Subgroups — C₇₃×#59975 #32969379

Order 18688.

1738 conjugacy classes of subgroups.

The subgroup lattice has 810 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇₃×#2763	C₂	1	1	yes	maximal, characteristic, complemented
2	C₇₃×#2757	C₂	1	2	yes	maximal, complemented
3	C₇₃×#2712	C₂	1	1	yes	maximal, characteristic
4	C₇₃×#2610	C₂	1	1	yes	maximal, characteristic
5	C₇₃×#2599	C₂	1	1	yes	maximal, characteristic, complemented
6	C₇₃×#2586	C₂	1	2	yes	maximal, complemented
7	C₇₃×#2532	C₂	1	2	yes	maximal, complemented
8	C₇₃×#2525	C₂	1	2	yes	maximal, complemented
9	C₇₃×#2523	C₂	1	1	yes	maximal, characteristic, complemented
10	C₇₃×#2518	C₂	1	2	yes	maximal, complemented
11	C₇₃×#2474	C₂	1	2	yes	maximal, complemented
12	C₇₃×#2474	C₂	1	2	yes	maximal, complemented
13	C₇₃×#2465	C₂	1	2	yes	maximal, complemented
14	C₇₃×#2463	C₂	1	1	yes	maximal, characteristic
15	C₇₃×#2367	C₂	1	2	yes	maximal, complemented
16	C₇₃×#2362	C₂	1	2	yes	maximal, complemented
17	C₇₃×#2356	C₂	1	2	yes	maximal, complemented
18	C₇₃×#2296	C₂	1	1	yes	maximal, characteristic, complemented
19	C₇₃×#2290	C₂	1	2	yes	maximal, complemented
20	C₂×#124×C₇₃	C₂²	1	2	yes	—
21	C₂×#124×C₇₃	C₂²	1	1	yes	characteristic
22	C₂×C₂²⋊Q₈×C₇₃	C₂²	1	2	yes	—
23	C₂×C₄×Q₈×C₇₃	C₂²	1	2	yes	—
24	C₂×C₄×Q₈×C₇₃	C₂²	1	1	yes	characteristic
25	C₂×C₄×D₄×C₇₃	C₂²	1	2	yes	—
26	C₂×#117×C₇₃	C₂²	1	1	yes	characteristic
27	C₂×#117×C₇₃	C₂²	1	2	yes	—
28	C₂×#117×C₇₃	C₂²	1	1	yes	characteristic
29	C₂²×C₄²×C₇₃	C₂²	1	1	yes	characteristic
30	#400×C₇₃	C₂²	1	2	yes	—
31	#398×C₇₃	C₂²	1	2	yes	—
32	#398×C₇₃	C₂²	1	1	yes	characteristic
33	#397×C₇₃	C₂²	1	1	yes	characteristic
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	#395×C₇₃	C₂²	1	1	yes	characteristic
40	#395×C₇₃	C₂²	1	2	yes	—
41	#395×C₇₃	C₂²	1	2	yes	—
42	#395×C₇₃	C₂²	1	1	yes	characteristic
43	#394×C₇₃	C₂²	1	2	yes	—
44	#394×C₇₃	C₂²	1	2	yes	—
45	#394×C₇₃	C₂²	1	1	yes	characteristic
46	#393×C₇₃	C₂²	1	2	yes	—
47	#393×C₇₃	C₂²	1	1	yes	characteristic
48	#393×C₇₃	C₂²	1	1	yes	characteristic
49	#392×C₇₃	C₂²	1	1	yes	characteristic
50	#391×C₇₃	C₂²	1	2	yes	—
51	#391×C₇₃	C₂²	1	2	yes	—
52	#391×C₇₃	C₂²	1	2	yes	—
53	#391×C₇₃	C₂²	1	2	yes	—
54	#391×C₇₃	C₂²	1	2	yes	—
55	#390×C₇₃	C₂²	1	2	yes	—
56	#389×C₇₃	C₂²	1	2	yes	—
57	#389×C₇₃	C₂²	1	2	yes	—
58	#389×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	#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	#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	#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	#386×C₇₃	C₂²	1	2	yes	—
83	#386×C₇₃	C₂²	1	2	yes	—
84	#386×C₇₃	C₂²	1	2	yes	—
85	#385×C₇₃	C₂²	1	1	yes	characteristic
86	#385×C₇₃	C₂²	1	1	yes	characteristic
87	#385×C₇₃	C₂²	1	2	yes	—
88	#385×C₇₃	C₂²	1	2	yes	—
89	#385×C₇₃	C₂²	1	1	yes	characteristic
90	#385×C₇₃	C₂²	1	2	yes	—
91	#385×C₇₃	C₂²	1	1	yes	characteristic
92	#383×C₇₃	C₂²	1	2	yes	—
93	#383×C₇₃	C₂²	1	2	yes	—
94	#383×C₇₃	C₂²	1	1	yes	characteristic
