Subgroups — C₇₃×#25680 #32935084

Order 18688.

1032 conjugacy classes of subgroups.

The subgroup lattice has 528 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#542×C₇₃	C₂	1	1	yes	maximal, characteristic
2	C₂×#498×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#489×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₇₃×#2628	C₂	1	1	yes	maximal, characteristic, complemented
5	C₇₃×#2035	C₂	1	2	yes	maximal, complemented
6	C₇₃×#2034	C₂	1	2	yes	maximal
7	C₇₃×#1993	C₂	1	1	yes	maximal, characteristic, complemented
8	C₇₃×#1958	C₂	1	1	yes	maximal, characteristic, complemented
9	C₇₃×#1865	C₂	1	2	yes	maximal, complemented
10	C₇₃×#1864	C₂	1	2	yes	maximal, complemented
11	C₇₃×#1750	C₂	1	1	yes	maximal, characteristic, complemented
12	#542×C₇₃	—	2	4	no	—
13	#542×C₇₃	—	2	4	no	—
14	C₂×C₄⋊Q₈×C₇₃	C₂²	1	1	yes	characteristic
15	C₂×C₄⋊Q₈×C₇₃	C₂²	1	1	yes	characteristic
16	C₂×#126×C₇₃	—	2	1	no	—
17	C₂×#124×C₇₃	—	2	1	no	—
18	C₂×#124×C₇₃	C₂²	1	1	yes	characteristic
19	C₂×#123×C₇₃	—	2	1	no	—
20	C₂×C₂²⋊Q₈×C₇₃	—	2	1	no	—
21	C₂×C₂²⋊Q₈×C₇₃	C₂²	1	1	yes	characteristic
22	C₂×#121×C₇₃	C₂²	1	1	yes	characteristic
23	C₂×C₄×Q₈×C₇₃	C₂²	1	1	yes	characteristic
24	C₂×C₄×D₄×C₇₃	C₂²	1	1	yes	characteristic
25	C₂×#117×C₇₃	C₂²	1	1	yes	characteristic
26	#498×C₇₃	—	2	4	no	—
27	#489×C₇₃	—	2	4	no	—
28	C₂×#106×C₇₃	C₂²	1	2	yes	—
29	C₂×#106×C₇₃	C₂²	1	2	yes	—
30	C₂×#103×C₇₃	C₂²	1	2	yes	—
31	C₂×#103×C₇₃	C₂²	1	2	yes	—
32	C₂×#102×C₇₃	C₂²	1	2	yes	—
33	C₂×#102×C₇₃	C₂²	1	2	yes	—
34	C₂×C₂²⋊C₈×C₇₃	C₂²	1	2	yes	—
35	C₂×#97×C₇₃	C₂²	1	1	yes	characteristic
36	C₂×C₄×C₈×C₇₃	C₂²	1	1	yes	characteristic
37	#400×C₇₃	—	2	1	no	—
38	#399×C₇₃	—	2	1	no	—
39	#395×C₇₃	—	2	1	no	—
40	#393×C₇₃	—	2	1	no	—
41	#389×C₇₃	C₂²	1	2	yes	—
42	#382×C₇₃	C₂²	1	1	yes	characteristic
43	#380×C₇₃	C₂²	1	2	yes	—
44	#340×C₇₃	C₂²	1	2	yes	—
45	#340×C₇₃	C₂²	1	2	yes	—
46	#336×C₇₃	C₂²	1	2	yes	—
47	C₂²×Q₈×C₇₃	—	2	1	no	—
48	C₂²×Q₈×C₇₃	—	2	1	no	—
49	C₂²×Q₈×C₇₃	C₂³	1	1	yes	characteristic
50	C₂²×D₄×C₇₃	—	2	1	no	—
51	C₂²×D₄×C₇₃	C₂³	1	1	yes	characteristic
