Subgroups — C₂²×#19099197 #35195178

Order 20224.

20038 conjugacy classes of subgroups.

The subgroup lattice has 606 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂⁴×D₃₁₆	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂³×D₄×D₇₉	C₂	1	2	yes	maximal, complemented
3	C₂³×D₄×D₇₉	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#19099197	C₂	1	48	yes	maximal, direct product factor
5	C₂²×#14579157	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×#14579136	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂²×#14579134	C₂	1	2	yes	maximal, complemented
8	C₂²×#14579131	C₂	1	2	yes	maximal, complemented
9	C₂²×#14579129	C₂	1	2	yes	maximal, complemented
10	C₂²×#14579123	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂²×C₄×C₂²⋊D₇₉	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×#121×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂⁵×D₇₉	C₂²	1	2	yes	complemented
14	C₂⁵×D₇₉	C₂²	1	2	yes	complemented
15	C₂³×D₃₁₆	—	2	16	no	—
16	C₂³×D₃₁₆	C₂²	1	1	yes	characteristic
17	C₂³×D₃₁₆	C₂²	1	2	yes	complemented
18	C₂³×D₃₁₆	C₂²	1	2	yes	complemented
19	C₂³×D₃₁₆	C₂²	1	1	yes	characteristic, complemented
20	C₂³×D₃₁₆	C₂²	1	24	yes	complemented
21	C₂³×C₂²⋊D₇₉	C₂²	1	1	yes	characteristic
22	C₂³×C₂²⋊D₇₉	C₂²	1	2	yes	complemented
23	C₂³×C₂²⋊D₇₉	C₂²	1	2	yes	complemented
24	C₂³×C₂²⋊D₇₉	C₂²	1	2	yes	complemented
25	C₂²×D₄×D₇₉	—	2	16	no	—
26	C₂²×D₄×D₇₉	—	2	32	no	—
27	C₂²×D₄×D₇₉	C₂²	1	48	yes	complemented
28	C₂²×D₄×D₇₉	C₂²	1	24	yes	complemented
29	C₂³×C₄×D₇₉	C₂²	1	1	yes	characteristic, complemented
30	C₂³×C₄×D₇₉	C₂²	1	2	yes	complemented
31	#19099197	C₂²	1	256	yes	direct product factor
32	C₂×#14579157	C₂²	1	24	yes	complemented
33	C₂×#14579136	C₂²	1	24	yes	complemented
34	C₂×#14579134	C₂²	1	48	yes	complemented
35	C₂×#14579131	C₂²	1	48	yes	complemented
36	C₂×#14579129	C₂²	1	48	yes	complemented
37	C₂×#14579123	C₂²	1	24	yes	complemented
38	C₂×C₄×C₂²⋊D₇₉	C₂²	1	24	yes	complemented
39	C₂²×Dic₇₉⋊C₄	C₂²	1	1	yes	characteristic, complemented
40	C₂²×C₂²⋊Dic₇₉	C₂²	1	1	yes	characteristic, complemented
41	C₂²×(C₂×D₇₉)⋊C₄	C₂²	1	1	yes	characteristic, complemented
42	C₂²×(C₂×D₇₉)⋊C₄	C₂²	1	2	yes	complemented
43	C₂²×(C₂×D₇₉)⋊C₄	C₂²	1	2	yes	complemented
44	C₂²×C₄×Dic₇₉	C₂²	1	1	yes	characteristic, complemented
45	C₂³×D₄×C₇₉	C₂²	1	2	yes	complemented
46	C₂³×D₄×C₇₉	C₂²	1	1	yes	characteristic, complemented
47	C₂⁴×C₄×C₇₉	C₂²	1	1	yes	characteristic, complemented
48	C₂×#121×C₇₉	C₂²	1	24	yes	complemented
49	C₂²×C₄⋊C₄×C₇₉	C₂²	1	1	yes	characteristic, complemented
50	C₂²×C₂²⋊C₄×C₇₉	C₂²	1	2	yes	complemented
51	C₂⁴×D₇₉	—	2	16	no	—
52	C₂⁴×D₇₉	—	2	16	no	—
53	C₂⁴×D₇₉	—	2	16	no	—
54	C₂⁴×D₇₉	—	2	16	no	—
55	C₂⁴×D₇₉	—	4	8	no	—
56	C₂⁴×D₇₉	—	4	8	no	—
57	C₂⁴×D₇₉	C₂³	1	2	yes	—
58	C₂⁴×D₇₉	C₂³	1	1	yes	characteristic
59	C₂⁴×D₇₉	C₂³	1	2	yes	—
60	C₂⁴×D₇₉	C₂³	1	24	yes	complemented
61	C₂⁴×D₇₉	C₂³	1	24	yes	complemented
62	C₂²×D₃₁₆	—	2	8	no	—
