Subgroups — C₇₃×#25660 #32935064

Order 18688.

1092 conjugacy classes of subgroups.

The subgroup lattice has 552 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#559×C₇₃	C₂	1	1	yes	maximal, characteristic
2	C₂×#489×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#474×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₇₃×#2567	C₂	1	1	yes	maximal, characteristic, complemented
5	C₇₃×#2042	C₂	1	2	yes	maximal, complemented
6	C₇₃×#2041	C₂	1	2	yes	maximal
7	C₇₃×#1985	C₂	1	1	yes	maximal, characteristic, complemented
8	C₇₃×#1983	C₂	1	1	yes	maximal, characteristic, complemented
9	C₇₃×#1863	C₂	1	2	yes	maximal, complemented
10	C₇₃×#1862	C₂	1	2	yes	maximal, complemented
11	C₇₃×#1762	C₂	1	1	yes	maximal, characteristic, complemented
12	#559×C₇₃	—	2	4	no	—
13	#559×C₇₃	—	2	4	no	—
14	C₂×C₄⋊Q₈×C₇₃	C₂²	1	1	yes	characteristic
15	C₂×#127×C₇₃	C₂²	1	1	yes	characteristic
16	C₂×#124×C₇₃	—	2	1	no	—
17	C₂×#124×C₇₃	C₂²	1	1	yes	characteristic
18	C₂×#124×C₇₃	C₂²	1	1	yes	characteristic
19	C₂×#123×C₇₃	—	2	1	no	—
20	C₂×#123×C₇₃	—	2	1	no	—
21	C₂×C₄×Q₈×C₇₃	C₂²	1	1	yes	characteristic
22	C₂×C₄×Q₈×C₇₃	C₂²	1	1	yes	characteristic
23	C₂×C₄×D₄×C₇₃	—	2	1	no	—
24	C₂×C₄×D₄×C₇₃	C₂²	1	1	yes	characteristic
25	C₂×C₄×D₄×C₇₃	C₂²	1	1	yes	characteristic
26	#489×C₇₃	—	2	4	no	—
27	#474×C₇₃	—	2	4	no	—
28	C₂×#107×C₇₃	C₂²	1	2	yes	—
29	C₂×C₄⋊C₈×C₇₃	C₂²	1	1	yes	characteristic
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×#102×C₇₃	C₂²	1	2	yes	—
35	C₂×#102×C₇₃	C₂²	1	2	yes	—
36	C₂×#97×C₇₃	C₂²	1	1	yes	characteristic
37	#395×C₇₃	—	2	1	no	—
38	#395×C₇₃	—	2	1	no	—
39	#391×C₇₃	—	2	1	no	—
40	#389×C₇₃	C₂²	1	2	yes	—
41	#389×C₇₃	C₂²	1	2	yes	—
42	#384×C₇₃	—	2	1	no	—
43	C₄×C₄⋊C₄×C₇₃	C₂²	1	1	yes	characteristic
44	#340×C₇₃	C₂²	1	2	yes	—
45	#336×C₇₃	C₂²	1	2	yes	—
46	#336×C₇₃	C₂²	1	2	yes	—
47	C₂²×Q₈×C₇₃	—	2	1	no	—
48	C₂²×Q₈×C₇₃	D₄	1	1	yes	characteristic
49	C₂²×Q₈×C₇₃	C₂³	1	1	yes	characteristic
50	C₂²×D₄×C₇₃	—	2	1	no	—
51	C₂²×D₄×C₇₃	—	2	1	no	—
52	C₂²×D₄×C₇₃	C₂³	1	1	yes	characteristic
53	C₂²×D₄×C₇₃	C₂³	1	1	yes	characteristic
54	C₂³×C₄×C₇₃	—	2	1	no	—
55	C₂³×C₄×C₇₃	—	2	1	no	—
