Subgroups — C₇₃×#24428 #32933832

Order 18688.

1632 conjugacy classes of subgroups.

The subgroup lattice has 960 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×#466×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#449×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#447×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#416×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
6	C₇₃×#2414	C₂	1	1	yes	maximal, characteristic, complemented
7	C₇₃×#2042	C₂	1	1	yes	maximal, characteristic, complemented
8	C₇₃×#2036	C₂	1	1	yes	maximal, characteristic, complemented
9	C₇₃×#2012	C₂	1	1	yes	maximal, characteristic, complemented
10	C₇₃×#2000	C₂	1	1	yes	maximal, characteristic, complemented
11	C₇₃×#1879	C₂	1	1	yes	maximal, characteristic, complemented
12	C₇₃×#1875	C₂	1	1	yes	maximal, characteristic, complemented
13	C₇₃×#1869	C₂	1	1	yes	maximal, characteristic, complemented
14	C₇₃×#1862	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×SD₁₆×C₇₃	C₂²	1	1	yes	characteristic, complemented
19	C₂²×D₈×C₇₃	C₂²	1	1	yes	characteristic
20	C₂²×D₈×C₇₃	C₂²	1	1	yes	characteristic
21	C₂³×C₈×C₇₃	C₂²	1	1	yes	characteristic, complemented
22	#546×C₇₃	—	2	4	no	—
23	#546×C₇₃	—	2	4	no	—
24	C₂×#124×C₇₃	C₂²	1	1	yes	characteristic
25	C₂×#123×C₇₃	—	2	1	no	—
26	C₂×C₂²⋊Q₈×C₇₃	C₂²	1	1	yes	characteristic
27	C₂×#121×C₇₃	—	2	1	no	—
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, complemented
31	C₂×#120×C₇₃	—	2	1	no	—
32	C₂×C₄×D₄×C₇₃	C₂²	1	1	yes	characteristic
33	C₂×C₄×D₄×C₇₃	C₂²	1	1	yes	characteristic
34	C₂×#117×C₇₃	C₂²	1	1	yes	characteristic, complemented
35	C₂²×C₂²⋊C₄×C₇₃	—	2	1	no	—
36	#466×C₇₃	—	2	4	no	—
37	#449×C₇₃	—	2	4	no	—
38	#447×C₇₃	—	2	4	no	—
39	C₂×#107×C₇₃	C₂²	1	1	yes	characteristic, complemented
40	#416×C₇₃	—	2	4	no	—
41	C₂×#103×C₇₃	C₂²	1	1	yes	characteristic, complemented
42	C₂×#103×C₇₃	C₂²	1	1	yes	characteristic, complemented
43	C₂×#103×C₇₃	C₂²	1	1	yes	characteristic, complemented
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
48	C₂×#102×C₇₃	C₂²	1	1	yes	characteristic
49	C₂×#102×C₇₃	C₂²	1	1	yes	characteristic
50	C₂×#102×C₇₃	C₂²	1	1	yes	characteristic, complemented
51	C₂×C₂²⋊C₈×C₇₃	C₂²	1	1	yes	characteristic
52	C₂×C₂²⋊C₈×C₇₃	C₂²	1	1	yes	characteristic
53	C₂×C₂²⋊C₈×C₇₃	C₂²	1	1	yes	characteristic, complemented
54	#394×C₇₃	—	2	1	no	—
55	#392×C₇₃	—	2	1	no	—
56	#390×C₇₃	—	2	1	no	—
57	#390×C₇₃	C₂²	1	1	yes	characteristic, complemented
58	#389×C₇₃	C₂²	1	1	yes	characteristic, complemented
59	#388×C₇₃	—	2	1	no	—
60	#380×C₇₃	C₂²	1	1	yes	characteristic
61	#340×C₇₃	C₂²	1	1	yes	characteristic, complemented
62	#340×C₇₃	C₂²	1	1	yes	characteristic, complemented
63	#336×C₇₃	C₂²	1	1	yes	characteristic, complemented
64	#336×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	—	4	1	no	—
70	C₂×#41×C₇₃	—	4	1	no	—
71	C₂×#41×C₇₃	D₄	1	4	yes	complemented
72	C₂²×Q₈×C₇₃	C₂³	1	1	yes	characteristic
73	C₂²×D₄×C₇₃	—	2	1	no	—
74	C₂²×D₄×C₇₃	—	2	1	no	—
75	C₂²×D₄×C₇₃	—	2	2	no	—
76	C₂²×D₄×C₇₃	—	2	2	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	—	4	1	no	—
83	C₂²×D₄×C₇₃	—	4	1	no	—
84	C₂²×D₄×C₇₃	D₄	1	1	yes	characteristic
85	C₂²×D₄×C₇₃	C₂³	1	1	yes	characteristic
86	C₂²×D₄×C₇₃	C₂³	1	1	yes	characteristic
87	C₂²×D₄×C₇₃	C₂³	1	1	yes	characteristic
88	C₂³×C₄×C₇₃	—	2	1	no	—
89	C₂³×C₄×C₇₃	—	2	1	no	—
90	C₂³×C₄×C₇₃	C₂³	1	1	yes	characteristic
91	C₂³×C₄×C₇₃	C₂³	1	1	yes	characteristic
92	C₂×SD₁₆×C₇₃	—	2	2	no	—
93	C₂×SD₁₆×C₇₃	—	4	1	no	—
94	C₂×SD₁₆×C₇₃	—	4	1	no	—
95	C₂×D₈×C₇₃	—	2	2	no	—
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	C₂²×C₈×C₇₃	—	2	2	no	—
