Subgroups — C₇₃×#25010 #32934414

Order 18688.

982 conjugacy classes of subgroups.

The subgroup lattice has 526 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#480×C₇₃	C₂	1	2	yes	maximal, complemented
2	C₇₃×#2537	C₂	1	1	yes	maximal, characteristic
3	D₄×C₄⋊C₄×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₇₃×#2075	C₂	1	2	yes	maximal, complemented
5	C₇₃×#2033	C₂	1	2	yes	maximal, complemented
6	C₇₃×#1954	C₂	1	1	yes	maximal, characteristic, complemented
7	C₇₃×#1947	C₂	1	1	yes	maximal, characteristic, complemented
8	C₇₃×#1852	C₂	1	2	yes	maximal, complemented
9	C₇₃×#1845	C₂	1	1	yes	maximal, characteristic, complemented
10	C₇₃×#1802	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄×#102×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#121×C₇₃	—	2	1	no	—
13	C₂×#121×C₇₃	C₂²	1	2	yes	—
14	C₂×C₄×D₄×C₇₃	—	2	1	no	—
15	C₂×C₄×D₄×C₇₃	C₂²	1	1	yes	characteristic
16	C₂×C₄×D₄×C₇₃	C₂²	1	1	yes	characteristic
17	C₂²×C₄⋊C₄×C₇₃	C₂²	1	2	yes	—
18	#480×C₇₃	—	2	8	no	—
19	C₂×#107×C₇₃	C₂²	1	2	yes	—
20	C₂×#107×C₇₃	C₂²	1	2	yes	—
21	C₂×#107×C₇₃	C₂²	1	2	yes	—
22	C₂×C₄⋊C₈×C₇₃	C₂²	1	1	yes	characteristic
23	C₂×#102×C₇₃	C₂²	1	1	yes	characteristic
24	C₂×#102×C₇₃	C₂²	1	2	yes	—
25	C₂×#102×C₇₃	C₂²	1	1	yes	characteristic
26	C₂×C₂²⋊C₈×C₇₃	C₂²	1	2	yes	—
27	C₂×C₂²⋊C₈×C₇₃	C₂²	1	2	yes	—
28	C₂×C₄×C₈×C₇₃	C₂²	1	1	yes	characteristic
29	#394×C₇₃	—	2	2	no	—
30	#389×C₇₃	—	2	1	no	—
31	#385×C₇₃	—	2	2	no	—
32	#384×C₇₃	C₂²	1	1	yes	characteristic
33	#384×C₇₃	C₂²	1	1	yes	characteristic
34	#380×C₇₃	—	2	1	no	—
35	#380×C₇₃	C₂²	1	2	yes	—
36	#380×C₇₃	C₂²	1	2	yes	—
37	C₄×C₄⋊C₄×C₇₃	C₂²	1	1	yes	characteristic
38	#340×C₇₃	C₂²	1	2	yes	—
39	#340×C₇₃	C₂²	1	1	yes	characteristic
40	#340×C₇₃	C₂²	1	1	yes	characteristic
41	#340×C₇₃	C₂²	1	2	yes	—
42	C₂²×D₄×C₇₃	—	2	2	no	—
43	C₂²×D₄×C₇₃	D₄	1	1	yes	characteristic
44	C₂²×D₄×C₇₃	C₂³	1	1	yes	characteristic
45	C₂³×C₄×C₇₃	—	2	2	no	—
46	C₂³×C₄×C₇₃	—	2	1	no	—
47	C₂³×C₄×C₇₃	C₂³	1	2	yes	—
48	C₂²×C₈×C₇₃	C₂³	1	2	yes	—
49	C₂²×C₈×C₇₃	C₂³	1	1	yes	characteristic
50	C₂²×C₈×C₇₃	C₂³	1	1	yes	characteristic
51	#121×C₇₃	—	2	4	no	—
52	#121×C₇₃	—	4	2	no	—
