Subgroups — C₇₃×#59825 #32969229

Order 18688.

2358 conjugacy classes of subgroups.

The subgroup lattice has 954 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#553×C₇₃	C₂	1	2	yes	maximal, complemented
2	C₇₃×#2727	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇₃×#2726	C₂	1	1	yes	maximal, characteristic, complemented
4	C₇₃×#2724	C₂	1	1	yes	maximal, characteristic, complemented
5	C₇₃×#2682	C₂	1	1	yes	maximal, characteristic, complemented
6	C₇₃×#2579	C₂	1	2	yes	maximal, complemented
7	C₇₃×#2553	C₂	1	2	yes	maximal, complemented
8	C₇₃×#2543	C₂	1	2	yes	maximal, complemented
9	C₇₃×#2519	C₂	1	2	yes	maximal, complemented
10	C₇₃×#2478	C₂	1	2	yes	maximal, complemented
11	C₇₃×#2455	C₂	1	2	yes	maximal, complemented
12	C₇₃×#2443	C₂	1	2	yes	maximal, complemented
13	C₇₃×#2443	C₂	1	2	yes	maximal, complemented
14	C₇₃×#2425	C₂	1	2	yes	maximal, complemented
15	C₇₃×#2359	C₂	1	2	yes	maximal, complemented
16	C₇₃×#2349	C₂	1	2	yes	maximal, complemented
17	C₄×#121×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
18	C₄×#121×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
19	C₂×#389×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
20	#553×C₇₃	—	2	16	no	—
21	C₂×#126×C₇₃	C₂²	1	2	yes	—
22	C₂×#126×C₇₃	C₂²	1	2	yes	—
23	C₂×#125×C₇₃	C₂²	1	2	yes	—
24	C₂×#123×C₇₃	C₂²	1	2	yes	—
25	C₂×#123×C₇₃	C₂²	1	2	yes	—
26	C₂×#123×C₇₃	C₂²	1	2	yes	—
27	C₂×#123×C₇₃	C₂²	1	2	yes	—
28	C₂×#121×C₇₃	C₂²	1	2	yes	—
29	C₂×#121×C₇₃	C₂²	1	2	yes	—
30	C₂×#121×C₇₃	C₂²	1	2	yes	—
31	C₂×#121×C₇₃	C₂²	1	1	yes	characteristic
32	C₂×#121×C₇₃	C₂²	1	1	yes	characteristic
33	C₂×C₄×D₄×C₇₃	C₂²	1	2	yes	—
34	C₂×C₄×D₄×C₇₃	C₂²	1	2	yes	—
35	C₂×C₄×D₄×C₇₃	C₂²	1	2	yes	—
36	C₂×C₄×D₄×C₇₃	C₂²	1	2	yes	—
37	C₂×C₄×D₄×C₇₃	C₂²	1	2	yes	—
38	C₂×C₄×D₄×C₇₃	C₂²	1	1	yes	characteristic
39	C₂×C₄×D₄×C₇₃	C₂²	1	1	yes	characteristic
40	C₂×#117×C₇₃	C₂²	1	2	yes	—
41	C₂²×C₄⋊C₄×C₇₃	C₂²	1	1	yes	characteristic
42	C₂²×C₄⋊C₄×C₇₃	C₂²	1	2	yes	—
43	C₂²×C₄⋊C₄×C₇₃	C₂²	1	1	yes	characteristic
44	C₂²×C₄²×C₇₃	C₂²	1	1	yes	characteristic
45	#399×C₇₃	C₂²	1	2	yes	—
46	#399×C₇₃	C₂²	1	2	yes	—
47	#398×C₇₃	C₂²	1	2	yes	—
48	#398×C₇₃	C₂²	1	2	yes	—
49	#398×C₇₃	C₂²	1	2	yes	—
50	#398×C₇₃	C₂²	1	2	yes	—
51	#398×C₇₃	C₂²	1	2	yes	—
52	#397×C₇₃	C₂²	1	2	yes	—
53	#397×C₇₃	C₂²	1	2	yes	—
54	#397×C₇₃	C₂²	1	2	yes	—
55	#396×C₇₃	C₂²	1	2	yes	—
56	#396×C₇₃	C₂²	1	2	yes	—
57	#394×C₇₃	C₂²	1	2	yes	—
58	#394×C₇₃	C₂²	1	2	yes	—
59	#394×C₇₃	C₂²	1	2	yes	—
60	#392×C₇₃	C₂²	1	2	yes	—
61	#390×C₇₃	C₂²	1	1	yes	characteristic
62	#390×C₇₃	C₂²	1	1	yes	characteristic
63	#389×C₇₃	C₂²	1	2	yes	—
64	#389×C₇₃	C₂²	1	2	yes	—
65	#389×C₇₃	C₂²	1	1	yes	characteristic
66	#389×C₇₃	C₂²	1	1	yes	characteristic
67	#389×C₇₃	C₂²	1	1	yes	characteristic
68	#389×C₇₃	C₂²	1	1	yes	characteristic
69	#389×C₇₃	C₂²	1	2	yes	—
70	#389×C₇₃	C₂²	1	2	yes	—
71	#389×C₇₃	C₂²	1	1	yes	characteristic
72	#389×C₇₃	C₂²	1	1	yes	characteristic
73	#388×C₇₃	C₂²	1	2	yes	—
74	#388×C₇₃	C₂²	1	2	yes	—
75	#388×C₇₃	C₂²	1	2	yes	—
76	#388×C₇₃	C₂²	1	2	yes	—
77	#388×C₇₃	C₂²	1	2	yes	—
78	#388×C₇₃	C₂²	1	2	yes	—
79	#387×C₇₃	C₂²	1	2	yes	—
80	#387×C₇₃	C₂²	1	2	yes	—
81	#387×C₇₃	C₂²	1	2	yes	—
82	#387×C₇₃	C₂²	1	2	yes	—
83	#386×C₇₃	C₂²	1	2	yes	—
84	#386×C₇₃	C₂²	1	2	yes	—
85	#386×C₇₃	C₂²	1	2	yes	—
86	#386×C₇₃	C₂²	1	2	yes	—
87	#386×C₇₃	C₂²	1	2	yes	—
88	#386×C₇₃	C₂²	1	2	yes	—
89	#385×C₇₃	C₂²	1	2	yes	—
90	#385×C₇₃	C₂²	1	2	yes	—
91	#385×C₇₃	C₂²	1	2	yes	—
92	#385×C₇₃	C₂²	1	2	yes	—
93	#385×C₇₃	C₂²	1	2	yes	—
94	#385×C₇₃	C₂²	1	2	yes	—
95	#385×C₇₃	C₂²	1	2	yes	—
96	#385×C₇₃	C₂²	1	2	yes	—
97	#382×C₇₃	C₂²	1	2	yes	—
98	#380×C₇₃	C₂²	1	2	yes	—
99	#380×C₇₃	C₂²	1	1	yes	characteristic
100	#380×C₇₃	C₂²	1	1	yes	characteristic
101	C₄×C₄⋊C₄×C₇₃	C₂²	1	1	yes	characteristic
102	C₄×C₄⋊C₄×C₇₃	C₂²	1	1	yes	characteristic
103	C₄×C₄⋊C₄×C₇₃	C₂²	1	2	yes	—
104	C₄×C₂²⋊C₄×C₇₃	C₂²	1	2	yes	—
105	C₄×C₂²⋊C₄×C₇₃	C₂²	1	2	yes	—
106	C₂×#95×C₇₃	C₂²	1	2	yes	—
107	C₂×#95×C₇₃	C₂²	1	2	yes	—
