Subgroups — C₇₃×#24069 #32933473

Order 18688.

1130 conjugacy classes of subgroups.

The subgroup lattice has 558 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#540×C₇₃	C₂	1	1	yes	maximal, characteristic
2	C₂×#481×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#480×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₇₃×#2317	C₂	1	1	yes	maximal, characteristic, complemented
5	C₇₃×#2059	C₂	1	2	yes	maximal, complemented
6	C₇₃×#2041	C₂	1	2	yes	maximal, complemented
7	C₇₃×#1875	C₂	1	1	yes	maximal, characteristic, complemented
8	C₇₃×#1875	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×#1818	C₂	1	1	yes	maximal, characteristic, complemented
12	#540×C₇₃	—	2	4	no	—
13	#540×C₇₃	—	2	4	no	—
14	C₂×#127×C₇₃	C₂²	1	1	yes	characteristic
15	C₂×#125×C₇₃	C₂²	1	1	yes	characteristic
16	C₂×#123×C₇₃	—	2	1	no	—
17	C₂×#123×C₇₃	—	2	1	no	—
18	C₂×#121×C₇₃	—	2	1	no	—
19	C₂×#121×C₇₃	—	2	1	no	—
20	C₂×#121×C₇₃	C₂²	1	1	yes	characteristic
21	C₂×#121×C₇₃	C₂²	1	1	yes	characteristic
22	C₂×C₄×D₄×C₇₃	C₂²	1	1	yes	characteristic
23	C₂×C₄×D₄×C₇₃	C₂²	1	1	yes	characteristic
24	C₂×#117×C₇₃	C₂²	1	1	yes	characteristic
25	C₂×#117×C₇₃	C₂²	1	1	yes	characteristic
26	C₂²×C₄⋊C₄×C₇₃	C₂²	1	1	yes	characteristic
27	#481×C₇₃	—	2	4	no	—
28	#480×C₇₃	—	2	4	no	—
29	C₂×#107×C₇₃	C₂²	1	2	yes	—
30	C₂×#106×C₇₃	C₂²	1	2	yes	—
31	C₂×#102×C₇₃	C₂²	1	2	yes	—
32	C₂×#102×C₇₃	C₂²	1	2	yes	—
33	C₂×#102×C₇₃	C₂²	1	2	yes	—
34	C₂×#102×C₇₃	C₂²	1	2	yes	—
35	C₂×C₂²⋊C₈×C₇₃	C₂²	1	1	yes	characteristic
36	C₂×C₂²⋊C₈×C₇₃	C₂²	1	1	yes	characteristic
37	#389×C₇₃	C₂²	1	2	yes	—
38	#389×C₇₃	C₂²	1	2	yes	—
39	#385×C₇₃	—	2	1	no	—
40	#385×C₇₃	—	2	1	no	—
41	#384×C₇₃	—	2	1	no	—
42	#382×C₇₃	—	2	1	no	—
43	#340×C₇₃	C₂²	1	2	yes	—
44	#340×C₇₃	C₂²	1	2	yes	—
45	#336×C₇₃	C₂²	1	2	yes	—
46	#336×C₇₃	C₂²	1	2	yes	—
47	C₂²×D₄×C₇₃	—	2	1	no	—
48	C₂²×D₄×C₇₃	—	2	1	no	—
49	C₂²×D₄×C₇₃	—	2	1	no	—
50	C₂²×D₄×C₇₃	—	2	1	no	—
51	C₂²×D₄×C₇₃	C₂³	1	1	yes	characteristic
52	C₂²×D₄×C₇₃	C₂³	1	1	yes	characteristic
53	C₂³×C₄×C₇₃	—	2	1	no	—
54	C₂³×C₄×C₇₃	—	2	1	no	—
55	C₂³×C₄×C₇₃	—	2	1	no	—
56	C₂³×C₄×C₇₃	C₂³	1	1	yes	characteristic
57	C₂²×C₈×C₇₃	C₂³	1	2	yes	—
58	C₂²×C₈×C₇₃	C₂³	1	2	yes	—
