Subgroups — C₇₃×#59547 #32968951

Order 18688.

1516 conjugacy classes of subgroups.

The subgroup lattice has 850 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇₃×#2766	C₂	1	2	yes	maximal
2	C₇₃×#2762	C₂	1	2	yes	maximal
3	C₇₃×#2612	C₂	1	2	yes	maximal
4	C₇₃×#2528	C₂	1	2	yes	maximal
5	C₇₃×#2528	C₂	1	2	yes	maximal
6	C₇₃×#2524	C₂	1	2	yes	maximal
7	C₇₃×#2514	C₂	1	1	yes	maximal, characteristic
8	C₇₃×#2514	C₂	1	1	yes	maximal, characteristic
9	C₇₃×#2508	C₂	1	1	yes	maximal, characteristic
10	C₇₃×#2508	C₂	1	1	yes	maximal, characteristic
11	C₇₃×#2462	C₂	1	2	yes	maximal
12	C₇₃×#2451	C₂	1	1	yes	maximal, characteristic
13	C₇₃×#2451	C₂	1	1	yes	maximal, characteristic
14	C₇₃×#2446	C₂	1	1	yes	maximal, characteristic
15	C₇₃×#2446	C₂	1	1	yes	maximal, characteristic
16	C₇₃×#2365	C₂	1	1	yes	maximal, characteristic
17	C₇₃×#2365	C₂	1	1	yes	maximal, characteristic
18	C₇₃×#2356	C₂	1	1	yes	maximal, characteristic
19	C₇₃×#2356	C₂	1	2	yes	maximal
20	C₇₃×#2351	C₂	1	1	yes	maximal, characteristic
21	C₄×#125×C₇₃	C₂	1	1	yes	maximal, characteristic
22	C₇₃×#2295	C₂	1	1	yes	maximal, characteristic
23	C₇₃×#2295	C₂	1	1	yes	maximal, characteristic
24	C₂×C₄⋊Q₈×C₇₃	C₂²	1	1	yes	characteristic
25	C₂×C₄⋊Q₈×C₇₃	C₂²	1	1	yes	characteristic
26	C₂×#125×C₇₃	C₂²	1	1	yes	characteristic
27	C₂×C₄×Q₈×C₇₃	C₂²	1	1	yes	characteristic
28	C₂×C₄×Q₈×C₇₃	C₂²	1	1	yes	characteristic
29	C₂×C₄×Q₈×C₇₃	C₂²	1	1	yes	characteristic
30	C₂×C₄×Q₈×C₇₃	C₂²	1	1	yes	characteristic
31	C₂×C₄×Q₈×C₇₃	C₂²	1	2	yes	—
32	#401×C₇₃	C₂²	1	2	yes	—
33	#401×C₇₃	C₂²	1	2	yes	—
34	#400×C₇₃	C₂²	1	2	yes	—
35	#400×C₇₃	C₂²	1	2	yes	—
36	#400×C₇₃	C₂²	1	2	yes	—
37	#400×C₇₃	C₂²	1	2	yes	—
38	#400×C₇₃	C₂²	1	2	yes	—
39	#400×C₇₃	C₂²	1	2	yes	—
40	#398×C₇₃	C₂²	1	2	yes	—
41	#398×C₇₃	C₂²	1	2	yes	—
42	#398×C₇₃	C₂²	1	2	yes	—
43	#398×C₇₃	C₂²	1	2	yes	—
44	#398×C₇₃	C₂²	1	2	yes	—
45	#398×C₇₃	C₂²	1	2	yes	—
46	#395×C₇₃	C₂²	1	2	yes	—
47	#395×C₇₃	C₂²	1	2	yes	—
48	#391×C₇₃	C₂²	1	1	yes	characteristic
49	#391×C₇₃	C₂²	1	1	yes	characteristic
50	#391×C₇₃	C₂²	1	1	yes	characteristic
51	#391×C₇₃	C₂²	1	1	yes	characteristic
52	#391×C₇₃	C₂²	1	1	yes	characteristic
53	#391×C₇₃	C₂²	1	1	yes	characteristic
54	#391×C₇₃	C₂²	1	2	yes	—
55	#391×C₇₃	C₂²	1	2	yes	—
56	#391×C₇₃	C₂²	1	2	yes	—
57	#391×C₇₃	C₂²	1	1	yes	characteristic
58	#391×C₇₃	C₂²	1	1	yes	characteristic
59	#389×C₇₃	C₂²	1	1	yes	characteristic
60	#389×C₇₃	C₂²	1	1	yes	characteristic
61	#389×C₇₃	C₂²	1	1	yes	characteristic
62	#389×C₇₃	C₂²	1	1	yes	characteristic
63	#389×C₇₃	C₂²	1	1	yes	characteristic
64	#389×C₇₃	C₂²	1	1	yes	characteristic
65	#389×C₇₃	C₂²	1	2	yes	—
66	#389×C₇₃	C₂²	1	2	yes	—
67	#389×C₇₃	C₂²	1	1	yes	characteristic
68	#389×C₇₃	C₂²	1	2	yes	—
69	#389×C₇₃	C₂²	1	1	yes	characteristic
70	#389×C₇₃	C₂²	1	1	yes	characteristic
71	#389×C₇₃	C₂²	1	1	yes	characteristic
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	#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	#387×C₇₃	C₂²	1	1	yes	characteristic
84	#387×C₇₃	C₂²	1	2	yes	—
85	#387×C₇₃	C₂²	1	2	yes	—
86	#387×C₇₃	C₂²	1	2	yes	—
87	#387×C₇₃	C₂²	1	2	yes	—
88	#387×C₇₃	C₂²	1	1	yes	characteristic
89	#387×C₇₃	C₂²	1	2	yes	—
90	#387×C₇₃	C₂²	1	2	yes	—
91	#387×C₇₃	C₂²	1	1	yes	characteristic
92	#387×C₇₃	C₂²	1	2	yes	—
93	#387×C₇₃	C₂²	1	2	yes	—
94	#387×C₇₃	C₂²	1	2	yes	—
