Subgroups — C₇₃×#59624 #32969028

Order 18688.

2154 conjugacy classes of subgroups.

The subgroup lattice has 908 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇₃×#2807	C₂	1	1	yes	maximal, characteristic, complemented
2	C₇₃×#2796	C₂	1	2	yes	maximal, complemented
3	C₇₃×#2712	C₂	1	1	yes	maximal, characteristic, complemented
4	C₇₃×#2602	C₂	1	2	yes	maximal, complemented
5	C₇₃×#2595	C₂	1	2	yes	maximal, complemented
6	C₇₃×#2589	C₂	1	2	yes	maximal, complemented
7	C₇₃×#2580	C₂	1	2	yes	maximal, complemented
8	C₇₃×#2539	C₂	1	1	yes	maximal, characteristic
9	C₇₃×#2517	C₂	1	1	yes	maximal, characteristic, complemented
10	C₇₃×#2488	C₂	1	2	yes	maximal, complemented
11	C₇₃×#2482	C₂	1	1	yes	maximal, characteristic, complemented
12	C₇₃×#2472	C₂	1	2	yes	maximal, complemented
13	C₇₃×#2455	C₂	1	1	yes	maximal, characteristic, complemented
14	C₇₃×#2443	C₂	1	2	yes	maximal, complemented
15	C₇₃×#2367	C₂	1	2	yes	maximal, complemented
16	C₇₃×#2360	C₂	1	2	yes	maximal, complemented
17	C₇₃×#2359	C₂	1	2	yes	maximal, complemented
18	C₄×#120×C₇₃	C₂	1	2	yes	maximal, complemented
19	C₂×#385×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂⁴×C₄×C₇₃	C₂²	1	1	yes	characteristic
21	C₂×#124×C₇₃	C₂²	1	2	yes	—
22	C₂×#123×C₇₃	C₂²	1	2	yes	—
23	C₂×#123×C₇₃	C₂²	1	2	yes	complemented
24	C₂×C₂²⋊Q₈×C₇₃	C₂²	1	2	yes	—
25	C₂×#121×C₇₃	C₂²	1	1	yes	characteristic
26	C₂×#120×C₇₃	C₂²	1	2	yes	—
27	C₂×C₄×Q₈×C₇₃	C₂²	1	2	yes	complemented
28	C₂×C₄×D₄×C₇₃	C₂²	1	2	yes	—
29	C₂×C₄×D₄×C₇₃	C₂²	1	2	yes	—
30	C₂×C₄×D₄×C₇₃	C₂²	1	2	yes	—
31	C₂×#117×C₇₃	C₂²	1	1	yes	characteristic
32	C₂²×C₄⋊C₄×C₇₃	C₂²	1	2	yes	—
33	C₂²×C₂²⋊C₄×C₇₃	C₂²	1	1	yes	characteristic
34	C₂²×C₂²⋊C₄×C₇₃	C₂²	1	1	yes	characteristic
35	#400×C₇₃	C₂²	1	2	yes	complemented
36	#400×C₇₃	C₂²	1	2	yes	complemented
37	#399×C₇₃	C₂²	1	1	yes	characteristic
38	#399×C₇₃	C₂²	1	1	yes	characteristic
39	#399×C₇₃	C₂²	1	1	yes	characteristic
40	#399×C₇₃	C₂²	1	1	yes	characteristic
41	#399×C₇₃	C₂²	1	2	yes	complemented
42	#398×C₇₃	C₂²	1	2	yes	complemented
43	#397×C₇₃	C₂²	1	1	yes	characteristic
44	#397×C₇₃	C₂²	1	2	yes	—
45	#397×C₇₃	C₂²	1	1	yes	characteristic
46	#397×C₇₃	C₂²	1	2	yes	complemented
47	#397×C₇₃	C₂²	1	2	yes	complemented
48	#394×C₇₃	C₂²	1	2	yes	—
49	#394×C₇₃	C₂²	1	2	yes	—
50	#394×C₇₃	C₂²	1	2	yes	complemented
51	#393×C₇₃	C₂²	1	2	yes	—
52	#393×C₇₃	C₂²	1	2	yes	complemented
53	#392×C₇₃	C₂²	1	1	yes	characteristic
54	#392×C₇₃	C₂²	1	1	yes	characteristic
55	#391×C₇₃	C₂²	1	2	yes	complemented
56	#391×C₇₃	C₂²	1	2	yes	complemented
57	#390×C₇₃	C₂²	1	2	yes	—
58	#390×C₇₃	C₂²	1	2	yes	—
59	#390×C₇₃	C₂²	1	2	yes	—
60	#389×C₇₃	C₂²	1	2	yes	complemented
61	#389×C₇₃	C₂²	1	2	yes	complemented
62	#389×C₇₃	C₂²	1	2	yes	complemented
63	#389×C₇₃	C₂²	1	2	yes	complemented
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	complemented
69	#388×C₇₃	C₂²	1	2	yes	complemented
70	#388×C₇₃	C₂²	1	2	yes	complemented
71	#388×C₇₃	C₂²	1	2	yes	complemented
72	#388×C₇₃	C₂²	1	2	yes	complemented
73	#387×C₇₃	C₂²	1	2	yes	complemented
74	#387×C₇₃	C₂²	1	2	yes	complemented
75	#387×C₇₃	C₂²	1	2	yes	complemented
76	#387×C₇₃	C₂²	1	2	yes	complemented
77	#387×C₇₃	C₂²	1	2	yes	complemented
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	2	yes	—
82	#386×C₇₃	C₂²	1	2	yes	—
83	#385×C₇₃	C₂²	1	2	yes	—
84	#385×C₇₃	C₂²	1	1	yes	characteristic
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	2	yes	—
90	#385×C₇₃	C₂²	1	1	yes	characteristic
91	#385×C₇₃	C₂²	1	2	yes	—
92	#385×C₇₃	C₂²	1	2	yes	—
93	#385×C₇₃	C₂²	1	2	yes	complemented
94	#385×C₇₃	C₂²	1	2	yes	complemented