59	#127×C₇₃	—	2	2	no	—
60	#127×C₇₃	—	2	2	no	—
61	#125×C₇₃	—	2	2	no	—
62	#125×C₇₃	—	2	2	no	—
63	#123×C₇₃	—	2	8	no	—
64	#123×C₇₃	—	2	8	no	—
65	#121×C₇₃	—	2	8	no	—
66	#121×C₇₃	—	2	8	no	—
67	#121×C₇₃	—	2	2	no	—
68	#121×C₇₃	—	2	2	no	—
69	#121×C₇₃	D₄	1	4	yes	—
70	#121×C₇₃	D₄	1	4	yes	—
71	C₄×D₄×C₇₃	—	2	2	no	—
72	C₄×D₄×C₇₃	—	2	2	no	—
73	C₄×D₄×C₇₃	—	2	2	no	—
74	C₄×D₄×C₇₃	—	2	2	no	—
75	#117×C₇₃	—	2	2	no	—
76	#117×C₇₃	—	2	2	no	—
77	#117×C₇₃	—	2	4	no	—
78	C₂×C₄⋊C₄×C₇₃	—	2	1	no	—
79	C₂×C₄⋊C₄×C₇₃	—	2	1	no	—
80	C₂×C₄⋊C₄×C₇₃	—	2	2	no	—
81	C₂×C₄⋊C₄×C₇₃	—	2	2	no	—
82	C₂×C₄⋊C₄×C₇₃	—	2	1	no	—
83	C₂×C₄⋊C₄×C₇₃	—	2	2	no	—
84	C₂×C₄⋊C₄×C₇₃	—	2	2	no	—
85	C₂×C₄⋊C₄×C₇₃	D₄	1	1	yes	characteristic
86	C₂×C₄⋊C₄×C₇₃	D₄	1	1	yes	characteristic
87	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
88	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
89	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
90	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
91	C₂×C₂²⋊C₄×C₇₃	—	2	1	no	—
92	C₂×C₂²⋊C₄×C₇₃	—	2	1	no	—
93	C₂×C₂²⋊C₄×C₇₃	—	2	1	no	—
94	C₂×C₂²⋊C₄×C₇₃	—	2	1	no	—
95	C₂×C₂²⋊C₄×C₇₃	—	2	1	no	—
96	C₂×C₂²⋊C₄×C₇₃	D₄	1	1	yes	characteristic
97	C₂×C₂²⋊C₄×C₇₃	D₄	1	1	yes	characteristic
98	C₂×C₄²×C₇₃	—	2	1	no	—
99	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
100	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
101	#107×C₇₃	—	2	4	no	—
102	#106×C₇₃	—	2	4	no	—
103	#102×C₇₃	—	2	4	no	—
104	#102×C₇₃	—	2	4	no	—
105	#102×C₇₃	—	2	4	no	—
106	#102×C₇₃	—	2	4	no	—
107	C₂²⋊C₈×C₇₃	—	2	2	no	—
108	C₂²⋊C₈×C₇₃	—	2	2	no	—
109	#95×C₇₃	—	2	2	no	—
110	#95×C₇₃	—	2	2	no	—
111	C₂⁴×C₇₃	—	2	1	no	—
112	C₂⁴×C₇₃	—	2	1	no	—
113	C₂⁴×C₇₃	C₂×D₄	1	1	yes	characteristic
114	C₂×D₄×C₇₃	—	2	4	no	—
115	C₂×D₄×C₇₃	—	2	4	no	—
116	C₂×D₄×C₇₃	—	2	4	no	—
117	C₂×D₄×C₇₃	—	2	4	no	—
118	C₂×D₄×C₇₃	—	2	1	no	—
119	C₂×D₄×C₇₃	—	2	1	no	—
120	C₂×D₄×C₇₃	—	2	2	no	—
121	C₂×D₄×C₇₃	—	2	2	no	—
122	C₂×D₄×C₇₃	—	2	2	no	—
123	C₂×D₄×C₇₃	—	2	2	no	—
124	C₂×D₄×C₇₃	—	8	2	no	—
125	C₂×D₄×C₇₃	—	8	2	no	—
126	C₂×D₄×C₇₃	—	8	2	no	—
127	C₂×D₄×C₇₃	—	8	2	no	—
128	C₂×D₄×C₇₃	C₂×D₄	1	2	yes	—
129	C₂×D₄×C₇₃	C₂×D₄	1	2	yes	—
130	C₂²×C₄×C₇₃	—	2	2	no	—
