Subgroups — C₇₃×#25655 #32935059

Order 18688.

1324 conjugacy classes of subgroups.

The subgroup lattice has 522 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#550×C₇₃	C₂	1	1	yes	maximal, characteristic
2	C₂×#490×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#478×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₇₃×#2584	C₂	1	1	yes	maximal, characteristic, complemented
5	C₇₃×#2041	C₂	1	2	yes	maximal, complemented
6	C₇₃×#2041	C₂	1	2	yes	maximal, complemented
7	C₇₃×#1985	C₂	1	1	yes	maximal, characteristic, complemented
8	C₇₃×#1982	C₂	1	1	yes	maximal, characteristic, complemented
9	C₇₃×#1864	C₂	1	2	yes	maximal, complemented
10	C₇₃×#1862	C₂	1	2	yes	maximal, complemented
11	C₇₃×#1762	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×#41×C₇₃	—	2	1	no	—
13	#550×C₇₃	—	2	4	no	—
14	#550×C₇₃	—	2	4	no	—
15	C₂×#127×C₇₃	C₂²	1	2	yes	—
16	C₂×#127×C₇₃	C₂²	1	1	yes	characteristic
17	C₂×#125×C₇₃	C₂²	1	1	yes	characteristic
18	C₂×#121×C₇₃	—	2	2	no	—
19	C₂×#121×C₇₃	—	2	1	no	—
20	C₂×C₄×Q₈×C₇₃	C₂²	1	1	yes	characteristic
21	C₂×C₄×D₄×C₇₃	C₂²	1	2	yes	—
22	C₂×C₄×D₄×C₇₃	C₂²	1	1	yes	characteristic
23	#490×C₇₃	—	2	4	no	—
24	#478×C₇₃	—	2	4	no	—
25	C₂×#107×C₇₃	C₂²	1	1	yes	characteristic
26	C₂×#106×C₇₃	C₂²	1	1	yes	characteristic
27	C₂×C₄⋊C₈×C₇₃	C₂²	1	1	yes	characteristic
28	C₂×#102×C₇₃	C₂²	1	2	yes	—
29	C₂×#102×C₇₃	C₂²	1	2	yes	—
30	C₂×#102×C₇₃	C₂²	1	2	yes	—
31	C₂×#102×C₇₃	C₂²	1	1	yes	characteristic
32	C₂×#102×C₇₃	C₂²	1	1	yes	characteristic
33	C₂×#102×C₇₃	C₂²	1	2	yes	—
34	C₂×#102×C₇₃	C₂²	1	2	yes	—
35	C₂×#97×C₇₃	C₂²	1	1	yes	characteristic
36	#398×C₇₃	—	2	1	no	—
37	#395×C₇₃	—	2	1	no	—
38	#389×C₇₃	—	2	2	no	—
39	#389×C₇₃	C₂²	1	2	yes	—
40	#389×C₇₃	C₂²	1	2	yes	—
41	C₄×C₄⋊C₄×C₇₃	C₂²	1	1	yes	characteristic
42	#340×C₇₃	C₂²	1	2	yes	—
43	#336×C₇₃	C₂²	1	2	yes	—
44	#336×C₇₃	C₂²	1	2	yes	—
45	C₂×#41×C₇₃	—	2	8	no	—
46	C₂×#41×C₇₃	—	4	8	no	—
47	C₂²×Q₈×C₇₃	D₄	1	1	yes	characteristic
48	C₂²×D₄×C₇₃	—	2	1	no	—
49	C₂²×D₄×C₇₃	—	2	2	no	—
50	C₂²×D₄×C₇₃	—	2	2	no	—
51	C₂²×D₄×C₇₃	—	2	1	no	—
