Subgroups — C₇₃×#25714 #32935118

Order 18688.

1122 conjugacy classes of subgroups.

The subgroup lattice has 570 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#553×C₇₃	C₂	1	1	yes	maximal, characteristic
2	C₂×#501×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#476×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₇₃×#2547	C₂	1	1	yes	maximal, characteristic, complemented
5	C₇₃×#2034	C₂	1	2	yes	maximal, complemented
6	C₇₃×#2033	C₂	1	2	yes	maximal, complemented
7	C₇₃×#1989	C₂	1	1	yes	maximal, characteristic, complemented
8	C₇₃×#1955	C₂	1	1	yes	maximal, characteristic, complemented
9	C₇₃×#1854	C₂	1	2	yes	maximal, complemented
10	C₇₃×#1853	C₂	1	2	yes	maximal, complemented
11	C₇₃×#1762	C₂	1	1	yes	maximal, characteristic, complemented
12	#553×C₇₃	—	2	4	no	—
13	#553×C₇₃	—	2	4	no	—
14	C₂×C₄⋊Q₈×C₇₃	C₂²	1	1	yes	characteristic
15	C₂×#126×C₇₃	—	2	1	no	—
16	C₂×#125×C₇₃	C₂²	1	1	yes	characteristic
17	C₂×#124×C₇₃	—	2	1	no	—
18	C₂×#123×C₇₃	—	2	1	no	—
19	C₂×#121×C₇₃	—	2	1	no	—
20	C₂×#121×C₇₃	C₂²	1	1	yes	characteristic
21	C₂×#121×C₇₃	C₂²	1	1	yes	characteristic
22	C₂×C₄×D₄×C₇₃	—	2	1	no	—
23	C₂×C₄×D₄×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	C₂²×C₄⋊C₄×C₇₃	C₂²	1	1	yes	characteristic
27	#501×C₇₃	—	2	4	no	—
28	#476×C₇₃	—	2	4	no	—
29	C₂×#107×C₇₃	C₂²	1	2	yes	—
30	C₂×#106×C₇₃	C₂²	1	2	yes	—
31	C₂×#106×C₇₃	C₂²	1	2	yes	—
32	C₂×C₄⋊C₈×C₇₃	C₂²	1	1	yes	characteristic
33	C₂×#102×C₇₃	C₂²	1	2	yes	—
34	C₂×#102×C₇₃	C₂²	1	2	yes	—
35	C₂×C₂²⋊C₈×C₇₃	C₂²	1	2	yes	—
36	C₂×C₂²⋊C₈×C₇₃	C₂²	1	2	yes	—
37	C₂×#97×C₇₃	C₂²	1	1	yes	characteristic
38	#397×C₇₃	—	2	1	no	—
39	#397×C₇₃	—	2	1	no	—
40	#391×C₇₃	—	2	1	no	—
41	#380×C₇₃	C₂²	1	2	yes	—
42	#380×C₇₃	C₂²	1	2	yes	—
43	C₄×C₄⋊C₄×C₇₃	C₂²	1	1	yes	characteristic
44	#340×C₇₃	C₂²	1	2	yes	—
45	#340×C₇₃	C₂²	1	2	yes	—
46	#340×C₇₃	C₂²	1	2	yes	—
47	C₂²×Q₈×C₇₃	—	2	1	no	—
48	C₂²×D₄×C₇₃	—	2	1	no	—
49	C₂²×D₄×C₇₃	—	2	1	no	—
50	C₂²×D₄×C₇₃	D₄	1	1	yes	characteristic
51	C₂²×D₄×C₇₃	C₂³	1	1	yes	characteristic
52	C₂³×C₄×C₇₃	—	2	1	no	—
53	C₂³×C₄×C₇₃	—	2	1	no	—
54	C₂³×C₄×C₇₃	C₂³	1	1	yes	characteristic
55	C₂³×C₄×C₇₃	C₂³	1	1	yes	characteristic
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	#126×C₇₃	—	2	8	no	—
61	#125×C₇₃	—	2	2	no	—