53	#121×C₇₃	—	4	4	no	—
54	C₄×D₄×C₇₃	—	2	2	no	—
55	C₄×D₄×C₇₃	—	2	2	no	—
56	C₄×D₄×C₇₃	—	2	2	no	—
57	C₄×D₄×C₇₃	—	2	2	no	—
58	C₄×D₄×C₇₃	—	4	4	no	—
59	C₂×C₄⋊C₄×C₇₃	—	2	4	no	—
60	C₂×C₄⋊C₄×C₇₃	—	2	1	no	—
61	C₂×C₄⋊C₄×C₇₃	—	2	1	no	—
62	C₂×C₄⋊C₄×C₇₃	—	2	2	no	—
63	C₂×C₄⋊C₄×C₇₃	—	2	1	no	—
64	C₂×C₄⋊C₄×C₇₃	—	2	1	no	—
65	C₂×C₄⋊C₄×C₇₃	—	4	2	no	—
66	C₂×C₄⋊C₄×C₇₃	D₄	1	1	yes	characteristic
67	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
68	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
69	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
70	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
71	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
72	C₂×C₂²⋊C₄×C₇₃	—	2	2	no	—
73	C₂×C₂²⋊C₄×C₇₃	—	2	2	no	—
74	C₂×C₂²⋊C₄×C₇₃	—	2	2	no	—
75	C₂×C₂²⋊C₄×C₇₃	—	2	1	no	—
76	C₂×C₂²⋊C₄×C₇₃	D₄	1	2	yes	—
77	C₂×C₄²×C₇₃	—	2	1	no	—
78	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
79	#107×C₇₃	—	2	4	no	—
80	#107×C₇₃	—	2	4	no	—
81	#107×C₇₃	—	4	2	no	—
82	C₄⋊C₈×C₇₃	—	2	2	no	—
83	#102×C₇₃	—	2	4	no	—
84	#102×C₇₃	—	2	2	no	—
85	#102×C₇₃	D₄	1	4	yes	complemented
86	C₂²⋊C₈×C₇₃	—	2	4	no	—
87	C₂²⋊C₈×C₇₃	—	2	4	no	—
88	C₄×C₈×C₇₃	—	2	2	no	—
89	#95×C₇₃	—	2	1	no	—
90	#95×C₇₃	—	2	2	no	—
91	#95×C₇₃	—	2	2	no	—
92	C₂⁴×C₇₃	—	2	1	no	—
93	C₂⁴×C₇₃	C₂×D₄	1	2	yes	—
94	C₂×D₄×C₇₃	—	2	2	no	—
95	C₂×D₄×C₇₃	—	2	2	no	—
96	C₂×D₄×C₇₃	—	2	1	no	—
97	C₂×D₄×C₇₃	—	2	1	no	—
98	C₂×D₄×C₇₃	—	2	1	no	—
99	C₂×D₄×C₇₃	—	2	1	no	—
100	C₂×D₄×C₇₃	—	2	1	no	—
101	C₂×D₄×C₇₃	—	4	4	no	—
102	C₂×D₄×C₇₃	—	4	4	no	—
103	C₂×D₄×C₇₃	—	8	2	no	—
104	C₂×D₄×C₇₃	D₈	1	4	yes	—
105	C₂×D₄×C₇₃	C₂×D₄	1	2	yes	—
106	C₂²×C₄×C₇₃	—	2	1	no	—
107	C₂²×C₄×C₇₃	—	2	2	no	—
108	C₂²×C₄×C₇₃	—	2	2	no	—
109	C₂²×C₄×C₇₃	—	2	2	no	—
110	C₂²×C₄×C₇₃	—	2	2	no	—
111	C₂²×C₄×C₇₃	—	2	2	no	—
112	C₂²×C₄×C₇₃	—	2	2	no	—
113	C₂²×C₄×C₇₃	—	2	1	no	—
114	C₂²×C₄×C₇₃	—	2	1	no	—
115	C₂²×C₄×C₇₃	—	2	2	no	—
116	C₂²×C₄×C₇₃	—	2	2	no	—
117	C₂²×C₄×C₇₃	—	4	4	no	—
118	C₂²×C₄×C₇₃	—	4	4	no	—
119	C₂²×C₄×C₇₃	—	4	2	no	—
120	C₂²×C₄×C₇₃	—	4	2	no	—
121	C₂²×C₄×C₇₃	—	4	2	no	—
122	C₂²×C₄×C₇₃	—	8	2	no	—
123	C₂²×C₄×C₇₃	C₂×D₄	1	2	yes	—
124	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
