Subgroups — C₇₃×#25762 #32935166

Order 18688.

1722 conjugacy classes of subgroups.

The subgroup lattice has 1006 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#546×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#495×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#463×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#452×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#449×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#450×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#447×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
8	C₇₃×#2540	C₂	1	1	yes	maximal, characteristic, complemented
9	C₇₃×#2001	C₂	1	1	yes	maximal, characteristic, complemented
10	C₇₃×#2000	C₂	1	1	yes	maximal, characteristic, complemented
11	C₇₃×#2000	C₂	1	1	yes	maximal, characteristic, complemented
12	C₇₃×#1999	C₂	1	1	yes	maximal, characteristic, complemented
13	C₇₃×#1983	C₂	1	1	yes	maximal, characteristic, complemented
14	C₇₃×#1954	C₂	1	1	yes	maximal, characteristic, complemented
15	C₄×#102×C₇₃	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×Q₁₆×C₇₃	C₂²	1	1	yes	characteristic, complemented
19	C₂²×SD₁₆×C₇₃	C₂²	1	1	yes	characteristic
20	C₂²×SD₁₆×C₇₃	C₂²	1	1	yes	characteristic
21	C₂²×SD₁₆×C₇₃	C₂²	1	1	yes	characteristic, complemented
22	C₂²×D₈×C₇₃	C₂²	1	1	yes	characteristic
23	C₂²×D₈×C₇₃	C₂²	1	1	yes	characteristic
24	#546×C₇₃	—	2	4	no	—
25	#546×C₇₃	—	2	4	no	—
26	C₂×#124×C₇₃	C₂²	1	1	yes	characteristic
27	C₂×#124×C₇₃	C₂²	1	1	yes	characteristic, complemented
28	C₂×#123×C₇₃	—	2	1	no	—
29	C₂×C₂²⋊Q₈×C₇₃	C₂²	1	1	yes	characteristic
30	C₂×C₂²⋊Q₈×C₇₃	C₂²	1	1	yes	characteristic
31	C₂×C₂²⋊Q₈×C₇₃	C₂²	1	1	yes	characteristic, complemented
32	C₂×#121×C₇₃	—	2	1	no	—
33	C₂×#121×C₇₃	C₂²	1	1	yes	characteristic
34	C₂×#121×C₇₃	C₂²	1	1	yes	characteristic
35	C₂×#121×C₇₃	C₂²	1	1	yes	characteristic, complemented
36	C₂×#120×C₇₃	—	2	1	no	—
37	C₂×C₄×D₄×C₇₃	C₂²	1	1	yes	characteristic
38	C₂×C₄×D₄×C₇₃	C₂²	1	1	yes	characteristic
39	C₂²×C₂²⋊C₄×C₇₃	—	2	1	no	—
40	#495×C₇₃	—	2	4	no	—
41	#463×C₇₃	—	2	4	no	—
42	#452×C₇₃	—	2	4	no	—
43	#450×C₇₃	—	2	4	no	—
44	#449×C₇₃	—	2	4	no	—
45	#447×C₇₃	—	2	4	no	—
46	C₂×C₄⋊C₈×C₇₃	C₂²	1	1	yes	characteristic, complemented
47	C₂×#103×C₇₃	C₂²	1	1	yes	characteristic, complemented
48	C₂×#103×C₇₃	C₂²	1	1	yes	characteristic, complemented
49	C₂×#103×C₇₃	C₂²	1	1	yes	characteristic, complemented
50	C₂×#102×C₇₃	C₂²	1	1	yes	characteristic
51	C₂×#102×C₇₃	C₂²	1	1	yes	characteristic
52	C₂×#102×C₇₃	C₂²	1	1	yes	characteristic
53	C₂×#102×C₇₃	C₂²	1	1	yes	characteristic
54	C₂×#102×C₇₃	C₂²	1	1	yes	characteristic, complemented
55	C₂×C₂²⋊C₈×C₇₃	C₂²	1	1	yes	characteristic
56	C₂×C₂²⋊C₈×C₇₃	C₂²	1	1	yes	characteristic
57	C₂×C₂²⋊C₈×C₇₃	C₂²	1	1	yes	characteristic, complemented
58	C₂×C₂²⋊C₈×C₇₃	C₂²	1	1	yes	characteristic, complemented
59	C₂×C₄×C₈×C₇₃	C₂²	1	1	yes	characteristic, complemented
60	#399×C₇₃	—	2	1	no	—
61	#392×C₇₃	—	2	1	no	—
62	#390×C₇₃	—	2	1	no	—
63	#390×C₇₃	—	2	1	no	—
64	C₄×C₄⋊C₄×C₇₃	C₂²	1	1	yes	characteristic, complemented
65	#340×C₇₃	C₂²	1	1	yes	characteristic, complemented
66	#340×C₇₃	C₂²	1	1	yes	characteristic, complemented
67	C₂⁵×C₇₃	—	2	1	no	—
68	C₂×#41×C₇₃	—	2	2	no	—
69	C₂×#41×C₇₃	—	2	2	no	—
70	C₂×#41×C₇₃	—	2	2	no	—
71	C₂×#41×C₇₃	—	2	2	no	—
72	C₂×#41×C₇₃	—	4	1	no	—
73	C₂×#41×C₇₃	—	4	1	no	—
74	C₂²×Q₈×C₇₃	C₂³	1	1	yes	characteristic
75	C₂²×Q₈×C₇₃	C₂³	1	1	yes	characteristic
76	C₂²×D₄×C₇₃	—	2	1	no	—
77	C₂²×D₄×C₇₃	—	2	1	no	—
78	C₂²×D₄×C₇₃	—	2	2	no	—
79	C₂²×D₄×C₇₃	—	2	2	no	—
80	C₂²×D₄×C₇₃	—	2	2	no	—
81	C₂²×D₄×C₇₃	—	2	2	no	—
82	C₂²×D₄×C₇₃	—	2	1	no	—
83	C₂²×D₄×C₇₃	—	2	1	no	—
84	C₂²×D₄×C₇₃	—	2	1	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	C₂³	1	1	yes	characteristic
