Subgroups — C₇₃×#13993 #32923397

Order 18688.

1746 conjugacy classes of subgroups.

The subgroup lattice has 814 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#389×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#380×C₇₃	C₂	1	1	yes	maximal, characteristic
3	C₂×#380×C₇₃	C₂	1	1	yes	maximal, characteristic
4	C₂×C₄×C₄⋊C₄×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₄×C₂²⋊C₄×C₇₃	C₂	1	1	yes	maximal, characteristic
6	C₇₃×#1443	C₂	1	2	yes	maximal, complemented
7	C₇₃×#1439	C₂	1	2	yes	maximal
8	C₇₃×#1437	C₂	1	2	yes	maximal
9	C₇₃×#1436	C₂	1	2	yes	maximal, complemented
10	C₇₃×C₄⋊#95	C₂	1	1	yes	maximal, characteristic, complemented
11	C₇₃×C₄⋊#95	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂⁴×C₄×C₇₃	C₂²	1	1	yes	characteristic
13	C₂²×C₄⋊C₄×C₇₃	C₂²	1	1	yes	characteristic
14	C₂²×C₄⋊C₄×C₇₃	C₂²	1	2	yes	—
15	C₂²×C₄⋊C₄×C₇₃	C₂²	1	1	yes	characteristic
16	C₂²×C₄⋊C₄×C₇₃	C₂²	1	1	yes	characteristic
17	C₂²×C₄⋊C₄×C₇₃	C₂²	1	1	yes	characteristic
18	C₂²×C₂²⋊C₄×C₇₃	C₂²	1	1	yes	characteristic
19	C₂²×C₂²⋊C₄×C₇₃	C₂²	1	2	yes	—
20	C₂²×C₂²⋊C₄×C₇₃	C₂²	1	1	yes	characteristic
21	C₂²×C₂²⋊C₄×C₇₃	C₂²	1	2	yes	—
22	C₂²×C₄²×C₇₃	C₂²	1	1	yes	characteristic
23	C₂²×C₄²×C₇₃	C₂²	1	1	yes	characteristic
24	C₂²×C₄²×C₇₃	C₂²	1	2	yes	—
25	#389×C₇₃	—	2	4	no	—
26	#380×C₇₃	—	2	4	no	—
27	#380×C₇₃	C₄	1	8	yes	complemented
28	C₄×C₄⋊C₄×C₇₃	—	2	4	no	—
29	C₄×C₂²⋊C₄×C₇₃	—	2	4	no	—
30	C₂×#95×C₇₃	C₂²	1	2	yes	—
31	C₂×#95×C₇₃	C₂²	1	1	yes	characteristic
32	C₂×#95×C₇₃	C₂²	1	2	yes	—
33	C₂×#95×C₇₃	C₂²	1	2	yes	—
34	C₂×#95×C₇₃	C₂²	1	2	yes	—
35	C₂×#95×C₇₃	C₂²	1	1	yes	characteristic
36	C₂×#95×C₇₃	C₂²	1	2	yes	—
37	C₂×#95×C₇₃	C₂²	1	2	yes	—
38	C₂×#95×C₇₃	C₂²	1	2	yes	—
39	C₂×#95×C₇₃	C₂²	1	2	yes	—
40	C₂⁵×C₇₃	C₂³	1	1	yes	characteristic
41	C₂³×C₄×C₇₃	—	2	2	no	—
42	C₂³×C₄×C₇₃	—	2	2	no	—
43	C₂³×C₄×C₇₃	—	2	2	no	—
44	C₂³×C₄×C₇₃	—	2	2	no	—
45	C₂³×C₄×C₇₃	—	2	2	no	—
46	C₂³×C₄×C₇₃	—	2	2	no	—
47	C₂³×C₄×C₇₃	C₂×C₄	1	4	yes	—
48	C₂³×C₄×C₇₃	C₂³	1	2	yes	—
49	C₂³×C₄×C₇₃	C₂³	1	2	yes	—
50	C₂³×C₄×C₇₃	C₂³	1	2	yes	—
51	C₂³×C₄×C₇₃	C₂³	1	1	yes	characteristic
52	C₂³×C₄×C₇₃	C₂³	1	2	yes	—
53	C₂³×C₄×C₇₃	C₂³	1	1	yes	characteristic
54	C₂³×C₄×C₇₃	C₂³	1	1	yes	characteristic
55	C₂³×C₄×C₇₃	C₂³	1	1	yes	characteristic
56	C₂³×C₄×C₇₃	C₂³	1	1	yes	characteristic
57	C₂³×C₄×C₇₃	C₂³	1	1	yes	characteristic
58	C₂×C₄⋊C₄×C₇₃	—	2	2	no	—
59	C₂×C₄⋊C₄×C₇₃	—	2	2	no	—
60	C₂×C₄⋊C₄×C₇₃	—	2	2	no	—
61	C₂×C₄⋊C₄×C₇₃	—	2	2	no	—
62	C₂×C₄⋊C₄×C₇₃	—	2	2	no	—
63	C₂×C₄⋊C₄×C₇₃	—	2	2	no	—
64	C₂×C₄⋊C₄×C₇₃	—	2	2	no	—
65	C₂×C₄⋊C₄×C₇₃	—	2	4	no	—
66	C₂×C₄⋊C₄×C₇₃	—	2	4	no	—
67	C₂×C₄⋊C₄×C₇₃	—	2	2	no	—
68	C₂×C₄⋊C₄×C₇₃	—	2	2	no	—
69	C₂×C₄⋊C₄×C₇₃	—	4	2	no	—
70	C₂×C₄⋊C₄×C₇₃	C₂×C₄	1	4	yes	—
71	C₂×C₄⋊C₄×C₇₃	C₂×C₄	1	4	yes	—
72	C₂×C₄⋊C₄×C₇₃	D₄	1	4	yes	—
73	C₂×C₂²⋊C₄×C₇₃	—	2	2	no	—
74	C₂×C₂²⋊C₄×C₇₃	—	2	2	no	—
75	C₂×C₂²⋊C₄×C₇₃	—	2	2	no	—
76	C₂×C₂²⋊C₄×C₇₃	—	2	2	no	—
77	C₂×C₂²⋊C₄×C₇₃	—	2	2	no	—
78	C₂×C₂²⋊C₄×C₇₃	—	2	4	no	—
79	C₂×C₂²⋊C₄×C₇₃	—	2	4	no	—
80	C₂×C₂²⋊C₄×C₇₃	—	4	2	no	—
81	C₂×C₂²⋊C₄×C₇₃	—	4	2	no	—
82	C₂×C₂²⋊C₄×C₇₃	—	4	2	no	—
83	C₂×C₂²⋊C₄×C₇₃	C₂×C₄	1	8	yes	—
84	C₂×C₂²⋊C₄×C₇₃	Q₈	1	4	yes	—
85	C₂×C₄²×C₇₃	—	2	2	no	—
