Subgroups — C₇₃×#59973 #32969377

Order 18688.

1964 conjugacy classes of subgroups.

The subgroup lattice has 922 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇₃×#2753	C₂	1	2	yes	maximal, complemented
2	C₇₃×#2748	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇₃×#2709	C₂	1	1	yes	maximal, characteristic, complemented
4	C₇₃×#2554	C₂	1	2	yes	maximal, complemented
5	C₇₃×#2526	C₂	1	2	yes	maximal, complemented
6	C₇₃×#2521	C₂	1	2	yes	maximal, complemented
7	C₇₃×#2520	C₂	1	2	yes	maximal, complemented
8	C₇₃×#2479	C₂	1	2	yes	maximal, complemented
9	C₇₃×#2476	C₂	1	2	yes	maximal, complemented
10	C₇₃×#2467	C₂	1	2	yes	maximal, complemented
11	C₇₃×#2467	C₂	1	2	yes	maximal, complemented
12	C₇₃×#2431	C₂	1	1	yes	maximal, characteristic
13	C₇₃×#2406	C₂	1	1	yes	maximal, characteristic, complemented
14	C₇₃×#2374	C₂	1	1	yes	maximal, characteristic, complemented
15	C₇₃×#2373	C₂	1	2	yes	maximal, complemented
16	C₇₃×#2366	C₂	1	1	yes	maximal, characteristic, complemented
17	C₇₃×#2352	C₂	1	2	yes	maximal, complemented
18	C₇₃×#2297	C₂	1	1	yes	maximal, characteristic, complemented
19	C₇₃×#2290	C₂	1	2	yes	maximal, complemented
20	C₂²×#41×C₇₃	C₂²	1	1	yes	characteristic
21	C₂×#127×C₇₃	C₂²	1	1	yes	characteristic
22	C₂×#126×C₇₃	C₂²	1	2	yes	—
23	C₂×#126×C₇₃	C₂²	1	2	yes	—
24	C₂×#124×C₇₃	C₂²	1	1	yes	characteristic
25	C₂×#123×C₇₃	C₂²	1	1	yes	characteristic
26	C₂×#123×C₇₃	C₂²	1	1	yes	characteristic
27	C₂×#121×C₇₃	C₂²	1	1	yes	characteristic
28	C₂×C₄×D₄×C₇₃	C₂²	1	2	yes	—
29	C₂×C₄×D₄×C₇₃	C₂²	1	2	yes	—
30	C₂×#117×C₇₃	C₂²	1	2	yes	—
31	C₂×#117×C₇₃	C₂²	1	1	yes	characteristic
32	C₂²×C₄⋊C₄×C₇₃	C₂²	1	1	yes	characteristic
33	C₂²×C₄²×C₇₃	C₂²	1	1	yes	characteristic
34	#400×C₇₃	C₂²	1	2	yes	—
35	#399×C₇₃	C₂²	1	2	yes	—
36	#399×C₇₃	C₂²	1	2	yes	—
37	#398×C₇₃	C₂²	1	2	yes	—
38	#398×C₇₃	C₂²	1	2	yes	—
39	#397×C₇₃	C₂²	1	2	yes	—
40	#396×C₇₃	C₂²	1	2	yes	—
41	#395×C₇₃	C₂²	1	2	yes	—
42	#394×C₇₃	C₂²	1	2	yes	—
43	#394×C₇₃	C₂²	1	2	yes	—
44	#394×C₇₃	C₂²	1	2	yes	—
45	#394×C₇₃	C₂²	1	2	yes	—
46	#394×C₇₃	C₂²	1	2	yes	—
47	#394×C₇₃	C₂²	1	2	yes	—
48	#392×C₇₃	C₂²	1	2	yes	—
49	#392×C₇₃	C₂²	1	2	yes	—
50	#391×C₇₃	C₂²	1	1	yes	characteristic
51	#391×C₇₃	C₂²	1	2	yes	—
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	#389×C₇₃	C₂²	1	2	yes	—
58	#388×C₇₃	C₂²	1	2	yes	—
59	#388×C₇₃	C₂²	1	2	yes	—
60	#388×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	#387×C₇₃	C₂²	1	2	yes	—
70	#387×C₇₃	C₂²	1	2	yes	—
71	#387×C₇₃	C₂²	1	2	yes	—
72	#387×C₇₃	C₂²	1	2	yes	—
73	#387×C₇₃	C₂²	1	2	yes	—
74	#387×C₇₃	C₂²	1	2	yes	—
75	#387×C₇₃	C₂²	1	2	yes	—
76	#387×C₇₃	C₂²	1	2	yes	—
77	#386×C₇₃	C₂²	1	1	yes	characteristic
78	#386×C₇₃	C₂²	1	2	yes	—
79	#386×C₇₃	C₂²	1	2	yes	—
80	#386×C₇₃	C₂²	1	2	yes	—
81	#386×C₇₃	C₂²	1	1	yes	characteristic
82	#386×C₇₃	C₂²	1	1	yes	characteristic
83	#386×C₇₃	C₂²	1	2	yes	—
84	#386×C₇₃	C₂²	1	2	yes	—
85	#386×C₇₃	C₂²	1	1	yes	characteristic
86	#386×C₇₃	C₂²	1	1	yes	characteristic
87	#386×C₇₃	C₂²	1	2	yes	—
88	#386×C₇₃	C₂²	1	1	yes	characteristic
89	#385×C₇₃	C₂²	1	2	yes	—
90	#385×C₇₃	C₂²	1	2	yes	—
91	#385×C₇₃	C₂²	1	2	yes	—
92	#382×C₇₃	C₂²	1	2	yes	—
93	#381×C₇₃	C₂²	1	1	yes	characteristic
94	#380×C₇₃	C₂²	1	2	yes	—
95	#380×C₇₃	C₂²	1	2	yes	—
96	C₄×C₄⋊C₄×C₇₃	C₂²	1	2	yes	—
97	C₄×C₄⋊C₄×C₇₃	C₂²	1	2	yes	—
98	C₄×C₄⋊C₄×C₇₃	C₂²	1	2	yes	—
99	C₄×C₄⋊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	C₄×C₂²⋊C₄×C₇₃	C₂²	1	1	yes	characteristic
106	#376×C₇₃	C₂²	1	2	yes	—