89	C₂²×D₄×C₇₃	C₂³	1	1	yes	characteristic
90	C₂²×D₄×C₇₃	C₂³	1	1	yes	characteristic
91	C₂³×C₄×C₇₃	—	2	1	no	—
92	C₂³×C₄×C₇₃	—	2	1	no	—
93	C₂³×C₄×C₇₃	C₂³	1	1	yes	characteristic
94	C₂³×C₄×C₇₃	C₂³	1	1	yes	characteristic
95	C₂×Q₁₆×C₇₃	—	2	2	no	—
96	C₂×Q₁₆×C₇₃	—	2	2	no	—
97	C₂×Q₁₆×C₇₃	—	4	1	no	—
98	C₂×SD₁₆×C₇₃	—	2	2	no	—
99	C₂×SD₁₆×C₇₃	—	2	2	no	—
100	C₂×SD₁₆×C₇₃	—	2	2	no	—
101	C₂×SD₁₆×C₇₃	—	2	2	no	—
102	C₂×SD₁₆×C₇₃	—	2	2	no	—
103	C₂×SD₁₆×C₇₃	—	2	2	no	—
104	C₂×SD₁₆×C₇₃	—	2	2	no	—
105	C₂×SD₁₆×C₇₃	—	4	1	no	—
106	C₂×SD₁₆×C₇₃	—	4	1	no	—
107	C₂×D₈×C₇₃	—	2	2	no	—
108	C₂×D₈×C₇₃	—	2	2	no	—
109	C₂×D₈×C₇₃	—	2	2	no	—
110	C₂×D₈×C₇₃	—	2	2	no	—
111	C₂×D₈×C₇₃	—	2	2	no	—
112	C₂×D₈×C₇₃	—	4	1	no	—
113	C₂²×C₈×C₇₃	C₂³	1	1	yes	characteristic
114	C₂²×C₈×C₇₃	C₂³	1	1	yes	characteristic
115	C₂²×C₈×C₇₃	C₂³	1	1	yes	characteristic
116	C₂²×C₈×C₇₃	C₂³	1	1	yes	characteristic
117	#124×C₇₃	—	2	2	no	—
118	#124×C₇₃	—	2	2	no	—
119	#124×C₇₃	—	2	2	no	—
120	#124×C₇₃	D₄	1	4	yes	complemented
121	#123×C₇₃	—	2	8	no	—
122	C₂²⋊Q₈×C₇₃	—	2	2	no	—
123	C₂²⋊Q₈×C₇₃	—	2	2	no	—
124	C₂²⋊Q₈×C₇₃	—	2	2	no	—
125	C₂²⋊Q₈×C₇₃	—	2	2	no	—
126	C₂²⋊Q₈×C₇₃	—	4	1	no	—
127	C₂²⋊Q₈×C₇₃	—	4	1	no	—
128	#121×C₇₃	—	2	8	no	—
129	#121×C₇₃	—	2	2	no	—
130	#121×C₇₃	—	2	2	no	—
131	#121×C₇₃	—	2	2	no	—
132	#121×C₇₃	—	2	2	no	—
133	#121×C₇₃	—	4	1	no	—
134	#121×C₇₃	—	4	1	no	—
135	#120×C₇₃	—	2	8	no	—
136	C₄×D₄×C₇₃	—	2	2	no	—
137	C₄×D₄×C₇₃	—	2	2	no	—
138	C₄×D₄×C₇₃	—	2	2	no	—
139	C₄×D₄×C₇₃	D₄	1	4	yes	complemented
140	C₂×C₄⋊C₄×C₇₃	—	2	1	no	—
141	C₂×C₄⋊C₄×C₇₃	—	2	1	no	—
142	C₂×C₄⋊C₄×C₇₃	—	2	1	no	—
143	C₂×C₄⋊C₄×C₇₃	D₄	1	1	yes	characteristic
144	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
145	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
146	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
147	C₂×C₂²⋊C₄×C₇₃	—	2	8	no	—
148	C₂×C₂²⋊C₄×C₇₃	—	2	1	no	—
149	C₂×C₂²⋊C₄×C₇₃	—	2	1	no	—
150	C₂×C₂²⋊C₄×C₇₃	—	2	1	no	—
151	C₂×C₂²⋊C₄×C₇₃	—	2	1	no	—
152	C₂×C₂²⋊C₄×C₇₃	—	2	1	no	—
153	C₂×C₂²⋊C₄×C₇₃	—	2	1	no	—
154	C₂×C₂²⋊C₄×C₇₃	—	2	1	no	—
155	C₂×C₂²⋊C₄×C₇₃	—	2	1	no	—
156	C₂×C₂²⋊C₄×C₇₃	—	2	1	no	—
157	C₂×C₂²⋊C₄×C₇₃	—	2	1	no	—
158	C₂×C₂²⋊C₄×C₇₃	—	2	1	no	—
159	C₂×C₂²⋊C₄×C₇₃	D₄	1	1	yes	characteristic
160	C₂×C₂²⋊C₄×C₇₃	D₄	1	1	yes	characteristic
161	C₂×C₄²×C₇₃	—	2	1	no	—
162	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
163	C₄⋊C₈×C₇₃	—	2	2	no	—
164	#103×C₇₃	—	2	2	no	—
165	#103×C₇₃	—	2	2	no	—
166	#103×C₇₃	—	2	2	no	—
167	#102×C₇₃	—	2	2	no	—
168	#102×C₇₃	—	2	2	no	—
169	#102×C₇₃	—	2	2	no	—
170	#102×C₇₃	D₄	1	4	yes	complemented
171	#102×C₇₃	D₄	1	4	yes	complemented
172	C₂²⋊C₈×C₇₃	—	2	2	no	—
173	C₂²⋊C₈×C₇₃	—	2	2	no	—
174	C₂²⋊C₈×C₇₃	—	2	2	no	—
175	C₂²⋊C₈×C₇₃	—	2	2	no	—
176	C₄×C₈×C₇₃	—	2	2	no	—
177	#95×C₇₃	—	2	1	no	—
178	C₂⁴×C₇₃	—	2	1	no	—
179	C₂⁴×C₇₃	—	2	4	no	—
180	C₂⁴×C₇₃	—	2	1	no	—
181	C₂⁴×C₇₃	—	2	1	no	—
182	C₂⁴×C₇₃	—	4	2	no	—
183	C₂⁴×C₇₃	—	4	2	no	—
184	C₂⁴×C₇₃	—	4	2	no	—
185	C₂⁴×C₇₃	—	4	2	no	—
186	C₂⁴×C₇₃	—	8	1	no	—
187	C₂⁴×C₇₃	—	8	1	no	—
188	C₂⁴×C₇₃	C₂×D₄	1	1	yes	characteristic
189	C₂⁴×C₇₃	C₂×D₄	1	1	yes	characteristic
190	#41×C₇₃	—	4	4	no	—
191	#41×C₇₃	—	4	4	no	—
192	#41×C₇₃	—	4	4	no	—
193	#41×C₇₃	—	4	4	no	—
194	C₂×Q₈×C₇₃	—	2	1	no	—
195	C₂×Q₈×C₇₃	—	2	1	no	—
196	C₂×Q₈×C₇₃	—	2	1	no	—
197	C₂×Q₈×C₇₃	—	2	1	no	—
198	C₂×Q₈×C₇₃	—	2	1	no	—
199	C₂×Q₈×C₇₃	—	2	1	no	—
200	C₂×Q₈×C₇₃	—	2	1	no	—
201	C₂×Q₈×C₇₃	—	2	1	no	—
202	C₂×Q₈×C₇₃	—	2	1	no	—
203	C₂×Q₈×C₇₃	—	2	1	no	—
204	C₂×Q₈×C₇₃	—	2	1	no	—
205	C₂×Q₈×C₇₃	C₂×D₄	1	2	yes	—
206	C₂×D₄×C₇₃	—	2	4	no	—
207	C₂×D₄×C₇₃	—	2	4	no	—
208	C₂×D₄×C₇₃	—	2	2	no	—
209	C₂×D₄×C₇₃	—	2	4	no	—
210	C₂×D₄×C₇₃	—	2	2	no	—
211	C₂×D₄×C₇₃	—	2	1	no	—
212	C₂×D₄×C₇₃	—	2	1	no	—
213	C₂×D₄×C₇₃	—	2	1	no	—