125	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
126	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
127	C₂×C₈×C₇₃	—	2	1	no	—
128	C₂×C₈×C₇₃	—	2	1	no	—
129	C₂×C₈×C₇₃	—	2	1	no	—
130	C₂×C₈×C₇₃	—	2	1	no	—
131	C₂×C₈×C₇₃	—	2	2	no	—
132	C₂×C₈×C₇₃	—	2	2	no	—
133	C₂×C₈×C₇₃	—	2	2	no	—
134	C₂×C₈×C₇₃	C₂×D₄	1	2	yes	—
135	C₂×C₈×C₇₃	#41	1	2	yes	—
136	C₄⋊C₄×C₇₃	—	2	2	no	—
137	C₄⋊C₄×C₇₃	—	2	1	no	—
138	C₄⋊C₄×C₇₃	—	2	2	no	—
139	C₄⋊C₄×C₇₃	—	2	2	no	—
140	C₄⋊C₄×C₇₃	—	2	1	no	—
141	C₄⋊C₄×C₇₃	—	2	1	no	—
142	C₄⋊C₄×C₇₃	—	2	1	no	—
143	C₄⋊C₄×C₇₃	—	2	2	no	—
144	C₄⋊C₄×C₇₃	—	2	2	no	—
145	C₄⋊C₄×C₇₃	—	2	1	no	—
146	C₄⋊C₄×C₇₃	—	4	4	no	—
147	C₄⋊C₄×C₇₃	—	4	2	no	—
148	C₄⋊C₄×C₇₃	—	4	2	no	—
149	C₄⋊C₄×C₇₃	—	8	1	no	—
150	C₄⋊C₄×C₇₃	—	8	1	no	—
151	C₄⋊C₄×C₇₃	C₂×D₄	1	2	yes	—
152	C₂²⋊C₄×C₇₃	—	2	4	no	—
153	C₂²⋊C₄×C₇₃	—	4	4	no	—
154	C₂²⋊C₄×C₇₃	—	4	4	no	—
155	C₂²⋊C₄×C₇₃	—	4	4	no	—
156	C₂²⋊C₄×C₇₃	—	4	2	no	—
157	C₄²×C₇₃	—	4	2	no	—
158	C₄²×C₇₃	#41	1	2	yes	—
159	C₄²×C₇₃	#41	1	2	yes	—
160	C₂³×C₇₃	—	2	2	no	—
161	C₂³×C₇₃	—	2	2	no	—
162	C₂³×C₇₃	—	2	2	no	—
163	C₂³×C₇₃	—	2	2	no	—
164	C₂³×C₇₃	—	2	2	no	—
165	C₂³×C₇₃	—	2	2	no	—
166	C₂³×C₇₃	—	2	2	no	—
167	C₂³×C₇₃	—	4	1	no	—
168	C₂³×C₇₃	—	4	1	no	—
169	C₂³×C₇₃	—	4	1	no	—
170	C₂³×C₇₃	—	4	1	no	—
171	C₂³×C₇₃	—	4	1	no	—
172	C₂³×C₇₃	—	4	1	no	—
173	C₂³×C₇₃	C₂×D₈	1	4	yes	—
174	C₂³×C₇₃	C₂²×D₄	1	1	yes	characteristic
175	D₄×C₇₃	—	2	2	no	—
176	D₄×C₇₃	—	2	2	no	—
177	D₄×C₇₃	—	2	8	no	—
178	D₄×C₇₃	—	4	1	no	—
179	D₄×C₇₃	—	4	1	no	—
180	D₄×C₇₃	—	8	8	no	—
181	C₂×C₄×C₇₃	—	2	1	no	—
182	C₂×C₄×C₇₃	—	2	1	no	—
183	C₂×C₄×C₇₃	—	2	2	no	—
184	C₂×C₄×C₇₃	—	2	2	no	—
185	C₂×C₄×C₇₃	—	2	2	no	—
186	C₂×C₄×C₇₃	—	2	2	no	—
187	C₂×C₄×C₇₃	—	4	1	no	—
188	C₂×C₄×C₇₃	—	4	1	no	—
189	C₂×C₄×C₇₃	—	4	2	no	—
190	C₂×C₄×C₇₃	—	4	2	no	—
191	C₂×C₄×C₇₃	—	4	2	no	—
192	C₂×C₄×C₇₃	—	4	2	no	—
193	C₂×C₄×C₇₃	—	4	1	no	—
194	C₂×C₄×C₇₃	—	4	2	no	—
195	C₂×C₄×C₇₃	—	4	2	no	—
196	C₂×C₄×C₇₃	—	4	1	no	—
197	C₂×C₄×C₇₃	—	4	1	no	—
198	C₂×C₄×C₇₃	—	4	1	no	—
199	C₂×C₄×C₇₃	—	4	2	no	—
200	C₂×C₄×C₇₃	—	4	2	no	—
201	C₂×C₄×C₇₃	—	4	1	no	—
202	C₂×C₄×C₇₃	—	4	2	no	—
203	C₂×C₄×C₇₃	—	4	2	no	—
204	C₂×C₄×C₇₃	—	4	1	no	—