63	C₂²×D₃₁₆	—	2	16	no	—
64	C₂²×D₃₁₆	—	2	16	no	—
65	C₂²×D₃₁₆	—	2	192	no	—
66	C₂²×D₃₁₆	D₄	1	16	yes	complemented
67	C₂²×D₃₁₆	C₂³	1	12	yes	—
68	C₂²×D₃₁₆	C₂³	1	64	yes	complemented
69	C₂²×D₃₁₆	C₂³	1	24	yes	complemented
70	C₂²×D₃₁₆	C₂³	1	24	yes	complemented
71	C₂²×D₃₁₆	C₂³	1	12	yes	complemented
72	C₂²×C₂²⋊D₇₉	—	2	16	no	—
73	C₂²×C₂²⋊D₇₉	—	2	16	no	—
74	C₂²×C₂²⋊D₇₉	—	4	8	no	—
75	C₂²×C₂²⋊D₇₉	D₄	1	16	yes	complemented
76	C₂²×C₂²⋊D₇₉	C₂³	1	12	yes	—
77	C₂²×C₂²⋊D₇₉	C₂³	1	24	yes	complemented
78	C₂²×C₂²⋊D₇₉	C₂³	1	24	yes	complemented
79	C₂²×C₂²⋊D₇₉	C₂³	1	24	yes	complemented
80	C₂×D₄×D₇₉	—	2	192	no	—
81	C₂×D₄×D₇₉	—	2	384	no	—
82	C₂×D₄×D₇₉	C₂³	1	128	yes	complemented
83	C₂×D₄×D₇₉	C₂³	1	64	yes	complemented
84	C₂³×Dic₇₉	C₂³	1	1	yes	characteristic
85	C₂³×Dic₇₉	C₂³	1	1	yes	characteristic
86	C₂³×Dic₇₉	C₂³	1	1	yes	characteristic
87	C₂²×C₄×D₇₉	—	2	8	no	—
88	C₂²×C₄×D₇₉	—	2	16	no	—
89	C₂²×C₄×D₇₉	C₂³	1	12	yes	complemented
90	C₂²×C₄×D₇₉	C₂³	1	24	yes	complemented
91	#14579157	C₂³	1	64	yes	complemented
92	#14579136	C₂³	1	64	yes	complemented
93	#14579134	C₂³	1	128	yes	complemented
94	#14579131	C₂³	1	128	yes	complemented
95	#14579129	C₂³	1	128	yes	complemented
96	#14579123	C₂³	1	64	yes	complemented
97	C₄×C₂²⋊D₇₉	C₂³	1	64	yes	complemented
98	C₂×Dic₇₉⋊C₄	C₂³	1	12	yes	complemented
99	C₂×C₂²⋊Dic₇₉	C₂³	1	12	yes	complemented
100	C₂×(C₂×D₇₉)⋊C₄	C₂³	1	12	yes	complemented
101	C₂×(C₂×D₇₉)⋊C₄	C₂³	1	24	yes	complemented
102	C₂×(C₂×D₇₉)⋊C₄	C₂³	1	24	yes	complemented
103	C₂×C₄×Dic₇₉	C₂³	1	12	yes	complemented
104	C₂⁵×C₇₉	C₂³	1	2	yes	—
105	C₂⁵×C₇₉	C₂³	1	1	yes	characteristic
106	C₂²×D₄×C₇₉	—	2	16	no	—
107	C₂²×D₄×C₇₉	—	2	8	no	—
108	C₂²×D₄×C₇₉	C₂³	1	24	yes	complemented
109	C₂²×D₄×C₇₉	C₂³	1	12	yes	complemented
110	C₂³×C₄×C₇₉	—	2	8	no	—
111	C₂³×C₄×C₇₉	C₂³	1	1	yes	characteristic
112	C₂³×C₄×C₇₉	C₂³	1	2	yes	—
113	C₂³×C₄×C₇₉	C₂³	1	1	yes	characteristic
114	C₂³×C₄×C₇₉	C₂³	1	12	yes	complemented
115	#121×C₇₉	C₂³	1	64	yes	complemented
116	C₂×C₄⋊C₄×C₇₉	C₂³	1	12	yes	complemented
117	C₂×C₂²⋊C₄×C₇₉	C₂³	1	24	yes	complemented
118	C₂³×D₇₉	—	2	4	no	—
119	C₂³×D₇₉	—	2	8	no	—
120	C₂³×D₇₉	—	2	4	no	—
121	C₂³×D₇₉	—	2	8	no	—
122	C₂³×D₇₉	—	2	8	no	—
123	C₂³×D₇₉	—	2	8	no	—
124	C₂³×D₇₉	—	2	96	no	—
125	C₂³×D₇₉	—	2	8	no	—
126	C₂³×D₇₉	—	2	96	no	—
127	C₂³×D₇₉	—	2	96	no	—
128	C₂³×D₇₉	—	2	96	no	—
129	C₂³×D₇₉	—	4	48	no	—
130	C₂³×D₇₉	—	4	48	no	—
131	C₂³×D₇₉	—	4	128	no	—
132	C₂³×D₇₉	—	4	128	no	—
133	C₂³×D₇₉	C₂×D₄	1	16	yes	complemented
134	C₂³×D₇₉	C₂×D₄	1	8	yes	complemented
135	C₂³×D₇₉	C₂⁴	1	12	yes	—
136	C₂³×D₇₉	C₂⁴	1	6	yes	—
137	C₂³×D₇₉	C₂⁴	1	12	yes	—
138	C₂³×D₇₉	C₂⁴	1	32	yes	complemented
139	C₂³×D₇₉	C₂⁴	1	32	yes	complemented
140	C₂×D₃₁₆	—	2	256	no	—
141	C₂×D₃₁₆	—	2	96	no	—
142	C₂×D₃₁₆	—	2	96	no	—
143	C₂×D₃₁₆	—	2	48	no	—
144	C₂×D₃₁₆	C₂×D₄	1	96	yes	complemented
145	C₂×D₃₁₆	C₂⁴	1	16	yes	—
146	C₂×D₃₁₆	C₂⁴	1	32	yes	complemented
147	C₂×D₃₁₆	C₂⁴	1	32	yes	complemented
148	C₂×D₃₁₆	C₂⁴	1	16	yes	complemented
