Subgroups — C₇₃×#24643 #32934047

Order 18688.

896 conjugacy classes of subgroups.

The subgroup lattice has 500 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#461×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#442×C₇₃	C₂	1	1	yes	maximal, characteristic
3	C₇₃×#2547	C₂	1	1	yes	maximal, characteristic, complemented
4	C₇₃×#2357	C₂	1	1	yes	maximal, characteristic, complemented
5	C₇₃×#2055	C₂	1	2	yes	maximal, complemented
6	C₇₃×#2012	C₂	1	2	yes	maximal
7	C₇₃×#1983	C₂	1	2	yes	maximal, complemented
8	C₇₃×#1960	C₂	1	1	yes	maximal, characteristic, complemented
9	C₇₃×#1940	C₂	1	1	yes	maximal, characteristic, complemented
10	C₇₃×#1927	C₂	1	2	yes	maximal, complemented
11	C₇₃×#1804	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×SD₁₆×C₇₃	C₂²	1	2	yes	—
13	C₂²×D₈×C₇₃	C₂²	1	1	yes	characteristic
14	C₂×C₄⋊Q₈×C₇₃	C₂²	1	1	yes	characteristic
15	C₂×#124×C₇₃	C₂²	1	2	yes	—
16	C₂×C₄×D₄×C₇₃	C₂²	1	1	yes	characteristic
17	C₂×C₄×D₄×C₇₃	C₂²	1	1	yes	characteristic
18	#461×C₇₃	—	2	4	no	—
19	#442×C₇₃	—	2	4	no	—
20	C₂×#106×C₇₃	C₂²	1	1	yes	characteristic
21	C₂×C₄⋊C₈×C₇₃	C₂²	1	1	yes	characteristic
22	C₂×C₄⋊C₈×C₇₃	C₂²	1	2	yes	—
23	C₂×#103×C₇₃	C₂²	1	2	yes	—
24	C₂×#103×C₇₃	C₂²	1	2	yes	—
25	C₂×#103×C₇₃	C₂²	1	2	yes	—
26	C₂×#102×C₇₃	C₂²	1	1	yes	characteristic
27	C₂×#102×C₇₃	C₂²	1	1	yes	characteristic
28	C₂×#102×C₇₃	C₂²	1	2	yes	—
29	C₂×#97×C₇₃	C₂²	1	1	yes	characteristic
30	#397×C₇₃	—	2	1	no	—
31	#397×C₇₃	—	2	1	no	—
32	#391×C₇₃	C₂²	1	2	yes	—
33	#390×C₇₃	C₂²	1	2	yes	—
34	#388×C₇₃	—	2	2	no	—
35	#382×C₇₃	C₂²	1	1	yes	characteristic
36	#381×C₇₃	—	2	1	no	—
37	#380×C₇₃	—	2	2	no	—
38	C₄×C₄⋊C₄×C₇₃	C₂²	1	2	yes	—
39	C₄×C₄⋊C₄×C₇₃	C₂²	1	1	yes	characteristic
40	C₄×C₂²⋊C₄×C₇₃	—	2	1	no	—
41	#340×C₇₃	C₂²	1	2	yes	—
42	#336×C₇₃	C₂²	1	2	yes	—
43	C₂²×Q₈×C₇₃	C₂³	1	2	yes	—
44	C₂²×D₄×C₇₃	C₂³	1	1	yes	characteristic
45	C₂²×D₄×C₇₃	C₂³	1	1	yes	characteristic
46	C₂³×C₄×C₇₃	—	2	1	no	—
47	C₂³×C₄×C₇₃	—	2	1	no	—
48	C₂×SD₁₆×C₇₃	—	2	4	no	—