205	C₂×C₄×C₇₃	—	8	8	no	—
206	C₂×C₄×C₇₃	—	8	4	no	—
207	C₂×C₄×C₇₃	#123	1	2	yes	—
208	C₂×C₄×C₇₃	#123	1	2	yes	—
209	C₂×C₄×C₇₃	C₂×D₈	1	2	yes	—
210	C₂×C₄×C₇₃	#137	1	2	yes	—
211	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
212	C₂×C₄×C₇₃	C₂×#41	1	1	yes	characteristic
213	C₂×C₄×C₇₃	C₂×#41	1	1	yes	characteristic
214	C₂×C₄×C₇₃	C₂×#41	1	1	yes	characteristic
215	C₂×C₄×C₇₃	H(5,𝔽₂)	1	1	yes	characteristic
216	C₂×C₄×C₇₃	2₋¹⁺⁴	1	1	yes	characteristic
217	C₈×C₇₃	—	2	2	no	—
218	C₈×C₇₃	—	2	2	no	—
219	C₈×C₇₃	—	4	2	no	—
220	C₂²×C₇₃	—	2	4	no	—
221	C₂²×C₇₃	—	2	4	no	—
222	C₂²×C₇₃	—	2	4	no	—
223	C₂²×C₇₃	—	4	2	no	—
224	C₂²×C₇₃	—	4	2	no	—
225	C₂²×C₇₃	—	4	2	no	—
226	C₂²×C₇₃	—	4	2	no	—
227	C₂²×C₇₃	—	4	2	no	—
228	C₂²×C₇₃	—	4	2	no	—
229	C₂²×C₇₃	—	4	2	no	—
230	C₂²×C₇₃	—	8	1	no	—
231	C₂²×C₇₃	—	8	1	no	—
232	C₂²×C₇₃	—	8	1	no	—
233	C₂²×C₇₃	—	8	1	no	—
234	C₂²×C₇₃	C₂×#123	1	1	yes	characteristic
235	C₂²×C₇₃	D₄²	1	1	yes	characteristic
236	C₂²×C₇₃	#547	1	1	yes	characteristic
237	C₂²×C₇₃	C₂²×D₈	1	1	yes	characteristic
238	C₂²×C₇₃	C₂×#137	1	1	yes	characteristic
239	C₂²×C₇₃	#576	1	1	yes	characteristic
240	C₂²×C₇₃	#578	1	1	yes	characteristic
241	C₄×C₇₃	—	2	2	no	—
242	C₄×C₇₃	—	4	2	no	—
243	C₄×C₇₃	—	4	2	no	—
244	C₄×C₇₃	—	8	1	no	—
245	C₄×C₇₃	—	8	1	no	—
246	C₄×C₇₃	—	8	2	no	—
247	C₄×C₇₃	—	8	2	no	—
248	C₄×C₇₃	#480	1	4	yes	complemented
249	C₄×C₇₃	#532	1	1	yes	characteristic
250	C₄×C₇₃	#542	1	1	yes	characteristic
251	C₄×C₇₃	#547	1	1	yes	characteristic
252	C₄×C₇₃	#553	1	1	yes	characteristic
253	#25010	C₇₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
254	C₂×C₇₃	—	4	4	no	—
255	C₂×C₇₃	—	8	2	no	—
256	C₂×C₇₃	#2422	1	1	yes	characteristic
257	C₂×C₇₃	C₂×#480	1	1	yes	characteristic
258	C₂×C₇₃	#3098	1	1	yes	characteristic
259	C₂×C₇₃	#3276	1	1	yes	characteristic
260	C₂×C₇₃	D₄×D₈	1	1	yes	characteristic
261	C₂×C₇₃	#3334	1	1	yes	characteristic
262	C₂×C₇₃	#3357	1	1	yes	characteristic
263	C₂×#480	C₂×C₇₃	1	2	yes	complemented
264	#2537	C₂×C₇₃	1	1	yes	characteristic
265	D₄×C₄⋊C₄	C₂×C₇₃	1	1	yes	characteristic, complemented
266	#2075	C₂×C₇₃	1	2	yes	complemented
267	#2033	C₂×C₇₃	1	2	yes	complemented
