Subgroups — C₇₃×#59743 #32969147

Order 18688.

1720 conjugacy classes of subgroups.

The subgroup lattice has 838 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇₃×#2783	C₂	1	2	yes	maximal, complemented
2	C₇₃×#2733	C₂	1	1	yes	maximal, characteristic
3	C₇₃×#2731	C₂	1	1	yes	maximal, characteristic, complemented
4	C₇₃×#2602	C₂	1	2	yes	maximal, complemented
5	C₇₃×#2565	C₂	1	1	yes	maximal, characteristic, complemented
6	C₇₃×#2558	C₂	1	2	yes	maximal, complemented
7	C₇₃×#2557	C₂	1	2	yes	maximal, complemented
8	C₇₃×#2554	C₂	1	2	yes	maximal, complemented
9	C₇₃×#2554	C₂	1	2	yes	maximal, complemented
10	C₇₃×#2545	C₂	1	1	yes	maximal, characteristic, complemented
11	C₇₃×#2532	C₂	1	2	yes	maximal, complemented
12	C₇₃×#2518	C₂	1	2	yes	maximal, complemented
13	C₇₃×#2512	C₂	1	2	yes	maximal, complemented
14	C₇₃×#2374	C₂	1	2	yes	maximal, complemented
15	C₇₃×#2373	C₂	1	2	yes	maximal, complemented
16	C₇₃×#2372	C₂	1	1	yes	maximal, characteristic, complemented
17	C₇₃×#2369	C₂	1	1	yes	maximal, characteristic, complemented
18	C₄×#126×C₇₃	C₂	1	2	yes	maximal, complemented
19	C₄×#124×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×C₄⋊Q₈×C₇₃	C₂²	1	1	yes	characteristic
21	C₂×#126×C₇₃	C₂²	1	2	yes	—
22	C₂×#126×C₇₃	C₂²	1	2	yes	—
23	C₂×#125×C₇₃	C₂²	1	1	yes	characteristic
24	C₂×#124×C₇₃	C₂²	1	1	yes	characteristic
25	C₂×#124×C₇₃	C₂²	1	1	yes	characteristic
26	C₂×#124×C₇₃	C₂²	1	1	yes	characteristic
27	C₂×#123×C₇₃	C₂²	1	2	yes	—
28	C₂×#123×C₇₃	C₂²	1	2	yes	—
29	C₂×C₄×Q₈×C₇₃	C₂²	1	1	yes	characteristic
30	C₂×C₄×D₄×C₇₃	C₂²	1	1	yes	characteristic
31	#400×C₇₃	C₂²	1	2	yes	—
32	#398×C₇₃	C₂²	1	2	yes	—
33	#398×C₇₃	C₂²	1	2	yes	—
34	#397×C₇₃	C₂²	1	2	yes	—
35	#397×C₇₃	C₂²	1	2	yes	—
36	#397×C₇₃	C₂²	1	2	yes	—
37	#396×C₇₃	C₂²	1	2	yes	—
38	#396×C₇₃	C₂²	1	2	yes	—
39	#396×C₇₃	C₂²	1	2	yes	—
40	#396×C₇₃	C₂²	1	2	yes	—
41	#394×C₇₃	C₂²	1	2	yes	—
42	#394×C₇₃	C₂²	1	2	yes	—
43	#394×C₇₃	C₂²	1	2	yes	—
44	#393×C₇₃	C₂²	1	2	yes	—
45	#392×C₇₃	C₂²	1	2	yes	—
46	#392×C₇₃	C₂²	1	2	yes	—
47	#391×C₇₃	C₂²	1	1	yes	characteristic
48	#391×C₇₃	C₂²	1	1	yes	characteristic
49	#391×C₇₃	C₂²	1	1	yes	characteristic
50	#391×C₇₃	C₂²	1	2	yes	—
51	#391×C₇₃	C₂²	1	1	yes	characteristic
52	#390×C₇₃	C₂²	1	2	yes	—
53	#390×C₇₃	C₂²	1	2	yes	—
54	#390×C₇₃	C₂²	1	2	yes	—
55	#390×C₇₃	C₂²	1	1	yes	characteristic
56	#390×C₇₃	C₂²	1	2	yes	—
57	#390×C₇₃	C₂²	1	1	yes	characteristic
58	#389×C₇₃	C₂²	1	2	yes	—
59	#389×C₇₃	C₂²	1	2	yes	—
60	#389×C₇₃	C₂²	1	2	yes	—
61	#388×C₇₃	C₂²	1	2	yes	—
62	#388×C₇₃	C₂²	1	2	yes	—
63	#388×C₇₃	C₂²	1	2	yes	—
64	#388×C₇₃	C₂²	1	2	yes	—
65	#388×C₇₃	C₂²	1	2	yes	—
66	#388×C₇₃	C₂²	1	2	yes	—
67	#388×C₇₃	C₂²	1	2	yes	—
68	#388×C₇₃	C₂²	1	2	yes	—
69	#388×C₇₃	C₂²	1	2	yes	—
70	#388×C₇₃	C₂²	1	2	yes	—
71	#388×C₇₃	C₂²	1	2	yes	—
72	#388×C₇₃	C₂²	1	2	yes	—
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	#387×C₇₃	C₂²	1	2	yes	—
78	#387×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	#385×C₇₃	C₂²	1	2	yes	—
87	#384×C₇₃	C₂²	1	1	yes	characteristic
88	#383×C₇₃	C₂²	1	2	yes	—
89	#382×C₇₃	C₂²	1	1	yes	characteristic
90	#382×C₇₃	C₂²	1	1	yes	characteristic
91	C₄×C₄⋊C₄×C₇₃	C₂²	1	2	yes	—
92	C₄×C₄⋊C₄×C₇₃	C₂²	1	2	yes	—
93	C₄×C₄⋊C₄×C₇₃	C₂²	1	1	yes	characteristic
94	C₄×C₄⋊C₄×C₇₃	C₂²	1	2	yes	—
95	C₄×C₄⋊C₄×C₇₃	C₂²	1	2	yes	—
96	C₄×C₄⋊C₄×C₇₃	C₂²	1	2	yes	—
97	C₄×C₄⋊C₄×C₇₃	C₂²	1	1	yes	characteristic
98	C₄×C₂²⋊C₄×C₇₃	C₂²	1	2	yes	—
99	C₄×C₂²⋊C₄×C₇₃	C₂²	1	2	yes	—
100	C₄×C₂²⋊C₄×C₇₃	C₂²	1	2	yes	—