49	C₂×SD₁₆×C₇₃	—	4	2	no	—
50	C₂×SD₁₆×C₇₃	—	4	2	no	—
51	C₂×D₈×C₇₃	—	2	2	no	—
52	C₂×D₈×C₇₃	—	2	2	no	—
53	C₂×D₈×C₇₃	—	2	2	no	—
54	C₂²×C₈×C₇₃	C₂³	1	1	yes	characteristic
55	C₂²×C₈×C₇₃	C₂³	1	2	yes	—
56	C₂²×C₈×C₇₃	C₂³	1	1	yes	characteristic
57	C₄⋊Q₈×C₇₃	—	2	2	no	—
58	C₄⋊Q₈×C₇₃	—	2	2	no	—
59	#124×C₇₃	—	2	4	no	—
60	#124×C₇₃	—	4	2	no	—
61	C₄×D₄×C₇₃	—	2	2	no	—
62	C₄×D₄×C₇₃	—	2	2	no	—
63	C₄×D₄×C₇₃	—	2	2	no	—
64	C₄×D₄×C₇₃	D₄	1	4	yes	—
65	C₂×C₄⋊C₄×C₇₃	—	2	1	no	—
66	C₂×C₄⋊C₄×C₇₃	—	2	1	no	—
67	C₂×C₄⋊C₄×C₇₃	D₄	1	2	yes	—
68	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
69	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
70	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
71	C₂×C₂²⋊C₄×C₇₃	—	2	1	no	—
72	C₂×C₂²⋊C₄×C₇₃	—	2	2	no	—
73	C₂×C₂²⋊C₄×C₇₃	—	2	2	no	—
74	C₂×C₂²⋊C₄×C₇₃	—	2	2	no	—
75	C₂×C₂²⋊C₄×C₇₃	—	2	1	no	—
76	C₂×C₂²⋊C₄×C₇₃	—	2	2	no	—
77	C₂×C₄²×C₇₃	—	2	2	no	—
78	C₂×C₄²×C₇₃	C₂³	1	2	yes	—
79	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
80	#106×C₇₃	—	2	2	no	—
81	C₄⋊C₈×C₇₃	—	2	2	no	—
82	C₄⋊C₈×C₇₃	—	4	2	no	—
83	#103×C₇₃	—	2	4	no	—
84	#103×C₇₃	—	2	4	no	—
85	#103×C₇₃	—	4	2	no	—
86	#102×C₇₃	—	2	2	no	—
87	#102×C₇₃	—	2	2	no	—
88	#102×C₇₃	—	4	2	no	—
89	#97×C₇₃	—	2	2	no	—
90	#95×C₇₃	—	2	1	no	—
91	#95×C₇₃	—	2	2	no	—
92	#95×C₇₃	—	2	2	no	—
93	#95×C₇₃	—	2	2	no	—
94	#95×C₇₃	—	2	1	no	—
95	#95×C₇₃	D₄	1	1	yes	characteristic
96	#95×C₇₃	D₄	1	1	yes	characteristic
97	C₂⁴×C₇₃	—	2	1	no	—
98	C₂⁴×C₇₃	—	2	1	no	—
99	C₂×Q₈×C₇₃	—	2	2	no	—
100	C₂×Q₈×C₇₃	—	2	2	no	—
101	C₂×Q₈×C₇₃	—	2	2	no	—
102	C₂×Q₈×C₇₃	—	2	2	no	—
103	C₂×Q₈×C₇₃	—	2	2	no	—
104	C₂×Q₈×C₇₃	—	2	2	no	—
105	C₂×D₄×C₇₃	—	2	1	no	—
106	C₂×D₄×C₇₃	—	2	1	no	—
107	C₂×D₄×C₇₃	—	2	1	no	—
108	C₂×D₄×C₇₃	—	2	1	no	—
109	C₂×D₄×C₇₃	—	2	1	no	—
110	C₂×D₄×C₇₃	—	2	1	no	—
111	C₂×D₄×C₇₃	—	2	1	no	—
112	C₂×D₄×C₇₃	—	2	1	no	—
113	C₂×D₄×C₇₃	—	2	1	no	—
114	C₂×D₄×C₇₃	—	2	1	no	—
115	C₂×D₄×C₇₃	C₂×D₄	1	2	yes	—
116	C₂×D₄×C₇₃	#41	1	2	yes	—
117	C₂²×C₄×C₇₃	—	2	1	no	—