214	C₂×D₄×C₇₃	—	2	1	no	—
215	C₂×D₄×C₇₃	—	2	1	no	—
216	C₂×D₄×C₇₃	—	2	1	no	—
217	C₂×D₄×C₇₃	—	2	1	no	—
218	C₂×D₄×C₇₃	—	2	1	no	—
219	C₂×D₄×C₇₃	—	2	1	no	—
220	C₂×D₄×C₇₃	—	2	1	no	—
221	C₂×D₄×C₇₃	—	2	1	no	—
222	C₂×D₄×C₇₃	—	2	1	no	—
223	C₂×D₄×C₇₃	—	2	1	no	—
224	C₂×D₄×C₇₃	—	2	1	no	—
225	C₂×D₄×C₇₃	—	4	1	no	—
226	C₂×D₄×C₇₃	—	4	2	no	—
227	C₂×D₄×C₇₃	—	4	2	no	—
228	C₂×D₄×C₇₃	—	4	2	no	—
229	C₂×D₄×C₇₃	—	4	2	no	—
230	C₂×D₄×C₇₃	—	4	4	no	—
231	C₂×D₄×C₇₃	—	4	4	no	—
232	C₂×D₄×C₇₃	—	4	4	no	—
233	C₂×D₄×C₇₃	—	4	2	no	—
234	C₂×D₄×C₇₃	—	4	2	no	—
235	C₂×D₄×C₇₃	—	4	4	no	—
236	C₂×D₄×C₇₃	—	4	2	no	—
237	C₂×D₄×C₇₃	—	4	2	no	—
238	C₂×D₄×C₇₃	—	8	1	no	—
239	C₂×D₄×C₇₃	—	8	1	no	—
240	C₂×D₄×C₇₃	—	8	1	no	—
241	C₂×D₄×C₇₃	—	8	1	no	—
242	C₂×D₄×C₇₃	C₂×D₄	1	2	yes	—
243	C₂×D₄×C₇₃	C₂×D₄	1	2	yes	—
244	C₂×D₄×C₇₃	C₂×D₄	1	2	yes	—
245	C₂×D₄×C₇₃	C₂×D₄	1	2	yes	—
246	C₂²×C₄×C₇₃	—	2	4	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	—	2	1	no	—
261	C₂²×C₄×C₇₃	—	2	1	no	—
262	C₂²×C₄×C₇₃	—	2	1	no	—
263	C₂²×C₄×C₇₃	—	2	4	no	—
264	C₂²×C₄×C₇₃	—	2	1	no	—
265	C₂²×C₄×C₇₃	—	4	2	no	—
266	C₂²×C₄×C₇₃	—	4	2	no	—
267	C₂²×C₄×C₇₃	—	8	1	no	—
268	C₂²×C₄×C₇₃	—	8	1	no	—
269	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
270	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
271	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
272	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
273	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
274	Q₁₆×C₇₃	—	4	4	no	—
275	SD₁₆×C₇₃	—	4	4	no	—
276	SD₁₆×C₇₃	—	4	4	no	—
277	SD₁₆×C₇₃	—	4	4	no	—
278	D₈×C₇₃	—	4	4	no	—
279	D₈×C₇₃	—	4	4	no	—
280	C₂×C₈×C₇₃	—	2	1	no	—
281	C₂×C₈×C₇₃	—	2	1	no	—
282	C₂×C₈×C₇₃	—	2	1	no	—
283	C₂×C₈×C₇₃	—	2	1	no	—
284	C₂×C₈×C₇₃	—	2	1	no	—
285	C₂×C₈×C₇₃	—	2	1	no	—
286	C₂×C₈×C₇₃	—	2	1	no	—
287	C₂×C₈×C₇₃	—	2	1	no	—
288	C₂×C₈×C₇₃	—	2	1	no	—
289	C₂×C₈×C₇₃	—	2	1	no	—
290	C₂×C₈×C₇₃	C₂×D₄	1	2	yes	—
291	C₂×C₈×C₇₃	C₂×D₄	1	2	yes	—
292	C₄⋊C₄×C₇₃	—	2	4	no	—
293	C₄⋊C₄×C₇₃	—	2	2	no	—
294	C₄⋊C₄×C₇₃	—	2	1	no	—
295	C₄⋊C₄×C₇₃	—	2	1	no	—
296	C₄⋊C₄×C₇₃	—	2	1	no	—
297	C₄⋊C₄×C₇₃	—	4	2	no	—
298	C₄⋊C₄×C₇₃	—	4	2	no	—
299	C₄⋊C₄×C₇₃	C₂×D₄	1	2	yes	—
300	C₄⋊C₄×C₇₃	C₂×D₄	1	2	yes	—
301	C₄⋊C₄×C₇₃	C₂×D₄	1	2	yes	—
302	C₂²⋊C₄×C₇₃	—	2	4	no	—
303	C₂²⋊C₄×C₇₃	—	2	4	no	—
304	C₂²⋊C₄×C₇₃	—	2	2	no	—
305	C₂²⋊C₄×C₇₃	—	2	4	no	—
306	C₂²⋊C₄×C₇₃	—	2	4	no	—
307	C₂²⋊C₄×C₇₃	—	2	4	no	—
308	C₂²⋊C₄×C₇₃	—	2	2	no	—
309	C₂²⋊C₄×C₇₃	—	4	2	no	—
310	C₂²⋊C₄×C₇₃	—	4	2	no	—
311	C₂²⋊C₄×C₇₃	—	4	2	no	—
312	C₂²⋊C₄×C₇₃	—	4	2	no	—
313	C₂²⋊C₄×C₇₃	—	4	2	no	—
314	C₂²⋊C₄×C₇₃	—	4	2	no	—
315	C₄²×C₇₃	—	8	1	no	—
316	C₄²×C₇₃	C₂×D₄	1	2	yes	—
317	C₄²×C₇₃	C₂×D₄	1	2	yes	—
318	C₂³×C₇₃	—	2	1	no	—
319	C₂³×C₇₃	—	2	2	no	—
320	C₂³×C₇₃	—	2	1	no	—
321	C₂³×C₇₃	—	2	1	no	—
322	C₂³×C₇₃	—	2	2	no	—
323	C₂³×C₇₃	—	2	2	no	—
324	C₂³×C₇₃	—	2	1	no	—
325	C₂³×C₇₃	—	2	1	no	—
326	C₂³×C₇₃	—	2	1	no	—
327	C₂³×C₇₃	—	2	2	no	—
328	C₂³×C₇₃	—	2	1	no	—
329	C₂³×C₇₃	—	2	1	no	—
330	C₂³×C₇₃	—	2	1	no	—
331	C₂³×C₇₃	—	2	1	no	—
332	C₂³×C₇₃	—	2	1	no	—
333	C₂³×C₇₃	—	2	1	no	—
334	C₂³×C₇₃	—	2	1	no	—
335	C₂³×C₇₃	—	4	8	no	—
336	C₂³×C₇₃	—	4	8	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	—	4	1	no	—
348	C₂³×C₇₃	—	4	1	no	—
349	C₂³×C₇₃	—	4	1	no	—
350	C₂³×C₇₃	—	4	1	no	—
351	C₂³×C₇₃	—	4	1	no	—
352	C₂³×C₇₃	—	4	1	no	—
353	C₂³×C₇₃	—	4	1	no	—
354	C₂³×C₇₃	—	8	4	no	—
355	C₂³×C₇₃	—	8	4	no	—
356	C₂³×C₇₃	—	8	4	no	—
357	C₂³×C₇₃	—	8	4	no	—
358	C₂³×C₇₃	—	8	4	no	—
359	C₂³×C₇₃	#135	1	2	yes	—
360	C₂³×C₇₃	C₂²×D₄	1	1	yes	characteristic
361	Q₈×C₇₃	—	2	2	no	—
362	Q₈×C₇₃	—	2	2	no	—
363	Q₈×C₇₃	—	4	1	no	—
364	Q₈×C₇₃	—	4	1	no	—
365	Q₈×C₇₃	—	4	1	no	—
366	Q₈×C₇₃	—	4	1	no	—
367	Q₈×C₇₃	—	4	1	no	—
368	Q₈×C₇₃	—	4	1	no	—
369	D₄×C₇₃	—	2	2	no	—
370	D₄×C₇₃	—	2	2	no	—
371	D₄×C₇₃	—	2	2	no	—