52	C₂²×D₄×C₇₃	C₂³	1	2	yes	—
53	C₂²×D₄×C₇₃	C₂³	1	1	yes	characteristic
54	C₂³×C₄×C₇₃	—	2	2	no	—
55	C₂³×C₄×C₇₃	—	2	1	no	—
56	C₂²×C₈×C₇₃	C₂³	1	2	yes	—
57	C₂²×C₈×C₇₃	C₂³	1	1	yes	characteristic
58	C₂²×C₈×C₇₃	C₂³	1	1	yes	characteristic
59	#127×C₇₃	—	2	4	no	—
60	#127×C₇₃	—	2	4	no	—
61	#127×C₇₃	—	2	2	no	—
62	#127×C₇₃	D₄	1	4	yes	—
63	#125×C₇₃	—	2	2	no	—
64	#125×C₇₃	—	2	2	no	—
65	#121×C₇₃	—	2	8	no	—
66	#121×C₇₃	—	2	16	no	—
67	C₄×Q₈×C₇₃	—	2	2	no	—
68	C₄×Q₈×C₇₃	—	2	2	no	—
69	C₄×D₄×C₇₃	—	2	4	no	—
70	C₄×D₄×C₇₃	—	2	4	no	—
71	C₄×D₄×C₇₃	—	2	2	no	—
72	C₄×D₄×C₇₃	D₄	1	4	yes	—
73	C₂×C₄⋊C₄×C₇₃	—	2	1	no	—
74	C₂×C₄⋊C₄×C₇₃	—	2	2	no	—
75	C₂×C₄⋊C₄×C₇₃	—	2	1	no	—
76	C₂×C₄⋊C₄×C₇₃	—	2	2	no	—
77	C₂×C₄⋊C₄×C₇₃	D₄	1	2	yes	—
78	C₂×C₄⋊C₄×C₇₃	D₄	1	1	yes	characteristic
79	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
80	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
81	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
82	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
83	C₂×C₂²⋊C₄×C₇₃	—	2	2	no	—
84	C₂×C₂²⋊C₄×C₇₃	—	2	1	no	—
85	C₂×C₄²×C₇₃	—	2	1	no	—
86	C₂×C₄²×C₇₃	C₂³	1	2	yes	—
87	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
88	#107×C₇₃	—	2	2	no	—
89	#106×C₇₃	—	2	2	no	—
90	C₄⋊C₈×C₇₃	—	2	2	no	—
91	#102×C₇₃	—	2	2	no	—
92	#102×C₇₃	—	2	2	no	—
93	#102×C₇₃	—	2	4	no	—
94	#102×C₇₃	—	2	4	no	—
95	#102×C₇₃	—	2	4	no	—
96	#102×C₇₃	—	2	4	no	—
97	#102×C₇₃	—	2	4	no	—
98	#97×C₇₃	—	2	2	no	—
99	#95×C₇₃	—	2	1	no	—
100	#95×C₇₃	—	2	2	no	—
101	#95×C₇₃	—	2	2	no	—
102	C₂⁴×C₇₃	—	2	2	no	—
103	C₂⁴×C₇₃	—	2	1	no	—
104	#41×C₇₃	—	4	32	no	—
105	C₂×Q₈×C₇₃	—	2	2	no	—
106	C₂×Q₈×C₇₃	—	2	4	no	—
107	C₂×D₄×C₇₃	—	2	8	no	—
108	C₂×D₄×C₇₃	—	2	8	no	—
109	C₂×D₄×C₇₃	—	2	4	no	—
110	C₂×D₄×C₇₃	—	2	4	no	—
111	C₂×D₄×C₇₃	—	2	2	no	—
112	C₂×D₄×C₇₃	—	2	1	no	—
113	C₂×D₄×C₇₃	—	2	2	no	—
114	C₂×D₄×C₇₃	—	2	2	no	—
115	C₂×D₄×C₇₃	—	2	2	no	—
116	C₂×D₄×C₇₃	—	2	2	no	—
117	C₂×D₄×C₇₃	—	2	2	no	—
118	C₂×D₄×C₇₃	—	2	2	no	—
119	C₂×D₄×C₇₃	—	4	4	no	—
120	C₂×D₄×C₇₃	—	4	4	no	—
121	C₂×D₄×C₇₃	—	4	4	no	—
122	C₂×D₄×C₇₃	—	8	1	no	—