268	#1954	C₂×C₇₃	1	1	yes	characteristic, complemented
269	#1947	C₂×C₇₃	1	1	yes	characteristic, complemented
270	#1852	C₂×C₇₃	1	2	yes	complemented
271	#1845	C₂×C₇₃	1	1	yes	characteristic, complemented
272	#1802	C₂×C₇₃	1	1	yes	characteristic, complemented
273	C₄×#102	C₂×C₇₃	1	1	yes	characteristic, complemented
274	C₇₃	#25010	1	1	yes	characteristic, direct product factor, Sylow
275	C₂×#121	—	2	1	no	—
276	C₂×#121	C₂²×C₇₃	1	2	yes	—
277	C₂×C₄×D₄	—	2	1	no	—
278	C₂×C₄×D₄	C₂²×C₇₃	1	1	yes	characteristic
279	C₂×C₄×D₄	C₂²×C₇₃	1	1	yes	characteristic
280	C₂²×C₄⋊C₄	C₂²×C₇₃	1	2	yes	—
281	#480	—	2	8	no	—
282	C₂×#107	C₂²×C₇₃	1	2	yes	—
283	C₂×#107	C₂²×C₇₃	1	2	yes	—
284	C₂×#107	C₂²×C₇₃	1	2	yes	—
285	C₂×C₄⋊C₈	C₂²×C₇₃	1	1	yes	characteristic
286	C₂×#102	C₂²×C₇₃	1	2	yes	—
287	C₂×#102	C₂²×C₇₃	1	1	yes	characteristic
288	C₂×#102	C₂²×C₇₃	1	1	yes	characteristic
289	C₂×C₂²⋊C₈	C₂²×C₇₃	1	2	yes	—
290	C₂×C₂²⋊C₈	C₂²×C₇₃	1	2	yes	—
291	C₂×C₄×C₈	C₂²×C₇₃	1	1	yes	characteristic
292	#394	—	2	2	no	—
293	#389	—	2	1	no	—
294	#385	—	2	2	no	—
295	#384	C₂²×C₇₃	1	1	yes	characteristic
296	#384	C₂²×C₇₃	1	1	yes	characteristic
297	#380	—	2	1	no	—
298	#380	C₂²×C₇₃	1	2	yes	—
299	#380	C₂²×C₇₃	1	2	yes	—
300	C₄×C₄⋊C₄	C₂²×C₇₃	1	1	yes	characteristic
301	#340	C₂²×C₇₃	1	2	yes	—
302	#340	C₂²×C₇₃	1	1	yes	characteristic
303	#340	C₂²×C₇₃	1	2	yes	—
304	#340	C₂²×C₇₃	1	1	yes	characteristic
305	C₂²×D₄	—	2	2	no	—
306	C₂²×D₄	D₄×C₇₃	1	1	yes	characteristic
307	C₂²×D₄	C₂³×C₇₃	1	1	yes	characteristic
308	C₂³×C₄	—	2	2	no	—
309	C₂³×C₄	—	2	1	no	—
310	C₂³×C₄	C₂³×C₇₃	1	2	yes	—
311	C₂²×C₈	C₂³×C₇₃	1	2	yes	—
312	C₂²×C₈	C₂³×C₇₃	1	1	yes	characteristic
313	C₂²×C₈	C₂³×C₇₃	1	1	yes	characteristic
314	#121	—	2	4	no	—
315	#121	—	4	2	no	—
316	#121	—	4	4	no	—
317	C₄×D₄	—	2	2	no	—
318	C₄×D₄	—	2	2	no	—
319	C₄×D₄	—	2	2	no	—
320	C₄×D₄	—	2	2	no	—
321	C₄×D₄	—	4	4	no	—
322	C₂×C₄⋊C₄	—	2	4	no	—
323	C₂×C₄⋊C₄	—	2	2	no	—
324	C₂×C₄⋊C₄	—	2	1	no	—
325	C₂×C₄⋊C₄	—	2	1	no	—
326	C₂×C₄⋊C₄	—	2	1	no	—
327	C₂×C₄⋊C₄	—	2	1	no	—
328	C₂×C₄⋊C₄	—	4	2	no	—
329	C₂×C₄⋊C₄	D₄×C₇₃	1	1	yes	characteristic
330	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
