Subgroups — C₇₃×#59846 #32969250

Order 18688.

2420 conjugacy classes of subgroups.

The subgroup lattice has 976 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#559×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#551×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇₃×#2717	C₂	1	1	yes	maximal, characteristic, complemented
4	C₇₃×#2672	C₂	1	2	yes	maximal, complemented
5	C₇₃×#2669	C₂	1	1	yes	maximal, characteristic
6	C₇₃×#2600	C₂	1	2	yes	maximal, complemented
7	C₇₃×#2557	C₂	1	2	yes	maximal, complemented
8	C₇₃×#2544	C₂	1	1	yes	maximal, characteristic, complemented
9	C₇₃×#2534	C₂	1	1	yes	maximal, characteristic, complemented
10	C₇₃×#2521	C₂	1	2	yes	maximal, complemented
11	C₇₃×#2472	C₂	1	2	yes	maximal, complemented
12	C₇₃×#2471	C₂	1	2	yes	maximal, complemented
13	C₇₃×#2466	C₂	1	2	yes	maximal, complemented
14	C₇₃×#2465	C₂	1	2	yes	maximal, complemented
15	C₇₃×#2461	C₂	1	2	yes	maximal, complemented
16	C₇₃×#2362	C₂	1	2	yes	maximal, complemented
17	C₇₃×#2358	C₂	1	2	yes	maximal, complemented
18	C₄×#123×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
19	C₄×#121×C₇₃	C₂	1	2	yes	maximal, complemented
20	#559×C₇₃	—	2	8	no	—
21	#551×C₇₃	—	2	8	no	—
22	C₂×#127×C₇₃	C₂²	1	1	yes	characteristic
23	C₂×#126×C₇₃	C₂²	1	2	yes	—
24	C₂×#124×C₇₃	C₂²	1	1	yes	characteristic
25	C₂×#124×C₇₃	C₂²	1	2	yes	—
26	C₂×#124×C₇₃	C₂²	1	2	yes	complemented
27	C₂×#124×C₇₃	C₂²	1	1	yes	characteristic, complemented
28	C₂×#123×C₇₃	C₂²	1	2	yes	—
29	C₂×#123×C₇₃	C₂²	1	1	yes	characteristic
30	C₂×#123×C₇₃	C₂²	1	1	yes	characteristic
31	C₂×#123×C₇₃	C₂²	1	2	yes	complemented
32	C₂×C₂²⋊Q₈×C₇₃	C₂²	1	2	yes	—
33	C₂×C₂²⋊Q₈×C₇₃	C₂²	1	2	yes	—
34	C₂×#121×C₇₃	C₂²	1	2	yes	—
35	C₂×#120×C₇₃	C₂²	1	1	yes	characteristic
36	C₂×#120×C₇₃	C₂²	1	2	yes	—
37	C₂×C₄×Q₈×C₇₃	C₂²	1	2	yes	complemented
38	C₂×C₄×D₄×C₇₃	C₂²	1	2	yes	—
39	C₂×C₄×D₄×C₇₃	C₂²	1	2	yes	—
40	C₂×C₄×D₄×C₇₃	C₂²	1	2	yes	—
41	C₂×C₄×D₄×C₇₃	C₂²	1	1	yes	characteristic
42	C₂×C₄×D₄×C₇₃	C₂²	1	2	yes	complemented
43	C₂×#117×C₇₃	C₂²	1	2	yes	—
44	C₂²×C₂²⋊C₄×C₇₃	C₂²	1	2	yes	—
45	C₂²×C₂²⋊C₄×C₇₃	C₂²	1	1	yes	characteristic
46	C₂²×C₄²×C₇₃	C₂²	1	1	yes	characteristic, complemented
47	#399×C₇₃	C₂²	1	2	yes	complemented
48	#397×C₇₃	C₂²	1	2	yes	—
49	#397×C₇₃	C₂²	1	2	yes	complemented
50	#397×C₇₃	C₂²	1	2	yes	complemented
51	#396×C₇₃	C₂²	1	2	yes	—
52	#396×C₇₃	C₂²	1	2	yes	complemented
53	#395×C₇₃	C₂²	1	2	yes	complemented
54	#395×C₇₃	C₂²	1	2	yes	complemented
55	#394×C₇₃	C₂²	1	2	yes	—
56	#394×C₇₃	C₂²	1	2	yes	—
57	#394×C₇₃	C₂²	1	2	yes	—
58	#394×C₇₃	C₂²	1	2	yes	—
59	#394×C₇₃	C₂²	1	2	yes	complemented
60	#393×C₇₃	C₂²	1	2	yes	—
61	#392×C₇₃	C₂²	1	2	yes	—
62	#392×C₇₃	C₂²	1	2	yes	—
63	#391×C₇₃	C₂²	1	1	yes	characteristic, complemented
64	#391×C₇₃	C₂²	1	2	yes	complemented
65	#390×C₇₃	C₂²	1	2	yes	—
66	#390×C₇₃	C₂²	1	2	yes	—
67	#390×C₇₃	C₂²	1	1	yes	characteristic, complemented
68	#389×C₇₃	C₂²	1	2	yes	complemented
69	#389×C₇₃	C₂²	1	2	yes	complemented
70	#388×C₇₃	C₂²	1	2	yes	—
71	#388×C₇₃	C₂²	1	2	yes	—
72	#388×C₇₃	C₂²	1	2	yes	—
73	#388×C₇₃	C₂²	1	2	yes	—
74	#388×C₇₃	C₂²	1	2	yes	—
75	#388×C₇₃	C₂²	1	2	yes	—
76	#388×C₇₃	C₂²	1	2	yes	complemented
77	#388×C₇₃	C₂²	1	2	yes	complemented
78	#388×C₇₃	C₂²	1	2	yes	complemented
79	#387×C₇₃	C₂²	1	2	yes	complemented
80	#387×C₇₃	C₂²	1	2	yes	complemented
81	#387×C₇₃	C₂²	1	2	yes	complemented
82	#387×C₇₃	C₂²	1	2	yes	complemented
83	#387×C₇₃	C₂²	1	2	yes	complemented
84	#386×C₇₃	C₂²	1	2	yes	—
85	#386×C₇₃	C₂²	1	1	yes	characteristic
86	#386×C₇₃	C₂²	1	2	yes	—
87	#386×C₇₃	C₂²	1	2	yes	—
88	#386×C₇₃	C₂²	1	2	yes	—
89	#386×C₇₃	C₂²	1	2	yes	—
90	#386×C₇₃	C₂²	1	2	yes	—
91	#386×C₇₃	C₂²	1	2	yes	complemented
92	#385×C₇₃	C₂²	1	2	yes	—
93	#385×C₇₃	C₂²	1	2	yes	—
94	#385×C₇₃	C₂²	1	2	yes	complemented
95	#385×C₇₃	C₂²	1	1	yes	characteristic, complemented
96	#381×C₇₃	C₂²	1	1	yes	characteristic
97	#381×C₇₃	C₂²	1	1	yes	characteristic, complemented
98	#380×C₇₃	C₂²	1	1	yes	characteristic
99	#380×C₇₃	C₂²	1	2	yes	complemented
100	#379×C₇₃	C₂²	1	1	yes	characteristic
101	C₄×C₄⋊C₄×C₇₃	C₂²	1	2	yes	complemented
102	C₄×C₄⋊C₄×C₇₃	C₂²	1	2	yes	complemented
