Subgroups — C₇₃×#23350 #32932754

Order 18688.

728 conjugacy classes of subgroups.

The subgroup lattice has 418 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇₃×#2398	C₂	1	1	yes	maximal, characteristic
2	C₇₃×#1985	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇₃×#1984	C₂	1	1	yes	maximal, characteristic, complemented
4	C₇₃×#1924	C₂	1	2	yes	maximal, complemented
5	C₇₃×#1923	C₂	1	2	yes	maximal, complemented
6	C₇₃×#1869	C₂	1	2	yes	maximal
7	C₇₃×#1850	C₂	1	2	yes	maximal, complemented
8	C₇₃×#1850	C₂	1	2	yes	maximal, complemented
9	C₇₃×#1832	C₂	1	2	yes	maximal, complemented
10	C₂³×C₈×C₇₃	C₂²	1	2	yes	—
11	C₂×C₄×Q₈×C₇₃	C₂²	1	1	yes	characteristic
12	C₂×C₄×D₄×C₇₃	C₂²	1	1	yes	characteristic
13	C₂×C₄⋊C₈×C₇₃	C₂²	1	1	yes	characteristic
14	C₂×C₄⋊C₈×C₇₃	C₂²	1	1	yes	characteristic
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×#97×C₇₃	C₂²	1	1	yes	characteristic
21	C₂×C₄×C₈×C₇₃	C₂²	1	1	yes	characteristic
22	#400×C₇₃	C₄	1	1	yes	characteristic
23	#400×C₇₃	C₄	1	1	yes	characteristic
24	#397×C₇₃	C₄	1	2	yes	—
25	#394×C₇₃	C₄	1	1	yes	characteristic
26	#394×C₇₃	C₄	1	1	yes	characteristic
27	#393×C₇₃	C₄	1	2	yes	—
28	C₄×C₂²⋊C₄×C₇₃	C₂²	1	2	yes	—
29	C₄×C₂²⋊C₄×C₇₃	C₂²	1	2	yes	—
30	#376×C₇₃	C₂²	1	1	yes	characteristic
31	#336×C₇₃	C₂²	1	2	yes	—
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×Q₈×C₇₃	C₂×C₄	1	1	yes	characteristic
38	C₂²×D₄×C₇₃	C₂×C₄	1	1	yes	characteristic
39	C₂³×C₄×C₇₃	C₂³	1	2	yes	—
40	C₂²×C₈×C₇₃	—	4	2	no	—
41	C₂²×C₈×C₇₃	—	4	2	no	—
42	C₂²×C₈×C₇₃	—	4	2	no	—
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	C₂²×C₈×C₇₃	C₂³	1	2	yes	—
47	C₄×Q₈×C₇₃	—	4	1	no	—
48	C₄×Q₈×C₇₃	—	4	1	no	—
49	C₄×D₄×C₇₃	—	4	1	no	—
50	C₄×D₄×C₇₃	—	4	1	no	—
51	C₂×C₄⋊C₄×C₇₃	C₂×C₄	1	1	yes	characteristic
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	2	yes	—
60	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
61	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