95	#382×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×C₄⋊C₄×C₇₃	C₂²	1	2	yes	—
101	C₄×C₄⋊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	#376×C₇₃	C₂²	1	1	yes	characteristic
107	C₂²×Q₈×C₇₃	C₂³	1	2	yes	—
108	C₂²×Q₈×C₇₃	C₂³	1	1	yes	characteristic
109	C₂²×Q₈×C₇₃	C₂³	1	1	yes	characteristic
110	C₂²×D₄×C₇₃	C₂³	1	2	yes	—
111	C₂²×D₄×C₇₃	C₂³	1	1	yes	characteristic
112	C₂³×C₄×C₇₃	C₂³	1	1	yes	characteristic
113	C₂³×C₄×C₇₃	C₂³	1	1	yes	characteristic
114	C₂³×C₄×C₇₃	C₂³	1	2	yes	—
115	C₂³×C₄×C₇₃	C₂³	1	1	yes	characteristic
116	#124×C₇₃	—	2	8	no	—
117	#124×C₇₃	—	4	2	no	—
118	C₂²⋊Q₈×C₇₃	—	2	8	no	—
119	C₄×Q₈×C₇₃	—	2	8	no	—
120	C₄×Q₈×C₇₃	—	4	2	no	—
121	C₄×D₄×C₇₃	—	2	8	no	—
122	#117×C₇₃	—	2	4	no	—
123	#117×C₇₃	—	4	2	no	—
124	#117×C₇₃	—	4	4	no	—
125	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
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	2	yes	—
137	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
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	2	yes	—
141	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
142	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
143	C₂×C₂²⋊C₄×C₇₃	C₂³	1	2	yes	—
144	C₂×C₂²⋊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	1	yes	characteristic
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	1	yes	characteristic
157	C₂×C₂²⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
162	C₂×C₄²×C₇₃	—	4	2	no	—
163	C₂×C₄²×C₇₃	C₂³	1	2	yes	—
164	C₂×C₄²×C₇₃	C₂³	1	2	yes	—
165	C₂×C₄²×C₇₃	C₂³	1	2	yes	—
166	C₂×C₄²×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	2	yes	—
172	C₂×C₄²×C₇₃	C₂³	1	2	yes	—
173	C₂×C₄²×C₇₃	C₂³	1	2	yes	—
174	C₂×C₄²×C₇₃	C₂³	1	2	yes	—
175	#95×C₇₃	C₂³	1	2	yes	—
176	#95×C₇₃	C₂³	1	2	yes	—
177	#95×C₇₃	C₂³	1	2	yes	—
178	#95×C₇₃	C₂³	1	2	yes	—
179	#95×C₇₃	C₂³	1	2	yes	—
180	#95×C₇₃	C₂³	1	2	yes	—
181	#95×C₇₃	C₂³	1	2	yes	—
182	#95×C₇₃	C₂³	1	2	yes	—
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	1	yes	characteristic
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	1	yes	characteristic
197	#95×C₇₃	C₂³	1	2	yes	—
198	#95×C₇₃	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
203	#95×C₇₃	C₂³	1	2	yes	—
204	C₂⁴×C₇₃	C₂⁴	1	2	yes	—
205	C₂⁴×C₇₃	C₂⁴	1	1	yes	characteristic
206	C₂×Q₈×C₇₃	—	2	4	no	—
207	C₂×Q₈×C₇₃	—	2	4	no	—
208	C₂×Q₈×C₇₃	—	2	4	no	—
209	C₂×Q₈×C₇₃	—	4	1	no	—
210	C₂×Q₈×C₇₃	—	4	2	no	—
211	C₂×Q₈×C₇₃	—	4	1	no	—
212	C₂×Q₈×C₇₃	—	4	2	no	—
213	C₂×D₄×C₇₃	—	2	4	no	—
214	C₂×D₄×C₇₃	—	2	4	no	—
215	C₂×D₄×C₇₃	—	4	2	no	—
216	C₂×D₄×C₇₃	—	4	1	no	—
217	C₂×D₄×C₇₃	—	4	2	no	—
218	C₂²×C₄×C₇₃	—	2	2	no	—
219	C₂²×C₄×C₇₃	—	2	2	no	—
220	C₂²×C₄×C₇₃	—	2	2	no	—
221	C₂²×C₄×C₇₃	—	2	4	no	—
222	C₂²×C₄×C₇₃	—	2	4	no	—
223	C₂²×C₄×C₇₃	—	2	4	no	—
224	C₂²×C₄×C₇₃	—	4	1	no	—
225	C₂²×C₄×C₇₃	—	4	1	no	—
226	C₂²×C₄×C₇₃	—	4	2	no	—
227	C₂²×C₄×C₇₃	—	4	2	no	—
228	C₂²×C₄×C₇₃	C₂⁴	1	2	yes	—
229	C₂²×C₄×C₇₃	C₂⁴	1	2	yes	—
230	C₂²×C₄×C₇₃	C₂⁴	1	2	yes	—