101	C₄×C₂²⋊C₄×C₇₃	C₂²	1	2	yes	—
102	C₄×C₂²⋊C₄×C₇₃	C₂²	1	2	yes	—
103	C₄×C₂²⋊C₄×C₇₃	C₂²	1	2	yes	—
104	C₄×C₂²⋊C₄×C₇₃	C₂²	1	2	yes	—
105	#376×C₇₃	C₂²	1	2	yes	—
106	C₄³×C₇₃	C₂²	1	1	yes	characteristic
107	C₂²×Q₈×C₇₃	C₂³	1	1	yes	characteristic
108	C₂²×Q₈×C₇₃	C₂³	1	1	yes	characteristic
109	C₂²×D₄×C₇₃	C₂³	1	1	yes	characteristic
110	C₂²×D₄×C₇₃	C₂³	1	2	yes	—
111	C₂²×D₄×C₇₃	C₂³	1	1	yes	characteristic
112	C₂²×D₄×C₇₃	C₂³	1	2	yes	—
113	C₂³×C₄×C₇₃	C₂³	1	2	yes	—
114	C₂³×C₄×C₇₃	C₂³	1	2	yes	—
115	C₄⋊Q₈×C₇₃	—	2	4	no	—
116	#126×C₇₃	—	2	8	no	—
117	#126×C₇₃	—	2	8	no	—
118	#125×C₇₃	—	4	2	no	—
119	#124×C₇₃	—	2	4	no	—
120	#124×C₇₃	—	2	4	no	—
121	#124×C₇₃	—	4	2	no	—
122	#123×C₇₃	—	2	8	no	—
123	#123×C₇₃	—	4	4	no	—
124	C₄×Q₈×C₇₃	—	4	2	no	—
125	C₄×D₄×C₇₃	—	4	2	no	—
126	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
127	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
128	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
129	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
130	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
131	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
132	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
133	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
134	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
135	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
136	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
137	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
138	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
139	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
140	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
141	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
142	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
143	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
144	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
145	C₂×C₂²⋊C₄×C₇₃	C₂³	1	2	yes	—
146	C₂×C₂²⋊C₄×C₇₃	C₂³	1	2	yes	—
147	C₂×C₂²⋊C₄×C₇₃	C₂³	1	2	yes	—
148	C₂×C₂²⋊C₄×C₇₃	C₂³	1	2	yes	—
149	C₂×C₂²⋊C₄×C₇₃	C₂³	1	2	yes	—
150	C₂×C₂²⋊C₄×C₇₃	C₂³	1	2	yes	—
151	C₂×C₂²⋊C₄×C₇₃	C₂³	1	2	yes	—
152	C₂×C₂²⋊C₄×C₇₃	C₂³	1	2	yes	—
153	C₂×C₂²⋊C₄×C₇₃	C₂³	1	2	yes	—
154	C₂×C₂²⋊C₄×C₇₃	C₂³	1	2	yes	—
155	C₂×C₂²⋊C₄×C₇₃	C₂³	1	2	yes	—
156	C₂×C₂²⋊C₄×C₇₃	C₂³	1	2	yes	—
157	C₂×C₂²⋊C₄×C₇₃	C₂³	1	2	yes	—
158	C₂×C₂²⋊C₄×C₇₃	C₂³	1	2	yes	—
159	C₂×C₂²⋊C₄×C₇₃	C₂³	1	2	yes	—
160	C₂×C₂²⋊C₄×C₇₃	C₂³	1	2	yes	—
161	C₂×C₂²⋊C₄×C₇₃	C₂³	1	2	yes	—
162	C₂×C₂²⋊C₄×C₇₃	C₂³	1	2	yes	—
163	C₂×C₂²⋊C₄×C₇₃	C₂³	1	2	yes	—
164	C₂×C₂²⋊C₄×C₇₃	C₂³	1	2	yes	—
165	C₂×C₂²⋊C₄×C₇₃	C₂³	1	2	yes	—
166	C₂×C₂²⋊C₄×C₇₃	C₂³	1	2	yes	—
167	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
168	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
169	C₂×C₄²×C₇₃	C₂³	1	2	yes	—
170	C₂×C₄²×C₇₃	C₂³	1	2	yes	—
171	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
172	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
173	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
174	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
175	C₂×C₄²×C₇₃	C₂³	1	2	yes	—
176	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
177	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
178	C₂×C₄²×C₇₃	C₂³	1	2	yes	—
179	C₂×C₄²×C₇₃	C₂³	1	2	yes	—
180	C₂×C₄²×C₇₃	C₂³	1	2	yes	—
181	C₂×C₄²×C₇₃	C₂³	1	2	yes	—
182	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
183	#95×C₇₃	C₂³	1	2	yes	—
184	#95×C₇₃	C₂³	1	2	yes	—
