Subgroups — C₂²×#19099203 #35195191

Order 20224.

14462 conjugacy classes of subgroups.

The subgroup lattice has 780 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	C₂⁴×C₂²⋊D₇₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#19099203	C₂	1	48	yes	maximal, direct product factor
4	C₂²×#14579147	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂²×#14579144	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×#14579143	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂²×#14579138	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×#14579135	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂²×#14579134	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂²×#14579134	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂²×#14579131	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×#14579130	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂²×C₄×C₂²⋊D₇₉	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂²×(C₂²⋊D₇₉)⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂²×C₂²⋊C₄×D₇₉	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂³×C₂²⋊C₄×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂⁵×D₇₉	C₂²	1	1	yes	characteristic
18	C₂²×#11929624	—	2	16	no	—
19	C₂²×#11929624	C₂²	1	24	yes	complemented
20	C₂³×Dic₁₅₈	C₂²	1	1	yes	characteristic, complemented
21	C₂³×D₃₁₆	C₂²	1	1	yes	characteristic, complemented
22	C₂³×D₃₁₆	C₂²	1	1	yes	characteristic, complemented
23	C₂³×C₂²⋊D₇₉	—	2	16	no	—
24	C₂³×C₂²⋊D₇₉	C₂²	1	1	yes	characteristic
25	C₂³×C₂²⋊D₇₉	C₂²	1	1	yes	characteristic
26	C₂³×C₂²⋊D₇₉	C₂²	1	1	yes	characteristic
27	C₂³×C₂²⋊D₇₉	C₂²	1	1	yes	characteristic
28	C₂³×C₂²⋊D₇₉	C₂²	1	1	yes	characteristic
29	C₂³×C₂²⋊D₇₉	C₂²	1	24	yes	complemented
30	C₂³×C₂²⋊D₇₉	C₂²	1	1	yes	characteristic, complemented
31	C₂³×C₂²⋊D₇₉	C₂²	1	1	yes	characteristic, complemented
32	C₂⁴×Dic₇₉	C₂²	1	1	yes	characteristic
33	C₂³×C₄×D₇₉	C₂²	1	1	yes	characteristic, complemented
34	C₂³×C₄×D₇₉	C₂²	1	1	yes	characteristic, complemented
35	C₂³×C₄×D₇₉	C₂²	1	1	yes	characteristic, complemented
36	#19099203	C₂²	1	256	yes	direct product factor
37	C₂×#14579147	C₂²	1	24	yes	complemented
38	C₂×#14579144	C₂²	1	24	yes	complemented
39	C₂×#14579143	C₂²	1	24	yes	complemented
40	C₂×#14579138	C₂²	1	24	yes	complemented
41	C₂×#14579135	C₂²	1	24	yes	complemented
42	C₂×#14579134	C₂²	1	24	yes	complemented
43	C₂×#14579134	C₂²	1	24	yes	complemented
44	C₂×#14579131	C₂²	1	24	yes	complemented
45	C₂×#14579130	C₂²	1	24	yes	complemented
46	C₂×C₄×C₂²⋊D₇₉	C₂²	1	24	yes	complemented
47	C₂×(C₂²⋊D₇₉)⋊C₄	C₂²	1	24	yes	complemented
48	C₂²×C₄⋊Dic₇₉	C₂²	1	1	yes	characteristic, complemented
49	C₂²×Dic₇₉⋊C₄	C₂²	1	1	yes	characteristic, complemented
50	C₂²×Dic₇₉⋊C₄	C₂²	1	1	yes	characteristic, complemented
51	C₂²×Dic₇₉⋊C₄	C₂²	1	1	yes	characteristic, complemented
52	C₂²×C₂²⋊Dic₇₉	C₂²	1	1	yes	characteristic
53	C₂²×C₂²⋊Dic₇₉	C₂²	1	1	yes	characteristic, complemented
54	C₂²×C₂²⋊Dic₇₉	C₂²	1	1	yes	characteristic, complemented
55	C₂²×(C₂×D₇₉)⋊C₄	C₂²	1	1	yes	characteristic, complemented
56	C₂²×(C₂×D₇₉)⋊C₄	C₂²	1	1	yes	characteristic, complemented
57	C₂²×(C₂×D₇₉)⋊C₄	C₂²	1	1	yes	characteristic, complemented
58	C₂²×(C₂×D₇₉)⋊C₄	C₂²	1	1	yes	characteristic, complemented
59	C₂²×(C₂×D₇₉)⋊C₄	C₂²	1	1	yes	characteristic, complemented
60	C₂×C₂²⋊C₄×D₇₉	C₂²	1	24	yes	complemented
61	C₂²×C₄×Dic₇₉	C₂²	1	1	yes	characteristic, complemented
62	C₂⁶×C₇₉	C₂²	1	1	yes	characteristic
63	C₂⁴×C₄×C₇₉	C₂²	1	1	yes	characteristic, complemented
64	C₂⁴×C₄×C₇₉	C₂²	1	1	yes	characteristic, complemented
65	C₂²×C₂²⋊C₄×C₇₉	C₂²	1	1	yes	characteristic
66	C₂²×C₂²⋊C₄×C₇₉	C₂²	1	1	yes	characteristic