56	C₂²×C₈×C₇₃	C₂³	1	2	yes	—
57	C₂²×C₈×C₇₃	C₂³	1	2	yes	—
58	C₄⋊Q₈×C₇₃	—	2	2	no	—
59	C₄⋊Q₈×C₇₃	—	2	2	no	—
60	#127×C₇₃	—	2	2	no	—
61	#127×C₇₃	—	2	2	no	—
62	#124×C₇₃	—	2	8	no	—
63	#124×C₇₃	—	2	2	no	—
64	#124×C₇₃	—	2	2	no	—
65	#124×C₇₃	—	2	2	no	—
66	#124×C₇₃	D₄	1	4	yes	—
67	#123×C₇₃	—	2	8	no	—
68	#123×C₇₃	—	2	8	no	—
69	C₄×Q₈×C₇₃	—	2	2	no	—
70	C₄×Q₈×C₇₃	—	2	2	no	—
71	C₄×Q₈×C₇₃	—	2	2	no	—
72	C₄×Q₈×C₇₃	—	2	2	no	—
73	C₄×D₄×C₇₃	—	2	8	no	—
74	C₄×D₄×C₇₃	—	2	2	no	—
75	C₄×D₄×C₇₃	—	2	2	no	—
76	C₄×D₄×C₇₃	—	2	2	no	—
77	C₄×D₄×C₇₃	D₄	1	4	yes	—
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	—	2	2	no	—
82	C₂×C₄⋊C₄×C₇₃	D₄	1	1	yes	characteristic
83	C₂×C₄⋊C₄×C₇₃	D₄	1	1	yes	characteristic
84	C₂×C₄⋊C₄×C₇₃	D₄	1	1	yes	characteristic
85	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
86	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
87	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
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	1	no	—
93	C₂×C₂²⋊C₄×C₇₃	—	2	1	no	—
94	C₂×C₄²×C₇₃	—	2	1	no	—
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	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
99	#107×C₇₃	—	2	4	no	—
100	C₄⋊C₈×C₇₃	—	2	2	no	—
101	#103×C₇₃	—	2	4	no	—
102	#103×C₇₃	—	2	4	no	—
103	#102×C₇₃	—	2	4	no	—
104	#102×C₇₃	—	2	4	no	—
105	#102×C₇₃	—	2	4	no	—
106	#102×C₇₃	—	2	4	no	—
107	#97×C₇₃	—	2	2	no	—
108	#95×C₇₃	—	2	1	no	—
109	#95×C₇₃	—	2	2	no	—
110	#95×C₇₃	—	2	2	no	—
111	C₂⁴×C₇₃	—	2	1	no	—
112	C₂⁴×C₇₃	—	2	1	no	—
113	C₂×Q₈×C₇₃	—	2	2	no	—
114	C₂×Q₈×C₇₃	—	2	2	no	—
115	C₂×Q₈×C₇₃	—	2	1	no	—
116	C₂×Q₈×C₇₃	—	2	2	no	—
117	C₂×Q₈×C₇₃	—	2	2	no	—
118	C₂×Q₈×C₇₃	—	4	1	no	—
119	C₂×Q₈×C₇₃	—	4	2	no	—
120	C₂×Q₈×C₇₃	—	8	2	no	—
121	C₂×Q₈×C₇₃	C₂×D₄	1	2	yes	—
122	C₂×D₄×C₇₃	—	2	4	no	—
123	C₂×D₄×C₇₃	—	2	4	no	—
124	C₂×D₄×C₇₃	—	2	1	no	—
125	C₂×D₄×C₇₃	—	2	1	no	—
126	C₂×D₄×C₇₃	—	2	2	no	—
127	C₂×D₄×C₇₃	—	2	2	no	—
128	C₂×D₄×C₇₃	—	2	2	no	—
129	C₂×D₄×C₇₃	—	2	2	no	—
130	C₂×D₄×C₇₃	—	4	2	no	—
131	C₂×D₄×C₇₃	—	4	2	no	—
132	C₂×D₄×C₇₃	—	8	2	no	—
133	C₂×D₄×C₇₃	C₂×D₄	1	2	yes	—
134	C₂×D₄×C₇₃	C₂×D₄	1	2	yes	—
135	C₂²×C₄×C₇₃	—	2	2	no	—
136	C₂²×C₄×C₇₃	—	2	1	no	—