95	#382×C₇₃	C₂²	1	2	yes	complemented
96	#381×C₇₃	C₂²	1	1	yes	characteristic
97	#379×C₇₃	C₂²	1	2	yes	—
98	C₄×C₄⋊C₄×C₇₃	C₂²	1	2	yes	complemented
99	C₄×C₄⋊C₄×C₇₃	C₂²	1	2	yes	complemented
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	1	yes	characteristic
104	C₄×C₂²⋊C₄×C₇₃	C₂²	1	2	yes	—
105	C₄×C₂²⋊C₄×C₇₃	C₂²	1	2	yes	complemented
106	C₂×#95×C₇₃	C₂²	1	2	yes	—
107	C₂⁵×C₇₃	C₂³	1	1	yes	characteristic
108	C₂²×Q₈×C₇₃	C₂³	1	2	yes	—
109	C₂²×D₄×C₇₃	C₂³	1	2	yes	—
110	C₂²×D₄×C₇₃	C₂³	1	2	yes	—
111	C₂²×D₄×C₇₃	C₂³	1	2	yes	—
112	C₂²×D₄×C₇₃	C₂³	1	1	yes	characteristic
113	C₂³×C₄×C₇₃	—	4	4	no	—
114	C₂³×C₄×C₇₃	—	4	2	no	—
115	C₂³×C₄×C₇₃	C₂³	1	1	yes	characteristic
116	C₂³×C₄×C₇₃	C₂³	1	1	yes	characteristic
117	C₂³×C₄×C₇₃	C₂³	1	2	yes	—
118	C₂³×C₄×C₇₃	C₂³	1	2	yes	—
119	C₂³×C₄×C₇₃	C₂³	1	2	yes	—
120	C₂³×C₄×C₇₃	C₂³	1	1	yes	characteristic
121	C₂³×C₄×C₇₃	C₂³	1	2	yes	—
122	C₂³×C₄×C₇₃	C₂³	1	1	yes	characteristic
123	#124×C₇₃	—	2	8	no	—
124	#123×C₇₃	—	2	8	no	—
125	#123×C₇₃	—	4	4	no	—
126	C₂²⋊Q₈×C₇₃	—	2	8	no	—
127	#121×C₇₃	—	4	2	no	—
128	#120×C₇₃	—	2	8	no	—
129	C₄×Q₈×C₇₃	—	4	4	no	—
130	C₄×D₄×C₇₃	—	4	4	no	—
131	C₄×D₄×C₇₃	—	4	4	no	—
132	C₄×D₄×C₇₃	—	4	4	no	—
133	#117×C₇₃	—	4	2	no	—
134	C₂×C₄⋊C₄×C₇₃	—	4	4	no	—
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	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	1	yes	characteristic
151	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
152	C₂×C₂²⋊C₄×C₇₃	—	2	4	no	—
153	C₂×C₂²⋊C₄×C₇₃	—	4	2	no	—
154	C₂×C₂²⋊C₄×C₇₃	C₂³	1	2	yes	—
155	C₂×C₂²⋊C₄×C₇₃	C₂³	1	2	yes	—
156	C₂×C₂²⋊C₄×C₇₃	C₂³	1	2	yes	—
157	C₂×C₂²⋊C₄×C₇₃	C₂³	1	2	yes	—
158	C₂×C₂²⋊C₄×C₇₃	C₂³	1	2	yes	—
159	C₂×C₂²⋊C₄×C₇₃	C₂³	1	2	yes	—
160	C₂×C₂²⋊C₄×C₇₃	C₂³	1	2	yes	—
161	C₂×C₂²⋊C₄×C₇₃	C₂³	1	2	yes	—
162	C₂×C₂²⋊C₄×C₇₃	C₂³	1	2	yes	—
163	C₂×C₂²⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
170	C₂×C₂²⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
171	C₂×C₂²⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
172	C₂×C₂²⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
173	C₂×C₂²⋊C₄×C₇₃	C₂³	1	2	yes	—
174	C₂×C₂²⋊C₄×C₇₃	C₂³	1	2	yes	—
175	C₂×C₂²⋊C₄×C₇₃	C₂³	1	2	yes	—
176	C₂×C₂²⋊C₄×C₇₃	C₂³	1	2	yes	—
177	C₂×C₂²⋊C₄×C₇₃	C₂³	1	2	yes	—
178	C₂×C₂²⋊C₄×C₇₃	C₂³	1	2	yes	—
179	C₂×C₂²⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
180	C₂×C₄²×C₇₃	C₂³	1	2	yes	—
181	C₂×C₄²×C₇₃	C₂³	1	2	yes	—
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	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	1	yes	characteristic
196	#95×C₇₃	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
201	#95×C₇₃	C₂³	1	2	yes	—
202	#95×C₇₃	C₂³	1	1	yes	characteristic
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	—	2	2	no	—
211	C₂⁴×C₇₃	—	2	2	no	—
212	C₂⁴×C₇₃	—	2	2	no	—
213	C₂⁴×C₇₃	—	2	4	no	—
214	C₂⁴×C₇₃	—	4	2	no	—
215	C₂⁴×C₇₃	C₂⁴	1	2	yes	—
216	C₂⁴×C₇₃	C₂⁴	1	1	yes	characteristic
217	C₂⁴×C₇₃	C₂⁴	1	1	yes	characteristic
218	C₂⁴×C₇₃	C₂⁴	1	1	yes	characteristic
219	C₂×Q₈×C₇₃	—	2	4	no	—
220	C₂×Q₈×C₇₃	—	2	4	no	—
221	C₂×Q₈×C₇₃	—	4	2	no	—
222	C₂×D₄×C₇₃	—	2	4	no	—
223	C₂×D₄×C₇₃	—	2	4	no	—
224	C₂×D₄×C₇₃	—	2	4	no	—
225	C₂×D₄×C₇₃	—	2	4	no	—
226	C₂×D₄×C₇₃	—	2	4	no	—
227	C₂×D₄×C₇₃	—	2	4	no	—
228	C₂×D₄×C₇₃	—	2	4	no	—
229	C₂×D₄×C₇₃	—	4	2	no	—
230	C₂×D₄×C₇₃	—	4	2	no	—
231	C₂×D₄×C₇₃	—	4	1	no	—
232	C₂×D₄×C₇₃	—	4	2	no	—
233	C₂²×C₄×C₇₃	—	2	4	no	—
234	C₂²×C₄×C₇₃	—	2	4	no	—
235	C₂²×C₄×C₇₃	—	2	2	no	—
236	C₂²×C₄×C₇₃	—	2	4	no	—
237	C₂²×C₄×C₇₃	—	2	2	no	—
238	C₂²×C₄×C₇₃	—	2	4	no	—
239	C₂²×C₄×C₇₃	—	2	4	no	—
240	C₂²×C₄×C₇₃	—	2	4	no	—
241	C₂²×C₄×C₇₃	—	2	4	no	—
242	C₂²×C₄×C₇₃	—	2	4	no	—
