Subgroups — C₇₃×#8429 #32917833

Order 18688.

936 conjugacy classes of subgroups.

The subgroup lattice has 518 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇₃×#3497	C₂	1	1	yes	maximal, characteristic
2	C₇₃×#1805	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇₃×#1540	C₂	1	1	yes	maximal, characteristic, complemented
4	C₇₃×#1517	C₂	1	1	yes	maximal, characteristic, complemented
5	C₇₃×#1517	C₂	1	1	yes	maximal, characteristic, complemented
6	C₇₃×#1480	C₂	1	1	yes	maximal, characteristic, complemented
7	C₇₃×#1479	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×2₋¹⁺⁴×C₇₃	—	2	1	no	—
9	#550×C₇₃	—	2	1	no	—
10	#550×C₇₃	C₄	1	2	yes	complemented
11	D₄×Q₈×C₇₃	—	2	1	no	—
12	D₄×Q₈×C₇₃	C₄	1	2	yes	complemented
13	#548×C₇₃	—	2	2	no	—
14	#548×C₇₃	—	2	2	no	—
15	#537×C₇₃	—	2	2	no	—
16	#537×C₇₃	—	2	1	no	—
17	#532×C₇₃	—	2	2	no	—
18	#532×C₇₃	C₂²	1	1	yes	characteristic
19	#532×C₇₃	C₂²	1	1	yes	characteristic
20	C₂×C₄×Q₈×C₇₃	C₂²	1	1	yes	characteristic
21	#431×C₇₃	C₂²	1	1	yes	characteristic
22	#431×C₇₃	C₂²	1	1	yes	characteristic
23	C₂×C₄⋊C₈×C₇₃	C₂²	1	1	yes	characteristic
24	C₂×#103×C₇₃	—	2	1	no	—
25	#382×C₇₃	C₂²	1	1	yes	characteristic
26	#340×C₇₃	—	2	1	no	—
27	#332×C₇₃	—	2	1	no	—
28	#331×C₇₃	—	2	1	no	—
29	#327×C₇₃	—	2	2	no	—
30	#327×C₇₃	—	2	2	no	—
31	Q₈⋊C₈×C₇₃	—	2	2	no	—
32	D₄⋊C₈×C₇₃	—	2	2	no	—
33	2₋¹⁺⁴×C₇₃	—	4	2	no	—
34	2₋¹⁺⁴×C₇₃	—	4	2	no	—
35	2₋¹⁺⁴×C₇₃	—	4	2	no	—
36	2₋¹⁺⁴×C₇₃	—	4	2	no	—
37	C₂×#41×C₇₃	—	2	4	no	—
38	C₂×#41×C₇₃	—	2	2	no	—
39	C₂×#41×C₇₃	—	2	2	no	—
40	C₂×#41×C₇₃	—	2	1	no	—
41	C₂×#41×C₇₃	—	2	1	no	—
42	C₂²×Q₈×C₇₃	—	2	2	no	—
43	C₂²×Q₈×C₇₃	—	2	2	no	—
44	C₂²×Q₈×C₇₃	D₄	1	1	yes	characteristic
45	C₂²×C₈×C₇₃	—	2	1	no	—
46	C₄⋊Q₈×C₇₃	—	2	2	no	—
47	C₄⋊Q₈×C₇₃	C₂×C₄	1	1	yes	characteristic
48	C₄⋊Q₈×C₇₃	D₄	1	1	yes	characteristic
49	#127×C₇₃	—	2	2	no	—
50	#127×C₇₃	C₂×C₄	1	1	yes	characteristic
51	#127×C₇₃	D₄	1	1	yes	characteristic
52	#124×C₇₃	—	2	4	no	—