149	C₂×C₂²⋊D₇₉	—	2	96	no	—
150	C₂×C₂²⋊D₇₉	—	2	96	no	—
151	C₂×C₂²⋊D₇₉	—	4	48	no	—
152	C₂×C₂²⋊D₇₉	C₂×D₄	1	96	yes	complemented
153	C₂×C₂²⋊D₇₉	C₂⁴	1	16	yes	—
154	C₂×C₂²⋊D₇₉	C₂⁴	1	32	yes	complemented
155	C₂×C₂²⋊D₇₉	C₂⁴	1	32	yes	complemented
156	C₂×C₂²⋊D₇₉	C₂⁴	1	32	yes	complemented
157	D₄×D₇₉	—	2	256	no	—
158	D₄×D₇₉	—	2	512	no	—
159	C₂²×Dic₇₉	—	2	4	no	—
160	C₂²×Dic₇₉	—	2	4	no	—
161	C₂²×Dic₇₉	C₂×D₄	1	8	yes	complemented
162	C₂²×Dic₇₉	C₂⁴	1	6	yes	—
163	C₂²×Dic₇₉	C₂⁴	1	6	yes	—
164	C₂²×Dic₇₉	C₂⁴	1	6	yes	—
165	C₂×C₄×D₇₉	—	2	96	no	—
166	C₂×C₄×D₇₉	—	2	48	no	—
167	C₂×C₄×D₇₉	C₂⁴	1	16	yes	complemented
168	C₂×C₄×D₇₉	C₂⁴	1	32	yes	complemented
169	Dic₇₉⋊C₄	C₂⁴	1	16	yes	complemented
170	C₂²⋊Dic₇₉	C₂⁴	1	16	yes	complemented
171	(C₂×D₇₉)⋊C₄	C₂⁴	1	16	yes	complemented
172	(C₂×D₇₉)⋊C₄	C₂⁴	1	32	yes	complemented
173	(C₂×D₇₉)⋊C₄	C₂⁴	1	32	yes	complemented
174	C₄×Dic₇₉	C₂⁴	1	16	yes	complemented
175	C₂⁴×C₇₉	—	2	4	no	—
176	C₂⁴×C₇₉	—	2	4	no	—
177	C₂⁴×C₇₉	—	2	8	no	—
178	C₂⁴×C₇₉	—	2	8	no	—
179	C₂⁴×C₇₉	—	2	8	no	—
180	C₂⁴×C₇₉	C₂×D₄	1	8	yes	complemented
181	C₂⁴×C₇₉	C₂⁴	1	12	yes	—
182	C₂⁴×C₇₉	C₂⁴	1	6	yes	—
183	C₂⁴×C₇₉	C₂⁴	1	1	yes	characteristic
184	C₂×D₄×C₇₉	—	2	96	no	—
185	C₂×D₄×C₇₉	—	2	48	no	—
186	C₂×D₄×C₇₉	C₂⁴	1	32	yes	complemented
187	C₂×D₄×C₇₉	C₂⁴	1	16	yes	complemented
188	C₂²×C₄×C₇₉	—	2	4	no	—
189	C₂²×C₄×C₇₉	—	2	8	no	—
190	C₂²×C₄×C₇₉	—	2	48	no	—
191	C₂²×C₄×C₇₉	C₂×D₄	1	8	yes	complemented
192	C₂²×C₄×C₇₉	C₂⁴	1	6	yes	—
193	C₂²×C₄×C₇₉	C₂⁴	1	12	yes	—
194	C₂²×C₄×C₇₉	C₂⁴	1	6	yes	—
195	C₂²×C₄×C₇₉	C₂⁴	1	16	yes	complemented
196	C₄⋊C₄×C₇₉	C₂⁴	1	16	yes	complemented
197	C₂²⋊C₄×C₇₉	C₂⁴	1	32	yes	complemented
198	C₂³×C₇₉	—	2	32	no	—
199	C₂³×C₇₉	—	2	12	no	—
200	C₂³×C₇₉	—	2	12	no	—
201	C₂³×C₇₉	—	2	24	no	—
202	C₂³×C₇₉	—	2	24	no	—
203	C₂³×C₇₉	—	2	24	no	—
204	C₂³×C₇₉	—	4	32	no	—
205	C₂³×C₇₉	C₂²×D₄	1	4	yes	—
206	C₂³×C₇₉	C₂²×D₄	1	4	yes	—
207	C₂³×C₇₉	C₂²×D₄	1	24	yes	complemented
208	C₂³×C₇₉	H(5,𝔽₂)	1	4	yes	—
209	C₂³×C₇₉	C₂⁵	1	8	yes	—
210	C₂³×C₇₉	C₂⁵	1	4	yes	—
211	C₂³×C₇₉	C₂⁵	1	3	yes	—
212	C₂²×D₇₉	—	2	32	no	—
213	C₂²×D₇₉	—	2	64	no	—
214	C₂²×D₇₉	—	2	24	no	—
215	C₂²×D₇₉	—	2	12	no	—
216	C₂²×D₇₉	—	2	12	no	—
217	C₂²×D₇₉	—	2	24	no	—
218	C₂²×D₇₉	—	2	24	no	—
219	C₂²×D₇₉	—	2	24	no	—
220	C₂²×D₇₉	—	2	64	no	—
221	C₂²×D₇₉	—	2	24	no	—
222	C₂²×D₇₉	—	2	64	no	—
223	C₂²×D₇₉	—	2	64	no	—
224	C₂²×D₇₉	—	2	64	no	—
225	C₂²×D₇₉	—	4	32	no	—
226	C₂²×D₇₉	—	4	32	no	—
227	C₂²×D₇₉	—	4	384	no	—
228	C₂²×D₇₉	—	4	384	no	—
229	C₂²×D₇₉	—	4	32	no	—
230	C₂²×D₇₉	C₂²×D₄	1	48	yes	complemented
231	C₂²×D₇₉	C₂²×D₄	1	24	yes	complemented
232	C₂²×D₇₉	C₂⁵	1	8	yes	—
233	C₂²×D₇₉	C₂⁵	1	4	yes	—
234	C₂²×D₇₉	C₂⁵	1	8	yes	—
235	D₄×C₇₉	—	2	64	no	—
236	D₄×C₇₉	—	2	32	no	—
237	C₂×C₄×C₇₉	—	2	24	no	—
238	C₂×C₄×C₇₉	—	2	12	no	—
239	C₂×C₄×C₇₉	—	2	32	no	—
240	C₂×C₄×C₇₉	C₂²×D₄	1	24	yes	complemented
241	C₂×C₄×C₇₉	C₂⁵	1	8	yes	—
242	C₂×C₄×C₇₉	C₂⁵	1	4	yes	—
243	C₂×C₄×C₇₉	C₂⁵	1	4	yes	—
244	C₂²⋊D₇₉	—	2	64	no	—