86	C₂×C₄²×C₇₃	—	2	2	no	—
87	C₂×C₄²×C₇₃	—	2	2	no	—
88	C₂×C₄²×C₇₃	—	2	4	no	—
89	C₂×C₄²×C₇₃	—	2	2	no	—
90	C₂×C₄²×C₇₃	—	2	2	no	—
91	C₂×C₄²×C₇₃	—	4	2	no	—
92	C₂×C₄²×C₇₃	—	4	2	no	—
93	C₂×C₄²×C₇₃	D₄	1	4	yes	—
94	#95×C₇₃	—	2	2	no	—
95	#95×C₇₃	—	2	2	no	—
96	#95×C₇₃	—	2	4	no	—
97	#95×C₇₃	—	2	4	no	—
98	#95×C₇₃	—	2	4	no	—
99	#95×C₇₃	—	2	4	no	—
100	#95×C₇₃	—	4	2	no	—
101	#95×C₇₃	—	4	2	no	—
102	#95×C₇₃	—	4	2	no	—
103	#95×C₇₃	C₂×C₄	1	8	yes	—
104	C₂⁴×C₇₃	—	2	1	no	—
105	C₂⁴×C₇₃	—	2	1	no	—
106	C₂⁴×C₇₃	—	2	1	no	—
107	C₂⁴×C₇₃	—	2	1	no	—
108	C₂⁴×C₇₃	—	2	1	no	—
109	C₂⁴×C₇₃	—	2	1	no	—
110	C₂⁴×C₇₃	—	2	1	no	—
111	C₂⁴×C₇₃	—	2	1	no	—
112	C₂⁴×C₇₃	—	2	1	no	—
113	C₂⁴×C₇₃	—	2	1	no	—
114	C₂⁴×C₇₃	—	2	1	no	—
115	C₂⁴×C₇₃	—	2	1	no	—
116	C₂⁴×C₇₃	C₂²×C₄	1	2	yes	—
117	C₂⁴×C₇₃	C₂×Q₈	1	2	yes	—
118	C₂⁴×C₇₃	#41	1	2	yes	—
119	C₂⁴×C₇₃	C₂⁴	1	1	yes	characteristic
120	C₂²×C₄×C₇₃	—	2	1	no	—
121	C₂²×C₄×C₇₃	—	2	1	no	—
122	C₂²×C₄×C₇₃	—	2	1	no	—
123	C₂²×C₄×C₇₃	—	2	1	no	—
124	C₂²×C₄×C₇₃	—	2	1	no	—
125	C₂²×C₄×C₇₃	—	2	1	no	—
126	C₂²×C₄×C₇₃	—	2	1	no	—
127	C₂²×C₄×C₇₃	—	2	1	no	—
128	C₂²×C₄×C₇₃	—	2	1	no	—
129	C₂²×C₄×C₇₃	—	2	2	no	—
130	C₂²×C₄×C₇₃	—	2	2	no	—
131	C₂²×C₄×C₇₃	—	2	2	no	—
132	C₂²×C₄×C₇₃	—	2	1	no	—
133	C₂²×C₄×C₇₃	—	2	2	no	—
134	C₂²×C₄×C₇₃	—	2	1	no	—
135	C₂²×C₄×C₇₃	—	2	1	no	—
136	C₂²×C₄×C₇₃	—	2	1	no	—
137	C₂²×C₄×C₇₃	—	2	1	no	—
138	C₂²×C₄×C₇₃	—	2	1	no	—
139	C₂²×C₄×C₇₃	—	2	1	no	—
140	C₂²×C₄×C₇₃	—	2	1	no	—
141	C₂²×C₄×C₇₃	—	2	1	no	—
142	C₂²×C₄×C₇₃	—	2	2	no	—
143	C₂²×C₄×C₇₃	—	2	2	no	—
144	C₂²×C₄×C₇₃	—	2	2	no	—
145	C₂²×C₄×C₇₃	—	2	2	no	—
146	C₂²×C₄×C₇₃	—	2	2	no	—
147	C₂²×C₄×C₇₃	—	2	2	no	—
148	C₂²×C₄×C₇₃	—	2	1	no	—
149	C₂²×C₄×C₇₃	—	2	1	no	—
150	C₂²×C₄×C₇₃	—	2	1	no	—
151	C₂²×C₄×C₇₃	—	2	1	no	—
152	C₂²×C₄×C₇₃	—	2	1	no	—
153	C₂²×C₄×C₇₃	—	2	1	no	—
154	C₂²×C₄×C₇₃	—	2	1	no	—
155	C₂²×C₄×C₇₃	—	2	2	no	—
156	C₂²×C₄×C₇₃	—	2	2	no	—
157	C₂²×C₄×C₇₃	—	2	2	no	—
158	C₂²×C₄×C₇₃	—	2	2	no	—
159	C₂²×C₄×C₇₃	—	2	2	no	—
160	C₂²×C₄×C₇₃	—	2	2	no	—
161	C₂²×C₄×C₇₃	—	2	2	no	—
162	C₂²×C₄×C₇₃	—	2	1	no	—
163	C₂²×C₄×C₇₃	—	2	2	no	—
164	C₂²×C₄×C₇₃	—	2	1	no	—
165	C₂²×C₄×C₇₃	—	2	1	no	—
166	C₂²×C₄×C₇₃	—	2	8	no	—
167	C₂²×C₄×C₇₃	—	2	8	no	—
168	C₂²×C₄×C₇₃	—	2	8	no	—
169	C₂²×C₄×C₇₃	—	2	2	no	—
170	C₂²×C₄×C₇₃	—	2	2	no	—
171	C₂²×C₄×C₇₃	—	2	2	no	—
172	C₂²×C₄×C₇₃	—	2	2	no	—
173	C₂²×C₄×C₇₃	—	2	2	no	—
174	C₂²×C₄×C₇₃	—	2	2	no	—
175	C₂²×C₄×C₇₃	—	2	2	no	—
176	C₂²×C₄×C₇₃	—	4	4	no	—
177	C₂²×C₄×C₇₃	—	4	4	no	—
178	C₂²×C₄×C₇₃	—	4	4	no	—
179	C₂²×C₄×C₇₃	—	4	4	no	—
180	C₂²×C₄×C₇₃	C₂²×C₄	1	2	yes	—
181	C₂²×C₄×C₇₃	C₂²×C₄	1	4	yes	—
182	C₂²×C₄×C₇₃	C₂²×C₄	1	4	yes	—
183	C₂²×C₄×C₇₃	C₂²×C₄	1	2	yes	—
184	C₂²×C₄×C₇₃	C₂×D₄	1	2	yes	—
185	C₂²×C₄×C₇₃	C₂×D₄	1	4	yes	—
186	C₂²×C₄×C₇₃	C₂×D₄	1	2	yes	—
187	C₂²×C₄×C₇₃	C₂×D₄	1	2	yes	—
188	C₂²×C₄×C₇₃	C₂×D₄	1	2	yes	—
189	C₂²×C₄×C₇₃	C₂×Q₈	1	2	yes	—
190	C₂²×C₄×C₇₃	C₂×Q₈	1	2	yes	—
191	C₂²×C₄×C₇₃	#41	1	2	yes	—
192	C₂²×C₄×C₇₃	#41	1	2	yes	—
193	C₂²×C₄×C₇₃	#41	1	2	yes	—
194	C₂²×C₄×C₇₃	#41	1	2	yes	—
195	C₂²×C₄×C₇₃	#41	1	2	yes	—
196	C₂²×C₄×C₇₃	#41	1	2	yes	—
197	C₄⋊C₄×C₇₃	—	2	8	no	—
198	C₄⋊C₄×C₇₃	—	2	8	no	—
199	C₄⋊C₄×C₇₃	—	2	8	no	—
200	C₄⋊C₄×C₇₃	—	4	8	no	—
201	C₄⋊C₄×C₇₃	—	4	4	no	—
