Subgroups — C₂²×#19099210 #35195192

Order 20224.

14462 conjugacy classes of subgroups.

The subgroup lattice has 546 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×#11929624	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂³×D₄×D₇₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#19099210	C₂	1	48	yes	maximal, direct product factor
4	C₂²×#14579148	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂²×#14579143	C₂	1	2	yes	maximal, complemented
6	C₂²×#14579141	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂²×#14579132	C₂	1	2	yes	maximal, complemented
8	C₂²×#14579129	C₂	1	2	yes	maximal, complemented
9	C₂²×#14579123	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂²×C₄×C₂²⋊D₇₉	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂²×C₂²⋊C₄×D₇₉	C₂	1	2	yes	maximal, complemented
12	C₂²×#121×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂⁵×D₇₉	C₂²	1	2	yes	—
14	C₂²×#11929624	—	2	16	no	—
15	C₂²×#11929624	C₂²	1	24	yes	complemented
16	C₂³×Dic₁₅₈	C₂²	1	1	yes	characteristic, complemented
17	C₂³×D₃₁₆	C₂²	1	1	yes	characteristic
18	C₂³×C₂²⋊D₇₉	C₂²	1	1	yes	characteristic
19	C₂³×C₂²⋊D₇₉	C₂²	1	2	yes	—
20	C₂³×C₂²⋊D₇₉	C₂²	1	2	yes	complemented
21	C₂²×D₄×D₇₉	—	2	16	no	—
22	C₂²×D₄×D₇₉	C₂²	1	24	yes	complemented
23	C₂³×C₄×D₇₉	C₂²	1	1	yes	characteristic
24	C₂³×C₄×D₇₉	C₂²	1	2	yes	complemented
25	C₂³×C₄×D₇₉	C₂²	1	2	yes	complemented
26	#19099210	C₂²	1	256	yes	direct product factor
27	C₂×#14579148	C₂²	1	24	yes	complemented
28	C₂×#14579143	C₂²	1	48	yes	complemented
29	C₂×#14579141	C₂²	1	24	yes	complemented
30	C₂×#14579132	C₂²	1	48	yes	complemented
31	C₂×#14579129	C₂²	1	48	yes	complemented
32	C₂×#14579123	C₂²	1	24	yes	complemented
33	C₂×C₄×C₂²⋊D₇₉	C₂²	1	24	yes	complemented
34	C₂²×C₄⋊Dic₇₉	C₂²	1	2	yes	complemented
35	C₂²×Dic₇₉⋊C₄	C₂²	1	1	yes	characteristic, complemented
36	C₂²×C₂²⋊Dic₇₉	C₂²	1	2	yes	complemented
37	C₂²×C₂²⋊Dic₇₉	C₂²	1	1	yes	characteristic, complemented
38	C₂²×C₂²⋊Dic₇₉	C₂²	1	2	yes	complemented
39	C₂²×(C₂×D₇₉)⋊C₄	C₂²	1	1	yes	characteristic
40	C₂²×(C₂×D₇₉)⋊C₄	C₂²	1	2	yes	—
41	C₂²×(C₂×D₇₉)⋊C₄	C₂²	1	2	yes	complemented
42	C₂×C₂²⋊C₄×D₇₉	C₂²	1	48	yes	complemented
43	C₂²×C₄×Dic₇₉	C₂²	1	1	yes	characteristic, complemented
44	C₂³×D₄×C₇₉	C₂²	1	1	yes	characteristic
45	C₂³×D₄×C₇₉	C₂²	1	2	yes	complemented
46	C₂⁴×C₄×C₇₉	C₂²	1	1	yes	characteristic, complemented
47	C₂×#121×C₇₉	C₂²	1	24	yes	complemented
48	C₂²×C₄⋊C₄×C₇₉	C₂²	1	1	yes	characteristic, complemented
49	C₂²×C₂²⋊C₄×C₇₉	C₂²	1	2	yes	complemented
50	C₂⁴×D₇₉	—	2	16	no	—
51	C₂⁴×D₇₉	—	2	16	no	—