231	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
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	1	yes	characteristic
236	C₂²×C₄×C₇₃	C₂⁴	1	2	yes	—
237	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
238	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
239	C₂²×C₄×C₇₃	C₂⁴	1	2	yes	—
240	C₂²×C₄×C₇₃	C₂⁴	1	2	yes	—
241	C₂²×C₄×C₇₃	C₂⁴	1	2	yes	—
242	C₂²×C₄×C₇₃	C₂⁴	1	2	yes	—
243	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
244	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
245	C₄⋊C₄×C₇₃	—	2	4	no	—
246	C₄⋊C₄×C₇₃	—	2	4	no	—
247	C₄⋊C₄×C₇₃	—	2	4	no	—
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	—	4	2	no	—
253	C₄⋊C₄×C₇₃	—	4	2	no	—
254	C₄⋊C₄×C₇₃	—	4	2	no	—
255	C₄⋊C₄×C₇₃	—	4	2	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	2	no	—
261	C₄⋊C₄×C₇₃	—	4	1	no	—
262	C₄⋊C₄×C₇₃	#41	1	8	yes	—
263	C₂²⋊C₄×C₇₃	—	2	2	no	—
264	C₂²⋊C₄×C₇₃	—	2	4	no	—
265	C₂²⋊C₄×C₇₃	—	2	4	no	—
266	C₂²⋊C₄×C₇₃	—	2	4	no	—
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	—	4	2	no	—
274	C₂²⋊C₄×C₇₃	—	4	2	no	—
275	C₂²⋊C₄×C₇₃	—	4	2	no	—
276	C₂²⋊C₄×C₇₃	—	4	2	no	—
277	C₂²⋊C₄×C₇₃	—	4	1	no	—
278	C₂²⋊C₄×C₇₃	—	4	2	no	—
279	C₂²⋊C₄×C₇₃	—	4	1	no	—
280	C₂²⋊C₄×C₇₃	—	4	2	no	—
281	C₂²⋊C₄×C₇₃	#41	1	4	yes	—
282	C₄²×C₇₃	—	2	4	no	—
283	C₄²×C₇₃	—	2	4	no	—
284	C₄²×C₇₃	—	2	4	no	—
285	C₄²×C₇₃	—	2	4	no	—
286	C₄²×C₇₃	—	2	4	no	—
287	C₄²×C₇₃	—	2	4	no	—
288	C₄²×C₇₃	—	2	4	no	—
289	C₄²×C₇₃	—	2	2	no	—
290	C₄²×C₇₃	—	2	2	no	—
291	C₄²×C₇₃	—	4	2	no	—
292	C₄²×C₇₃	—	4	2	no	—
293	C₄²×C₇₃	—	4	2	no	—
294	C₂³×C₇₃	—	2	2	no	—
295	C₂³×C₇₃	—	2	1	no	—
296	C₂³×C₇₃	—	2	1	no	—
297	C₂³×C₇₃	—	2	2	no	—
298	C₂³×C₇₃	—	2	2	no	—
299	C₂³×C₇₃	—	2	2	no	—
300	C₂³×C₇₃	—	2	2	no	—
301	C₂³×C₇₃	—	2	2	no	—
302	C₂³×C₇₃	—	2	2	no	—
303	C₂³×C₇₃	—	2	2	no	—
304	C₂³×C₇₃	—	2	2	no	—
305	C₂³×C₇₃	C₂×#41	1	2	yes	—
306	C₂³×C₇₃	C₂⁵	1	1	yes	characteristic
307	Q₈×C₇₃	—	4	8	no	—
308	Q₈×C₇₃	—	4	4	no	—
309	Q₈×C₇₃	—	8	2	no	—
310	D₄×C₇₃	—	4	8	no	—
311	D₄×C₇₃	—	8	2	no	—
312	C₂×C₄×C₇₃	—	2	8	no	—
313	C₂×C₄×C₇₃	—	2	1	no	—
314	C₂×C₄×C₇₃	—	2	2	no	—
315	C₂×C₄×C₇₃	—	2	2	no	—
316	C₂×C₄×C₇₃	—	2	2	no	—
317	C₂×C₄×C₇₃	—	2	1	no	—
318	C₂×C₄×C₇₃	—	2	2	no	—
319	C₂×C₄×C₇₃	—	2	2	no	—
320	C₂×C₄×C₇₃	—	2	1	no	—
321	C₂×C₄×C₇₃	—	2	2	no	—
322	C₂×C₄×C₇₃	—	2	1	no	—
323	C₂×C₄×C₇₃	—	2	2	no	—
324	C₂×C₄×C₇₃	—	2	2	no	—
325	C₂×C₄×C₇₃	—	2	2	no	—
326	C₂×C₄×C₇₃	—	2	2	no	—
327	C₂×C₄×C₇₃	—	2	2	no	—
328	C₂×C₄×C₇₃	—	2	2	no	—
329	C₂×C₄×C₇₃	—	2	2	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	1	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	2	no	—
351	C₂×C₄×C₇₃	—	2	2	no	—
352	C₂×C₄×C₇₃	—	2	2	no	—
353	C₂×C₄×C₇₃	—	2	2	no	—
354	C₂×C₄×C₇₃	—	4	4	no	—
355	C₂×C₄×C₇₃	—	4	8	no	—
356	C₂×C₄×C₇₃	—	4	4	no	—
357	C₂×C₄×C₇₃	C₂×#41	1	4	yes	—
358	C₂×C₄×C₇₃	C₂×#41	1	4	yes	—
359	C₂×C₄×C₇₃	C₂×#41	1	4	yes	—
360	C₂×C₄×C₇₃	C₂×#41	1	4	yes	—
361	C₂×C₄×C₇₃	H(5,𝔽₂)	1	2	yes	—
362	C₂×C₄×C₇₃	2₋¹⁺⁴	1	2	yes	—