95	#387×C₇₃	C₂²	1	1	yes	characteristic
96	#383×C₇₃	C₂²	1	2	yes	—
97	#383×C₇₃	C₂²	1	2	yes	—
98	#383×C₇₃	C₂²	1	2	yes	—
99	#382×C₇₃	C₂²	1	2	yes	—
100	#382×C₇₃	C₂²	1	2	yes	—
101	#382×C₇₃	C₂²	1	1	yes	characteristic
102	#382×C₇₃	C₂²	1	1	yes	characteristic
103	#382×C₇₃	C₂²	1	2	yes	—
104	#382×C₇₃	C₂²	1	1	yes	characteristic
105	C₄×C₄⋊C₄×C₇₃	C₂²	1	1	yes	characteristic
106	C₄×C₄⋊C₄×C₇₃	C₂²	1	1	yes	characteristic
107	C₄×C₄⋊C₄×C₇₃	C₂²	1	1	yes	characteristic
108	C₄×C₄⋊C₄×C₇₃	C₂²	1	1	yes	characteristic
109	C₄×C₄⋊C₄×C₇₃	C₂²	1	2	yes	—
110	C₄×C₄⋊C₄×C₇₃	C₂²	1	1	yes	characteristic
111	C₄×C₄⋊C₄×C₇₃	C₂²	1	1	yes	characteristic
112	C₄×C₄⋊C₄×C₇₃	C₂²	1	1	yes	characteristic
113	C₄×C₄⋊C₄×C₇₃	C₂²	1	1	yes	characteristic
114	C₄×C₄⋊C₄×C₇₃	C₂²	1	1	yes	characteristic
115	C₄×C₄⋊C₄×C₇₃	C₂²	1	1	yes	characteristic
116	C₄×C₄⋊C₄×C₇₃	C₂²	1	2	yes	—
117	C₄×C₄⋊C₄×C₇₃	C₂²	1	2	yes	—
118	C₄×C₄⋊C₄×C₇₃	C₂²	1	2	yes	—
119	#376×C₇₃	C₂²	1	2	yes	—
120	#376×C₇₃	C₂²	1	2	yes	—
121	#376×C₇₃	C₂²	1	2	yes	—
122	C₄³×C₇₃	C₂²	1	1	yes	characteristic
123	C₂²×Q₈×C₇₃	C₂³	1	1	yes	characteristic
124	C₂²×Q₈×C₇₃	C₂³	1	2	yes	—
125	C₂²×Q₈×C₇₃	C₂³	1	1	yes	characteristic
126	C₄⋊Q₈×C₇₃	—	2	4	no	—
127	C₄⋊Q₈×C₇₃	—	2	4	no	—
128	#125×C₇₃	—	2	4	no	—
129	C₄×Q₈×C₇₃	—	2	4	no	—
130	C₄×Q₈×C₇₃	—	2	4	no	—
131	C₄×Q₈×C₇₃	—	2	8	no	—
132	C₄×Q₈×C₇₃	—	2	4	no	—
133	C₄×Q₈×C₇₃	—	2	4	no	—
134	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
135	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
136	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
141	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
142	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
143	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
144	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
145	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
146	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
147	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
148	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
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	2	yes	—
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	1	yes	characteristic
167	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
168	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
169	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
170	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
171	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
172	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
173	C₂×C₄²×C₇₃	C₂³	1	2	yes	—
174	C₂×C₄²×C₇₃	C₂³	1	2	yes	—
175	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
176	C₂×C₄²×C₇₃	C₂³	1	2	yes	—
177	C₂×C₄²×C₇₃	C₂³	1	2	yes	—
178	C₂×C₄²×C₇₃	C₂³	1	2	yes	—
179	C₂×C₄²×C₇₃	C₂³	1	2	yes	—
180	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
185	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
186	#95×C₇₃	C₂³	1	1	yes	characteristic
187	#95×C₇₃	C₂³	1	2	yes	—
188	#95×C₇₃	C₂³	1	1	yes	characteristic
189	#95×C₇₃	C₂³	1	1	yes	characteristic
190	#95×C₇₃	C₂³	1	1	yes	characteristic
191	#95×C₇₃	C₂³	1	1	yes	characteristic
192	#95×C₇₃	C₂³	1	1	yes	characteristic
193	#95×C₇₃	C₂³	1	1	yes	characteristic
194	#95×C₇₃	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
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	1	yes	characteristic
