Subgroups — C₇₃×#23308 #32932712

Order 18688.

1046 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	C₄×#120×C₇₃	C₂	1	1	yes	maximal, characteristic
2	C₇₃×#1955	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇₃×#1954	C₂	1	2	yes	maximal, complemented
4	C₇₃×#1924	C₂	1	2	yes	maximal, complemented
5	C₇₃×#1923	C₂	1	2	yes	maximal, complemented
6	C₇₃×#1923	C₂	1	2	yes	maximal, complemented
7	C₇₃×#1870	C₂	1	1	yes	maximal, characteristic, complemented
8	C₇₃×#1870	C₂	1	2	yes	maximal, complemented
9	C₇₃×#1779	C₂	1	2	yes	maximal, complemented
10	C₂⁴×C₄×C₇₃	C₂²	1	1	yes	characteristic
11	C₂²×M₁₆×C₇₃	C₂²	1	1	yes	characteristic, complemented
12	C₂×#120×C₇₃	C₄	1	1	yes	characteristic
13	C₂×C₄×D₄×C₇₃	C₂²	1	2	yes	—
14	C₂×C₄×D₄×C₇₃	C₂²	1	1	yes	characteristic
15	C₂×C₄⋊C₈×C₇₃	C₂²	1	2	yes	complemented
16	C₂×C₄⋊C₈×C₇₃	C₂²	1	1	yes	characteristic, complemented
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	2	yes	—
21	C₂×C₂²⋊C₈×C₇₃	C₂²	1	2	yes	—
22	C₂×C₂²⋊C₈×C₇₃	C₂²	1	2	yes	—
23	C₂×C₂²⋊C₈×C₇₃	C₂²	1	1	yes	characteristic, complemented
24	C₂×C₂²⋊C₈×C₇₃	C₂²	1	2	yes	complemented
25	C₂×#97×C₇₃	C₂²	1	1	yes	characteristic, complemented
26	C₂×C₄×C₈×C₇₃	C₂²	1	2	yes	complemented
27	#386×C₇₃	C₄	1	2	yes	—
28	#386×C₇₃	C₄	1	1	yes	characteristic
29	#385×C₇₃	C₄	1	2	yes	—
30	#385×C₇₃	C₄	1	1	yes	characteristic
31	#379×C₇₃	C₄	1	1	yes	characteristic
32	C₄×C₂²⋊C₄×C₇₃	C₂²	1	1	yes	characteristic
33	C₄×C₂²⋊C₄×C₇₃	C₂²	1	2	yes	—
34	#336×C₇₃	C₂²	1	2	yes	complemented
35	#336×C₇₃	C₂²	1	2	yes	complemented
36	#336×C₇₃	C₂²	1	2	yes	complemented
37	C₂⁵×C₇₃	C₂×C₄	1	1	yes	characteristic
38	C₂²×D₄×C₇₃	C₂×C₄	1	2	yes	—
39	C₂²×D₄×C₇₃	C₂×C₄	1	1	yes	characteristic
40	C₂³×C₄×C₇₃	—	4	2	no	—
41	C₂³×C₄×C₇₃	—	4	1	no	—
42	C₂³×C₄×C₇₃	—	4	2	no	—
43	C₂³×C₄×C₇₃	—	4	1	no	—
44	C₂³×C₄×C₇₃	C₂×C₄	1	1	yes	characteristic
45	C₂³×C₄×C₇₃	C₂×C₄	1	2	yes	—
46	C₂³×C₄×C₇₃	C₂³	1	1	yes	characteristic
47	C₂³×C₄×C₇₃	C₂³	1	2	yes	—
48	C₂³×C₄×C₇₃	C₂³	1	1	yes	characteristic
49	C₂×M₁₆×C₇₃	—	4	2	no	—
50	C₂×M₁₆×C₇₃	—	4	1	no	—
51	C₂²×C₈×C₇₃	C₂³	1	2	yes	—
52	C₂²×C₈×C₇₃	C₂³	1	2	yes	—