363	C₂²×C₇₃	—	2	4	no	—
364	C₂²×C₇₃	—	2	2	no	—
365	C₂²×C₇₃	—	4	1	no	—
366	C₂²×C₇₃	—	4	2	no	—
367	C₂²×C₇₃	—	4	1	no	—
368	C₂²×C₇₃	—	4	2	no	—
369	C₂²×C₇₃	—	4	2	no	—
370	C₂²×C₇₃	—	4	2	no	—
371	C₂²×C₇₃	—	4	2	no	—
372	C₂²×C₇₃	—	4	2	no	—
373	C₂²×C₇₃	—	4	2	no	—
374	C₂²×C₇₃	—	4	2	no	—
375	C₂²×C₇₃	C₂²×#41	1	1	yes	characteristic
376	C₂²×C₇₃	C₂²×#41	1	2	yes	—
377	C₂²×C₇₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
378	C₂²×C₇₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
379	C₂²×C₇₃	#585	1	2	yes	—
380	C₄×C₇₃	—	2	4	no	—
381	C₄×C₇₃	—	2	4	no	—
382	C₄×C₇₃	—	2	4	no	—
383	C₄×C₇₃	—	2	4	no	—
384	C₄×C₇₃	—	2	2	no	—
385	C₄×C₇₃	—	2	2	no	—
386	C₄×C₇₃	—	4	2	no	—
387	C₄×C₇₃	—	4	2	no	—
388	C₄×C₇₃	—	4	1	no	—
389	C₄×C₇₃	—	4	1	no	—
390	C₄×C₇₃	—	4	2	no	—
391	C₄×C₇₃	—	4	2	no	—
392	C₄×C₇₃	—	4	2	no	—
393	C₄×C₇₃	—	4	1	no	—
394	C₄×C₇₃	—	4	2	no	—
395	C₄×C₇₃	—	4	1	no	—
396	C₄×C₇₃	—	4	2	no	—
397	#59975	C₇₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
398	C₂×C₇₃	—	4	2	no	—
399	C₂×C₇₃	—	8	2	no	—
400	C₂×C₇₃	#3475	1	2	yes	—
401	C₂×C₇₃	#3481	1	1	yes	characteristic
402	C₂×C₇₃	#3492	1	1	yes	characteristic
403	C₂×C₇₃	#3518	1	2	yes	—
404	C₂×C₇₃	#3540	1	1	yes	characteristic
405	#2763	C₂×C₇₃	1	1	yes	characteristic, complemented
406	#2757	C₂×C₇₃	1	2	yes	complemented
407	#2712	C₂×C₇₃	1	1	yes	characteristic
408	#2610	C₂×C₇₃	1	1	yes	characteristic
409	#2599	C₂×C₇₃	1	1	yes	characteristic, complemented
410	#2586	C₂×C₇₃	1	2	yes	complemented
411	#2532	C₂×C₇₃	1	2	yes	complemented
412	#2525	C₂×C₇₃	1	2	yes	complemented
413	#2523	C₂×C₇₃	1	1	yes	characteristic, complemented
414	#2518	C₂×C₇₃	1	2	yes	complemented
415	#2474	C₂×C₇₃	1	2	yes	complemented
416	#2474	C₂×C₇₃	1	2	yes	complemented
417	#2465	C₂×C₇₃	1	2	yes	complemented
418	#2463	C₂×C₇₃	1	1	yes	characteristic
419	#2367	C₂×C₇₃	1	2	yes	complemented
420	#2362	C₂×C₇₃	1	2	yes	complemented
421	#2356	C₂×C₇₃	1	2	yes	complemented
422	#2296	C₂×C₇₃	1	1	yes	characteristic, complemented
423	#2290	C₂×C₇₃	1	2	yes	complemented
424	C₇₃	#59975	1	1	yes	characteristic, direct product factor, Sylow
425	C₂×#124	C₂²×C₇₃	1	2	yes	—
426	C₂×#124	C₂²×C₇₃	1	1	yes	characteristic
427	C₂×C₂²⋊Q₈	C₂²×C₇₃	1	2	yes	—
428	C₂×C₄×Q₈	C₂²×C₇₃	1	2	yes	—
429	C₂×C₄×Q₈	C₂²×C₇₃	1	1	yes	characteristic
430	C₂×C₄×D₄	C₂²×C₇₃	1	2	yes	—
431	C₂×#117	C₂²×C₇₃	1	1	yes	characteristic
432	C₂×#117	C₂²×C₇₃	1	1	yes	characteristic
433	C₂×#117	C₂²×C₇₃	1	2	yes	—
434	C₂²×C₄²	C₂²×C₇₃	1	1	yes	characteristic
435	#400	C₂²×C₇₃	1	2	yes	—
436	#398	C₂²×C₇₃	1	2	yes	—
437	#398	C₂²×C₇₃	1	1	yes	characteristic
438	#397	C₂²×C₇₃	1	1	yes	characteristic
439	#397	C₂²×C₇₃	1	2	yes	—
440	#397	C₂²×C₇₃	1	2	yes	—
441	#397	C₂²×C₇₃	1	2	yes	—
442	#396	C₂²×C₇₃	1	2	yes	—
443	#396	C₂²×C₇₃	1	2	yes	—
444	#395	C₂²×C₇₃	1	1	yes	characteristic
445	#395	C₂²×C₇₃	1	2	yes	—
446	#395	C₂²×C₇₃	1	2	yes	—
447	#395	C₂²×C₇₃	1	1	yes	characteristic
448	#394	C₂²×C₇₃	1	1	yes	characteristic