52	C₂³×C₄×C₇₃	—	2	1	no	—
53	C₂³×C₄×C₇₃	C₂³	1	1	yes	characteristic
54	C₂²×C₈×C₇₃	C₂³	1	2	yes	—
55	C₂²×C₈×C₇₃	C₂³	1	2	yes	—
56	C₄⋊Q₈×C₇₃	—	2	2	no	—
57	C₄⋊Q₈×C₇₃	—	2	2	no	—
58	C₄⋊Q₈×C₇₃	—	2	2	no	—
59	C₄⋊Q₈×C₇₃	D₄	1	4	yes	—
60	#126×C₇₃	—	2	8	no	—
61	#124×C₇₃	—	2	8	no	—
62	#124×C₇₃	—	2	2	no	—
63	#124×C₇₃	D₄	1	4	yes	—
64	#123×C₇₃	—	2	8	no	—
65	C₂²⋊Q₈×C₇₃	—	2	8	no	—
66	C₂²⋊Q₈×C₇₃	—	2	2	no	—
67	C₂²⋊Q₈×C₇₃	—	2	2	no	—
68	#121×C₇₃	—	2	2	no	—
69	#121×C₇₃	—	2	2	no	—
70	C₄×Q₈×C₇₃	—	2	2	no	—
71	C₄×Q₈×C₇₃	—	2	2	no	—
72	C₄×D₄×C₇₃	—	2	2	no	—
73	C₄×D₄×C₇₃	—	2	2	no	—
74	#117×C₇₃	—	2	2	no	—
75	#117×C₇₃	—	2	2	no	—
76	C₂×C₄⋊C₄×C₇₃	—	2	1	no	—
77	C₂×C₄⋊C₄×C₇₃	—	2	1	no	—
78	C₂×C₄⋊C₄×C₇₃	—	2	1	no	—
79	C₂×C₄⋊C₄×C₇₃	—	2	1	no	—
80	C₂×C₄⋊C₄×C₇₃	—	2	2	no	—
81	C₂×C₄⋊C₄×C₇₃	D₄	1	1	yes	characteristic
82	C₂×C₄⋊C₄×C₇₃	D₄	1	1	yes	characteristic
83	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
84	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
85	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
86	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
87	C₂×C₂²⋊C₄×C₇₃	—	2	1	no	—
88	C₂×C₂²⋊C₄×C₇₃	—	2	1	no	—
89	C₂×C₂²⋊C₄×C₇₃	—	2	1	no	—
90	C₂×C₂²⋊C₄×C₇₃	—	2	1	no	—
91	C₂×C₂²⋊C₄×C₇₃	—	2	1	no	—
92	C₂×C₂²⋊C₄×C₇₃	—	2	2	no	—
93	C₂×C₂²⋊C₄×C₇₃	D₄	1	1	yes	characteristic
94	C₂×C₂²⋊C₄×C₇₃	D₄	1	1	yes	characteristic
95	C₂×C₄²×C₇₃	—	2	1	no	—
96	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
97	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
98	#106×C₇₃	—	2	4	no	—
99	#106×C₇₃	—	2	4	no	—
100	#103×C₇₃	—	2	4	no	—
101	#103×C₇₃	—	2	4	no	—
102	#102×C₇₃	—	2	4	no	—
103	#102×C₇₃	—	2	4	no	—
104	C₂²⋊C₈×C₇₃	—	2	4	no	—
105	#97×C₇₃	—	2	2	no	—
106	C₄×C₈×C₇₃	—	2	2	no	—
107	#95×C₇₃	—	2	2	no	—
108	#95×C₇₃	—	2	1	no	—
109	#95×C₇₃	—	2	1	no	—
110	#95×C₇₃	—	2	2	no	—
111	C₂⁴×C₇₃	—	2	1	no	—
112	C₂⁴×C₇₃	C₂×D₄	1	1	yes	characteristic
113	C₂×Q₈×C₇₃	—	2	4	no	—
114	C₂×Q₈×C₇₃	—	2	1	no	—
115	C₂×Q₈×C₇₃	—	2	2	no	—
116	C₂×Q₈×C₇₃	—	2	2	no	—
117	C₂×Q₈×C₇₃	—	4	2	no	—
118	C₂×Q₈×C₇₃	—	8	2	no	—
119	C₂×Q₈×C₇₃	—	8	2	no	—
