Subgroups — C₇₃×#59697 #32969101

Order 18688.

1790 conjugacy classes of subgroups.

The subgroup lattice has 970 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇₃×#2777	C₂	1	2	yes	maximal, complemented
2	C₇₃×#2718	C₂	1	2	yes	maximal, complemented
3	C₇₃×#2596	C₂	1	2	yes	maximal, complemented
4	C₇₃×#2558	C₂	1	2	yes	maximal, complemented
5	C₇₃×#2545	C₂	1	1	yes	maximal, characteristic, complemented
6	C₇₃×#2522	C₂	1	2	yes	maximal, complemented
7	C₇₃×#2511	C₂	1	1	yes	maximal, characteristic, complemented
8	C₇₃×#2506	C₂	1	1	yes	maximal, characteristic, complemented
9	C₇₃×#2501	C₂	1	1	yes	maximal, characteristic
10	C₇₃×#2470	C₂	1	2	yes	maximal, complemented
11	C₇₃×#2448	C₂	1	1	yes	maximal, characteristic, complemented
12	C₇₃×#2441	C₂	1	2	yes	maximal, complemented
13	C₇₃×#2429	C₂	1	1	yes	maximal, characteristic, complemented
14	C₇₃×#2427	C₂	1	1	yes	maximal, characteristic
15	C₇₃×#2426	C₂	1	1	yes	maximal, characteristic
16	C₇₃×#2374	C₂	1	2	yes	maximal, complemented
17	C₇₃×#2367	C₂	1	1	yes	maximal, characteristic, complemented
18	C₇₃×#2360	C₂	1	1	yes	maximal, characteristic, complemented
19	C₇₃×#2360	C₂	1	1	yes	maximal, characteristic, complemented
20	Q₈×C₄⋊C₄×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
21	C₄×C₄⋊Q₈×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
22	C₄×#126×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
23	C₇₃×#2293	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×C₄⋊Q₈×C₇₃	C₂²	1	1	yes	characteristic
25	C₂×#126×C₇₃	C₂²	1	1	yes	characteristic
26	C₂×#125×C₇₃	C₂²	1	2	yes	—
27	C₂×#124×C₇₃	C₂²	1	1	yes	characteristic
28	C₂×#124×C₇₃	C₂²	1	1	yes	characteristic
29	C₂×#123×C₇₃	C₂²	1	2	yes	—
30	C₂×#123×C₇₃	C₂²	1	2	yes	—
31	C₂×C₂²⋊Q₈×C₇₃	C₂²	1	1	yes	characteristic
32	C₂×C₂²⋊Q₈×C₇₃	C₂²	1	1	yes	characteristic
33	C₂×#121×C₇₃	C₂²	1	1	yes	characteristic
34	C₂×C₄×Q₈×C₇₃	C₂²	1	1	yes	characteristic
35	C₂×C₄×Q₈×C₇₃	C₂²	1	1	yes	characteristic
36	C₂×C₄×Q₈×C₇₃	C₂²	1	1	yes	characteristic
37	C₂×C₄×Q₈×C₇₃	C₂²	1	1	yes	characteristic
38	C₂×C₄×D₄×C₇₃	C₂²	1	1	yes	characteristic
39	C₂×#117×C₇₃	C₂²	1	2	yes	—
40	C₂²×C₄⋊C₄×C₇₃	C₂²	1	1	yes	characteristic
41	#400×C₇₃	C₂²	1	2	yes	—
42	#400×C₇₃	C₂²	1	2	yes	—
43	#400×C₇₃	C₂²	1	2	yes	—
44	#399×C₇₃	C₂²	1	2	yes	—
45	#399×C₇₃	C₂²	1	2	yes	—
46	#399×C₇₃	C₂²	1	2	yes	—
47	#398×C₇₃	C₂²	1	2	yes	—
48	#398×C₇₃	C₂²	1	2	yes	—
49	#397×C₇₃	C₂²	1	2	yes	—
50	#397×C₇₃	C₂²	1	2	yes	—
51	#396×C₇₃	C₂²	1	2	yes	—
52	#396×C₇₃	C₂²	1	2	yes	—
53	#396×C₇₃	C₂²	1	2	yes	—
54	#396×C₇₃	C₂²	1	2	yes	—
55	#394×C₇₃	C₂²	1	2	yes	—
56	#394×C₇₃	C₂²	1	2	yes	—
57	#391×C₇₃	C₂²	1	1	yes	characteristic
58	#391×C₇₃	C₂²	1	1	yes	characteristic
59	#391×C₇₃	C₂²	1	1	yes	characteristic
60	#391×C₇₃	C₂²	1	1	yes	characteristic
61	#390×C₇₃	C₂²	1	1	yes	characteristic
62	#390×C₇₃	C₂²	1	1	yes	characteristic
63	#390×C₇₃	C₂²	1	1	yes	characteristic
64	#390×C₇₃	C₂²	1	2	yes	—
65	#389×C₇₃	C₂²	1	2	yes	—
66	#389×C₇₃	C₂²	1	2	yes	—
67	#389×C₇₃	C₂²	1	2	yes	—
68	#389×C₇₃	C₂²	1	2	yes	—
69	#389×C₇₃	C₂²	1	1	yes	characteristic
70	#389×C₇₃	C₂²	1	2	yes	—
71	#389×C₇₃	C₂²	1	2	yes	—
72	#389×C₇₃	C₂²	1	1	yes	characteristic
73	#389×C₇₃	C₂²	1	1	yes	characteristic
74	#389×C₇₃	C₂²	1	1	yes	characteristic
75	#389×C₇₃	C₂²	1	2	yes	—
76	#389×C₇₃	C₂²	1	1	yes	characteristic
77	#388×C₇₃	C₂²	1	2	yes	—
78	#388×C₇₃	C₂²	1	2	yes	—
79	#388×C₇₃	C₂²	1	2	yes	—
80	#388×C₇₃	C₂²	1	2	yes	—
81	#388×C₇₃	C₂²	1	2	yes	—
82	#388×C₇₃	C₂²	1	1	yes	characteristic
83	#388×C₇₃	C₂²	1	2	yes	—
84	#388×C₇₃	C₂²	1	2	yes	—
85	#388×C₇₃	C₂²	1	2	yes	—
86	#388×C₇₃	C₂²	1	2	yes	—
87	#388×C₇₃	C₂²	1	2	yes	—
88	#388×C₇₃	C₂²	1	1	yes	characteristic
89	#388×C₇₃	C₂²	1	1	yes	characteristic
90	#387×C₇₃	C₂²	1	1	yes	characteristic
91	#387×C₇₃	C₂²	1	2	yes	—
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	#387×C₇₃	C₂²	1	2	yes	—
97	#387×C₇₃	C₂²	1	1	yes	characteristic
98	#386×C₇₃	C₂²	1	2	yes	—
99	#385×C₇₃	C₂²	1	2	yes	—
100	#385×C₇₃	C₂²	1	2	yes	—
101	#385×C₇₃	C₂²	1	2	yes	—
102	#384×C₇₃	C₂²	1	2	yes	—