53	#124×C₇₃	—	2	1	no	—
54	#124×C₇₃	—	2	1	no	—
55	C₂²⋊Q₈×C₇₃	—	2	2	no	—
56	C₂²⋊Q₈×C₇₃	—	2	4	no	—
57	C₂²⋊Q₈×C₇₃	—	2	2	no	—
58	C₂²⋊Q₈×C₇₃	—	2	4	no	—
59	#121×C₇₃	—	2	4	no	—
60	#121×C₇₃	—	2	2	no	—
61	#121×C₇₃	—	2	4	no	—
62	#121×C₇₃	—	2	4	no	—
63	#121×C₇₃	—	2	1	no	—
64	#121×C₇₃	—	2	1	no	—
65	#121×C₇₃	—	2	2	no	—
66	#121×C₇₃	D₄	1	2	yes	—
67	#121×C₇₃	D₄	1	2	yes	—
68	C₄×Q₈×C₇₃	—	2	1	no	—
69	C₄×Q₈×C₇₃	—	2	1	no	—
70	C₄×Q₈×C₇₃	C₂×C₄	1	2	yes	—
71	C₄×Q₈×C₇₃	D₄	1	2	yes	—
72	C₄×D₄×C₇₃	—	2	4	no	—
73	C₄×D₄×C₇₃	—	2	2	no	—
74	C₄×D₄×C₇₃	—	2	2	no	—
75	C₄×D₄×C₇₃	—	2	1	no	—
76	C₄×D₄×C₇₃	—	2	1	no	—
77	C₄×D₄×C₇₃	C₂×C₄	1	2	yes	—
78	C₄×D₄×C₇₃	D₄	1	2	yes	—
79	C₂×C₄⋊C₄×C₇₃	—	2	1	no	—
80	C₂×C₄⋊C₄×C₇₃	—	2	1	no	—
81	C₂×C₄⋊C₄×C₇₃	D₄	1	1	yes	characteristic
82	C₂×C₄²×C₇₃	—	2	1	no	—
83	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
84	C₄⋊C₈×C₇₃	—	2	1	no	—
85	C₄⋊C₈×C₇₃	—	2	1	no	—
86	C₄⋊C₈×C₇₃	—	2	1	no	—
87	C₄⋊C₈×C₇₃	—	2	1	no	—
88	#103×C₇₃	—	4	2	no	—
89	C₂²⋊C₈×C₇₃	—	2	1	no	—
90	C₂²⋊C₈×C₇₃	—	2	1	no	—
91	C₄×C₈×C₇₃	—	2	1	no	—
92	C₄×C₈×C₇₃	—	2	1	no	—
93	#95×C₇₃	—	2	1	no	—
94	#95×C₇₃	—	2	1	no	—
95	#41×C₇₃	—	4	8	no	—
96	#41×C₇₃	—	4	8	no	—
97	#41×C₇₃	—	4	4	no	—
98	#41×C₇₃	—	4	4	no	—
99	#41×C₇₃	—	4	4	no	—
100	#41×C₇₃	—	4	4	no	—
101	#41×C₇₃	—	4	1	no	—
102	#41×C₇₃	—	4	1	no	—
103	#41×C₇₃	—	4	1	no	—
104	#41×C₇₃	—	4	1	no	—
105	#41×C₇₃	—	4	1	no	—
106	#41×C₇₃	—	4	1	no	—
107	#41×C₇₃	—	4	1	no	—
108	#41×C₇₃	—	4	1	no	—
109	C₂×Q₈×C₇₃	—	2	4	no	—
110	C₂×Q₈×C₇₃	—	2	1	no	—
111	C₂×Q₈×C₇₃	—	2	1	no	—
112	C₂×Q₈×C₇₃	—	2	1	no	—
113	C₂×Q₈×C₇₃	—	2	1	no	—
114	C₂×Q₈×C₇₃	—	2	1	no	—
115	C₂×Q₈×C₇₃	—	4	4	no	—
116	C₂×Q₈×C₇₃	—	4	4	no	—
117	C₂×Q₈×C₇₃	—	4	4	no	—
118	C₂×Q₈×C₇₃	—	4	4	no	—
119	C₂×Q₈×C₇₃	C₂²⋊C₄	1	2	yes	—
120	C₂×Q₈×C₇₃	D₈	1	2	yes	—
121	C₂×Q₈×C₇₃	SD₁₆	1	2	yes	—
122	C₂×D₄×C₇₃	—	2	4	no	—
123	C₂×D₄×C₇₃	—	2	2	no	—
124	C₂×D₄×C₇₃	—	2	2	no	—
125	C₂×D₄×C₇₃	—	2	4	no	—
126	C₂×D₄×C₇₃	—	2	1	no	—
127	C₂×D₄×C₇₃	—	2	1	no	—
128	C₂×D₄×C₇₃	—	2	1	no	—