67	C₂²×C₂²⋊C₄×C₇₉	C₂²	1	24	yes	complemented
68	C₂²×C₂²⋊C₄×C₇₉	C₂²	1	1	yes	characteristic, complemented
69	C₂²×C₂²⋊C₄×C₇₉	C₂²	1	1	yes	characteristic, complemented
70	C₂⁴×D₇₉	—	2	8	no	—
71	C₂⁴×D₇₉	—	2	8	no	—
72	C₂⁴×D₇₉	—	4	4	no	—
73	C₂⁴×D₇₉	C₂³	1	1	yes	characteristic
74	C₂⁴×D₇₉	C₂³	1	1	yes	characteristic
75	C₂⁴×D₇₉	C₂³	1	12	yes	—
76	C₂⁴×D₇₉	C₂³	1	1	yes	characteristic
77	C₂×#11929624	—	2	192	no	—
78	C₂×#11929624	C₂³	1	64	yes	complemented
79	C₂²×Dic₁₅₈	—	2	8	no	—
80	C₂²×Dic₁₅₈	C₂³	1	12	yes	complemented
81	C₂²×D₃₁₆	—	2	8	no	—
82	C₂²×D₃₁₆	—	4	4	no	—
83	C₂²×D₃₁₆	C₂³	1	12	yes	complemented
84	C₂²×D₃₁₆	C₂³	1	12	yes	complemented
85	C₂²×C₂²⋊D₇₉	—	2	8	no	—
86	C₂²×C₂²⋊D₇₉	—	2	8	no	—
87	C₂²×C₂²⋊D₇₉	—	2	8	no	—
88	C₂²×C₂²⋊D₇₉	—	2	8	no	—
89	C₂²×C₂²⋊D₇₉	—	2	192	no	—
90	C₂²×C₂²⋊D₇₉	—	2	8	no	—
91	C₂²×C₂²⋊D₇₉	—	4	4	no	—
92	C₂²×C₂²⋊D₇₉	D₄	1	16	yes	complemented
93	C₂²×C₂²⋊D₇₉	C₂³	1	12	yes	—
94	C₂²×C₂²⋊D₇₉	C₂³	1	12	yes	—
95	C₂²×C₂²⋊D₇₉	C₂³	1	12	yes	—
96	C₂²×C₂²⋊D₇₉	C₂³	1	12	yes	—
97	C₂²×C₂²⋊D₇₉	C₂³	1	12	yes	—
98	C₂²×C₂²⋊D₇₉	C₂³	1	64	yes	complemented
99	C₂²×C₂²⋊D₇₉	C₂³	1	12	yes	complemented
100	C₂²×C₂²⋊D₇₉	C₂³	1	12	yes	complemented
101	C₂³×Dic₇₉	—	2	8	no	—
102	C₂³×Dic₇₉	C₂³	1	1	yes	characteristic
103	C₂³×Dic₇₉	C₂³	1	1	yes	characteristic
104	C₂³×Dic₇₉	C₂³	1	1	yes	characteristic
105	C₂³×Dic₇₉	C₂³	1	1	yes	characteristic
106	C₂³×Dic₇₉	C₂³	1	12	yes	—
107	C₂³×Dic₇₉	C₂³	1	1	yes	characteristic
108	C₂²×C₄×D₇₉	—	2	8	no	—
109	C₂²×C₄×D₇₉	—	2	8	no	—
110	C₂²×C₄×D₇₉	—	4	4	no	—
111	C₂²×C₄×D₇₉	C₂³	1	12	yes	complemented
112	C₂²×C₄×D₇₉	C₂³	1	12	yes	complemented
113	C₂²×C₄×D₇₉	C₂³	1	12	yes	complemented
114	#14579147	C₂³	1	64	yes	complemented
115	#14579144	C₂³	1	64	yes	complemented
116	#14579143	C₂³	1	64	yes	complemented
117	#14579138	C₂³	1	64	yes	complemented
118	#14579135	C₂³	1	64	yes	complemented
119	#14579134	C₂³	1	64	yes	complemented
120	#14579134	C₂³	1	64	yes	complemented
121	#14579131	C₂³	1	64	yes	complemented
122	#14579130	C₂³	1	64	yes	complemented
123	C₄×C₂²⋊D₇₉	C₂³	1	64	yes	complemented
124	(C₂²⋊D₇₉)⋊C₄	C₂³	1	64	yes	complemented
125	C₂×C₄⋊Dic₇₉	C₂³	1	12	yes	complemented
126	C₂×Dic₇₉⋊C₄	C₂³	1	12	yes	complemented
127	C₂×Dic₇₉⋊C₄	C₂³	1	12	yes	complemented
128	C₂×Dic₇₉⋊C₄	C₂³	1	12	yes	complemented
129	C₂×C₂²⋊Dic₇₉	C₂³	1	12	yes	—
130	C₂×C₂²⋊Dic₇₉	C₂³	1	12	yes	complemented
131	C₂×C₂²⋊Dic₇₉	C₂³	1	12	yes	complemented
132	C₂×(C₂×D₇₉)⋊C₄	C₂³	1	12	yes	complemented
133	C₂×(C₂×D₇₉)⋊C₄	C₂³	1	12	yes	complemented
134	C₂×(C₂×D₇₉)⋊C₄	C₂³	1	12	yes	complemented
135	C₂×(C₂×D₇₉)⋊C₄	C₂³	1	12	yes	complemented
136	C₂×(C₂×D₇₉)⋊C₄	C₂³	1	12	yes	complemented
137	C₂²⋊C₄×D₇₉	C₂³	1	64	yes	complemented
138	C₂×C₄×Dic₇₉	C₂³	1	12	yes	complemented
139	C₂⁵×C₇₉	—	2	8	no	—
140	C₂⁵×C₇₉	—	2	8	no	—
141	C₂⁵×C₇₉	—	4	4	no	—
142	C₂⁵×C₇₉	C₂³	1	1	yes	characteristic
143	C₂⁵×C₇₉	C₂³	1	12	yes	—
144	C₂⁵×C₇₉	C₂³	1	1	yes	characteristic
145	C₂⁵×C₇₉	C₂³	1	1	yes	characteristic
146	C₂³×C₄×C₇₉	—	2	8	no	—
147	C₂³×C₄×C₇₉	—	4	4	no	—
148	C₂³×C₄×C₇₉	C₂³	1	1	yes	characteristic
149	C₂³×C₄×C₇₉	C₂³	1	1	yes	characteristic
150	C₂³×C₄×C₇₉	C₂³	1	1	yes	characteristic
151	C₂³×C₄×C₇₉	C₂³	1	1	yes	characteristic
152	C₂³×C₄×C₇₉	C₂³	1	12	yes	complemented
153	C₂³×C₄×C₇₉	C₂³	1	12	yes	complemented
154	C₂×C₂²⋊C₄×C₇₉	C₂³	1	12	yes	—
155	C₂×C₂²⋊C₄×C₇₉	C₂³	1	12	yes	—
156	C₂×C₂²⋊C₄×C₇₉	C₂³	1	64	yes	complemented
157	C₂×C₂²⋊C₄×C₇₉	C₂³	1	12	yes	complemented
158	C₂×C₂²⋊C₄×C₇₉	C₂³	1	12	yes	complemented
159	C₂³×D₇₉	—	2	4	no	—
160	C₂³×D₇₉	—	2	4	no	—
161	C₂³×D₇₉	—	2	4	no	—
162	C₂³×D₇₉	—	2	4	no	—
163	C₂³×D₇₉	—	2	4	no	—
164	C₂³×D₇₉	—	2	4	no	—
165	C₂³×D₇₉	—	2	48	no	—
166	C₂³×D₇₉	—	2	4	no	—
167	C₂³×D₇₉	—	2	4	no	—
168	C₂³×D₇₉	—	2	48	no	—