123	C₂×D₄×C₇₃	—	8	1	no	—
124	C₂×D₄×C₇₃	—	8	2	no	—
125	C₂×D₄×C₇₃	—	8	2	no	—
126	C₂×D₄×C₇₃	C₂×D₄	1	4	yes	—
127	C₂×D₄×C₇₃	C₂×D₄	1	2	yes	—
128	C₂²×C₄×C₇₃	—	2	8	no	—
129	C₂²×C₄×C₇₃	—	2	2	no	—
130	C₂²×C₄×C₇₃	—	2	1	no	—
131	C₂²×C₄×C₇₃	—	2	4	no	—
132	C₂²×C₄×C₇₃	—	2	1	no	—
133	C₂²×C₄×C₇₃	—	2	1	no	—
134	C₂²×C₄×C₇₃	—	4	4	no	—
135	C₂²×C₄×C₇₃	—	4	4	no	—
136	C₂²×C₄×C₇₃	—	4	4	no	—
137	C₂²×C₄×C₇₃	C₂×D₄	1	2	yes	—
138	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
139	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
140	C₂²×C₄×C₇₃	C₂×D₄	1	2	yes	—
141	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
142	C₂×C₈×C₇₃	—	2	2	no	—
143	C₂×C₈×C₇₃	—	2	1	no	—
144	C₂×C₈×C₇₃	—	2	1	no	—
145	C₂×C₈×C₇₃	—	2	2	no	—
146	C₂×C₈×C₇₃	—	2	2	no	—
147	C₂×C₈×C₇₃	—	2	2	no	—
148	C₂×C₈×C₇₃	—	2	2	no	—
149	C₄⋊C₄×C₇₃	—	2	4	no	—
150	C₄⋊C₄×C₇₃	—	2	2	no	—
151	C₄⋊C₄×C₇₃	—	2	1	no	—
152	C₄⋊C₄×C₇₃	—	2	2	no	—
153	C₄⋊C₄×C₇₃	—	2	1	no	—
154	C₄⋊C₄×C₇₃	—	2	1	no	—
155	C₄⋊C₄×C₇₃	—	2	1	no	—
156	C₄⋊C₄×C₇₃	—	2	1	no	—
157	C₄⋊C₄×C₇₃	—	4	2	no	—
158	C₄⋊C₄×C₇₃	—	4	2	no	—
159	C₄⋊C₄×C₇₃	—	4	4	no	—
160	C₄⋊C₄×C₇₃	—	8	2	no	—
161	C₄⋊C₄×C₇₃	C₂×D₄	1	2	yes	—
162	C₄⋊C₄×C₇₃	#41	1	4	yes	complemented
163	C₂²⋊C₄×C₇₃	—	2	8	no	—
164	C₂²⋊C₄×C₇₃	—	2	4	no	—
165	C₄²×C₇₃	—	2	2	no	—
166	C₄²×C₇₃	—	2	2	no	—
167	C₄²×C₇₃	—	8	1	no	—
168	C₄²×C₇₃	C₂×D₄	1	2	yes	—
169	C₄²×C₇₃	C₂×D₄	1	2	yes	—
170	C₂³×C₇₃	—	2	4	no	—
171	C₂³×C₇₃	—	2	2	no	—
172	C₂³×C₇₃	—	4	2	no	—
173	C₂³×C₇₃	—	4	2	no	—
174	C₂³×C₇₃	—	4	2	no	—
175	C₂³×C₇₃	—	4	2	no	—
176	C₂³×C₇₃	—	4	2	no	—
177	C₂³×C₇₃	—	4	2	no	—
178	C₂³×C₇₃	—	4	2	no	—
179	C₂³×C₇₃	—	4	1	no	—
180	C₂³×C₇₃	—	4	2	no	—
181	C₂³×C₇₃	—	4	1	no	—
182	C₂³×C₇₃	C₂²×D₄	1	1	yes	characteristic
183	Q₈×C₇₃	—	2	8	no	—
184	D₄×C₇₃	—	2	2	no	—
185	D₄×C₇₃	—	2	2	no	—
186	D₄×C₇₃	—	2	4	no	—
187	D₄×C₇₃	—	2	4	no	—
188	D₄×C₇₃	—	4	8	no	—
189	D₄×C₇₃	—	4	16	no	—
190	D₄×C₇₃	—	4	2	no	—
191	D₄×C₇₃	—	4	2	no	—
192	D₄×C₇₃	—	4	2	no	—
193	D₄×C₇₃	—	8	4	no	—
194	D₄×C₇₃	—	8	8	no	—
195	C₂×C₄×C₇₃	—	2	2	no	—
196	C₂×C₄×C₇₃	—	2	2	no	—
197	C₂×C₄×C₇₃	—	2	2	no	—