52	C₂⁴×D₇₉	—	4	8	no	—
53	C₂⁴×D₇₉	C₂³	1	24	yes	—
54	C₂⁴×D₇₉	C₂³	1	2	yes	—
55	C₂⁴×D₇₉	C₂³	1	1	yes	characteristic
56	C₂×#11929624	—	2	192	no	—
57	C₂×#11929624	C₂³	1	64	yes	complemented
58	C₂²×Dic₁₅₈	—	2	8	no	—
59	C₂²×Dic₁₅₈	C₂³	1	12	yes	complemented
60	C₂²×D₃₁₆	D₄	1	16	yes	complemented
61	C₂²×D₃₁₆	C₂³	1	12	yes	—
62	C₂²×C₂²⋊D₇₉	—	2	16	no	—
63	C₂²×C₂²⋊D₇₉	—	2	16	no	—
64	C₂²×C₂²⋊D₇₉	—	2	8	no	—
65	C₂²×C₂²⋊D₇₉	C₂³	1	12	yes	—
66	C₂²×C₂²⋊D₇₉	C₂³	1	24	yes	—
67	C₂²×C₂²⋊D₇₉	C₂³	1	24	yes	complemented
68	C₂×D₄×D₇₉	—	2	192	no	—
69	C₂×D₄×D₇₉	C₂³	1	64	yes	complemented
70	C₂³×Dic₇₉	C₂³	1	1	yes	characteristic
71	C₂³×Dic₇₉	C₂³	1	1	yes	characteristic
72	C₂³×Dic₇₉	C₂³	1	2	yes	—
73	C₂³×Dic₇₉	C₂³	1	1	yes	characteristic
74	C₂²×C₄×D₇₉	—	2	8	no	—
75	C₂²×C₄×D₇₉	—	2	16	no	—
76	C₂²×C₄×D₇₉	—	4	8	no	—
77	C₂²×C₄×D₇₉	C₂³	1	12	yes	—
78	C₂²×C₄×D₇₉	C₂³	1	24	yes	complemented
79	C₂²×C₄×D₇₉	C₂³	1	24	yes	complemented
80	#14579148	C₂³	1	64	yes	complemented
81	#14579143	C₂³	1	128	yes	complemented
82	#14579141	C₂³	1	64	yes	complemented
83	#14579132	C₂³	1	128	yes	complemented
84	#14579129	C₂³	1	128	yes	complemented
85	#14579123	C₂³	1	64	yes	complemented
86	C₄×C₂²⋊D₇₉	C₂³	1	64	yes	complemented
87	C₂×C₄⋊Dic₇₉	C₂³	1	24	yes	complemented
88	C₂×Dic₇₉⋊C₄	C₂³	1	12	yes	complemented
89	C₂×C₂²⋊Dic₇₉	C₂³	1	24	yes	complemented
90	C₂×C₂²⋊Dic₇₉	C₂³	1	12	yes	complemented
91	C₂×C₂²⋊Dic₇₉	C₂³	1	24	yes	complemented
92	C₂×(C₂×D₇₉)⋊C₄	C₂³	1	12	yes	—
93	C₂×(C₂×D₇₉)⋊C₄	C₂³	1	24	yes	—
94	C₂×(C₂×D₇₉)⋊C₄	C₂³	1	24	yes	complemented
95	C₂²⋊C₄×D₇₉	C₂³	1	128	yes	complemented
96	C₂×C₄×Dic₇₉	C₂³	1	12	yes	complemented
97	C₂⁵×C₇₉	C₂³	1	2	yes	—
98	C₂⁵×C₇₉	C₂³	1	1	yes	characteristic
99	C₂²×D₄×C₇₉	—	2	8	no	—
100	C₂²×D₄×C₇₉	—	4	8	no	—
101	C₂²×D₄×C₇₉	C₂³	1	12	yes	—
102	C₂²×D₄×C₇₉	C₂³	1	24	yes	complemented
103	C₂³×C₄×C₇₉	—	2	8	no	—
104	C₂³×C₄×C₇₉	C₂³	1	1	yes	characteristic
105	C₂³×C₄×C₇₉	C₂³	1	2	yes	—
106	C₂³×C₄×C₇₉	C₂³	1	1	yes	characteristic
107	C₂³×C₄×C₇₉	C₂³	1	12	yes	complemented
108	#121×C₇₉	C₂³	1	64	yes	complemented
109	C₂×C₄⋊C₄×C₇₉	C₂³	1	12	yes	complemented
110	C₂×C₂²⋊C₄×C₇₉	C₂³	1	24	yes	complemented
111	C₂³×D₇₉	—	2	4	no	—
112	C₂³×D₇₉	—	2	8	no	—
113	C₂³×D₇₉	—	2	4	no	—
114	C₂³×D₇₉	—	2	8	no	—
115	C₂³×D₇₉	—	2	96	no	—
116	C₂³×D₇₉	—	2	96	no	—
117	C₂³×D₇₉	—	4	48	no	—
118	C₂³×D₇₉	—	4	128	no	—
119	C₂³×D₇₉	C₂×D₄	1	16	yes	—
120	C₂³×D₇₉	#41	1	8	yes	complemented
121	C₂³×D₇₉	C₂⁴	1	32	yes	—
122	C₂³×D₇₉	C₂⁴	1	12	yes	—
123	C₂³×D₇₉	C₂⁴	1	6	yes	—
124	#11929624	—	2	256	no	—
125	C₂×Dic₁₅₈	—	2	48	no	—
126	C₂×Dic₁₅₈	C₂⁴	1	16	yes	complemented