169	C₂³×D₇₉	—	4	24	no	—
170	C₂³×D₇₉	—	4	64	no	—
171	C₂³×D₇₉	C₂×D₄	1	8	yes	—
172	C₂³×D₇₉	C₂⁴	1	6	yes	—
173	C₂³×D₇₉	C₂⁴	1	6	yes	—
174	C₂³×D₇₉	C₂⁴	1	16	yes	—
175	C₂³×D₇₉	C₂⁴	1	6	yes	—
176	#11929624	—	2	256	no	—
177	C₂×Dic₁₅₈	—	2	48	no	—
178	C₂×Dic₁₅₈	C₂⁴	1	16	yes	complemented
179	C₂×D₃₁₆	—	2	48	no	—
180	C₂×D₃₁₆	—	4	24	no	—
181	C₂×D₃₁₆	C₂⁴	1	16	yes	complemented
182	C₂×D₃₁₆	C₂⁴	1	16	yes	complemented
183	C₂×C₂²⋊D₇₉	—	2	48	no	—
184	C₂×C₂²⋊D₇₉	—	2	48	no	—
185	C₂×C₂²⋊D₇₉	—	2	48	no	—
186	C₂×C₂²⋊D₇₉	—	2	48	no	—
187	C₂×C₂²⋊D₇₉	—	2	48	no	—
188	C₂×C₂²⋊D₇₉	—	2	256	no	—
189	C₂×C₂²⋊D₇₉	—	4	24	no	—
190	C₂×C₂²⋊D₇₉	C₂×D₄	1	96	yes	complemented
191	C₂×C₂²⋊D₇₉	C₂⁴	1	16	yes	—
192	C₂×C₂²⋊D₇₉	C₂⁴	1	16	yes	—
193	C₂×C₂²⋊D₇₉	C₂⁴	1	16	yes	—
194	C₂×C₂²⋊D₇₉	C₂⁴	1	16	yes	—
195	C₂×C₂²⋊D₇₉	C₂⁴	1	16	yes	—
196	C₂×C₂²⋊D₇₉	C₂⁴	1	16	yes	complemented
197	C₂×C₂²⋊D₇₉	C₂⁴	1	16	yes	complemented
198	C₂²×Dic₇₉	—	2	48	no	—
199	C₂²×Dic₇₉	—	2	4	no	—
200	C₂²×Dic₇₉	—	2	4	no	—
201	C₂²×Dic₇₉	—	2	4	no	—
202	C₂²×Dic₇₉	—	2	4	no	—
203	C₂²×Dic₇₉	C₂×D₄	1	8	yes	—
204	C₂²×Dic₇₉	C₂⁴	1	6	yes	—
205	C₂²×Dic₇₉	C₂⁴	1	6	yes	—
206	C₂²×Dic₇₉	C₂⁴	1	6	yes	—
207	C₂²×Dic₇₉	C₂⁴	1	6	yes	—
208	C₂²×Dic₇₉	C₂⁴	1	16	yes	—
209	C₂²×Dic₇₉	C₂⁴	1	6	yes	—
210	C₂×C₄×D₇₉	—	2	48	no	—
211	C₂×C₄×D₇₉	—	2	48	no	—
212	C₂×C₄×D₇₉	—	4	24	no	—
213	C₂×C₄×D₇₉	C₂⁴	1	16	yes	complemented
214	C₂×C₄×D₇₉	C₂⁴	1	16	yes	complemented
215	C₂×C₄×D₇₉	C₂⁴	1	16	yes	complemented
216	C₄⋊Dic₇₉	C₂⁴	1	16	yes	complemented
217	Dic₇₉⋊C₄	C₂⁴	1	16	yes	complemented
218	Dic₇₉⋊C₄	C₂⁴	1	16	yes	complemented
219	Dic₇₉⋊C₄	C₂⁴	1	16	yes	complemented
220	C₂²⋊Dic₇₉	C₂⁴	1	16	yes	—
221	C₂²⋊Dic₇₉	C₂⁴	1	16	yes	complemented
222	C₂²⋊Dic₇₉	C₂⁴	1	16	yes	complemented
223	(C₂×D₇₉)⋊C₄	C₂⁴	1	16	yes	complemented
224	(C₂×D₇₉)⋊C₄	C₂⁴	1	16	yes	complemented
225	(C₂×D₇₉)⋊C₄	C₂⁴	1	16	yes	complemented
226	(C₂×D₇₉)⋊C₄	C₂⁴	1	16	yes	complemented
227	(C₂×D₇₉)⋊C₄	C₂⁴	1	16	yes	complemented
228	C₄×Dic₇₉	C₂⁴	1	16	yes	complemented
229	C₂⁴×C₇₉	—	2	4	no	—
230	C₂⁴×C₇₉	—	2	4	no	—
231	C₂⁴×C₇₉	—	2	4	no	—
232	C₂⁴×C₇₉	—	2	4	no	—
233	C₂⁴×C₇₉	—	2	48	no	—
234	C₂⁴×C₇₉	—	2	4	no	—
235	C₂⁴×C₇₉	—	2	4	no	—
236	C₂⁴×C₇₉	—	2	48	no	—
237	C₂⁴×C₇₉	—	2	4	no	—
238	C₂⁴×C₇₉	—	4	24	no	—
239	C₂⁴×C₇₉	—	4	64	no	—
240	C₂⁴×C₇₉	C₂×D₄	1	8	yes	—
241	C₂⁴×C₇₉	#41	1	8	yes	complemented
242	C₂⁴×C₇₉	C₂⁴	1	6	yes	—
243	C₂⁴×C₇₉	C₂⁴	1	16	yes	—
244	C₂⁴×C₇₉	C₂⁴	1	6	yes	—
245	C₂⁴×C₇₉	C₂⁴	1	6	yes	—
246	C₂⁴×C₇₉	C₂⁴	1	1	yes	characteristic
247	C₂²×C₄×C₇₉	—	2	4	no	—
248	C₂²×C₄×C₇₉	—	2	48	no	—
249	C₂²×C₄×C₇₉	—	2	4	no	—
250	C₂²×C₄×C₇₉	—	2	4	no	—
251	C₂²×C₄×C₇₉	—	2	4	no	—
252	C₂²×C₄×C₇₉	—	4	24	no	—
253	C₂²×C₄×C₇₉	C₂⁴	1	6	yes	—
254	C₂²×C₄×C₇₉	C₂⁴	1	6	yes	—
255	C₂²×C₄×C₇₉	C₂⁴	1	6	yes	—
256	C₂²×C₄×C₇₉	C₂⁴	1	6	yes	—
257	C₂²×C₄×C₇₉	C₂⁴	1	16	yes	complemented
258	C₂²×C₄×C₇₉	C₂⁴	1	16	yes	complemented
259	C₂²⋊C₄×C₇₉	C₂⁴	1	16	yes	—
260	C₂²⋊C₄×C₇₉	C₂⁴	1	16	yes	—
261	C₂²⋊C₄×C₇₉	C₂⁴	1	16	yes	complemented
262	C₂²⋊C₄×C₇₉	C₂⁴	1	16	yes	complemented
263	C₂³×C₇₉	—	2	32	no	—
264	C₂³×C₇₉	—	2	32	no	—
265	C₂³×C₇₉	—	2	12	no	—
266	C₂³×C₇₉	—	2	12	no	—
267	C₂³×C₇₉	—	2	12	no	—
268	C₂³×C₇₉	—	2	12	no	—
269	C₂³×C₇₉	—	2	32	no	—
270	C₂³×C₇₉	—	2	12	no	—
271	C₂³×C₇₉	—	2	12	no	—
272	C₂³×C₇₉	—	2	32	no	—
273	C₂³×C₇₉	—	2	12	no	—
274	C₂³×C₇₉	—	4	16	no	—
275	C₂³×C₇₉	—	4	192	no	—
276	C₂³×C₇₉	—	4	16	no	—
277	C₂³×C₇₉	C₂²×D₄	1	24	yes	—
278	C₂³×C₇₉	C₂²×D₄	1	4	yes	—
279	C₂³×C₇₉	C₂×#41	1	4	yes	—
280	C₂³×C₇₉	C₂×#41	1	24	yes	complemented
281	C₂³×C₇₉	H(5,𝔽₂)	1	4	yes	—
282	C₂³×C₇₉	C₂⁵	1	4	yes	—
283	C₂³×C₇₉	C₂⁵	1	4	yes	—
284	C₂³×C₇₉	C₂⁵	1	4	yes	—
285	C₂³×C₇₉	C₂⁵	1	3	yes	—
286	C₂²×D₇₉	—	2	32	no	—
287	C₂²×D₇₉	—	2	12	no	—
288	C₂²×D₇₉	—	2	12	no	—
289	C₂²×D₇₉	—	2	12	no	—
