Subgroups — C₇₃×#59866 #32969270

Order 18688.

1666 conjugacy classes of subgroups.

The subgroup lattice has 808 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇₃×#2809	C₂	1	1	yes	maximal, characteristic, complemented
2	C₇₃×#2806	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇₃×#2805	C₂	1	1	yes	maximal, characteristic, complemented
4	C₇₃×#2726	C₂	1	1	yes	maximal, characteristic, complemented
5	C₇₃×#2590	C₂	1	2	yes	maximal, complemented
6	C₇₃×#2585	C₂	1	2	yes	maximal, complemented
7	C₇₃×#2585	C₂	1	2	yes	maximal, complemented
8	C₇₃×#2583	C₂	1	2	yes	maximal
9	C₇₃×#2569	C₂	1	2	yes	maximal
10	C₇₃×#2473	C₂	1	2	yes	maximal
11	C₇₃×#2473	C₂	1	2	yes	maximal
12	C₇₃×#2462	C₂	1	2	yes	maximal, complemented
13	C₇₃×#2453	C₂	1	2	yes	maximal, complemented
14	C₇₃×#2370	C₂	1	2	yes	maximal, complemented
15	C₇₃×#2368	C₂	1	2	yes	maximal
16	C₇₃×#2345	C₂	1	2	yes	maximal
17	C₄×C₂²⋊Q₈×C₇₃	C₂	1	1	yes	maximal, characteristic
18	C₄×C₂²⋊Q₈×C₇₃	C₂	1	1	yes	maximal, characteristic
19	C₂×#389×C₇₃	C₂	1	1	yes	maximal, characteristic
20	C₂×#125×C₇₃	C₂²	1	2	yes	—
21	C₂×#125×C₇₃	C₂²	1	2	yes	—
22	C₂×C₂²⋊Q₈×C₇₃	C₂²	1	1	yes	characteristic
23	C₂×C₂²⋊Q₈×C₇₃	C₂²	1	1	yes	characteristic
24	C₂×C₄×Q₈×C₇₃	C₂²	1	1	yes	characteristic
25	C₂×C₄×Q₈×C₇₃	C₂²	1	1	yes	characteristic
26	C₂²×C₄⋊C₄×C₇₃	C₂²	1	1	yes	characteristic
27	C₂²×C₄⋊C₄×C₇₃	C₂²	1	2	yes	—
28	C₂²×C₄⋊C₄×C₇₃	C₂²	1	1	yes	characteristic
29	C₂²×C₄²×C₇₃	C₂²	1	1	yes	characteristic
30	#400×C₇₃	C₂²	1	2	yes	—
31	#400×C₇₃	C₂²	1	2	yes	—
32	#400×C₇₃	C₂²	1	2	yes	—
33	#400×C₇₃	C₂²	1	2	yes	—
34	#398×C₇₃	C₂²	1	2	yes	—
35	#398×C₇₃	C₂²	1	2	yes	—
36	#398×C₇₃	C₂²	1	2	yes	—
37	#398×C₇₃	C₂²	1	2	yes	—
38	#398×C₇₃	C₂²	1	2	yes	—
39	#398×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	#395×C₇₃	C₂²	1	2	yes	—
45	#395×C₇₃	C₂²	1	2	yes	—
46	#391×C₇₃	C₂²	1	2	yes	—
47	#391×C₇₃	C₂²	1	2	yes	—
48	#391×C₇₃	C₂²	1	1	yes	characteristic
49	#391×C₇₃	C₂²	1	1	yes	characteristic
50	#389×C₇₃	C₂²	1	2	yes	—
51	#389×C₇₃	C₂²	1	2	yes	—
52	#389×C₇₃	C₂²	1	2	yes	—
53	#389×C₇₃	C₂²	1	2	yes	—
54	#389×C₇₃	C₂²	1	2	yes	—
55	#389×C₇₃	C₂²	1	2	yes	—
56	#389×C₇₃	C₂²	1	1	yes	characteristic
57	#389×C₇₃	C₂²	1	1	yes	characteristic
58	#389×C₇₃	C₂²	1	1	yes	characteristic
59	#389×C₇₃	C₂²	1	2	yes	—
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	2	yes	—
64	#389×C₇₃	C₂²	1	2	yes	—
65	#389×C₇₃	C₂²	1	2	yes	—
66	#387×C₇₃	C₂²	1	2	yes	—
67	#387×C₇₃	C₂²	1	2	yes	—
68	#387×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	#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	2	yes	—
84	#385×C₇₃	C₂²	1	2	yes	—
85	#385×C₇₃	C₂²	1	2	yes	—
86	#385×C₇₃	C₂²	1	2	yes	—
87	#385×C₇₃	C₂²	1	2	yes	—
88	#385×C₇₃	C₂²	1	2	yes	—
89	#385×C₇₃	C₂²	1	2	yes	—