331	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
332	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
333	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
334	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
335	C₂×C₂²⋊C₄	—	2	2	no	—
336	C₂×C₂²⋊C₄	—	2	2	no	—
337	C₂×C₂²⋊C₄	—	2	1	no	—
338	C₂×C₂²⋊C₄	—	2	2	no	—
339	C₂×C₂²⋊C₄	D₄×C₇₃	1	2	yes	—
340	C₂×C₄²	—	2	1	no	—
341	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
342	#107	—	2	4	no	—
343	#107	—	2	4	no	—
344	#107	—	4	2	no	—
345	C₄⋊C₈	—	2	2	no	—
346	#102	—	2	4	no	—
347	#102	—	2	2	no	—
348	#102	D₄×C₇₃	1	4	yes	complemented
349	C₂²⋊C₈	—	2	4	no	—
350	C₂²⋊C₈	—	2	4	no	—
351	C₄×C₈	—	2	2	no	—
352	#95	—	2	1	no	—
353	#95	—	2	2	no	—
354	#95	—	2	2	no	—
355	C₂⁴	—	2	1	no	—
356	C₂⁴	C₂×D₄×C₇₃	1	2	yes	—
357	C₂×D₄	—	2	2	no	—
358	C₂×D₄	—	2	2	no	—
359	C₂×D₄	—	2	1	no	—
360	C₂×D₄	—	2	1	no	—
361	C₂×D₄	—	2	1	no	—
362	C₂×D₄	—	2	1	no	—
363	C₂×D₄	—	2	1	no	—
364	C₂×D₄	—	4	4	no	—
365	C₂×D₄	—	4	4	no	—
366	C₂×D₄	—	8	2	no	—
367	C₂×D₄	D₈×C₇₃	1	4	yes	—
368	C₂×D₄	C₂×D₄×C₇₃	1	2	yes	—
369	C₂²×C₄	—	2	1	no	—
370	C₂²×C₄	—	2	2	no	—
371	C₂²×C₄	—	2	2	no	—
372	C₂²×C₄	—	2	2	no	—
373	C₂²×C₄	—	2	2	no	—
374	C₂²×C₄	—	2	2	no	—
375	C₂²×C₄	—	2	2	no	—
376	C₂²×C₄	—	2	1	no	—
377	C₂²×C₄	—	2	1	no	—
378	C₂²×C₄	—	2	2	no	—
379	C₂²×C₄	—	2	2	no	—
380	C₂²×C₄	—	4	4	no	—
381	C₂²×C₄	—	4	4	no	—
382	C₂²×C₄	—	4	2	no	—
383	C₂²×C₄	—	4	2	no	—
384	C₂²×C₄	—	4	2	no	—
385	C₂²×C₄	—	8	2	no	—
386	C₂²×C₄	C₂×D₄×C₇₃	1	2	yes	—
387	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
388	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
389	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
390	C₂×C₈	—	2	1	no	—
391	C₂×C₈	—	2	1	no	—
392	C₂×C₈	—	2	1	no	—
393	C₂×C₈	—	2	1	no	—
394	C₂×C₈	—	2	2	no	—
395	C₂×C₈	—	2	2	no	—
396	C₂×C₈	—	2	2	no	—
397	C₂×C₈	C₂×D₄×C₇₃	1	2	yes	—
398	C₂×C₈	#41×C₇₃	1	2	yes	—
399	C₄⋊C₄	—	2	2	no	—
400	C₄⋊C₄	—	2	1	no	—
401	C₄⋊C₄	—	2	2	no	—
402	C₄⋊C₄	—	2	2	no	—
403	C₄⋊C₄	—	2	1	no	—
404	C₄⋊C₄	—	2	1	no	—
405	C₄⋊C₄	—	2	1	no	—
406	C₄⋊C₄	—	2	2	no	—
407	C₄⋊C₄	—	2	2	no	—
408	C₄⋊C₄	—	2	1	no	—
409	C₄⋊C₄	—	4	4	no	—
410	C₄⋊C₄	—	4	2	no	—