198	C₂×C₄×C₇₃	—	2	1	no	—
199	C₂×C₄×C₇₃	—	2	1	no	—
200	C₂×C₄×C₇₃	—	2	2	no	—
201	C₂×C₄×C₇₃	—	2	2	no	—
202	C₂×C₄×C₇₃	—	2	4	no	—
203	C₂×C₄×C₇₃	—	2	2	no	—
204	C₂×C₄×C₇₃	—	2	2	no	—
205	C₂×C₄×C₇₃	—	4	8	no	—
206	C₂×C₄×C₇₃	—	4	16	no	—
207	C₂×C₄×C₇₃	—	4	2	no	—
208	C₂×C₄×C₇₃	—	4	2	no	—
209	C₂×C₄×C₇₃	—	4	2	no	—
210	C₂×C₄×C₇₃	—	4	1	no	—
211	C₂×C₄×C₇₃	—	4	1	no	—
212	C₂×C₄×C₇₃	—	4	2	no	—
213	C₂×C₄×C₇₃	—	4	1	no	—
214	C₂×C₄×C₇₃	—	4	1	no	—
215	C₂×C₄×C₇₃	#120	1	2	yes	—
216	C₂×C₄×C₇₃	#120	1	2	yes	—
217	C₂×C₄×C₇₃	AGL(1,ℤ/8)	1	4	yes	—
218	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
219	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
220	C₂×C₄×C₇₃	C₂×#41	1	2	yes	—
221	C₂×C₄×C₇₃	2₋¹⁺⁴	1	2	yes	—
222	C₈×C₇₃	—	4	1	no	—
223	C₈×C₇₃	—	4	1	no	—
224	C₈×C₇₃	—	4	2	no	—
225	C₂²×C₇₃	—	4	2	no	—
226	C₂²×C₇₃	—	4	4	no	—
227	C₂²×C₇₃	—	4	2	no	—
228	C₂²×C₇₃	—	4	4	no	—
229	C₂²×C₇₃	—	4	4	no	—
230	C₂²×C₇₃	—	4	2	no	—
231	C₂²×C₇₃	—	8	2	no	—
232	C₂²×C₇₃	—	8	2	no	—
233	C₂²×C₇₃	—	8	2	no	—
234	C₂²×C₇₃	—	8	2	no	—
235	C₂²×C₇₃	—	8	2	no	—
236	C₂²×C₇₃	—	8	2	no	—
237	C₂²×C₇₃	C₂×#120	1	1	yes	characteristic
238	C₂²×C₇₃	#548	1	2	yes	—
239	C₂²×C₇₃	C₂×AGL(1,ℤ/8)	1	2	yes	—
240	C₂²×C₇₃	#576	1	1	yes	characteristic
241	C₂²×C₇₃	#577	1	1	yes	characteristic
242	C₄×C₇₃	—	2	2	no	—
243	C₄×C₇₃	—	2	4	no	—
244	C₄×C₇₃	—	2	2	no	—
245	C₄×C₇₃	—	4	4	no	—
246	C₄×C₇₃	—	4	2	no	—
247	C₄×C₇₃	—	4	2	no	—
248	C₄×C₇₃	—	8	1	no	—
249	C₄×C₇₃	—	8	1	no	—
250	C₄×C₇₃	#532	1	1	yes	characteristic
251	C₄×C₇₃	#536	1	1	yes	characteristic
252	C₄×C₇₃	#547	1	2	yes	—
253	#25655	C₇₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
254	C₂×C₇₃	—	8	2	no	—
255	C₂×C₇₃	—	8	4	no	—
256	C₂×C₇₃	#2432	1	1	yes	characteristic
257	C₂×C₇₃	#3003	1	1	yes	characteristic
258	C₂×C₇₃	#3012	1	1	yes	characteristic
259	C₂×C₇₃	#3366	1	2	yes	—
260	C₂×C₇₃	#3368	1	2	yes	—
261	C₂×#550	C₂×C₇₃	1	1	yes	characteristic
262	C₂×#490	C₂×C₇₃	1	1	yes	characteristic, complemented
263	C₂×#478	C₂×C₇₃	1	1	yes	characteristic, complemented
264	#2584	C₂×C₇₃	1	1	yes	characteristic, complemented