90	#380×C₇₃	C₂²	1	2	yes	—
91	#380×C₇₃	C₂²	1	2	yes	—
92	#380×C₇₃	C₂²	1	1	yes	characteristic
93	#380×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	1	yes	characteristic
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	1	yes	characteristic
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	C₄×C₂²⋊C₄×C₇₃	C₂²	1	2	yes	—
106	C₂×#95×C₇₃	C₂²	1	2	yes	—
107	C₂²×Q₈×C₇₃	C₂³	1	1	yes	characteristic
108	C₂²×Q₈×C₇₃	C₂³	1	1	yes	characteristic
109	C₂³×C₄×C₇₃	C₂³	1	1	yes	characteristic
110	C₂³×C₄×C₇₃	C₂³	1	2	yes	—
111	C₂³×C₄×C₇₃	C₂³	1	2	yes	—
112	C₂³×C₄×C₇₃	C₂³	1	1	yes	characteristic
113	C₂³×C₄×C₇₃	C₂³	1	1	yes	characteristic
114	#125×C₇₃	—	2	8	no	—
115	#125×C₇₃	—	4	4	no	—
116	C₂²⋊Q₈×C₇₃	—	2	4	no	—
117	C₂²⋊Q₈×C₇₃	Q₈	1	8	yes	complemented
118	C₄×Q₈×C₇₃	—	4	2	no	—
119	C₄×Q₈×C₇₃	—	4	2	no	—
120	C₂×C₄⋊C₄×C₇₃	—	2	8	no	—
121	C₂×C₄⋊C₄×C₇₃	—	2	4	no	—
122	C₂×C₄⋊C₄×C₇₃	—	4	2	no	—
123	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
124	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
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	1	yes	characteristic
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×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
144	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
145	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
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	2	yes	—
149	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
150	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
151	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
152	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
153	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
154	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
155	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
156	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
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×C₄²×C₇₃	—	4	2	no	—
162	C₂×C₄²×C₇₃	C₂³	1	2	yes	—
163	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
164	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
165	C₂×C₄²×C₇₃	C₂³	1	2	yes	—
166	C₂×C₄²×C₇₃	C₂³	1	2	yes	—
167	C₂×C₄²×C₇₃	C₂³	1	2	yes	—
168	C₂×C₄²×C₇₃	C₂³	1	2	yes	—
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	1	yes	characteristic
173	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
174	#95×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	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	C₂⁴×C₇₃	C₂⁴	1	1	yes	characteristic
205	C₂×Q₈×C₇₃	—	2	2	no	—
206	C₂×Q₈×C₇₃	—	4	1	no	—
207	C₂×Q₈×C₇₃	—	4	1	no	—
208	C₂×Q₈×C₇₃	—	4	1	no	—
209	C₂×Q₈×C₇₃	—	4	1	no	—
210	C₂×Q₈×C₇₃	C₂×Q₈	1	4	yes	—
211	C₂²×C₄×C₇₃	—	2	2	no	—
