Subgroups — C₂×#560×D₇₉ #35195134

Order 20224.

9606 conjugacy classes of subgroups.

The subgroup lattice has 628 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#19099304	C₂	1	2	yes	maximal, complemented
2	C₂×#19099303	C₂	1	3	yes	maximal, complemented
3	C₂×#19099302	C₂	1	3	yes	maximal, complemented
4	C₂×#19099301	C₂	1	6	yes	maximal, complemented
5	C₂×#19099300	C₂	1	1	yes	maximal, characteristic, complemented
6	#560×D₇₉	C₂	1	32	yes	maximal, direct product factor
7	C₂×#127×D₇₉	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#126×D₇₉	C₂	1	2	yes	maximal, complemented
9	C₂×#123×D₇₉	C₂	1	3	yes	maximal, complemented
10	C₂×#121×D₇₉	C₂	1	6	yes	maximal, complemented
11	C₂×#120×D₇₉	C₂	1	3	yes	maximal, complemented
12	C₂×#560×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂⁵×D₇₉	C₂²	1	1	yes	characteristic
14	C₂²×D₄×D₇₉	C₂²	1	6	yes	—
15	C₂²×D₄×D₇₉	C₂²	1	3	yes	—
16	C₂²×D₄×D₇₉	C₂²	1	3	yes	complemented
17	C₂³×C₄×D₇₉	C₂²	1	3	yes	complemented
18	#19099304	C₂²	1	32	yes	complemented
19	#19099303	C₂²	1	48	yes	complemented
20	#19099302	C₂²	1	48	yes	complemented
21	#19099301	C₂²	1	96	yes	complemented
22	#19099300	C₂²	1	16	yes	complemented
23	C₂×#14579158	C₂²	1	1	yes	characteristic, complemented
24	C₂×#14579157	C₂²	1	3	yes	complemented
25	C₂×#14579157	C₂²	1	3	yes	complemented
26	#127×D₇₉	C₂²	1	16	yes	complemented
27	C₂×#14579156	C₂²	1	6	yes	complemented
28	C₂×#14579155	C₂²	1	2	yes	complemented
29	C₂×#14579154	C₂²	1	6	yes	complemented
30	#126×D₇₉	C₂²	1	32	yes	complemented
31	C₂×#14579146	C₂²	1	6	yes	complemented
32	C₂×#14579145	C₂²	1	3	yes	complemented
33	C₂×#14579144	C₂²	1	3	yes	complemented
34	C₂×#14579143	C₂²	1	6	yes	complemented
35	C₂×#14579142	C₂²	1	3	yes	complemented
36	#123×D₇₉	C₂²	1	48	yes	complemented
37	C₂×#14579136	C₂²	1	6	yes	complemented
38	C₂×#14579135	C₂²	1	6	yes	complemented
39	C₂×#14579134	C₂²	1	6	yes	complemented
40	C₂×#14579134	C₂²	1	6	yes	complemented
41	C₂×#14579133	C₂²	1	6	yes	complemented
42	C₂×#14579133	C₂²	1	6	yes	complemented
43	C₂×#14579132	C₂²	1	6	yes	complemented
44	#121×D₇₉	C₂²	1	96	yes	complemented
45	C₂×#14579131	C₂²	1	6	yes	complemented
46	C₂×#14579131	C₂²	1	3	yes	complemented
47	C₂×#14579130	C₂²	1	3	yes	complemented
48	C₂×#14579129	C₂²	1	3	yes	complemented
49	C₂×#14579129	C₂²	1	6	yes	complemented
50	#120×D₇₉	C₂²	1	48	yes	complemented
51	C₂×C₄⋊C₄×D₇₉	C₂²	1	6	yes	complemented
52	C₂×C₂²⋊C₄×D₇₉	C₂²	1	6	yes	—
53	C₂×C₂²⋊C₄×D₇₉	C₂²	1	3	yes	—
54	C₂×C₂²⋊C₄×D₇₉	C₂²	1	3	yes	complemented
55	C₂×C₄²×D₇₉	C₂²	1	1	yes	characteristic, complemented
56	#560×C₇₉	C₂²	1	16	yes	complemented
57	C₂×#127×C₇₉	C₂²	1	1	yes	characteristic, complemented
58	C₂×#126×C₇₉	C₂²	1	2	yes	complemented
59	C₂×#123×C₇₉	C₂²	1	3	yes	complemented
60	C₂×#121×C₇₉	C₂²	1	6	yes	complemented
61	C₂×#120×C₇₉	C₂²	1	3	yes	complemented
62	C₂⁴×D₇₉	—	4	12	no	—
63	C₂⁴×D₇₉	C₂³	1	2	yes	—
64	C₂⁴×D₇₉	C₂³	1	1	yes	characteristic
65	C₂⁴×D₇₉	C₂³	1	3	yes	—
66	C₂⁴×D₇₉	C₂³	1	8	yes	—