118	C₂²×C₄×C₇₃	—	2	4	no	—
119	C₂²×C₄×C₇₃	—	2	1	no	—
120	C₂²×C₄×C₇₃	—	2	2	no	—
121	C₂²×C₄×C₇₃	—	2	2	no	—
122	C₂²×C₄×C₇₃	—	4	4	no	—
123	C₂²×C₄×C₇₃	—	4	2	no	—
124	C₂²×C₄×C₇₃	—	8	2	no	—
125	C₂²×C₄×C₇₃	C₂×D₄	1	2	yes	—
126	C₂²×C₄×C₇₃	C₂×D₄	1	2	yes	—
127	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
128	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
129	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
130	SD₁₆×C₇₃	—	4	8	no	—
131	D₈×C₇₃	—	2	8	no	—
132	C₂×C₈×C₇₃	—	2	1	no	—
133	C₂×C₈×C₇₃	—	2	1	no	—
134	C₂×C₈×C₇₃	—	2	1	no	—
135	C₂×C₈×C₇₃	—	2	2	no	—
136	C₂×C₈×C₇₃	—	2	2	no	—
137	C₂×C₈×C₇₃	—	2	1	no	—
138	C₂×C₈×C₇₃	—	2	1	no	—
139	C₂×C₈×C₇₃	—	2	2	no	—
140	C₂×C₈×C₇₃	#41	1	2	yes	—
141	C₄⋊C₄×C₇₃	—	2	1	no	—
142	C₄⋊C₄×C₇₃	—	2	1	no	—
143	C₄⋊C₄×C₇₃	—	2	2	no	—
144	C₄⋊C₄×C₇₃	—	2	1	no	—
145	C₄⋊C₄×C₇₃	—	2	2	no	—
146	C₄⋊C₄×C₇₃	—	4	2	no	—
147	C₄⋊C₄×C₇₃	—	4	2	no	—
148	C₄⋊C₄×C₇₃	—	4	2	no	—
149	C₄⋊C₄×C₇₃	C₂×D₄	1	2	yes	—
150	C₂²⋊C₄×C₇₃	—	2	4	no	—
151	C₂²⋊C₄×C₇₃	—	4	4	no	—
152	C₂²⋊C₄×C₇₃	—	4	4	no	—
153	C₂²⋊C₄×C₇₃	—	4	4	no	—
154	C₂²⋊C₄×C₇₃	—	4	2	no	—
155	C₂²⋊C₄×C₇₃	—	8	2	no	—
156	C₄²×C₇₃	—	2	2	no	—
157	C₄²×C₇₃	—	2	2	no	—
158	C₄²×C₇₃	—	8	2	no	—
159	C₄²×C₇₃	C₂×D₄	1	2	yes	—
160	C₄²×C₇₃	#41	1	2	yes	—
161	C₂³×C₇₃	—	2	2	no	—
162	C₂³×C₇₃	—	2	2	no	—
163	C₂³×C₇₃	—	4	1	no	—
164	C₂³×C₇₃	—	4	1	no	—
165	C₂³×C₇₃	—	4	1	no	—
166	C₂³×C₇₃	—	4	1	no	—
167	C₂³×C₇₃	—	4	2	no	—
168	C₂³×C₇₃	—	4	2	no	—
169	C₂³×C₇₃	—	4	2	no	—
170	C₂³×C₇₃	—	4	2	no	—
171	C₂³×C₇₃	C₂²×D₄	1	1	yes	characteristic
172	Q₈×C₇₃	—	4	2	no	—
173	Q₈×C₇₃	—	4	2	no	—
174	Q₈×C₇₃	—	4	2	no	—
175	Q₈×C₇₃	—	4	2	no	—
176	D₄×C₇₃	—	2	2	no	—
177	D₄×C₇₃	—	2	2	no	—
178	D₄×C₇₃	—	2	2	no	—
179	D₄×C₇₃	—	2	2	no	—
180	D₄×C₇₃	—	4	1	no	—
181	D₄×C₇₃	—	4	1	no	—
182	D₄×C₇₃	—	4	1	no	—
183	D₄×C₇₃	—	4	1	no	—
184	C₂×C₄×C₇₃	—	2	2	no	—
185	C₂×C₄×C₇₃	—	2	2	no	—
186	C₂×C₄×C₇₃	—	2	2	no	—
187	C₂×C₄×C₇₃	—	2	2	no	—
188	C₂×C₄×C₇₃	—	2	2	no	—
189	C₂×C₄×C₇₃	—	2	2	no	—
190	C₂×C₄×C₇₃	—	2	2	no	—