108	C₂²×D₄×C₇₃	C₂³	1	2	yes	—
109	C₂²×D₄×C₇₃	C₂³	1	2	yes	—
110	C₂²×D₄×C₇₃	C₂³	1	2	yes	—
111	C₂²×D₄×C₇₃	C₂³	1	2	yes	—
112	C₂²×D₄×C₇₃	C₂³	1	1	yes	characteristic
113	C₂²×D₄×C₇₃	C₂³	1	1	yes	characteristic
114	C₂³×C₄×C₇₃	C₂³	1	1	yes	characteristic
115	C₂³×C₄×C₇₃	C₂³	1	2	yes	—
116	C₂³×C₄×C₇₃	C₂³	1	2	yes	—
117	C₂³×C₄×C₇₃	C₂³	1	2	yes	—
118	C₂³×C₄×C₇₃	C₂³	1	2	yes	—
119	C₂³×C₄×C₇₃	C₂³	1	2	yes	—
120	C₂³×C₄×C₇₃	C₂³	1	2	yes	—
121	C₂³×C₄×C₇₃	C₂³	1	1	yes	characteristic
122	C₂³×C₄×C₇₃	C₂³	1	1	yes	characteristic
123	#126×C₇₃	—	2	8	no	—
124	#126×C₇₃	—	2	8	no	—
125	#125×C₇₃	—	2	8	no	—
126	#123×C₇₃	—	2	8	no	—
127	#123×C₇₃	—	2	8	no	—
128	#123×C₇₃	—	2	8	no	—
129	#123×C₇₃	—	4	4	no	—
130	#121×C₇₃	—	2	8	no	—
131	#121×C₇₃	—	2	8	no	—
132	#121×C₇₃	—	2	8	no	—
133	#121×C₇₃	—	2	4	no	—
134	#121×C₇₃	D₄	1	8	yes	complemented
135	C₄×D₄×C₇₃	—	2	8	no	—
136	C₄×D₄×C₇₃	—	2	8	no	—
137	C₄×D₄×C₇₃	—	2	8	no	—
138	C₄×D₄×C₇₃	—	2	8	no	—
139	C₄×D₄×C₇₃	—	2	8	no	—
140	C₄×D₄×C₇₃	—	4	2	no	—
141	C₄×D₄×C₇₃	—	4	2	no	—
142	#117×C₇₃	—	2	8	no	—
143	C₂×C₄⋊C₄×C₇₃	—	2	8	no	—
144	C₂×C₄⋊C₄×C₇₃	—	2	4	no	—
145	C₂×C₄⋊C₄×C₇₃	—	4	2	no	—
146	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
147	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
148	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
149	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
150	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
151	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
152	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
153	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
154	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
155	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
156	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
157	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
158	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
159	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
160	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
161	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
162	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
163	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
164	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
165	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
166	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
167	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
168	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
169	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
170	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
171	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
172	C₂×C₂²⋊C₄×C₇₃	C₂³	1	2	yes	—
173	C₂×C₂²⋊C₄×C₇₃	C₂³	1	2	yes	—
174	C₂×C₂²⋊C₄×C₇₃	C₂³	1	2	yes	—
175	C₂×C₂²⋊C₄×C₇₃	C₂³	1	2	yes	—
176	C₂×C₂²⋊C₄×C₇₃	C₂³	1	2	yes	—
177	C₂×C₂²⋊C₄×C₇₃	C₂³	1	2	yes	—
178	C₂×C₂²⋊C₄×C₇₃	C₂³	1	2	yes	—
179	C₂×C₂²⋊C₄×C₇₃	C₂³	1	2	yes	—
180	C₂×C₂²⋊C₄×C₇₃	C₂³	1	2	yes	—
181	C₂×C₂²⋊C₄×C₇₃	C₂³	1	2	yes	—
182	C₂×C₂²⋊C₄×C₇₃	C₂³	1	2	yes	—
183	C₂×C₂²⋊C₄×C₇₃	C₂³	1	2	yes	—
184	C₂×C₂²⋊C₄×C₇₃	C₂³	1	2	yes	—
185	C₂×C₂²⋊C₄×C₇₃	C₂³	1	2	yes	—
186	C₂×C₂²⋊C₄×C₇₃	C₂³	1	2	yes	—
187	C₂×C₂²⋊C₄×C₇₃	C₂³	1	2	yes	—
188	C₂×C₂²⋊C₄×C₇₃	C₂³	1	2	yes	—
189	C₂×C₂²⋊C₄×C₇₃	C₂³	1	2	yes	—
190	C₂×C₂²⋊C₄×C₇₃	C₂³	1	2	yes	—
191	C₂×C₂²⋊C₄×C₇₃	C₂³	1	2	yes	—
192	C₂×C₄²×C₇₃	—	4	2	no	—
193	C₂×C₄²×C₇₃	C₂³	1	2	yes	—
194	C₂×C₄²×C₇₃	C₂³	1	2	yes	—
195	C₂×C₄²×C₇₃	C₂³	1	2	yes	—
196	C₂×C₄²×C₇₃	C₂³	1	2	yes	—
197	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
198	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
199	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
200	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
201	#95×C₇₃	C₂³	1	2	yes	—
202	#95×C₇₃	C₂³	1	2	yes	—
203	#95×C₇₃	C₂³	1	2	yes	—
204	#95×C₇₃	C₂³	1	2	yes	—
205	#95×C₇₃	C₂³	1	2	yes	—
206	#95×C₇₃	C₂³	1	2	yes	—
207	#95×C₇₃	C₂³	1	2	yes	—
