Subgroups — C₇₃×#23325 #32932729

Order 18688.

680 conjugacy classes of subgroups.

The subgroup lattice has 426 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇₃×#2395	C₂	1	1	yes	maximal, characteristic
2	C₇₃×#1954	C₂	1	1	yes	maximal, characteristic
3	C₇₃×#1940	C₂	1	2	yes	maximal, complemented
4	C₇₃×#1924	C₂	1	2	yes	maximal, complemented
5	C₇₃×#1924	C₂	1	2	yes	maximal, complemented
6	C₇₃×#1916	C₂	1	2	yes	maximal, complemented
7	C₇₃×#1870	C₂	1	1	yes	maximal, characteristic
8	C₇₃×#1851	C₂	1	2	yes	maximal, complemented
9	C₇₃×#1798	C₂	1	2	yes	maximal, complemented
10	C₂²×M₁₆×C₇₃	C₂²	1	1	yes	characteristic
11	C₂×C₄×D₄×C₇₃	C₂²	1	1	yes	characteristic
12	C₂×#117×C₇₃	C₂²	1	1	yes	characteristic
13	C₂×C₄⋊C₈×C₇₃	C₂²	1	1	yes	characteristic
14	C₂×C₄⋊C₈×C₇₃	C₂²	1	2	yes	—
15	C₂×C₄⋊C₈×C₇₃	C₂²	1	2	yes	—
16	C₂×C₄⋊C₈×C₇₃	C₂²	1	2	yes	—
17	C₂×C₂²⋊C₈×C₇₃	C₂²	1	2	yes	—
18	C₂×C₂²⋊C₈×C₇₃	C₂²	1	2	yes	—
19	C₂×C₂²⋊C₈×C₇₃	C₂²	1	2	yes	—
20	C₂×C₂²⋊C₈×C₇₃	C₂²	1	1	yes	characteristic
21	C₂×#97×C₇₃	C₂²	1	2	yes	—
22	C₂×C₄×C₈×C₇₃	C₂²	1	1	yes	characteristic
23	#400×C₇₃	C₄	1	1	yes	characteristic
24	#399×C₇₃	C₄	1	1	yes	characteristic
25	#398×C₇₃	C₄	1	1	yes	characteristic
26	#397×C₇₃	C₄	1	2	yes	—
27	#397×C₇₃	C₄	1	1	yes	characteristic
28	#394×C₇₃	C₄	1	2	yes	—
29	C₄×C₄⋊C₄×C₇₃	C₂²	1	2	yes	—
30	C₄×C₂²⋊C₄×C₇₃	C₂²	1	2	yes	—
31	C₄×C₂²⋊C₄×C₇₃	C₂²	1	1	yes	characteristic
32	#336×C₇₃	C₂²	1	2	yes	—
33	#336×C₇₃	C₂²	1	2	yes	—
34	#336×C₇₃	C₂²	1	2	yes	—
35	#336×C₇₃	C₂²	1	2	yes	—
36	#336×C₇₃	C₂²	1	2	yes	—
37	C₂²×D₄×C₇₃	C₂×C₄	1	1	yes	characteristic
38	C₂³×C₄×C₇₃	C₂³	1	1	yes	characteristic
39	C₂³×C₄×C₇₃	C₂³	1	1	yes	characteristic
40	C₂×M₁₆×C₇₃	—	4	2	no	—
41	C₂×M₁₆×C₇₃	—	4	1	no	—
42	C₂²×C₈×C₇₃	C₂³	1	2	yes	—
43	C₂²×C₈×C₇₃	C₂³	1	2	yes	—
44	C₂²×C₈×C₇₃	C₂³	1	2	yes	—
45	C₂²×C₈×C₇₃	C₂³	1	2	yes	—
46	C₄×D₄×C₇₃	—	4	1	no	—
47	C₄×D₄×C₇₃	—	4	1	no	—
48	#117×C₇₃	—	4	1	no	—
49	#117×C₇₃	—	4	1	no	—
50	C₂×C₄⋊C₄×C₇₃	C₂×C₄	1	2	yes	—