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	1	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	#97×C₇₃	—	4	1	no	—
72	C₄×C₈×C₇₃	—	4	1	no	—
73	#95×C₇₃	C₂×C₄	1	2	yes	—
74	#95×C₇₃	C₂×C₄	1	2	yes	—
75	#95×C₇₃	C₂×C₄	1	2	yes	—
76	#95×C₇₃	C₂×C₄	1	2	yes	—
77	#95×C₇₃	C₂×C₄	1	2	yes	—
78	#95×C₇₃	C₂×C₄	1	1	yes	characteristic
79	#95×C₇₃	C₂×C₄	1	1	yes	characteristic
80	C₂⁴×C₇₃	C₂²×C₄	1	2	yes	—
81	C₂×Q₈×C₇₃	—	2	2	no	—
82	C₂×Q₈×C₇₃	—	4	1	no	—
83	C₂×Q₈×C₇₃	—	4	1	no	—
84	C₂×D₄×C₇₃	—	2	4	no	—
85	C₂×D₄×C₇₃	—	4	1	no	—
86	C₂²×C₄×C₇₃	—	2	2	no	—
87	C₂²×C₄×C₇₃	—	2	2	no	—
88	C₂²×C₄×C₇₃	—	2	2	no	—
89	C₂²×C₄×C₇₃	—	2	2	no	—
90	C₂²×C₄×C₇₃	—	2	2	no	—
91	C₂²×C₄×C₇₃	—	2	2	no	—
92	C₂²×C₄×C₇₃	C₂²×C₄	1	2	yes	—
93	C₂²×C₄×C₇₃	C₂²×C₄	1	2	yes	—
94	C₂²×C₄×C₇₃	C₂²×C₄	1	2	yes	—
95	C₂²×C₄×C₇₃	C₂²×C₄	1	1	yes	characteristic
96	C₂²×C₄×C₇₃	C₂²×C₄	1	1	yes	characteristic
97	C₂²×C₄×C₇₃	C₂²×C₄	1	1	yes	characteristic
98	C₂²×C₄×C₇₃	C₂²×C₄	1	1	yes	characteristic
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	C₂×C₈×C₇₃	—	2	2	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	—	4	8	no	—
115	C₄⋊C₄×C₇₃	—	4	1	no	—
116	C₄⋊C₄×C₇₃	—	4	1	no	—
117	C₄⋊C₄×C₇₃	—	4	1	no	—
118	C₄⋊C₄×C₇₃	—	4	1	no	—
119	C₂²⋊C₄×C₇₃	—	2	4	no	—
120	C₂²⋊C₄×C₇₃	—	2	4	no	—
121	C₂²⋊C₄×C₇₃	—	2	4	no	—
122	C₂²⋊C₄×C₇₃	—	4	2	no	—
123	C₂²⋊C₄×C₇₃	—	4	2	no	—
124	C₄²×C₇₃	—	2	1	no	—
125	C₄²×C₇₃	—	2	1	no	—
126	C₄²×C₇₃	—	2	2	no	—
127	C₄²×C₇₃	—	2	1	no	—
128	C₄²×C₇₃	—	2	1	no	—
129	C₄²×C₇₃	—	2	1	no	—
130	C₄²×C₇₃	—	2	1	no	—
131	C₄²×C₇₃	—	2	2	no	—
132	C₂³×C₇₃	—	2	2	no	—
133	C₂³×C₇₃	—	2	2	no	—
134	C₂³×C₇₃	—	2	2	no	—
135	C₂³×C₇₃	—	2	2	no	—
136	C₂³×C₇₃	—	2	2	no	—
137	C₂³×C₇₃	—	2	2	no	—
138	C₂³×C₇₃	#131	1	4	yes	—
139	C₂³×C₇₃	C₂³×C₄	1	1	yes	characteristic
140	Q₈×C₇₃	—	4	4	no	—
141	D₄×C₇₃	—	4	4	no	—
142	C₂×C₄×C₇₃	—	2	1	no	—
143	C₂×C₄×C₇₃	—	2	1	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	1	no	—
148	C₂×C₄×C₇₃	—	2	1	no	—
149	C₂×C₄×C₇₃	—	2	2	no	—
150	C₂×C₄×C₇₃	—	2	2	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	1	no	—