245	C₂²⋊D₇₉	—	2	64	no	—
246	C₂²⋊D₇₉	—	4	32	no	—
247	C₂²⋊D₇₉	C₂²×D₄	1	64	yes	complemented
248	C₂×Dic₇₉	—	2	12	no	—
249	C₂×Dic₇₉	—	2	12	no	—
250	C₂×Dic₇₉	C₂²×D₄	1	24	yes	complemented
251	C₂×Dic₇₉	C₂⁵	1	4	yes	—
252	C₂×Dic₇₉	C₂⁵	1	4	yes	—
253	C₂×Dic₇₉	C₂⁵	1	4	yes	—
254	D₃₁₆	—	2	64	no	—
255	D₃₁₆	—	2	64	no	—
256	D₃₁₆	—	2	32	no	—
257	D₃₁₆	C₂²×D₄	1	64	yes	complemented
258	C₄×D₇₉	—	2	32	no	—
259	C₄×D₇₉	—	2	64	no	—
260	C₂²×C₇₉	—	2	4	no	—
261	C₂²×C₇₉	—	2	4	no	—
262	C₂²×C₇₉	—	2	48	no	—
263	C₂²×C₇₉	—	2	8	no	—
264	C₂²×C₇₉	—	2	8	no	—
265	C₂²×C₇₉	—	2	8	no	—
266	C₂²×C₇₉	—	4	48	no	—
267	C₂²×C₇₉	D₄²	1	16	yes	complemented
268	C₂²×C₇₉	C₂³×D₄	1	6	yes	—
269	C₂²×C₇₉	C₂³×D₄	1	6	yes	—
270	C₂²×C₇₉	C₂³×D₄	1	8	yes	complemented
271	C₂²×C₇₉	C₂×H(5,𝔽₂)	1	6	yes	—
272	C₂²×C₇₉	C₂⁶	1	1	yes	characteristic
273	C₂×D₇₉	—	2	4	no	—
274	C₂×D₇₉	—	2	8	no	—
275	C₂×D₇₉	—	2	4	no	—
276	C₂×D₇₉	—	2	8	no	—
277	C₂×D₇₉	—	2	48	no	—
278	C₂×D₇₉	—	2	96	no	—
279	C₂×D₇₉	—	2	8	no	—
280	C₂×D₇₉	—	2	8	no	—
281	C₂×D₇₉	—	2	8	no	—
282	C₂×D₇₉	—	4	128	no	—
283	C₂×D₇₉	—	4	128	no	—
284	C₂×D₇₉	—	4	48	no	—
285	C₂×D₇₉	C₂³×D₄	1	16	yes	complemented
286	C₂×D₇₉	C₂³×D₄	1	8	yes	complemented
287	C₄×C₇₉	—	2	4	no	—
288	C₄×C₇₉	—	2	8	no	—
289	C₄×C₇₉	C₂³×D₄	1	8	yes	complemented
290	Dic₇₉	—	2	4	no	—
291	Dic₇₉	—	2	4	no	—
292	Dic₇₉	C₂³×D₄	1	8	yes	complemented
293	C₂²×D₄²	—	79	1	no	maximal, Sylow
294	C₂×C₇₉	—	2	8	no	—
295	C₂×C₇₉	—	4	8	no	—
296	C₂×C₇₉	C₂×D₄²	1	12	yes	complemented
297	C₂×C₇₉	C₂⁴×D₄	1	1	yes	characteristic
298	C₂×C₇₉	C₂⁴×D₄	1	1	yes	characteristic
299	C₂×C₇₉	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
300	D₇₉	—	2	8	no	—
301	D₇₉	—	2	16	no	—
302	D₇₉	—	4	8	no	—
303	C₂⁴×D₄	—	79	2	no	—
304	C₂⁴×D₄	—	79	1	no	—
305	C₂⁴×D₄	—	79	1	no	—
306	C₂×D₄²	—	79	48	no	—
307	C₂²×#127	—	79	1	no	—
308	C₂²×#121	—	79	1	no	—
309	C₂²×#121	—	79	2	no	—
310	C₂²×#121	D₇₉	1	1	yes	characteristic, complemented
311	C₂²×#120	—	79	2	no	—
312	C₂²×#120	—	79	2	no	—
313	C₂²×C₄×D₄	—	79	1	no	—
314	C₂²×C₄×D₄	—	79	1	no	—
315	C₇₉	C₂²×D₄²	1	1	yes	characteristic, complemented, Sylow
316	C₂⁶	—	79	2	no	—
317	C₂⁶	—	79	2	no	—
318	C₂³×D₄	—	79	2	no	—
319	C₂³×D₄	—	79	1	no	—
320	C₂³×D₄	—	79	2	no	—
321	C₂³×D₄	—	79	2	no	—
322	C₂³×D₄	—	79	48	no	—
323	C₂³×D₄	—	79	24	no	—
324	C₂³×D₄	—	79	1	no	—
325	C₂³×D₄	—	79	2	no	—
326	C₂³×D₄	—	79	2	no	—
327	C₂³×D₄	—	79	1	no	—
328	C₂³×D₄	—	79	24	no	—
329	C₂³×D₄	—	158	16	no	—
330	C₂³×D₄	—	158	32	no	—
331	C₂³×D₄	—	158	16	no	—
332	C₂³×D₄	C₂×D₇₉	1	2	yes	complemented
333	C₂³×D₄	C₂×D₇₉	1	1	yes	characteristic, complemented
334	C₂⁴×C₄	—	79	2	no	—
335	C₂⁴×C₄	—	79	1	no	—
336	C₂⁴×C₄	C₂×D₇₉	1	1	yes	characteristic, complemented
337	D₄²	—	79	256	no	—
338	C₂×#127	—	79	24	no	—
339	C₂×#121	—	79	24	no	—
340	C₂×#121	—	79	48	no	—
341	C₂×#121	C₂×D₇₉	1	24	yes	complemented
342	C₂×#120	—	79	48	no	—
343	C₂×#120	—	79	48	no	—
344	C₂×C₄×D₄	—	79	24	no	—
345	C₂×C₄×D₄	—	79	24	no	—
346	C₂²×C₄⋊C₄	—	79	1	no	—