207	#95×C₇₃	C₂³	1	1	yes	characteristic
208	#95×C₇₃	C₂³	1	1	yes	characteristic
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	#95×C₇₃	C₂³	1	2	yes	—
220	#95×C₇₃	C₂³	1	2	yes	—
221	#95×C₇₃	C₂³	1	2	yes	—
222	#95×C₇₃	C₂³	1	2	yes	—
223	#95×C₇₃	C₂³	1	2	yes	—
224	#95×C₇₃	C₂³	1	2	yes	—
225	#95×C₇₃	C₂³	1	2	yes	—
226	#95×C₇₃	C₂³	1	2	yes	—
227	#95×C₇₃	C₂³	1	2	yes	—
228	#95×C₇₃	C₂³	1	2	yes	—
229	#95×C₇₃	C₂³	1	2	yes	—
230	C₂×Q₈×C₇₃	—	2	2	no	—
231	C₂×Q₈×C₇₃	—	2	4	no	—
232	C₂×Q₈×C₇₃	—	2	2	no	—
233	C₂×Q₈×C₇₃	—	2	4	no	—
234	C₂×Q₈×C₇₃	—	2	2	no	—
235	C₂×Q₈×C₇₃	—	2	2	no	—
236	C₂×Q₈×C₇₃	—	2	2	no	—
237	C₂×Q₈×C₇₃	—	4	2	no	—
238	C₂×Q₈×C₇₃	#41	1	4	yes	—
239	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
240	C₂²×C₄×C₇₃	C₂⁴	1	2	yes	—
241	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
242	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
243	C₂²×C₄×C₇₃	C₂⁴	1	2	yes	—
244	C₂²×C₄×C₇₃	C₂⁴	1	2	yes	—
245	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
246	C₂²×C₄×C₇₃	C₂⁴	1	2	yes	—
247	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
248	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
249	C₂²×C₄×C₇₃	C₂⁴	1	2	yes	—
250	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
251	C₂²×C₄×C₇₃	C₂⁴	1	2	yes	—
252	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
253	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
254	C₂²×C₄×C₇₃	C₂⁴	1	2	yes	—
255	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
256	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
257	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
258	C₂²×C₄×C₇₃	C₂⁴	1	2	yes	—
259	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
260	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
261	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
262	C₄⋊C₄×C₇₃	—	2	4	no	—
263	C₄⋊C₄×C₇₃	—	2	4	no	—
264	C₄⋊C₄×C₇₃	—	2	4	no	—
265	C₄⋊C₄×C₇₃	—	2	4	no	—
266	C₄⋊C₄×C₇₃	—	2	2	no	—
267	C₄⋊C₄×C₇₃	—	2	2	no	—
268	C₄⋊C₄×C₇₃	—	2	4	no	—
269	C₄⋊C₄×C₇₃	—	2	4	no	—
270	C₄⋊C₄×C₇₃	—	2	2	no	—
271	C₄⋊C₄×C₇₃	—	2	2	no	—
272	C₄⋊C₄×C₇₃	—	2	2	no	—
273	C₄⋊C₄×C₇₃	—	2	2	no	—
274	C₄⋊C₄×C₇₃	—	2	2	no	—
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	2	no	—
279	C₄⋊C₄×C₇₃	—	2	2	no	—
280	C₄⋊C₄×C₇₃	—	2	2	no	—
281	C₄⋊C₄×C₇₃	—	2	2	no	—
282	C₄⋊C₄×C₇₃	—	2	2	no	—
283	C₄⋊C₄×C₇₃	—	2	4	no	—
284	C₄⋊C₄×C₇₃	—	2	2	no	—
285	C₄⋊C₄×C₇₃	—	2	2	no	—
286	C₄⋊C₄×C₇₃	—	4	2	no	—
287	C₄⋊C₄×C₇₃	—	4	2	no	—
288	C₄⋊C₄×C₇₃	—	4	1	no	—
289	C₄⋊C₄×C₇₃	—	4	1	no	—
290	C₄⋊C₄×C₇₃	—	4	2	no	—
291	C₄⋊C₄×C₇₃	—	4	2	no	—
292	C₄⋊C₄×C₇₃	—	4	2	no	—
293	C₄⋊C₄×C₇₃	#41	1	4	yes	—
294	C₄⋊C₄×C₇₃	#41	1	4	yes	—
295	C₄²×C₇₃	—	2	4	no	—
296	C₄²×C₇₃	—	2	2	no	—
297	C₄²×C₇₃	—	2	2	no	—
298	C₄²×C₇₃	—	2	4	no	—
299	C₄²×C₇₃	—	2	4	no	—
300	C₄²×C₇₃	—	2	4	no	—
301	C₄²×C₇₃	—	2	4	no	—
302	C₄²×C₇₃	—	2	4	no	—
303	C₄²×C₇₃	—	2	2	no	—
304	C₄²×C₇₃	—	2	2	no	—
305	C₄²×C₇₃	—	2	4	no	—
306	C₄²×C₇₃	—	2	2	no	—
307	C₄²×C₇₃	—	2	2	no	—
308	C₄²×C₇₃	—	2	2	no	—
309	C₄²×C₇₃	—	2	2	no	—
310	C₄²×C₇₃	—	2	2	no	—
311	C₄²×C₇₃	—	2	2	no	—
312	C₄²×C₇₃	—	2	4	no	—
313	C₄²×C₇₃	—	4	1	no	—
314	C₂³×C₇₃	C₂⁵	1	1	yes	characteristic
315	Q₈×C₇₃	—	2	8	no	—
316	Q₈×C₇₃	—	4	8	no	—
317	Q₈×C₇₃	—	4	4	no	—
318	C₂×C₄×C₇₃	—	2	1	no	—
319	C₂×C₄×C₇₃	—	2	1	no	—
320	C₂×C₄×C₇₃	—	2	1	no	—
321	C₂×C₄×C₇₃	—	2	1	no	—
322	C₂×C₄×C₇₃	—	2	2	no	—
323	C₂×C₄×C₇₃	—	2	2	no	—
