Subgroups — C₇₃×#24390 #32933794

Order 18688.

1636 conjugacy classes of subgroups.

The subgroup lattice has 1004 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#535×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#469×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#466×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#447×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#408×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
6	C₇₃×#2615	C₂	1	1	yes	maximal, characteristic, complemented
7	C₇₃×#2034	C₂	1	1	yes	maximal, characteristic, complemented
8	C₇₃×#2033	C₂	1	1	yes	maximal, characteristic, complemented
9	C₇₃×#1999	C₂	1	1	yes	maximal, characteristic, complemented
10	C₇₃×#1999	C₂	1	1	yes	maximal, characteristic, complemented
11	C₇₃×#1895	C₂	1	1	yes	maximal, characteristic, complemented
12	C₇₃×#1893	C₂	1	1	yes	maximal, characteristic, complemented
13	C₇₃×#1875	C₂	1	1	yes	maximal, characteristic, complemented
14	C₇₃×#1854	C₂	1	1	yes	maximal, characteristic, complemented
15	C₇₃×#1786	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×#41×C₇₃	C₂²	1	1	yes	characteristic
17	C₂³×D₄×C₇₃	C₂²	1	1	yes	characteristic
18	C₂²×D₈×C₇₃	C₂²	1	1	yes	characteristic
19	C₂²×D₈×C₇₃	C₂²	1	1	yes	characteristic
20	C₂²×M₁₆×C₇₃	C₂²	1	1	yes	characteristic, complemented
21	C₂³×C₈×C₇₃	C₂²	1	1	yes	characteristic, complemented
22	#535×C₇₃	—	2	4	no	—
23	#535×C₇₃	—	2	4	no	—
24	C₂×#127×C₇₃	—	2	1	no	—
25	C₂×#124×C₇₃	—	2	1	no	—
26	C₂×#121×C₇₃	C₂²	1	1	yes	characteristic
27	C₂×#121×C₇₃	C₂²	1	1	yes	characteristic
28	C₂×#121×C₇₃	C₂²	1	1	yes	characteristic
29	C₂×#121×C₇₃	C₂²	1	1	yes	characteristic
30	C₂×#121×C₇₃	C₂²	1	1	yes	characteristic
31	C₂×#121×C₇₃	C₂²	1	1	yes	characteristic, complemented
32	C₂×#121×C₇₃	C₂²	1	1	yes	characteristic, complemented
33	C₂×#120×C₇₃	—	2	1	no	—
34	C₂×#120×C₇₃	—	2	1	no	—
35	C₂×#117×C₇₃	C₂²	1	1	yes	characteristic
36	#469×C₇₃	—	2	4	no	—
37	#466×C₇₃	—	2	4	no	—
38	#447×C₇₃	—	2	4	no	—
39	C₂×#107×C₇₃	C₂²	1	1	yes	characteristic, complemented
40	C₂×#106×C₇₃	C₂²	1	1	yes	characteristic, complemented
41	C₂×#102×C₇₃	C₂²	1	1	yes	characteristic
42	C₂×#102×C₇₃	C₂²	1	1	yes	characteristic
43	C₂×#102×C₇₃	C₂²	1	1	yes	characteristic
44	C₂×#102×C₇₃	C₂²	1	1	yes	characteristic
45	C₂×#102×C₇₃	C₂²	1	1	yes	characteristic
46	C₂×#102×C₇₃	C₂²	1	1	yes	characteristic
47	C₂×#102×C₇₃	C₂²	1	1	yes	characteristic, complemented
48	C₂×#102×C₇₃	C₂²	1	1	yes	characteristic, complemented
49	#408×C₇₃	—	2	4	no	—
50	C₂×C₂²⋊C₈×C₇₃	C₂²	1	1	yes	characteristic
51	C₂×C₂²⋊C₈×C₇₃	C₂²	1	1	yes	characteristic
52	C₂×C₂²⋊C₈×C₇₃	C₂²	1	1	yes	characteristic, complemented
53	C₂×C₂²⋊C₈×C₇₃	C₂²	1	1	yes	characteristic, complemented
54	#393×C₇₃	—	2	1	no	—
55	#392×C₇₃	—	2	1	no	—
56	#392×C₇₃	—	2	1	no	—
57	#392×C₇₃	—	2	1	no	—
58	#380×C₇₃	C₂²	1	1	yes	characteristic
59	#380×C₇₃	C₂²	1	1	yes	characteristic, complemented
60	#380×C₇₃	C₂²	1	1	yes	characteristic, complemented
61	#340×C₇₃	C₂²	1	1	yes	characteristic, complemented
62	#340×C₇₃	C₂²	1	1	yes	characteristic, complemented
63	#340×C₇₃	C₂²	1	1	yes	characteristic, complemented
64	#340×C₇₃	C₂²	1	1	yes	characteristic, complemented
65	C₂⁵×C₇₃	—	2	1	no	—
66	C₂×#41×C₇₃	—	2	2	no	—
67	C₂×#41×C₇₃	—	2	2	no	—
68	C₂×#41×C₇₃	—	2	2	no	—
69	C₂×#41×C₇₃	—	2	2	no	—
70	C₂×#41×C₇₃	—	4	1	no	—
71	C₂×#41×C₇₃	—	4	1	no	—
72	C₂²×Q₈×C₇₃	D₄	1	1	yes	characteristic
73	C₂²×D₄×C₇₃	—	2	1	no	—
74	C₂²×D₄×C₇₃	—	2	1	no	—
75	C₂²×D₄×C₇₃	—	2	1	no	—
76	C₂²×D₄×C₇₃	—	2	1	no	—
77	C₂²×D₄×C₇₃	—	2	2	no	—
78	C₂²×D₄×C₇₃	—	2	2	no	—
79	C₂²×D₄×C₇₃	—	2	1	no	—
80	C₂²×D₄×C₇₃	—	2	1	no	—
81	C₂²×D₄×C₇₃	—	2	1	no	—
82	C₂²×D₄×C₇₃	—	2	1	no	—
83	C₂²×D₄×C₇₃	—	2	2	no	—
84	C₂²×D₄×C₇₃	—	2	2	no	—
85	C₂²×D₄×C₇₃	—	4	1	no	—
86	C₂²×D₄×C₇₃	—	4	1	no	—
87	C₂²×D₄×C₇₃	D₄	1	1	yes	characteristic
88	C₂²×D₄×C₇₃	D₄	1	1	yes	characteristic
89	C₂²×D₄×C₇₃	D₄	1	1	yes	characteristic