120	C₂×Q₈×C₇₃	C₂×D₄	1	2	yes	—
121	C₂×D₄×C₇₃	—	2	4	no	—
122	C₂×D₄×C₇₃	—	2	1	no	—
123	C₂×D₄×C₇₃	—	2	2	no	—
124	C₂×D₄×C₇₃	—	2	2	no	—
125	C₂×D₄×C₇₃	—	8	2	no	—
126	C₂×D₄×C₇₃	C₂×D₄	1	2	yes	—
127	C₂²×C₄×C₇₃	—	2	1	no	—
128	C₂²×C₄×C₇₃	—	2	1	no	—
129	C₂²×C₄×C₇₃	—	2	1	no	—
130	C₂²×C₄×C₇₃	—	2	4	no	—
131	C₂²×C₄×C₇₃	—	2	1	no	—
132	C₂²×C₄×C₇₃	—	2	1	no	—
133	C₂²×C₄×C₇₃	—	2	2	no	—
134	C₂²×C₄×C₇₃	—	2	2	no	—
135	C₂²×C₄×C₇₃	—	2	2	no	—
136	C₂²×C₄×C₇₃	—	2	2	no	—
137	C₂²×C₄×C₇₃	—	8	2	no	—
138	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
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	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
143	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
144	C₂×C₈×C₇₃	—	2	2	no	—
145	C₂×C₈×C₇₃	—	2	2	no	—
146	C₂×C₈×C₇₃	—	2	2	no	—
147	C₂×C₈×C₇₃	—	2	2	no	—
148	C₂×C₈×C₇₃	—	2	2	no	—
149	C₂×C₈×C₇₃	#41	1	4	yes	—
150	C₄⋊C₄×C₇₃	—	2	4	no	—
151	C₄⋊C₄×C₇₃	—	2	4	no	—
152	C₄⋊C₄×C₇₃	—	2	4	no	—
153	C₄⋊C₄×C₇₃	—	2	2	no	—
154	C₄⋊C₄×C₇₃	—	2	2	no	—
155	C₄⋊C₄×C₇₃	—	2	1	no	—
156	C₄⋊C₄×C₇₃	—	2	1	no	—
157	C₄⋊C₄×C₇₃	—	2	2	no	—
158	C₄⋊C₄×C₇₃	—	2	2	no	—
159	C₄⋊C₄×C₇₃	—	2	2	no	—
160	C₄⋊C₄×C₇₃	—	2	2	no	—
161	C₄⋊C₄×C₇₃	—	4	2	no	—
162	C₄⋊C₄×C₇₃	—	8	2	no	—
163	C₄⋊C₄×C₇₃	C₂×D₄	1	2	yes	—
164	C₄⋊C₄×C₇₃	C₂×D₄	1	2	yes	—
165	C₂²⋊C₄×C₇₃	—	2	4	no	—
166	C₂²⋊C₄×C₇₃	—	2	4	no	—
167	C₂²⋊C₄×C₇₃	—	2	4	no	—
168	C₂²⋊C₄×C₇₃	—	2	4	no	—
169	C₂²⋊C₄×C₇₃	—	2	4	no	—
170	C₂²⋊C₄×C₇₃	—	2	2	no	—
171	C₂²⋊C₄×C₇₃	—	2	2	no	—
172	C₂²⋊C₄×C₇₃	—	8	2	no	—
173	C₄²×C₇₃	—	2	4	no	—
174	C₄²×C₇₃	—	2	1	no	—
175	C₄²×C₇₃	—	2	1	no	—
176	C₄²×C₇₃	C₂×D₄	1	2	yes	—
177	C₄²×C₇₃	C₂×D₄	1	2	yes	—
178	C₂³×C₇₃	—	2	1	no	—
179	C₂³×C₇₃	—	2	2	no	—
180	C₂³×C₇₃	—	2	1	no	—
181	C₂³×C₇₃	—	2	1	no	—
182	C₂³×C₇₃	—	2	2	no	—
183	C₂³×C₇₃	—	2	2	no	—
184	C₂³×C₇₃	—	4	1	no	—
185	C₂³×C₇₃	—	4	1	no	—
186	C₂³×C₇₃	—	4	2	no	—
187	C₂³×C₇₃	—	4	2	no	—
188	C₂³×C₇₃	C₂²×D₄	1	1	yes	characteristic
189	Q₈×C₇₃	—	2	4	no	—
190	Q₈×C₇₃	—	4	2	no	—
191	Q₈×C₇₃	—	8	4	no	—
192	Q₈×C₇₃	—	8	4	no	—
193	D₄×C₇₃	—	2	4	no	—
194	D₄×C₇₃	—	4	2	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	1	no	—