212	C₂²×C₄×C₇₃	—	2	2	no	—
213	C₂²×C₄×C₇₃	—	2	2	no	—
214	C₂²×C₄×C₇₃	—	2	4	no	—
215	C₂²×C₄×C₇₃	—	2	4	no	—
216	C₂²×C₄×C₇₃	—	2	4	no	—
217	C₂²×C₄×C₇₃	—	4	1	no	—
218	C₂²×C₄×C₇₃	—	4	1	no	—
219	C₂²×C₄×C₇₃	—	4	1	no	—
220	C₂²×C₄×C₇₃	—	4	1	no	—
221	C₂²×C₄×C₇₃	—	4	2	no	—
222	C₂²×C₄×C₇₃	—	4	2	no	—
223	C₂²×C₄×C₇₃	—	4	2	no	—
224	C₂²×C₄×C₇₃	C₂×Q₈	1	4	yes	—
225	C₂²×C₄×C₇₃	#41	1	4	yes	—
226	C₂²×C₄×C₇₃	C₂⁴	1	2	yes	—
227	C₂²×C₄×C₇₃	C₂⁴	1	2	yes	—
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	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	1	yes	characteristic
236	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
237	C₂²×C₄×C₇₃	C₂⁴	1	2	yes	—
238	C₂²×C₄×C₇₃	C₂⁴	1	2	yes	—
239	C₂²×C₄×C₇₃	C₂⁴	1	2	yes	—
240	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
241	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
242	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
243	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
244	C₄⋊C₄×C₇₃	—	2	4	no	—
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	2	no	—
249	C₄⋊C₄×C₇₃	—	2	4	no	—
250	C₄⋊C₄×C₇₃	—	2	2	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	—	2	4	no	—
257	C₄⋊C₄×C₇₃	—	2	4	no	—
258	C₄⋊C₄×C₇₃	—	2	4	no	—
259	C₄⋊C₄×C₇₃	—	2	4	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	2	no	—
264	C₄⋊C₄×C₇₃	—	4	2	no	—
265	C₄⋊C₄×C₇₃	—	4	1	no	—
266	C₄⋊C₄×C₇₃	—	4	1	no	—
267	C₄⋊C₄×C₇₃	—	4	2	no	—
268	C₄⋊C₄×C₇₃	—	4	2	no	—
269	C₄⋊C₄×C₇₃	—	4	2	no	—
270	C₄⋊C₄×C₇₃	—	4	1	no	—
271	C₄⋊C₄×C₇₃	—	4	1	no	—
272	C₄⋊C₄×C₇₃	—	4	2	no	—
273	C₄⋊C₄×C₇₃	—	4	2	no	—
274	C₄⋊C₄×C₇₃	—	4	2	no	—
275	C₄⋊C₄×C₇₃	C₂×Q₈	1	4	yes	—
276	C₄⋊C₄×C₇₃	C₂×Q₈	1	8	yes	—
277	C₄⋊C₄×C₇₃	#41	1	4	yes	—
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	C₂×Q₈	1	8	yes	—
282	C₄²×C₇₃	—	2	4	no	—
283	C₄²×C₇₃	—	2	2	no	—
284	C₄²×C₇₃	—	2	2	no	—
285	C₄²×C₇₃	—	4	1	no	—
286	C₄²×C₇₃	—	4	1	no	—
287	C₄²×C₇₃	—	4	2	no	—
288	C₄²×C₇₃	—	4	2	no	—
289	C₄²×C₇₃	—	4	2	no	—
290	C₄²×C₇₃	—	4	2	no	—
291	C₄²×C₇₃	—	4	2	no	—
292	C₄²×C₇₃	—	4	2	no	—
293	C₄²×C₇₃	—	4	2	no	—
294	C₂³×C₇₃	—	2	1	no	—
295	C₂³×C₇₃	—	2	1	no	—
296	C₂³×C₇₃	—	2	1	no	—
297	C₂³×C₇₃	—	2	1	no	—
298	C₂³×C₇₃	C₂²×Q₈	1	2	yes	—
299	C₂³×C₇₃	C₂×#41	1	2	yes	—
300	C₂³×C₇₃	2₋¹⁺⁴	1	2	yes	—
301	C₂³×C₇₃	C₂⁵	1	1	yes	characteristic
302	Q₈×C₇₃	—	4	4	no	—
303	Q₈×C₇₃	—	4	4	no	—
304	C₂×C₄×C₇₃	—	2	8	no	—
305	C₂×C₄×C₇₃	—	2	2	no	—
306	C₂×C₄×C₇₃	—	2	2	no	—
307	C₂×C₄×C₇₃	—	2	1	no	—
308	C₂×C₄×C₇₃	—	2	1	no	—
309	C₂×C₄×C₇₃	—	2	1	no	—
310	C₂×C₄×C₇₃	—	2	1	no	—
311	C₂×C₄×C₇₃	—	2	1	no	—
312	C₂×C₄×C₇₃	—	2	2	no	—
313	C₂×C₄×C₇₃	—	2	1	no	—
314	C₂×C₄×C₇₃	—	2	1	no	—
315	C₂×C₄×C₇₃	—	2	1	no	—
316	C₂×C₄×C₇₃	—	2	2	no	—
317	C₂×C₄×C₇₃	—	2	1	no	—
318	C₂×C₄×C₇₃	—	2	1	no	—
319	C₂×C₄×C₇₃	—	2	2	no	—