67	C₂⁴×D₇₉	C₂³	1	1	yes	characteristic
68	C₂⁴×D₇₉	C₂³	1	2	yes	—
69	C₂²×D₃₁₆	C₂³	1	6	yes	—
70	C₂²×D₃₁₆	C₂³	1	3	yes	—
71	C₂²×D₃₁₆	C₂³	1	3	yes	complemented
72	C₂²×C₂²⋊D₇₉	C₂³	1	6	yes	—
73	C₂²×C₂²⋊D₇₉	C₂³	1	3	yes	—
74	C₂²×C₂²⋊D₇₉	C₂³	1	6	yes	—
75	C₂²×C₂²⋊D₇₉	C₂³	1	3	yes	—
76	C₂²×C₂²⋊D₇₉	C₂³	1	6	yes	complemented
77	C₂×D₄×D₇₉	—	4	24	no	—
78	C₂×D₄×D₇₉	—	4	12	no	—
79	C₂×D₄×D₇₉	—	4	12	no	—
80	C₂×D₄×D₇₉	C₂³	1	48	yes	—
81	C₂×D₄×D₇₉	C₂³	1	24	yes	—
82	C₂×D₄×D₇₉	C₂³	1	24	yes	complemented
83	C₂³×Dic₇₉	C₂³	1	3	yes	complemented
84	C₂²×C₄×D₇₉	—	4	12	no	—
85	C₂²×C₄×D₇₉	C₂³	1	3	yes	—
86	C₂²×C₄×D₇₉	C₂³	1	6	yes	—
87	C₂²×C₄×D₇₉	C₂³	1	24	yes	complemented
88	C₂²×C₄×D₇₉	C₂³	1	6	yes	complemented
89	#14579158	C₂³	1	8	yes	complemented
90	#14579157	C₂³	1	24	yes	complemented
91	#14579157	C₂³	1	24	yes	complemented
92	#14579156	C₂³	1	48	yes	complemented
93	#14579155	C₂³	1	16	yes	complemented
94	#14579154	C₂³	1	48	yes	complemented
95	#14579146	C₂³	1	48	yes	complemented
96	#14579145	C₂³	1	24	yes	complemented
97	#14579144	C₂³	1	24	yes	complemented
98	#14579143	C₂³	1	48	yes	complemented
99	#14579142	C₂³	1	24	yes	complemented
100	#14579136	C₂³	1	48	yes	complemented
101	#14579135	C₂³	1	48	yes	complemented
102	#14579134	C₂³	1	48	yes	complemented
103	#14579134	C₂³	1	48	yes	complemented
104	#14579133	C₂³	1	48	yes	complemented
105	#14579133	C₂³	1	48	yes	complemented
106	#14579132	C₂³	1	48	yes	complemented
107	#14579131	C₂³	1	48	yes	complemented
108	#14579131	C₂³	1	24	yes	complemented
109	#14579130	C₂³	1	24	yes	complemented
110	#14579129	C₂³	1	24	yes	complemented
111	#14579129	C₂³	1	48	yes	complemented
112	C₂×C₄⋊Dic₇₉	C₂³	1	6	yes	complemented
113	C₂×Dic₇₉⋊C₄	C₂³	1	6	yes	complemented
114	C₂×Dic₇₉⋊C₄	C₂³	1	6	yes	complemented
115	C₄⋊C₄×D₇₉	C₂³	1	48	yes	complemented
116	C₂×C₂²⋊Dic₇₉	C₂³	1	6	yes	—
117	C₂×C₂²⋊Dic₇₉	C₂³	1	3	yes	—
118	C₂×C₂²⋊Dic₇₉	C₂³	1	3	yes	complemented
119	C₂×(C₂×D₇₉)⋊C₄	C₂³	1	6	yes	—
120	C₂×(C₂×D₇₉)⋊C₄	C₂³	1	6	yes	—
121	C₂×(C₂×D₇₉)⋊C₄	C₂³	1	6	yes	—
122	C₂×(C₂×D₇₉)⋊C₄	C₂³	1	6	yes	complemented
123	C₂²⋊C₄×D₇₉	C₂³	1	48	yes	—
124	C₂²⋊C₄×D₇₉	C₂³	1	24	yes	—
125	C₂²⋊C₄×D₇₉	C₂³	1	24	yes	complemented
126	C₂×C₄×Dic₇₉	C₂³	1	3	yes	complemented
127	C₄²×D₇₉	C₂³	1	8	yes	complemented
128	C₂⁵×C₇₉	C₂³	1	1	yes	characteristic
129	C₂²×D₄×C₇₉	C₂³	1	6	yes	—
130	C₂²×D₄×C₇₉	C₂³	1	3	yes	—
131	C₂²×D₄×C₇₉	C₂³	1	3	yes	complemented
132	C₂³×C₄×C₇₉	C₂³	1	3	yes	complemented
133	#127×C₇₉	C₂³	1	8	yes	complemented
134	#126×C₇₉	C₂³	1	16	yes	complemented
135	#123×C₇₉	C₂³	1	24	yes	complemented
136	#121×C₇₉	C₂³	1	48	yes	complemented
137	#120×C₇₉	C₂³	1	24	yes	complemented
138	C₂×C₄⋊C₄×C₇₉	C₂³	1	6	yes	complemented
139	C₂×C₂²⋊C₄×C₇₉	C₂³	1	6	yes	—
140	C₂×C₂²⋊C₄×C₇₉	C₂³	1	3	yes	—
141	C₂×C₂²⋊C₄×C₇₉	C₂³	1	3	yes	complemented
142	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic, complemented
143	C₂³×D₇₉	—	2	24	no	—
144	C₂³×D₇₉	—	2	12	no	—
145	C₂³×D₇₉	—	2	12	no	—
146	C₂³×D₇₉	—	2	24	no	—
147	C₂³×D₇₉	—	4	48	no	—