185	#95×C₇₃	C₂³	1	2	yes	—
186	#95×C₇₃	C₂³	1	2	yes	—
187	#95×C₇₃	C₂³	1	2	yes	—
188	#95×C₇₃	C₂³	1	2	yes	—
189	#95×C₇₃	C₂³	1	2	yes	—
190	#95×C₇₃	C₂³	1	2	yes	—
191	#95×C₇₃	C₂³	1	2	yes	—
192	#95×C₇₃	C₂³	1	2	yes	—
193	#95×C₇₃	C₂³	1	2	yes	—
194	#95×C₇₃	C₂³	1	2	yes	—
195	#95×C₇₃	C₂³	1	2	yes	—
196	#95×C₇₃	C₂³	1	2	yes	—
197	#95×C₇₃	C₂³	1	2	yes	—
198	#95×C₇₃	C₂³	1	2	yes	—
199	#95×C₇₃	C₂³	1	2	yes	—
200	#95×C₇₃	C₂³	1	2	yes	—
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	C₂⁴×C₇₃	C₂⁴	1	2	yes	—
206	C₂⁴×C₇₃	C₂⁴	1	2	yes	—
207	C₂×Q₈×C₇₃	—	2	2	no	—
208	C₂×Q₈×C₇₃	—	4	1	no	—
209	C₂×Q₈×C₇₃	—	4	1	no	—
210	C₂×Q₈×C₇₃	—	4	1	no	—
211	C₂×Q₈×C₇₃	—	4	1	no	—
212	C₂×Q₈×C₇₃	#41	1	4	yes	—
213	C₂×D₄×C₇₃	—	2	2	no	—
214	C₂×D₄×C₇₃	—	2	4	no	—
215	C₂×D₄×C₇₃	—	2	2	no	—
216	C₂×D₄×C₇₃	—	4	1	no	—
217	C₂×D₄×C₇₃	—	4	1	no	—
218	C₂×D₄×C₇₃	—	4	2	no	—
219	C₂×D₄×C₇₃	—	4	1	no	—
220	C₂×D₄×C₇₃	—	4	2	no	—
221	C₂×D₄×C₇₃	—	4	2	no	—
222	C₂×D₄×C₇₃	—	4	1	no	—
223	C₂×D₄×C₇₃	—	4	2	no	—
224	C₂×D₄×C₇₃	—	4	2	no	—
225	C₂²×C₄×C₇₃	—	2	4	no	—
226	C₂²×C₄×C₇₃	—	2	4	no	—
227	C₂²×C₄×C₇₃	—	4	2	no	—
228	C₂²×C₄×C₇₃	—	4	2	no	—
229	C₂²×C₄×C₇₃	—	4	2	no	—
230	C₂²×C₄×C₇₃	—	4	2	no	—
231	C₂²×C₄×C₇₃	C₂⁴	1	2	yes	—
232	C₂²×C₄×C₇₃	C₂⁴	1	2	yes	—
233	C₂²×C₄×C₇₃	C₂⁴	1	2	yes	—
234	C₂²×C₄×C₇₃	C₂⁴	1	2	yes	—
235	C₂²×C₄×C₇₃	C₂⁴	1	2	yes	—
236	C₂²×C₄×C₇₃	C₂⁴	1	2	yes	—
237	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
238	C₂²×C₄×C₇₃	C₂⁴	1	2	yes	—
239	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
240	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
241	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
242	C₂²×C₄×C₇₃	C₂⁴	1	2	yes	—
243	C₂²×C₄×C₇₃	C₂⁴	1	2	yes	—
244	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
245	C₂²×C₄×C₇₃	C₂⁴	1	2	yes	—
246	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
247	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
248	C₄⋊C₄×C₇₃	—	2	4	no	—
249	C₄⋊C₄×C₇₃	—	2	4	no	—
250	C₄⋊C₄×C₇₃	—	2	4	no	—
251	C₄⋊C₄×C₇₃	—	2	4	no	—
252	C₄⋊C₄×C₇₃	—	2	4	no	—
253	C₄⋊C₄×C₇₃	—	2	4	no	—
254	C₄⋊C₄×C₇₃	—	2	4	no	—
255	C₄⋊C₄×C₇₃	—	2	4	no	—
256	C₄⋊C₄×C₇₃	—	4	2	no	—
257	C₄⋊C₄×C₇₃	—	4	2	no	—
258	C₄⋊C₄×C₇₃	—	4	1	no	—
259	C₄⋊C₄×C₇₃	—	4	1	no	—
260	C₄⋊C₄×C₇₃	—	4	1	no	—
261	C₄⋊C₄×C₇₃	—	4	1	no	—
262	C₄⋊C₄×C₇₃	—	4	2	no	—
263	C₄⋊C₄×C₇₃	—	4	1	no	—
264	C₄⋊C₄×C₇₃	—	4	1	no	—
265	C₄⋊C₄×C₇₃	—	4	2	no	—
266	C₄⋊C₄×C₇₃	#41	1	8	yes	—
267	C₂²⋊C₄×C₇₃	—	2	4	no	—
268	C₂²⋊C₄×C₇₃	—	2	4	no	—
269	C₂²⋊C₄×C₇₃	—	2	4	no	—
270	C₂²⋊C₄×C₇₃	—	2	4	no	—
271	C₂²⋊C₄×C₇₃	—	2	4	no	—
272	C₂²⋊C₄×C₇₃	—	2	4	no	—
273	C₂²⋊C₄×C₇₃	—	2	4	no	—
274	C₂²⋊C₄×C₇₃	—	2	4	no	—
275	C₂²⋊C₄×C₇₃	—	2	4	no	—
276	C₂²⋊C₄×C₇₃	—	2	4	no	—
277	C₂²⋊C₄×C₇₃	—	2	4	no	—
278	C₂²⋊C₄×C₇₃	—	2	4	no	—
279	C₂²⋊C₄×C₇₃	—	2	4	no	—
280	C₂²⋊C₄×C₇₃	—	2	4	no	—
281	C₂²⋊C₄×C₇₃	—	4	2	no	—
282	C₂²⋊C₄×C₇₃	—	4	2	no	—
283	C₂²⋊C₄×C₇₃	—	4	2	no	—
284	C₂²⋊C₄×C₇₃	—	4	2	no	—
285	C₂²⋊C₄×C₇₃	—	4	2	no	—
286	C₂²⋊C₄×C₇₃	—	4	2	no	—
287	C₂²⋊C₄×C₇₃	—	4	2	no	—
288	C₂²⋊C₄×C₇₃	—	4	2	no	—
289	C₄²×C₇₃	—	2	2	no	—
290	C₄²×C₇₃	—	2	2	no	—
291	C₄²×C₇₃	—	2	4	no	—
292	C₄²×C₇₃	—	2	4	no	—
293	C₄²×C₇₃	—	2	2	no	—
294	C₄²×C₇₃	—	2	2	no	—
295	C₄²×C₇₃	—	2	2	no	—
296	C₄²×C₇₃	—	2	2	no	—
297	C₄²×C₇₃	—	4	2	no	—
298	C₄²×C₇₃	—	4	2	no	—
299	C₄²×C₇₃	—	4	1	no	—
300	C₄²×C₇₃	—	4	2	no	—
301	C₄²×C₇₃	—	4	2	no	—
302	C₄²×C₇₃	—	4	1	no	—
303	C₄²×C₇₃	—	4	1	no	—
304	C₄²×C₇₃	—	4	2	no	—
305	C₂³×C₇₃	—	2	2	no	—
306	C₂³×C₇₃	—	2	2	no	—
307	C₂³×C₇₃	—	2	2	no	—
308	C₂³×C₇₃	—	2	2	no	—