51	C₂×C₄⋊C₄×C₇₃	C₂×C₄	1	2	yes	—
52	C₂×C₄⋊C₄×C₇₃	C₂×C₄	1	1	yes	characteristic
53	C₂×C₄⋊C₄×C₇₃	C₂×C₄	1	1	yes	characteristic
54	C₂×C₄⋊C₄×C₇₃	C₂×C₄	1	1	yes	characteristic
55	C₂×C₂²⋊C₄×C₇₃	C₂×C₄	1	2	yes	—
56	C₂×C₂²⋊C₄×C₇₃	C₂×C₄	1	2	yes	—
57	C₂×C₂²⋊C₄×C₇₃	C₂×C₄	1	2	yes	—
58	C₂×C₂²⋊C₄×C₇₃	C₂×C₄	1	2	yes	—
59	C₂×C₂²⋊C₄×C₇₃	C₂×C₄	1	1	yes	characteristic
60	C₂×C₂²⋊C₄×C₇₃	C₂×C₄	1	1	yes	characteristic
61	C₂×C₄²×C₇₃	C₂³	1	2	yes	—
62	C₂×C₄²×C₇₃	C₂³	1	2	yes	—
63	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
64	C₄⋊C₈×C₇₃	—	4	2	no	—
65	C₄⋊C₈×C₇₃	—	4	2	no	—
66	C₄⋊C₈×C₇₃	—	4	2	no	—
67	C₄⋊C₈×C₇₃	—	4	1	no	—
68	C₂²⋊C₈×C₇₃	—	4	2	no	—
69	C₂²⋊C₈×C₇₃	—	4	2	no	—
70	C₂²⋊C₈×C₇₃	—	4	2	no	—
71	C₂²⋊C₈×C₇₃	—	4	1	no	—
72	#97×C₇₃	—	4	2	no	—
73	C₄×C₈×C₇₃	—	4	1	no	—
74	#95×C₇₃	C₂×C₄	1	2	yes	—
75	#95×C₇₃	C₂×C₄	1	1	yes	characteristic
76	#95×C₇₃	C₂×C₄	1	2	yes	—
77	#95×C₇₃	C₂×C₄	1	1	yes	characteristic
78	#95×C₇₃	C₂×C₄	1	2	yes	—
79	#95×C₇₃	C₂×C₄	1	2	yes	—
80	C₂⁴×C₇₃	C₂²×C₄	1	1	yes	characteristic
81	C₂⁴×C₇₃	C₂²×C₄	1	1	yes	characteristic
82	C₂×D₄×C₇₃	—	2	2	no	—
83	C₂×D₄×C₇₃	—	4	1	no	—
84	C₂×D₄×C₇₃	—	4	1	no	—
85	C₂²×C₄×C₇₃	—	2	2	no	—
86	C₂²×C₄×C₇₃	—	2	1	no	—
87	C₂²×C₄×C₇₃	—	2	2	no	—
88	C₂²×C₄×C₇₃	—	2	1	no	—
89	C₂²×C₄×C₇₃	—	2	1	no	—
90	C₂²×C₄×C₇₃	—	2	1	no	—
91	C₂²×C₄×C₇₃	—	2	2	no	—
92	C₂²×C₄×C₇₃	—	2	2	no	—
93	C₂²×C₄×C₇₃	C₂²×C₄	1	2	yes	—
94	C₂²×C₄×C₇₃	C₂²×C₄	1	1	yes	characteristic
95	C₂²×C₄×C₇₃	C₂²×C₄	1	1	yes	characteristic
96	C₂²×C₄×C₇₃	C₂²×C₄	1	2	yes	—
97	C₂²×C₄×C₇₃	C₂²×C₄	1	2	yes	—
98	C₂²×C₄×C₇₃	C₂²×C₄	1	2	yes	—
99	C₂²×C₄×C₇₃	C₂²×C₄	1	1	yes	characteristic
100	C₂²×C₄×C₇₃	C₂²×C₄	1	1	yes	characteristic
101	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
102	M₁₆×C₇₃	—	4	4	no	—
103	C₂×C₈×C₇₃	—	2	2	no	—
104	C₂×C₈×C₇₃	—	2	2	no	—
105	C₂×C₈×C₇₃	—	2	2	no	—
106	C₂×C₈×C₇₃	—	2	2	no	—
107	C₂×C₈×C₇₃	—	2	2	no	—
108	C₂×C₈×C₇₃	—	2	2	no	—
109	C₂×C₈×C₇₃	—	2	2	no	—
110	C₂×C₈×C₇₃	—	2	2	no	—