243	C₂²×C₄×C₇₃	—	4	2	no	—
244	C₂²×C₄×C₇₃	—	4	1	no	—
245	C₂²×C₄×C₇₃	—	4	2	no	—
246	C₂²×C₄×C₇₃	—	4	2	no	—
247	C₂²×C₄×C₇₃	—	4	2	no	—
248	C₂²×C₄×C₇₃	—	4	1	no	—
249	C₂²×C₄×C₇₃	—	4	2	no	—
250	C₂²×C₄×C₇₃	—	4	2	no	—
251	C₂²×C₄×C₇₃	—	4	2	no	—
252	C₂²×C₄×C₇₃	—	4	2	no	—
253	C₂²×C₄×C₇₃	—	4	16	no	—
254	C₂²×C₄×C₇₃	C₂⁴	1	2	yes	—
255	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
256	C₂²×C₄×C₇₃	C₂⁴	1	2	yes	—
257	C₂²×C₄×C₇₃	C₂⁴	1	2	yes	—
258	C₂²×C₄×C₇₃	C₂⁴	1	2	yes	—
259	C₂²×C₄×C₇₃	C₂⁴	1	2	yes	—
260	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
261	C₂²×C₄×C₇₃	C₂⁴	1	2	yes	—
262	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
263	C₂²×C₄×C₇₃	C₂⁴	1	2	yes	—
264	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
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	C₄⋊C₄×C₇₃	—	2	4	no	—
270	C₄⋊C₄×C₇₃	—	2	4	no	—
271	C₄⋊C₄×C₇₃	—	2	4	no	—
272	C₄⋊C₄×C₇₃	—	2	4	no	—
273	C₄⋊C₄×C₇₃	—	2	4	no	—
274	C₄⋊C₄×C₇₃	—	2	4	no	—
275	C₄⋊C₄×C₇₃	—	2	4	no	—
276	C₄⋊C₄×C₇₃	—	2	4	no	—
277	C₄⋊C₄×C₇₃	—	4	2	no	—
278	C₄⋊C₄×C₇₃	—	4	2	no	—
279	C₄⋊C₄×C₇₃	—	4	1	no	—
280	C₄⋊C₄×C₇₃	—	4	1	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	1	no	—
285	C₄⋊C₄×C₇₃	—	4	2	no	—
286	C₂²⋊C₄×C₇₃	—	2	2	no	—
287	C₂²⋊C₄×C₇₃	—	2	4	no	—
288	C₂²⋊C₄×C₇₃	—	2	4	no	—
289	C₂²⋊C₄×C₇₃	—	2	4	no	—
290	C₂²⋊C₄×C₇₃	—	2	4	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	—	4	1	no	—
300	C₂²⋊C₄×C₇₃	—	4	1	no	—
301	C₂²⋊C₄×C₇₃	—	4	1	no	—
302	C₂²⋊C₄×C₇₃	—	4	1	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	2	no	—
309	C₂²⋊C₄×C₇₃	—	4	2	no	—
310	C₂²⋊C₄×C₇₃	#41	1	4	yes	—
311	C₂²⋊C₄×C₇₃	#41	1	8	yes	—
312	C₄²×C₇₃	—	2	4	no	—
313	C₄²×C₇₃	—	2	4	no	—
314	C₄²×C₇₃	—	4	2	no	—
315	C₄²×C₇₃	—	4	2	no	—
316	C₄²×C₇₃	—	4	2	no	—
317	C₄²×C₇₃	—	4	2	no	—
318	C₄²×C₇₃	—	4	2	no	—
319	C₂³×C₇₃	—	2	1	no	—
320	C₂³×C₇₃	—	2	2	no	—
321	C₂³×C₇₃	—	2	1	no	—
322	C₂³×C₇₃	—	2	8	no	—
323	C₂³×C₇₃	—	2	1	no	—
324	C₂³×C₇₃	—	2	2	no	—
325	C₂³×C₇₃	—	2	2	no	—
326	C₂³×C₇₃	—	2	1	no	—
327	C₂³×C₇₃	—	2	1	no	—
328	C₂³×C₇₃	—	2	2	no	—
329	C₂³×C₇₃	—	2	2	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	2	no	—
337	C₂³×C₇₃	—	2	2	no	—
338	C₂³×C₇₃	—	4	8	no	—
339	C₂³×C₇₃	—	4	8	no	—
340	C₂³×C₇₃	—	4	4	no	—
341	C₂³×C₇₃	—	4	4	no	—
342	C₂³×C₇₃	C₂×#41	1	2	yes	—
343	C₂³×C₇₃	C₂×#41	1	4	yes	—
344	C₂³×C₇₃	H(5,𝔽₂)	1	2	yes	—
345	C₂³×C₇₃	2₋¹⁺⁴	1	2	yes	—
346	C₂³×C₇₃	C₂⁵	1	1	yes	characteristic
347	Q₈×C₇₃	—	4	8	no	—
348	D₄×C₇₃	—	4	8	no	—
349	D₄×C₇₃	—	4	8	no	—
350	D₄×C₇₃	—	4	8	no	—
351	D₄×C₇₃	—	8	2	no	—
352	C₂×C₄×C₇₃	—	2	2	no	—
353	C₂×C₄×C₇₃	—	2	2	no	—
354	C₂×C₄×C₇₃	—	2	2	no	—
355	C₂×C₄×C₇₃	—	2	2	no	—
356	C₂×C₄×C₇₃	—	2	2	no	—
357	C₂×C₄×C₇₃	—	2	2	no	—
358	C₂×C₄×C₇₃	—	2	2	no	—
359	C₂×C₄×C₇₃	—	2	2	no	—
360	C₂×C₄×C₇₃	—	2	2	no	—
361	C₂×C₄×C₇₃	—	2	2	no	—
362	C₂×C₄×C₇₃	—	2	2	no	—
363	C₂×C₄×C₇₃	—	2	2	no	—
364	C₂×C₄×C₇₃	—	2	2	no	—
365	C₂×C₄×C₇₃	—	2	2	no	—
366	C₂×C₄×C₇₃	—	2	2	no	—
367	C₂×C₄×C₇₃	—	2	2	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	1	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	2	no	—
377	C₂×C₄×C₇₃	—	2	2	no	—
378	C₂×C₄×C₇₃	—	2	1	no	—
379	C₂×C₄×C₇₃	—	2	2	no	—
380	C₂×C₄×C₇₃	—	2	1	no	—
381	C₂×C₄×C₇₃	—	2	2	no	—
382	C₂×C₄×C₇₃	—	2	1	no	—
383	C₂×C₄×C₇₃	—	2	2	no	—
384	C₂×C₄×C₇₃	—	2	2	no	—
385	C₂×C₄×C₇₃	—	2	2	no	—
386	C₂×C₄×C₇₃	—	2	2	no	—
387	C₂×C₄×C₇₃	—	2	2	no	—
388	C₂×C₄×C₇₃	—	2	2	no	—
389	C₂×C₄×C₇₃	—	4	4	no	—
390	C₂×C₄×C₇₃	—	4	8	no	—
391	C₂×C₄×C₇₃	—	4	8	no	—
392	C₂×C₄×C₇₃	—	4	8	no	—
393	C₂×C₄×C₇₃	—	4	4	no	—
394	C₂×C₄×C₇₃	—	4	4	no	—
395	C₂×C₄×C₇₃	—	8	4	no	—
396	C₂×C₄×C₇₃	—	8	2	no	—
397	C₂×C₄×C₇₃	C₂×#41	1	4	yes	—
398	C₂×C₄×C₇₃	C₂×#41	1	4	yes	—