129	C₂×D₄×C₇₃	—	2	1	no	—
130	C₂×D₄×C₇₃	C₂²⋊C₄	1	2	yes	—
131	C₂×D₄×C₇₃	C₂²⋊C₄	1	2	yes	—
132	C₂²×C₄×C₇₃	—	2	1	no	—
133	C₂²×C₄×C₇₃	—	2	4	no	—
134	C₂²×C₄×C₇₃	—	2	4	no	—
135	C₂²×C₄×C₇₃	—	2	1	no	—
136	C₂²×C₄×C₇₃	—	2	2	no	—
137	C₂²×C₄×C₇₃	—	2	2	no	—
138	C₂²×C₄×C₇₃	—	4	1	no	—
139	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
140	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
141	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
142	C₂×C₈×C₇₃	—	4	1	no	—
143	C₂×C₈×C₇₃	—	4	1	no	—
144	C₂×C₈×C₇₃	—	4	1	no	—
145	C₂×C₈×C₇₃	—	4	1	no	—
146	C₂×C₈×C₇₃	—	4	1	no	—
147	C₄⋊C₄×C₇₃	—	2	4	no	—
148	C₄⋊C₄×C₇₃	—	2	2	no	—
149	C₄⋊C₄×C₇₃	—	2	1	no	—
150	C₄⋊C₄×C₇₃	—	2	2	no	—
151	C₄⋊C₄×C₇₃	—	2	1	no	—
152	C₄⋊C₄×C₇₃	—	2	1	no	—
153	C₄⋊C₄×C₇₃	—	4	1	no	—
154	C₄⋊C₄×C₇₃	—	4	1	no	—
155	C₄⋊C₄×C₇₃	C₂²⋊C₄	1	2	yes	—
156	C₄⋊C₄×C₇₃	C₂²⋊C₄	1	2	yes	—
157	C₄⋊C₄×C₇₃	C₂²⋊C₄	1	2	yes	—
158	C₂²⋊C₄×C₇₃	—	2	4	no	—
159	C₂²⋊C₄×C₇₃	—	2	4	no	—
160	C₂²⋊C₄×C₇₃	—	2	2	no	—
161	C₂²⋊C₄×C₇₃	—	2	2	no	—
162	C₂²⋊C₄×C₇₃	—	2	2	no	—
163	C₂²⋊C₄×C₇₃	—	2	2	no	—
164	C₄²×C₇₃	—	2	2	no	—
165	C₄²×C₇₃	—	2	2	no	—
166	C₄²×C₇₃	C₂²×C₄	1	1	yes	characteristic
167	C₄²×C₇₃	C₂×D₄	1	1	yes	characteristic
168	C₄²×C₇₃	C₂×D₄	1	1	yes	characteristic
169	C₄²×C₇₃	C₂×D₄	1	1	yes	characteristic
170	C₂³×C₇₃	—	2	2	no	—
171	C₂³×C₇₃	—	2	2	no	—
172	C₂³×C₇₃	#120	1	1	yes	characteristic
173	Q₈×C₇₃	—	2	2	no	—
174	Q₈×C₇₃	—	2	2	no	—
175	Q₈×C₇₃	—	2	2	no	—
176	Q₈×C₇₃	—	4	8	no	—
177	Q₈×C₇₃	—	4	1	no	—
178	Q₈×C₇₃	—	4	1	no	—
179	Q₈×C₇₃	—	4	1	no	—
180	Q₈×C₇₃	—	4	1	no	—
181	Q₈×C₇₃	#102	1	4	yes	—
182	D₄×C₇₃	—	4	2	no	—
183	D₄×C₇₃	—	4	2	no	—
184	D₄×C₇₃	—	4	2	no	—
185	D₄×C₇₃	—	4	8	no	—
186	D₄×C₇₃	—	4	2	no	—
187	D₄×C₇₃	—	4	2	no	—
188	D₄×C₇₃	—	4	2	no	—
189	D₄×C₇₃	—	4	2	no	—
190	D₄×C₇₃	—	4	1	no	—
191	D₄×C₇₃	—	4	1	no	—
192	D₄×C₇₃	—	4	1	no	—
193	D₄×C₇₃	—	4	1	no	—
194	D₄×C₇₃	—	8	1	no	—
195	D₄×C₇₃	—	8	4	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	2	no	—