161	C₂×C₄×C₇₃	—	2	1	no	—
162	C₂×C₄×C₇₃	—	2	1	no	—
163	C₂×C₄×C₇₃	—	2	2	no	—
164	C₂×C₄×C₇₃	—	2	1	no	—
165	C₂×C₄×C₇₃	—	4	2	no	—
166	C₂×C₄×C₇₃	—	4	2	no	—
167	C₂×C₄×C₇₃	—	4	2	no	—
168	C₂×C₄×C₇₃	—	4	2	no	—
169	C₂×C₄×C₇₃	#131	1	2	yes	—
170	C₂×C₄×C₇₃	H(5,𝔽₂)	1	2	yes	—
171	C₂×C₄×C₇₃	H(5,𝔽₂)	1	1	yes	characteristic
172	C₂×C₄×C₇₃	H(5,𝔽₂)	1	1	yes	characteristic
173	C₂×C₄×C₇₃	2₋¹⁺⁴	1	2	yes	—
174	C₈×C₇₃	—	4	2	no	—
175	C₈×C₇₃	—	4	2	no	—
176	C₈×C₇₃	—	4	2	no	—
177	C₈×C₇₃	—	4	2	no	—
178	C₂²×C₇₃	—	2	4	no	—
179	C₂²×C₇₃	—	2	4	no	—
180	C₂²×C₇₃	—	2	4	no	—
181	C₂²×C₇₃	—	4	2	no	—
182	C₂²×C₇₃	—	4	2	no	—
183	C₂²×C₇₃	—	4	2	no	—
184	C₂²×C₇₃	—	4	2	no	—
185	C₂²×C₇₃	#518	1	1	yes	characteristic
186	C₂²×C₇₃	#520	1	2	yes	—
187	C₂²×C₇₃	C₂×#131	1	1	yes	characteristic
188	C₂²×C₇₃	C₂×#131	1	2	yes	—
189	C₂²×C₇₃	#568	1	1	yes	characteristic
190	C₄×C₇₃	—	2	2	no	—
191	C₄×C₇₃	—	4	2	no	—
192	C₄×C₇₃	—	4	1	no	—
193	C₄×C₇₃	—	4	1	no	—
194	C₄×C₇₃	—	4	1	no	—
195	C₄×C₇₃	—	4	1	no	—
196	C₄×C₇₃	—	4	1	no	—
197	C₄×C₇₃	—	4	2	no	—
198	C₄×C₇₃	—	4	2	no	—
199	C₄×C₇₃	H(3,𝔽₄)	1	1	yes	characteristic
200	C₄×C₇₃	#562	1	2	yes	—
201	C₄×C₇₃	#563	1	1	yes	characteristic
202	#23350	C₇₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
203	C₂×C₇₃	—	4	4	no	—
204	C₂×C₇₃	#2379	1	1	yes	characteristic
205	C₂×C₇₃	#2976	1	1	yes	characteristic
206	C₂×C₇₃	#2977	1	1	yes	characteristic
207	C₂×C₇₃	#2992	1	2	yes	—
208	C₂×C₇₃	#2994	1	2	yes	—
209	#2398	C₂×C₇₃	1	1	yes	characteristic
210	#1985	C₂×C₇₃	1	1	yes	characteristic, complemented
211	#1984	C₂×C₇₃	1	1	yes	characteristic, complemented
212	#1924	C₂×C₇₃	1	2	yes	complemented
213	#1923	C₂×C₇₃	1	2	yes	complemented
214	#1869	C₂×C₇₃	1	2	yes	—
215	#1850	C₂×C₇₃	1	2	yes	complemented
216	#1850	C₂×C₇₃	1	2	yes	complemented
217	#1832	C₂×C₇₃	1	2	yes	complemented
218	C₇₃	#23350	1	1	yes	characteristic, direct product factor, Sylow
219	C₂³×C₈	C₂²×C₇₃	1	2	yes	—
220	C₂×C₄×Q₈	C₂²×C₇₃	1	1	yes	characteristic
221	C₂×C₄×D₄	C₂²×C₇₃	1	1	yes	characteristic