148	C₂³×D₇₉	—	4	6	no	—
149	C₂³×D₇₉	—	4	12	no	—
150	C₂³×D₇₉	—	4	64	no	—
151	C₂³×D₇₉	C₂⁴	1	8	yes	—
152	C₂³×D₇₉	C₂⁴	1	4	yes	—
153	C₂³×D₇₉	C₂⁴	1	2	yes	—
154	C₂³×D₇₉	C₂⁴	1	1	yes	characteristic
155	C₂³×D₇₉	C₂⁴	1	12	yes	—
156	C₂³×D₇₉	C₂⁴	1	3	yes	—
157	C₂³×D₇₉	C₂⁴	1	4	yes	—
158	C₂³×D₇₉	C₂⁴	1	8	yes	—
159	C₂³×D₇₉	C₂⁴	1	1	yes	characteristic
160	C₂×D₃₁₆	—	4	12	no	—
161	C₂×D₃₁₆	—	4	6	no	—
162	C₂×D₃₁₆	—	4	6	no	—
163	C₂×D₃₁₆	C₂⁴	1	24	yes	—
164	C₂×D₃₁₆	C₂⁴	1	12	yes	—
165	C₂×D₃₁₆	C₂⁴	1	12	yes	complemented
166	C₂×C₂²⋊D₇₉	—	4	6	no	—
167	C₂×C₂²⋊D₇₉	—	4	12	no	—
168	C₂×C₂²⋊D₇₉	—	4	6	no	—
169	C₂×C₂²⋊D₇₉	—	4	12	no	—
170	C₂×C₂²⋊D₇₉	—	4	12	no	—
171	C₂×C₂²⋊D₇₉	C₂⁴	1	24	yes	—
172	C₂×C₂²⋊D₇₉	C₂⁴	1	12	yes	—
173	C₂×C₂²⋊D₇₉	C₂⁴	1	24	yes	—
174	C₂×C₂²⋊D₇₉	C₂⁴	1	12	yes	—
175	C₂×C₂²⋊D₇₉	C₂⁴	1	24	yes	complemented
176	D₄×D₇₉	—	4	48	no	—
177	D₄×D₇₉	—	4	96	no	—
178	D₄×D₇₉	—	4	48	no	—
179	C₂²×Dic₇₉	—	4	6	no	—
180	C₂²×Dic₇₉	C₂⁴	1	3	yes	—
181	C₂²×Dic₇₉	C₂⁴	1	6	yes	—
182	C₂²×Dic₇₉	C₂⁴	1	12	yes	complemented
183	C₂×C₄×D₇₉	—	2	24	no	—
184	C₂×C₄×D₇₉	—	2	12	no	—
185	C₂×C₄×D₇₉	—	4	12	no	—
186	C₂×C₄×D₇₉	—	4	48	no	—
187	C₂×C₄×D₇₉	C₂⁴	1	12	yes	—
188	C₂×C₄×D₇₉	C₂⁴	1	24	yes	—
189	C₂×C₄×D₇₉	C₂⁴	1	24	yes	complemented
190	C₄⋊Dic₇₉	C₂⁴	1	24	yes	complemented
191	Dic₇₉⋊C₄	C₂⁴	1	24	yes	complemented
192	Dic₇₉⋊C₄	C₂⁴	1	24	yes	complemented
193	C₂²⋊Dic₇₉	C₂⁴	1	24	yes	—
194	C₂²⋊Dic₇₉	C₂⁴	1	12	yes	—
195	C₂²⋊Dic₇₉	C₂⁴	1	12	yes	complemented
196	(C₂×D₇₉)⋊C₄	C₂⁴	1	24	yes	—
197	(C₂×D₇₉)⋊C₄	C₂⁴	1	24	yes	—
198	(C₂×D₇₉)⋊C₄	C₂⁴	1	24	yes	—
199	(C₂×D₇₉)⋊C₄	C₂⁴	1	24	yes	complemented
200	C₄×Dic₇₉	C₂⁴	1	12	yes	complemented
201	C₂⁴×C₇₉	—	4	6	no	—
202	C₂⁴×C₇₉	C₂⁴	1	2	yes	—
203	C₂⁴×C₇₉	C₂⁴	1	1	yes	characteristic
204	C₂⁴×C₇₉	C₂⁴	1	3	yes	—
205	C₂⁴×C₇₉	C₂⁴	1	4	yes	—
206	C₂×D₄×C₇₉	—	4	12	no	—
207	C₂×D₄×C₇₉	—	4	6	no	—
208	C₂×D₄×C₇₉	—	4	6	no	—
209	C₂×D₄×C₇₉	C₂⁴	1	24	yes	—
210	C₂×D₄×C₇₉	C₂⁴	1	12	yes	—
211	C₂×D₄×C₇₉	C₂⁴	1	12	yes	complemented
212	C₂²×C₄×C₇₉	—	4	6	no	—
213	C₂²×C₄×C₇₉	C₂⁴	1	3	yes	—
214	C₂²×C₄×C₇₉	C₂⁴	1	6	yes	—
215	C₂²×C₄×C₇₉	C₂⁴	1	12	yes	complemented
216	C₄⋊C₄×C₇₉	C₂⁴	1	24	yes	complemented
217	C₂²⋊C₄×C₇₉	C₂⁴	1	24	yes	—
218	C₂²⋊C₄×C₇₉	C₂⁴	1	12	yes	—
219	C₂²⋊C₄×C₇₉	C₂⁴	1	12	yes	complemented
220	C₄²×C₇₉	C₂⁴	1	4	yes	complemented
221	C₂³×C₇₉	—	2	6	no	—
222	C₂³×C₇₉	—	2	12	no	—
223	C₂³×C₇₉	—	2	6	no	—
224	C₂³×C₇₉	—	2	12	no	—
225	C₂³×C₇₉	—	4	12	no	—
226	C₂³×C₇₉	—	4	16	no	—
227	C₂³×C₇₉	C₂⁵	1	4	yes	—
228	C₂³×C₇₉	C₂⁵	1	2	yes	—
229	C₂³×C₇₉	C₂⁵	1	6	yes	—
230	C₂³×C₇₉	C₂⁵	1	1	yes	characteristic
231	C₂²×D₇₉	—	2	6	no	—
232	C₂²×D₇₉	—	2	12	no	—
233	C₂²×D₇₉	—	2	6	no	—
234	C₂²×D₇₉	—	2	12	no	—
235	C₂²×D₇₉	—	2	24	no	—
236	C₂²×D₇₉	—	2	48	no	—
237	C₂²×D₇₉	—	2	24	no	—
238	C₂²×D₇₉	—	2	48	no	—
239	C₂²×D₇₉	—	4	12	no	—
240	C₂²×D₇₉	—	4	24	no	—
241	C₂²×D₇₉	—	4	16	no	—
242	C₂²×D₇₉	—	4	32	no	—
243	C₂²×D₇₉	—	4	128	no	—
244	C₂²×D₇₉	—	4	48	no	—
245	C₂²×D₇₉	—	4	32	no	—
246	C₂²×D₇₉	—	4	16	no	—
247	C₂²×D₇₉	H(5,𝔽₂)	1	12	yes	—
248	C₂²×D₇₉	C₂⁵	1	4	yes	—
249	C₂²×D₇₉	C₂⁵	1	2	yes	—