103	C₄×C₄⋊C₄×C₇₃	C₂²	1	1	yes	characteristic, complemented
104	C₄×C₂²⋊C₄×C₇₃	C₂²	1	2	yes	—
105	C₄×C₂²⋊C₄×C₇₃	C₂²	1	2	yes	—
106	C₄×C₂²⋊C₄×C₇₃	C₂²	1	2	yes	—
107	C₄×C₂²⋊C₄×C₇₃	C₂²	1	2	yes	complemented
108	C₄×C₂²⋊C₄×C₇₃	C₂²	1	1	yes	characteristic, complemented
109	C₂⁵×C₇₃	C₂³	1	1	yes	characteristic
110	C₂²×Q₈×C₇₃	C₂³	1	2	yes	—
111	C₂²×Q₈×C₇₃	C₂³	1	1	yes	characteristic
112	C₂²×D₄×C₇₃	C₂³	1	2	yes	—
113	C₂²×D₄×C₇₃	C₂³	1	2	yes	—
114	C₂²×D₄×C₇₃	C₂³	1	2	yes	—
115	C₂²×D₄×C₇₃	C₂³	1	2	yes	—
116	C₂²×D₄×C₇₃	C₂³	1	2	yes	—
117	C₂²×D₄×C₇₃	C₂³	1	1	yes	characteristic
118	C₂²×D₄×C₇₃	C₂³	1	1	yes	characteristic
119	C₂³×C₄×C₇₃	C₂³	1	2	yes	—
120	C₂³×C₄×C₇₃	C₂³	1	1	yes	characteristic
121	C₂³×C₄×C₇₃	C₂³	1	1	yes	characteristic
122	C₂³×C₄×C₇₃	C₂³	1	2	yes	—
123	C₂³×C₄×C₇₃	C₂³	1	2	yes	—
124	C₂³×C₄×C₇₃	C₂³	1	1	yes	characteristic
125	C₂³×C₄×C₇₃	C₂³	1	1	yes	characteristic
126	C₂³×C₄×C₇₃	C₂³	1	1	yes	characteristic
127	#127×C₇₃	—	2	4	no	—
128	#126×C₇₃	—	2	8	no	—
129	#124×C₇₃	—	2	4	no	—
130	#124×C₇₃	—	2	8	no	—
131	#124×C₇₃	—	2	8	no	—
132	#124×C₇₃	—	4	2	no	—
133	#123×C₇₃	—	2	4	no	—
134	#123×C₇₃	—	2	8	no	—
135	#123×C₇₃	—	2	8	no	—
136	#123×C₇₃	D₄	1	8	yes	complemented
137	C₂²⋊Q₈×C₇₃	—	2	8	no	—
138	C₂²⋊Q₈×C₇₃	—	2	8	no	—
139	#121×C₇₃	—	2	8	no	—
140	#120×C₇₃	—	2	4	no	—
141	#120×C₇₃	—	2	8	no	—
142	C₄×Q₈×C₇₃	—	2	8	no	—
143	C₄×D₄×C₇₃	—	2	8	no	—
144	C₄×D₄×C₇₃	—	2	8	no	—
145	C₄×D₄×C₇₃	—	2	8	no	—
146	C₄×D₄×C₇₃	—	4	4	no	—
147	C₄×D₄×C₇₃	—	4	2	no	—
148	#117×C₇₃	—	2	8	no	—
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	2	yes	—
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	2	yes	—
161	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
162	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
163	C₂×C₂²⋊C₄×C₇₃	—	2	8	no	—
164	C₂×C₂²⋊C₄×C₇₃	—	4	2	no	—
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	2	yes	—
171	C₂×C₂²⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
172	C₂×C₂²⋊C₄×C₇₃	C₂³	1	2	yes	—
173	C₂×C₂²⋊C₄×C₇₃	C₂³	1	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	2	yes	—
180	C₂×C₂²⋊C₄×C₇₃	C₂³	1	2	yes	—
181	C₂×C₂²⋊C₄×C₇₃	C₂³	1	2	yes	—
182	C₂×C₂²⋊C₄×C₇₃	C₂³	1	2	yes	—
183	C₂×C₂²⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
184	C₂×C₂²⋊C₄×C₇₃	C₂³	1	2	yes	—
185	C₂×C₂²⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
186	C₂×C₂²⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
187	C₂×C₂²⋊C₄×C₇₃	C₂³	1	2	yes	—
188	C₂×C₂²⋊C₄×C₇₃	C₂³	1	2	yes	—
189	C₂×C₂²⋊C₄×C₇₃	C₂³	1	2	yes	—
190	C₂×C₂²⋊C₄×C₇₃	C₂³	1	2	yes	—
191	C₂×C₂²⋊C₄×C₇₃	C₂³	1	2	yes	—
192	C₂×C₂²⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
193	C₂×C₂²⋊C₄×C₇₃	C₂³	1	2	yes	—
194	C₂×C₄²×C₇₃	—	4	2	no	—
195	C₂×C₄²×C₇₃	C₂³	1	2	yes	—
196	C₂×C₄²×C₇₃	C₂³	1	2	yes	—
197	C₂×C₄²×C₇₃	C₂³	1	2	yes	—
198	C₂×C₄²×C₇₃	C₂³	1	2	yes	—
199	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
200	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
201	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
202	C₂×C₄²×C₇₃	C₂³	1	2	yes	—
203	C₂×C₄²×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	#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	C₂⁴×C₇₃	—	2	2	no	—
222	C₂⁴×C₇₃	—	2	4	no	—
223	C₂⁴×C₇₃	—	4	1	no	—
224	C₂⁴×C₇₃	—	4	2	no	—
225	C₂⁴×C₇₃	—	4	1	no	—
226	C₂⁴×C₇₃	C₂⁴	1	2	yes	—
227	C₂⁴×C₇₃	C₂⁴	1	1	yes	characteristic
228	C₂⁴×C₇₃	C₂⁴	1	1	yes	characteristic
229	C₂⁴×C₇₃	C₂⁴	1	2	yes	—
230	C₂×Q₈×C₇₃	—	2	4	no	—
231	C₂×Q₈×C₇₃	—	2	2	no	—
232	C₂×Q₈×C₇₃	—	2	4	no	—
233	C₂×Q₈×C₇₃	—	4	2	no	—
234	C₂×Q₈×C₇₃	—	4	1	no	—
235	C₂×Q₈×C₇₃	—	4	1	no	—
236	C₂×D₄×C₇₃	—	2	4	no	—
237	C₂×D₄×C₇₃	—	2	4	no	—
238	C₂×D₄×C₇₃	—	2	4	no	—
239	C₂×D₄×C₇₃	—	2	4	no	—
240	C₂×D₄×C₇₃	—	2	4	no	—
241	C₂×D₄×C₇₃	—	2	4	no	—
242	C₂×D₄×C₇₃	—	2	2	no	—
243	C₂×D₄×C₇₃	—	2	4	no	—
244	C₂×D₄×C₇₃	—	2	4	no	—
245	C₂×D₄×C₇₃	—	2	4	no	—
246	C₂×D₄×C₇₃	—	4	2	no	—
247	C₂×D₄×C₇₃	—	4	1	no	—
248	C₂×D₄×C₇₃	—	4	1	no	—
249	C₂×D₄×C₇₃	—	4	2	no	—
250	C₂×D₄×C₇₃	—	4	2	no	—
251	C₂×D₄×C₇₃	—	4	2	no	—
252	C₂×D₄×C₇₃	—	4	1	no	—
253	C₂×D₄×C₇₃	—	4	1	no	—
254	C₂×D₄×C₇₃	—	4	2	no	—
255	C₂×D₄×C₇₃	—	4	2	no	—
256	C₂×D₄×C₇₃	C₂×D₄	1	4	yes	—
