Subgroups — C₇₃×#24409 #32933813

Order 18688.

1336 conjugacy classes of subgroups.

The subgroup lattice has 590 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇₃×#3585	C₂	1	1	yes	maximal, characteristic
2	C₇₃×#3042	C₂	1	2	yes	maximal, complemented
3	C₇₃×#3028	C₂	1	1	yes	maximal, characteristic, complemented
4	C₇₃×#3009	C₂	1	1	yes	maximal, characteristic, complemented
5	C₇₃×#2883	C₂	1	1	yes	maximal, characteristic, complemented
6	C₇₃×#2053	C₂	1	2	yes	maximal, complemented
7	C₇₃×#2009	C₂	1	2	yes	maximal, complemented
8	C₇₃×#1909	C₂	1	1	yes	maximal, characteristic, complemented
9	C₇₃×#1904	C₂	1	2	yes	maximal, complemented
10	C₇₃×#1868	C₂	1	1	yes	maximal, characteristic, complemented
11	C₇₃×#1794	C₂	1	1	yes	maximal, characteristic, complemented
12	#585×C₇₃	C₂²	1	1	yes	characteristic
13	C₂×H(5,𝔽₂)×C₇₃	C₂²	1	1	yes	characteristic
14	#577×C₇₃	—	2	4	no	—
15	#576×C₇₃	—	2	4	no	—
16	#575×C₇₃	—	2	2	no	—
17	#575×C₇₃	C₂²	1	2	yes	—
18	C₂×#137×C₇₃	C₂²	1	1	yes	characteristic, complemented
19	C₂×AGL(1,ℤ/8)×C₇₃	—	2	2	no	—
20	C₂×AGL(1,ℤ/8)×C₇₃	C₂²	1	2	yes	—
21	C₂²×SD₁₆×C₇₃	C₂²	1	1	yes	characteristic, complemented
22	#568×C₇₃	C₂²	1	1	yes	characteristic
23	#536×C₇₃	C₂²	1	1	yes	characteristic
24	#536×C₇₃	C₂²	1	2	yes	complemented
25	#518×C₇₃	C₂²	1	2	yes	complemented
26	#463×C₇₃	—	2	4	no	—
27	#461×C₇₃	—	2	4	no	—
28	#458×C₇₃	—	2	4	no	—
29	#452×C₇₃	—	2	2	no	—
30	#450×C₇₃	—	2	2	no	—
31	#424×C₇₃	C₂²	1	2	yes	complemented
32	#421×C₇₃	C₂²	1	2	yes	complemented
33	#419×C₇₃	C₂²	1	2	yes	complemented
34	#418×C₇₃	C₂²	1	1	yes	characteristic, complemented
35	#416×C₇₃	C₂²	1	1	yes	characteristic, complemented
36	#416×C₇₃	C₂²	1	2	yes	complemented
37	#410×C₇₃	C₂²	1	1	yes	characteristic
38	#410×C₇₃	C₂²	1	1	yes	characteristic
39	#410×C₇₃	C₂²	1	2	yes	complemented
40	#410×C₇₃	C₂²	1	2	yes	complemented
41	C₂×#99×C₇₃	—	2	4	no	—
42	#408×C₇₃	C₂²	1	1	yes	characteristic
43	#344×C₇₃	C₂²	1	2	yes	complemented
44	H(3,ℤ/4)×C₇₃	C₂²	1	2	yes	complemented
45	2₋¹⁺⁴×C₇₃	—	2	2	no	—
46	2₋¹⁺⁴×C₇₃	—	2	1	no	—
47	H(5,𝔽₂)×C₇₃	—	2	2	no	—
48	H(5,𝔽₂)×C₇₃	—	2	4	no	—
49	H(5,𝔽₂)×C₇₃	—	2	2	no	—
50	H(5,𝔽₂)×C₇₃	—	2	1	no	—
51	H(5,𝔽₂)×C₇₃	—	4	2	no	—
52	C₂×#41×C₇₃	—	2	1	no	—
53	C₂×#41×C₇₃	—	2	2	no	—
54	C₂×#41×C₇₃	—	4	2	no	—
55	C₂×#41×C₇₃	D₄	1	2	yes	—