208	#95×C₇₃	C₂³	1	2	yes	—
209	#95×C₇₃	C₂³	1	2	yes	—
210	#95×C₇₃	C₂³	1	2	yes	—
211	#95×C₇₃	C₂³	1	2	yes	—
212	#95×C₇₃	C₂³	1	2	yes	—
213	#95×C₇₃	C₂³	1	2	yes	—
214	#95×C₇₃	C₂³	1	2	yes	—
215	#95×C₇₃	C₂³	1	2	yes	—
216	#95×C₇₃	C₂³	1	2	yes	—
217	#95×C₇₃	C₂³	1	2	yes	—
218	#95×C₇₃	C₂³	1	2	yes	—
219	C₂⁴×C₇₃	C₂⁴	1	2	yes	—
220	C₂⁴×C₇₃	C₂⁴	1	2	yes	—
221	C₂⁴×C₇₃	C₂⁴	1	1	yes	characteristic
222	C₂×D₄×C₇₃	—	2	4	no	—
223	C₂×D₄×C₇₃	—	2	4	no	—
224	C₂×D₄×C₇₃	—	2	4	no	—
225	C₂×D₄×C₇₃	—	2	4	no	—
226	C₂×D₄×C₇₃	—	2	4	no	—
227	C₂×D₄×C₇₃	—	2	4	no	—
228	C₂×D₄×C₇₃	—	2	4	no	—
229	C₂×D₄×C₇₃	—	2	2	no	—
230	C₂×D₄×C₇₃	—	2	4	no	—
231	C₂×D₄×C₇₃	—	4	1	no	—
232	C₂×D₄×C₇₃	—	4	1	no	—
233	C₂×D₄×C₇₃	—	4	1	no	—
234	C₂×D₄×C₇₃	—	4	1	no	—
235	C₂×D₄×C₇₃	—	4	2	no	—
236	C₂×D₄×C₇₃	—	4	2	no	—
237	C₂×D₄×C₇₃	—	4	2	no	—
238	C₂×D₄×C₇₃	C₂×D₄	1	8	yes	—
239	C₂×D₄×C₇₃	C₂×D₄	1	4	yes	—
240	C₂²×C₄×C₇₃	—	2	2	no	—
241	C₂²×C₄×C₇₃	—	2	2	no	—
242	C₂²×C₄×C₇₃	—	2	2	no	—
243	C₂²×C₄×C₇₃	—	2	4	no	—
244	C₂²×C₄×C₇₃	—	2	4	no	—
245	C₂²×C₄×C₇₃	—	2	4	no	—
246	C₂²×C₄×C₇₃	—	2	4	no	—
247	C₂²×C₄×C₇₃	—	2	4	no	—
248	C₂²×C₄×C₇₃	—	2	4	no	—
249	C₂²×C₄×C₇₃	—	2	4	no	—
250	C₂²×C₄×C₇₃	—	2	4	no	—
251	C₂²×C₄×C₇₃	—	4	1	no	—
252	C₂²×C₄×C₇₃	—	4	1	no	—
253	C₂²×C₄×C₇₃	—	4	1	no	—
254	C₂²×C₄×C₇₃	—	4	1	no	—
255	C₂²×C₄×C₇₃	—	4	2	no	—
256	C₂²×C₄×C₇₃	—	4	2	no	—
257	C₂²×C₄×C₇₃	—	4	2	no	—
258	C₂²×C₄×C₇₃	—	4	2	no	—
259	C₂²×C₄×C₇₃	—	4	2	no	—
260	C₂²×C₄×C₇₃	—	4	2	no	—
261	C₂²×C₄×C₇₃	—	4	2	no	—
262	C₂²×C₄×C₇₃	—	4	2	no	—
263	C₂²×C₄×C₇₃	—	4	2	no	—
264	C₂²×C₄×C₇₃	—	4	2	no	—
265	C₂²×C₄×C₇₃	C₂×D₄	1	4	yes	—
266	C₂²×C₄×C₇₃	#41	1	4	yes	—
267	C₂²×C₄×C₇₃	C₂⁴	1	2	yes	—
268	C₂²×C₄×C₇₃	C₂⁴	1	2	yes	—
269	C₂²×C₄×C₇₃	C₂⁴	1	2	yes	—
270	C₂²×C₄×C₇₃	C₂⁴	1	2	yes	—
271	C₂²×C₄×C₇₃	C₂⁴	1	2	yes	—
272	C₂²×C₄×C₇₃	C₂⁴	1	2	yes	—
273	C₂²×C₄×C₇₃	C₂⁴	1	2	yes	—
274	C₂²×C₄×C₇₃	C₂⁴	1	2	yes	—
275	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
276	C₂²×C₄×C₇₃	C₂⁴	1	2	yes	—
277	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
278	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
279	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
280	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
281	C₂²×C₄×C₇₃	C₂⁴	1	2	yes	—
282	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
283	C₄⋊C₄×C₇₃	—	2	4	no	—
284	C₄⋊C₄×C₇₃	—	2	4	no	—
285	C₄⋊C₄×C₇₃	—	2	4	no	—
286	C₄⋊C₄×C₇₃	—	2	4	no	—
287	C₄⋊C₄×C₇₃	—	2	4	no	—
288	C₄⋊C₄×C₇₃	—	2	4	no	—
289	C₄⋊C₄×C₇₃	—	2	4	no	—
290	C₄⋊C₄×C₇₃	—	2	4	no	—
291	C₄⋊C₄×C₇₃	—	2	4	no	—
292	C₄⋊C₄×C₇₃	—	2	4	no	—
293	C₄⋊C₄×C₇₃	—	2	2	no	—
294	C₄⋊C₄×C₇₃	—	2	4	no	—
295	C₄⋊C₄×C₇₃	—	2	2	no	—
296	C₄⋊C₄×C₇₃	—	2	4	no	—
297	C₄⋊C₄×C₇₃	—	2	4	no	—
298	C₄⋊C₄×C₇₃	—	4	1	no	—
299	C₄⋊C₄×C₇₃	—	4	1	no	—
300	C₄⋊C₄×C₇₃	—	4	1	no	—
301	C₄⋊C₄×C₇₃	—	4	1	no	—
302	C₄⋊C₄×C₇₃	—	4	2	no	—
303	C₄⋊C₄×C₇₃	—	4	2	no	—
304	C₄⋊C₄×C₇₃	—	4	1	no	—
305	C₄⋊C₄×C₇₃	—	4	1	no	—
306	C₄⋊C₄×C₇₃	—	4	2	no	—
307	C₄⋊C₄×C₇₃	C₂×D₄	1	4	yes	—
308	C₄⋊C₄×C₇₃	#41	1	4	yes	—
309	C₂²⋊C₄×C₇₃	—	2	4	no	—
310	C₂²⋊C₄×C₇₃	—	2	4	no	—
311	C₂²⋊C₄×C₇₃	—	2	4	no	—
312	C₂²⋊C₄×C₇₃	—	2	4	no	—
313	C₂²⋊C₄×C₇₃	—	2	4	no	—
314	C₂²⋊C₄×C₇₃	—	2	4	no	—
315	C₂²⋊C₄×C₇₃	—	2	4	no	—
316	C₂²⋊C₄×C₇₃	—	2	4	no	—
317	C₂²⋊C₄×C₇₃	—	2	4	no	—
318	C₂²⋊C₄×C₇₃	—	2	4	no	—
319	C₂²⋊C₄×C₇₃	—	2	4	no	—
320	C₂²⋊C₄×C₇₃	—	2	4	no	—
321	C₂²⋊C₄×C₇₃	—	2	4	no	—
322	C₂²⋊C₄×C₇₃	—	2	4	no	—
323	C₂²⋊C₄×C₇₃	—	2	4	no	—
324	C₂²⋊C₄×C₇₃	—	2	4	no	—
325	C₂²⋊C₄×C₇₃	—	4	2	no	—
326	C₂²⋊C₄×C₇₃	—	4	2	no	—
327	C₂²⋊C₄×C₇₃	—	4	2	no	—
328	C₂²⋊C₄×C₇₃	C₂×D₄	1	8	yes	—
329	C₄²×C₇₃	—	2	4	no	—
330	C₄²×C₇₃	—	2	4	no	—
331	C₄²×C₇₃	—	2	4	no	—
332	C₄²×C₇₃	—	2	4	no	—
333	C₄²×C₇₃	—	2	2	no	—
334	C₄²×C₇₃	—	2	2	no	—
335	C₄²×C₇₃	—	4	1	no	—
336	C₄²×C₇₃	—	4	1	no	—
337	C₂³×C₇₃	—	2	1	no	—
338	C₂³×C₇₃	—	2	1	no	—
339	C₂³×C₇₃	—	2	1	no	—
340	C₂³×C₇₃	—	2	1	no	—
341	C₂³×C₇₃	—	2	2	no	—
342	C₂³×C₇₃	—	2	2	no	—
343	C₂³×C₇₃	—	2	2	no	—
344	C₂³×C₇₃	—	2	2	no	—
345	C₂³×C₇₃	—	2	2	no	—
346	C₂³×C₇₃	—	2	2	no	—
347	C₂³×C₇₃	—	2	2	no	—