290	C₂²×D₇₉	—	2	12	no	—
291	C₂²×D₇₉	—	2	12	no	—
292	C₂²×D₇₉	—	2	12	no	—
293	C₂²×D₇₉	—	2	32	no	—
294	C₂²×D₇₉	—	2	12	no	—
295	C₂²×D₇₉	—	2	12	no	—
296	C₂²×D₇₉	—	2	32	no	—
297	C₂²×D₇₉	—	4	16	no	—
298	C₂²×D₇₉	—	4	192	no	—
299	C₂²×D₇₉	—	4	16	no	—
300	C₂²×D₇₉	—	4	16	no	—
301	C₂²×D₇₉	C₂²×D₄	1	24	yes	—
302	C₂²×D₇₉	C₂⁵	1	4	yes	—
303	C₂²×D₇₉	C₂⁵	1	4	yes	—
304	C₂²×D₇₉	C₂⁵	1	4	yes	—
305	C₂×C₄×C₇₉	—	2	12	no	—
306	C₂×C₄×C₇₉	—	2	12	no	—
307	C₂×C₄×C₇₉	—	2	32	no	—
308	C₂×C₄×C₇₉	—	2	12	no	—
309	C₂×C₄×C₇₉	—	2	12	no	—
310	C₂×C₄×C₇₉	—	4	16	no	—
311	C₂×C₄×C₇₉	C₂⁵	1	4	yes	—
312	C₂×C₄×C₇₉	C₂⁵	1	4	yes	—
313	C₂×C₄×C₇₉	C₂⁵	1	4	yes	—
314	C₂×C₄×C₇₉	C₂⁵	1	4	yes	—
315	C₂²⋊D₇₉	—	2	32	no	—
316	C₂²⋊D₇₉	—	2	32	no	—
317	C₂²⋊D₇₉	—	2	32	no	—
318	C₂²⋊D₇₉	—	2	32	no	—
319	C₂²⋊D₇₉	—	2	32	no	—
320	C₂²⋊D₇₉	—	4	16	no	—
321	C₂²⋊D₇₉	C₂²×D₄	1	64	yes	complemented
322	C₂×Dic₇₉	—	2	12	no	—
323	C₂×Dic₇₉	—	2	12	no	—
324	C₂×Dic₇₉	—	2	12	no	—
325	C₂×Dic₇₉	—	2	12	no	—
326	C₂×Dic₇₉	—	2	32	no	—
327	C₂×Dic₇₉	C₂²×D₄	1	24	yes	—
328	C₂×Dic₇₉	C₂⁵	1	4	yes	—
329	C₂×Dic₇₉	C₂⁵	1	4	yes	—
330	C₂×Dic₇₉	C₂⁵	1	4	yes	—
331	C₂×Dic₇₉	C₂⁵	1	4	yes	—
332	C₂×Dic₇₉	C₂⁵	1	4	yes	—
333	D₃₁₆	—	2	32	no	—
334	D₃₁₆	—	4	16	no	—
335	C₄×D₇₉	—	2	32	no	—
336	C₄×D₇₉	—	2	32	no	—
337	C₄×D₇₉	—	4	16	no	—
338	Dic₁₅₈	—	2	32	no	—
339	C₂²×C₇₉	—	2	4	no	—
340	C₂²×C₇₉	—	2	4	no	—
341	C₂²×C₇₉	—	2	4	no	—
342	C₂²×C₇₉	—	2	4	no	—
343	C₂²×C₇₉	—	2	48	no	—
344	C₂²×C₇₉	—	2	48	no	—
345	C₂²×C₇₉	—	2	4	no	—
346	C₂²×C₇₉	—	2	4	no	—
347	C₂²×C₇₉	—	2	4	no	—
348	C₂²×C₇₉	—	4	64	no	—
349	C₂²×C₇₉	—	4	24	no	—
350	C₂²×C₇₉	#546	1	16	yes	complemented
351	C₂²×C₇₉	C₂³×D₄	1	8	yes	—
352	C₂²×C₇₉	C₂³×D₄	1	6	yes	—
353	C₂²×C₇₉	C₂²×#41	1	6	yes	—
354	C₂²×C₇₉	C₂²×#41	1	8	yes	complemented
355	C₂²×C₇₉	C₂×H(5,𝔽₂)	1	6	yes	—
356	C₂²×C₇₉	C₂⁶	1	1	yes	characteristic
357	C₂×D₇₉	—	2	4	no	—
358	C₂×D₇₉	—	2	4	no	—
359	C₂×D₇₉	—	2	48	no	—
360	C₂×D₇₉	—	2	4	no	—
361	C₂×D₇₉	—	2	4	no	—
362	C₂×D₇₉	—	2	4	no	—
363	C₂×D₇₉	—	2	4	no	—
364	C₂×D₇₉	—	2	4	no	—
365	C₂×D₇₉	—	2	4	no	—
366	C₂×D₇₉	—	4	64	no	—
367	C₂×D₇₉	—	4	24	no	—
368	C₂×D₇₉	—	4	24	no	—
369	C₂×D₇₉	C₂³×D₄	1	8	yes	—
370	C₄×C₇₉	—	2	4	no	—
371	C₄×C₇₉	—	2	4	no	—
372	C₄×C₇₉	—	2	4	no	—
373	C₄×C₇₉	—	2	4	no	—
374	Dic₇₉	—	2	4	no	—
375	Dic₇₉	—	2	4	no	—
376	Dic₇₉	—	2	4	no	—
377	Dic₇₉	—	2	4	no	—
378	Dic₇₉	C₂³×D₄	1	8	yes	—
379	C₂²×#546	—	79	1	no	maximal, Sylow
380	C₂×C₇₉	—	2	8	no	—
381	C₂×C₇₉	—	2	8	no	—
382	C₂×C₇₉	—	4	4	no	—
383	C₂×C₇₉	C₂×#546	1	12	yes	complemented
384	C₂×C₇₉	C₂⁴×D₄	1	1	yes	characteristic
385	C₂×C₇₉	C₂³×#41	1	1	yes	characteristic
386	C₂×C₇₉	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
387	D₇₉	—	2	8	no	—
388	D₇₉	—	4	4	no	—
389	D₇₉	—	4	4	no	—
390	C₂³×#41	—	79	1	no	—
391	C₂⁴×D₄	—	79	1	no	—
392	C₂×#546	—	79	48	no	—
393	C₂²×#124	—	79	1	no	—
394	C₂²×#123	—	79	1	no	—
395	C₂²×#123	—	79	1	no	—
396	C₂²×C₂²⋊Q₈	—	79	1	no	—
397	C₂²×#121	—	79	1	no	—
398	C₂²×#121	—	79	1	no	—
399	C₂²×#121	—	79	1	no	—
400	C₂²×#120	—	79	1	no	—
401	C₂²×#120	—	79	1	no	—
402	C₂²×C₄×D₄	—	79	1	no	—
403	C₂²×C₄×D₄	—	79	1	no	—
404	C₂³×C₂²⋊C₄	—	79	1	no	—
405	C₂³×C₂²⋊C₄	D₇₉	1	1	yes	characteristic, complemented
406	C₇₉	C₂²×#546	1	1	yes	characteristic, complemented, Sylow
407	C₂⁶	—	79	1	no	—
408	C₂⁶	C₂×D₇₉	1	1	yes	characteristic
409	C₂²×#41	—	79	24	no	—
410	C₂²×#41	—	158	16	no	—
411	C₂³×Q₈	—	79	1	no	—
412	C₂³×D₄	—	79	1	no	—
413	C₂³×D₄	—	79	1	no	—
414	C₂³×D₄	—	79	1	no	—
415	C₂³×D₄	—	79	1	no	—
416	C₂³×D₄	—	79	1	no	—
417	C₂³×D₄	—	79	24	no	—
418	C₂³×D₄	—	79	1	no	—
419	C₂³×D₄	—	79	1	no	—
420	C₂³×D₄	—	79	1	no	—
421	C₂³×D₄	—	79	1	no	—
422	C₂³×D₄	—	158	16	no	—
423	C₂⁴×C₄	—	79	1	no	—
424	C₂⁴×C₄	—	79	1	no	—
425	C₂⁴×C₄	—	79	1	no	—
426	C₂⁴×C₄	—	79	1	no	—