200	C₂×C₄×C₇₃	—	2	2	no	—
201	C₂×C₄×C₇₃	—	2	2	no	—
202	C₂×C₄×C₇₃	—	4	1	no	—
203	C₂×C₄×C₇₃	—	4	1	no	—
204	C₂×C₄×C₇₃	—	4	8	no	—
205	C₂×C₄×C₇₃	—	4	8	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	2	no	—
210	C₂×C₄×C₇₃	—	8	1	no	—
211	C₂×C₄×C₇₃	—	8	1	no	—
212	C₂×C₄×C₇₃	—	8	1	no	—
213	C₂×C₄×C₇₃	—	8	1	no	—
214	C₂×C₄×C₇₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
215	C₂×C₄×C₇₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
216	C₂×C₄×C₇₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
217	C₂×C₄×C₇₃	#120	1	1	yes	characteristic
218	C₂×C₄×C₇₃	#120	1	1	yes	characteristic
219	C₂×C₄×C₇₃	#120	1	1	yes	characteristic
220	C₂×C₄×C₇₃	C₂×D₈	1	1	yes	characteristic
221	C₂×C₄×C₇₃	C₂×SD₁₆	1	1	yes	characteristic
222	C₂×C₄×C₇₃	AGL(1,ℤ/8)	1	1	yes	characteristic
223	C₂×C₄×C₇₃	AGL(1,ℤ/8)	1	1	yes	characteristic
224	C₈×C₇₃	—	8	1	no	—
225	C₈×C₇₃	—	8	1	no	—
226	C₈×C₇₃	—	8	1	no	—
227	C₂²×C₇₃	—	2	1	no	—
228	C₂²×C₇₃	—	2	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	2	no	—
234	C₂²×C₇₃	—	4	2	no	—
235	C₂²×C₇₃	#379	1	1	yes	characteristic
236	C₂²×C₇₃	#447	1	1	yes	characteristic
237	C₂²×C₇₃	#450	1	1	yes	characteristic
238	C₄×C₇₃	—	2	1	no	—
239	C₄×C₇₃	—	2	1	no	—
240	C₄×C₇₃	—	2	1	no	—
241	C₄×C₇₃	—	2	1	no	—
242	C₄×C₇₃	—	2	4	no	—
243	C₄×C₇₃	—	4	2	no	—
244	C₄×C₇₃	—	4	2	no	—
245	C₄×C₇₃	—	4	2	no	—
246	C₄×C₇₃	—	16	1	no	—
247	C₄×C₇₃	C₂×#102	1	1	yes	characteristic
248	C₄×C₇₃	#418	1	1	yes	characteristic
249	C₄×C₇₃	#447	1	1	yes	characteristic
250	C₄×C₇₃	#450	1	1	yes	characteristic
251	#8429	C₇₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
252	C₂×C₇₃	—	2	1	no	—
253	C₂×C₇₃	—	2	1	no	—
254	C₂×C₇₃	—	8	2	no	—
255	C₂×C₇₃	—	8	2	no	—
256	C₂×C₇₃	#1786	1	1	yes	characteristic
257	C₂×C₇₃	#1794	1	1	yes	characteristic
258	C₂×C₇₃	#1796	1	1	yes	characteristic
259	#3497	C₂×C₇₃	1	1	yes	characteristic
260	#1805	C₂×C₇₃	1	1	yes	characteristic, complemented