348	C₂³×C₇₃	—	2	2	no	—
349	C₂³×C₇₃	—	2	2	no	—
350	C₂³×C₇₃	—	2	2	no	—
351	C₂³×C₇₃	—	2	2	no	—
352	C₂³×C₇₃	—	2	2	no	—
353	C₂³×C₇₃	—	2	2	no	—
354	C₂³×C₇₃	C₂²×D₄	1	4	yes	—
355	C₂³×C₇₃	C₂²×D₄	1	2	yes	—
356	C₂³×C₇₃	C₂×#41	1	2	yes	—
357	C₂³×C₇₃	2₋¹⁺⁴	1	2	yes	—
358	C₂³×C₇₃	C₂⁵	1	1	yes	characteristic
359	D₄×C₇₃	—	2	16	no	—
360	D₄×C₇₃	—	4	4	no	—
361	D₄×C₇₃	—	4	8	no	—
362	D₄×C₇₃	—	4	4	no	—
363	D₄×C₇₃	—	4	8	no	—
364	D₄×C₇₃	—	8	4	no	—
365	C₂×C₄×C₇₃	—	2	8	no	—
366	C₂×C₄×C₇₃	—	2	2	no	—
367	C₂×C₄×C₇₃	—	2	2	no	—
368	C₂×C₄×C₇₃	—	2	1	no	—
369	C₂×C₄×C₇₃	—	2	1	no	—
370	C₂×C₄×C₇₃	—	2	1	no	—
371	C₂×C₄×C₇₃	—	2	1	no	—
372	C₂×C₄×C₇₃	—	2	1	no	—
373	C₂×C₄×C₇₃	—	2	1	no	—
374	C₂×C₄×C₇₃	—	2	1	no	—
375	C₂×C₄×C₇₃	—	2	1	no	—
376	C₂×C₄×C₇₃	—	2	2	no	—
377	C₂×C₄×C₇₃	—	2	1	no	—
378	C₂×C₄×C₇₃	—	2	1	no	—
379	C₂×C₄×C₇₃	—	2	1	no	—
380	C₂×C₄×C₇₃	—	2	1	no	—
381	C₂×C₄×C₇₃	—	2	2	no	—
382	C₂×C₄×C₇₃	—	2	2	no	—
383	C₂×C₄×C₇₃	—	2	2	no	—
384	C₂×C₄×C₇₃	—	2	2	no	—
385	C₂×C₄×C₇₃	—	2	2	no	—
386	C₂×C₄×C₇₃	—	2	2	no	—
387	C₂×C₄×C₇₃	—	2	2	no	—
388	C₂×C₄×C₇₃	—	2	2	no	—
389	C₂×C₄×C₇₃	—	2	2	no	—
390	C₂×C₄×C₇₃	—	2	2	no	—
391	C₂×C₄×C₇₃	—	2	2	no	—
392	C₂×C₄×C₇₃	—	2	2	no	—
393	C₂×C₄×C₇₃	—	2	2	no	—
394	C₂×C₄×C₇₃	—	2	2	no	—
395	C₂×C₄×C₇₃	—	2	2	no	—
396	C₂×C₄×C₇₃	—	2	2	no	—
397	C₂×C₄×C₇₃	—	2	2	no	—
398	C₂×C₄×C₇₃	—	2	2	no	—
399	C₂×C₄×C₇₃	—	2	2	no	—
400	C₂×C₄×C₇₃	—	2	2	no	—
401	C₂×C₄×C₇₃	—	2	2	no	—
402	C₂×C₄×C₇₃	—	2	2	no	—
403	C₂×C₄×C₇₃	—	2	2	no	—
404	C₂×C₄×C₇₃	—	2	2	no	—
405	C₂×C₄×C₇₃	—	2	2	no	—
406	C₂×C₄×C₇₃	—	4	4	no	—
407	C₂×C₄×C₇₃	—	4	4	no	—
408	C₂×C₄×C₇₃	—	4	8	no	—
409	C₂×C₄×C₇₃	—	4	8	no	—
410	C₂×C₄×C₇₃	—	8	4	no	—
411	C₂×C₄×C₇₃	—	8	4	no	—
412	C₂×C₄×C₇₃	—	8	4	no	—
413	C₂×C₄×C₇₃	—	8	4	no	—
414	C₂×C₄×C₇₃	C₂²×D₄	1	4	yes	—
415	C₂×C₄×C₇₃	C₂²×D₄	1	2	yes	—
416	C₂×C₄×C₇₃	C₂²×D₄	1	2	yes	—
417	C₂×C₄×C₇₃	C₂×#41	1	2	yes	—
418	C₂×C₄×C₇₃	C₂×#41	1	2	yes	—
419	C₂×C₄×C₇₃	C₂×#41	1	2	yes	—
420	C₂×C₄×C₇₃	C₂×#41	1	4	yes	—
421	C₂×C₄×C₇₃	H(5,𝔽₂)	1	2	yes	—
422	C₂²×C₇₃	—	2	2	no	—
423	C₂²×C₇₃	—	2	2	no	—
424	C₂²×C₇₃	—	2	2	no	—
425	C₂²×C₇₃	—	2	2	no	—
426	C₂²×C₇₃	—	2	2	no	—
427	C₂²×C₇₃	—	2	2	no	—
428	C₂²×C₇₃	—	2	4	no	—
429	C₂²×C₇₃	—	2	4	no	—
430	C₂²×C₇₃	—	2	4	no	—
431	C₂²×C₇₃	—	4	2	no	—
432	C₂²×C₇₃	—	4	2	no	—
433	C₂²×C₇₃	—	4	2	no	—
434	C₂²×C₇₃	—	4	2	no	—
435	C₂²×C₇₃	—	4	2	no	—
436	C₂²×C₇₃	—	4	2	no	—
437	C₂²×C₇₃	—	4	2	no	—
438	C₂²×C₇₃	—	4	2	no	—
439	C₂²×C₇₃	—	4	2	no	—
440	C₂²×C₇₃	—	4	2	no	—
441	C₂²×C₇₃	—	4	2	no	—
442	C₂²×C₇₃	#547	1	4	yes	—
443	C₂²×C₇₃	C₂³×D₄	1	1	yes	characteristic
444	C₂²×C₇₃	C₂²×#41	1	1	yes	characteristic
445	C₂²×C₇₃	C₂²×#41	1	1	yes	characteristic
446	C₂²×C₇₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
447	C₂²×C₇₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
448	C₂²×C₇₃	#585	1	1	yes	characteristic
449	C₂²×C₇₃	#585	1	1	yes	characteristic
450	C₄×C₇₃	—	2	4	no	—
451	C₄×C₇₃	—	2	4	no	—
452	C₄×C₇₃	—	2	2	no	—
453	C₄×C₇₃	—	2	2	no	—
454	C₄×C₇₃	—	2	2	no	—
455	C₄×C₇₃	—	2	2	no	—
456	C₄×C₇₃	—	2	2	no	—
457	C₄×C₇₃	—	2	2	no	—
458	C₄×C₇₃	—	4	2	no	—
459	C₄×C₇₃	—	4	2	no	—
460	C₄×C₇₃	—	4	2	no	—
461	C₄×C₇₃	—	4	2	no	—
462	C₄×C₇₃	—	4	2	no	—
463	C₄×C₇₃	—	4	2	no	—
464	C₄×C₇₃	—	4	2	no	—
465	C₄×C₇₃	—	4	2	no	—
466	#59825	C₇₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
467	C₂×C₇₃	—	2	4	no	—
468	C₂×C₇₃	—	4	4	no	—
469	C₂×C₇₃	—	8	2	no	—
470	C₂×C₇₃	C₂×#547	1	1	yes	characteristic
471	C₂×C₇₃	D₄×#41	1	1	yes	characteristic
472	C₂×C₇₃	#3480	1	1	yes	characteristic
473	C₂×C₇₃	#3492	1	1	yes	characteristic
474	C₂×C₇₃	#3496	1	1	yes	characteristic
475	C₂×C₇₃	#3505	1	1	yes	characteristic
476	C₂×C₇₃	#3553	1	1	yes	characteristic
477	C₂×#553	C₂×C₇₃	1	2	yes	complemented
478	#2727	C₂×C₇₃	1	1	yes	characteristic, complemented
479	#2726	C₂×C₇₃	1	1	yes	characteristic, complemented
480	#2724	C₂×C₇₃	1	1	yes	characteristic, complemented
481	#2682	C₂×C₇₃	1	1	yes	characteristic, complemented
482	#2579	C₂×C₇₃	1	2	yes	complemented
483	#2553	C₂×C₇₃	1	2	yes	complemented