90	C₂²×D₄×C₇₃	C₂³	1	1	yes	characteristic
91	C₂²×D₄×C₇₃	C₂³	1	1	yes	characteristic
92	C₂²×D₄×C₇₃	C₂³	1	1	yes	characteristic
93	C₂³×C₄×C₇₃	C₂³	1	1	yes	characteristic
94	C₂³×C₄×C₇₃	C₂³	1	1	yes	characteristic
95	C₂³×C₄×C₇₃	C₂³	1	1	yes	characteristic
96	C₂×D₈×C₇₃	—	2	2	no	—
97	C₂×D₈×C₇₃	—	2	2	no	—
98	C₂×D₈×C₇₃	—	2	2	no	—
99	C₂×D₈×C₇₃	—	2	2	no	—
100	C₂×D₈×C₇₃	—	4	1	no	—
101	C₂×D₈×C₇₃	—	4	1	no	—
102	C₂×M₁₆×C₇₃	—	2	2	no	—
103	C₂×M₁₆×C₇₃	—	2	2	no	—
104	C₂×M₁₆×C₇₃	—	4	1	no	—
105	C₂²×C₈×C₇₃	—	2	2	no	—
106	C₂²×C₈×C₇₃	—	2	2	no	—
107	C₂²×C₈×C₇₃	—	4	1	no	—
108	C₂²×C₈×C₇₃	C₂³	1	1	yes	characteristic
109	C₂²×C₈×C₇₃	C₂³	1	1	yes	characteristic
110	C₂²×C₈×C₇₃	C₂³	1	1	yes	characteristic
111	C₂²×C₈×C₇₃	C₂³	1	1	yes	characteristic
112	#127×C₇₃	—	2	8	no	—
113	#124×C₇₃	—	2	8	no	—
114	#121×C₇₃	—	2	2	no	—
115	#121×C₇₃	—	2	2	no	—
116	#121×C₇₃	—	2	2	no	—
117	#121×C₇₃	—	2	2	no	—
118	#121×C₇₃	—	2	2	no	—
119	#121×C₇₃	—	2	2	no	—
120	#121×C₇₃	—	2	2	no	—
121	#121×C₇₃	—	2	2	no	—
122	#121×C₇₃	—	2	2	no	—
123	#121×C₇₃	—	2	2	no	—
124	#121×C₇₃	—	4	1	no	—
125	#121×C₇₃	—	4	1	no	—
126	#121×C₇₃	D₄	1	4	yes	complemented
127	#121×C₇₃	D₄	1	4	yes	complemented
128	#120×C₇₃	—	2	8	no	—
129	#120×C₇₃	—	2	8	no	—
130	#117×C₇₃	—	2	2	no	—
131	#117×C₇₃	—	2	2	no	—
132	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
133	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
134	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
135	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
136	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
137	C₂×C₂²⋊C₄×C₇₃	—	2	1	no	—
138	C₂×C₂²⋊C₄×C₇₃	—	2	1	no	—
139	C₂×C₂²⋊C₄×C₇₃	—	2	1	no	—
140	C₂×C₂²⋊C₄×C₇₃	—	2	1	no	—
141	C₂×C₂²⋊C₄×C₇₃	—	2	1	no	—
142	C₂×C₂²⋊C₄×C₇₃	—	2	1	no	—
143	C₂×C₂²⋊C₄×C₇₃	—	2	1	no	—
144	C₂×C₂²⋊C₄×C₇₃	—	2	1	no	—
145	C₂×C₂²⋊C₄×C₇₃	—	2	1	no	—
146	C₂×C₂²⋊C₄×C₇₃	—	2	1	no	—
147	C₂×C₂²⋊C₄×C₇₃	—	2	1	no	—
148	C₂×C₄²×C₇₃	—	2	1	no	—
149	#107×C₇₃	—	2	2	no	—
150	#106×C₇₃	—	2	2	no	—
151	#102×C₇₃	—	2	2	no	—
152	#102×C₇₃	—	2	2	no	—
153	#102×C₇₃	—	2	2	no	—
154	#102×C₇₃	—	2	2	no	—
155	#102×C₇₃	—	2	2	no	—
156	#102×C₇₃	—	2	2	no	—
157	#102×C₇₃	—	4	1	no	—
158	#102×C₇₃	—	4	1	no	—
159	C₂²⋊C₈×C₇₃	—	2	2	no	—
160	C₂²⋊C₈×C₇₃	—	2	2	no	—
161	C₂²⋊C₈×C₇₃	—	2	2	no	—
162	C₂²⋊C₈×C₇₃	D₄	1	4	yes	complemented
163	#95×C₇₃	—	2	1	no	—
164	#95×C₇₃	—	2	1	no	—
165	#95×C₇₃	—	2	1	no	—
166	C₂⁴×C₇₃	—	2	4	no	—
167	C₂⁴×C₇₃	—	2	1	no	—
168	C₂⁴×C₇₃	—	2	1	no	—
169	C₂⁴×C₇₃	—	2	1	no	—
170	C₂⁴×C₇₃	—	4	2	no	—
171	C₂⁴×C₇₃	—	4	2	no	—
172	C₂⁴×C₇₃	—	8	1	no	—
173	C₂⁴×C₇₃	—	8	1	no	—
174	C₂⁴×C₇₃	—	8	1	no	—
175	C₂⁴×C₇₃	—	8	1	no	—
176	C₂⁴×C₇₃	C₂×D₄	1	1	yes	characteristic
177	C₂⁴×C₇₃	C₂×D₄	1	1	yes	characteristic
178	C₂⁴×C₇₃	C₂×D₄	1	1	yes	characteristic
179	#41×C₇₃	—	4	4	no	—
180	#41×C₇₃	—	4	4	no	—
181	#41×C₇₃	—	4	4	no	—
182	#41×C₇₃	—	4	4	no	—
183	C₂×Q₈×C₇₃	—	2	2	no	—
184	C₂×Q₈×C₇₃	—	2	2	no	—
185	C₂×Q₈×C₇₃	—	4	1	no	—
186	C₂×D₄×C₇₃	—	2	4	no	—
187	C₂×D₄×C₇₃	—	2	2	no	—
188	C₂×D₄×C₇₃	—	2	2	no	—
189	C₂×D₄×C₇₃	—	2	2	no	—
190	C₂×D₄×C₇₃	—	2	2	no	—
191	C₂×D₄×C₇₃	—	2	4	no	—
192	C₂×D₄×C₇₃	—	2	4	no	—
193	C₂×D₄×C₇₃	—	2	4	no	—
194	C₂×D₄×C₇₃	—	2	4	no	—
195	C₂×D₄×C₇₃	—	2	2	no	—
196	C₂×D₄×C₇₃	—	2	2	no	—
197	C₂×D₄×C₇₃	—	2	1	no	—
198	C₂×D₄×C₇₃	—	2	1	no	—
199	C₂×D₄×C₇₃	—	2	1	no	—
200	C₂×D₄×C₇₃	—	2	1	no	—
201	C₂×D₄×C₇₃	—	2	1	no	—
202	C₂×D₄×C₇₃	—	2	1	no	—
203	C₂×D₄×C₇₃	—	2	1	no	—
204	C₂×D₄×C₇₃	—	2	1	no	—
205	C₂×D₄×C₇₃	—	2	1	no	—
206	C₂×D₄×C₇₃	—	2	1	no	—
207	C₂×D₄×C₇₃	—	2	1	no	—
208	C₂×D₄×C₇₃	—	2	1	no	—
209	C₂×D₄×C₇₃	—	2	1	no	—
210	C₂×D₄×C₇₃	—	2	1	no	—
211	C₂×D₄×C₇₃	—	2	1	no	—
212	C₂×D₄×C₇₃	—	2	1	no	—
213	C₂×D₄×C₇₃	—	4	4	no	—
214	C₂×D₄×C₇₃	—	4	4	no	—
215	C₂×D₄×C₇₃	—	4	4	no	—
216	C₂×D₄×C₇₃	—	4	4	no	—
217	C₂×D₄×C₇₃	—	4	1	no	—
218	C₂×D₄×C₇₃	—	4	1	no	—
219	C₂×D₄×C₇₃	—	4	1	no	—
220	C₂×D₄×C₇₃	—	4	2	no	—
221	C₂×D₄×C₇₃	—	4	2	no	—
222	C₂×D₄×C₇₃	—	4	2	no	—
223	C₂×D₄×C₇₃	—	4	2	no	—
224	C₂×D₄×C₇₃	—	4	2	no	—