324	C₂×C₄×C₇₃	—	2	1	no	—
325	C₂×C₄×C₇₃	—	2	1	no	—
326	C₂×C₄×C₇₃	—	2	1	no	—
327	C₂×C₄×C₇₃	—	2	1	no	—
328	C₂×C₄×C₇₃	—	2	1	no	—
329	C₂×C₄×C₇₃	—	2	2	no	—
330	C₂×C₄×C₇₃	—	2	2	no	—
331	C₂×C₄×C₇₃	—	2	1	no	—
332	C₂×C₄×C₇₃	—	2	1	no	—
333	C₂×C₄×C₇₃	—	2	1	no	—
334	C₂×C₄×C₇₃	—	2	2	no	—
335	C₂×C₄×C₇₃	—	2	1	no	—
336	C₂×C₄×C₇₃	—	2	1	no	—
337	C₂×C₄×C₇₃	—	2	1	no	—
338	C₂×C₄×C₇₃	—	2	2	no	—
339	C₂×C₄×C₇₃	—	2	1	no	—
340	C₂×C₄×C₇₃	—	2	2	no	—
341	C₂×C₄×C₇₃	—	2	1	no	—
342	C₂×C₄×C₇₃	—	2	2	no	—
343	C₂×C₄×C₇₃	—	2	1	no	—
344	C₂×C₄×C₇₃	—	2	1	no	—
345	C₂×C₄×C₇₃	—	2	2	no	—
346	C₂×C₄×C₇₃	—	2	2	no	—
347	C₂×C₄×C₇₃	—	2	1	no	—
348	C₂×C₄×C₇₃	—	2	1	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	1	no	—
353	C₂×C₄×C₇₃	—	2	1	no	—
354	C₂×C₄×C₇₃	—	2	1	no	—
355	C₂×C₄×C₇₃	—	2	2	no	—
356	C₂×C₄×C₇₃	—	2	1	no	—
357	C₂×C₄×C₇₃	—	2	1	no	—
358	C₂×C₄×C₇₃	—	2	1	no	—
359	C₂×C₄×C₇₃	—	2	2	no	—
360	C₂×C₄×C₇₃	—	2	2	no	—
361	C₂×C₄×C₇₃	—	2	1	no	—
362	C₂×C₄×C₇₃	—	2	1	no	—
363	C₂×C₄×C₇₃	—	2	1	no	—
364	C₂×C₄×C₇₃	—	2	2	no	—
365	C₂×C₄×C₇₃	—	2	1	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	2	no	—
374	C₂×C₄×C₇₃	—	2	1	no	—
375	C₂×C₄×C₇₃	—	2	2	no	—
376	C₂×C₄×C₇₃	—	2	2	no	—
377	C₂×C₄×C₇₃	C₂×#41	1	2	yes	—
378	C₂×C₄×C₇₃	C₂×#41	1	2	yes	—
379	C₂×C₄×C₇₃	C₂×#41	1	4	yes	—
380	C₂×C₄×C₇₃	C₂×#41	1	4	yes	—
381	C₂×C₄×C₇₃	C₂×#41	1	2	yes	—
382	C₂×C₄×C₇₃	C₂×#41	1	2	yes	—
383	C₂×C₄×C₇₃	C₂×#41	1	2	yes	—
384	C₂×C₄×C₇₃	2₋¹⁺⁴	1	2	yes	—
385	C₂×C₄×C₇₃	2₋¹⁺⁴	1	2	yes	—
386	C₂×C₄×C₇₃	2₋¹⁺⁴	1	2	yes	—
387	C₂²×C₇₃	C₂²×#41	1	1	yes	characteristic
388	C₂²×C₇₃	C₂²×#41	1	1	yes	characteristic
389	C₂²×C₇₃	C₂²×#41	1	1	yes	characteristic
390	C₂²×C₇₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
391	C₂²×C₇₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
392	C₂²×C₇₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
393	C₂²×C₇₃	#585	1	1	yes	characteristic
394	C₄×C₇₃	—	2	4	no	—
395	C₄×C₇₃	—	2	4	no	—
396	C₄×C₇₃	—	2	2	no	—
397	C₄×C₇₃	—	2	2	no	—
398	C₄×C₇₃	—	2	2	no	—
399	C₄×C₇₃	—	2	2	no	—
400	C₄×C₇₃	—	2	2	no	—
401	C₄×C₇₃	—	4	2	no	—
402	C₄×C₇₃	—	4	1	no	—
403	C₄×C₇₃	—	4	1	no	—
404	C₄×C₇₃	—	4	2	no	—
405	C₄×C₇₃	—	4	2	no	—
406	C₄×C₇₃	—	4	1	no	—
407	C₄×C₇₃	—	4	1	no	—
408	C₄×C₇₃	—	4	1	no	—
409	C₄×C₇₃	—	4	2	no	—
410	C₄×C₇₃	—	4	1	no	—
411	C₄×C₇₃	—	4	1	no	—
412	C₄×C₇₃	—	4	2	no	—
413	C₄×C₇₃	—	4	1	no	—
414	C₄×C₇₃	—	4	1	no	—
415	C₄×C₇₃	—	4	2	no	—
416	C₄×C₇₃	#552	1	4	yes	—
417	#59547	C₇₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
418	C₂×C₇₃	C₂×#552	1	1	yes	characteristic
419	C₂×C₇₃	#3475	1	1	yes	characteristic
420	C₂×C₇₃	#3482	1	1	yes	characteristic
421	C₂×C₇₃	#3518	1	1	yes	characteristic
422	C₂×C₇₃	#3523	1	1	yes	characteristic
423	C₂×C₇₃	#3523	1	1	yes	characteristic
424	C₂×C₇₃	#3555	1	1	yes	characteristic
425	#2766	C₂×C₇₃	1	2	yes	—
426	#2762	C₂×C₇₃	1	2	yes	—
427	#2612	C₂×C₇₃	1	2	yes	—
428	#2528	C₂×C₇₃	1	2	yes	—
429	#2528	C₂×C₇₃	1	2	yes	—
430	#2524	C₂×C₇₃	1	2	yes	—
431	#2514	C₂×C₇₃	1	1	yes	characteristic
432	#2514	C₂×C₇₃	1	1	yes	characteristic
433	#2508	C₂×C₇₃	1	1	yes	characteristic
434	#2508	C₂×C₇₃	1	1	yes	characteristic
435	#2462	C₂×C₇₃	1	2	yes	—
436	#2451	C₂×C₇₃	1	1	yes	characteristic
437	#2451	C₂×C₇₃	1	1	yes	characteristic
438	#2446	C₂×C₇₃	1	1	yes	characteristic
439	#2446	C₂×C₇₃	1	1	yes	characteristic
440	#2365	C₂×C₇₃	1	1	yes	characteristic