265	#2041	C₂×C₇₃	1	2	yes	complemented
266	#2041	C₂×C₇₃	1	2	yes	complemented
267	#1985	C₂×C₇₃	1	1	yes	characteristic, complemented
268	#1982	C₂×C₇₃	1	1	yes	characteristic, complemented
269	#1864	C₂×C₇₃	1	2	yes	complemented
270	#1862	C₂×C₇₃	1	2	yes	complemented
271	#1762	C₂×C₇₃	1	1	yes	characteristic, complemented
272	C₇₃	#25655	1	1	yes	characteristic, direct product factor, Sylow
273	C₂²×#41	—	2	1	no	—
274	#550	—	2	4	no	—
275	#550	—	2	4	no	—
276	C₂×#127	C₂²×C₇₃	1	2	yes	—
277	C₂×#127	C₂²×C₇₃	1	1	yes	characteristic
278	C₂×#125	C₂²×C₇₃	1	1	yes	characteristic
279	C₂×#121	—	2	2	no	—
280	C₂×#121	—	2	1	no	—
281	C₂×C₄×Q₈	C₂²×C₇₃	1	1	yes	characteristic
282	C₂×C₄×D₄	C₂²×C₇₃	1	2	yes	—
283	C₂×C₄×D₄	C₂²×C₇₃	1	1	yes	characteristic
284	#490	—	2	4	no	—
285	#478	—	2	4	no	—
286	C₂×#107	C₂²×C₇₃	1	1	yes	characteristic
287	C₂×#106	C₂²×C₇₃	1	1	yes	characteristic
288	C₂×C₄⋊C₈	C₂²×C₇₃	1	1	yes	characteristic
289	C₂×#102	C₂²×C₇₃	1	1	yes	characteristic
290	C₂×#102	C₂²×C₇₃	1	1	yes	characteristic
291	C₂×#102	C₂²×C₇₃	1	2	yes	—
292	C₂×#102	C₂²×C₇₃	1	2	yes	—
293	C₂×#102	C₂²×C₇₃	1	2	yes	—
294	C₂×#102	C₂²×C₇₃	1	2	yes	—
295	C₂×#102	C₂²×C₇₃	1	2	yes	—
296	C₂×#97	C₂²×C₇₃	1	1	yes	characteristic
297	#398	—	2	1	no	—
298	#395	—	2	1	no	—
299	#389	—	2	2	no	—
300	#389	C₂²×C₇₃	1	2	yes	—
301	#389	C₂²×C₇₃	1	2	yes	—
302	C₄×C₄⋊C₄	C₂²×C₇₃	1	1	yes	characteristic
303	#340	C₂²×C₇₃	1	2	yes	—
304	#336	C₂²×C₇₃	1	2	yes	—
305	#336	C₂²×C₇₃	1	2	yes	—
306	C₂×#41	—	2	8	no	—
307	C₂×#41	—	4	8	no	—
308	C₂²×Q₈	D₄×C₇₃	1	1	yes	characteristic
309	C₂²×D₄	—	2	1	no	—
310	C₂²×D₄	—	2	2	no	—
311	C₂²×D₄	—	2	2	no	—
312	C₂²×D₄	—	2	1	no	—
313	C₂²×D₄	C₂³×C₇₃	1	2	yes	—
314	C₂²×D₄	C₂³×C₇₃	1	1	yes	characteristic
315	C₂³×C₄	—	2	2	no	—
316	C₂³×C₄	—	2	1	no	—
317	C₂²×C₈	C₂³×C₇₃	1	2	yes	—
318	C₂²×C₈	C₂³×C₇₃	1	1	yes	characteristic
319	C₂²×C₈	C₂³×C₇₃	1	1	yes	characteristic
320	#127	—	2	4	no	—
321	#127	—	2	4	no	—
322	#127	—	2	2	no	—
323	#127	D₄×C₇₃	1	4	yes	—
324	#125	—	2	2	no	—
325	#125	—	2	2	no	—
326	#121	—	2	8	no	—