102	C₂²×C₈×C₇₃	—	2	2	no	—
103	C₂²×C₈×C₇₃	—	4	1	no	—
104	C₂²×C₈×C₇₃	C₂³	1	1	yes	characteristic
105	C₂²×C₈×C₇₃	C₂³	1	1	yes	characteristic
106	C₂²×C₈×C₇₃	C₂³	1	1	yes	characteristic
107	C₂²×C₈×C₇₃	C₂³	1	1	yes	characteristic
108	#124×C₇₃	—	2	2	no	—
109	#124×C₇₃	—	2	2	no	—
110	#123×C₇₃	—	2	8	no	—
111	C₂²⋊Q₈×C₇₃	—	2	2	no	—
112	C₂²⋊Q₈×C₇₃	—	2	2	no	—
113	#121×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	—	4	1	no	—
119	#121×C₇₃	D₄	1	4	yes	complemented
120	#120×C₇₃	—	2	8	no	—
121	C₄×D₄×C₇₃	—	2	2	no	—
122	C₄×D₄×C₇₃	—	2	2	no	—
123	C₄×D₄×C₇₃	—	2	2	no	—
124	C₄×D₄×C₇₃	—	2	2	no	—
125	#117×C₇₃	—	2	2	no	—
126	#117×C₇₃	—	4	1	no	—
127	C₂×C₄⋊C₄×C₇₃	—	2	1	no	—
128	C₂×C₄⋊C₄×C₇₃	—	2	1	no	—
129	C₂×C₄⋊C₄×C₇₃	D₄	1	1	yes	characteristic
130	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
131	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
132	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
133	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
134	C₂×C₂²⋊C₄×C₇₃	—	2	8	no	—
135	C₂×C₂²⋊C₄×C₇₃	—	2	1	no	—
136	C₂×C₂²⋊C₄×C₇₃	—	2	1	no	—
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	D₄	1	1	yes	characteristic
147	C₂×C₂²⋊C₄×C₇₃	D₄	1	1	yes	characteristic
148	C₂×C₄²×C₇₃	—	2	1	no	—
149	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
150	#107×C₇₃	—	2	2	no	—
151	#103×C₇₃	—	2	2	no	—
152	#103×C₇₃	—	2	2	no	—
153	#103×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	—	2	2	no	—
158	#102×C₇₃	—	2	2	no	—
159	#102×C₇₃	—	4	1	no	—
160	#102×C₇₃	D₄	1	4	yes	complemented
161	C₂²⋊C₈×C₇₃	—	2	2	no	—
162	C₂²⋊C₈×C₇₃	—	2	2	no	—
163	C₂²⋊C₈×C₇₃	—	4	1	no	—
164	#95×C₇₃	—	2	1	no	—
165	#95×C₇₃	—	2	1	no	—
166	C₂⁴×C₇₃	—	2	1	no	—
167	C₂⁴×C₇₃	—	2	4	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	—	4	2	no	—
173	C₂⁴×C₇₃	—	4	2	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	#41×C₇₃	—	2	8	no	—
179	#41×C₇₃	—	4	4	no	—
180	#41×C₇₃	—	4	4	no	—
181	#41×C₇₃	—	4	4	no	—
182	C₂×Q₈×C₇₃	—	2	1	no	—
183	C₂×Q₈×C₇₃	—	2	1	no	—
184	C₂×Q₈×C₇₃	—	2	1	no	—
185	C₂×Q₈×C₇₃	—	2	1	no	—
186	C₂×Q₈×C₇₃	—	2	1	no	—
187	C₂×Q₈×C₇₃	C₂×D₄	1	2	yes	—
188	C₂×D₄×C₇₃	—	2	4	no	—
189	C₂×D₄×C₇₃	—	2	2	no	—
190	C₂×D₄×C₇₃	—	2	4	no	—
191	C₂×D₄×C₇₃	—	2	2	no	—
192	C₂×D₄×C₇₃	—	2	4	no	—
193	C₂×D₄×C₇₃	—	2	1	no	—
194	C₂×D₄×C₇₃	—	2	1	no	—
195	C₂×D₄×C₇₃	—	2	1	no	—
196	C₂×D₄×C₇₃	—	2	1	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	—	4	1	no	—
208	C₂×D₄×C₇₃	—	4	2	no	—
209	C₂×D₄×C₇₃	—	4	2	no	—
210	C₂×D₄×C₇₃	—	4	2	no	—
211	C₂×D₄×C₇₃	—	4	4	no	—
212	C₂×D₄×C₇₃	—	4	4	no	—
213	C₂×D₄×C₇₃	—	4	4	no	—
214	C₂×D₄×C₇₃	—	4	2	no	—
215	C₂×D₄×C₇₃	—	4	2	no	—
216	C₂×D₄×C₇₃	—	4	4	no	—
217	C₂×D₄×C₇₃	—	4	2	no	—
218	C₂×D₄×C₇₃	—	4	2	no	—
219	C₂×D₄×C₇₃	—	8	1	no	—
220	C₂×D₄×C₇₃	—	8	1	no	—
221	C₂×D₄×C₇₃	—	8	1	no	—
222	C₂×D₄×C₇₃	—	8	1	no	—
223	C₂×D₄×C₇₃	—	8	1	no	—
224	C₂×D₄×C₇₃	C₂×D₄	1	2	yes	—
225	C₂×D₄×C₇₃	C₂×D₄	1	2	yes	—
226	C₂×D₄×C₇₃	C₂×D₄	1	2	yes	—
227	C₂×D₄×C₇₃	#41	1	2	yes	—
228	C₂²×C₄×C₇₃	—	2	1	no	—
229	C₂²×C₄×C₇₃	—	2	1	no	—
230	C₂²×C₄×C₇₃	—	2	1	no	—
231	C₂²×C₄×C₇₃	—	2	1	no	—
232	C₂²×C₄×C₇₃	—	2	1	no	—
233	C₂²×C₄×C₇₃	—	2	1	no	—
234	C₂²×C₄×C₇₃	—	2	1	no	—
235	C₂²×C₄×C₇₃	—	2	4	no	—
236	C₂²×C₄×C₇₃	—	2	4	no	—
237	C₂²×C₄×C₇₃	—	2	1	no	—
238	C₂²×C₄×C₇₃	—	2	1	no	—
239	C₂²×C₄×C₇₃	—	2	1	no	—
240	C₂²×C₄×C₇₃	—	2	1	no	—
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	—	4	2	no	—
246	C₂²×C₄×C₇₃	—	4	2	no	—
247	C₂²×C₄×C₇₃	—	8	1	no	—
248	C₂²×C₄×C₇₃	—	8	1	no	—
249	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
250	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