372	D₄×C₇₃	—	2	2	no	—
373	D₄×C₇₃	—	2	2	no	—
374	D₄×C₇₃	—	4	4	no	—
375	D₄×C₇₃	—	4	8	no	—
376	D₄×C₇₃	—	4	8	no	—
377	D₄×C₇₃	—	4	1	no	—
378	D₄×C₇₃	—	4	1	no	—
379	D₄×C₇₃	—	4	1	no	—
380	D₄×C₇₃	—	4	1	no	—
381	D₄×C₇₃	—	4	1	no	—
382	D₄×C₇₃	—	4	1	no	—
383	D₄×C₇₃	—	8	4	no	—
384	D₄×C₇₃	—	8	4	no	—
385	D₄×C₇₃	—	8	4	no	—
386	D₄×C₇₃	#127	1	4	yes	—
387	C₂×C₄×C₇₃	—	2	1	no	—
388	C₂×C₄×C₇₃	—	2	1	no	—
389	C₂×C₄×C₇₃	—	2	1	no	—
390	C₂×C₄×C₇₃	—	2	1	no	—
391	C₂×C₄×C₇₃	—	2	2	no	—
392	C₂×C₄×C₇₃	—	2	1	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	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	—	4	8	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	—	4	1	no	—
415	C₂×C₄×C₇₃	—	4	1	no	—
416	C₂×C₄×C₇₃	—	4	1	no	—
417	C₂×C₄×C₇₃	—	4	1	no	—
418	C₂×C₄×C₇₃	—	4	1	no	—
419	C₂×C₄×C₇₃	—	4	1	no	—
420	C₂×C₄×C₇₃	—	4	1	no	—
421	C₂×C₄×C₇₃	—	8	4	no	—
422	C₂×C₄×C₇₃	#120	1	2	yes	—
423	C₂×C₄×C₇₃	#120	1	2	yes	—
424	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
425	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
426	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
427	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
428	C₂×C₄×C₇₃	H(5,𝔽₂)	1	1	yes	characteristic
429	C₂×C₄×C₇₃	H(5,𝔽₂)	1	1	yes	characteristic
430	C₈×C₇₃	—	2	2	no	—
431	C₈×C₇₃	—	2	2	no	—
432	C₈×C₇₃	—	4	1	no	—
433	C₈×C₇₃	—	4	1	no	—
434	C₂²×C₇₃	—	2	4	no	—
435	C₂²×C₇₃	—	2	2	no	—
436	C₂²×C₇₃	—	2	2	no	—
437	C₂²×C₇₃	—	2	2	no	—
438	C₂²×C₇₃	—	4	1	no	—
439	C₂²×C₇₃	—	4	2	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	1	no	—
445	C₂²×C₇₃	—	4	2	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	1	no	—
451	C₂²×C₇₃	—	4	2	no	—
452	C₂²×C₇₃	—	4	1	no	—
453	C₂²×C₇₃	—	4	2	no	—
454	C₂²×C₇₃	—	4	1	no	—
455	C₂²×C₇₃	—	4	1	no	—
456	C₂²×C₇₃	—	4	1	no	—
457	C₂²×C₇₃	—	4	1	no	—
458	C₂²×C₇₃	—	8	16	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	—	8	1	no	—
470	C₂²×C₇₃	C₂×#120	1	1	yes	characteristic
471	C₂²×C₇₃	D₄²	1	1	yes	characteristic
472	C₂²×C₇₃	D₄²	1	1	yes	characteristic
473	C₂²×C₇₃	C₂×#135	1	1	yes	characteristic
474	C₂²×C₇₃	#575	1	1	yes	characteristic
475	C₂²×C₇₃	#576	1	1	yes	characteristic
476	C₂²×C₇₃	#577	1	1	yes	characteristic
477	C₄×C₇₃	—	2	2	no	—
478	C₄×C₇₃	—	2	2	no	—
479	C₄×C₇₃	—	4	1	no	—
480	C₄×C₇₃	—	4	1	no	—
481	C₄×C₇₃	—	4	2	no	—
482	C₄×C₇₃	—	4	2	no	—
483	C₄×C₇₃	—	4	2	no	—
484	C₄×C₇₃	—	4	2	no	—
485	C₄×C₇₃	—	8	1	no	—
486	C₄×C₇₃	C₂×#127	1	1	yes	characteristic
487	C₄×C₇₃	#535	1	1	yes	characteristic
488	C₄×C₇₃	D₄²	1	1	yes	characteristic
489	C₄×C₇₃	D₄²	1	1	yes	characteristic
490	#25762	C₇₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
491	C₂×C₇₃	—	4	2	no	—
492	C₂×C₇₃	—	4	4	no	—
493	C₂×C₇₃	—	8	1	no	—
494	C₂×C₇₃	—	8	2	no	—
495	C₂×C₇₃	—	16	1	no	—
496	C₂×C₇₃	#2433	1	1	yes	characteristic
497	C₂×C₇₃	#3002	1	1	yes	characteristic
498	C₂×C₇₃	#3012	1	1	yes	characteristic
499	C₂×C₇₃	#3273	1	1	yes	characteristic
500	C₂×C₇₃	#3275	1	1	yes	characteristic
501	C₂×C₇₃	#3280	1	1	yes	characteristic
502	C₂×C₇₃	#3282	1	1	yes	characteristic
503	C₂×#546	C₂×C₇₃	1	1	yes	characteristic, complemented
504	C₂×#495	C₂×C₇₃	1	1	yes	characteristic, complemented
505	C₂×#463	C₂×C₇₃	1	1	yes	characteristic, complemented
506	C₂×#452	C₂×C₇₃	1	1	yes	characteristic, complemented
507	C₂×#449	C₂×C₇₃	1	1	yes	characteristic, complemented
508	C₂×#450	C₂×C₇₃	1	1	yes	characteristic, complemented
509	C₂×#447	C₂×C₇₃	1	1	yes	characteristic, complemented
510	#2540	C₂×C₇₃	1	1	yes	characteristic, complemented
511	#2001	C₂×C₇₃	1	1	yes	characteristic, complemented
512	#2000	C₂×C₇₃	1	1	yes	characteristic, complemented
513	#2000	C₂×C₇₃	1	1	yes	characteristic, complemented
514	#1999	C₂×C₇₃	1	1	yes	characteristic, complemented