127	C₂×D₃₁₆	C₂×D₄	1	96	yes	complemented
128	C₂×D₃₁₆	C₂⁴	1	16	yes	—
129	C₂×C₂²⋊D₇₉	—	2	96	no	—
130	C₂×C₂²⋊D₇₉	—	2	96	no	—
131	C₂×C₂²⋊D₇₉	—	2	48	no	—
132	C₂×C₂²⋊D₇₉	C₂⁴	1	16	yes	—
133	C₂×C₂²⋊D₇₉	C₂⁴	1	32	yes	—
134	C₂×C₂²⋊D₇₉	C₂⁴	1	32	yes	complemented
135	D₄×D₇₉	—	2	256	no	—
136	C₂²×Dic₇₉	—	2	8	no	—
137	C₂²×Dic₇₉	—	2	4	no	—
138	C₂²×Dic₇₉	—	2	4	no	—
139	C₂²×Dic₇₉	—	2	4	no	—
140	C₂²×Dic₇₉	C₂⁴	1	12	yes	—
141	C₂²×Dic₇₉	C₂⁴	1	6	yes	—
142	C₂²×Dic₇₉	C₂⁴	1	6	yes	—
143	C₂²×Dic₇₉	C₂⁴	1	6	yes	—
144	C₂×C₄×D₇₉	—	2	96	no	—
145	C₂×C₄×D₇₉	—	2	48	no	—
146	C₂×C₄×D₇₉	—	4	48	no	—
147	C₂×C₄×D₇₉	C₂⁴	1	16	yes	—
148	C₂×C₄×D₇₉	C₂⁴	1	32	yes	complemented
149	C₂×C₄×D₇₉	C₂⁴	1	32	yes	complemented
150	C₄⋊Dic₇₉	C₂⁴	1	32	yes	complemented
151	Dic₇₉⋊C₄	C₂⁴	1	16	yes	complemented
152	C₂²⋊Dic₇₉	C₂⁴	1	32	yes	complemented
153	C₂²⋊Dic₇₉	C₂⁴	1	16	yes	complemented
154	C₂²⋊Dic₇₉	C₂⁴	1	32	yes	complemented
155	(C₂×D₇₉)⋊C₄	C₂⁴	1	16	yes	—
156	(C₂×D₇₉)⋊C₄	C₂⁴	1	32	yes	—
157	(C₂×D₇₉)⋊C₄	C₂⁴	1	32	yes	complemented
158	C₄×Dic₇₉	C₂⁴	1	16	yes	complemented
159	C₂⁴×C₇₉	—	2	8	no	—
160	C₂⁴×C₇₉	—	2	4	no	—
161	C₂⁴×C₇₉	—	2	8	no	—
162	C₂⁴×C₇₉	—	2	4	no	—
163	C₂⁴×C₇₉	—	2	8	no	—
164	C₂⁴×C₇₉	—	2	4	no	—
165	C₂⁴×C₇₉	C₂⁴	1	12	yes	—
166	C₂⁴×C₇₉	C₂⁴	1	6	yes	—
167	C₂⁴×C₇₉	C₂⁴	1	1	yes	characteristic
168	C₂×D₄×C₇₉	—	2	48	no	—
169	C₂×D₄×C₇₉	—	4	48	no	—
170	C₂×D₄×C₇₉	C₂⁴	1	16	yes	—
171	C₂×D₄×C₇₉	C₂⁴	1	32	yes	complemented
172	C₂²×C₄×C₇₉	—	2	4	no	—
173	C₂²×C₄×C₇₉	—	2	8	no	—
174	C₂²×C₄×C₇₉	—	2	48	no	—
175	C₂²×C₄×C₇₉	C₂×D₄	1	8	yes	—
176	C₂²×C₄×C₇₉	C₂⁴	1	6	yes	—
177	C₂²×C₄×C₇₉	C₂⁴	1	12	yes	—
178	C₂²×C₄×C₇₉	C₂⁴	1	6	yes	—
179	C₂²×C₄×C₇₉	C₂⁴	1	16	yes	complemented
180	C₄⋊C₄×C₇₉	C₂⁴	1	16	yes	complemented
181	C₂²⋊C₄×C₇₉	C₂⁴	1	32	yes	complemented
182	C₂³×C₇₉	—	2	12	no	—
183	C₂³×C₇₉	—	2	24	no	—
184	C₂³×C₇₉	—	2	12	no	—
185	C₂³×C₇₉	—	2	24	no	—
186	C₂³×C₇₉	—	2	24	no	—
187	C₂³×C₇₉	—	2	12	no	—
188	C₂³×C₇₉	—	4	32	no	—
189	C₂³×C₇₉	—	4	16	no	—
190	C₂³×C₇₉	C₂²×D₄	1	4	yes	—
191	C₂³×C₇₉	C₂×#41	1	4	yes	—
192	C₂³×C₇₉	H(5,𝔽₂)	1	4	yes	—
193	C₂³×C₇₉	C₂⁵	1	8	yes	—
194	C₂³×C₇₉	C₂⁵	1	4	yes	—
195	C₂³×C₇₉	C₂⁵	1	3	yes	—
196	C₂²×D₇₉	—	2	32	no	—
197	C₂²×D₇₉	—	2	64	no	—
198	C₂²×D₇₉	—	2	12	no	—
199	C₂²×D₇₉	—	2	24	no	—
200	C₂²×D₇₉	—	2	24	no	—
201	C₂²×D₇₉	—	2	12	no	—
202	C₂²×D₇₉	—	2	64	no	—
203	C₂²×D₇₉	—	2	64	no	—
204	C₂²×D₇₉	—	4	32	no	—
205	C₂²×D₇₉	—	4	384	no	—
206	C₂²×D₇₉	C₂²×D₄	1	48	yes	—
207	C₂²×D₇₉	C₂×#41	1	24	yes	complemented
208	C₂²×D₇₉	C₂⁵	1	8	yes	—
209	C₂²×D₇₉	C₂⁵	1	4	yes	—
210	D₄×C₇₉	—	2	32	no	—
211	D₄×C₇₉	—	4	32	no	—
212	C₂×C₄×C₇₉	—	2	12	no	—
213	C₂×C₄×C₇₉	—	2	24	no	—