427	C₂⁴×C₄	C₂×D₇₉	1	1	yes	characteristic, complemented
428	C₂⁴×C₄	C₂×D₇₉	1	1	yes	characteristic, complemented
429	#546	—	79	256	no	—
430	C₂×#124	—	79	24	no	—
431	C₂×#123	—	79	24	no	—
432	C₂×#123	—	79	24	no	—
433	C₂×C₂²⋊Q₈	—	79	24	no	—
434	C₂×#121	—	79	24	no	—
435	C₂×#121	—	79	24	no	—
436	C₂×#121	—	79	24	no	—
437	C₂×#120	—	79	24	no	—
438	C₂×#120	—	79	24	no	—
439	C₂×C₄×D₄	—	79	24	no	—
440	C₂×C₄×D₄	—	79	24	no	—
441	C₂²×C₄⋊C₄	—	79	1	no	—
442	C₂²×C₄⋊C₄	—	79	1	no	—
443	C₂²×C₄⋊C₄	—	79	1	no	—
444	C₂²×C₄⋊C₄	—	79	1	no	—
445	C₂²×C₂²⋊C₄	—	79	1	no	—
446	C₂²×C₂²⋊C₄	—	79	1	no	—
447	C₂²×C₂²⋊C₄	—	79	1	no	—
448	C₂²×C₂²⋊C₄	—	79	1	no	—
449	C₂²×C₂²⋊C₄	—	79	1	no	—
450	C₂²×C₂²⋊C₄	—	79	1	no	—
451	C₂²×C₂²⋊C₄	—	79	1	no	—
452	C₂²×C₂²⋊C₄	—	79	1	no	—
453	C₂²×C₂²⋊C₄	—	79	24	no	—
454	C₂²×C₂²⋊C₄	C₂×D₇₉	1	1	yes	characteristic
455	C₂²×C₂²⋊C₄	C₂×D₇₉	1	1	yes	characteristic
456	C₂²×C₂²⋊C₄	C₂×D₇₉	1	24	yes	complemented
457	C₂²×C₂²⋊C₄	C₂×D₇₉	1	1	yes	characteristic, complemented
458	C₂²×C₂²⋊C₄	C₂×D₇₉	1	1	yes	characteristic, complemented
459	C₂²×C₄²	—	79	1	no	—
460	C₂⁵	—	2	8	no	—
461	C₂⁵	—	2	8	no	—
462	C₂⁵	—	4	4	no	—
463	C₂⁵	—	316	4	no	—
464	C₂⁵	—	79	12	no	—
465	C₂⁵	—	79	1	no	—
466	C₂⁵	—	79	1	no	—
467	C₂⁵	—	79	1	no	—
468	C₂⁵	—	158	8	no	—
469	C₂⁵	—	158	8	no	—
470	C₂⁵	C₂²×D₇₉	1	1	yes	characteristic
471	C₂⁵	C₂²×D₇₉	1	12	yes	—
472	C₂⁵	C₂²×D₇₉	1	1	yes	characteristic
473	C₂⁵	C₂²×D₇₉	1	1	yes	characteristic
474	C₂×#41	—	79	64	no	—
475	C₂×#41	—	158	192	no	—
476	C₂²×Q₈	—	79	12	no	—
477	C₂²×Q₈	—	158	8	no	—
478	C₂²×D₄	—	316	4	no	—
479	C₂²×D₄	—	316	4	no	—
480	C₂²×D₄	—	79	12	no	—
481	C₂²×D₄	—	79	16	no	—
482	C₂²×D₄	—	79	12	no	—
483	C₂²×D₄	—	79	12	no	—
484	C₂²×D₄	—	79	12	no	—
485	C₂²×D₄	—	79	12	no	—
486	C₂²×D₄	—	79	12	no	—
487	C₂²×D₄	—	79	12	no	—
488	C₂²×D₄	—	79	64	no	—
489	C₂²×D₄	—	79	12	no	—
490	C₂²×D₄	—	79	12	no	—
491	C₂²×D₄	—	158	8	no	—
492	C₂²×D₄	—	158	8	no	—
493	C₂²×D₄	—	158	192	no	—
494	C₂²×D₄	—	158	8	no	—
495	C₂²×D₄	—	158	8	no	—
496	C₂²×D₄	—	158	8	no	—
497	C₂²×D₄	—	158	8	no	—
498	C₂³×C₄	—	2	8	no	—
499	C₂³×C₄	—	4	4	no	—
500	C₂³×C₄	—	316	4	no	—
501	C₂³×C₄	—	79	12	no	—
502	C₂³×C₄	—	79	1	no	—
503	C₂³×C₄	—	79	12	no	—
504	C₂³×C₄	—	79	1	no	—
505	C₂³×C₄	—	79	1	no	—
506	C₂³×C₄	—	79	1	no	—
507	C₂³×C₄	—	79	1	no	—
508	C₂³×C₄	—	79	12	no	—
509	C₂³×C₄	—	79	12	no	—
510	C₂³×C₄	—	158	8	no	—
511	C₂³×C₄	—	158	8	no	—
512	C₂³×C₄	—	158	8	no	—
513	C₂³×C₄	C₂²×D₇₉	1	1	yes	characteristic
514	C₂³×C₄	C₂²×D₇₉	1	1	yes	characteristic
515	C₂³×C₄	C₂²×D₇₉	1	1	yes	characteristic
516	C₂³×C₄	C₂²×D₇₉	1	1	yes	characteristic
517	C₂³×C₄	C₂²×D₇₉	1	12	yes	complemented
518	C₂³×C₄	C₂²×D₇₉	1	12	yes	complemented
519	#124	—	79	64	no	—
520	#123	—	79	64	no	—
521	#123	—	79	64	no	—
522	C₂²⋊Q₈	—	79	64	no	—
523	#121	—	79	64	no	—
524	#121	—	79	64	no	—
525	#121	—	79	64	no	—
526	#120	—	79	64	no	—
527	#120	—	79	64	no	—
528	C₄×D₄	—	79	64	no	—
529	C₄×D₄	—	79	64	no	—
530	C₂×C₄⋊C₄	—	79	12	no	—
531	C₂×C₄⋊C₄	—	79	12	no	—
532	C₂×C₄⋊C₄	—	79	12	no	—
533	C₂×C₄⋊C₄	—	79	12	no	—
534	C₂×C₂²⋊C₄	—	79	12	no	—
535	C₂×C₂²⋊C₄	—	79	12	no	—
536	C₂×C₂²⋊C₄	—	79	12	no	—
537	C₂×C₂²⋊C₄	—	79	12	no	—
538	C₂×C₂²⋊C₄	—	79	12	no	—
539	C₂×C₂²⋊C₄	—	79	12	no	—
540	C₂×C₂²⋊C₄	—	79	12	no	—
541	C₂×C₂²⋊C₄	—	79	12	no	—
542	C₂×C₂²⋊C₄	—	79	64	no	—
543	C₂×C₂²⋊C₄	C₂²×D₇₉	1	12	yes	—
544	C₂×C₂²⋊C₄	C₂²×D₇₉	1	12	yes	—
545	C₂×C₂²⋊C₄	C₂²×D₇₉	1	64	yes	complemented
546	C₂×C₂²⋊C₄	C₂²×D₇₉	1	12	yes	complemented
547	C₂×C₂²⋊C₄	C₂²×D₇₉	1	12	yes	complemented
548	C₂×C₄²	—	79	12	no	—
549	C₂⁴	—	2	4	no	—
550	C₂⁴	—	2	4	no	—
551	C₂⁴	—	2	4	no	—
552	C₂⁴	—	2	4	no	—
553	C₂⁴	—	2	4	no	—
554	C₂⁴	—	2	48	no	—
555	C₂⁴	—	2	4	no	—
556	C₂⁴	—	2	48	no	—
557	C₂⁴	—	2	4	no	—