327	#121	—	2	16	no	—
328	C₄×Q₈	—	2	2	no	—
329	C₄×Q₈	—	2	2	no	—
330	C₄×D₄	—	2	4	no	—
331	C₄×D₄	—	2	4	no	—
332	C₄×D₄	—	2	2	no	—
333	C₄×D₄	D₄×C₇₃	1	4	yes	—
334	C₂×C₄⋊C₄	—	2	1	no	—
335	C₂×C₄⋊C₄	—	2	1	no	—
336	C₂×C₄⋊C₄	—	2	2	no	—
337	C₂×C₄⋊C₄	—	2	2	no	—
338	C₂×C₄⋊C₄	D₄×C₇₃	1	2	yes	—
339	C₂×C₄⋊C₄	D₄×C₇₃	1	1	yes	characteristic
340	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
341	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
342	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
343	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
344	C₂×C₂²⋊C₄	—	2	2	no	—
345	C₂×C₂²⋊C₄	—	2	1	no	—
346	C₂×C₄²	—	2	1	no	—
347	C₂×C₄²	C₂³×C₇₃	1	2	yes	—
348	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
349	#107	—	2	2	no	—
350	#106	—	2	2	no	—
351	C₄⋊C₈	—	2	2	no	—
352	#102	—	2	2	no	—
353	#102	—	2	2	no	—
354	#102	—	2	4	no	—
355	#102	—	2	4	no	—
356	#102	—	2	4	no	—
357	#102	—	2	4	no	—
358	#102	—	2	4	no	—
359	#97	—	2	2	no	—
360	#95	—	2	1	no	—
361	#95	—	2	2	no	—
362	#95	—	2	2	no	—
363	C₂⁴	—	2	2	no	—
364	C₂⁴	—	2	1	no	—
365	#41	—	4	32	no	—
366	C₂×Q₈	—	2	2	no	—
367	C₂×Q₈	—	2	4	no	—
368	C₂×D₄	—	2	8	no	—
369	C₂×D₄	—	2	8	no	—
370	C₂×D₄	—	2	4	no	—
371	C₂×D₄	—	2	4	no	—
372	C₂×D₄	—	2	2	no	—
373	C₂×D₄	—	2	1	no	—
374	C₂×D₄	—	2	2	no	—
375	C₂×D₄	—	2	2	no	—
376	C₂×D₄	—	2	2	no	—
377	C₂×D₄	—	2	2	no	—
378	C₂×D₄	—	2	2	no	—
379	C₂×D₄	—	2	2	no	—
380	C₂×D₄	—	4	4	no	—
381	C₂×D₄	—	4	4	no	—
382	C₂×D₄	—	4	4	no	—
383	C₂×D₄	—	8	1	no	—
384	C₂×D₄	—	8	1	no	—
385	C₂×D₄	—	8	2	no	—
386	C₂×D₄	—	8	2	no	—
387	C₂×D₄	C₂×D₄×C₇₃	1	4	yes	—
388	C₂×D₄	C₂×D₄×C₇₃	1	2	yes	—
389	C₂²×C₄	—	2	8	no	—
390	C₂²×C₄	—	2	2	no	—
391	C₂²×C₄	—	2	1	no	—
392	C₂²×C₄	—	2	4	no	—
393	C₂²×C₄	—	2	1	no	—
394	C₂²×C₄	—	2	1	no	—
395	C₂²×C₄	—	4	4	no	—
396	C₂²×C₄	—	4	4	no	—
397	C₂²×C₄	—	4	4	no	—
398	C₂²×C₄	C₂×D₄×C₇₃	1	2	yes	—
399	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
400	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
401	C₂²×C₄	C₂×D₄×C₇₃	1	2	yes	—
402	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
