Subgroups — C₇₃×#23860 #32933264

Order 18688.

2240 conjugacy classes of subgroups.

The subgroup lattice has 1088 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×AGL(1,ℤ/8)×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×D₄²×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#449×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#450×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#447×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
6	C₇₃×#2407	C₂	1	1	yes	maximal, characteristic, complemented
7	C₇₃×#2014	C₂	1	1	yes	maximal, characteristic, complemented
8	C₇₃×#2011	C₂	1	1	yes	maximal, characteristic, complemented
9	C₇₃×#2000	C₂	1	1	yes	maximal, characteristic, complemented
10	C₇₃×#1999	C₂	1	1	yes	maximal, characteristic, complemented
11	C₇₃×#1895	C₂	1	1	yes	maximal, characteristic, complemented
12	C₇₃×#1879	C₂	1	1	yes	maximal, characteristic, complemented
13	C₇₃×#1877	C₂	1	1	yes	maximal, characteristic, complemented
14	C₇₃×#1870	C₂	1	1	yes	maximal, characteristic, complemented
15	C₇₃×#1786	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×#41×C₇₃	C₂²	1	1	yes	characteristic, complemented
17	C₂³×D₄×C₇₃	—	2	1	no	—
18	C₂³×D₄×C₇₃	C₂²	1	1	yes	characteristic
19	C₂³×D₄×C₇₃	C₂²	1	1	yes	characteristic
20	C₂×AGL(1,ℤ/8)×C₇₃	—	2	4	no	—
21	C₂×AGL(1,ℤ/8)×C₇₃	—	2	4	no	—
22	C₂×AGL(1,ℤ/8)×C₇₃	—	2	4	no	—
23	C₂²×SD₁₆×C₇₃	C₂²	1	1	yes	characteristic
24	C₂²×SD₁₆×C₇₃	C₂²	1	1	yes	characteristic, complemented
25	C₂²×SD₁₆×C₇₃	C₂²	1	1	yes	characteristic, complemented
26	C₂²×D₈×C₇₃	C₂²	1	1	yes	characteristic
27	C₂²×D₈×C₇₃	C₂²	1	1	yes	characteristic, complemented
28	C₂²×D₈×C₇₃	C₂²	1	1	yes	characteristic, complemented
29	C₂²×M₁₆×C₇₃	C₂²	1	1	yes	characteristic, complemented
30	D₄²×C₇₃	—	2	4	no	—
31	D₄²×C₇₃	—	2	4	no	—
32	C₂×#127×C₇₃	C₂²	1	1	yes	characteristic
33	C₂×C₂²⋊Q₈×C₇₃	C₂²	1	1	yes	characteristic, complemented
34	C₂×#121×C₇₃	—	2	1	no	—
35	C₂×#121×C₇₃	C₂²	1	1	yes	characteristic
36	C₂×#121×C₇₃	C₂²	1	1	yes	characteristic
37	C₂×#121×C₇₃	C₂²	1	1	yes	characteristic, complemented
38	C₂×#120×C₇₃	—	2	1	no	—
39	C₂×#120×C₇₃	—	2	1	no	—
40	C₂×C₄×D₄×C₇₃	C₂²	1	1	yes	characteristic
41	C₂×C₄×D₄×C₇₃	C₂²	1	1	yes	characteristic
42	#450×C₇₃	—	2	4	no	—
43	#449×C₇₃	—	2	4	no	—
44	#447×C₇₃	—	2	4	no	—
45	C₂×#103×C₇₃	C₂²	1	1	yes	characteristic, complemented
46	C₂×#102×C₇₃	C₂²	1	1	yes	characteristic
47	C₂×#102×C₇₃	C₂²	1	1	yes	characteristic
48	C₂×#102×C₇₃	C₂²	1	1	yes	characteristic, complemented
49	C₂×#102×C₇₃	C₂²	1	1	yes	characteristic, complemented
50	C₂×#102×C₇₃	C₂²	1	1	yes	characteristic, complemented
51	C₂×#102×C₇₃	C₂²	1	1	yes	characteristic, complemented
52	C₂×#102×C₇₃	C₂²	1	1	yes	characteristic, complemented
53	C₂×C₂²⋊C₈×C₇₃	C₂²	1	1	yes	characteristic, complemented
54	C₂×C₂²⋊C₈×C₇₃	C₂²	1	1	yes	characteristic, complemented
55	C₂×C₂²⋊C₈×C₇₃	C₂²	1	1	yes	characteristic, complemented
56	#394×C₇₃	—	2	1	no	—
57	#392×C₇₃	—	2	1	no	—
58	#391×C₇₃	C₂²	1	1	yes	characteristic, complemented
59	#390×C₇₃	C₂²	1	1	yes	characteristic, complemented
60	#386×C₇₃	—	2	1	no	—
61	#385×C₇₃	—	2	1	no	—
62	#380×C₇₃	C₂²	1	1	yes	characteristic, complemented
63	#340×C₇₃	C₂²	1	1	yes	characteristic, complemented
64	#340×C₇₃	C₂²	1	1	yes	characteristic, complemented
65	#336×C₇₃	C₂²	1	1	yes	characteristic, complemented
66	#336×C₇₃	C₂²	1	1	yes	characteristic, complemented
67	C₂⁵×C₇₃	—	2	1	no	—
68	C₂⁵×C₇₃	—	2	1	no	—
69	C₂×#41×C₇₃	—	2	2	no	—
70	C₂×#41×C₇₃	—	2	2	no	—
71	C₂×#41×C₇₃	—	2	2	no	—
72	C₂×#41×C₇₃	—	2	2	no	—
73	C₂×#41×C₇₃	—	4	1	no	—
74	C₂×#41×C₇₃	—	4	1	no	—
75	C₂²×Q₈×C₇₃	C₂³	1	1	yes	characteristic
76	C₂²×D₄×C₇₃	—	2	2	no	—
77	C₂²×D₄×C₇₃	—	2	2	no	—
78	C₂²×D₄×C₇₃	—	2	8	no	—
79	C₂²×D₄×C₇₃	—	2	1	no	—
80	C₂²×D₄×C₇₃	—	2	1	no	—
81	C₂²×D₄×C₇₃	—	2	2	no	—
82	C₂²×D₄×C₇₃	—	2	2	no	—
83	C₂²×D₄×C₇₃	—	2	2	no	—
84	C₂²×D₄×C₇₃	—	2	2	no	—
85	C₂²×D₄×C₇₃	—	2	1	no	—
86	C₂²×D₄×C₇₃	—	2	1	no	—
87	C₂²×D₄×C₇₃	—	2	1	no	—
88	C₂²×D₄×C₇₃	—	2	1	no	—
89	C₂²×D₄×C₇₃	—	2	1	no	—
90	C₂²×D₄×C₇₃	—	2	2	no	—
91	C₂²×D₄×C₇₃	—	2	1	no	—
92	C₂²×D₄×C₇₃	—	4	1	no	—
93	C₂²×D₄×C₇₃	—	4	1	no	—
94	C₂²×D₄×C₇₃	—	4	1	no	—
95	C₂²×D₄×C₇₃	—	4	1	no	—
96	C₂²×D₄×C₇₃	—	4	4	no	—
97	C₂²×D₄×C₇₃	—	4	4	no	—
98	C₂²×D₄×C₇₃	D₄	1	1	yes	characteristic
99	C₂²×D₄×C₇₃	D₄	1	4	yes	complemented
100	C₂²×D₄×C₇₃	C₂³	1	1	yes	characteristic
101	C₂²×D₄×C₇₃	C₂³	1	1	yes	characteristic
102	C₂²×D₄×C₇₃	C₂³	1	1	yes	characteristic