558	C₂⁴	—	4	24	no	—
559	C₂⁴	—	4	64	no	—
560	C₂⁴	—	316	64	no	—
561	C₂⁴	—	316	24	no	—
562	C₂⁴	—	79	16	no	—
563	C₂⁴	—	79	6	no	—
564	C₂⁴	—	79	8	no	—
565	C₂⁴	—	79	6	no	—
566	C₂⁴	—	79	6	no	—
567	C₂⁴	—	158	48	no	—
568	C₂⁴	—	158	4	no	—
569	C₂⁴	—	158	4	no	—
570	C₂⁴	—	158	48	no	—
571	C₂⁴	—	158	4	no	—
572	C₂⁴	—	158	4	no	—
573	C₂⁴	—	158	4	no	—
574	C₂⁴	—	158	4	no	—
575	C₂⁴	—	158	4	no	—
576	C₂⁴	—	158	4	no	—
577	C₂⁴	D₄×D₇₉	1	8	yes	—
578	C₂⁴	#11929624	1	8	yes	complemented
579	C₂⁴	C₂³×D₇₉	1	6	yes	—
580	C₂⁴	C₂³×D₇₉	1	16	yes	—
581	C₂⁴	C₂³×D₇₉	1	6	yes	—
582	C₂⁴	C₂³×D₇₉	1	6	yes	—
583	C₂⁴	C₂³×D₇₉	1	1	yes	characteristic
584	#41	—	158	256	no	—
585	C₂×Q₈	—	79	16	no	—
586	C₂×Q₈	—	158	48	no	—
587	C₂×D₄	—	316	24	no	—
588	C₂×D₄	—	316	24	no	—
589	C₂×D₄	—	79	16	no	—
590	C₂×D₄	—	79	16	no	—
591	C₂×D₄	—	79	96	no	—
592	C₂×D₄	—	79	16	no	—
593	C₂×D₄	—	79	16	no	—
594	C₂×D₄	—	79	16	no	—
595	C₂×D₄	—	79	16	no	—
596	C₂×D₄	—	79	16	no	—
597	C₂×D₄	—	79	16	no	—
598	C₂×D₄	—	79	16	no	—
599	C₂×D₄	—	158	48	no	—
600	C₂×D₄	—	158	48	no	—
601	C₂×D₄	—	158	256	no	—
602	C₂×D₄	—	158	48	no	—
603	C₂×D₄	—	158	48	no	—
604	C₂×D₄	—	158	48	no	—
605	C₂×D₄	—	158	48	no	—
606	C₂²×C₄	—	2	4	no	—
607	C₂²×C₄	—	2	4	no	—
608	C₂²×C₄	—	2	4	no	—
609	C₂²×C₄	—	2	4	no	—
610	C₂²×C₄	—	2	48	no	—
611	C₂²×C₄	—	4	24	no	—
612	C₂²×C₄	—	316	24	no	—
613	C₂²×C₄	—	79	16	no	—
614	C₂²×C₄	—	79	6	no	—
615	C₂²×C₄	—	79	8	no	—
616	C₂²×C₄	—	79	6	no	—
617	C₂²×C₄	—	79	6	no	—
618	C₂²×C₄	—	79	6	no	—
619	C₂²×C₄	—	79	6	no	—
620	C₂²×C₄	—	79	16	no	—
621	C₂²×C₄	—	79	16	no	—
622	C₂²×C₄	—	79	16	no	—
623	C₂²×C₄	—	158	48	no	—
624	C₂²×C₄	—	158	48	no	—
625	C₂²×C₄	—	158	48	no	—
626	C₂²×C₄	—	158	4	no	—
627	C₂²×C₄	—	158	4	no	—
628	C₂²×C₄	—	158	4	no	—
629	C₂²×C₄	—	158	4	no	—
630	C₂²×C₄	C₂³×D₇₉	1	6	yes	—
631	C₂²×C₄	C₂³×D₇₉	1	6	yes	—
632	C₂²×C₄	C₂³×D₇₉	1	6	yes	—
633	C₂²×C₄	C₂³×D₇₉	1	6	yes	—
634	C₂²×C₄	C₂³×D₇₉	1	16	yes	complemented
635	C₂²×C₄	C₂³×D₇₉	1	16	yes	complemented
636	C₄⋊C₄	—	79	16	no	—
637	C₄⋊C₄	—	79	16	no	—
638	C₄⋊C₄	—	79	16	no	—
639	C₄⋊C₄	—	79	16	no	—
640	C₂²⋊C₄	—	79	16	no	—
641	C₂²⋊C₄	—	79	16	no	—
642	C₂²⋊C₄	—	79	16	no	—
643	C₂²⋊C₄	—	79	16	no	—
644	C₂²⋊C₄	—	79	16	no	—
645	C₂²⋊C₄	—	79	16	no	—
646	C₂²⋊C₄	—	79	16	no	—
647	C₂²⋊C₄	—	79	16	no	—
648	C₂²⋊C₄	C₂³×D₇₉	1	16	yes	—
649	C₂²⋊C₄	C₂³×D₇₉	1	16	yes	—
650	C₂²⋊C₄	C₂³×D₇₉	1	16	yes	complemented
651	C₂²⋊C₄	C₂³×D₇₉	1	16	yes	complemented
652	C₄²	—	79	16	no	—
653	C₂³	—	2	12	no	—
654	C₂³	—	2	12	no	—
655	C₂³	—	2	32	no	—
656	C₂³	—	2	32	no	—
657	C₂³	—	2	12	no	—
658	C₂³	—	2	12	no	—
659	C₂³	—	2	12	no	—
660	C₂³	—	2	32	no	—
661	C₂³	—	2	12	no	—
662	C₂³	—	2	12	no	—
663	C₂³	—	2	32	no	—
664	C₂³	—	4	16	no	—
665	C₂³	—	4	192	no	—
666	C₂³	—	4	16	no	—
667	C₂³	—	316	192	no	—
668	C₂³	—	316	16	no	—
669	C₂³	—	316	16	no	—
670	C₂³	—	316	16	no	—
671	C₂³	—	79	4	no	—
672	C₂³	—	79	24	no	—
673	C₂³	—	79	4	no	—
674	C₂³	—	79	4	no	—
675	C₂³	—	158	32	no	—
676	C₂³	—	158	12	no	—
677	C₂³	—	158	12	no	—
678	C₂³	—	158	12	no	—
679	C₂³	—	158	12	no	—
680	C₂³	—	158	12	no	—
681	C₂³	—	158	12	no	—
682	C₂³	—	158	32	no	—
683	C₂³	—	158	12	no	—
684	C₂³	—	158	32	no	—
685	C₂³	—	158	12	no	—
686	C₂³	C₂×D₄×D₇₉	1	24	yes	—
687	C₂³	C₂×D₄×D₇₉	1	4	yes	—
688	C₂³	C₂×#11929624	1	4	yes	—
689	C₂³	C₂×#11929624	1	24	yes	complemented
690	C₂³	#14579206	1	4	yes	—
691	C₂³	C₂⁴×D₇₉	1	4	yes	—
692	C₂³	C₂⁴×D₇₉	1	4	yes	—
693	C₂³	C₂⁴×D₇₉	1	4	yes	—
694	C₂³	C₂⁴×D₇₉	1	3	yes	—
695	Q₈	—	158	32	no	—
696	D₄	—	316	16	no	—
697	D₄	—	316	16	no	—
698	D₄	—	79	64	no	—
699	D₄	—	158	32	no	—
700	D₄	—	158	32	no	—
701	D₄	—	158	32	no	—
702	D₄	—	158	32	no	—
703	D₄	—	158	32	no	—
704	D₄	—	158	32	no	—
705	C₂×C₄	—	2	12	no	—
706	C₂×C₄	—	2	12	no	—
707	C₂×C₄	—	2	12	no	—