320	C₂×C₄×C₇₃	—	2	2	no	—
321	C₂×C₄×C₇₃	—	2	1	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	2	no	—
335	C₂×C₄×C₇₃	—	2	2	no	—
336	C₂×C₄×C₇₃	—	2	2	no	—
337	C₂×C₄×C₇₃	—	2	2	no	—
338	C₂×C₄×C₇₃	—	2	2	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	—	4	4	no	—
351	C₂×C₄×C₇₃	—	4	4	no	—
352	C₂×C₄×C₇₃	—	4	8	no	—
353	C₂×C₄×C₇₃	—	8	4	no	—
354	C₂×C₄×C₇₃	C₂²×Q₈	1	4	yes	—
355	C₂×C₄×C₇₃	C₂²×Q₈	1	4	yes	—
356	C₂×C₄×C₇₃	C₂²×Q₈	1	2	yes	—
357	C₂×C₄×C₇₃	C₂²×Q₈	1	2	yes	—
358	C₂×C₄×C₇₃	C₂×#41	1	4	yes	—
359	C₂×C₄×C₇₃	C₂×#41	1	2	yes	—
360	C₂×C₄×C₇₃	C₂×#41	1	2	yes	—
361	C₂×C₄×C₇₃	C₂×#41	1	2	yes	—
362	C₂×C₄×C₇₃	H(5,𝔽₂)	1	2	yes	—
363	C₂²×C₇₃	—	2	2	no	—
364	C₂²×C₇₃	—	2	2	no	—
365	C₂²×C₇₃	—	2	2	no	—
366	C₂²×C₇₃	—	2	2	no	—
367	C₂²×C₇₃	—	2	2	no	—
368	C₂²×C₇₃	—	2	2	no	—
369	C₂²×C₇₃	#557	1	4	yes	—
370	C₂²×C₇₃	C₂³×Q₈	1	1	yes	characteristic
371	C₂²×C₇₃	C₂²×#41	1	1	yes	characteristic
372	C₂²×C₇₃	C₂²×#41	1	1	yes	characteristic
373	C₂²×C₇₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
374	C₂²×C₇₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
375	C₂²×C₇₃	#585	1	1	yes	characteristic
376	C₂²×C₇₃	#585	1	1	yes	characteristic
377	C₄×C₇₃	—	2	4	no	—
378	C₄×C₇₃	—	2	4	no	—
379	C₄×C₇₃	—	2	2	no	—
380	C₄×C₇₃	—	2	2	no	—
381	C₄×C₇₃	—	2	2	no	—
382	C₄×C₇₃	—	2	2	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	2	no	—
389	C₄×C₇₃	—	4	2	no	—
390	C₄×C₇₃	—	4	2	no	—
391	C₄×C₇₃	—	4	2	no	—
392	C₄×C₇₃	—	4	2	no	—
393	C₄×C₇₃	—	4	2	no	—
394	C₄×C₇₃	—	4	2	no	—
395	#59866	C₇₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
396	C₂×C₇₃	—	2	4	no	—
397	C₂×C₇₃	#3475	1	1	yes	characteristic
398	C₂×C₇₃	C₂×#557	1	1	yes	characteristic
399	C₂×C₇₃	Q₈×#41	1	1	yes	characteristic
400	C₂×C₇₃	#3492	1	1	yes	characteristic
401	C₂×C₇₃	#3501	1	1	yes	characteristic
402	C₂×C₇₃	#3505	1	1	yes	characteristic
403	C₂×C₇₃	#3553	1	1	yes	characteristic
404	#2809	C₂×C₇₃	1	1	yes	characteristic, complemented
405	#2806	C₂×C₇₃	1	1	yes	characteristic, complemented
406	#2805	C₂×C₇₃	1	1	yes	characteristic, complemented
407	#2726	C₂×C₇₃	1	1	yes	characteristic, complemented
408	#2590	C₂×C₇₃	1	2	yes	complemented
409	#2585	C₂×C₇₃	1	2	yes	complemented
410	#2585	C₂×C₇₃	1	2	yes	complemented
411	#2583	C₂×C₇₃	1	2	yes	—
412	#2569	C₂×C₇₃	1	2	yes	—
413	#2473	C₂×C₇₃	1	2	yes	—
414	#2473	C₂×C₇₃	1	2	yes	—
415	#2462	C₂×C₇₃	1	2	yes	complemented
416	#2453	C₂×C₇₃	1	2	yes	complemented
417	#2370	C₂×C₇₃	1	2	yes	complemented
418	#2368	C₂×C₇₃	1	2	yes	—
419	#2345	C₂×C₇₃	1	2	yes	—
420	C₄×C₂²⋊Q₈	C₂×C₇₃	1	1	yes	characteristic
421	C₄×C₂²⋊Q₈	C₂×C₇₃	1	1	yes	characteristic
422	C₂×#389	C₂×C₇₃	1	1	yes	characteristic
423	C₇₃	#59866	1	1	yes	characteristic, direct product factor, Sylow
424	C₂×#125	C₂²×C₇₃	1	2	yes	—