103	#384×C₇₃	C₂²	1	1	yes	characteristic
104	#384×C₇₃	C₂²	1	1	yes	characteristic
105	#383×C₇₃	C₂²	1	1	yes	characteristic
106	#380×C₇₃	C₂²	1	2	yes	—
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	1	yes	characteristic
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	2	yes	—
113	C₄×C₄⋊C₄×C₇₃	C₂²	1	2	yes	—
114	C₄×C₄⋊C₄×C₇₃	C₂²	1	2	yes	—
115	C₄×C₂²⋊C₄×C₇₃	C₂²	1	2	yes	—
116	C₄×C₂²⋊C₄×C₇₃	C₂²	1	2	yes	—
117	C₄×C₂²⋊C₄×C₇₃	C₂²	1	1	yes	characteristic
118	C₄×C₂²⋊C₄×C₇₃	C₂²	1	2	yes	—
119	C₄×C₂²⋊C₄×C₇₃	C₂²	1	2	yes	—
120	C₄×C₂²⋊C₄×C₇₃	C₂²	1	1	yes	characteristic
121	C₄×C₂²⋊C₄×C₇₃	C₂²	1	1	yes	characteristic
122	C₄³×C₇₃	C₂²	1	1	yes	characteristic
123	C₂²×Q₈×C₇₃	C₂³	1	1	yes	characteristic
124	C₂²×Q₈×C₇₃	C₂³	1	1	yes	characteristic
125	C₂²×D₄×C₇₃	C₂³	1	1	yes	characteristic
126	C₂²×D₄×C₇₃	C₂³	1	2	yes	—
127	C₂³×C₄×C₇₃	C₂³	1	1	yes	characteristic
128	C₂³×C₄×C₇₃	C₂³	1	2	yes	—
129	C₂³×C₄×C₇₃	C₂³	1	2	yes	—
130	C₄⋊Q₈×C₇₃	—	2	4	no	—
131	#126×C₇₃	—	2	4	no	—
132	#125×C₇₃	—	4	4	no	—
133	#124×C₇₃	—	2	4	no	—
134	#124×C₇₃	—	4	2	no	—
135	#123×C₇₃	—	2	8	no	—
136	#123×C₇₃	—	4	4	no	—
137	C₂²⋊Q₈×C₇₃	—	2	4	no	—
138	C₂²⋊Q₈×C₇₃	—	2	4	no	—
139	#121×C₇₃	—	4	2	no	—
140	C₄×Q₈×C₇₃	—	2	4	no	—
141	C₄×Q₈×C₇₃	—	4	2	no	—
142	C₄×Q₈×C₇₃	—	4	2	no	—
143	C₄×Q₈×C₇₃	—	4	2	no	—
144	C₄×D₄×C₇₃	—	2	4	no	—
145	#117×C₇₃	—	4	4	no	—
146	C₂×C₄⋊C₄×C₇₃	—	4	2	no	—
147	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
148	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
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	1	yes	characteristic
155	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
156	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
157	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
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	2	yes	—
162	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
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	2	yes	—
166	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
167	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
168	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
169	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
170	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
171	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
172	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
173	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
174	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
175	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
176	C₂×C₂²⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
177	C₂×C₂²⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
178	C₂×C₂²⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
179	C₂×C₂²⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
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	2	yes	—
184	C₂×C₂²⋊C₄×C₇₃	C₂³	1	2	yes	—
185	C₂×C₂²⋊C₄×C₇₃	C₂³	1	2	yes	—
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	2	yes	—
193	C₂×C₂²⋊C₄×C₇₃	C₂³	1	2	yes	—
194	C₂×C₂²⋊C₄×C₇₃	C₂³	1	2	yes	—
195	C₂×C₂²⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
196	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
197	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
198	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
199	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
200	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
201	C₂×C₄²×C₇₃	C₂³	1	2	yes	—
202	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
203	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
204	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
205	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
206	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
207	C₂×C₄²×C₇₃	C₂³	1	2	yes	—
208	C₂×C₄²×C₇₃	C₂³	1	2	yes	—
209	C₂×C₄²×C₇₃	C₂³	1	2	yes	—
210	C₂×C₄²×C₇₃	C₂³	1	2	yes	—
211	C₂×C₄²×C₇₃	C₂³	1	2	yes	—
212	#95×C₇₃	C₂³	1	2	yes	—
213	#95×C₇₃	C₂³	1	1	yes	characteristic
214	#95×C₇₃	C₂³	1	2	yes	—