107	C₂×#41×C₇₃	—	2	4	no	—
108	C₂×#41×C₇₃	—	4	2	no	—
109	C₂×#41×C₇₃	—	4	2	no	—
110	C₂²×Q₈×C₇₃	C₂³	1	1	yes	characteristic
111	C₂²×D₄×C₇₃	C₂³	1	2	yes	—
112	C₂²×D₄×C₇₃	C₂³	1	2	yes	—
113	C₂²×D₄×C₇₃	C₂³	1	1	yes	characteristic
114	C₂²×D₄×C₇₃	C₂³	1	1	yes	characteristic
115	C₂²×D₄×C₇₃	C₂³	1	1	yes	characteristic
116	C₂²×D₄×C₇₃	C₂³	1	2	yes	—
117	C₂²×D₄×C₇₃	C₂³	1	1	yes	characteristic
118	C₂³×C₄×C₇₃	C₂³	1	1	yes	characteristic
119	C₂³×C₄×C₇₃	C₂³	1	1	yes	characteristic
120	C₂³×C₄×C₇₃	C₂³	1	1	yes	characteristic
121	C₂³×C₄×C₇₃	C₂³	1	1	yes	characteristic
122	C₂³×C₄×C₇₃	C₂³	1	2	yes	—
123	C₂³×C₄×C₇₃	C₂³	1	1	yes	characteristic
124	C₂³×C₄×C₇₃	C₂³	1	1	yes	characteristic
125	C₂³×C₄×C₇₃	C₂³	1	1	yes	characteristic
126	#127×C₇₃	—	2	4	no	—
127	#126×C₇₃	—	2	8	no	—
128	#126×C₇₃	—	4	4	no	—
129	#124×C₇₃	—	4	2	no	—
130	#123×C₇₃	—	2	4	no	—
131	#123×C₇₃	—	4	2	no	—
132	#121×C₇₃	—	4	2	no	—
133	C₄×D₄×C₇₃	—	2	8	no	—
134	C₄×D₄×C₇₃	—	2	8	no	—
135	#117×C₇₃	—	4	4	no	—
136	#117×C₇₃	—	4	2	no	—
137	C₂×C₄⋊C₄×C₇₃	—	4	2	no	—
138	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
139	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
140	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
141	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
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×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
146	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
147	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
148	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
149	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
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×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	1	yes	characteristic
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×C₂²⋊C₄×C₇₃	C₂³	1	2	yes	—
168	C₂×C₂²⋊C₄×C₇₃	C₂³	1	2	yes	—
169	C₂×C₂²⋊C₄×C₇₃	C₂³	1	2	yes	—
170	C₂×C₂²⋊C₄×C₇₃	C₂³	1	2	yes	—
171	C₂×C₂²⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
172	C₂×C₂²⋊C₄×C₇₃	C₂³	1	2	yes	—
173	C₂×C₂²⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
174	C₂×C₂²⋊C₄×C₇₃	C₂³	1	2	yes	—
175	C₂×C₂²⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
176	C₂×C₂²⋊C₄×C₇₃	C₂³	1	2	yes	—
177	C₂×C₂²⋊C₄×C₇₃	C₂³	1	2	yes	—
178	C₂×C₄²×C₇₃	—	4	2	no	—
179	C₂×C₄²×C₇₃	C₂³	1	2	yes	—
180	C₂×C₄²×C₇₃	C₂³	1	2	yes	—
181	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
182	C₂×C₄²×C₇₃	C₂³	1	2	yes	—
183	C₂×C₄²×C₇₃	C₂³	1	2	yes	—
184	C₂×C₄²×C₇₃	C₂³	1	2	yes	—
185	C₂×C₄²×C₇₃	C₂³	1	2	yes	—
186	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
187	C₂×C₄²×C₇₃	C₂³	1	2	yes	—
188	C₂×C₄²×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	#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	C₂⁴×C₇₃	C₂⁴	1	1	yes	characteristic
211	C₂⁴×C₇₃	C₂⁴	1	2	yes	—
212	C₂⁴×C₇₃	C₂⁴	1	1	yes	characteristic
213	C₂⁴×C₇₃	C₂⁴	1	1	yes	characteristic
214	#41×C₇₃	—	4	16	no	—
215	C₂×Q₈×C₇₃	—	2	2	no	—
216	C₂×Q₈×C₇₃	—	2	2	no	—
217	C₂×Q₈×C₇₃	—	4	1	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	2	no	—
222	C₂×D₄×C₇₃	—	2	4	no	—
223	C₂×D₄×C₇₃	—	2	4	no	—
224	C₂×D₄×C₇₃	—	2	2	no	—
225	C₂×D₄×C₇₃	—	2	2	no	—
226	C₂×D₄×C₇₃	—	4	2	no	—
227	C₂×D₄×C₇₃	—	4	2	no	—
228	C₂×D₄×C₇₃	—	4	1	no	—
229	C₂×D₄×C₇₃	—	4	1	no	—
230	C₂×D₄×C₇₃	—	4	1	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	2	no	—
235	C₂×D₄×C₇₃	—	4	1	no	—
236	C₂×D₄×C₇₃	—	4	2	no	—
237	C₂×D₄×C₇₃	—	4	2	no	—