309	C₂³×C₇₃	—	2	2	no	—
310	C₂³×C₇₃	—	2	2	no	—
311	C₂³×C₇₃	—	2	2	no	—
312	C₂³×C₇₃	—	2	2	no	—
313	C₂³×C₇₃	—	2	2	no	—
314	C₂³×C₇₃	—	2	2	no	—
315	C₂³×C₇₃	—	2	2	no	—
316	C₂³×C₇₃	—	2	2	no	—
317	C₂³×C₇₃	—	2	2	no	—
318	C₂³×C₇₃	—	2	2	no	—
319	C₂³×C₇₃	C₂⁵	1	1	yes	characteristic
320	Q₈×C₇₃	—	4	4	no	—
321	Q₈×C₇₃	—	8	2	no	—
322	D₄×C₇₃	—	4	4	no	—
323	D₄×C₇₃	—	8	2	no	—
324	D₄×C₇₃	—	8	4	no	—
325	D₄×C₇₃	—	8	4	no	—
326	C₂×C₄×C₇₃	—	2	2	no	—
327	C₂×C₄×C₇₃	—	2	1	no	—
328	C₂×C₄×C₇₃	—	2	1	no	—
329	C₂×C₄×C₇₃	—	2	1	no	—
330	C₂×C₄×C₇₃	—	2	2	no	—
331	C₂×C₄×C₇₃	—	2	2	no	—
332	C₂×C₄×C₇₃	—	2	2	no	—
333	C₂×C₄×C₇₃	—	2	2	no	—
334	C₂×C₄×C₇₃	—	2	1	no	—
335	C₂×C₄×C₇₃	—	2	2	no	—
336	C₂×C₄×C₇₃	—	2	2	no	—
337	C₂×C₄×C₇₃	—	2	1	no	—
338	C₂×C₄×C₇₃	—	2	1	no	—
339	C₂×C₄×C₇₃	—	2	2	no	—
340	C₂×C₄×C₇₃	—	2	2	no	—
341	C₂×C₄×C₇₃	—	2	2	no	—
342	C₂×C₄×C₇₃	—	2	2	no	—
343	C₂×C₄×C₇₃	—	2	2	no	—
344	C₂×C₄×C₇₃	—	2	2	no	—
345	C₂×C₄×C₇₃	—	2	2	no	—
346	C₂×C₄×C₇₃	—	2	2	no	—
347	C₂×C₄×C₇₃	—	2	2	no	—
348	C₂×C₄×C₇₃	—	2	2	no	—
349	C₂×C₄×C₇₃	—	2	2	no	—
350	C₂×C₄×C₇₃	—	2	1	no	—
351	C₂×C₄×C₇₃	—	2	1	no	—
352	C₂×C₄×C₇₃	—	2	1	no	—
353	C₂×C₄×C₇₃	—	2	2	no	—
354	C₂×C₄×C₇₃	—	2	2	no	—
355	C₂×C₄×C₇₃	—	2	2	no	—
356	C₂×C₄×C₇₃	—	2	2	no	—
357	C₂×C₄×C₇₃	—	2	2	no	—
358	C₂×C₄×C₇₃	—	2	2	no	—
359	C₂×C₄×C₇₃	—	2	2	no	—
360	C₂×C₄×C₇₃	—	2	2	no	—
361	C₂×C₄×C₇₃	—	2	2	no	—
362	C₂×C₄×C₇₃	—	2	2	no	—
363	C₂×C₄×C₇₃	—	2	2	no	—
364	C₂×C₄×C₇₃	—	2	2	no	—
365	C₂×C₄×C₇₃	—	2	2	no	—
366	C₂×C₄×C₇₃	—	8	4	no	—
367	C₂×C₄×C₇₃	—	8	4	no	—
368	C₂×C₄×C₇₃	C₂×#41	1	4	yes	—
369	C₂×C₄×C₇₃	C₂×#41	1	2	yes	—
370	C₂×C₄×C₇₃	C₂×#41	1	2	yes	—
371	C₂×C₄×C₇₃	C₂×#41	1	4	yes	—
372	C₂×C₄×C₇₃	C₂×#41	1	2	yes	—
373	C₂×C₄×C₇₃	C₂×#41	1	4	yes	—
374	C₂×C₄×C₇₃	H(5,𝔽₂)	1	2	yes	—
375	C₂²×C₇₃	—	4	2	no	—
376	C₂²×C₇₃	—	4	2	no	—
377	C₂²×C₇₃	—	4	2	no	—
378	C₂²×C₇₃	—	4	2	no	—
379	C₂²×C₇₃	—	4	2	no	—
380	C₂²×C₇₃	—	4	2	no	—
381	C₂²×C₇₃	—	4	2	no	—
382	C₂²×C₇₃	—	4	2	no	—
383	C₂²×C₇₃	—	4	2	no	—
384	C₂²×C₇₃	—	4	2	no	—
385	C₂²×C₇₃	—	4	2	no	—
386	C₂²×C₇₃	—	4	2	no	—
387	C₂²×C₇₃	—	4	2	no	—
388	C₂²×C₇₃	—	4	2	no	—
389	C₂²×C₇₃	C₂²×#41	1	1	yes	characteristic
390	C₂²×C₇₃	C₂²×#41	1	2	yes	—
391	C₂²×C₇₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
392	C₂²×C₇₃	#585	1	2	yes	—
393	C₂²×C₇₃	#585	1	1	yes	characteristic
394	C₄×C₇₃	—	2	4	no	—
395	C₄×C₇₃	—	2	2	no	—
396	C₄×C₇₃	—	2	2	no	—
397	C₄×C₇₃	—	2	2	no	—
398	C₄×C₇₃	—	2	4	no	—
399	C₄×C₇₃	—	2	4	no	—
400	C₄×C₇₃	—	2	2	no	—
401	C₄×C₇₃	—	4	2	no	—
402	C₄×C₇₃	—	4	2	no	—
403	C₄×C₇₃	—	4	1	no	—
404	C₄×C₇₃	—	4	2	no	—
405	C₄×C₇₃	—	4	1	no	—
406	C₄×C₇₃	—	4	1	no	—
407	C₄×C₇₃	—	4	2	no	—
408	C₄×C₇₃	—	4	2	no	—
409	C₄×C₇₃	—	4	2	no	—
410	C₄×C₇₃	—	4	2	no	—
411	#59743	C₇₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
412	C₂×C₇₃	—	8	2	no	—
413	C₂×C₇₃	—	8	2	no	—
414	C₂×C₇₃	#3480	1	2	yes	—
415	C₂×C₇₃	#3483	1	1	yes	characteristic
416	C₂×C₇₃	#3505	1	1	yes	characteristic
417	C₂×C₇₃	#3521	1	2	yes	—
418	C₂×C₇₃	#3545	1	1	yes	characteristic
419	#2783	C₂×C₇₃	1	2	yes	complemented
420	#2733	C₂×C₇₃	1	1	yes	characteristic
421	#2731	C₂×C₇₃	1	1	yes	characteristic, complemented
422	#2602	C₂×C₇₃	1	2	yes	complemented
423	#2565	C₂×C₇₃	1	1	yes	characteristic, complemented
424	#2558	C₂×C₇₃	1	2	yes	complemented
425	#2557	C₂×C₇₃	1	2	yes	complemented
426	#2554	C₂×C₇₃	1	2	yes	complemented
427	#2554	C₂×C₇₃	1	2	yes	complemented
428	#2545	C₂×C₇₃	1	1	yes	characteristic, complemented
429	#2532	C₂×C₇₃	1	2	yes	complemented
