no	—
546	C₂×C₄	—	158	2	no	—
547	C₂×C₄	—	158	2	no	—
548	C₂×C₄	C₂³×D₇₉	1	2	yes	—
549	C₂×C₄	C₂³×D₇₉	1	2	yes	—
550	C₂×C₄	C₂³×D₇₉	1	2	yes	—
551	C₂×C₄	C₂³×D₇₉	1	1	yes	characteristic
552	C₂×C₄	C₂³×D₇₉	1	2	yes	—
553	C₂²	—	2	1	no	—
554	C₂²	—	2	2	no	—
555	C₂²	—	2	2	no	—
556	C₂²	—	2	1	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	—	2	2	no	—
563	C₂²	—	4	4	no	—
564	C₂²	—	8	2	no	—
565	C₂²	—	632	2	no	—
566	C₂²	—	158	1	no	—
567	C₂²	—	158	2	no	—
568	C₂²	—	158	2	no	—
569	C₂²	—	158	2	no	—
570	C₂²	—	158	2	no	—
571	C₂²	C₂⁴×D₇₉	1	1	yes	characteristic
572	C₄	—	2	2	no	—
573	C₄	—	2	1	no	—
574	C₄	—	2	2	no	—
575	C₄	—	2	2	no	—
576	C₄	—	2	2	no	—
577	C₄	—	79	2	no	—
578	C₄	—	158	2	no	—
579	C₄	—	158	1	no	—
580	C₄	—	158	2	no	—
581	C₄	—	158	1	no	—
582	C₄	—	158	2	no	—
583	C₄	—	158	2	no	—
584	C₄	—	158	2	no	—
585	C₂	—	4	1	no	—
586	C₂	—	4	2	no	—
587	C₂	—	4	1	no	—
588	C₂	—	4	2	no	—
589	C₂	—	316	2	no	—
590	C₂	—	316	1	no	—
591	C₂	H(5,𝔽₂)×D₇₉	1	1	yes	characteristic
592	C₂	#19099398	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₇₉
commutator, socle, cosocle	C₂²×C₇₉	C₂⁵
Fitting	H(3,𝔽₄)×C₇₉	C₂
hypercenter	H(3,𝔽₄)	D₇₉
hypocenter	C₇₉	#3540
LCS	G ▷ C₂²×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂² ◁ H(3,𝔽₄)

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. #19099295	C₂	semidirect
4. #19099282	C₂	semidirect
5. #19099275	C₂	semidirect
6. #19099244	C₂	semidirect
7. #19099243	C₂	semidirect
8. #19099221	C₂	semidirect
9. #19099200	C₂	semidirect
10. #19099182	C₂	semidirect
11. #19099177	C₂	semidirect
12. #19099177	C₂	semidirect
13. #19099148	C₂	semidirect
14. #19099147	C₂	semidirect
15. #19099133	C₂	semidirect
16. #19099128	C₂	semidirect
17. #19099069	C₂	semidirect
18. #19099069	C₂	semidirect
19. H(3,𝔽₄)×C₇₉	C₂	semidirect
22. C₂×Q₈×D₇₉	C₂²	semidirect
23. C₂²×C₂²⋊D₇₉	C₂²	semidirect
24. C₂³×Dic₇₉	C₂²	semidirect
25. #14579161	C₂²	semidirect
26. #14579159	C₂²	semidirect
27. #14579159	C₂²	semidirect
29. #14579155	C₂²	semidirect
30. #14579154	C₂²	semidirect
31. #14579154	C₂²	semidirect
32. #14579154	C₂²	semidirect
33. #14579154	C₂²	semidirect
34. #14579154	C₂²	semidirect
35. #14579150	C₂²	semidirect
38. #14579147	C₂²	semidirect
39. #14579147	C₂²	semidirect
40. #14579147	C₂²	semidirect
41. #14579147	C₂²	semidirect
42. #14579147	C₂²	semidirect
43. #14579147	C₂²	semidirect
44. #14579145	C₂²	semidirect
45. #14579145	C₂²	semidirect
46. #14579145	C₂²	semidirect
47. #14579143	C₂²	semidirect
48. #14579143	C₂²	semidirect
49. #14579143	C₂²	semidirect
50. #14579143	C₂²	semidirect
52. #14579142	C₂²	semidirect
53. #14579142	C₂²	semidirect
54. #14579138	C₂²	semidirect
55. #14579138	C₂²	semidirect
56. #14579138	C₂²	semidirect
57. #14579138	C₂²	semidirect
58. #14579138	C₂²	semidirect
59. #14579138	C₂²	semidirect
60. #14579137	C₂²	semidirect
61. #14579137	C₂²	semidirect
62. #14579134	C₂²	semidirect
63. #14579134	C₂²	semidirect
64. #14579134	C₂²	semidirect
69. #14579133	C₂²	semidirect
71. #14579132	C₂²	semidirect
72. #14579131	C₂²	semidirect
73. #14579130	C₂²	semidirect
74. #14579130	C₂²	semidirect
75. #14579130	C₂²	semidirect
78. Q₈×Dic₇₉	C₂²	semidirect
79. C₄×Dic₁₅₈	C₂²	semidirect
80. C₄×Dic₁₅₈	C₂²	semidirect
81. C₄×D₃₁₆	C₂²	semidirect
83. D₄×Dic₇₉	C₂²	semidirect
84. D₄×Dic₇₉	C₂²	semidirect
85. (C₂²⋊D₇₉)⋊C₄	C₂²	semidirect
86. (C₂²⋊D₇₉)⋊C₄	C₂²	semidirect
87. (C₂²⋊D₇₉)⋊C₄	C₂²	semidirect
88. (C₂²⋊D₇₉)⋊C₄	C₂²	semidirect
89. (C₂²⋊D₇₉)⋊C₄	C₂²	semidirect
90. #14579118	C₂²	semidirect
91. #14579118	C₂²	semidirect
92. #14579117	C₂²	semidirect
93. #14579117	C₂²	semidirect
94. #14579117	C₂²	semidirect
95. #14579117	C₂²	semidirect
96. C₂×C₂²⋊Dic₇₉	C₂²	semidirect
97. C₂²⋊C₄×D₇₉	C₂²	semidirect
100. #124×C₇₉	C₂²	semidirect
101. #124×C₇₉	C₂²	semidirect
102. #124×C₇₉	C₂²	semidirect
106. #120×C₇₉	C₂²	semidirect
297. C₇₉	#3540	semidirect
299. H(3,𝔽₄)	D₇₉	semidirect
343. #124	C₂×D₇₉	semidirect
344. #124	C₂×D₇₉	semidirect
345. #124	C₂×D₇₉	semidirect
383. #120	C₂×D₇₉	semidirect