250	C₂²×D₇₉	C₂⁵	1	6	yes	—
251	C₂²×D₇₉	C₂⁵	1	2	yes	—
252	D₄×C₇₉	—	4	24	no	—
253	D₄×C₇₉	—	4	12	no	—
254	D₄×C₇₉	—	4	12	no	—
255	C₂×C₄×C₇₉	—	2	12	no	—
256	C₂×C₄×C₇₉	—	2	6	no	—
257	C₂×C₄×C₇₉	—	4	12	no	—
258	C₂×C₄×C₇₉	C₂⁵	1	6	yes	—
259	C₂×C₄×C₇₉	C₂⁵	1	12	yes	—
260	C₂²⋊D₇₉	—	4	12	no	—
261	C₂²⋊D₇₉	—	4	12	no	—
262	C₂²⋊D₇₉	—	4	24	no	—
263	C₂²⋊D₇₉	—	4	24	no	—
264	C₂²⋊D₇₉	—	4	24	no	—
265	C₂×Dic₇₉	—	2	12	no	—
266	C₂×Dic₇₉	—	2	6	no	—
267	C₂×Dic₇₉	—	4	12	no	—
268	C₂×Dic₇₉	C₂⁵	1	6	yes	—
269	C₂×Dic₇₉	C₂⁵	1	12	yes	—
270	D₃₁₆	—	4	24	no	—
271	D₃₁₆	—	4	12	no	—
272	D₃₁₆	—	4	12	no	—
273	C₄×D₇₉	—	2	48	no	—
274	C₄×D₇₉	—	2	24	no	—
275	C₄×D₇₉	—	4	24	no	—
276	C₂²×C₇₉	—	2	12	no	—
277	C₂²×C₇₉	—	2	6	no	—
278	C₂²×C₇₉	—	2	6	no	—
279	C₂²×C₇₉	—	2	12	no	—
280	C₂²×C₇₉	—	4	16	no	—
281	C₂²×C₇₉	—	4	4	no	—
282	C₂²×C₇₉	—	4	8	no	—
283	C₂²×C₇₉	—	4	12	no	—
284	C₂²×C₇₉	C₂×H(5,𝔽₂)	1	6	yes	—
285	C₂²×C₇₉	C₂⁶	1	1	yes	characteristic
286	C₂×D₇₉	—	2	12	no	—
287	C₂×D₇₉	—	2	6	no	—
288	C₂×D₇₉	—	2	12	no	—
289	C₂×D₇₉	—	2	6	no	—
290	C₂×D₇₉	—	4	16	no	—
291	C₂×D₇₉	—	4	32	no	—
292	C₂×D₇₉	—	4	12	no	—
293	C₂×D₇₉	—	4	4	no	—
294	C₂×D₇₉	—	4	8	no	—
295	C₂×D₇₉	—	4	48	no	—
296	C₂×D₇₉	—	4	16	no	—
297	C₂×D₇₉	—	4	32	no	—
298	C₂×D₇₉	#560	1	16	yes	direct product factor
299	C₂×D₇₉	C₂×H(5,𝔽₂)	1	12	yes	—
300	C₄×C₇₉	—	2	12	no	—
301	C₄×C₇₉	—	2	6	no	—
302	Dic₇₉	—	2	6	no	—
303	Dic₇₉	—	2	12	no	—
304	C₂²×#560	—	79	1	no	maximal, Sylow
305	C₂×C₇₉	—	4	2	no	—
306	C₂×C₇₉	—	4	4	no	—
307	C₂×C₇₉	—	4	6	no	—
308	C₂×C₇₉	C₂×#560	1	4	yes	complemented
309	C₂×C₇₉	C₂²×H(5,𝔽₂)	1	3	yes	—
310	D₇₉	—	4	6	no	—
311	D₇₉	—	4	2	no	—
312	D₇₉	—	4	4	no	—
313	D₇₉	C₂×#560	1	8	yes	direct product factor
314	C₂×#560	—	79	32	no	—
315	C₂×#560	—	79	1	no	—
316	C₂×#560	—	79	2	no	—
317	C₂×#560	—	79	3	no	—
318	C₂×#560	—	79	6	no	—
319	C₂×#560	—	79	3	no	—
320	C₂×#560	D₇₉	1	1	yes	characteristic, direct product factor
321	C₂²×#127	—	79	1	no	—
322	C₂²×#126	—	79	2	no	—
323	C₂²×#123	—	79	3	no	—
324	C₂²×#121	—	79	6	no	—
325	C₂²×#120	—	79	3	no	—
326	C₇₉	C₂²×#560	1	1	yes	characteristic, complemented, Sylow
327	C₂⁶	—	79	1	no	—
328	C₂³×D₄	—	79	6	no	—
329	C₂³×D₄	—	79	3	no	—
330	C₂³×D₄	—	79	3	no	—
331	C₂⁴×C₄	—	79	3	no	—
332	#560	—	79	16	no	—
333	#560	—	79	32	no	—
334	#560	—	79	48	no	—
335	#560	—	79	96	no	—
336	#560	—	79	48	no	—
337	#560	C₂×D₇₉	1	16	yes	direct product factor
338	C₂×#127	—	79	3	no	—
339	C₂×#127	—	79	3	no	—
340	C₂×#127	—	79	16	no	—
341	C₂×#127	—	79	1	no	—
342	C₂×#127	C₂×D₇₉	1	1	yes	characteristic, complemented
343	C₂×#126	—	79	32	no	—
344	C₂×#126	—	79	6	no	—
345	C₂×#126	—	79	6	no	—
346	C₂×#126	—	79	2	no	—
347	C₂×#126	C₂×D₇₉	1	2	yes	complemented
348	C₂×#123	—	79	3	no	—
349	C₂×#123	—	79	3	no	—
350	C₂×#123	—	79	48	no	—
351	C₂×#123	—	79	6	no	—
352	C₂×#123	—	79	6	no	—
353	C₂×#123	—	79	3	no	—
354	C₂×#123	C₂×D₇₉	1	3	yes	complemented
355	C₂×#121	—	79	6	no	—
356	C₂×#121	—	79	6	no	—
357	C₂×#121	—	79	6	no	—
358	C₂×#121	—	79	6	no	—
359	C₂×#121	—	79	96	no	—
360	C₂×#121	—	79	6	no	—