199	C₂×C₄×C₇₃	—	2	2	no	—
200	C₂×C₄×C₇₃	—	2	1	no	—
201	C₂×C₄×C₇₃	—	2	2	no	—
202	C₂×C₄×C₇₃	—	2	1	no	—
203	C₂×C₄×C₇₃	—	2	2	no	—
204	C₂×C₄×C₇₃	—	2	1	no	—
205	C₂×C₄×C₇₃	—	2	1	no	—
206	C₂×C₄×C₇₃	—	2	2	no	—
207	C₂×C₄×C₇₃	—	2	2	no	—
208	C₂×C₄×C₇₃	—	4	1	no	—
209	C₂×C₄×C₇₃	—	4	1	no	—
210	C₂×C₄×C₇₃	—	4	2	no	—
211	C₂×C₄×C₇₃	—	4	2	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	2	no	—
216	C₂×C₄×C₇₃	—	4	2	no	—
217	C₂×C₄×C₇₃	—	4	2	no	—
218	C₂×C₄×C₇₃	—	4	2	no	—
219	C₂×C₄×C₇₃	—	4	2	no	—
220	C₂×C₄×C₇₃	—	8	4	no	—
221	C₂×C₄×C₇₃	#120	1	2	yes	—
222	C₂×C₄×C₇₃	#120	1	2	yes	—
223	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
224	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
225	C₂×C₄×C₇₃	C₂×#41	1	2	yes	—
226	C₂×C₄×C₇₃	2₋¹⁺⁴	1	2	yes	—
227	C₈×C₇₃	—	2	4	no	—
228	C₈×C₇₃	—	4	2	no	—
229	C₂²×C₇₃	—	4	2	no	—
230	C₂²×C₇₃	—	4	1	no	—
231	C₂²×C₇₃	—	4	2	no	—
232	C₂²×C₇₃	—	4	2	no	—
233	C₂²×C₇₃	—	4	2	no	—
234	C₂²×C₇₃	—	4	1	no	—
235	C₂²×C₇₃	—	4	1	no	—
236	C₂²×C₇₃	—	4	2	no	—
237	C₂²×C₇₃	—	8	2	no	—
238	C₂²×C₇₃	—	8	2	no	—
239	C₂²×C₇₃	C₂×#120	1	1	yes	characteristic
240	C₂²×C₇₃	#532	1	1	yes	characteristic
241	C₂²×C₇₃	#536	1	1	yes	characteristic
242	C₂²×C₇₃	#577	1	2	yes	—
243	C₂²×C₇₃	#577	1	2	yes	—
244	C₄×C₇₃	—	2	2	no	—
245	C₄×C₇₃	—	2	2	no	—
246	C₄×C₇₃	—	4	1	no	—
247	C₄×C₇₃	—	4	2	no	—
248	C₄×C₇₃	—	4	1	no	—
249	C₄×C₇₃	—	4	2	no	—
250	C₄×C₇₃	—	4	2	no	—
251	C₄×C₇₃	—	4	1	no	—
252	C₄×C₇₃	—	8	2	no	—
253	C₄×C₇₃	—	8	2	no	—
254	C₄×C₇₃	#547	1	2	yes	—
255	C₄×C₇₃	#548	1	2	yes	—
256	#25680	C₇₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
257	C₂×C₇₃	—	8	1	no	—
258	C₂×C₇₃	—	8	2	no	—
259	C₂×C₇₃	#2432	1	1	yes	characteristic
260	C₂×C₇₃	#3009	1	1	yes	characteristic
261	C₂×C₇₃	#3010	1	1	yes	characteristic
262	C₂×C₇₃	#3173	1	2	yes	—
263	C₂×C₇₃	#3244	1	2	yes	—
264	C₂×#542	C₂×C₇₃	1	1	yes	characteristic
265	C₂×#498	C₂×C₇₃	1	1	yes	characteristic, complemented
266	C₂×#489	C₂×C₇₃	1	1	yes	characteristic, complemented
267	#2628	C₂×C₇₃	1	1	yes	characteristic, complemented