347	C₂²×C₄⋊C₄	C₂×D₇₉	1	1	yes	characteristic, complemented
348	C₂²×C₂²⋊C₄	—	79	1	no	—
349	C₂²×C₂²⋊C₄	—	79	2	no	—
350	C₂²×C₂²⋊C₄	—	79	1	no	—
351	C₂²×C₂²⋊C₄	—	79	2	no	—
352	C₂²×C₂²⋊C₄	C₂×D₇₉	1	2	yes	complemented
353	C₂²×C₄²	—	79	1	no	—
354	C₂⁵	—	316	8	no	—
355	C₂⁵	—	316	8	no	—
356	C₂⁵	—	79	24	no	—
357	C₂⁵	—	79	24	no	—
358	C₂⁵	—	79	1	no	—
359	C₂⁵	—	79	2	no	—
360	C₂⁵	—	79	2	no	—
361	C₂⁵	—	158	16	no	—
362	C₂⁵	—	158	16	no	—
363	C₂⁵	—	158	16	no	—
364	C₂⁵	—	158	16	no	—
365	C₂⁵	C₂²×D₇₉	1	2	yes	—
366	C₂⁵	C₂²×D₇₉	1	1	yes	characteristic
367	C₂²×D₄	—	2	16	no	—
368	C₂²×D₄	—	2	8	no	—
369	C₂²×D₄	—	316	8	no	—
370	C₂²×D₄	—	79	24	no	—
371	C₂²×D₄	—	79	16	no	—
372	C₂²×D₄	—	79	12	no	—
373	C₂²×D₄	—	79	24	no	—
374	C₂²×D₄	—	79	24	no	—
375	C₂²×D₄	—	79	128	no	—
376	C₂²×D₄	—	79	64	no	—
377	C₂²×D₄	—	79	16	no	—
378	C₂²×D₄	—	79	12	no	—
379	C₂²×D₄	—	79	24	no	—
380	C₂²×D₄	—	79	24	no	—
381	C₂²×D₄	—	79	12	no	—
382	C₂²×D₄	—	79	64	no	—
383	C₂²×D₄	—	158	192	no	—
384	C₂²×D₄	—	158	16	no	—
385	C₂²×D₄	—	158	16	no	—
386	C₂²×D₄	—	158	16	no	—
387	C₂²×D₄	—	158	384	no	—
388	C₂²×D₄	—	158	192	no	—
389	C₂²×D₄	—	158	16	no	—
390	C₂²×D₄	—	158	8	no	—
391	C₂²×D₄	C₂²×D₇₉	1	24	yes	complemented
392	C₂²×D₄	C₂²×D₇₉	1	12	yes	complemented
393	C₂³×C₄	—	2	8	no	—
394	C₂³×C₄	—	79	1	no	—
395	C₂³×C₄	—	79	1	no	—
396	C₂³×C₄	—	79	1	no	—
397	C₂³×C₄	—	79	24	no	—
398	C₂³×C₄	—	79	12	no	—
399	C₂³×C₄	—	158	16	no	—
400	C₂³×C₄	—	158	8	no	—
401	C₂³×C₄	C₂²×D₇₉	1	2	yes	—
402	C₂³×C₄	C₂²×D₇₉	1	1	yes	characteristic
403	C₂³×C₄	C₂²×D₇₉	1	1	yes	characteristic
404	C₂³×C₄	C₂²×D₇₉	1	12	yes	complemented
405	#127	—	79	64	no	—
406	#121	—	79	64	no	—
407	#121	—	79	128	no	—
408	#121	C₂²×D₇₉	1	64	yes	complemented
409	#120	—	79	128	no	—
410	#120	—	79	128	no	—
411	C₄×D₄	—	79	64	no	—
412	C₄×D₄	—	79	64	no	—
413	C₂×C₄⋊C₄	—	79	12	no	—
414	C₂×C₄⋊C₄	C₂²×D₇₉	1	12	yes	complemented
415	C₂×C₂²⋊C₄	—	79	12	no	—
416	C₂×C₂²⋊C₄	—	79	24	no	—
417	C₂×C₂²⋊C₄	—	79	12	no	—
418	C₂×C₂²⋊C₄	—	79	24	no	—
419	C₂×C₂²⋊C₄	C₂²×D₇₉	1	24	yes	complemented
420	C₂×C₄²	—	79	12	no	—
421	C₂⁴	—	2	4	no	—
422	C₂⁴	—	2	4	no	—
423	C₂⁴	—	2	8	no	—
424	C₂⁴	—	2	8	no	—
425	C₂⁴	—	2	8	no	—
426	C₂⁴	—	316	128	no	—
427	C₂⁴	—	316	48	no	—
428	C₂⁴	—	316	48	no	—
429	C₂⁴	—	316	128	no	—
430	C₂⁴	—	79	32	no	—
431	C₂⁴	—	79	32	no	—
432	C₂⁴	—	79	6	no	—
433	C₂⁴	—	79	12	no	—
434	C₂⁴	—	79	8	no	—
435	C₂⁴	—	79	16	no	—
436	C₂⁴	—	79	12	no	—
437	C₂⁴	—	158	96	no	—
438	C₂⁴	—	158	96	no	—
439	C₂⁴	—	158	96	no	—
440	C₂⁴	—	158	8	no	—
441	C₂⁴	—	158	8	no	—
442	C₂⁴	—	158	8	no	—
443	C₂⁴	—	158	96	no	—
444	C₂⁴	—	158	8	no	—
445	C₂⁴	—	158	4	no	—
446	C₂⁴	—	158	8	no	—
447	C₂⁴	—	158	4	no	—
448	C₂⁴	D₄×D₇₉	1	8	yes	complemented
449	C₂⁴	C₂³×D₇₉	1	12	yes	—
450	C₂⁴	C₂³×D₇₉	1	6	yes	—
451	C₂⁴	C₂³×D₇₉	1	1	yes	characteristic
452	C₂×D₄	—	2	96	no	—
453	C₂×D₄	—	2	48	no	—
454	C₂×D₄	—	316	48	no	—
455	C₂×D₄	—	79	32	no	—
456	C₂×D₄	—	79	16	no	—
457	C₂×D₄	—	79	96	no	—
458	C₂×D₄	—	79	32	no	—
459	C₂×D₄	—	79	32	no	—