441	#2365	C₂×C₇₃	1	1	yes	characteristic
442	#2356	C₂×C₇₃	1	1	yes	characteristic
443	#2356	C₂×C₇₃	1	2	yes	—
444	#2351	C₂×C₇₃	1	1	yes	characteristic
445	C₄×#125	C₂×C₇₃	1	1	yes	characteristic
446	#2295	C₂×C₇₃	1	1	yes	characteristic
447	#2295	C₂×C₇₃	1	1	yes	characteristic
448	C₇₃	#59547	1	1	yes	characteristic, direct product factor, Sylow
449	C₂×C₄⋊Q₈	C₂²×C₇₃	1	1	yes	characteristic
450	C₂×C₄⋊Q₈	C₂²×C₇₃	1	1	yes	characteristic
451	C₂×#125	C₂²×C₇₃	1	1	yes	characteristic
452	C₂×C₄×Q₈	C₂²×C₇₃	1	1	yes	characteristic
453	C₂×C₄×Q₈	C₂²×C₇₃	1	1	yes	characteristic
454	C₂×C₄×Q₈	C₂²×C₇₃	1	1	yes	characteristic
455	C₂×C₄×Q₈	C₂²×C₇₃	1	2	yes	—
456	C₂×C₄×Q₈	C₂²×C₇₃	1	1	yes	characteristic
457	#401	C₂²×C₇₃	1	2	yes	—
458	#401	C₂²×C₇₃	1	2	yes	—
459	#400	C₂²×C₇₃	1	2	yes	—
460	#400	C₂²×C₇₃	1	2	yes	—
461	#400	C₂²×C₇₃	1	2	yes	—
462	#400	C₂²×C₇₃	1	2	yes	—
463	#400	C₂²×C₇₃	1	2	yes	—
464	#400	C₂²×C₇₃	1	2	yes	—
465	#398	C₂²×C₇₃	1	2	yes	—
466	#398	C₂²×C₇₃	1	2	yes	—
467	#398	C₂²×C₇₃	1	2	yes	—
468	#398	C₂²×C₇₃	1	2	yes	—
469	#398	C₂²×C₇₃	1	2	yes	—
470	#398	C₂²×C₇₃	1	2	yes	—
471	#395	C₂²×C₇₃	1	2	yes	—
472	#395	C₂²×C₇₃	1	2	yes	—
473	#391	C₂²×C₇₃	1	2	yes	—
474	#391	C₂²×C₇₃	1	1	yes	characteristic
475	#391	C₂²×C₇₃	1	1	yes	characteristic
476	#391	C₂²×C₇₃	1	2	yes	—
477	#391	C₂²×C₇₃	1	2	yes	—
478	#391	C₂²×C₇₃	1	1	yes	characteristic
479	#391	C₂²×C₇₃	1	1	yes	characteristic
480	#391	C₂²×C₇₃	1	1	yes	characteristic
481	#391	C₂²×C₇₃	1	1	yes	characteristic
482	#391	C₂²×C₇₃	1	1	yes	characteristic
483	#391	C₂²×C₇₃	1	1	yes	characteristic
484	#389	C₂²×C₇₃	1	1	yes	characteristic
485	#389	C₂²×C₇₃	1	1	yes	characteristic
486	#389	C₂²×C₇₃	1	2	yes	—
487	#389	C₂²×C₇₃	1	1	yes	characteristic
488	#389	C₂²×C₇₃	1	1	yes	characteristic
489	#389	C₂²×C₇₃	1	2	yes	—
490	#389	C₂²×C₇₃	1	1	yes	characteristic
491	#389	C₂²×C₇₃	1	2	yes	—
492	#389	C₂²×C₇₃	1	1	yes	characteristic
493	#389	C₂²×C₇₃	1	1	yes	characteristic
494	#389	C₂²×C₇₃	1	1	yes	characteristic
495	#389	C₂²×C₇₃	1	1	yes	characteristic
496	#389	C₂²×C₇₃	1	1	yes	characteristic
497	#387	C₂²×C₇₃	1	1	yes	characteristic
498	#387	C₂²×C₇₃	1	1	yes	characteristic
499	#387	C₂²×C₇₃	1	1	yes	characteristic
500	#387	C₂²×C₇₃	1	1	yes	characteristic
501	#387	C₂²×C₇₃	1	2	yes	—
502	#387	C₂²×C₇₃	1	2	yes	—
503	#387	C₂²×C₇₃	1	2	yes	—
504	#387	C₂²×C₇₃	1	2	yes	—
505	#387	C₂²×C₇₃	1	2	yes	—
506	#387	C₂²×C₇₃	1	2	yes	—
507	#387	C₂²×C₇₃	1	2	yes	—
508	#387	C₂²×C₇₃	1	2	yes	—
509	#387	C₂²×C₇₃	1	2	yes	—
510	#387	C₂²×C₇₃	1	2	yes	—
511	#387	C₂²×C₇₃	1	2	yes	—
512	#387	C₂²×C₇₃	1	2	yes	—
513	#387	C₂²×C₇₃	1	2	yes	—
514	#387	C₂²×C₇₃	1	2	yes	—
515	#387	C₂²×C₇₃	1	2	yes	—
516	#387	C₂²×C₇₃	1	2	yes	—
517	#387	C₂²×C₇₃	1	2	yes	—
518	#387	C₂²×C₇₃	1	2	yes	—
519	#387	C₂²×C₇₃	1	2	yes	—
520	#387	C₂²×C₇₃	1	2	yes	—
521	#383	C₂²×C₇₃	1	2	yes	—
522	#383	C₂²×C₇₃	1	2	yes	—
523	#383	C₂²×C₇₃	1	2	yes	—
524	#382	C₂²×C₇₃	1	1	yes	characteristic
525	#382	C₂²×C₇₃	1	2	yes	—
526	#382	C₂²×C₇₃	1	1	yes	characteristic
527	#382	C₂²×C₇₃	1	2	yes	—
528	#382	C₂²×C₇₃	1	1	yes	characteristic
529	#382	C₂²×C₇₃	1	2	yes	—
530	C₄×C₄⋊C₄	C₂²×C₇₃	1	1	yes	characteristic
531	C₄×C₄⋊C₄	C₂²×C₇₃	1	1	yes	characteristic
532	C₄×C₄⋊C₄	C₂²×C₇₃	1	1	yes	characteristic
533	C₄×C₄⋊C₄	C₂²×C₇₃	1	1	yes	characteristic
534	C₄×C₄⋊C₄	C₂²×C₇₃	1	1	yes	characteristic