449	#394	C₂²×C₇₃	1	2	yes	—
450	#394	C₂²×C₇₃	1	2	yes	—
451	#393	C₂²×C₇₃	1	1	yes	characteristic
452	#393	C₂²×C₇₃	1	1	yes	characteristic
453	#393	C₂²×C₇₃	1	2	yes	—
454	#392	C₂²×C₇₃	1	1	yes	characteristic
455	#391	C₂²×C₇₃	1	2	yes	—
456	#391	C₂²×C₇₃	1	2	yes	—
457	#391	C₂²×C₇₃	1	2	yes	—
458	#391	C₂²×C₇₃	1	2	yes	—
459	#391	C₂²×C₇₃	1	2	yes	—
460	#390	C₂²×C₇₃	1	2	yes	—
461	#389	C₂²×C₇₃	1	2	yes	—
462	#389	C₂²×C₇₃	1	2	yes	—
463	#389	C₂²×C₇₃	1	2	yes	—
464	#388	C₂²×C₇₃	1	2	yes	—
465	#388	C₂²×C₇₃	1	2	yes	—
466	#388	C₂²×C₇₃	1	2	yes	—
467	#388	C₂²×C₇₃	1	2	yes	—
468	#388	C₂²×C₇₃	1	2	yes	—
469	#388	C₂²×C₇₃	1	2	yes	—
470	#388	C₂²×C₇₃	1	2	yes	—
471	#388	C₂²×C₇₃	1	2	yes	—
472	#388	C₂²×C₇₃	1	2	yes	—
473	#388	C₂²×C₇₃	1	2	yes	—
474	#388	C₂²×C₇₃	1	2	yes	—
475	#388	C₂²×C₇₃	1	2	yes	—
476	#388	C₂²×C₇₃	1	2	yes	—
477	#388	C₂²×C₇₃	1	2	yes	—
478	#387	C₂²×C₇₃	1	2	yes	—
479	#387	C₂²×C₇₃	1	2	yes	—
480	#387	C₂²×C₇₃	1	2	yes	—
481	#387	C₂²×C₇₃	1	2	yes	—
482	#387	C₂²×C₇₃	1	2	yes	—
483	#387	C₂²×C₇₃	1	2	yes	—
484	#387	C₂²×C₇₃	1	2	yes	—
485	#387	C₂²×C₇₃	1	2	yes	—
486	#387	C₂²×C₇₃	1	2	yes	—
487	#386	C₂²×C₇₃	1	2	yes	—
488	#386	C₂²×C₇₃	1	2	yes	—
489	#386	C₂²×C₇₃	1	2	yes	—
490	#385	C₂²×C₇₃	1	2	yes	—
491	#385	C₂²×C₇₃	1	1	yes	characteristic
492	#385	C₂²×C₇₃	1	2	yes	—
493	#385	C₂²×C₇₃	1	1	yes	characteristic
494	#385	C₂²×C₇₃	1	1	yes	characteristic
495	#385	C₂²×C₇₃	1	1	yes	characteristic
496	#385	C₂²×C₇₃	1	2	yes	—
497	#383	C₂²×C₇₃	1	1	yes	characteristic
498	#383	C₂²×C₇₃	1	2	yes	—
499	#383	C₂²×C₇₃	1	2	yes	—
500	#382	C₂²×C₇₃	1	2	yes	—
501	C₄×C₄⋊C₄	C₂²×C₇₃	1	2	yes	—
502	C₄×C₄⋊C₄	C₂²×C₇₃	1	2	yes	—
503	C₄×C₄⋊C₄	C₂²×C₇₃	1	2	yes	—
504	C₄×C₄⋊C₄	C₂²×C₇₃	1	2	yes	—
505	C₄×C₄⋊C₄	C₂²×C₇₃	1	2	yes	—
506	C₄×C₄⋊C₄	C₂²×C₇₃	1	2	yes	—
507	C₄×C₂²⋊C₄	C₂²×C₇₃	1	2	yes	—
508	C₄×C₂²⋊C₄	C₂²×C₇₃	1	2	yes	—
509	C₄×C₂²⋊C₄	C₂²×C₇₃	1	2	yes	—
510	#376	C₂²×C₇₃	1	1	yes	characteristic
511	#376	C₂²×C₇₃	1	2	yes	—
512	C₂²×Q₈	C₂³×C₇₃	1	1	yes	characteristic
513	C₂²×Q₈	C₂³×C₇₃	1	2	yes	—
514	C₂²×Q₈	C₂³×C₇₃	1	1	yes	characteristic
515	C₂²×D₄	C₂³×C₇₃	1	2	yes	—
516	C₂²×D₄	C₂³×C₇₃	1	1	yes	characteristic
517	C₂³×C₄	C₂³×C₇₃	1	1	yes	characteristic
518	C₂³×C₄	C₂³×C₇₃	1	2	yes	—
519	C₂³×C₄	C₂³×C₇₃	1	1	yes	characteristic
520	C₂³×C₄	C₂³×C₇₃	1	1	yes	characteristic
521	#124	—	2	8	no	—
522	#124	—	4	2	no	—
523	C₂²⋊Q₈	—	2	8	no	—
524	C₄×Q₈	—	2	8	no	—
525	C₄×Q₈	—	4	2	no	—
526	C₄×D₄	—	2	8	no	—
527	#117	—	2	4	no	—
528	#117	—	4	2	no	—
529	#117	—	4	4	no	—
530	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
531	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
532	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
533	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
534	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
535	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
536	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
537	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