131	C₂²×C₄×C₇₃	—	2	2	no	—
132	C₂²×C₄×C₇₃	—	2	2	no	—
133	C₂²×C₄×C₇₃	—	2	1	no	—
134	C₂²×C₄×C₇₃	—	2	1	no	—
135	C₂²×C₄×C₇₃	—	2	4	no	—
136	C₂²×C₄×C₇₃	—	2	4	no	—
137	C₂²×C₄×C₇₃	—	2	2	no	—
138	C₂²×C₄×C₇₃	—	4	2	no	—
139	C₂²×C₄×C₇₃	—	8	2	no	—
140	C₂²×C₄×C₇₃	—	8	2	no	—
141	C₂²×C₄×C₇₃	—	8	2	no	—
142	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
143	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
144	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
145	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
146	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
147	C₂²×C₄×C₇₃	C₂×D₄	1	2	yes	—
148	C₂²×C₄×C₇₃	C₂×D₄	1	2	yes	—
149	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
150	C₂×C₈×C₇₃	—	2	2	no	—
151	C₂×C₈×C₇₃	—	2	2	no	—
152	C₂×C₈×C₇₃	—	2	2	no	—
153	C₂×C₈×C₇₃	—	2	2	no	—
154	C₂×C₈×C₇₃	—	2	2	no	—
155	C₂×C₈×C₇₃	—	2	2	no	—
156	C₄⋊C₄×C₇₃	—	2	4	no	—
157	C₄⋊C₄×C₇₃	—	2	4	no	—
158	C₄⋊C₄×C₇₃	—	2	2	no	—
159	C₄⋊C₄×C₇₃	—	2	2	no	—
160	C₄⋊C₄×C₇₃	—	2	1	no	—
161	C₄⋊C₄×C₇₃	—	2	1	no	—
162	C₄⋊C₄×C₇₃	—	2	2	no	—
163	C₄⋊C₄×C₇₃	—	2	2	no	—
164	C₄⋊C₄×C₇₃	—	2	2	no	—
165	C₄⋊C₄×C₇₃	—	4	2	no	—
166	C₄⋊C₄×C₇₃	—	8	2	no	—
167	C₄⋊C₄×C₇₃	—	8	2	no	—
168	C₄⋊C₄×C₇₃	C₂×D₄	1	2	yes	—
169	C₄⋊C₄×C₇₃	C₂×D₄	1	2	yes	—
170	C₄⋊C₄×C₇₃	#41	1	4	yes	—
171	C₂²⋊C₄×C₇₃	—	2	4	no	—
172	C₂²⋊C₄×C₇₃	—	2	4	no	—
173	C₂²⋊C₄×C₇₃	—	2	4	no	—
174	C₂²⋊C₄×C₇₃	—	2	2	no	—
175	C₂²⋊C₄×C₇₃	—	2	2	no	—
176	C₂²⋊C₄×C₇₃	—	2	4	no	—
177	C₂²⋊C₄×C₇₃	—	2	4	no	—
178	C₄²×C₇₃	—	2	4	no	—
179	C₄²×C₇₃	—	2	1	no	—
180	C₄²×C₇₃	—	2	1	no	—
181	C₄²×C₇₃	—	2	1	no	—
182	C₄²×C₇₃	—	2	1	no	—
183	C₂³×C₇₃	—	2	1	no	—
184	C₂³×C₇₃	—	2	1	no	—
185	C₂³×C₇₃	—	2	2	no	—
186	C₂³×C₇₃	—	2	2	no	—
187	C₂³×C₇₃	—	2	2	no	—
188	C₂³×C₇₃	—	2	2	no	—
189	C₂³×C₇₃	—	4	1	no	—
190	C₂³×C₇₃	—	4	1	no	—
191	C₂³×C₇₃	—	4	1	no	—
192	C₂³×C₇₃	—	4	1	no	—
193	C₂³×C₇₃	—	4	2	no	—
194	C₂³×C₇₃	—	4	2	no	—
195	C₂³×C₇₃	—	4	2	no	—
196	C₂³×C₇₃	—	4	2	no	—
197	C₂³×C₇₃	#120	1	2	yes	—
198	C₂³×C₇₃	C₂²×D₄	1	1	yes	characteristic
199	D₄×C₇₃	—	2	4	no	—
200	D₄×C₇₃	—	2	4	no	—
201	D₄×C₇₃	—	4	2	no	—
202	D₄×C₇₃	—	4	2	no	—
203	D₄×C₇₃	—	8	4	no	—
204	D₄×C₇₃	—	8	4	no	—
205	D₄×C₇₃	—	8	4	no	—
206	D₄×C₇₃	—	8	4	no	—