403	C₂×C₈	—	2	2	no	—
404	C₂×C₈	—	2	1	no	—
405	C₂×C₈	—	2	1	no	—
406	C₂×C₈	—	2	2	no	—
407	C₂×C₈	—	2	2	no	—
408	C₂×C₈	—	2	2	no	—
409	C₂×C₈	—	2	2	no	—
410	C₄⋊C₄	—	2	4	no	—
411	C₄⋊C₄	—	2	2	no	—
412	C₄⋊C₄	—	2	1	no	—
413	C₄⋊C₄	—	2	2	no	—
414	C₄⋊C₄	—	2	1	no	—
415	C₄⋊C₄	—	2	1	no	—
416	C₄⋊C₄	—	2	1	no	—
417	C₄⋊C₄	—	2	1	no	—
418	C₄⋊C₄	—	4	2	no	—
419	C₄⋊C₄	—	4	2	no	—
420	C₄⋊C₄	—	4	4	no	—
421	C₄⋊C₄	—	8	2	no	—
422	C₄⋊C₄	C₂×D₄×C₇₃	1	2	yes	—
423	C₄⋊C₄	#41×C₇₃	1	4	yes	complemented
424	C₂²⋊C₄	—	2	8	no	—
425	C₂²⋊C₄	—	2	4	no	—
426	C₄²	—	2	2	no	—
427	C₄²	—	2	2	no	—
428	C₄²	—	8	1	no	—
429	C₄²	C₂×D₄×C₇₃	1	2	yes	—
430	C₄²	C₂×D₄×C₇₃	1	2	yes	—
431	C₂³	—	2	4	no	—
432	C₂³	—	2	2	no	—
433	C₂³	—	4	2	no	—
434	C₂³	—	4	2	no	—
435	C₂³	—	4	2	no	—
436	C₂³	—	4	2	no	—
437	C₂³	—	4	2	no	—
438	C₂³	—	4	2	no	—
439	C₂³	—	4	2	no	—
440	C₂³	—	4	1	no	—
441	C₂³	—	4	2	no	—
442	C₂³	—	4	1	no	—
443	C₂³	C₂²×D₄×C₇₃	1	1	yes	characteristic
444	Q₈	—	2	8	no	—
445	D₄	—	2	2	no	—
446	D₄	—	2	2	no	—
447	D₄	—	2	4	no	—
448	D₄	—	2	4	no	—
449	D₄	—	4	8	no	—
450	D₄	—	4	16	no	—
451	D₄	—	4	2	no	—
452	D₄	—	4	2	no	—
453	D₄	—	4	2	no	—
454	D₄	—	8	4	no	—
455	D₄	—	8	8	no	—
456	C₂×C₄	—	2	2	no	—
457	C₂×C₄	—	2	2	no	—
458	C₂×C₄	—	2	2	no	—
459	C₂×C₄	—	2	1	no	—
460	C₂×C₄	—	2	1	no	—
461	C₂×C₄	—	2	2	no	—
462	C₂×C₄	—	2	2	no	—
463	C₂×C₄	—	2	4	no	—
464	C₂×C₄	—	2	2	no	—
465	C₂×C₄	—	2	2	no	—
466	C₂×C₄	—	4	8	no	—
467	C₂×C₄	—	4	16	no	—
468	C₂×C₄	—	4	2	no	—
469	C₂×C₄	—	4	2	no	—
470	C₂×C₄	—	4	2	no	—
471	C₂×C₄	—	4	1	no	—
472	C₂×C₄	—	4	1	no	—
473	C₂×C₄	—	4	2	no	—
474	C₂×C₄	—	4	1	no	—
475	C₂×C₄	—	4	1	no	—
476	C₂×C₄	#120×C₇₃	1	2	yes	—
477	C₂×C₄	#120×C₇₃	1	2	yes	—
478	C₂×C₄	AGL(1,ℤ/8)×C₇₃	1	4	yes	—
479	C₂×C₄	C₂²×D₄×C₇₃	1	1	yes	characteristic
480	C₂×C₄	C₂²×D₄×C₇₃	1	1	yes	characteristic
481	C₂×C₄	C₂×#41×C₇₃	1	2	yes	—
482	C₂×C₄	2₋¹⁺⁴×C₇₃	1	2	yes	—
483	C₈	—	4	1	no	—
484	C₈	—	4	1	no	—
485	C₈	—	4	2	no	—
486	C₂²	—	4	2	no	—
487	C₂²	—	4	4	no	—
488	C₂²	—	4	4	no	—
489	C₂²	—	4	2	no	—
490	C₂²	—	4	2	no	—
491	C₂²	—	4	4	no	—
492	C₂²	—	8	2	no	—
493	C₂²	—	8	2	no	—