251	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
252	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
253	C₂²×C₄×C₇₃	C₂×D₄	1	2	yes	—
254	C₂²×C₄×C₇₃	C₂×D₄	1	2	yes	—
255	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
256	SD₁₆×C₇₃	—	4	4	no	—
257	D₈×C₇₃	—	4	4	no	—
258	D₈×C₇₃	—	4	4	no	—
259	C₂×C₈×C₇₃	—	2	1	no	—
260	C₂×C₈×C₇₃	—	2	1	no	—
261	C₂×C₈×C₇₃	—	2	1	no	—
262	C₂×C₈×C₇₃	—	2	1	no	—
263	C₂×C₈×C₇₃	—	2	1	no	—
264	C₂×C₈×C₇₃	—	2	1	no	—
265	C₂×C₈×C₇₃	—	2	1	no	—
266	C₂×C₈×C₇₃	—	2	1	no	—
267	C₂×C₈×C₇₃	—	2	1	no	—
268	C₂×C₈×C₇₃	—	2	1	no	—
269	C₂×C₈×C₇₃	—	2	1	no	—
270	C₂×C₈×C₇₃	—	4	4	no	—
271	C₂×C₈×C₇₃	C₂×D₄	1	2	yes	—
272	C₄⋊C₄×C₇₃	—	2	4	no	—
273	C₄⋊C₄×C₇₃	—	2	2	no	—
274	C₄⋊C₄×C₇₃	—	2	1	no	—
275	C₄⋊C₄×C₇₃	—	2	1	no	—
276	C₄⋊C₄×C₇₃	—	2	1	no	—
277	C₄⋊C₄×C₇₃	—	2	1	no	—
278	C₄⋊C₄×C₇₃	—	2	1	no	—
279	C₄⋊C₄×C₇₃	—	2	1	no	—
280	C₄⋊C₄×C₇₃	—	8	1	no	—
281	C₄⋊C₄×C₇₃	C₂×D₄	1	2	yes	—
282	C₄⋊C₄×C₇₃	C₂×D₄	1	2	yes	—
283	C₂²⋊C₄×C₇₃	—	2	4	no	—
284	C₂²⋊C₄×C₇₃	—	2	4	no	—
285	C₂²⋊C₄×C₇₃	—	2	4	no	—
286	C₂²⋊C₄×C₇₃	—	2	4	no	—
287	C₂²⋊C₄×C₇₃	—	2	2	no	—
288	C₂²⋊C₄×C₇₃	—	2	2	no	—
289	C₂²⋊C₄×C₇₃	—	2	4	no	—
290	C₂²⋊C₄×C₇₃	—	4	2	no	—
291	C₂²⋊C₄×C₇₃	—	4	2	no	—
292	C₂²⋊C₄×C₇₃	—	4	2	no	—
293	C₂²⋊C₄×C₇₃	—	4	2	no	—
294	C₂²⋊C₄×C₇₃	—	8	1	no	—
295	C₂²⋊C₄×C₇₃	—	8	1	no	—
296	C₄²×C₇₃	—	2	1	no	—
297	C₄²×C₇₃	—	2	1	no	—
298	C₄²×C₇₃	—	4	2	no	—
299	C₂³×C₇₃	—	2	1	no	—
300	C₂³×C₇₃	—	2	2	no	—
301	C₂³×C₇₃	—	2	1	no	—
302	C₂³×C₇₃	—	2	1	no	—
303	C₂³×C₇₃	—	2	2	no	—
304	C₂³×C₇₃	—	2	1	no	—
305	C₂³×C₇₃	—	2	1	no	—
306	C₂³×C₇₃	—	2	2	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	2	no	—
315	C₂³×C₇₃	—	4	8	no	—
316	C₂³×C₇₃	—	4	8	no	—
317	C₂³×C₇₃	—	4	1	no	—
318	C₂³×C₇₃	—	4	1	no	—
319	C₂³×C₇₃	—	4	1	no	—
320	C₂³×C₇₃	—	4	1	no	—
321	C₂³×C₇₃	—	4	1	no	—
322	C₂³×C₇₃	—	4	1	no	—
323	C₂³×C₇₃	—	4	1	no	—
324	C₂³×C₇₃	—	4	1	no	—
325	C₂³×C₇₃	—	4	1	no	—
326	C₂³×C₇₃	—	4	1	no	—
327	C₂³×C₇₃	—	4	1	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	—	8	4	no	—
335	C₂³×C₇₃	—	8	4	no	—
336	C₂³×C₇₃	—	8	4	no	—
337	C₂³×C₇₃	—	8	4	no	—
338	C₂³×C₇₃	—	8	4	no	—
339	C₂³×C₇₃	#120	1	2	yes	—
340	C₂³×C₇₃	#135	1	2	yes	—
341	C₂³×C₇₃	C₂²×D₄	1	1	yes	characteristic
342	Q₈×C₇₃	—	2	2	no	—
343	Q₈×C₇₃	—	2	2	no	—
344	Q₈×C₇₃	—	4	1	no	—
345	Q₈×C₇₃	—	4	1	no	—
346	D₄×C₇₃	—	2	2	no	—
347	D₄×C₇₃	—	2	2	no	—
348	D₄×C₇₃	—	2	2	no	—
349	D₄×C₇₃	—	2	2	no	—
350	D₄×C₇₃	—	2	2	no	—
351	D₄×C₇₃	—	4	4	no	—
352	D₄×C₇₃	—	4	8	no	—
353	D₄×C₇₃	—	4	8	no	—
354	D₄×C₇₃	—	4	1	no	—
355	D₄×C₇₃	—	4	1	no	—
356	D₄×C₇₃	—	4	1	no	—
357	D₄×C₇₃	—	4	1	no	—
358	D₄×C₇₃	—	4	1	no	—
359	D₄×C₇₃	—	4	1	no	—
360	D₄×C₇₃	—	8	4	no	—
361	D₄×C₇₃	—	8	4	no	—
362	D₄×C₇₃	—	8	4	no	—
363	D₄×C₇₃	#121	1	4	yes	—
364	C₂×C₄×C₇₃	—	2	1	no	—
365	C₂×C₄×C₇₃	—	2	1	no	—
366	C₂×C₄×C₇₃	—	2	2	no	—
367	C₂×C₄×C₇₃	—	2	2	no	—
368	C₂×C₄×C₇₃	—	2	2	no	—
369	C₂×C₄×C₇₃	—	2	2	no	—
370	C₂×C₄×C₇₃	—	2	1	no	—
371	C₂×C₄×C₇₃	—	2	1	no	—
372	C₂×C₄×C₇₃	—	2	2	no	—
373	C₂×C₄×C₇₃	—	2	2	no	—
374	C₂×C₄×C₇₃	—	2	1	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	1	no	—
381	C₂×C₄×C₇₃	—	2	1	no	—
382	C₂×C₄×C₇₃	—	4	8	no	—
383	C₂×C₄×C₇₃	—	4	1	no	—
384	C₂×C₄×C₇₃	—	4	1	no	—
385	C₂×C₄×C₇₃	—	4	1	no	—
386	C₂×C₄×C₇₃	—	4	1	no	—
387	C₂×C₄×C₇₃	—	4	1	no	—
388	C₂×C₄×C₇₃	—	4	1	no	—
389	C₂×C₄×C₇₃	—	4	1	no	—
390	C₂×C₄×C₇₃	—	4	1	no	—
391	C₂×C₄×C₇₃	—	4	1	no	—
392	C₂×C₄×C₇₃	—	4	1	no	—
393	C₂×C₄×C₇₃	—	4	1	no	—
394	C₂×C₄×C₇₃	—	4	1	no	—
395	C₂×C₄×C₇₃	—	4	1	no	—
396	C₂×C₄×C₇₃	—	4	1	no	—
397	C₂×C₄×C₇₃	—	4	1	no	—
398	C₂×C₄×C₇₃	—	4	1	no	—
399	C₂×C₄×C₇₃	—	8	4	no	—
400	C₂×C₄×C₇₃	#120	1	2	yes	—
401	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