225	C₂×D₄×C₇₃	—	8	1	no	—
226	C₂×D₄×C₇₃	—	8	1	no	—
227	C₂×D₄×C₇₃	—	8	1	no	—
228	C₂×D₄×C₇₃	—	8	1	no	—
229	C₂×D₄×C₇₃	—	8	1	no	—
230	C₂×D₄×C₇₃	—	8	1	no	—
231	C₂×D₄×C₇₃	—	8	1	no	—
232	C₂×D₄×C₇₃	—	8	1	no	—
233	C₂×D₄×C₇₃	—	8	1	no	—
234	C₂×D₄×C₇₃	—	8	1	no	—
235	C₂×D₄×C₇₃	—	8	1	no	—
236	C₂×D₄×C₇₃	—	8	1	no	—
237	C₂×D₄×C₇₃	—	8	1	no	—
238	C₂×D₄×C₇₃	—	8	1	no	—
239	C₂×D₄×C₇₃	C₂×D₄	1	2	yes	—
240	C₂×D₄×C₇₃	C₂×D₄	1	2	yes	—
241	C₂²×C₄×C₇₃	—	2	1	no	—
242	C₂²×C₄×C₇₃	—	2	1	no	—
243	C₂²×C₄×C₇₃	—	2	1	no	—
244	C₂²×C₄×C₇₃	—	2	1	no	—
245	C₂²×C₄×C₇₃	—	2	1	no	—
246	C₂²×C₄×C₇₃	—	2	1	no	—
247	C₂²×C₄×C₇₃	—	2	1	no	—
248	C₂²×C₄×C₇₃	—	2	1	no	—
249	C₂²×C₄×C₇₃	—	2	1	no	—
250	C₂²×C₄×C₇₃	—	2	1	no	—
251	C₂²×C₄×C₇₃	—	2	1	no	—
252	C₂²×C₄×C₇₃	—	2	1	no	—
253	C₂²×C₄×C₇₃	—	2	1	no	—
254	C₂²×C₄×C₇₃	—	2	1	no	—
255	C₂²×C₄×C₇₃	—	2	1	no	—
256	C₂²×C₄×C₇₃	—	2	1	no	—
257	C₂²×C₄×C₇₃	—	2	1	no	—
258	C₂²×C₄×C₇₃	—	2	1	no	—
259	C₂²×C₄×C₇₃	—	2	1	no	—
260	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
261	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
262	C₂²×C₄×C₇₃	C₂×D₄	1	2	yes	—
263	C₂²×C₄×C₇₃	C₂×D₄	1	2	yes	—
264	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
265	C₂²×C₄×C₇₃	C₂×D₄	1	2	yes	—
266	C₂²×C₄×C₇₃	#41	1	2	yes	—
267	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
268	D₈×C₇₃	—	4	4	no	—
269	D₈×C₇₃	—	4	4	no	—
270	M₁₆×C₇₃	—	4	4	no	—
271	C₂×C₈×C₇₃	—	2	1	no	—
272	C₂×C₈×C₇₃	—	2	1	no	—
273	C₂×C₈×C₇₃	—	2	1	no	—
274	C₂×C₈×C₇₃	—	2	1	no	—
275	C₂×C₈×C₇₃	—	2	1	no	—
276	C₂×C₈×C₇₃	—	2	1	no	—
277	C₂×C₈×C₇₃	—	2	1	no	—
278	C₂×C₈×C₇₃	—	2	1	no	—
279	C₂×C₈×C₇₃	—	2	1	no	—
280	C₂×C₈×C₇₃	—	2	1	no	—
281	C₂×C₈×C₇₃	—	4	4	no	—
282	C₂×C₈×C₇₃	C₂×D₄	1	2	yes	—
283	C₂×C₈×C₇₃	C₂×D₄	1	2	yes	—
284	C₄⋊C₄×C₇₃	—	2	1	no	—
285	C₄⋊C₄×C₇₃	—	2	1	no	—
286	C₄⋊C₄×C₇₃	—	2	1	no	—
287	C₄⋊C₄×C₇₃	—	2	1	no	—
288	C₄⋊C₄×C₇₃	—	2	1	no	—
289	C₄⋊C₄×C₇₃	—	2	1	no	—
290	C₄⋊C₄×C₇₃	—	2	1	no	—
291	C₄⋊C₄×C₇₃	—	2	1	no	—
292	C₄⋊C₄×C₇₃	C₂×D₄	1	2	yes	—
293	C₄⋊C₄×C₇₃	C₂×D₄	1	2	yes	—
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	2	no	—
300	C₂²⋊C₄×C₇₃	—	4	2	no	—
301	C₂²⋊C₄×C₇₃	—	4	2	no	—
302	C₂²⋊C₄×C₇₃	—	8	1	no	—
303	C₂²⋊C₄×C₇₃	—	8	1	no	—
304	C₂²⋊C₄×C₇₃	—	8	1	no	—
305	C₄²×C₇₃	—	2	4	no	—
306	C₂³×C₇₃	—	2	1	no	—
307	C₂³×C₇₃	—	2	1	no	—
308	C₂³×C₇₃	—	2	1	no	—
309	C₂³×C₇₃	—	2	1	no	—
310	C₂³×C₇₃	—	2	1	no	—
311	C₂³×C₇₃	—	2	1	no	—
312	C₂³×C₇₃	—	2	1	no	—
313	C₂³×C₇₃	—	2	1	no	—
314	C₂³×C₇₃	—	2	1	no	—
315	C₂³×C₇₃	—	2	1	no	—
316	C₂³×C₇₃	—	2	1	no	—
317	C₂³×C₇₃	—	2	1	no	—
318	C₂³×C₇₃	—	2	2	no	—
319	C₂³×C₇₃	—	2	2	no	—
320	C₂³×C₇₃	—	2	1	no	—
321	C₂³×C₇₃	—	2	1	no	—
322	C₂³×C₇₃	—	2	1	no	—
323	C₂³×C₇₃	—	2	1	no	—
324	C₂³×C₇₃	—	2	1	no	—
325	C₂³×C₇₃	—	2	1	no	—
326	C₂³×C₇₃	—	2	1	no	—
327	C₂³×C₇₃	—	4	8	no	—
328	C₂³×C₇₃	—	4	1	no	—
329	C₂³×C₇₃	—	4	1	no	—
330	C₂³×C₇₃	—	4	1	no	—
331	C₂³×C₇₃	—	4	1	no	—
332	C₂³×C₇₃	—	4	1	no	—
333	C₂³×C₇₃	—	4	1	no	—
334	C₂³×C₇₃	—	4	1	no	—
335	C₂³×C₇₃	—	4	1	no	—
336	C₂³×C₇₃	—	4	1	no	—
337	C₂³×C₇₃	—	4	1	no	—
338	C₂³×C₇₃	—	4	1	no	—
339	C₂³×C₇₃	—	4	1	no	—
340	C₂³×C₇₃	—	4	1	no	—
341	C₂³×C₇₃	—	4	1	no	—
342	C₂³×C₇₃	—	4	1	no	—
343	C₂³×C₇₃	—	4	1	no	—
344	C₂³×C₇₃	—	4	1	no	—
345	C₂³×C₇₃	—	4	1	no	—
346	C₂³×C₇₃	—	4	1	no	—
347	C₂³×C₇₃	—	8	4	no	—
348	C₂³×C₇₃	—	8	4	no	—
349	C₂³×C₇₃	—	8	4	no	—
350	C₂³×C₇₃	—	8	4	no	—
351	C₂³×C₇₃	—	8	4	no	—
352	C₂³×C₇₃	—	8	4	no	—
353	C₂³×C₇₃	#120	1	2	yes	—
354	C₂³×C₇₃	#121	1	2	yes	—
355	C₂³×C₇₃	C₂²×D₄	1	1	yes	characteristic
356	Q₈×C₇₃	—	4	4	no	—
357	D₄×C₇₃	—	2	2	no	—
358	D₄×C₇₃	—	2	2	no	—
359	D₄×C₇₃	—	2	2	no	—
360	D₄×C₇₃	—	2	2	no	—
361	D₄×C₇₃	—	4	4	no	—
362	D₄×C₇₃	—	4	4	no	—
363	D₄×C₇₃	—	4	8	no	—
364	D₄×C₇₃	—	4	4	no	—
365	D₄×C₇₃	—	4	1	no	—
366	D₄×C₇₃	—	4	1	no	—
367	D₄×C₇₃	—	4	1	no	—
368	D₄×C₇₃	—	4	1	no	—
369	D₄×C₇₃	—	4	1	no	—
370	D₄×C₇₃	—	4	1	no	—
371	D₄×C₇₃	—	4	1	no	—
372	D₄×C₇₃	—	4	1	no	—
373	D₄×C₇₃	—	8	4	no	—
374	D₄×C₇₃	—	8	4	no	—
375	D₄×C₇₃	—	8	4	no	—
376	D₄×C₇₃	—	8	4	no	—
