Subgroups — C₇₃×#18720 #32928124

Order 18688.

998 conjugacy classes of subgroups.

The subgroup lattice has 468 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇₃×#3543	C₂	1	1	yes	maximal, characteristic
2	C₇₃×#3248	C₂	1	2	yes	maximal, complemented
3	C₇₃×#3138	C₂	1	1	yes	maximal, characteristic, complemented
4	C₇₃×#1642	C₂	1	2	yes	maximal, complemented
5	C₇₃×#1641	C₂	1	2	yes	maximal, complemented
6	C₇₃×#1640	C₂	1	2	yes	maximal, complemented
7	C₇₃×#1639	C₂	1	2	yes	maximal, complemented
8	C₂×#331×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
9	C₇₃×#1483	C₂	1	2	yes	maximal, complemented
10	#560×C₇₃	—	2	2	no	—
11	#559×C₇₃	C₂²	1	1	yes	characteristic
12	#550×C₇₃	C₂²	1	2	yes	—
13	#546×C₇₃	—	2	2	no	—
14	D₄²×C₇₃	—	2	2	no	—
15	D₄²×C₇₃	C₂²	1	1	yes	characteristic
16	#540×C₇₃	—	2	2	no	—
17	#535×C₇₃	—	2	2	no	—
18	#534×C₇₃	—	2	2	no	—
19	#533×C₇₃	C₂²	1	1	yes	characteristic, complemented
20	C₂×#127×C₇₃	C₂²	1	1	yes	characteristic
21	#529×C₇₃	C₂²	1	2	yes	—
22	#490×C₇₃	—	2	2	no	—
23	#486×C₇₃	C₂²	1	2	yes	—
24	#486×C₇₃	C₂²	1	2	yes	complemented
25	#479×C₇₃	—	2	2	no	—
26	#475×C₇₃	C₂²	1	2	yes	complemented
27	#474×C₇₃	C₂²	1	2	yes	complemented
28	#467×C₇₃	—	2	2	no	—
29	#465×C₇₃	—	2	2	no	—
30	#464×C₇₃	—	2	2	no	—
31	#462×C₇₃	C₂²	1	2	yes	complemented
32	#461×C₇₃	C₂²	1	2	yes	complemented
33	C₂×C₄⋊C₈×C₇₃	C₂²	1	2	yes	complemented
34	#418×C₇₃	—	2	2	no	—
35	C₄×M₁₆×C₇₃	C₂²	1	1	yes	characteristic, complemented
36	#331×C₇₃	C₂²	1	2	yes	—
37	#331×C₇₃	C₂²	1	1	yes	characteristic, complemented
38	#331×C₇₃	C₂²	1	1	yes	characteristic, complemented
39	Q₈⋊C₈×C₇₃	C₂²	1	2	yes	complemented
40	Q₈⋊C₈×C₇₃	C₂²	1	2	yes	complemented
41	D₄⋊C₈×C₇₃	C₂²	1	2	yes	complemented
42	D₄⋊C₈×C₇₃	C₂²	1	2	yes	complemented
43	C₂×#41×C₇₃	—	2	2	no	—
44	C₂²×D₄×C₇₃	—	2	2	no	—
45	C₂²×D₄×C₇₃	—	2	2	no	—
46	C₂²×D₄×C₇₃	—	2	2	no	—
47	C₂²×D₄×C₇₃	D₄	1	2	yes	—
48	C₂×Q₁₆×C₇₃	—	2	2	no	—
49	C₂×SD₁₆×C₇₃	—	2	2	no	—
50	C₂×M₁₆×C₇₃	—	2	1	no	—
51	C₂²×C₈×C₇₃	—	2	2	no	—
52	C₄⋊Q₈×C₇₃	C₂³	1	2	yes	—
53	#127×C₇₃	—	2	2	no	—
54	#127×C₇₃	—	2	2	no	—