430	#2518	C₂×C₇₃	1	2	yes	complemented
431	#2512	C₂×C₇₃	1	2	yes	complemented
432	#2374	C₂×C₇₃	1	2	yes	complemented
433	#2373	C₂×C₇₃	1	2	yes	complemented
434	#2372	C₂×C₇₃	1	1	yes	characteristic, complemented
435	#2369	C₂×C₇₃	1	1	yes	characteristic, complemented
436	C₄×#126	C₂×C₇₃	1	2	yes	complemented
437	C₄×#124	C₂×C₇₃	1	1	yes	characteristic, complemented
438	C₇₃	#59743	1	1	yes	characteristic, direct product factor, Sylow
439	C₂×C₄⋊Q₈	C₂²×C₇₃	1	1	yes	characteristic
440	C₂×#126	C₂²×C₇₃	1	2	yes	—
441	C₂×#126	C₂²×C₇₃	1	2	yes	—
442	C₂×#125	C₂²×C₇₃	1	1	yes	characteristic
443	C₂×#124	C₂²×C₇₃	1	1	yes	characteristic
444	C₂×#124	C₂²×C₇₃	1	1	yes	characteristic
445	C₂×#124	C₂²×C₇₃	1	1	yes	characteristic
446	C₂×#123	C₂²×C₇₃	1	2	yes	—
447	C₂×#123	C₂²×C₇₃	1	2	yes	—
448	C₂×C₄×Q₈	C₂²×C₇₃	1	1	yes	characteristic
449	C₂×C₄×D₄	C₂²×C₇₃	1	1	yes	characteristic
450	#400	C₂²×C₇₃	1	2	yes	—
451	#398	C₂²×C₇₃	1	2	yes	—
452	#398	C₂²×C₇₃	1	2	yes	—
453	#397	C₂²×C₇₃	1	2	yes	—
454	#397	C₂²×C₇₃	1	2	yes	—
455	#397	C₂²×C₇₃	1	2	yes	—
456	#396	C₂²×C₇₃	1	2	yes	—
457	#396	C₂²×C₇₃	1	2	yes	—
458	#396	C₂²×C₇₃	1	2	yes	—
459	#396	C₂²×C₇₃	1	2	yes	—
460	#394	C₂²×C₇₃	1	2	yes	—
461	#394	C₂²×C₇₃	1	2	yes	—
462	#394	C₂²×C₇₃	1	2	yes	—
463	#393	C₂²×C₇₃	1	2	yes	—
464	#392	C₂²×C₇₃	1	2	yes	—
465	#392	C₂²×C₇₃	1	2	yes	—
466	#391	C₂²×C₇₃	1	1	yes	characteristic
467	#391	C₂²×C₇₃	1	1	yes	characteristic
468	#391	C₂²×C₇₃	1	1	yes	characteristic
469	#391	C₂²×C₇₃	1	2	yes	—
470	#391	C₂²×C₇₃	1	1	yes	characteristic
471	#390	C₂²×C₇₃	1	2	yes	—
472	#390	C₂²×C₇₃	1	2	yes	—
473	#390	C₂²×C₇₃	1	2	yes	—
474	#390	C₂²×C₇₃	1	1	yes	characteristic
475	#390	C₂²×C₇₃	1	2	yes	—
476	#390	C₂²×C₇₃	1	1	yes	characteristic
477	#389	C₂²×C₇₃	1	2	yes	—
478	#389	C₂²×C₇₃	1	2	yes	—
479	#389	C₂²×C₇₃	1	2	yes	—
480	#388	C₂²×C₇₃	1	2	yes	—
481	#388	C₂²×C₇₃	1	2	yes	—
482	#388	C₂²×C₇₃	1	2	yes	—
483	#388	C₂²×C₇₃	1	2	yes	—
484	#388	C₂²×C₇₃	1	2	yes	—
485	#388	C₂²×C₇₃	1	2	yes	—
486	#388	C₂²×C₇₃	1	2	yes	—
487	#388	C₂²×C₇₃	1	2	yes	—
488	#388	C₂²×C₇₃	1	2	yes	—
489	#388	C₂²×C₇₃	1	2	yes	—
490	#388	C₂²×C₇₃	1	2	yes	—
491	#388	C₂²×C₇₃	1	2	yes	—
492	#388	C₂²×C₇₃	1	2	yes	—
493	#388	C₂²×C₇₃	1	2	yes	—
494	#388	C₂²×C₇₃	1	2	yes	—
495	#388	C₂²×C₇₃	1	2	yes	—
496	#387	C₂²×C₇₃	1	2	yes	—
497	#387	C₂²×C₇₃	1	2	yes	—
498	#387	C₂²×C₇₃	1	2	yes	—
499	#387	C₂²×C₇₃	1	2	yes	—
500	#387	C₂²×C₇₃	1	2	yes	—
501	#387	C₂²×C₇₃	1	2	yes	—
502	#386	C₂²×C₇₃	1	2	yes	—
503	#386	C₂²×C₇₃	1	2	yes	—
504	#386	C₂²×C₇₃	1	2	yes	—
505	#385	C₂²×C₇₃	1	2	yes	—
506	#384	C₂²×C₇₃	1	1	yes	characteristic
507	#383	C₂²×C₇₃	1	2	yes	—
508	#382	C₂²×C₇₃	1	1	yes	characteristic
509	#382	C₂²×C₇₃	1	1	yes	characteristic
510	C₄×C₄⋊C₄	C₂²×C₇₃	1	2	yes	—
511	C₄×C₄⋊C₄	C₂²×C₇₃	1	2	yes	—
512	C₄×C₄⋊C₄	C₂²×C₇₃	1	2	yes	—
513	C₄×C₄⋊C₄	C₂²×C₇₃	1	1	yes	characteristic
514	C₄×C₄⋊C₄	C₂²×C₇₃	1	2	yes	—
515	C₄×C₄⋊C₄	C₂²×C₇₃	1	2	yes	—
516	C₄×C₄⋊C₄	C₂²×C₇₃	1	1	yes	characteristic
517	C₄×C₂²⋊C₄	C₂²×C₇₃	1	2	yes	—
518	C₄×C₂²⋊C₄	C₂²×C₇₃	1	2	yes	—
519	C₄×C₂²⋊C₄	C₂²×C₇₃	1	2	yes	—
520	C₄×C₂²⋊C₄	C₂²×C₇₃	1	2	yes	—
521	C₄×C₂²⋊C₄	C₂²×C₇₃	1	2	yes	—
522	C₄×C₂²⋊C₄	C₂²×C₇₃	1	2	yes	—
523	C₄×C₂²⋊C₄	C₂²×C₇₃	1	2	yes	—
524	#376	C₂²×C₇₃	1	2	yes	—
525	C₄³	C₂²×C₇₃	1	1	yes	characteristic
526	C₂²×Q₈	C₂³×C₇₃	1	1	yes	characteristic
527	C₂²×Q₈	C₂³×C₇₃	1	1	yes	characteristic
528	C₂²×D₄	C₂³×C₇₃	1	1	yes	characteristic
529	C₂²×D₄	C₂³×C₇₃	1	2	yes	—
530	C₂²×D₄	C₂³×C₇₃	1	1	yes	characteristic
531	C₂²×D₄	C₂³×C₇₃	1	2	yes	—