515	#1983	C₂×C₇₃	1	1	yes	characteristic, complemented
516	#1954	C₂×C₇₃	1	1	yes	characteristic, complemented
517	C₄×#102	C₂×C₇₃	1	1	yes	characteristic, complemented
518	C₇₃	#25762	1	1	yes	characteristic, direct product factor, Sylow
519	C₂²×#41	C₂²×C₇₃	1	1	yes	characteristic
520	C₂³×D₄	C₂²×C₇₃	1	1	yes	characteristic
521	C₂²×Q₁₆	C₂²×C₇₃	1	1	yes	characteristic, complemented
522	C₂²×SD₁₆	C₂²×C₇₃	1	1	yes	characteristic
523	C₂²×SD₁₆	C₂²×C₇₃	1	1	yes	characteristic
524	C₂²×SD₁₆	C₂²×C₇₃	1	1	yes	characteristic, complemented
525	C₂²×D₈	C₂²×C₇₃	1	1	yes	characteristic
526	C₂²×D₈	C₂²×C₇₃	1	1	yes	characteristic
527	#546	—	2	4	no	—
528	#546	—	2	4	no	—
529	C₂×#124	C₂²×C₇₃	1	1	yes	characteristic
530	C₂×#124	C₂²×C₇₃	1	1	yes	characteristic, complemented
531	C₂×#123	—	2	1	no	—
532	C₂×C₂²⋊Q₈	C₂²×C₇₃	1	1	yes	characteristic
533	C₂×C₂²⋊Q₈	C₂²×C₇₃	1	1	yes	characteristic
534	C₂×C₂²⋊Q₈	C₂²×C₇₃	1	1	yes	characteristic, complemented
535	C₂×#121	—	2	1	no	—
536	C₂×#121	C₂²×C₇₃	1	1	yes	characteristic
537	C₂×#121	C₂²×C₇₃	1	1	yes	characteristic
538	C₂×#121	C₂²×C₇₃	1	1	yes	characteristic, complemented
539	C₂×#120	—	2	1	no	—
540	C₂×C₄×D₄	C₂²×C₇₃	1	1	yes	characteristic
541	C₂×C₄×D₄	C₂²×C₇₃	1	1	yes	characteristic
542	C₂²×C₂²⋊C₄	—	2	1	no	—
543	#495	—	2	4	no	—
544	#463	—	2	4	no	—
545	#452	—	2	4	no	—
546	#450	—	2	4	no	—
547	#449	—	2	4	no	—
548	#447	—	2	4	no	—
549	C₂×C₄⋊C₈	C₂²×C₇₃	1	1	yes	characteristic, complemented
550	C₂×#103	C₂²×C₇₃	1	1	yes	characteristic, complemented
551	C₂×#103	C₂²×C₇₃	1	1	yes	characteristic, complemented
552	C₂×#103	C₂²×C₇₃	1	1	yes	characteristic, complemented
553	C₂×#102	C₂²×C₇₃	1	1	yes	characteristic
554	C₂×#102	C₂²×C₇₃	1	1	yes	characteristic
555	C₂×#102	C₂²×C₇₃	1	1	yes	characteristic
556	C₂×#102	C₂²×C₇₃	1	1	yes	characteristic
557	C₂×#102	C₂²×C₇₃	1	1	yes	characteristic, complemented
558	C₂×C₂²⋊C₈	C₂²×C₇₃	1	1	yes	characteristic
559	C₂×C₂²⋊C₈	C₂²×C₇₃	1	1	yes	characteristic
560	C₂×C₂²⋊C₈	C₂²×C₇₃	1	1	yes	characteristic, complemented
561	C₂×C₂²⋊C₈	C₂²×C₇₃	1	1	yes	characteristic, complemented
562	C₂×C₄×C₈	C₂²×C₇₃	1	1	yes	characteristic, complemented
563	#399	—	2	1	no	—
564	#392	—	2	1	no	—
565	#390	—	2	1	no	—
566	#390	—	2	1	no	—
567	C₄×C₄⋊C₄	C₂²×C₇₃	1	1	yes	characteristic, complemented
568	#340	C₂²×C₇₃	1	1	yes	characteristic, complemented
569	#340	C₂²×C₇₃	1	1	yes	characteristic, complemented
570	C₂⁵	—	2	1	no	—
571	C₂×#41	—	2	2	no	—
572	C₂×#41	—	2	2	no	—
573	C₂×#41	—	2	2	no	—
574	C₂×#41	—	2	2	no	—
575	C₂×#41	—	4	1	no	—
576	C₂×#41	—	4	1	no	—
577	C₂²×Q₈	C₂³×C₇₃	1	1	yes	characteristic
578	C₂²×Q₈	C₂³×C₇₃	1	1	yes	characteristic
579	C₂²×D₄	—	2	1	no	—
580	C₂²×D₄	—	2	1	no	—
581	C₂²×D₄	—	2	2	no	—
582	C₂²×D₄	—	2	2	no	—
583	C₂²×D₄	—	2	2	no	—
584	C₂²×D₄	—	2	2	no	—
585	C₂²×D₄	—	2	1	no	—
586	C₂²×D₄	—	2	1	no	—
587	C₂²×D₄	—	2	1	no	—
588	C₂²×D₄	—	4	1	no	—
589	C₂²×D₄	—	4	1	no	—
590	C₂²×D₄	D₄×C₇₃	1	1	yes	characteristic
591	C₂²×D₄	C₂³×C₇₃	1	1	yes	characteristic
592	C₂²×D₄	C₂³×C₇₃	1	1	yes	characteristic
593	C₂²×D₄	C₂³×C₇₃	1	1	yes	characteristic
594	C₂³×C₄	—	2	1	no	—
595	C₂³×C₄	—	2	1	no	—
596	C₂³×C₄	C₂³×C₇₃	1	1	yes	characteristic
597	C₂³×C₄	C₂³×C₇₃	1	1	yes	characteristic
598	C₂×Q₁₆	—	2	2	no	—
599	C₂×Q₁₆	—	2	2	no	—
600	C₂×Q₁₆	—	4	1	no	—
601	C₂×SD₁₆	—	2	2	no	—
602	C₂×SD₁₆	—	2	2	no	—
603	C₂×SD₁₆	—	2	2	no	—
604	C₂×SD₁₆	—	2	2	no	—
605	C₂×SD₁₆	—	2	2	no	—
606	C₂×SD₁₆	—	2	2	no	—
607	C₂×SD₁₆	—	2	2	no	—
608	C₂×SD₁₆	—	4	1	no	—
609	C₂×SD₁₆	—	4	1	no	—
610	C₂×D₈	—	2	2	no	—
611	C₂×D₈	—	2	2	no	—
612	C₂×D₈	—	2	2	no	—
613	C₂×D₈	—	2	2	no	—
614	C₂×D₈	—	2	2	no	—
615	C₂×D₈	—	4	1	no	—
616	C₂²×C₈	C₂³×C₇₃	1	1	yes	characteristic
617	C₂²×C₈	C₂³×C₇₃	1	1	yes	characteristic
618	C₂²×C₈	C₂³×C₇₃	1	1	yes	characteristic