484	#2543	C₂×C₇₃	1	2	yes	complemented
485	#2519	C₂×C₇₃	1	2	yes	complemented
486	#2478	C₂×C₇₃	1	2	yes	complemented
487	#2455	C₂×C₇₃	1	2	yes	complemented
488	#2443	C₂×C₇₃	1	2	yes	complemented
489	#2443	C₂×C₇₃	1	2	yes	complemented
490	#2425	C₂×C₇₃	1	2	yes	complemented
491	#2359	C₂×C₇₃	1	2	yes	complemented
492	#2349	C₂×C₇₃	1	2	yes	complemented
493	C₄×#121	C₂×C₇₃	1	1	yes	characteristic, complemented
494	C₄×#121	C₂×C₇₃	1	1	yes	characteristic, complemented
495	C₂×#389	C₂×C₇₃	1	1	yes	characteristic, complemented
496	C₇₃	#59825	1	1	yes	characteristic, direct product factor, Sylow
497	#553	—	2	16	no	—
498	C₂×#126	C₂²×C₇₃	1	2	yes	—
499	C₂×#126	C₂²×C₇₃	1	2	yes	—
500	C₂×#125	C₂²×C₇₃	1	2	yes	—
501	C₂×#123	C₂²×C₇₃	1	2	yes	—
502	C₂×#123	C₂²×C₇₃	1	2	yes	—
503	C₂×#123	C₂²×C₇₃	1	2	yes	—
504	C₂×#123	C₂²×C₇₃	1	2	yes	—
505	C₂×#121	C₂²×C₇₃	1	2	yes	—
506	C₂×#121	C₂²×C₇₃	1	2	yes	—
507	C₂×#121	C₂²×C₇₃	1	2	yes	—
508	C₂×#121	C₂²×C₇₃	1	1	yes	characteristic
509	C₂×#121	C₂²×C₇₃	1	1	yes	characteristic
510	C₂×C₄×D₄	C₂²×C₇₃	1	2	yes	—
511	C₂×C₄×D₄	C₂²×C₇₃	1	2	yes	—
512	C₂×C₄×D₄	C₂²×C₇₃	1	2	yes	—
513	C₂×C₄×D₄	C₂²×C₇₃	1	2	yes	—
514	C₂×C₄×D₄	C₂²×C₇₃	1	2	yes	—
515	C₂×C₄×D₄	C₂²×C₇₃	1	1	yes	characteristic
516	C₂×C₄×D₄	C₂²×C₇₃	1	1	yes	characteristic
517	C₂×#117	C₂²×C₇₃	1	2	yes	—
518	C₂²×C₄⋊C₄	C₂²×C₇₃	1	2	yes	—
519	C₂²×C₄⋊C₄	C₂²×C₇₃	1	1	yes	characteristic
520	C₂²×C₄⋊C₄	C₂²×C₇₃	1	1	yes	characteristic
521	C₂²×C₄²	C₂²×C₇₃	1	1	yes	characteristic
522	#399	C₂²×C₇₃	1	2	yes	—
523	#399	C₂²×C₇₃	1	2	yes	—
524	#398	C₂²×C₇₃	1	2	yes	—
525	#398	C₂²×C₇₃	1	2	yes	—
526	#398	C₂²×C₇₃	1	2	yes	—
527	#398	C₂²×C₇₃	1	2	yes	—
528	#398	C₂²×C₇₃	1	2	yes	—
529	#397	C₂²×C₇₃	1	2	yes	—
530	#397	C₂²×C₇₃	1	2	yes	—
531	#397	C₂²×C₇₃	1	2	yes	—
532	#396	C₂²×C₇₃	1	2	yes	—
533	#396	C₂²×C₇₃	1	2	yes	—
534	#394	C₂²×C₇₃	1	2	yes	—
535	#394	C₂²×C₇₃	1	2	yes	—
536	#394	C₂²×C₇₃	1	2	yes	—
537	#392	C₂²×C₇₃	1	2	yes	—
538	#390	C₂²×C₇₃	1	1	yes	characteristic
539	#390	C₂²×C₇₃	1	1	yes	characteristic
540	#389	C₂²×C₇₃	1	2	yes	—
541	#389	C₂²×C₇₃	1	2	yes	—
542	#389	C₂²×C₇₃	1	1	yes	characteristic
543	#389	C₂²×C₇₃	1	2	yes	—
544	#389	C₂²×C₇₃	1	1	yes	characteristic
545	#389	C₂²×C₇₃	1	2	yes	—
546	#389	C₂²×C₇₃	1	1	yes	characteristic
547	#389	C₂²×C₇₃	1	1	yes	characteristic
548	#389	C₂²×C₇₃	1	1	yes	characteristic
549	#389	C₂²×C₇₃	1	1	yes	characteristic
550	#388	C₂²×C₇₃	1	2	yes	—
551	#388	C₂²×C₇₃	1	2	yes	—
552	#388	C₂²×C₇₃	1	2	yes	—
553	#388	C₂²×C₇₃	1	2	yes	—
554	#388	C₂²×C₇₃	1	2	yes	—
555	#388	C₂²×C₇₃	1	2	yes	—
556	#387	C₂²×C₇₃	1	2	yes	—
557	#387	C₂²×C₇₃	1	2	yes	—
558	#387	C₂²×C₇₃	1	2	yes	—
559	#387	C₂²×C₇₃	1	2	yes	—
560	#386	C₂²×C₇₃	1	2	yes	—
561	#386	C₂²×C₇₃	1	2	yes	—
562	#386	C₂²×C₇₃	1	2	yes	—
563	#386	C₂²×C₇₃	1	2	yes	—
564	#386	C₂²×C₇₃	1	2	yes	—
565	#386	C₂²×C₇₃	1	2	yes	—
566	#385	C₂²×C₇₃	1	2	yes	—
567	#385	C₂²×C₇₃	1	2	yes	—
568	#385	C₂²×C₇₃	1	2	yes	—
569	#385	C₂²×C₇₃	1	2	yes	—
570	#385	C₂²×C₇₃	1	2	yes	—
571	#385	C₂²×C₇₃	1	2	yes	—
572	#385	C₂²×C₇₃	1	2	yes	—
573	#385	C₂²×C₇₃	1	2	yes	—
574	#382	C₂²×C₇₃	1	2	yes	—
575	#380	C₂²×C₇₃	1	1	yes	characteristic
576	#380	C₂²×C₇₃	1	1	yes	characteristic
577	#380	C₂²×C₇₃	1	2	yes	—
578	C₄×C₄⋊C₄	C₂²×C₇₃	1	2	yes	—
579	C₄×C₄⋊C₄	C₂²×C₇₃	1	1	yes	characteristic
580	C₄×C₄⋊C₄	C₂²×C₇₃	1	1	yes	characteristic
581	C₄×C₂²⋊C₄	C₂²×C₇₃	1	2	yes	—
582	C₄×C₂²⋊C₄	C₂²×C₇₃	1	2	yes	—
583	C₂×#95	C₂²×C₇₃	1	2	yes	—
584	C₂×#95	C₂²×C₇₃	1	2	yes	—
585	C₂²×D₄	C₂³×C₇₃	1	2	yes	—
586	C₂²×D₄	C₂³×C₇₃	1	2	yes	—
587	C₂²×D₄	C₂³×C₇₃	1	2	yes	—
588	C₂²×D₄	C₂³×C₇₃	1	1	yes	characteristic
589	C₂²×D₄	C₂³×C₇₃	1	2	yes	—
590	C₂²×D₄	C₂³×C₇₃	1	1	yes	characteristic
591	C₂³×C₄	C₂³×C₇₃	1	1	yes	characteristic
592	C₂³×C₄	C₂³×C₇₃	1	2	yes	—
593	C₂³×C₄	C₂³×C₇₃	1	2	yes	—
594	C₂³×C₄	C₂³×C₇₃	1	2	yes	—
595	C₂³×C₄	C₂³×C₇₃	1	2	yes	—
596	C₂³×C₄	C₂³×C₇₃	1	2	yes	—
597	C₂³×C₄	C₂³×C₇₃	1	2	yes	—
598	C₂³×C₄	C₂³×C₇₃	1	1	yes	characteristic
599	C₂³×C₄	C₂³×C₇₃	1	1	yes	characteristic