425	C₂×#125	C₂²×C₇₃	1	2	yes	—
426	C₂×C₂²⋊Q₈	C₂²×C₇₃	1	1	yes	characteristic
427	C₂×C₂²⋊Q₈	C₂²×C₇₃	1	1	yes	characteristic
428	C₂×C₄×Q₈	C₂²×C₇₃	1	1	yes	characteristic
429	C₂×C₄×Q₈	C₂²×C₇₃	1	1	yes	characteristic
430	C₂²×C₄⋊C₄	C₂²×C₇₃	1	2	yes	—
431	C₂²×C₄⋊C₄	C₂²×C₇₃	1	1	yes	characteristic
432	C₂²×C₄⋊C₄	C₂²×C₇₃	1	1	yes	characteristic
433	C₂²×C₄²	C₂²×C₇₃	1	1	yes	characteristic
434	#400	C₂²×C₇₃	1	2	yes	—
435	#400	C₂²×C₇₃	1	2	yes	—
436	#400	C₂²×C₇₃	1	2	yes	—
437	#400	C₂²×C₇₃	1	2	yes	—
438	#398	C₂²×C₇₃	1	2	yes	—
439	#398	C₂²×C₇₃	1	2	yes	—
440	#398	C₂²×C₇₃	1	2	yes	—
441	#398	C₂²×C₇₃	1	2	yes	—
442	#398	C₂²×C₇₃	1	2	yes	—
443	#398	C₂²×C₇₃	1	2	yes	—
444	#398	C₂²×C₇₃	1	2	yes	—
445	#398	C₂²×C₇₃	1	2	yes	—
446	#398	C₂²×C₇₃	1	2	yes	—
447	#398	C₂²×C₇₃	1	2	yes	—
448	#395	C₂²×C₇₃	1	2	yes	—
449	#395	C₂²×C₇₃	1	2	yes	—
450	#391	C₂²×C₇₃	1	2	yes	—
451	#391	C₂²×C₇₃	1	2	yes	—
452	#391	C₂²×C₇₃	1	1	yes	characteristic
453	#391	C₂²×C₇₃	1	1	yes	characteristic
454	#389	C₂²×C₇₃	1	2	yes	—
455	#389	C₂²×C₇₃	1	2	yes	—
456	#389	C₂²×C₇₃	1	2	yes	—
457	#389	C₂²×C₇₃	1	2	yes	—
458	#389	C₂²×C₇₃	1	1	yes	characteristic
459	#389	C₂²×C₇₃	1	2	yes	—
460	#389	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	#389	C₂²×C₇₃	1	1	yes	characteristic
465	#389	C₂²×C₇₃	1	2	yes	—
466	#389	C₂²×C₇₃	1	1	yes	characteristic
467	#389	C₂²×C₇₃	1	1	yes	characteristic
468	#389	C₂²×C₇₃	1	1	yes	characteristic
469	#389	C₂²×C₇₃	1	1	yes	characteristic
470	#387	C₂²×C₇₃	1	2	yes	—
471	#387	C₂²×C₇₃	1	2	yes	—
472	#387	C₂²×C₇₃	1	2	yes	—
473	#387	C₂²×C₇₃	1	2	yes	—
474	#387	C₂²×C₇₃	1	2	yes	—
475	#387	C₂²×C₇₃	1	2	yes	—
476	#387	C₂²×C₇₃	1	2	yes	—
477	#387	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	#387	C₂²×C₇₃	1	2	yes	—
488	#385	C₂²×C₇₃	1	2	yes	—
489	#385	C₂²×C₇₃	1	2	yes	—
490	#385	C₂²×C₇₃	1	2	yes	—
491	#385	C₂²×C₇₃	1	2	yes	—
492	#385	C₂²×C₇₃	1	2	yes	—
493	#385	C₂²×C₇₃	1	2	yes	—
494	#380	C₂²×C₇₃	1	1	yes	characteristic
495	#380	C₂²×C₇₃	1	2	yes	—
496	#380	C₂²×C₇₃	1	2	yes	—
497	#380	C₂²×C₇₃	1	1	yes	characteristic
498	C₄×C₄⋊C₄	C₂²×C₇₃	1	1	yes	characteristic
499	C₄×C₄⋊C₄	C₂²×C₇₃	1	2	yes	—
500	C₄×C₄⋊C₄	C₂²×C₇₃	1	2	yes	—
501	C₄×C₄⋊C₄	C₂²×C₇₃	1	2	yes	—
502	C₄×C₄⋊C₄	C₂²×C₇₃	1	1	yes	characteristic
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×C₂²⋊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	C₂×#95	C₂²×C₇₃	1	2	yes	—
511	C₂²×Q₈	C₂³×C₇₃	1	1	yes	characteristic
512	C₂²×Q₈	C₂³×C₇₃	1	1	yes	characteristic
513	C₂³×C₄	C₂³×C₇₃	1	1	yes	characteristic
514	C₂³×C₄	C₂³×C₇₃	1	2	yes	—
515	C₂³×C₄	C₂³×C₇₃	1	2	yes	—
516	C₂³×C₄	C₂³×C₇₃	1	1	yes	characteristic
517	C₂³×C₄	C₂³×C₇₃	1	1	yes	characteristic
518	#125	—	2	8	no	—
519	#125	—	4	4	no	—
520	C₂²⋊Q₈	—	2	4	no	—