56	C₂×#41×C₇₃	C₂³	1	1	yes	characteristic
57	C₂×#41×C₇₃	C₂³	1	2	yes	—
58	C₂×#41×C₇₃	C₂³	1	1	yes	characteristic
59	C₂²×Q₈×C₇₃	C₂³	1	1	yes	characteristic
60	C₂²×D₄×C₇₃	—	2	2	no	—
61	C₂²×D₄×C₇₃	—	2	1	no	—
62	C₂²×D₄×C₇₃	D₄	1	2	yes	—
63	C₂²×D₄×C₇₃	C₂³	1	1	yes	characteristic
64	#137×C₇₃	—	2	4	no	—
65	#137×C₇₃	—	2	2	no	—
66	#137×C₇₃	—	2	2	no	—
67	#137×C₇₃	—	4	2	no	—
68	AGL(1,ℤ/8)×C₇₃	—	2	8	no	—
69	AGL(1,ℤ/8)×C₇₃	—	2	4	no	—
70	AGL(1,ℤ/8)×C₇₃	—	2	2	no	—
71	AGL(1,ℤ/8)×C₇₃	—	2	4	no	—
72	AGL(1,ℤ/8)×C₇₃	—	2	4	no	—
73	AGL(1,ℤ/8)×C₇₃	—	2	2	no	—
74	#135×C₇₃	—	2	8	no	—
75	#135×C₇₃	—	2	4	no	—
76	C₂×Q₁₆×C₇₃	—	2	1	no	—
77	C₂×SD₁₆×C₇₃	—	2	4	no	—
78	C₂×SD₁₆×C₇₃	—	2	1	no	—
79	C₂×SD₁₆×C₇₃	—	2	2	no	—
80	C₂×SD₁₆×C₇₃	—	2	4	no	—
81	C₂×SD₁₆×C₇₃	D₄	1	4	yes	—
82	C₂×D₈×C₇₃	—	2	4	no	—
83	C₂×D₈×C₇₃	D₄	1	4	yes	—
84	#131×C₇₃	—	2	4	no	—
85	C₂×M₁₆×C₇₃	—	2	2	no	—
86	C₂×M₁₆×C₇₃	C₂³	1	1	yes	characteristic
87	C₂×M₁₆×C₇₃	C₂³	1	2	yes	—
88	C₂²×C₈×C₇₃	C₂³	1	1	yes	characteristic
89	C₄⋊Q₈×C₇₃	—	2	2	no	—
90	C₄⋊Q₈×C₇₃	—	2	1	no	—
91	#124×C₇₃	—	2	2	no	—
92	#124×C₇₃	—	2	1	no	—
93	#123×C₇₃	—	2	2	no	—
94	#123×C₇₃	—	2	4	no	—
95	C₂²⋊Q₈×C₇₃	—	2	2	no	—
96	C₂²⋊Q₈×C₇₃	—	4	2	no	—
97	C₄×D₄×C₇₃	—	2	4	no	—
98	C₄×D₄×C₇₃	—	4	2	no	—
99	#117×C₇₃	C₂³	1	2	yes	—
100	#117×C₇₃	C₂³	1	1	yes	characteristic
101	#117×C₇₃	C₂³	1	2	yes	—
102	C₂×C₂²⋊C₄×C₇₃	—	2	4	no	—
103	C₄⋊C₈×C₇₃	—	2	4	no	—
104	#104×C₇₃	—	4	2	no	—
105	#103×C₇₃	—	2	1	no	—
106	#103×C₇₃	—	2	2	no	—
107	#103×C₇₃	—	2	4	no	—
108	#102×C₇₃	—	2	1	no	—
109	#102×C₇₃	—	2	2	no	—
110	#102×C₇₃	—	2	2	no	—
111	#99×C₇₃	—	2	2	no	—
112	#99×C₇₃	—	2	4	no	—
113	#99×C₇₃	—	2	4	no	—
114	#99×C₇₃	D₄	1	4	yes	—
115	C₂²⋊C₈×C₇₃	—	2	2	no	—
116	C₂⁴×C₇₃	—	2	1	no	—
117	C₂⁴×C₇₃	—	2	2	no	—
118	#41×C₇₃	—	2	2	no	—
119	#41×C₇₃	—	2	2	no	—
120	#41×C₇₃	—	2	4	no	—
121	#41×C₇₃	—	2	4	no	—
122	#41×C₇₃	—	2	2	no	—
123	#41×C₇₃	—	2	2	no	—
124	#41×C₇₃	—	2	2	no	—
125	#41×C₇₃	—	2	2	no	—
126	#41×C₇₃	—	2	2	no	—
127	#41×C₇₃	—	2	2	no	—
128	#41×C₇₃	—	4	2	no	—
129	#41×C₇₃	—	4	4	no	—
130	#41×C₇₃	—	4	2	no	—
131	#41×C₇₃	—	4	4	no	—
132	#41×C₇₃	—	4	2	no	—
133	#41×C₇₃	—	4	2	no	—
134	#41×C₇₃	—	4	2	no	—
135	C₂×Q₈×C₇₃	—	2	2	no	—
136	C₂×Q₈×C₇₃	—	2	2	no	—
137	C₂×Q₈×C₇₃	—	2	1	no	—
138	C₂×Q₈×C₇₃	—	2	1	no	—
139	C₂×Q₈×C₇₃	—	2	2	no	—
140	C₂×Q₈×C₇₃	—	4	2	no	—
141	C₂×Q₈×C₇₃	C₂×D₄	1	2	yes	—