55	#127×C₇₃	D₄	1	2	yes	—
56	#127×C₇₃	C₂³	1	1	yes	characteristic
57	#127×C₇₃	C₂³	1	1	yes	characteristic
58	#126×C₇₃	—	2	2	no	—
59	#125×C₇₃	—	2	1	no	—
60	#125×C₇₃	D₄	1	2	yes	—
61	#124×C₇₃	—	2	2	no	—
62	#124×C₇₃	D₄	1	2	yes	—
63	#123×C₇₃	—	2	2	no	—
64	#123×C₇₃	—	2	4	no	—
65	#123×C₇₃	—	2	2	no	—
66	#123×C₇₃	—	2	2	no	—
67	C₂²⋊Q₈×C₇₃	—	2	2	no	—
68	C₂²⋊Q₈×C₇₃	D₄	1	2	yes	—
69	#121×C₇₃	—	2	4	no	—
70	#121×C₇₃	—	2	4	no	—
71	#121×C₇₃	—	2	4	no	—
72	#121×C₇₃	—	2	4	no	—
73	#121×C₇₃	—	2	2	no	—
74	#121×C₇₃	—	2	2	no	—
75	#121×C₇₃	D₄	1	2	yes	—
76	#120×C₇₃	—	2	2	no	—
77	#120×C₇₃	—	2	4	no	—
78	#120×C₇₃	—	2	4	no	—
79	#120×C₇₃	—	2	2	no	—
80	C₄×Q₈×C₇₃	—	2	2	no	—
81	C₄×Q₈×C₇₃	C₂³	1	2	yes	—
82	C₄×D₄×C₇₃	—	2	2	no	—
83	C₄×D₄×C₇₃	—	2	2	no	—
84	C₄×D₄×C₇₃	—	2	2	no	—
85	C₄×D₄×C₇₃	C₂³	1	2	yes	—
86	#117×C₇₃	—	2	2	no	—
87	#117×C₇₃	—	2	1	no	—
88	C₂×C₂²⋊C₄×C₇₃	—	2	2	no	—
89	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
90	#107×C₇₃	—	2	2	no	—
91	#106×C₇₃	—	2	2	no	—
92	C₄⋊C₈×C₇₃	—	2	2	no	—
93	C₄⋊C₈×C₇₃	C₂³	1	2	yes	—
94	C₄⋊C₈×C₇₃	C₂³	1	2	yes	—
95	#103×C₇₃	—	2	2	no	—
96	#103×C₇₃	—	2	2	no	—
97	#103×C₇₃	—	2	2	no	—
98	#102×C₇₃	—	2	4	no	—
99	#102×C₇₃	—	2	4	no	—
100	#102×C₇₃	—	2	2	no	—
101	#97×C₇₃	—	2	1	no	—
102	C₄×C₈×C₇₃	C₂³	1	2	yes	—
103	C₂⁴×C₇₃	—	2	2	no	—
104	C₂⁴×C₇₃	—	2	2	no	—
105	#41×C₇₃	—	8	2	no	—
106	#41×C₇₃	—	8	2	no	—
107	C₂×Q₈×C₇₃	—	2	2	no	—
108	C₂×Q₈×C₇₃	C₂×D₄	1	2	yes	—
109	C₂×D₄×C₇₃	—	2	2	no	—
110	C₂×D₄×C₇₃	—	2	4	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	4	no	—
115	C₂×D₄×C₇₃	—	2	2	no	—
116	C₂×D₄×C₇₃	—	2	2	no	—
117	C₂×D₄×C₇₃	—	4	4	no	—
118	C₂×D₄×C₇₃	—	8	2	no	—
119	C₂×D₄×C₇₃	—	8	2	no	—
120	C₂×D₄×C₇₃	—	8	2	no	—
121	C₂×D₄×C₇₃	—	8	2	no	—
122	C₂×D₄×C₇₃	—	8	4	no	—
123	C₂×D₄×C₇₃	C₂×D₄	1	2	yes	—
124	C₂×D₄×C₇₃	C₂×D₄	1	2	yes	—
125	C₂×D₄×C₇₃	C₂×D₄	1	2	yes	—
126	C₂²×C₄×C₇₃	—	2	4	no	—
127	C₂²×C₄×C₇₃	—	2	2	no	—
128	C₂²×C₄×C₇₃	—	2	2	no	—
129	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
130	C₂²×C₄×C₇₃	C₂×D₄	1	2	yes	—
131	Q₁₆×C₇₃	—	8	2	no	—
132	SD₁₆×C₇₃	—	8	2	no	—
133	M₁₆×C₇₃	—	4	2	no	—
134	C₂×C₈×C₇₃	—	2	2	no	—