708	C₂×C₄	—	2	12	no	—
709	C₂×C₄	—	2	32	no	—
710	C₂×C₄	—	4	16	no	—
711	C₂×C₄	—	316	16	no	—
712	C₂×C₄	—	79	4	no	—
713	C₂×C₄	—	79	24	no	—
714	C₂×C₄	—	79	4	no	—
715	C₂×C₄	—	79	4	no	—
716	C₂×C₄	—	79	4	no	—
717	C₂×C₄	—	79	4	no	—
718	C₂×C₄	—	158	32	no	—
719	C₂×C₄	—	158	32	no	—
720	C₂×C₄	—	158	32	no	—
721	C₂×C₄	—	158	12	no	—
722	C₂×C₄	—	158	12	no	—
723	C₂×C₄	—	158	12	no	—
724	C₂×C₄	—	158	12	no	—
725	C₂×C₄	C₂⁴×D₇₉	1	4	yes	—
726	C₂×C₄	C₂⁴×D₇₉	1	4	yes	—
727	C₂×C₄	C₂⁴×D₇₉	1	4	yes	—
728	C₂×C₄	C₂⁴×D₇₉	1	4	yes	—
729	C₂²	—	2	48	no	—
730	C₂²	—	2	48	no	—
731	C₂²	—	2	4	no	—
732	C₂²	—	2	4	no	—
733	C₂²	—	2	4	no	—
734	C₂²	—	2	4	no	—
735	C₂²	—	2	4	no	—
736	C₂²	—	2	4	no	—
737	C₂²	—	2	4	no	—
738	C₂²	—	4	64	no	—
739	C₂²	—	4	24	no	—
740	C₂²	—	316	64	no	—
741	C₂²	—	316	24	no	—
742	C₂²	—	316	24	no	—
743	C₂²	—	79	8	no	—
744	C₂²	—	158	4	no	—
745	C₂²	—	158	4	no	—
746	C₂²	—	158	4	no	—
747	C₂²	—	158	4	no	—
748	C₂²	—	158	4	no	—
749	C₂²	—	158	4	no	—
750	C₂²	—	158	48	no	—
751	C₂²	—	158	4	no	—
752	C₂²	—	158	4	no	—
753	C₂²	#19099203	1	16	yes	direct product factor
754	C₂²	C₂²×D₄×D₇₉	1	8	yes	—
755	C₂²	C₂²×D₄×D₇₉	1	6	yes	—
756	C₂²	C₂²×#11929624	1	6	yes	—
757	C₂²	C₂²×#11929624	1	8	yes	complemented
758	C₂²	C₂×#14579206	1	6	yes	—
759	C₂²	C₂⁵×D₇₉	1	1	yes	characteristic
760	C₄	—	2	4	no	—
761	C₄	—	2	4	no	—
762	C₄	—	2	4	no	—
763	C₄	—	2	4	no	—
764	C₄	—	79	8	no	—
765	C₄	—	158	4	no	—
766	C₄	—	158	4	no	—
767	C₄	—	158	4	no	—
768	C₄	—	158	4	no	—
769	C₂	—	2	8	no	—
770	C₂	—	2	8	no	—
771	C₂	—	4	4	no	—
772	C₂	—	316	4	no	—
773	C₂	—	316	4	no	—
774	C₂	—	158	8	no	—
775	C₂	C₂×#19099203	1	12	yes	direct product factor
776	C₂	C₂³×D₄×D₇₉	1	1	yes	characteristic
777	C₂	C₂³×#11929624	1	1	yes	characteristic
778	C₂	C₂²×#14579206	1	1	yes	characteristic

	subgroup	G/H
center	C₂⁴	C₂³×D₇₉
commutator, cosocle	C₂²×C₇₉	C₂⁶
Frattini	C₂²	C₂⁵×D₇₉
Fitting	C₂³×C₂²⋊C₄×C₇₉	C₂
socle	C₂⁴×C₇₉	C₂⁴
hypercenter	C₂³×C₂²⋊C₄	D₇₉
hypocenter	C₇₉	C₂²×#546
LCS	G ▷ C₂²×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂⁴ ◁ C₂³×C₂²⋊C₄

Complements

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

N	H ≅ G/N	type
1. C₂³×#11929624	C₂	semidirect
2. C₂⁴×C₂²⋊D₇₉	C₂	semidirect
3. C₂×#19099203	C₂	direct (N × H)
4. C₂²×#14579147	C₂	semidirect
5. C₂²×#14579144	C₂	semidirect
6. C₂²×#14579143	C₂	semidirect
7. C₂²×#14579138	C₂	semidirect
8. C₂²×#14579135	C₂	semidirect
9. C₂²×#14579134	C₂	semidirect
10. C₂²×#14579134	C₂	semidirect
11. C₂²×#14579131	C₂	semidirect
12. C₂²×#14579130	C₂	semidirect
13. C₂²×C₄×C₂²⋊D₇₉	C₂	semidirect
14. C₂²×(C₂²⋊D₇₉)⋊C₄	C₂	semidirect
15. C₂²×C₂²⋊C₄×D₇₉	C₂	semidirect
16. C₂³×C₂²⋊C₄×C₇₉	C₂	semidirect
19. C₂²×#11929624	C₂²	semidirect
20. C₂³×Dic₁₅₈	C₂²	semidirect
21. C₂³×D₃₁₆	C₂²	semidirect
22. C₂³×D₃₁₆	C₂²	semidirect
29. C₂³×C₂²⋊D₇₉	C₂²	semidirect
30. C₂³×C₂²⋊D₇₉	C₂²	semidirect
31. C₂³×C₂²⋊D₇₉	C₂²	semidirect
33. C₂³×C₄×D₇₉	C₂²	semidirect
34. C₂³×C₄×D₇₉	C₂²	semidirect
35. C₂³×C₄×D₇₉	C₂²	semidirect
36. #19099203	C₂²	direct (N × H)
37. C₂×#14579147	C₂²	semidirect
38. C₂×#14579144	C₂²	semidirect
39. C₂×#14579143	C₂²	semidirect
40. C₂×#14579138	C₂²	semidirect
41. C₂×#14579135	C₂²	semidirect
42. C₂×#14579134	C₂²	semidirect
43. C₂×#14579134	C₂²	semidirect
44. C₂×#14579131	C₂²	semidirect
45. C₂×#14579130	C₂²	semidirect
46. C₂×C₄×C₂²⋊D₇₉	C₂²	semidirect
47. C₂×(C₂²⋊D₇₉)⋊C₄	C₂²	semidirect
48. C₂²×C₄⋊Dic₇₉	C₂²	semidirect
49. C₂²×Dic₇₉⋊C₄	C₂²	semidirect
50. C₂²×Dic₇₉⋊C₄	C₂²	semidirect
51. C₂²×Dic₇₉⋊C₄	C₂²	semidirect
53. C₂²×C₂²⋊Dic₇₉	C₂²	semidirect
54. C₂²×C₂²⋊Dic₇₉	C₂²	semidirect
55. C₂²×(C₂×D₇₉)⋊C₄	C₂²	semidirect
56. C₂²×(C₂×D₇₉)⋊C₄	C₂²	semidirect
57. C₂²×(C₂×D₇₉)⋊C₄	C₂²	semidirect