535	C₄×C₄⋊C₄	C₂²×C₇₃	1	1	yes	characteristic
536	C₄×C₄⋊C₄	C₂²×C₇₃	1	2	yes	—
537	C₄×C₄⋊C₄	C₂²×C₇₃	1	1	yes	characteristic
538	C₄×C₄⋊C₄	C₂²×C₇₃	1	2	yes	—
539	C₄×C₄⋊C₄	C₂²×C₇₃	1	1	yes	characteristic
540	C₄×C₄⋊C₄	C₂²×C₇₃	1	2	yes	—
541	C₄×C₄⋊C₄	C₂²×C₇₃	1	1	yes	characteristic
542	C₄×C₄⋊C₄	C₂²×C₇₃	1	1	yes	characteristic
543	C₄×C₄⋊C₄	C₂²×C₇₃	1	2	yes	—
544	#376	C₂²×C₇₃	1	2	yes	—
545	#376	C₂²×C₇₃	1	2	yes	—
546	#376	C₂²×C₇₃	1	2	yes	—
547	C₄³	C₂²×C₇₃	1	1	yes	characteristic
548	C₂²×Q₈	C₂³×C₇₃	1	1	yes	characteristic
549	C₂²×Q₈	C₂³×C₇₃	1	2	yes	—
550	C₂²×Q₈	C₂³×C₇₃	1	1	yes	characteristic
551	C₄⋊Q₈	—	2	4	no	—
552	C₄⋊Q₈	—	2	4	no	—
553	#125	—	2	4	no	—
554	C₄×Q₈	—	2	4	no	—
555	C₄×Q₈	—	2	4	no	—
556	C₄×Q₈	—	2	8	no	—
557	C₄×Q₈	—	2	4	no	—
558	C₄×Q₈	—	2	4	no	—
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	1	yes	characteristic
564	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
565	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
566	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
567	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
568	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
569	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
570	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
571	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
572	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
573	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
574	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
575	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
576	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
577	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
578	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
579	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
580	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
581	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
582	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
583	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
584	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
585	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
586	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
587	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
588	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
589	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
590	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
591	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
592	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
593	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
594	C₂×C₄²	C₂³×C₇₃	1	2	yes	—
595	C₂×C₄²	C₂³×C₇₃	1	2	yes	—
596	C₂×C₄²	C₂³×C₇₃	1	2	yes	—
597	C₂×C₄²	C₂³×C₇₃	1	2	yes	—
598	C₂×C₄²	C₂³×C₇₃	1	2	yes	—
599	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
600	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
601	C₂×C₄²	C₂³×C₇₃	1	2	yes	—
602	C₂×C₄²	C₂³×C₇₃	1	2	yes	—
603	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
604	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
605	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
606	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
607	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
608	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