111	C₂×C₈×C₇₃	—	2	2	no	—
112	C₂×C₈×C₇₃	—	2	2	no	—
113	C₂×C₈×C₇₃	—	2	2	no	—
114	C₂×C₈×C₇₃	—	2	2	no	—
115	C₄⋊C₄×C₇₃	—	2	4	no	—
116	C₄⋊C₄×C₇₃	—	4	2	no	—
117	C₄⋊C₄×C₇₃	—	4	1	no	—
118	C₄⋊C₄×C₇₃	—	4	1	no	—
119	C₄⋊C₄×C₇₃	—	4	1	no	—
120	C₂²⋊C₄×C₇₃	—	4	2	no	—
121	C₂²⋊C₄×C₇₃	—	4	2	no	—
122	C₂²⋊C₄×C₇₃	—	4	2	no	—
123	C₂²⋊C₄×C₇₃	—	4	2	no	—
124	C₂²⋊C₄×C₇₃	—	4	1	no	—
125	C₂²⋊C₄×C₇₃	—	4	1	no	—
126	C₄²×C₇₃	—	2	1	no	—
127	C₄²×C₇₃	—	2	2	no	—
128	C₄²×C₇₃	—	2	2	no	—
129	C₄²×C₇₃	—	2	2	no	—
130	C₄²×C₇₃	—	2	1	no	—
131	C₄²×C₇₃	—	2	2	no	—
132	C₂³×C₇₃	—	2	1	no	—
133	C₂³×C₇₃	—	2	1	no	—
134	C₂³×C₇₃	—	2	2	no	—
135	C₂³×C₇₃	—	2	2	no	—
136	C₂³×C₇₃	—	2	1	no	—
137	C₂³×C₇₃	—	2	1	no	—
138	C₂³×C₇₃	—	2	1	no	—
139	C₂³×C₇₃	—	2	2	no	—
140	C₂³×C₇₃	—	2	2	no	—
141	C₂³×C₇₃	—	2	1	no	—
142	C₂³×C₇₃	C₂³×C₄	1	1	yes	characteristic
143	D₄×C₇₃	—	4	4	no	—
144	C₂×C₄×C₇₃	—	2	1	no	—
145	C₂×C₄×C₇₃	—	2	1	no	—
146	C₂×C₄×C₇₃	—	2	1	no	—
147	C₂×C₄×C₇₃	—	2	2	no	—
148	C₂×C₄×C₇₃	—	2	2	no	—
149	C₂×C₄×C₇₃	—	2	1	no	—
150	C₂×C₄×C₇₃	—	2	1	no	—
151	C₂×C₄×C₇₃	—	2	2	no	—
152	C₂×C₄×C₇₃	—	2	2	no	—
153	C₂×C₄×C₇₃	—	2	2	no	—
154	C₂×C₄×C₇₃	—	2	2	no	—
155	C₂×C₄×C₇₃	—	2	2	no	—
156	C₂×C₄×C₇₃	—	2	2	no	—
157	C₂×C₄×C₇₃	—	2	2	no	—
158	C₂×C₄×C₇₃	—	2	2	no	—
159	C₂×C₄×C₇₃	—	2	2	no	—
160	C₂×C₄×C₇₃	—	2	2	no	—
161	C₂×C₄×C₇₃	—	2	2	no	—
162	C₂×C₄×C₇₃	—	2	2	no	—
163	C₂×C₄×C₇₃	—	2	2	no	—
164	C₂×C₄×C₇₃	—	4	1	no	—
165	C₂×C₄×C₇₃	—	4	1	no	—
166	C₂×C₄×C₇₃	—	4	2	no	—
167	C₂×C₄×C₇₃	—	4	2	no	—
168	C₂×C₄×C₇₃	—	4	1	no	—
169	C₂×C₄×C₇₃	—	4	1	no	—
170	C₂×C₄×C₇₃	#131	1	2	yes	—
171	C₂×C₄×C₇₃	H(5,𝔽₂)	1	2	yes	—
172	C₂×C₄×C₇₃	H(5,𝔽₂)	1	1	yes	characteristic
173	C₂×C₄×C₇₃	H(5,𝔽₂)	1	1	yes	characteristic
174	C₂×C₄×C₇₃	2₋¹⁺⁴	1	2	yes	—
175	C₈×C₇₃	—	4	2	no	—
176	C₈×C₇₃	—	4	2	no	—
177	C₈×C₇₃	—	4	2	no	—
178	C₈×C₇₃	—	4	2	no	—
179	C₂²×C₇₃	—	4	1	no	—
180	C₂²×C₇₃	—	4	1	no	—
181	C₂²×C₇₃	—	4	1	no	—
182	C₂²×C₇₃	—	4	1	no	—
183	C₂²×C₇₃	—	4	1	no	—
184	C₂²×C₇₃	—	4	1	no	—