268	#2035	C₂×C₇₃	1	2	yes	complemented
269	#2034	C₂×C₇₃	1	2	yes	—
270	#1993	C₂×C₇₃	1	1	yes	characteristic, complemented
271	#1958	C₂×C₇₃	1	1	yes	characteristic, complemented
272	#1865	C₂×C₇₃	1	2	yes	complemented
273	#1864	C₂×C₇₃	1	2	yes	complemented
274	#1750	C₂×C₇₃	1	1	yes	characteristic, complemented
275	C₇₃	#25680	1	1	yes	characteristic, direct product factor, Sylow
276	#542	—	2	4	no	—
277	#542	—	2	4	no	—
278	C₂×C₄⋊Q₈	C₂²×C₇₃	1	1	yes	characteristic
279	C₂×C₄⋊Q₈	C₂²×C₇₃	1	1	yes	characteristic
280	C₂×#126	—	2	1	no	—
281	C₂×#124	—	2	1	no	—
282	C₂×#124	C₂²×C₇₃	1	1	yes	characteristic
283	C₂×#123	—	2	1	no	—
284	C₂×C₂²⋊Q₈	—	2	1	no	—
285	C₂×C₂²⋊Q₈	C₂²×C₇₃	1	1	yes	characteristic
286	C₂×#121	C₂²×C₇₃	1	1	yes	characteristic
287	C₂×C₄×Q₈	C₂²×C₇₃	1	1	yes	characteristic
288	C₂×C₄×D₄	C₂²×C₇₃	1	1	yes	characteristic
289	C₂×#117	C₂²×C₇₃	1	1	yes	characteristic
290	#498	—	2	4	no	—
291	#489	—	2	4	no	—
292	C₂×#106	C₂²×C₇₃	1	2	yes	—
293	C₂×#106	C₂²×C₇₃	1	2	yes	—
294	C₂×#103	C₂²×C₇₃	1	2	yes	—
295	C₂×#103	C₂²×C₇₃	1	2	yes	—
296	C₂×#102	C₂²×C₇₃	1	2	yes	—
297	C₂×#102	C₂²×C₇₃	1	2	yes	—
298	C₂×C₂²⋊C₈	C₂²×C₇₃	1	2	yes	—
299	C₂×#97	C₂²×C₇₃	1	1	yes	characteristic
300	C₂×C₄×C₈	C₂²×C₇₃	1	1	yes	characteristic
301	#400	—	2	1	no	—
302	#399	—	2	1	no	—
303	#395	—	2	1	no	—
304	#393	—	2	1	no	—
305	#389	C₂²×C₇₃	1	2	yes	—
306	#382	C₂²×C₇₃	1	1	yes	characteristic
307	#380	C₂²×C₇₃	1	2	yes	—
308	#340	C₂²×C₇₃	1	2	yes	—
309	#340	C₂²×C₇₃	1	2	yes	—
310	#336	C₂²×C₇₃	1	2	yes	—
311	C₂²×Q₈	—	2	1	no	—
312	C₂²×Q₈	—	2	1	no	—
313	C₂²×Q₈	C₂³×C₇₃	1	1	yes	characteristic
314	C₂²×D₄	—	2	1	no	—
315	C₂²×D₄	C₂³×C₇₃	1	1	yes	characteristic
316	C₂³×C₄	—	2	1	no	—
317	C₂³×C₄	C₂³×C₇₃	1	1	yes	characteristic
318	C₂²×C₈	C₂³×C₇₃	1	2	yes	—
319	C₂²×C₈	C₂³×C₇₃	1	2	yes	—
320	C₄⋊Q₈	—	2	2	no	—
321	C₄⋊Q₈	—	2	2	no	—
322	C₄⋊Q₈	—	2	2	no	—
323	C₄⋊Q₈	D₄×C₇₃	1	4	yes	—
324	#126	—	2	8	no	—
325	#124	—	2	8	no	—
326	#124	—	2	2	no	—
327	#124	D₄×C₇₃	1	4	yes	—
328	#123	—	2	8	no	—
329	C₂²⋊Q₈	—	2	8	no	—
330	C₂²⋊Q₈	—	2	2	no	—
331	C₂²⋊Q₈	—	2	2	no	—
332	#121	—	2	2	no	—