202	C₂²⋊C₄×C₇₃	—	2	8	no	—
203	C₂²⋊C₄×C₇₃	—	2	8	no	—
204	C₂²⋊C₄×C₇₃	—	4	8	no	—
205	C₂²⋊C₄×C₇₃	—	4	8	no	—
206	C₄²×C₇₃	—	2	8	no	—
207	C₄²×C₇₃	—	4	8	no	—
208	C₄²×C₇₃	—	4	4	no	—
209	C₂³×C₇₃	—	2	2	no	—
210	C₂³×C₇₃	—	2	2	no	—
211	C₂³×C₇₃	—	2	2	no	—
212	C₂³×C₇₃	—	2	2	no	—
213	C₂³×C₇₃	—	2	2	no	—
214	C₂³×C₇₃	—	2	2	no	—
215	C₂³×C₇₃	—	2	2	no	—
216	C₂³×C₇₃	—	2	2	no	—
217	C₂³×C₇₃	—	2	2	no	—
218	C₂³×C₇₃	—	2	2	no	—
219	C₂³×C₇₃	—	2	2	no	—
220	C₂³×C₇₃	—	2	2	no	—
221	C₂³×C₇₃	—	2	2	no	—
222	C₂³×C₇₃	—	2	2	no	—
223	C₂³×C₇₃	—	2	2	no	—
224	C₂³×C₇₃	—	2	2	no	—
225	C₂³×C₇₃	—	2	2	no	—
226	C₂³×C₇₃	—	2	2	no	—
227	C₂³×C₇₃	—	4	1	no	—
228	C₂³×C₇₃	—	4	1	no	—
229	C₂³×C₇₃	—	4	1	no	—
230	C₂³×C₇₃	—	4	1	no	—
231	C₂³×C₇₃	—	4	1	no	—
232	C₂³×C₇₃	—	4	1	no	—
233	C₂³×C₇₃	—	4	1	no	—
234	C₂³×C₇₃	—	4	1	no	—
235	C₂³×C₇₃	—	4	1	no	—
236	C₂³×C₇₃	—	4	1	no	—
237	C₂³×C₇₃	—	4	1	no	—
238	C₂³×C₇₃	—	4	1	no	—
239	C₂³×C₇₃	—	4	1	no	—
240	C₂³×C₇₃	—	4	1	no	—
241	C₂³×C₇₃	—	4	1	no	—
242	C₂³×C₇₃	—	4	1	no	—
243	C₂³×C₇₃	C₄×Q₈	1	4	yes	—
244	C₂³×C₇₃	C₂³×C₄	1	1	yes	characteristic
245	C₂³×C₇₃	C₂²×D₄	1	1	yes	characteristic
246	C₂³×C₇₃	C₂²×D₄	1	1	yes	characteristic
247	C₂³×C₇₃	C₂²×Q₈	1	1	yes	characteristic
248	C₂³×C₇₃	C₂×#41	1	1	yes	characteristic
249	C₂³×C₇₃	C₂×#41	1	1	yes	characteristic
250	C₂³×C₇₃	C₂×#41	1	1	yes	characteristic
251	C₂³×C₇₃	C₂×#41	1	1	yes	characteristic
252	C₂³×C₇₃	C₂×#41	1	1	yes	characteristic
253	C₂³×C₇₃	C₂×#41	1	1	yes	characteristic
254	C₂³×C₇₃	C₂×#41	1	1	yes	characteristic
255	C₂³×C₇₃	H(5,𝔽₂)	1	1	yes	characteristic
256	C₂³×C₇₃	H(5,𝔽₂)	1	1	yes	characteristic
257	C₂³×C₇₃	H(5,𝔽₂)	1	1	yes	characteristic
258	C₂³×C₇₃	2₋¹⁺⁴	1	1	yes	characteristic
259	C₂×C₄×C₇₃	—	2	2	no	—
260	C₂×C₄×C₇₃	—	2	2	no	—
261	C₂×C₄×C₇₃	—	2	2	no	—
262	C₂×C₄×C₇₃	—	2	2	no	—
263	C₂×C₄×C₇₃	—	2	2	no	—
264	C₂×C₄×C₇₃	—	2	2	no	—
265	C₂×C₄×C₇₃	—	2	2	no	—
266	C₂×C₄×C₇₃	—	2	4	no	—
267	C₂×C₄×C₇₃	—	2	4	no	—
268	C₂×C₄×C₇₃	—	2	2	no	—
269	C₂×C₄×C₇₃	—	2	2	no	—
270	C₂×C₄×C₇₃	—	2	4	no	—
271	C₂×C₄×C₇₃	—	2	4	no	—
272	C₂×C₄×C₇₃	—	2	4	no	—
273	C₂×C₄×C₇₃	—	2	4	no	—
274	C₂×C₄×C₇₃	—	2	4	no	—
275	C₂×C₄×C₇₃	—	2	2	no	—
276	C₂×C₄×C₇₃	—	2	2	no	—
277	C₂×C₄×C₇₃	—	2	2	no	—
278	C₂×C₄×C₇₃	—	2	2	no	—
279	C₂×C₄×C₇₃	—	2	2	no	—
280	C₂×C₄×C₇₃	—	2	4	no	—
281	C₂×C₄×C₇₃	—	2	2	no	—
282	C₂×C₄×C₇₃	—	2	4	no	—
283	C₂×C₄×C₇₃	—	2	2	no	—
284	C₂×C₄×C₇₃	—	2	2	no	—
285	C₂×C₄×C₇₃	—	2	2	no	—
286	C₂×C₄×C₇₃	—	4	1	no	—
287	C₂×C₄×C₇₃	—	4	1	no	—
288	C₂×C₄×C₇₃	—	4	1	no	—
289	C₂×C₄×C₇₃	—	4	1	no	—
290	C₂×C₄×C₇₃	—	4	2	no	—
291	C₂×C₄×C₇₃	—	4	1	no	—
292	C₂×C₄×C₇₃	—	4	1	no	—
293	C₂×C₄×C₇₃	—	4	2	no	—
294	C₂×C₄×C₇₃	—	4	2	no	—
295	C₂×C₄×C₇₃	—	4	1	no	—
296	C₂×C₄×C₇₃	—	4	2	no	—
297	C₂×C₄×C₇₃	—	4	1	no	—
298	C₂×C₄×C₇₃	—	4	2	no	—
299	C₂×C₄×C₇₃	—	4	2	no	—
300	C₂×C₄×C₇₃	—	4	2	no	—
301	C₂×C₄×C₇₃	—	4	1	no	—
302	C₂×C₄×C₇₃	—	4	2	no	—
303	C₂×C₄×C₇₃	—	4	1	no	—
304	C₂×C₄×C₇₃	—	4	1	no	—
305	C₂×C₄×C₇₃	—	4	2	no	—
306	C₂×C₄×C₇₃	—	4	1	no	—
307	C₂×C₄×C₇₃	—	4	1	no	—
308	C₂×C₄×C₇₃	—	4	2	no	—
309	C₂×C₄×C₇₃	—	4	2	no	—
310	C₂×C₄×C₇₃	—	4	2	no	—
311	C₂×C₄×C₇₃	—	4	1	no	—
312	C₂×C₄×C₇₃	—	4	1	no	—
313	C₂×C₄×C₇₃	—	4	1	no	—
314	C₂×C₄×C₇₃	—	4	16	no	—
315	C₂×C₄×C₇₃	—	4	2	no	—