185	C₂²×C₇₃	—	4	2	no	—
186	C₂²×C₇₃	—	4	2	no	—
187	C₂²×C₇₃	—	4	2	no	—
188	C₂²×C₇₃	—	4	2	no	—
189	C₂²×C₇₃	#518	1	1	yes	characteristic
190	C₂²×C₇₃	#520	1	2	yes	—
191	C₂²×C₇₃	C₂×#131	1	1	yes	characteristic
192	C₂²×C₇₃	#568	1	1	yes	characteristic
193	C₂²×C₇₃	#568	1	2	yes	—
194	C₄×C₇₃	—	2	2	no	—
195	C₄×C₇₃	—	4	1	no	—
196	C₄×C₇₃	—	4	1	no	—
197	C₄×C₇₃	—	4	2	no	—
198	C₄×C₇₃	—	4	1	no	—
199	C₄×C₇₃	—	4	2	no	—
200	C₄×C₇₃	—	4	2	no	—
201	C₄×C₇₃	—	4	2	no	—
202	C₄×C₇₃	#560	1	1	yes	characteristic
203	C₄×C₇₃	#562	1	2	yes	—
204	C₄×C₇₃	#563	1	1	yes	characteristic
205	#23325	C₇₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
206	C₂×C₇₃	—	8	1	no	—
207	C₂×C₇₃	—	8	1	no	—
208	C₂×C₇₃	#2376	1	1	yes	characteristic
209	C₂×C₇₃	#2976	1	1	yes	characteristic
210	C₂×C₇₃	#2980	1	1	yes	characteristic
211	C₂×C₇₃	#2993	1	2	yes	—
212	C₂×C₇₃	#2995	1	2	yes	—
213	#2395	C₂×C₇₃	1	1	yes	characteristic
214	#1954	C₂×C₇₃	1	1	yes	characteristic
215	#1940	C₂×C₇₃	1	2	yes	complemented
216	#1924	C₂×C₇₃	1	2	yes	complemented
217	#1924	C₂×C₇₃	1	2	yes	complemented
218	#1916	C₂×C₇₃	1	2	yes	complemented
219	#1870	C₂×C₇₃	1	1	yes	characteristic
220	#1851	C₂×C₇₃	1	2	yes	complemented
221	#1798	C₂×C₇₃	1	2	yes	complemented
222	C₇₃	#23325	1	1	yes	characteristic, direct product factor, Sylow
223	C₂²×M₁₆	C₂²×C₇₃	1	1	yes	characteristic
224	C₂×C₄×D₄	C₂²×C₇₃	1	1	yes	characteristic
225	C₂×#117	C₂²×C₇₃	1	1	yes	characteristic
226	C₂×C₄⋊C₈	C₂²×C₇₃	1	2	yes	—
227	C₂×C₄⋊C₈	C₂²×C₇₃	1	2	yes	—
228	C₂×C₄⋊C₈	C₂²×C₇₃	1	2	yes	—
229	C₂×C₄⋊C₈	C₂²×C₇₃	1	1	yes	characteristic
230	C₂×C₂²⋊C₈	C₂²×C₇₃	1	2	yes	—
231	C₂×C₂²⋊C₈	C₂²×C₇₃	1	2	yes	—
232	C₂×C₂²⋊C₈	C₂²×C₇₃	1	2	yes	—
233	C₂×C₂²⋊C₈	C₂²×C₇₃	1	1	yes	characteristic
234	C₂×#97	C₂²×C₇₃	1	2	yes	—
235	C₂×C₄×C₈	C₂²×C₇₃	1	1	yes	characteristic
236	#400	C₄×C₇₃	1	1	yes	characteristic
237	#399	C₄×C₇₃	1	1	yes	characteristic
238	#398	C₄×C₇₃	1	1	yes	characteristic
239	#397	C₄×C₇₃	1	2	yes	—