521	C₂²⋊Q₈	Q₈×C₇₃	1	8	yes	complemented
522	C₄×Q₈	—	4	2	no	—
523	C₄×Q₈	—	4	2	no	—
524	C₂×C₄⋊C₄	—	2	8	no	—
525	C₂×C₄⋊C₄	—	2	4	no	—
526	C₂×C₄⋊C₄	—	4	2	no	—
527	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
528	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
529	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
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	1	yes	characteristic
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	1	yes	characteristic
538	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
539	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
540	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
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	1	yes	characteristic
544	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
545	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
546	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
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	1	yes	characteristic
551	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
552	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
553	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
554	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
555	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
556	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
557	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
558	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
559	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
560	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
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×C₄²	—	4	2	no	—
566	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
567	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
568	C₂×C₄²	C₂³×C₇₃	1	2	yes	—
569	C₂×C₄²	C₂³×C₇₃	1	2	yes	—
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	1	yes	characteristic
577	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
578	#95	C₂³×C₇₃	1	2	yes	—
579	#95	C₂³×C₇₃	1	2	yes	—
580	#95	C₂³×C₇₃	1	2	yes	—
581	#95	C₂³×C₇₃	1	2	yes	—
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	2	yes	—
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	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	C₂⁴	C₂⁴×C₇₃	1	1	yes	characteristic
609	C₂×Q₈	—	2	2	no	—
610	C₂×Q₈	—	4	1	no	—
611	C₂×Q₈	—	4	1	no	—
612	C₂×Q₈	—	4	1	no	—
613	C₂×Q₈	—	4	1	no	—
614	C₂×Q₈	C₂×Q₈×C₇₃	1	4	yes	—
615	C₂²×C₄	—	2	2	no	—
616	C₂²×C₄	—	2	2	no	—
617	C₂²×C₄	—	2	2	no	—
618	C₂²×C₄	—	2	4	no	—
619	C₂²×C₄	—	2	4	no	—
620	C₂²×C₄	—	2	4	no	—
621	C₂²×C₄	—	4	1	no	—
622	C₂²×C₄	—	4	1	no	—
623	C₂²×C₄	—	4	1	no	—
624	C₂²×C₄	—	4	1	no	—
625	C₂²×C₄	—	4	2	no	—
626	C₂²×C₄	—	4	2	no	—