238	C₂×D₄×C₇₃	#41	1	4	yes	—
239	C₂²×C₄×C₇₃	—	2	2	no	—
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	2	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	2	no	—
249	C₂²×C₄×C₇₃	—	2	2	no	—
250	C₂²×C₄×C₇₃	—	2	2	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	2	no	—
255	C₂²×C₄×C₇₃	—	4	2	no	—
256	C₂²×C₄×C₇₃	—	4	1	no	—
257	C₂²×C₄×C₇₃	—	4	1	no	—
258	C₂²×C₄×C₇₃	—	4	1	no	—
259	C₂²×C₄×C₇₃	—	4	1	no	—
260	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
261	C₂²×C₄×C₇₃	C₂⁴	1	2	yes	—
262	C₂²×C₄×C₇₃	C₂⁴	1	2	yes	—
263	C₂²×C₄×C₇₃	C₂⁴	1	2	yes	—
264	C₂²×C₄×C₇₃	C₂⁴	1	2	yes	—
265	C₂²×C₄×C₇₃	C₂⁴	1	2	yes	—
266	C₂²×C₄×C₇₃	C₂⁴	1	2	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	1	yes	characteristic
271	C₂²×C₄×C₇₃	C₂⁴	1	2	yes	—
272	C₂²×C₄×C₇₃	C₂⁴	1	2	yes	—
273	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
274	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
275	C₄⋊C₄×C₇₃	—	2	4	no	—
276	C₄⋊C₄×C₇₃	—	2	4	no	—
277	C₄⋊C₄×C₇₃	—	2	4	no	—
278	C₄⋊C₄×C₇₃	—	2	4	no	—
279	C₄⋊C₄×C₇₃	—	2	4	no	—
280	C₄⋊C₄×C₇₃	—	2	4	no	—
281	C₄⋊C₄×C₇₃	—	4	2	no	—
282	C₄⋊C₄×C₇₃	—	4	2	no	—
283	C₄⋊C₄×C₇₃	—	4	2	no	—
284	C₄⋊C₄×C₇₃	—	4	2	no	—
285	C₄⋊C₄×C₇₃	—	4	2	no	—
286	C₄⋊C₄×C₇₃	—	4	2	no	—
287	C₄⋊C₄×C₇₃	—	4	1	no	—
288	C₄⋊C₄×C₇₃	—	4	2	no	—
289	C₄⋊C₄×C₇₃	#41	1	8	yes	complemented
290	C₂²⋊C₄×C₇₃	—	2	2	no	—
291	C₂²⋊C₄×C₇₃	—	2	4	no	—
292	C₂²⋊C₄×C₇₃	—	2	4	no	—
293	C₂²⋊C₄×C₇₃	—	2	4	no	—
294	C₂²⋊C₄×C₇₃	—	2	4	no	—
295	C₂²⋊C₄×C₇₃	—	2	4	no	—
296	C₂²⋊C₄×C₇₃	—	2	4	no	—
297	C₂²⋊C₄×C₇₃	—	2	4	no	—
298	C₂²⋊C₄×C₇₃	—	2	4	no	—
299	C₂²⋊C₄×C₇₃	—	2	4	no	—
300	C₂²⋊C₄×C₇₃	—	2	4	no	—
301	C₂²⋊C₄×C₇₃	—	4	2	no	—
302	C₂²⋊C₄×C₇₃	—	4	2	no	—
303	C₂²⋊C₄×C₇₃	—	4	2	no	—
304	C₂²⋊C₄×C₇₃	—	4	2	no	—
305	C₂²⋊C₄×C₇₃	—	4	2	no	—
306	C₂²⋊C₄×C₇₃	—	4	2	no	—
307	C₂²⋊C₄×C₇₃	—	4	2	no	—
308	C₂²⋊C₄×C₇₃	—	4	1	no	—
309	C₂²⋊C₄×C₇₃	—	4	1	no	—
310	C₂²⋊C₄×C₇₃	—	4	2	no	—
311	C₂²⋊C₄×C₇₃	—	4	1	no	—
312	C₂²⋊C₄×C₇₃	—	4	2	no	—
313	C₂²⋊C₄×C₇₃	—	4	2	no	—
314	C₂²⋊C₄×C₇₃	—	4	2	no	—
315	C₄²×C₇₃	—	2	4	no	—
316	C₄²×C₇₃	—	2	4	no	—
317	C₄²×C₇₃	—	2	4	no	—
318	C₄²×C₇₃	—	2	2	no	—
319	C₄²×C₇₃	—	2	4	no	—
320	C₄²×C₇₃	—	4	2	no	—
321	C₄²×C₇₃	—	4	2	no	—
322	C₄²×C₇₃	—	4	2	no	—
323	C₄²×C₇₃	—	4	1	no	—
324	C₄²×C₇₃	—	4	2	no	—
325	C₂³×C₇₃	—	2	2	no	—
326	C₂³×C₇₃	—	2	2	no	—
327	C₂³×C₇₃	—	2	1	no	—
328	C₂³×C₇₃	—	2	1	no	—
329	C₂³×C₇₃	—	2	1	no	—
330	C₂³×C₇₃	—	2	1	no	—
331	C₂³×C₇₃	—	2	2	no	—
332	C₂³×C₇₃	—	2	2	no	—
333	C₂³×C₇₃	—	2	2	no	—
334	C₂³×C₇₃	—	2	2	no	—
335	C₂³×C₇₃	—	2	2	no	—
336	C₂³×C₇₃	—	2	1	no	—
337	C₂³×C₇₃	—	2	2	no	—
338	C₂³×C₇₃	—	2	2	no	—
339	C₂³×C₇₃	—	2	2	no	—
340	C₂³×C₇₃	—	2	1	no	—
341	C₂³×C₇₃	—	2	1	no	—
342	C₂³×C₇₃	—	2	2	no	—
343	C₂³×C₇₃	—	2	2	no	—
344	C₂³×C₇₃	—	2	2	no	—
345	C₂³×C₇₃	C₂×#41	1	2	yes	—
346	C₂³×C₇₃	C₂×#41	1	2	yes	—
347	C₂³×C₇₃	C₂⁵	1	1	yes	characteristic
348	Q₈×C₇₃	—	4	4	no	—
349	D₄×C₇₃	—	4	4	no	—
350	D₄×C₇₃	—	4	8	no	—
351	D₄×C₇₃	—	4	8	no	—
352	D₄×C₇₃	—	4	4	no	—
353	D₄×C₇₃	—	4	4	no	—
354	D₄×C₇₃	—	8	2	no	—
355	D₄×C₇₃	—	8	4	no	—
356	C₂×C₄×C₇₃	—	2	8	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	1	no	—
361	C₂×C₄×C₇₃	—	2	1	no	—
362	C₂×C₄×C₇₃	—	2	2	no	—
363	C₂×C₄×C₇₃	—	2	1	no	—
364	C₂×C₄×C₇₃	—	2	1	no	—
365	C₂×C₄×C₇₃	—	2	1	no	—
366	C₂×C₄×C₇₃	—	2	2	no	—
367	C₂×C₄×C₇₃	—	2	1	no	—
368	C₂×C₄×C₇₃	—	2	2	no	—
369	C₂×C₄×C₇₃	—	2	2	no	—
370	C₂×C₄×C₇₃	—	2	2	no	—
371	C₂×C₄×C₇₃	—	2	2	no	—
372	C₂×C₄×C₇₃	—	2	2	no	—
373	C₂×C₄×C₇₃	—	2	2	no	—
374	C₂×C₄×C₇₃	—	2	2	no	—
375	C₂×C₄×C₇₃	—	2	2	no	—