215	#95×C₇₃	C₂³	1	1	yes	characteristic
216	#95×C₇₃	C₂³	1	1	yes	characteristic
217	#95×C₇₃	C₂³	1	1	yes	characteristic
218	#95×C₇₃	C₂³	1	1	yes	characteristic
219	#95×C₇₃	C₂³	1	1	yes	characteristic
220	#95×C₇₃	C₂³	1	2	yes	—
221	#95×C₇₃	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
226	#95×C₇₃	C₂³	1	1	yes	characteristic
227	#95×C₇₃	C₂³	1	1	yes	characteristic
228	#95×C₇₃	C₂³	1	2	yes	—
229	#95×C₇₃	C₂³	1	2	yes	—
230	#95×C₇₃	C₂³	1	2	yes	—
231	#95×C₇₃	C₂³	1	2	yes	—
232	#95×C₇₃	C₂³	1	1	yes	characteristic
233	#95×C₇₃	C₂³	1	1	yes	characteristic
234	#95×C₇₃	C₂³	1	2	yes	—
235	#95×C₇₃	C₂³	1	2	yes	—
236	#95×C₇₃	C₂³	1	2	yes	—
237	#95×C₇₃	C₂³	1	2	yes	—
238	#95×C₇₃	C₂³	1	2	yes	—
239	C₂⁴×C₇₃	C₂⁴	1	2	yes	—
240	C₂⁴×C₇₃	C₂⁴	1	1	yes	characteristic
241	C₂×Q₈×C₇₃	—	2	2	no	—
242	C₂×Q₈×C₇₃	—	2	2	no	—
243	C₂×Q₈×C₇₃	—	2	2	no	—
244	C₂×Q₈×C₇₃	—	2	2	no	—
245	C₂×Q₈×C₇₃	—	2	2	no	—
246	C₂×Q₈×C₇₃	#41	1	4	yes	—
247	C₂×D₄×C₇₃	—	2	4	no	—
248	C₂×D₄×C₇₃	—	2	2	no	—
249	C₂×D₄×C₇₃	—	2	2	no	—
250	C₂×D₄×C₇₃	—	2	2	no	—
251	C₂×D₄×C₇₃	—	4	2	no	—
252	C₂×D₄×C₇₃	—	4	2	no	—
253	C₂²×C₄×C₇₃	—	2	4	no	—
254	C₂²×C₄×C₇₃	—	2	4	no	—
255	C₂²×C₄×C₇₃	—	2	2	no	—
256	C₂²×C₄×C₇₃	—	2	2	no	—
257	C₂²×C₄×C₇₃	—	2	2	no	—
258	C₂²×C₄×C₇₃	—	2	4	no	—
259	C₂²×C₄×C₇₃	—	4	2	no	—
260	C₂²×C₄×C₇₃	—	4	2	no	—
261	C₂²×C₄×C₇₃	—	4	2	no	—
262	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
263	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
264	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
265	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
266	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
267	C₂²×C₄×C₇₃	C₂⁴	1	2	yes	—
268	C₂²×C₄×C₇₃	C₂⁴	1	2	yes	—
269	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
270	C₂²×C₄×C₇₃	C₂⁴	1	2	yes	—
271	C₂²×C₄×C₇₃	C₂⁴	1	2	yes	—
272	C₂²×C₄×C₇₃	C₂⁴	1	2	yes	—
273	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
274	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
275	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
276	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
277	C₂²×C₄×C₇₃	C₂⁴	1	2	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	1	yes	characteristic
282	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
283	C₄⋊C₄×C₇₃	—	2	4	no	—
284	C₄⋊C₄×C₇₃	—	2	2	no	—
285	C₄⋊C₄×C₇₃	—	2	4	no	—
286	C₄⋊C₄×C₇₃	—	2	4	no	—
287	C₄⋊C₄×C₇₃	—	2	4	no	—
288	C₄⋊C₄×C₇₃	—	2	4	no	—
289	C₄⋊C₄×C₇₃	—	2	2	no	—
290	C₄⋊C₄×C₇₃	—	2	2	no	—
291	C₄⋊C₄×C₇₃	—	2	2	no	—
292	C₄⋊C₄×C₇₃	—	2	4	no	—
293	C₄⋊C₄×C₇₃	—	2	4	no	—
294	C₄⋊C₄×C₇₃	—	2	2	no	—
295	C₄⋊C₄×C₇₃	—	2	2	no	—
296	C₄⋊C₄×C₇₃	—	2	4	no	—
297	C₄⋊C₄×C₇₃	—	2	2	no	—
298	C₄⋊C₄×C₇₃	—	2	4	no	—
299	C₄⋊C₄×C₇₃	—	2	2	no	—
300	C₄⋊C₄×C₇₃	—	2	2	no	—
301	C₄⋊C₄×C₇₃	—	2	2	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	2	no	—
306	C₄⋊C₄×C₇₃	—	4	2	no	—
307	C₄⋊C₄×C₇₃	—	4	2	no	—
308	C₄⋊C₄×C₇₃	—	4	2	no	—
309	C₄⋊C₄×C₇₃	—	4	2	no	—
310	C₄⋊C₄×C₇₃	—	4	2	no	—
311	C₄⋊C₄×C₇₃	#41	1	4	yes	—
312	C₂²⋊C₄×C₇₃	—	2	2	no	—
313	C₂²⋊C₄×C₇₃	—	2	2	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	2	no	—
323	C₂²⋊C₄×C₇₃	—	2	2	no	—
324	C₂²⋊C₄×C₇₃	—	2	4	no	—
325	C₂²⋊C₄×C₇₃	—	2	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	2	no	—
330	C₂²⋊C₄×C₇₃	—	4	2	no	—
331	C₂²⋊C₄×C₇₃	#41	1	4	yes	—
332	C₄²×C₇₃	—	2	2	no	—
333	C₄²×C₇₃	—	2	4	no	—
334	C₄²×C₇₃	—	2	2	no	—
335	C₄²×C₇₃	—	2	2	no	—
336	C₄²×C₇₃	—	2	2	no	—
337	C₄²×C₇₃	—	2	2	no	—
338	C₄²×C₇₃	—	2	2	no	—
339	C₄²×C₇₃	—	2	2	no	—
340	C₄²×C₇₃	—	2	2	no	—
341	C₄²×C₇₃	—	2	2	no	—
342	C₄²×C₇₃	—	2	2	no	—
343	C₄²×C₇₃	—	4	2	no	—
344	C₄²×C₇₃	—	4	2	no	—
345	C₄²×C₇₃	—	4	2	no	—
346	C₄²×C₇₃	—	4	2	no	—
347	C₄²×C₇₃	—	4	2	no	—
348	C₂³×C₇₃	—	2	1	no	—
349	C₂³×C₇₃	—	2	1	no	—
350	C₂³×C₇₃	—	2	1	no	—
351	C₂³×C₇₃	—	2	1	no	—
352	C₂³×C₇₃	—	2	1	no	—
353	C₂³×C₇₃	—	2	1	no	—
354	C₂³×C₇₃	—	2	2	no	—
355	C₂³×C₇₃	—	2	2	no	—
356	C₂³×C₇₃	—	2	2	no	—
357	C₂³×C₇₃	—	2	2	no	—
358	C₂³×C₇₃	—	2	2	no	—
359	C₂³×C₇₃	—	2	2	no	—
360	C₂³×C₇₃	—	2	2	no	—
361	C₂³×C₇₃	C₂×#41	1	2	yes	—
362	C₂³×C₇₃	C₂⁵	1	1	yes	characteristic
363	Q₈×C₇₃	—	2	8	no	—
