Subgroups — C₇₃×#25753 #32935157

Order 18688.

1998 conjugacy classes of subgroups.

The subgroup lattice has 536 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₄²×C₇₃	C₂	1	1	yes	maximal, characteristic
2	C₂×#492×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#461×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#450×C₇₃	C₂	1	4	yes	maximal, complemented
5	C₇₃×#2542	C₂	1	1	yes	maximal, characteristic, complemented
6	C₇₃×#2000	C₂	1	4	yes	maximal, complemented
7	C₇₃×#1982	C₂	1	1	yes	maximal, characteristic, complemented
8	C₇₃×#1954	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄×#102×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂³×D₄×C₇₃	—	2	1	no	—
11	C₂³×D₄×C₇₃	C₂²	1	2	yes	—
12	C₂²×SD₁₆×C₇₃	C₂²	1	2	yes	—
13	C₂²×SD₁₆×C₇₃	C₂²	1	4	yes	complemented
14	D₄²×C₇₃	—	2	4	no	—
15	D₄²×C₇₃	—	2	4	no	—
16	C₂×C₄⋊Q₈×C₇₃	C₂²	1	1	yes	characteristic, complemented
17	C₂×#127×C₇₃	C₂²	1	1	yes	characteristic
18	C₂×C₂²⋊Q₈×C₇₃	C₂²	1	4	yes	complemented
19	C₂×#121×C₇₃	—	2	1	no	—
20	C₂×#121×C₇₃	C₂²	1	2	yes	—
21	C₂×#120×C₇₃	—	2	2	no	—
22	C₂×C₄×D₄×C₇₃	C₂²	1	1	yes	characteristic
23	C₂×C₄×D₄×C₇₃	C₂²	1	1	yes	characteristic
24	#492×C₇₃	—	2	4	no	—
25	#461×C₇₃	—	2	4	no	—
26	#450×C₇₃	—	2	16	no	—
27	C₂×C₄⋊C₈×C₇₃	C₂²	1	1	yes	characteristic, complemented
28	C₂×#103×C₇₃	C₂²	1	2	yes	complemented
29	C₂×#102×C₇₃	C₂²	1	2	yes	—
30	C₂×#102×C₇₃	C₂²	1	4	yes	complemented
31	C₂×C₂²⋊C₈×C₇₃	C₂²	1	4	yes	complemented
32	C₂×C₄×C₈×C₇₃	C₂²	1	1	yes	characteristic, complemented
33	#399×C₇₃	—	2	2	no	—
34	#390×C₇₃	—	2	1	no	—
35	#384×C₇₃	—	2	1	no	—
36	C₄×C₄⋊C₄×C₇₃	C₂²	1	1	yes	characteristic, complemented
37	#340×C₇₃	C₂²	1	2	yes	complemented
38	C₂⁵×C₇₃	—	2	2	no	—
39	C₂²×Q₈×C₇₃	C₂³	1	2	yes	—
40	C₂²×D₄×C₇₃	—	2	8	no	—
41	C₂²×D₄×C₇₃	—	2	2	no	—
42	C₂²×D₄×C₇₃	—	2	4	no	—
43	C₂²×D₄×C₇₃	—	2	4	no	—
44	C₂²×D₄×C₇₃	—	2	8	no	—
45	C₂²×D₄×C₇₃	—	2	2	no	—
46	C₂²×D₄×C₇₃	—	2	1	no	—
47	C₂²×D₄×C₇₃	—	2	1	no	—
48	C₂²×D₄×C₇₃	—	4	4	no	—
49	C₂²×D₄×C₇₃	—	4	4	no	—
50	C₂²×D₄×C₇₃	—	4	4	no	—
51	C₂²×D₄×C₇₃	D₄	1	1	yes	characteristic
52	C₂²×D₄×C₇₃	C₂³	1	2	yes	—
53	C₂²×D₄×C₇₃	C₂³	1	1	yes	characteristic
54	C₂³×C₄×C₇₃	—	2	1	no	—
55	C₂³×C₄×C₇₃	C₂³	1	2	yes	—