257	C₂²×C₄×C₇₃	—	2	4	no	—
258	C₂²×C₄×C₇₃	—	2	2	no	—
259	C₂²×C₄×C₇₃	—	2	4	no	—
260	C₂²×C₄×C₇₃	—	2	4	no	—
261	C₂²×C₄×C₇₃	—	2	2	no	—
262	C₂²×C₄×C₇₃	—	2	4	no	—
263	C₂²×C₄×C₇₃	—	2	4	no	—
264	C₂²×C₄×C₇₃	—	2	2	no	—
265	C₂²×C₄×C₇₃	—	4	1	no	—
266	C₂²×C₄×C₇₃	—	4	1	no	—
267	C₂²×C₄×C₇₃	—	4	2	no	—
268	C₂²×C₄×C₇₃	—	4	2	no	—
269	C₂²×C₄×C₇₃	—	4	1	no	—
270	C₂²×C₄×C₇₃	—	4	1	no	—
271	C₂²×C₄×C₇₃	—	4	2	no	—
272	C₂²×C₄×C₇₃	—	4	2	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	1	no	—
277	C₂²×C₄×C₇₃	C₂×D₄	1	4	yes	—
278	C₂²×C₄×C₇₃	C₂⁴	1	2	yes	—
279	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
280	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
281	C₂²×C₄×C₇₃	C₂⁴	1	2	yes	—
282	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
283	C₂²×C₄×C₇₃	C₂⁴	1	2	yes	—
284	C₂²×C₄×C₇₃	C₂⁴	1	2	yes	—
285	C₂²×C₄×C₇₃	C₂⁴	1	2	yes	—
286	C₂²×C₄×C₇₃	C₂⁴	1	2	yes	—
287	C₂²×C₄×C₇₃	C₂⁴	1	2	yes	—
288	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
289	C₂²×C₄×C₇₃	C₂⁴	1	2	yes	—
290	C₂²×C₄×C₇₃	C₂⁴	1	2	yes	—
291	C₂²×C₄×C₇₃	C₂⁴	1	2	yes	—
292	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
293	C₄⋊C₄×C₇₃	—	2	4	no	—
294	C₄⋊C₄×C₇₃	—	2	4	no	—
295	C₄⋊C₄×C₇₃	—	2	4	no	—
296	C₄⋊C₄×C₇₃	—	2	4	no	—
297	C₄⋊C₄×C₇₃	—	2	4	no	—
298	C₄⋊C₄×C₇₃	—	2	4	no	—
299	C₄⋊C₄×C₇₃	—	2	4	no	—
300	C₄⋊C₄×C₇₃	—	2	4	no	—
301	C₄⋊C₄×C₇₃	—	2	4	no	—
302	C₄⋊C₄×C₇₃	—	4	2	no	—
303	C₄⋊C₄×C₇₃	—	4	2	no	—
304	C₄⋊C₄×C₇₃	—	4	2	no	—
305	C₄⋊C₄×C₇₃	—	4	1	no	—
306	C₄⋊C₄×C₇₃	C₂×D₄	1	8	yes	—
307	C₂²⋊C₄×C₇₃	—	2	4	no	—
308	C₂²⋊C₄×C₇₃	—	2	4	no	—
309	C₂²⋊C₄×C₇₃	—	2	4	no	—
310	C₂²⋊C₄×C₇₃	—	2	2	no	—
311	C₂²⋊C₄×C₇₃	—	2	2	no	—
312	C₂²⋊C₄×C₇₃	—	2	4	no	—
313	C₂²⋊C₄×C₇₃	—	2	4	no	—
314	C₂²⋊C₄×C₇₃	—	2	4	no	—
315	C₂²⋊C₄×C₇₃	—	2	4	no	—
316	C₂²⋊C₄×C₇₃	—	2	4	no	—
317	C₂²⋊C₄×C₇₃	—	2	4	no	—
318	C₂²⋊C₄×C₇₃	—	2	4	no	—
319	C₂²⋊C₄×C₇₃	—	2	4	no	—
320	C₂²⋊C₄×C₇₃	—	2	4	no	—
321	C₂²⋊C₄×C₇₃	—	2	4	no	—
322	C₂²⋊C₄×C₇₃	—	2	4	no	—
323	C₂²⋊C₄×C₇₃	—	2	4	no	—
324	C₂²⋊C₄×C₇₃	—	4	2	no	—
325	C₂²⋊C₄×C₇₃	—	4	2	no	—
326	C₂²⋊C₄×C₇₃	—	4	2	no	—
327	C₂²⋊C₄×C₇₃	—	4	2	no	—
328	C₂²⋊C₄×C₇₃	—	4	2	no	—
329	C₂²⋊C₄×C₇₃	—	4	1	no	—
330	C₂²⋊C₄×C₇₃	—	4	1	no	—
331	C₂²⋊C₄×C₇₃	—	4	1	no	—
332	C₂²⋊C₄×C₇₃	—	4	2	no	—
333	C₂²⋊C₄×C₇₃	C₂×D₄	1	8	yes	—
334	C₂²⋊C₄×C₇₃	C₂×D₄	1	4	yes	—
335	C₂²⋊C₄×C₇₃	#41	1	8	yes	—
336	C₄²×C₇₃	—	2	2	no	—
337	C₄²×C₇₃	—	2	4	no	—
338	C₄²×C₇₃	—	2	4	no	—
339	C₄²×C₇₃	—	2	4	no	—
340	C₄²×C₇₃	—	2	2	no	—
341	C₄²×C₇₃	—	2	4	no	—
342	C₄²×C₇₃	—	2	2	no	—
343	C₄²×C₇₃	—	4	2	no	—
344	C₄²×C₇₃	—	4	2	no	—
345	C₂³×C₇₃	—	2	2	no	—
346	C₂³×C₇₃	—	2	2	no	—
347	C₂³×C₇₃	—	2	2	no	—
348	C₂³×C₇₃	—	2	2	no	—
349	C₂³×C₇₃	—	2	2	no	—
350	C₂³×C₇₃	—	2	1	no	—
351	C₂³×C₇₃	—	2	1	no	—
352	C₂³×C₇₃	—	2	1	no	—
353	C₂³×C₇₃	—	2	2	no	—
354	C₂³×C₇₃	—	2	2	no	—
355	C₂³×C₇₃	—	2	2	no	—
356	C₂³×C₇₃	—	2	2	no	—
357	C₂³×C₇₃	—	2	1	no	—
358	C₂³×C₇₃	—	2	2	no	—
359	C₂³×C₇₃	—	2	2	no	—
360	C₂³×C₇₃	—	2	2	no	—
361	C₂³×C₇₃	—	2	2	no	—
362	C₂³×C₇₃	—	2	2	no	—
363	C₂³×C₇₃	—	2	2	no	—
364	C₂³×C₇₃	—	2	2	no	—
365	C₂³×C₇₃	—	2	2	no	—
366	C₂³×C₇₃	—	4	8	no	—
367	C₂³×C₇₃	—	4	4	no	—
368	C₂³×C₇₃	—	8	2	no	—
369	C₂³×C₇₃	—	8	4	no	—
370	C₂³×C₇₃	—	8	2	no	—
371	C₂³×C₇₃	C₂²×D₄	1	2	yes	—
372	C₂³×C₇₃	C₂²×D₄	1	2	yes	—
373	C₂³×C₇₃	C₂×#41	1	4	yes	—
374	C₂³×C₇₃	C₂⁵	1	1	yes	characteristic
375	Q₈×C₇₃	—	4	8	no	—
376	Q₈×C₇₃	—	8	2	no	—
377	D₄×C₇₃	—	4	4	no	—
378	D₄×C₇₃	—	4	8	no	—
379	D₄×C₇₃	—	4	8	no	—
380	D₄×C₇₃	—	4	8	no	—
381	D₄×C₇₃	—	4	8	no	—
382	D₄×C₇₃	—	8	2	no	—
383	D₄×C₇₃	—	8	4	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	—	2	1	no	—
390	C₂×C₄×C₇₃	—	2	2	no	—
391	C₂×C₄×C₇₃	—	2	2	no	—
392	C₂×C₄×C₇₃	—	2	2	no	—
393	C₂×C₄×C₇₃	—	2	2	no	—
394	C₂×C₄×C₇₃	—	2	1	no	—
395	C₂×C₄×C₇₃	—	2	2	no	—
396	C₂×C₄×C₇₃	—	2	2	no	—
397	C₂×C₄×C₇₃	—	2	2	no	—
398	C₂×C₄×C₇₃	—	2	2	no	—
399	C₂×C₄×C₇₃	—	2	2	no	—
400	C₂×C₄×C₇₃	—	2	2	no	—
401	C₂×C₄×C₇₃	—	2	2	no	—
402	C₂×C₄×C₇₃	—	2	2	no	—
403	C₂×C₄×C₇₃	—	2	2	no	—
404	C₂×C₄×C₇₃	—	2	2	no	—
405	C₂×C₄×C₇₃	—	2	1	no	—
406	C₂×C₄×C₇₃	—	2	1	no	—
407	C₂×C₄×C₇₃	—	2	2	no	—
408	C₂×C₄×C₇₃	—	2	2	no	—
409	C₂×C₄×C₇₃	—	2	1	no	—
410	C₂×C₄×C₇₃	—	2	2	no	—
411	C₂×C₄×C₇₃	—	2	2	no	—
412	C₂×C₄×C₇₃	—	2	2	no	—