494	C₂²	—	8	2	no	—
495	C₂²	—	8	2	no	—
496	C₂²	—	8	2	no	—
497	C₂²	—	8	2	no	—
498	C₂²	C₂×#120×C₇₃	1	1	yes	characteristic
499	C₂²	#548×C₇₃	1	2	yes	—
500	C₂²	C₂×AGL(1,ℤ/8)×C₇₃	1	2	yes	—
501	C₂²	#576×C₇₃	1	1	yes	characteristic
502	C₂²	#577×C₇₃	1	1	yes	characteristic
503	C₄	—	2	2	no	—
504	C₄	—	2	4	no	—
505	C₄	—	2	2	no	—
506	C₄	—	4	2	no	—
507	C₄	—	4	2	no	—
508	C₄	—	4	4	no	—
509	C₄	—	8	1	no	—
510	C₄	—	8	1	no	—
511	C₄	#532×C₇₃	1	1	yes	characteristic
512	C₄	#536×C₇₃	1	1	yes	characteristic
513	C₄	#547×C₇₃	1	2	yes	—
514	C₂	—	8	4	no	—
515	C₂	—	8	2	no	—
516	C₂	C₇₃×#2432	1	1	yes	characteristic
517	C₂	C₇₃×#3003	1	1	yes	characteristic
518	C₂	C₇₃×#3012	1	1	yes	characteristic
519	C₂	C₇₃×#3366	1	2	yes	—
520	C₂	C₇₃×#3368	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₇₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₇₃
prime radical	C₂×#550×C₇₃	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₇₃ ◁ C₂×C₄×Q₈×C₇₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×#490×C₇₃	C₂	semidirect
3. C₂×#478×C₇₃	C₂	semidirect
4. C₇₃×#2584	C₂	semidirect
5. C₇₃×#2041	C₂	semidirect
6. C₇₃×#2041	C₂	semidirect
7. C₇₃×#1985	C₂	semidirect
8. C₇₃×#1982	C₂	semidirect
9. C₇₃×#1864	C₂	semidirect
10. C₇₃×#1862	C₂	semidirect
11. C₇₃×#1762	C₂	semidirect
162. C₄⋊C₄×C₇₃	#41	semidirect
253. #25655	C₇₃	direct (N × H)
262. C₂×#490	C₂×C₇₃	semidirect
263. C₂×#478	C₂×C₇₃	semidirect
264. #2584	C₂×C₇₃	semidirect
265. #2041	C₂×C₇₃	semidirect
266. #2041	C₂×C₇₃	semidirect
267. #1985	C₂×C₇₃	semidirect
268. #1982	C₂×C₇₃	semidirect
269. #1864	C₂×C₇₃	semidirect
270. #1862	C₂×C₇₃	semidirect
271. #1762	C₂×C₇₃	semidirect
272. C₇₃	#25655	direct (N × H)
423. C₄⋊C₄	#41×C₇₃	semidirect

Maximal subgroups

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

subgroup	index
C₂×#550×C₇₃	2
C₂×#490×C₇₃	2
C₂×#478×C₇₃	2
C₇₃×#2584	2
C₇₃×#2041	2
C₇₃×#1985	2
C₇₃×#1982	2
C₇₃×#1864	2
C₇₃×#1862	2
C₇₃×#1762	2
#25655	73

Subgroups — C73×#25655 #32935059

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₃×#25655 #32935059