103	C₂²×D₄×C₇₃	C₂³	1	1	yes	characteristic
104	C₂³×C₄×C₇₃	—	2	1	no	—
105	C₂³×C₄×C₇₃	—	2	1	no	—
106	C₂³×C₄×C₇₃	C₂³	1	1	yes	characteristic
107	C₂³×C₄×C₇₃	C₂³	1	1	yes	characteristic
108	AGL(1,ℤ/8)×C₇₃	—	2	32	no	—
109	C₂×SD₁₆×C₇₃	—	2	2	no	—
110	C₂×SD₁₆×C₇₃	—	2	2	no	—
111	C₂×SD₁₆×C₇₃	—	2	2	no	—
112	C₂×SD₁₆×C₇₃	—	2	2	no	—
113	C₂×SD₁₆×C₇₃	—	2	2	no	—
114	C₂×SD₁₆×C₇₃	—	2	2	no	—
115	C₂×SD₁₆×C₇₃	—	2	2	no	—
116	C₂×SD₁₆×C₇₃	—	4	1	no	—
117	C₂×SD₁₆×C₇₃	D₄	1	4	yes	complemented
118	C₂×D₈×C₇₃	—	2	2	no	—
119	C₂×D₈×C₇₃	—	2	2	no	—
120	C₂×D₈×C₇₃	—	2	2	no	—
121	C₂×D₈×C₇₃	—	2	2	no	—
122	C₂×D₈×C₇₃	—	2	2	no	—
123	C₂×D₈×C₇₃	—	2	2	no	—
124	C₂×D₈×C₇₃	—	2	2	no	—
125	C₂×D₈×C₇₃	—	4	1	no	—
126	C₂×D₈×C₇₃	D₄	1	4	yes	complemented
127	C₂×M₁₆×C₇₃	—	2	2	no	—
128	C₂×M₁₆×C₇₃	—	2	2	no	—
129	C₂×M₁₆×C₇₃	—	2	2	no	—
130	C₂²×C₈×C₇₃	C₂³	1	1	yes	characteristic
131	C₂²×C₈×C₇₃	C₂³	1	1	yes	characteristic
132	C₂²×C₈×C₇₃	C₂³	1	1	yes	characteristic
133	C₂²×C₈×C₇₃	C₂³	1	1	yes	characteristic
134	#127×C₇₃	—	2	2	no	—
135	#127×C₇₃	—	2	2	no	—
136	C₂²⋊Q₈×C₇₃	—	2	2	no	—
137	C₂²⋊Q₈×C₇₃	—	4	1	no	—
138	#121×C₇₃	—	2	8	no	—
139	#121×C₇₃	—	2	2	no	—
140	#121×C₇₃	—	2	2	no	—
141	#121×C₇₃	—	2	2	no	—
142	#121×C₇₃	—	2	2	no	—
143	#121×C₇₃	—	4	1	no	—
144	#121×C₇₃	D₄	1	4	yes	complemented
145	#120×C₇₃	—	2	8	no	—
146	#120×C₇₃	—	2	8	no	—
147	C₄×D₄×C₇₃	—	2	2	no	—
148	C₄×D₄×C₇₃	—	2	2	no	—
149	C₄×D₄×C₇₃	—	2	2	no	—
150	C₄×D₄×C₇₃	—	2	2	no	—
151	C₂×C₄⋊C₄×C₇₃	—	2	1	no	—
152	C₂×C₄⋊C₄×C₇₃	D₄	1	1	yes	characteristic
153	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
154	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
155	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
156	C₂×C₂²⋊C₄×C₇₃	—	2	1	no	—
157	C₂×C₂²⋊C₄×C₇₃	—	2	1	no	—
158	C₂×C₂²⋊C₄×C₇₃	—	2	1	no	—
159	C₂×C₂²⋊C₄×C₇₃	—	2	1	no	—
160	C₂×C₂²⋊C₄×C₇₃	—	2	1	no	—
161	C₂×C₂²⋊C₄×C₇₃	—	2	1	no	—
162	C₂×C₂²⋊C₄×C₇₃	—	2	1	no	—
163	C₂×C₂²⋊C₄×C₇₃	—	2	1	no	—
164	C₂×C₂²⋊C₄×C₇₃	D₄	1	1	yes	characteristic
165	C₂×C₂²⋊C₄×C₇₃	D₄	1	1	yes	characteristic
166	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
167	#103×C₇₃	—	2	2	no	—
168	#102×C₇₃	—	2	2	no	—
169	#102×C₇₃	—	2	2	no	—
170	#102×C₇₃	—	2	2	no	—
171	#102×C₇₃	—	2	2	no	—
172	#102×C₇₃	—	2	2	no	—
173	#102×C₇₃	—	4	1	no	—
174	#102×C₇₃	—	4	1	no	—
175	C₂²⋊C₈×C₇₃	—	2	2	no	—
176	C₂²⋊C₈×C₇₃	—	2	2	no	—
177	C₂²⋊C₈×C₇₃	—	2	2	no	—
178	#95×C₇₃	—	2	1	no	—
179	#95×C₇₃	—	2	1	no	—
180	#95×C₇₃	—	2	1	no	—
181	C₂⁴×C₇₃	—	2	1	no	—
182	C₂⁴×C₇₃	—	2	4	no	—
183	C₂⁴×C₇₃	—	2	1	no	—
184	C₂⁴×C₇₃	—	2	1	no	—
185	C₂⁴×C₇₃	—	2	1	no	—
186	C₂⁴×C₇₃	—	2	4	no	—
187	C₂⁴×C₇₃	—	4	2	no	—
188	C₂⁴×C₇₃	—	4	2	no	—
189	C₂⁴×C₇₃	—	4	2	no	—
190	C₂⁴×C₇₃	—	4	2	no	—
191	C₂⁴×C₇₃	—	4	2	no	—
192	C₂⁴×C₇₃	—	4	2	no	—
193	C₂⁴×C₇₃	—	4	2	no	—
194	C₂⁴×C₇₃	—	4	2	no	—
195	C₂⁴×C₇₃	—	8	1	no	—
196	C₂⁴×C₇₃	—	8	1	no	—
197	C₂⁴×C₇₃	—	8	1	no	—
198	C₂⁴×C₇₃	—	8	1	no	—
199	C₂⁴×C₇₃	C₂×D₄	1	1	yes	characteristic
200	C₂⁴×C₇₃	C₂×D₄	1	1	yes	characteristic
201	#41×C₇₃	—	2	8	no	—
202	#41×C₇₃	—	4	4	no	—
203	#41×C₇₃	—	4	4	no	—
204	#41×C₇₃	—	4	4	no	—
205	C₂×Q₈×C₇₃	—	2	1	no	—
206	C₂×Q₈×C₇₃	—	2	1	no	—
207	C₂×Q₈×C₇₃	—	2	1	no	—
208	C₂×Q₈×C₇₃	—	2	1	no	—
209	C₂×Q₈×C₇₃	—	2	1	no	—
210	C₂×Q₈×C₇₃	C₂×D₄	1	2	yes	complemented
211	C₂×D₄×C₇₃	—	2	2	no	—
212	C₂×D₄×C₇₃	—	2	2	no	—
213	C₂×D₄×C₇₃	—	2	8	no	—
214	C₂×D₄×C₇₃	—	2	4	no	—
215	C₂×D₄×C₇₃	—	2	4	no	—
216	C₂×D₄×C₇₃	—	2	4	no	—
217	C₂×D₄×C₇₃	—	2	4	no	—
218	C₂×D₄×C₇₃	—	2	4	no	—
219	C₂×D₄×C₇₃	—	2	4	no	—
220	C₂×D₄×C₇₃	—	2	2	no	—
221	C₂×D₄×C₇₃	—	2	1	no	—
222	C₂×D₄×C₇₃	—	2	1	no	—
223	C₂×D₄×C₇₃	—	2	1	no	—
224	C₂×D₄×C₇₃	—	2	1	no	—
225	C₂×D₄×C₇₃	—	2	1	no	—
226	C₂×D₄×C₇₃	—	2	1	no	—
227	C₂×D₄×C₇₃	—	2	1	no	—
228	C₂×D₄×C₇₃	—	2	1	no	—
229	C₂×D₄×C₇₃	—	2	1	no	—
230	C₂×D₄×C₇₃	—	2	1	no	—
231	C₂×D₄×C₇₃	—	2	1	no	—
232	C₂×D₄×C₇₃	—	2	1	no	—
233	C₂×D₄×C₇₃	—	2	1	no	—
234	C₂×D₄×C₇₃	—	2	1	no	—
235	C₂×D₄×C₇₃	—	2	1	no	—
236	C₂×D₄×C₇₃	—	2	1	no	—
237	C₂×D₄×C₇₃	—	2	1	no	—
238	C₂×D₄×C₇₃	—	2	1	no	—
239	C₂×D₄×C₇₃	—	4	4	no	—
240	C₂×D₄×C₇₃	—	4	4	no	—
241	C₂×D₄×C₇₃	—	4	4	no	—
242	C₂×D₄×C₇₃	—	4	2	no	—
243	C₂×D₄×C₇₃	—	4	2	no	—
244	C₂×D₄×C₇₃	—	4	2	no	—
245	C₂×D₄×C₇₃	—	4	2	no	—
246	C₂×D₄×C₇₃	—	4	2	no	—
247	C₂×D₄×C₇₃	—	4	2	no	—
248	C₂×D₄×C₇₃	—	4	4	no	—
249	C₂×D₄×C₇₃	—	4	4	no	—
250	C₂×D₄×C₇₃	—	4	32	no	—
251	C₂×D₄×C₇₃	—	4	4	no	—
252	C₂×D₄×C₇₃	—	4	2	no	—
253	C₂×D₄×C₇₃	—	4	2	no	—
254	C₂×D₄×C₇₃	—	4	2	no	—
255	C₂×D₄×C₇₃	—	4	2	no	—
256	C₂×D₄×C₇₃	—	4	2	no	—
257	C₂×D₄×C₇₃	—	4	2	no	—
258	C₂×D₄×C₇₃	—	4	4	no	—