316	C₂×C₄×C₇₃	—	4	2	no	—
317	C₂×C₄×C₇₃	—	4	2	no	—
318	C₂×C₄×C₇₃	—	4	2	no	—
319	C₂×C₄×C₇₃	—	4	2	no	—
320	C₂×C₄×C₇₃	—	4	2	no	—
321	C₂×C₄×C₇₃	—	4	2	no	—
322	C₂×C₄×C₇₃	#117	1	4	yes	—
323	C₂×C₄×C₇₃	C₄×D₄	1	4	yes	—
324	C₂×C₄×C₇₃	C₄×D₄	1	4	yes	—
325	C₂×C₄×C₇₃	#121	1	4	yes	—
326	C₂×C₄×C₇₃	C₂²⋊Q₈	1	4	yes	—
327	C₂×C₄×C₇₃	#123	1	4	yes	—
328	C₂×C₄×C₇₃	#124	1	4	yes	—
329	C₂×C₄×C₇₃	#126	1	4	yes	—
330	C₂²×C₇₃	—	2	4	no	—
331	C₂²×C₇₃	—	2	4	no	—
332	C₂²×C₇₃	—	2	4	no	—
333	C₂²×C₇₃	—	4	2	no	—
334	C₂²×C₇₃	—	4	2	no	—
335	C₂²×C₇₃	—	4	2	no	—
336	C₂²×C₇₃	—	4	2	no	—
337	C₂²×C₇₃	—	4	2	no	—
338	C₂²×C₇₃	—	4	2	no	—
339	C₂²×C₇₃	—	4	2	no	—
340	C₂²×C₇₃	—	4	2	no	—
341	C₂²×C₇₃	—	4	2	no	—
342	C₂²×C₇₃	—	4	2	no	—
343	C₂²×C₇₃	—	4	2	no	—
344	C₂²×C₇₃	—	4	2	no	—
345	C₂²×C₇₃	C₂×#117	1	1	yes	characteristic
346	C₂²×C₇₃	C₂×C₄×D₄	1	1	yes	characteristic
347	C₂²×C₇₃	C₂×C₄×D₄	1	1	yes	characteristic
348	C₂²×C₇₃	C₂×C₄×Q₈	1	1	yes	characteristic
349	C₂²×C₇₃	C₄×#41	1	1	yes	characteristic
350	C₂²×C₇₃	#518	1	1	yes	characteristic
351	C₂²×C₇₃	#520	1	1	yes	characteristic
352	C₂²×C₇₃	C₂×#121	1	1	yes	characteristic
353	C₂²×C₇₃	C₂×C₂²⋊Q₈	1	1	yes	characteristic
354	C₂²×C₇₃	C₂×#123	1	1	yes	characteristic
355	C₂²×C₇₃	#525	1	1	yes	characteristic
356	C₂²×C₇₃	C₂×#124	1	1	yes	characteristic
357	C₂²×C₇₃	C₂×#126	1	1	yes	characteristic
358	C₂²×C₇₃	#529	1	1	yes	characteristic
359	C₂²×C₇₃	#533	1	1	yes	characteristic
360	C₂²×C₇₃	#535	1	1	yes	characteristic
361	C₂²×C₇₃	#537	1	1	yes	characteristic
362	C₂²×C₇₃	#540	1	1	yes	characteristic
363	C₂²×C₇₃	#542	1	1	yes	characteristic
364	C₂²×C₇₃	#546	1	1	yes	characteristic
365	C₂²×C₇₃	#546	1	1	yes	characteristic
366	C₂²×C₇₃	D₄×Q₈	1	1	yes	characteristic
367	C₂²×C₇₃	#550	1	1	yes	characteristic
368	C₂²×C₇₃	#552	1	1	yes	characteristic
369	C₂²×C₇₃	#553	1	1	yes	characteristic
370	C₂²×C₇₃	#553	1	1	yes	characteristic
371	C₂²×C₇₃	#553	1	1	yes	characteristic
372	C₂²×C₇₃	#553	1	1	yes	characteristic
373	C₂²×C₇₃	#553	1	1	yes	characteristic
374	C₂²×C₇₃	#554	1	1	yes	characteristic
375	C₂²×C₇₃	#554	1	1	yes	characteristic
376	C₂²×C₇₃	#554	1	1	yes	characteristic
377	C₂²×C₇₃	#555	1	1	yes	characteristic
378	C₂²×C₇₃	#556	1	1	yes	characteristic
379	C₂²×C₇₃	#556	1	1	yes	characteristic
380	C₄×C₇₃	—	2	4	no	—
381	C₄×C₇₃	—	4	4	no	—
382	C₄×C₇₃	—	4	4	no	—
383	C₄×C₇₃	—	4	2	no	—
384	C₄×C₇₃	—	4	4	no	—
385	C₄×C₇₃	—	4	2	no	—
386	C₄×C₇₃	—	4	2	no	—
387	C₄×C₇₃	—	4	2	no	—
388	C₄×C₇₃	—	8	2	no	—
389	C₄×C₇₃	#388	1	8	yes	—
390	#13993	C₇₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
391	C₂×C₇₃	—	4	4	no	—
392	C₂×C₇₃	C₂×#388	1	1	yes	characteristic
393	C₂×C₇₃	C₄×C₂²⋊Q₈	1	1	yes	characteristic
394	C₂×C₇₃	#2324	1	1	yes	characteristic
395	C₂×C₇₃	#2345	1	1	yes	characteristic
396	C₂×C₇₃	#2347	1	1	yes	characteristic
397	C₂×C₇₃	#2360	1	1	yes	characteristic
398	C₂×C₇₃	#2363	1	1	yes	characteristic
399	C₂×C₇₃	#2485	1	1	yes	characteristic
400	C₂×C₇₃	#2487	1	1	yes	characteristic
401	C₂×C₇₃	#2490	1	1	yes	characteristic
402	C₂×C₇₃	#2492	1	1	yes	characteristic
403	C₂×C₇₃	#2494	1	1	yes	characteristic
404	C₂×C₇₃	#2497	1	1	yes	characteristic