619	C₂²×C₈	C₂³×C₇₃	1	1	yes	characteristic
620	#124	—	2	2	no	—
621	#124	—	2	2	no	—
622	#124	—	2	2	no	—
623	#124	D₄×C₇₃	1	4	yes	complemented
624	#123	—	2	8	no	—
625	C₂²⋊Q₈	—	2	2	no	—
626	C₂²⋊Q₈	—	2	2	no	—
627	C₂²⋊Q₈	—	2	2	no	—
628	C₂²⋊Q₈	—	2	2	no	—
629	C₂²⋊Q₈	—	4	1	no	—
630	C₂²⋊Q₈	—	4	1	no	—
631	#121	—	2	8	no	—
632	#121	—	2	2	no	—
633	#121	—	2	2	no	—
634	#121	—	2	2	no	—
635	#121	—	2	2	no	—
636	#121	—	4	1	no	—
637	#121	—	4	1	no	—
638	#120	—	2	8	no	—
639	C₄×D₄	—	2	2	no	—
640	C₄×D₄	—	2	2	no	—
641	C₄×D₄	—	2	2	no	—
642	C₄×D₄	D₄×C₇₃	1	4	yes	complemented
643	C₂×C₄⋊C₄	—	2	1	no	—
644	C₂×C₄⋊C₄	—	2	1	no	—
645	C₂×C₄⋊C₄	—	2	1	no	—
646	C₂×C₄⋊C₄	D₄×C₇₃	1	1	yes	characteristic
647	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
648	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
649	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
650	C₂×C₂²⋊C₄	—	2	8	no	—
651	C₂×C₂²⋊C₄	—	2	1	no	—
652	C₂×C₂²⋊C₄	—	2	1	no	—
653	C₂×C₂²⋊C₄	—	2	1	no	—
654	C₂×C₂²⋊C₄	—	2	1	no	—
655	C₂×C₂²⋊C₄	—	2	1	no	—
656	C₂×C₂²⋊C₄	—	2	1	no	—
657	C₂×C₂²⋊C₄	—	2	1	no	—
658	C₂×C₂²⋊C₄	—	2	1	no	—
659	C₂×C₂²⋊C₄	—	2	1	no	—
660	C₂×C₂²⋊C₄	—	2	1	no	—
661	C₂×C₂²⋊C₄	—	2	1	no	—
662	C₂×C₂²⋊C₄	D₄×C₇₃	1	1	yes	characteristic
663	C₂×C₂²⋊C₄	D₄×C₇₃	1	1	yes	characteristic
664	C₂×C₄²	—	2	1	no	—
665	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
666	C₄⋊C₈	—	2	2	no	—
667	#103	—	2	2	no	—
668	#103	—	2	2	no	—
669	#103	—	2	2	no	—
670	#102	—	2	2	no	—
671	#102	—	2	2	no	—
672	#102	—	2	2	no	—
673	#102	D₄×C₇₃	1	4	yes	complemented
674	#102	D₄×C₇₃	1	4	yes	complemented
675	C₂²⋊C₈	—	2	2	no	—
676	C₂²⋊C₈	—	2	2	no	—
677	C₂²⋊C₈	—	2	2	no	—
678	C₂²⋊C₈	—	2	2	no	—
679	C₄×C₈	—	2	2	no	—
680	#95	—	2	1	no	—
681	C₂⁴	—	2	1	no	—
682	C₂⁴	—	2	4	no	—
683	C₂⁴	—	2	1	no	—
684	C₂⁴	—	2	1	no	—
685	C₂⁴	—	4	2	no	—
686	C₂⁴	—	4	2	no	—
687	C₂⁴	—	4	2	no	—
688	C₂⁴	—	4	2	no	—
689	C₂⁴	—	8	1	no	—
690	C₂⁴	—	8	1	no	—
691	C₂⁴	C₂×D₄×C₇₃	1	1	yes	characteristic
692	C₂⁴	C₂×D₄×C₇₃	1	1	yes	characteristic
693	#41	—	4	4	no	—
694	#41	—	4	4	no	—
695	#41	—	4	4	no	—
696	#41	—	4	4	no	—
697	C₂×Q₈	—	2	1	no	—
698	C₂×Q₈	—	2	1	no	—
699	C₂×Q₈	—	2	1	no	—
700	C₂×Q₈	—	2	1	no	—
701	C₂×Q₈	—	2	1	no	—
702	C₂×Q₈	—	2	1	no	—
703	C₂×Q₈	—	2	1	no	—
704	C₂×Q₈	—	2	1	no	—
705	C₂×Q₈	—	2	1	no	—
706	C₂×Q₈	—	2	1	no	—
707	C₂×Q₈	—	2	1	no	—
708	C₂×Q₈	C₂×D₄×C₇₃	1	2	yes	—
709	C₂×D₄	—	2	4	no	—
710	C₂×D₄	—	2	4	no	—
711	C₂×D₄	—	2	2	no	—
712	C₂×D₄	—	2	4	no	—
713	C₂×D₄	—	2	2	no	—
714	C₂×D₄	—	2	1	no	—
715	C₂×D₄	—	2	1	no	—
716	C₂×D₄	—	2	1	no	—
717	C₂×D₄	—	2	1	no	—
718	C₂×D₄	—	2	1	no	—
719	C₂×D₄	—	2	1	no	—
720	C₂×D₄	—	2	1	no	—
721	C₂×D₄	—	2	1	no	—
722	C₂×D₄	—	2	1	no	—
723	C₂×D₄	—	2	1	no	—
724	C₂×D₄	—	2	1	no	—
725	C₂×D₄	—	2	1	no	—
726	C₂×D₄	—	2	1	no	—
727	C₂×D₄	—	2	1	no	—
728	C₂×D₄	—	4	1	no	—
729	C₂×D₄	—	4	2	no	—
730	C₂×D₄	—	4	2	no	—
731	C₂×D₄	—	4	2	no	—
732	C₂×D₄	—	4	2	no	—
733	C₂×D₄	—	4	4	no	—
734	C₂×D₄	—	4	4	no	—
735	C₂×D₄	—	4	4	no	—
736	C₂×D₄	—	4	2	no	—
737	C₂×D₄	—	4	2	no	—
738	C₂×D₄	—	4	4	no	—
739	C₂×D₄	—	4	2	no	—
740	C₂×D₄	—	4	2	no	—
741	C₂×D₄	—	8	1	no	—
742	C₂×D₄	—	8	1	no	—
743	C₂×D₄	—	8	1	no	—
744	C₂×D₄	—	8	1	no	—
745	C₂×D₄	C₂×D₄×C₇₃	1	2	yes	—
746	C₂×D₄	C₂×D₄×C₇₃	1	2	yes	—
747	C₂×D₄	C₂×D₄×C₇₃	1	2	yes	—
748	C₂×D₄	C₂×D₄×C₇₃	1	2	yes	—
749	C₂²×C₄	—	2	4	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	—	2	1	no	—
763	C₂²×C₄	—	2	1	no	—
764	C₂²×C₄	—	2	1	no	—
765	C₂²×C₄	—	2	1	no	—
766	C₂²×C₄	—	2	4	no	—
767	C₂²×C₄	—	2	1	no	—
768	C₂²×C₄	—	4	2	no	—
769	C₂²×C₄	—	4	2	no	—
770	C₂²×C₄	—	8	1	no	—
771	C₂²×C₄	—	8	1	no	—
772	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
773	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
774	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