214	C₂×C₄×C₇₉	—	2	32	no	—
215	C₂×C₄×C₇₉	C₂²×D₄	1	24	yes	—
216	C₂×C₄×C₇₉	C₂⁵	1	8	yes	—
217	C₂×C₄×C₇₉	C₂⁵	1	4	yes	—
218	C₂×C₄×C₇₉	C₂⁵	1	4	yes	—
219	C₂²⋊D₇₉	—	2	64	no	—
220	C₂²⋊D₇₉	—	2	64	no	—
221	C₂²⋊D₇₉	—	2	32	no	—
222	C₂×Dic₇₉	—	2	12	no	—
223	C₂×Dic₇₉	—	2	24	no	—
224	C₂×Dic₇₉	—	2	12	no	—
225	C₂×Dic₇₉	—	2	12	no	—
226	C₂×Dic₇₉	C₂⁵	1	4	yes	—
227	C₂×Dic₇₉	C₂⁵	1	4	yes	—
228	C₂×Dic₇₉	C₂⁵	1	8	yes	—
229	C₂×Dic₇₉	C₂⁵	1	4	yes	—
230	D₃₁₆	C₂²×D₄	1	64	yes	complemented
231	C₄×D₇₉	—	2	64	no	—
232	C₄×D₇₉	—	2	32	no	—
233	C₄×D₇₉	—	4	32	no	—
234	Dic₁₅₈	—	2	32	no	—
235	C₂²×C₇₉	—	2	4	no	—
236	C₂²×C₇₉	—	2	8	no	—
237	C₂²×C₇₉	—	2	4	no	—
238	C₂²×C₇₉	—	2	8	no	—
239	C₂²×C₇₉	—	2	4	no	—
240	C₂²×C₇₉	—	2	8	no	—
241	C₂²×C₇₉	—	4	48	no	—
242	C₂²×C₇₉	—	4	24	no	—
243	C₂²×C₇₉	#546	1	16	yes	complemented
244	C₂²×C₇₉	C₂³×D₄	1	6	yes	—
245	C₂²×C₇₉	C₂²×#41	1	6	yes	—
246	C₂²×C₇₉	C₂×H(5,𝔽₂)	1	6	yes	—
247	C₂²×C₇₉	C₂⁶	1	1	yes	characteristic
248	C₂×D₇₉	—	2	4	no	—
249	C₂×D₇₉	—	2	8	no	—
250	C₂×D₇₉	—	2	4	no	—
251	C₂×D₇₉	—	2	8	no	—
252	C₂×D₇₉	—	2	48	no	—
253	C₂×D₇₉	—	2	96	no	—
254	C₂×D₇₉	—	4	128	no	—
255	C₂×D₇₉	C₂³×D₄	1	16	yes	—
256	C₂×D₇₉	C₂²×#41	1	8	yes	complemented
257	C₄×C₇₉	—	2	4	no	—
258	C₄×C₇₉	—	2	8	no	—
259	C₄×C₇₉	C₂³×D₄	1	8	yes	—
260	Dic₇₉	—	2	4	no	—
261	Dic₇₉	—	2	8	no	—
262	Dic₇₉	—	2	4	no	—
263	Dic₇₉	—	2	4	no	—
264	C₂²×#546	—	79	1	no	maximal, Sylow
265	C₂×C₇₉	—	4	8	no	—
266	C₂×C₇₉	—	4	4	no	—
267	C₂×C₇₉	C₂×#546	1	12	yes	complemented
268	C₂×C₇₉	C₂⁴×D₄	1	1	yes	characteristic
269	C₂×C₇₉	C₂³×#41	1	1	yes	characteristic
270	C₂×C₇₉	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
271	D₇₉	—	2	8	no	—
272	D₇₉	—	2	16	no	—
273	C₂³×#41	—	79	1	no	—
274	C₂⁴×D₄	—	79	1	no	—
275	C₂×#546	—	79	48	no	—
276	C₂²×#124	—	79	1	no	—
277	C₂²×#123	—	79	2	no	—
278	C₂²×C₂²⋊Q₈	—	79	1	no	—
279	C₂²×#121	—	79	2	no	—
280	C₂²×#121	D₇₉	1	1	yes	characteristic, complemented
281	C₂²×#120	—	79	2	no	—
282	C₂²×C₄×D₄	—	79	1	no	—
283	C₂²×C₄×D₄	—	79	1	no	—
284	C₂³×C₂²⋊C₄	—	79	2	no	—
285	C₇₉	C₂²×#546	1	1	yes	characteristic, complemented, Sylow
286	C₂⁶	—	79	2	no	—
287	C₂²×#41	—	79	24	no	—
288	C₂²×#41	—	158	16	no	—
289	C₂³×Q₈	—	79	1	no	—
290	C₂³×D₄	—	79	2	no	—
291	C₂³×D₄	—	79	2	no	—
292	C₂³×D₄	—	79	1	no	—
293	C₂³×D₄	—	79	24	no	—
294	C₂³×D₄	—	79	1	no	—
295	C₂³×D₄	—	158	16	no	—
296	C₂³×D₄	C₂×D₇₉	1	1	yes	characteristic
297	C₂³×D₄	C₂×D₇₉	1	2	yes	complemented
298	C₂⁴×C₄	—	79	2	no	—
299	C₂⁴×C₄	—	79	1	no	—
300	C₂⁴×C₄	—	79	2	no	—
301	C₂⁴×C₄	C₂×D₇₉	1	1	yes	characteristic, complemented
302	#546	—	79	256	no	—
303	C₂×#124	—	79	24	no	—
304	C₂×#123	—	79	48	no	—