609	C₂×C₄²	C₂³×C₇₃	1	2	yes	—
610	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
611	#95	C₂³×C₇₃	1	2	yes	—
612	#95	C₂³×C₇₃	1	1	yes	characteristic
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	1	yes	characteristic
623	#95	C₂³×C₇₃	1	2	yes	—
624	#95	C₂³×C₇₃	1	1	yes	characteristic
625	#95	C₂³×C₇₃	1	1	yes	characteristic
626	#95	C₂³×C₇₃	1	1	yes	characteristic
627	#95	C₂³×C₇₃	1	1	yes	characteristic
628	#95	C₂³×C₇₃	1	1	yes	characteristic
629	#95	C₂³×C₇₃	1	1	yes	characteristic
630	#95	C₂³×C₇₃	1	1	yes	characteristic
631	#95	C₂³×C₇₃	1	2	yes	—
632	#95	C₂³×C₇₃	1	2	yes	—
633	#95	C₂³×C₇₃	1	2	yes	—
634	#95	C₂³×C₇₃	1	2	yes	—
635	#95	C₂³×C₇₃	1	2	yes	—
636	#95	C₂³×C₇₃	1	2	yes	—
637	#95	C₂³×C₇₃	1	1	yes	characteristic
638	#95	C₂³×C₇₃	1	2	yes	—
639	#95	C₂³×C₇₃	1	2	yes	—
640	#95	C₂³×C₇₃	1	2	yes	—
641	#95	C₂³×C₇₃	1	1	yes	characteristic
642	#95	C₂³×C₇₃	1	1	yes	characteristic
643	#95	C₂³×C₇₃	1	2	yes	—
644	#95	C₂³×C₇₃	1	2	yes	—
645	#95	C₂³×C₇₃	1	2	yes	—
646	#95	C₂³×C₇₃	1	2	yes	—
647	#95	C₂³×C₇₃	1	2	yes	—
648	#95	C₂³×C₇₃	1	2	yes	—
649	#95	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	C₂×Q₈	—	2	2	no	—
656	C₂×Q₈	—	2	4	no	—
657	C₂×Q₈	—	2	2	no	—
658	C₂×Q₈	—	2	4	no	—
659	C₂×Q₈	—	2	2	no	—
660	C₂×Q₈	—	2	2	no	—
661	C₂×Q₈	—	2	2	no	—
662	C₂×Q₈	—	4	2	no	—
663	C₂×Q₈	#41×C₇₃	1	4	yes	—
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	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
668	C₂²×C₄	C₂⁴×C₇₃	1	2	yes	—
669	C₂²×C₄	C₂⁴×C₇₃	1	2	yes	—
670	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
671	C₂²×C₄	C₂⁴×C₇₃	1	2	yes	—
672	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
673	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
674	C₂²×C₄	C₂⁴×C₇₃	1	2	yes	—
675	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
676	C₂²×C₄	C₂⁴×C₇₃	1	2	yes	—
677	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
678	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
679	C₂²×C₄	C₂⁴×C₇₃	1	2	yes	—
680	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
681	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
682	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
683	C₂²×C₄	C₂⁴×C₇₃	1	2	yes	—
684	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
685	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
686	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
687	C₄⋊C₄	—	2	4	no	—
688	C₄⋊C₄	—	2	4	no	—
689	C₄⋊C₄	—	2	4	no	—
690	C₄⋊C₄	—	2	4	no	—
691	C₄⋊C₄	—	2	2	no	—
692	C₄⋊C₄	—	2	2	no	—
693	C₄⋊C₄	—	2	4	no	—
694	C₄⋊C₄	—	2	4	no	—
695	C₄⋊C₄	—	2	2	no	—
696	C₄⋊C₄	—	2	2	no	—
697	C₄⋊C₄	—	2	2	no	—
698	C₄⋊C₄	—	2	2	no	—
699	C₄⋊C₄	—	2	2	no	—
700	C₄⋊C₄	—	2	4	no	—
701	C₄⋊C₄	—	2	4	no	—
702	C₄⋊C₄	—	2	4	no	—
703	C₄⋊C₄	—	2	2	no	—
704	C₄⋊C₄	—	2	2	no	—
705	C₄⋊C₄	—	2	2	no	—
706	C₄⋊C₄	—	2	2	no	—
707	C₄⋊C₄	—	2	2	no	—
708	C₄⋊C₄	—	2	4	no	—
709	C₄⋊C₄	—	2	2	no	—
710	C₄⋊C₄	—	2	2	no	—
711	C₄⋊C₄	—	4	2	no	—
712	C₄⋊C₄	—	4	2	no	—
713	C₄⋊C₄	—	4	1	no	—
714	C₄⋊C₄	—	4	1	no	—
715	C₄⋊C₄	—	4	2	no	—
716	C₄⋊C₄	—	4	2	no	—
717	C₄⋊C₄	—	4	2	no	—
718	C₄⋊C₄	#41×C₇₃	1	4	yes	—
719	C₄⋊C₄	#41×C₇₃	1	4	yes	—
720	C₄²	—	2	4	no	—
721	C₄²	—	2	2	no	—
722	C₄²	—	2	2	no	—
723	C₄²	—	2	4	no	—
724	C₄²	—	2	4	no	—
725	C₄²	—	2	4	no	—
726	C₄²	—	2	4	no	—
727	C₄²	—	2	4	no	—
728	C₄²	—	2	2	no	—
729	C₄²	—	2	2	no	—
730	C₄²	—	2	4	no	—