600	#126	—	2	8	no	—
601	#126	—	2	8	no	—
602	#125	—	2	8	no	—
603	#123	—	2	8	no	—
604	#123	—	2	8	no	—
605	#123	—	2	8	no	—
606	#123	—	4	4	no	—
607	#121	—	2	8	no	—
608	#121	—	2	8	no	—
609	#121	—	2	8	no	—
610	#121	—	2	4	no	—
611	#121	D₄×C₇₃	1	8	yes	complemented
612	C₄×D₄	—	2	8	no	—
613	C₄×D₄	—	2	8	no	—
614	C₄×D₄	—	2	8	no	—
615	C₄×D₄	—	2	8	no	—
616	C₄×D₄	—	2	8	no	—
617	C₄×D₄	—	4	2	no	—
618	C₄×D₄	—	4	2	no	—
619	#117	—	2	8	no	—
620	C₂×C₄⋊C₄	—	2	8	no	—
621	C₂×C₄⋊C₄	—	2	4	no	—
622	C₂×C₄⋊C₄	—	4	2	no	—
623	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
624	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
625	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
626	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
627	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
628	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
629	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
630	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
631	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
632	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
633	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
634	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
635	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
636	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
637	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
638	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
639	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
640	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
641	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
642	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
643	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
644	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
645	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
646	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
647	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
648	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
649	C₂×C₂²⋊C₄	C₂³×C₇₃	1	2	yes	—
650	C₂×C₂²⋊C₄	C₂³×C₇₃	1	2	yes	—
651	C₂×C₂²⋊C₄	C₂³×C₇₃	1	2	yes	—
652	C₂×C₂²⋊C₄	C₂³×C₇₃	1	2	yes	—
653	C₂×C₂²⋊C₄	C₂³×C₇₃	1	2	yes	—
654	C₂×C₂²⋊C₄	C₂³×C₇₃	1	2	yes	—
655	C₂×C₂²⋊C₄	C₂³×C₇₃	1	2	yes	—
656	C₂×C₂²⋊C₄	C₂³×C₇₃	1	2	yes	—
657	C₂×C₂²⋊C₄	C₂³×C₇₃	1	2	yes	—
658	C₂×C₂²⋊C₄	C₂³×C₇₃	1	2	yes	—
659	C₂×C₂²⋊C₄	C₂³×C₇₃	1	2	yes	—
660	C₂×C₂²⋊C₄	C₂³×C₇₃	1	2	yes	—
661	C₂×C₂²⋊C₄	C₂³×C₇₃	1	2	yes	—
662	C₂×C₂²⋊C₄	C₂³×C₇₃	1	2	yes	—
663	C₂×C₂²⋊C₄	C₂³×C₇₃	1	2	yes	—
664	C₂×C₂²⋊C₄	C₂³×C₇₃	1	2	yes	—
665	C₂×C₂²⋊C₄	C₂³×C₇₃	1	2	yes	—
666	C₂×C₂²⋊C₄	C₂³×C₇₃	1	2	yes	—
667	C₂×C₂²⋊C₄	C₂³×C₇₃	1	2	yes	—
668	C₂×C₂²⋊C₄	C₂³×C₇₃	1	2	yes	—
669	C₂×C₄²	—	4	2	no	—
670	C₂×C₄²	C₂³×C₇₃	1	2	yes	—
671	C₂×C₄²	C₂³×C₇₃	1	2	yes	—
672	C₂×C₄²	C₂³×C₇₃	1	2	yes	—
673	C₂×C₄²	C₂³×C₇₃	1	2	yes	—
674	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
675	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
676	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
677	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
678	#95	C₂³×C₇₃	1	2	yes	—
679	#95	C₂³×C₇₃	1	2	yes	—
680	#95	C₂³×C₇₃	1	2	yes	—
681	#95	C₂³×C₇₃	1	2	yes	—
682	#95	C₂³×C₇₃	1	2	yes	—
683	#95	C₂³×C₇₃	1	2	yes	—
684	#95	C₂³×C₇₃	1	2	yes	—
685	#95	C₂³×C₇₃	1	2	yes	—
686	#95	C₂³×C₇₃	1	2	yes	—
687	#95	C₂³×C₇₃	1	2	yes	—
688	#95	C₂³×C₇₃	1	2	yes	—
689	#95	C₂³×C₇₃	1	2	yes	—
690	#95	C₂³×C₇₃	1	2	yes	—
691	#95	C₂³×C₇₃	1	2	yes	—
692	#95	C₂³×C₇₃	1	2	yes	—
693	#95	C₂³×C₇₃	1	2	yes	—
694	#95	C₂³×C₇₃	1	2	yes	—
695	#95	C₂³×C₇₃	1	2	yes	—
696	C₂⁴	C₂⁴×C₇₃	1	2	yes	—
697	C₂⁴	C₂⁴×C₇₃	1	2	yes	—
698	C₂⁴	C₂⁴×C₇₃	1	1	yes	characteristic
699	C₂×D₄	—	2	4	no	—
700	C₂×D₄	—	2	4	no	—
701	C₂×D₄	—	2	4	no	—
702	C₂×D₄	—	2	4	no	—
703	C₂×D₄	—	2	4	no	—
704	C₂×D₄	—	2	4	no	—
705	C₂×D₄	—	2	4	no	—
706	C₂×D₄	—	2	2	no	—
707	C₂×D₄	—	2	4	no	—
708	C₂×D₄	—	4	1	no	—