377	D₄×C₇₃	—	8	4	no	—
378	D₄×C₇₃	—	8	4	no	—
379	D₄×C₇₃	—	8	4	no	—
380	C₂×C₄×C₇₃	—	2	1	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	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	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	2	no	—
394	C₂×C₄×C₇₃	—	2	1	no	—
395	C₂×C₄×C₇₃	—	2	1	no	—
396	C₂×C₄×C₇₃	—	2	1	no	—
397	C₂×C₄×C₇₃	—	4	1	no	—
398	C₂×C₄×C₇₃	—	4	1	no	—
399	C₂×C₄×C₇₃	—	4	1	no	—
400	C₂×C₄×C₇₃	—	4	1	no	—
401	C₂×C₄×C₇₃	—	4	1	no	—
402	C₂×C₄×C₇₃	—	4	1	no	—
403	C₂×C₄×C₇₃	—	4	1	no	—
404	C₂×C₄×C₇₃	—	4	1	no	—
405	C₂×C₄×C₇₃	—	4	1	no	—
406	C₂×C₄×C₇₃	—	4	1	no	—
407	C₂×C₄×C₇₃	—	4	1	no	—
408	C₂×C₄×C₇₃	—	4	1	no	—
409	C₂×C₄×C₇₃	—	4	1	no	—
410	C₂×C₄×C₇₃	—	4	1	no	—
411	C₂×C₄×C₇₃	—	4	1	no	—
412	C₂×C₄×C₇₃	—	4	1	no	—
413	C₂×C₄×C₇₃	—	4	1	no	—
414	C₂×C₄×C₇₃	#120	1	2	yes	—
415	C₂×C₄×C₇₃	#121	1	2	yes	—
416	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
417	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
418	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
419	C₂×C₄×C₇₃	C₂×#41	1	1	yes	characteristic
420	C₂×C₄×C₇₃	H(5,𝔽₂)	1	1	yes	characteristic
421	C₂×C₄×C₇₃	H(5,𝔽₂)	1	1	yes	characteristic
422	C₈×C₇₃	—	2	2	no	—
423	C₈×C₇₃	—	2	2	no	—
424	C₈×C₇₃	—	4	1	no	—
425	C₈×C₇₃	—	4	1	no	—
426	C₂²×C₇₃	—	2	2	no	—
427	C₂²×C₇₃	—	2	2	no	—
428	C₂²×C₇₃	—	2	2	no	—
429	C₂²×C₇₃	—	2	2	no	—
430	C₂²×C₇₃	—	2	2	no	—
431	C₂²×C₇₃	—	2	2	no	—
432	C₂²×C₇₃	—	4	1	no	—
433	C₂²×C₇₃	—	4	1	no	—
434	C₂²×C₇₃	—	4	1	no	—
435	C₂²×C₇₃	—	4	1	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	1	no	—
441	C₂²×C₇₃	—	4	2	no	—
442	C₂²×C₇₃	—	4	2	no	—
443	C₂²×C₇₃	—	4	1	no	—
444	C₂²×C₇₃	—	4	1	no	—
445	C₂²×C₇₃	—	4	1	no	—
446	C₂²×C₇₃	—	4	2	no	—
447	C₂²×C₇₃	—	4	2	no	—
448	C₂²×C₇₃	—	4	1	no	—
449	C₂²×C₇₃	—	4	2	no	—
450	C₂²×C₇₃	—	4	2	no	—
451	C₂²×C₇₃	—	4	1	no	—
452	C₂²×C₇₃	—	4	1	no	—
453	C₂²×C₇₃	—	8	16	no	—
454	C₂²×C₇₃	—	8	1	no	—
455	C₂²×C₇₃	—	8	1	no	—
456	C₂²×C₇₃	—	8	1	no	—
457	C₂²×C₇₃	—	8	1	no	—
458	C₂²×C₇₃	—	8	1	no	—
459	C₂²×C₇₃	—	8	1	no	—
460	C₂²×C₇₃	—	8	1	no	—
461	C₂²×C₇₃	—	8	1	no	—
462	C₂²×C₇₃	—	8	1	no	—
463	C₂²×C₇₃	—	8	1	no	—
464	C₂²×C₇₃	—	8	1	no	—
465	C₂²×C₇₃	—	8	1	no	—
466	C₂²×C₇₃	—	8	1	no	—
467	C₂²×C₇₃	—	8	1	no	—
468	C₂²×C₇₃	—	8	1	no	—
469	C₂²×C₇₃	C₂×#120	1	1	yes	characteristic
470	C₂²×C₇₃	C₂×#121	1	1	yes	characteristic
471	C₂²×C₇₃	#534	1	1	yes	characteristic
472	C₂²×C₇₃	#576	1	1	yes	characteristic
473	C₂²×C₇₃	#576	1	1	yes	characteristic
474	C₂²×C₇₃	#576	1	1	yes	characteristic
475	C₂²×C₇₃	#577	1	1	yes	characteristic
476	C₄×C₇₃	—	2	2	no	—
477	C₄×C₇₃	—	2	2	no	—
478	C₄×C₇₃	—	4	1	no	—
479	C₄×C₇₃	—	4	2	no	—
480	C₄×C₇₃	—	4	2	no	—
481	C₄×C₇₃	—	8	1	no	—
482	C₄×C₇₃	—	8	1	no	—
483	C₄×C₇₃	—	8	1	no	—
484	C₄×C₇₃	D₄²	1	1	yes	characteristic
485	C₄×C₇₃	D₄²	1	1	yes	characteristic
486	C₄×C₇₃	#546	1	1	yes	characteristic
487	C₄×C₇₃	#546	1	1	yes	characteristic
488	#24390	C₇₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
489	C₂×C₇₃	—	4	2	no	—
490	C₂×C₇₃	—	4	2	no	—
491	C₂×C₇₃	—	8	1	no	—
492	C₂×C₇₃	—	8	2	no	—
493	C₂×C₇₃	—	8	2	no	—
494	C₂×C₇₃	—	16	1	no	—
495	C₂×C₇₃	#2410	1	1	yes	characteristic
496	C₂×C₇₃	#3008	1	1	yes	characteristic
497	C₂×C₇₃	#3012	1	1	yes	characteristic
498	C₂×C₇₃	#3058	1	1	yes	characteristic
499	C₂×C₇₃	#3062	1	1	yes	characteristic
500	C₂×C₇₃	#3198	1	1	yes	characteristic
501	C₂×C₇₃	#3199	1	1	yes	characteristic
502	C₂×#535	C₂×C₇₃	1	1	yes	characteristic, complemented
503	C₂×#469	C₂×C₇₃	1	1	yes	characteristic, complemented
504	C₂×#466	C₂×C₇₃	1	1	yes	characteristic, complemented
505	C₂×#447	C₂×C₇₃	1	1	yes	characteristic, complemented
506	C₂×#408	C₂×C₇₃	1	1	yes	characteristic, complemented
507	#2615	C₂×C₇₃	1	1	yes	characteristic, complemented
508	#2034	C₂×C₇₃	1	1	yes	characteristic, complemented
509	#2033	C₂×C₇₃	1	1	yes	characteristic, complemented
510	#1999	C₂×C₇₃	1	1	yes	characteristic, complemented