413	C₂×C₄×C₇₃	—	2	2	no	—
414	C₂×C₄×C₇₃	—	2	2	no	—
415	C₂×C₄×C₇₃	—	2	2	no	—
416	C₂×C₄×C₇₃	—	2	2	no	—
417	C₂×C₄×C₇₃	—	2	2	no	—
418	C₂×C₄×C₇₃	—	2	2	no	—
419	C₂×C₄×C₇₃	—	4	4	no	—
420	C₂×C₄×C₇₃	—	4	4	no	—
421	C₂×C₄×C₇₃	—	4	8	no	—
422	C₂×C₄×C₇₃	—	4	4	no	—
423	C₂×C₄×C₇₃	—	8	4	no	—
424	C₂×C₄×C₇₃	—	8	4	no	—
425	C₂×C₄×C₇₃	—	8	2	no	—
426	C₂×C₄×C₇₃	—	8	2	no	—
427	C₂×C₄×C₇₃	C₂²×D₄	1	4	yes	—
428	C₂×C₄×C₇₃	C₂²×D₄	1	2	yes	—
429	C₂×C₄×C₇₃	C₂²×D₄	1	4	yes	—
430	C₂×C₄×C₇₃	C₂×#41	1	4	yes	—
431	C₂×C₄×C₇₃	C₂×#41	1	4	yes	—
432	C₂×C₄×C₇₃	H(5,𝔽₂)	1	2	yes	—
433	C₂²×C₇₃	—	2	4	no	—
434	C₂²×C₇₃	—	2	4	no	—
435	C₂²×C₇₃	—	2	4	no	—
436	C₂²×C₇₃	—	2	4	no	—
437	C₂²×C₇₃	—	2	2	no	—
438	C₂²×C₇₃	—	2	2	no	—
439	C₂²×C₇₃	—	2	4	no	—
440	C₂²×C₇₃	—	4	2	no	—
441	C₂²×C₇₃	—	4	1	no	—
442	C₂²×C₇₃	—	4	1	no	—
443	C₂²×C₇₃	—	4	2	no	—
444	C₂²×C₇₃	—	4	2	no	—
445	C₂²×C₇₃	—	4	2	no	—
446	C₂²×C₇₃	—	4	2	no	—
447	C₂²×C₇₃	—	4	1	no	—
448	C₂²×C₇₃	—	4	1	no	—
449	C₂²×C₇₃	—	4	2	no	—
450	C₂²×C₇₃	—	4	2	no	—
451	C₂²×C₇₃	—	4	2	no	—
452	C₂²×C₇₃	—	4	2	no	—
453	C₂²×C₇₃	—	4	2	no	—
454	C₂²×C₇₃	—	4	2	no	—
455	C₂²×C₇₃	—	4	2	no	—
456	C₂²×C₇₃	—	4	2	no	—
457	C₂²×C₇₃	—	8	8	no	—
458	C₂²×C₇₃	C₂³×D₄	1	1	yes	characteristic
459	C₂²×C₇₃	C₂²×#41	1	2	yes	—
460	C₂²×C₇₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
461	C₂²×C₇₃	#585	1	2	yes	—
462	C₂²×C₇₃	#585	1	1	yes	characteristic
463	C₄×C₇₃	—	2	4	no	—
464	C₄×C₇₃	—	2	4	no	—
465	C₄×C₇₃	—	2	4	no	—
466	C₄×C₇₃	—	2	4	no	—
467	C₄×C₇₃	—	2	2	no	—
468	C₄×C₇₃	—	2	2	no	—
469	C₄×C₇₃	—	4	2	no	—
470	C₄×C₇₃	—	4	2	no	—
471	C₄×C₇₃	—	4	2	no	—
472	C₄×C₇₃	—	4	1	no	—
473	C₄×C₇₃	—	4	2	no	—
474	C₄×C₇₃	—	4	2	no	—
475	C₄×C₇₃	—	4	2	no	—
476	C₄×C₇₃	—	4	1	no	—
477	C₄×C₇₃	—	4	1	no	—
478	#59846	C₇₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
479	C₂×C₇₃	—	4	2	no	—
480	C₂×C₇₃	—	4	4	no	—
481	C₂×C₇₃	—	4	2	no	—
482	C₂×C₇₃	—	8	2	no	—
483	C₂×C₇₃	D₄×#41	1	2	yes	—
484	C₂×C₇₃	#3481	1	1	yes	characteristic
485	C₂×C₇₃	#3496	1	1	yes	characteristic
486	C₂×C₇₃	#3510	1	2	yes	—
487	C₂×C₇₃	#3533	1	1	yes	characteristic
488	C₂×#559	C₂×C₇₃	1	1	yes	characteristic, complemented
489	C₂×#551	C₂×C₇₃	1	1	yes	characteristic, complemented
490	#2717	C₂×C₇₃	1	1	yes	characteristic, complemented
491	#2672	C₂×C₇₃	1	2	yes	complemented
492	#2669	C₂×C₇₃	1	1	yes	characteristic
493	#2600	C₂×C₇₃	1	2	yes	complemented
494	#2557	C₂×C₇₃	1	2	yes	complemented
495	#2544	C₂×C₇₃	1	1	yes	characteristic, complemented
496	#2534	C₂×C₇₃	1	1	yes	characteristic, complemented
497	#2521	C₂×C₇₃	1	2	yes	complemented
498	#2472	C₂×C₇₃	1	2	yes	complemented
499	#2471	C₂×C₇₃	1	2	yes	complemented
500	#2466	C₂×C₇₃	1	2	yes	complemented
501	#2465	C₂×C₇₃	1	2	yes	complemented
502	#2461	C₂×C₇₃	1	2	yes	complemented
503	#2362	C₂×C₇₃	1	2	yes	complemented
504	#2358	C₂×C₇₃	1	2	yes	complemented
505	C₄×#123	C₂×C₇₃	1	1	yes	characteristic, complemented
506	C₄×#121	C₂×C₇₃	1	2	yes	complemented
507	C₇₃	#59846	1	1	yes	characteristic, direct product factor, Sylow
508	#559	—	2	8	no	—
509	#551	—	2	8	no	—
510	C₂×#127	C₂²×C₇₃	1	1	yes	characteristic
511	C₂×#126	C₂²×C₇₃	1	2	yes	—
512	C₂×#124	C₂²×C₇₃	1	1	yes	characteristic
513	C₂×#124	C₂²×C₇₃	1	2	yes	—
514	C₂×#124	C₂²×C₇₃	1	2	yes	complemented
515	C₂×#124	C₂²×C₇₃	1	1	yes	characteristic, complemented
516	C₂×#123	C₂²×C₇₃	1	2	yes	—
517	C₂×#123	C₂²×C₇₃	1	1	yes	characteristic
518	C₂×#123	C₂²×C₇₃	1	1	yes	characteristic
519	C₂×#123	C₂²×C₇₃	1	2	yes	complemented
520	C₂×C₂²⋊Q₈	C₂²×C₇₃	1	2	yes	—
521	C₂×C₂²⋊Q₈	C₂²×C₇₃	1	2	yes	—
522	C₂×#121	C₂²×C₇₃	1	2	yes	—
523	C₂×#120	C₂²×C₇₃	1	2	yes	—
524	C₂×#120	C₂²×C₇₃	1	1	yes	characteristic
525	C₂×C₄×Q₈	C₂²×C₇₃	1	2	yes	complemented
526	C₂×C₄×D₄	C₂²×C₇₃	1	2	yes	—
527	C₂×C₄×D₄	C₂²×C₇₃	1	2	yes	—
528	C₂×C₄×D₄	C₂²×C₇₃	1	2	yes	—
529	C₂×C₄×D₄	C₂²×C₇₃	1	1	yes	characteristic
530	C₂×C₄×D₄	C₂²×C₇₃	1	2	yes	complemented
531	C₂×#117	C₂²×C₇₃	1	2	yes	—
532	C₂²×C₂²⋊C₄	C₂²×C₇₃	1	2	yes	—
533	C₂²×C₂²⋊C₄	C₂²×C₇₃	1	1	yes	characteristic
534	C₂²×C₄²	C₂²×C₇₃	1	1	yes	characteristic, complemented
535	#399	C₂²×C₇₃	1	2	yes	complemented
536	#397	C₂²×C₇₃	1	2	yes	—
537	#397	C₂²×C₇₃	1	2	yes	complemented