376	C₂×C₄×C₇₃	—	2	1	no	—
377	C₂×C₄×C₇₃	—	2	2	no	—
378	C₂×C₄×C₇₃	—	2	2	no	—
379	C₂×C₄×C₇₃	—	2	2	no	—
380	C₂×C₄×C₇₃	—	2	2	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	1	no	—
386	C₂×C₄×C₇₃	—	2	1	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	—	4	4	no	—
397	C₂×C₄×C₇₃	—	4	4	no	—
398	C₂×C₄×C₇₃	—	4	8	no	—
399	C₂×C₄×C₇₃	—	4	4	no	—
400	C₂×C₄×C₇₃	—	4	4	no	—
401	C₂×C₄×C₇₃	—	4	4	no	—
402	C₂×C₄×C₇₃	—	8	2	no	—
403	C₂×C₄×C₇₃	C₂×#41	1	4	yes	—
404	C₂×C₄×C₇₃	C₂×#41	1	4	yes	—
405	C₂×C₄×C₇₃	C₂×#41	1	2	yes	—
406	C₂×C₄×C₇₃	C₂×#41	1	4	yes	—
407	C₂×C₄×C₇₃	H(5,𝔽₂)	1	2	yes	—
408	C₂×C₄×C₇₃	H(5,𝔽₂)	1	2	yes	—
409	C₂²×C₇₃	—	2	4	no	—
410	C₂²×C₇₃	—	2	4	no	—
411	C₂²×C₇₃	—	2	2	no	—
412	C₂²×C₇₃	—	2	2	no	—
413	C₂²×C₇₃	—	4	1	no	—
414	C₂²×C₇₃	—	4	1	no	—
415	C₂²×C₇₃	—	4	2	no	—
416	C₂²×C₇₃	—	4	2	no	—
417	C₂²×C₇₃	—	4	1	no	—
418	C₂²×C₇₃	—	4	1	no	—
419	C₂²×C₇₃	—	4	2	no	—
420	C₂²×C₇₃	—	4	2	no	—
421	C₂²×C₇₃	—	4	2	no	—
422	C₂²×C₇₃	—	4	2	no	—
423	C₂²×C₇₃	—	4	1	no	—
424	C₂²×C₇₃	—	4	1	no	—
425	C₂²×C₇₃	—	4	2	no	—
426	C₂²×C₇₃	—	4	2	no	—
427	C₂²×C₇₃	—	4	2	no	—
428	C₂²×C₇₃	—	4	2	no	—
429	C₂²×C₇₃	—	4	1	no	—
430	C₂²×C₇₃	—	4	2	no	—
431	C₂²×C₇₃	C₂²×#41	1	1	yes	characteristic
432	C₂²×C₇₃	C₂²×#41	1	2	yes	—
433	C₂²×C₇₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
434	C₂²×C₇₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
435	C₂²×C₇₃	#585	1	2	yes	—
436	C₄×C₇₃	—	2	4	no	—
437	C₄×C₇₃	—	2	4	no	—
438	C₄×C₇₃	—	2	4	no	—
439	C₄×C₇₃	—	2	2	no	—
440	C₄×C₇₃	—	2	2	no	—
441	C₄×C₇₃	—	2	2	no	—
442	C₄×C₇₃	—	4	2	no	—
443	C₄×C₇₃	—	4	1	no	—
444	C₄×C₇₃	—	4	2	no	—
445	C₄×C₇₃	—	4	2	no	—
446	C₄×C₇₃	—	4	2	no	—
447	C₄×C₇₃	—	4	2	no	—
448	C₄×C₇₃	—	4	2	no	—
449	C₄×C₇₃	—	4	2	no	—
450	C₄×C₇₃	—	4	2	no	—
451	#59973	C₇₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
452	C₂×C₇₃	—	4	2	no	—
453	C₂×C₇₃	—	4	2	no	—
454	C₂×C₇₃	—	8	2	no	—
455	C₂×C₇₃	—	8	1	no	—
456	C₂×C₇₃	#3475	1	2	yes	—
457	C₂×C₇₃	#3481	1	1	yes	characteristic
458	C₂×C₇₃	#3490	1	1	yes	characteristic
459	C₂×C₇₃	#3517	1	2	yes	—
460	C₂×C₇₃	#3540	1	1	yes	characteristic
461	#2753	C₂×C₇₃	1	2	yes	complemented
462	#2748	C₂×C₇₃	1	1	yes	characteristic, complemented
463	#2709	C₂×C₇₃	1	1	yes	characteristic, complemented
464	#2554	C₂×C₇₃	1	2	yes	complemented
465	#2526	C₂×C₇₃	1	2	yes	complemented
466	#2521	C₂×C₇₃	1	2	yes	complemented
467	#2520	C₂×C₇₃	1	2	yes	complemented
468	#2479	C₂×C₇₃	1	2	yes	complemented
469	#2476	C₂×C₇₃	1	2	yes	complemented
470	#2467	C₂×C₇₃	1	2	yes	complemented
471	#2467	C₂×C₇₃	1	2	yes	complemented
472	#2431	C₂×C₇₃	1	1	yes	characteristic
473	#2406	C₂×C₇₃	1	1	yes	characteristic, complemented
474	#2374	C₂×C₇₃	1	1	yes	characteristic, complemented
475	#2373	C₂×C₇₃	1	2	yes	complemented
476	#2366	C₂×C₇₃	1	1	yes	characteristic, complemented
477	#2352	C₂×C₇₃	1	2	yes	complemented
478	#2297	C₂×C₇₃	1	1	yes	characteristic, complemented
479	#2290	C₂×C₇₃	1	2	yes	complemented
480	C₇₃	#59973	1	1	yes	characteristic, direct product factor, Sylow
481	C₂²×#41	C₂²×C₇₃	1	1	yes	characteristic
482	C₂×#127	C₂²×C₇₃	1	1	yes	characteristic
483	C₂×#126	C₂²×C₇₃	1	2	yes	—
484	C₂×#126	C₂²×C₇₃	1	2	yes	—
485	C₂×#124	C₂²×C₇₃	1	1	yes	characteristic
486	C₂×#123	C₂²×C₇₃	1	1	yes	characteristic
487	C₂×#123	C₂²×C₇₃	1	1	yes	characteristic
488	C₂×#121	C₂²×C₇₃	1	1	yes	characteristic
489	C₂×C₄×D₄	C₂²×C₇₃	1	2	yes	—
490	C₂×C₄×D₄	C₂²×C₇₃	1	2	yes	—
491	C₂×#117	C₂²×C₇₃	1	2	yes	—
492	C₂×#117	C₂²×C₇₃	1	1	yes	characteristic