135	C₂×C₈×C₇₃	—	2	2	no	—
136	C₂×C₈×C₇₃	—	2	2	no	—
137	C₂×C₈×C₇₃	—	8	2	no	—
138	C₄⋊C₄×C₇₃	—	2	2	no	—
139	C₄⋊C₄×C₇₃	—	2	2	no	—
140	C₄⋊C₄×C₇₃	—	2	2	no	—
141	C₄⋊C₄×C₇₃	—	2	2	no	—
142	C₄⋊C₄×C₇₃	—	2	2	no	—
143	C₄⋊C₄×C₇₃	—	2	2	no	—
144	C₄⋊C₄×C₇₃	—	4	2	no	—
145	C₄⋊C₄×C₇₃	C₂×D₄	1	2	yes	—
146	C₄⋊C₄×C₇₃	C₂×D₄	1	2	yes	—
147	C₂²⋊C₄×C₇₃	—	2	2	no	—
148	C₂²⋊C₄×C₇₃	—	2	2	no	—
149	C₂²⋊C₄×C₇₃	—	2	4	no	—
150	C₂²⋊C₄×C₇₃	—	2	4	no	—
151	C₂²⋊C₄×C₇₃	—	2	2	no	—
152	C₂²⋊C₄×C₇₃	—	2	2	no	—
153	C₂²⋊C₄×C₇₃	—	2	2	no	—
154	C₂²⋊C₄×C₇₃	—	2	2	no	—
155	C₂²⋊C₄×C₇₃	—	2	2	no	—
156	C₂²⋊C₄×C₇₃	—	4	1	no	—
157	C₄²×C₇₃	—	2	2	no	—
158	C₄²×C₇₃	—	4	1	no	—
159	C₄²×C₇₃	C₂×D₄	1	1	yes	characteristic
160	C₄²×C₇₃	C₂×D₄	1	2	yes	—
161	C₄²×C₇₃	C₂⁴	1	1	yes	characteristic
162	C₂³×C₇₃	—	2	2	no	—
163	C₂³×C₇₃	—	2	2	no	—
164	C₂³×C₇₃	—	2	2	no	—
165	C₂³×C₇₃	—	4	4	no	—
166	C₂³×C₇₃	—	8	4	no	—
167	C₂³×C₇₃	—	8	4	no	—
168	C₂³×C₇₃	—	8	2	no	—
169	C₂³×C₇₃	#120	1	1	yes	characteristic
170	Q₈×C₇₃	—	2	2	no	—
171	Q₈×C₇₃	—	2	2	no	—
172	Q₈×C₇₃	—	4	2	no	—
173	Q₈×C₇₃	—	4	2	no	—
174	D₄×C₇₃	—	2	2	no	—
175	D₄×C₇₃	—	2	2	no	—
176	D₄×C₇₃	—	4	2	no	—
177	D₄×C₇₃	—	4	2	no	—
178	D₄×C₇₃	—	4	4	no	—
179	D₄×C₇₃	—	4	2	no	—
180	D₄×C₇₃	—	4	2	no	—
181	D₄×C₇₃	—	4	2	no	—
182	D₄×C₇₃	—	4	2	no	—
183	D₄×C₇₃	—	8	2	no	—
184	D₄×C₇₃	—	8	4	no	—
185	D₄×C₇₃	—	8	4	no	—
186	D₄×C₇₃	—	8	4	no	—
187	D₄×C₇₃	—	8	4	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	—	2	2	no	—
194	C₂×C₄×C₇₃	—	4	2	no	—
195	C₂×C₄×C₇₃	—	4	2	no	—
196	C₂×C₄×C₇₃	—	4	2	no	—
197	C₂×C₄×C₇₃	—	8	2	no	—
198	C₂×C₄×C₇₃	—	8	4	no	—
199	C₂×C₄×C₇₃	#120	1	1	yes	characteristic
200	C₂×C₄×C₇₃	#120	1	2	yes	—
201	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
202	C₂×C₄×C₇₃	C₂²×D₄	1	2	yes	—
203	C₈×C₇₃	—	4	2	no	—
204	C₈×C₇₃	—	4	2	no	—
205	C₈×C₇₃	—	4	2	no	—
206	C₂²×C₇₃	—	2	2	no	—
207	C₂²×C₇₃	—	4	2	no	—
208	C₂²×C₇₃	—	4	4	no	—
209	C₂²×C₇₃	—	4	2	no	—
210	C₂²×C₇₃	—	4	4	no	—
211	C₂²×C₇₃	—	4	2	no	—
212	C₂²×C₇₃	—	4	2	no	—
213	C₂²×C₇₃	—	4	2	no	—
214	C₂²×C₇₃	—	16	4	no	—
215	C₂²×C₇₃	—	16	4	no	—
216	C₂²×C₇₃	#455	1	2	yes	—