56	C₂×SD₁₆×C₇₃	—	2	8	no	—
57	C₂×SD₁₆×C₇₃	—	2	4	no	—
58	C₂×SD₁₆×C₇₃	—	2	8	no	—
59	C₂×SD₁₆×C₇₃	—	2	8	no	—
60	C₂×SD₁₆×C₇₃	—	4	4	no	—
61	C₂²×C₈×C₇₃	C₂³	1	2	yes	—
62	C₂²×C₈×C₇₃	C₂³	1	2	yes	—
63	C₄⋊Q₈×C₇₃	—	2	2	no	—
64	C₄⋊Q₈×C₇₃	—	2	2	no	—
65	#127×C₇₃	—	2	2	no	—
66	#127×C₇₃	D₄	1	4	yes	—
67	C₂²⋊Q₈×C₇₃	—	2	8	no	—
68	C₂²⋊Q₈×C₇₃	—	4	4	no	—
69	#121×C₇₃	—	2	8	no	—
70	#121×C₇₃	—	2	4	no	—
71	#121×C₇₃	—	2	4	no	—
72	#120×C₇₃	—	2	16	no	—
73	C₄×D₄×C₇₃	—	2	2	no	—
74	C₄×D₄×C₇₃	—	2	2	no	—
75	C₄×D₄×C₇₃	—	2	2	no	—
76	C₄×D₄×C₇₃	D₄	1	4	yes	—
77	C₂×C₄⋊C₄×C₇₃	—	2	1	no	—
78	C₂×C₄⋊C₄×C₇₃	—	2	4	no	—
79	C₂×C₄⋊C₄×C₇₃	—	2	1	no	—
80	C₂×C₄⋊C₄×C₇₃	D₄	1	1	yes	characteristic
81	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
82	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
83	C₂×C₂²⋊C₄×C₇₃	—	2	1	no	—
84	C₂×C₂²⋊C₄×C₇₃	—	2	2	no	—
85	C₂×C₂²⋊C₄×C₇₃	—	2	4	no	—
86	C₂×C₂²⋊C₄×C₇₃	D₄	1	2	yes	—
87	C₂×C₄²×C₇₃	—	2	1	no	—
88	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
89	C₄⋊C₈×C₇₃	—	2	2	no	—
90	#103×C₇₃	—	2	4	no	—
91	#102×C₇₃	—	2	8	no	—
92	#102×C₇₃	D₄	1	8	yes	complemented
93	C₂²⋊C₈×C₇₃	—	2	8	no	—
94	C₄×C₈×C₇₃	—	2	2	no	—
95	#95×C₇₃	—	2	1	no	—
96	C₂⁴×C₇₃	—	2	1	no	—
97	C₂⁴×C₇₃	—	2	8	no	—
98	C₂⁴×C₇₃	—	2	2	no	—
99	C₂⁴×C₇₃	—	4	8	no	—
100	C₂⁴×C₇₃	—	4	4	no	—
101	C₂⁴×C₇₃	—	4	4	no	—
102	C₂⁴×C₇₃	—	8	4	no	—
103	C₂⁴×C₇₃	C₂×D₄	1	2	yes	—
104	C₂×Q₈×C₇₃	—	2	2	no	—
105	C₂×Q₈×C₇₃	—	2	4	no	—
106	C₂×Q₈×C₇₃	—	2	2	no	—
107	C₂×Q₈×C₇₃	—	2	4	no	—
108	C₂×D₄×C₇₃	—	2	8	no	—
109	C₂×D₄×C₇₃	—	2	8	no	—
110	C₂×D₄×C₇₃	—	2	2	no	—
111	C₂×D₄×C₇₃	—	2	4	no	—
112	C₂×D₄×C₇₃	—	2	4	no	—
113	C₂×D₄×C₇₃	—	2	2	no	—
114	C₂×D₄×C₇₃	—	2	1	no	—
115	C₂×D₄×C₇₃	—	2	4	no	—
116	C₂×D₄×C₇₃	—	2	2	no	—
117	C₂×D₄×C₇₃	—	2	2	no	—
118	C₂×D₄×C₇₃	—	2	4	no	—
119	C₂×D₄×C₇₃	—	4	8	no	—
120	C₂×D₄×C₇₃	—	4	16	no	—
121	C₂×D₄×C₇₃	—	4	8	no	—
122	C₂×D₄×C₇₃	—	4	32	no	—
123	C₂×D₄×C₇₃	—	4	4	no	—
124	C₂×D₄×C₇₃	—	4	4	no	—
125	C₂×D₄×C₇₃	—	4	8	no	—
126	C₂×D₄×C₇₃	—	4	2	no	—
127	C₂×D₄×C₇₃	—	4	2	no	—
128	C₂×D₄×C₇₃	—	8	2	no	—
129	C₂×D₄×C₇₃	SD₁₆	1	4	yes	complemented
130	C₂×D₄×C₇₃	C₂×D₄	1	4	yes	—
131	C₂×D₄×C₇₃	C₂×D₄	1	4	yes	—
132	C₂×D₄×C₇₃	C₂×D₄	1	2	yes	—