775	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
776	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
777	Q₁₆	—	4	4	no	—
778	SD₁₆	—	4	4	no	—
779	SD₁₆	—	4	4	no	—
780	SD₁₆	—	4	4	no	—
781	D₈	—	4	4	no	—
782	D₈	—	4	4	no	—
783	C₂×C₈	—	2	1	no	—
784	C₂×C₈	—	2	1	no	—
785	C₂×C₈	—	2	1	no	—
786	C₂×C₈	—	2	1	no	—
787	C₂×C₈	—	2	1	no	—
788	C₂×C₈	—	2	1	no	—
789	C₂×C₈	—	2	1	no	—
790	C₂×C₈	—	2	1	no	—
791	C₂×C₈	—	2	1	no	—
792	C₂×C₈	—	2	1	no	—
793	C₂×C₈	C₂×D₄×C₇₃	1	2	yes	—
794	C₂×C₈	C₂×D₄×C₇₃	1	2	yes	—
795	C₄⋊C₄	—	2	4	no	—
796	C₄⋊C₄	—	2	2	no	—
797	C₄⋊C₄	—	2	1	no	—
798	C₄⋊C₄	—	2	1	no	—
799	C₄⋊C₄	—	2	1	no	—
800	C₄⋊C₄	—	4	2	no	—
801	C₄⋊C₄	—	4	2	no	—
802	C₄⋊C₄	C₂×D₄×C₇₃	1	2	yes	—
803	C₄⋊C₄	C₂×D₄×C₇₃	1	2	yes	—
804	C₄⋊C₄	C₂×D₄×C₇₃	1	2	yes	—
805	C₂²⋊C₄	—	2	4	no	—
806	C₂²⋊C₄	—	2	4	no	—
807	C₂²⋊C₄	—	2	2	no	—
808	C₂²⋊C₄	—	2	4	no	—
809	C₂²⋊C₄	—	2	4	no	—
810	C₂²⋊C₄	—	2	4	no	—
811	C₂²⋊C₄	—	2	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	—	4	2	no	—
817	C₂²⋊C₄	—	4	2	no	—
818	C₄²	—	8	1	no	—
819	C₄²	C₂×D₄×C₇₃	1	2	yes	—
820	C₄²	C₂×D₄×C₇₃	1	2	yes	—
821	C₂³	—	2	1	no	—
822	C₂³	—	2	2	no	—
823	C₂³	—	2	1	no	—
824	C₂³	—	2	1	no	—
825	C₂³	—	2	2	no	—
826	C₂³	—	2	2	no	—
827	C₂³	—	2	1	no	—
828	C₂³	—	2	1	no	—
829	C₂³	—	2	1	no	—
830	C₂³	—	2	2	no	—
831	C₂³	—	2	1	no	—
832	C₂³	—	2	1	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	—	4	8	no	—
839	C₂³	—	4	8	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	—	4	1	no	—
850	C₂³	—	4	1	no	—
851	C₂³	—	4	1	no	—
852	C₂³	—	4	1	no	—
853	C₂³	—	4	1	no	—
854	C₂³	—	4	1	no	—
855	C₂³	—	4	1	no	—
856	C₂³	—	4	1	no	—
857	C₂³	—	8	4	no	—
858	C₂³	—	8	4	no	—
859	C₂³	—	8	4	no	—
860	C₂³	—	8	4	no	—
861	C₂³	—	8	4	no	—
862	C₂³	#135×C₇₃	1	2	yes	—
863	C₂³	C₂²×D₄×C₇₃	1	1	yes	characteristic
864	Q₈	—	2	2	no	—
865	Q₈	—	2	2	no	—
866	Q₈	—	4	1	no	—
867	Q₈	—	4	1	no	—
868	Q₈	—	4	1	no	—
869	Q₈	—	4	1	no	—
870	Q₈	—	4	1	no	—
871	Q₈	—	4	1	no	—
872	D₄	—	2	2	no	—
873	D₄	—	2	2	no	—
874	D₄	—	2	2	no	—
875	D₄	—	2	2	no	—
876	D₄	—	2	2	no	—
877	D₄	—	4	4	no	—
878	D₄	—	4	8	no	—
879	D₄	—	4	8	no	—
880	D₄	—	4	1	no	—
881	D₄	—	4	1	no	—
882	D₄	—	4	1	no	—
883	D₄	—	4	1	no	—
884	D₄	—	4	1	no	—
885	D₄	—	4	1	no	—
886	D₄	—	8	4	no	—
887	D₄	—	8	4	no	—
888	D₄	—	8	4	no	—
889	D₄	#127×C₇₃	1	4	yes	—
890	C₂×C₄	—	2	1	no	—
891	C₂×C₄	—	2	1	no	—
892	C₂×C₄	—	2	1	no	—
893	C₂×C₄	—	2	1	no	—
894	C₂×C₄	—	2	2	no	—
895	C₂×C₄	—	2	1	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	1	no	—
901	C₂×C₄	—	2	1	no	—
902	C₂×C₄	—	2	1	no	—
903	C₂×C₄	—	2	1	no	—
904	C₂×C₄	—	4	8	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	—	4	1	no	—
917	C₂×C₄	—	4	1	no	—
918	C₂×C₄	—	4	1	no	—
919	C₂×C₄	—	4	1	no	—
920	C₂×C₄	—	4	1	no	—
921	C₂×C₄	—	4	1	no	—
922	C₂×C₄	—	4	1	no	—
923	C₂×C₄	—	4	1	no	—
924	C₂×C₄	—	8	4	no	—
925	C₂×C₄	#120×C₇₃	1	2	yes	—
926	C₂×C₄	#120×C₇₃	1	2	yes	—
927	C₂×C₄	C₂²×D₄×C₇₃	1	1	yes	characteristic
928	C₂×C₄	C₂²×D₄×C₇₃	1	1	yes	characteristic
929	C₂×C₄	C₂²×D₄×C₇₃	1	1	yes	characteristic
930	C₂×C₄	C₂²×D₄×C₇₃	1	1	yes	characteristic
931	C₂×C₄	H(5,𝔽₂)×C₇₃	1	1	yes	characteristic
932	C₂×C₄	H(5,𝔽₂)×C₇₃	1	1	yes	characteristic
933	C₈	—	2	2	no	—
934	C₈	—	2	2	no	—
935	C₈	—	4	1	no	—
936	C₈	—	4	1	no	—
937	C₂²	—	2	2	no	—
938	C₂²	—	2	2	no	—
939	C₂²	—	2	2	no	—
940	C₂²	—	2	4	no	—
941	C₂²	—	4	2	no	—
942	C₂²	—	4	2	no	—
943	C₂²	—	4	1	no	—
944	C₂²	—	4	1	no	—
945	C₂²	—	4	2	no	—
946	C₂²	—	4	1	no	—
947	C₂²	—	4	2	no	—
948	C₂²	—	4	2	no	—
949	C₂²	—	4	2	no	—
950	C₂²	—	4	1	no	—
951	C₂²	—	4	1	no	—
952	C₂²	—	4	2	no	—
953	C₂²	—	4	1	no	—
954	C₂²	—	4	2	no	—
955	C₂²	—	4	1	no	—
956	C₂²	—	4	1	no	—
957	C₂²	—	4	1	no	—
958	C₂²	—	4	1	no	—
959	C₂²	—	4	1	no	—
960	C₂²	—	4	2	no	—
961	C₂²	—	8	16	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	—	8	1	no	—