191	C₂×C₄×C₇₃	—	2	2	no	—
192	C₂×C₄×C₇₃	—	2	2	no	—
193	C₂×C₄×C₇₃	—	4	2	no	—
194	C₂×C₄×C₇₃	—	4	1	no	—
195	C₂×C₄×C₇₃	—	4	2	no	—
196	C₂×C₄×C₇₃	—	4	2	no	—
197	C₂×C₄×C₇₃	—	4	2	no	—
198	C₂×C₄×C₇₃	—	4	2	no	—
199	C₂×C₄×C₇₃	—	4	2	no	—
200	C₂×C₄×C₇₃	—	4	2	no	—
201	C₂×C₄×C₇₃	—	4	2	no	—
202	C₂×C₄×C₇₃	—	8	4	no	—
203	C₂×C₄×C₇₃	—	8	4	no	—
204	C₂×C₄×C₇₃	#121	1	2	yes	—
205	C₂×C₄×C₇₃	#121	1	2	yes	—
206	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
207	C₂×C₄×C₇₃	C₂×#41	1	1	yes	characteristic
208	C₂×C₄×C₇₃	C₂×#41	1	1	yes	characteristic
209	C₂×C₄×C₇₃	C₂×#41	1	1	yes	characteristic
210	C₂×C₄×C₇₃	H(5,𝔽₂)	1	1	yes	characteristic
211	C₂×C₄×C₇₃	H(5,𝔽₂)	1	1	yes	characteristic
212	C₈×C₇₃	—	2	2	no	—
213	C₈×C₇₃	—	4	1	no	—
214	C₈×C₇₃	—	4	2	no	—
215	C₂²×C₇₃	—	4	2	no	—
216	C₂²×C₇₃	—	4	2	no	—
217	C₂²×C₇₃	—	4	2	no	—
218	C₂²×C₇₃	—	4	2	no	—
219	C₂²×C₇₃	—	4	4	no	—
220	C₂²×C₇₃	—	8	2	no	—
221	C₂²×C₇₃	—	8	2	no	—
222	C₂²×C₇₃	—	8	1	no	—
223	C₂²×C₇₃	—	8	1	no	—
224	C₂²×C₇₃	—	8	2	no	—
225	C₂²×C₇₃	C₂×#121	1	1	yes	characteristic
226	C₂²×C₇₃	#546	1	1	yes	characteristic
227	C₂²×C₇₃	#550	1	1	yes	characteristic
228	C₂²×C₇₃	#575	1	2	yes	—
229	C₂²×C₇₃	#577	1	2	yes	—
230	C₄×C₇₃	—	2	2	no	—
231	C₄×C₇₃	—	2	2	no	—
232	C₄×C₇₃	—	4	2	no	—
233	C₄×C₇₃	—	4	2	no	—
234	C₄×C₇₃	—	4	2	no	—
235	C₄×C₇₃	—	8	2	no	—
236	C₄×C₇₃	—	8	2	no	—
237	C₄×C₇₃	—	8	1	no	—
238	C₄×C₇₃	#525	1	1	yes	characteristic
239	C₄×C₇₃	#535	1	1	yes	characteristic
240	C₄×C₇₃	#553	1	1	yes	characteristic
241	C₄×C₇₃	#555	1	1	yes	characteristic
242	#24643	C₇₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
243	C₂×C₇₃	—	8	2	no	—
244	C₂×C₇₃	—	8	2	no	—
245	C₂×C₇₃	#2414	1	1	yes	characteristic
246	C₂×C₇₃	#3040	1	1	yes	characteristic
247	C₂×C₇₃	#3042	1	1	yes	characteristic
248	C₂×C₇₃	#3307	1	2	yes	—
249	C₂×C₇₃	#3401	1	2	yes	—
250	C₂×#461	C₂×C₇₃	1	1	yes	characteristic, complemented
251	C₂×#442	C₂×C₇₃	1	1	yes	characteristic
252	#2547	C₂×C₇₃	1	1	yes	characteristic, complemented