538	#397	C₂²×C₇₃	1	2	yes	complemented
539	#396	C₂²×C₇₃	1	2	yes	—
540	#396	C₂²×C₇₃	1	2	yes	complemented
541	#395	C₂²×C₇₃	1	2	yes	complemented
542	#395	C₂²×C₇₃	1	2	yes	complemented
543	#394	C₂²×C₇₃	1	2	yes	—
544	#394	C₂²×C₇₃	1	2	yes	—
545	#394	C₂²×C₇₃	1	2	yes	—
546	#394	C₂²×C₇₃	1	2	yes	—
547	#394	C₂²×C₇₃	1	2	yes	complemented
548	#393	C₂²×C₇₃	1	2	yes	—
549	#392	C₂²×C₇₃	1	2	yes	—
550	#392	C₂²×C₇₃	1	2	yes	—
551	#391	C₂²×C₇₃	1	2	yes	complemented
552	#391	C₂²×C₇₃	1	1	yes	characteristic, complemented
553	#390	C₂²×C₇₃	1	2	yes	—
554	#390	C₂²×C₇₃	1	2	yes	—
555	#390	C₂²×C₇₃	1	1	yes	characteristic, complemented
556	#389	C₂²×C₇₃	1	2	yes	complemented
557	#389	C₂²×C₇₃	1	2	yes	complemented
558	#388	C₂²×C₇₃	1	2	yes	—
559	#388	C₂²×C₇₃	1	2	yes	—
560	#388	C₂²×C₇₃	1	2	yes	—
561	#388	C₂²×C₇₃	1	2	yes	—
562	#388	C₂²×C₇₃	1	2	yes	—
563	#388	C₂²×C₇₃	1	2	yes	—
564	#388	C₂²×C₇₃	1	2	yes	complemented
565	#388	C₂²×C₇₃	1	2	yes	complemented
566	#388	C₂²×C₇₃	1	2	yes	complemented
567	#387	C₂²×C₇₃	1	2	yes	complemented
568	#387	C₂²×C₇₃	1	2	yes	complemented
569	#387	C₂²×C₇₃	1	2	yes	complemented
570	#387	C₂²×C₇₃	1	2	yes	complemented
571	#387	C₂²×C₇₃	1	2	yes	complemented
572	#386	C₂²×C₇₃	1	2	yes	—
573	#386	C₂²×C₇₃	1	2	yes	—
574	#386	C₂²×C₇₃	1	2	yes	—
575	#386	C₂²×C₇₃	1	2	yes	—
576	#386	C₂²×C₇₃	1	1	yes	characteristic
577	#386	C₂²×C₇₃	1	2	yes	—
578	#386	C₂²×C₇₃	1	2	yes	—
579	#386	C₂²×C₇₃	1	2	yes	complemented
580	#385	C₂²×C₇₃	1	2	yes	—
581	#385	C₂²×C₇₃	1	2	yes	—
582	#385	C₂²×C₇₃	1	2	yes	complemented
583	#385	C₂²×C₇₃	1	1	yes	characteristic, complemented
584	#381	C₂²×C₇₃	1	1	yes	characteristic
585	#381	C₂²×C₇₃	1	1	yes	characteristic, complemented
586	#380	C₂²×C₇₃	1	1	yes	characteristic
587	#380	C₂²×C₇₃	1	2	yes	complemented
588	#379	C₂²×C₇₃	1	1	yes	characteristic
589	C₄×C₄⋊C₄	C₂²×C₇₃	1	1	yes	characteristic, complemented
590	C₄×C₄⋊C₄	C₂²×C₇₃	1	2	yes	complemented
591	C₄×C₄⋊C₄	C₂²×C₇₃	1	2	yes	complemented
592	C₄×C₂²⋊C₄	C₂²×C₇₃	1	2	yes	—
593	C₄×C₂²⋊C₄	C₂²×C₇₃	1	2	yes	—
594	C₄×C₂²⋊C₄	C₂²×C₇₃	1	2	yes	—
595	C₄×C₂²⋊C₄	C₂²×C₇₃	1	2	yes	complemented
596	C₄×C₂²⋊C₄	C₂²×C₇₃	1	1	yes	characteristic, complemented
597	C₂⁵	C₂³×C₇₃	1	1	yes	characteristic
598	C₂²×Q₈	C₂³×C₇₃	1	2	yes	—
599	C₂²×Q₈	C₂³×C₇₃	1	1	yes	characteristic
600	C₂²×D₄	C₂³×C₇₃	1	2	yes	—
601	C₂²×D₄	C₂³×C₇₃	1	2	yes	—
602	C₂²×D₄	C₂³×C₇₃	1	2	yes	—
603	C₂²×D₄	C₂³×C₇₃	1	2	yes	—
604	C₂²×D₄	C₂³×C₇₃	1	2	yes	—
605	C₂²×D₄	C₂³×C₇₃	1	1	yes	characteristic
606	C₂²×D₄	C₂³×C₇₃	1	1	yes	characteristic
607	C₂³×C₄	C₂³×C₇₃	1	2	yes	—
608	C₂³×C₄	C₂³×C₇₃	1	1	yes	characteristic
609	C₂³×C₄	C₂³×C₇₃	1	2	yes	—
610	C₂³×C₄	C₂³×C₇₃	1	1	yes	characteristic
611	C₂³×C₄	C₂³×C₇₃	1	1	yes	characteristic
612	C₂³×C₄	C₂³×C₇₃	1	2	yes	—
613	C₂³×C₄	C₂³×C₇₃	1	1	yes	characteristic
614	C₂³×C₄	C₂³×C₇₃	1	1	yes	characteristic
615	#127	—	2	4	no	—
616	#126	—	2	8	no	—
617	#124	—	2	4	no	—
618	#124	—	2	8	no	—
619	#124	—	2	8	no	—
620	#124	—	4	2	no	—
621	#123	—	2	4	no	—
622	#123	—	2	8	no	—
623	#123	—	2	8	no	—
624	#123	D₄×C₇₃	1	8	yes	complemented
625	C₂²⋊Q₈	—	2	8	no	—
626	C₂²⋊Q₈	—	2	8	no	—
627	#121	—	2	8	no	—
628	#120	—	2	4	no	—
629	#120	—	2	8	no	—
630	C₄×Q₈	—	2	8	no	—
631	C₄×D₄	—	2	8	no	—
632	C₄×D₄	—	2	8	no	—
633	C₄×D₄	—	2	8	no	—
634	C₄×D₄	—	4	4	no	—
635	C₄×D₄	—	4	2	no	—
636	#117	—	2	8	no	—
637	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
638	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
639	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
640	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
641	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
642	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
643	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
644	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
645	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
646	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
647	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
648	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
649	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