53	C₂²×C₈×C₇₃	C₂³	1	2	yes	—
54	C₂²×C₈×C₇₃	C₂³	1	2	yes	—
55	#120×C₇₃	—	2	4	no	—
56	C₄×D₄×C₇₃	—	4	2	no	—
57	C₄×D₄×C₇₃	—	4	1	no	—
58	C₄×D₄×C₇₃	—	4	2	no	—
59	C₄×D₄×C₇₃	—	4	1	no	—
60	C₂×C₄⋊C₄×C₇₃	C₂×C₄	1	1	yes	characteristic
61	C₂×C₄⋊C₄×C₇₃	C₂×C₄	1	2	yes	—
62	C₂×C₂²⋊C₄×C₇₃	C₂×C₄	1	2	yes	—
63	C₂×C₂²⋊C₄×C₇₃	C₂×C₄	1	2	yes	—
64	C₂×C₂²⋊C₄×C₇₃	C₂×C₄	1	1	yes	characteristic
65	C₂×C₂²⋊C₄×C₇₃	C₂×C₄	1	1	yes	characteristic
66	C₂×C₂²⋊C₄×C₇₃	C₂×C₄	1	2	yes	—
67	C₂×C₂²⋊C₄×C₇₃	C₂×C₄	1	2	yes	—
68	C₂×C₂²⋊C₄×C₇₃	C₂×C₄	1	1	yes	characteristic
69	C₂×C₂²⋊C₄×C₇₃	C₂×C₄	1	1	yes	characteristic
70	C₂×C₄²×C₇₃	C₂³	1	2	yes	—
71	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
72	C₄⋊C₈×C₇₃	—	4	2	no	—
73	C₄⋊C₈×C₇₃	—	4	1	no	—
74	C₂²⋊C₈×C₇₃	—	4	2	no	—
75	C₂²⋊C₈×C₇₃	—	4	2	no	—
76	C₂²⋊C₈×C₇₃	—	4	2	no	—
77	C₂²⋊C₈×C₇₃	—	4	2	no	—
78	C₂²⋊C₈×C₇₃	—	4	2	no	—
79	C₂²⋊C₈×C₇₃	—	4	2	no	—
80	C₂²⋊C₈×C₇₃	—	4	1	no	—
81	C₂²⋊C₈×C₇₃	—	4	2	no	—
82	#97×C₇₃	—	4	1	no	—
83	C₄×C₈×C₇₃	—	4	2	no	—
84	#95×C₇₃	C₂×C₄	1	2	yes	—
85	#95×C₇₃	C₂×C₄	1	2	yes	—
86	#95×C₇₃	C₂×C₄	1	2	yes	—
87	C₂⁴×C₇₃	—	2	2	no	—
88	C₂⁴×C₇₃	—	2	4	no	—
89	C₂⁴×C₇₃	—	4	2	no	—
90	C₂⁴×C₇₃	—	4	1	no	—
91	C₂⁴×C₇₃	—	4	1	no	—
92	C₂⁴×C₇₃	C₂²×C₄	1	1	yes	characteristic
93	C₂⁴×C₇₃	C₂²×C₄	1	1	yes	characteristic
94	C₂⁴×C₇₃	C₂²×C₄	1	2	yes	—
95	C₂×D₄×C₇₃	—	2	2	no	—
96	C₂×D₄×C₇₃	—	2	4	no	—
97	C₂×D₄×C₇₃	—	2	4	no	—
98	C₂×D₄×C₇₃	—	4	2	no	—
99	C₂×D₄×C₇₃	—	4	1	no	—
100	C₂×D₄×C₇₃	—	4	1	no	—
101	C₂²×C₄×C₇₃	—	2	2	no	—
102	C₂²×C₄×C₇₃	—	2	1	no	—
103	C₂²×C₄×C₇₃	—	2	2	no	—
104	C₂²×C₄×C₇₃	—	2	2	no	—
105	C₂²×C₄×C₇₃	—	2	2	no	—
106	C₂²×C₄×C₇₃	—	2	2	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	1	no	—
111	C₂²×C₄×C₇₃	—	2	2	no	—
112	C₂²×C₄×C₇₃	—	2	1	no	—
113	C₂²×C₄×C₇₃	—	2	2	no	—
114	C₂²×C₄×C₇₃	—	2	1	no	—
115	C₂²×C₄×C₇₃	—	4	2	no	—
116	C₂²×C₄×C₇₃	—	4	2	no	—
117	C₂²×C₄×C₇₃	—	4	2	no	—
118	C₂²×C₄×C₇₃	—	4	2	no	—
119	C₂²×C₄×C₇₃	—	4	1	no	—
120	C₂²×C₄×C₇₃	—	4	8	no	—
121	C₂²×C₄×C₇₃	—	4	4	no	—
122	C₂²×C₄×C₇₃	—	4	4	no	—
123	C₂²×C₄×C₇₃	C₂²×C₄	1	1	yes	characteristic
124	C₂²×C₄×C₇₃	C₂²×C₄	1	2	yes	—
125	C₂²×C₄×C₇₃	C₂²×C₄	1	1	yes	characteristic