333	#121	—	2	2	no	—
334	C₄×Q₈	—	2	2	no	—
335	C₄×Q₈	—	2	2	no	—
336	C₄×D₄	—	2	2	no	—
337	C₄×D₄	—	2	2	no	—
338	#117	—	2	2	no	—
339	#117	—	2	2	no	—
340	C₂×C₄⋊C₄	—	2	1	no	—
341	C₂×C₄⋊C₄	—	2	1	no	—
342	C₂×C₄⋊C₄	—	2	1	no	—
343	C₂×C₄⋊C₄	—	2	1	no	—
344	C₂×C₄⋊C₄	—	2	2	no	—
345	C₂×C₄⋊C₄	D₄×C₇₃	1	1	yes	characteristic
346	C₂×C₄⋊C₄	D₄×C₇₃	1	1	yes	characteristic
347	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
348	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
349	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
350	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
351	C₂×C₂²⋊C₄	—	2	1	no	—
352	C₂×C₂²⋊C₄	—	2	1	no	—
353	C₂×C₂²⋊C₄	—	2	1	no	—
354	C₂×C₂²⋊C₄	—	2	1	no	—
355	C₂×C₂²⋊C₄	—	2	1	no	—
356	C₂×C₂²⋊C₄	—	2	2	no	—
357	C₂×C₂²⋊C₄	D₄×C₇₃	1	1	yes	characteristic
358	C₂×C₂²⋊C₄	D₄×C₇₃	1	1	yes	characteristic
359	C₂×C₄²	—	2	1	no	—
360	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
361	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
362	#106	—	2	4	no	—
363	#106	—	2	4	no	—
364	#103	—	2	4	no	—
365	#103	—	2	4	no	—
366	#102	—	2	4	no	—
367	#102	—	2	4	no	—
368	C₂²⋊C₈	—	2	4	no	—
369	#97	—	2	2	no	—
370	C₄×C₈	—	2	2	no	—
371	#95	—	2	2	no	—
372	#95	—	2	1	no	—
373	#95	—	2	1	no	—
374	#95	—	2	2	no	—
375	C₂⁴	—	2	1	no	—
376	C₂⁴	C₂×D₄×C₇₃	1	1	yes	characteristic
377	C₂×Q₈	—	2	4	no	—
378	C₂×Q₈	—	2	1	no	—
379	C₂×Q₈	—	2	2	no	—
380	C₂×Q₈	—	2	2	no	—
381	C₂×Q₈	—	4	2	no	—
382	C₂×Q₈	—	8	2	no	—
383	C₂×Q₈	—	8	2	no	—
384	C₂×Q₈	C₂×D₄×C₇₃	1	2	yes	—
385	C₂×D₄	—	2	4	no	—
386	C₂×D₄	—	2	1	no	—
387	C₂×D₄	—	2	2	no	—
388	C₂×D₄	—	2	2	no	—
389	C₂×D₄	—	8	2	no	—
390	C₂×D₄	C₂×D₄×C₇₃	1	2	yes	—
391	C₂²×C₄	—	2	1	no	—
392	C₂²×C₄	—	2	1	no	—
393	C₂²×C₄	—	2	1	no	—
394	C₂²×C₄	—	2	4	no	—
395	C₂²×C₄	—	2	1	no	—
396	C₂²×C₄	—	2	1	no	—
397	C₂²×C₄	—	2	2	no	—
398	C₂²×C₄	—	2	2	no	—
399	C₂²×C₄	—	2	2	no	—
400	C₂²×C₄	—	2	2	no	—
401	C₂²×C₄	—	8	2	no	—
402	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
403	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
404	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