405	C₂×C₇₃	#2535	1	1	yes	characteristic
406	C₂×C₇₃	#2538	1	1	yes	characteristic
407	C₂×#389	C₂×C₇₃	1	1	yes	characteristic, complemented
408	C₂×#380	C₂×C₇₃	1	1	yes	characteristic
409	C₂×#380	C₂×C₇₃	1	1	yes	characteristic
410	C₂×C₄×C₄⋊C₄	C₂×C₇₃	1	1	yes	characteristic, complemented
411	C₂×C₄×C₂²⋊C₄	C₂×C₇₃	1	1	yes	characteristic
412	#1443	C₂×C₇₃	1	2	yes	complemented
413	#1439	C₂×C₇₃	1	2	yes	—
414	#1437	C₂×C₇₃	1	2	yes	—
415	#1436	C₂×C₇₃	1	2	yes	complemented
416	C₄⋊#95	C₂×C₇₃	1	1	yes	characteristic, complemented
417	C₄⋊#95	C₂×C₇₃	1	1	yes	characteristic, complemented
418	C₇₃	#13993	1	1	yes	characteristic, direct product factor, Sylow
419	C₂⁴×C₄	C₂²×C₇₃	1	1	yes	characteristic
420	C₂²×C₄⋊C₄	C₂²×C₇₃	1	1	yes	characteristic
421	C₂²×C₄⋊C₄	C₂²×C₇₃	1	2	yes	—
422	C₂²×C₄⋊C₄	C₂²×C₇₃	1	1	yes	characteristic
423	C₂²×C₄⋊C₄	C₂²×C₇₃	1	1	yes	characteristic
424	C₂²×C₄⋊C₄	C₂²×C₇₃	1	1	yes	characteristic
425	C₂²×C₂²⋊C₄	C₂²×C₇₃	1	1	yes	characteristic
426	C₂²×C₂²⋊C₄	C₂²×C₇₃	1	2	yes	—
427	C₂²×C₂²⋊C₄	C₂²×C₇₃	1	1	yes	characteristic
428	C₂²×C₂²⋊C₄	C₂²×C₇₃	1	2	yes	—
429	C₂²×C₄²	C₂²×C₇₃	1	1	yes	characteristic
430	C₂²×C₄²	C₂²×C₇₃	1	1	yes	characteristic
431	C₂²×C₄²	C₂²×C₇₃	1	2	yes	—
432	#389	—	2	4	no	—
433	#380	—	2	4	no	—
434	#380	C₄×C₇₃	1	8	yes	complemented
435	C₄×C₄⋊C₄	—	2	4	no	—
436	C₄×C₂²⋊C₄	—	2	4	no	—
437	C₂×#95	C₂²×C₇₃	1	2	yes	—
438	C₂×#95	C₂²×C₇₃	1	1	yes	characteristic
439	C₂×#95	C₂²×C₇₃	1	2	yes	—
440	C₂×#95	C₂²×C₇₃	1	2	yes	—
441	C₂×#95	C₂²×C₇₃	1	2	yes	—
442	C₂×#95	C₂²×C₇₃	1	1	yes	characteristic
443	C₂×#95	C₂²×C₇₃	1	2	yes	—
444	C₂×#95	C₂²×C₇₃	1	2	yes	—
445	C₂×#95	C₂²×C₇₃	1	2	yes	—
446	C₂×#95	C₂²×C₇₃	1	2	yes	—
447	C₂⁵	C₂³×C₇₃	1	1	yes	characteristic
448	C₂³×C₄	—	2	2	no	—
449	C₂³×C₄	—	2	2	no	—
450	C₂³×C₄	—	2	2	no	—
451	C₂³×C₄	—	2	2	no	—
452	C₂³×C₄	—	2	2	no	—
453	C₂³×C₄	—	2	2	no	—
454	C₂³×C₄	C₂×C₄×C₇₃	1	4	yes	—
455	C₂³×C₄	C₂³×C₇₃	1	2	yes	—
456	C₂³×C₄	C₂³×C₇₃	1	2	yes	—
457	C₂³×C₄	C₂³×C₇₃	1	2	yes	—
458	C₂³×C₄	C₂³×C₇₃	1	1	yes	characteristic
459	C₂³×C₄	C₂³×C₇₃	1	2	yes	—
460	C₂³×C₄	C₂³×C₇₃	1	1	yes	characteristic
461	C₂³×C₄	C₂³×C₇₃	1	1	yes	characteristic
462	C₂³×C₄	C₂³×C₇₃	1	1	yes	characteristic
463	C₂³×C₄	C₂³×C₇₃	1	1	yes	characteristic
464	C₂³×C₄	C₂³×C₇₃	1	1	yes	characteristic
465	C₂×C₄⋊C₄	—	2	2	no	—
466	C₂×C₄⋊C₄	—	2	2	no	—
467	C₂×C₄⋊C₄	—	2	2	no	—
468	C₂×C₄⋊C₄	—	2	2	no	—
469	C₂×C₄⋊C₄	—	2	2	no	—
470	C₂×C₄⋊C₄	—	2	2	no	—
471	C₂×C₄⋊C₄	—	2	2	no	—
472	C₂×C₄⋊C₄	—	2	4	no	—
473	C₂×C₄⋊C₄	—	2	4	no	—
474	C₂×C₄⋊C₄	—	2	2	no	—
475	C₂×C₄⋊C₄	—	2	2	no	—
476	C₂×C₄⋊C₄	—	4	2	no	—
477	C₂×C₄⋊C₄	C₂×C₄×C₇₃	1	4	yes	—
478	C₂×C₄⋊C₄	C₂×C₄×C₇₃	1	4	yes	—
479	C₂×C₄⋊C₄	D₄×C₇₃	1	4	yes	—
480	C₂×C₂²⋊C₄	—	2	2	no	—
481	C₂×C₂²⋊C₄	—	2	2	no	—
482	C₂×C₂²⋊C₄	—	2	2	no	—
483	C₂×C₂²⋊C₄	—	2	2	no	—
484	C₂×C₂²⋊C₄	—	2	2	no	—
485	C₂×C₂²⋊C₄	—	2	4	no	—
486	C₂×C₂²⋊C₄	—	2	4	no	—
487	C₂×C₂²⋊C₄	—	4	2	no	—
488	C₂×C₂²⋊C₄	—	4	2	no	—
489	C₂×C₂²⋊C₄	—	4	2	no	—
490	C₂×C₂²⋊C₄	C₂×C₄×C₇₃	1	8	yes	—
491	C₂×C₂²⋊C₄	Q₈×C₇₃	1	4	yes	—
492	C₂×C₄²	—	2	2	no	—
493	C₂×C₄²	—	2	2	no	—
494	C₂×C₄²	—	2	2	no	—
495	C₂×C₄²	—	2	4	no	—
496	C₂×C₄²	—	2	2	no	—
497	C₂×C₄²	—	2	2	no	—
498	C₂×C₄²	—	4	2	no	—
499	C₂×C₄²	—	4	2	no	—