240	#397	C₄×C₇₃	1	1	yes	characteristic
241	#394	C₄×C₇₃	1	2	yes	—
242	C₄×C₄⋊C₄	C₂²×C₇₃	1	2	yes	—
243	C₄×C₂²⋊C₄	C₂²×C₇₃	1	2	yes	—
244	C₄×C₂²⋊C₄	C₂²×C₇₃	1	1	yes	characteristic
245	#336	C₂²×C₇₃	1	2	yes	—
246	#336	C₂²×C₇₃	1	2	yes	—
247	#336	C₂²×C₇₃	1	2	yes	—
248	#336	C₂²×C₇₃	1	2	yes	—
249	#336	C₂²×C₇₃	1	2	yes	—
250	C₂²×D₄	C₂×C₄×C₇₃	1	1	yes	characteristic
251	C₂³×C₄	C₂³×C₇₃	1	1	yes	characteristic
252	C₂³×C₄	C₂³×C₇₃	1	1	yes	characteristic
253	C₂×M₁₆	—	4	2	no	—
254	C₂×M₁₆	—	4	1	no	—
255	C₂²×C₈	C₂³×C₇₃	1	2	yes	—
256	C₂²×C₈	C₂³×C₇₃	1	2	yes	—
257	C₂²×C₈	C₂³×C₇₃	1	2	yes	—
258	C₂²×C₈	C₂³×C₇₃	1	2	yes	—
259	C₄×D₄	—	4	1	no	—
260	C₄×D₄	—	4	1	no	—
261	#117	—	4	1	no	—
262	#117	—	4	1	no	—
263	C₂×C₄⋊C₄	C₂×C₄×C₇₃	1	2	yes	—
264	C₂×C₄⋊C₄	C₂×C₄×C₇₃	1	1	yes	characteristic
265	C₂×C₄⋊C₄	C₂×C₄×C₇₃	1	1	yes	characteristic
266	C₂×C₄⋊C₄	C₂×C₄×C₇₃	1	1	yes	characteristic
267	C₂×C₄⋊C₄	C₂×C₄×C₇₃	1	2	yes	—
268	C₂×C₂²⋊C₄	C₂×C₄×C₇₃	1	2	yes	—
269	C₂×C₂²⋊C₄	C₂×C₄×C₇₃	1	1	yes	characteristic
270	C₂×C₂²⋊C₄	C₂×C₄×C₇₃	1	1	yes	characteristic
271	C₂×C₂²⋊C₄	C₂×C₄×C₇₃	1	2	yes	—
272	C₂×C₂²⋊C₄	C₂×C₄×C₇₃	1	2	yes	—
273	C₂×C₂²⋊C₄	C₂×C₄×C₇₃	1	2	yes	—
274	C₂×C₄²	C₂³×C₇₃	1	2	yes	—
275	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
276	C₂×C₄²	C₂³×C₇₃	1	2	yes	—
277	C₄⋊C₈	—	4	2	no	—
278	C₄⋊C₈	—	4	2	no	—
279	C₄⋊C₈	—	4	2	no	—
280	C₄⋊C₈	—	4	1	no	—
281	C₂²⋊C₈	—	4	2	no	—
282	C₂²⋊C₈	—	4	2	no	—
283	C₂²⋊C₈	—	4	2	no	—
284	C₂²⋊C₈	—	4	1	no	—
285	#97	—	4	2	no	—
286	C₄×C₈	—	4	1	no	—
287	#95	C₂×C₄×C₇₃	1	2	yes	—
288	#95	C₂×C₄×C₇₃	1	1	yes	characteristic
289	#95	C₂×C₄×C₇₃	1	2	yes	—
290	#95	C₂×C₄×C₇₃	1	1	yes	characteristic
291	#95	C₂×C₄×C₇₃	1	2	yes	—
292	#95	C₂×C₄×C₇₃	1	2	yes	—
293	C₂⁴	C₂²×C₄×C₇₃	1	1	yes	characteristic
294	C₂⁴	C₂²×C₄×C₇₃	1	1	yes	characteristic
295	C₂×D₄	—	2	2	no	—
296	C₂×D₄	—	4	1	no	—
297	C₂×D₄	—	4	1	no	—
298	C₂²×C₄	—	2	2	no	—
299	C₂²×C₄	—	2	1	no	—
300	C₂²×C₄	—	2	2	no	—
301	C₂²×C₄	—	2	1	no	—
302	C₂²×C₄	—	2	1	no	—