126	C₂²×C₄×C₇₃	C₂²×C₄	1	2	yes	—
127	C₂²×C₄×C₇₃	C₂²×C₄	1	1	yes	characteristic
128	C₂²×C₄×C₇₃	C₂²×C₄	1	1	yes	characteristic
129	C₂²×C₄×C₇₃	C₂²×C₄	1	2	yes	—
130	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
131	M₁₆×C₇₃	—	4	4	no	—
132	C₂×C₈×C₇₃	—	2	2	no	—
133	C₂×C₈×C₇₃	—	2	2	no	—
134	C₂×C₈×C₇₃	—	2	2	no	—
135	C₂×C₈×C₇₃	—	2	2	no	—
136	C₂×C₈×C₇₃	—	2	2	no	—
137	C₂×C₈×C₇₃	—	2	2	no	—
138	C₂×C₈×C₇₃	—	2	2	no	—
139	C₂×C₈×C₇₃	—	2	2	no	—
140	C₂×C₈×C₇₃	—	2	2	no	—
141	C₂×C₈×C₇₃	—	2	2	no	—
142	C₂×C₈×C₇₃	—	2	2	no	—
143	C₂×C₈×C₇₃	—	2	2	no	—
144	C₄⋊C₄×C₇₃	—	4	2	no	—
145	C₄⋊C₄×C₇₃	—	4	1	no	—
146	C₂²⋊C₄×C₇₃	—	2	4	no	—
147	C₂²⋊C₄×C₇₃	—	2	4	no	—
148	C₂²⋊C₄×C₇₃	—	4	1	no	—
149	C₂²⋊C₄×C₇₃	—	4	2	no	—
150	C₂²⋊C₄×C₇₃	—	4	1	no	—
151	C₂²⋊C₄×C₇₃	—	4	2	no	—
152	C₂²⋊C₄×C₇₃	—	4	1	no	—
153	C₂²⋊C₄×C₇₃	M₁₆	1	4	yes	complemented
154	C₄²×C₇₃	—	2	2	no	—
155	C₄²×C₇₃	—	2	1	no	—
156	C₄²×C₇₃	—	2	2	no	—
157	C₄²×C₇₃	—	2	1	no	—
158	C₂³×C₇₃	—	2	2	no	—
159	C₂³×C₇₃	—	2	1	no	—
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	1	no	—
167	C₂³×C₇₃	—	2	2	no	—
168	C₂³×C₇₃	—	2	2	no	—
169	C₂³×C₇₃	—	2	1	no	—
170	C₂³×C₇₃	—	2	1	no	—
171	C₂³×C₇₃	—	2	2	no	—
172	C₂³×C₇₃	—	2	1	no	—
173	C₂³×C₇₃	—	4	8	no	—
174	C₂³×C₇₃	—	4	4	no	—
175	C₂³×C₇₃	—	4	4	no	—
176	C₂³×C₇₃	—	4	8	no	—
177	C₂³×C₇₃	—	4	4	no	—
178	C₂³×C₇₃	C₂×M₁₆	1	2	yes	—
179	C₂³×C₇₃	#131	1	4	yes	—
180	C₂³×C₇₃	C₂³×C₄	1	1	yes	characteristic
181	D₄×C₇₃	—	4	8	no	—
182	D₄×C₇₃	—	4	4	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	1	no	—
187	C₂×C₄×C₇₃	—	2	1	no	—
188	C₂×C₄×C₇₃	—	2	2	no	—
189	C₂×C₄×C₇₃	—	2	1	no	—
190	C₂×C₄×C₇₃	—	2	2	no	—
191	C₂×C₄×C₇₃	—	2	1	no	—
192	C₂×C₄×C₇₃	—	2	2	no	—
193	C₂×C₄×C₇₃	—	2	2	no	—
194	C₂×C₄×C₇₃	—	2	2	no	—
195	C₂×C₄×C₇₃	—	2	1	no	—
196	C₂×C₄×C₇₃	—	2	2	no	—
197	C₂×C₄×C₇₃	—	2	2	no	—
198	C₂×C₄×C₇₃	—	2	2	no	—
199	C₂×C₄×C₇₃	—	2	1	no	—
200	C₂×C₄×C₇₃	—	4	4	no	—
201	C₂×C₄×C₇₃	—	4	8	no	—
202	C₂×C₄×C₇₃	—	4	1	no	—
203	C₂×C₄×C₇₃	—	4	2	no	—
204	C₂×C₄×C₇₃	—	4	2	no	—
205	C₂×C₄×C₇₃	—	4	1	no	—
206	C₂×C₄×C₇₃	—	4	2	no	—
207	C₂×C₄×C₇₃	—	4	2	no	—
208	C₂×C₄×C₇₃	—	4	2	no	—