222	C₂×C₄⋊C₈	C₂²×C₇₃	1	2	yes	—
223	C₂×C₄⋊C₈	C₂²×C₇₃	1	2	yes	—
224	C₂×C₄⋊C₈	C₂²×C₇₃	1	1	yes	characteristic
225	C₂×C₄⋊C₈	C₂²×C₇₃	1	1	yes	characteristic
226	C₂×C₂²⋊C₈	C₂²×C₇₃	1	2	yes	—
227	C₂×C₂²⋊C₈	C₂²×C₇₃	1	2	yes	—
228	C₂×C₂²⋊C₈	C₂²×C₇₃	1	2	yes	—
229	C₂×#97	C₂²×C₇₃	1	1	yes	characteristic
230	C₂×C₄×C₈	C₂²×C₇₃	1	1	yes	characteristic
231	#400	C₄×C₇₃	1	1	yes	characteristic
232	#400	C₄×C₇₃	1	1	yes	characteristic
233	#397	C₄×C₇₃	1	2	yes	—
234	#394	C₄×C₇₃	1	1	yes	characteristic
235	#394	C₄×C₇₃	1	1	yes	characteristic
236	#393	C₄×C₇₃	1	2	yes	—
237	C₄×C₂²⋊C₄	C₂²×C₇₃	1	2	yes	—
238	C₄×C₂²⋊C₄	C₂²×C₇₃	1	2	yes	—
239	#376	C₂²×C₇₃	1	1	yes	characteristic
240	#336	C₂²×C₇₃	1	2	yes	—
241	#336	C₂²×C₇₃	1	2	yes	—
242	#336	C₂²×C₇₃	1	2	yes	—
243	#336	C₂²×C₇₃	1	2	yes	—
244	#336	C₂²×C₇₃	1	2	yes	—
245	#336	C₂²×C₇₃	1	2	yes	—
246	C₂²×Q₈	C₂×C₄×C₇₃	1	1	yes	characteristic
247	C₂²×D₄	C₂×C₄×C₇₃	1	1	yes	characteristic
248	C₂³×C₄	C₂³×C₇₃	1	2	yes	—
249	C₂²×C₈	—	4	2	no	—
250	C₂²×C₈	—	4	2	no	—
251	C₂²×C₈	—	4	2	no	—
252	C₂²×C₈	C₂³×C₇₃	1	2	yes	—
253	C₂²×C₈	C₂³×C₇₃	1	2	yes	—
254	C₂²×C₈	C₂³×C₇₃	1	2	yes	—
255	C₂²×C₈	C₂³×C₇₃	1	2	yes	—
256	C₄×Q₈	—	4	1	no	—
257	C₄×Q₈	—	4	1	no	—
258	C₄×D₄	—	4	1	no	—
259	C₄×D₄	—	4	1	no	—
260	C₂×C₄⋊C₄	C₂×C₄×C₇₃	1	1	yes	characteristic
261	C₂×C₄⋊C₄	C₂×C₄×C₇₃	1	1	yes	characteristic
262	C₂×C₄⋊C₄	C₂×C₄×C₇₃	1	1	yes	characteristic
263	C₂×C₄⋊C₄	C₂×C₄×C₇₃	1	1	yes	characteristic
264	C₂×C₂²⋊C₄	C₂×C₄×C₇₃	1	2	yes	—
265	C₂×C₂²⋊C₄	C₂×C₄×C₇₃	1	2	yes	—
266	C₂×C₂²⋊C₄	C₂×C₄×C₇₃	1	2	yes	—
267	C₂×C₂²⋊C₄	C₂×C₄×C₇₃	1	2	yes	—
268	C₂×C₂²⋊C₄	C₂×C₄×C₇₃	1	2	yes	—
269	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
270	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
271	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
272	C₂×C₄²	C₂³×C₇₃	1	2	yes	—
273	C₄⋊C₈	—	4	2	no	—
274	C₄⋊C₈	—	4	2	no	—
275	C₄⋊C₈	—	4	1	no	—
276	C₄⋊C₈	—	4	1	no	—
277	C₂²⋊C₈	—	4	2	no	—
278	C₂²⋊C₈	—	4	2	no	—
279	C₂²⋊C₈	—	4	2	no	—
280	#97	—	4	1	no	—
281	C₄×C₈	—	4	1	no	—