511	#1999	C₂×C₇₃	1	1	yes	characteristic, complemented
512	#1895	C₂×C₇₃	1	1	yes	characteristic, complemented
513	#1893	C₂×C₇₃	1	1	yes	characteristic, complemented
514	#1875	C₂×C₇₃	1	1	yes	characteristic, complemented
515	#1854	C₂×C₇₃	1	1	yes	characteristic, complemented
516	#1786	C₂×C₇₃	1	1	yes	characteristic, complemented
517	C₇₃	#24390	1	1	yes	characteristic, direct product factor, Sylow
518	C₂²×#41	C₂²×C₇₃	1	1	yes	characteristic
519	C₂³×D₄	C₂²×C₇₃	1	1	yes	characteristic
520	C₂²×D₈	C₂²×C₇₃	1	1	yes	characteristic
521	C₂²×D₈	C₂²×C₇₃	1	1	yes	characteristic
522	C₂²×M₁₆	C₂²×C₇₃	1	1	yes	characteristic, complemented
523	C₂³×C₈	C₂²×C₇₃	1	1	yes	characteristic, complemented
524	#535	—	2	4	no	—
525	#535	—	2	4	no	—
526	C₂×#127	—	2	1	no	—
527	C₂×#124	—	2	1	no	—
528	C₂×#121	C₂²×C₇₃	1	1	yes	characteristic
529	C₂×#121	C₂²×C₇₃	1	1	yes	characteristic
530	C₂×#121	C₂²×C₇₃	1	1	yes	characteristic
531	C₂×#121	C₂²×C₇₃	1	1	yes	characteristic
532	C₂×#121	C₂²×C₇₃	1	1	yes	characteristic
533	C₂×#121	C₂²×C₇₃	1	1	yes	characteristic, complemented
534	C₂×#121	C₂²×C₇₃	1	1	yes	characteristic, complemented
535	C₂×#120	—	2	1	no	—
536	C₂×#120	—	2	1	no	—
537	C₂×#117	C₂²×C₇₃	1	1	yes	characteristic
538	#469	—	2	4	no	—
539	#466	—	2	4	no	—
540	#447	—	2	4	no	—
541	C₂×#107	C₂²×C₇₃	1	1	yes	characteristic, complemented
542	C₂×#106	C₂²×C₇₃	1	1	yes	characteristic, complemented
543	C₂×#102	C₂²×C₇₃	1	1	yes	characteristic
544	C₂×#102	C₂²×C₇₃	1	1	yes	characteristic
545	C₂×#102	C₂²×C₇₃	1	1	yes	characteristic
546	C₂×#102	C₂²×C₇₃	1	1	yes	characteristic
547	C₂×#102	C₂²×C₇₃	1	1	yes	characteristic
548	C₂×#102	C₂²×C₇₃	1	1	yes	characteristic
549	C₂×#102	C₂²×C₇₃	1	1	yes	characteristic, complemented
550	C₂×#102	C₂²×C₇₃	1	1	yes	characteristic, complemented
551	#408	—	2	4	no	—
552	C₂×C₂²⋊C₈	C₂²×C₇₃	1	1	yes	characteristic
553	C₂×C₂²⋊C₈	C₂²×C₇₃	1	1	yes	characteristic
554	C₂×C₂²⋊C₈	C₂²×C₇₃	1	1	yes	characteristic, complemented
555	C₂×C₂²⋊C₈	C₂²×C₇₃	1	1	yes	characteristic, complemented
556	#393	—	2	1	no	—
557	#392	—	2	1	no	—
558	#392	—	2	1	no	—
559	#392	—	2	1	no	—
560	#380	C₂²×C₇₃	1	1	yes	characteristic
561	#380	C₂²×C₇₃	1	1	yes	characteristic, complemented
562	#380	C₂²×C₇₃	1	1	yes	characteristic, complemented
563	#340	C₂²×C₇₃	1	1	yes	characteristic, complemented
564	#340	C₂²×C₇₃	1	1	yes	characteristic, complemented
565	#340	C₂²×C₇₃	1	1	yes	characteristic, complemented
566	#340	C₂²×C₇₃	1	1	yes	characteristic, complemented
567	C₂⁵	—	2	1	no	—
568	C₂×#41	—	2	2	no	—
569	C₂×#41	—	2	2	no	—
570	C₂×#41	—	2	2	no	—
571	C₂×#41	—	2	2	no	—
572	C₂×#41	—	4	1	no	—
573	C₂×#41	—	4	1	no	—
574	C₂²×Q₈	D₄×C₇₃	1	1	yes	characteristic
575	C₂²×D₄	—	2	1	no	—
576	C₂²×D₄	—	2	1	no	—
577	C₂²×D₄	—	2	1	no	—
578	C₂²×D₄	—	2	1	no	—
579	C₂²×D₄	—	2	2	no	—
580	C₂²×D₄	—	2	2	no	—
581	C₂²×D₄	—	2	1	no	—
582	C₂²×D₄	—	2	1	no	—
583	C₂²×D₄	—	2	1	no	—
584	C₂²×D₄	—	2	1	no	—
585	C₂²×D₄	—	2	2	no	—
586	C₂²×D₄	—	2	2	no	—
587	C₂²×D₄	—	4	1	no	—
588	C₂²×D₄	—	4	1	no	—
589	C₂²×D₄	D₄×C₇₃	1	1	yes	characteristic
590	C₂²×D₄	D₄×C₇₃	1	1	yes	characteristic
591	C₂²×D₄	D₄×C₇₃	1	1	yes	characteristic
592	C₂²×D₄	C₂³×C₇₃	1	1	yes	characteristic
593	C₂²×D₄	C₂³×C₇₃	1	1	yes	characteristic
594	C₂²×D₄	C₂³×C₇₃	1	1	yes	characteristic
595	C₂³×C₄	C₂³×C₇₃	1	1	yes	characteristic
596	C₂³×C₄	C₂³×C₇₃	1	1	yes	characteristic
597	C₂³×C₄	C₂³×C₇₃	1	1	yes	characteristic
598	C₂×D₈	—	2	2	no	—
599	C₂×D₈	—	2	2	no	—
600	C₂×D₈	—	2	2	no	—
601	C₂×D₈	—	2	2	no	—
602	C₂×D₈	—	4	1	no	—
603	C₂×D₈	—	4	1	no	—
604	C₂×M₁₆	—	2	2	no	—
605	C₂×M₁₆	—	2	2	no	—
606	C₂×M₁₆	—	4	1	no	—
607	C₂²×C₈	—	2	2	no	—
608	C₂²×C₈	—	2	2	no	—
609	C₂²×C₈	—	4	1	no	—
610	C₂²×C₈	C₂³×C₇₃	1	1	yes	characteristic
611	C₂²×C₈	C₂³×C₇₃	1	1	yes	characteristic
612	C₂²×C₈	C₂³×C₇₃	1	1	yes	characteristic
613	C₂²×C₈	C₂³×C₇₃	1	1	yes	characteristic
614	#127	—	2	8	no	—
615	#124	—	2	8	no	—
616	#121	—	2	2	no	—
617	#121	—	2	2	no	—
618	#121	—	2	2	no	—