209	C₂×C₄×C₇₃	—	4	1	no	—
210	C₂×C₄×C₇₃	—	4	2	no	—
211	C₂×C₄×C₇₃	—	4	1	no	—
212	C₂×C₄×C₇₃	C₂×M₁₆	1	4	yes	—
213	C₂×C₄×C₇₃	H(5,𝔽₂)	1	2	yes	—
214	C₂×C₄×C₇₃	H(5,𝔽₂)	1	1	yes	characteristic
215	C₂×C₄×C₇₃	H(5,𝔽₂)	1	2	yes	—
216	C₂×C₄×C₇₃	H(5,𝔽₂)	1	1	yes	characteristic
217	C₈×C₇₃	—	4	2	no	—
218	C₈×C₇₃	—	4	2	no	—
219	C₈×C₇₃	—	4	2	no	—
220	C₈×C₇₃	—	4	2	no	—
221	C₂²×C₇₃	—	2	4	no	—
222	C₂²×C₇₃	—	2	4	no	—
223	C₂²×C₇₃	—	2	2	no	—
224	C₂²×C₇₃	—	2	4	no	—
225	C₂²×C₇₃	—	2	4	no	—
226	C₂²×C₇₃	—	4	16	no	—
227	C₂²×C₇₃	—	4	2	no	—
228	C₂²×C₇₃	—	4	1	no	—
229	C₂²×C₇₃	—	4	2	no	—
230	C₂²×C₇₃	—	4	2	no	—
231	C₂²×C₇₃	—	4	2	no	—
232	C₂²×C₇₃	—	4	2	no	—
233	C₂²×C₇₃	—	4	1	no	—
234	C₂²×C₇₃	—	4	1	no	—
235	C₂²×C₇₃	—	4	2	no	—
236	C₂²×C₇₃	—	4	1	no	—
237	C₂²×C₇₃	—	4	2	no	—
238	C₂²×C₇₃	—	4	1	no	—
239	C₂²×C₇₃	#518	1	2	yes	—
240	C₂²×C₇₃	#518	1	1	yes	characteristic
241	C₂²×C₇₃	C₂²×M₁₆	1	1	yes	characteristic
242	C₂²×C₇₃	C₂×#131	1	2	yes	—
243	C₂²×C₇₃	#568	1	1	yes	characteristic
244	C₄×C₇₃	—	2	4	no	—
245	C₄×C₇₃	—	4	1	no	—
246	C₄×C₇₃	—	4	2	no	—
247	C₄×C₇₃	—	4	1	no	—
248	C₄×C₇₃	—	4	1	no	—
249	C₄×C₇₃	—	4	2	no	—
250	C₄×C₇₃	—	4	1	no	—
251	C₄×C₇₃	#560	1	1	yes	characteristic
252	C₄×C₇₃	#560	1	2	yes	—
253	C₄×C₇₃	H(3,𝔽₄)	1	1	yes	characteristic
254	#23308	C₇₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
255	C₂×C₇₃	—	4	4	no	—
256	C₂×C₇₃	—	4	2	no	—
257	C₂×C₇₃	—	8	1	no	—
258	C₂×C₇₃	#2375	1	1	yes	characteristic
259	C₂×C₇₃	#2974	1	2	yes	—
260	C₂×C₇₃	#2975	1	1	yes	characteristic
261	C₂×C₇₃	#2976	1	2	yes	—
262	C₂×C₇₃	#2977	1	1	yes	characteristic
263	C₄×#120	C₂×C₇₃	1	1	yes	characteristic
264	#1955	C₂×C₇₃	1	1	yes	characteristic, complemented
265	#1954	C₂×C₇₃	1	2	yes	complemented
266	#1924	C₂×C₇₃	1	2	yes	complemented
267	#1923	C₂×C₇₃	1	2	yes	complemented
268	#1923	C₂×C₇₃	1	2	yes	complemented
269	#1870	C₂×C₇₃	1	2	yes	complemented
270	#1870	C₂×C₇₃	1	1	yes	characteristic, complemented
271	#1779	C₂×C₇₃	1	2	yes	complemented
272	C₇₃	#23308	1	1	yes	characteristic, direct product factor, Sylow
273	C₂⁴×C₄	C₂²×C₇₃	1	1	yes	characteristic
274	C₂²×M₁₆	C₂²×C₇₃	1	1	yes	characteristic, complemented