500	C₂×C₄²	D₄×C₇₃	1	4	yes	—
501	#95	—	2	2	no	—
502	#95	—	2	2	no	—
503	#95	—	2	4	no	—
504	#95	—	2	4	no	—
505	#95	—	2	4	no	—
506	#95	—	2	4	no	—
507	#95	—	4	2	no	—
508	#95	—	4	2	no	—
509	#95	—	4	2	no	—
510	#95	C₂×C₄×C₇₃	1	8	yes	—
511	C₂⁴	—	2	1	no	—
512	C₂⁴	—	2	1	no	—
513	C₂⁴	—	2	1	no	—
514	C₂⁴	—	2	1	no	—
515	C₂⁴	—	2	1	no	—
516	C₂⁴	—	2	1	no	—
517	C₂⁴	—	2	1	no	—
518	C₂⁴	—	2	1	no	—
519	C₂⁴	—	2	1	no	—
520	C₂⁴	—	2	1	no	—
521	C₂⁴	—	2	1	no	—
522	C₂⁴	—	2	1	no	—
523	C₂⁴	C₂²×C₄×C₇₃	1	2	yes	—
524	C₂⁴	C₂×Q₈×C₇₃	1	2	yes	—
525	C₂⁴	#41×C₇₃	1	2	yes	—
526	C₂⁴	C₂⁴×C₇₃	1	1	yes	characteristic
527	C₂²×C₄	—	2	1	no	—
528	C₂²×C₄	—	2	1	no	—
529	C₂²×C₄	—	2	1	no	—
530	C₂²×C₄	—	2	1	no	—
531	C₂²×C₄	—	2	1	no	—
532	C₂²×C₄	—	2	1	no	—
533	C₂²×C₄	—	2	1	no	—
534	C₂²×C₄	—	2	1	no	—
535	C₂²×C₄	—	2	1	no	—
536	C₂²×C₄	—	2	2	no	—
537	C₂²×C₄	—	2	2	no	—
538	C₂²×C₄	—	2	2	no	—
539	C₂²×C₄	—	2	1	no	—
540	C₂²×C₄	—	2	2	no	—
541	C₂²×C₄	—	2	1	no	—
542	C₂²×C₄	—	2	1	no	—
543	C₂²×C₄	—	2	1	no	—
544	C₂²×C₄	—	2	1	no	—
545	C₂²×C₄	—	2	1	no	—
546	C₂²×C₄	—	2	1	no	—
547	C₂²×C₄	—	2	1	no	—
548	C₂²×C₄	—	2	1	no	—
549	C₂²×C₄	—	2	2	no	—
550	C₂²×C₄	—	2	2	no	—
551	C₂²×C₄	—	2	2	no	—
552	C₂²×C₄	—	2	2	no	—
553	C₂²×C₄	—	2	2	no	—
554	C₂²×C₄	—	2	2	no	—
555	C₂²×C₄	—	2	1	no	—
556	C₂²×C₄	—	2	1	no	—
557	C₂²×C₄	—	2	1	no	—
558	C₂²×C₄	—	2	1	no	—
559	C₂²×C₄	—	2	1	no	—
560	C₂²×C₄	—	2	1	no	—
561	C₂²×C₄	—	2	1	no	—
562	C₂²×C₄	—	2	2	no	—
563	C₂²×C₄	—	2	2	no	—
564	C₂²×C₄	—	2	2	no	—
565	C₂²×C₄	—	2	2	no	—
566	C₂²×C₄	—	2	2	no	—
567	C₂²×C₄	—	2	2	no	—
568	C₂²×C₄	—	2	2	no	—
569	C₂²×C₄	—	2	1	no	—
570	C₂²×C₄	—	2	2	no	—
571	C₂²×C₄	—	2	1	no	—
572	C₂²×C₄	—	2	1	no	—
573	C₂²×C₄	—	2	8	no	—
574	C₂²×C₄	—	2	8	no	—
575	C₂²×C₄	—	2	8	no	—
576	C₂²×C₄	—	2	2	no	—
577	C₂²×C₄	—	2	2	no	—
578	C₂²×C₄	—	2	2	no	—
579	C₂²×C₄	—	2	2	no	—
580	C₂²×C₄	—	2	2	no	—
581	C₂²×C₄	—	2	2	no	—
582	C₂²×C₄	—	2	2	no	—
583	C₂²×C₄	—	4	4	no	—
584	C₂²×C₄	—	4	4	no	—
585	C₂²×C₄	—	4	4	no	—
586	C₂²×C₄	—	4	4	no	—
587	C₂²×C₄	C₂²×C₄×C₇₃	1	2	yes	—
588	C₂²×C₄	C₂²×C₄×C₇₃	1	4	yes	—
589	C₂²×C₄	C₂²×C₄×C₇₃	1	4	yes	—
590	C₂²×C₄	C₂²×C₄×C₇₃	1	2	yes	—
591	C₂²×C₄	C₂×D₄×C₇₃	1	2	yes	—
592	C₂²×C₄	C₂×D₄×C₇₃	1	4	yes	—
593	C₂²×C₄	C₂×D₄×C₇₃	1	2	yes	—
594	C₂²×C₄	C₂×D₄×C₇₃	1	2	yes	—
595	C₂²×C₄	C₂×D₄×C₇₃	1	2	yes	—
596	C₂²×C₄	C₂×Q₈×C₇₃	1	2	yes	—
597	C₂²×C₄	C₂×Q₈×C₇₃	1	2	yes	—
598	C₂²×C₄	#41×C₇₃	1	2	yes	—
599	C₂²×C₄	#41×C₇₃	1	2	yes	—
600	C₂²×C₄	#41×C₇₃	1	2	yes	—
601	C₂²×C₄	#41×C₇₃	1	2	yes	—
602	C₂²×C₄	#41×C₇₃	1	2	yes	—
603	C₂²×C₄	#41×C₇₃	1	2	yes	—
604	C₄⋊C₄	—	2	8	no	—
605	C₄⋊C₄	—	2	8	no	—
606	C₄⋊C₄	—	2	8	no	—
607	C₄⋊C₄	—	4	8	no	—
608	C₄⋊C₄	—	4	4	no	—
609	C₂²⋊C₄	—	2	8	no	—
610	C₂²⋊C₄	—	2	8	no	—
611	C₂²⋊C₄	—	4	8	no	—
612	C₂²⋊C₄	—	4	8	no	—
613	C₄²	—	2	8	no	—
614	C₄²	—	4	8	no	—
615	C₄²	—	4	4	no	—
616	C₂³	—	2	2	no	—
617	C₂³	—	2	2	no	—
618	C₂³	—	2	2	no	—
619	C₂³	—	2	2	no	—
620	C₂³	—	2	2	no	—
621	C₂³	—	2	2	no	—
622	C₂³	—	2	2	no	—
623	C₂³	—	2	2	no	—
624	C₂³	—	2	2	no	—
625	C₂³	—	2	2	no	—
626	C₂³	—	2	2	no	—
627	C₂³	—	2	2	no	—
628	C₂³	—	2	2	no	—
629	C₂³	—	2	2	no	—
630	C₂³	—	2	2	no	—
631	C₂³	—	2	2	no	—
632	C₂³	—	2	2	no	—
633	C₂³	—	2	2	no	—
634	C₂³	—	4	1	no	—