137	C₂²×C₄×C₇₃	—	2	1	no	—
138	C₂²×C₄×C₇₃	—	2	4	no	—
139	C₂²×C₄×C₇₃	—	2	4	no	—
140	C₂²×C₄×C₇₃	—	2	2	no	—
141	C₂²×C₄×C₇₃	—	8	2	no	—
142	C₂²×C₄×C₇₃	—	8	2	no	—
143	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
144	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
145	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
146	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
147	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
148	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
149	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
150	C₂×C₈×C₇₃	—	2	2	no	—
151	C₂×C₈×C₇₃	—	2	2	no	—
152	C₂×C₈×C₇₃	—	2	2	no	—
153	C₂×C₈×C₇₃	—	2	2	no	—
154	C₂×C₈×C₇₃	—	2	2	no	—
155	C₂×C₈×C₇₃	—	2	2	no	—
156	C₄⋊C₄×C₇₃	—	2	4	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	1	no	—
161	C₄⋊C₄×C₇₃	—	2	2	no	—
162	C₄⋊C₄×C₇₃	—	2	2	no	—
163	C₄⋊C₄×C₇₃	—	2	2	no	—
164	C₄⋊C₄×C₇₃	—	4	2	no	—
165	C₄⋊C₄×C₇₃	—	8	2	no	—
166	C₄⋊C₄×C₇₃	—	8	2	no	—
167	C₄⋊C₄×C₇₃	C₂×D₄	1	2	yes	—
168	C₄⋊C₄×C₇₃	#41	1	4	yes	—
169	C₂²⋊C₄×C₇₃	—	2	4	no	—
170	C₂²⋊C₄×C₇₃	—	2	4	no	—
171	C₂²⋊C₄×C₇₃	—	2	4	no	—
172	C₂²⋊C₄×C₇₃	—	2	4	no	—
173	C₂²⋊C₄×C₇₃	—	2	4	no	—
174	C₂²⋊C₄×C₇₃	—	2	4	no	—
175	C₄²×C₇₃	—	2	4	no	—
176	C₄²×C₇₃	—	2	1	no	—
177	C₄²×C₇₃	—	2	1	no	—
178	C₄²×C₇₃	—	2	1	no	—
179	C₄²×C₇₃	—	2	1	no	—
180	C₄²×C₇₃	—	4	2	no	—
181	C₄²×C₇₃	C₂×D₄	1	2	yes	—
182	C₄²×C₇₃	C₂×D₄	1	2	yes	—
183	C₂³×C₇₃	—	2	2	no	—
184	C₂³×C₇₃	—	2	2	no	—
185	C₂³×C₇₃	—	4	2	no	—
186	C₂³×C₇₃	—	4	2	no	—
187	C₂³×C₇₃	—	4	1	no	—
188	C₂³×C₇₃	—	4	1	no	—
189	C₂³×C₇₃	—	4	1	no	—
190	C₂³×C₇₃	—	4	1	no	—
191	C₂³×C₇₃	—	4	2	no	—
192	C₂³×C₇₃	—	4	2	no	—
193	C₂³×C₇₃	C₂²×D₄	1	1	yes	characteristic
194	Q₈×C₇₃	—	2	4	no	—
195	Q₈×C₇₃	—	4	4	no	—
196	Q₈×C₇₃	—	4	1	no	—
197	Q₈×C₇₃	—	4	1	no	—
198	Q₈×C₇₃	—	8	4	no	—
199	D₄×C₇₃	—	2	2	no	—
200	D₄×C₇₃	—	2	2	no	—
201	D₄×C₇₃	—	2	4	no	—
202	D₄×C₇₃	—	4	8	no	—
203	D₄×C₇₃	—	4	1	no	—
204	D₄×C₇₃	—	4	1	no	—
205	D₄×C₇₃	—	4	2	no	—
206	D₄×C₇₃	—	8	4	no	—
207	C₂×C₄×C₇₃	—	2	1	no	—
208	C₂×C₄×C₇₃	—	2	1	no	—
209	C₂×C₄×C₇₃	—	2	1	no	—
210	C₂×C₄×C₇₃	—	2	1	no	—
211	C₂×C₄×C₇₃	—	2	2	no	—