305	C₂×C₂²⋊Q₈	—	79	24	no	—
306	C₂×#121	—	79	48	no	—
307	C₂×#121	C₂×D₇₉	1	24	yes	complemented
308	C₂×#120	—	79	48	no	—
309	C₂×C₄×D₄	—	79	24	no	—
310	C₂×C₄×D₄	—	79	24	no	—
311	C₂²×C₄⋊C₄	—	79	1	no	—
312	C₂²×C₄⋊C₄	—	79	2	no	—
313	C₂²×C₄⋊C₄	C₂×D₇₉	1	1	yes	characteristic, complemented
314	C₂²×C₂²⋊C₄	—	79	2	no	—
315	C₂²×C₂²⋊C₄	—	79	1	no	—
316	C₂²×C₂²⋊C₄	—	79	2	no	—
317	C₂²×C₂²⋊C₄	—	79	1	no	—
318	C₂²×C₂²⋊C₄	—	79	2	no	—
319	C₂²×C₂²⋊C₄	—	79	2	no	—
320	C₂²×C₂²⋊C₄	—	79	48	no	—
321	C₂²×C₂²⋊C₄	C₂×D₇₉	1	2	yes	complemented
322	C₂²×C₄²	—	79	1	no	—
323	C₂⁵	—	316	8	no	—
324	C₂⁵	—	79	24	no	—
325	C₂⁵	—	79	1	no	—
326	C₂⁵	—	79	2	no	—
327	C₂⁵	—	158	16	no	—
328	C₂⁵	—	158	16	no	—
329	C₂⁵	C₂²×D₇₉	1	2	yes	—
330	C₂⁵	C₂²×D₇₉	1	1	yes	characteristic
331	C₂×#41	—	79	64	no	—
332	C₂×#41	—	158	192	no	—
333	C₂²×Q₈	—	79	12	no	—
334	C₂²×Q₈	—	158	8	no	—
335	C₂²×D₄	—	2	8	no	—
336	C₂²×D₄	—	4	8	no	—
337	C₂²×D₄	—	79	12	no	—
338	C₂²×D₄	—	79	24	no	—
339	C₂²×D₄	—	79	24	no	—
340	C₂²×D₄	—	79	64	no	—
341	C₂²×D₄	—	79	16	no	—
342	C₂²×D₄	—	79	12	no	—
343	C₂²×D₄	—	158	192	no	—
344	C₂²×D₄	—	158	16	no	—
345	C₂²×D₄	—	158	16	no	—
346	C₂²×D₄	—	158	8	no	—
347	C₂²×D₄	C₂²×D₇₉	1	12	yes	—
348	C₂²×D₄	C₂²×D₇₉	1	24	yes	complemented
349	C₂³×C₄	—	2	8	no	—
350	C₂³×C₄	—	316	8	no	—
351	C₂³×C₄	—	79	24	no	—
352	C₂³×C₄	—	79	1	no	—
353	C₂³×C₄	—	79	1	no	—
354	C₂³×C₄	—	79	2	no	—
355	C₂³×C₄	—	79	1	no	—
356	C₂³×C₄	—	79	24	no	—
357	C₂³×C₄	—	79	12	no	—
358	C₂³×C₄	—	158	16	no	—
359	C₂³×C₄	—	158	8	no	—
360	C₂³×C₄	C₂²×D₇₉	1	2	yes	—
361	C₂³×C₄	C₂²×D₇₉	1	1	yes	characteristic
362	C₂³×C₄	C₂²×D₇₉	1	1	yes	characteristic
363	C₂³×C₄	C₂²×D₇₉	1	12	yes	complemented
364	#124	—	79	64	no	—
365	#123	—	79	128	no	—
366	C₂²⋊Q₈	—	79	64	no	—
367	#121	—	79	128	no	—
368	#121	C₂²×D₇₉	1	64	yes	complemented
369	#120	—	79	128	no	—
370	C₄×D₄	—	79	64	no	—
371	C₄×D₄	—	79	64	no	—
372	C₂×C₄⋊C₄	—	79	12	no	—
373	C₂×C₄⋊C₄	—	79	24	no	—
374	C₂×C₄⋊C₄	C₂²×D₇₉	1	12	yes	complemented
375	C₂×C₂²⋊C₄	—	79	24	no	—
376	C₂×C₂²⋊C₄	—	79	12	no	—
377	C₂×C₂²⋊C₄	—	79	24	no	—
378	C₂×C₂²⋊C₄	—	79	12	no	—
379	C₂×C₂²⋊C₄	—	79	24	no	—
380	C₂×C₂²⋊C₄	—	79	24	no	—
381	C₂×C₂²⋊C₄	—	79	128	no	—
382	C₂×C₂²⋊C₄	C₂²×D₇₉	1	24	yes	complemented
383	C₂×C₄²	—	79	12	no	—
384	C₂⁴	—	2	4	no	—
385	C₂⁴	—	2	8	no	—
386	C₂⁴	—	2	4	no	—
387	C₂⁴	—	2	8	no	—
388	C₂⁴	—	2	4	no	—
389	C₂⁴	—	2	8	no	—
390	C₂⁴	—	316	48	no	—
391	C₂⁴	—	316	128	no	—
392	C₂⁴	—	79	32	no	—
393	C₂⁴	—	79	8	no	—
394	C₂⁴	—	79	6	no	—
395	C₂⁴	—	79	12	no	—
396	C₂⁴	—	79	16	no	—
397	C₂⁴	—	158	96	no	—
398	C₂⁴	—	158	96	no	—
399	C₂⁴	—	158	8	no	—
400	C₂⁴	—	158	8	no	—