142	C₂×Q₈×C₇₃	C₂×D₄	1	1	yes	characteristic
143	C₂×Q₈×C₇₃	#41	1	1	yes	characteristic
144	C₂×D₄×C₇₃	—	2	2	no	—
145	C₂×D₄×C₇₃	—	2	4	no	—
146	C₂×D₄×C₇₃	—	2	2	no	—
147	C₂×D₄×C₇₃	—	2	1	no	—
148	C₂×D₄×C₇₃	—	2	2	no	—
149	C₂×D₄×C₇₃	—	2	2	no	—
150	C₂×D₄×C₇₃	—	2	1	no	—
151	C₂×D₄×C₇₃	—	2	2	no	—
152	C₂×D₄×C₇₃	—	4	2	no	—
153	C₂×D₄×C₇₃	—	4	4	no	—
154	C₂×D₄×C₇₃	—	4	2	no	—
155	C₂×D₄×C₇₃	—	4	8	no	—
156	C₂×D₄×C₇₃	—	4	4	no	—
157	C₂×D₄×C₇₃	—	4	2	no	—
158	C₂×D₄×C₇₃	C₂×D₄	1	2	yes	—
159	C₂×D₄×C₇₃	C₂×D₄	1	2	yes	—
160	C₂×D₄×C₇₃	C₂×D₄	1	1	yes	characteristic
161	C₂×D₄×C₇₃	C₂×D₄	1	2	yes	—
162	C₂×D₄×C₇₃	C₂×D₄	1	4	yes	—
163	C₂×D₄×C₇₃	#41	1	1	yes	characteristic
164	C₂²×C₄×C₇₃	—	2	2	no	—
165	C₂²×C₄×C₇₃	—	2	1	no	—
166	C₂²×C₄×C₇₃	—	2	2	no	—
167	C₂²×C₄×C₇₃	—	2	1	no	—
168	C₂²×C₄×C₇₃	—	4	2	no	—
169	C₂²×C₄×C₇₃	—	4	4	no	—
170	C₂²×C₄×C₇₃	C₂×D₄	1	2	yes	—
171	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
172	Q₁₆×C₇₃	—	2	4	no	—
173	Q₁₆×C₇₃	—	4	2	no	—
174	SD₁₆×C₇₃	—	2	4	no	—
175	SD₁₆×C₇₃	—	2	4	no	—
176	SD₁₆×C₇₃	—	2	8	no	—
177	SD₁₆×C₇₃	—	4	2	no	—
178	SD₁₆×C₇₃	—	4	4	no	—
179	D₈×C₇₃	—	2	4	no	—
180	D₈×C₇₃	—	2	8	no	—
181	M₁₆×C₇₃	—	2	4	no	—
182	M₁₆×C₇₃	—	2	2	no	—
183	M₁₆×C₇₃	—	2	2	no	—
184	M₁₆×C₇₃	—	2	2	no	—
185	C₂×C₈×C₇₃	—	2	4	no	—
186	C₂×C₈×C₇₃	—	2	1	no	—
187	C₂×C₈×C₇₃	—	2	1	no	—
188	C₂×C₈×C₇₃	—	2	2	no	—
189	C₂×C₈×C₇₃	C₂×D₄	1	4	yes	—
190	C₄⋊C₄×C₇₃	—	2	2	no	—
191	C₄⋊C₄×C₇₃	—	2	1	no	—
192	C₄⋊C₄×C₇₃	—	2	2	no	—
193	C₄⋊C₄×C₇₃	—	4	4	no	—
194	C₄⋊C₄×C₇₃	—	4	2	no	—
195	C₂²⋊C₄×C₇₃	—	2	2	no	—
196	C₂²⋊C₄×C₇₃	—	2	1	no	—
197	C₂²⋊C₄×C₇₃	—	4	4	no	—
198	C₂²⋊C₄×C₇₃	—	4	4	no	—
199	C₂²⋊C₄×C₇₃	—	4	2	no	—
200	C₂²⋊C₄×C₇₃	C₂×D₄	1	4	yes	—
201	C₄²×C₇₃	—	2	2	no	—
202	C₄²×C₇₃	—	2	1	no	—
203	C₄²×C₇₃	—	2	2	no	—
204	C₂³×C₇₃	—	2	2	no	—
205	C₂³×C₇₃	—	2	4	no	—
206	C₂³×C₇₃	—	2	1	no	—
207	C₂³×C₇₃	—	2	2	no	—
208	C₂³×C₇₃	—	4	4	no	—
209	C₂³×C₇₃	—	4	2	no	—
210	C₂³×C₇₃	—	16	1	no	—
211	C₂³×C₇₃	—	16	2	no	—
212	C₂³×C₇₃	#121	1	2	yes	—
213	C₂³×C₇₃	C₂²×D₄	1	1	yes	characteristic
214	Q₈×C₇₃	—	2	2	no	—
215	Q₈×C₇₃	—	2	2	no	—
216	Q₈×C₇₃	—	2	1	no	—
217	Q₈×C₇₃	—	2	1	no	—
218	Q₈×C₇₃	—	2	2	no	—
219	Q₈×C₇₃	—	4	2	no	—
220	Q₈×C₇₃	—	4	1	no	—
221	Q₈×C₇₃	—	4	1	no	—
222	Q₈×C₇₃	—	4	2	no	—
223	D₄×C₇₃	—	2	4	no	—
224	D₄×C₇₃	—	2	2	no	—
225	D₄×C₇₃	—	2	1	no	—
226	D₄×C₇₃	—	2	2	no	—
227	D₄×C₇₃	—	2	1	no	—
228	D₄×C₇₃	—	2	4	no	—