212	C₂×C₄×C₇₃	—	2	2	no	—
213	C₂×C₄×C₇₃	—	2	1	no	—
214	C₂×C₄×C₇₃	—	2	1	no	—
215	C₂×C₄×C₇₃	—	2	2	no	—
216	C₂×C₄×C₇₃	—	2	1	no	—
217	C₂×C₄×C₇₃	—	2	4	no	—
218	C₂×C₄×C₇₃	—	2	1	no	—
219	C₂×C₄×C₇₃	—	2	1	no	—
220	C₂×C₄×C₇₃	—	2	2	no	—
221	C₂×C₄×C₇₃	—	2	2	no	—
222	C₂×C₄×C₇₃	—	4	2	no	—
223	C₂×C₄×C₇₃	—	4	2	no	—
224	C₂×C₄×C₇₃	—	4	2	no	—
225	C₂×C₄×C₇₃	—	4	2	no	—
226	C₂×C₄×C₇₃	—	4	2	no	—
227	C₂×C₄×C₇₃	—	4	2	no	—
228	C₂×C₄×C₇₃	—	4	2	no	—
229	C₂×C₄×C₇₃	—	8	4	no	—
230	C₂×C₄×C₇₃	—	8	4	no	—
231	C₂×C₄×C₇₃	#120	1	2	yes	—
232	C₂×C₄×C₇₃	#120	1	2	yes	—
233	C₂×C₄×C₇₃	#137	1	2	yes	—
234	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
235	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
236	C₂×C₄×C₇₃	C₂×#41	1	2	yes	—
237	C₂×C₄×C₇₃	2₋¹⁺⁴	1	2	yes	—
238	C₈×C₇₃	—	4	2	no	—
239	C₈×C₇₃	—	4	2	no	—
240	C₂²×C₇₃	—	4	2	no	—
241	C₂²×C₇₃	—	4	2	no	—
242	C₂²×C₇₃	—	4	2	no	—
243	C₂²×C₇₃	—	4	2	no	—
244	C₂²×C₇₃	—	4	2	no	—
245	C₂²×C₇₃	—	4	2	no	—
246	C₂²×C₇₃	—	8	2	no	—
247	C₂²×C₇₃	—	8	2	no	—
248	C₂²×C₇₃	—	8	2	no	—
249	C₂²×C₇₃	—	8	2	no	—
250	C₂²×C₇₃	C₂×#120	1	1	yes	characteristic
251	C₂²×C₇₃	#548	1	2	yes	—
252	C₂²×C₇₃	C₂×#137	1	1	yes	characteristic
253	C₂²×C₇₃	#575	1	1	yes	characteristic
254	C₂²×C₇₃	#576	1	2	yes	—
255	C₄×C₇₃	—	2	2	no	—
256	C₄×C₇₃	—	2	2	no	—
257	C₄×C₇₃	—	2	2	no	—
258	C₄×C₇₃	—	4	4	no	—
259	C₄×C₇₃	—	4	2	no	—
260	C₄×C₇₃	—	4	1	no	—
261	C₄×C₇₃	—	4	1	no	—
262	C₄×C₇₃	—	4	1	no	—
263	C₄×C₇₃	—	4	2	no	—
264	C₄×C₇₃	—	8	2	no	—
265	C₄×C₇₃	#532	1	1	yes	characteristic
266	C₄×C₇₃	#536	1	1	yes	characteristic
267	C₄×C₇₃	#547	1	2	yes	—
268	#25660	C₇₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
269	C₂×C₇₃	—	8	2	no	—
270	C₂×C₇₃	—	8	2	no	—
271	C₂×C₇₃	#2432	1	1	yes	characteristic
272	C₂×C₇₃	#3007	1	1	yes	characteristic
273	C₂×C₇₃	#3008	1	1	yes	characteristic
274	C₂×C₇₃	#3370	1	2	yes	—
275	C₂×C₇₃	#3375	1	2	yes	—
276	C₂×#559	C₂×C₇₃	1	1	yes	characteristic
277	C₂×#489	C₂×C₇₃	1	1	yes	characteristic, complemented
278	C₂×#474	C₂×C₇₃	1	1	yes	characteristic, complemented
279	#2567	C₂×C₇₃	1	1	yes	characteristic, complemented
280	#2042	C₂×C₇₃	1	2	yes	complemented