253	#2357	C₂×C₇₃	1	1	yes	characteristic, complemented
254	#2055	C₂×C₇₃	1	2	yes	complemented
255	#2012	C₂×C₇₃	1	2	yes	—
256	#1983	C₂×C₇₃	1	2	yes	complemented
257	#1960	C₂×C₇₃	1	1	yes	characteristic, complemented
258	#1940	C₂×C₇₃	1	1	yes	characteristic, complemented
259	#1927	C₂×C₇₃	1	2	yes	complemented
260	#1804	C₂×C₇₃	1	1	yes	characteristic, complemented
261	C₇₃	#24643	1	1	yes	characteristic, direct product factor, Sylow
262	C₂²×SD₁₆	C₂²×C₇₃	1	2	yes	—
263	C₂²×D₈	C₂²×C₇₃	1	1	yes	characteristic
264	C₂×C₄⋊Q₈	C₂²×C₇₃	1	1	yes	characteristic
265	C₂×#124	C₂²×C₇₃	1	2	yes	—
266	C₂×C₄×D₄	C₂²×C₇₃	1	1	yes	characteristic
267	C₂×C₄×D₄	C₂²×C₇₃	1	1	yes	characteristic
268	#461	—	2	4	no	—
269	#442	—	2	4	no	—
270	C₂×#106	C₂²×C₇₃	1	1	yes	characteristic
271	C₂×C₄⋊C₈	C₂²×C₇₃	1	1	yes	characteristic
272	C₂×C₄⋊C₈	C₂²×C₇₃	1	2	yes	—
273	C₂×#103	C₂²×C₇₃	1	2	yes	—
274	C₂×#103	C₂²×C₇₃	1	2	yes	—
275	C₂×#103	C₂²×C₇₃	1	2	yes	—
276	C₂×#102	C₂²×C₇₃	1	1	yes	characteristic
277	C₂×#102	C₂²×C₇₃	1	1	yes	characteristic
278	C₂×#102	C₂²×C₇₃	1	2	yes	—
279	C₂×#97	C₂²×C₇₃	1	1	yes	characteristic
280	#397	—	2	1	no	—
281	#397	—	2	1	no	—
282	#391	C₂²×C₇₃	1	2	yes	—
283	#390	C₂²×C₇₃	1	2	yes	—
284	#388	—	2	2	no	—
285	#382	C₂²×C₇₃	1	1	yes	characteristic
286	#381	—	2	1	no	—
287	#380	—	2	2	no	—
288	C₄×C₄⋊C₄	C₂²×C₇₃	1	2	yes	—
289	C₄×C₄⋊C₄	C₂²×C₇₃	1	1	yes	characteristic
290	C₄×C₂²⋊C₄	—	2	1	no	—
291	#340	C₂²×C₇₃	1	2	yes	—
292	#336	C₂²×C₇₃	1	2	yes	—
293	C₂²×Q₈	C₂³×C₇₃	1	2	yes	—
294	C₂²×D₄	C₂³×C₇₃	1	1	yes	characteristic
295	C₂²×D₄	C₂³×C₇₃	1	1	yes	characteristic
296	C₂³×C₄	—	2	1	no	—
297	C₂³×C₄	—	2	1	no	—
298	C₂×SD₁₆	—	2	4	no	—
299	C₂×SD₁₆	—	4	2	no	—
300	C₂×SD₁₆	—	4	2	no	—
301	C₂×D₈	—	2	2	no	—
302	C₂×D₈	—	2	2	no	—
303	C₂×D₈	—	2	2	no	—
304	C₂²×C₈	C₂³×C₇₃	1	2	yes	—
305	C₂²×C₈	C₂³×C₇₃	1	1	yes	characteristic
306	C₂²×C₈	C₂³×C₇₃	1	1	yes	characteristic
307	C₄⋊Q₈	—	2	2	no	—
308	C₄⋊Q₈	—	2	2	no	—
309	#124	—	2	4	no	—
310	#124	—	4	2	no	—