261	#1540	C₂×C₇₃	1	1	yes	characteristic, complemented
262	#1517	C₂×C₇₃	1	1	yes	characteristic, complemented
263	#1517	C₂×C₇₃	1	1	yes	characteristic, complemented
264	#1480	C₂×C₇₃	1	1	yes	characteristic, complemented
265	#1479	C₂×C₇₃	1	1	yes	characteristic, complemented
266	C₇₃	#8429	1	1	yes	characteristic, direct product factor, Sylow
267	C₂×2₋¹⁺⁴	—	2	1	no	—
268	#550	—	2	1	no	—
269	#550	C₄×C₇₃	1	2	yes	complemented
270	D₄×Q₈	—	2	1	no	—
271	D₄×Q₈	C₄×C₇₃	1	2	yes	complemented
272	#548	—	2	2	no	—
273	#548	—	2	2	no	—
274	#537	—	2	2	no	—
275	#537	—	2	1	no	—
276	#532	—	2	2	no	—
277	#532	C₂²×C₇₃	1	1	yes	characteristic
278	#532	C₂²×C₇₃	1	1	yes	characteristic
279	C₂×C₄×Q₈	C₂²×C₇₃	1	1	yes	characteristic
280	#431	C₂²×C₇₃	1	1	yes	characteristic
281	#431	C₂²×C₇₃	1	1	yes	characteristic
282	C₂×C₄⋊C₈	C₂²×C₇₃	1	1	yes	characteristic
283	C₂×#103	—	2	1	no	—
284	#382	C₂²×C₇₃	1	1	yes	characteristic
285	#340	—	2	1	no	—
286	#332	—	2	1	no	—
287	#331	—	2	1	no	—
288	#327	—	2	2	no	—
289	#327	—	2	2	no	—
290	Q₈⋊C₈	—	2	2	no	—
291	D₄⋊C₈	—	2	2	no	—
292	2₋¹⁺⁴	—	4	2	no	—
293	2₋¹⁺⁴	—	4	2	no	—
294	2₋¹⁺⁴	—	4	2	no	—
295	2₋¹⁺⁴	—	4	2	no	—
296	C₂×#41	—	2	4	no	—
297	C₂×#41	—	2	2	no	—
298	C₂×#41	—	2	2	no	—
299	C₂×#41	—	2	1	no	—
300	C₂×#41	—	2	1	no	—
301	C₂²×Q₈	—	2	2	no	—
302	C₂²×Q₈	—	2	2	no	—
303	C₂²×Q₈	D₄×C₇₃	1	1	yes	characteristic
304	C₂²×C₈	—	2	1	no	—
305	C₄⋊Q₈	—	2	2	no	—
306	C₄⋊Q₈	C₂×C₄×C₇₃	1	1	yes	characteristic
307	C₄⋊Q₈	D₄×C₇₃	1	1	yes	characteristic
308	#127	—	2	2	no	—
309	#127	C₂×C₄×C₇₃	1	1	yes	characteristic
310	#127	D₄×C₇₃	1	1	yes	characteristic
311	#124	—	2	4	no	—
312	#124	—	2	1	no	—
313	#124	—	2	1	no	—
314	C₂²⋊Q₈	—	2	2	no	—
315	C₂²⋊Q₈	—	2	4	no	—
316	C₂²⋊Q₈	—	2	2	no	—
317	C₂²⋊Q₈	—	2	4	no	—
318	#121	—	2	4	no	—
319	#121	—	2	2	no	—
320	#121	—	2	4	no	—
321	#121	—	2	4	no	—
322	#121	—	2	1	no	—
323	#121	—	2	1	no	—
324	#121	—	2	2	no	—
325	#121	D₄×C₇₃	1	2	yes	—
326	#121	D₄×C₇₃	1	2	yes	—
327	C₄×Q₈	—	2	1	no	—