364	Q₈×C₇₃	—	4	4	no	—
365	D₄×C₇₃	—	4	4	no	—
366	D₄×C₇₃	—	8	4	no	—
367	C₂×C₄×C₇₃	—	2	1	no	—
368	C₂×C₄×C₇₃	—	2	1	no	—
369	C₂×C₄×C₇₃	—	2	1	no	—
370	C₂×C₄×C₇₃	—	2	2	no	—
371	C₂×C₄×C₇₃	—	2	1	no	—
372	C₂×C₄×C₇₃	—	2	1	no	—
373	C₂×C₄×C₇₃	—	2	1	no	—
374	C₂×C₄×C₇₃	—	2	2	no	—
375	C₂×C₄×C₇₃	—	2	2	no	—
376	C₂×C₄×C₇₃	—	2	1	no	—
377	C₂×C₄×C₇₃	—	2	1	no	—
378	C₂×C₄×C₇₃	—	2	1	no	—
379	C₂×C₄×C₇₃	—	2	1	no	—
380	C₂×C₄×C₇₃	—	2	2	no	—
381	C₂×C₄×C₇₃	—	2	1	no	—
382	C₂×C₄×C₇₃	—	2	1	no	—
383	C₂×C₄×C₇₃	—	2	1	no	—
384	C₂×C₄×C₇₃	—	2	1	no	—
385	C₂×C₄×C₇₃	—	2	1	no	—
386	C₂×C₄×C₇₃	—	2	1	no	—
387	C₂×C₄×C₇₃	—	2	1	no	—
388	C₂×C₄×C₇₃	—	2	1	no	—
389	C₂×C₄×C₇₃	—	2	2	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	1	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	1	no	—
398	C₂×C₄×C₇₃	—	2	1	no	—
399	C₂×C₄×C₇₃	—	2	1	no	—
400	C₂×C₄×C₇₃	—	2	1	no	—
401	C₂×C₄×C₇₃	—	2	1	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	2	no	—
406	C₂×C₄×C₇₃	—	2	2	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	1	no	—
411	C₂×C₄×C₇₃	—	2	1	no	—
412	C₂×C₄×C₇₃	—	2	2	no	—
413	C₂×C₄×C₇₃	—	2	1	no	—
414	C₂×C₄×C₇₃	—	2	1	no	—
415	C₂×C₄×C₇₃	—	2	2	no	—
416	C₂×C₄×C₇₃	—	2	1	no	—
417	C₂×C₄×C₇₃	—	2	1	no	—
418	C₂×C₄×C₇₃	—	2	1	no	—
419	C₂×C₄×C₇₃	—	2	1	no	—
420	C₂×C₄×C₇₃	—	4	8	no	—
421	C₂×C₄×C₇₃	—	4	4	no	—
422	C₂×C₄×C₇₃	—	8	4	no	—
423	C₂×C₄×C₇₃	C₂×#41	1	2	yes	—
424	C₂×C₄×C₇₃	C₂×#41	1	4	yes	—
425	C₂×C₄×C₇₃	C₂×#41	1	4	yes	—
426	C₂×C₄×C₇₃	C₂×#41	1	2	yes	—
427	C₂×C₄×C₇₃	C₂×#41	1	2	yes	—
428	C₂×C₄×C₇₃	C₂×#41	1	2	yes	—
429	C₂×C₄×C₇₃	H(5,𝔽₂)	1	2	yes	—
430	C₂×C₄×C₇₃	H(5,𝔽₂)	1	2	yes	—
431	C₂×C₄×C₇₃	2₋¹⁺⁴	1	2	yes	—
432	C₂×C₄×C₇₃	2₋¹⁺⁴	1	2	yes	—
433	C₂²×C₇₃	—	2	2	no	—
434	C₂²×C₇₃	—	2	2	no	—
435	C₂²×C₇₃	—	2	2	no	—
436	C₂²×C₇₃	—	4	1	no	—
437	C₂²×C₇₃	—	4	1	no	—
438	C₂²×C₇₃	—	4	1	no	—
439	C₂²×C₇₃	—	4	1	no	—
440	C₂²×C₇₃	—	4	2	no	—
441	C₂²×C₇₃	—	4	2	no	—
442	C₂²×C₇₃	—	4	2	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	C₂²×#41	1	1	yes	characteristic
448	C₂²×C₇₃	C₂²×#41	1	1	yes	characteristic
449	C₂²×C₇₃	C₂²×#41	1	1	yes	characteristic
450	C₂²×C₇₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
451	C₂²×C₇₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
452	C₂²×C₇₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
453	C₂²×C₇₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
454	C₄×C₇₃	—	2	4	no	—
455	C₄×C₇₃	—	2	2	no	—
456	C₄×C₇₃	—	2	2	no	—
457	C₄×C₇₃	—	2	2	no	—
458	C₄×C₇₃	—	2	4	no	—
459	C₄×C₇₃	—	2	2	no	—
460	C₄×C₇₃	—	2	2	no	—
461	C₄×C₇₃	—	4	1	no	—
462	C₄×C₇₃	—	4	2	no	—
463	C₄×C₇₃	—	4	1	no	—
464	C₄×C₇₃	—	4	1	no	—
465	C₄×C₇₃	—	4	1	no	—
466	C₄×C₇₃	—	4	1	no	—
467	C₄×C₇₃	—	4	2	no	—
468	C₄×C₇₃	—	4	2	no	—
469	C₄×C₇₃	—	4	2	no	—
470	C₄×C₇₃	—	4	1	no	—
471	C₄×C₇₃	—	4	1	no	—
472	C₄×C₇₃	—	4	2	no	—
473	C₄×C₇₃	—	4	1	no	—
474	C₄×C₇₃	#553	1	4	yes	—
475	#59697	C₇₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
476	C₂×C₇₃	—	4	2	no	—
477	C₂×C₇₃	—	8	2	no	—
478	C₂×C₇₃	C₂×#553	1	1	yes	characteristic
479	C₂×C₇₃	#3482	1	1	yes	characteristic
480	C₂×C₇₃	#3482	1	1	yes	characteristic
481	C₂×C₇₃	#3508	1	1	yes	characteristic
482	C₂×C₇₃	#3520	1	1	yes	characteristic
483	C₂×C₇₃	#3522	1	1	yes	characteristic
484	C₂×C₇₃	#3552	1	1	yes	characteristic
485	#2777	C₂×C₇₃	1	2	yes	complemented
486	#2718	C₂×C₇₃	1	2	yes	complemented
487	#2596	C₂×C₇₃	1	2	yes	complemented
488	#2558	C₂×C₇₃	1	2	yes	complemented
489	#2545	C₂×C₇₃	1	1	yes	characteristic, complemented
490	#2522	C₂×C₇₃	1	2	yes	complemented
491	#2511	C₂×C₇₃	1	1	yes	characteristic, complemented
492	#2506	C₂×C₇₃	1	1	yes	characteristic, complemented
493	#2501	C₂×C₇₃	1	1	yes	characteristic
494	#2470	C₂×C₇₃	1	2	yes	complemented
495	#2448	C₂×C₇₃	1	1	yes	characteristic, complemented
496	#2441	C₂×C₇₃	1	2	yes	complemented
497	#2429	C₂×C₇₃	1	1	yes	characteristic, complemented
498	#2427	C₂×C₇₃	1	1	yes	characteristic
499	#2426	C₂×C₇₃	1	1	yes	characteristic
500	#2374	C₂×C₇₃	1	2	yes	complemented
501	#2367	C₂×C₇₃	1	1	yes	characteristic, complemented