62	#125×C₇₃	D₄	1	4	yes	—
63	#124×C₇₃	—	4	4	no	—
64	#123×C₇₃	—	2	8	no	—
65	#121×C₇₃	—	2	8	no	—
66	#121×C₇₃	—	2	2	no	—
67	#121×C₇₃	—	2	2	no	—
68	#121×C₇₃	—	2	2	no	—
69	#121×C₇₃	—	2	2	no	—
70	C₄×D₄×C₇₃	—	2	8	no	—
71	C₄×D₄×C₇₃	—	2	2	no	—
72	C₄×D₄×C₇₃	—	2	2	no	—
73	C₄×D₄×C₇₃	—	2	2	no	—
74	C₄×D₄×C₇₃	D₄	1	4	yes	—
75	#117×C₇₃	—	2	2	no	—
76	#117×C₇₃	—	2	2	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	—	2	2	no	—
82	C₂×C₄⋊C₄×C₇₃	—	2	1	no	—
83	C₂×C₄⋊C₄×C₇₃	D₄	1	1	yes	characteristic
84	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
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	1	yes	characteristic
88	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
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	2	no	—
94	C₂×C₂²⋊C₄×C₇₃	—	2	2	no	—
95	C₂×C₂²⋊C₄×C₇₃	D₄	1	1	yes	characteristic
96	C₂×C₂²⋊C₄×C₇₃	D₄	1	1	yes	characteristic
97	C₂×C₄²×C₇₃	—	2	1	no	—
98	C₂×C₄²×C₇₃	—	2	1	no	—
99	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
100	#107×C₇₃	—	2	4	no	—
101	#106×C₇₃	—	2	4	no	—
102	#106×C₇₃	—	2	4	no	—
103	C₄⋊C₈×C₇₃	—	2	2	no	—
104	#102×C₇₃	—	2	4	no	—
105	#102×C₇₃	—	2	4	no	—
106	C₂²⋊C₈×C₇₃	—	2	4	no	—
107	C₂²⋊C₈×C₇₃	—	2	4	no	—
108	#97×C₇₃	—	2	2	no	—
109	#95×C₇₃	—	2	1	no	—
110	#95×C₇₃	—	2	2	no	—
111	#95×C₇₃	—	2	2	no	—
112	C₂⁴×C₇₃	—	2	1	no	—
113	C₂⁴×C₇₃	C₂×D₄	1	1	yes	characteristic
114	C₂⁴×C₇₃	C₂×D₄	1	1	yes	characteristic
115	C₂×Q₈×C₇₃	—	4	2	no	—
116	C₂×Q₈×C₇₃	—	4	2	no	—
117	C₂×Q₈×C₇₃	—	4	2	no	—
118	C₂×D₄×C₇₃	—	2	4	no	—
119	C₂×D₄×C₇₃	—	2	2	no	—
120	C₂×D₄×C₇₃	—	2	4	no	—
121	C₂×D₄×C₇₃	—	2	2	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	—	4	1	no	—
126	C₂×D₄×C₇₃	—	4	2	no	—
127	C₂×D₄×C₇₃	—	4	2	no	—
128	C₂×D₄×C₇₃	—	8	2	no	—
129	C₂×D₄×C₇₃	C₂×D₄	1	2	yes	—
130	C₂²×C₄×C₇₃	—	2	1	no	—
131	C₂²×C₄×C₇₃	—	2	1	no	—
132	C₂²×C₄×C₇₃	—	2	1	no	—
133	C₂²×C₄×C₇₃	—	2	4	no	—
134	C₂²×C₄×C₇₃	—	2	1	no	—
135	C₂²×C₄×C₇₃	—	2	1	no	—
136	C₂²×C₄×C₇₃	—	2	1	no	—
137	C₂²×C₄×C₇₃	—	2	1	no	—
138	C₂²×C₄×C₇₃	—	2	2	no	—
139	C₂²×C₄×C₇₃	—	2	2	no	—
140	C₂²×C₄×C₇₃	—	2	2	no	—
141	C₂²×C₄×C₇₃	—	2	2	no	—
142	C₂²×C₄×C₇₃	—	2	4	no	—
143	C₂²×C₄×C₇₃	—	2	2	no	—
144	C₂²×C₄×C₇₃	—	2	2	no	—
145	C₂²×C₄×C₇₃	—	8	2	no	—
146	C₂²×C₄×C₇₃	—	8	2	no	—
147	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