650	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
651	C₂×C₂²⋊C₄	—	2	8	no	—
652	C₂×C₂²⋊C₄	—	4	2	no	—
653	C₂×C₂²⋊C₄	C₂³×C₇₃	1	2	yes	—
654	C₂×C₂²⋊C₄	C₂³×C₇₃	1	2	yes	—
655	C₂×C₂²⋊C₄	C₂³×C₇₃	1	2	yes	—
656	C₂×C₂²⋊C₄	C₂³×C₇₃	1	2	yes	—
657	C₂×C₂²⋊C₄	C₂³×C₇₃	1	2	yes	—
658	C₂×C₂²⋊C₄	C₂³×C₇₃	1	2	yes	—
659	C₂×C₂²⋊C₄	C₂³×C₇₃	1	2	yes	—
660	C₂×C₂²⋊C₄	C₂³×C₇₃	1	2	yes	—
661	C₂×C₂²⋊C₄	C₂³×C₇₃	1	2	yes	—
662	C₂×C₂²⋊C₄	C₂³×C₇₃	1	2	yes	—
663	C₂×C₂²⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
664	C₂×C₂²⋊C₄	C₂³×C₇₃	1	2	yes	—
665	C₂×C₂²⋊C₄	C₂³×C₇₃	1	2	yes	—
666	C₂×C₂²⋊C₄	C₂³×C₇₃	1	2	yes	—
667	C₂×C₂²⋊C₄	C₂³×C₇₃	1	2	yes	—
668	C₂×C₂²⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
669	C₂×C₂²⋊C₄	C₂³×C₇₃	1	2	yes	—
670	C₂×C₂²⋊C₄	C₂³×C₇₃	1	2	yes	—
671	C₂×C₂²⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
672	C₂×C₂²⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
673	C₂×C₂²⋊C₄	C₂³×C₇₃	1	2	yes	—
674	C₂×C₂²⋊C₄	C₂³×C₇₃	1	2	yes	—
675	C₂×C₂²⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
676	C₂×C₂²⋊C₄	C₂³×C₇₃	1	2	yes	—
677	C₂×C₂²⋊C₄	C₂³×C₇₃	1	2	yes	—
678	C₂×C₂²⋊C₄	C₂³×C₇₃	1	2	yes	—
679	C₂×C₂²⋊C₄	C₂³×C₇₃	1	2	yes	—
680	C₂×C₂²⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
681	C₂×C₂²⋊C₄	C₂³×C₇₃	1	2	yes	—
682	C₂×C₄²	—	4	2	no	—
683	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
684	C₂×C₄²	C₂³×C₇₃	1	2	yes	—
685	C₂×C₄²	C₂³×C₇₃	1	2	yes	—
686	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
687	C₂×C₄²	C₂³×C₇₃	1	2	yes	—
688	C₂×C₄²	C₂³×C₇₃	1	2	yes	—
689	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
690	C₂×C₄²	C₂³×C₇₃	1	2	yes	—
691	C₂×C₄²	C₂³×C₇₃	1	2	yes	—
692	#95	C₂³×C₇₃	1	2	yes	—
693	#95	C₂³×C₇₃	1	2	yes	—
694	#95	C₂³×C₇₃	1	2	yes	—
695	#95	C₂³×C₇₃	1	2	yes	—
696	#95	C₂³×C₇₃	1	2	yes	—
697	#95	C₂³×C₇₃	1	2	yes	—
698	#95	C₂³×C₇₃	1	2	yes	—
699	#95	C₂³×C₇₃	1	2	yes	—
700	#95	C₂³×C₇₃	1	2	yes	—
701	#95	C₂³×C₇₃	1	2	yes	—
702	#95	C₂³×C₇₃	1	2	yes	—
703	#95	C₂³×C₇₃	1	2	yes	—
704	#95	C₂³×C₇₃	1	2	yes	—
705	#95	C₂³×C₇₃	1	2	yes	—
706	#95	C₂³×C₇₃	1	2	yes	—
707	#95	C₂³×C₇₃	1	2	yes	—
708	#95	C₂³×C₇₃	1	2	yes	—
709	C₂⁴	—	2	2	no	—
710	C₂⁴	—	2	4	no	—
711	C₂⁴	—	4	1	no	—
712	C₂⁴	—	4	2	no	—
713	C₂⁴	—	4	1	no	—
714	C₂⁴	C₂⁴×C₇₃	1	2	yes	—
715	C₂⁴	C₂⁴×C₇₃	1	1	yes	characteristic
716	C₂⁴	C₂⁴×C₇₃	1	1	yes	characteristic
717	C₂⁴	C₂⁴×C₇₃	1	2	yes	—
718	C₂×Q₈	—	2	4	no	—
719	C₂×Q₈	—	2	2	no	—
720	C₂×Q₈	—	2	4	no	—
721	C₂×Q₈	—	4	2	no	—
722	C₂×Q₈	—	4	1	no	—
723	C₂×Q₈	—	4	1	no	—
724	C₂×D₄	—	2	4	no	—
725	C₂×D₄	—	2	4	no	—
726	C₂×D₄	—	2	4	no	—
727	C₂×D₄	—	2	4	no	—
728	C₂×D₄	—	2	4	no	—
729	C₂×D₄	—	2	4	no	—
730	C₂×D₄	—	2	2	no	—
731	C₂×D₄	—	2	4	no	—
732	C₂×D₄	—	2	4	no	—
733	C₂×D₄	—	2	4	no	—
734	C₂×D₄	—	4	2	no	—
735	C₂×D₄	—	4	1	no	—
736	C₂×D₄	—	4	1	no	—
737	C₂×D₄	—	4	2	no	—
738	C₂×D₄	—	4	2	no	—
739	C₂×D₄	—	4	2	no	—
740	C₂×D₄	—	4	1	no	—
741	C₂×D₄	—	4	1	no	—
742	C₂×D₄	—	4	2	no	—
743	C₂×D₄	—	4	2	no	—
744	C₂×D₄	C₂×D₄×C₇₃	1	4	yes	—
745	C₂²×C₄	—	2	4	no	—
746	C₂²×C₄	—	2	2	no	—
747	C₂²×C₄	—	2	4	no	—
748	C₂²×C₄	—	2	4	no	—
749	C₂²×C₄	—	2	2	no	—
750	C₂²×C₄	—	2	4	no	—
751	C₂²×C₄	—	2	4	no	—
752	C₂²×C₄	—	2	2	no	—
753	C₂²×C₄	—	4	1	no	—
754	C₂²×C₄	—	4	1	no	—
755	C₂²×C₄	—	4	2	no	—
756	C₂²×C₄	—	4	2	no	—
757	C₂²×C₄	—	4	1	no	—
758	C₂²×C₄	—	4	1	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	—	4	1	no	—
765	C₂²×C₄	C₂×D₄×C₇₃	1	4	yes	—
766	C₂²×C₄	C₂⁴×C₇₃	1	2	yes	—
767	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
768	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
769	C₂²×C₄	C₂⁴×C₇₃	1	2	yes	—
770	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
771	C₂²×C₄	C₂⁴×C₇₃	1	2	yes	—
772	C₂²×C₄	C₂⁴×C₇₃	1	2	yes	—
773	C₂²×C₄	C₂⁴×C₇₃	1	2	yes	—
774	C₂²×C₄	C₂⁴×C₇₃	1	2	yes	—
775	C₂²×C₄	C₂⁴×C₇₃	1	2	yes	—
776	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
777	C₂²×C₄	C₂⁴×C₇₃	1	2	yes	—
778	C₂²×C₄	C₂⁴×C₇₃	1	2	yes	—
779	C₂²×C₄	C₂⁴×C₇₃	1	2	yes	—
780	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
781	C₄⋊C₄	—	2	4	no	—
782	C₄⋊C₄	—	2	4	no	—
783	C₄⋊C₄	—	2	4	no	—
784	C₄⋊C₄	—	2	4	no	—
785	C₄⋊C₄	—	2	4	no	—
786	C₄⋊C₄	—	2	4	no	—
787	C₄⋊C₄	—	2	4	no	—