229	D₄×C₇₃	—	2	2	no	—
230	D₄×C₇₃	—	2	2	no	—
231	D₄×C₇₃	—	4	4	no	—
232	D₄×C₇₃	—	4	2	no	—
233	D₄×C₇₃	—	4	4	no	—
234	D₄×C₇₃	—	4	4	no	—
235	D₄×C₇₃	—	4	2	no	—
236	D₄×C₇₃	—	4	2	no	—
237	D₄×C₇₃	—	4	2	no	—
238	D₄×C₇₃	#120	1	4	yes	—
239	C₂×C₄×C₇₃	—	2	2	no	—
240	C₂×C₄×C₇₃	—	2	2	no	—
241	C₂×C₄×C₇₃	—	2	1	no	—
242	C₂×C₄×C₇₃	—	2	4	no	—
243	C₂×C₄×C₇₃	—	2	2	no	—
244	C₂×C₄×C₇₃	—	4	4	no	—
245	C₂×C₄×C₇₃	—	4	4	no	—
246	C₂×C₄×C₇₃	—	4	2	no	—
247	C₂×C₄×C₇₃	—	4	2	no	—
248	C₂×C₄×C₇₃	—	4	2	no	—
249	C₂×C₄×C₇₃	—	4	2	no	—
250	C₂×C₄×C₇₃	—	4	1	no	—
251	C₂×C₄×C₇₃	—	4	1	no	—
252	C₂×C₄×C₇₃	—	4	2	no	—
253	C₂×C₄×C₇₃	—	4	2	no	—
254	C₂×C₄×C₇₃	—	16	4	no	—
255	C₂×C₄×C₇₃	#121	1	2	yes	—
256	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
257	C₂×C₄×C₇₃	C₂²×D₄	1	2	yes	—
258	C₂×C₄×C₇₃	C₂×#41	1	1	yes	characteristic
259	C₂×C₄×C₇₃	H(5,𝔽₂)	1	2	yes	—
260	C₈×C₇₃	—	2	4	no	—
261	C₈×C₇₃	—	4	1	no	—
262	C₈×C₇₃	—	4	1	no	—
263	C₂²×C₇₃	—	2	2	no	—
264	C₂²×C₇₃	—	2	4	no	—
265	C₂²×C₇₃	—	4	1	no	—
266	C₂²×C₇₃	—	4	2	no	—
267	C₂²×C₇₃	—	4	2	no	—
268	C₂²×C₇₃	—	4	1	no	—
269	C₂²×C₇₃	—	8	4	no	—
270	C₂²×C₇₃	—	8	2	no	—
271	C₂²×C₇₃	—	8	2	no	—
272	C₂²×C₇₃	—	8	1	no	—
273	C₂²×C₇₃	—	16	4	no	—
274	C₂²×C₇₃	—	16	2	no	—
275	C₂²×C₇₃	C₂×#121	1	1	yes	characteristic
276	C₂²×C₇₃	D₄²	1	2	yes	—
277	C₄×C₇₃	—	2	2	no	—
278	C₄×C₇₃	—	4	4	no	—
279	C₄×C₇₃	—	4	1	no	—
280	C₄×C₇₃	—	4	2	no	—
281	C₄×C₇₃	—	8	1	no	—
282	C₄×C₇₃	—	8	2	no	—
283	C₄×C₇₃	—	8	1	no	—
284	C₄×C₇₃	C₂×#120	1	1	yes	characteristic
285	C₄×C₇₃	#534	1	1	yes	characteristic
286	C₄×C₇₃	#546	1	2	yes	—
287	#24409	C₇₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
288	C₂×C₇₃	—	2	2	no	—
289	C₂×C₇₃	—	2	1	no	—
290	C₂×C₇₃	—	4	2	no	—
291	C₂×C₇₃	—	4	4	no	—
292	C₂×C₇₃	—	8	2	no	—
293	C₂×C₇₃	—	8	1	no	—
294	C₂×C₇₃	#2410	1	1	yes	characteristic
295	#3585	C₂×C₇₃	1	1	yes	characteristic
296	#3042	C₂×C₇₃	1	2	yes	complemented
297	#3028	C₂×C₇₃	1	1	yes	characteristic, complemented
298	#3009	C₂×C₇₃	1	1	yes	characteristic, complemented
299	#2883	C₂×C₇₃	1	1	yes	characteristic, complemented
300	#2053	C₂×C₇₃	1	2	yes	complemented
301	#2009	C₂×C₇₃	1	2	yes	complemented
302	#1909	C₂×C₇₃	1	1	yes	characteristic, complemented
303	#1904	C₂×C₇₃	1	2	yes	complemented
304	#1868	C₂×C₇₃	1	1	yes	characteristic, complemented
305	#1794	C₂×C₇₃	1	1	yes	characteristic, complemented