399	C₂×C₄×C₇₃	C₂×#41	1	4	yes	—
400	C₂×C₄×C₇₃	H(5,𝔽₂)	1	4	yes	—
401	C₂²×C₇₃	—	2	4	no	—
402	C₂²×C₇₃	—	2	2	no	—
403	C₂²×C₇₃	—	2	4	no	—
404	C₂²×C₇₃	—	2	2	no	—
405	C₂²×C₇₃	—	2	4	no	—
406	C₂²×C₇₃	—	2	2	no	—
407	C₂²×C₇₃	—	2	2	no	—
408	C₂²×C₇₃	—	2	4	no	—
409	C₂²×C₇₃	—	4	16	no	—
410	C₂²×C₇₃	—	4	1	no	—
411	C₂²×C₇₃	—	4	1	no	—
412	C₂²×C₇₃	—	4	2	no	—
413	C₂²×C₇₃	—	4	2	no	—
414	C₂²×C₇₃	—	4	1	no	—
415	C₂²×C₇₃	—	4	1	no	—
416	C₂²×C₇₃	—	4	2	no	—
417	C₂²×C₇₃	—	4	2	no	—
418	C₂²×C₇₃	—	4	2	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	#559	1	4	yes	—
424	C₂²×C₇₃	C₂²×#41	1	2	yes	—
425	C₂²×C₇₃	C₂²×#41	1	1	yes	characteristic
426	C₂²×C₇₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
427	C₂²×C₇₃	C₂×H(5,𝔽₂)	1	2	yes	—
428	C₂²×C₇₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
429	C₄×C₇₃	—	2	4	no	—
430	C₄×C₇₃	—	2	4	no	—
431	C₄×C₇₃	—	2	4	no	—
432	C₄×C₇₃	—	2	4	no	—
433	C₄×C₇₃	—	4	1	no	—
434	C₄×C₇₃	—	4	1	no	—
435	C₄×C₇₃	—	4	2	no	—
436	C₄×C₇₃	—	4	2	no	—
437	C₄×C₇₃	—	4	2	no	—
438	C₄×C₇₃	—	4	2	no	—
439	C₄×C₇₃	—	4	2	no	—
440	C₄×C₇₃	—	4	2	no	—
441	C₄×C₇₃	—	4	2	no	—
442	C₄×C₇₃	—	4	1	no	—
443	C₄×C₇₃	—	4	1	no	—
444	#59624	C₇₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
445	C₂×C₇₃	—	2	4	no	—
446	C₂×C₇₃	—	4	2	no	—
447	C₂×C₇₃	—	4	2	no	—
448	C₂×C₇₃	—	8	2	no	—
449	C₂×C₇₃	C₂×#559	1	1	yes	characteristic
450	C₂×C₇₃	#3481	1	2	yes	—
451	C₂×C₇₃	#3492	1	1	yes	characteristic
452	C₂×C₇₃	#3520	1	2	yes	—
453	C₂×C₇₃	#3532	1	1	yes	characteristic
454	#2807	C₂×C₇₃	1	1	yes	characteristic, complemented
455	#2796	C₂×C₇₃	1	2	yes	complemented
456	#2712	C₂×C₇₃	1	1	yes	characteristic, complemented
457	#2602	C₂×C₇₃	1	2	yes	complemented
458	#2595	C₂×C₇₃	1	2	yes	complemented
459	#2589	C₂×C₇₃	1	2	yes	complemented
460	#2580	C₂×C₇₃	1	2	yes	complemented
461	#2539	C₂×C₇₃	1	1	yes	characteristic
462	#2517	C₂×C₇₃	1	1	yes	characteristic, complemented
463	#2488	C₂×C₇₃	1	2	yes	complemented
464	#2482	C₂×C₇₃	1	1	yes	characteristic, complemented
465	#2472	C₂×C₇₃	1	2	yes	complemented
466	#2455	C₂×C₇₃	1	1	yes	characteristic, complemented
467	#2443	C₂×C₇₃	1	2	yes	complemented
468	#2367	C₂×C₇₃	1	2	yes	complemented
469	#2360	C₂×C₇₃	1	2	yes	complemented
470	#2359	C₂×C₇₃	1	2	yes	complemented
471	C₄×#120	C₂×C₇₃	1	2	yes	complemented
472	C₂×#385	C₂×C₇₃	1	1	yes	characteristic, complemented
473	C₇₃	#59624	1	1	yes	characteristic, direct product factor, Sylow
474	C₂⁴×C₄	C₂²×C₇₃	1	1	yes	characteristic
475	C₂×#124	C₂²×C₇₃	1	2	yes	—
476	C₂×#123	C₂²×C₇₃	1	2	yes	—
477	C₂×#123	C₂²×C₇₃	1	2	yes	complemented
478	C₂×C₂²⋊Q₈	C₂²×C₇₃	1	2	yes	—
479	C₂×#121	C₂²×C₇₃	1	1	yes	characteristic
480	C₂×#120	C₂²×C₇₃	1	2	yes	—
481	C₂×C₄×Q₈	C₂²×C₇₃	1	2	yes	complemented
482	C₂×C₄×D₄	C₂²×C₇₃	1	2	yes	—
483	C₂×C₄×D₄	C₂²×C₇₃	1	2	yes	—
484	C₂×C₄×D₄	C₂²×C₇₃	1	2	yes	—
485	C₂×#117	C₂²×C₇₃	1	1	yes	characteristic
486	C₂²×C₄⋊C₄	C₂²×C₇₃	1	2	yes	—
487	C₂²×C₂²⋊C₄	C₂²×C₇₃	1	1	yes	characteristic
488	C₂²×C₂²⋊C₄	C₂²×C₇₃	1	1	yes	characteristic
489	#400	C₂²×C₇₃	1	2	yes	complemented
490	#400	C₂²×C₇₃	1	2	yes	complemented
491	#399	C₂²×C₇₃	1	1	yes	characteristic
492	#399	C₂²×C₇₃	1	1	yes	characteristic
493	#399	C₂²×C₇₃	1	1	yes	characteristic
494	#399	C₂²×C₇₃	1	1	yes	characteristic
495	#399	C₂²×C₇₃	1	2	yes	complemented
496	#398	C₂²×C₇₃	1	2	yes	complemented
497	#397	C₂²×C₇₃	1	1	yes	characteristic
498	#397	C₂²×C₇₃	1	1	yes	characteristic
499	#397	C₂²×C₇₃	1	2	yes	—
500	#397	C₂²×C₇₃	1	2	yes	complemented
501	#397	C₂²×C₇₃	1	2	yes	complemented
502	#394	C₂²×C₇₃	1	2	yes	—
503	#394	C₂²×C₇₃	1	2	yes	—
504	#394	C₂²×C₇₃	1	2	yes	complemented