788	C₄⋊C₄	—	2	4	no	—
789	C₄⋊C₄	—	2	4	no	—
790	C₄⋊C₄	—	4	2	no	—
791	C₄⋊C₄	—	4	2	no	—
792	C₄⋊C₄	—	4	2	no	—
793	C₄⋊C₄	—	4	1	no	—
794	C₄⋊C₄	C₂×D₄×C₇₃	1	8	yes	—
795	C₂²⋊C₄	—	2	4	no	—
796	C₂²⋊C₄	—	2	4	no	—
797	C₂²⋊C₄	—	2	4	no	—
798	C₂²⋊C₄	—	2	2	no	—
799	C₂²⋊C₄	—	2	2	no	—
800	C₂²⋊C₄	—	2	4	no	—
801	C₂²⋊C₄	—	2	4	no	—
802	C₂²⋊C₄	—	2	4	no	—
803	C₂²⋊C₄	—	2	4	no	—
804	C₂²⋊C₄	—	2	4	no	—
805	C₂²⋊C₄	—	2	4	no	—
806	C₂²⋊C₄	—	2	4	no	—
807	C₂²⋊C₄	—	2	4	no	—
808	C₂²⋊C₄	—	2	4	no	—
809	C₂²⋊C₄	—	2	4	no	—
810	C₂²⋊C₄	—	2	4	no	—
811	C₂²⋊C₄	—	2	4	no	—
812	C₂²⋊C₄	—	4	2	no	—
813	C₂²⋊C₄	—	4	2	no	—
814	C₂²⋊C₄	—	4	2	no	—
815	C₂²⋊C₄	—	4	2	no	—
816	C₂²⋊C₄	—	4	2	no	—
817	C₂²⋊C₄	—	4	1	no	—
818	C₂²⋊C₄	—	4	1	no	—
819	C₂²⋊C₄	—	4	1	no	—
820	C₂²⋊C₄	—	4	2	no	—
821	C₂²⋊C₄	C₂×D₄×C₇₃	1	8	yes	—
822	C₂²⋊C₄	C₂×D₄×C₇₃	1	4	yes	—
823	C₂²⋊C₄	#41×C₇₃	1	8	yes	—
824	C₄²	—	2	2	no	—
825	C₄²	—	2	4	no	—
826	C₄²	—	2	4	no	—
827	C₄²	—	2	4	no	—
828	C₄²	—	2	2	no	—
829	C₄²	—	2	4	no	—
830	C₄²	—	2	2	no	—
831	C₄²	—	4	2	no	—
832	C₄²	—	4	2	no	—
833	C₂³	—	2	2	no	—
834	C₂³	—	2	2	no	—
835	C₂³	—	2	2	no	—
836	C₂³	—	2	2	no	—
837	C₂³	—	2	2	no	—
838	C₂³	—	2	1	no	—
839	C₂³	—	2	1	no	—
840	C₂³	—	2	1	no	—
841	C₂³	—	2	2	no	—
842	C₂³	—	2	2	no	—
843	C₂³	—	2	2	no	—
844	C₂³	—	2	2	no	—
845	C₂³	—	2	1	no	—
846	C₂³	—	2	2	no	—
847	C₂³	—	2	2	no	—
848	C₂³	—	2	2	no	—
849	C₂³	—	2	2	no	—
850	C₂³	—	2	2	no	—
851	C₂³	—	2	2	no	—
852	C₂³	—	2	2	no	—
853	C₂³	—	2	2	no	—
854	C₂³	—	4	8	no	—
855	C₂³	—	4	4	no	—
856	C₂³	—	8	2	no	—
857	C₂³	—	8	4	no	—
858	C₂³	—	8	2	no	—
859	C₂³	C₂²×D₄×C₇₃	1	2	yes	—
860	C₂³	C₂²×D₄×C₇₃	1	2	yes	—
861	C₂³	C₂×#41×C₇₃	1	4	yes	—
862	C₂³	C₂⁵×C₇₃	1	1	yes	characteristic
863	Q₈	—	4	8	no	—
864	Q₈	—	8	2	no	—
865	D₄	—	4	4	no	—
866	D₄	—	4	8	no	—
867	D₄	—	4	8	no	—
868	D₄	—	4	8	no	—
869	D₄	—	4	8	no	—
870	D₄	—	8	2	no	—
871	D₄	—	8	4	no	—
872	C₂×C₄	—	2	2	no	—
873	C₂×C₄	—	2	2	no	—
874	C₂×C₄	—	2	2	no	—
875	C₂×C₄	—	2	2	no	—
876	C₂×C₄	—	2	2	no	—
877	C₂×C₄	—	2	1	no	—
878	C₂×C₄	—	2	2	no	—
879	C₂×C₄	—	2	2	no	—
880	C₂×C₄	—	2	2	no	—
881	C₂×C₄	—	2	2	no	—
882	C₂×C₄	—	2	1	no	—
883	C₂×C₄	—	2	2	no	—
884	C₂×C₄	—	2	2	no	—
885	C₂×C₄	—	2	2	no	—
886	C₂×C₄	—	2	2	no	—
887	C₂×C₄	—	2	2	no	—
888	C₂×C₄	—	2	2	no	—
889	C₂×C₄	—	2	2	no	—
890	C₂×C₄	—	2	2	no	—
891	C₂×C₄	—	2	2	no	—
892	C₂×C₄	—	2	2	no	—
893	C₂×C₄	—	2	1	no	—
894	C₂×C₄	—	2	1	no	—
895	C₂×C₄	—	2	2	no	—
896	C₂×C₄	—	2	2	no	—
897	C₂×C₄	—	2	1	no	—
898	C₂×C₄	—	2	2	no	—
899	C₂×C₄	—	2	2	no	—
900	C₂×C₄	—	2	2	no	—
901	C₂×C₄	—	2	2	no	—
902	C₂×C₄	—	2	2	no	—
903	C₂×C₄	—	2	2	no	—
904	C₂×C₄	—	2	2	no	—
905	C₂×C₄	—	2	2	no	—
906	C₂×C₄	—	2	2	no	—
907	C₂×C₄	—	4	4	no	—
908	C₂×C₄	—	4	4	no	—
909	C₂×C₄	—	4	8	no	—
910	C₂×C₄	—	4	4	no	—
911	C₂×C₄	—	8	4	no	—
912	C₂×C₄	—	8	4	no	—
913	C₂×C₄	—	8	2	no	—
914	C₂×C₄	—	8	2	no	—
915	C₂×C₄	C₂²×D₄×C₇₃	1	4	yes	—
916	C₂×C₄	C₂²×D₄×C₇₃	1	2	yes	—
917	C₂×C₄	C₂²×D₄×C₇₃	1	4	yes	—
918	C₂×C₄	C₂×#41×C₇₃	1	4	yes	—
919	C₂×C₄	C₂×#41×C₇₃	1	4	yes	—
920	C₂×C₄	H(5,𝔽₂)×C₇₃	1	2	yes	—
921	C₂²	—	2	4	no	—
922	C₂²	—	2	4	no	—
923	C₂²	—	2	4	no	—
924	C₂²	—	2	4	no	—
925	C₂²	—	2	2	no	—
926	C₂²	—	2	2	no	—
927	C₂²	—	2	4	no	—
928	C₂²	—	4	2	no	—
929	C₂²	—	4	1	no	—
930	C₂²	—	4	1	no	—
931	C₂²	—	4	2	no	—
932	C₂²	—	4	2	no	—
933	C₂²	—	4	2	no	—
934	C₂²	—	4	2	no	—
935	C₂²	—	4	1	no	—
936	C₂²	—	4	1	no	—
937	C₂²	—	4	2	no	—
938	C₂²	—	4	2	no	—
939	C₂²	—	4	2	no	—
940	C₂²	—	4	2	no	—
941	C₂²	—	4	2	no	—
942	C₂²	—	4	2	no	—
943	C₂²	—	4	2	no	—
944	C₂²	—	4	2	no	—
945	C₂²	—	8	8	no	—
946	C₂²	C₂³×D₄×C₇₃	1	1	yes	characteristic
947	C₂²	C₂²×#41×C₇₃	1	2	yes	—
948	C₂²	C₂×H(5,𝔽₂)×C₇₃	1	1	yes	characteristic
949	C₂²	#585×C₇₃	1	2	yes	—
950	C₂²	#585×C₇₃	1	1	yes	characteristic
951	C₄	—	2	4	no	—
952	C₄	—	2	4	no	—
953	C₄	—	2	4	no	—
954	C₄	—	2	4	no	—
955	C₄	—	2	2	no	—
956	C₄	—	2	2	no	—
957	C₄	—	4	2	no	—
958	C₄	—	4	2	no	—
959	C₄	—	4	2	no	—
960	C₄	—	4	1	no	—
961	C₄	—	4	2	no	—
962	C₄	—	4	2	no	—
963	C₄	—	4	2	no	—
964	C₄	—	4	1	no	—
965	C₄	—	4	1	no	—
966	C₂	—	4	4	no	—
967	C₂	—	4	2	no	—
968	C₂	—	4	2	no	—
969	C₂	—	8	2	no	—
970	C₂	D₄×#41×C₇₃	1	2	yes	—
971	C₂	C₇₃×#3481	1	1	yes	characteristic
972	C₂	C₇₃×#3496	1	1	yes	characteristic