148	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
149	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
150	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
151	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
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	C₂×C₈×C₇₃	—	2	2	no	—
157	C₂×C₈×C₇₃	#41	1	4	yes	—
158	C₄⋊C₄×C₇₃	—	2	4	no	—
159	C₄⋊C₄×C₇₃	—	2	4	no	—
160	C₄⋊C₄×C₇₃	—	2	4	no	—
161	C₄⋊C₄×C₇₃	—	2	2	no	—
162	C₄⋊C₄×C₇₃	—	2	1	no	—
163	C₄⋊C₄×C₇₃	—	2	1	no	—
164	C₄⋊C₄×C₇₃	—	2	1	no	—
165	C₄⋊C₄×C₇₃	—	2	2	no	—
166	C₄⋊C₄×C₇₃	—	2	2	no	—
167	C₄⋊C₄×C₇₃	—	2	2	no	—
168	C₄⋊C₄×C₇₃	—	2	2	no	—
169	C₄⋊C₄×C₇₃	—	4	2	no	—
170	C₄⋊C₄×C₇₃	C₂×D₄	1	2	yes	—
171	C₄⋊C₄×C₇₃	C₂×D₄	1	2	yes	—
172	C₄⋊C₄×C₇₃	C₂×D₄	1	2	yes	—
173	C₂²⋊C₄×C₇₃	—	2	4	no	—
174	C₂²⋊C₄×C₇₃	—	2	4	no	—
175	C₂²⋊C₄×C₇₃	—	2	4	no	—
176	C₂²⋊C₄×C₇₃	—	2	4	no	—
177	C₂²⋊C₄×C₇₃	—	2	2	no	—
178	C₂²⋊C₄×C₇₃	—	2	2	no	—
179	C₂²⋊C₄×C₇₃	—	4	4	no	—
180	C₂²⋊C₄×C₇₃	—	4	4	no	—
181	C₄²×C₇₃	—	2	4	no	—
182	C₄²×C₇₃	—	4	2	no	—
183	C₄²×C₇₃	C₂×D₄	1	2	yes	—
184	C₄²×C₇₃	C₂×D₄	1	2	yes	—
185	C₂³×C₇₃	—	2	1	no	—
186	C₂³×C₇₃	—	2	2	no	—
187	C₂³×C₇₃	—	2	1	no	—
188	C₂³×C₇₃	—	2	2	no	—
189	C₂³×C₇₃	—	2	1	no	—
190	C₂³×C₇₃	—	2	2	no	—
191	C₂³×C₇₃	—	2	2	no	—
192	C₂³×C₇₃	—	2	1	no	—
193	C₂³×C₇₃	—	2	1	no	—
194	C₂³×C₇₃	—	2	2	no	—
195	C₂³×C₇₃	—	4	2	no	—
196	C₂³×C₇₃	—	4	1	no	—
197	C₂³×C₇₃	—	4	1	no	—
198	C₂³×C₇₃	—	4	2	no	—
199	C₂³×C₇₃	AGL(1,ℤ/8)	1	2	yes	—
200	C₂³×C₇₃	C₂²×D₄	1	1	yes	characteristic
201	Q₈×C₇₃	—	8	4	no	—
202	D₄×C₇₃	—	2	2	no	—
203	D₄×C₇₃	—	2	2	no	—
204	D₄×C₇₃	—	4	4	no	—
205	D₄×C₇₃	—	4	8	no	—
206	D₄×C₇₃	—	4	2	no	—
207	D₄×C₇₃	—	8	4	no	—
208	C₂×C₄×C₇₃	—	2	1	no	—
209	C₂×C₄×C₇₃	—	2	1	no	—
210	C₂×C₄×C₇₃	—	2	2	no	—
211	C₂×C₄×C₇₃	—	2	1	no	—
212	C₂×C₄×C₇₃	—	2	2	no	—
213	C₂×C₄×C₇₃	—	2	2	no	—
214	C₂×C₄×C₇₃	—	2	1	no	—
215	C₂×C₄×C₇₃	—	2	2	no	—
216	C₂×C₄×C₇₃	—	2	2	no	—
217	C₂×C₄×C₇₃	—	2	2	no	—
218	C₂×C₄×C₇₃	—	4	1	no	—
219	C₂×C₄×C₇₃	—	4	1	no	—
220	C₂×C₄×C₇₃	—	4	2	no	—
221	C₂×C₄×C₇₃	—	4	2	no	—
222	C₂×C₄×C₇₃	—	4	1	no	—
223	C₂×C₄×C₇₃	—	4	1	no	—
224	C₂×C₄×C₇₃	—	4	1	no	—
225	C₂×C₄×C₇₃	—	4	1	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	—	4	2	no	—
230	C₂×C₄×C₇₃	—	4	2	no	—
231	C₂×C₄×C₇₃	—	4	2	no	—