411	C₄⋊C₄	—	4	2	no	—
412	C₄⋊C₄	—	8	1	no	—
413	C₄⋊C₄	—	8	1	no	—
414	C₄⋊C₄	C₂×D₄×C₇₃	1	2	yes	—
415	C₂²⋊C₄	—	2	4	no	—
416	C₂²⋊C₄	—	4	4	no	—
417	C₂²⋊C₄	—	4	4	no	—
418	C₂²⋊C₄	—	4	4	no	—
419	C₂²⋊C₄	—	4	2	no	—
420	C₄²	—	4	2	no	—
421	C₄²	#41×C₇₃	1	2	yes	—
422	C₄²	#41×C₇₃	1	2	yes	—
423	C₂³	—	2	2	no	—
424	C₂³	—	2	2	no	—
425	C₂³	—	2	2	no	—
426	C₂³	—	2	2	no	—
427	C₂³	—	2	2	no	—
428	C₂³	—	2	2	no	—
429	C₂³	—	2	2	no	—
430	C₂³	—	4	1	no	—
431	C₂³	—	4	1	no	—
432	C₂³	—	4	1	no	—
433	C₂³	—	4	1	no	—
434	C₂³	—	4	1	no	—
435	C₂³	—	4	1	no	—
436	C₂³	C₂×D₈×C₇₃	1	4	yes	—
437	C₂³	C₂²×D₄×C₇₃	1	1	yes	characteristic
438	D₄	—	2	8	no	—
439	D₄	—	2	2	no	—
440	D₄	—	2	2	no	—
441	D₄	—	4	1	no	—
442	D₄	—	4	1	no	—
443	D₄	—	8	8	no	—
444	C₂×C₄	—	2	1	no	—
445	C₂×C₄	—	2	1	no	—
446	C₂×C₄	—	2	2	no	—
447	C₂×C₄	—	2	2	no	—
448	C₂×C₄	—	2	2	no	—
449	C₂×C₄	—	2	2	no	—
450	C₂×C₄	—	4	1	no	—
451	C₂×C₄	—	4	1	no	—
452	C₂×C₄	—	4	2	no	—
453	C₂×C₄	—	4	2	no	—
454	C₂×C₄	—	4	2	no	—
455	C₂×C₄	—	4	2	no	—
456	C₂×C₄	—	4	1	no	—
457	C₂×C₄	—	4	2	no	—
458	C₂×C₄	—	4	2	no	—
459	C₂×C₄	—	4	1	no	—
460	C₂×C₄	—	4	1	no	—
461	C₂×C₄	—	4	1	no	—
462	C₂×C₄	—	4	2	no	—
463	C₂×C₄	—	4	2	no	—
464	C₂×C₄	—	4	1	no	—
465	C₂×C₄	—	4	2	no	—
466	C₂×C₄	—	4	2	no	—
467	C₂×C₄	—	4	1	no	—
468	C₂×C₄	—	8	8	no	—
469	C₂×C₄	—	8	4	no	—
470	C₂×C₄	#123×C₇₃	1	2	yes	—
471	C₂×C₄	#123×C₇₃	1	2	yes	—
472	C₂×C₄	C₂×D₈×C₇₃	1	2	yes	—
473	C₂×C₄	#137×C₇₃	1	2	yes	—
474	C₂×C₄	C₂²×D₄×C₇₃	1	1	yes	characteristic
475	C₂×C₄	C₂×#41×C₇₃	1	1	yes	characteristic
476	C₂×C₄	C₂×#41×C₇₃	1	1	yes	characteristic
477	C₂×C₄	C₂×#41×C₇₃	1	1	yes	characteristic
478	C₂×C₄	H(5,𝔽₂)×C₇₃	1	1	yes	characteristic
479	C₂×C₄	2₋¹⁺⁴×C₇₃	1	1	yes	characteristic
480	C₈	—	2	2	no	—
481	C₈	—	2	2	no	—
482	C₈	—	4	2	no	—
483	C₂²	—	2	4	no	—
484	C₂²	—	2	4	no	—
485	C₂²	—	2	4	no	—
486	C₂²	—	4	2	no	—
487	C₂²	—	4	2	no	—
488	C₂²	—	4	2	no	—
489	C₂²	—	4	2	no	—
490	C₂²	—	4	2	no	—
491	C₂²	—	4	2	no	—
492	C₂²	—	4	2	no	—
493	C₂²	—	8	1	no	—
494	C₂²	—	8	1	no	—
495	C₂²	—	8	1	no	—
496	C₂²	—	8	1	no	—
497	C₂²	C₂×#123×C₇₃	1	1	yes	characteristic
498	C₂²	D₄²×C₇₃	1	1	yes	characteristic
499	C₂²	#547×C₇₃	1	1	yes	characteristic