635	C₂³	—	4	1	no	—
636	C₂³	—	4	1	no	—
637	C₂³	—	4	1	no	—
638	C₂³	—	4	1	no	—
639	C₂³	—	4	1	no	—
640	C₂³	—	4	1	no	—
641	C₂³	—	4	1	no	—
642	C₂³	—	4	1	no	—
643	C₂³	—	4	1	no	—
644	C₂³	—	4	1	no	—
645	C₂³	—	4	1	no	—
646	C₂³	—	4	1	no	—
647	C₂³	—	4	1	no	—
648	C₂³	—	4	1	no	—
649	C₂³	—	4	1	no	—
650	C₂³	C₄×Q₈×C₇₃	1	4	yes	—
651	C₂³	C₂³×C₄×C₇₃	1	1	yes	characteristic
652	C₂³	C₂²×D₄×C₇₃	1	1	yes	characteristic
653	C₂³	C₂²×D₄×C₇₃	1	1	yes	characteristic
654	C₂³	C₂²×Q₈×C₇₃	1	1	yes	characteristic
655	C₂³	C₂×#41×C₇₃	1	1	yes	characteristic
656	C₂³	C₂×#41×C₇₃	1	1	yes	characteristic
657	C₂³	C₂×#41×C₇₃	1	1	yes	characteristic
658	C₂³	C₂×#41×C₇₃	1	1	yes	characteristic
659	C₂³	C₂×#41×C₇₃	1	1	yes	characteristic
660	C₂³	C₂×#41×C₇₃	1	1	yes	characteristic
661	C₂³	C₂×#41×C₇₃	1	1	yes	characteristic
662	C₂³	H(5,𝔽₂)×C₇₃	1	1	yes	characteristic
663	C₂³	H(5,𝔽₂)×C₇₃	1	1	yes	characteristic
664	C₂³	H(5,𝔽₂)×C₇₃	1	1	yes	characteristic
665	C₂³	2₋¹⁺⁴×C₇₃	1	1	yes	characteristic
666	C₂×C₄	—	2	2	no	—
667	C₂×C₄	—	2	2	no	—
668	C₂×C₄	—	2	2	no	—
669	C₂×C₄	—	2	2	no	—
670	C₂×C₄	—	2	2	no	—
671	C₂×C₄	—	2	2	no	—
672	C₂×C₄	—	2	2	no	—
673	C₂×C₄	—	2	4	no	—
674	C₂×C₄	—	2	4	no	—
675	C₂×C₄	—	2	2	no	—
676	C₂×C₄	—	2	2	no	—
677	C₂×C₄	—	2	4	no	—
678	C₂×C₄	—	2	4	no	—
679	C₂×C₄	—	2	4	no	—
680	C₂×C₄	—	2	4	no	—
681	C₂×C₄	—	2	4	no	—
682	C₂×C₄	—	2	2	no	—
683	C₂×C₄	—	2	2	no	—
684	C₂×C₄	—	2	2	no	—
685	C₂×C₄	—	2	2	no	—
686	C₂×C₄	—	2	2	no	—
687	C₂×C₄	—	2	4	no	—
688	C₂×C₄	—	2	2	no	—
689	C₂×C₄	—	2	4	no	—
690	C₂×C₄	—	2	2	no	—
691	C₂×C₄	—	2	2	no	—
692	C₂×C₄	—	2	2	no	—
693	C₂×C₄	—	4	1	no	—
694	C₂×C₄	—	4	1	no	—
695	C₂×C₄	—	4	1	no	—
696	C₂×C₄	—	4	1	no	—
697	C₂×C₄	—	4	2	no	—
698	C₂×C₄	—	4	1	no	—
699	C₂×C₄	—	4	1	no	—
700	C₂×C₄	—	4	2	no	—
701	C₂×C₄	—	4	2	no	—
702	C₂×C₄	—	4	1	no	—
703	C₂×C₄	—	4	1	no	—
704	C₂×C₄	—	4	2	no	—
705	C₂×C₄	—	4	2	no	—
706	C₂×C₄	—	4	2	no	—
707	C₂×C₄	—	4	2	no	—
708	C₂×C₄	—	4	1	no	—
709	C₂×C₄	—	4	1	no	—
710	C₂×C₄	—	4	2	no	—
711	C₂×C₄	—	4	1	no	—
712	C₂×C₄	—	4	1	no	—
713	C₂×C₄	—	4	1	no	—
714	C₂×C₄	—	4	2	no	—
715	C₂×C₄	—	4	2	no	—
716	C₂×C₄	—	4	2	no	—
717	C₂×C₄	—	4	1	no	—
718	C₂×C₄	—	4	2	no	—
719	C₂×C₄	—	4	1	no	—
720	C₂×C₄	—	4	1	no	—
721	C₂×C₄	—	4	16	no	—
722	C₂×C₄	—	4	2	no	—
723	C₂×C₄	—	4	2	no	—
724	C₂×C₄	—	4	2	no	—
725	C₂×C₄	—	4	2	no	—
726	C₂×C₄	—	4	2	no	—
727	C₂×C₄	—	4	2	no	—
728	C₂×C₄	—	4	2	no	—
729	C₂×C₄	#117×C₇₃	1	4	yes	—
730	C₂×C₄	C₄×D₄×C₇₃	1	4	yes	—
731	C₂×C₄	C₄×D₄×C₇₃	1	4	yes	—
732	C₂×C₄	#121×C₇₃	1	4	yes	—
733	C₂×C₄	C₂²⋊Q₈×C₇₃	1	4	yes	—
734	C₂×C₄	#123×C₇₃	1	4	yes	—
735	C₂×C₄	#124×C₇₃	1	4	yes	—
736	C₂×C₄	#126×C₇₃	1	4	yes	—
737	C₂²	—	2	4	no	—
738	C₂²	—	2	4	no	—
739	C₂²	—	2	4	no	—
740	C₂²	—	4	2	no	—
741	C₂²	—	4	2	no	—
742	C₂²	—	4	2	no	—
743	C₂²	—	4	2	no	—
744	C₂²	—	4	2	no	—
745	C₂²	—	4	2	no	—
746	C₂²	—	4	2	no	—
747	C₂²	—	4	2	no	—
748	C₂²	—	4	2	no	—
749	C₂²	—	4	2	no	—
750	C₂²	—	4	2	no	—
751	C₂²	—	4	2	no	—
752	C₂²	C₂×#117×C₇₃	1	1	yes	characteristic
753	C₂²	C₂×C₄×D₄×C₇₃	1	1	yes	characteristic
754	C₂²	C₂×C₄×D₄×C₇₃	1	1	yes	characteristic
755	C₂²	C₂×C₄×Q₈×C₇₃	1	1	yes	characteristic
756	C₂²	C₄×#41×C₇₃	1	1	yes	characteristic
757	C₂²	#518×C₇₃	1	1	yes	characteristic