133	C₂²×C₄×C₇₃	—	2	2	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	—	2	2	no	—
139	C₂²×C₄×C₇₃	—	2	4	no	—
140	C₂²×C₄×C₇₃	—	2	2	no	—
141	C₂²×C₄×C₇₃	—	4	2	no	—
142	C₂²×C₄×C₇₃	—	4	2	no	—
143	C₂²×C₄×C₇₃	C₂×D₄	1	2	yes	—
144	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
145	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
146	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
147	SD₁₆×C₇₃	—	4	16	no	—
148	SD₁₆×C₇₃	—	4	8	no	—
149	C₂×C₈×C₇₃	—	2	2	no	—
150	C₂×C₈×C₇₃	—	2	2	no	—
151	C₂×C₈×C₇₃	—	2	4	no	—
152	C₂×C₈×C₇₃	—	2	2	no	—
153	C₂×C₈×C₇₃	C₂×D₄	1	4	yes	complemented
154	C₄⋊C₄×C₇₃	—	2	2	no	—
155	C₄⋊C₄×C₇₃	—	2	1	no	—
156	C₄⋊C₄×C₇₃	—	2	2	no	—
157	C₄⋊C₄×C₇₃	—	4	8	no	—
158	C₄⋊C₄×C₇₃	—	4	2	no	—
159	C₄⋊C₄×C₇₃	—	4	2	no	—
160	C₄⋊C₄×C₇₃	C₂×D₄	1	2	yes	—
161	C₄⋊C₄×C₇₃	C₂×D₄	1	4	yes	complemented
162	C₂²⋊C₄×C₇₃	—	2	8	no	—
163	C₂²⋊C₄×C₇₃	—	2	4	no	—
164	C₂²⋊C₄×C₇₃	—	2	4	no	—
165	C₂²⋊C₄×C₇₃	—	4	8	no	—
166	C₄²×C₇₃	—	4	2	no	—
167	C₄²×C₇₃	C₂×D₄	1	2	yes	—
168	C₄²×C₇₃	C₂×D₄	1	2	yes	—
169	C₂³×C₇₃	—	2	2	no	—
170	C₂³×C₇₃	—	2	2	no	—
171	C₂³×C₇₃	—	2	4	no	—
172	C₂³×C₇₃	—	2	4	no	—
173	C₂³×C₇₃	—	2	2	no	—
174	C₂³×C₇₃	—	2	4	no	—
175	C₂³×C₇₃	—	2	4	no	—
176	C₂³×C₇₃	—	4	16	no	—
177	C₂³×C₇₃	—	4	16	no	—
178	C₂³×C₇₃	—	4	1	no	—
179	C₂³×C₇₃	—	4	1	no	—
180	C₂³×C₇₃	—	4	2	no	—
181	C₂³×C₇₃	—	4	4	no	—
182	C₂³×C₇₃	—	4	2	no	—
183	C₂³×C₇₃	—	4	2	no	—
184	C₂³×C₇₃	—	4	4	no	—
185	C₂³×C₇₃	—	8	16	no	—
186	C₂³×C₇₃	—	8	8	no	—
187	C₂³×C₇₃	—	8	16	no	—
188	C₂³×C₇₃	C₂×SD₁₆	1	4	yes	—
189	C₂³×C₇₃	C₂²×D₄	1	1	yes	characteristic
190	Q₈×C₇₃	—	4	2	no	—
191	Q₈×C₇₃	—	4	2	no	—
192	Q₈×C₇₃	—	4	4	no	—
193	D₄×C₇₃	—	2	2	no	—
194	D₄×C₇₃	—	2	4	no	—
195	D₄×C₇₃	—	2	8	no	—
196	D₄×C₇₃	—	2	8	no	—
197	D₄×C₇₃	—	4	16	no	—
198	D₄×C₇₃	—	4	16	no	—
199	D₄×C₇₃	—	4	2	no	—
200	D₄×C₇₃	—	4	2	no	—
201	D₄×C₇₃	—	4	8	no	—
202	D₄×C₇₃	—	8	4	no	—
203	D₄×C₇₃	#127	1	4	yes	—
204	C₂×C₄×C₇₃	—	2	2	no	—
205	C₂×C₄×C₇₃	—	2	2	no	—
206	C₂×C₄×C₇₃	—	2	2	no	—
207	C₂×C₄×C₇₃	—	2	4	no	—
208	C₂×C₄×C₇₃	—	2	4	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	—	4	2	no	—
213	C₂×C₄×C₇₃	—	4	2	no	—
214	C₂×C₄×C₇₃	—	4	2	no	—
215	C₂×C₄×C₇₃	—	4	4	no	—
216	C₂×C₄×C₇₃	—	4	8	no	—
217	C₂×C₄×C₇₃	—	4	2	no	—
218	C₂×C₄×C₇₃	—	4	4	no	—