281	#2041	C₂×C₇₃	1	2	yes	—
282	#1985	C₂×C₇₃	1	1	yes	characteristic, complemented
283	#1983	C₂×C₇₃	1	1	yes	characteristic, complemented
284	#1863	C₂×C₇₃	1	2	yes	complemented
285	#1862	C₂×C₇₃	1	2	yes	complemented
286	#1762	C₂×C₇₃	1	1	yes	characteristic, complemented
287	C₇₃	#25660	1	1	yes	characteristic, direct product factor, Sylow
288	#559	—	2	4	no	—
289	#559	—	2	4	no	—
290	C₂×C₄⋊Q₈	C₂²×C₇₃	1	1	yes	characteristic
291	C₂×#127	C₂²×C₇₃	1	1	yes	characteristic
292	C₂×#124	—	2	1	no	—
293	C₂×#124	C₂²×C₇₃	1	1	yes	characteristic
294	C₂×#124	C₂²×C₇₃	1	1	yes	characteristic
295	C₂×#123	—	2	1	no	—
296	C₂×#123	—	2	1	no	—
297	C₂×C₄×Q₈	C₂²×C₇₃	1	1	yes	characteristic
298	C₂×C₄×Q₈	C₂²×C₇₃	1	1	yes	characteristic
299	C₂×C₄×D₄	—	2	1	no	—
300	C₂×C₄×D₄	C₂²×C₇₃	1	1	yes	characteristic
301	C₂×C₄×D₄	C₂²×C₇₃	1	1	yes	characteristic
302	#489	—	2	4	no	—
303	#474	—	2	4	no	—
304	C₂×#107	C₂²×C₇₃	1	2	yes	—
305	C₂×C₄⋊C₈	C₂²×C₇₃	1	1	yes	characteristic
306	C₂×#103	C₂²×C₇₃	1	2	yes	—
307	C₂×#103	C₂²×C₇₃	1	2	yes	—
308	C₂×#102	C₂²×C₇₃	1	2	yes	—
309	C₂×#102	C₂²×C₇₃	1	2	yes	—
310	C₂×#102	C₂²×C₇₃	1	2	yes	—
311	C₂×#102	C₂²×C₇₃	1	2	yes	—
312	C₂×#97	C₂²×C₇₃	1	1	yes	characteristic
313	#395	—	2	1	no	—
314	#395	—	2	1	no	—
315	#391	—	2	1	no	—
316	#389	C₂²×C₇₃	1	2	yes	—
317	#389	C₂²×C₇₃	1	2	yes	—
318	#384	—	2	1	no	—
319	C₄×C₄⋊C₄	C₂²×C₇₃	1	1	yes	characteristic
320	#340	C₂²×C₇₃	1	2	yes	—
321	#336	C₂²×C₇₃	1	2	yes	—
322	#336	C₂²×C₇₃	1	2	yes	—
323	C₂²×Q₈	—	2	1	no	—
324	C₂²×Q₈	D₄×C₇₃	1	1	yes	characteristic
325	C₂²×Q₈	C₂³×C₇₃	1	1	yes	characteristic
326	C₂²×D₄	—	2	1	no	—
327	C₂²×D₄	—	2	1	no	—
328	C₂²×D₄	C₂³×C₇₃	1	1	yes	characteristic
329	C₂²×D₄	C₂³×C₇₃	1	1	yes	characteristic
330	C₂³×C₄	—	2	1	no	—
331	C₂³×C₄	—	2	1	no	—
332	C₂²×C₈	C₂³×C₇₃	1	2	yes	—
333	C₂²×C₈	C₂³×C₇₃	1	2	yes	—
334	C₄⋊Q₈	—	2	2	no	—
335	C₄⋊Q₈	—	2	2	no	—
336	#127	—	2	2	no	—
337	#127	—	2	2	no	—
338	#124	—	2	8	no	—
339	#124	—	2	2	no	—
340	#124	—	2	2	no	—
341	#124	—	2	2	no	—
342	#124	D₄×C₇₃	1	4	yes	—
343	#123	—	2	8	no	—
344	#123	—	2	8	no	—
345	C₄×Q₈	—	2	2	no	—
346	C₄×Q₈	—	2	2	no	—
347	C₄×Q₈	—	2	2	no	—
348	C₄×Q₈	—	2	2	no	—