401	C₂⁴	—	158	4	no	—
402	C₂⁴	—	158	4	no	—
403	C₂⁴	C₂³×D₇₉	1	12	yes	—
404	C₂⁴	C₂³×D₇₉	1	6	yes	—
405	C₂⁴	C₂³×D₇₉	1	1	yes	characteristic
406	#41	—	158	256	no	—
407	C₂×Q₈	—	79	16	no	—
408	C₂×Q₈	—	158	48	no	—
409	C₂×D₄	—	2	48	no	—
410	C₂×D₄	—	4	48	no	—
411	C₂×D₄	—	79	16	no	—
412	C₂×D₄	—	79	32	no	—
413	C₂×D₄	—	79	32	no	—
414	C₂×D₄	—	79	16	no	—
415	C₂×D₄	—	79	96	no	—
416	C₂×D₄	—	158	256	no	—
417	C₂×D₄	—	158	48	no	—
418	C₂×D₄	—	158	96	no	—
419	C₂×D₄	—	158	96	no	—
420	C₂×D₄	C₂³×D₇₉	1	16	yes	—
421	C₂×D₄	C₂³×D₇₉	1	32	yes	complemented
422	C₂²×C₄	—	2	8	no	—
423	C₂²×C₄	—	2	4	no	—
424	C₂²×C₄	—	2	48	no	—
425	C₂²×C₄	—	316	48	no	—
426	C₂²×C₄	—	79	32	no	—
427	C₂²×C₄	—	79	6	no	—
428	C₂²×C₄	—	79	6	no	—
429	C₂²×C₄	—	79	12	no	—
430	C₂²×C₄	—	79	6	no	—
431	C₂²×C₄	—	79	16	no	—
432	C₂²×C₄	—	79	32	no	—
433	C₂²×C₄	—	158	96	no	—
434	C₂²×C₄	—	158	4	no	—
435	C₂²×C₄	—	158	4	no	—
436	C₂²×C₄	—	158	4	no	—
437	C₂²×C₄	—	158	8	no	—
438	C₂²×C₄	—	158	48	no	—
439	C₂²×C₄	D₄×D₇₉	1	8	yes	—
440	C₂²×C₄	C₂³×D₇₉	1	12	yes	—
441	C₂²×C₄	C₂³×D₇₉	1	6	yes	—
442	C₂²×C₄	C₂³×D₇₉	1	6	yes	—
443	C₂²×C₄	C₂³×D₇₉	1	16	yes	complemented
444	C₄⋊C₄	—	79	16	no	—
445	C₄⋊C₄	—	79	32	no	—
446	C₄⋊C₄	C₂³×D₇₉	1	16	yes	complemented
447	C₂²⋊C₄	—	79	32	no	—
448	C₂²⋊C₄	—	79	16	no	—
449	C₂²⋊C₄	—	79	32	no	—
450	C₂²⋊C₄	—	79	16	no	—
451	C₂²⋊C₄	—	79	32	no	—
452	C₂²⋊C₄	—	79	32	no	—
453	C₂²⋊C₄	C₂³×D₇₉	1	32	yes	complemented
454	C₄²	—	79	16	no	—
455	C₂³	—	2	12	no	—
456	C₂³	—	2	24	no	—
457	C₂³	—	2	12	no	—
458	C₂³	—	2	24	no	—
459	C₂³	—	2	12	no	—
460	C₂³	—	2	24	no	—
461	C₂³	—	4	16	no	—
462	C₂³	—	4	32	no	—
463	C₂³	—	316	32	no	—
464	C₂³	—	316	384	no	—
465	C₂³	—	79	4	no	—
466	C₂³	—	79	8	no	—
467	C₂³	—	79	48	no	—
468	C₂³	—	79	24	no	—
469	C₂³	—	158	64	no	—
470	C₂³	—	158	64	no	—
471	C₂³	—	158	24	no	—
472	C₂³	—	158	12	no	—
473	C₂³	—	158	32	no	—
474	C₂³	—	158	64	no	—
475	C₂³	—	158	12	no	—
476	C₂³	—	158	24	no	—
477	C₂³	C₂×D₄×D₇₉	1	4	yes	—
478	C₂³	#41×D₇₉	1	4	yes	—
479	C₂³	#14579206	1	4	yes	—
480	C₂³	C₂⁴×D₇₉	1	8	yes	—
481	C₂³	C₂⁴×D₇₉	1	4	yes	—
482	C₂³	C₂⁴×D₇₉	1	3	yes	—
483	Q₈	—	158	32	no	—
484	D₄	—	2	32	no	—
485	D₄	—	4	32	no	—
486	D₄	—	79	64	no	—
487	D₄	—	158	32	no	—
488	D₄	—	158	64	no	—
489	D₄	—	158	64	no	—
490	C₂×C₄	—	2	24	no	—
491	C₂×C₄	—	2	12	no	—
492	C₂×C₄	—	2	32	no	—
493	C₂×C₄	—	316	32	no	—
494	C₂×C₄	—	79	4	no	—
495	C₂×C₄	—	79	4	no	—
496	C₂×C₄	—	79	8	no	—
497	C₂×C₄	—	79	4	no	—
498	C₂×C₄	—	158	64	no	—
499	C₂×C₄	—	158	12	no	—
500	C₂×C₄	—	158	12	no	—
501	C₂×C₄	—	158	24	no	—
502	C₂×C₄	—	158	12	no	—
503	C₂×C₄	—	158	32	no	—
504	C₂×C₄	C₂×D₄×D₇₉	1	24	yes	—