505	#393	C₂²×C₇₃	1	2	yes	—
506	#393	C₂²×C₇₃	1	2	yes	complemented
507	#392	C₂²×C₇₃	1	1	yes	characteristic
508	#392	C₂²×C₇₃	1	1	yes	characteristic
509	#391	C₂²×C₇₃	1	2	yes	complemented
510	#391	C₂²×C₇₃	1	2	yes	complemented
511	#390	C₂²×C₇₃	1	2	yes	—
512	#390	C₂²×C₇₃	1	2	yes	—
513	#390	C₂²×C₇₃	1	2	yes	—
514	#389	C₂²×C₇₃	1	2	yes	complemented
515	#389	C₂²×C₇₃	1	2	yes	complemented
516	#389	C₂²×C₇₃	1	2	yes	complemented
517	#389	C₂²×C₇₃	1	2	yes	complemented
518	#388	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	complemented
523	#388	C₂²×C₇₃	1	2	yes	complemented
524	#388	C₂²×C₇₃	1	2	yes	complemented
525	#388	C₂²×C₇₃	1	2	yes	complemented
526	#388	C₂²×C₇₃	1	2	yes	complemented
527	#387	C₂²×C₇₃	1	2	yes	complemented
528	#387	C₂²×C₇₃	1	2	yes	complemented
529	#387	C₂²×C₇₃	1	2	yes	complemented
530	#387	C₂²×C₇₃	1	2	yes	complemented
531	#387	C₂²×C₇₃	1	2	yes	complemented
532	#386	C₂²×C₇₃	1	2	yes	—
533	#386	C₂²×C₇₃	1	2	yes	—
534	#386	C₂²×C₇₃	1	2	yes	—
535	#386	C₂²×C₇₃	1	2	yes	—
536	#386	C₂²×C₇₃	1	2	yes	—
537	#385	C₂²×C₇₃	1	2	yes	—
538	#385	C₂²×C₇₃	1	2	yes	—
539	#385	C₂²×C₇₃	1	2	yes	—
540	#385	C₂²×C₇₃	1	2	yes	—
541	#385	C₂²×C₇₃	1	2	yes	—
542	#385	C₂²×C₇₃	1	1	yes	characteristic
543	#385	C₂²×C₇₃	1	1	yes	characteristic
544	#385	C₂²×C₇₃	1	1	yes	characteristic
545	#385	C₂²×C₇₃	1	1	yes	characteristic
546	#385	C₂²×C₇₃	1	2	yes	—
547	#385	C₂²×C₇₃	1	2	yes	complemented
548	#385	C₂²×C₇₃	1	2	yes	complemented
549	#382	C₂²×C₇₃	1	2	yes	complemented
550	#381	C₂²×C₇₃	1	1	yes	characteristic
551	#379	C₂²×C₇₃	1	2	yes	—
552	C₄×C₄⋊C₄	C₂²×C₇₃	1	2	yes	complemented
553	C₄×C₄⋊C₄	C₂²×C₇₃	1	2	yes	complemented
554	C₄×C₂²⋊C₄	C₂²×C₇₃	1	2	yes	—
555	C₄×C₂²⋊C₄	C₂²×C₇₃	1	2	yes	—
556	C₄×C₂²⋊C₄	C₂²×C₇₃	1	1	yes	characteristic
557	C₄×C₂²⋊C₄	C₂²×C₇₃	1	2	yes	—
558	C₄×C₂²⋊C₄	C₂²×C₇₃	1	2	yes	—
559	C₄×C₂²⋊C₄	C₂²×C₇₃	1	2	yes	complemented
560	C₂×#95	C₂²×C₇₃	1	2	yes	—
561	C₂⁵	C₂³×C₇₃	1	1	yes	characteristic
562	C₂²×Q₈	C₂³×C₇₃	1	2	yes	—
563	C₂²×D₄	C₂³×C₇₃	1	2	yes	—
564	C₂²×D₄	C₂³×C₇₃	1	2	yes	—
565	C₂²×D₄	C₂³×C₇₃	1	2	yes	—
566	C₂²×D₄	C₂³×C₇₃	1	1	yes	characteristic
567	C₂³×C₄	—	4	4	no	—
568	C₂³×C₄	—	4	2	no	—
569	C₂³×C₄	C₂³×C₇₃	1	1	yes	characteristic
570	C₂³×C₄	C₂³×C₇₃	1	2	yes	—
571	C₂³×C₄	C₂³×C₇₃	1	2	yes	—
572	C₂³×C₄	C₂³×C₇₃	1	1	yes	characteristic
573	C₂³×C₄	C₂³×C₇₃	1	1	yes	characteristic
574	C₂³×C₄	C₂³×C₇₃	1	2	yes	—
575	C₂³×C₄	C₂³×C₇₃	1	2	yes	—
576	C₂³×C₄	C₂³×C₇₃	1	1	yes	characteristic
577	#124	—	2	8	no	—
578	#123	—	2	8	no	—
579	#123	—	4	4	no	—
580	C₂²⋊Q₈	—	2	8	no	—
581	#121	—	4	2	no	—
582	#120	—	2	8	no	—
583	C₄×Q₈	—	4	4	no	—
584	C₄×D₄	—	4	4	no	—
585	C₄×D₄	—	4	4	no	—
586	C₄×D₄	—	4	4	no	—
587	#117	—	4	2	no	—
588	C₂×C₄⋊C₄	—	4	4	no	—
589	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
590	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
591	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
592	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
593	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
594	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
595	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
596	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
597	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
598	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
599	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
600	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
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	1	yes	characteristic
605	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