259	C₂×D₄×C₇₃	—	4	2	no	—
260	C₂×D₄×C₇₃	—	4	2	no	—
261	C₂×D₄×C₇₃	—	4	2	no	—
262	C₂×D₄×C₇₃	—	8	1	no	—
263	C₂×D₄×C₇₃	—	8	1	no	—
264	C₂×D₄×C₇₃	—	8	1	no	—
265	C₂×D₄×C₇₃	C₂×D₄	1	2	yes	—
266	C₂×D₄×C₇₃	C₂×D₄	1	2	yes	—
267	C₂×D₄×C₇₃	C₂×D₄	1	2	yes	—
268	C₂×D₄×C₇₃	C₂×D₄	1	2	yes	—
269	C₂×D₄×C₇₃	C₂×D₄	1	2	yes	—
270	C₂×D₄×C₇₃	C₂×D₄	1	2	yes	complemented
271	C₂²×C₄×C₇₃	—	2	1	no	—
272	C₂²×C₄×C₇₃	—	2	1	no	—
273	C₂²×C₄×C₇₃	—	2	1	no	—
274	C₂²×C₄×C₇₃	—	2	1	no	—
275	C₂²×C₄×C₇₃	—	2	4	no	—
276	C₂²×C₄×C₇₃	—	2	1	no	—
277	C₂²×C₄×C₇₃	—	2	1	no	—
278	C₂²×C₄×C₇₃	—	2	1	no	—
279	C₂²×C₄×C₇₃	—	2	1	no	—
280	C₂²×C₄×C₇₃	—	2	1	no	—
281	C₂²×C₄×C₇₃	—	2	1	no	—
282	C₂²×C₄×C₇₃	—	2	1	no	—
283	C₂²×C₄×C₇₃	—	2	1	no	—
284	C₂²×C₄×C₇₃	—	2	1	no	—
285	C₂²×C₄×C₇₃	—	2	1	no	—
286	C₂²×C₄×C₇₃	—	4	2	no	—
287	C₂²×C₄×C₇₃	—	4	2	no	—
288	C₂²×C₄×C₇₃	—	4	2	no	—
289	C₂²×C₄×C₇₃	—	4	2	no	—
290	C₂²×C₄×C₇₃	—	4	2	no	—
291	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
292	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
293	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
294	C₂²×C₄×C₇₃	C₂×D₄	1	2	yes	—
295	C₂²×C₄×C₇₃	C₂×D₄	1	2	yes	—
296	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
297	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
298	SD₁₆×C₇₃	—	2	8	no	—
299	SD₁₆×C₇₃	—	2	8	no	—
300	SD₁₆×C₇₃	—	4	4	no	—
301	D₈×C₇₃	—	2	8	no	—
302	D₈×C₇₃	—	2	8	no	—
303	D₈×C₇₃	—	4	4	no	—
304	M₁₆×C₇₃	—	2	8	no	—
305	C₂×C₈×C₇₃	—	2	1	no	—
306	C₂×C₈×C₇₃	—	2	1	no	—
307	C₂×C₈×C₇₃	—	2	1	no	—
308	C₂×C₈×C₇₃	—	2	1	no	—
309	C₂×C₈×C₇₃	—	2	1	no	—
310	C₂×C₈×C₇₃	—	2	1	no	—
311	C₂×C₈×C₇₃	—	2	1	no	—
312	C₂×C₈×C₇₃	—	2	1	no	—
313	C₂×C₈×C₇₃	—	2	1	no	—
314	C₂×C₈×C₇₃	—	2	1	no	—
315	C₂×C₈×C₇₃	C₂×D₄	1	2	yes	complemented
316	C₂×C₈×C₇₃	C₂×D₄	1	2	yes	complemented
317	C₄⋊C₄×C₇₃	—	2	2	no	—
318	C₄⋊C₄×C₇₃	—	2	1	no	—
319	C₄⋊C₄×C₇₃	—	2	1	no	—
320	C₄⋊C₄×C₇₃	—	2	1	no	—
321	C₄⋊C₄×C₇₃	—	2	1	no	—
322	C₄⋊C₄×C₇₃	—	2	1	no	—
323	C₄⋊C₄×C₇₃	—	4	2	no	—
324	C₄⋊C₄×C₇₃	C₂×D₄	1	2	yes	—
325	C₂²⋊C₄×C₇₃	—	2	4	no	—
326	C₂²⋊C₄×C₇₃	—	2	4	no	—
327	C₂²⋊C₄×C₇₃	—	2	2	no	—
328	C₂²⋊C₄×C₇₃	—	2	4	no	—
329	C₂²⋊C₄×C₇₃	—	2	2	no	—
330	C₂²⋊C₄×C₇₃	—	4	2	no	—
331	C₂²⋊C₄×C₇₃	—	4	2	no	—
332	C₂²⋊C₄×C₇₃	—	4	2	no	—
333	C₂²⋊C₄×C₇₃	—	8	1	no	—
334	C₂²⋊C₄×C₇₃	—	8	1	no	—
335	C₄²×C₇₃	—	2	1	no	—
336	C₄²×C₇₃	—	2	1	no	—
337	C₂³×C₇₃	—	2	1	no	—
338	C₂³×C₇₃	—	2	2	no	—
339	C₂³×C₇₃	—	2	1	no	—
340	C₂³×C₇₃	—	2	1	no	—
341	C₂³×C₇₃	—	2	1	no	—
342	C₂³×C₇₃	—	2	1	no	—
343	C₂³×C₇₃	—	2	2	no	—
344	C₂³×C₇₃	—	2	2	no	—
345	C₂³×C₇₃	—	2	1	no	—
346	C₂³×C₇₃	—	2	1	no	—
347	C₂³×C₇₃	—	2	1	no	—
348	C₂³×C₇₃	—	2	1	no	—
349	C₂³×C₇₃	—	2	1	no	—
350	C₂³×C₇₃	—	2	1	no	—
351	C₂³×C₇₃	—	2	1	no	—
352	C₂³×C₇₃	—	2	2	no	—
353	C₂³×C₇₃	—	2	2	no	—
354	C₂³×C₇₃	—	2	2	no	—
355	C₂³×C₇₃	—	4	8	no	—
356	C₂³×C₇₃	—	4	8	no	—
357	C₂³×C₇₃	—	4	8	no	—
358	C₂³×C₇₃	—	4	8	no	—
359	C₂³×C₇₃	—	4	1	no	—
360	C₂³×C₇₃	—	4	1	no	—
361	C₂³×C₇₃	—	4	1	no	—
362	C₂³×C₇₃	—	4	1	no	—
363	C₂³×C₇₃	—	4	1	no	—
364	C₂³×C₇₃	—	4	1	no	—
365	C₂³×C₇₃	—	4	1	no	—
366	C₂³×C₇₃	—	4	1	no	—
367	C₂³×C₇₃	—	4	1	no	—
368	C₂³×C₇₃	—	4	1	no	—
369	C₂³×C₇₃	—	4	1	no	—
370	C₂³×C₇₃	—	4	1	no	—
371	C₂³×C₇₃	—	4	1	no	—
372	C₂³×C₇₃	—	4	1	no	—
373	C₂³×C₇₃	—	4	1	no	—
374	C₂³×C₇₃	—	4	1	no	—
375	C₂³×C₇₃	—	4	1	no	—
376	C₂³×C₇₃	—	4	1	no	—
377	C₂³×C₇₃	—	4	1	no	—
378	C₂³×C₇₃	—	4	1	no	—
379	C₂³×C₇₃	—	4	1	no	—
380	C₂³×C₇₃	—	4	1	no	—
381	C₂³×C₇₃	—	8	4	no	—
382	C₂³×C₇₃	—	8	4	no	—
383	C₂³×C₇₃	—	8	4	no	—
384	C₂³×C₇₃	—	8	4	no	—
385	C₂³×C₇₃	—	8	4	no	—
386	C₂³×C₇₃	—	8	4	no	—
387	C₂³×C₇₃	—	8	4	no	—
388	C₂³×C₇₃	—	8	4	no	—
389	C₂³×C₇₃	—	8	4	no	—
390	C₂³×C₇₃	—	8	4	no	—
391	C₂³×C₇₃	#120	1	2	yes	—
392	C₂³×C₇₃	AGL(1,ℤ/8)	1	2	yes	complemented
393	C₂³×C₇₃	C₂²×D₄	1	1	yes	characteristic
394	Q₈×C₇₃	—	2	2	no	—
395	Q₈×C₇₃	—	2	2	no	—
396	Q₈×C₇₃	—	4	1	no	—
397	Q₈×C₇₃	—	4	1	no	—
398	D₄×C₇₃	—	2	8	no	—
399	D₄×C₇₃	—	2	2	no	—
400	D₄×C₇₃	—	2	2	no	—
401	D₄×C₇₃	—	2	2	no	—
402	D₄×C₇₃	—	2	2	no	—
403	D₄×C₇₃	—	2	2	no	—
404	D₄×C₇₃	—	2	2	no	—
405	D₄×C₇₃	—	2	2	no	—
406	D₄×C₇₃	—	2	2	no	—
407	D₄×C₇₃	—	2	2	no	—
408	D₄×C₇₃	—	4	8	no	—
409	D₄×C₇₃	—	4	8	no	—
410	D₄×C₇₃	—	4	8	no	—
411	D₄×C₇₃	—	4	8	no	—
412	D₄×C₇₃	—	4	8	no	—
413	D₄×C₇₃	—	4	8	no	—
414	D₄×C₇₃	—	4	1	no	—
415	D₄×C₇₃	—	4	1	no	—
416	D₄×C₇₃	—	4	1	no	—
417	D₄×C₇₃	—	4	1	no	—
418	D₄×C₇₃	—	4	1	no	—
419	D₄×C₇₃	—	4	1	no	—
420	D₄×C₇₃	—	8	4	no	—
421	D₄×C₇₃	—	8	4	no	—
422	D₄×C₇₃	#120	1	4	yes	—
423	C₂×C₄×C₇₃	—	2	1	no	—
424	C₂×C₄×C₇₃	—	2	1	no	—
425	C₂×C₄×C₇₃	—	2	1	no	—