538	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
539	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
540	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
541	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
542	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
543	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
544	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
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×C₂²⋊C₄	C₂³×C₇₃	1	2	yes	—
549	C₂×C₂²⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
550	C₂×C₂²⋊C₄	C₂³×C₇₃	1	2	yes	—
551	C₂×C₂²⋊C₄	C₂³×C₇₃	1	2	yes	—
552	C₂×C₂²⋊C₄	C₂³×C₇₃	1	2	yes	—
553	C₂×C₂²⋊C₄	C₂³×C₇₃	1	2	yes	—
554	C₂×C₂²⋊C₄	C₂³×C₇₃	1	2	yes	—
555	C₂×C₂²⋊C₄	C₂³×C₇₃	1	2	yes	—
556	C₂×C₂²⋊C₄	C₂³×C₇₃	1	2	yes	—
557	C₂×C₂²⋊C₄	C₂³×C₇₃	1	2	yes	—
558	C₂×C₂²⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
559	C₂×C₂²⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
560	C₂×C₂²⋊C₄	C₂³×C₇₃	1	2	yes	—
561	C₂×C₂²⋊C₄	C₂³×C₇₃	1	2	yes	—
562	C₂×C₂²⋊C₄	C₂³×C₇₃	1	2	yes	—
563	C₂×C₂²⋊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	1	yes	characteristic
567	C₂×C₄²	—	4	2	no	—
568	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
569	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
570	C₂×C₄²	C₂³×C₇₃	1	2	yes	—
571	C₂×C₄²	C₂³×C₇₃	1	2	yes	—
572	C₂×C₄²	C₂³×C₇₃	1	2	yes	—
573	C₂×C₄²	C₂³×C₇₃	1	2	yes	—
574	C₂×C₄²	C₂³×C₇₃	1	2	yes	—
575	C₂×C₄²	C₂³×C₇₃	1	2	yes	—
576	C₂×C₄²	C₂³×C₇₃	1	2	yes	—
577	C₂×C₄²	C₂³×C₇₃	1	2	yes	—
578	C₂×C₄²	C₂³×C₇₃	1	2	yes	—
579	C₂×C₄²	C₂³×C₇₃	1	2	yes	—
580	#95	C₂³×C₇₃	1	2	yes	—
581	#95	C₂³×C₇₃	1	1	yes	characteristic
582	#95	C₂³×C₇₃	1	2	yes	—
583	#95	C₂³×C₇₃	1	2	yes	—
584	#95	C₂³×C₇₃	1	2	yes	—
585	#95	C₂³×C₇₃	1	1	yes	characteristic
586	#95	C₂³×C₇₃	1	2	yes	—
587	#95	C₂³×C₇₃	1	2	yes	—
588	#95	C₂³×C₇₃	1	2	yes	—
589	#95	C₂³×C₇₃	1	2	yes	—
590	#95	C₂³×C₇₃	1	2	yes	—
591	#95	C₂³×C₇₃	1	2	yes	—
592	#95	C₂³×C₇₃	1	2	yes	—
593	#95	C₂³×C₇₃	1	2	yes	—
594	#95	C₂³×C₇₃	1	2	yes	—
595	#95	C₂³×C₇₃	1	2	yes	—
596	#95	C₂³×C₇₃	1	2	yes	—
597	#95	C₂³×C₇₃	1	2	yes	—
598	#95	C₂³×C₇₃	1	2	yes	—
599	#95	C₂³×C₇₃	1	2	yes	—
600	#95	C₂³×C₇₃	1	2	yes	—
601	#95	C₂³×C₇₃	1	2	yes	—
602	#95	C₂³×C₇₃	1	2	yes	—
603	#95	C₂³×C₇₃	1	1	yes	characteristic
604	#95	C₂³×C₇₃	1	2	yes	—
605	#95	C₂³×C₇₃	1	1	yes	characteristic
606	#95	C₂³×C₇₃	1	2	yes	—
607	#95	C₂³×C₇₃	1	2	yes	—
608	#95	C₂³×C₇₃	1	2	yes	—
609	C₂⁴	C₂⁴×C₇₃	1	2	yes	—
610	C₂⁴	C₂⁴×C₇₃	1	1	yes	characteristic
611	C₂×Q₈	—	2	4	no	—
612	C₂×Q₈	—	2	4	no	—
613	C₂×Q₈	—	2	4	no	—
614	C₂×Q₈	—	4	1	no	—
615	C₂×Q₈	—	4	2	no	—
616	C₂×Q₈	—	4	1	no	—
617	C₂×Q₈	—	4	2	no	—
618	C₂×D₄	—	2	4	no	—
619	C₂×D₄	—	2	4	no	—
620	C₂×D₄	—	4	2	no	—
621	C₂×D₄	—	4	1	no	—
622	C₂×D₄	—	4	2	no	—
623	C₂²×C₄	—	2	2	no	—
624	C₂²×C₄	—	2	2	no	—
625	C₂²×C₄	—	2	2	no	—
626	C₂²×C₄	—	2	4	no	—
627	C₂²×C₄	—	2	4	no	—
628	C₂²×C₄	—	2	4	no	—
629	C₂²×C₄	—	4	1	no	—