619	#121	—	2	2	no	—
620	#121	—	2	2	no	—
621	#121	—	2	2	no	—
622	#121	—	2	2	no	—
623	#121	—	2	2	no	—
624	#121	—	2	2	no	—
625	#121	—	2	2	no	—
626	#121	—	4	1	no	—
627	#121	—	4	1	no	—
628	#121	D₄×C₇₃	1	4	yes	complemented
629	#121	D₄×C₇₃	1	4	yes	complemented
630	#120	—	2	8	no	—
631	#120	—	2	8	no	—
632	#117	—	2	2	no	—
633	#117	—	2	2	no	—
634	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
635	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
636	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
637	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
638	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
639	C₂×C₂²⋊C₄	—	2	1	no	—
640	C₂×C₂²⋊C₄	—	2	1	no	—
641	C₂×C₂²⋊C₄	—	2	1	no	—
642	C₂×C₂²⋊C₄	—	2	1	no	—
643	C₂×C₂²⋊C₄	—	2	1	no	—
644	C₂×C₂²⋊C₄	—	2	1	no	—
645	C₂×C₂²⋊C₄	—	2	1	no	—
646	C₂×C₂²⋊C₄	—	2	1	no	—
647	C₂×C₂²⋊C₄	—	2	1	no	—
648	C₂×C₂²⋊C₄	—	2	1	no	—
649	C₂×C₂²⋊C₄	—	2	1	no	—
650	C₂×C₄²	—	2	1	no	—
651	#107	—	2	2	no	—
652	#106	—	2	2	no	—
653	#102	—	2	2	no	—
654	#102	—	2	2	no	—
655	#102	—	2	2	no	—
656	#102	—	2	2	no	—
657	#102	—	2	2	no	—
658	#102	—	2	2	no	—
659	#102	—	4	1	no	—
660	#102	—	4	1	no	—
661	C₂²⋊C₈	—	2	2	no	—
662	C₂²⋊C₈	—	2	2	no	—
663	C₂²⋊C₈	—	2	2	no	—
664	C₂²⋊C₈	D₄×C₇₃	1	4	yes	complemented
665	#95	—	2	1	no	—
666	#95	—	2	1	no	—
667	#95	—	2	1	no	—
668	C₂⁴	—	2	4	no	—
669	C₂⁴	—	2	1	no	—
670	C₂⁴	—	2	1	no	—
671	C₂⁴	—	2	1	no	—
672	C₂⁴	—	4	2	no	—
673	C₂⁴	—	4	2	no	—
674	C₂⁴	—	8	1	no	—
675	C₂⁴	—	8	1	no	—
676	C₂⁴	—	8	1	no	—
677	C₂⁴	—	8	1	no	—
678	C₂⁴	C₂×D₄×C₇₃	1	1	yes	characteristic
679	C₂⁴	C₂×D₄×C₇₃	1	1	yes	characteristic
680	C₂⁴	C₂×D₄×C₇₃	1	1	yes	characteristic
681	#41	—	4	4	no	—
682	#41	—	4	4	no	—
683	#41	—	4	4	no	—
684	#41	—	4	4	no	—
685	C₂×Q₈	—	2	2	no	—
686	C₂×Q₈	—	2	2	no	—
687	C₂×Q₈	—	4	1	no	—
688	C₂×D₄	—	2	4	no	—
689	C₂×D₄	—	2	2	no	—
690	C₂×D₄	—	2	2	no	—
691	C₂×D₄	—	2	2	no	—
692	C₂×D₄	—	2	2	no	—
693	C₂×D₄	—	2	4	no	—
694	C₂×D₄	—	2	4	no	—
695	C₂×D₄	—	2	4	no	—
696	C₂×D₄	—	2	4	no	—
697	C₂×D₄	—	2	2	no	—
698	C₂×D₄	—	2	2	no	—
699	C₂×D₄	—	2	1	no	—
700	C₂×D₄	—	2	1	no	—
701	C₂×D₄	—	2	1	no	—
702	C₂×D₄	—	2	1	no	—
703	C₂×D₄	—	2	1	no	—
704	C₂×D₄	—	2	1	no	—
705	C₂×D₄	—	2	1	no	—
706	C₂×D₄	—	2	1	no	—
707	C₂×D₄	—	2	1	no	—
708	C₂×D₄	—	2	1	no	—
709	C₂×D₄	—	2	1	no	—
710	C₂×D₄	—	2	1	no	—
711	C₂×D₄	—	2	1	no	—
712	C₂×D₄	—	2	1	no	—
713	C₂×D₄	—	2	1	no	—
714	C₂×D₄	—	2	1	no	—
715	C₂×D₄	—	4	4	no	—
716	C₂×D₄	—	4	4	no	—
717	C₂×D₄	—	4	4	no	—
718	C₂×D₄	—	4	4	no	—
719	C₂×D₄	—	4	1	no	—
720	C₂×D₄	—	4	1	no	—
721	C₂×D₄	—	4	1	no	—
722	C₂×D₄	—	4	2	no	—
723	C₂×D₄	—	4	2	no	—
724	C₂×D₄	—	4	2	no	—
725	C₂×D₄	—	4	2	no	—
726	C₂×D₄	—	4	2	no	—
727	C₂×D₄	—	8	1	no	—
728	C₂×D₄	—	8	1	no	—
729	C₂×D₄	—	8	1	no	—
730	C₂×D₄	—	8	1	no	—
731	C₂×D₄	—	8	1	no	—
732	C₂×D₄	—	8	1	no	—
733	C₂×D₄	—	8	1	no	—
734	C₂×D₄	—	8	1	no	—
735	C₂×D₄	—	8	1	no	—
736	C₂×D₄	—	8	1	no	—
737	C₂×D₄	—	8	1	no	—
738	C₂×D₄	—	8	1	no	—
739	C₂×D₄	—	8	1	no	—
740	C₂×D₄	—	8	1	no	—
741	C₂×D₄	C₂×D₄×C₇₃	1	2	yes	—
742	C₂×D₄	C₂×D₄×C₇₃	1	2	yes	—
743	C₂²×C₄	—	2	1	no	—
744	C₂²×C₄	—	2	1	no	—
745	C₂²×C₄	—	2	1	no	—
746	C₂²×C₄	—	2	1	no	—
747	C₂²×C₄	—	2	1	no	—
748	C₂²×C₄	—	2	1	no	—
749	C₂²×C₄	—	2	1	no	—
750	C₂²×C₄	—	2	1	no	—
751	C₂²×C₄	—	2	1	no	—
752	C₂²×C₄	—	2	1	no	—
753	C₂²×C₄	—	2	1	no	—
754	C₂²×C₄	—	2	1	no	—
755	C₂²×C₄	—	2	1	no	—
756	C₂²×C₄	—	2	1	no	—
757	C₂²×C₄	—	2	1	no	—
758	C₂²×C₄	—	2	1	no	—
759	C₂²×C₄	—	2	1	no	—
760	C₂²×C₄	—	2	1	no	—
761	C₂²×C₄	—	2	1	no	—
762	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
763	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
764	C₂²×C₄	C₂×D₄×C₇₃	1	2	yes	—
765	C₂²×C₄	C₂×D₄×C₇₃	1	2	yes	—
766	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
767	C₂²×C₄	C₂×D₄×C₇₃	1	2	yes	—
768	C₂²×C₄	#41×C₇₃	1	2	yes	—
769	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
770	D₈	—	4	4	no	—
771	D₈	—	4	4	no	—
772	M₁₆	—	4	4	no	—
773	C₂×C₈	—	2	1	no	—
774	C₂×C₈	—	2	1	no	—