275	C₂×#120	C₄×C₇₃	1	1	yes	characteristic
276	C₂×C₄×D₄	C₂²×C₇₃	1	2	yes	—
277	C₂×C₄×D₄	C₂²×C₇₃	1	1	yes	characteristic
278	C₂×C₄⋊C₈	C₂²×C₇₃	1	1	yes	characteristic, complemented
279	C₂×C₄⋊C₈	C₂²×C₇₃	1	2	yes	complemented
280	C₂×C₂²⋊C₈	C₂²×C₇₃	1	2	yes	—
281	C₂×C₂²⋊C₈	C₂²×C₇₃	1	2	yes	—
282	C₂×C₂²⋊C₈	C₂²×C₇₃	1	2	yes	—
283	C₂×C₂²⋊C₈	C₂²×C₇₃	1	2	yes	—
284	C₂×C₂²⋊C₈	C₂²×C₇₃	1	2	yes	—
285	C₂×C₂²⋊C₈	C₂²×C₇₃	1	2	yes	—
286	C₂×C₂²⋊C₈	C₂²×C₇₃	1	1	yes	characteristic, complemented
287	C₂×C₂²⋊C₈	C₂²×C₇₃	1	2	yes	complemented
288	C₂×#97	C₂²×C₇₃	1	1	yes	characteristic, complemented
289	C₂×C₄×C₈	C₂²×C₇₃	1	2	yes	complemented
290	#386	C₄×C₇₃	1	2	yes	—
291	#386	C₄×C₇₃	1	1	yes	characteristic
292	#385	C₄×C₇₃	1	2	yes	—
293	#385	C₄×C₇₃	1	1	yes	characteristic
294	#379	C₄×C₇₃	1	1	yes	characteristic
295	C₄×C₂²⋊C₄	C₂²×C₇₃	1	1	yes	characteristic
296	C₄×C₂²⋊C₄	C₂²×C₇₃	1	2	yes	—
297	#336	C₂²×C₇₃	1	2	yes	complemented
298	#336	C₂²×C₇₃	1	2	yes	complemented
299	#336	C₂²×C₇₃	1	2	yes	complemented
300	C₂⁵	C₂×C₄×C₇₃	1	1	yes	characteristic
301	C₂²×D₄	C₂×C₄×C₇₃	1	2	yes	—
302	C₂²×D₄	C₂×C₄×C₇₃	1	1	yes	characteristic
303	C₂³×C₄	—	4	2	no	—
304	C₂³×C₄	—	4	1	no	—
305	C₂³×C₄	—	4	2	no	—
306	C₂³×C₄	—	4	1	no	—
307	C₂³×C₄	C₂×C₄×C₇₃	1	1	yes	characteristic
308	C₂³×C₄	C₂×C₄×C₇₃	1	2	yes	—
309	C₂³×C₄	C₂³×C₇₃	1	1	yes	characteristic
310	C₂³×C₄	C₂³×C₇₃	1	1	yes	characteristic
311	C₂³×C₄	C₂³×C₇₃	1	2	yes	—
312	C₂×M₁₆	—	4	2	no	—
313	C₂×M₁₆	—	4	1	no	—
314	C₂²×C₈	C₂³×C₇₃	1	2	yes	—
315	C₂²×C₈	C₂³×C₇₃	1	2	yes	—
316	C₂²×C₈	C₂³×C₇₃	1	2	yes	—
317	C₂²×C₈	C₂³×C₇₃	1	2	yes	—
318	#120	—	2	4	no	—
319	C₄×D₄	—	4	2	no	—
320	C₄×D₄	—	4	1	no	—
321	C₄×D₄	—	4	2	no	—
322	C₄×D₄	—	4	1	no	—
323	C₂×C₄⋊C₄	C₂×C₄×C₇₃	1	1	yes	characteristic
324	C₂×C₄⋊C₄	C₂×C₄×C₇₃	1	2	yes	—
325	C₂×C₂²⋊C₄	C₂×C₄×C₇₃	1	2	yes	—
326	C₂×C₂²⋊C₄	C₂×C₄×C₇₃	1	2	yes	—
327	C₂×C₂²⋊C₄	C₂×C₄×C₇₃	1	1	yes	characteristic
328	C₂×C₂²⋊C₄	C₂×C₄×C₇₃	1	2	yes	—
329	C₂×C₂²⋊C₄	C₂×C₄×C₇₃	1	2	yes	—
330	C₂×C₂²⋊C₄	C₂×C₄×C₇₃	1	1	yes	characteristic
331	C₂×C₂²⋊C₄	C₂×C₄×C₇₃	1	1	yes	characteristic
332	C₂×C₂²⋊C₄	C₂×C₄×C₇₃	1	1	yes	characteristic