502	#2360	C₂×C₇₃	1	1	yes	characteristic, complemented
503	#2360	C₂×C₇₃	1	1	yes	characteristic, complemented
504	Q₈×C₄⋊C₄	C₂×C₇₃	1	1	yes	characteristic, complemented
505	C₄×C₄⋊Q₈	C₂×C₇₃	1	1	yes	characteristic, complemented
506	C₄×#126	C₂×C₇₃	1	1	yes	characteristic, complemented
507	#2293	C₂×C₇₃	1	1	yes	characteristic, complemented
508	C₇₃	#59697	1	1	yes	characteristic, direct product factor, Sylow
509	C₂×C₄⋊Q₈	C₂²×C₇₃	1	1	yes	characteristic
510	C₂×#126	C₂²×C₇₃	1	1	yes	characteristic
511	C₂×#125	C₂²×C₇₃	1	2	yes	—
512	C₂×#124	C₂²×C₇₃	1	1	yes	characteristic
513	C₂×#124	C₂²×C₇₃	1	1	yes	characteristic
514	C₂×#123	C₂²×C₇₃	1	2	yes	—
515	C₂×#123	C₂²×C₇₃	1	2	yes	—
516	C₂×C₂²⋊Q₈	C₂²×C₇₃	1	1	yes	characteristic
517	C₂×C₂²⋊Q₈	C₂²×C₇₃	1	1	yes	characteristic
518	C₂×#121	C₂²×C₇₃	1	1	yes	characteristic
519	C₂×C₄×Q₈	C₂²×C₇₃	1	1	yes	characteristic
520	C₂×C₄×Q₈	C₂²×C₇₃	1	1	yes	characteristic
521	C₂×C₄×Q₈	C₂²×C₇₃	1	1	yes	characteristic
522	C₂×C₄×Q₈	C₂²×C₇₃	1	1	yes	characteristic
523	C₂×C₄×D₄	C₂²×C₇₃	1	1	yes	characteristic
524	C₂×#117	C₂²×C₇₃	1	2	yes	—
525	C₂²×C₄⋊C₄	C₂²×C₇₃	1	1	yes	characteristic
526	#400	C₂²×C₇₃	1	2	yes	—
527	#400	C₂²×C₇₃	1	2	yes	—
528	#400	C₂²×C₇₃	1	2	yes	—
529	#399	C₂²×C₇₃	1	2	yes	—
530	#399	C₂²×C₇₃	1	2	yes	—
531	#399	C₂²×C₇₃	1	2	yes	—
532	#398	C₂²×C₇₃	1	2	yes	—
533	#398	C₂²×C₇₃	1	2	yes	—
534	#397	C₂²×C₇₃	1	2	yes	—
535	#397	C₂²×C₇₃	1	2	yes	—
536	#396	C₂²×C₇₃	1	2	yes	—
537	#396	C₂²×C₇₃	1	2	yes	—
538	#396	C₂²×C₇₃	1	2	yes	—
539	#396	C₂²×C₇₃	1	2	yes	—
540	#394	C₂²×C₇₃	1	2	yes	—
541	#394	C₂²×C₇₃	1	2	yes	—
542	#391	C₂²×C₇₃	1	1	yes	characteristic
543	#391	C₂²×C₇₃	1	1	yes	characteristic
544	#391	C₂²×C₇₃	1	1	yes	characteristic
545	#391	C₂²×C₇₃	1	1	yes	characteristic
546	#390	C₂²×C₇₃	1	1	yes	characteristic
547	#390	C₂²×C₇₃	1	2	yes	—
548	#390	C₂²×C₇₃	1	1	yes	characteristic
549	#390	C₂²×C₇₃	1	1	yes	characteristic
550	#389	C₂²×C₇₃	1	2	yes	—
551	#389	C₂²×C₇₃	1	2	yes	—
552	#389	C₂²×C₇₃	1	2	yes	—
553	#389	C₂²×C₇₃	1	1	yes	characteristic
554	#389	C₂²×C₇₃	1	1	yes	characteristic
555	#389	C₂²×C₇₃	1	2	yes	—
556	#389	C₂²×C₇₃	1	2	yes	—
557	#389	C₂²×C₇₃	1	2	yes	—
558	#389	C₂²×C₇₃	1	2	yes	—
559	#389	C₂²×C₇₃	1	1	yes	characteristic
560	#389	C₂²×C₇₃	1	1	yes	characteristic
561	#389	C₂²×C₇₃	1	1	yes	characteristic
562	#388	C₂²×C₇₃	1	1	yes	characteristic
563	#388	C₂²×C₇₃	1	1	yes	characteristic
564	#388	C₂²×C₇₃	1	1	yes	characteristic
565	#388	C₂²×C₇₃	1	2	yes	—
566	#388	C₂²×C₇₃	1	2	yes	—
567	#388	C₂²×C₇₃	1	2	yes	—
568	#388	C₂²×C₇₃	1	2	yes	—
569	#388	C₂²×C₇₃	1	2	yes	—
570	#388	C₂²×C₇₃	1	2	yes	—
571	#388	C₂²×C₇₃	1	2	yes	—
572	#388	C₂²×C₇₃	1	2	yes	—
573	#388	C₂²×C₇₃	1	2	yes	—
574	#388	C₂²×C₇₃	1	2	yes	—
575	#387	C₂²×C₇₃	1	1	yes	characteristic
576	#387	C₂²×C₇₃	1	1	yes	characteristic
577	#387	C₂²×C₇₃	1	1	yes	characteristic
578	#387	C₂²×C₇₃	1	2	yes	—
579	#387	C₂²×C₇₃	1	2	yes	—
580	#387	C₂²×C₇₃	1	2	yes	—
581	#387	C₂²×C₇₃	1	2	yes	—
582	#387	C₂²×C₇₃	1	2	yes	—
583	#386	C₂²×C₇₃	1	2	yes	—
584	#385	C₂²×C₇₃	1	2	yes	—
585	#385	C₂²×C₇₃	1	2	yes	—
586	#385	C₂²×C₇₃	1	2	yes	—
587	#384	C₂²×C₇₃	1	1	yes	characteristic
588	#384	C₂²×C₇₃	1	2	yes	—
589	#384	C₂²×C₇₃	1	1	yes	characteristic
590	#383	C₂²×C₇₃	1	1	yes	characteristic
591	#380	C₂²×C₇₃	1	2	yes	—
592	C₄×C₄⋊C₄	C₂²×C₇₃	1	1	yes	characteristic
593	C₄×C₄⋊C₄	C₂²×C₇₃	1	1	yes	characteristic
594	C₄×C₄⋊C₄	C₂²×C₇₃	1	1	yes	characteristic
595	C₄×C₄⋊C₄	C₂²×C₇₃	1	2	yes	—
596	C₄×C₄⋊C₄	C₂²×C₇₃	1	2	yes	—
597	C₄×C₄⋊C₄	C₂²×C₇₃	1	2	yes	—
598	C₄×C₄⋊C₄	C₂²×C₇₃	1	1	yes	characteristic
599	C₄×C₄⋊C₄	C₂²×C₇₃	1	1	yes	characteristic
600	C₄×C₂²⋊C₄	C₂²×C₇₃	1	1	yes	characteristic
601	C₄×C₂²⋊C₄	C₂²×C₇₃	1	1	yes	characteristic
602	C₄×C₂²⋊C₄	C₂²×C₇₃	1	1	yes	characteristic
603	C₄×C₂²⋊C₄	C₂²×C₇₃	1	2	yes	—
604	C₄×C₂²⋊C₄	C₂²×C₇₃	1	2	yes	—
605	C₄×C₂²⋊C₄	C₂²×C₇₃	1	2	yes	—
606	C₄×C₂²⋊C₄	C₂²×C₇₃	1	2	yes	—
607	C₄³	C₂²×C₇₃	1	1	yes	characteristic
608	C₂²×Q₈	C₂³×C₇₃	1	1	yes	characteristic
609	C₂²×Q₈	C₂³×C₇₃	1	1	yes	characteristic
610	C₂²×D₄	C₂³×C₇₃	1	1	yes	characteristic