207	C₂×C₄×C₇₃	—	2	1	no	—
208	C₂×C₄×C₇₃	—	2	1	no	—
209	C₂×C₄×C₇₃	—	2	4	no	—
210	C₂×C₄×C₇₃	—	2	4	no	—
211	C₂×C₄×C₇₃	—	2	1	no	—
212	C₂×C₄×C₇₃	—	2	1	no	—
213	C₂×C₄×C₇₃	—	2	1	no	—
214	C₂×C₄×C₇₃	—	2	1	no	—
215	C₂×C₄×C₇₃	—	2	2	no	—
216	C₂×C₄×C₇₃	—	2	2	no	—
217	C₂×C₄×C₇₃	—	2	4	no	—
218	C₂×C₄×C₇₃	—	2	2	no	—
219	C₂×C₄×C₇₃	—	2	2	no	—
220	C₂×C₄×C₇₃	—	2	2	no	—
221	C₂×C₄×C₇₃	—	2	2	no	—
222	C₂×C₄×C₇₃	—	4	2	no	—
223	C₂×C₄×C₇₃	—	4	2	no	—
224	C₂×C₄×C₇₃	—	4	2	no	—
225	C₂×C₄×C₇₃	—	4	2	no	—
226	C₂×C₄×C₇₃	—	4	2	no	—
227	C₂×C₄×C₇₃	—	4	2	no	—
228	C₂×C₄×C₇₃	—	4	2	no	—
229	C₂×C₄×C₇₃	—	8	4	no	—
230	C₂×C₄×C₇₃	—	8	4	no	—
231	C₂×C₄×C₇₃	—	8	4	no	—
232	C₂×C₄×C₇₃	#120	1	2	yes	—
233	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
234	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
235	C₂×C₄×C₇₃	C₂×#41	1	2	yes	—
236	C₂×C₄×C₇₃	2₋¹⁺⁴	1	2	yes	—
237	C₈×C₇₃	—	4	2	no	—
238	C₈×C₇₃	—	4	2	no	—
239	C₂²×C₇₃	—	2	2	no	—
240	C₂²×C₇₃	—	2	2	no	—
241	C₂²×C₇₃	—	2	2	no	—
242	C₂²×C₇₃	—	4	2	no	—
243	C₂²×C₇₃	—	4	2	no	—
244	C₂²×C₇₃	—	4	2	no	—
245	C₂²×C₇₃	—	4	2	no	—
246	C₂²×C₇₃	—	4	2	no	—
247	C₂²×C₇₃	—	4	2	no	—
248	C₂²×C₇₃	—	4	2	no	—
249	C₂²×C₇₃	—	4	2	no	—
250	C₂²×C₇₃	—	8	2	no	—
251	C₂²×C₇₃	—	8	2	no	—
252	C₂²×C₇₃	—	8	2	no	—
253	C₂²×C₇₃	—	8	2	no	—
254	C₂²×C₇₃	C₂×#120	1	1	yes	characteristic
255	C₂²×C₇₃	#525	1	1	yes	characteristic
256	C₂²×C₇₃	#536	1	1	yes	characteristic
257	C₂²×C₇₃	#576	1	2	yes	—
258	C₂²×C₇₃	#577	1	2	yes	—
259	C₄×C₇₃	—	2	2	no	—
260	C₄×C₇₃	—	4	4	no	—
261	C₄×C₇₃	—	4	1	no	—
262	C₄×C₇₃	—	4	1	no	—
263	C₄×C₇₃	—	4	2	no	—
264	C₄×C₇₃	—	4	1	no	—
265	C₄×C₇₃	—	4	1	no	—
266	C₄×C₇₃	—	4	2	no	—
267	C₄×C₇₃	—	8	2	no	—
268	C₄×C₇₃	#547	1	2	yes	—
269	C₄×C₇₃	#547	1	2	yes	—
270	#24069	C₇₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
271	C₂×C₇₃	—	4	2	no	—
272	C₂×C₇₃	—	8	2	no	—
273	C₂×C₇₃	—	8	2	no	—
274	C₂×C₇₃	#2406	1	1	yes	characteristic
275	C₂×C₇₃	#3008	1	1	yes	characteristic
276	C₂×C₇₃	#3009	1	1	yes	characteristic
277	C₂×C₇₃	#3119	1	2	yes	—
278	C₂×C₇₃	#3241	1	2	yes	—
279	C₂×#540	C₂×C₇₃	1	1	yes	characteristic
280	C₂×#481	C₂×C₇₃	1	1	yes	characteristic, complemented
281	C₂×#480	C₂×C₇₃	1	1	yes	characteristic, complemented