333	C₂×C₄²	C₂³×C₇₃	1	2	yes	—
334	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
335	C₄⋊C₈	—	4	1	no	—
336	C₄⋊C₈	—	4	2	no	—
337	C₂²⋊C₈	—	4	2	no	—
338	C₂²⋊C₈	—	4	2	no	—
339	C₂²⋊C₈	—	4	2	no	—
340	C₂²⋊C₈	—	4	2	no	—
341	C₂²⋊C₈	—	4	2	no	—
342	C₂²⋊C₈	—	4	2	no	—
343	C₂²⋊C₈	—	4	1	no	—
344	C₂²⋊C₈	—	4	2	no	—
345	#97	—	4	1	no	—
346	C₄×C₈	—	4	2	no	—
347	#95	C₂×C₄×C₇₃	1	2	yes	—
348	#95	C₂×C₄×C₇₃	1	2	yes	—
349	#95	C₂×C₄×C₇₃	1	2	yes	—
350	C₂⁴	—	2	2	no	—
351	C₂⁴	—	2	4	no	—
352	C₂⁴	—	4	2	no	—
353	C₂⁴	—	4	1	no	—
354	C₂⁴	—	4	1	no	—
355	C₂⁴	C₂²×C₄×C₇₃	1	1	yes	characteristic
356	C₂⁴	C₂²×C₄×C₇₃	1	1	yes	characteristic
357	C₂⁴	C₂²×C₄×C₇₃	1	2	yes	—
358	C₂×D₄	—	2	2	no	—
359	C₂×D₄	—	2	4	no	—
360	C₂×D₄	—	2	4	no	—
361	C₂×D₄	—	4	2	no	—
362	C₂×D₄	—	4	1	no	—
363	C₂×D₄	—	4	1	no	—
364	C₂²×C₄	—	2	2	no	—
365	C₂²×C₄	—	2	1	no	—
366	C₂²×C₄	—	2	2	no	—
367	C₂²×C₄	—	2	2	no	—
368	C₂²×C₄	—	2	2	no	—
369	C₂²×C₄	—	2	2	no	—
370	C₂²×C₄	—	2	2	no	—
371	C₂²×C₄	—	2	2	no	—
372	C₂²×C₄	—	2	2	no	—
373	C₂²×C₄	—	2	1	no	—
374	C₂²×C₄	—	2	2	no	—
375	C₂²×C₄	—	2	1	no	—
376	C₂²×C₄	—	2	2	no	—
377	C₂²×C₄	—	2	1	no	—
378	C₂²×C₄	—	4	2	no	—
379	C₂²×C₄	—	4	2	no	—
380	C₂²×C₄	—	4	2	no	—
381	C₂²×C₄	—	4	2	no	—
382	C₂²×C₄	—	4	1	no	—
383	C₂²×C₄	—	4	8	no	—
384	C₂²×C₄	—	4	4	no	—
385	C₂²×C₄	—	4	4	no	—
386	C₂²×C₄	C₂²×C₄×C₇₃	1	1	yes	characteristic
387	C₂²×C₄	C₂²×C₄×C₇₃	1	2	yes	—
388	C₂²×C₄	C₂²×C₄×C₇₃	1	1	yes	characteristic
389	C₂²×C₄	C₂²×C₄×C₇₃	1	2	yes	—
390	C₂²×C₄	C₂²×C₄×C₇₃	1	1	yes	characteristic
391	C₂²×C₄	C₂²×C₄×C₇₃	1	1	yes	characteristic
392	C₂²×C₄	C₂²×C₄×C₇₃	1	2	yes	—
393	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
394	M₁₆	—	4	4	no	—
395	C₂×C₈	—	2	2	no	—
396	C₂×C₈	—	2	2	no	—
397	C₂×C₈	—	2	2	no	—
398	C₂×C₈	—	2	2	no	—
399	C₂×C₈	—	2	2	no	—
400	C₂×C₈	—	2	2	no	—
401	C₂×C₈	—	2	2	no	—
402	C₂×C₈	—	2	2	no	—
403	C₂×C₈	—	2	2	no	—
404	C₂×C₈	—	2	2	no	—
405	C₂×C₈	—	2	2	no	—
406	C₂×C₈	—	2	2	no	—
407	C₄⋊C₄	—	4	2	no	—
408	C₄⋊C₄	—	4	1	no	—
409	C₂²⋊C₄	—	2	4	no	—
410	C₂²⋊C₄	—	2	4	no	—
411	C₂²⋊C₄	—	4	1	no	—
412	C₂²⋊C₄	—	4	2	no	—
413	C₂²⋊C₄	—	4	1	no	—