426	C₂×C₄×C₇₃	—	2	1	no	—
427	C₂×C₄×C₇₃	—	2	2	no	—
428	C₂×C₄×C₇₃	—	2	2	no	—
429	C₂×C₄×C₇₃	—	2	2	no	—
430	C₂×C₄×C₇₃	—	2	2	no	—
431	C₂×C₄×C₇₃	—	2	1	no	—
432	C₂×C₄×C₇₃	—	2	1	no	—
433	C₂×C₄×C₇₃	—	2	2	no	—
434	C₂×C₄×C₇₃	—	2	1	no	—
435	C₂×C₄×C₇₃	—	2	2	no	—
436	C₂×C₄×C₇₃	—	2	1	no	—
437	C₂×C₄×C₇₃	—	2	1	no	—
438	C₂×C₄×C₇₃	—	2	1	no	—
439	C₂×C₄×C₇₃	—	4	8	no	—
440	C₂×C₄×C₇₃	—	4	8	no	—
441	C₂×C₄×C₇₃	—	4	1	no	—
442	C₂×C₄×C₇₃	—	4	1	no	—
443	C₂×C₄×C₇₃	—	4	1	no	—
444	C₂×C₄×C₇₃	—	4	1	no	—
445	C₂×C₄×C₇₃	—	4	1	no	—
446	C₂×C₄×C₇₃	—	4	1	no	—
447	C₂×C₄×C₇₃	—	4	1	no	—
448	C₂×C₄×C₇₃	—	4	1	no	—
449	C₂×C₄×C₇₃	—	4	1	no	—
450	C₂×C₄×C₇₃	—	4	1	no	—
451	C₂×C₄×C₇₃	—	4	1	no	—
452	C₂×C₄×C₇₃	—	4	1	no	—
453	C₂×C₄×C₇₃	—	4	1	no	—
454	C₂×C₄×C₇₃	—	4	1	no	—
455	C₂×C₄×C₇₃	#120	1	2	yes	—
456	C₂×C₄×C₇₃	AGL(1,ℤ/8)	1	2	yes	complemented
457	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
458	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
459	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
460	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
461	C₂×C₄×C₇₃	H(5,𝔽₂)	1	1	yes	characteristic
462	C₂×C₄×C₇₃	H(5,𝔽₂)	1	1	yes	characteristic
463	C₈×C₇₃	—	2	2	no	—
464	C₈×C₇₃	—	2	2	no	—
465	C₈×C₇₃	—	4	1	no	—
466	C₈×C₇₃	—	4	1	no	—
467	C₂²×C₇₃	—	2	2	no	—
468	C₂²×C₇₃	—	2	4	no	—
469	C₂²×C₇₃	—	2	2	no	—
470	C₂²×C₇₃	—	2	2	no	—
471	C₂²×C₇₃	—	2	2	no	—
472	C₂²×C₇₃	—	2	2	no	—
473	C₂²×C₇₃	—	2	2	no	—
474	C₂²×C₇₃	—	4	1	no	—
475	C₂²×C₇₃	—	4	2	no	—
476	C₂²×C₇₃	—	4	1	no	—
477	C₂²×C₇₃	—	4	2	no	—
478	C₂²×C₇₃	—	4	1	no	—
479	C₂²×C₇₃	—	4	2	no	—
480	C₂²×C₇₃	—	4	1	no	—
481	C₂²×C₇₃	—	4	2	no	—
482	C₂²×C₇₃	—	4	1	no	—
483	C₂²×C₇₃	—	4	1	no	—
484	C₂²×C₇₃	—	4	2	no	—
485	C₂²×C₇₃	—	4	1	no	—
486	C₂²×C₇₃	—	4	1	no	—
487	C₂²×C₇₃	—	4	2	no	—
488	C₂²×C₇₃	—	4	2	no	—
489	C₂²×C₇₃	—	4	2	no	—
490	C₂²×C₇₃	—	4	2	no	—
491	C₂²×C₇₃	—	4	2	no	—
492	C₂²×C₇₃	—	4	2	no	—
493	C₂²×C₇₃	—	4	2	no	—
494	C₂²×C₇₃	—	4	2	no	—
495	C₂²×C₇₃	—	4	2	no	—
496	C₂²×C₇₃	—	4	2	no	—
497	C₂²×C₇₃	—	8	16	no	—
498	C₂²×C₇₃	—	8	16	no	—
499	C₂²×C₇₃	—	8	1	no	—
500	C₂²×C₇₃	—	8	1	no	—
501	C₂²×C₇₃	—	8	1	no	—
502	C₂²×C₇₃	—	8	1	no	—
503	C₂²×C₇₃	—	8	1	no	—
504	C₂²×C₇₃	—	8	1	no	—
505	C₂²×C₇₃	—	8	1	no	—
506	C₂²×C₇₃	—	8	1	no	—
507	C₂²×C₇₃	—	8	1	no	—
508	C₂²×C₇₃	—	8	1	no	—
509	C₂²×C₇₃	—	8	1	no	—
510	C₂²×C₇₃	—	8	1	no	—
511	C₂²×C₇₃	C₂×#120	1	1	yes	characteristic
512	C₂²×C₇₃	D₄²	1	1	yes	characteristic
513	C₂²×C₇₃	D₄²	1	1	yes	characteristic
514	C₂²×C₇₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
515	C₂²×C₇₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
516	C₂²×C₇₃	#576	1	1	yes	characteristic
517	C₂²×C₇₃	#577	1	1	yes	characteristic
518	C₄×C₇₃	—	2	2	no	—
519	C₄×C₇₃	—	2	2	no	—
520	C₄×C₇₃	—	4	1	no	—
521	C₄×C₇₃	—	4	2	no	—
522	C₄×C₇₃	—	4	2	no	—
523	C₄×C₇₃	—	4	1	no	—
524	C₄×C₇₃	—	8	1	no	—
525	C₄×C₇₃	—	8	1	no	—
526	C₄×C₇₃	C₂×#120	1	1	yes	characteristic
527	C₄×C₇₃	#534	1	1	yes	characteristic
528	C₄×C₇₃	D₄²	1	1	yes	characteristic
529	C₄×C₇₃	D₄²	1	1	yes	characteristic
530	#23860	C₇₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
531	C₂×C₇₃	—	4	2	no	—
532	C₂×C₇₃	—	4	2	no	—
533	C₂×C₇₃	—	4	4	no	—
534	C₂×C₇₃	—	8	2	no	—
535	C₂×C₇₃	—	8	2	no	—
536	C₂×C₇₃	—	8	2	no	—
537	C₂×C₇₃	#2403	1	1	yes	characteristic
538	C₂×C₇₃	#3003	1	1	yes	characteristic
539	C₂×C₇₃	#3012	1	1	yes	characteristic
540	C₂×C₇₃	#3264	1	1	yes	characteristic
541	C₂×C₇₃	#3265	1	1	yes	characteristic
542	C₂×C₇₃	#3272	1	1	yes	characteristic
543	C₂×C₇₃	#3274	1	1	yes	characteristic
544	C₂²×AGL(1,ℤ/8)	C₂×C₇₃	1	1	yes	characteristic, complemented
545	C₂×D₄²	C₂×C₇₃	1	1	yes	characteristic, complemented
546	C₂×#449	C₂×C₇₃	1	1	yes	characteristic, complemented
547	C₂×#450	C₂×C₇₃	1	1	yes	characteristic, complemented
548	C₂×#447	C₂×C₇₃	1	1	yes	characteristic, complemented
549	#2407	C₂×C₇₃	1	1	yes	characteristic, complemented
550	#2014	C₂×C₇₃	1	1	yes	characteristic, complemented
551	#2011	C₂×C₇₃	1	1	yes	characteristic, complemented
552	#2000	C₂×C₇₃	1	1	yes	characteristic, complemented
553	#1999	C₂×C₇₃	1	1	yes	characteristic, complemented
554	#1895	C₂×C₇₃	1	1	yes	characteristic, complemented
555	#1879	C₂×C₇₃	1	1	yes	characteristic, complemented
556	#1877	C₂×C₇₃	1	1	yes	characteristic, complemented
557	#1870	C₂×C₇₃	1	1	yes	characteristic, complemented
558	#1786	C₂×C₇₃	1	1	yes	characteristic, complemented
559	C₇₃	#23860	1	1	yes	characteristic, direct product factor, Sylow