505	C₂×C₄	C₂⁴×D₇₉	1	8	yes	—
506	C₂×C₄	C₂⁴×D₇₉	1	4	yes	—
507	C₂×C₄	C₂⁴×D₇₉	1	4	yes	—
508	C₂²	—	2	4	no	—
509	C₂²	—	2	8	no	—
510	C₂²	—	2	4	no	—
511	C₂²	—	2	8	no	—
512	C₂²	—	2	4	no	—
513	C₂²	—	2	8	no	—
514	C₂²	—	4	48	no	—
515	C₂²	—	4	24	no	—
516	C₂²	—	316	128	no	—
517	C₂²	—	79	16	no	—
518	C₂²	—	79	8	no	—
519	C₂²	—	158	48	no	—
520	C₂²	—	158	96	no	—
521	C₂²	—	158	4	no	—
522	C₂²	—	158	8	no	—
523	C₂²	—	158	8	no	—
524	C₂²	—	158	4	no	—
525	C₂²	#19099210	1	16	yes	direct product factor
526	C₂²	C₂²×D₄×D₇₉	1	6	yes	—
527	C₂²	C₂×#41×D₇₉	1	6	yes	—
528	C₂²	C₂×#14579206	1	6	yes	—
529	C₂²	C₂⁵×D₇₉	1	1	yes	characteristic
530	C₄	—	2	4	no	—
531	C₄	—	2	8	no	—
532	C₄	—	158	4	no	—
533	C₄	—	158	8	no	—
534	C₄	—	158	4	no	—
535	C₄	—	158	4	no	—
536	C₄	C₂²×D₄×D₇₉	1	8	yes	—
537	C₂	—	4	8	no	—
538	C₂	—	4	4	no	—
539	C₂	—	158	8	no	—
540	C₂	—	158	16	no	—
541	C₂	C₂×#19099210	1	12	yes	direct product factor
542	C₂	C₂³×D₄×D₇₉	1	1	yes	characteristic
543	C₂	C₂²×#41×D₇₉	1	1	yes	characteristic
544	C₂	C₂²×#14579206	1	1	yes	characteristic

	subgroup	G/H
center	C₂⁴	C₂³×D₇₉
commutator, cosocle	C₂²×C₇₉	C₂⁶
Frattini	C₂²	C₂⁵×D₇₉
Fitting	C₂²×#121×C₇₉	C₂
socle	C₂⁴×C₇₉	C₂⁴
hypercenter	C₂²×#121	D₇₉
hypocenter	C₇₉	C₂²×#546
LCS	G ▷ C₂²×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂⁴ ◁ C₂²×#121

Complements

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

N	H ≅ G/N	type
1. C₂³×#11929624	C₂	semidirect
2. C₂³×D₄×D₇₉	C₂	semidirect
3. C₂×#19099210	C₂	direct (N × H)
4. C₂²×#14579148	C₂	semidirect
5. C₂²×#14579143	C₂	semidirect
6. C₂²×#14579141	C₂	semidirect
7. C₂²×#14579132	C₂	semidirect
8. C₂²×#14579129	C₂	semidirect
9. C₂²×#14579123	C₂	semidirect
10. C₂²×C₄×C₂²⋊D₇₉	C₂	semidirect
11. C₂²×C₂²⋊C₄×D₇₉	C₂	semidirect
12. C₂²×#121×C₇₉	C₂	semidirect
15. C₂²×#11929624	C₂²	semidirect
16. C₂³×Dic₁₅₈	C₂²	semidirect
20. C₂³×C₂²⋊D₇₉	C₂²	semidirect
22. C₂²×D₄×D₇₉	C₂²	semidirect
24. C₂³×C₄×D₇₉	C₂²	semidirect
25. C₂³×C₄×D₇₉	C₂²	semidirect
26. #19099210	C₂²	direct (N × H)
27. C₂×#14579148	C₂²	semidirect
28. C₂×#14579143	C₂²	semidirect
29. C₂×#14579141	C₂²	semidirect
30. C₂×#14579132	C₂²	semidirect
31. C₂×#14579129	C₂²	semidirect
32. C₂×#14579123	C₂²	semidirect
33. C₂×C₄×C₂²⋊D₇₉	C₂²	semidirect
34. C₂²×C₄⋊Dic₇₉	C₂²	semidirect
35. C₂²×Dic₇₉⋊C₄	C₂²	semidirect
36. C₂²×C₂²⋊Dic₇₉	C₂²	semidirect
37. C₂²×C₂²⋊Dic₇₉	C₂²	semidirect
38. C₂²×C₂²⋊Dic₇₉	C₂²	semidirect
41. C₂²×(C₂×D₇₉)⋊C₄	C₂²	semidirect
42. C₂×C₂²⋊C₄×D₇₉	C₂²	semidirect
43. C₂²×C₄×Dic₇₉	C₂²	semidirect
45. C₂³×D₄×C₇₉	C₂²	semidirect
46. C₂⁴×C₄×C₇₉	C₂²	semidirect