282	#2317	C₂×C₇₃	1	1	yes	characteristic, complemented
283	#2059	C₂×C₇₃	1	2	yes	complemented
284	#2041	C₂×C₇₃	1	2	yes	complemented
285	#1875	C₂×C₇₃	1	1	yes	characteristic, complemented
286	#1875	C₂×C₇₃	1	1	yes	characteristic, complemented
287	#1864	C₂×C₇₃	1	2	yes	complemented
288	#1862	C₂×C₇₃	1	2	yes	complemented
289	#1818	C₂×C₇₃	1	1	yes	characteristic, complemented
290	C₇₃	#24069	1	1	yes	characteristic, direct product factor, Sylow
291	#540	—	2	4	no	—
292	#540	—	2	4	no	—
293	C₂×#127	C₂²×C₇₃	1	1	yes	characteristic
294	C₂×#125	C₂²×C₇₃	1	1	yes	characteristic
295	C₂×#123	—	2	1	no	—
296	C₂×#123	—	2	1	no	—
297	C₂×#121	—	2	1	no	—
298	C₂×#121	—	2	1	no	—
299	C₂×#121	C₂²×C₇₃	1	1	yes	characteristic
300	C₂×#121	C₂²×C₇₃	1	1	yes	characteristic
301	C₂×C₄×D₄	C₂²×C₇₃	1	1	yes	characteristic
302	C₂×C₄×D₄	C₂²×C₇₃	1	1	yes	characteristic
303	C₂×#117	C₂²×C₇₃	1	1	yes	characteristic
304	C₂×#117	C₂²×C₇₃	1	1	yes	characteristic
305	C₂²×C₄⋊C₄	C₂²×C₇₃	1	1	yes	characteristic
306	#481	—	2	4	no	—
307	#480	—	2	4	no	—
308	C₂×#107	C₂²×C₇₃	1	2	yes	—
309	C₂×#106	C₂²×C₇₃	1	2	yes	—
310	C₂×#102	C₂²×C₇₃	1	2	yes	—
311	C₂×#102	C₂²×C₇₃	1	2	yes	—
312	C₂×#102	C₂²×C₇₃	1	2	yes	—
313	C₂×#102	C₂²×C₇₃	1	2	yes	—
314	C₂×C₂²⋊C₈	C₂²×C₇₃	1	1	yes	characteristic
315	C₂×C₂²⋊C₈	C₂²×C₇₃	1	1	yes	characteristic
316	#389	C₂²×C₇₃	1	2	yes	—
317	#389	C₂²×C₇₃	1	2	yes	—
318	#385	—	2	1	no	—
319	#385	—	2	1	no	—
320	#384	—	2	1	no	—
321	#382	—	2	1	no	—
322	#340	C₂²×C₇₃	1	2	yes	—
323	#340	C₂²×C₇₃	1	2	yes	—
324	#336	C₂²×C₇₃	1	2	yes	—
325	#336	C₂²×C₇₃	1	2	yes	—
326	C₂²×D₄	—	2	1	no	—
327	C₂²×D₄	—	2	1	no	—
328	C₂²×D₄	—	2	1	no	—
329	C₂²×D₄	—	2	1	no	—
330	C₂²×D₄	C₂³×C₇₃	1	1	yes	characteristic
331	C₂²×D₄	C₂³×C₇₃	1	1	yes	characteristic
332	C₂³×C₄	—	2	1	no	—
333	C₂³×C₄	—	2	1	no	—
334	C₂³×C₄	—	2	1	no	—
335	C₂³×C₄	C₂³×C₇₃	1	1	yes	characteristic
336	C₂²×C₈	C₂³×C₇₃	1	2	yes	—
337	C₂²×C₈	C₂³×C₇₃	1	2	yes	—
338	#127	—	2	2	no	—
339	#127	—	2	2	no	—
340	#125	—	2	2	no	—
341	#125	—	2	2	no	—
342	#123	—	2	8	no	—
343	#123	—	2	8	no	—
344	#121	—	2	8	no	—
345	#121	—	2	8	no	—
346	#121	—	2	2	no	—
347	#121	—	2	2	no	—
348	#121	D₄×C₇₃	1	4	yes	—
349	#121	D₄×C₇₃	1	4	yes	—