328	C₄×Q₈	—	2	1	no	—
329	C₄×Q₈	C₂×C₄×C₇₃	1	2	yes	—
330	C₄×Q₈	D₄×C₇₃	1	2	yes	—
331	C₄×D₄	—	2	4	no	—
332	C₄×D₄	—	2	2	no	—
333	C₄×D₄	—	2	2	no	—
334	C₄×D₄	—	2	1	no	—
335	C₄×D₄	—	2	1	no	—
336	C₄×D₄	C₂×C₄×C₇₃	1	2	yes	—
337	C₄×D₄	D₄×C₇₃	1	2	yes	—
338	C₂×C₄⋊C₄	—	2	1	no	—
339	C₂×C₄⋊C₄	—	2	1	no	—
340	C₂×C₄⋊C₄	D₄×C₇₃	1	1	yes	characteristic
341	C₂×C₄²	—	2	1	no	—
342	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
343	C₄⋊C₈	—	2	1	no	—
344	C₄⋊C₈	—	2	1	no	—
345	C₄⋊C₈	—	2	1	no	—
346	C₄⋊C₈	—	2	1	no	—
347	#103	—	4	2	no	—
348	C₂²⋊C₈	—	2	1	no	—
349	C₂²⋊C₈	—	2	1	no	—
350	C₄×C₈	—	2	1	no	—
351	C₄×C₈	—	2	1	no	—
352	#95	—	2	1	no	—
353	#95	—	2	1	no	—
354	#41	—	4	8	no	—
355	#41	—	4	8	no	—
356	#41	—	4	4	no	—
357	#41	—	4	4	no	—
358	#41	—	4	4	no	—
359	#41	—	4	4	no	—
360	#41	—	4	1	no	—
361	#41	—	4	1	no	—
362	#41	—	4	1	no	—
363	#41	—	4	1	no	—
364	#41	—	4	1	no	—
365	#41	—	4	1	no	—
366	#41	—	4	1	no	—
367	#41	—	4	1	no	—
368	C₂×Q₈	—	2	4	no	—
369	C₂×Q₈	—	2	1	no	—
370	C₂×Q₈	—	2	1	no	—
371	C₂×Q₈	—	2	1	no	—
372	C₂×Q₈	—	2	1	no	—
373	C₂×Q₈	—	2	1	no	—
374	C₂×Q₈	—	4	4	no	—
375	C₂×Q₈	—	4	4	no	—
376	C₂×Q₈	—	4	4	no	—
377	C₂×Q₈	—	4	4	no	—
378	C₂×Q₈	C₂²⋊C₄×C₇₃	1	2	yes	—
379	C₂×Q₈	D₈×C₇₃	1	2	yes	—
380	C₂×Q₈	SD₁₆×C₇₃	1	2	yes	—
381	C₂×D₄	—	2	4	no	—
382	C₂×D₄	—	2	2	no	—
383	C₂×D₄	—	2	2	no	—
384	C₂×D₄	—	2	4	no	—
385	C₂×D₄	—	2	1	no	—
386	C₂×D₄	—	2	1	no	—
387	C₂×D₄	—	2	1	no	—
388	C₂×D₄	—	2	1	no	—
389	C₂×D₄	C₂²⋊C₄×C₇₃	1	2	yes	—
390	C₂×D₄	C₂²⋊C₄×C₇₃	1	2	yes	—
391	C₂²×C₄	—	2	1	no	—
392	C₂²×C₄	—	2	4	no	—
393	C₂²×C₄	—	2	4	no	—
394	C₂²×C₄	—	2	1	no	—
395	C₂²×C₄	—	2	2	no	—
396	C₂²×C₄	—	2	2	no	—
397	C₂²×C₄	—	4	1	no	—
398	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
399	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
400	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
401	C₂×C₈	—	4	1	no	—
402	C₂×C₈	—	4	1	no	—
403	C₂×C₈	—	4	1	no	—
404	C₂×C₈	—	4	1	no	—
405	C₂×C₈	—	4	1	no	—
406	C₄⋊C₄	—	2	4	no	—