414	C₂²⋊C₄	—	4	2	no	—
415	C₂²⋊C₄	—	4	1	no	—
416	C₂²⋊C₄	M₁₆×C₇₃	1	4	yes	complemented
417	C₄²	—	2	2	no	—
418	C₄²	—	2	1	no	—
419	C₄²	—	2	2	no	—
420	C₄²	—	2	1	no	—
421	C₂³	—	2	2	no	—
422	C₂³	—	2	1	no	—
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	1	no	—
430	C₂³	—	2	2	no	—
431	C₂³	—	2	2	no	—
432	C₂³	—	2	1	no	—
433	C₂³	—	2	1	no	—
434	C₂³	—	2	2	no	—
435	C₂³	—	2	1	no	—
436	C₂³	—	4	8	no	—
437	C₂³	—	4	4	no	—
438	C₂³	—	4	4	no	—
439	C₂³	—	4	8	no	—
440	C₂³	—	4	4	no	—
441	C₂³	C₂×M₁₆×C₇₃	1	2	yes	—
442	C₂³	#131×C₇₃	1	4	yes	—
443	C₂³	C₂³×C₄×C₇₃	1	1	yes	characteristic
444	D₄	—	4	8	no	—
445	D₄	—	4	4	no	—
446	C₂×C₄	—	2	2	no	—
447	C₂×C₄	—	2	2	no	—
448	C₂×C₄	—	2	2	no	—
449	C₂×C₄	—	2	1	no	—
450	C₂×C₄	—	2	1	no	—
451	C₂×C₄	—	2	2	no	—
452	C₂×C₄	—	2	1	no	—
453	C₂×C₄	—	2	2	no	—
454	C₂×C₄	—	2	1	no	—
455	C₂×C₄	—	2	2	no	—
456	C₂×C₄	—	2	2	no	—
457	C₂×C₄	—	2	2	no	—
458	C₂×C₄	—	2	1	no	—
459	C₂×C₄	—	2	2	no	—
460	C₂×C₄	—	2	2	no	—
461	C₂×C₄	—	2	2	no	—
462	C₂×C₄	—	2	1	no	—
463	C₂×C₄	—	4	4	no	—
464	C₂×C₄	—	4	8	no	—
465	C₂×C₄	—	4	2	no	—
466	C₂×C₄	—	4	1	no	—
467	C₂×C₄	—	4	2	no	—
468	C₂×C₄	—	4	2	no	—
469	C₂×C₄	—	4	2	no	—
470	C₂×C₄	—	4	1	no	—
471	C₂×C₄	—	4	2	no	—
472	C₂×C₄	—	4	1	no	—
473	C₂×C₄	—	4	2	no	—
474	C₂×C₄	—	4	1	no	—
475	C₂×C₄	C₂×M₁₆×C₇₃	1	4	yes	—
476	C₂×C₄	H(5,𝔽₂)×C₇₃	1	2	yes	—
477	C₂×C₄	H(5,𝔽₂)×C₇₃	1	1	yes	characteristic
478	C₂×C₄	H(5,𝔽₂)×C₇₃	1	2	yes	—
479	C₂×C₄	H(5,𝔽₂)×C₇₃	1	1	yes	characteristic
480	C₈	—	4	2	no	—
481	C₈	—	4	2	no	—
482	C₈	—	4	2	no	—
483	C₈	—	4	2	no	—
484	C₂²	—	2	4	no	—
485	C₂²	—	2	4	no	—
486	C₂²	—	2	2	no	—
487	C₂²	—	2	4	no	—
488	C₂²	—	2	4	no	—
489	C₂²	—	4	16	no	—
490	C₂²	—	4	2	no	—
491	C₂²	—	4	2	no	—
492	C₂²	—	4	2	no	—
493	C₂²	—	4	2	no	—
494	C₂²	—	4	1	no	—
495	C₂²	—	4	2	no	—
496	C₂²	—	4	1	no	—
497	C₂²	—	4	2	no	—
498	C₂²	—	4	1	no	—
499	C₂²	—	4	2	no	—
500	C₂²	—	4	1	no	—
501	C₂²	—	4	1	no	—
502	C₂²	#518×C₇₃	1	2	yes	—
503	C₂²	#518×C₇₃	1	1	yes	characteristic
504	C₂²	C₂²×M₁₆×C₇₃	1	1	yes	characteristic
505	C₂²	C₂×#131×C₇₃	1	2	yes	—
506	C₂²	#568×C₇₃	1	1	yes	characteristic
507	C₄	—	2	4	no	—
508	C₄	—	4	1	no	—