775	C₂×C₈	—	2	1	no	—
776	C₂×C₈	—	2	1	no	—
777	C₂×C₈	—	2	1	no	—
778	C₂×C₈	—	2	1	no	—
779	C₂×C₈	—	2	1	no	—
780	C₂×C₈	—	2	1	no	—
781	C₂×C₈	—	2	1	no	—
782	C₂×C₈	—	2	1	no	—
783	C₂×C₈	—	4	4	no	—
784	C₂×C₈	C₂×D₄×C₇₃	1	2	yes	—
785	C₂×C₈	C₂×D₄×C₇₃	1	2	yes	—
786	C₄⋊C₄	—	2	1	no	—
787	C₄⋊C₄	—	2	1	no	—
788	C₄⋊C₄	—	2	1	no	—
789	C₄⋊C₄	—	2	1	no	—
790	C₄⋊C₄	—	2	1	no	—
791	C₄⋊C₄	—	2	1	no	—
792	C₄⋊C₄	—	2	1	no	—
793	C₄⋊C₄	—	2	1	no	—
794	C₄⋊C₄	C₂×D₄×C₇₃	1	2	yes	—
795	C₄⋊C₄	C₂×D₄×C₇₃	1	2	yes	—
796	C₂²⋊C₄	—	2	4	no	—
797	C₂²⋊C₄	—	2	4	no	—
798	C₂²⋊C₄	—	2	4	no	—
799	C₂²⋊C₄	—	2	4	no	—
800	C₂²⋊C₄	—	2	4	no	—
801	C₂²⋊C₄	—	4	2	no	—
802	C₂²⋊C₄	—	4	2	no	—
803	C₂²⋊C₄	—	4	2	no	—
804	C₂²⋊C₄	—	8	1	no	—
805	C₂²⋊C₄	—	8	1	no	—
806	C₂²⋊C₄	—	8	1	no	—
807	C₄²	—	2	4	no	—
808	C₂³	—	2	1	no	—
809	C₂³	—	2	1	no	—
810	C₂³	—	2	1	no	—
811	C₂³	—	2	1	no	—
812	C₂³	—	2	1	no	—
813	C₂³	—	2	1	no	—
814	C₂³	—	2	1	no	—
815	C₂³	—	2	1	no	—
816	C₂³	—	2	1	no	—
817	C₂³	—	2	1	no	—
818	C₂³	—	2	1	no	—
819	C₂³	—	2	1	no	—
820	C₂³	—	2	2	no	—
821	C₂³	—	2	2	no	—
822	C₂³	—	2	1	no	—
823	C₂³	—	2	1	no	—
824	C₂³	—	2	1	no	—
825	C₂³	—	2	1	no	—
826	C₂³	—	2	1	no	—
827	C₂³	—	2	1	no	—
828	C₂³	—	2	1	no	—
829	C₂³	—	4	8	no	—
830	C₂³	—	4	1	no	—
831	C₂³	—	4	1	no	—
832	C₂³	—	4	1	no	—
833	C₂³	—	4	1	no	—
834	C₂³	—	4	1	no	—
835	C₂³	—	4	1	no	—
836	C₂³	—	4	1	no	—
837	C₂³	—	4	1	no	—
838	C₂³	—	4	1	no	—
839	C₂³	—	4	1	no	—
840	C₂³	—	4	1	no	—
841	C₂³	—	4	1	no	—
842	C₂³	—	4	1	no	—
843	C₂³	—	4	1	no	—
844	C₂³	—	4	1	no	—
845	C₂³	—	4	1	no	—
846	C₂³	—	4	1	no	—
847	C₂³	—	4	1	no	—
848	C₂³	—	4	1	no	—
849	C₂³	—	8	4	no	—
850	C₂³	—	8	4	no	—
851	C₂³	—	8	4	no	—
852	C₂³	—	8	4	no	—
853	C₂³	—	8	4	no	—
854	C₂³	—	8	4	no	—
855	C₂³	#120×C₇₃	1	2	yes	—
856	C₂³	#121×C₇₃	1	2	yes	—
857	C₂³	C₂²×D₄×C₇₃	1	1	yes	characteristic
858	Q₈	—	4	4	no	—
859	D₄	—	2	2	no	—
860	D₄	—	2	2	no	—
861	D₄	—	2	2	no	—
862	D₄	—	2	2	no	—
863	D₄	—	4	4	no	—
864	D₄	—	4	4	no	—
865	D₄	—	4	8	no	—
866	D₄	—	4	4	no	—
867	D₄	—	4	1	no	—
868	D₄	—	4	1	no	—
869	D₄	—	4	1	no	—
870	D₄	—	4	1	no	—
871	D₄	—	4	1	no	—
872	D₄	—	4	1	no	—
873	D₄	—	4	1	no	—
874	D₄	—	4	1	no	—
875	D₄	—	8	4	no	—
876	D₄	—	8	4	no	—
877	D₄	—	8	4	no	—
878	D₄	—	8	4	no	—
879	D₄	—	8	4	no	—
880	D₄	—	8	4	no	—
881	D₄	—	8	4	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	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	2	no	—
894	C₂×C₄	—	2	2	no	—
895	C₂×C₄	—	2	2	no	—
896	C₂×C₄	—	2	1	no	—
897	C₂×C₄	—	2	1	no	—
898	C₂×C₄	—	2	1	no	—
899	C₂×C₄	—	4	1	no	—
900	C₂×C₄	—	4	1	no	—
901	C₂×C₄	—	4	1	no	—
902	C₂×C₄	—	4	1	no	—
903	C₂×C₄	—	4	1	no	—
904	C₂×C₄	—	4	1	no	—
905	C₂×C₄	—	4	1	no	—
906	C₂×C₄	—	4	1	no	—
907	C₂×C₄	—	4	1	no	—
908	C₂×C₄	—	4	1	no	—
909	C₂×C₄	—	4	1	no	—
910	C₂×C₄	—	4	1	no	—
911	C₂×C₄	—	4	1	no	—
912	C₂×C₄	—	4	1	no	—
913	C₂×C₄	—	4	1	no	—
914	C₂×C₄	—	4	1	no	—
915	C₂×C₄	—	4	1	no	—
916	C₂×C₄	#120×C₇₃	1	2	yes	—
917	C₂×C₄	#121×C₇₃	1	2	yes	—
918	C₂×C₄	C₂²×D₄×C₇₃	1	1	yes	characteristic
919	C₂×C₄	C₂²×D₄×C₇₃	1	1	yes	characteristic
920	C₂×C₄	C₂²×D₄×C₇₃	1	1	yes	characteristic
921	C₂×C₄	C₂×#41×C₇₃	1	1	yes	characteristic
922	C₂×C₄	H(5,𝔽₂)×C₇₃	1	1	yes	characteristic
923	C₂×C₄	H(5,𝔽₂)×C₇₃	1	1	yes	characteristic
924	C₈	—	2	2	no	—
925	C₈	—	2	2	no	—
926	C₈	—	4	1	no	—
927	C₈	—	4	1	no	—
928	C₂²	—	2	2	no	—
929	C₂²	—	2	2	no	—
930	C₂²	—	2	2	no	—
931	C₂²	—	2	2	no	—
932	C₂²	—	2	2	no	—
933	C₂²	—	2	2	no	—
934	C₂²	—	4	1	no	—
935	C₂²	—	4	1	no	—
936	C₂²	—	4	1	no	—
937	C₂²	—	4	1	no	—
938	C₂²	—	4	1	no	—
939	C₂²	—	4	1	no	—
940	C₂²	—	4	1	no	—
941	C₂²	—	4	1	no	—
942	C₂²	—	4	1	no	—
943	C₂²	—	4	2	no	—
944	C₂²	—	4	2	no	—
945	C₂²	—	4	1	no	—
946	C₂²	—	4	2	no	—
947	C₂²	—	4	2	no	—
948	C₂²	—	4	1	no	—
949	C₂²	—	4	1	no	—
950	C₂²	—	4	1	no	—
951	C₂²	—	4	2	no	—
952	C₂²	—	4	2	no	—
953	C₂²	—	4	1	no	—
954	C₂²	—	4	1	no	—
955	C₂²	—	8	16	no	—
956	C₂²	—	8	1	no	—
957	C₂²	—	8	1	no	—
958	C₂²	—	8	1	no	—
959	C₂²	—	8	1	no	—
960	C₂²	—	8	1	no	—