402	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
403	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
404	C₂×C₄×C₇₃	C₂×#41	1	1	yes	characteristic
405	C₂×C₄×C₇₃	H(5,𝔽₂)	1	1	yes	characteristic
406	C₂×C₄×C₇₃	H(5,𝔽₂)	1	1	yes	characteristic
407	C₈×C₇₃	—	2	2	no	—
408	C₈×C₇₃	—	4	1	no	—
409	C₈×C₇₃	—	4	1	no	—
410	C₈×C₇₃	—	4	1	no	—
411	C₂²×C₇₃	—	2	2	no	—
412	C₂²×C₇₃	—	2	4	no	—
413	C₂²×C₇₃	—	2	2	no	—
414	C₂²×C₇₃	—	2	2	no	—
415	C₂²×C₇₃	—	2	2	no	—
416	C₂²×C₇₃	—	2	2	no	—
417	C₂²×C₇₃	—	2	2	no	—
418	C₂²×C₇₃	—	4	1	no	—
419	C₂²×C₇₃	—	4	2	no	—
420	C₂²×C₇₃	—	4	2	no	—
421	C₂²×C₇₃	—	4	1	no	—
422	C₂²×C₇₃	—	4	1	no	—
423	C₂²×C₇₃	—	4	1	no	—
424	C₂²×C₇₃	—	4	2	no	—
425	C₂²×C₇₃	—	4	1	no	—
426	C₂²×C₇₃	—	4	2	no	—
427	C₂²×C₇₃	—	4	1	no	—
428	C₂²×C₇₃	—	4	2	no	—
429	C₂²×C₇₃	—	4	1	no	—
430	C₂²×C₇₃	—	4	1	no	—
431	C₂²×C₇₃	—	4	2	no	—
432	C₂²×C₇₃	—	4	2	no	—
433	C₂²×C₇₃	—	4	2	no	—
434	C₂²×C₇₃	—	4	2	no	—
435	C₂²×C₇₃	—	8	16	no	—
436	C₂²×C₇₃	—	8	1	no	—
437	C₂²×C₇₃	—	8	1	no	—
438	C₂²×C₇₃	—	8	1	no	—
439	C₂²×C₇₃	—	8	1	no	—
440	C₂²×C₇₃	—	8	1	no	—
441	C₂²×C₇₃	—	8	1	no	—
442	C₂²×C₇₃	—	8	1	no	—
443	C₂²×C₇₃	—	8	1	no	—
444	C₂²×C₇₃	—	8	1	no	—
445	C₂²×C₇₃	—	8	1	no	—
446	C₂²×C₇₃	—	8	1	no	—
447	C₂²×C₇₃	C₂×#120	1	1	yes	characteristic
448	C₂²×C₇₃	D₄²	1	1	yes	characteristic
449	C₂²×C₇₃	#546	1	1	yes	characteristic
450	C₂²×C₇₃	C₂×#135	1	1	yes	characteristic
451	C₂²×C₇₃	#575	1	1	yes	characteristic
452	C₂²×C₇₃	#576	1	1	yes	characteristic
453	C₂²×C₇₃	#576	1	1	yes	characteristic
454	C₄×C₇₃	—	2	2	no	—
455	C₄×C₇₃	—	4	1	no	—
456	C₄×C₇₃	—	4	2	no	—
457	C₄×C₇₃	—	4	1	no	—
458	C₄×C₇₃	—	4	1	no	—
459	C₄×C₇₃	—	4	2	no	—
460	C₄×C₇₃	—	4	2	no	—
461	C₄×C₇₃	—	8	1	no	—
462	C₄×C₇₃	—	8	1	no	—
463	C₄×C₇₃	C₂×#121	1	1	yes	characteristic
464	C₄×C₇₃	#534	1	1	yes	characteristic
465	C₄×C₇₃	D₄²	1	1	yes	characteristic
466	C₄×C₇₃	#546	1	1	yes	characteristic
467	#24428	C₇₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
468	C₂×C₇₃	—	4	2	no	—
469	C₂×C₇₃	—	4	2	no	—
470	C₂×C₇₃	—	4	4	no	—
471	C₂×C₇₃	—	8	2	no	—
472	C₂×C₇₃	—	16	1	no	—
473	C₂×C₇₃	#2410	1	1	yes	characteristic
474	C₂×C₇₃	#3002	1	1	yes	characteristic
475	C₂×C₇₃	#3008	1	1	yes	characteristic
476	C₂×C₇₃	#3268	1	1	yes	characteristic
477	C₂×C₇₃	#3280	1	1	yes	characteristic
478	C₂×C₇₃	#3297	1	1	yes	characteristic
479	C₂×C₇₃	#3319	1	1	yes	characteristic
480	C₂×#546	C₂×C₇₃	1	1	yes	characteristic, complemented
481	C₂×#466	C₂×C₇₃	1	1	yes	characteristic, complemented
482	C₂×#449	C₂×C₇₃	1	1	yes	characteristic, complemented
483	C₂×#447	C₂×C₇₃	1	1	yes	characteristic, complemented
484	C₂×#416	C₂×C₇₃	1	1	yes	characteristic, complemented
485	#2414	C₂×C₇₃	1	1	yes	characteristic, complemented
486	#2042	C₂×C₇₃	1	1	yes	characteristic, complemented
487	#2036	C₂×C₇₃	1	1	yes	characteristic, complemented
488	#2012	C₂×C₇₃	1	1	yes	characteristic, complemented
489	#2000	C₂×C₇₃	1	1	yes	characteristic, complemented
490	#1879	C₂×C₇₃	1	1	yes	characteristic, complemented
491	#1875	C₂×C₇₃	1	1	yes	characteristic, complemented
492	#1869	C₂×C₇₃	1	1	yes	characteristic, complemented
493	#1862	C₂×C₇₃	1	1	yes	characteristic, complemented
494	#1786	C₂×C₇₃	1	1	yes	characteristic, complemented
495	C₇₃	#24428	1	1	yes	characteristic, direct product factor, Sylow
496	C₂²×#41	C₂²×C₇₃	1	1	yes	characteristic
497	C₂³×D₄	C₂²×C₇₃	1	1	yes	characteristic
498	C₂²×SD₁₆	C₂²×C₇₃	1	1	yes	characteristic, complemented
499	C₂²×D₈	C₂²×C₇₃	1	1	yes	characteristic
500	C₂²×D₈	C₂²×C₇₃	1	1	yes	characteristic
501	C₂³×C₈	C₂²×C₇₃	1	1	yes	characteristic, complemented
502	#546	—	2	4	no	—
503	#546	—	2	4	no	—