758	C₂²	#520×C₇₃	1	1	yes	characteristic
759	C₂²	C₂×#121×C₇₃	1	1	yes	characteristic
760	C₂²	C₂×C₂²⋊Q₈×C₇₃	1	1	yes	characteristic
761	C₂²	C₂×#123×C₇₃	1	1	yes	characteristic
762	C₂²	#525×C₇₃	1	1	yes	characteristic
763	C₂²	C₂×#124×C₇₃	1	1	yes	characteristic
764	C₂²	C₂×#126×C₇₃	1	1	yes	characteristic
765	C₂²	#529×C₇₃	1	1	yes	characteristic
766	C₂²	#533×C₇₃	1	1	yes	characteristic
767	C₂²	#535×C₇₃	1	1	yes	characteristic
768	C₂²	#537×C₇₃	1	1	yes	characteristic
769	C₂²	#540×C₇₃	1	1	yes	characteristic
770	C₂²	#542×C₇₃	1	1	yes	characteristic
771	C₂²	#546×C₇₃	1	1	yes	characteristic
772	C₂²	#546×C₇₃	1	1	yes	characteristic
773	C₂²	D₄×Q₈×C₇₃	1	1	yes	characteristic
774	C₂²	#550×C₇₃	1	1	yes	characteristic
775	C₂²	#552×C₇₃	1	1	yes	characteristic
776	C₂²	#553×C₇₃	1	1	yes	characteristic
777	C₂²	#553×C₇₃	1	1	yes	characteristic
778	C₂²	#553×C₇₃	1	1	yes	characteristic
779	C₂²	#553×C₇₃	1	1	yes	characteristic
780	C₂²	#553×C₇₃	1	1	yes	characteristic
781	C₂²	#554×C₇₃	1	1	yes	characteristic
782	C₂²	#554×C₇₃	1	1	yes	characteristic
783	C₂²	#554×C₇₃	1	1	yes	characteristic
784	C₂²	#555×C₇₃	1	1	yes	characteristic
785	C₂²	#556×C₇₃	1	1	yes	characteristic
786	C₂²	#556×C₇₃	1	1	yes	characteristic
787	C₄	—	2	4	no	—
788	C₄	—	4	2	no	—
789	C₄	—	4	4	no	—
790	C₄	—	4	2	no	—
791	C₄	—	4	2	no	—
792	C₄	—	4	2	no	—
793	C₄	—	4	4	no	—
794	C₄	—	4	4	no	—
795	C₄	—	8	2	no	—
796	C₄	#388×C₇₃	1	8	yes	—
797	C₂	—	4	4	no	—
798	C₂	C₂×#388×C₇₃	1	1	yes	characteristic
799	C₂	C₄×C₂²⋊Q₈×C₇₃	1	1	yes	characteristic
800	C₂	C₇₃×#2324	1	1	yes	characteristic
801	C₂	C₇₃×#2345	1	1	yes	characteristic
802	C₂	C₇₃×#2347	1	1	yes	characteristic
803	C₂	C₇₃×#2360	1	1	yes	characteristic
804	C₂	C₇₃×#2363	1	1	yes	characteristic
805	C₂	C₇₃×#2485	1	1	yes	characteristic
806	C₂	C₇₃×#2487	1	1	yes	characteristic
807	C₂	C₇₃×#2490	1	1	yes	characteristic
808	C₂	C₇₃×#2492	1	1	yes	characteristic
809	C₂	C₇₃×#2494	1	1	yes	characteristic
810	C₂	C₇₃×#2497	1	1	yes	characteristic
811	C₂	C₇₃×#2535	1	1	yes	characteristic
812	C₂	C₇₃×#2538	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂⁴×C₇₃	C₂⁴
commutator	C₂³	C₂³×C₄×C₇₃
Frattini, cosocle	C₂⁴	C₂⁴×C₇₃
prime radical	C₂⁵×C₇₃	C₂³
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂⁴×C₇₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×#389×C₇₃	C₂	semidirect
4. C₂×C₄×C₄⋊C₄×C₇₃	C₂	semidirect
6. C₇₃×#1443	C₂	semidirect
9. C₇₃×#1436	C₂	semidirect
10. C₇₃×C₄⋊#95	C₂	semidirect
11. C₇₃×C₄⋊#95	C₂	semidirect
27. #380×C₇₃	C₄	semidirect
390. #13993	C₇₃	direct (N × H)
407. C₂×#389	C₂×C₇₃	semidirect
410. C₂×C₄×C₄⋊C₄	C₂×C₇₃	semidirect
412. #1443	C₂×C₇₃	semidirect
415. #1436	C₂×C₇₃	semidirect
416. C₄⋊#95	C₂×C₇₃	semidirect
417. C₄⋊#95	C₂×C₇₃	semidirect
418. C₇₃	#13993	direct (N × H)
434. #380	C₄×C₇₃	semidirect

Maximal subgroups

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

subgroup	index
C₂×#389×C₇₃	2
C₂×#380×C₇₃	2
C₂×C₄×C₄⋊C₄×C₇₃	2
C₂×C₄×C₂²⋊C₄×C₇₃	2
C₇₃×#1443	2
C₇₃×#1439	2
C₇₃×#1437	2
C₇₃×#1436	2
C₇₃×C₄⋊#95	2
#13993	73

Subgroups — C73×#13993 #32923397

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₃×#13993 #32923397