493	C₂²×C₄⋊C₄	C₂²×C₇₃	1	1	yes	characteristic
494	C₂²×C₄²	C₂²×C₇₃	1	1	yes	characteristic
495	#400	C₂²×C₇₃	1	2	yes	—
496	#399	C₂²×C₇₃	1	2	yes	—
497	#399	C₂²×C₇₃	1	2	yes	—
498	#398	C₂²×C₇₃	1	2	yes	—
499	#398	C₂²×C₇₃	1	2	yes	—
500	#397	C₂²×C₇₃	1	2	yes	—
501	#396	C₂²×C₇₃	1	2	yes	—
502	#395	C₂²×C₇₃	1	2	yes	—
503	#394	C₂²×C₇₃	1	2	yes	—
504	#394	C₂²×C₇₃	1	2	yes	—
505	#394	C₂²×C₇₃	1	2	yes	—
506	#394	C₂²×C₇₃	1	2	yes	—
507	#394	C₂²×C₇₃	1	2	yes	—
508	#394	C₂²×C₇₃	1	2	yes	—
509	#392	C₂²×C₇₃	1	2	yes	—
510	#392	C₂²×C₇₃	1	2	yes	—
511	#391	C₂²×C₇₃	1	1	yes	characteristic
512	#391	C₂²×C₇₃	1	2	yes	—
513	#390	C₂²×C₇₃	1	2	yes	—
514	#390	C₂²×C₇₃	1	2	yes	—
515	#390	C₂²×C₇₃	1	1	yes	characteristic
516	#390	C₂²×C₇₃	1	2	yes	—
517	#390	C₂²×C₇₃	1	2	yes	—
518	#389	C₂²×C₇₃	1	2	yes	—
519	#388	C₂²×C₇₃	1	2	yes	—
520	#388	C₂²×C₇₃	1	2	yes	—
521	#388	C₂²×C₇₃	1	2	yes	—
522	#388	C₂²×C₇₃	1	2	yes	—
523	#388	C₂²×C₇₃	1	2	yes	—
524	#388	C₂²×C₇₃	1	2	yes	—
525	#388	C₂²×C₇₃	1	2	yes	—
526	#388	C₂²×C₇₃	1	2	yes	—
527	#388	C₂²×C₇₃	1	2	yes	—
528	#388	C₂²×C₇₃	1	2	yes	—
529	#388	C₂²×C₇₃	1	2	yes	—
530	#387	C₂²×C₇₃	1	2	yes	—
531	#387	C₂²×C₇₃	1	2	yes	—
532	#387	C₂²×C₇₃	1	2	yes	—
533	#387	C₂²×C₇₃	1	2	yes	—
534	#387	C₂²×C₇₃	1	2	yes	—
535	#387	C₂²×C₇₃	1	2	yes	—
536	#387	C₂²×C₇₃	1	2	yes	—
537	#387	C₂²×C₇₃	1	2	yes	—
538	#386	C₂²×C₇₃	1	2	yes	—
539	#386	C₂²×C₇₃	1	2	yes	—
540	#386	C₂²×C₇₃	1	1	yes	characteristic
541	#386	C₂²×C₇₃	1	1	yes	characteristic
542	#386	C₂²×C₇₃	1	2	yes	—
543	#386	C₂²×C₇₃	1	1	yes	characteristic
544	#386	C₂²×C₇₃	1	2	yes	—
545	#386	C₂²×C₇₃	1	1	yes	characteristic
546	#386	C₂²×C₇₃	1	2	yes	—
547	#386	C₂²×C₇₃	1	2	yes	—
548	#386	C₂²×C₇₃	1	1	yes	characteristic
549	#386	C₂²×C₇₃	1	1	yes	characteristic
550	#385	C₂²×C₇₃	1	2	yes	—
551	#385	C₂²×C₇₃	1	2	yes	—
552	#385	C₂²×C₇₃	1	2	yes	—
553	#382	C₂²×C₇₃	1	2	yes	—
554	#381	C₂²×C₇₃	1	1	yes	characteristic
555	#380	C₂²×C₇₃	1	2	yes	—
556	#380	C₂²×C₇₃	1	2	yes	—
557	C₄×C₄⋊C₄	C₂²×C₇₃	1	2	yes	—
558	C₄×C₄⋊C₄	C₂²×C₇₃	1	2	yes	—
559	C₄×C₄⋊C₄	C₂²×C₇₃	1	2	yes	—
560	C₄×C₄⋊C₄	C₂²×C₇₃	1	2	yes	—
561	C₄×C₂²⋊C₄	C₂²×C₇₃	1	2	yes	—
562	C₄×C₂²⋊C₄	C₂²×C₇₃	1	2	yes	—
563	C₄×C₂²⋊C₄	C₂²×C₇₃	1	1	yes	characteristic
564	C₄×C₂²⋊C₄	C₂²×C₇₃	1	2	yes	—
565	C₄×C₂²⋊C₄	C₂²×C₇₃	1	2	yes	—
566	C₄×C₂²⋊C₄	C₂²×C₇₃	1	2	yes	—
567	#376	C₂²×C₇₃	1	2	yes	—
568	C₂×#41	—	2	4	no	—
569	C₂×#41	—	4	2	no	—
570	C₂×#41	—	4	2	no	—
571	C₂²×Q₈	C₂³×C₇₃	1	1	yes	characteristic
572	C₂²×D₄	C₂³×C₇₃	1	2	yes	—
573	C₂²×D₄	C₂³×C₇₃	1	2	yes	—
574	C₂²×D₄	C₂³×C₇₃	1	1	yes	characteristic
575	C₂²×D₄	C₂³×C₇₃	1	1	yes	characteristic
576	C₂²×D₄	C₂³×C₇₃	1	1	yes	characteristic
577	C₂²×D₄	C₂³×C₇₃	1	2	yes	—
578	C₂²×D₄	C₂³×C₇₃	1	1	yes	characteristic
579	C₂³×C₄	C₂³×C₇₃	1	1	yes	characteristic
580	C₂³×C₄	C₂³×C₇₃	1	1	yes	characteristic
581	C₂³×C₄	C₂³×C₇₃	1	1	yes	characteristic
582	C₂³×C₄	C₂³×C₇₃	1	2	yes	—
583	C₂³×C₄	C₂³×C₇₃	1	1	yes	characteristic
584	C₂³×C₄	C₂³×C₇₃	1	1	yes	characteristic
585	C₂³×C₄	C₂³×C₇₃	1	1	yes	characteristic
586	C₂³×C₄	C₂³×C₇₃	1	1	yes	characteristic
587	#127	—	2	4	no	—
588	#126	—	2	8	no	—
589	#126	—	4	4	no	—
590	#124	—	4	2	no	—
591	#123	—	2	4	no	—
592	#123	—	4	2	no	—
593	#121	—	4	2	no	—
594	C₄×D₄	—	2	8	no	—
595	C₄×D₄	—	2	8	no	—
596	#117	—	4	4	no	—
597	#117	—	4	2	no	—
598	C₂×C₄⋊C₄	—	4	2	no	—
599	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
600	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