217	C₂²×C₇₃	C₂×#120	1	1	yes	characteristic
218	C₄×C₇₃	—	2	2	no	—
219	C₄×C₇₃	—	2	1	no	—
220	C₄×C₇₃	—	2	1	no	—
221	C₄×C₇₃	—	4	2	no	—
222	C₄×C₇₃	—	4	2	no	—
223	C₄×C₇₃	—	4	2	no	—
224	C₄×C₇₃	—	8	2	no	—
225	C₄×C₇₃	#576	1	2	yes	—
226	C₄×C₇₃	#577	1	2	yes	—
227	#18720	C₇₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
228	C₂×C₇₃	—	2	2	no	—
229	C₂×C₇₃	—	8	2	no	—
230	C₂×C₇₃	—	8	2	no	—
231	C₂×C₇₃	—	8	2	no	—
232	C₂×C₇₃	#3012	1	2	yes	—
233	C₂×C₇₃	C₂×#455	1	1	yes	characteristic
234	#3543	C₂×C₇₃	1	1	yes	characteristic
235	#3248	C₂×C₇₃	1	2	yes	complemented
236	#3138	C₂×C₇₃	1	1	yes	characteristic, complemented
237	#1642	C₂×C₇₃	1	2	yes	complemented
238	#1641	C₂×C₇₃	1	2	yes	complemented
239	#1640	C₂×C₇₃	1	2	yes	complemented
240	#1639	C₂×C₇₃	1	2	yes	complemented
241	C₂×#331	C₂×C₇₃	1	1	yes	characteristic, complemented
242	#1483	C₂×C₇₃	1	2	yes	complemented
243	C₇₃	#18720	1	1	yes	characteristic, direct product factor, Sylow
244	#560	—	2	2	no	—
245	#559	C₂²×C₇₃	1	1	yes	characteristic
246	#550	C₂²×C₇₃	1	2	yes	—
247	#546	—	2	2	no	—
248	D₄²	—	2	2	no	—
249	D₄²	C₂²×C₇₃	1	1	yes	characteristic
250	#540	—	2	2	no	—
251	#535	—	2	2	no	—
252	#534	—	2	2	no	—
253	#533	C₂²×C₇₃	1	1	yes	characteristic, complemented
254	C₂×#127	C₂²×C₇₃	1	1	yes	characteristic
255	#529	C₂²×C₇₃	1	2	yes	—
256	#490	—	2	2	no	—
257	#486	C₂²×C₇₃	1	2	yes	—
258	#486	C₂²×C₇₃	1	2	yes	complemented
259	#479	—	2	2	no	—
260	#475	C₂²×C₇₃	1	2	yes	complemented
261	#474	C₂²×C₇₃	1	2	yes	complemented
262	#467	—	2	2	no	—
263	#465	—	2	2	no	—
264	#464	—	2	2	no	—
265	#462	C₂²×C₇₃	1	2	yes	complemented
266	#461	C₂²×C₇₃	1	2	yes	complemented
267	C₂×C₄⋊C₈	C₂²×C₇₃	1	2	yes	complemented
268	#418	—	2	2	no	—
269	C₄×M₁₆	C₂²×C₇₃	1	1	yes	characteristic, complemented
270	#331	C₂²×C₇₃	1	2	yes	—
271	#331	C₂²×C₇₃	1	1	yes	characteristic, complemented
272	#331	C₂²×C₇₃	1	1	yes	characteristic, complemented
273	Q₈⋊C₈	C₂²×C₇₃	1	2	yes	complemented
274	Q₈⋊C₈	C₂²×C₇₃	1	2	yes	complemented
275	D₄⋊C₈	C₂²×C₇₃	1	2	yes	complemented
276	D₄⋊C₈	C₂²×C₇₃	1	2	yes	complemented
277	C₂×#41	—	2	2	no	—