973	C₂	C₇₃×#3510	1	2	yes	—
974	C₂	C₇₃×#3533	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₇₃	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₇₃
prime radical	C₇₃×#2669	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. C₂×#559×C₇₃	C₂	semidirect
2. C₂×#551×C₇₃	C₂	semidirect
3. C₇₃×#2717	C₂	semidirect
4. C₇₃×#2672	C₂	semidirect
6. C₇₃×#2600	C₂	semidirect
7. C₇₃×#2557	C₂	semidirect
8. C₇₃×#2544	C₂	semidirect
9. C₇₃×#2534	C₂	semidirect
10. C₇₃×#2521	C₂	semidirect
11. C₇₃×#2472	C₂	semidirect
12. C₇₃×#2471	C₂	semidirect
13. C₇₃×#2466	C₂	semidirect
14. C₇₃×#2465	C₂	semidirect
15. C₇₃×#2461	C₂	semidirect
16. C₇₃×#2362	C₂	semidirect
17. C₇₃×#2358	C₂	semidirect
18. C₄×#123×C₇₃	C₂	semidirect
19. C₄×#121×C₇₃	C₂	semidirect
26. C₂×#124×C₇₃	C₂²	semidirect
27. C₂×#124×C₇₃	C₂²	semidirect
31. C₂×#123×C₇₃	C₂²	semidirect
37. C₂×C₄×Q₈×C₇₃	C₂²	semidirect
42. C₂×C₄×D₄×C₇₃	C₂²	semidirect
46. C₂²×C₄²×C₇₃	C₂²	semidirect
47. #399×C₇₃	C₂²	semidirect
49. #397×C₇₃	C₂²	semidirect
50. #397×C₇₃	C₂²	semidirect
52. #396×C₇₃	C₂²	semidirect
53. #395×C₇₃	C₂²	semidirect
54. #395×C₇₃	C₂²	semidirect
59. #394×C₇₃	C₂²	semidirect
63. #391×C₇₃	C₂²	semidirect
64. #391×C₇₃	C₂²	semidirect
67. #390×C₇₃	C₂²	semidirect
68. #389×C₇₃	C₂²	semidirect
69. #389×C₇₃	C₂²	semidirect
76. #388×C₇₃	C₂²	semidirect
77. #388×C₇₃	C₂²	semidirect
78. #388×C₇₃	C₂²	semidirect
79. #387×C₇₃	C₂²	semidirect
80. #387×C₇₃	C₂²	semidirect
81. #387×C₇₃	C₂²	semidirect
82. #387×C₇₃	C₂²	semidirect
83. #387×C₇₃	C₂²	semidirect
91. #386×C₇₃	C₂²	semidirect
94. #385×C₇₃	C₂²	semidirect
95. #385×C₇₃	C₂²	semidirect
97. #381×C₇₃	C₂²	semidirect
99. #380×C₇₃	C₂²	semidirect
101. C₄×C₄⋊C₄×C₇₃	C₂²	semidirect
102. C₄×C₄⋊C₄×C₇₃	C₂²	semidirect
103. C₄×C₄⋊C₄×C₇₃	C₂²	semidirect
107. C₄×C₂²⋊C₄×C₇₃	C₂²	semidirect
108. C₄×C₂²⋊C₄×C₇₃	C₂²	semidirect
136. #123×C₇₃	D₄	semidirect
478. #59846	C₇₃	direct (N × H)
488. C₂×#559	C₂×C₇₃	semidirect
489. C₂×#551	C₂×C₇₃	semidirect
490. #2717	C₂×C₇₃	semidirect
491. #2672	C₂×C₇₃	semidirect
493. #2600	C₂×C₇₃	semidirect
494. #2557	C₂×C₇₃	semidirect
495. #2544	C₂×C₇₃	semidirect
496. #2534	C₂×C₇₃	semidirect
497. #2521	C₂×C₇₃	semidirect
498. #2472	C₂×C₇₃	semidirect
499. #2471	C₂×C₇₃	semidirect
500. #2466	C₂×C₇₃	semidirect
501. #2465	C₂×C₇₃	semidirect
502. #2461	C₂×C₇₃	semidirect
503. #2362	C₂×C₇₃	semidirect
504. #2358	C₂×C₇₃	semidirect
505. C₄×#123	C₂×C₇₃	semidirect
506. C₄×#121	C₂×C₇₃	semidirect
507. C₇₃	#59846	direct (N × H)
514. C₂×#124	C₂²×C₇₃	semidirect
515. C₂×#124	C₂²×C₇₃	semidirect
519. C₂×#123	C₂²×C₇₃	semidirect
525. C₂×C₄×Q₈	C₂²×C₇₃	semidirect
530. C₂×C₄×D₄	C₂²×C₇₃	semidirect
534. C₂²×C₄²	C₂²×C₇₃	semidirect
535. #399	C₂²×C₇₃	semidirect
537. #397	C₂²×C₇₃	semidirect
538. #397	C₂²×C₇₃	semidirect
540. #396	C₂²×C₇₃	semidirect
541. #395	C₂²×C₇₃	semidirect
542. #395	C₂²×C₇₃	semidirect
547. #394	C₂²×C₇₃	semidirect
551. #391	C₂²×C₇₃	semidirect
552. #391	C₂²×C₇₃	semidirect
555. #390	C₂²×C₇₃	semidirect
556. #389	C₂²×C₇₃	semidirect
557. #389	C₂²×C₇₃	semidirect
564. #388	C₂²×C₇₃	semidirect
565. #388	C₂²×C₇₃	semidirect
566. #388	C₂²×C₇₃	semidirect
567. #387	C₂²×C₇₃	semidirect
568. #387	C₂²×C₇₃	semidirect
569. #387	C₂²×C₇₃	semidirect
570. #387	C₂²×C₇₃	semidirect
571. #387	C₂²×C₇₃	semidirect
579. #386	C₂²×C₇₃	semidirect
582. #385	C₂²×C₇₃	semidirect
583. #385	C₂²×C₇₃	semidirect
585. #381	C₂²×C₇₃	semidirect
587. #380	C₂²×C₇₃	semidirect
589. C₄×C₄⋊C₄	C₂²×C₇₃	semidirect
590. C₄×C₄⋊C₄	C₂²×C₇₃	semidirect
591. C₄×C₄⋊C₄	C₂²×C₇₃	semidirect
595. C₄×C₂²⋊C₄	C₂²×C₇₃	semidirect
596. C₄×C₂²⋊C₄	C₂²×C₇₃	semidirect
624. #123	D₄×C₇₃	semidirect

Maximal subgroups

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

subgroup	index
C₂×#559×C₇₃	2
C₂×#551×C₇₃	2
C₇₃×#2717	2
C₇₃×#2672	2
C₇₃×#2669	2
C₇₃×#2600	2
C₇₃×#2557	2
C₇₃×#2544	2
C₇₃×#2534	2
C₇₃×#2521	2
C₇₃×#2472	2
C₇₃×#2471	2
C₇₃×#2466	2
C₇₃×#2465	2
C₇₃×#2461	2
C₇₃×#2362	2
C₇₃×#2358	2
C₄×#123×C₇₃	2
C₄×#121×C₇₃	2
#59846	73

Subgroups — C73×#59846 #32969250

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₃×#59846 #32969250