361	C₂×#121	—	79	6	no	—
362	C₂×#121	—	79	6	no	—
363	C₂×#121	C₂×D₇₉	1	6	yes	complemented
364	C₂×#120	—	79	3	no	—
365	C₂×#120	—	79	6	no	—
366	C₂×#120	—	79	3	no	—
367	C₂×#120	—	79	48	no	—
368	C₂×#120	—	79	3	no	—
369	C₂×#120	—	79	6	no	—
370	C₂×#120	C₂×D₇₉	1	3	yes	complemented
371	C₂²×C₄⋊C₄	—	79	6	no	—
372	C₂²×C₂²⋊C₄	—	79	6	no	—
373	C₂²×C₂²⋊C₄	—	79	3	no	—
374	C₂²×C₂²⋊C₄	—	79	3	no	—
375	C₂²×C₄²	—	79	1	no	—
376	C₂⁵	—	316	12	no	—
377	C₂⁵	—	79	1	no	—
378	C₂⁵	—	79	2	no	—
379	C₂⁵	—	79	8	no	—
380	C₂⁵	—	79	2	no	—
381	C₂⁵	—	79	1	no	—
382	C₂⁵	—	79	3	no	—
383	C₂⁵	C₂²×D₇₉	1	1	yes	characteristic
384	C₂²×D₄	—	316	24	no	—
385	C₂²×D₄	—	316	12	no	—
386	C₂²×D₄	—	316	12	no	—
387	C₂²×D₄	—	79	6	no	—
388	C₂²×D₄	—	79	6	no	—
389	C₂²×D₄	—	79	3	no	—
390	C₂²×D₄	—	79	3	no	—
391	C₂²×D₄	—	79	6	no	—
392	C₂²×D₄	—	79	48	no	—
393	C₂²×D₄	—	79	24	no	—
394	C₂²×D₄	—	79	24	no	—
395	C₂²×D₄	—	79	6	no	—
396	C₂²×D₄	—	79	3	no	—
397	C₂²×D₄	—	79	3	no	—
398	C₂²×D₄	C₂²×D₇₉	1	6	yes	—
399	C₂²×D₄	C₂²×D₇₉	1	3	yes	—
400	C₂²×D₄	C₂²×D₇₉	1	3	yes	complemented
401	C₂³×C₄	—	316	12	no	—
402	C₂³×C₄	—	79	3	no	—
403	C₂³×C₄	—	79	6	no	—
404	C₂³×C₄	—	79	24	no	—
405	C₂³×C₄	—	79	6	no	—
406	C₂³×C₄	—	79	3	no	—
407	C₂³×C₄	C₂²×D₇₉	1	3	yes	complemented
408	#127	—	79	24	no	—
409	#127	—	79	24	no	—
410	#127	—	79	8	no	—
411	#127	C₂²×D₇₉	1	8	yes	complemented
412	#126	—	79	48	no	—
413	#126	—	79	48	no	—
414	#126	—	79	16	no	—
415	#126	C₂²×D₇₉	1	16	yes	complemented
416	#123	—	79	24	no	—
417	#123	—	79	24	no	—
418	#123	—	79	48	no	—
419	#123	—	79	48	no	—
420	#123	—	79	24	no	—
421	#123	C₂²×D₇₉	1	24	yes	complemented
422	#121	—	79	48	no	—
423	#121	—	79	48	no	—
424	#121	—	79	48	no	—
425	#121	—	79	48	no	—
426	#121	—	79	48	no	—
427	#121	—	79	48	no	—
428	#121	—	79	48	no	—
429	#121	C₂²×D₇₉	1	48	yes	complemented
430	#120	—	79	24	no	—
431	#120	—	79	48	no	—
432	#120	—	79	24	no	—
433	#120	—	79	24	no	—
434	#120	—	79	48	no	—
435	#120	C₂²×D₇₉	1	24	yes	complemented
436	C₂×C₄⋊C₄	—	79	6	no	—
437	C₂×C₄⋊C₄	—	79	6	no	—
438	C₂×C₄⋊C₄	—	79	6	no	—
439	C₂×C₄⋊C₄	—	79	48	no	—
440	C₂×C₄⋊C₄	C₂²×D₇₉	1	6	yes	complemented
441	C₂×C₂²⋊C₄	—	79	6	no	—
442	C₂×C₂²⋊C₄	—	79	3	no	—
443	C₂×C₂²⋊C₄	—	79	3	no	—
444	C₂×C₂²⋊C₄	—	79	6	no	—
445	C₂×C₂²⋊C₄	—	79	6	no	—
446	C₂×C₂²⋊C₄	—	79	6	no	—
447	C₂×C₂²⋊C₄	—	79	6	no	—
448	C₂×C₂²⋊C₄	—	79	48	no	—
449	C₂×C₂²⋊C₄	—	79	24	no	—
450	C₂×C₂²⋊C₄	—	79	24	no	—
451	C₂×C₂²⋊C₄	C₂²×D₇₉	1	6	yes	—
452	C₂×C₂²⋊C₄	C₂²×D₇₉	1	3	yes	—
453	C₂×C₂²⋊C₄	C₂²×D₇₉	1	3	yes	complemented
454	C₂×C₄²	—	79	3	no	—
455	C₂×C₄²	—	79	8	no	—
456	C₂×C₄²	C₂²×D₇₉	1	1	yes	characteristic, complemented
457	C₂⁴	—	4	6	no	—
458	C₂⁴	—	316	12	no	—
459	C₂⁴	—	316	6	no	—
460	C₂⁴	—	316	64	no	—
461	C₂⁴	—	316	48	no	—
462	C₂⁴	—	79	4	no	—
463	C₂⁴	—	79	8	no	—
464	C₂⁴	—	79	1	no	—
465	C₂⁴	—	79	8	no	—
466	C₂⁴	—	79	4	no	—
467	C₂⁴	—	79	12	no	—
468	C₂⁴	—	79	2	no	—
469	C₂⁴	—	79	1	no	—
470	C₂⁴	—	79	3	no	—
471	C₂⁴	—	158	12	no	—
472	C₂⁴	—	158	24	no	—
473	C₂⁴	—	158	24	no	—
474	C₂⁴	—	158	12	no	—