460	C₂×D₄	—	79	16	no	—
461	C₂×D₄	—	79	32	no	—
462	C₂×D₄	—	79	32	no	—
463	C₂×D₄	—	79	16	no	—
464	C₂×D₄	—	79	96	no	—
465	C₂×D₄	—	158	256	no	—
466	C₂×D₄	—	158	96	no	—
467	C₂×D₄	—	158	96	no	—
468	C₂×D₄	—	158	96	no	—
469	C₂×D₄	—	158	512	no	—
470	C₂×D₄	—	158	256	no	—
471	C₂×D₄	—	158	96	no	—
472	C₂×D₄	—	158	48	no	—
473	C₂×D₄	C₂³×D₇₉	1	32	yes	complemented
474	C₂×D₄	C₂³×D₇₉	1	16	yes	complemented
475	C₂²×C₄	—	2	4	no	—
476	C₂²×C₄	—	2	8	no	—
477	C₂²×C₄	—	2	48	no	—
478	C₂²×C₄	—	79	6	no	—
479	C₂²×C₄	—	79	8	no	—
480	C₂²×C₄	—	79	6	no	—
481	C₂²×C₄	—	79	6	no	—
482	C₂²×C₄	—	79	32	no	—
483	C₂²×C₄	—	79	16	no	—
484	C₂²×C₄	—	158	96	no	—
485	C₂²×C₄	—	158	4	no	—
486	C₂²×C₄	—	158	4	no	—
487	C₂²×C₄	—	158	48	no	—
488	C₂²×C₄	D₄×D₇₉	1	8	yes	complemented
489	C₂²×C₄	C₂³×D₇₉	1	12	yes	—
490	C₂²×C₄	C₂³×D₇₉	1	6	yes	—
491	C₂²×C₄	C₂³×D₇₉	1	6	yes	—
492	C₂²×C₄	C₂³×D₇₉	1	16	yes	complemented
493	C₄⋊C₄	—	79	16	no	—
494	C₄⋊C₄	C₂³×D₇₉	1	16	yes	complemented
495	C₂²⋊C₄	—	79	16	no	—
496	C₂²⋊C₄	—	79	32	no	—
497	C₂²⋊C₄	—	79	16	no	—
498	C₂²⋊C₄	—	79	32	no	—
499	C₂²⋊C₄	C₂³×D₇₉	1	32	yes	complemented
500	C₄²	—	79	16	no	—
501	C₂³	—	2	12	no	—
502	C₂³	—	2	32	no	—
503	C₂³	—	2	12	no	—
504	C₂³	—	2	24	no	—
505	C₂³	—	2	24	no	—
506	C₂³	—	2	24	no	—
507	C₂³	—	4	32	no	—
508	C₂³	—	316	384	no	—
509	C₂³	—	316	32	no	—
510	C₂³	—	316	32	no	—
511	C₂³	—	316	384	no	—
512	C₂³	—	316	32	no	—
513	C₂³	—	79	4	no	—
514	C₂³	—	79	8	no	—
515	C₂³	—	79	24	no	—
516	C₂³	—	79	48	no	—
517	C₂³	—	79	8	no	—
518	C₂³	—	158	64	no	—
519	C₂³	—	158	64	no	—
520	C₂³	—	158	64	no	—
521	C₂³	—	158	24	no	—
522	C₂³	—	158	24	no	—
523	C₂³	—	158	24	no	—
524	C₂³	—	158	64	no	—
525	C₂³	—	158	24	no	—
526	C₂³	—	158	12	no	—
527	C₂³	—	158	64	no	—
528	C₂³	—	158	32	no	—
529	C₂³	—	158	24	no	—
530	C₂³	—	158	12	no	—
531	C₂³	C₂×D₄×D₇₉	1	4	yes	—
532	C₂³	C₂×D₄×D₇₉	1	4	yes	—
533	C₂³	C₂×D₄×D₇₉	1	24	yes	complemented
534	C₂³	#14579207	1	4	yes	—
535	C₂³	C₂⁴×D₇₉	1	8	yes	—
536	C₂³	C₂⁴×D₇₉	1	4	yes	—
537	C₂³	C₂⁴×D₇₉	1	3	yes	—
538	D₄	—	2	64	no	—
539	D₄	—	2	32	no	—
540	D₄	—	316	32	no	—
541	D₄	—	79	64	no	—
542	D₄	—	79	64	no	—
543	D₄	—	158	64	no	—
544	D₄	—	158	64	no	—
545	D₄	—	158	64	no	—
546	D₄	—	158	64	no	—
547	D₄	—	158	32	no	—
548	C₂×C₄	—	2	12	no	—
549	C₂×C₄	—	2	24	no	—
550	C₂×C₄	—	2	32	no	—
551	C₂×C₄	—	79	4	no	—
552	C₂×C₄	—	79	24	no	—
553	C₂×C₄	—	79	4	no	—
554	C₂×C₄	—	79	4	no	—
555	C₂×C₄	—	158	64	no	—
556	C₂×C₄	—	158	12	no	—
557	C₂×C₄	—	158	12	no	—
558	C₂×C₄	—	158	32	no	—
559	C₂×C₄	C₂×D₄×D₇₉	1	24	yes	complemented
560	C₂×C₄	C₂⁴×D₇₉	1	8	yes	—
561	C₂×C₄	C₂⁴×D₇₉	1	4	yes	—
562	C₂×C₄	C₂⁴×D₇₉	1	4	yes	—
563	C₂²	—	2	48	no	—
564	C₂²	—	2	4	no	—
565	C₂²	—	2	4	no	—
566	C₂²	—	2	8	no	—
567	C₂²	—	2	8	no	—
568	C₂²	—	2	8	no	—
569	C₂²	—	4	48	no	—
570	C₂²	—	316	128	no	—
571	C₂²	—	316	128	no	—
572	C₂²	—	316	48	no	—
573	C₂²	—	79	8	no	—
574	C₂²	—	79	16	no	—
575	C₂²	—	158	8	no	—
576	C₂²	—	158	8	no	—
577	C₂²	—	158	8	no	—
578	C₂²	—	158	96	no	—