311	C₄×D₄	—	2	2	no	—
312	C₄×D₄	—	2	2	no	—
313	C₄×D₄	—	2	2	no	—
314	C₄×D₄	D₄×C₇₃	1	4	yes	—
315	C₂×C₄⋊C₄	—	2	1	no	—
316	C₂×C₄⋊C₄	—	2	1	no	—
317	C₂×C₄⋊C₄	D₄×C₇₃	1	2	yes	—
318	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
319	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
320	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
321	C₂×C₂²⋊C₄	—	2	1	no	—
322	C₂×C₂²⋊C₄	—	2	1	no	—
323	C₂×C₂²⋊C₄	—	2	2	no	—
324	C₂×C₂²⋊C₄	—	2	2	no	—
325	C₂×C₂²⋊C₄	—	2	2	no	—
326	C₂×C₂²⋊C₄	—	2	2	no	—
327	C₂×C₄²	—	2	2	no	—
328	C₂×C₄²	C₂³×C₇₃	1	2	yes	—
329	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
330	#106	—	2	2	no	—
331	C₄⋊C₈	—	2	2	no	—
332	C₄⋊C₈	—	4	2	no	—
333	#103	—	2	4	no	—
334	#103	—	2	4	no	—
335	#103	—	4	2	no	—
336	#102	—	2	2	no	—
337	#102	—	2	2	no	—
338	#102	—	4	2	no	—
339	#97	—	2	2	no	—
340	#95	—	2	1	no	—
341	#95	—	2	2	no	—
342	#95	—	2	2	no	—
343	#95	—	2	2	no	—
344	#95	—	2	1	no	—
345	#95	D₄×C₇₃	1	1	yes	characteristic
346	#95	D₄×C₇₃	1	1	yes	characteristic
347	C₂⁴	—	2	1	no	—
348	C₂⁴	—	2	1	no	—
349	C₂×Q₈	—	2	2	no	—
350	C₂×Q₈	—	2	2	no	—
351	C₂×Q₈	—	2	2	no	—
352	C₂×Q₈	—	2	2	no	—
353	C₂×Q₈	—	2	2	no	—
354	C₂×Q₈	—	2	2	no	—
355	C₂×D₄	—	2	1	no	—
356	C₂×D₄	—	2	1	no	—
357	C₂×D₄	—	2	1	no	—
358	C₂×D₄	—	2	1	no	—
359	C₂×D₄	—	2	1	no	—
360	C₂×D₄	—	2	1	no	—
361	C₂×D₄	—	2	1	no	—
362	C₂×D₄	—	2	1	no	—
363	C₂×D₄	—	2	1	no	—
364	C₂×D₄	—	2	1	no	—
365	C₂×D₄	C₂×D₄×C₇₃	1	2	yes	—
366	C₂×D₄	#41×C₇₃	1	2	yes	—
367	C₂²×C₄	—	2	1	no	—
368	C₂²×C₄	—	2	4	no	—
369	C₂²×C₄	—	2	1	no	—
370	C₂²×C₄	—	2	2	no	—
371	C₂²×C₄	—	2	2	no	—
372	C₂²×C₄	—	4	4	no	—
373	C₂²×C₄	—	4	2	no	—
374	C₂²×C₄	—	8	2	no	—
375	C₂²×C₄	C₂×D₄×C₇₃	1	2	yes	—
376	C₂²×C₄	C₂×D₄×C₇₃	1	2	yes	—
377	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
378	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
379	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
380	SD₁₆	—	4	8	no	—
381	D₈	—	2	8	no	—
382	C₂×C₈	—	2	1	no	—
383	C₂×C₈	—	2	1	no	—