475	C₂⁴	C₂³×D₇₉	1	2	yes	—
476	C₂⁴	C₂³×D₇₉	1	1	yes	characteristic
477	C₂⁴	C₂³×D₇₉	1	3	yes	—
478	C₂⁴	C₂³×D₇₉	1	4	yes	—
479	C₂×D₄	—	4	12	no	—
480	C₂×D₄	—	4	6	no	—
481	C₂×D₄	—	4	6	no	—
482	C₂×D₄	—	316	12	no	—
483	C₂×D₄	—	316	6	no	—
484	C₂×D₄	—	316	6	no	—
485	C₂×D₄	—	316	96	no	—
486	C₂×D₄	—	316	48	no	—
487	C₂×D₄	—	316	48	no	—
488	C₂×D₄	—	316	12	no	—
489	C₂×D₄	—	316	12	no	—
490	C₂×D₄	—	316	6	no	—
491	C₂×D₄	—	316	12	no	—
492	C₂×D₄	—	316	6	no	—
493	C₂×D₄	—	79	24	no	—
494	C₂×D₄	—	79	24	no	—
495	C₂×D₄	—	79	12	no	—
496	C₂×D₄	—	79	12	no	—
497	C₂×D₄	—	79	24	no	—
498	C₂×D₄	—	79	24	no	—
499	C₂×D₄	—	79	12	no	—
500	C₂×D₄	—	79	12	no	—
501	C₂×D₄	C₂³×D₇₉	1	24	yes	—
502	C₂×D₄	C₂³×D₇₉	1	12	yes	—
503	C₂×D₄	C₂³×D₇₉	1	12	yes	complemented
504	C₂²×C₄	—	4	6	no	—
505	C₂²×C₄	—	316	12	no	—
506	C₂²×C₄	—	316	48	no	—
507	C₂²×C₄	—	316	6	no	—
508	C₂²×C₄	—	79	12	no	—
509	C₂²×C₄	—	79	24	no	—
510	C₂²×C₄	—	79	3	no	—
511	C₂²×C₄	—	79	6	no	—
512	C₂²×C₄	—	79	12	no	—
513	C₂²×C₄	—	79	24	no	—
514	C₂²×C₄	—	158	24	no	—
515	C₂²×C₄	—	158	12	no	—
516	C₂²×C₄	C₂³×D₇₉	1	3	yes	—
517	C₂²×C₄	C₂³×D₇₉	1	6	yes	—
518	C₂²×C₄	C₂³×D₇₉	1	12	yes	complemented
519	C₄⋊C₄	—	79	24	no	—
520	C₄⋊C₄	—	79	24	no	—
521	C₄⋊C₄	—	79	24	no	—
522	C₄⋊C₄	C₂³×D₇₉	1	24	yes	complemented
523	C₂²⋊C₄	—	79	24	no	—
524	C₂²⋊C₄	—	79	12	no	—
525	C₂²⋊C₄	—	79	12	no	—
526	C₂²⋊C₄	—	79	24	no	—
527	C₂²⋊C₄	—	79	24	no	—
528	C₂²⋊C₄	—	79	24	no	—
529	C₂²⋊C₄	—	79	24	no	—
530	C₂²⋊C₄	C₂³×D₇₉	1	24	yes	—
531	C₂²⋊C₄	C₂³×D₇₉	1	12	yes	—
532	C₂²⋊C₄	C₂³×D₇₉	1	12	yes	complemented
533	C₄²	—	79	12	no	—
534	C₄²	C₂³×D₇₉	1	4	yes	complemented
535	C₂³	—	2	6	no	—
536	C₂³	—	2	12	no	—
537	C₂³	—	2	12	no	—
538	C₂³	—	2	6	no	—
539	C₂³	—	4	12	no	—
540	C₂³	—	4	16	no	—
541	C₂³	—	316	24	no	—
542	C₂³	—	316	12	no	—
543	C₂³	—	316	128	no	—
544	C₂³	—	316	32	no	—
545	C₂³	—	316	16	no	—
546	C₂³	—	316	32	no	—
547	C₂³	—	316	16	no	—
548	C₂³	—	316	48	no	—
549	C₂³	—	79	12	no	—
550	C₂³	—	79	2	no	—
551	C₂³	—	79	4	no	—
552	C₂³	—	79	2	no	—
553	C₂³	—	79	6	no	—
554	C₂³	—	158	24	no	—
555	C₂³	—	158	48	no	—
556	C₂³	—	158	48	no	—
557	C₂³	—	158	24	no	—
558	C₂³	—	158	6	no	—
559	C₂³	—	158	12	no	—
560	C₂³	—	158	12	no	—
561	C₂³	—	158	6	no	—
562	C₂³	C₂⁴×D₇₉	1	4	yes	—
563	C₂³	C₂⁴×D₇₉	1	2	yes	—
564	C₂³	C₂⁴×D₇₉	1	6	yes	—
565	C₂³	C₂⁴×D₇₉	1	1	yes	characteristic
566	D₄	—	4	24	no	—
567	D₄	—	4	12	no	—
568	D₄	—	4	12	no	—
569	D₄	—	316	24	no	—
570	D₄	—	316	12	no	—
571	D₄	—	316	12	no	—
572	D₄	—	316	24	no	—
573	D₄	—	316	24	no	—
574	D₄	—	316	12	no	—
575	D₄	—	316	24	no	—
576	D₄	—	316	12	no	—
577	C₂×C₄	—	2	12	no	—
578	C₂×C₄	—	2	6	no	—
579	C₂×C₄	—	4	12	no	—
580	C₂×C₄	—	316	24	no	—
581	C₂×C₄	—	316	12	no	—
582	C₂×C₄	—	79	6	no	—
583	C₂×C₄	—	79	12	no	—
584	C₂×C₄	—	158	48	no	—
585	C₂×C₄	—	158	24	no	—
586	C₂×C₄	—	158	12	no	—
587	C₂×C₄	—	158	6	no	—
588	C₂×C₄	C₂⁴×D₇₉	1	6	yes	—
589	C₂×C₄	C₂⁴×D₇₉	1	12	yes	—
590	C₂²	—	2	6	no	—
591	C₂²	—	2	12	no	—
592	C₂²	—	2	12	no	—
593	C₂²	—	2	6	no	—
594	C₂²	—	4	16	no	—
595	C₂²	—	4	8	no	—
596	C₂²	—	4	4	no	—