349	C₄×D₄	—	2	8	no	—
350	C₄×D₄	—	2	2	no	—
351	C₄×D₄	—	2	2	no	—
352	C₄×D₄	—	2	2	no	—
353	C₄×D₄	D₄×C₇₃	1	4	yes	—
354	C₂×C₄⋊C₄	—	2	1	no	—
355	C₂×C₄⋊C₄	—	2	1	no	—
356	C₂×C₄⋊C₄	—	2	2	no	—
357	C₂×C₄⋊C₄	—	2	2	no	—
358	C₂×C₄⋊C₄	D₄×C₇₃	1	1	yes	characteristic
359	C₂×C₄⋊C₄	D₄×C₇₃	1	1	yes	characteristic
360	C₂×C₄⋊C₄	D₄×C₇₃	1	1	yes	characteristic
361	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
362	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
363	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
364	C₂×C₂²⋊C₄	—	2	1	no	—
365	C₂×C₂²⋊C₄	—	2	1	no	—
366	C₂×C₂²⋊C₄	—	2	1	no	—
367	C₂×C₂²⋊C₄	—	2	1	no	—
368	C₂×C₂²⋊C₄	—	2	1	no	—
369	C₂×C₂²⋊C₄	—	2	1	no	—
370	C₂×C₄²	—	2	1	no	—
371	C₂×C₄²	—	2	1	no	—
372	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
373	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
374	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
375	#107	—	2	4	no	—
376	C₄⋊C₈	—	2	2	no	—
377	#103	—	2	4	no	—
378	#103	—	2	4	no	—
379	#102	—	2	4	no	—
380	#102	—	2	4	no	—
381	#102	—	2	4	no	—
382	#102	—	2	4	no	—
383	#97	—	2	2	no	—
384	#95	—	2	1	no	—
385	#95	—	2	2	no	—
386	#95	—	2	2	no	—
387	C₂⁴	—	2	1	no	—
388	C₂⁴	—	2	1	no	—
389	C₂×Q₈	—	2	2	no	—
390	C₂×Q₈	—	2	2	no	—
391	C₂×Q₈	—	2	1	no	—
392	C₂×Q₈	—	2	2	no	—
393	C₂×Q₈	—	2	2	no	—
394	C₂×Q₈	—	4	1	no	—
395	C₂×Q₈	—	4	2	no	—
396	C₂×Q₈	—	8	2	no	—
397	C₂×Q₈	C₂×D₄×C₇₃	1	2	yes	—
398	C₂×D₄	—	2	4	no	—
399	C₂×D₄	—	2	4	no	—
400	C₂×D₄	—	2	1	no	—
401	C₂×D₄	—	2	1	no	—
402	C₂×D₄	—	2	2	no	—
403	C₂×D₄	—	2	2	no	—
404	C₂×D₄	—	2	2	no	—
405	C₂×D₄	—	2	2	no	—
406	C₂×D₄	—	4	2	no	—
407	C₂×D₄	—	4	2	no	—
408	C₂×D₄	—	8	2	no	—
409	C₂×D₄	C₂×D₄×C₇₃	1	2	yes	—
410	C₂×D₄	C₂×D₄×C₇₃	1	2	yes	—
411	C₂²×C₄	—	2	2	no	—
412	C₂²×C₄	—	2	1	no	—
413	C₂²×C₄	—	2	1	no	—
414	C₂²×C₄	—	2	4	no	—
415	C₂²×C₄	—	2	4	no	—
416	C₂²×C₄	—	2	2	no	—
417	C₂²×C₄	—	8	2	no	—
418	C₂²×C₄	—	8	2	no	—
419	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
420	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
421	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
422	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