532	C₂³×C₄	C₂³×C₇₃	1	2	yes	—
533	C₂³×C₄	C₂³×C₇₃	1	2	yes	—
534	C₄⋊Q₈	—	2	4	no	—
535	#126	—	2	8	no	—
536	#126	—	2	8	no	—
537	#125	—	4	2	no	—
538	#124	—	2	4	no	—
539	#124	—	2	4	no	—
540	#124	—	4	2	no	—
541	#123	—	2	8	no	—
542	#123	—	4	4	no	—
543	C₄×Q₈	—	4	2	no	—
544	C₄×D₄	—	4	2	no	—
545	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
546	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
547	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
548	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
549	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
550	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
551	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
552	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
553	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
554	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
555	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
556	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
557	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
558	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
559	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
560	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
561	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
562	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
563	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
564	C₂×C₂²⋊C₄	C₂³×C₇₃	1	2	yes	—
565	C₂×C₂²⋊C₄	C₂³×C₇₃	1	2	yes	—
566	C₂×C₂²⋊C₄	C₂³×C₇₃	1	2	yes	—
567	C₂×C₂²⋊C₄	C₂³×C₇₃	1	2	yes	—
568	C₂×C₂²⋊C₄	C₂³×C₇₃	1	2	yes	—
569	C₂×C₂²⋊C₄	C₂³×C₇₃	1	2	yes	—
570	C₂×C₂²⋊C₄	C₂³×C₇₃	1	2	yes	—
571	C₂×C₂²⋊C₄	C₂³×C₇₃	1	2	yes	—
572	C₂×C₂²⋊C₄	C₂³×C₇₃	1	2	yes	—
573	C₂×C₂²⋊C₄	C₂³×C₇₃	1	2	yes	—
574	C₂×C₂²⋊C₄	C₂³×C₇₃	1	2	yes	—
575	C₂×C₂²⋊C₄	C₂³×C₇₃	1	2	yes	—
576	C₂×C₂²⋊C₄	C₂³×C₇₃	1	2	yes	—
577	C₂×C₂²⋊C₄	C₂³×C₇₃	1	2	yes	—
578	C₂×C₂²⋊C₄	C₂³×C₇₃	1	2	yes	—
579	C₂×C₂²⋊C₄	C₂³×C₇₃	1	2	yes	—
580	C₂×C₂²⋊C₄	C₂³×C₇₃	1	2	yes	—
581	C₂×C₂²⋊C₄	C₂³×C₇₃	1	2	yes	—
582	C₂×C₂²⋊C₄	C₂³×C₇₃	1	2	yes	—
583	C₂×C₂²⋊C₄	C₂³×C₇₃	1	2	yes	—
584	C₂×C₂²⋊C₄	C₂³×C₇₃	1	2	yes	—
585	C₂×C₂²⋊C₄	C₂³×C₇₃	1	2	yes	—
586	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
587	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
588	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
589	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
590	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
591	C₂×C₄²	C₂³×C₇₃	1	2	yes	—
592	C₂×C₄²	C₂³×C₇₃	1	2	yes	—
593	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
594	C₂×C₄²	C₂³×C₇₃	1	2	yes	—
595	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
596	C₂×C₄²	C₂³×C₇₃	1	2	yes	—
597	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
598	C₂×C₄²	C₂³×C₇₃	1	2	yes	—
599	C₂×C₄²	C₂³×C₇₃	1	2	yes	—
600	C₂×C₄²	C₂³×C₇₃	1	2	yes	—
601	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
602	#95	C₂³×C₇₃	1	2	yes	—
603	#95	C₂³×C₇₃	1	2	yes	—
604	#95	C₂³×C₇₃	1	2	yes	—
605	#95	C₂³×C₇₃	1	2	yes	—
606	#95	C₂³×C₇₃	1	2	yes	—
607	#95	C₂³×C₇₃	1	2	yes	—
608	#95	C₂³×C₇₃	1	2	yes	—
609	#95	C₂³×C₇₃	1	2	yes	—
610	#95	C₂³×C₇₃	1	2	yes	—
611	#95	C₂³×C₇₃	1	2	yes	—
612	#95	C₂³×C₇₃	1	2	yes	—
613	#95	C₂³×C₇₃	1	2	yes	—
614	#95	C₂³×C₇₃	1	2	yes	—
615	#95	C₂³×C₇₃	1	2	yes	—
616	#95	C₂³×C₇₃	1	2	yes	—
617	#95	C₂³×C₇₃	1	2	yes	—
618	#95	C₂³×C₇₃	1	2	yes	—
619	#95	C₂³×C₇₃	1	2	yes	—
620	#95	C₂³×C₇₃	1	2	yes	—
621	#95	C₂³×C₇₃	1	2	yes	—