282	#95	C₂×C₄×C₇₃	1	2	yes	—
283	#95	C₂×C₄×C₇₃	1	1	yes	characteristic
284	#95	C₂×C₄×C₇₃	1	1	yes	characteristic
285	#95	C₂×C₄×C₇₃	1	2	yes	—
286	#95	C₂×C₄×C₇₃	1	2	yes	—
287	#95	C₂×C₄×C₇₃	1	2	yes	—
288	#95	C₂×C₄×C₇₃	1	2	yes	—
289	C₂⁴	C₂²×C₄×C₇₃	1	2	yes	—
290	C₂×Q₈	—	2	2	no	—
291	C₂×Q₈	—	4	1	no	—
292	C₂×Q₈	—	4	1	no	—
293	C₂×D₄	—	2	4	no	—
294	C₂×D₄	—	4	1	no	—
295	C₂²×C₄	—	2	2	no	—
296	C₂²×C₄	—	2	2	no	—
297	C₂²×C₄	—	2	2	no	—
298	C₂²×C₄	—	2	2	no	—
299	C₂²×C₄	—	2	2	no	—
300	C₂²×C₄	—	2	2	no	—
301	C₂²×C₄	C₂²×C₄×C₇₃	1	2	yes	—
302	C₂²×C₄	C₂²×C₄×C₇₃	1	2	yes	—
303	C₂²×C₄	C₂²×C₄×C₇₃	1	2	yes	—
304	C₂²×C₄	C₂²×C₄×C₇₃	1	1	yes	characteristic
305	C₂²×C₄	C₂²×C₄×C₇₃	1	1	yes	characteristic
306	C₂²×C₄	C₂²×C₄×C₇₃	1	1	yes	characteristic
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	1	yes	characteristic
310	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
311	C₂×C₈	—	2	2	no	—
312	C₂×C₈	—	2	2	no	—
313	C₂×C₈	—	2	2	no	—
314	C₂×C₈	—	2	2	no	—
315	C₂×C₈	—	2	2	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	—	4	8	no	—
324	C₄⋊C₄	—	4	1	no	—
325	C₄⋊C₄	—	4	1	no	—
326	C₄⋊C₄	—	4	1	no	—
327	C₄⋊C₄	—	4	1	no	—
328	C₂²⋊C₄	—	2	4	no	—
329	C₂²⋊C₄	—	2	4	no	—
330	C₂²⋊C₄	—	2	4	no	—
331	C₂²⋊C₄	—	4	2	no	—
332	C₂²⋊C₄	—	4	2	no	—
333	C₄²	—	2	1	no	—
334	C₄²	—	2	1	no	—
335	C₄²	—	2	2	no	—
336	C₄²	—	2	1	no	—
337	C₄²	—	2	1	no	—
338	C₄²	—	2	1	no	—
339	C₄²	—	2	1	no	—
340	C₄²	—	2	2	no	—
341	C₂³	—	2	2	no	—
342	C₂³	—	2	2	no	—
343	C₂³	—	2	2	no	—
344	C₂³	—	2	2	no	—
345	C₂³	—	2	2	no	—
346	C₂³	—	2	2	no	—
347	C₂³	#131×C₇₃	1	4	yes	—
348	C₂³	C₂³×C₄×C₇₃	1	1	yes	characteristic
349	Q₈	—	4	4	no	—
350	D₄	—	4	4	no	—
351	C₂×C₄	—	2	1	no	—
352	C₂×C₄	—	2	1	no	—
353	C₂×C₄	—	2	1	no	—
354	C₂×C₄	—	2	1	no	—
355	C₂×C₄	—	2	1	no	—
356	C₂×C₄	—	2	1	no	—
357	C₂×C₄	—	2	1	no	—
358	C₂×C₄	—	2	2	no	—
359	C₂×C₄	—	2	2	no	—
360	C₂×C₄	—	2	2	no	—
361	C₂×C₄	—	2	2	no	—
362	C₂×C₄	—	2	2	no	—
363	C₂×C₄	—	2	2	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	1	no	—
370	C₂×C₄	—	2	1	no	—