58. C₂²×(C₂×D₇₉)⋊C₄	C₂²	semidirect
59. C₂²×(C₂×D₇₉)⋊C₄	C₂²	semidirect
60. C₂×C₂²⋊C₄×D₇₉	C₂²	semidirect
61. C₂²×C₄×Dic₇₉	C₂²	semidirect
63. C₂⁴×C₄×C₇₉	C₂²	semidirect
64. C₂⁴×C₄×C₇₉	C₂²	semidirect
67. C₂²×C₂²⋊C₄×C₇₉	C₂²	semidirect
68. C₂²×C₂²⋊C₄×C₇₉	C₂²	semidirect
69. C₂²×C₂²⋊C₄×C₇₉	C₂²	semidirect
78. C₂×#11929624	C₂³	semidirect
80. C₂²×Dic₁₅₈	C₂³	semidirect
83. C₂²×D₃₁₆	C₂³	semidirect
84. C₂²×D₃₁₆	C₂³	semidirect
92. C₂²×C₂²⋊D₇₉	D₄	semidirect
98. C₂²×C₂²⋊D₇₉	C₂³	semidirect
99. C₂²×C₂²⋊D₇₉	C₂³	semidirect
100. C₂²×C₂²⋊D₇₉	C₂³	semidirect
111. C₂²×C₄×D₇₉	C₂³	semidirect
112. C₂²×C₄×D₇₉	C₂³	semidirect
113. C₂²×C₄×D₇₉	C₂³	semidirect
114. #14579147	C₂³	semidirect
115. #14579144	C₂³	semidirect
116. #14579143	C₂³	semidirect
117. #14579138	C₂³	semidirect
118. #14579135	C₂³	semidirect
119. #14579134	C₂³	semidirect
120. #14579134	C₂³	semidirect
121. #14579131	C₂³	semidirect
122. #14579130	C₂³	semidirect
123. C₄×C₂²⋊D₇₉	C₂³	semidirect
124. (C₂²⋊D₇₉)⋊C₄	C₂³	semidirect
125. C₂×C₄⋊Dic₇₉	C₂³	semidirect
126. C₂×Dic₇₉⋊C₄	C₂³	semidirect
127. C₂×Dic₇₉⋊C₄	C₂³	semidirect
128. C₂×Dic₇₉⋊C₄	C₂³	semidirect
130. C₂×C₂²⋊Dic₇₉	C₂³	semidirect
131. C₂×C₂²⋊Dic₇₉	C₂³	semidirect
132. C₂×(C₂×D₇₉)⋊C₄	C₂³	semidirect
133. C₂×(C₂×D₇₉)⋊C₄	C₂³	semidirect
134. C₂×(C₂×D₇₉)⋊C₄	C₂³	semidirect
135. C₂×(C₂×D₇₉)⋊C₄	C₂³	semidirect
136. C₂×(C₂×D₇₉)⋊C₄	C₂³	semidirect
137. C₂²⋊C₄×D₇₉	C₂³	semidirect
138. C₂×C₄×Dic₇₉	C₂³	semidirect
152. C₂³×C₄×C₇₉	C₂³	semidirect
153. C₂³×C₄×C₇₉	C₂³	semidirect
156. C₂×C₂²⋊C₄×C₇₉	C₂³	semidirect
157. C₂×C₂²⋊C₄×C₇₉	C₂³	semidirect
158. C₂×C₂²⋊C₄×C₇₉	C₂³	semidirect
178. C₂×Dic₁₅₈	C₂⁴	semidirect
181. C₂×D₃₁₆	C₂⁴	semidirect
182. C₂×D₃₁₆	C₂⁴	semidirect
190. C₂×C₂²⋊D₇₉	C₂×D₄	semidirect
196. C₂×C₂²⋊D₇₉	C₂⁴	semidirect
197. C₂×C₂²⋊D₇₉	C₂⁴	semidirect
213. C₂×C₄×D₇₉	C₂⁴	semidirect
214. C₂×C₄×D₇₉	C₂⁴	semidirect
215. C₂×C₄×D₇₉	C₂⁴	semidirect
216. C₄⋊Dic₇₉	C₂⁴	semidirect
217. Dic₇₉⋊C₄	C₂⁴	semidirect
218. Dic₇₉⋊C₄	C₂⁴	semidirect
219. Dic₇₉⋊C₄	C₂⁴	semidirect
221. C₂²⋊Dic₇₉	C₂⁴	semidirect
222. C₂²⋊Dic₇₉	C₂⁴	semidirect
223. (C₂×D₇₉)⋊C₄	C₂⁴	semidirect
224. (C₂×D₇₉)⋊C₄	C₂⁴	semidirect
225. (C₂×D₇₉)⋊C₄	C₂⁴	semidirect
226. (C₂×D₇₉)⋊C₄	C₂⁴	semidirect
227. (C₂×D₇₉)⋊C₄	C₂⁴	semidirect
228. C₄×Dic₇₉	C₂⁴	semidirect
241. C₂⁴×C₇₉	#41	semidirect
257. C₂²×C₄×C₇₉	C₂⁴	semidirect
258. C₂²×C₄×C₇₉	C₂⁴	semidirect
261. C₂²⋊C₄×C₇₉	C₂⁴	semidirect
262. C₂²⋊C₄×C₇₉	C₂⁴	semidirect
280. C₂³×C₇₉	C₂×#41	semidirect
321. C₂²⋊D₇₉	C₂²×D₄	semidirect
350. C₂²×C₇₉	#546	semidirect
354. C₂²×C₇₉	C₂²×#41	semidirect
383. C₂×C₇₉	C₂×#546	semidirect
405. C₂³×C₂²⋊C₄	D₇₉	semidirect
406. C₇₉	C₂²×#546	semidirect
427. C₂⁴×C₄	C₂×D₇₉	semidirect
428. C₂⁴×C₄	C₂×D₇₉	semidirect
456. C₂²×C₂²⋊C₄	C₂×D₇₉	semidirect
457. C₂²×C₂²⋊C₄	C₂×D₇₉	semidirect
458. C₂²×C₂²⋊C₄	C₂×D₇₉	semidirect
517. C₂³×C₄	C₂²×D₇₉	semidirect
518. C₂³×C₄	C₂²×D₇₉	semidirect
545. C₂×C₂²⋊C₄	C₂²×D₇₉	semidirect
546. C₂×C₂²⋊C₄	C₂²×D₇₉	semidirect
547. C₂×C₂²⋊C₄	C₂²×D₇₉	semidirect
578. C₂⁴	#11929624	semidirect
634. C₂²×C₄	C₂³×D₇₉	semidirect
635. C₂²×C₄	C₂³×D₇₉	semidirect
650. C₂²⋊C₄	C₂³×D₇₉	semidirect
651. C₂²⋊C₄	C₂³×D₇₉	semidirect
689. C₂³	C₂×#11929624	semidirect
753. C₂²	#19099203	direct (N × H)
757. C₂²	C₂²×#11929624	semidirect
775. C₂	C₂×#19099203	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
C₂⁴×C₂²⋊D₇₉	2
C₂×#19099203	2
C₂²×#14579147	2
C₂²×#14579144	2
C₂²×#14579143	2
C₂²×#14579138	2
C₂²×#14579135	2
C₂²×#14579134	2
C₂²×#14579131	2
C₂²×#14579130	2
C₂²×C₄×C₂²⋊D₇₉	2
C₂²×(C₂²⋊D₇₉)⋊C₄	2
C₂²×C₂²⋊C₄×D₇₉	2
C₂³×C₂²⋊C₄×C₇₉	2
C₂²×#546	79

Subgroups — C22×#19099203 #35195191

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×#19099203 #35195191