611	C₂²×D₄	C₂³×C₇₃	1	2	yes	—
612	C₂³×C₄	C₂³×C₇₃	1	1	yes	characteristic
613	C₂³×C₄	C₂³×C₇₃	1	2	yes	—
614	C₂³×C₄	C₂³×C₇₃	1	2	yes	—
615	C₄⋊Q₈	—	2	4	no	—
616	#126	—	2	4	no	—
617	#125	—	4	4	no	—
618	#124	—	2	4	no	—
619	#124	—	4	2	no	—
620	#123	—	2	8	no	—
621	#123	—	4	4	no	—
622	C₂²⋊Q₈	—	2	4	no	—
623	C₂²⋊Q₈	—	2	4	no	—
624	#121	—	4	2	no	—
625	C₄×Q₈	—	2	4	no	—
626	C₄×Q₈	—	4	2	no	—
627	C₄×Q₈	—	4	2	no	—
628	C₄×Q₈	—	4	2	no	—
629	C₄×D₄	—	2	4	no	—
630	#117	—	4	4	no	—
631	C₂×C₄⋊C₄	—	4	2	no	—
632	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
633	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
634	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
635	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
636	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
637	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
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	1	yes	characteristic
644	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
645	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
646	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
647	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
648	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
649	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
650	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
651	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
652	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
653	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
654	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
655	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
656	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
657	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
658	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
659	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
660	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
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	2	yes	—
664	C₂×C₂²⋊C₄	C₂³×C₇₃	1	2	yes	—
665	C₂×C₂²⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
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	2	yes	—
669	C₂×C₂²⋊C₄	C₂³×C₇₃	1	2	yes	—
670	C₂×C₂²⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
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	1	yes	characteristic
674	C₂×C₂²⋊C₄	C₂³×C₇₃	1	2	yes	—
675	C₂×C₂²⋊C₄	C₂³×C₇₃	1	2	yes	—
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×C₄²	C₂³×C₇₃	1	1	yes	characteristic
682	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
683	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
684	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
685	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
686	C₂×C₄²	C₂³×C₇₃	1	2	yes	—
687	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
688	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
689	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
690	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
691	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
692	C₂×C₄²	C₂³×C₇₃	1	2	yes	—
693	C₂×C₄²	C₂³×C₇₃	1	2	yes	—
694	C₂×C₄²	C₂³×C₇₃	1	2	yes	—
695	C₂×C₄²	C₂³×C₇₃	1	2	yes	—
696	C₂×C₄²	C₂³×C₇₃	1	2	yes	—
697	#95	C₂³×C₇₃	1	2	yes	—
698	#95	C₂³×C₇₃	1	1	yes	characteristic
699	#95	C₂³×C₇₃	1	2	yes	—
700	#95	C₂³×C₇₃	1	1	yes	characteristic
701	#95	C₂³×C₇₃	1	1	yes	characteristic
702	#95	C₂³×C₇₃	1	1	yes	characteristic
703	#95	C₂³×C₇₃	1	1	yes	characteristic
704	#95	C₂³×C₇₃	1	1	yes	characteristic
705	#95	C₂³×C₇₃	1	2	yes	—
706	#95	C₂³×C₇₃	1	1	yes	characteristic
707	#95	C₂³×C₇₃	1	2	yes	—
708	#95	C₂³×C₇₃	1	2	yes	—
709	#95	C₂³×C₇₃	1	2	yes	—
710	#95	C₂³×C₇₃	1	1	yes	characteristic
711	#95	C₂³×C₇₃	1	1	yes	characteristic
712	#95	C₂³×C₇₃	1	1	yes	characteristic
713	#95	C₂³×C₇₃	1	2	yes	—
714	#95	C₂³×C₇₃	1	2	yes	—
715	#95	C₂³×C₇₃	1	2	yes	—
716	#95	C₂³×C₇₃	1	2	yes	—
717	#95	C₂³×C₇₃	1	1	yes	characteristic
718	#95	C₂³×C₇₃	1	1	yes	characteristic
719	#95	C₂³×C₇₃	1	2	yes	—