597	C₂²	—	4	12	no	—
598	C₂²	—	316	32	no	—
599	C₂²	—	316	16	no	—
600	C₂²	—	316	32	no	—
601	C₂²	—	316	16	no	—
602	C₂²	—	316	48	no	—
603	C₂²	—	316	8	no	—
604	C₂²	—	316	4	no	—
605	C₂²	—	316	12	no	—
606	C₂²	—	79	12	no	—
607	C₂²	—	79	16	no	—
608	C₂²	—	158	6	no	—
609	C₂²	—	158	12	no	—
610	C₂²	—	158	12	no	—
611	C₂²	—	158	6	no	—
612	C₂²	H(5,𝔽₂)×D₇₉	1	6	yes	—
613	C₂²	C₂⁵×D₇₉	1	1	yes	characteristic
614	C₄	—	2	12	no	—
615	C₄	—	2	6	no	—
616	C₄	—	158	12	no	—
617	C₄	—	158	6	no	—
618	C₂	—	4	4	no	—
619	C₂	—	4	2	no	—
620	C₂	—	4	6	no	—
621	C₂	—	316	4	no	—
622	C₂	—	316	2	no	—
623	C₂	—	316	6	no	—
624	C₂	—	79	8	no	—
625	C₂	#560×D₇₉	1	4	yes	direct product factor
626	C₂	C₂×H(5,𝔽₂)×D₇₉	1	3	yes	—

	subgroup	G/H
center	C₂³	C₂⁴×D₇₉
commutator, cosocle	C₂²×C₇₉	C₂⁶
Frattini	C₂²	C₂⁵×D₇₉
Fitting	C₂×#560×C₇₉	C₂
socle	C₂³×C₇₉	C₂⁵
hypercenter	C₂×#560	D₇₉
hypocenter	C₇₉	C₂²×#560
LCS	G ▷ C₂²×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂³ ◁ C₂×#560

Complements

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

N	H ≅ G/N	type
1. C₂×#19099304	C₂	semidirect
2. C₂×#19099303	C₂	semidirect
3. C₂×#19099302	C₂	semidirect
4. C₂×#19099301	C₂	semidirect
5. C₂×#19099300	C₂	semidirect
6. #560×D₇₉	C₂	direct (N × H)
7. C₂×#127×D₇₉	C₂	semidirect
8. C₂×#126×D₇₉	C₂	semidirect
9. C₂×#123×D₇₉	C₂	semidirect
10. C₂×#121×D₇₉	C₂	semidirect
11. C₂×#120×D₇₉	C₂	semidirect
12. C₂×#560×C₇₉	C₂	semidirect
16. C₂²×D₄×D₇₉	C₂²	semidirect
17. C₂³×C₄×D₇₉	C₂²	semidirect
18. #19099304	C₂²	semidirect
19. #19099303	C₂²	semidirect
20. #19099302	C₂²	semidirect
21. #19099301	C₂²	semidirect
22. #19099300	C₂²	semidirect
23. C₂×#14579158	C₂²	semidirect
24. C₂×#14579157	C₂²	semidirect
25. C₂×#14579157	C₂²	semidirect
26. #127×D₇₉	C₂²	semidirect
27. C₂×#14579156	C₂²	semidirect
28. C₂×#14579155	C₂²	semidirect
29. C₂×#14579154	C₂²	semidirect
30. #126×D₇₉	C₂²	semidirect
31. C₂×#14579146	C₂²	semidirect
32. C₂×#14579145	C₂²	semidirect
33. C₂×#14579144	C₂²	semidirect
34. C₂×#14579143	C₂²	semidirect
35. C₂×#14579142	C₂²	semidirect
36. #123×D₇₉	C₂²	semidirect
37. C₂×#14579136	C₂²	semidirect
38. C₂×#14579135	C₂²	semidirect
39. C₂×#14579134	C₂²	semidirect
40. C₂×#14579134	C₂²	semidirect
41. C₂×#14579133	C₂²	semidirect
42. C₂×#14579133	C₂²	semidirect
43. C₂×#14579132	C₂²	semidirect
44. #121×D₇₉	C₂²	semidirect
45. C₂×#14579131	C₂²	semidirect
46. C₂×#14579131	C₂²	semidirect
47. C₂×#14579130	C₂²	semidirect
48. C₂×#14579129	C₂²	semidirect
49. C₂×#14579129	C₂²	semidirect
50. #120×D₇₉	C₂²	semidirect
51. C₂×C₄⋊C₄×D₇₉	C₂²	semidirect
54. C₂×C₂²⋊C₄×D₇₉	C₂²	semidirect
55. C₂×C₄²×D₇₉	C₂²	semidirect
56. #560×C₇₉	C₂²	semidirect
57. C₂×#127×C₇₉	C₂²	semidirect
58. C₂×#126×C₇₉	C₂²	semidirect
59. C₂×#123×C₇₉	C₂²	semidirect
60. C₂×#121×C₇₉	C₂²	semidirect
61. C₂×#120×C₇₉	C₂²	semidirect
71. C₂²×D₃₁₆	C₂³	semidirect
76. C₂²×C₂²⋊D₇₉	C₂³	semidirect
82. C₂×D₄×D₇₉	C₂³	semidirect
83. C₂³×Dic₇₉	C₂³	semidirect
87. C₂²×C₄×D₇₉	C₂³	semidirect