709	C₂×D₄	—	4	1	no	—
710	C₂×D₄	—	4	1	no	—
711	C₂×D₄	—	4	1	no	—
712	C₂×D₄	—	4	2	no	—
713	C₂×D₄	—	4	2	no	—
714	C₂×D₄	—	4	2	no	—
715	C₂×D₄	C₂×D₄×C₇₃	1	8	yes	—
716	C₂×D₄	C₂×D₄×C₇₃	1	4	yes	—
717	C₂²×C₄	—	2	2	no	—
718	C₂²×C₄	—	2	2	no	—
719	C₂²×C₄	—	2	2	no	—
720	C₂²×C₄	—	2	4	no	—
721	C₂²×C₄	—	2	4	no	—
722	C₂²×C₄	—	2	4	no	—
723	C₂²×C₄	—	2	4	no	—
724	C₂²×C₄	—	2	4	no	—
725	C₂²×C₄	—	2	4	no	—
726	C₂²×C₄	—	2	4	no	—
727	C₂²×C₄	—	2	4	no	—
728	C₂²×C₄	—	4	1	no	—
729	C₂²×C₄	—	4	1	no	—
730	C₂²×C₄	—	4	1	no	—
731	C₂²×C₄	—	4	1	no	—
732	C₂²×C₄	—	4	2	no	—
733	C₂²×C₄	—	4	2	no	—
734	C₂²×C₄	—	4	2	no	—
735	C₂²×C₄	—	4	2	no	—
736	C₂²×C₄	—	4	2	no	—
737	C₂²×C₄	—	4	2	no	—
738	C₂²×C₄	—	4	2	no	—
739	C₂²×C₄	—	4	2	no	—
740	C₂²×C₄	—	4	2	no	—
741	C₂²×C₄	—	4	2	no	—
742	C₂²×C₄	C₂×D₄×C₇₃	1	4	yes	—
743	C₂²×C₄	#41×C₇₃	1	4	yes	—
744	C₂²×C₄	C₂⁴×C₇₃	1	2	yes	—
745	C₂²×C₄	C₂⁴×C₇₃	1	2	yes	—
746	C₂²×C₄	C₂⁴×C₇₃	1	2	yes	—
747	C₂²×C₄	C₂⁴×C₇₃	1	2	yes	—
748	C₂²×C₄	C₂⁴×C₇₃	1	2	yes	—
749	C₂²×C₄	C₂⁴×C₇₃	1	2	yes	—
750	C₂²×C₄	C₂⁴×C₇₃	1	2	yes	—
751	C₂²×C₄	C₂⁴×C₇₃	1	2	yes	—
752	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
753	C₂²×C₄	C₂⁴×C₇₃	1	2	yes	—
754	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
755	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
756	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
757	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
758	C₂²×C₄	C₂⁴×C₇₃	1	2	yes	—
759	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
760	C₄⋊C₄	—	2	4	no	—
761	C₄⋊C₄	—	2	4	no	—
762	C₄⋊C₄	—	2	4	no	—
763	C₄⋊C₄	—	2	4	no	—
764	C₄⋊C₄	—	2	4	no	—
765	C₄⋊C₄	—	2	4	no	—
766	C₄⋊C₄	—	2	4	no	—
767	C₄⋊C₄	—	2	4	no	—
768	C₄⋊C₄	—	2	4	no	—
769	C₄⋊C₄	—	2	4	no	—
770	C₄⋊C₄	—	2	2	no	—
771	C₄⋊C₄	—	2	4	no	—
772	C₄⋊C₄	—	2	2	no	—
773	C₄⋊C₄	—	2	4	no	—
774	C₄⋊C₄	—	2	4	no	—
775	C₄⋊C₄	—	4	1	no	—
776	C₄⋊C₄	—	4	1	no	—
777	C₄⋊C₄	—	4	1	no	—
778	C₄⋊C₄	—	4	1	no	—
779	C₄⋊C₄	—	4	2	no	—
780	C₄⋊C₄	—	4	2	no	—
781	C₄⋊C₄	—	4	1	no	—
782	C₄⋊C₄	—	4	1	no	—
783	C₄⋊C₄	—	4	2	no	—
784	C₄⋊C₄	C₂×D₄×C₇₃	1	4	yes	—
785	C₄⋊C₄	#41×C₇₃	1	4	yes	—
786	C₂²⋊C₄	—	2	4	no	—
787	C₂²⋊C₄	—	2	4	no	—
788	C₂²⋊C₄	—	2	4	no	—
789	C₂²⋊C₄	—	2	4	no	—
790	C₂²⋊C₄	—	2	4	no	—
791	C₂²⋊C₄	—	2	4	no	—
792	C₂²⋊C₄	—	2	4	no	—
793	C₂²⋊C₄	—	2	4	no	—
794	C₂²⋊C₄	—	2	4	no	—
795	C₂²⋊C₄	—	2	4	no	—
796	C₂²⋊C₄	—	2	4	no	—
797	C₂²⋊C₄	—	2	4	no	—
798	C₂²⋊C₄	—	2	4	no	—
799	C₂²⋊C₄	—	2	4	no	—
800	C₂²⋊C₄	—	2	4	no	—
801	C₂²⋊C₄	—	2	4	no	—
802	C₂²⋊C₄	—	4	2	no	—
803	C₂²⋊C₄	—	4	2	no	—
804	C₂²⋊C₄	—	4	2	no	—
805	C₂²⋊C₄	C₂×D₄×C₇₃	1	8	yes	—
806	C₄²	—	2	4	no	—
807	C₄²	—	2	4	no	—
808	C₄²	—	2	4	no	—
809	C₄²	—	2	4	no	—
810	C₄²	—	2	2	no	—
811	C₄²	—	2	2	no	—
812	C₄²	—	4	1	no	—
813	C₄²	—	4	1	no	—
814	C₂³	—	2	1	no	—
815	C₂³	—	2	1	no	—
816	C₂³	—	2	1	no	—
817	C₂³	—	2	1	no	—
818	C₂³	—	2	2	no	—
819	C₂³	—	2	2	no	—
820	C₂³	—	2	2	no	—
821	C₂³	—	2	2	no	—
822	C₂³	—	2	2	no	—
823	C₂³	—	2	2	no	—
824	C₂³	—	2	2	no	—
825	C₂³	—	2	2	no	—
826	C₂³	—	2	2	no	—
827	C₂³	—	2	2	no	—
828	C₂³	—	2	2	no	—
829	C₂³	—	2	2	no	—
830	C₂³	—	2	2	no	—
831	C₂³	C₂²×D₄×C₇₃	1	4	yes	—
832	C₂³	C₂²×D₄×C₇₃	1	2	yes	—
833	C₂³	C₂×#41×C₇₃	1	2	yes	—
834	C₂³	2₋¹⁺⁴×C₇₃	1	2	yes	—
835	C₂³	C₂⁵×C₇₃	1	1	yes	characteristic
836	D₄	—	2	16	no	—
837	D₄	—	4	4	no	—
838	D₄	—	4	8	no	—
839	D₄	—	4	4	no	—
840	D₄	—	4	8	no	—
841	D₄	—	8	4	no	—
842	C₂×C₄	—	2	8	no	—
843	C₂×C₄	—	2	2	no	—
844	C₂×C₄	—	2	2	no	—
845	C₂×C₄	—	2	1	no	—
846	C₂×C₄	—	2	1	no	—
847	C₂×C₄	—	2	1	no	—
848	C₂×C₄	—	2	1	no	—
849	C₂×C₄	—	2	1	no	—
850	C₂×C₄	—	2	1	no	—
851	C₂×C₄	—	2	1	no	—
852	C₂×C₄	—	2	1	no	—
853	C₂×C₄	—	2	2	no	—
854	C₂×C₄	—	2	1	no	—
855	C₂×C₄	—	2	1	no	—
856	C₂×C₄	—	2	1	no	—
857	C₂×C₄	—	2	1	no	—
858	C₂×C₄	—	2	2	no	—
859	C₂×C₄	—	2	2	no	—
860	C₂×C₄	—	2	2	no	—
861	C₂×C₄	—	2	2	no	—
862	C₂×C₄	—	2	2	no	—
863	C₂×C₄	—	2	2	no	—
864	C₂×C₄	—	2	2	no	—
865	C₂×C₄	—	2	2	no	—
866	C₂×C₄	—	2	2	no	—
867	C₂×C₄	—	2	2	no	—
868	C₂×C₄	—	2	2	no	—
869	C₂×C₄	—	2	2	no	—
870	C₂×C₄	—	2	2	no	—
871	C₂×C₄	—	2	2	no	—