500	C₂²	C₂²×D₈×C₇₃	1	1	yes	characteristic
501	C₂²	C₂×#137×C₇₃	1	1	yes	characteristic
502	C₂²	#576×C₇₃	1	1	yes	characteristic
503	C₂²	#578×C₇₃	1	1	yes	characteristic
504	C₄	—	2	2	no	—
505	C₄	—	4	2	no	—
506	C₄	—	4	2	no	—
507	C₄	—	8	2	no	—
508	C₄	—	8	2	no	—
509	C₄	—	8	1	no	—
510	C₄	—	8	1	no	—
511	C₄	#480×C₇₃	1	4	yes	complemented
512	C₄	#532×C₇₃	1	1	yes	characteristic
513	C₄	#542×C₇₃	1	1	yes	characteristic
514	C₄	#547×C₇₃	1	1	yes	characteristic
515	C₄	#553×C₇₃	1	1	yes	characteristic
516	C₂	—	4	4	no	—
517	C₂	—	8	2	no	—
518	C₂	C₇₃×#2422	1	1	yes	characteristic
519	C₂	C₂×#480×C₇₃	1	1	yes	characteristic
520	C₂	C₇₃×#3098	1	1	yes	characteristic
521	C₂	C₇₃×#3276	1	1	yes	characteristic
522	C₂	D₄×D₈×C₇₃	1	1	yes	characteristic
523	C₂	C₇₃×#3334	1	1	yes	characteristic
524	C₂	C₇₃×#3357	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₇₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₇₃
prime radical	C₇₃×#2537	C₂
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×#480×C₇₃	C₂	semidirect
3. D₄×C₄⋊C₄×C₇₃	C₂	semidirect
4. C₇₃×#2075	C₂	semidirect
5. C₇₃×#2033	C₂	semidirect
6. C₇₃×#1954	C₂	semidirect
7. C₇₃×#1947	C₂	semidirect
8. C₇₃×#1852	C₂	semidirect
9. C₇₃×#1845	C₂	semidirect
10. C₇₃×#1802	C₂	semidirect
11. C₄×#102×C₇₃	C₂	semidirect
85. #102×C₇₃	D₄	semidirect
248. C₄×C₇₃	#480	semidirect
253. #25010	C₇₃	direct (N × H)
263. C₂×#480	C₂×C₇₃	semidirect
265. D₄×C₄⋊C₄	C₂×C₇₃	semidirect
266. #2075	C₂×C₇₃	semidirect
267. #2033	C₂×C₇₃	semidirect
268. #1954	C₂×C₇₃	semidirect
269. #1947	C₂×C₇₃	semidirect
270. #1852	C₂×C₇₃	semidirect
271. #1845	C₂×C₇₃	semidirect
272. #1802	C₂×C₇₃	semidirect
273. C₄×#102	C₂×C₇₃	semidirect
274. C₇₃	#25010	direct (N × H)
348. #102	D₄×C₇₃	semidirect
511. C₄	#480×C₇₃	semidirect

Maximal subgroups

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

subgroup	index
C₂×#480×C₇₃	2
C₇₃×#2537	2
D₄×C₄⋊C₄×C₇₃	2
C₇₃×#2075	2
C₇₃×#2033	2
C₇₃×#1954	2
C₇₃×#1947	2
C₇₃×#1852	2
C₇₃×#1845	2
C₇₃×#1802	2
C₄×#102×C₇₃	2
#25010	73

Subgroups — C73×#25010 #32934414

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₃×#25010 #32934414