560	C₂²×#41	C₂²×C₇₃	1	1	yes	characteristic, complemented
561	C₂³×D₄	—	2	1	no	—
562	C₂³×D₄	C₂²×C₇₃	1	1	yes	characteristic
563	C₂³×D₄	C₂²×C₇₃	1	1	yes	characteristic
564	C₂×AGL(1,ℤ/8)	—	2	4	no	—
565	C₂×AGL(1,ℤ/8)	—	2	4	no	—
566	C₂×AGL(1,ℤ/8)	—	2	4	no	—
567	C₂²×SD₁₆	C₂²×C₇₃	1	1	yes	characteristic
568	C₂²×SD₁₆	C₂²×C₇₃	1	1	yes	characteristic, complemented
569	C₂²×SD₁₆	C₂²×C₇₃	1	1	yes	characteristic, complemented
570	C₂²×D₈	C₂²×C₇₃	1	1	yes	characteristic
571	C₂²×D₈	C₂²×C₇₃	1	1	yes	characteristic, complemented
572	C₂²×D₈	C₂²×C₇₃	1	1	yes	characteristic, complemented
573	C₂²×M₁₆	C₂²×C₇₃	1	1	yes	characteristic, complemented
574	D₄²	—	2	4	no	—
575	D₄²	—	2	4	no	—
576	C₂×#127	C₂²×C₇₃	1	1	yes	characteristic
577	C₂×C₂²⋊Q₈	C₂²×C₇₃	1	1	yes	characteristic, complemented
578	C₂×#121	—	2	1	no	—
579	C₂×#121	C₂²×C₇₃	1	1	yes	characteristic
580	C₂×#121	C₂²×C₇₃	1	1	yes	characteristic
581	C₂×#121	C₂²×C₇₃	1	1	yes	characteristic, complemented
582	C₂×#120	—	2	1	no	—
583	C₂×#120	—	2	1	no	—
584	C₂×C₄×D₄	C₂²×C₇₃	1	1	yes	characteristic
585	C₂×C₄×D₄	C₂²×C₇₃	1	1	yes	characteristic
586	#450	—	2	4	no	—
587	#449	—	2	4	no	—
588	#447	—	2	4	no	—
589	C₂×#103	C₂²×C₇₃	1	1	yes	characteristic, complemented
590	C₂×#102	C₂²×C₇₃	1	1	yes	characteristic
591	C₂×#102	C₂²×C₇₃	1	1	yes	characteristic
592	C₂×#102	C₂²×C₇₃	1	1	yes	characteristic, complemented
593	C₂×#102	C₂²×C₇₃	1	1	yes	characteristic, complemented
594	C₂×#102	C₂²×C₇₃	1	1	yes	characteristic, complemented
595	C₂×#102	C₂²×C₇₃	1	1	yes	characteristic, complemented
596	C₂×#102	C₂²×C₇₃	1	1	yes	characteristic, complemented
597	C₂×C₂²⋊C₈	C₂²×C₇₃	1	1	yes	characteristic, complemented
598	C₂×C₂²⋊C₈	C₂²×C₇₃	1	1	yes	characteristic, complemented
599	C₂×C₂²⋊C₈	C₂²×C₇₃	1	1	yes	characteristic, complemented
600	#394	—	2	1	no	—
601	#392	—	2	1	no	—
602	#391	C₂²×C₇₃	1	1	yes	characteristic, complemented
603	#390	C₂²×C₇₃	1	1	yes	characteristic, complemented
604	#386	—	2	1	no	—
605	#385	—	2	1	no	—
606	#380	C₂²×C₇₃	1	1	yes	characteristic, complemented
607	#340	C₂²×C₇₃	1	1	yes	characteristic, complemented
608	#340	C₂²×C₇₃	1	1	yes	characteristic, complemented
609	#336	C₂²×C₇₃	1	1	yes	characteristic, complemented
610	#336	C₂²×C₇₃	1	1	yes	characteristic, complemented
611	C₂⁵	—	2	1	no	—
612	C₂⁵	—	2	1	no	—
613	C₂×#41	—	2	2	no	—
614	C₂×#41	—	2	2	no	—
615	C₂×#41	—	2	2	no	—
616	C₂×#41	—	2	2	no	—
617	C₂×#41	—	4	1	no	—
618	C₂×#41	—	4	1	no	—
619	C₂²×Q₈	C₂³×C₇₃	1	1	yes	characteristic
620	C₂²×D₄	—	2	2	no	—
621	C₂²×D₄	—	2	2	no	—
622	C₂²×D₄	—	2	8	no	—
623	C₂²×D₄	—	2	1	no	—
624	C₂²×D₄	—	2	1	no	—
625	C₂²×D₄	—	2	2	no	—
626	C₂²×D₄	—	2	2	no	—
627	C₂²×D₄	—	2	2	no	—
628	C₂²×D₄	—	2	2	no	—
629	C₂²×D₄	—	2	1	no	—
630	C₂²×D₄	—	2	1	no	—
631	C₂²×D₄	—	2	1	no	—
632	C₂²×D₄	—	2	1	no	—
633	C₂²×D₄	—	2	1	no	—
634	C₂²×D₄	—	2	2	no	—
635	C₂²×D₄	—	2	1	no	—
636	C₂²×D₄	—	4	1	no	—
637	C₂²×D₄	—	4	1	no	—
638	C₂²×D₄	—	4	1	no	—
639	C₂²×D₄	—	4	1	no	—
640	C₂²×D₄	—	4	4	no	—
641	C₂²×D₄	—	4	4	no	—
642	C₂²×D₄	D₄×C₇₃	1	1	yes	characteristic
643	C₂²×D₄	D₄×C₇₃	1	4	yes	complemented
644	C₂²×D₄	C₂³×C₇₃	1	1	yes	characteristic
645	C₂²×D₄	C₂³×C₇₃	1	1	yes	characteristic
646	C₂²×D₄	C₂³×C₇₃	1	1	yes	characteristic
647	C₂²×D₄	C₂³×C₇₃	1	1	yes	characteristic
648	C₂³×C₄	—	2	1	no	—
649	C₂³×C₄	—	2	1	no	—
650	C₂³×C₄	C₂³×C₇₃	1	1	yes	characteristic
651	C₂³×C₄	C₂³×C₇₃	1	1	yes	characteristic
652	AGL(1,ℤ/8)	—	2	32	no	—
653	C₂×SD₁₆	—	2	2	no	—
654	C₂×SD₁₆	—	2	2	no	—
655	C₂×SD₁₆	—	2	2	no	—
656	C₂×SD₁₆	—	2	2	no	—
657	C₂×SD₁₆	—	2	2	no	—
658	C₂×SD₁₆	—	2	2	no	—
659	C₂×SD₁₆	—	2	2	no	—
660	C₂×SD₁₆	—	4	1	no	—
661	C₂×SD₁₆	D₄×C₇₃	1	4	yes	complemented
662	C₂×D₈	—	2	2	no	—
663	C₂×D₈	—	2	2	no	—
664	C₂×D₈	—	2	2	no	—
665	C₂×D₈	—	2	2	no	—
666	C₂×D₈	—	2	2	no	—
667	C₂×D₈	—	2	2	no	—
668	C₂×D₈	—	2	2	no	—
669	C₂×D₈	—	4	1	no	—
670	C₂×D₈	D₄×C₇₃	1	4	yes	complemented
671	C₂×M₁₆	—	2	2	no	—
672	C₂×M₁₆	—	2	2	no	—
673	C₂×M₁₆	—	2	2	no	—
674	C₂²×C₈	C₂³×C₇₃	1	1	yes	characteristic
675	C₂²×C₈	C₂³×C₇₃	1	1	yes	characteristic
676	C₂²×C₈	C₂³×C₇₃	1	1	yes	characteristic
677	C₂²×C₈	C₂³×C₇₃	1	1	yes	characteristic
678	#127	—	2	2	no	—
679	#127	—	2	2	no	—
680	C₂²⋊Q₈	—	2	2	no	—
681	C₂²⋊Q₈	—	4	1	no	—
682	#121	—	2	8	no	—
683	#121	—	2	2	no	—
684	#121	—	2	2	no	—
685	#121	—	2	2	no	—
686	#121	—	2	2	no	—
687	#121	—	4	1	no	—
688	#121	D₄×C₇₃	1	4	yes	complemented
689	#120	—	2	8	no	—
690	#120	—	2	8	no	—
691	C₄×D₄	—	2	2	no	—
692	C₄×D₄	—	2	2	no	—
693	C₄×D₄	—	2	2	no	—