423	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
424	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
425	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
426	C₂×C₈	—	2	2	no	—
427	C₂×C₈	—	2	2	no	—
428	C₂×C₈	—	2	2	no	—
429	C₂×C₈	—	2	2	no	—
430	C₂×C₈	—	2	2	no	—
431	C₂×C₈	—	2	2	no	—
432	C₄⋊C₄	—	2	4	no	—
433	C₄⋊C₄	—	2	2	no	—
434	C₄⋊C₄	—	2	2	no	—
435	C₄⋊C₄	—	2	2	no	—
436	C₄⋊C₄	—	2	1	no	—
437	C₄⋊C₄	—	2	2	no	—
438	C₄⋊C₄	—	2	2	no	—
439	C₄⋊C₄	—	2	2	no	—
440	C₄⋊C₄	—	4	2	no	—
441	C₄⋊C₄	—	8	2	no	—
442	C₄⋊C₄	—	8	2	no	—
443	C₄⋊C₄	C₂×D₄×C₇₃	1	2	yes	—
444	C₄⋊C₄	#41×C₇₃	1	4	yes	—
445	C₂²⋊C₄	—	2	4	no	—
446	C₂²⋊C₄	—	2	4	no	—
447	C₂²⋊C₄	—	2	4	no	—
448	C₂²⋊C₄	—	2	4	no	—
449	C₂²⋊C₄	—	2	4	no	—
450	C₂²⋊C₄	—	2	4	no	—
451	C₄²	—	2	4	no	—
452	C₄²	—	2	1	no	—
453	C₄²	—	2	1	no	—
454	C₄²	—	2	1	no	—
455	C₄²	—	2	1	no	—
456	C₄²	—	4	2	no	—
457	C₄²	C₂×D₄×C₇₃	1	2	yes	—
458	C₄²	C₂×D₄×C₇₃	1	2	yes	—
459	C₂³	—	2	2	no	—
460	C₂³	—	2	2	no	—
461	C₂³	—	4	2	no	—
462	C₂³	—	4	2	no	—
463	C₂³	—	4	1	no	—
464	C₂³	—	4	1	no	—
465	C₂³	—	4	1	no	—
466	C₂³	—	4	1	no	—
467	C₂³	—	4	2	no	—
468	C₂³	—	4	2	no	—
469	C₂³	C₂²×D₄×C₇₃	1	1	yes	characteristic
470	Q₈	—	2	4	no	—
471	Q₈	—	4	4	no	—
472	Q₈	—	4	1	no	—
473	Q₈	—	4	1	no	—
474	Q₈	—	8	4	no	—
475	D₄	—	2	2	no	—
476	D₄	—	2	2	no	—
477	D₄	—	2	4	no	—
478	D₄	—	4	8	no	—
479	D₄	—	4	1	no	—
480	D₄	—	4	1	no	—
481	D₄	—	4	2	no	—
482	D₄	—	8	4	no	—
483	C₂×C₄	—	2	1	no	—
484	C₂×C₄	—	2	1	no	—
485	C₂×C₄	—	2	1	no	—
486	C₂×C₄	—	2	1	no	—
487	C₂×C₄	—	2	2	no	—
488	C₂×C₄	—	2	2	no	—
489	C₂×C₄	—	2	1	no	—
490	C₂×C₄	—	2	1	no	—
491	C₂×C₄	—	2	2	no	—
492	C₂×C₄	—	2	1	no	—
493	C₂×C₄	—	2	4	no	—
494	C₂×C₄	—	2	1	no	—
495	C₂×C₄	—	2	1	no	—
496	C₂×C₄	—	2	2	no	—
497	C₂×C₄	—	2	2	no	—
498	C₂×C₄	—	4	2	no	—
499	C₂×C₄	—	4	2	no	—
500	C₂×C₄	—	4	2	no	—
501	C₂×C₄	—	4	2	no	—
502	C₂×C₄	—	4	2	no	—
503	C₂×C₄	—	4	2	no	—
504	C₂×C₄	—	4	2	no	—
505	C₂×C₄	—	8	4	no	—
506	C₂×C₄	—	8	4	no	—
507	C₂×C₄	#120×C₇₃	1	2	yes	—
508	C₂×C₄	#120×C₇₃	1	2	yes	—
509	C₂×C₄	#137×C₇₃	1	2	yes	—
510	C₂×C₄	C₂²×D₄×C₇₃	1	1	yes	characteristic
511	C₂×C₄	C₂²×D₄×C₇₃	1	1	yes	characteristic
512	C₂×C₄	C₂×#41×C₇₃	1	2	yes	—