606	C₂×C₂²⋊C₄	—	2	4	no	—
607	C₂×C₂²⋊C₄	—	4	2	no	—
608	C₂×C₂²⋊C₄	C₂³×C₇₃	1	2	yes	—
609	C₂×C₂²⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
610	C₂×C₂²⋊C₄	C₂³×C₇₃	1	2	yes	—
611	C₂×C₂²⋊C₄	C₂³×C₇₃	1	2	yes	—
612	C₂×C₂²⋊C₄	C₂³×C₇₃	1	2	yes	—
613	C₂×C₂²⋊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	2	yes	—
621	C₂×C₂²⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
622	C₂×C₂²⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
623	C₂×C₂²⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
624	C₂×C₂²⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
625	C₂×C₂²⋊C₄	C₂³×C₇₃	1	2	yes	—
626	C₂×C₂²⋊C₄	C₂³×C₇₃	1	2	yes	—
627	C₂×C₂²⋊C₄	C₂³×C₇₃	1	2	yes	—
628	C₂×C₂²⋊C₄	C₂³×C₇₃	1	2	yes	—
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	1	yes	characteristic
633	C₂×C₂²⋊C₄	C₂³×C₇₃	1	2	yes	—
634	C₂×C₄²	C₂³×C₇₃	1	2	yes	—
635	C₂×C₄²	C₂³×C₇₃	1	2	yes	—
636	C₂×C₄²	C₂³×C₇₃	1	2	yes	—
637	C₂×C₄²	C₂³×C₇₃	1	2	yes	—
638	C₂×C₄²	C₂³×C₇₃	1	2	yes	—
639	C₂×C₄²	C₂³×C₇₃	1	2	yes	—
640	C₂×C₄²	C₂³×C₇₃	1	2	yes	—
641	#95	C₂³×C₇₃	1	2	yes	—
642	#95	C₂³×C₇₃	1	2	yes	—
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	1	yes	characteristic
654	#95	C₂³×C₇₃	1	1	yes	characteristic
655	#95	C₂³×C₇₃	1	2	yes	—
656	#95	C₂³×C₇₃	1	2	yes	—
657	#95	C₂³×C₇₃	1	1	yes	characteristic
658	#95	C₂³×C₇₃	1	2	yes	—
659	#95	C₂³×C₇₃	1	1	yes	characteristic
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	C₂⁴	—	2	2	no	—
665	C₂⁴	—	2	2	no	—
666	C₂⁴	—	2	2	no	—
667	C₂⁴	—	2	4	no	—
668	C₂⁴	—	4	2	no	—
669	C₂⁴	C₂⁴×C₇₃	1	2	yes	—
670	C₂⁴	C₂⁴×C₇₃	1	1	yes	characteristic
671	C₂⁴	C₂⁴×C₇₃	1	1	yes	characteristic
672	C₂⁴	C₂⁴×C₇₃	1	1	yes	characteristic
673	C₂×Q₈	—	2	4	no	—
674	C₂×Q₈	—	2	4	no	—
675	C₂×Q₈	—	4	2	no	—
676	C₂×D₄	—	2	4	no	—
677	C₂×D₄	—	2	4	no	—
678	C₂×D₄	—	2	4	no	—
679	C₂×D₄	—	2	4	no	—
680	C₂×D₄	—	2	4	no	—
681	C₂×D₄	—	2	4	no	—
682	C₂×D₄	—	2	4	no	—
683	C₂×D₄	—	4	2	no	—
684	C₂×D₄	—	4	2	no	—
685	C₂×D₄	—	4	1	no	—
686	C₂×D₄	—	4	2	no	—
687	C₂²×C₄	—	2	4	no	—
688	C₂²×C₄	—	2	4	no	—
689	C₂²×C₄	—	2	2	no	—
690	C₂²×C₄	—	2	4	no	—
691	C₂²×C₄	—	2	2	no	—
692	C₂²×C₄	—	2	4	no	—
693	C₂²×C₄	—	2	4	no	—
694	C₂²×C₄	—	2	4	no	—
695	C₂²×C₄	—	2	4	no	—
696	C₂²×C₄	—	2	4	no	—
697	C₂²×C₄	—	4	2	no	—
698	C₂²×C₄	—	4	1	no	—
699	C₂²×C₄	—	4	2	no	—
700	C₂²×C₄	—	4	2	no	—
701	C₂²×C₄	—	4	2	no	—
702	C₂²×C₄	—	4	1	no	—
703	C₂²×C₄	—	4	2	no	—
704	C₂²×C₄	—	4	2	no	—
705	C₂²×C₄	—	4	2	no	—
706	C₂²×C₄	—	4	2	no	—
707	C₂²×C₄	—	4	16	no	—
708	C₂²×C₄	C₂⁴×C₇₃	1	2	yes	—
709	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
710	C₂²×C₄	C₂⁴×C₇₃	1	2	yes	—
711	C₂²×C₄	C₂⁴×C₇₃	1	2	yes	—
712	C₂²×C₄	C₂⁴×C₇₃	1	2	yes	—
713	C₂²×C₄	C₂⁴×C₇₃	1	2	yes	—
714	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
715	C₂²×C₄	C₂⁴×C₇₃	1	2	yes	—
716	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
717	C₂²×C₄	C₂⁴×C₇₃	1	2	yes	—
718	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
719	C₂²×C₄	C₂⁴×C₇₃	1	2	yes	—
720	C₂²×C₄	C₂⁴×C₇₃	1	2	yes	—
721	C₂²×C₄	C₂⁴×C₇₃	1	2	yes	—
722	C₂²×C₄	C₂⁴×C₇₃	1	2	yes	—
723	C₄⋊C₄	—	2	4	no	—
724	C₄⋊C₄	—	2	4	no	—
725	C₄⋊C₄	—	2	4	no	—
726	C₄⋊C₄	—	2	4	no	—
727	C₄⋊C₄	—	2	4	no	—
728	C₄⋊C₄	—	2	4	no	—
729	C₄⋊C₄	—	2	4	no	—
730	C₄⋊C₄	—	2	4	no	—
731	C₄⋊C₄	—	4	2	no	—
732	C₄⋊C₄	—	4	2	no	—
733	C₄⋊C₄	—	4	1	no	—
734	C₄⋊C₄	—	4	1	no	—
735	C₄⋊C₄	—	4	2	no	—
736	C₄⋊C₄	—	4	2	no	—
737	C₄⋊C₄	—	4	2	no	—
738	C₄⋊C₄	—	4	1	no	—
739	C₄⋊C₄	—	4	2	no	—
740	C₂²⋊C₄	—	2	2	no	—
741	C₂²⋊C₄	—	2	4	no	—
742	C₂²⋊C₄	—	2	4	no	—
743	C₂²⋊C₄	—	2	4	no	—
744	C₂²⋊C₄	—	2	4	no	—
745	C₂²⋊C₄	—	2	4	no	—
746	C₂²⋊C₄	—	2	4	no	—
747	C₂²⋊C₄	—	2	4	no	—