405	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
406	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
407	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
408	C₂×C₈	—	2	2	no	—
409	C₂×C₈	—	2	2	no	—
410	C₂×C₈	—	2	2	no	—
411	C₂×C₈	—	2	2	no	—
412	C₂×C₈	—	2	2	no	—
413	C₂×C₈	#41×C₇₃	1	4	yes	—
414	C₄⋊C₄	—	2	4	no	—
415	C₄⋊C₄	—	2	4	no	—
416	C₄⋊C₄	—	2	4	no	—
417	C₄⋊C₄	—	2	2	no	—
418	C₄⋊C₄	—	2	2	no	—
419	C₄⋊C₄	—	2	1	no	—
420	C₄⋊C₄	—	2	1	no	—
421	C₄⋊C₄	—	2	2	no	—
422	C₄⋊C₄	—	2	2	no	—
423	C₄⋊C₄	—	2	2	no	—
424	C₄⋊C₄	—	2	2	no	—
425	C₄⋊C₄	—	4	2	no	—
426	C₄⋊C₄	—	8	2	no	—
427	C₄⋊C₄	C₂×D₄×C₇₃	1	2	yes	—
428	C₄⋊C₄	C₂×D₄×C₇₃	1	2	yes	—
429	C₂²⋊C₄	—	2	4	no	—
430	C₂²⋊C₄	—	2	4	no	—
431	C₂²⋊C₄	—	2	4	no	—
432	C₂²⋊C₄	—	2	4	no	—
433	C₂²⋊C₄	—	2	4	no	—
434	C₂²⋊C₄	—	2	2	no	—
435	C₂²⋊C₄	—	2	2	no	—
436	C₂²⋊C₄	—	8	2	no	—
437	C₄²	—	2	4	no	—
438	C₄²	—	2	1	no	—
439	C₄²	—	2	1	no	—
440	C₄²	C₂×D₄×C₇₃	1	2	yes	—
441	C₄²	C₂×D₄×C₇₃	1	2	yes	—
442	C₂³	—	2	1	no	—
443	C₂³	—	2	2	no	—
444	C₂³	—	2	1	no	—
445	C₂³	—	2	1	no	—
446	C₂³	—	2	2	no	—
447	C₂³	—	2	2	no	—
448	C₂³	—	4	1	no	—
449	C₂³	—	4	1	no	—
450	C₂³	—	4	2	no	—
451	C₂³	—	4	2	no	—
452	C₂³	C₂²×D₄×C₇₃	1	1	yes	characteristic
453	Q₈	—	2	4	no	—
454	Q₈	—	4	2	no	—
455	Q₈	—	8	4	no	—
456	Q₈	—	8	4	no	—
457	D₄	—	2	4	no	—
458	D₄	—	4	2	no	—
459	D₄	—	8	4	no	—
460	C₂×C₄	—	2	2	no	—
461	C₂×C₄	—	2	2	no	—
462	C₂×C₄	—	2	1	no	—
463	C₂×C₄	—	2	2	no	—
464	C₂×C₄	—	2	1	no	—
465	C₂×C₄	—	2	2	no	—
466	C₂×C₄	—	2	1	no	—
467	C₂×C₄	—	2	2	no	—
468	C₂×C₄	—	2	1	no	—
469	C₂×C₄	—	2	1	no	—
470	C₂×C₄	—	2	2	no	—
471	C₂×C₄	—	2	2	no	—
472	C₂×C₄	—	4	1	no	—
473	C₂×C₄	—	4	1	no	—
474	C₂×C₄	—	4	2	no	—
475	C₂×C₄	—	4	2	no	—
476	C₂×C₄	—	4	2	no	—
477	C₂×C₄	—	4	2	no	—
478	C₂×C₄	—	4	2	no	—
479	C₂×C₄	—	4	2	no	—
480	C₂×C₄	—	4	2	no	—
481	C₂×C₄	—	4	2	no	—
482	C₂×C₄	—	4	2	no	—
483	C₂×C₄	—	4	2	no	—
484	C₂×C₄	—	8	4	no	—
485	C₂×C₄	#120×C₇₃	1	2	yes	—
486	C₂×C₄	#120×C₇₃	1	2	yes	—
487	C₂×C₄	C₂²×D₄×C₇₃	1	1	yes	characteristic
488	C₂×C₄	C₂²×D₄×C₇₃	1	1	yes	characteristic
489	C₂×C₄	C₂×#41×C₇₃	1	2	yes	—