306	C₇₃	#24409	1	1	yes	characteristic, direct product factor, Sylow
307	#585	C₂²×C₇₃	1	1	yes	characteristic
308	C₂×H(5,𝔽₂)	C₂²×C₇₃	1	1	yes	characteristic
309	#577	—	2	4	no	—
310	#576	—	2	4	no	—
311	#575	—	2	2	no	—
312	#575	C₂²×C₇₃	1	2	yes	—
313	C₂×#137	C₂²×C₇₃	1	1	yes	characteristic, complemented
314	C₂×AGL(1,ℤ/8)	—	2	2	no	—
315	C₂×AGL(1,ℤ/8)	C₂²×C₇₃	1	2	yes	—
316	C₂²×SD₁₆	C₂²×C₇₃	1	1	yes	characteristic, complemented
317	#568	C₂²×C₇₃	1	1	yes	characteristic
318	#536	C₂²×C₇₃	1	1	yes	characteristic
319	#536	C₂²×C₇₃	1	2	yes	complemented
320	#518	C₂²×C₇₃	1	2	yes	complemented
321	#463	—	2	4	no	—
322	#461	—	2	4	no	—
323	#458	—	2	4	no	—
324	#452	—	2	2	no	—
325	#450	—	2	2	no	—
326	#424	C₂²×C₇₃	1	2	yes	complemented
327	#421	C₂²×C₇₃	1	2	yes	complemented
328	#419	C₂²×C₇₃	1	2	yes	complemented
329	#418	C₂²×C₇₃	1	1	yes	characteristic, complemented
330	#416	C₂²×C₇₃	1	2	yes	complemented
331	#416	C₂²×C₇₃	1	1	yes	characteristic, complemented
332	#410	C₂²×C₇₃	1	1	yes	characteristic
333	#410	C₂²×C₇₃	1	1	yes	characteristic
334	#410	C₂²×C₇₃	1	2	yes	complemented
335	#410	C₂²×C₇₃	1	2	yes	complemented
336	C₂×#99	—	2	4	no	—
337	#408	C₂²×C₇₃	1	1	yes	characteristic
338	#344	C₂²×C₇₃	1	2	yes	complemented
339	H(3,ℤ/4)	C₂²×C₇₃	1	2	yes	complemented
340	2₋¹⁺⁴	—	2	2	no	—
341	2₋¹⁺⁴	—	2	1	no	—
342	H(5,𝔽₂)	—	2	2	no	—
343	H(5,𝔽₂)	—	2	4	no	—
344	H(5,𝔽₂)	—	2	2	no	—
345	H(5,𝔽₂)	—	2	1	no	—
346	H(5,𝔽₂)	—	4	2	no	—
347	C₂×#41	—	2	1	no	—
348	C₂×#41	—	2	2	no	—
349	C₂×#41	—	4	2	no	—
350	C₂×#41	D₄×C₇₃	1	2	yes	—
351	C₂×#41	C₂³×C₇₃	1	2	yes	—
352	C₂×#41	C₂³×C₇₃	1	1	yes	characteristic
353	C₂×#41	C₂³×C₇₃	1	1	yes	characteristic
354	C₂²×Q₈	C₂³×C₇₃	1	1	yes	characteristic
355	C₂²×D₄	—	2	2	no	—
356	C₂²×D₄	—	2	1	no	—
357	C₂²×D₄	D₄×C₇₃	1	2	yes	—
358	C₂²×D₄	C₂³×C₇₃	1	1	yes	characteristic
359	#137	—	2	4	no	—
360	#137	—	2	2	no	—
361	#137	—	2	2	no	—
362	#137	—	4	2	no	—
363	AGL(1,ℤ/8)	—	2	8	no	—
364	AGL(1,ℤ/8)	—	2	4	no	—
365	AGL(1,ℤ/8)	—	2	2	no	—
366	AGL(1,ℤ/8)	—	2	4	no	—
367	AGL(1,ℤ/8)	—	2	4	no	—
368	AGL(1,ℤ/8)	—	2	2	no	—
369	#135	—	2	8	no	—
370	#135	—	2	4	no	—
371	C₂×Q₁₆	—	2	1	no	—
372	C₂×SD₁₆	—	2	4	no	—
373	C₂×SD₁₆	—	2	2	no	—
374	C₂×SD₁₆	—	2	4	no	—
375	C₂×SD₁₆	—	2	1	no	—
376	C₂×SD₁₆	D₄×C₇₃	1	4	yes	—
377	C₂×D₈	—	2	4	no	—
378	C₂×D₈	D₄×C₇₃	1	4	yes	—