504	C₂×#124	C₂²×C₇₃	1	1	yes	characteristic
505	C₂×#123	—	2	1	no	—
506	C₂×C₂²⋊Q₈	C₂²×C₇₃	1	1	yes	characteristic
507	C₂×#121	—	2	1	no	—
508	C₂×#121	C₂²×C₇₃	1	1	yes	characteristic
509	C₂×#121	C₂²×C₇₃	1	1	yes	characteristic
510	C₂×#121	C₂²×C₇₃	1	1	yes	characteristic, complemented
511	C₂×#120	—	2	1	no	—
512	C₂×C₄×D₄	C₂²×C₇₃	1	1	yes	characteristic
513	C₂×C₄×D₄	C₂²×C₇₃	1	1	yes	characteristic
514	C₂×#117	C₂²×C₇₃	1	1	yes	characteristic, complemented
515	C₂²×C₂²⋊C₄	—	2	1	no	—
516	#466	—	2	4	no	—
517	#449	—	2	4	no	—
518	#447	—	2	4	no	—
519	C₂×#107	C₂²×C₇₃	1	1	yes	characteristic, complemented
520	#416	—	2	4	no	—
521	C₂×#103	C₂²×C₇₃	1	1	yes	characteristic, complemented
522	C₂×#103	C₂²×C₇₃	1	1	yes	characteristic, complemented
523	C₂×#103	C₂²×C₇₃	1	1	yes	characteristic, complemented
524	C₂×#102	C₂²×C₇₃	1	1	yes	characteristic
525	C₂×#102	C₂²×C₇₃	1	1	yes	characteristic
526	C₂×#102	C₂²×C₇₃	1	1	yes	characteristic
527	C₂×#102	C₂²×C₇₃	1	1	yes	characteristic
528	C₂×#102	C₂²×C₇₃	1	1	yes	characteristic
529	C₂×#102	C₂²×C₇₃	1	1	yes	characteristic
530	C₂×#102	C₂²×C₇₃	1	1	yes	characteristic, complemented
531	C₂×C₂²⋊C₈	C₂²×C₇₃	1	1	yes	characteristic
532	C₂×C₂²⋊C₈	C₂²×C₇₃	1	1	yes	characteristic
533	C₂×C₂²⋊C₈	C₂²×C₇₃	1	1	yes	characteristic, complemented
534	#394	—	2	1	no	—
535	#392	—	2	1	no	—
536	#390	—	2	1	no	—
537	#390	C₂²×C₇₃	1	1	yes	characteristic, complemented
538	#389	C₂²×C₇₃	1	1	yes	characteristic, complemented
539	#388	—	2	1	no	—
540	#380	C₂²×C₇₃	1	1	yes	characteristic
541	#340	C₂²×C₇₃	1	1	yes	characteristic, complemented
542	#340	C₂²×C₇₃	1	1	yes	characteristic, complemented
543	#336	C₂²×C₇₃	1	1	yes	characteristic, complemented
544	#336	C₂²×C₇₃	1	1	yes	characteristic, complemented
545	C₂⁵	—	2	1	no	—
546	C₂×#41	—	2	2	no	—
547	C₂×#41	—	2	2	no	—
548	C₂×#41	—	2	2	no	—
549	C₂×#41	—	4	1	no	—
550	C₂×#41	—	4	1	no	—
551	C₂×#41	D₄×C₇₃	1	4	yes	complemented
552	C₂²×Q₈	C₂³×C₇₃	1	1	yes	characteristic
553	C₂²×D₄	—	2	1	no	—
554	C₂²×D₄	—	2	1	no	—
555	C₂²×D₄	—	2	2	no	—
556	C₂²×D₄	—	2	2	no	—
557	C₂²×D₄	—	2	2	no	—
558	C₂²×D₄	—	2	2	no	—
559	C₂²×D₄	—	2	1	no	—
560	C₂²×D₄	—	2	1	no	—
561	C₂²×D₄	—	2	1	no	—
562	C₂²×D₄	—	4	1	no	—
563	C₂²×D₄	—	4	1	no	—
564	C₂²×D₄	D₄×C₇₃	1	1	yes	characteristic
565	C₂²×D₄	C₂³×C₇₃	1	1	yes	characteristic
566	C₂²×D₄	C₂³×C₇₃	1	1	yes	characteristic
567	C₂²×D₄	C₂³×C₇₃	1	1	yes	characteristic
568	C₂³×C₄	—	2	1	no	—
569	C₂³×C₄	—	2	1	no	—
570	C₂³×C₄	C₂³×C₇₃	1	1	yes	characteristic
571	C₂³×C₄	C₂³×C₇₃	1	1	yes	characteristic
572	C₂×SD₁₆	—	2	2	no	—
573	C₂×SD₁₆	—	4	1	no	—
574	C₂×SD₁₆	—	4	1	no	—
575	C₂×D₈	—	2	2	no	—
576	C₂×D₈	—	2	2	no	—
577	C₂×D₈	—	2	2	no	—
578	C₂×D₈	—	2	2	no	—
579	C₂×D₈	—	2	2	no	—
580	C₂×D₈	—	4	1	no	—
581	C₂²×C₈	—	2	2	no	—
582	C₂²×C₈	—	2	2	no	—
583	C₂²×C₈	—	4	1	no	—
584	C₂²×C₈	C₂³×C₇₃	1	1	yes	characteristic
585	C₂²×C₈	C₂³×C₇₃	1	1	yes	characteristic
586	C₂²×C₈	C₂³×C₇₃	1	1	yes	characteristic
587	C₂²×C₈	C₂³×C₇₃	1	1	yes	characteristic
588	#124	—	2	2	no	—
589	#124	—	2	2	no	—
590	#123	—	2	8	no	—
591	C₂²⋊Q₈	—	2	2	no	—
592	C₂²⋊Q₈	—	2	2	no	—
593	#121	—	2	8	no	—
594	#121	—	2	2	no	—
595	#121	—	2	2	no	—
596	#121	—	2	2	no	—
597	#121	—	2	2	no	—
598	#121	—	4	1	no	—
599	#121	D₄×C₇₃	1	4	yes	complemented
600	#120	—	2	8	no	—
601	C₄×D₄	—	2	2	no	—
602	C₄×D₄	—	2	2	no	—
603	C₄×D₄	—	2	2	no	—
604	C₄×D₄	—	2	2	no	—
605	#117	—	2	2	no	—
606	#117	—	4	1	no	—
607	C₂×C₄⋊C₄	—	2	1	no	—
608	C₂×C₄⋊C₄	—	2	1	no	—
609	C₂×C₄⋊C₄	D₄×C₇₃	1	1	yes	characteristic
610	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
611	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