509	C₄	—	4	2	no	—
510	C₄	—	4	1	no	—
511	C₄	—	4	2	no	—
512	C₄	—	4	1	no	—
513	C₄	—	4	1	no	—
514	C₄	#560×C₇₃	1	1	yes	characteristic
515	C₄	#560×C₇₃	1	2	yes	—
516	C₄	H(3,𝔽₄)×C₇₃	1	1	yes	characteristic
517	C₂	—	4	4	no	—
518	C₂	—	4	2	no	—
519	C₂	—	8	1	no	—
520	C₂	C₇₃×#2375	1	1	yes	characteristic
521	C₂	C₇₃×#2974	1	2	yes	—
522	C₂	C₇₃×#2975	1	1	yes	characteristic
523	C₂	C₇₃×#2976	1	2	yes	—
524	C₂	C₇₃×#2977	1	1	yes	characteristic

	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	C₂×#120×C₇₃	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
2. C₇₃×#1955	C₂	semidirect
3. C₇₃×#1954	C₂	semidirect
4. C₇₃×#1924	C₂	semidirect
5. C₇₃×#1923	C₂	semidirect
6. C₇₃×#1923	C₂	semidirect
7. C₇₃×#1870	C₂	semidirect
8. C₇₃×#1870	C₂	semidirect
9. C₇₃×#1779	C₂	semidirect
11. C₂²×M₁₆×C₇₃	C₂²	semidirect
15. C₂×C₄⋊C₈×C₇₃	C₂²	semidirect
16. C₂×C₄⋊C₈×C₇₃	C₂²	semidirect
23. C₂×C₂²⋊C₈×C₇₃	C₂²	semidirect
24. C₂×C₂²⋊C₈×C₇₃	C₂²	semidirect
25. C₂×#97×C₇₃	C₂²	semidirect
26. C₂×C₄×C₈×C₇₃	C₂²	semidirect
34. #336×C₇₃	C₂²	semidirect
35. #336×C₇₃	C₂²	semidirect
36. #336×C₇₃	C₂²	semidirect
153. C₂²⋊C₄×C₇₃	M₁₆	semidirect
254. #23308	C₇₃	direct (N × H)
264. #1955	C₂×C₇₃	semidirect
265. #1954	C₂×C₇₃	semidirect
266. #1924	C₂×C₇₃	semidirect
267. #1923	C₂×C₇₃	semidirect
268. #1923	C₂×C₇₃	semidirect
269. #1870	C₂×C₇₃	semidirect
270. #1870	C₂×C₇₃	semidirect
271. #1779	C₂×C₇₃	semidirect
272. C₇₃	#23308	direct (N × H)
274. C₂²×M₁₆	C₂²×C₇₃	semidirect
278. C₂×C₄⋊C₈	C₂²×C₇₃	semidirect
279. C₂×C₄⋊C₈	C₂²×C₇₃	semidirect
286. C₂×C₂²⋊C₈	C₂²×C₇₃	semidirect
287. C₂×C₂²⋊C₈	C₂²×C₇₃	semidirect
288. C₂×#97	C₂²×C₇₃	semidirect
289. C₂×C₄×C₈	C₂²×C₇₃	semidirect
297. #336	C₂²×C₇₃	semidirect
298. #336	C₂²×C₇₃	semidirect
299. #336	C₂²×C₇₃	semidirect
416. C₂²⋊C₄	M₁₆×C₇₃	semidirect

Maximal subgroups

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

subgroup	index
C₄×#120×C₇₃	2
C₇₃×#1955	2
C₇₃×#1954	2
C₇₃×#1924	2
C₇₃×#1923	2
C₇₃×#1870	2
C₇₃×#1779	2
#23308	73

Subgroups — C73×#23308 #32932712

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₃×#23308 #32932712