731	C₄²	—	2	2	no	—
732	C₄²	—	2	2	no	—
733	C₄²	—	2	2	no	—
734	C₄²	—	2	2	no	—
735	C₄²	—	2	2	no	—
736	C₄²	—	2	2	no	—
737	C₄²	—	2	4	no	—
738	C₄²	—	4	1	no	—
739	C₂³	C₂⁵×C₇₃	1	1	yes	characteristic
740	Q₈	—	2	8	no	—
741	Q₈	—	4	8	no	—
742	Q₈	—	4	4	no	—
743	C₂×C₄	—	2	1	no	—
744	C₂×C₄	—	2	1	no	—
745	C₂×C₄	—	2	1	no	—
746	C₂×C₄	—	2	1	no	—
747	C₂×C₄	—	2	2	no	—
748	C₂×C₄	—	2	2	no	—
749	C₂×C₄	—	2	1	no	—
750	C₂×C₄	—	2	1	no	—
751	C₂×C₄	—	2	1	no	—
752	C₂×C₄	—	2	1	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	1	no	—
759	C₂×C₄	—	2	2	no	—
760	C₂×C₄	—	2	1	no	—
761	C₂×C₄	—	2	1	no	—
762	C₂×C₄	—	2	1	no	—
763	C₂×C₄	—	2	2	no	—
764	C₂×C₄	—	2	1	no	—
765	C₂×C₄	—	2	2	no	—
766	C₂×C₄	—	2	1	no	—
767	C₂×C₄	—	2	2	no	—
768	C₂×C₄	—	2	1	no	—
769	C₂×C₄	—	2	1	no	—
770	C₂×C₄	—	2	2	no	—
771	C₂×C₄	—	2	2	no	—
772	C₂×C₄	—	2	1	no	—
773	C₂×C₄	—	2	1	no	—
774	C₂×C₄	—	2	2	no	—
775	C₂×C₄	—	2	2	no	—
776	C₂×C₄	—	2	2	no	—
777	C₂×C₄	—	2	1	no	—
778	C₂×C₄	—	2	1	no	—
779	C₂×C₄	—	2	1	no	—
780	C₂×C₄	—	2	2	no	—
781	C₂×C₄	—	2	1	no	—
782	C₂×C₄	—	2	1	no	—
783	C₂×C₄	—	2	1	no	—
784	C₂×C₄	—	2	2	no	—
785	C₂×C₄	—	2	2	no	—
786	C₂×C₄	—	2	1	no	—
787	C₂×C₄	—	2	1	no	—
788	C₂×C₄	—	2	1	no	—
789	C₂×C₄	—	2	2	no	—
790	C₂×C₄	—	2	1	no	—
791	C₂×C₄	—	2	2	no	—
792	C₂×C₄	—	2	2	no	—
793	C₂×C₄	—	2	1	no	—
794	C₂×C₄	—	2	1	no	—
795	C₂×C₄	—	2	1	no	—
796	C₂×C₄	—	2	1	no	—
797	C₂×C₄	—	2	1	no	—
798	C₂×C₄	—	2	2	no	—
799	C₂×C₄	—	2	1	no	—
800	C₂×C₄	—	2	2	no	—
801	C₂×C₄	—	2	2	no	—
802	C₂×C₄	C₂×#41×C₇₃	1	2	yes	—
803	C₂×C₄	C₂×#41×C₇₃	1	2	yes	—
804	C₂×C₄	C₂×#41×C₇₃	1	4	yes	—
805	C₂×C₄	C₂×#41×C₇₃	1	4	yes	—
806	C₂×C₄	C₂×#41×C₇₃	1	2	yes	—
807	C₂×C₄	C₂×#41×C₇₃	1	2	yes	—
808	C₂×C₄	C₂×#41×C₇₃	1	2	yes	—
809	C₂×C₄	2₋¹⁺⁴×C₇₃	1	2	yes	—
810	C₂×C₄	2₋¹⁺⁴×C₇₃	1	2	yes	—
811	C₂×C₄	2₋¹⁺⁴×C₇₃	1	2	yes	—
812	C₂²	C₂²×#41×C₇₃	1	1	yes	characteristic
813	C₂²	C₂²×#41×C₇₃	1	1	yes	characteristic
814	C₂²	C₂²×#41×C₇₃	1	1	yes	characteristic
815	C₂²	C₂×2₋¹⁺⁴×C₇₃	1	1	yes	characteristic
816	C₂²	C₂×2₋¹⁺⁴×C₇₃	1	1	yes	characteristic
817	C₂²	C₂×2₋¹⁺⁴×C₇₃	1	1	yes	characteristic
818	C₂²	#585×C₇₃	1	1	yes	characteristic
819	C₄	—	2	4	no	—
820	C₄	—	2	2	no	—
821	C₄	—	2	4	no	—
822	C₄	—	2	2	no	—
823	C₄	—	2	2	no	—
824	C₄	—	2	2	no	—
825	C₄	—	2	2	no	—
826	C₄	—	4	2	no	—
827	C₄	—	4	2	no	—
828	C₄	—	4	1	no	—
829	C₄	—	4	1	no	—
830	C₄	—	4	2	no	—
831	C₄	—	4	1	no	—
832	C₄	—	4	1	no	—
833	C₄	—	4	1	no	—
834	C₄	—	4	2	no	—
835	C₄	—	4	1	no	—
836	C₄	—	4	1	no	—
837	C₄	—	4	2	no	—
838	C₄	—	4	1	no	—
839	C₄	—	4	1	no	—
840	C₄	—	4	2	no	—
841	C₄	#552×C₇₃	1	4	yes	—
842	C₂	C₂×#552×C₇₃	1	1	yes	characteristic
843	C₂	C₇₃×#3475	1	1	yes	characteristic
844	C₂	C₇₃×#3482	1	1	yes	characteristic
845	C₂	C₇₃×#3518	1	1	yes	characteristic
846	C₂	C₇₃×#3523	1	1	yes	characteristic
847	C₂	C₇₃×#3523	1	1	yes	characteristic
848	C₂	C₇₃×#3555	1	1	yes	characteristic

	subgroup	G/H
center, socle, prime radical	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
417. #59547	C₇₃	direct (N × H)
448. C₇₃	#59547	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×#2766	2
C₇₃×#2762	2
C₇₃×#2612	2
C₇₃×#2528	2
C₇₃×#2524	2
C₇₃×#2514	2
C₇₃×#2508	2
C₇₃×#2462	2
C₇₃×#2451	2
C₇₃×#2446	2
C₇₃×#2365	2
C₇₃×#2356	2
C₇₃×#2351	2
C₄×#125×C₇₃	2
C₇₃×#2295	2
#59547	73

Subgroups — C73×#59547 #32968951

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₃×#59547 #32968951