694	C₄×D₄	—	2	2	no	—
695	C₂×C₄⋊C₄	—	2	1	no	—
696	C₂×C₄⋊C₄	D₄×C₇₃	1	1	yes	characteristic
697	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
698	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
699	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
700	C₂×C₂²⋊C₄	—	2	1	no	—
701	C₂×C₂²⋊C₄	—	2	1	no	—
702	C₂×C₂²⋊C₄	—	2	1	no	—
703	C₂×C₂²⋊C₄	—	2	1	no	—
704	C₂×C₂²⋊C₄	—	2	1	no	—
705	C₂×C₂²⋊C₄	—	2	1	no	—
706	C₂×C₂²⋊C₄	—	2	1	no	—
707	C₂×C₂²⋊C₄	—	2	1	no	—
708	C₂×C₂²⋊C₄	D₄×C₇₃	1	1	yes	characteristic
709	C₂×C₂²⋊C₄	D₄×C₇₃	1	1	yes	characteristic
710	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
711	#103	—	2	2	no	—
712	#102	—	2	2	no	—
713	#102	—	2	2	no	—
714	#102	—	2	2	no	—
715	#102	—	2	2	no	—
716	#102	—	2	2	no	—
717	#102	—	4	1	no	—
718	#102	—	4	1	no	—
719	C₂²⋊C₈	—	2	2	no	—
720	C₂²⋊C₈	—	2	2	no	—
721	C₂²⋊C₈	—	2	2	no	—
722	#95	—	2	1	no	—
723	#95	—	2	1	no	—
724	#95	—	2	1	no	—
725	C₂⁴	—	2	1	no	—
726	C₂⁴	—	2	4	no	—
727	C₂⁴	—	2	1	no	—
728	C₂⁴	—	2	1	no	—
729	C₂⁴	—	2	1	no	—
730	C₂⁴	—	2	4	no	—
731	C₂⁴	—	4	2	no	—
732	C₂⁴	—	4	2	no	—
733	C₂⁴	—	4	2	no	—
734	C₂⁴	—	4	2	no	—
735	C₂⁴	—	4	2	no	—
736	C₂⁴	—	4	2	no	—
737	C₂⁴	—	4	2	no	—
738	C₂⁴	—	4	2	no	—
739	C₂⁴	—	8	1	no	—
740	C₂⁴	—	8	1	no	—
741	C₂⁴	—	8	1	no	—
742	C₂⁴	—	8	1	no	—
743	C₂⁴	C₂×D₄×C₇₃	1	1	yes	characteristic
744	C₂⁴	C₂×D₄×C₇₃	1	1	yes	characteristic
745	#41	—	2	8	no	—
746	#41	—	4	4	no	—
747	#41	—	4	4	no	—
748	#41	—	4	4	no	—
749	C₂×Q₈	—	2	1	no	—
750	C₂×Q₈	—	2	1	no	—
751	C₂×Q₈	—	2	1	no	—
752	C₂×Q₈	—	2	1	no	—
753	C₂×Q₈	—	2	1	no	—
754	C₂×Q₈	C₂×D₄×C₇₃	1	2	yes	complemented
755	C₂×D₄	—	2	2	no	—
756	C₂×D₄	—	2	2	no	—
757	C₂×D₄	—	2	8	no	—
758	C₂×D₄	—	2	4	no	—
759	C₂×D₄	—	2	4	no	—
760	C₂×D₄	—	2	4	no	—
761	C₂×D₄	—	2	4	no	—
762	C₂×D₄	—	2	4	no	—
763	C₂×D₄	—	2	4	no	—
764	C₂×D₄	—	2	2	no	—
765	C₂×D₄	—	2	1	no	—
766	C₂×D₄	—	2	1	no	—
767	C₂×D₄	—	2	1	no	—
768	C₂×D₄	—	2	1	no	—
769	C₂×D₄	—	2	1	no	—
770	C₂×D₄	—	2	1	no	—
771	C₂×D₄	—	2	1	no	—
772	C₂×D₄	—	2	1	no	—
773	C₂×D₄	—	2	1	no	—
774	C₂×D₄	—	2	1	no	—
775	C₂×D₄	—	2	1	no	—
776	C₂×D₄	—	2	1	no	—
777	C₂×D₄	—	2	1	no	—
778	C₂×D₄	—	2	1	no	—
779	C₂×D₄	—	2	1	no	—
780	C₂×D₄	—	2	1	no	—
781	C₂×D₄	—	2	1	no	—
782	C₂×D₄	—	2	1	no	—
783	C₂×D₄	—	4	4	no	—
784	C₂×D₄	—	4	4	no	—
785	C₂×D₄	—	4	4	no	—
786	C₂×D₄	—	4	2	no	—
787	C₂×D₄	—	4	2	no	—
788	C₂×D₄	—	4	2	no	—
789	C₂×D₄	—	4	2	no	—
790	C₂×D₄	—	4	2	no	—
791	C₂×D₄	—	4	2	no	—
792	C₂×D₄	—	4	4	no	—
793	C₂×D₄	—	4	4	no	—
794	C₂×D₄	—	4	32	no	—
795	C₂×D₄	—	4	4	no	—
796	C₂×D₄	—	4	2	no	—
797	C₂×D₄	—	4	2	no	—
798	C₂×D₄	—	4	2	no	—
799	C₂×D₄	—	4	2	no	—
800	C₂×D₄	—	4	2	no	—
801	C₂×D₄	—	4	2	no	—
802	C₂×D₄	—	4	4	no	—
803	C₂×D₄	—	4	2	no	—
804	C₂×D₄	—	4	2	no	—
805	C₂×D₄	—	4	2	no	—
806	C₂×D₄	—	8	1	no	—
807	C₂×D₄	—	8	1	no	—
808	C₂×D₄	—	8	1	no	—
809	C₂×D₄	C₂×D₄×C₇₃	1	2	yes	—
810	C₂×D₄	C₂×D₄×C₇₃	1	2	yes	—
811	C₂×D₄	C₂×D₄×C₇₃	1	2	yes	—
812	C₂×D₄	C₂×D₄×C₇₃	1	2	yes	—
813	C₂×D₄	C₂×D₄×C₇₃	1	2	yes	—
814	C₂×D₄	C₂×D₄×C₇₃	1	2	yes	complemented
815	C₂²×C₄	—	2	1	no	—
816	C₂²×C₄	—	2	1	no	—
817	C₂²×C₄	—	2	1	no	—
818	C₂²×C₄	—	2	1	no	—
819	C₂²×C₄	—	2	4	no	—
820	C₂²×C₄	—	2	1	no	—
821	C₂²×C₄	—	2	1	no	—
822	C₂²×C₄	—	2	1	no	—
823	C₂²×C₄	—	2	1	no	—
824	C₂²×C₄	—	2	1	no	—
825	C₂²×C₄	—	2	1	no	—
826	C₂²×C₄	—	2	1	no	—
827	C₂²×C₄	—	2	1	no	—
828	C₂²×C₄	—	2	1	no	—
829	C₂²×C₄	—	2	1	no	—
830	C₂²×C₄	—	4	2	no	—
831	C₂²×C₄	—	4	2	no	—
832	C₂²×C₄	—	4	2	no	—
833	C₂²×C₄	—	4	2	no	—
834	C₂²×C₄	—	4	2	no	—
835	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
836	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
837	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
838	C₂²×C₄	C₂×D₄×C₇₃	1	2	yes	—
839	C₂²×C₄	C₂×D₄×C₇₃	1	2	yes	—
840	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
841	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
842	SD₁₆	—	2	8	no	—
843	SD₁₆	—	2	8	no	—
844	SD₁₆	—	4	4	no	—
845	D₈	—	2	8	no	—
846	D₈	—	2	8	no	—
847	D₈	—	4	4	no	—
848	M₁₆	—	2	8	no	—
849	C₂×C₈	—	2	1	no	—
850	C₂×C₈	—	2	1	no	—
851	C₂×C₈	—	2	1	no	—
852	C₂×C₈	—	2	1	no	—
853	C₂×C₈	—	2	1	no	—
854	C₂×C₈	—	2	1	no	—
855	C₂×C₈	—	2	1	no	—
856	C₂×C₈	—	2	1	no	—
857	C₂×C₈	—	2	1	no	—
858	C₂×C₈	—	2	1	no	—
859	C₂×C₈	C₂×D₄×C₇₃	1	2	yes	complemented
860	C₂×C₈	C₂×D₄×C₇₃	1	2	yes	complemented
861	C₄⋊C₄	—	2	2	no	—
862	C₄⋊C₄	—	2	1	no	—
863	C₄⋊C₄	—	2	1	no	—
864	C₄⋊C₄	—	2	1	no	—
865	C₄⋊C₄	—	2	1	no	—
866	C₄⋊C₄	—	2	1	no	—
867	C₄⋊C₄	—	4	2	no	—
868	C₄⋊C₄	C₂×D₄×C₇₃	1	2	yes	—
869	C₂²⋊C₄	—	2	4	no	—