622	#95	C₂³×C₇₃	1	2	yes	—
623	#95	C₂³×C₇₃	1	2	yes	—
624	C₂⁴	C₂⁴×C₇₃	1	2	yes	—
625	C₂⁴	C₂⁴×C₇₃	1	2	yes	—
626	C₂×Q₈	—	2	2	no	—
627	C₂×Q₈	—	4	1	no	—
628	C₂×Q₈	—	4	1	no	—
629	C₂×Q₈	—	4	1	no	—
630	C₂×Q₈	—	4	1	no	—
631	C₂×Q₈	#41×C₇₃	1	4	yes	—
632	C₂×D₄	—	2	2	no	—
633	C₂×D₄	—	2	4	no	—
634	C₂×D₄	—	2	2	no	—
635	C₂×D₄	—	4	1	no	—
636	C₂×D₄	—	4	1	no	—
637	C₂×D₄	—	4	2	no	—
638	C₂×D₄	—	4	1	no	—
639	C₂×D₄	—	4	2	no	—
640	C₂×D₄	—	4	2	no	—
641	C₂×D₄	—	4	1	no	—
642	C₂×D₄	—	4	2	no	—
643	C₂×D₄	—	4	2	no	—
644	C₂²×C₄	—	2	4	no	—
645	C₂²×C₄	—	2	4	no	—
646	C₂²×C₄	—	4	2	no	—
647	C₂²×C₄	—	4	2	no	—
648	C₂²×C₄	—	4	2	no	—
649	C₂²×C₄	—	4	2	no	—
650	C₂²×C₄	C₂⁴×C₇₃	1	2	yes	—
651	C₂²×C₄	C₂⁴×C₇₃	1	2	yes	—
652	C₂²×C₄	C₂⁴×C₇₃	1	2	yes	—
653	C₂²×C₄	C₂⁴×C₇₃	1	2	yes	—
654	C₂²×C₄	C₂⁴×C₇₃	1	2	yes	—
655	C₂²×C₄	C₂⁴×C₇₃	1	2	yes	—
656	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
657	C₂²×C₄	C₂⁴×C₇₃	1	2	yes	—
658	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
659	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
660	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
661	C₂²×C₄	C₂⁴×C₇₃	1	2	yes	—
662	C₂²×C₄	C₂⁴×C₇₃	1	2	yes	—
663	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
664	C₂²×C₄	C₂⁴×C₇₃	1	2	yes	—
665	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
666	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
667	C₄⋊C₄	—	2	4	no	—
668	C₄⋊C₄	—	2	4	no	—
669	C₄⋊C₄	—	2	4	no	—
670	C₄⋊C₄	—	2	4	no	—
671	C₄⋊C₄	—	2	4	no	—
672	C₄⋊C₄	—	2	4	no	—
673	C₄⋊C₄	—	2	4	no	—
674	C₄⋊C₄	—	2	4	no	—
675	C₄⋊C₄	—	4	2	no	—
676	C₄⋊C₄	—	4	2	no	—
677	C₄⋊C₄	—	4	1	no	—
678	C₄⋊C₄	—	4	1	no	—
679	C₄⋊C₄	—	4	1	no	—
680	C₄⋊C₄	—	4	1	no	—
681	C₄⋊C₄	—	4	2	no	—
682	C₄⋊C₄	—	4	1	no	—
683	C₄⋊C₄	—	4	1	no	—
684	C₄⋊C₄	—	4	2	no	—
685	C₄⋊C₄	#41×C₇₃	1	8	yes	—
686	C₂²⋊C₄	—	2	4	no	—
687	C₂²⋊C₄	—	2	4	no	—
688	C₂²⋊C₄	—	2	4	no	—
689	C₂²⋊C₄	—	2	4	no	—
690	C₂²⋊C₄	—	2	4	no	—
691	C₂²⋊C₄	—	2	4	no	—
692	C₂²⋊C₄	—	2	4	no	—
693	C₂²⋊C₄	—	2	4	no	—
694	C₂²⋊C₄	—	2	4	no	—
695	C₂²⋊C₄	—	2	4	no	—
696	C₂²⋊C₄	—	2	4	no	—
697	C₂²⋊C₄	—	2	4	no	—
698	C₂²⋊C₄	—	2	4	no	—
699	C₂²⋊C₄	—	2	4	no	—
700	C₂²⋊C₄	—	4	2	no	—
701	C₂²⋊C₄	—	4	2	no	—
702	C₂²⋊C₄	—	4	2	no	—
703	C₂²⋊C₄	—	4	2	no	—
704	C₂²⋊C₄	—	4	2	no	—
705	C₂²⋊C₄	—	4	2	no	—
706	C₂²⋊C₄	—	4	2	no	—
707	C₂²⋊C₄	—	4	2	no	—
708	C₄²	—	2	2	no	—
709	C₄²	—	2	2	no	—
710	C₄²	—	2	4	no	—
711	C₄²	—	2	4	no	—
712	C₄²	—	2	2	no	—
713	C₄²	—	2	2	no	—
714	C₄²	—	2	2	no	—
715	C₄²	—	2	2	no	—
716	C₄²	—	4	2	no	—
717	C₄²	—	4	2	no	—
718	C₄²	—	4	1	no	—
719	C₄²	—	4	2	no	—
720	C₄²	—	4	2	no	—
721	C₄²	—	4	1	no	—
722	C₄²	—	4	1	no	—
723	C₄²	—	4	2	no	—
724	C₂³	—	2	2	no	—
725	C₂³	—	2	2	no	—
726	C₂³	—	2	2	no	—
727	C₂³	—	2	2	no	—
728	C₂³	—	2	2	no	—
729	C₂³	—	2	2	no	—
730	C₂³	—	2	2	no	—
731	C₂³	—	2	2	no	—
732	C₂³	—	2	2	no	—
733	C₂³	—	2	2	no	—
734	C₂³	—	2	2	no	—
735	C₂³	—	2	2	no	—
736	C₂³	—	2	2	no	—
737	C₂³	—	2	2	no	—
738	C₂³	C₂⁵×C₇₃	1	1	yes	characteristic
739	Q₈	—	4	4	no	—
740	Q₈	—	8	2	no	—
741	D₄	—	4	4	no	—
742	D₄	—	8	2	no	—
743	D₄	—	8	4	no	—
744	D₄	—	8	4	no	—
745	C₂×C₄	—	2	2	no	—
746	C₂×C₄	—	2	1	no	—
747	C₂×C₄	—	2	1	no	—
748	C₂×C₄	—	2	1	no	—
749	C₂×C₄	—	2	2	no	—
750	C₂×C₄	—	2	2	no	—
751	C₂×C₄	—	2	2	no	—
752	C₂×C₄	—	2	2	no	—
753	C₂×C₄	—	2	1	no	—
754	C₂×C₄	—	2	2	no	—
755	C₂×C₄	—	2	2	no	—
756	C₂×C₄	—	2	1	no	—
757	C₂×C₄	—	2	1	no	—
758	C₂×C₄	—	2	2	no	—
759	C₂×C₄	—	2	2	no	—
760	C₂×C₄	—	2	2	no	—
761	C₂×C₄	—	2	2	no	—
762	C₂×C₄	—	2	2	no	—
763	C₂×C₄	—	2	2	no	—
764	C₂×C₄	—	2	2	no	—