350	C₄×D₄	—	2	2	no	—
351	C₄×D₄	—	2	2	no	—
352	C₄×D₄	—	2	2	no	—
353	C₄×D₄	—	2	2	no	—
354	#117	—	2	2	no	—
355	#117	—	2	2	no	—
356	#117	—	2	4	no	—
357	C₂×C₄⋊C₄	—	2	1	no	—
358	C₂×C₄⋊C₄	—	2	1	no	—
359	C₂×C₄⋊C₄	—	2	2	no	—
360	C₂×C₄⋊C₄	—	2	2	no	—
361	C₂×C₄⋊C₄	—	2	1	no	—
362	C₂×C₄⋊C₄	—	2	2	no	—
363	C₂×C₄⋊C₄	—	2	2	no	—
364	C₂×C₄⋊C₄	D₄×C₇₃	1	1	yes	characteristic
365	C₂×C₄⋊C₄	D₄×C₇₃	1	1	yes	characteristic
366	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
367	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
368	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
369	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
370	C₂×C₂²⋊C₄	—	2	1	no	—
371	C₂×C₂²⋊C₄	—	2	1	no	—
372	C₂×C₂²⋊C₄	—	2	1	no	—
373	C₂×C₂²⋊C₄	—	2	1	no	—
374	C₂×C₂²⋊C₄	—	2	1	no	—
375	C₂×C₂²⋊C₄	D₄×C₇₃	1	1	yes	characteristic
376	C₂×C₂²⋊C₄	D₄×C₇₃	1	1	yes	characteristic
377	C₂×C₄²	—	2	1	no	—
378	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
379	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
380	#107	—	2	4	no	—
381	#106	—	2	4	no	—
382	#102	—	2	4	no	—
383	#102	—	2	4	no	—
384	#102	—	2	4	no	—
385	#102	—	2	4	no	—
386	C₂²⋊C₈	—	2	2	no	—
387	C₂²⋊C₈	—	2	2	no	—
388	#95	—	2	2	no	—
389	#95	—	2	2	no	—
390	C₂⁴	—	2	1	no	—
391	C₂⁴	—	2	1	no	—
392	C₂⁴	C₂×D₄×C₇₃	1	1	yes	characteristic
393	C₂×D₄	—	2	4	no	—
394	C₂×D₄	—	2	4	no	—
395	C₂×D₄	—	2	4	no	—
396	C₂×D₄	—	2	4	no	—
397	C₂×D₄	—	2	1	no	—
398	C₂×D₄	—	2	1	no	—
399	C₂×D₄	—	2	2	no	—
400	C₂×D₄	—	2	2	no	—
401	C₂×D₄	—	2	2	no	—
402	C₂×D₄	—	2	2	no	—
403	C₂×D₄	—	8	2	no	—
404	C₂×D₄	—	8	2	no	—
405	C₂×D₄	—	8	2	no	—
406	C₂×D₄	—	8	2	no	—
407	C₂×D₄	C₂×D₄×C₇₃	1	2	yes	—
408	C₂×D₄	C₂×D₄×C₇₃	1	2	yes	—
409	C₂²×C₄	—	2	2	no	—
410	C₂²×C₄	—	2	2	no	—
411	C₂²×C₄	—	2	2	no	—
412	C₂²×C₄	—	2	1	no	—
413	C₂²×C₄	—	2	1	no	—
414	C₂²×C₄	—	2	4	no	—
415	C₂²×C₄	—	2	4	no	—
416	C₂²×C₄	—	2	2	no	—
417	C₂²×C₄	—	4	2	no	—
418	C₂²×C₄	—	8	2	no	—
419	C₂²×C₄	—	8	2	no	—
420	C₂²×C₄	—	8	2	no	—
421	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
422	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
423	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
424	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