601	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
602	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
603	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
604	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
605	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
606	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
607	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
608	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
609	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
610	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
611	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
612	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
613	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
614	C₂×C₂²⋊C₄	C₂³×C₇₃	1	2	yes	—
615	C₂×C₂²⋊C₄	C₂³×C₇₃	1	2	yes	—
616	C₂×C₂²⋊C₄	C₂³×C₇₃	1	2	yes	—
617	C₂×C₂²⋊C₄	C₂³×C₇₃	1	2	yes	—
618	C₂×C₂²⋊C₄	C₂³×C₇₃	1	2	yes	—
619	C₂×C₂²⋊C₄	C₂³×C₇₃	1	2	yes	—
620	C₂×C₂²⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
621	C₂×C₂²⋊C₄	C₂³×C₇₃	1	2	yes	—
622	C₂×C₂²⋊C₄	C₂³×C₇₃	1	2	yes	—
623	C₂×C₂²⋊C₄	C₂³×C₇₃	1	2	yes	—
624	C₂×C₂²⋊C₄	C₂³×C₇₃	1	2	yes	—
625	C₂×C₂²⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
626	C₂×C₂²⋊C₄	C₂³×C₇₃	1	2	yes	—
627	C₂×C₂²⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
628	C₂×C₂²⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
629	C₂×C₂²⋊C₄	C₂³×C₇₃	1	2	yes	—
630	C₂×C₂²⋊C₄	C₂³×C₇₃	1	2	yes	—
631	C₂×C₂²⋊C₄	C₂³×C₇₃	1	2	yes	—
632	C₂×C₂²⋊C₄	C₂³×C₇₃	1	2	yes	—
633	C₂×C₂²⋊C₄	C₂³×C₇₃	1	2	yes	—
634	C₂×C₂²⋊C₄	C₂³×C₇₃	1	2	yes	—
635	C₂×C₂²⋊C₄	C₂³×C₇₃	1	2	yes	—
636	C₂×C₂²⋊C₄	C₂³×C₇₃	1	2	yes	—
637	C₂×C₂²⋊C₄	C₂³×C₇₃	1	2	yes	—
638	C₂×C₂²⋊C₄	C₂³×C₇₃	1	2	yes	—
639	C₂×C₄²	—	4	2	no	—
640	C₂×C₄²	C₂³×C₇₃	1	2	yes	—
641	C₂×C₄²	C₂³×C₇₃	1	2	yes	—
642	C₂×C₄²	C₂³×C₇₃	1	2	yes	—
643	C₂×C₄²	C₂³×C₇₃	1	2	yes	—
644	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
645	C₂×C₄²	C₂³×C₇₃	1	2	yes	—
646	C₂×C₄²	C₂³×C₇₃	1	2	yes	—
647	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
648	C₂×C₄²	C₂³×C₇₃	1	2	yes	—
649	C₂×C₄²	C₂³×C₇₃	1	2	yes	—
650	#95	C₂³×C₇₃	1	2	yes	—
651	#95	C₂³×C₇₃	1	2	yes	—
652	#95	C₂³×C₇₃	1	2	yes	—
653	#95	C₂³×C₇₃	1	2	yes	—
654	#95	C₂³×C₇₃	1	2	yes	—
655	#95	C₂³×C₇₃	1	2	yes	—
656	#95	C₂³×C₇₃	1	2	yes	—
657	#95	C₂³×C₇₃	1	2	yes	—
658	#95	C₂³×C₇₃	1	2	yes	—
659	#95	C₂³×C₇₃	1	2	yes	—
660	#95	C₂³×C₇₃	1	2	yes	—
661	#95	C₂³×C₇₃	1	2	yes	—
662	#95	C₂³×C₇₃	1	2	yes	—
663	#95	C₂³×C₇₃	1	2	yes	—
664	#95	C₂³×C₇₃	1	2	yes	—
665	#95	C₂³×C₇₃	1	2	yes	—
666	#95	C₂³×C₇₃	1	2	yes	—
667	#95	C₂³×C₇₃	1	2	yes	—
668	#95	C₂³×C₇₃	1	2	yes	—
669	#95	C₂³×C₇₃	1	2	yes	—
670	#95	C₂³×C₇₃	1	2	yes	—
671	C₂⁴	C₂⁴×C₇₃	1	1	yes	characteristic
672	C₂⁴	C₂⁴×C₇₃	1	2	yes	—
673	C₂⁴	C₂⁴×C₇₃	1	1	yes	characteristic
674	C₂⁴	C₂⁴×C₇₃	1	1	yes	characteristic
675	#41	—	4	16	no	—
676	C₂×Q₈	—	2	2	no	—
677	C₂×Q₈	—	2	2	no	—
678	C₂×Q₈	—	4	1	no	—
679	C₂×D₄	—	2	4	no	—
680	C₂×D₄	—	2	4	no	—
681	C₂×D₄	—	2	2	no	—
682	C₂×D₄	—	2	2	no	—
683	C₂×D₄	—	2	4	no	—
684	C₂×D₄	—	2	4	no	—
685	C₂×D₄	—	2	2	no	—
686	C₂×D₄	—	2	2	no	—
687	C₂×D₄	—	4	2	no	—
688	C₂×D₄	—	4	2	no	—
689	C₂×D₄	—	4	1	no	—
690	C₂×D₄	—	4	1	no	—
691	C₂×D₄	—	4	1	no	—
692	C₂×D₄	—	4	1	no	—
693	C₂×D₄	—	4	1	no	—
694	C₂×D₄	—	4	1	no	—
695	C₂×D₄	—	4	2	no	—
696	C₂×D₄	—	4	1	no	—
697	C₂×D₄	—	4	2	no	—
698	C₂×D₄	—	4	2	no	—
699	C₂×D₄	#41×C₇₃	1	4	yes	—
700	C₂²×C₄	—	2	2	no	—
701	C₂²×C₄	—	2	2	no	—
702	C₂²×C₄	—	2	2	no	—