219	C₂×C₄×C₇₃	#120	1	2	yes	—
220	C₂×C₄×C₇₃	#120	1	2	yes	—
221	C₂×C₄×C₇₃	C₂×SD₁₆	1	2	yes	—
222	C₂×C₄×C₇₃	AGL(1,ℤ/8)	1	2	yes	—
223	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
224	C₂×C₄×C₇₃	C₂²×D₄	1	2	yes	—
225	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
226	C₂×C₄×C₇₃	H(5,𝔽₂)	1	2	yes	—
227	C₈×C₇₃	—	2	4	no	—
228	C₈×C₇₃	—	4	2	no	—
229	C₂²×C₇₃	—	2	4	no	—
230	C₂²×C₇₃	—	2	4	no	—
231	C₂²×C₇₃	—	2	8	no	—
232	C₂²×C₇₃	—	4	2	no	—
233	C₂²×C₇₃	—	4	2	no	—
234	C₂²×C₇₃	—	4	2	no	—
235	C₂²×C₇₃	—	4	2	no	—
236	C₂²×C₇₃	—	4	4	no	—
237	C₂²×C₇₃	—	4	4	no	—
238	C₂²×C₇₃	—	4	4	no	—
239	C₂²×C₇₃	—	4	4	no	—
240	C₂²×C₇₃	—	4	4	no	—
241	C₂²×C₇₃	—	4	4	no	—
242	C₂²×C₇₃	—	8	32	no	—
243	C₂²×C₇₃	—	8	4	no	—
244	C₂²×C₇₃	—	8	4	no	—
245	C₂²×C₇₃	C₂×#120	1	1	yes	characteristic
246	C₂²×C₇₃	D₄²	1	2	yes	—
247	C₂²×C₇₃	C₂²×SD₁₆	1	1	yes	characteristic
248	C₂²×C₇₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
249	C₂²×C₇₃	#577	1	2	yes	—
250	C₄×C₇₃	—	2	2	no	—
251	C₄×C₇₃	—	4	2	no	—
252	C₄×C₇₃	—	4	2	no	—
253	C₄×C₇₃	—	4	4	no	—
254	C₄×C₇₃	—	8	2	no	—
255	C₄×C₇₃	#450	1	4	yes	complemented
256	C₄×C₇₃	C₂×#127	1	1	yes	characteristic
257	C₄×C₇₃	#535	1	1	yes	characteristic
258	C₄×C₇₃	D₄²	1	2	yes	—
259	#25753	C₇₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
260	C₂×C₇₃	—	4	4	no	—
261	C₂×C₇₃	—	4	4	no	—
262	C₂×C₇₃	—	8	4	no	—
263	C₂×C₇₃	#2433	1	1	yes	characteristic
264	C₂×C₇₃	C₂×#450	1	1	yes	characteristic
265	C₂×C₇₃	#3009	1	1	yes	characteristic
266	C₂×C₇₃	#3272	1	2	yes	—
267	C₂×C₇₃	D₄×SD₁₆	1	2	yes	—
268	C₂×D₄²	C₂×C₇₃	1	1	yes	characteristic
269	C₂×#492	C₂×C₇₃	1	1	yes	characteristic, complemented
270	C₂×#461	C₂×C₇₃	1	1	yes	characteristic, complemented
271	C₂×#450	C₂×C₇₃	1	4	yes	complemented
272	#2542	C₂×C₇₃	1	1	yes	characteristic, complemented
273	#2000	C₂×C₇₃	1	4	yes	complemented
274	#1982	C₂×C₇₃	1	1	yes	characteristic, complemented
275	#1954	C₂×C₇₃	1	1	yes	characteristic, complemented
276	C₄×#102	C₂×C₇₃	1	1	yes	characteristic, complemented
277	C₇₃	#25753	1	1	yes	characteristic, direct product factor, Sylow
278	C₂³×D₄	—	2	1	no	—
279	C₂³×D₄	C₂²×C₇₃	1	2	yes	—
280	C₂²×SD₁₆	C₂²×C₇₃	1	2	yes	—