384	C₂×C₈	—	2	1	no	—
385	C₂×C₈	—	2	2	no	—
386	C₂×C₈	—	2	2	no	—
387	C₂×C₈	—	2	1	no	—
388	C₂×C₈	—	2	1	no	—
389	C₂×C₈	—	2	2	no	—
390	C₂×C₈	#41×C₇₃	1	2	yes	—
391	C₄⋊C₄	—	2	1	no	—
392	C₄⋊C₄	—	2	1	no	—
393	C₄⋊C₄	—	2	2	no	—
394	C₄⋊C₄	—	2	1	no	—
395	C₄⋊C₄	—	2	2	no	—
396	C₄⋊C₄	—	4	2	no	—
397	C₄⋊C₄	—	4	2	no	—
398	C₄⋊C₄	—	4	2	no	—
399	C₄⋊C₄	C₂×D₄×C₇₃	1	2	yes	—
400	C₂²⋊C₄	—	2	4	no	—
401	C₂²⋊C₄	—	4	4	no	—
402	C₂²⋊C₄	—	4	4	no	—
403	C₂²⋊C₄	—	4	4	no	—
404	C₂²⋊C₄	—	4	2	no	—
405	C₂²⋊C₄	—	8	2	no	—
406	C₄²	—	2	2	no	—
407	C₄²	—	2	2	no	—
408	C₄²	—	8	2	no	—
409	C₄²	C₂×D₄×C₇₃	1	2	yes	—
410	C₄²	#41×C₇₃	1	2	yes	—
411	C₂³	—	2	2	no	—
412	C₂³	—	2	2	no	—
413	C₂³	—	4	1	no	—
414	C₂³	—	4	1	no	—
415	C₂³	—	4	1	no	—
416	C₂³	—	4	1	no	—
417	C₂³	—	4	2	no	—
418	C₂³	—	4	2	no	—
419	C₂³	—	4	2	no	—
420	C₂³	—	4	2	no	—
421	C₂³	C₂²×D₄×C₇₃	1	1	yes	characteristic
422	Q₈	—	4	2	no	—
423	Q₈	—	4	2	no	—
424	Q₈	—	4	2	no	—
425	Q₈	—	4	2	no	—
426	D₄	—	2	2	no	—
427	D₄	—	2	2	no	—
428	D₄	—	2	2	no	—
429	D₄	—	2	2	no	—
430	D₄	—	4	1	no	—
431	D₄	—	4	1	no	—
432	D₄	—	4	1	no	—
433	D₄	—	4	1	no	—
434	C₂×C₄	—	2	2	no	—
435	C₂×C₄	—	2	2	no	—
436	C₂×C₄	—	2	2	no	—
437	C₂×C₄	—	2	2	no	—
438	C₂×C₄	—	2	2	no	—
439	C₂×C₄	—	2	2	no	—
440	C₂×C₄	—	2	2	no	—
441	C₂×C₄	—	2	2	no	—
442	C₂×C₄	—	2	2	no	—
443	C₂×C₄	—	4	2	no	—
444	C₂×C₄	—	4	1	no	—
445	C₂×C₄	—	4	2	no	—
446	C₂×C₄	—	4	2	no	—
447	C₂×C₄	—	4	2	no	—
448	C₂×C₄	—	4	2	no	—
449	C₂×C₄	—	4	2	no	—
450	C₂×C₄	—	4	2	no	—
451	C₂×C₄	—	4	2	no	—
452	C₂×C₄	—	8	4	no	—
453	C₂×C₄	—	8	4	no	—
454	C₂×C₄	#121×C₇₃	1	2	yes	—
455	C₂×C₄	#121×C₇₃	1	2	yes	—
456	C₂×C₄	C₂²×D₄×C₇₃	1	1	yes	characteristic
457	C₂×C₄	C₂×#41×C₇₃	1	1	yes	characteristic
458	C₂×C₄	C₂×#41×C₇₃	1	1	yes	characteristic
459	C₂×C₄	C₂×#41×C₇₃	1	1	yes	characteristic
460	C₂×C₄	H(5,𝔽₂)×C₇₃	1	1	yes	characteristic
461	C₂×C₄	H(5,𝔽₂)×C₇₃	1	1	yes	characteristic
462	C₈	—	2	2	no	—
463	C₈	—	4	2	no	—
464	C₈	—	4	1	no	—
465	C₂²	—	4	2	no	—
466	C₂²	—	4	2	no	—
467	C₂²	—	4	4	no	—
468	C₂²	—	4	2	no	—