379	#131	—	2	4	no	—
380	C₂×M₁₆	—	2	2	no	—
381	C₂×M₁₆	C₂³×C₇₃	1	1	yes	characteristic
382	C₂×M₁₆	C₂³×C₇₃	1	2	yes	—
383	C₂²×C₈	C₂³×C₇₃	1	1	yes	characteristic
384	C₄⋊Q₈	—	2	2	no	—
385	C₄⋊Q₈	—	2	1	no	—
386	#124	—	2	2	no	—
387	#124	—	2	1	no	—
388	#123	—	2	2	no	—
389	#123	—	2	4	no	—
390	C₂²⋊Q₈	—	2	2	no	—
391	C₂²⋊Q₈	—	4	2	no	—
392	C₄×D₄	—	2	4	no	—
393	C₄×D₄	—	4	2	no	—
394	#117	C₂³×C₇₃	1	2	yes	—
395	#117	C₂³×C₇₃	1	1	yes	characteristic
396	#117	C₂³×C₇₃	1	2	yes	—
397	C₂×C₂²⋊C₄	—	2	4	no	—
398	C₄⋊C₈	—	2	4	no	—
399	#104	—	4	2	no	—
400	#103	—	2	1	no	—
401	#103	—	2	2	no	—
402	#103	—	2	4	no	—
403	#102	—	2	1	no	—
404	#102	—	2	2	no	—
405	#102	—	2	2	no	—
406	#99	—	2	2	no	—
407	#99	—	2	4	no	—
408	#99	—	2	4	no	—
409	#99	D₄×C₇₃	1	4	yes	—
410	C₂²⋊C₈	—	2	2	no	—
411	C₂⁴	—	2	1	no	—
412	C₂⁴	—	2	2	no	—
413	#41	—	2	2	no	—
414	#41	—	2	2	no	—
415	#41	—	2	4	no	—
416	#41	—	2	4	no	—
417	#41	—	2	2	no	—
418	#41	—	2	2	no	—
419	#41	—	2	2	no	—
420	#41	—	2	2	no	—
421	#41	—	2	2	no	—
422	#41	—	2	2	no	—
423	#41	—	4	2	no	—
424	#41	—	4	4	no	—
425	#41	—	4	2	no	—
426	#41	—	4	4	no	—
427	#41	—	4	2	no	—
428	#41	—	4	2	no	—
429	#41	—	4	2	no	—
430	C₂×Q₈	—	2	2	no	—
431	C₂×Q₈	—	2	2	no	—
432	C₂×Q₈	—	2	1	no	—
433	C₂×Q₈	—	2	1	no	—
434	C₂×Q₈	—	2	2	no	—
435	C₂×Q₈	—	4	2	no	—
436	C₂×Q₈	C₂×D₄×C₇₃	1	2	yes	—
437	C₂×Q₈	C₂×D₄×C₇₃	1	1	yes	characteristic
438	C₂×Q₈	#41×C₇₃	1	1	yes	characteristic
439	C₂×D₄	—	2	2	no	—
440	C₂×D₄	—	2	4	no	—
441	C₂×D₄	—	2	2	no	—
442	C₂×D₄	—	2	1	no	—
443	C₂×D₄	—	2	2	no	—
444	C₂×D₄	—	2	2	no	—
445	C₂×D₄	—	2	1	no	—
446	C₂×D₄	—	2	2	no	—
447	C₂×D₄	—	4	2	no	—
448	C₂×D₄	—	4	4	no	—
449	C₂×D₄	—	4	2	no	—
450	C₂×D₄	—	4	8	no	—
451	C₂×D₄	—	4	4	no	—
452	C₂×D₄	—	4	2	no	—
453	C₂×D₄	C₂×D₄×C₇₃	1	2	yes	—
454	C₂×D₄	C₂×D₄×C₇₃	1	2	yes	—
455	C₂×D₄	C₂×D₄×C₇₃	1	1	yes	characteristic
456	C₂×D₄	C₂×D₄×C₇₃	1	2	yes	—
457	C₂×D₄	C₂×D₄×C₇₃	1	4	yes	—
458	C₂×D₄	#41×C₇₃	1	1	yes	characteristic
459	C₂²×C₄	—	2	2	no	—
460	C₂²×C₄	—	2	1	no	—
461	C₂²×C₄	—	2	2	no	—
462	C₂²×C₄	—	2	1	no	—
463	C₂²×C₄	—	4	2	no	—
464	C₂²×C₄	—	4	4	no	—
465	C₂²×C₄	C₂×D₄×C₇₃	1	2	yes	—
466	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
467	Q₁₆	—	2	4	no	—
468	Q₁₆	—	4	2	no	—
469	SD₁₆	—	2	4	no	—
470	SD₁₆	—	2	4	no	—
471	SD₁₆	—	2	8	no	—
472	SD₁₆	—	4	2	no	—
473	SD₁₆	—	4	4	no	—
474	D₈	—	2	4	no	—