281	C₂²×SD₁₆	C₂²×C₇₃	1	4	yes	complemented
282	D₄²	—	2	4	no	—
283	D₄²	—	2	4	no	—
284	C₂×C₄⋊Q₈	C₂²×C₇₃	1	1	yes	characteristic, complemented
285	C₂×#127	C₂²×C₇₃	1	1	yes	characteristic
286	C₂×C₂²⋊Q₈	C₂²×C₇₃	1	4	yes	complemented
287	C₂×#121	—	2	1	no	—
288	C₂×#121	C₂²×C₇₃	1	2	yes	—
289	C₂×#120	—	2	2	no	—
290	C₂×C₄×D₄	C₂²×C₇₃	1	1	yes	characteristic
291	C₂×C₄×D₄	C₂²×C₇₃	1	1	yes	characteristic
292	#492	—	2	4	no	—
293	#461	—	2	4	no	—
294	#450	—	2	16	no	—
295	C₂×C₄⋊C₈	C₂²×C₇₃	1	1	yes	characteristic, complemented
296	C₂×#103	C₂²×C₇₃	1	2	yes	complemented
297	C₂×#102	C₂²×C₇₃	1	2	yes	—
298	C₂×#102	C₂²×C₇₃	1	4	yes	complemented
299	C₂×C₂²⋊C₈	C₂²×C₇₃	1	4	yes	complemented
300	C₂×C₄×C₈	C₂²×C₇₃	1	1	yes	characteristic, complemented
301	#399	—	2	2	no	—
302	#390	—	2	1	no	—
303	#384	—	2	1	no	—
304	C₄×C₄⋊C₄	C₂²×C₇₃	1	1	yes	characteristic, complemented
305	#340	C₂²×C₇₃	1	2	yes	complemented
306	C₂⁵	—	2	2	no	—
307	C₂²×Q₈	C₂³×C₇₃	1	2	yes	—
308	C₂²×D₄	—	2	8	no	—
309	C₂²×D₄	—	2	2	no	—
310	C₂²×D₄	—	2	4	no	—
311	C₂²×D₄	—	2	4	no	—
312	C₂²×D₄	—	2	8	no	—
313	C₂²×D₄	—	2	2	no	—
314	C₂²×D₄	—	2	1	no	—
315	C₂²×D₄	—	2	1	no	—
316	C₂²×D₄	—	4	4	no	—
317	C₂²×D₄	—	4	4	no	—
318	C₂²×D₄	—	4	4	no	—
319	C₂²×D₄	D₄×C₇₃	1	1	yes	characteristic
320	C₂²×D₄	C₂³×C₇₃	1	2	yes	—
321	C₂²×D₄	C₂³×C₇₃	1	1	yes	characteristic
322	C₂³×C₄	—	2	1	no	—
323	C₂³×C₄	C₂³×C₇₃	1	2	yes	—
324	C₂×SD₁₆	—	2	8	no	—
325	C₂×SD₁₆	—	2	4	no	—
326	C₂×SD₁₆	—	2	8	no	—
327	C₂×SD₁₆	—	2	8	no	—
328	C₂×SD₁₆	—	4	4	no	—
329	C₂²×C₈	C₂³×C₇₃	1	2	yes	—
330	C₂²×C₈	C₂³×C₇₃	1	2	yes	—
331	C₄⋊Q₈	—	2	2	no	—
332	C₄⋊Q₈	—	2	2	no	—
333	#127	—	2	2	no	—
334	#127	D₄×C₇₃	1	4	yes	—
335	C₂²⋊Q₈	—	2	8	no	—
336	C₂²⋊Q₈	—	4	4	no	—
337	#121	—	2	8	no	—
338	#121	—	2	4	no	—
339	#121	—	2	4	no	—
340	#120	—	2	16	no	—
341	C₄×D₄	—	2	2	no	—
342	C₄×D₄	—	2	2	no	—
343	C₄×D₄	—	2	2	no	—
344	C₄×D₄	D₄×C₇₃	1	4	yes	—
345	C₂×C₄⋊C₄	—	2	4	no	—
346	C₂×C₄⋊C₄	—	2	1	no	—
347	C₂×C₄⋊C₄	—	2	1	no	—
348	C₂×C₄⋊C₄	D₄×C₇₃	1	1	yes	characteristic
349	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
350	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
351	C₂×C₂²⋊C₄	—	2	1	no	—
352	C₂×C₂²⋊C₄	—	2	2	no	—
353	C₂×C₂²⋊C₄	—	2	4	no	—
354	C₂×C₂²⋊C₄	D₄×C₇₃	1	2	yes	—