972	C₂²	—	8	1	no	—
973	C₂²	C₂×#120×C₇₃	1	1	yes	characteristic
974	C₂²	D₄²×C₇₃	1	1	yes	characteristic
975	C₂²	D₄²×C₇₃	1	1	yes	characteristic
976	C₂²	C₂×#135×C₇₃	1	1	yes	characteristic
977	C₂²	#575×C₇₃	1	1	yes	characteristic
978	C₂²	#576×C₇₃	1	1	yes	characteristic
979	C₂²	#577×C₇₃	1	1	yes	characteristic
980	C₄	—	2	2	no	—
981	C₄	—	2	2	no	—
982	C₄	—	4	2	no	—
983	C₄	—	4	2	no	—
984	C₄	—	4	2	no	—
985	C₄	—	4	1	no	—
986	C₄	—	4	1	no	—
987	C₄	—	4	2	no	—
988	C₄	—	8	1	no	—
989	C₄	C₂×#127×C₇₃	1	1	yes	characteristic
990	C₄	#535×C₇₃	1	1	yes	characteristic
991	C₄	D₄²×C₇₃	1	1	yes	characteristic
992	C₄	D₄²×C₇₃	1	1	yes	characteristic
993	C₂	—	4	2	no	—
994	C₂	—	4	4	no	—
995	C₂	—	8	1	no	—
996	C₂	—	8	2	no	—
997	C₂	—	16	1	no	—
998	C₂	C₇₃×#2433	1	1	yes	characteristic
999	C₂	C₇₃×#3002	1	1	yes	characteristic
1000	C₂	C₇₃×#3012	1	1	yes	characteristic
1001	C₂	C₇₃×#3273	1	1	yes	characteristic
1002	C₂	C₇₃×#3275	1	1	yes	characteristic
1003	C₂	C₇₃×#3280	1	1	yes	characteristic
1004	C₂	C₇₃×#3282	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 ◁ C₂×C₄×D₄×C₇₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×#546×C₇₃	C₂	semidirect
2. C₂×#495×C₇₃	C₂	semidirect
3. C₂×#463×C₇₃	C₂	semidirect
4. C₂×#452×C₇₃	C₂	semidirect
5. C₂×#449×C₇₃	C₂	semidirect
6. C₂×#450×C₇₃	C₂	semidirect
7. C₂×#447×C₇₃	C₂	semidirect
8. C₇₃×#2540	C₂	semidirect
9. C₇₃×#2001	C₂	semidirect
10. C₇₃×#2000	C₂	semidirect
11. C₇₃×#2000	C₂	semidirect
12. C₇₃×#1999	C₂	semidirect
13. C₇₃×#1983	C₂	semidirect
14. C₇₃×#1954	C₂	semidirect
15. C₄×#102×C₇₃	C₂	semidirect
18. C₂²×Q₁₆×C₇₃	C₂²	semidirect
21. C₂²×SD₁₆×C₇₃	C₂²	semidirect
27. C₂×#124×C₇₃	C₂²	semidirect
31. C₂×C₂²⋊Q₈×C₇₃	C₂²	semidirect
35. C₂×#121×C₇₃	C₂²	semidirect
46. C₂×C₄⋊C₈×C₇₃	C₂²	semidirect
47. C₂×#103×C₇₃	C₂²	semidirect
48. C₂×#103×C₇₃	C₂²	semidirect
49. C₂×#103×C₇₃	C₂²	semidirect
54. C₂×#102×C₇₃	C₂²	semidirect
57. C₂×C₂²⋊C₈×C₇₃	C₂²	semidirect
58. C₂×C₂²⋊C₈×C₇₃	C₂²	semidirect
59. C₂×C₄×C₈×C₇₃	C₂²	semidirect
64. C₄×C₄⋊C₄×C₇₃	C₂²	semidirect
65. #340×C₇₃	C₂²	semidirect
66. #340×C₇₃	C₂²	semidirect
120. #124×C₇₃	D₄	semidirect
139. C₄×D₄×C₇₃	D₄	semidirect
170. #102×C₇₃	D₄	semidirect
171. #102×C₇₃	D₄	semidirect
490. #25762	C₇₃	direct (N × H)
503. C₂×#546	C₂×C₇₃	semidirect
504. C₂×#495	C₂×C₇₃	semidirect
505. C₂×#463	C₂×C₇₃	semidirect
506. C₂×#452	C₂×C₇₃	semidirect
507. C₂×#449	C₂×C₇₃	semidirect
508. C₂×#450	C₂×C₇₃	semidirect
509. C₂×#447	C₂×C₇₃	semidirect
510. #2540	C₂×C₇₃	semidirect
511. #2001	C₂×C₇₃	semidirect
512. #2000	C₂×C₇₃	semidirect
513. #2000	C₂×C₇₃	semidirect
514. #1999	C₂×C₇₃	semidirect
515. #1983	C₂×C₇₃	semidirect
516. #1954	C₂×C₇₃	semidirect
517. C₄×#102	C₂×C₇₃	semidirect
518. C₇₃	#25762	direct (N × H)
521. C₂²×Q₁₆	C₂²×C₇₃	semidirect
524. C₂²×SD₁₆	C₂²×C₇₃	semidirect
530. C₂×#124	C₂²×C₇₃	semidirect
534. C₂×C₂²⋊Q₈	C₂²×C₇₃	semidirect
538. C₂×#121	C₂²×C₇₃	semidirect
549. C₂×C₄⋊C₈	C₂²×C₇₃	semidirect
550. C₂×#103	C₂²×C₇₃	semidirect
551. C₂×#103	C₂²×C₇₃	semidirect
552. C₂×#103	C₂²×C₇₃	semidirect
557. C₂×#102	C₂²×C₇₃	semidirect
560. C₂×C₂²⋊C₈	C₂²×C₇₃	semidirect
561. C₂×C₂²⋊C₈	C₂²×C₇₃	semidirect
562. C₂×C₄×C₈	C₂²×C₇₃	semidirect
567. C₄×C₄⋊C₄	C₂²×C₇₃	semidirect
568. #340	C₂²×C₇₃	semidirect
569. #340	C₂²×C₇₃	semidirect
623. #124	D₄×C₇₃	semidirect
642. C₄×D₄	D₄×C₇₃	semidirect
673. #102	D₄×C₇₃	semidirect
674. #102	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×#546×C₇₃	2
C₂×#495×C₇₃	2
C₂×#463×C₇₃	2
C₂×#452×C₇₃	2
C₂×#449×C₇₃	2
C₂×#450×C₇₃	2
C₂×#447×C₇₃	2
C₇₃×#2540	2
C₇₃×#2001	2
C₇₃×#2000	2
C₇₃×#1999	2
C₇₃×#1983	2
C₇₃×#1954	2
C₄×#102×C₇₃	2
#25762	73

Subgroups — C73×#25762 #32935166

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₃×#25762 #32935166