630	C₂²×C₄	—	4	1	no	—
631	C₂²×C₄	—	4	2	no	—
632	C₂²×C₄	—	4	2	no	—
633	C₂²×C₄	C₂⁴×C₇₃	1	2	yes	—
634	C₂²×C₄	C₂⁴×C₇₃	1	2	yes	—
635	C₂²×C₄	C₂⁴×C₇₃	1	2	yes	—
636	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
637	C₂²×C₄	C₂⁴×C₇₃	1	2	yes	—
638	C₂²×C₄	C₂⁴×C₇₃	1	2	yes	—
639	C₂²×C₄	C₂⁴×C₇₃	1	2	yes	—
640	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
641	C₂²×C₄	C₂⁴×C₇₃	1	2	yes	—
642	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
643	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
644	C₂²×C₄	C₂⁴×C₇₃	1	2	yes	—
645	C₂²×C₄	C₂⁴×C₇₃	1	2	yes	—
646	C₂²×C₄	C₂⁴×C₇₃	1	2	yes	—
647	C₂²×C₄	C₂⁴×C₇₃	1	2	yes	—
648	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
649	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
650	C₄⋊C₄	—	2	4	no	—
651	C₄⋊C₄	—	2	4	no	—
652	C₄⋊C₄	—	2	4	no	—
653	C₄⋊C₄	—	2	4	no	—
654	C₄⋊C₄	—	2	4	no	—
655	C₄⋊C₄	—	2	4	no	—
656	C₄⋊C₄	—	2	4	no	—
657	C₄⋊C₄	—	4	2	no	—
658	C₄⋊C₄	—	4	2	no	—
659	C₄⋊C₄	—	4	2	no	—
660	C₄⋊C₄	—	4	2	no	—
661	C₄⋊C₄	—	4	2	no	—
662	C₄⋊C₄	—	4	2	no	—
663	C₄⋊C₄	—	4	1	no	—
664	C₄⋊C₄	—	4	1	no	—
665	C₄⋊C₄	—	4	2	no	—
666	C₄⋊C₄	—	4	1	no	—
667	C₄⋊C₄	#41×C₇₃	1	8	yes	—
668	C₂²⋊C₄	—	2	2	no	—
669	C₂²⋊C₄	—	2	4	no	—
670	C₂²⋊C₄	—	2	4	no	—
671	C₂²⋊C₄	—	2	4	no	—
672	C₂²⋊C₄	—	2	4	no	—
673	C₂²⋊C₄	—	2	4	no	—
674	C₂²⋊C₄	—	2	4	no	—
675	C₂²⋊C₄	—	2	4	no	—
676	C₂²⋊C₄	—	2	4	no	—
677	C₂²⋊C₄	—	2	4	no	—
678	C₂²⋊C₄	—	4	2	no	—
679	C₂²⋊C₄	—	4	2	no	—
680	C₂²⋊C₄	—	4	2	no	—
681	C₂²⋊C₄	—	4	2	no	—
682	C₂²⋊C₄	—	4	1	no	—
683	C₂²⋊C₄	—	4	2	no	—
684	C₂²⋊C₄	—	4	1	no	—
685	C₂²⋊C₄	—	4	2	no	—
686	C₂²⋊C₄	#41×C₇₃	1	4	yes	—
687	C₄²	—	2	4	no	—
688	C₄²	—	2	4	no	—
689	C₄²	—	2	4	no	—
690	C₄²	—	2	4	no	—
691	C₄²	—	2	4	no	—
692	C₄²	—	2	4	no	—
693	C₄²	—	2	4	no	—
694	C₄²	—	2	2	no	—
695	C₄²	—	2	2	no	—
696	C₄²	—	4	2	no	—
697	C₄²	—	4	2	no	—
698	C₄²	—	4	2	no	—
699	C₂³	—	2	2	no	—
700	C₂³	—	2	1	no	—
701	C₂³	—	2	1	no	—
702	C₂³	—	2	2	no	—
703	C₂³	—	2	2	no	—
704	C₂³	—	2	2	no	—
705	C₂³	—	2	2	no	—
706	C₂³	—	2	2	no	—
707	C₂³	—	2	2	no	—
708	C₂³	—	2	2	no	—
709	C₂³	—	2	2	no	—
710	C₂³	C₂×#41×C₇₃	1	2	yes	—
711	C₂³	C₂⁵×C₇₃	1	1	yes	characteristic
712	Q₈	—	4	8	no	—
713	Q₈	—	4	4	no	—
714	Q₈	—	8	2	no	—
715	D₄	—	4	8	no	—
716	D₄	—	8	2	no	—
717	C₂×C₄	—	2	8	no	—
718	C₂×C₄	—	2	1	no	—
719	C₂×C₄	—	2	2	no	—
720	C₂×C₄	—	2	2	no	—
721	C₂×C₄	—	2	2	no	—
722	C₂×C₄	—	2	1	no	—
723	C₂×C₄	—	2	2	no	—
724	C₂×C₄	—	2	2	no	—
725	C₂×C₄	—	2	1	no	—
726	C₂×C₄	—	2	2	no	—
727	C₂×C₄	—	2	1	no	—
728	C₂×C₄	—	2	2	no	—
729	C₂×C₄	—	2	2	no	—
730	C₂×C₄	—	2	2	no	—
731	C₂×C₄	—	2	2	no	—
732	C₂×C₄	—	2	2	no	—
733	C₂×C₄	—	2	2	no	—
734	C₂×C₄	—	2	2	no	—
735	C₂×C₄	—	2	2	no	—
736	C₂×C₄	—	2	2	no	—
737	C₂×C₄	—	2	2	no	—
738	C₂×C₄	—	2	2	no	—
739	C₂×C₄	—	2	1	no	—
740	C₂×C₄	—	2	2	no	—
741	C₂×C₄	—	2	1	no	—
742	C₂×C₄	—	2	1	no	—
743	C₂×C₄	—	2	1	no	—
744	C₂×C₄	—	2	2	no	—
745	C₂×C₄	—	2	2	no	—
746	C₂×C₄	—	2	2	no	—
747	C₂×C₄	—	2	2	no	—