355	C₂×C₄²	—	2	1	no	—
356	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
357	C₄⋊C₈	—	2	2	no	—
358	#103	—	2	4	no	—
359	#102	—	2	8	no	—
360	#102	D₄×C₇₃	1	8	yes	complemented
361	C₂²⋊C₈	—	2	8	no	—
362	C₄×C₈	—	2	2	no	—
363	#95	—	2	1	no	—
364	C₂⁴	—	2	1	no	—
365	C₂⁴	—	2	8	no	—
366	C₂⁴	—	2	2	no	—
367	C₂⁴	—	4	8	no	—
368	C₂⁴	—	4	4	no	—
369	C₂⁴	—	4	4	no	—
370	C₂⁴	—	8	4	no	—
371	C₂⁴	C₂×D₄×C₇₃	1	2	yes	—
372	C₂×Q₈	—	2	2	no	—
373	C₂×Q₈	—	2	4	no	—
374	C₂×Q₈	—	2	2	no	—
375	C₂×Q₈	—	2	4	no	—
376	C₂×D₄	—	2	8	no	—
377	C₂×D₄	—	2	8	no	—
378	C₂×D₄	—	2	2	no	—
379	C₂×D₄	—	2	4	no	—
380	C₂×D₄	—	2	4	no	—
381	C₂×D₄	—	2	2	no	—
382	C₂×D₄	—	2	1	no	—
383	C₂×D₄	—	2	4	no	—
384	C₂×D₄	—	2	2	no	—
385	C₂×D₄	—	2	2	no	—
386	C₂×D₄	—	2	4	no	—
387	C₂×D₄	—	4	8	no	—
388	C₂×D₄	—	4	16	no	—
389	C₂×D₄	—	4	32	no	—
390	C₂×D₄	—	4	8	no	—
391	C₂×D₄	—	4	4	no	—
392	C₂×D₄	—	4	4	no	—
393	C₂×D₄	—	4	8	no	—
394	C₂×D₄	—	4	2	no	—
395	C₂×D₄	—	4	2	no	—
396	C₂×D₄	—	8	2	no	—
397	C₂×D₄	SD₁₆×C₇₃	1	4	yes	complemented
398	C₂×D₄	C₂×D₄×C₇₃	1	4	yes	—
399	C₂×D₄	C₂×D₄×C₇₃	1	4	yes	—
400	C₂×D₄	C₂×D₄×C₇₃	1	2	yes	—
401	C₂²×C₄	—	2	2	no	—
402	C₂²×C₄	—	2	1	no	—
403	C₂²×C₄	—	2	4	no	—
404	C₂²×C₄	—	2	4	no	—
405	C₂²×C₄	—	2	2	no	—
406	C₂²×C₄	—	2	2	no	—
407	C₂²×C₄	—	2	4	no	—
408	C₂²×C₄	—	2	2	no	—
409	C₂²×C₄	—	4	2	no	—
410	C₂²×C₄	—	4	2	no	—
411	C₂²×C₄	C₂×D₄×C₇₃	1	2	yes	—
412	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
413	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
414	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
415	SD₁₆	—	4	16	no	—
416	SD₁₆	—	4	8	no	—
417	C₂×C₈	—	2	2	no	—
418	C₂×C₈	—	2	2	no	—
419	C₂×C₈	—	2	4	no	—
420	C₂×C₈	—	2	2	no	—
421	C₂×C₈	C₂×D₄×C₇₃	1	4	yes	complemented
422	C₄⋊C₄	—	2	2	no	—
423	C₄⋊C₄	—	2	1	no	—
424	C₄⋊C₄	—	2	2	no	—
425	C₄⋊C₄	—	4	8	no	—
426	C₄⋊C₄	—	4	2	no	—
427	C₄⋊C₄	—	4	2	no	—
428	C₄⋊C₄	C₂×D₄×C₇₃	1	2	yes	—
429	C₄⋊C₄	C₂×D₄×C₇₃	1	4	yes	complemented
430	C₂²⋊C₄	—	2	8	no	—
431	C₂²⋊C₄	—	2	4	no	—
432	C₂²⋊C₄	—	2	4	no	—
433	C₂²⋊C₄	—	4	8	no	—
434	C₄²	—	4	2	no	—
435	C₄²	C₂×D₄×C₇₃	1	2	yes	—
436	C₄²	C₂×D₄×C₇₃	1	2	yes	—
437	C₂³	—	2	2	no	—
438	C₂³	—	2	2	no	—
439	C₂³	—	2	4	no	—
440	C₂³	—	2	4	no	—
441	C₂³	—	2	2	no	—