88. C₂²×C₄×D₇₉	C₂³	semidirect
89. #14579158	C₂³	semidirect
90. #14579157	C₂³	semidirect
91. #14579157	C₂³	semidirect
92. #14579156	C₂³	semidirect
93. #14579155	C₂³	semidirect
94. #14579154	C₂³	semidirect
95. #14579146	C₂³	semidirect
96. #14579145	C₂³	semidirect
97. #14579144	C₂³	semidirect
98. #14579143	C₂³	semidirect
99. #14579142	C₂³	semidirect
100. #14579136	C₂³	semidirect
101. #14579135	C₂³	semidirect
102. #14579134	C₂³	semidirect
103. #14579134	C₂³	semidirect
104. #14579133	C₂³	semidirect
105. #14579133	C₂³	semidirect
106. #14579132	C₂³	semidirect
107. #14579131	C₂³	semidirect
108. #14579131	C₂³	semidirect
109. #14579130	C₂³	semidirect
110. #14579129	C₂³	semidirect
111. #14579129	C₂³	semidirect
112. C₂×C₄⋊Dic₇₉	C₂³	semidirect
113. C₂×Dic₇₉⋊C₄	C₂³	semidirect
114. C₂×Dic₇₉⋊C₄	C₂³	semidirect
115. C₄⋊C₄×D₇₉	C₂³	semidirect
118. C₂×C₂²⋊Dic₇₉	C₂³	semidirect
122. C₂×(C₂×D₇₉)⋊C₄	C₂³	semidirect
125. C₂²⋊C₄×D₇₉	C₂³	semidirect
126. C₂×C₄×Dic₇₉	C₂³	semidirect
127. C₄²×D₇₉	C₂³	semidirect
131. C₂²×D₄×C₇₉	C₂³	semidirect
132. C₂³×C₄×C₇₉	C₂³	semidirect
133. #127×C₇₉	C₂³	semidirect
134. #126×C₇₉	C₂³	semidirect
135. #123×C₇₉	C₂³	semidirect
136. #121×C₇₉	C₂³	semidirect
137. #120×C₇₉	C₂³	semidirect
138. C₂×C₄⋊C₄×C₇₉	C₂³	semidirect
141. C₂×C₂²⋊C₄×C₇₉	C₂³	semidirect
142. C₂×C₄²×C₇₉	C₂³	semidirect
165. C₂×D₃₁₆	C₂⁴	semidirect
175. C₂×C₂²⋊D₇₉	C₂⁴	semidirect
182. C₂²×Dic₇₉	C₂⁴	semidirect
189. C₂×C₄×D₇₉	C₂⁴	semidirect
190. C₄⋊Dic₇₉	C₂⁴	semidirect
191. Dic₇₉⋊C₄	C₂⁴	semidirect
192. Dic₇₉⋊C₄	C₂⁴	semidirect
195. C₂²⋊Dic₇₉	C₂⁴	semidirect
199. (C₂×D₇₉)⋊C₄	C₂⁴	semidirect
200. C₄×Dic₇₉	C₂⁴	semidirect
211. C₂×D₄×C₇₉	C₂⁴	semidirect
215. C₂²×C₄×C₇₉	C₂⁴	semidirect
216. C₄⋊C₄×C₇₉	C₂⁴	semidirect
219. C₂²⋊C₄×C₇₉	C₂⁴	semidirect
220. C₄²×C₇₉	C₂⁴	semidirect
298. C₂×D₇₉	#560	direct (N × H)
308. C₂×C₇₉	C₂×#560	semidirect
313. D₇₉	C₂×#560	direct (N × H)
320. C₂×#560	D₇₉	direct (N × H)
326. C₇₉	C₂²×#560	semidirect
337. #560	C₂×D₇₉	direct (N × H)
342. C₂×#127	C₂×D₇₉	semidirect
347. C₂×#126	C₂×D₇₉	semidirect
354. C₂×#123	C₂×D₇₉	semidirect
363. C₂×#121	C₂×D₇₉	semidirect
370. C₂×#120	C₂×D₇₉	semidirect
400. C₂²×D₄	C₂²×D₇₉	semidirect
407. C₂³×C₄	C₂²×D₇₉	semidirect
411. #127	C₂²×D₇₉	semidirect
415. #126	C₂²×D₇₉	semidirect
421. #123	C₂²×D₇₉	semidirect
429. #121	C₂²×D₇₉	semidirect
435. #120	C₂²×D₇₉	semidirect
440. C₂×C₄⋊C₄	C₂²×D₇₉	semidirect
453. C₂×C₂²⋊C₄	C₂²×D₇₉	semidirect
456. C₂×C₄²	C₂²×D₇₉	semidirect
503. C₂×D₄	C₂³×D₇₉	semidirect
518. C₂²×C₄	C₂³×D₇₉	semidirect
522. C₄⋊C₄	C₂³×D₇₉	semidirect
532. C₂²⋊C₄	C₂³×D₇₉	semidirect
534. C₄²	C₂³×D₇₉	semidirect
625. C₂	#560×D₇₉	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×#19099304	2
C₂×#19099303	2
C₂×#19099302	2
C₂×#19099301	2
C₂×#19099300	2
#560×D₇₉	2
C₂×#127×D₇₉	2
C₂×#126×D₇₉	2
C₂×#123×D₇₉	2
C₂×#121×D₇₉	2
C₂×#120×D₇₉	2
C₂×#560×C₇₉	2
C₂²×#560	79

Subgroups — C2×#560×D79 #35195134

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#560×D₇₉ #35195134