748	C₂×C₄	—	2	2	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	2	no	—
754	C₂×C₄	—	2	2	no	—
755	C₂×C₄	—	2	2	no	—
756	C₂×C₄	—	2	2	no	—
757	C₂×C₄	—	2	2	no	—
758	C₂×C₄	—	2	2	no	—
759	C₂×C₄	—	4	4	no	—
760	C₂×C₄	—	4	8	no	—
761	C₂×C₄	—	4	4	no	—
762	C₂×C₄	C₂×#41×C₇₃	1	4	yes	—
763	C₂×C₄	C₂×#41×C₇₃	1	4	yes	—
764	C₂×C₄	C₂×#41×C₇₃	1	4	yes	—
765	C₂×C₄	C₂×#41×C₇₃	1	4	yes	—
766	C₂×C₄	H(5,𝔽₂)×C₇₃	1	2	yes	—
767	C₂×C₄	2₋¹⁺⁴×C₇₃	1	2	yes	—
768	C₂²	—	2	4	no	—
769	C₂²	—	2	2	no	—
770	C₂²	—	4	1	no	—
771	C₂²	—	4	2	no	—
772	C₂²	—	4	1	no	—
773	C₂²	—	4	2	no	—
774	C₂²	—	4	2	no	—
775	C₂²	—	4	2	no	—
776	C₂²	—	4	2	no	—
777	C₂²	—	4	2	no	—
778	C₂²	—	4	2	no	—
779	C₂²	—	4	2	no	—
780	C₂²	C₂²×#41×C₇₃	1	1	yes	characteristic
781	C₂²	C₂²×#41×C₇₃	1	2	yes	—
782	C₂²	C₂×H(5,𝔽₂)×C₇₃	1	1	yes	characteristic
783	C₂²	C₂×2₋¹⁺⁴×C₇₃	1	1	yes	characteristic
784	C₂²	#585×C₇₃	1	2	yes	—
785	C₄	—	2	4	no	—
786	C₄	—	2	4	no	—
787	C₄	—	2	4	no	—
788	C₄	—	2	4	no	—
789	C₄	—	2	2	no	—
790	C₄	—	2	2	no	—
791	C₄	—	4	2	no	—
792	C₄	—	4	2	no	—
793	C₄	—	4	1	no	—
794	C₄	—	4	1	no	—
795	C₄	—	4	2	no	—
796	C₄	—	4	2	no	—
797	C₄	—	4	2	no	—
798	C₄	—	4	2	no	—
799	C₄	—	4	1	no	—
800	C₄	—	4	2	no	—
801	C₄	—	4	1	no	—
802	C₂	—	4	2	no	—
803	C₂	—	8	2	no	—
804	C₂	C₇₃×#3475	1	2	yes	—
805	C₂	C₇₃×#3481	1	1	yes	characteristic
806	C₂	C₇₃×#3492	1	1	yes	characteristic
807	C₂	C₇₃×#3518	1	2	yes	—
808	C₂	C₇₃×#3540	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₇₃	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₇₃
prime radical	#392×C₇₃	C₂²
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×#2763	C₂	semidirect
2. C₇₃×#2757	C₂	semidirect
5. C₇₃×#2599	C₂	semidirect
6. C₇₃×#2586	C₂	semidirect
7. C₇₃×#2532	C₂	semidirect
8. C₇₃×#2525	C₂	semidirect
9. C₇₃×#2523	C₂	semidirect
10. C₇₃×#2518	C₂	semidirect
11. C₇₃×#2474	C₂	semidirect
12. C₇₃×#2474	C₂	semidirect
13. C₇₃×#2465	C₂	semidirect
15. C₇₃×#2367	C₂	semidirect
16. C₇₃×#2362	C₂	semidirect
17. C₇₃×#2356	C₂	semidirect
18. C₇₃×#2296	C₂	semidirect
19. C₇₃×#2290	C₂	semidirect
397. #59975	C₇₃	direct (N × H)
405. #2763	C₂×C₇₃	semidirect
406. #2757	C₂×C₇₃	semidirect
409. #2599	C₂×C₇₃	semidirect
410. #2586	C₂×C₇₃	semidirect
411. #2532	C₂×C₇₃	semidirect
412. #2525	C₂×C₇₃	semidirect
413. #2523	C₂×C₇₃	semidirect
414. #2518	C₂×C₇₃	semidirect
415. #2474	C₂×C₇₃	semidirect
416. #2474	C₂×C₇₃	semidirect
417. #2465	C₂×C₇₃	semidirect
419. #2367	C₂×C₇₃	semidirect
420. #2362	C₂×C₇₃	semidirect
421. #2356	C₂×C₇₃	semidirect
422. #2296	C₂×C₇₃	semidirect
423. #2290	C₂×C₇₃	semidirect
424. C₇₃	#59975	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×#2763	2
C₇₃×#2757	2
C₇₃×#2712	2
C₇₃×#2610	2
C₇₃×#2599	2
C₇₃×#2586	2
C₇₃×#2532	2
C₇₃×#2525	2
C₇₃×#2523	2
C₇₃×#2518	2
C₇₃×#2474	2
C₇₃×#2465	2
C₇₃×#2463	2
C₇₃×#2367	2
C₇₃×#2362	2
C₇₃×#2356	2
C₇₃×#2296	2
C₇₃×#2290	2
#59975	73

Subgroups — C73×#59975 #32969379

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₃×#59975 #32969379