748	C₂²⋊C₄	—	2	4	no	—
749	C₂²⋊C₄	—	2	4	no	—
750	C₂²⋊C₄	—	2	4	no	—
751	C₂²⋊C₄	—	2	4	no	—
752	C₂²⋊C₄	—	2	4	no	—
753	C₂²⋊C₄	—	4	1	no	—
754	C₂²⋊C₄	—	4	1	no	—
755	C₂²⋊C₄	—	4	1	no	—
756	C₂²⋊C₄	—	4	1	no	—
757	C₂²⋊C₄	—	4	2	no	—
758	C₂²⋊C₄	—	4	2	no	—
759	C₂²⋊C₄	—	4	2	no	—
760	C₂²⋊C₄	—	4	2	no	—
761	C₂²⋊C₄	—	4	2	no	—
762	C₂²⋊C₄	—	4	2	no	—
763	C₂²⋊C₄	—	4	2	no	—
764	C₂²⋊C₄	#41×C₇₃	1	4	yes	—
765	C₂²⋊C₄	#41×C₇₃	1	8	yes	—
766	C₄²	—	2	4	no	—
767	C₄²	—	2	4	no	—
768	C₄²	—	4	2	no	—
769	C₄²	—	4	2	no	—
770	C₄²	—	4	2	no	—
771	C₄²	—	4	2	no	—
772	C₄²	—	4	2	no	—
773	C₂³	—	2	1	no	—
774	C₂³	—	2	2	no	—
775	C₂³	—	2	1	no	—
776	C₂³	—	2	8	no	—
777	C₂³	—	2	1	no	—
778	C₂³	—	2	2	no	—
779	C₂³	—	2	2	no	—
780	C₂³	—	2	1	no	—
781	C₂³	—	2	1	no	—
782	C₂³	—	2	2	no	—
783	C₂³	—	2	2	no	—
784	C₂³	—	2	1	no	—
785	C₂³	—	2	2	no	—
786	C₂³	—	2	2	no	—
787	C₂³	—	2	2	no	—
788	C₂³	—	2	2	no	—
789	C₂³	—	2	2	no	—
790	C₂³	—	2	2	no	—
791	C₂³	—	2	2	no	—
792	C₂³	—	4	8	no	—
793	C₂³	—	4	8	no	—
794	C₂³	—	4	4	no	—
795	C₂³	—	4	4	no	—
796	C₂³	C₂×#41×C₇₃	1	2	yes	—
797	C₂³	C₂×#41×C₇₃	1	4	yes	—
798	C₂³	H(5,𝔽₂)×C₇₃	1	2	yes	—
799	C₂³	2₋¹⁺⁴×C₇₃	1	2	yes	—
800	C₂³	C₂⁵×C₇₃	1	1	yes	characteristic
801	Q₈	—	4	8	no	—
802	D₄	—	4	8	no	—
803	D₄	—	4	8	no	—
804	D₄	—	4	8	no	—
805	D₄	—	8	2	no	—
806	C₂×C₄	—	2	2	no	—
807	C₂×C₄	—	2	2	no	—
808	C₂×C₄	—	2	2	no	—
809	C₂×C₄	—	2	2	no	—
810	C₂×C₄	—	2	2	no	—
811	C₂×C₄	—	2	2	no	—
812	C₂×C₄	—	2	2	no	—
813	C₂×C₄	—	2	2	no	—
814	C₂×C₄	—	2	2	no	—
815	C₂×C₄	—	2	2	no	—
816	C₂×C₄	—	2	2	no	—
817	C₂×C₄	—	2	2	no	—
818	C₂×C₄	—	2	2	no	—
819	C₂×C₄	—	2	2	no	—
820	C₂×C₄	—	2	2	no	—
821	C₂×C₄	—	2	2	no	—
822	C₂×C₄	—	2	2	no	—
823	C₂×C₄	—	2	2	no	—
824	C₂×C₄	—	2	2	no	—
825	C₂×C₄	—	2	2	no	—
826	C₂×C₄	—	2	1	no	—
827	C₂×C₄	—	2	2	no	—
828	C₂×C₄	—	2	2	no	—
829	C₂×C₄	—	2	2	no	—
830	C₂×C₄	—	2	2	no	—
831	C₂×C₄	—	2	2	no	—
832	C₂×C₄	—	2	1	no	—
833	C₂×C₄	—	2	2	no	—
834	C₂×C₄	—	2	1	no	—
835	C₂×C₄	—	2	2	no	—
836	C₂×C₄	—	2	1	no	—
837	C₂×C₄	—	2	2	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	—	4	4	no	—
844	C₂×C₄	—	4	8	no	—
845	C₂×C₄	—	4	8	no	—
846	C₂×C₄	—	4	8	no	—
847	C₂×C₄	—	4	4	no	—
848	C₂×C₄	—	4	4	no	—
849	C₂×C₄	—	8	4	no	—
850	C₂×C₄	—	8	2	no	—
851	C₂×C₄	C₂×#41×C₇₃	1	4	yes	—
852	C₂×C₄	C₂×#41×C₇₃	1	4	yes	—
853	C₂×C₄	C₂×#41×C₇₃	1	4	yes	—
854	C₂×C₄	H(5,𝔽₂)×C₇₃	1	4	yes	—
855	C₂²	—	2	4	no	—
856	C₂²	—	2	2	no	—
857	C₂²	—	2	4	no	—
858	C₂²	—	2	2	no	—
859	C₂²	—	2	4	no	—
860	C₂²	—	2	2	no	—
861	C₂²	—	2	2	no	—
862	C₂²	—	2	4	no	—
863	C₂²	—	4	16	no	—
864	C₂²	—	4	1	no	—
865	C₂²	—	4	1	no	—
866	C₂²	—	4	2	no	—
867	C₂²	—	4	2	no	—
868	C₂²	—	4	1	no	—
869	C₂²	—	4	1	no	—
870	C₂²	—	4	2	no	—
871	C₂²	—	4	2	no	—
872	C₂²	—	4	2	no	—
873	C₂²	—	4	2	no	—
874	C₂²	—	4	2	no	—
875	C₂²	—	4	2	no	—
876	C₂²	—	4	2	no	—
877	C₂²	#559×C₇₃	1	4	yes	—
878	C₂²	C₂²×#41×C₇₃	1	2	yes	—
879	C₂²	C₂²×#41×C₇₃	1	1	yes	characteristic
880	C₂²	C₂×H(5,𝔽₂)×C₇₃	1	1	yes	characteristic
881	C₂²	C₂×H(5,𝔽₂)×C₇₃	1	2	yes	—
882	C₂²	C₂×2₋¹⁺⁴×C₇₃	1	1	yes	characteristic
883	C₄	—	2	4	no	—
884	C₄	—	2	4	no	—
885	C₄	—	2	4	no	—
886	C₄	—	2	4	no	—
887	C₄	—	4	1	no	—
888	C₄	—	4	1	no	—
889	C₄	—	4	2	no	—
890	C₄	—	4	2	no	—
891	C₄	—	4	2	no	—
892	C₄	—	4	2	no	—
893	C₄	—	4	2	no	—
894	C₄	—	4	2	no	—
895	C₄	—	4	1	no	—
896	C₄	—	4	2	no	—
897	C₄	—	4	1	no	—
898	C₂	—	2	4	no	—
899	C₂	—	4	2	no	—
900	C₂	—	4	2	no	—
901	C₂	—	8	2	no	—
902	C₂	C₂×#559×C₇₃	1	1	yes	characteristic
903	C₂	C₇₃×#3481	1	2	yes	—
904	C₂	C₇₃×#3492	1	1	yes	characteristic
905	C₂	C₇₃×#3520	1	2	yes	—
906	C₂	C₇₃×#3532	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₇₃	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₇₃