612	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
613	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
614	C₂×C₂²⋊C₄	—	2	8	no	—
615	C₂×C₂²⋊C₄	—	2	1	no	—
616	C₂×C₂²⋊C₄	—	2	1	no	—
617	C₂×C₂²⋊C₄	—	2	1	no	—
618	C₂×C₂²⋊C₄	—	2	1	no	—
619	C₂×C₂²⋊C₄	—	2	1	no	—
620	C₂×C₂²⋊C₄	—	2	1	no	—
621	C₂×C₂²⋊C₄	—	2	1	no	—
622	C₂×C₂²⋊C₄	—	2	1	no	—
623	C₂×C₂²⋊C₄	—	2	1	no	—
624	C₂×C₂²⋊C₄	—	2	1	no	—
625	C₂×C₂²⋊C₄	—	2	1	no	—
626	C₂×C₂²⋊C₄	D₄×C₇₃	1	1	yes	characteristic
627	C₂×C₂²⋊C₄	D₄×C₇₃	1	1	yes	characteristic
628	C₂×C₄²	—	2	1	no	—
629	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
630	#107	—	2	2	no	—
631	#103	—	2	2	no	—
632	#103	—	2	2	no	—
633	#103	—	2	2	no	—
634	#102	—	2	2	no	—
635	#102	—	2	2	no	—
636	#102	—	2	2	no	—
637	#102	—	2	2	no	—
638	#102	—	2	2	no	—
639	#102	—	4	1	no	—
640	#102	D₄×C₇₃	1	4	yes	complemented
641	C₂²⋊C₈	—	2	2	no	—
642	C₂²⋊C₈	—	2	2	no	—
643	C₂²⋊C₈	—	4	1	no	—
644	#95	—	2	1	no	—
645	#95	—	2	1	no	—
646	C₂⁴	—	2	1	no	—
647	C₂⁴	—	2	4	no	—
648	C₂⁴	—	2	1	no	—
649	C₂⁴	—	2	1	no	—
650	C₂⁴	—	4	2	no	—
651	C₂⁴	—	4	2	no	—
652	C₂⁴	—	4	2	no	—
653	C₂⁴	—	4	2	no	—
654	C₂⁴	—	8	1	no	—
655	C₂⁴	—	8	1	no	—
656	C₂⁴	C₂×D₄×C₇₃	1	1	yes	characteristic
657	C₂⁴	C₂×D₄×C₇₃	1	1	yes	characteristic
658	#41	—	2	8	no	—
659	#41	—	4	4	no	—
660	#41	—	4	4	no	—
661	#41	—	4	4	no	—
662	C₂×Q₈	—	2	1	no	—
663	C₂×Q₈	—	2	1	no	—
664	C₂×Q₈	—	2	1	no	—
665	C₂×Q₈	—	2	1	no	—
666	C₂×Q₈	—	2	1	no	—
667	C₂×Q₈	C₂×D₄×C₇₃	1	2	yes	—
668	C₂×D₄	—	2	4	no	—
669	C₂×D₄	—	2	2	no	—
670	C₂×D₄	—	2	4	no	—
671	C₂×D₄	—	2	2	no	—
672	C₂×D₄	—	2	4	no	—
673	C₂×D₄	—	2	1	no	—
674	C₂×D₄	—	2	1	no	—
675	C₂×D₄	—	2	1	no	—
676	C₂×D₄	—	2	1	no	—
677	C₂×D₄	—	2	1	no	—
678	C₂×D₄	—	2	1	no	—
679	C₂×D₄	—	2	1	no	—
680	C₂×D₄	—	2	1	no	—
681	C₂×D₄	—	2	1	no	—
682	C₂×D₄	—	2	1	no	—
683	C₂×D₄	—	2	1	no	—
684	C₂×D₄	—	2	1	no	—
685	C₂×D₄	—	2	1	no	—
686	C₂×D₄	—	2	1	no	—
687	C₂×D₄	—	4	1	no	—
688	C₂×D₄	—	4	2	no	—
689	C₂×D₄	—	4	2	no	—
690	C₂×D₄	—	4	2	no	—
691	C₂×D₄	—	4	4	no	—
692	C₂×D₄	—	4	4	no	—
693	C₂×D₄	—	4	4	no	—
694	C₂×D₄	—	4	2	no	—
695	C₂×D₄	—	4	2	no	—
696	C₂×D₄	—	4	4	no	—
697	C₂×D₄	—	4	2	no	—
698	C₂×D₄	—	4	2	no	—
699	C₂×D₄	—	8	1	no	—
700	C₂×D₄	—	8	1	no	—
701	C₂×D₄	—	8	1	no	—
702	C₂×D₄	—	8	1	no	—
703	C₂×D₄	—	8	1	no	—
704	C₂×D₄	C₂×D₄×C₇₃	1	2	yes	—
705	C₂×D₄	C₂×D₄×C₇₃	1	2	yes	—
706	C₂×D₄	C₂×D₄×C₇₃	1	2	yes	—
707	C₂×D₄	#41×C₇₃	1	2	yes	—
708	C₂²×C₄	—	2	1	no	—
709	C₂²×C₄	—	2	1	no	—
710	C₂²×C₄	—	2	1	no	—
711	C₂²×C₄	—	2	1	no	—
712	C₂²×C₄	—	2	1	no	—
713	C₂²×C₄	—	2	1	no	—
714	C₂²×C₄	—	2	1	no	—
715	C₂²×C₄	—	2	4	no	—
716	C₂²×C₄	—	2	4	no	—
717	C₂²×C₄	—	2	1	no	—
718	C₂²×C₄	—	2	1	no	—
719	C₂²×C₄	—	2	1	no	—
720	C₂²×C₄	—	2	1	no	—
721	C₂²×C₄	—	2	1	no	—
722	C₂²×C₄	—	2	1	no	—
723	C₂²×C₄	—	2	1	no	—
724	C₂²×C₄	—	2	1	no	—
725	C₂²×C₄	—	4	2	no	—
726	C₂²×C₄	—	4	2	no	—
727	C₂²×C₄	—	8	1	no	—
728	C₂²×C₄	—	8	1	no	—
729	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
730	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
731	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
732	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
733	C₂²×C₄	C₂×D₄×C₇₃	1	2	yes	—
734	C₂²×C₄	C₂×D₄×C₇₃	1	2	yes	—
735	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
736	SD₁₆	—	4	4	no	—
737	D₈	—	4	4	no	—
738	D₈	—	4	4	no	—
739	C₂×C₈	—	2	1	no	—
740	C₂×C₈	—	2	1	no	—
741	C₂×C₈	—	2	1	no	—
742	C₂×C₈	—	2	1	no	—
743	C₂×C₈	—	2	1	no	—
744	C₂×C₈	—	2	1	no	—
745	C₂×C₈	—	2	1	no	—
746	C₂×C₈	—	2	1	no	—
747	C₂×C₈	—	2	1	no	—
748	C₂×C₈	—	2	1	no	—
749	C₂×C₈	—	2	1	no	—
750	C₂×C₈	—	4	4	no	—
751	C₂×C₈	C₂×D₄×C₇₃	1	2	yes	—
752	C₄⋊C₄	—	2	4	no	—