870	C₂²⋊C₄	—	2	4	no	—
871	C₂²⋊C₄	—	2	2	no	—
872	C₂²⋊C₄	—	2	4	no	—
873	C₂²⋊C₄	—	2	2	no	—
874	C₂²⋊C₄	—	4	2	no	—
875	C₂²⋊C₄	—	4	2	no	—
876	C₂²⋊C₄	—	4	2	no	—
877	C₂²⋊C₄	—	8	1	no	—
878	C₂²⋊C₄	—	8	1	no	—
879	C₄²	—	2	1	no	—
880	C₄²	—	2	1	no	—
881	C₂³	—	2	1	no	—
882	C₂³	—	2	2	no	—
883	C₂³	—	2	1	no	—
884	C₂³	—	2	1	no	—
885	C₂³	—	2	1	no	—
886	C₂³	—	2	1	no	—
887	C₂³	—	2	2	no	—
888	C₂³	—	2	2	no	—
889	C₂³	—	2	1	no	—
890	C₂³	—	2	1	no	—
891	C₂³	—	2	1	no	—
892	C₂³	—	2	1	no	—
893	C₂³	—	2	1	no	—
894	C₂³	—	2	1	no	—
895	C₂³	—	2	1	no	—
896	C₂³	—	2	2	no	—
897	C₂³	—	2	2	no	—
898	C₂³	—	2	2	no	—
899	C₂³	—	4	8	no	—
900	C₂³	—	4	8	no	—
901	C₂³	—	4	8	no	—
902	C₂³	—	4	8	no	—
903	C₂³	—	4	1	no	—
904	C₂³	—	4	1	no	—
905	C₂³	—	4	1	no	—
906	C₂³	—	4	1	no	—
907	C₂³	—	4	1	no	—
908	C₂³	—	4	1	no	—
909	C₂³	—	4	1	no	—
910	C₂³	—	4	1	no	—
911	C₂³	—	4	1	no	—
912	C₂³	—	4	1	no	—
913	C₂³	—	4	1	no	—
914	C₂³	—	4	1	no	—
915	C₂³	—	4	1	no	—
916	C₂³	—	4	1	no	—
917	C₂³	—	4	1	no	—
918	C₂³	—	4	1	no	—
919	C₂³	—	4	1	no	—
920	C₂³	—	4	1	no	—
921	C₂³	—	4	1	no	—
922	C₂³	—	4	1	no	—
923	C₂³	—	4	1	no	—
924	C₂³	—	4	1	no	—
925	C₂³	—	8	4	no	—
926	C₂³	—	8	4	no	—
927	C₂³	—	8	4	no	—
928	C₂³	—	8	4	no	—
929	C₂³	—	8	4	no	—
930	C₂³	—	8	4	no	—
931	C₂³	—	8	4	no	—
932	C₂³	—	8	4	no	—
933	C₂³	—	8	4	no	—
934	C₂³	—	8	4	no	—
935	C₂³	#120×C₇₃	1	2	yes	—
936	C₂³	AGL(1,ℤ/8)×C₇₃	1	2	yes	complemented
937	C₂³	C₂²×D₄×C₇₃	1	1	yes	characteristic
938	Q₈	—	2	2	no	—
939	Q₈	—	2	2	no	—
940	Q₈	—	4	1	no	—
941	Q₈	—	4	1	no	—
942	D₄	—	2	8	no	—
943	D₄	—	2	2	no	—
944	D₄	—	2	2	no	—
945	D₄	—	2	2	no	—
946	D₄	—	2	2	no	—
947	D₄	—	2	2	no	—
948	D₄	—	2	2	no	—
949	D₄	—	2	2	no	—
950	D₄	—	2	2	no	—
951	D₄	—	2	2	no	—
952	D₄	—	4	8	no	—
953	D₄	—	4	8	no	—
954	D₄	—	4	8	no	—
955	D₄	—	4	8	no	—
956	D₄	—	4	8	no	—
957	D₄	—	4	8	no	—
958	D₄	—	4	1	no	—
959	D₄	—	4	1	no	—
960	D₄	—	4	1	no	—
961	D₄	—	4	1	no	—
962	D₄	—	4	1	no	—
963	D₄	—	4	1	no	—
964	D₄	—	8	4	no	—
965	D₄	—	8	4	no	—
966	D₄	#120×C₇₃	1	4	yes	—
967	C₂×C₄	—	2	1	no	—
968	C₂×C₄	—	2	1	no	—
969	C₂×C₄	—	2	1	no	—
970	C₂×C₄	—	2	1	no	—
971	C₂×C₄	—	2	2	no	—
972	C₂×C₄	—	2	2	no	—
973	C₂×C₄	—	2	2	no	—
974	C₂×C₄	—	2	2	no	—
975	C₂×C₄	—	2	1	no	—
976	C₂×C₄	—	2	1	no	—
977	C₂×C₄	—	2	2	no	—
978	C₂×C₄	—	2	1	no	—
979	C₂×C₄	—	2	2	no	—
980	C₂×C₄	—	2	1	no	—
981	C₂×C₄	—	2	1	no	—
982	C₂×C₄	—	2	1	no	—
983	C₂×C₄	—	4	8	no	—
984	C₂×C₄	—	4	8	no	—
985	C₂×C₄	—	4	1	no	—
986	C₂×C₄	—	4	1	no	—
987	C₂×C₄	—	4	1	no	—
988	C₂×C₄	—	4	1	no	—
989	C₂×C₄	—	4	1	no	—
990	C₂×C₄	—	4	1	no	—
991	C₂×C₄	—	4	1	no	—
992	C₂×C₄	—	4	1	no	—
993	C₂×C₄	—	4	1	no	—
994	C₂×C₄	—	4	1	no	—
995	C₂×C₄	—	4	1	no	—
996	C₂×C₄	—	4	1	no	—
997	C₂×C₄	—	4	1	no	—
998	C₂×C₄	—	4	1	no	—
999	C₂×C₄	#120×C₇₃	1	2	yes	—
1000	C₂×C₄	AGL(1,ℤ/8)×C₇₃	1	2	yes	complemented
1001	C₂×C₄	C₂²×D₄×C₇₃	1	1	yes	characteristic
1002	C₂×C₄	C₂²×D₄×C₇₃	1	1	yes	characteristic
1003	C₂×C₄	C₂²×D₄×C₇₃	1	1	yes	characteristic
1004	C₂×C₄	C₂²×D₄×C₇₃	1	1	yes	characteristic
1005	C₂×C₄	H(5,𝔽₂)×C₇₃	1	1	yes	characteristic
1006	C₂×C₄	H(5,𝔽₂)×C₇₃	1	1	yes	characteristic
1007	C₈	—	2	2	no	—
1008	C₈	—	2	2	no	—
1009	C₈	—	4	1	no	—
1010	C₈	—	4	1	no	—
1011	C₂²	—	2	2	no	—
1012	C₂²	—	2	2	no	—
1013	C₂²	—	2	2	no	—
1014	C₂²	—	2	2	no	—
1015	C₂²	—	2	2	no	—
1016	C₂²	—	2	2	no	—
1017	C₂²	—	2	4	no	—
1018	C₂²	—	4	2	no	—
1019	C₂²	—	4	1	no	—
1020	C₂²	—	4	2	no	—
1021	C₂²	—	4	1	no	—
1022	C₂²	—	4	2	no	—
1023	C₂²	—	4	1	no	—
1024	C₂²	—	4	2	no	—
1025	C₂²	—	4	1	no	—
1026	C₂²	—	4	1	no	—
1027	C₂²	—	4	2	no	—
1028	C₂²	—	4	1	no	—
1029	C₂²	—	4	1	no	—
1030	C₂²	—	4	2	no	—
1031	C₂²	—	4	1	no	—
1032	C₂²	—	4	2	no	—
1033	C₂²	—	4	2	no	—
1034	C₂²	—	4	2	no	—
1035	C₂²	—	4	2	no	—
1036	C₂²	—	4	2	no	—
1037	C₂²	—	4	2	no	—
1038	C₂²	—	4	2	no	—
1039	C₂²	—	4	2	no	—
1040	C₂²	—	4	2	no	—
1041	C₂²	—	8	16	no	—
1042	C₂²	—	8	16	no	—
1043	C₂²	—	8	1	no	—
1044	C₂²	—	8	1	no	—
1045	C₂²	—	8	1	no	—
1046	C₂²	—	8	1	no	—
1047	C₂²	—	8	1	no	—
1048	C₂²	—	8	1	no	—
1049	C₂²	—	8	1	no	—
1050	C₂²	—	8	1	no	—
1051	C₂²	—	8	1	no	—
1052	C₂²	—	8	1	no	—
1053	C₂²	—	8	1	no	—
1054	C₂²	—	8	1	no	—
1055	C₂²	C₂×#120×C₇₃	1	1	yes	characteristic
1056	C₂²	D₄²×C₇₃	1	1	yes	characteristic
1057	C₂²	D₄²×C₇₃	1	1	yes	characteristic
1058	C₂²	C₂×AGL(1,ℤ/8)×C₇₃	1	1	yes	characteristic
1059	C₂²	C₂×AGL(1,ℤ/8)×C₇₃	1	1	yes	characteristic
1060	C₂²	#576×C₇₃	1	1	yes	characteristic
1061	C₂²	#577×C₇₃	1	1	yes	characteristic
1062	C₄	—	2	2	no	—
1063	C₄	—	2	2	no	—
1064	C₄	—	4	2	no	—
1065	C₄	—	4	1	no	—
1066	C₄	—	4	1	no	—