579	C₂²	—	158	48	no	—
580	C₂²	—	158	8	no	—
581	C₂²	—	158	4	no	—
582	C₂²	—	158	8	no	—
583	C₂²	—	158	4	no	—
584	C₂²	#19099197	1	16	yes	direct product factor
585	C₂²	C₂²×D₄×D₇₉	1	6	yes	—
586	C₂²	C₂²×D₄×D₇₉	1	6	yes	—
587	C₂²	C₂²×D₄×D₇₉	1	8	yes	complemented
588	C₂²	C₂×#14579207	1	6	yes	—
589	C₂²	C₂⁵×D₇₉	1	1	yes	characteristic
590	C₄	—	2	4	no	—
591	C₄	—	2	8	no	—
592	C₄	—	79	8	no	—
593	C₄	—	158	4	no	—
594	C₄	—	158	4	no	—
595	C₄	C₂²×D₄×D₇₉	1	8	yes	complemented
596	C₂	—	2	8	no	—
597	C₂	—	4	8	no	—
598	C₂	—	316	8	no	—
599	C₂	—	158	16	no	—
600	C₂	—	158	8	no	—
601	C₂	C₂×#19099197	1	12	yes	direct product factor
602	C₂	C₂³×D₄×D₇₉	1	1	yes	characteristic
603	C₂	C₂³×D₄×D₇₉	1	1	yes	characteristic
604	C₂	C₂²×#14579207	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×D₄²
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. C₂⁴×D₃₁₆	C₂	semidirect
2. C₂³×D₄×D₇₉	C₂	semidirect
3. C₂³×D₄×D₇₉	C₂	semidirect
4. C₂×#19099197	C₂	direct (N × H)
5. C₂²×#14579157	C₂	semidirect
6. C₂²×#14579136	C₂	semidirect
7. C₂²×#14579134	C₂	semidirect
8. C₂²×#14579131	C₂	semidirect
9. C₂²×#14579129	C₂	semidirect
10. C₂²×#14579123	C₂	semidirect
11. C₂²×C₄×C₂²⋊D₇₉	C₂	semidirect
12. C₂²×#121×C₇₉	C₂	semidirect
13. C₂⁵×D₇₉	C₂²	semidirect
14. C₂⁵×D₇₉	C₂²	semidirect
17. C₂³×D₃₁₆	C₂²	semidirect
18. C₂³×D₃₁₆	C₂²	semidirect
19. C₂³×D₃₁₆	C₂²	semidirect
20. C₂³×D₃₁₆	C₂²	semidirect
22. C₂³×C₂²⋊D₇₉	C₂²	semidirect
23. C₂³×C₂²⋊D₇₉	C₂²	semidirect
24. C₂³×C₂²⋊D₇₉	C₂²	semidirect
27. C₂²×D₄×D₇₉	C₂²	semidirect
28. C₂²×D₄×D₇₉	C₂²	semidirect
29. C₂³×C₄×D₇₉	C₂²	semidirect
30. C₂³×C₄×D₇₉	C₂²	semidirect
31. #19099197	C₂²	direct (N × H)
32. C₂×#14579157	C₂²	semidirect
33. C₂×#14579136	C₂²	semidirect
34. C₂×#14579134	C₂²	semidirect
35. C₂×#14579131	C₂²	semidirect
36. C₂×#14579129	C₂²	semidirect
37. C₂×#14579123	C₂²	semidirect
38. C₂×C₄×C₂²⋊D₇₉	C₂²	semidirect
39. C₂²×Dic₇₉⋊C₄	C₂²	semidirect
40. C₂²×C₂²⋊Dic₇₉	C₂²	semidirect
41. C₂²×(C₂×D₇₉)⋊C₄	C₂²	semidirect
42. C₂²×(C₂×D₇₉)⋊C₄	C₂²	semidirect
43. C₂²×(C₂×D₇₉)⋊C₄	C₂²	semidirect
44. C₂²×C₄×Dic₇₉	C₂²	semidirect
45. C₂³×D₄×C₇₉	C₂²	semidirect
46. C₂³×D₄×C₇₉	C₂²	semidirect
47. C₂⁴×C₄×C₇₉	C₂²	semidirect
48. C₂×#121×C₇₉	C₂²	semidirect
49. C₂²×C₄⋊C₄×C₇₉	C₂²	semidirect
50. C₂²×C₂²⋊C₄×C₇₉	C₂²	semidirect
60. C₂⁴×D₇₉	C₂³	semidirect
61. C₂⁴×D₇₉	C₂³	semidirect
66. C₂²×D₃₁₆	D₄	semidirect
68. C₂²×D₃₁₆	C₂³	semidirect
69. C₂²×D₃₁₆	C₂³	semidirect
70. C₂²×D₃₁₆	C₂³	semidirect
71. C₂²×D₃₁₆	C₂³	semidirect
75. C₂²×C₂²⋊D₇₉	D₄	semidirect
77. C₂²×C₂²⋊D₇₉	C₂³	semidirect
78. C₂²×C₂²⋊D₇₉	C₂³	semidirect
79. C₂²×C₂²⋊D₇₉	C₂³	semidirect
82. C₂×D₄×D₇₉	C₂³	semidirect
83. C₂×D₄×D₇₉	C₂³	semidirect
89. C₂²×C₄×D₇₉	C₂³	semidirect
90. C₂²×C₄×D₇₉	C₂³	semidirect
91. #14579157	C₂³	semidirect
92. #14579136	C₂³	semidirect
93. #14579134	C₂³	semidirect
94. #14579131	C₂³	semidirect
95. #14579129	C₂³	semidirect
96. #14579123	C₂³	semidirect