753	C₄⋊C₄	—	2	2	no	—
754	C₄⋊C₄	—	2	1	no	—
755	C₄⋊C₄	—	2	1	no	—
756	C₄⋊C₄	—	2	1	no	—
757	C₄⋊C₄	—	2	1	no	—
758	C₄⋊C₄	—	2	1	no	—
759	C₄⋊C₄	—	2	1	no	—
760	C₄⋊C₄	—	8	1	no	—
761	C₄⋊C₄	C₂×D₄×C₇₃	1	2	yes	—
762	C₄⋊C₄	C₂×D₄×C₇₃	1	2	yes	—
763	C₂²⋊C₄	—	2	4	no	—
764	C₂²⋊C₄	—	2	4	no	—
765	C₂²⋊C₄	—	2	4	no	—
766	C₂²⋊C₄	—	2	4	no	—
767	C₂²⋊C₄	—	2	2	no	—
768	C₂²⋊C₄	—	2	2	no	—
769	C₂²⋊C₄	—	2	4	no	—
770	C₂²⋊C₄	—	4	2	no	—
771	C₂²⋊C₄	—	4	2	no	—
772	C₂²⋊C₄	—	4	2	no	—
773	C₂²⋊C₄	—	4	2	no	—
774	C₂²⋊C₄	—	8	1	no	—
775	C₂²⋊C₄	—	8	1	no	—
776	C₄²	—	2	1	no	—
777	C₄²	—	2	1	no	—
778	C₄²	—	4	2	no	—
779	C₂³	—	2	1	no	—
780	C₂³	—	2	2	no	—
781	C₂³	—	2	1	no	—
782	C₂³	—	2	1	no	—
783	C₂³	—	2	2	no	—
784	C₂³	—	2	1	no	—
785	C₂³	—	2	1	no	—
786	C₂³	—	2	2	no	—
787	C₂³	—	2	1	no	—
788	C₂³	—	2	1	no	—
789	C₂³	—	2	1	no	—
790	C₂³	—	2	1	no	—
791	C₂³	—	2	1	no	—
792	C₂³	—	2	1	no	—
793	C₂³	—	2	1	no	—
794	C₂³	—	2	2	no	—
795	C₂³	—	4	8	no	—
796	C₂³	—	4	8	no	—
797	C₂³	—	4	1	no	—
798	C₂³	—	4	1	no	—
799	C₂³	—	4	1	no	—
800	C₂³	—	4	1	no	—
801	C₂³	—	4	1	no	—
802	C₂³	—	4	1	no	—
803	C₂³	—	4	1	no	—
804	C₂³	—	4	1	no	—
805	C₂³	—	4	1	no	—
806	C₂³	—	4	1	no	—
807	C₂³	—	4	1	no	—
808	C₂³	—	4	1	no	—
809	C₂³	—	4	1	no	—
810	C₂³	—	4	1	no	—
811	C₂³	—	4	1	no	—
812	C₂³	—	4	1	no	—
813	C₂³	—	4	1	no	—
814	C₂³	—	8	4	no	—
815	C₂³	—	8	4	no	—
816	C₂³	—	8	4	no	—
817	C₂³	—	8	4	no	—
818	C₂³	—	8	4	no	—
819	C₂³	#120×C₇₃	1	2	yes	—
820	C₂³	#135×C₇₃	1	2	yes	—
821	C₂³	C₂²×D₄×C₇₃	1	1	yes	characteristic
822	Q₈	—	2	2	no	—
823	Q₈	—	2	2	no	—
824	Q₈	—	4	1	no	—
825	Q₈	—	4	1	no	—
826	D₄	—	2	2	no	—
827	D₄	—	2	2	no	—
828	D₄	—	2	2	no	—
829	D₄	—	2	2	no	—
830	D₄	—	2	2	no	—
831	D₄	—	4	4	no	—
832	D₄	—	4	8	no	—
833	D₄	—	4	8	no	—
834	D₄	—	4	1	no	—
835	D₄	—	4	1	no	—
836	D₄	—	4	1	no	—
837	D₄	—	4	1	no	—
838	D₄	—	4	1	no	—
839	D₄	—	4	1	no	—
840	D₄	—	8	4	no	—
841	D₄	—	8	4	no	—
842	D₄	—	8	4	no	—
843	D₄	#121×C₇₃	1	4	yes	—
844	C₂×C₄	—	2	1	no	—
845	C₂×C₄	—	2	1	no	—
846	C₂×C₄	—	2	2	no	—
847	C₂×C₄	—	2	2	no	—
848	C₂×C₄	—	2	2	no	—
849	C₂×C₄	—	2	2	no	—
850	C₂×C₄	—	2	1	no	—
851	C₂×C₄	—	2	1	no	—
852	C₂×C₄	—	2	2	no	—
853	C₂×C₄	—	2	2	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	1	no	—
860	C₂×C₄	—	2	1	no	—
861	C₂×C₄	—	2	1	no	—
862	C₂×C₄	—	4	8	no	—
863	C₂×C₄	—	4	1	no	—
864	C₂×C₄	—	4	1	no	—
865	C₂×C₄	—	4	1	no	—
866	C₂×C₄	—	4	1	no	—
867	C₂×C₄	—	4	1	no	—
868	C₂×C₄	—	4	1	no	—
869	C₂×C₄	—	4	1	no	—
870	C₂×C₄	—	4	1	no	—
871	C₂×C₄	—	4	1	no	—
872	C₂×C₄	—	4	1	no	—
873	C₂×C₄	—	4	1	no	—
874	C₂×C₄	—	4	1	no	—
875	C₂×C₄	—	4	1	no	—
876	C₂×C₄	—	4	1	no	—
877	C₂×C₄	—	4	1	no	—
878	C₂×C₄	—	4	1	no	—
879	C₂×C₄	—	8	4	no	—
880	C₂×C₄	#120×C₇₃	1	2	yes	—
881	C₂×C₄	C₂²×D₄×C₇₃	1	1	yes	characteristic
882	C₂×C₄	C₂²×D₄×C₇₃	1	1	yes	characteristic
883	C₂×C₄	C₂²×D₄×C₇₃	1	1	yes	characteristic
884	C₂×C₄	C₂×#41×C₇₃	1	1	yes	characteristic
885	C₂×C₄	H(5,𝔽₂)×C₇₃	1	1	yes	characteristic
886	C₂×C₄	H(5,𝔽₂)×C₇₃	1	1	yes	characteristic
887	C₈	—	2	2	no	—
888	C₈	—	4	1	no	—
889	C₈	—	4	1	no	—
890	C₈	—	4	1	no	—
891	C₂²	—	2	2	no	—
892	C₂²	—	2	2	no	—
893	C₂²	—	2	2	no	—
894	C₂²	—	2	2	no	—
895	C₂²	—	2	2	no	—
896	C₂²	—	2	2	no	—
897	C₂²	—	2	4	no	—
898	C₂²	—	4	2	no	—
899	C₂²	—	4	2	no	—
900	C₂²	—	4	1	no	—
901	C₂²	—	4	1	no	—
902	C₂²	—	4	1	no	—
903	C₂²	—	4	2	no	—
904	C₂²	—	4	1	no	—
905	C₂²	—	4	2	no	—
906	C₂²	—	4	1	no	—
907	C₂²	—	4	2	no	—
908	C₂²	—	4	1	no	—
909	C₂²	—	4	1	no	—
910	C₂²	—	4	2	no	—
911	C₂²	—	4	1	no	—
912	C₂²	—	4	2	no	—
913	C₂²	—	4	2	no	—
914	C₂²	—	4	2	no	—
915	C₂²	—	8	16	no	—
916	C₂²	—	8	1	no	—
917	C₂²	—	8	1	no	—
918	C₂²	—	8	1	no	—
919	C₂²	—	8	1	no	—
920	C₂²	—	8	1	no	—
921	C₂²	—	8	1	no	—