371	C₂×C₄	—	2	1	no	—
372	C₂×C₄	—	2	2	no	—
373	C₂×C₄	—	2	1	no	—
374	C₂×C₄	—	4	2	no	—
375	C₂×C₄	—	4	2	no	—
376	C₂×C₄	—	4	2	no	—
377	C₂×C₄	—	4	2	no	—
378	C₂×C₄	#131×C₇₃	1	2	yes	—
379	C₂×C₄	H(5,𝔽₂)×C₇₃	1	2	yes	—
380	C₂×C₄	H(5,𝔽₂)×C₇₃	1	1	yes	characteristic
381	C₂×C₄	H(5,𝔽₂)×C₇₃	1	1	yes	characteristic
382	C₂×C₄	2₋¹⁺⁴×C₇₃	1	2	yes	—
383	C₈	—	4	2	no	—
384	C₈	—	4	2	no	—
385	C₈	—	4	2	no	—
386	C₈	—	4	2	no	—
387	C₂²	—	2	4	no	—
388	C₂²	—	2	4	no	—
389	C₂²	—	2	4	no	—
390	C₂²	—	4	2	no	—
391	C₂²	—	4	2	no	—
392	C₂²	—	4	2	no	—
393	C₂²	—	4	2	no	—
394	C₂²	#518×C₇₃	1	1	yes	characteristic
395	C₂²	#520×C₇₃	1	2	yes	—
396	C₂²	C₂×#131×C₇₃	1	1	yes	characteristic
397	C₂²	C₂×#131×C₇₃	1	2	yes	—
398	C₂²	#568×C₇₃	1	1	yes	characteristic
399	C₄	—	2	2	no	—
400	C₄	—	4	1	no	—
401	C₄	—	4	1	no	—
402	C₄	—	4	1	no	—
403	C₄	—	4	1	no	—
404	C₄	—	4	1	no	—
405	C₄	—	4	2	no	—
406	C₄	—	4	2	no	—
407	C₄	—	4	2	no	—
408	C₄	H(3,𝔽₄)×C₇₃	1	1	yes	characteristic
409	C₄	#562×C₇₃	1	2	yes	—
410	C₄	#563×C₇₃	1	1	yes	characteristic
411	C₂	—	4	4	no	—
412	C₂	C₇₃×#2379	1	1	yes	characteristic
413	C₂	C₇₃×#2976	1	1	yes	characteristic
414	C₂	C₇₃×#2977	1	1	yes	characteristic
415	C₂	C₇₃×#2992	1	2	yes	—
416	C₂	C₇₃×#2994	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
2. C₇₃×#1985	C₂	semidirect
3. C₇₃×#1984	C₂	semidirect
4. C₇₃×#1924	C₂	semidirect
5. C₇₃×#1923	C₂	semidirect
7. C₇₃×#1850	C₂	semidirect
8. C₇₃×#1850	C₂	semidirect
9. C₇₃×#1832	C₂	semidirect
202. #23350	C₇₃	direct (N × H)
210. #1985	C₂×C₇₃	semidirect
211. #1984	C₂×C₇₃	semidirect
212. #1924	C₂×C₇₃	semidirect
213. #1923	C₂×C₇₃	semidirect
215. #1850	C₂×C₇₃	semidirect
216. #1850	C₂×C₇₃	semidirect
217. #1832	C₂×C₇₃	semidirect
218. C₇₃	#23350	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×#2398	2
C₇₃×#1985	2
C₇₃×#1984	2
C₇₃×#1924	2
C₇₃×#1923	2
C₇₃×#1869	2
C₇₃×#1850	2
C₇₃×#1832	2
#23350	73

Subgroups — C73×#23350 #32932754

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₃×#23350 #32932754