627	C₂²×C₄	—	4	2	no	—
628	C₂²×C₄	C₂×Q₈×C₇₃	1	4	yes	—
629	C₂²×C₄	#41×C₇₃	1	4	yes	—
630	C₂²×C₄	C₂⁴×C₇₃	1	2	yes	—
631	C₂²×C₄	C₂⁴×C₇₃	1	2	yes	—
632	C₂²×C₄	C₂⁴×C₇₃	1	2	yes	—
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	2	yes	—
637	C₂²×C₄	C₂⁴×C₇₃	1	2	yes	—
638	C₂²×C₄	C₂⁴×C₇₃	1	2	yes	—
639	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
640	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
641	C₂²×C₄	C₂⁴×C₇₃	1	2	yes	—
642	C₂²×C₄	C₂⁴×C₇₃	1	2	yes	—
643	C₂²×C₄	C₂⁴×C₇₃	1	2	yes	—
644	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
645	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
646	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
647	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
648	C₄⋊C₄	—	2	4	no	—
649	C₄⋊C₄	—	2	4	no	—
650	C₄⋊C₄	—	2	4	no	—
651	C₄⋊C₄	—	2	4	no	—
652	C₄⋊C₄	—	2	2	no	—
653	C₄⋊C₄	—	2	4	no	—
654	C₄⋊C₄	—	2	2	no	—
655	C₄⋊C₄	—	2	4	no	—
656	C₄⋊C₄	—	2	4	no	—
657	C₄⋊C₄	—	2	4	no	—
658	C₄⋊C₄	—	2	4	no	—
659	C₄⋊C₄	—	2	4	no	—
660	C₄⋊C₄	—	2	4	no	—
661	C₄⋊C₄	—	2	4	no	—
662	C₄⋊C₄	—	2	4	no	—
663	C₄⋊C₄	—	2	4	no	—
664	C₄⋊C₄	—	4	1	no	—
665	C₄⋊C₄	—	4	1	no	—
666	C₄⋊C₄	—	4	2	no	—
667	C₄⋊C₄	—	4	2	no	—
668	C₄⋊C₄	—	4	2	no	—
669	C₄⋊C₄	—	4	1	no	—
670	C₄⋊C₄	—	4	1	no	—
671	C₄⋊C₄	—	4	2	no	—
672	C₄⋊C₄	—	4	2	no	—
673	C₄⋊C₄	—	4	2	no	—
674	C₄⋊C₄	—	4	1	no	—
675	C₄⋊C₄	—	4	1	no	—
676	C₄⋊C₄	—	4	2	no	—
677	C₄⋊C₄	—	4	2	no	—
678	C₄⋊C₄	—	4	2	no	—
679	C₄⋊C₄	C₂×Q₈×C₇₃	1	4	yes	—
680	C₄⋊C₄	C₂×Q₈×C₇₃	1	8	yes	—
681	C₄⋊C₄	#41×C₇₃	1	4	yes	—
682	C₂²⋊C₄	—	2	4	no	—
683	C₂²⋊C₄	—	2	4	no	—
684	C₂²⋊C₄	—	2	4	no	—
685	C₂²⋊C₄	C₂×Q₈×C₇₃	1	8	yes	—
686	C₄²	—	2	4	no	—
687	C₄²	—	2	2	no	—
688	C₄²	—	2	2	no	—
689	C₄²	—	4	1	no	—
690	C₄²	—	4	1	no	—
691	C₄²	—	4	2	no	—
692	C₄²	—	4	2	no	—
693	C₄²	—	4	2	no	—
694	C₄²	—	4	2	no	—
695	C₄²	—	4	2	no	—
696	C₄²	—	4	2	no	—
697	C₄²	—	4	2	no	—
698	C₂³	—	2	1	no	—
699	C₂³	—	2	1	no	—
700	C₂³	—	2	1	no	—
701	C₂³	—	2	1	no	—
702	C₂³	C₂²×Q₈×C₇₃	1	2	yes	—
703	C₂³	C₂×#41×C₇₃	1	2	yes	—
704	C₂³	2₋¹⁺⁴×C₇₃	1	2	yes	—
705	C₂³	C₂⁵×C₇₃	1	1	yes	characteristic
706	Q₈	—	4	4	no	—
707	Q₈	—	4	4	no	—
708	C₂×C₄	—	2	8	no	—
709	C₂×C₄	—	2	2	no	—
710	C₂×C₄	—	2	2	no	—
711	C₂×C₄	—	2	1	no	—
712	C₂×C₄	—	2	1	no	—
713	C₂×C₄	—	2	1	no	—
714	C₂×C₄	—	2	1	no	—
715	C₂×C₄	—	2	1	no	—
716	C₂×C₄	—	2	2	no	—
717	C₂×C₄	—	2	1	no	—
718	C₂×C₄	—	2	1	no	—
719	C₂×C₄	—	2	1	no	—
720	C₂×C₄	—	2	2	no	—
721	C₂×C₄	—	2	1	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	1	no	—
727	C₂×C₄	—	2	2	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	2	no	—
740	C₂×C₄	—	2	2	no	—
741	C₂×C₄	—	2	2	no	—
742	C₂×C₄	—	2	2	no	—
743	C₂×C₄	—	2	2	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	—	4	4	no	—
755	C₂×C₄	—	4	4	no	—