922	C₂²	—	8	1	no	—
923	C₂²	—	8	1	no	—
924	C₂²	—	8	1	no	—
925	C₂²	—	8	1	no	—
926	C₂²	—	8	1	no	—
927	C₂²	C₂×#120×C₇₃	1	1	yes	characteristic
928	C₂²	D₄²×C₇₃	1	1	yes	characteristic
929	C₂²	#546×C₇₃	1	1	yes	characteristic
930	C₂²	C₂×#135×C₇₃	1	1	yes	characteristic
931	C₂²	#575×C₇₃	1	1	yes	characteristic
932	C₂²	#576×C₇₃	1	1	yes	characteristic
933	C₂²	#576×C₇₃	1	1	yes	characteristic
934	C₄	—	2	2	no	—
935	C₄	—	4	1	no	—
936	C₄	—	4	1	no	—
937	C₄	—	4	2	no	—
938	C₄	—	4	2	no	—
939	C₄	—	4	1	no	—
940	C₄	—	4	2	no	—
941	C₄	—	8	1	no	—
942	C₄	—	8	1	no	—
943	C₄	C₂×#121×C₇₃	1	1	yes	characteristic
944	C₄	#534×C₇₃	1	1	yes	characteristic
945	C₄	D₄²×C₇₃	1	1	yes	characteristic
946	C₄	#546×C₇₃	1	1	yes	characteristic
947	C₂	—	4	2	no	—
948	C₂	—	4	2	no	—
949	C₂	—	4	4	no	—
950	C₂	—	8	2	no	—
951	C₂	—	16	1	no	—
952	C₂	C₇₃×#2410	1	1	yes	characteristic
953	C₂	C₇₃×#3002	1	1	yes	characteristic
954	C₂	C₇₃×#3008	1	1	yes	characteristic
955	C₂	C₇₃×#3268	1	1	yes	characteristic
956	C₂	C₇₃×#3280	1	1	yes	characteristic
957	C₂	C₇₃×#3297	1	1	yes	characteristic
958	C₂	C₇₃×#3319	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×#466×C₇₃	C₂	semidirect
3. C₂×#449×C₇₃	C₂	semidirect
4. C₂×#447×C₇₃	C₂	semidirect
5. C₂×#416×C₇₃	C₂	semidirect
6. C₇₃×#2414	C₂	semidirect
7. C₇₃×#2042	C₂	semidirect
8. C₇₃×#2036	C₂	semidirect
9. C₇₃×#2012	C₂	semidirect
10. C₇₃×#2000	C₂	semidirect
11. C₇₃×#1879	C₂	semidirect
12. C₇₃×#1875	C₂	semidirect
13. C₇₃×#1869	C₂	semidirect
14. C₇₃×#1862	C₂	semidirect
15. C₇₃×#1786	C₂	semidirect
18. C₂²×SD₁₆×C₇₃	C₂²	semidirect
21. C₂³×C₈×C₇₃	C₂²	semidirect
30. C₂×#121×C₇₃	C₂²	semidirect
34. C₂×#117×C₇₃	C₂²	semidirect
39. C₂×#107×C₇₃	C₂²	semidirect
41. C₂×#103×C₇₃	C₂²	semidirect
42. C₂×#103×C₇₃	C₂²	semidirect
43. C₂×#103×C₇₃	C₂²	semidirect
50. C₂×#102×C₇₃	C₂²	semidirect
53. C₂×C₂²⋊C₈×C₇₃	C₂²	semidirect
57. #390×C₇₃	C₂²	semidirect
58. #389×C₇₃	C₂²	semidirect
61. #340×C₇₃	C₂²	semidirect
62. #340×C₇₃	C₂²	semidirect
63. #336×C₇₃	C₂²	semidirect
64. #336×C₇₃	C₂²	semidirect
71. C₂×#41×C₇₃	D₄	semidirect
119. #121×C₇₃	D₄	semidirect
160. #102×C₇₃	D₄	semidirect
467. #24428	C₇₃	direct (N × H)
480. C₂×#546	C₂×C₇₃	semidirect
481. C₂×#466	C₂×C₇₃	semidirect
482. C₂×#449	C₂×C₇₃	semidirect
483. C₂×#447	C₂×C₇₃	semidirect
484. C₂×#416	C₂×C₇₃	semidirect
485. #2414	C₂×C₇₃	semidirect
486. #2042	C₂×C₇₃	semidirect
487. #2036	C₂×C₇₃	semidirect
488. #2012	C₂×C₇₃	semidirect
489. #2000	C₂×C₇₃	semidirect
490. #1879	C₂×C₇₃	semidirect
491. #1875	C₂×C₇₃	semidirect
492. #1869	C₂×C₇₃	semidirect
493. #1862	C₂×C₇₃	semidirect
494. #1786	C₂×C₇₃	semidirect
495. C₇₃	#24428	direct (N × H)
498. C₂²×SD₁₆	C₂²×C₇₃	semidirect
501. C₂³×C₈	C₂²×C₇₃	semidirect
510. C₂×#121	C₂²×C₇₃	semidirect
514. C₂×#117	C₂²×C₇₃	semidirect
519. C₂×#107	C₂²×C₇₃	semidirect
521. C₂×#103	C₂²×C₇₃	semidirect
522. C₂×#103	C₂²×C₇₃	semidirect
523. C₂×#103	C₂²×C₇₃	semidirect
530. C₂×#102	C₂²×C₇₃	semidirect
533. C₂×C₂²⋊C₈	C₂²×C₇₃	semidirect
537. #390	C₂²×C₇₃	semidirect
538. #389	C₂²×C₇₃	semidirect
541. #340	C₂²×C₇₃	semidirect
542. #340	C₂²×C₇₃	semidirect
543. #336	C₂²×C₇₃	semidirect
544. #336	C₂²×C₇₃	semidirect
551. C₂×#41	D₄×C₇₃	semidirect
599. #121	D₄×C₇₃	semidirect
640. #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×#466×C₇₃	2
C₂×#449×C₇₃	2
C₂×#447×C₇₃	2
C₂×#416×C₇₃	2
C₇₃×#2414	2
C₇₃×#2042	2
C₇₃×#2036	2
C₇₃×#2012	2
C₇₃×#2000	2
C₇₃×#1879	2
C₇₃×#1875	2
C₇₃×#1869	2
C₇₃×#1862	2
C₇₃×#1786	2
#24428	73

Subgroups — C73×#24428 #32933832

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₃×#24428 #32933832