442	C₂³	—	2	4	no	—
443	C₂³	—	2	4	no	—
444	C₂³	—	4	16	no	—
445	C₂³	—	4	16	no	—
446	C₂³	—	4	1	no	—
447	C₂³	—	4	1	no	—
448	C₂³	—	4	2	no	—
449	C₂³	—	4	4	no	—
450	C₂³	—	4	2	no	—
451	C₂³	—	4	2	no	—
452	C₂³	—	4	4	no	—
453	C₂³	—	8	16	no	—
454	C₂³	—	8	8	no	—
455	C₂³	—	8	16	no	—
456	C₂³	C₂×SD₁₆×C₇₃	1	4	yes	—
457	C₂³	C₂²×D₄×C₇₃	1	1	yes	characteristic
458	Q₈	—	4	2	no	—
459	Q₈	—	4	2	no	—
460	Q₈	—	4	4	no	—
461	D₄	—	2	8	no	—
462	D₄	—	2	2	no	—
463	D₄	—	2	4	no	—
464	D₄	—	2	8	no	—
465	D₄	—	4	16	no	—
466	D₄	—	4	16	no	—
467	D₄	—	4	8	no	—
468	D₄	—	4	2	no	—
469	D₄	—	4	2	no	—
470	D₄	—	8	4	no	—
471	D₄	#127×C₇₃	1	4	yes	—
472	C₂×C₄	—	2	2	no	—
473	C₂×C₄	—	2	2	no	—
474	C₂×C₄	—	2	2	no	—
475	C₂×C₄	—	2	4	no	—
476	C₂×C₄	—	2	4	no	—
477	C₂×C₄	—	4	1	no	—
478	C₂×C₄	—	4	2	no	—
479	C₂×C₄	—	4	1	no	—
480	C₂×C₄	—	4	2	no	—
481	C₂×C₄	—	4	8	no	—
482	C₂×C₄	—	4	2	no	—
483	C₂×C₄	—	4	2	no	—
484	C₂×C₄	—	4	4	no	—
485	C₂×C₄	—	4	2	no	—
486	C₂×C₄	—	4	4	no	—
487	C₂×C₄	#120×C₇₃	1	2	yes	—
488	C₂×C₄	#120×C₇₃	1	2	yes	—
489	C₂×C₄	C₂×SD₁₆×C₇₃	1	2	yes	—
490	C₂×C₄	AGL(1,ℤ/8)×C₇₃	1	2	yes	—
491	C₂×C₄	C₂²×D₄×C₇₃	1	1	yes	characteristic
492	C₂×C₄	C₂²×D₄×C₇₃	1	2	yes	—
493	C₂×C₄	C₂²×D₄×C₇₃	1	1	yes	characteristic
494	C₂×C₄	H(5,𝔽₂)×C₇₃	1	2	yes	—
495	C₈	—	2	4	no	—
496	C₈	—	4	2	no	—
497	C₂²	—	2	4	no	—
498	C₂²	—	2	8	no	—
499	C₂²	—	2	4	no	—
500	C₂²	—	4	2	no	—
501	C₂²	—	4	2	no	—
502	C₂²	—	4	2	no	—
503	C₂²	—	4	4	no	—
504	C₂²	—	4	4	no	—
505	C₂²	—	4	4	no	—
506	C₂²	—	4	2	no	—
507	C₂²	—	4	4	no	—
508	C₂²	—	4	4	no	—
509	C₂²	—	4	4	no	—
510	C₂²	—	8	32	no	—
511	C₂²	—	8	4	no	—
512	C₂²	—	8	4	no	—
513	C₂²	C₂×#120×C₇₃	1	1	yes	characteristic
514	C₂²	D₄²×C₇₃	1	2	yes	—
515	C₂²	C₂²×SD₁₆×C₇₃	1	1	yes	characteristic
516	C₂²	C₂×AGL(1,ℤ/8)×C₇₃	1	1	yes	characteristic
517	C₂²	#577×C₇₃	1	2	yes	—
518	C₄	—	2	2	no	—
519	C₄	—	4	2	no	—
520	C₄	—	4	4	no	—
521	C₄	—	4	2	no	—
522	C₄	—	8	2	no	—
523	C₄	#450×C₇₃	1	4	yes	complemented
524	C₄	C₂×#127×C₇₃	1	1	yes	characteristic
525	C₄	#535×C₇₃	1	1	yes	characteristic
526	C₄	D₄²×C₇₃	1	2	yes	—
527	C₂	—	4	4	no	—
528	C₂	—	4	4	no	—
529	C₂	—	8	4	no	—
530	C₂	C₇₃×#2433	1	1	yes	characteristic
531	C₂	C₂×#450×C₇₃	1	1	yes	characteristic