prime radical	C₇₃×#2539	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×#2807	C₂	semidirect
2. C₇₃×#2796	C₂	semidirect
3. C₇₃×#2712	C₂	semidirect
4. C₇₃×#2602	C₂	semidirect
5. C₇₃×#2595	C₂	semidirect
6. C₇₃×#2589	C₂	semidirect
7. C₇₃×#2580	C₂	semidirect
9. C₇₃×#2517	C₂	semidirect
10. C₇₃×#2488	C₂	semidirect
11. C₇₃×#2482	C₂	semidirect
12. C₇₃×#2472	C₂	semidirect
13. C₇₃×#2455	C₂	semidirect
14. C₇₃×#2443	C₂	semidirect
15. C₇₃×#2367	C₂	semidirect
16. C₇₃×#2360	C₂	semidirect
17. C₇₃×#2359	C₂	semidirect
18. C₄×#120×C₇₃	C₂	semidirect
19. C₂×#385×C₇₃	C₂	semidirect
23. C₂×#123×C₇₃	C₂²	semidirect
27. C₂×C₄×Q₈×C₇₃	C₂²	semidirect
35. #400×C₇₃	C₂²	semidirect
36. #400×C₇₃	C₂²	semidirect
41. #399×C₇₃	C₂²	semidirect
42. #398×C₇₃	C₂²	semidirect
46. #397×C₇₃	C₂²	semidirect
47. #397×C₇₃	C₂²	semidirect
50. #394×C₇₃	C₂²	semidirect
52. #393×C₇₃	C₂²	semidirect
55. #391×C₇₃	C₂²	semidirect
56. #391×C₇₃	C₂²	semidirect
60. #389×C₇₃	C₂²	semidirect
61. #389×C₇₃	C₂²	semidirect
62. #389×C₇₃	C₂²	semidirect
63. #389×C₇₃	C₂²	semidirect
68. #388×C₇₃	C₂²	semidirect
69. #388×C₇₃	C₂²	semidirect
70. #388×C₇₃	C₂²	semidirect
71. #388×C₇₃	C₂²	semidirect
72. #388×C₇₃	C₂²	semidirect
73. #387×C₇₃	C₂²	semidirect
74. #387×C₇₃	C₂²	semidirect
75. #387×C₇₃	C₂²	semidirect
76. #387×C₇₃	C₂²	semidirect
77. #387×C₇₃	C₂²	semidirect
93. #385×C₇₃	C₂²	semidirect
94. #385×C₇₃	C₂²	semidirect
95. #382×C₇₃	C₂²	semidirect
98. C₄×C₄⋊C₄×C₇₃	C₂²	semidirect
99. C₄×C₄⋊C₄×C₇₃	C₂²	semidirect
105. C₄×C₂²⋊C₄×C₇₃	C₂²	semidirect
444. #59624	C₇₃	direct (N × H)
454. #2807	C₂×C₇₃	semidirect
455. #2796	C₂×C₇₃	semidirect
456. #2712	C₂×C₇₃	semidirect
457. #2602	C₂×C₇₃	semidirect
458. #2595	C₂×C₇₃	semidirect
459. #2589	C₂×C₇₃	semidirect
460. #2580	C₂×C₇₃	semidirect
462. #2517	C₂×C₇₃	semidirect
463. #2488	C₂×C₇₃	semidirect
464. #2482	C₂×C₇₃	semidirect
465. #2472	C₂×C₇₃	semidirect
466. #2455	C₂×C₇₃	semidirect
467. #2443	C₂×C₇₃	semidirect
468. #2367	C₂×C₇₃	semidirect
469. #2360	C₂×C₇₃	semidirect
470. #2359	C₂×C₇₃	semidirect
471. C₄×#120	C₂×C₇₃	semidirect
472. C₂×#385	C₂×C₇₃	semidirect
473. C₇₃	#59624	direct (N × H)
477. C₂×#123	C₂²×C₇₃	semidirect
481. C₂×C₄×Q₈	C₂²×C₇₃	semidirect
489. #400	C₂²×C₇₃	semidirect
490. #400	C₂²×C₇₃	semidirect
495. #399	C₂²×C₇₃	semidirect
496. #398	C₂²×C₇₃	semidirect
500. #397	C₂²×C₇₃	semidirect
501. #397	C₂²×C₇₃	semidirect
504. #394	C₂²×C₇₃	semidirect
506. #393	C₂²×C₇₃	semidirect
509. #391	C₂²×C₇₃	semidirect
510. #391	C₂²×C₇₃	semidirect
514. #389	C₂²×C₇₃	semidirect
515. #389	C₂²×C₇₃	semidirect
516. #389	C₂²×C₇₃	semidirect
517. #389	C₂²×C₇₃	semidirect
522. #388	C₂²×C₇₃	semidirect
523. #388	C₂²×C₇₃	semidirect
524. #388	C₂²×C₇₃	semidirect
525. #388	C₂²×C₇₃	semidirect
526. #388	C₂²×C₇₃	semidirect
527. #387	C₂²×C₇₃	semidirect
528. #387	C₂²×C₇₃	semidirect
529. #387	C₂²×C₇₃	semidirect
530. #387	C₂²×C₇₃	semidirect
531. #387	C₂²×C₇₃	semidirect
547. #385	C₂²×C₇₃	semidirect
548. #385	C₂²×C₇₃	semidirect
549. #382	C₂²×C₇₃	semidirect
552. C₄×C₄⋊C₄	C₂²×C₇₃	semidirect
553. C₄×C₄⋊C₄	C₂²×C₇₃	semidirect
559. C₄×C₂²⋊C₄	C₂²×C₇₃	semidirect

Maximal subgroups

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

subgroup	index
C₇₃×#2807	2
C₇₃×#2796	2
C₇₃×#2712	2
C₇₃×#2602	2
C₇₃×#2595	2
C₇₃×#2589	2
C₇₃×#2580	2
C₇₃×#2539	2
C₇₃×#2517	2
C₇₃×#2488	2
C₇₃×#2482	2
C₇₃×#2472	2
C₇₃×#2455	2
C₇₃×#2443	2
C₇₃×#2367	2
C₇₃×#2360	2
C₇₃×#2359	2
C₄×#120×C₇₃	2
C₂×#385×C₇₃	2
#59624	73

Subgroups — C73×#59624 #32969028

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₃×#59624 #32969028