303	C₂²×C₄	—	2	1	no	—
304	C₂²×C₄	—	2	2	no	—
305	C₂²×C₄	—	2	2	no	—
306	C₂²×C₄	C₂²×C₄×C₇₃	1	2	yes	—
307	C₂²×C₄	C₂²×C₄×C₇₃	1	1	yes	characteristic
308	C₂²×C₄	C₂²×C₄×C₇₃	1	1	yes	characteristic
309	C₂²×C₄	C₂²×C₄×C₇₃	1	2	yes	—
310	C₂²×C₄	C₂²×C₄×C₇₃	1	2	yes	—
311	C₂²×C₄	C₂²×C₄×C₇₃	1	2	yes	—
312	C₂²×C₄	C₂²×C₄×C₇₃	1	1	yes	characteristic
313	C₂²×C₄	C₂²×C₄×C₇₃	1	1	yes	characteristic
314	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
315	M₁₆	—	4	4	no	—
316	C₂×C₈	—	2	2	no	—
317	C₂×C₈	—	2	2	no	—
318	C₂×C₈	—	2	2	no	—
319	C₂×C₈	—	2	2	no	—
320	C₂×C₈	—	2	2	no	—
321	C₂×C₈	—	2	2	no	—
322	C₂×C₈	—	2	2	no	—
323	C₂×C₈	—	2	2	no	—
324	C₂×C₈	—	2	2	no	—
325	C₂×C₈	—	2	2	no	—
326	C₂×C₈	—	2	2	no	—
327	C₂×C₈	—	2	2	no	—
328	C₄⋊C₄	—	2	4	no	—
329	C₄⋊C₄	—	4	2	no	—
330	C₄⋊C₄	—	4	1	no	—
331	C₄⋊C₄	—	4	1	no	—
332	C₄⋊C₄	—	4	1	no	—
333	C₂²⋊C₄	—	4	2	no	—
334	C₂²⋊C₄	—	4	2	no	—
335	C₂²⋊C₄	—	4	2	no	—
336	C₂²⋊C₄	—	4	2	no	—
337	C₂²⋊C₄	—	4	1	no	—
338	C₂²⋊C₄	—	4	1	no	—
339	C₄²	—	2	1	no	—
340	C₄²	—	2	2	no	—
341	C₄²	—	2	2	no	—
342	C₄²	—	2	2	no	—
343	C₄²	—	2	1	no	—
344	C₄²	—	2	2	no	—
345	C₂³	—	2	1	no	—
346	C₂³	—	2	1	no	—
347	C₂³	—	2	2	no	—
348	C₂³	—	2	2	no	—
349	C₂³	—	2	1	no	—
350	C₂³	—	2	1	no	—
351	C₂³	—	2	1	no	—
352	C₂³	—	2	2	no	—
353	C₂³	—	2	2	no	—
354	C₂³	—	2	1	no	—
355	C₂³	C₂³×C₄×C₇₃	1	1	yes	characteristic
356	D₄	—	4	4	no	—
357	C₂×C₄	—	2	1	no	—
358	C₂×C₄	—	2	1	no	—
359	C₂×C₄	—	2	1	no	—
360	C₂×C₄	—	2	2	no	—
361	C₂×C₄	—	2	2	no	—
362	C₂×C₄	—	2	1	no	—
363	C₂×C₄	—	2	1	no	—
364	C₂×C₄	—	2	2	no	—
365	C₂×C₄	—	2	2	no	—
366	C₂×C₄	—	2	2	no	—
367	C₂×C₄	—	2	2	no	—
368	C₂×C₄	—	2	2	no	—
369	C₂×C₄	—	2	2	no	—
370	C₂×C₄	—	2	2	no	—
371	C₂×C₄	—	2	2	no	—
372	C₂×C₄	—	2	2	no	—
373	C₂×C₄	—	2	2	no	—
374	C₂×C₄	—	2	2	no	—
375	C₂×C₄	—	2	2	no	—
376	C₂×C₄	—	2	2	no	—
377	C₂×C₄	—	4	1	no	—
378	C₂×C₄	—	4	1	no	—
379	C₂×C₄	—	4	2	no	—
380	C₂×C₄	—	4	2	no	—
381	C₂×C₄	—	4	1	no	—
382	C₂×C₄	—	4	1	no	—
383	C₂×C₄	#131×C₇₃	1	2	yes	—