513	C₂×C₄	2₋¹⁺⁴×C₇₃	1	2	yes	—
514	C₈	—	4	2	no	—
515	C₈	—	4	2	no	—
516	C₂²	—	4	2	no	—
517	C₂²	—	4	2	no	—
518	C₂²	—	4	2	no	—
519	C₂²	—	4	2	no	—
520	C₂²	—	4	2	no	—
521	C₂²	—	4	2	no	—
522	C₂²	—	8	2	no	—
523	C₂²	—	8	2	no	—
524	C₂²	—	8	2	no	—
525	C₂²	—	8	2	no	—
526	C₂²	C₂×#120×C₇₃	1	1	yes	characteristic
527	C₂²	#548×C₇₃	1	2	yes	—
528	C₂²	C₂×#137×C₇₃	1	1	yes	characteristic
529	C₂²	#575×C₇₃	1	1	yes	characteristic
530	C₂²	#576×C₇₃	1	2	yes	—
531	C₄	—	2	2	no	—
532	C₄	—	2	2	no	—
533	C₄	—	2	2	no	—
534	C₄	—	4	1	no	—
535	C₄	—	4	1	no	—
536	C₄	—	4	1	no	—
537	C₄	—	4	2	no	—
538	C₄	—	4	4	no	—
539	C₄	—	4	2	no	—
540	C₄	—	8	2	no	—
541	C₄	#532×C₇₃	1	1	yes	characteristic
542	C₄	#536×C₇₃	1	1	yes	characteristic
543	C₄	#547×C₇₃	1	2	yes	—
544	C₂	—	8	2	no	—
545	C₂	—	8	2	no	—
546	C₂	C₇₃×#2432	1	1	yes	characteristic
547	C₂	C₇₃×#3007	1	1	yes	characteristic
548	C₂	C₇₃×#3008	1	1	yes	characteristic
549	C₂	C₇₃×#3370	1	2	yes	—
550	C₂	C₇₃×#3375	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₇₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₇₃
prime radical	C₂×#127×C₇₃	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₇₃ ◁ C₂×C₄×Q₈×C₇₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×#489×C₇₃	C₂	semidirect
3. C₂×#474×C₇₃	C₂	semidirect
4. C₇₃×#2567	C₂	semidirect
5. C₇₃×#2042	C₂	semidirect
7. C₇₃×#1985	C₂	semidirect
8. C₇₃×#1983	C₂	semidirect
9. C₇₃×#1863	C₂	semidirect
10. C₇₃×#1862	C₂	semidirect
11. C₇₃×#1762	C₂	semidirect
268. #25660	C₇₃	direct (N × H)
277. C₂×#489	C₂×C₇₃	semidirect
278. C₂×#474	C₂×C₇₃	semidirect
279. #2567	C₂×C₇₃	semidirect
280. #2042	C₂×C₇₃	semidirect
282. #1985	C₂×C₇₃	semidirect
283. #1983	C₂×C₇₃	semidirect
284. #1863	C₂×C₇₃	semidirect
285. #1862	C₂×C₇₃	semidirect
286. #1762	C₂×C₇₃	semidirect
287. C₇₃	#25660	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×#559×C₇₃	2
C₂×#489×C₇₃	2
C₂×#474×C₇₃	2
C₇₃×#2567	2
C₇₃×#2042	2
C₇₃×#2041	2
C₇₃×#1985	2
C₇₃×#1983	2
C₇₃×#1863	2
C₇₃×#1862	2
C₇₃×#1762	2
#25660	73

Subgroups — C73×#25660 #32935064

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₃×#25660 #32935064