1067	C₄	—	4	2	no	—
1068	C₄	—	8	1	no	—
1069	C₄	—	8	1	no	—
1070	C₄	C₂×#120×C₇₃	1	1	yes	characteristic
1071	C₄	#534×C₇₃	1	1	yes	characteristic
1072	C₄	D₄²×C₇₃	1	1	yes	characteristic
1073	C₄	D₄²×C₇₃	1	1	yes	characteristic
1074	C₂	—	4	2	no	—
1075	C₂	—	4	2	no	—
1076	C₂	—	4	4	no	—
1077	C₂	—	8	2	no	—
1078	C₂	—	8	2	no	—
1079	C₂	—	8	2	no	—
1080	C₂	C₇₃×#2403	1	1	yes	characteristic
1081	C₂	C₇₃×#3003	1	1	yes	characteristic
1082	C₂	C₇₃×#3012	1	1	yes	characteristic
1083	C₂	C₇₃×#3264	1	1	yes	characteristic
1084	C₂	C₇₃×#3265	1	1	yes	characteristic
1085	C₂	C₇₃×#3272	1	1	yes	characteristic
1086	C₂	C₇₃×#3274	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₇₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₇₃
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₇₃ ◁ C₂×C₄×D₄×C₇₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂²×AGL(1,ℤ/8)×C₇₃	C₂	semidirect
2. C₂×D₄²×C₇₃	C₂	semidirect
3. C₂×#449×C₇₃	C₂	semidirect
4. C₂×#450×C₇₃	C₂	semidirect
5. C₂×#447×C₇₃	C₂	semidirect
6. C₇₃×#2407	C₂	semidirect
7. C₇₃×#2014	C₂	semidirect
8. C₇₃×#2011	C₂	semidirect
9. C₇₃×#2000	C₂	semidirect
10. C₇₃×#1999	C₂	semidirect
11. C₇₃×#1895	C₂	semidirect
12. C₇₃×#1879	C₂	semidirect
13. C₇₃×#1877	C₂	semidirect
14. C₇₃×#1870	C₂	semidirect
15. C₇₃×#1786	C₂	semidirect
16. C₂²×#41×C₇₃	C₂²	semidirect
24. C₂²×SD₁₆×C₇₃	C₂²	semidirect
25. C₂²×SD₁₆×C₇₃	C₂²	semidirect
27. C₂²×D₈×C₇₃	C₂²	semidirect
28. C₂²×D₈×C₇₃	C₂²	semidirect
29. C₂²×M₁₆×C₇₃	C₂²	semidirect
33. C₂×C₂²⋊Q₈×C₇₃	C₂²	semidirect
37. C₂×#121×C₇₃	C₂²	semidirect
45. C₂×#103×C₇₃	C₂²	semidirect
48. C₂×#102×C₇₃	C₂²	semidirect
49. C₂×#102×C₇₃	C₂²	semidirect
50. C₂×#102×C₇₃	C₂²	semidirect
51. C₂×#102×C₇₃	C₂²	semidirect
52. C₂×#102×C₇₃	C₂²	semidirect
53. C₂×C₂²⋊C₈×C₇₃	C₂²	semidirect
54. C₂×C₂²⋊C₈×C₇₃	C₂²	semidirect
55. C₂×C₂²⋊C₈×C₇₃	C₂²	semidirect
58. #391×C₇₃	C₂²	semidirect
59. #390×C₇₃	C₂²	semidirect
62. #380×C₇₃	C₂²	semidirect
63. #340×C₇₃	C₂²	semidirect
64. #340×C₇₃	C₂²	semidirect
65. #336×C₇₃	C₂²	semidirect
66. #336×C₇₃	C₂²	semidirect
99. C₂²×D₄×C₇₃	D₄	semidirect
117. C₂×SD₁₆×C₇₃	D₄	semidirect
126. C₂×D₈×C₇₃	D₄	semidirect
144. #121×C₇₃	D₄	semidirect
210. C₂×Q₈×C₇₃	C₂×D₄	semidirect
270. C₂×D₄×C₇₃	C₂×D₄	semidirect
315. C₂×C₈×C₇₃	C₂×D₄	semidirect
316. C₂×C₈×C₇₃	C₂×D₄	semidirect
392. C₂³×C₇₃	AGL(1,ℤ/8)	semidirect
456. C₂×C₄×C₇₃	AGL(1,ℤ/8)	semidirect
530. #23860	C₇₃	direct (N × H)
544. C₂²×AGL(1,ℤ/8)	C₂×C₇₃	semidirect
545. C₂×D₄²	C₂×C₇₃	semidirect
546. C₂×#449	C₂×C₇₃	semidirect
547. C₂×#450	C₂×C₇₃	semidirect
548. C₂×#447	C₂×C₇₃	semidirect
549. #2407	C₂×C₇₃	semidirect
550. #2014	C₂×C₇₃	semidirect
551. #2011	C₂×C₇₃	semidirect
552. #2000	C₂×C₇₃	semidirect
553. #1999	C₂×C₇₃	semidirect
554. #1895	C₂×C₇₃	semidirect
555. #1879	C₂×C₇₃	semidirect
556. #1877	C₂×C₇₃	semidirect
557. #1870	C₂×C₇₃	semidirect
558. #1786	C₂×C₇₃	semidirect
559. C₇₃	#23860	direct (N × H)
560. C₂²×#41	C₂²×C₇₃	semidirect
568. C₂²×SD₁₆	C₂²×C₇₃	semidirect
569. C₂²×SD₁₆	C₂²×C₇₃	semidirect
571. C₂²×D₈	C₂²×C₇₃	semidirect
572. C₂²×D₈	C₂²×C₇₃	semidirect
573. C₂²×M₁₆	C₂²×C₇₃	semidirect
577. C₂×C₂²⋊Q₈	C₂²×C₇₃	semidirect
581. C₂×#121	C₂²×C₇₃	semidirect
589. C₂×#103	C₂²×C₇₃	semidirect
592. C₂×#102	C₂²×C₇₃	semidirect
593. C₂×#102	C₂²×C₇₃	semidirect
594. C₂×#102	C₂²×C₇₃	semidirect
595. C₂×#102	C₂²×C₇₃	semidirect
596. C₂×#102	C₂²×C₇₃	semidirect
597. C₂×C₂²⋊C₈	C₂²×C₇₃	semidirect
598. C₂×C₂²⋊C₈	C₂²×C₇₃	semidirect
599. C₂×C₂²⋊C₈	C₂²×C₇₃	semidirect
602. #391	C₂²×C₇₃	semidirect
603. #390	C₂²×C₇₃	semidirect
606. #380	C₂²×C₇₃	semidirect
607. #340	C₂²×C₇₃	semidirect
608. #340	C₂²×C₇₃	semidirect
609. #336	C₂²×C₇₃	semidirect
610. #336	C₂²×C₇₃	semidirect
643. C₂²×D₄	D₄×C₇₃	semidirect
661. C₂×SD₁₆	D₄×C₇₃	semidirect
670. C₂×D₈	D₄×C₇₃	semidirect
688. #121	D₄×C₇₃	semidirect
754. C₂×Q₈	C₂×D₄×C₇₃	semidirect
814. C₂×D₄	C₂×D₄×C₇₃	semidirect
859. C₂×C₈	C₂×D₄×C₇₃	semidirect
860. C₂×C₈	C₂×D₄×C₇₃	semidirect
936. C₂³	AGL(1,ℤ/8)×C₇₃	semidirect
1000. C₂×C₄	AGL(1,ℤ/8)×C₇₃	semidirect

Maximal subgroups

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

subgroup	index
C₂²×AGL(1,ℤ/8)×C₇₃	2
C₂×D₄²×C₇₃	2
C₂×#449×C₇₃	2
C₂×#450×C₇₃	2
C₂×#447×C₇₃	2
C₇₃×#2407	2
C₇₃×#2014	2
C₇₃×#2011	2
C₇₃×#2000	2
C₇₃×#1999	2
C₇₃×#1895	2
C₇₃×#1879	2
C₇₃×#1877	2
C₇₃×#1870	2
C₇₃×#1786	2
#23860	73

Subgroups — C73×#23860 #32933264

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₃×#23860 #32933264