872	C₂×C₄	—	2	2	no	—
873	C₂×C₄	—	2	2	no	—
874	C₂×C₄	—	2	2	no	—
875	C₂×C₄	—	2	2	no	—
876	C₂×C₄	—	2	2	no	—
877	C₂×C₄	—	2	2	no	—
878	C₂×C₄	—	2	2	no	—
879	C₂×C₄	—	2	2	no	—
880	C₂×C₄	—	2	2	no	—
881	C₂×C₄	—	2	2	no	—
882	C₂×C₄	—	2	2	no	—
883	C₂×C₄	—	4	4	no	—
884	C₂×C₄	—	4	4	no	—
885	C₂×C₄	—	4	8	no	—
886	C₂×C₄	—	4	8	no	—
887	C₂×C₄	—	8	4	no	—
888	C₂×C₄	—	8	4	no	—
889	C₂×C₄	—	8	4	no	—
890	C₂×C₄	—	8	4	no	—
891	C₂×C₄	C₂²×D₄×C₇₃	1	4	yes	—
892	C₂×C₄	C₂²×D₄×C₇₃	1	2	yes	—
893	C₂×C₄	C₂²×D₄×C₇₃	1	2	yes	—
894	C₂×C₄	C₂×#41×C₇₃	1	2	yes	—
895	C₂×C₄	C₂×#41×C₇₃	1	2	yes	—
896	C₂×C₄	C₂×#41×C₇₃	1	2	yes	—
897	C₂×C₄	C₂×#41×C₇₃	1	4	yes	—
898	C₂×C₄	H(5,𝔽₂)×C₇₃	1	2	yes	—
899	C₂²	—	2	2	no	—
900	C₂²	—	2	2	no	—
901	C₂²	—	2	2	no	—
902	C₂²	—	2	2	no	—
903	C₂²	—	2	2	no	—
904	C₂²	—	2	2	no	—
905	C₂²	—	2	4	no	—
906	C₂²	—	2	4	no	—
907	C₂²	—	2	4	no	—
908	C₂²	—	4	2	no	—
909	C₂²	—	4	2	no	—
910	C₂²	—	4	2	no	—
911	C₂²	—	4	2	no	—
912	C₂²	—	4	2	no	—
913	C₂²	—	4	2	no	—
914	C₂²	—	4	2	no	—
915	C₂²	—	4	2	no	—
916	C₂²	—	4	2	no	—
917	C₂²	—	4	2	no	—
918	C₂²	—	4	2	no	—
919	C₂²	#547×C₇₃	1	4	yes	—
920	C₂²	C₂³×D₄×C₇₃	1	1	yes	characteristic
921	C₂²	C₂²×#41×C₇₃	1	1	yes	characteristic
922	C₂²	C₂²×#41×C₇₃	1	1	yes	characteristic
923	C₂²	C₂×H(5,𝔽₂)×C₇₃	1	1	yes	characteristic
924	C₂²	C₂×2₋¹⁺⁴×C₇₃	1	1	yes	characteristic
925	C₂²	#585×C₇₃	1	1	yes	characteristic
926	C₂²	#585×C₇₃	1	1	yes	characteristic
927	C₄	—	2	4	no	—
928	C₄	—	2	4	no	—
929	C₄	—	2	2	no	—
930	C₄	—	2	2	no	—
931	C₄	—	2	2	no	—
932	C₄	—	2	2	no	—
933	C₄	—	2	2	no	—
934	C₄	—	2	2	no	—
935	C₄	—	4	2	no	—
936	C₄	—	4	2	no	—
937	C₄	—	4	2	no	—
938	C₄	—	4	2	no	—
939	C₄	—	4	2	no	—
940	C₄	—	4	2	no	—
941	C₄	—	4	2	no	—
942	C₄	—	4	2	no	—
943	C₂	—	2	4	no	—
944	C₂	—	4	4	no	—
945	C₂	—	8	2	no	—
946	C₂	C₂×#547×C₇₃	1	1	yes	characteristic
947	C₂	D₄×#41×C₇₃	1	1	yes	characteristic
948	C₂	C₇₃×#3480	1	1	yes	characteristic
949	C₂	C₇₃×#3492	1	1	yes	characteristic
950	C₂	C₇₃×#3496	1	1	yes	characteristic
951	C₂	C₇₃×#3505	1	1	yes	characteristic
952	C₂	C₇₃×#3553	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₇₃	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₇₃
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₇₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×#553×C₇₃	C₂	semidirect
2. C₇₃×#2727	C₂	semidirect
3. C₇₃×#2726	C₂	semidirect
4. C₇₃×#2724	C₂	semidirect
5. C₇₃×#2682	C₂	semidirect
6. C₇₃×#2579	C₂	semidirect
7. C₇₃×#2553	C₂	semidirect
8. C₇₃×#2543	C₂	semidirect
9. C₇₃×#2519	C₂	semidirect
10. C₇₃×#2478	C₂	semidirect
11. C₇₃×#2455	C₂	semidirect
12. C₇₃×#2443	C₂	semidirect
13. C₇₃×#2443	C₂	semidirect
14. C₇₃×#2425	C₂	semidirect
15. C₇₃×#2359	C₂	semidirect
16. C₇₃×#2349	C₂	semidirect
17. C₄×#121×C₇₃	C₂	semidirect
18. C₄×#121×C₇₃	C₂	semidirect
19. C₂×#389×C₇₃	C₂	semidirect
134. #121×C₇₃	D₄	semidirect
466. #59825	C₇₃	direct (N × H)
477. C₂×#553	C₂×C₇₃	semidirect
478. #2727	C₂×C₇₃	semidirect
479. #2726	C₂×C₇₃	semidirect
480. #2724	C₂×C₇₃	semidirect
481. #2682	C₂×C₇₃	semidirect
482. #2579	C₂×C₇₃	semidirect
483. #2553	C₂×C₇₃	semidirect
484. #2543	C₂×C₇₃	semidirect
485. #2519	C₂×C₇₃	semidirect
486. #2478	C₂×C₇₃	semidirect
487. #2455	C₂×C₇₃	semidirect
488. #2443	C₂×C₇₃	semidirect
489. #2443	C₂×C₇₃	semidirect
490. #2425	C₂×C₇₃	semidirect
491. #2359	C₂×C₇₃	semidirect
492. #2349	C₂×C₇₃	semidirect
493. C₄×#121	C₂×C₇₃	semidirect
494. C₄×#121	C₂×C₇₃	semidirect
495. C₂×#389	C₂×C₇₃	semidirect
496. C₇₃	#59825	direct (N × H)
611. #121	D₄×C₇₃	semidirect

Maximal subgroups

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

subgroup	index
C₂×#553×C₇₃	2
C₇₃×#2727	2
C₇₃×#2726	2
C₇₃×#2724	2
C₇₃×#2682	2
C₇₃×#2579	2
C₇₃×#2553	2
C₇₃×#2543	2
C₇₃×#2519	2
C₇₃×#2478	2
C₇₃×#2455	2
C₇₃×#2443	2
C₇₃×#2425	2
C₇₃×#2359	2
C₇₃×#2349	2
C₄×#121×C₇₃	2
C₂×#389×C₇₃	2
#59825	73

Subgroups — C73×#59825 #32969229

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₃×#59825 #32969229