425	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
426	C₂²×C₄	C₂×D₄×C₇₃	1	2	yes	—
427	C₂²×C₄	C₂×D₄×C₇₃	1	2	yes	—
428	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
429	C₂×C₈	—	2	2	no	—
430	C₂×C₈	—	2	2	no	—
431	C₂×C₈	—	2	2	no	—
432	C₂×C₈	—	2	2	no	—
433	C₂×C₈	—	2	2	no	—
434	C₂×C₈	—	2	2	no	—
435	C₄⋊C₄	—	2	4	no	—
436	C₄⋊C₄	—	2	4	no	—
437	C₄⋊C₄	—	2	2	no	—
438	C₄⋊C₄	—	2	2	no	—
439	C₄⋊C₄	—	2	1	no	—
440	C₄⋊C₄	—	2	1	no	—
441	C₄⋊C₄	—	2	2	no	—
442	C₄⋊C₄	—	2	2	no	—
443	C₄⋊C₄	—	2	2	no	—
444	C₄⋊C₄	—	4	2	no	—
445	C₄⋊C₄	—	8	2	no	—
446	C₄⋊C₄	—	8	2	no	—
447	C₄⋊C₄	C₂×D₄×C₇₃	1	2	yes	—
448	C₄⋊C₄	C₂×D₄×C₇₃	1	2	yes	—
449	C₄⋊C₄	#41×C₇₃	1	4	yes	—
450	C₂²⋊C₄	—	2	4	no	—
451	C₂²⋊C₄	—	2	4	no	—
452	C₂²⋊C₄	—	2	4	no	—
453	C₂²⋊C₄	—	2	2	no	—
454	C₂²⋊C₄	—	2	2	no	—
455	C₂²⋊C₄	—	2	4	no	—
456	C₂²⋊C₄	—	2	4	no	—
457	C₄²	—	2	4	no	—
458	C₄²	—	2	1	no	—
459	C₄²	—	2	1	no	—
460	C₄²	—	2	1	no	—
461	C₄²	—	2	1	no	—
462	C₂³	—	2	1	no	—
463	C₂³	—	2	1	no	—
464	C₂³	—	2	2	no	—
465	C₂³	—	2	2	no	—
466	C₂³	—	2	2	no	—
467	C₂³	—	2	2	no	—
468	C₂³	—	4	1	no	—
469	C₂³	—	4	1	no	—
470	C₂³	—	4	1	no	—
471	C₂³	—	4	1	no	—
472	C₂³	—	4	2	no	—
473	C₂³	—	4	2	no	—
474	C₂³	—	4	2	no	—
475	C₂³	—	4	2	no	—
476	C₂³	#120×C₇₃	1	2	yes	—
477	C₂³	C₂²×D₄×C₇₃	1	1	yes	characteristic
478	D₄	—	2	4	no	—
479	D₄	—	2	4	no	—
480	D₄	—	4	2	no	—
481	D₄	—	4	2	no	—
482	D₄	—	8	4	no	—
483	D₄	—	8	4	no	—
484	D₄	—	8	4	no	—
485	D₄	—	8	4	no	—
486	C₂×C₄	—	2	1	no	—
487	C₂×C₄	—	2	1	no	—
488	C₂×C₄	—	2	4	no	—
489	C₂×C₄	—	2	4	no	—
490	C₂×C₄	—	2	1	no	—
491	C₂×C₄	—	2	1	no	—
492	C₂×C₄	—	2	1	no	—
493	C₂×C₄	—	2	1	no	—
494	C₂×C₄	—	2	2	no	—
495	C₂×C₄	—	2	2	no	—
496	C₂×C₄	—	2	4	no	—
497	C₂×C₄	—	2	2	no	—
498	C₂×C₄	—	2	2	no	—
499	C₂×C₄	—	2	2	no	—
500	C₂×C₄	—	2	2	no	—
501	C₂×C₄	—	4	2	no	—
502	C₂×C₄	—	4	2	no	—
503	C₂×C₄	—	4	2	no	—
504	C₂×C₄	—	4	2	no	—
505	C₂×C₄	—	4	2	no	—
506	C₂×C₄	—	4	2	no	—
507	C₂×C₄	—	4	2	no	—
508	C₂×C₄	—	8	4	no	—
509	C₂×C₄	—	8	4	no	—
510	C₂×C₄	—	8	4	no	—
511	C₂×C₄	#120×C₇₃	1	2	yes	—
512	C₂×C₄	C₂²×D₄×C₇₃	1	1	yes	characteristic
513	C₂×C₄	C₂²×D₄×C₇₃	1	1	yes	characteristic
514	C₂×C₄	C₂×#41×C₇₃	1	2	yes	—
515	C₂×C₄	2₋¹⁺⁴×C₇₃	1	2	yes	—