703	C₂²×C₄	—	2	2	no	—
704	C₂²×C₄	—	2	2	no	—
705	C₂²×C₄	—	2	4	no	—
706	C₂²×C₄	—	2	4	no	—
707	C₂²×C₄	—	2	4	no	—
708	C₂²×C₄	—	2	4	no	—
709	C₂²×C₄	—	2	2	no	—
710	C₂²×C₄	—	2	2	no	—
711	C₂²×C₄	—	2	2	no	—
712	C₂²×C₄	—	4	1	no	—
713	C₂²×C₄	—	4	1	no	—
714	C₂²×C₄	—	4	1	no	—
715	C₂²×C₄	—	4	2	no	—
716	C₂²×C₄	—	4	2	no	—
717	C₂²×C₄	—	4	1	no	—
718	C₂²×C₄	—	4	1	no	—
719	C₂²×C₄	—	4	1	no	—
720	C₂²×C₄	—	4	1	no	—
721	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
722	C₂²×C₄	C₂⁴×C₇₃	1	2	yes	—
723	C₂²×C₄	C₂⁴×C₇₃	1	2	yes	—
724	C₂²×C₄	C₂⁴×C₇₃	1	2	yes	—
725	C₂²×C₄	C₂⁴×C₇₃	1	2	yes	—
726	C₂²×C₄	C₂⁴×C₇₃	1	2	yes	—
727	C₂²×C₄	C₂⁴×C₇₃	1	2	yes	—
728	C₂²×C₄	C₂⁴×C₇₃	1	2	yes	—
729	C₂²×C₄	C₂⁴×C₇₃	1	2	yes	—
730	C₂²×C₄	C₂⁴×C₇₃	1	2	yes	—
731	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
732	C₂²×C₄	C₂⁴×C₇₃	1	2	yes	—
733	C₂²×C₄	C₂⁴×C₇₃	1	2	yes	—
734	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
735	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
736	C₄⋊C₄	—	2	4	no	—
737	C₄⋊C₄	—	2	4	no	—
738	C₄⋊C₄	—	2	4	no	—
739	C₄⋊C₄	—	2	4	no	—
740	C₄⋊C₄	—	2	4	no	—
741	C₄⋊C₄	—	2	4	no	—
742	C₄⋊C₄	—	4	2	no	—
743	C₄⋊C₄	—	4	2	no	—
744	C₄⋊C₄	—	4	2	no	—
745	C₄⋊C₄	—	4	2	no	—
746	C₄⋊C₄	—	4	2	no	—
747	C₄⋊C₄	—	4	2	no	—
748	C₄⋊C₄	—	4	1	no	—
749	C₄⋊C₄	—	4	2	no	—
750	C₄⋊C₄	#41×C₇₃	1	8	yes	complemented
751	C₂²⋊C₄	—	2	2	no	—
752	C₂²⋊C₄	—	2	4	no	—
753	C₂²⋊C₄	—	2	4	no	—
754	C₂²⋊C₄	—	2	4	no	—
755	C₂²⋊C₄	—	2	4	no	—
756	C₂²⋊C₄	—	2	4	no	—
757	C₂²⋊C₄	—	2	4	no	—
758	C₂²⋊C₄	—	2	4	no	—
759	C₂²⋊C₄	—	2	4	no	—
760	C₂²⋊C₄	—	2	4	no	—
761	C₂²⋊C₄	—	2	4	no	—
762	C₂²⋊C₄	—	4	2	no	—
763	C₂²⋊C₄	—	4	2	no	—
764	C₂²⋊C₄	—	4	2	no	—
765	C₂²⋊C₄	—	4	2	no	—
766	C₂²⋊C₄	—	4	2	no	—
767	C₂²⋊C₄	—	4	2	no	—
768	C₂²⋊C₄	—	4	2	no	—
769	C₂²⋊C₄	—	4	1	no	—
770	C₂²⋊C₄	—	4	1	no	—
771	C₂²⋊C₄	—	4	2	no	—
772	C₂²⋊C₄	—	4	1	no	—
773	C₂²⋊C₄	—	4	2	no	—
774	C₂²⋊C₄	—	4	2	no	—
775	C₂²⋊C₄	—	4	2	no	—
776	C₄²	—	2	4	no	—
777	C₄²	—	2	4	no	—
778	C₄²	—	2	4	no	—
779	C₄²	—	2	2	no	—
780	C₄²	—	2	4	no	—
781	C₄²	—	4	2	no	—
782	C₄²	—	4	2	no	—
783	C₄²	—	4	2	no	—
784	C₄²	—	4	1	no	—
785	C₄²	—	4	2	no	—
786	C₂³	—	2	2	no	—
787	C₂³	—	2	2	no	—
788	C₂³	—	2	1	no	—
789	C₂³	—	2	1	no	—
790	C₂³	—	2	1	no	—
791	C₂³	—	2	1	no	—
792	C₂³	—	2	2	no	—
793	C₂³	—	2	2	no	—
794	C₂³	—	2	2	no	—
795	C₂³	—	2	2	no	—
796	C₂³	—	2	2	no	—
797	C₂³	—	2	1	no	—
798	C₂³	—	2	2	no	—
799	C₂³	—	2	2	no	—
800	C₂³	—	2	2	no	—
801	C₂³	—	2	1	no	—
802	C₂³	—	2	1	no	—
803	C₂³	—	2	2	no	—
804	C₂³	—	2	2	no	—
805	C₂³	—	2	2	no	—
806	C₂³	C₂×#41×C₇₃	1	2	yes	—
807	C₂³	C₂×#41×C₇₃	1	2	yes	—
808	C₂³	C₂⁵×C₇₃	1	1	yes	characteristic
809	Q₈	—	4	4	no	—
810	D₄	—	4	4	no	—
811	D₄	—	4	4	no	—
812	D₄	—	4	8	no	—
813	D₄	—	4	8	no	—
814	D₄	—	4	4	no	—
815	D₄	—	8	2	no	—
816	D₄	—	8	4	no	—
817	C₂×C₄	—	2	8	no	—
818	C₂×C₄	—	2	2	no	—
819	C₂×C₄	—	2	2	no	—
820	C₂×C₄	—	2	2	no	—
821	C₂×C₄	—	2	1	no	—
822	C₂×C₄	—	2	1	no	—
823	C₂×C₄	—	2	2	no	—
824	C₂×C₄	—	2	1	no	—
825	C₂×C₄	—	2	1	no	—
826	C₂×C₄	—	2	1	no	—
827	C₂×C₄	—	2	2	no	—
828	C₂×C₄	—	2	1	no	—
829	C₂×C₄	—	2	2	no	—
830	C₂×C₄	—	2	2	no	—
831	C₂×C₄	—	2	2	no	—
832	C₂×C₄	—	2	2	no	—
833	C₂×C₄	—	2	2	no	—
834	C₂×C₄	—	2	2	no	—
835	C₂×C₄	—	2	2	no	—
836	C₂×C₄	—	2	2	no	—
837	C₂×C₄	—	2	1	no	—
838	C₂×C₄	—	2	2	no	—
839	C₂×C₄	—	2	2	no	—
840	C₂×C₄	—	2	2	no	—
841	C₂×C₄	—	2	2	no	—
842	C₂×C₄	—	2	2	no	—
843	C₂×C₄	—	2	2	no	—
844	C₂×C₄	—	2	2	no	—
845	C₂×C₄	—	2	2	no	—
846	C₂×C₄	—	2	1	no	—
847	C₂×C₄	—	2	1	no	—
848	C₂×C₄	—	2	2	no	—
849	C₂×C₄	—	2	2	no	—