532	C₂	C₇₃×#3009	1	1	yes	characteristic
533	C₂	C₇₃×#3272	1	2	yes	—
534	C₂	D₄×SD₁₆×C₇₃	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₇₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₇₃
prime radical	C₂×D₄²×C₇₃	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₇₃ ◁ C₂×C₄×D₄×C₇₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×#492×C₇₃	C₂	semidirect
3. C₂×#461×C₇₃	C₂	semidirect
4. C₂×#450×C₇₃	C₂	semidirect
5. C₇₃×#2542	C₂	semidirect
6. C₇₃×#2000	C₂	semidirect
7. C₇₃×#1982	C₂	semidirect
8. C₇₃×#1954	C₂	semidirect
9. C₄×#102×C₇₃	C₂	semidirect
13. C₂²×SD₁₆×C₇₃	C₂²	semidirect
16. C₂×C₄⋊Q₈×C₇₃	C₂²	semidirect
18. C₂×C₂²⋊Q₈×C₇₃	C₂²	semidirect
27. C₂×C₄⋊C₈×C₇₃	C₂²	semidirect
28. C₂×#103×C₇₃	C₂²	semidirect
30. C₂×#102×C₇₃	C₂²	semidirect
31. C₂×C₂²⋊C₈×C₇₃	C₂²	semidirect
32. C₂×C₄×C₈×C₇₃	C₂²	semidirect
36. C₄×C₄⋊C₄×C₇₃	C₂²	semidirect
37. #340×C₇₃	C₂²	semidirect
92. #102×C₇₃	D₄	semidirect
129. C₂×D₄×C₇₃	SD₁₆	semidirect
153. C₂×C₈×C₇₃	C₂×D₄	semidirect
161. C₄⋊C₄×C₇₃	C₂×D₄	semidirect
255. C₄×C₇₃	#450	semidirect
259. #25753	C₇₃	direct (N × H)
269. C₂×#492	C₂×C₇₃	semidirect
270. C₂×#461	C₂×C₇₃	semidirect
271. C₂×#450	C₂×C₇₃	semidirect
272. #2542	C₂×C₇₃	semidirect
273. #2000	C₂×C₇₃	semidirect
274. #1982	C₂×C₇₃	semidirect
275. #1954	C₂×C₇₃	semidirect
276. C₄×#102	C₂×C₇₃	semidirect
277. C₇₃	#25753	direct (N × H)
281. C₂²×SD₁₆	C₂²×C₇₃	semidirect
284. C₂×C₄⋊Q₈	C₂²×C₇₃	semidirect
286. C₂×C₂²⋊Q₈	C₂²×C₇₃	semidirect
295. C₂×C₄⋊C₈	C₂²×C₇₃	semidirect
296. C₂×#103	C₂²×C₇₃	semidirect
298. C₂×#102	C₂²×C₇₃	semidirect
299. C₂×C₂²⋊C₈	C₂²×C₇₃	semidirect
300. C₂×C₄×C₈	C₂²×C₇₃	semidirect
304. C₄×C₄⋊C₄	C₂²×C₇₃	semidirect
305. #340	C₂²×C₇₃	semidirect
360. #102	D₄×C₇₃	semidirect
397. C₂×D₄	SD₁₆×C₇₃	semidirect
421. C₂×C₈	C₂×D₄×C₇₃	semidirect
429. C₄⋊C₄	C₂×D₄×C₇₃	semidirect
523. C₄	#450×C₇₃	semidirect

Maximal subgroups

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

subgroup	index
C₂×D₄²×C₇₃	2
C₂×#492×C₇₃	2
C₂×#461×C₇₃	2
C₂×#450×C₇₃	2
C₇₃×#2542	2
C₇₃×#2000	2
C₇₃×#1982	2
C₇₃×#1954	2
C₄×#102×C₇₃	2
#25753	73

Subgroups — C73×#25753 #32935157

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₃×#25753 #32935157