475	D₈	—	2	8	no	—
476	M₁₆	—	2	4	no	—
477	M₁₆	—	2	2	no	—
478	M₁₆	—	2	2	no	—
479	M₁₆	—	2	2	no	—
480	C₂×C₈	—	2	4	no	—
481	C₂×C₈	—	2	1	no	—
482	C₂×C₈	—	2	1	no	—
483	C₂×C₈	—	2	2	no	—
484	C₂×C₈	C₂×D₄×C₇₃	1	4	yes	—
485	C₄⋊C₄	—	2	2	no	—
486	C₄⋊C₄	—	2	1	no	—
487	C₄⋊C₄	—	2	2	no	—
488	C₄⋊C₄	—	4	4	no	—
489	C₄⋊C₄	—	4	2	no	—
490	C₂²⋊C₄	—	2	2	no	—
491	C₂²⋊C₄	—	2	1	no	—
492	C₂²⋊C₄	—	4	4	no	—
493	C₂²⋊C₄	—	4	4	no	—
494	C₂²⋊C₄	—	4	2	no	—
495	C₂²⋊C₄	C₂×D₄×C₇₃	1	4	yes	—
496	C₄²	—	2	2	no	—
497	C₄²	—	2	1	no	—
498	C₄²	—	2	2	no	—
499	C₂³	—	2	2	no	—
500	C₂³	—	2	4	no	—
501	C₂³	—	2	1	no	—
502	C₂³	—	2	2	no	—
503	C₂³	—	4	4	no	—
504	C₂³	—	4	2	no	—
505	C₂³	—	16	1	no	—
506	C₂³	—	16	2	no	—
507	C₂³	#121×C₇₃	1	2	yes	—
508	C₂³	C₂²×D₄×C₇₃	1	1	yes	characteristic
509	Q₈	—	2	2	no	—
510	Q₈	—	2	2	no	—
511	Q₈	—	2	1	no	—
512	Q₈	—	2	1	no	—
513	Q₈	—	2	2	no	—
514	Q₈	—	4	2	no	—
515	Q₈	—	4	1	no	—
516	Q₈	—	4	1	no	—
517	Q₈	—	4	2	no	—
518	D₄	—	2	4	no	—
519	D₄	—	2	2	no	—
520	D₄	—	2	1	no	—
521	D₄	—	2	2	no	—
522	D₄	—	2	1	no	—
523	D₄	—	2	4	no	—
524	D₄	—	2	2	no	—
525	D₄	—	2	2	no	—
526	D₄	—	4	4	no	—
527	D₄	—	4	2	no	—
528	D₄	—	4	4	no	—
529	D₄	—	4	4	no	—
530	D₄	—	4	2	no	—
531	D₄	—	4	2	no	—
532	D₄	—	4	2	no	—
533	D₄	#120×C₇₃	1	4	yes	—
534	C₂×C₄	—	2	2	no	—
535	C₂×C₄	—	2	2	no	—
536	C₂×C₄	—	2	1	no	—
537	C₂×C₄	—	2	4	no	—
538	C₂×C₄	—	2	2	no	—
539	C₂×C₄	—	4	4	no	—
540	C₂×C₄	—	4	4	no	—
541	C₂×C₄	—	4	2	no	—
542	C₂×C₄	—	4	2	no	—
543	C₂×C₄	—	4	2	no	—
544	C₂×C₄	—	4	2	no	—
545	C₂×C₄	—	4	1	no	—
546	C₂×C₄	—	4	1	no	—
547	C₂×C₄	—	4	2	no	—
548	C₂×C₄	—	4	2	no	—
549	C₂×C₄	—	16	4	no	—
550	C₂×C₄	#121×C₇₃	1	2	yes	—
551	C₂×C₄	C₂²×D₄×C₇₃	1	1	yes	characteristic
552	C₂×C₄	C₂²×D₄×C₇₃	1	2	yes	—
553	C₂×C₄	C₂×#41×C₇₃	1	1	yes	characteristic
554	C₂×C₄	H(5,𝔽₂)×C₇₃	1	2	yes	—
555	C₈	—	2	4	no	—
556	C₈	—	4	1	no	—
557	C₈	—	4	1	no	—
558	C₂²	—	2	2	no	—
559	C₂²	—	2	4	no	—
560	C₂²	—	4	1	no	—
561	C₂²	—	4	2	no	—
562	C₂²	—	4	2	no	—
563	C₂²	—	4	1	no	—
564	C₂²	—	8	4	no	—
565	C₂²	—	8	2	no	—
566	C₂²	—	8	1	no	—
567	C₂²	—	8	2	no	—
568	C₂²	—	16	4	no	—
569	C₂²	—	16	2	no	—
570	C₂²	C₂×#121×C₇₃	1	1	yes	characteristic
571	C₂²	D₄²×C₇₃	1	2	yes	—
572	C₄	—	2	2	no	—
573	C₄	—	4	4	no	—
574	C₄	—	4	1	no	—
575	C₄	—	4	2	no	—
576	C₄	—	8	2	no	—
577	C₄	—	8	1	no	—
578	C₄	—	8	1	no	—
579	C₄	C₂×#120×C₇₃	1	1	yes	characteristic