720	#95	C₂³×C₇₃	1	2	yes	—
721	#95	C₂³×C₇₃	1	2	yes	—
722	#95	C₂³×C₇₃	1	2	yes	—
723	#95	C₂³×C₇₃	1	2	yes	—
724	C₂⁴	C₂⁴×C₇₃	1	2	yes	—
725	C₂⁴	C₂⁴×C₇₃	1	1	yes	characteristic
726	C₂×Q₈	—	2	2	no	—
727	C₂×Q₈	—	2	2	no	—
728	C₂×Q₈	—	2	2	no	—
729	C₂×Q₈	—	2	2	no	—
730	C₂×Q₈	—	2	2	no	—
731	C₂×Q₈	#41×C₇₃	1	4	yes	—
732	C₂×D₄	—	2	4	no	—
733	C₂×D₄	—	2	2	no	—
734	C₂×D₄	—	2	2	no	—
735	C₂×D₄	—	2	2	no	—
736	C₂×D₄	—	4	2	no	—
737	C₂×D₄	—	4	2	no	—
738	C₂²×C₄	—	2	4	no	—
739	C₂²×C₄	—	2	4	no	—
740	C₂²×C₄	—	2	2	no	—
741	C₂²×C₄	—	2	2	no	—
742	C₂²×C₄	—	2	2	no	—
743	C₂²×C₄	—	2	4	no	—
744	C₂²×C₄	—	4	2	no	—
745	C₂²×C₄	—	4	2	no	—
746	C₂²×C₄	—	4	2	no	—
747	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
748	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
749	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
750	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
751	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
752	C₂²×C₄	C₂⁴×C₇₃	1	2	yes	—
753	C₂²×C₄	C₂⁴×C₇₃	1	2	yes	—
754	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
755	C₂²×C₄	C₂⁴×C₇₃	1	2	yes	—
756	C₂²×C₄	C₂⁴×C₇₃	1	2	yes	—
757	C₂²×C₄	C₂⁴×C₇₃	1	2	yes	—
758	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
759	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
760	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
761	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
762	C₂²×C₄	C₂⁴×C₇₃	1	2	yes	—
763	C₂²×C₄	C₂⁴×C₇₃	1	2	yes	—
764	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
765	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
766	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
767	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
768	C₄⋊C₄	—	2	4	no	—
769	C₄⋊C₄	—	2	2	no	—
770	C₄⋊C₄	—	2	4	no	—
771	C₄⋊C₄	—	2	4	no	—
772	C₄⋊C₄	—	2	4	no	—
773	C₄⋊C₄	—	2	4	no	—
774	C₄⋊C₄	—	2	2	no	—
775	C₄⋊C₄	—	2	2	no	—
776	C₄⋊C₄	—	2	2	no	—
777	C₄⋊C₄	—	2	4	no	—
778	C₄⋊C₄	—	2	4	no	—
779	C₄⋊C₄	—	2	2	no	—
780	C₄⋊C₄	—	2	2	no	—
781	C₄⋊C₄	—	2	4	no	—
782	C₄⋊C₄	—	2	2	no	—
783	C₄⋊C₄	—	2	4	no	—
784	C₄⋊C₄	—	2	2	no	—
785	C₄⋊C₄	—	2	2	no	—
786	C₄⋊C₄	—	2	2	no	—
787	C₄⋊C₄	—	4	2	no	—
788	C₄⋊C₄	—	4	2	no	—
789	C₄⋊C₄	—	4	2	no	—
790	C₄⋊C₄	—	4	2	no	—
791	C₄⋊C₄	—	4	2	no	—
792	C₄⋊C₄	—	4	2	no	—
793	C₄⋊C₄	—	4	2	no	—
794	C₄⋊C₄	—	4	2	no	—
795	C₄⋊C₄	—	4	2	no	—
796	C₄⋊C₄	#41×C₇₃	1	4	yes	—
797	C₂²⋊C₄	—	2	2	no	—
798	C₂²⋊C₄	—	2	2	no	—
799	C₂²⋊C₄	—	2	4	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	2	no	—
808	C₂²⋊C₄	—	2	2	no	—
809	C₂²⋊C₄	—	2	4	no	—
810	C₂²⋊C₄	—	2	2	no	—
811	C₂²⋊C₄	—	4	2	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	#41×C₇₃	1	4	yes	—
817	C₄²	—	2	2	no	—
818	C₄²	—	2	4	no	—
819	C₄²	—	2	2	no	—
820	C₄²	—	2	2	no	—
821	C₄²	—	2	2	no	—
822	C₄²	—	2	2	no	—
823	C₄²	—	2	2	no	—
824	C₄²	—	2	2	no	—
825	C₄²	—	2	2	no	—
826	C₄²	—	2	2	no	—
827	C₄²	—	2	2	no	—
828	C₄²	—	4	2	no	—
829	C₄²	—	4	2	no	—
830	C₄²	—	4	2	no	—
831	C₄²	—	4	2	no	—
832	C₄²	—	4	2	no	—
833	C₂³	—	2	1	no	—
834	C₂³	—	2	1	no	—
835	C₂³	—	2	1	no	—
836	C₂³	—	2	1	no	—
837	C₂³	—	2	1	no	—
838	C₂³	—	2	1	no	—
839	C₂³	—	2	2	no	—
840	C₂³	—	2	2	no	—
841	C₂³	—	2	2	no	—
842	C₂³	—	2	2	no	—
843	C₂³	—	2	2	no	—
844	C₂³	—	2	2	no	—
845	C₂³	—	2	2	no	—
846	C₂³	C₂×#41×C₇₃	1	2	yes	—
847	C₂³	C₂⁵×C₇₃	1	1	yes	characteristic
848	Q₈	—	2	8	no	—
849	Q₈	—	4	4	no	—
850	D₄	—	4	4	no	—
851	D₄	—	8	4	no	—
852	C₂×C₄	—	2	1	no	—
853	C₂×C₄	—	2	1	no	—
854	C₂×C₄	—	2	1	no	—
855	C₂×C₄	—	2	2	no	—
856	C₂×C₄	—	2	1	no	—
857	C₂×C₄	—	2	1	no	—
858	C₂×C₄	—	2	1	no	—
859	C₂×C₄	—	2	2	no	—
860	C₂×C₄	—	2	2	no	—
861	C₂×C₄	—	2	1	no	—
862	C₂×C₄	—	2	1	no	—
863	C₂×C₄	—	2	1	no	—
864	C₂×C₄	—	2	1	no	—
865	C₂×C₄	—	2	2	no	—
866	C₂×C₄	—	2	1	no	—
867	C₂×C₄	—	2	1	no	—
868	C₂×C₄	—	2	1	no	—
869	C₂×C₄	—	2	1	no	—
870	C₂×C₄	—	2	1	no	—
871	C₂×C₄	—	2	1	no	—
872	C₂×C₄	—	2	1	no	—
873	C₂×C₄	—	2	1	no	—
874	C₂×C₄	—	2	2	no	—
875	C₂×C₄	—	2	2	no	—
876	C₂×C₄	—	2	2	no	—
877	C₂×C₄	—	2	2	no	—
878	C₂×C₄	—	2	1	no	—
879	C₂×C₄	—	2	1	no	—
880	C₂×C₄	—	2	2	no	—
881	C₂×C₄	—	2	2	no	—
882	C₂×C₄	—	2	1	no	—