407	C₄⋊C₄	—	2	2	no	—
408	C₄⋊C₄	—	2	1	no	—
409	C₄⋊C₄	—	2	2	no	—
410	C₄⋊C₄	—	2	1	no	—
411	C₄⋊C₄	—	2	1	no	—
412	C₄⋊C₄	—	4	1	no	—
413	C₄⋊C₄	—	4	1	no	—
414	C₄⋊C₄	C₂²⋊C₄×C₇₃	1	2	yes	—
415	C₄⋊C₄	C₂²⋊C₄×C₇₃	1	2	yes	—
416	C₄⋊C₄	C₂²⋊C₄×C₇₃	1	2	yes	—
417	C₂²⋊C₄	—	2	4	no	—
418	C₂²⋊C₄	—	2	4	no	—
419	C₂²⋊C₄	—	2	2	no	—
420	C₂²⋊C₄	—	2	2	no	—
421	C₂²⋊C₄	—	2	2	no	—
422	C₂²⋊C₄	—	2	2	no	—
423	C₄²	—	2	2	no	—
424	C₄²	—	2	2	no	—
425	C₄²	C₂²×C₄×C₇₃	1	1	yes	characteristic
426	C₄²	C₂×D₄×C₇₃	1	1	yes	characteristic
427	C₄²	C₂×D₄×C₇₃	1	1	yes	characteristic
428	C₄²	C₂×D₄×C₇₃	1	1	yes	characteristic
429	C₂³	—	2	2	no	—
430	C₂³	—	2	2	no	—
431	C₂³	#120×C₇₃	1	1	yes	characteristic
432	Q₈	—	2	2	no	—
433	Q₈	—	2	2	no	—
434	Q₈	—	2	2	no	—
435	Q₈	—	4	8	no	—
436	Q₈	—	4	1	no	—
437	Q₈	—	4	1	no	—
438	Q₈	—	4	1	no	—
439	Q₈	—	4	1	no	—
440	Q₈	#102×C₇₃	1	4	yes	—
441	D₄	—	4	2	no	—
442	D₄	—	4	2	no	—
443	D₄	—	4	8	no	—
444	D₄	—	4	2	no	—
445	D₄	—	4	2	no	—
446	D₄	—	4	2	no	—
447	D₄	—	4	2	no	—
448	D₄	—	4	2	no	—
449	D₄	—	4	1	no	—
450	D₄	—	4	1	no	—
451	D₄	—	4	1	no	—
452	D₄	—	4	1	no	—
453	D₄	—	8	1	no	—
454	D₄	—	8	4	no	—
455	C₂×C₄	—	2	2	no	—
456	C₂×C₄	—	2	2	no	—
457	C₂×C₄	—	2	2	no	—
458	C₂×C₄	—	2	2	no	—
459	C₂×C₄	—	2	2	no	—
460	C₂×C₄	—	2	2	no	—
461	C₂×C₄	—	4	1	no	—
462	C₂×C₄	—	4	1	no	—
463	C₂×C₄	—	4	8	no	—
464	C₂×C₄	—	4	8	no	—
465	C₂×C₄	—	4	2	no	—
466	C₂×C₄	—	4	2	no	—
467	C₂×C₄	—	4	2	no	—
468	C₂×C₄	—	4	2	no	—
469	C₂×C₄	—	8	1	no	—
470	C₂×C₄	—	8	1	no	—
471	C₂×C₄	—	8	1	no	—
472	C₂×C₄	—	8	1	no	—
473	C₂×C₄	C₂×C₂²⋊C₄×C₇₃	1	1	yes	characteristic
474	C₂×C₄	C₂×C₂²⋊C₄×C₇₃	1	1	yes	characteristic
475	C₂×C₄	C₂×C₂²⋊C₄×C₇₃	1	1	yes	characteristic
476	C₂×C₄	#120×C₇₃	1	1	yes	characteristic
477	C₂×C₄	#120×C₇₃	1	1	yes	characteristic
478	C₂×C₄	#120×C₇₃	1	1	yes	characteristic
479	C₂×C₄	C₂×D₈×C₇₃	1	1	yes	characteristic
480	C₂×C₄	C₂×SD₁₆×C₇₃	1	1	yes	characteristic
481	C₂×C₄	AGL(1,ℤ/8)×C₇₃	1	1	yes	characteristic
482	C₂×C₄	AGL(1,ℤ/8)×C₇₃	1	1	yes	characteristic