97. C₄×C₂²⋊D₇₉	C₂³	semidirect
98. C₂×Dic₇₉⋊C₄	C₂³	semidirect
99. C₂×C₂²⋊Dic₇₉	C₂³	semidirect
100. C₂×(C₂×D₇₉)⋊C₄	C₂³	semidirect
101. C₂×(C₂×D₇₉)⋊C₄	C₂³	semidirect
102. C₂×(C₂×D₇₉)⋊C₄	C₂³	semidirect
103. C₂×C₄×Dic₇₉	C₂³	semidirect
108. C₂²×D₄×C₇₉	C₂³	semidirect
109. C₂²×D₄×C₇₉	C₂³	semidirect
114. C₂³×C₄×C₇₉	C₂³	semidirect
115. #121×C₇₉	C₂³	semidirect
116. C₂×C₄⋊C₄×C₇₉	C₂³	semidirect
117. C₂×C₂²⋊C₄×C₇₉	C₂³	semidirect
133. C₂³×D₇₉	C₂×D₄	semidirect
134. C₂³×D₇₉	C₂×D₄	semidirect
138. C₂³×D₇₉	C₂⁴	semidirect
139. C₂³×D₇₉	C₂⁴	semidirect
144. C₂×D₃₁₆	C₂×D₄	semidirect
146. C₂×D₃₁₆	C₂⁴	semidirect
147. C₂×D₃₁₆	C₂⁴	semidirect
148. C₂×D₃₁₆	C₂⁴	semidirect
152. C₂×C₂²⋊D₇₉	C₂×D₄	semidirect
154. C₂×C₂²⋊D₇₉	C₂⁴	semidirect
155. C₂×C₂²⋊D₇₉	C₂⁴	semidirect
156. C₂×C₂²⋊D₇₉	C₂⁴	semidirect
161. C₂²×Dic₇₉	C₂×D₄	semidirect
167. C₂×C₄×D₇₉	C₂⁴	semidirect
168. C₂×C₄×D₇₉	C₂⁴	semidirect
169. Dic₇₉⋊C₄	C₂⁴	semidirect
170. C₂²⋊Dic₇₉	C₂⁴	semidirect
171. (C₂×D₇₉)⋊C₄	C₂⁴	semidirect
172. (C₂×D₇₉)⋊C₄	C₂⁴	semidirect
173. (C₂×D₇₉)⋊C₄	C₂⁴	semidirect
174. C₄×Dic₇₉	C₂⁴	semidirect
180. C₂⁴×C₇₉	C₂×D₄	semidirect
186. C₂×D₄×C₇₉	C₂⁴	semidirect
187. C₂×D₄×C₇₉	C₂⁴	semidirect
191. C₂²×C₄×C₇₉	C₂×D₄	semidirect
195. C₂²×C₄×C₇₉	C₂⁴	semidirect
196. C₄⋊C₄×C₇₉	C₂⁴	semidirect
197. C₂²⋊C₄×C₇₉	C₂⁴	semidirect
207. C₂³×C₇₉	C₂²×D₄	semidirect
230. C₂²×D₇₉	C₂²×D₄	semidirect
231. C₂²×D₇₉	C₂²×D₄	semidirect
240. C₂×C₄×C₇₉	C₂²×D₄	semidirect
247. C₂²⋊D₇₉	C₂²×D₄	semidirect
250. C₂×Dic₇₉	C₂²×D₄	semidirect
257. D₃₁₆	C₂²×D₄	semidirect
267. C₂²×C₇₉	D₄²	semidirect
270. C₂²×C₇₉	C₂³×D₄	semidirect
285. C₂×D₇₉	C₂³×D₄	semidirect
286. C₂×D₇₉	C₂³×D₄	semidirect
289. C₄×C₇₉	C₂³×D₄	semidirect
292. Dic₇₉	C₂³×D₄	semidirect
296. C₂×C₇₉	C₂×D₄²	semidirect
310. C₂²×#121	D₇₉	semidirect
315. C₇₉	C₂²×D₄²	semidirect
332. C₂³×D₄	C₂×D₇₉	semidirect
333. C₂³×D₄	C₂×D₇₉	semidirect
336. C₂⁴×C₄	C₂×D₇₉	semidirect
341. C₂×#121	C₂×D₇₉	semidirect
347. C₂²×C₄⋊C₄	C₂×D₇₉	semidirect
352. C₂²×C₂²⋊C₄	C₂×D₇₉	semidirect
391. C₂²×D₄	C₂²×D₇₉	semidirect
392. C₂²×D₄	C₂²×D₇₉	semidirect
404. C₂³×C₄	C₂²×D₇₉	semidirect
408. #121	C₂²×D₇₉	semidirect
414. C₂×C₄⋊C₄	C₂²×D₇₉	semidirect
419. C₂×C₂²⋊C₄	C₂²×D₇₉	semidirect
448. C₂⁴	D₄×D₇₉	semidirect
473. C₂×D₄	C₂³×D₇₉	semidirect
474. C₂×D₄	C₂³×D₇₉	semidirect
488. C₂²×C₄	D₄×D₇₉	semidirect
492. C₂²×C₄	C₂³×D₇₉	semidirect
494. C₄⋊C₄	C₂³×D₇₉	semidirect
499. C₂²⋊C₄	C₂³×D₇₉	semidirect
533. C₂³	C₂×D₄×D₇₉	semidirect
559. C₂×C₄	C₂×D₄×D₇₉	semidirect
584. C₂²	#19099197	direct (N × H)
587. C₂²	C₂²×D₄×D₇₉	semidirect
595. C₄	C₂²×D₄×D₇₉	semidirect
601. C₂	C₂×#19099197	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂⁴×D₃₁₆	2
C₂³×D₄×D₇₉	2
C₂×#19099197	2
C₂²×#14579157	2
C₂²×#14579136	2
C₂²×#14579134	2
C₂²×#14579131	2
C₂²×#14579129	2
C₂²×#14579123	2
C₂²×C₄×C₂²⋊D₇₉	2
C₂²×#121×C₇₉	2
C₂²×D₄²	79

Subgroups — C22×#19099197 #35195178

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×#19099197 #35195178