469	C₂²	—	4	2	no	—
470	C₂²	—	8	1	no	—
471	C₂²	—	8	1	no	—
472	C₂²	—	8	2	no	—
473	C₂²	—	8	2	no	—
474	C₂²	—	8	2	no	—
475	C₂²	C₂×#121×C₇₃	1	1	yes	characteristic
476	C₂²	#546×C₇₃	1	1	yes	characteristic
477	C₂²	#550×C₇₃	1	1	yes	characteristic
478	C₂²	#575×C₇₃	1	2	yes	—
479	C₂²	#577×C₇₃	1	2	yes	—
480	C₄	—	2	2	no	—
481	C₄	—	2	2	no	—
482	C₄	—	4	2	no	—
483	C₄	—	4	2	no	—
484	C₄	—	4	2	no	—
485	C₄	—	8	1	no	—
486	C₄	—	8	2	no	—
487	C₄	—	8	2	no	—
488	C₄	#525×C₇₃	1	1	yes	characteristic
489	C₄	#535×C₇₃	1	1	yes	characteristic
490	C₄	#553×C₇₃	1	1	yes	characteristic
491	C₄	#555×C₇₃	1	1	yes	characteristic
492	C₂	—	8	2	no	—
493	C₂	—	8	2	no	—
494	C₂	C₇₃×#2414	1	1	yes	characteristic
495	C₂	C₇₃×#3040	1	1	yes	characteristic
496	C₂	C₇₃×#3042	1	1	yes	characteristic
497	C₂	C₇₃×#3307	1	2	yes	—
498	C₂	C₇₃×#3401	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₇₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₇₃
prime radical	C₂²×D₈×C₇₃	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₇₃ ◁ C₄×C₄⋊C₄×C₇₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×#461×C₇₃	C₂	semidirect
3. C₇₃×#2547	C₂	semidirect
4. C₇₃×#2357	C₂	semidirect
5. C₇₃×#2055	C₂	semidirect
7. C₇₃×#1983	C₂	semidirect
8. C₇₃×#1960	C₂	semidirect
9. C₇₃×#1940	C₂	semidirect
10. C₇₃×#1927	C₂	semidirect
11. C₇₃×#1804	C₂	semidirect
242. #24643	C₇₃	direct (N × H)
250. C₂×#461	C₂×C₇₃	semidirect
252. #2547	C₂×C₇₃	semidirect
253. #2357	C₂×C₇₃	semidirect
254. #2055	C₂×C₇₃	semidirect
256. #1983	C₂×C₇₃	semidirect
257. #1960	C₂×C₇₃	semidirect
258. #1940	C₂×C₇₃	semidirect
259. #1927	C₂×C₇₃	semidirect
260. #1804	C₂×C₇₃	semidirect
261. C₇₃	#24643	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×#461×C₇₃	2
C₂×#442×C₇₃	2
C₇₃×#2547	2
C₇₃×#2357	2
C₇₃×#2055	2
C₇₃×#2012	2
C₇₃×#1983	2
C₇₃×#1960	2
C₇₃×#1940	2
C₇₃×#1927	2
C₇₃×#1804	2
#24643	73

Subgroups — C73×#24643 #32934047

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₃×#24643 #32934047