850	C₂×C₄	—	2	2	no	—
851	C₂×C₄	—	2	2	no	—
852	C₂×C₄	—	2	2	no	—
853	C₂×C₄	—	2	2	no	—
854	C₂×C₄	—	2	2	no	—
855	C₂×C₄	—	2	2	no	—
856	C₂×C₄	—	2	2	no	—
857	C₂×C₄	—	4	4	no	—
858	C₂×C₄	—	4	4	no	—
859	C₂×C₄	—	4	4	no	—
860	C₂×C₄	—	4	8	no	—
861	C₂×C₄	—	4	4	no	—
862	C₂×C₄	—	4	4	no	—
863	C₂×C₄	—	8	2	no	—
864	C₂×C₄	C₂×#41×C₇₃	1	4	yes	—
865	C₂×C₄	C₂×#41×C₇₃	1	4	yes	—
866	C₂×C₄	C₂×#41×C₇₃	1	2	yes	—
867	C₂×C₄	C₂×#41×C₇₃	1	4	yes	—
868	C₂×C₄	H(5,𝔽₂)×C₇₃	1	2	yes	—
869	C₂×C₄	H(5,𝔽₂)×C₇₃	1	2	yes	—
870	C₂²	—	2	4	no	—
871	C₂²	—	2	4	no	—
872	C₂²	—	2	2	no	—
873	C₂²	—	2	2	no	—
874	C₂²	—	4	1	no	—
875	C₂²	—	4	1	no	—
876	C₂²	—	4	2	no	—
877	C₂²	—	4	2	no	—
878	C₂²	—	4	1	no	—
879	C₂²	—	4	1	no	—
880	C₂²	—	4	2	no	—
881	C₂²	—	4	2	no	—
882	C₂²	—	4	2	no	—
883	C₂²	—	4	2	no	—
884	C₂²	—	4	1	no	—
885	C₂²	—	4	1	no	—
886	C₂²	—	4	2	no	—
887	C₂²	—	4	2	no	—
888	C₂²	—	4	2	no	—
889	C₂²	—	4	2	no	—
890	C₂²	—	4	1	no	—
891	C₂²	—	4	2	no	—
892	C₂²	C₂²×#41×C₇₃	1	1	yes	characteristic
893	C₂²	C₂²×#41×C₇₃	1	2	yes	—
894	C₂²	C₂×H(5,𝔽₂)×C₇₃	1	1	yes	characteristic
895	C₂²	C₂×H(5,𝔽₂)×C₇₃	1	1	yes	characteristic
896	C₂²	#585×C₇₃	1	2	yes	—
897	C₄	—	2	4	no	—
898	C₄	—	2	4	no	—
899	C₄	—	2	4	no	—
900	C₄	—	2	2	no	—
901	C₄	—	2	2	no	—
902	C₄	—	2	2	no	—
903	C₄	—	4	2	no	—
904	C₄	—	4	1	no	—
905	C₄	—	4	2	no	—
906	C₄	—	4	2	no	—
907	C₄	—	4	2	no	—
908	C₄	—	4	2	no	—
909	C₄	—	4	2	no	—
910	C₄	—	4	2	no	—
911	C₄	—	4	2	no	—
912	C₂	—	4	2	no	—
913	C₂	—	4	2	no	—
914	C₂	—	8	2	no	—
915	C₂	—	8	1	no	—
916	C₂	C₇₃×#3475	1	2	yes	—
917	C₂	C₇₃×#3481	1	1	yes	characteristic
918	C₂	C₇₃×#3490	1	1	yes	characteristic
919	C₂	C₇₃×#3517	1	2	yes	—
920	C₂	C₇₃×#3540	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₇₃	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₇₃
prime radical	C₇₃×#2431	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×#2753	C₂	semidirect
2. C₇₃×#2748	C₂	semidirect
3. C₇₃×#2709	C₂	semidirect
4. C₇₃×#2554	C₂	semidirect
5. C₇₃×#2526	C₂	semidirect
6. C₇₃×#2521	C₂	semidirect
7. C₇₃×#2520	C₂	semidirect
8. C₇₃×#2479	C₂	semidirect
9. C₇₃×#2476	C₂	semidirect
10. C₇₃×#2467	C₂	semidirect
11. C₇₃×#2467	C₂	semidirect
13. C₇₃×#2406	C₂	semidirect
14. C₇₃×#2374	C₂	semidirect
15. C₇₃×#2373	C₂	semidirect
16. C₇₃×#2366	C₂	semidirect
17. C₇₃×#2352	C₂	semidirect
18. C₇₃×#2297	C₂	semidirect
19. C₇₃×#2290	C₂	semidirect
289. C₄⋊C₄×C₇₃	#41	semidirect
451. #59973	C₇₃	direct (N × H)
461. #2753	C₂×C₇₃	semidirect
462. #2748	C₂×C₇₃	semidirect
463. #2709	C₂×C₇₃	semidirect
464. #2554	C₂×C₇₃	semidirect
465. #2526	C₂×C₇₃	semidirect
466. #2521	C₂×C₇₃	semidirect
467. #2520	C₂×C₇₃	semidirect
468. #2479	C₂×C₇₃	semidirect
469. #2476	C₂×C₇₃	semidirect
470. #2467	C₂×C₇₃	semidirect
471. #2467	C₂×C₇₃	semidirect
473. #2406	C₂×C₇₃	semidirect
474. #2374	C₂×C₇₃	semidirect
475. #2373	C₂×C₇₃	semidirect
476. #2366	C₂×C₇₃	semidirect
477. #2352	C₂×C₇₃	semidirect
478. #2297	C₂×C₇₃	semidirect
479. #2290	C₂×C₇₃	semidirect
480. C₇₃	#59973	direct (N × H)
750. C₄⋊C₄	#41×C₇₃	semidirect

Maximal subgroups

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

subgroup	index
C₇₃×#2753	2
C₇₃×#2748	2
C₇₃×#2709	2
C₇₃×#2554	2
C₇₃×#2526	2
C₇₃×#2521	2
C₇₃×#2520	2
C₇₃×#2479	2
C₇₃×#2476	2
C₇₃×#2467	2
C₇₃×#2431	2
C₇₃×#2406	2
C₇₃×#2374	2
C₇₃×#2373	2
C₇₃×#2366	2
C₇₃×#2352	2
C₇₃×#2297	2
C₇₃×#2290	2
#59973	73

Subgroups — C73×#59973 #32969377

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₃×#59973 #32969377