278	C₂²×D₄	—	2	2	no	—
279	C₂²×D₄	—	2	2	no	—
280	C₂²×D₄	—	2	2	no	—
281	C₂²×D₄	D₄×C₇₃	1	2	yes	—
282	C₂×Q₁₆	—	2	2	no	—
283	C₂×SD₁₆	—	2	2	no	—
284	C₂×M₁₆	—	2	1	no	—
285	C₂²×C₈	—	2	2	no	—
286	C₄⋊Q₈	C₂³×C₇₃	1	2	yes	—
287	#127	—	2	2	no	—
288	#127	—	2	2	no	—
289	#127	D₄×C₇₃	1	2	yes	—
290	#127	C₂³×C₇₃	1	1	yes	characteristic
291	#127	C₂³×C₇₃	1	1	yes	characteristic
292	#126	—	2	2	no	—
293	#125	—	2	1	no	—
294	#125	D₄×C₇₃	1	2	yes	—
295	#124	—	2	2	no	—
296	#124	D₄×C₇₃	1	2	yes	—
297	#123	—	2	2	no	—
298	#123	—	2	4	no	—
299	#123	—	2	2	no	—
300	#123	—	2	2	no	—
301	C₂²⋊Q₈	—	2	2	no	—
302	C₂²⋊Q₈	D₄×C₇₃	1	2	yes	—
303	#121	—	2	4	no	—
304	#121	—	2	4	no	—
305	#121	—	2	4	no	—
306	#121	—	2	4	no	—
307	#121	—	2	2	no	—
308	#121	—	2	2	no	—
309	#121	D₄×C₇₃	1	2	yes	—
310	#120	—	2	2	no	—
311	#120	—	2	4	no	—
312	#120	—	2	4	no	—
313	#120	—	2	2	no	—
314	C₄×Q₈	—	2	2	no	—
315	C₄×Q₈	C₂³×C₇₃	1	2	yes	—
316	C₄×D₄	—	2	2	no	—
317	C₄×D₄	—	2	2	no	—
318	C₄×D₄	—	2	2	no	—
319	C₄×D₄	C₂³×C₇₃	1	2	yes	—
320	#117	—	2	2	no	—
321	#117	—	2	1	no	—
322	C₂×C₂²⋊C₄	—	2	2	no	—
323	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
324	#107	—	2	2	no	—
325	#106	—	2	2	no	—
326	C₄⋊C₈	—	2	2	no	—
327	C₄⋊C₈	C₂³×C₇₃	1	2	yes	—
328	C₄⋊C₈	C₂³×C₇₃	1	2	yes	—
329	#103	—	2	2	no	—
330	#103	—	2	2	no	—
331	#103	—	2	2	no	—
332	#102	—	2	4	no	—
333	#102	—	2	4	no	—
334	#102	—	2	2	no	—
335	#97	—	2	1	no	—
336	C₄×C₈	C₂³×C₇₃	1	2	yes	—
337	C₂⁴	—	2	2	no	—
338	C₂⁴	—	2	2	no	—
339	#41	—	8	2	no	—
340	#41	—	8	2	no	—
341	C₂×Q₈	—	2	2	no	—
342	C₂×Q₈	C₂×D₄×C₇₃	1	2	yes	—
343	C₂×D₄	—	2	2	no	—
344	C₂×D₄	—	2	4	no	—
345	C₂×D₄	—	2	4	no	—
346	C₂×D₄	—	2	4	no	—
347	C₂×D₄	—	2	2	no	—
348	C₂×D₄	—	2	4	no	—
349	C₂×D₄	—	2	2	no	—
350	C₂×D₄	—	2	2	no	—
351	C₂×D₄	—	4	4	no	—
352	C₂×D₄	—	8	2	no	—
353	C₂×D₄	—	8	2	no	—
354	C₂×D₄	—	8	2	no	—
355	C₂×D₄	—	8	2	no	—
356	C₂×D₄	—	8	4	no	—
357	C₂×D₄	C₂×D₄×C₇₃	1	2	yes	—
358	C₂×D₄	C₂×D₄×C₇₃	1	2	yes	—
359	C₂×D₄	C₂×D₄×C₇₃	1	2	yes	—
360	C₂²×C₄	—	2	4	no	—
361	C₂²×C₄	—	2	2	no	—
362	C₂²×C₄	—	2	2	no	—
363	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