961	C₂²	—	8	1	no	—
962	C₂²	—	8	1	no	—
963	C₂²	—	8	1	no	—
964	C₂²	—	8	1	no	—
965	C₂²	—	8	1	no	—
966	C₂²	—	8	1	no	—
967	C₂²	—	8	1	no	—
968	C₂²	—	8	1	no	—
969	C₂²	—	8	1	no	—
970	C₂²	—	8	1	no	—
971	C₂²	C₂×#120×C₇₃	1	1	yes	characteristic
972	C₂²	C₂×#121×C₇₃	1	1	yes	characteristic
973	C₂²	#534×C₇₃	1	1	yes	characteristic
974	C₂²	#576×C₇₃	1	1	yes	characteristic
975	C₂²	#576×C₇₃	1	1	yes	characteristic
976	C₂²	#576×C₇₃	1	1	yes	characteristic
977	C₂²	#577×C₇₃	1	1	yes	characteristic
978	C₄	—	2	2	no	—
979	C₄	—	2	2	no	—
980	C₄	—	4	2	no	—
981	C₄	—	4	2	no	—
982	C₄	—	4	1	no	—
983	C₄	—	8	1	no	—
984	C₄	—	8	1	no	—
985	C₄	—	8	1	no	—
986	C₄	D₄²×C₇₃	1	1	yes	characteristic
987	C₄	D₄²×C₇₃	1	1	yes	characteristic
988	C₄	#546×C₇₃	1	1	yes	characteristic
989	C₄	#546×C₇₃	1	1	yes	characteristic
990	C₂	—	4	2	no	—
991	C₂	—	4	2	no	—
992	C₂	—	8	1	no	—
993	C₂	—	8	2	no	—
994	C₂	—	8	2	no	—
995	C₂	—	16	1	no	—
996	C₂	C₇₃×#2410	1	1	yes	characteristic
997	C₂	C₇₃×#3008	1	1	yes	characteristic
998	C₂	C₇₃×#3012	1	1	yes	characteristic
999	C₂	C₇₃×#3058	1	1	yes	characteristic
1000	C₂	C₇₃×#3062	1	1	yes	characteristic
1001	C₂	C₇₃×#3198	1	1	yes	characteristic
1002	C₂	C₇₃×#3199	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₇₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₇₃
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₇₃ ◁ C₂²×#41×C₇₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×#535×C₇₃	C₂	semidirect
2. C₂×#469×C₇₃	C₂	semidirect
3. C₂×#466×C₇₃	C₂	semidirect
4. C₂×#447×C₇₃	C₂	semidirect
5. C₂×#408×C₇₃	C₂	semidirect
6. C₇₃×#2615	C₂	semidirect
7. C₇₃×#2034	C₂	semidirect
8. C₇₃×#2033	C₂	semidirect
9. C₇₃×#1999	C₂	semidirect
10. C₇₃×#1999	C₂	semidirect
11. C₇₃×#1895	C₂	semidirect
12. C₇₃×#1893	C₂	semidirect
13. C₇₃×#1875	C₂	semidirect
14. C₇₃×#1854	C₂	semidirect
15. C₇₃×#1786	C₂	semidirect
20. C₂²×M₁₆×C₇₃	C₂²	semidirect
21. C₂³×C₈×C₇₃	C₂²	semidirect
31. C₂×#121×C₇₃	C₂²	semidirect
32. C₂×#121×C₇₃	C₂²	semidirect
39. C₂×#107×C₇₃	C₂²	semidirect
40. C₂×#106×C₇₃	C₂²	semidirect
47. C₂×#102×C₇₃	C₂²	semidirect
48. C₂×#102×C₇₃	C₂²	semidirect
52. C₂×C₂²⋊C₈×C₇₃	C₂²	semidirect
53. C₂×C₂²⋊C₈×C₇₃	C₂²	semidirect
59. #380×C₇₃	C₂²	semidirect
60. #380×C₇₃	C₂²	semidirect
61. #340×C₇₃	C₂²	semidirect
62. #340×C₇₃	C₂²	semidirect
63. #340×C₇₃	C₂²	semidirect
64. #340×C₇₃	C₂²	semidirect
126. #121×C₇₃	D₄	semidirect
127. #121×C₇₃	D₄	semidirect
162. C₂²⋊C₈×C₇₃	D₄	semidirect
488. #24390	C₇₃	direct (N × H)
502. C₂×#535	C₂×C₇₃	semidirect
503. C₂×#469	C₂×C₇₃	semidirect
504. C₂×#466	C₂×C₇₃	semidirect
505. C₂×#447	C₂×C₇₃	semidirect
506. C₂×#408	C₂×C₇₃	semidirect
507. #2615	C₂×C₇₃	semidirect
508. #2034	C₂×C₇₃	semidirect
509. #2033	C₂×C₇₃	semidirect
510. #1999	C₂×C₇₃	semidirect
511. #1999	C₂×C₇₃	semidirect
512. #1895	C₂×C₇₃	semidirect
513. #1893	C₂×C₇₃	semidirect
514. #1875	C₂×C₇₃	semidirect
515. #1854	C₂×C₇₃	semidirect
516. #1786	C₂×C₇₃	semidirect
517. C₇₃	#24390	direct (N × H)
522. C₂²×M₁₆	C₂²×C₇₃	semidirect
523. C₂³×C₈	C₂²×C₇₃	semidirect
533. C₂×#121	C₂²×C₇₃	semidirect
534. C₂×#121	C₂²×C₇₃	semidirect
541. C₂×#107	C₂²×C₇₃	semidirect
542. C₂×#106	C₂²×C₇₃	semidirect
549. C₂×#102	C₂²×C₇₃	semidirect
550. C₂×#102	C₂²×C₇₃	semidirect
554. C₂×C₂²⋊C₈	C₂²×C₇₃	semidirect
555. C₂×C₂²⋊C₈	C₂²×C₇₃	semidirect
561. #380	C₂²×C₇₃	semidirect
562. #380	C₂²×C₇₃	semidirect
563. #340	C₂²×C₇₃	semidirect
564. #340	C₂²×C₇₃	semidirect
565. #340	C₂²×C₇₃	semidirect
566. #340	C₂²×C₇₃	semidirect
628. #121	D₄×C₇₃	semidirect
629. #121	D₄×C₇₃	semidirect
664. C₂²⋊C₈	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×#535×C₇₃	2
C₂×#469×C₇₃	2
C₂×#466×C₇₃	2
C₂×#447×C₇₃	2
C₂×#408×C₇₃	2
C₇₃×#2615	2
C₇₃×#2034	2
C₇₃×#2033	2
C₇₃×#1999	2
C₇₃×#1895	2
C₇₃×#1893	2
C₇₃×#1875	2
C₇₃×#1854	2
C₇₃×#1786	2
#24390	73

Subgroups — C73×#24390 #32933794

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₃×#24390 #32933794