490	C₂×C₄	2₋¹⁺⁴×C₇₃	1	2	yes	—
491	C₈	—	2	4	no	—
492	C₈	—	4	2	no	—
493	C₂²	—	4	2	no	—
494	C₂²	—	4	2	no	—
495	C₂²	—	4	1	no	—
496	C₂²	—	4	1	no	—
497	C₂²	—	4	2	no	—
498	C₂²	—	4	2	no	—
499	C₂²	—	4	1	no	—
500	C₂²	—	4	2	no	—
501	C₂²	—	8	2	no	—
502	C₂²	—	8	2	no	—
503	C₂²	C₂×#120×C₇₃	1	1	yes	characteristic
504	C₂²	#532×C₇₃	1	1	yes	characteristic
505	C₂²	#536×C₇₃	1	1	yes	characteristic
506	C₂²	#577×C₇₃	1	2	yes	—
507	C₂²	#577×C₇₃	1	2	yes	—
508	C₄	—	2	2	no	—
509	C₄	—	2	2	no	—
510	C₄	—	4	1	no	—
511	C₄	—	4	2	no	—
512	C₄	—	4	2	no	—
513	C₄	—	4	1	no	—
514	C₄	—	4	1	no	—
515	C₄	—	4	2	no	—
516	C₄	—	8	2	no	—
517	C₄	—	8	2	no	—
518	C₄	#547×C₇₃	1	2	yes	—
519	C₄	#548×C₇₃	1	2	yes	—
520	C₂	—	8	1	no	—
521	C₂	—	8	2	no	—
522	C₂	C₇₃×#2432	1	1	yes	characteristic
523	C₂	C₇₃×#3009	1	1	yes	characteristic
524	C₂	C₇₃×#3010	1	1	yes	characteristic
525	C₂	C₇₃×#3173	1	2	yes	—
526	C₂	C₇₃×#3244	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₇₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₇₃
prime radical	C₂×#121×C₇₃	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₇₃ ◁ C₂×#117×C₇₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×#498×C₇₃	C₂	semidirect
3. C₂×#489×C₇₃	C₂	semidirect
4. C₇₃×#2628	C₂	semidirect
5. C₇₃×#2035	C₂	semidirect
7. C₇₃×#1993	C₂	semidirect
8. C₇₃×#1958	C₂	semidirect
9. C₇₃×#1865	C₂	semidirect
10. C₇₃×#1864	C₂	semidirect
11. C₇₃×#1750	C₂	semidirect
256. #25680	C₇₃	direct (N × H)
265. C₂×#498	C₂×C₇₃	semidirect
266. C₂×#489	C₂×C₇₃	semidirect
267. #2628	C₂×C₇₃	semidirect
268. #2035	C₂×C₇₃	semidirect
270. #1993	C₂×C₇₃	semidirect
271. #1958	C₂×C₇₃	semidirect
272. #1865	C₂×C₇₃	semidirect
273. #1864	C₂×C₇₃	semidirect
274. #1750	C₂×C₇₃	semidirect
275. C₇₃	#25680	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×#542×C₇₃	2
C₂×#498×C₇₃	2
C₂×#489×C₇₃	2
C₇₃×#2628	2
C₇₃×#2035	2
C₇₃×#2034	2
C₇₃×#1993	2
C₇₃×#1958	2
C₇₃×#1865	2
C₇₃×#1864	2
C₇₃×#1750	2
#25680	73

Subgroups — C73×#25680 #32935084

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₃×#25680 #32935084