384	C₂×C₄	H(5,𝔽₂)×C₇₃	1	2	yes	—
385	C₂×C₄	H(5,𝔽₂)×C₇₃	1	1	yes	characteristic
386	C₂×C₄	H(5,𝔽₂)×C₇₃	1	1	yes	characteristic
387	C₂×C₄	2₋¹⁺⁴×C₇₃	1	2	yes	—
388	C₈	—	4	2	no	—
389	C₈	—	4	2	no	—
390	C₈	—	4	2	no	—
391	C₈	—	4	2	no	—
392	C₂²	—	4	1	no	—
393	C₂²	—	4	1	no	—
394	C₂²	—	4	1	no	—
395	C₂²	—	4	1	no	—
396	C₂²	—	4	2	no	—
397	C₂²	—	4	2	no	—
398	C₂²	—	4	2	no	—
399	C₂²	—	4	2	no	—
400	C₂²	—	4	1	no	—
401	C₂²	—	4	1	no	—
402	C₂²	#518×C₇₃	1	1	yes	characteristic
403	C₂²	#520×C₇₃	1	2	yes	—
404	C₂²	C₂×#131×C₇₃	1	1	yes	characteristic
405	C₂²	#568×C₇₃	1	1	yes	characteristic
406	C₂²	#568×C₇₃	1	2	yes	—
407	C₄	—	2	2	no	—
408	C₄	—	4	2	no	—
409	C₄	—	4	1	no	—
410	C₄	—	4	2	no	—
411	C₄	—	4	2	no	—
412	C₄	—	4	2	no	—
413	C₄	—	4	1	no	—
414	C₄	—	4	1	no	—
415	C₄	#560×C₇₃	1	1	yes	characteristic
416	C₄	#562×C₇₃	1	2	yes	—
417	C₄	#563×C₇₃	1	1	yes	characteristic
418	C₂	—	8	1	no	—
419	C₂	—	8	1	no	—
420	C₂	C₇₃×#2376	1	1	yes	characteristic
421	C₂	C₇₃×#2976	1	1	yes	characteristic
422	C₂	C₇₃×#2980	1	1	yes	characteristic
423	C₂	C₇₃×#2993	1	2	yes	—
424	C₂	C₇₃×#2995	1	2	yes	—

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

Complements

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

N	H ≅ G/N	type
3. C₇₃×#1940	C₂	semidirect
4. C₇₃×#1924	C₂	semidirect
5. C₇₃×#1924	C₂	semidirect
6. C₇₃×#1916	C₂	semidirect
8. C₇₃×#1851	C₂	semidirect
9. C₇₃×#1798	C₂	semidirect
205. #23325	C₇₃	direct (N × H)
215. #1940	C₂×C₇₃	semidirect
216. #1924	C₂×C₇₃	semidirect
217. #1924	C₂×C₇₃	semidirect
218. #1916	C₂×C₇₃	semidirect
220. #1851	C₂×C₇₃	semidirect
221. #1798	C₂×C₇₃	semidirect
222. C₇₃	#23325	direct (N × H)

Maximal subgroups

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

subgroup	index
C₇₃×#2395	2
C₇₃×#1954	2
C₇₃×#1940	2
C₇₃×#1924	2
C₇₃×#1916	2
C₇₃×#1870	2
C₇₃×#1851	2
C₇₃×#1798	2
#23325	73

Subgroups — C73×#23325 #32932729

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₃×#23325 #32932729