47. C₂×#121×C₇₉	C₂²	semidirect
48. C₂²×C₄⋊C₄×C₇₉	C₂²	semidirect
49. C₂²×C₂²⋊C₄×C₇₉	C₂²	semidirect
57. C₂×#11929624	C₂³	semidirect
59. C₂²×Dic₁₅₈	C₂³	semidirect
60. C₂²×D₃₁₆	D₄	semidirect
67. C₂²×C₂²⋊D₇₉	C₂³	semidirect
69. C₂×D₄×D₇₉	C₂³	semidirect
78. C₂²×C₄×D₇₉	C₂³	semidirect
79. C₂²×C₄×D₇₉	C₂³	semidirect
80. #14579148	C₂³	semidirect
81. #14579143	C₂³	semidirect
82. #14579141	C₂³	semidirect
83. #14579132	C₂³	semidirect
84. #14579129	C₂³	semidirect
85. #14579123	C₂³	semidirect
86. C₄×C₂²⋊D₇₉	C₂³	semidirect
87. C₂×C₄⋊Dic₇₉	C₂³	semidirect
88. C₂×Dic₇₉⋊C₄	C₂³	semidirect
89. C₂×C₂²⋊Dic₇₉	C₂³	semidirect
90. C₂×C₂²⋊Dic₇₉	C₂³	semidirect
91. C₂×C₂²⋊Dic₇₉	C₂³	semidirect
94. C₂×(C₂×D₇₉)⋊C₄	C₂³	semidirect
95. C₂²⋊C₄×D₇₉	C₂³	semidirect
96. C₂×C₄×Dic₇₉	C₂³	semidirect
102. C₂²×D₄×C₇₉	C₂³	semidirect
107. C₂³×C₄×C₇₉	C₂³	semidirect
108. #121×C₇₉	C₂³	semidirect
109. C₂×C₄⋊C₄×C₇₉	C₂³	semidirect
110. C₂×C₂²⋊C₄×C₇₉	C₂³	semidirect
120. C₂³×D₇₉	#41	semidirect
126. C₂×Dic₁₅₈	C₂⁴	semidirect
127. C₂×D₃₁₆	C₂×D₄	semidirect
134. C₂×C₂²⋊D₇₉	C₂⁴	semidirect
148. C₂×C₄×D₇₉	C₂⁴	semidirect
149. C₂×C₄×D₇₉	C₂⁴	semidirect
150. C₄⋊Dic₇₉	C₂⁴	semidirect
151. Dic₇₉⋊C₄	C₂⁴	semidirect
152. C₂²⋊Dic₇₉	C₂⁴	semidirect
153. C₂²⋊Dic₇₉	C₂⁴	semidirect
154. C₂²⋊Dic₇₉	C₂⁴	semidirect
157. (C₂×D₇₉)⋊C₄	C₂⁴	semidirect
158. C₄×Dic₇₉	C₂⁴	semidirect
171. C₂×D₄×C₇₉	C₂⁴	semidirect
179. C₂²×C₄×C₇₉	C₂⁴	semidirect
180. C₄⋊C₄×C₇₉	C₂⁴	semidirect
181. C₂²⋊C₄×C₇₉	C₂⁴	semidirect
207. C₂²×D₇₉	C₂×#41	semidirect
230. D₃₁₆	C₂²×D₄	semidirect
243. C₂²×C₇₉	#546	semidirect
256. C₂×D₇₉	C₂²×#41	semidirect
267. C₂×C₇₉	C₂×#546	semidirect
280. C₂²×#121	D₇₉	semidirect
285. C₇₉	C₂²×#546	semidirect
297. C₂³×D₄	C₂×D₇₉	semidirect
301. C₂⁴×C₄	C₂×D₇₉	semidirect
307. C₂×#121	C₂×D₇₉	semidirect
313. C₂²×C₄⋊C₄	C₂×D₇₉	semidirect
321. C₂²×C₂²⋊C₄	C₂×D₇₉	semidirect
348. C₂²×D₄	C₂²×D₇₉	semidirect
363. C₂³×C₄	C₂²×D₇₉	semidirect
368. #121	C₂²×D₇₉	semidirect
374. C₂×C₄⋊C₄	C₂²×D₇₉	semidirect
382. C₂×C₂²⋊C₄	C₂²×D₇₉	semidirect
421. C₂×D₄	C₂³×D₇₉	semidirect
443. C₂²×C₄	C₂³×D₇₉	semidirect
446. C₄⋊C₄	C₂³×D₇₉	semidirect
453. C₂²⋊C₄	C₂³×D₇₉	semidirect
525. C₂²	#19099210	direct (N × H)
541. C₂	C₂×#19099210	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂³×#11929624	2
C₂³×D₄×D₇₉	2
C₂×#19099210	2
C₂²×#14579148	2
C₂²×#14579143	2
C₂²×#14579141	2
C₂²×#14579132	2
C₂²×#14579129	2
C₂²×#14579123	2
C₂²×C₄×C₂²⋊D₇₉	2
C₂²×C₂²⋊C₄×D₇₉	2
C₂²×#121×C₇₉	2
C₂²×#546	79

Subgroups — C22×#19099210 #35195192

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×#19099210 #35195192