483	C₈	—	8	1	no	—
484	C₈	—	8	1	no	—
485	C₈	—	8	1	no	—
486	C₂²	—	2	1	no	—
487	C₂²	—	2	1	no	—
488	C₂²	—	4	2	no	—
489	C₂²	—	4	2	no	—
490	C₂²	—	4	2	no	—
491	C₂²	—	4	2	no	—
492	C₂²	—	4	2	no	—
493	C₂²	—	4	2	no	—
494	C₂²	#379×C₇₃	1	1	yes	characteristic
495	C₂²	#447×C₇₃	1	1	yes	characteristic
496	C₂²	#450×C₇₃	1	1	yes	characteristic
497	C₄	—	2	4	no	—
498	C₄	—	2	1	no	—
499	C₄	—	2	1	no	—
500	C₄	—	2	1	no	—
501	C₄	—	2	1	no	—
502	C₄	—	4	2	no	—
503	C₄	—	4	2	no	—
504	C₄	—	4	2	no	—
505	C₄	—	16	1	no	—
506	C₄	C₂×#102×C₇₃	1	1	yes	characteristic
507	C₄	#418×C₇₃	1	1	yes	characteristic
508	C₄	#447×C₇₃	1	1	yes	characteristic
509	C₄	#450×C₇₃	1	1	yes	characteristic
510	C₂	—	2	1	no	—
511	C₂	—	2	1	no	—
512	C₂	—	8	2	no	—
513	C₂	—	8	2	no	—
514	C₂	C₇₃×#1786	1	1	yes	characteristic
515	C₂	C₇₃×#1794	1	1	yes	characteristic
516	C₂	C₇₃×#1796	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₇₃	#379
commutator	C₄²	C₂²×C₄×C₇₃
Frattini, cosocle	C₂×C₄²	C₂³×C₇₃
prime radical	C₇₃×#3497	C₂
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₇₃ ◁ C₂×C₄²×C₇₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₇₃×#1805	C₂	semidirect
3. C₇₃×#1540	C₂	semidirect
4. C₇₃×#1517	C₂	semidirect
5. C₇₃×#1517	C₂	semidirect
6. C₇₃×#1480	C₂	semidirect
7. C₇₃×#1479	C₂	semidirect
10. #550×C₇₃	C₄	semidirect
12. D₄×Q₈×C₇₃	C₄	semidirect
251. #8429	C₇₃	direct (N × H)
260. #1805	C₂×C₇₃	semidirect
261. #1540	C₂×C₇₃	semidirect
262. #1517	C₂×C₇₃	semidirect
263. #1517	C₂×C₇₃	semidirect
264. #1480	C₂×C₇₃	semidirect
265. #1479	C₂×C₇₃	semidirect
266. C₇₃	#8429	direct (N × H)
269. #550	C₄×C₇₃	semidirect
271. D₄×Q₈	C₄×C₇₃	semidirect

Maximal subgroups

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

subgroup	index
C₇₃×#3497	2
C₇₃×#1805	2
C₇₃×#1540	2
C₇₃×#1517	2
C₇₃×#1480	2
C₇₃×#1479	2
#8429	73

Subgroups — C73×#8429 #32917833

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₃×#8429 #32917833