580	C₄	#534×C₇₃	1	1	yes	characteristic
581	C₄	#546×C₇₃	1	2	yes	—
582	C₂	—	2	2	no	—
583	C₂	—	2	1	no	—
584	C₂	—	4	2	no	—
585	C₂	—	4	4	no	—
586	C₂	—	8	1	no	—
587	C₂	—	8	2	no	—
588	C₂	C₇₃×#2410	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂×C₇₃	#2410
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₇₃
prime radical	C₇₃×#3585	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₇₃ ◁ C₂²×C₄×C₇₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₇₃×#3042	C₂	semidirect
3. C₇₃×#3028	C₂	semidirect
4. C₇₃×#3009	C₂	semidirect
5. C₇₃×#2883	C₂	semidirect
6. C₇₃×#2053	C₂	semidirect
7. C₇₃×#2009	C₂	semidirect
8. C₇₃×#1909	C₂	semidirect
9. C₇₃×#1904	C₂	semidirect
10. C₇₃×#1868	C₂	semidirect
11. C₇₃×#1794	C₂	semidirect
18. C₂×#137×C₇₃	C₂²	semidirect
21. C₂²×SD₁₆×C₇₃	C₂²	semidirect
24. #536×C₇₃	C₂²	semidirect
25. #518×C₇₃	C₂²	semidirect
31. #424×C₇₃	C₂²	semidirect
32. #421×C₇₃	C₂²	semidirect
33. #419×C₇₃	C₂²	semidirect
34. #418×C₇₃	C₂²	semidirect
35. #416×C₇₃	C₂²	semidirect
36. #416×C₇₃	C₂²	semidirect
39. #410×C₇₃	C₂²	semidirect
40. #410×C₇₃	C₂²	semidirect
43. #344×C₇₃	C₂²	semidirect
44. H(3,ℤ/4)×C₇₃	C₂²	semidirect
287. #24409	C₇₃	direct (N × H)
296. #3042	C₂×C₇₃	semidirect
297. #3028	C₂×C₇₃	semidirect
298. #3009	C₂×C₇₃	semidirect
299. #2883	C₂×C₇₃	semidirect
300. #2053	C₂×C₇₃	semidirect
301. #2009	C₂×C₇₃	semidirect
302. #1909	C₂×C₇₃	semidirect
303. #1904	C₂×C₇₃	semidirect
304. #1868	C₂×C₇₃	semidirect
305. #1794	C₂×C₇₃	semidirect
306. C₇₃	#24409	direct (N × H)
313. C₂×#137	C₂²×C₇₃	semidirect
316. C₂²×SD₁₆	C₂²×C₇₃	semidirect
319. #536	C₂²×C₇₃	semidirect
320. #518	C₂²×C₇₃	semidirect
326. #424	C₂²×C₇₃	semidirect
327. #421	C₂²×C₇₃	semidirect
328. #419	C₂²×C₇₃	semidirect
329. #418	C₂²×C₇₃	semidirect
330. #416	C₂²×C₇₃	semidirect
331. #416	C₂²×C₇₃	semidirect
334. #410	C₂²×C₇₃	semidirect
335. #410	C₂²×C₇₃	semidirect
338. #344	C₂²×C₇₃	semidirect
339. H(3,ℤ/4)	C₂²×C₇₃	semidirect

Maximal subgroups

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

subgroup	index
C₇₃×#3585	2
C₇₃×#3042	2
C₇₃×#3028	2
C₇₃×#3009	2
C₇₃×#2883	2
C₇₃×#2053	2
C₇₃×#2009	2
C₇₃×#1909	2
C₇₃×#1904	2
C₇₃×#1868	2
C₇₃×#1794	2
#24409	73

Subgroups — C73×#24409 #32933813

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₃×#24409 #32933813