883	C₂×C₄	—	2	1	no	—
884	C₂×C₄	—	2	1	no	—
885	C₂×C₄	—	2	1	no	—
886	C₂×C₄	—	2	1	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	2	no	—
894	C₂×C₄	—	2	1	no	—
895	C₂×C₄	—	2	1	no	—
896	C₂×C₄	—	2	1	no	—
897	C₂×C₄	—	2	2	no	—
898	C₂×C₄	—	2	1	no	—
899	C₂×C₄	—	2	1	no	—
900	C₂×C₄	—	2	2	no	—
901	C₂×C₄	—	2	1	no	—
902	C₂×C₄	—	2	1	no	—
903	C₂×C₄	—	2	1	no	—
904	C₂×C₄	—	2	1	no	—
905	C₂×C₄	—	4	8	no	—
906	C₂×C₄	—	4	4	no	—
907	C₂×C₄	—	8	4	no	—
908	C₂×C₄	C₂×#41×C₇₃	1	2	yes	—
909	C₂×C₄	C₂×#41×C₇₃	1	4	yes	—
910	C₂×C₄	C₂×#41×C₇₃	1	4	yes	—
911	C₂×C₄	C₂×#41×C₇₃	1	2	yes	—
912	C₂×C₄	C₂×#41×C₇₃	1	2	yes	—
913	C₂×C₄	C₂×#41×C₇₃	1	2	yes	—
914	C₂×C₄	H(5,𝔽₂)×C₇₃	1	2	yes	—
915	C₂×C₄	H(5,𝔽₂)×C₇₃	1	2	yes	—
916	C₂×C₄	2₋¹⁺⁴×C₇₃	1	2	yes	—
917	C₂×C₄	2₋¹⁺⁴×C₇₃	1	2	yes	—
918	C₂²	—	2	2	no	—
919	C₂²	—	2	2	no	—
920	C₂²	—	2	2	no	—
921	C₂²	—	4	1	no	—
922	C₂²	—	4	1	no	—
923	C₂²	—	4	1	no	—
924	C₂²	—	4	1	no	—
925	C₂²	—	4	2	no	—
926	C₂²	—	4	2	no	—
927	C₂²	—	4	2	no	—
928	C₂²	—	4	2	no	—
929	C₂²	—	4	2	no	—
930	C₂²	—	4	2	no	—
931	C₂²	—	4	2	no	—
932	C₂²	C₂²×#41×C₇₃	1	1	yes	characteristic
933	C₂²	C₂²×#41×C₇₃	1	1	yes	characteristic
934	C₂²	C₂²×#41×C₇₃	1	1	yes	characteristic
935	C₂²	C₂×H(5,𝔽₂)×C₇₃	1	1	yes	characteristic
936	C₂²	C₂×H(5,𝔽₂)×C₇₃	1	1	yes	characteristic
937	C₂²	C₂×2₋¹⁺⁴×C₇₃	1	1	yes	characteristic
938	C₂²	C₂×2₋¹⁺⁴×C₇₃	1	1	yes	characteristic
939	C₄	—	2	4	no	—
940	C₄	—	2	2	no	—
941	C₄	—	2	2	no	—
942	C₄	—	2	2	no	—
943	C₄	—	2	4	no	—
944	C₄	—	2	2	no	—
945	C₄	—	2	2	no	—
946	C₄	—	4	1	no	—
947	C₄	—	4	2	no	—
948	C₄	—	4	1	no	—
949	C₄	—	4	1	no	—
950	C₄	—	4	2	no	—
951	C₄	—	4	2	no	—
952	C₄	—	4	2	no	—
953	C₄	—	4	1	no	—
954	C₄	—	4	1	no	—
955	C₄	—	4	1	no	—
956	C₄	—	4	1	no	—
957	C₄	—	4	2	no	—
958	C₄	—	4	1	no	—
959	C₄	#553×C₇₃	1	4	yes	—
960	C₂	—	4	2	no	—
961	C₂	—	8	2	no	—
962	C₂	C₂×#553×C₇₃	1	1	yes	characteristic
963	C₂	C₇₃×#3482	1	1	yes	characteristic
964	C₂	C₇₃×#3482	1	1	yes	characteristic
965	C₂	C₇₃×#3508	1	1	yes	characteristic
966	C₂	C₇₃×#3520	1	1	yes	characteristic
967	C₂	C₇₃×#3522	1	1	yes	characteristic
968	C₂	C₇₃×#3552	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₇₃	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₇₃
prime radical	C₂×#121×C₇₃	C₂²
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₇₃ ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. C₇₃×#2777	C₂	semidirect
2. C₇₃×#2718	C₂	semidirect
3. C₇₃×#2596	C₂	semidirect
4. C₇₃×#2558	C₂	semidirect
5. C₇₃×#2545	C₂	semidirect
6. C₇₃×#2522	C₂	semidirect
7. C₇₃×#2511	C₂	semidirect
8. C₇₃×#2506	C₂	semidirect
10. C₇₃×#2470	C₂	semidirect
11. C₇₃×#2448	C₂	semidirect
12. C₇₃×#2441	C₂	semidirect
13. C₇₃×#2429	C₂	semidirect
16. C₇₃×#2374	C₂	semidirect
17. C₇₃×#2367	C₂	semidirect
18. C₇₃×#2360	C₂	semidirect
19. C₇₃×#2360	C₂	semidirect
20. Q₈×C₄⋊C₄×C₇₃	C₂	semidirect
21. C₄×C₄⋊Q₈×C₇₃	C₂	semidirect
22. C₄×#126×C₇₃	C₂	semidirect
23. C₇₃×#2293	C₂	semidirect
475. #59697	C₇₃	direct (N × H)
485. #2777	C₂×C₇₃	semidirect
486. #2718	C₂×C₇₃	semidirect
487. #2596	C₂×C₇₃	semidirect
488. #2558	C₂×C₇₃	semidirect
489. #2545	C₂×C₇₃	semidirect
490. #2522	C₂×C₇₃	semidirect
491. #2511	C₂×C₇₃	semidirect
492. #2506	C₂×C₇₃	semidirect
494. #2470	C₂×C₇₃	semidirect
495. #2448	C₂×C₇₃	semidirect
496. #2441	C₂×C₇₃	semidirect
497. #2429	C₂×C₇₃	semidirect
500. #2374	C₂×C₇₃	semidirect
501. #2367	C₂×C₇₃	semidirect
502. #2360	C₂×C₇₃	semidirect
503. #2360	C₂×C₇₃	semidirect
504. Q₈×C₄⋊C₄	C₂×C₇₃	semidirect
505. C₄×C₄⋊Q₈	C₂×C₇₃	semidirect
506. C₄×#126	C₂×C₇₃	semidirect
507. #2293	C₂×C₇₃	semidirect
508. C₇₃	#59697	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×#2777	2
C₇₃×#2718	2
C₇₃×#2596	2
C₇₃×#2558	2
C₇₃×#2545	2
C₇₃×#2522	2
C₇₃×#2511	2
C₇₃×#2506	2
C₇₃×#2501	2
C₇₃×#2470	2
C₇₃×#2448	2
C₇₃×#2441	2
C₇₃×#2429	2
C₇₃×#2427	2
C₇₃×#2426	2
C₇₃×#2374	2
C₇₃×#2367	2
C₇₃×#2360	2
Q₈×C₄⋊C₄×C₇₃	2
C₄×C₄⋊Q₈×C₇₃	2
C₄×#126×C₇₃	2
C₇₃×#2293	2
#59697	73

Subgroups — C73×#59697 #32969101

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₃×#59697 #32969101