364	C₂²×C₄	C₂×D₄×C₇₃	1	2	yes	—
365	Q₁₆	—	8	2	no	—
366	SD₁₆	—	8	2	no	—
367	M₁₆	—	4	2	no	—
368	C₂×C₈	—	2	2	no	—
369	C₂×C₈	—	2	2	no	—
370	C₂×C₈	—	2	2	no	—
371	C₂×C₈	—	8	2	no	—
372	C₄⋊C₄	—	2	2	no	—
373	C₄⋊C₄	—	2	2	no	—
374	C₄⋊C₄	—	2	2	no	—
375	C₄⋊C₄	—	2	2	no	—
376	C₄⋊C₄	—	2	2	no	—
377	C₄⋊C₄	—	2	2	no	—
378	C₄⋊C₄	—	4	2	no	—
379	C₄⋊C₄	C₂×D₄×C₇₃	1	2	yes	—
380	C₄⋊C₄	C₂×D₄×C₇₃	1	2	yes	—
381	C₂²⋊C₄	—	2	2	no	—
382	C₂²⋊C₄	—	2	2	no	—
383	C₂²⋊C₄	—	2	4	no	—
384	C₂²⋊C₄	—	2	4	no	—
385	C₂²⋊C₄	—	2	2	no	—
386	C₂²⋊C₄	—	2	2	no	—
387	C₂²⋊C₄	—	2	2	no	—
388	C₂²⋊C₄	—	2	2	no	—
389	C₂²⋊C₄	—	2	2	no	—
390	C₂²⋊C₄	—	4	1	no	—
391	C₄²	—	2	2	no	—
392	C₄²	—	4	1	no	—
393	C₄²	C₂×D₄×C₇₃	1	1	yes	characteristic
394	C₄²	C₂×D₄×C₇₃	1	2	yes	—
395	C₄²	C₂⁴×C₇₃	1	1	yes	characteristic
396	C₂³	—	2	2	no	—
397	C₂³	—	2	2	no	—
398	C₂³	—	2	2	no	—
399	C₂³	—	4	4	no	—
400	C₂³	—	8	4	no	—
401	C₂³	—	8	4	no	—
402	C₂³	—	8	2	no	—
403	C₂³	#120×C₇₃	1	1	yes	characteristic
404	Q₈	—	2	2	no	—
405	Q₈	—	2	2	no	—
406	Q₈	—	4	2	no	—
407	Q₈	—	4	2	no	—
408	D₄	—	2	2	no	—
409	D₄	—	2	2	no	—
410	D₄	—	4	2	no	—
411	D₄	—	4	2	no	—
412	D₄	—	4	4	no	—
413	D₄	—	4	2	no	—
414	D₄	—	4	2	no	—
415	D₄	—	4	2	no	—
416	D₄	—	4	2	no	—
417	D₄	—	8	2	no	—
418	D₄	—	8	4	no	—
419	D₄	—	8	4	no	—
420	D₄	—	8	4	no	—
421	D₄	—	8	4	no	—
422	C₂×C₄	—	2	2	no	—
423	C₂×C₄	—	2	2	no	—
424	C₂×C₄	—	2	2	no	—
425	C₂×C₄	—	2	2	no	—
426	C₂×C₄	—	2	2	no	—
427	C₂×C₄	—	2	2	no	—
428	C₂×C₄	—	4	2	no	—
429	C₂×C₄	—	4	2	no	—
430	C₂×C₄	—	4	2	no	—
431	C₂×C₄	—	8	2	no	—
432	C₂×C₄	—	8	4	no	—
433	C₂×C₄	#120×C₇₃	1	1	yes	characteristic
434	C₂×C₄	#120×C₇₃	1	2	yes	—
435	C₂×C₄	C₂²×D₄×C₇₃	1	1	yes	characteristic
436	C₂×C₄	C₂²×D₄×C₇₃	1	2	yes	—
437	C₈	—	4	2	no	—
438	C₈	—	4	2	no	—
439	C₈	—	4	2	no	—
440	C₂²	—	2	2	no	—
441	C₂²	—	4	2	no	—
442	C₂²	—	4	4	no	—
443	C₂²	—	4	2	no	—
444	C₂²	—	4	4	no	—
445	C₂²	—	4	2	no	—
446	C₂²	—	4	2	no	—
447	C₂²	—	4	2	no	—
448	C₂²	—	16	4	no	—
449	C₂²	—	16	4	no	—
450	C₂²	#455×C₇₃	1	2	yes	—
451	C₂²	C₂×#120×C₇₃	1	1	yes	characteristic
452	C₄	—	2	2	no	—
453	C₄	—	2	1	no	—
454	C₄	—	2	1	no	—