756	C₂×C₄	—	4	8	no	—
757	C₂×C₄	—	8	4	no	—
758	C₂×C₄	C₂²×Q₈×C₇₃	1	4	yes	—
759	C₂×C₄	C₂²×Q₈×C₇₃	1	4	yes	—
760	C₂×C₄	C₂²×Q₈×C₇₃	1	2	yes	—
761	C₂×C₄	C₂²×Q₈×C₇₃	1	2	yes	—
762	C₂×C₄	C₂×#41×C₇₃	1	4	yes	—
763	C₂×C₄	C₂×#41×C₇₃	1	2	yes	—
764	C₂×C₄	C₂×#41×C₇₃	1	2	yes	—
765	C₂×C₄	C₂×#41×C₇₃	1	2	yes	—
766	C₂×C₄	H(5,𝔽₂)×C₇₃	1	2	yes	—
767	C₂²	—	2	2	no	—
768	C₂²	—	2	2	no	—
769	C₂²	—	2	2	no	—
770	C₂²	—	2	2	no	—
771	C₂²	—	2	2	no	—
772	C₂²	—	2	2	no	—
773	C₂²	#557×C₇₃	1	4	yes	—
774	C₂²	C₂³×Q₈×C₇₃	1	1	yes	characteristic
775	C₂²	C₂²×#41×C₇₃	1	1	yes	characteristic
776	C₂²	C₂²×#41×C₇₃	1	1	yes	characteristic
777	C₂²	C₂×H(5,𝔽₂)×C₇₃	1	1	yes	characteristic
778	C₂²	C₂×2₋¹⁺⁴×C₇₃	1	1	yes	characteristic
779	C₂²	#585×C₇₃	1	1	yes	characteristic
780	C₂²	#585×C₇₃	1	1	yes	characteristic
781	C₄	—	2	4	no	—
782	C₄	—	2	4	no	—
783	C₄	—	2	2	no	—
784	C₄	—	2	2	no	—
785	C₄	—	2	2	no	—
786	C₄	—	2	2	no	—
787	C₄	—	2	4	no	—
788	C₄	—	2	2	no	—
789	C₄	—	2	2	no	—
790	C₄	—	4	2	no	—
791	C₄	—	4	2	no	—
792	C₄	—	4	2	no	—
793	C₄	—	4	2	no	—
794	C₄	—	4	2	no	—
795	C₄	—	4	2	no	—
796	C₄	—	4	2	no	—
797	C₄	—	4	2	no	—
798	C₄	—	4	2	no	—
799	C₂	—	2	4	no	—
800	C₂	C₇₃×#3475	1	1	yes	characteristic
801	C₂	C₂×#557×C₇₃	1	1	yes	characteristic
802	C₂	Q₈×#41×C₇₃	1	1	yes	characteristic
803	C₂	C₇₃×#3492	1	1	yes	characteristic
804	C₂	C₇₃×#3501	1	1	yes	characteristic
805	C₂	C₇₃×#3505	1	1	yes	characteristic
806	C₂	C₇₃×#3553	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₇₃	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₇₃
prime radical	C₂⁴×C₇₃	C₂⁴
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×#2809	C₂	semidirect
2. C₇₃×#2806	C₂	semidirect
3. C₇₃×#2805	C₂	semidirect
4. C₇₃×#2726	C₂	semidirect
5. C₇₃×#2590	C₂	semidirect
6. C₇₃×#2585	C₂	semidirect
7. C₇₃×#2585	C₂	semidirect
12. C₇₃×#2462	C₂	semidirect
13. C₇₃×#2453	C₂	semidirect
14. C₇₃×#2370	C₂	semidirect
117. C₂²⋊Q₈×C₇₃	Q₈	semidirect
395. #59866	C₇₃	direct (N × H)
404. #2809	C₂×C₇₃	semidirect
405. #2806	C₂×C₇₃	semidirect
406. #2805	C₂×C₇₃	semidirect
407. #2726	C₂×C₇₃	semidirect
408. #2590	C₂×C₇₃	semidirect
409. #2585	C₂×C₇₃	semidirect
410. #2585	C₂×C₇₃	semidirect
415. #2462	C₂×C₇₃	semidirect
416. #2453	C₂×C₇₃	semidirect
417. #2370	C₂×C₇₃	semidirect
423. C₇₃	#59866	direct (N × H)
521. C₂²⋊Q₈	Q₈×C₇₃	semidirect

Maximal subgroups

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

subgroup	index
C₇₃×#2809	2
C₇₃×#2806	2
C₇₃×#2805	2
C₇₃×#2726	2
C₇₃×#2590	2
C₇₃×#2585	2
C₇₃×#2583	2
C₇₃×#2569	2
C₇₃×#2473	2
C₇₃×#2462	2
C₇₃×#2453	2
C₇₃×#2370	2
C₇₃×#2368	2
C₇₃×#2345	2
C₄×C₂²⋊Q₈×C₇₃	2
C₂×#389×C₇₃	2
#59866	73

Subgroups — C73×#59866 #32969270

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₃×#59866 #32969270