765	C₂×C₄	—	2	2	no	—
766	C₂×C₄	—	2	2	no	—
767	C₂×C₄	—	2	2	no	—
768	C₂×C₄	—	2	2	no	—
769	C₂×C₄	—	2	1	no	—
770	C₂×C₄	—	2	1	no	—
771	C₂×C₄	—	2	1	no	—
772	C₂×C₄	—	2	2	no	—
773	C₂×C₄	—	2	2	no	—
774	C₂×C₄	—	2	2	no	—
775	C₂×C₄	—	2	2	no	—
776	C₂×C₄	—	2	2	no	—
777	C₂×C₄	—	2	2	no	—
778	C₂×C₄	—	2	2	no	—
779	C₂×C₄	—	2	2	no	—
780	C₂×C₄	—	2	2	no	—
781	C₂×C₄	—	2	2	no	—
782	C₂×C₄	—	2	2	no	—
783	C₂×C₄	—	2	2	no	—
784	C₂×C₄	—	2	2	no	—
785	C₂×C₄	—	8	4	no	—
786	C₂×C₄	—	8	4	no	—
787	C₂×C₄	C₂×#41×C₇₃	1	4	yes	—
788	C₂×C₄	C₂×#41×C₇₃	1	2	yes	—
789	C₂×C₄	C₂×#41×C₇₃	1	2	yes	—
790	C₂×C₄	C₂×#41×C₇₃	1	4	yes	—
791	C₂×C₄	C₂×#41×C₇₃	1	2	yes	—
792	C₂×C₄	C₂×#41×C₇₃	1	4	yes	—
793	C₂×C₄	H(5,𝔽₂)×C₇₃	1	2	yes	—
794	C₂²	—	4	2	no	—
795	C₂²	—	4	2	no	—
796	C₂²	—	4	2	no	—
797	C₂²	—	4	2	no	—
798	C₂²	—	4	2	no	—
799	C₂²	—	4	2	no	—
800	C₂²	—	4	2	no	—
801	C₂²	—	4	2	no	—
802	C₂²	—	4	2	no	—
803	C₂²	—	4	2	no	—
804	C₂²	—	4	2	no	—
805	C₂²	—	4	2	no	—
806	C₂²	—	4	2	no	—
807	C₂²	—	4	2	no	—
808	C₂²	C₂²×#41×C₇₃	1	1	yes	characteristic
809	C₂²	C₂²×#41×C₇₃	1	2	yes	—
810	C₂²	C₂×H(5,𝔽₂)×C₇₃	1	1	yes	characteristic
811	C₂²	#585×C₇₃	1	2	yes	—
812	C₂²	#585×C₇₃	1	1	yes	characteristic
813	C₄	—	2	4	no	—
814	C₄	—	2	2	no	—
815	C₄	—	2	2	no	—
816	C₄	—	2	2	no	—
817	C₄	—	2	4	no	—
818	C₄	—	2	4	no	—
819	C₄	—	2	2	no	—
820	C₄	—	4	2	no	—
821	C₄	—	4	2	no	—
822	C₄	—	4	1	no	—
823	C₄	—	4	2	no	—
824	C₄	—	4	1	no	—
825	C₄	—	4	1	no	—
826	C₄	—	4	2	no	—
827	C₄	—	4	2	no	—
828	C₄	—	4	2	no	—
829	C₄	—	4	2	no	—
830	C₂	—	8	2	no	—
831	C₂	—	8	2	no	—
832	C₂	C₇₃×#3480	1	2	yes	—
833	C₂	C₇₃×#3483	1	1	yes	characteristic
834	C₂	C₇₃×#3505	1	1	yes	characteristic
835	C₂	C₇₃×#3521	1	2	yes	—
836	C₂	C₇₃×#3545	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₇₃	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₇₃
prime radical	C₇₃×#2733	C₂
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. C₇₃×#2783	C₂	semidirect
3. C₇₃×#2731	C₂	semidirect
4. C₇₃×#2602	C₂	semidirect
5. C₇₃×#2565	C₂	semidirect
6. C₇₃×#2558	C₂	semidirect
7. C₇₃×#2557	C₂	semidirect
8. C₇₃×#2554	C₂	semidirect
9. C₇₃×#2554	C₂	semidirect
10. C₇₃×#2545	C₂	semidirect
11. C₇₃×#2532	C₂	semidirect
12. C₇₃×#2518	C₂	semidirect
13. C₇₃×#2512	C₂	semidirect
14. C₇₃×#2374	C₂	semidirect
15. C₇₃×#2373	C₂	semidirect
16. C₇₃×#2372	C₂	semidirect
17. C₇₃×#2369	C₂	semidirect
18. C₄×#126×C₇₃	C₂	semidirect
19. C₄×#124×C₇₃	C₂	semidirect
411. #59743	C₇₃	direct (N × H)
419. #2783	C₂×C₇₃	semidirect
421. #2731	C₂×C₇₃	semidirect
422. #2602	C₂×C₇₃	semidirect
423. #2565	C₂×C₇₃	semidirect
424. #2558	C₂×C₇₃	semidirect
425. #2557	C₂×C₇₃	semidirect
426. #2554	C₂×C₇₃	semidirect
427. #2554	C₂×C₇₃	semidirect
428. #2545	C₂×C₇₃	semidirect
429. #2532	C₂×C₇₃	semidirect
430. #2518	C₂×C₇₃	semidirect
431. #2512	C₂×C₇₃	semidirect
432. #2374	C₂×C₇₃	semidirect
433. #2373	C₂×C₇₃	semidirect
434. #2372	C₂×C₇₃	semidirect
435. #2369	C₂×C₇₃	semidirect
436. C₄×#126	C₂×C₇₃	semidirect
437. C₄×#124	C₂×C₇₃	semidirect
438. C₇₃	#59743	direct (N × H)

Maximal subgroups

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

subgroup	index
C₇₃×#2783	2
C₇₃×#2733	2
C₇₃×#2731	2
C₇₃×#2602	2
C₇₃×#2565	2
C₇₃×#2558	2
C₇₃×#2557	2
C₇₃×#2554	2
C₇₃×#2545	2
C₇₃×#2532	2
C₇₃×#2518	2
C₇₃×#2512	2
C₇₃×#2374	2
C₇₃×#2373	2
C₇₃×#2372	2
C₇₃×#2369	2
C₄×#126×C₇₃	2
C₄×#124×C₇₃	2
#59743	73

Subgroups — C73×#59743 #32969147

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₃×#59743 #32969147