455	C₄	—	4	2	no	—
456	C₄	—	4	2	no	—
457	C₄	—	4	2	no	—
458	C₄	—	8	2	no	—
459	C₄	#576×C₇₃	1	2	yes	—
460	C₄	#577×C₇₃	1	2	yes	—
461	C₂	—	2	2	no	—
462	C₂	—	8	2	no	—
463	C₂	—	8	2	no	—
464	C₂	—	8	2	no	—
465	C₂	C₇₃×#3012	1	2	yes	—
466	C₂	C₂×#455×C₇₃	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₇₃	C₂×#120
commutator, Frattini, cosocle	C₄²	C₂⁴×C₇₃
prime radical	C₇₃×#3543	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×#3248	C₂	semidirect
3. C₇₃×#3138	C₂	semidirect
4. C₇₃×#1642	C₂	semidirect
5. C₇₃×#1641	C₂	semidirect
6. C₇₃×#1640	C₂	semidirect
7. C₇₃×#1639	C₂	semidirect
8. C₂×#331×C₇₃	C₂	semidirect
9. C₇₃×#1483	C₂	semidirect
19. #533×C₇₃	C₂²	semidirect
24. #486×C₇₃	C₂²	semidirect
26. #475×C₇₃	C₂²	semidirect
27. #474×C₇₃	C₂²	semidirect
31. #462×C₇₃	C₂²	semidirect
32. #461×C₇₃	C₂²	semidirect
33. C₂×C₄⋊C₈×C₇₃	C₂²	semidirect
35. C₄×M₁₆×C₇₃	C₂²	semidirect
37. #331×C₇₃	C₂²	semidirect
38. #331×C₇₃	C₂²	semidirect
39. Q₈⋊C₈×C₇₃	C₂²	semidirect
40. Q₈⋊C₈×C₇₃	C₂²	semidirect
41. D₄⋊C₈×C₇₃	C₂²	semidirect
42. D₄⋊C₈×C₇₃	C₂²	semidirect
227. #18720	C₇₃	direct (N × H)
235. #3248	C₂×C₇₃	semidirect
236. #3138	C₂×C₇₃	semidirect
237. #1642	C₂×C₇₃	semidirect
238. #1641	C₂×C₇₃	semidirect
239. #1640	C₂×C₇₃	semidirect
240. #1639	C₂×C₇₃	semidirect
241. C₂×#331	C₂×C₇₃	semidirect
242. #1483	C₂×C₇₃	semidirect
243. C₇₃	#18720	direct (N × H)
253. #533	C₂²×C₇₃	semidirect
258. #486	C₂²×C₇₃	semidirect
260. #475	C₂²×C₇₃	semidirect
261. #474	C₂²×C₇₃	semidirect
265. #462	C₂²×C₇₃	semidirect
266. #461	C₂²×C₇₃	semidirect
267. C₂×C₄⋊C₈	C₂²×C₇₃	semidirect
269. C₄×M₁₆	C₂²×C₇₃	semidirect
271. #331	C₂²×C₇₃	semidirect
272. #331	C₂²×C₇₃	semidirect
273. Q₈⋊C₈	C₂²×C₇₃	semidirect
274. Q₈⋊C₈	C₂²×C₇₃	semidirect
275. D₄⋊C₈	C₂²×C₇₃	semidirect
276. D₄⋊C₈	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×#3543	2
C₇₃×#3248	2
C₇₃×#3138	2
C₇₃×#1642	2
C₇₃×#1641	2
C₇₃×#1640	2
C₇₃×#1639	2
C₂×#331×C₇₃	2
C₇₃×#1483	2
#18720	73

Subgroups — C73×#18720 #32928124

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₃×#18720 #32928124