516	C₈	—	4	2	no	—
517	C₈	—	4	2	no	—
518	C₂²	—	2	2	no	—
519	C₂²	—	2	2	no	—
520	C₂²	—	2	2	no	—
521	C₂²	—	4	2	no	—
522	C₂²	—	4	2	no	—
523	C₂²	—	4	2	no	—
524	C₂²	—	4	2	no	—
525	C₂²	—	4	2	no	—
526	C₂²	—	4	2	no	—
527	C₂²	—	4	2	no	—
528	C₂²	—	4	2	no	—
529	C₂²	—	8	2	no	—
530	C₂²	—	8	2	no	—
531	C₂²	—	8	2	no	—
532	C₂²	—	8	2	no	—
533	C₂²	C₂×#120×C₇₃	1	1	yes	characteristic
534	C₂²	#525×C₇₃	1	1	yes	characteristic
535	C₂²	#536×C₇₃	1	1	yes	characteristic
536	C₂²	#576×C₇₃	1	2	yes	—
537	C₂²	#577×C₇₃	1	2	yes	—
538	C₄	—	2	2	no	—
539	C₄	—	4	1	no	—
540	C₄	—	4	1	no	—
541	C₄	—	4	2	no	—
542	C₄	—	4	1	no	—
543	C₄	—	4	1	no	—
544	C₄	—	4	2	no	—
545	C₄	—	4	4	no	—
546	C₄	—	8	2	no	—
547	C₄	#547×C₇₃	1	2	yes	—
548	C₄	#547×C₇₃	1	2	yes	—
549	C₂	—	4	2	no	—
550	C₂	—	8	2	no	—
551	C₂	—	8	2	no	—
552	C₂	C₇₃×#2406	1	1	yes	characteristic
553	C₂	C₇₃×#3008	1	1	yes	characteristic
554	C₂	C₇₃×#3009	1	1	yes	characteristic
555	C₂	C₇₃×#3119	1	2	yes	—
556	C₂	C₇₃×#3241	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₇₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₇₃
prime radical	C₂×#540×C₇₃	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₇₃ ◁ C₂×#117×C₇₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×#481×C₇₃	C₂	semidirect
3. C₂×#480×C₇₃	C₂	semidirect
4. C₇₃×#2317	C₂	semidirect
5. C₇₃×#2059	C₂	semidirect
6. C₇₃×#2041	C₂	semidirect
7. C₇₃×#1875	C₂	semidirect
8. C₇₃×#1875	C₂	semidirect
9. C₇₃×#1864	C₂	semidirect
10. C₇₃×#1862	C₂	semidirect
11. C₇₃×#1818	C₂	semidirect
270. #24069	C₇₃	direct (N × H)
280. C₂×#481	C₂×C₇₃	semidirect
281. C₂×#480	C₂×C₇₃	semidirect
282. #2317	C₂×C₇₃	semidirect
283. #2059	C₂×C₇₃	semidirect
284. #2041	C₂×C₇₃	semidirect
285. #1875	C₂×C₇₃	semidirect
286. #1875	C₂×C₇₃	semidirect
287. #1864	C₂×C₇₃	semidirect
288. #1862	C₂×C₇₃	semidirect
289. #1818	C₂×C₇₃	semidirect
290. C₇₃	#24069	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×#540×C₇₃	2
C₂×#481×C₇₃	2
C₂×#480×C₇₃	2
C₇₃×#2317	2
C₇₃×#2059	2
C₇₃×#2041	2
C₇₃×#1875	2
C₇₃×#1864	2
C₇₃×#1862	2
C₇₃×#1818	2
#24069	73

Subgroups — C73×#24069 #32933473

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₃×#24069 #32933473