232	C₂×C₄×C₇₃	—	4	2	no	—
233	C₂×C₄×C₇₃	—	4	2	no	—
234	C₂×C₄×C₇₃	—	8	4	no	—
235	C₂×C₄×C₇₃	—	8	4	no	—
236	C₂×C₄×C₇₃	#120	1	2	yes	—
237	C₂×C₄×C₇₃	#120	1	2	yes	—
238	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
239	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
240	C₂×C₄×C₇₃	C₂×#41	1	2	yes	—
241	C₂×C₄×C₇₃	2₋¹⁺⁴	1	2	yes	—
242	C₈×C₇₃	—	2	4	no	—
243	C₈×C₇₃	—	4	2	no	—
244	C₂²×C₇₃	—	2	4	no	—
245	C₂²×C₇₃	—	2	2	no	—
246	C₂²×C₇₃	—	4	2	no	—
247	C₂²×C₇₃	—	4	1	no	—
248	C₂²×C₇₃	—	4	1	no	—
249	C₂²×C₇₃	—	4	2	no	—
250	C₂²×C₇₃	—	4	2	no	—
251	C₂²×C₇₃	—	4	1	no	—
252	C₂²×C₇₃	—	4	2	no	—
253	C₂²×C₇₃	—	4	1	no	—
254	C₂²×C₇₃	—	4	2	no	—
255	C₂²×C₇₃	—	4	2	no	—
256	C₂²×C₇₃	—	4	1	no	—
257	C₂²×C₇₃	—	8	2	no	—
258	C₂²×C₇₃	—	8	2	no	—
259	C₂²×C₇₃	C₂×#120	1	1	yes	characteristic
260	C₂²×C₇₃	#547	1	2	yes	—
261	C₂²×C₇₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
262	C₂²×C₇₃	#575	1	1	yes	characteristic
263	C₂²×C₇₃	#577	1	2	yes	—
264	C₄×C₇₃	—	2	2	no	—
265	C₄×C₇₃	—	2	2	no	—
266	C₄×C₇₃	—	4	1	no	—
267	C₄×C₇₃	—	4	1	no	—
268	C₄×C₇₃	—	4	2	no	—
269	C₄×C₇₃	—	4	2	no	—
270	C₄×C₇₃	—	4	2	no	—
271	C₄×C₇₃	—	8	2	no	—
272	C₄×C₇₃	—	8	2	no	—
273	C₄×C₇₃	#532	1	1	yes	characteristic
274	C₄×C₇₃	#536	1	1	yes	characteristic
275	C₄×C₇₃	#548	1	2	yes	—
276	#25714	C₇₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
277	C₂×C₇₃	—	4	2	no	—
278	C₂×C₇₃	—	8	1	no	—
279	C₂×C₇₃	—	8	2	no	—
280	C₂×C₇₃	#2432	1	1	yes	characteristic
281	C₂×C₇₃	#3006	1	1	yes	characteristic
282	C₂×C₇₃	#3009	1	1	yes	characteristic
283	C₂×C₇₃	#3345	1	2	yes	—
284	C₂×C₇₃	#3350	1	2	yes	—
285	C₂×#553	C₂×C₇₃	1	1	yes	characteristic
286	C₂×#501	C₂×C₇₃	1	1	yes	characteristic, complemented
287	C₂×#476	C₂×C₇₃	1	1	yes	characteristic, complemented
288	#2547	C₂×C₇₃	1	1	yes	characteristic, complemented
289	#2034	C₂×C₇₃	1	2	yes	complemented
290	#2033	C₂×C₇₃	1	2	yes	complemented
291	#1989	C₂×C₇₃	1	1	yes	characteristic, complemented
292	#1955	C₂×C₇₃	1	1	yes	characteristic, complemented
293	#1854	C₂×C₇₃	1	2	yes	complemented
294	#1853	C₂×C₇₃	1	2	yes	complemented
295	#1762	C₂×C₇₃	1	1	yes	characteristic, complemented
296	C₇₃	#25714	1	1	yes	characteristic, direct product factor, Sylow
297	#553	—	2	4	no	—
298	#553	—	2	4	no	—
299	C₂×C₄⋊Q₈	C₂²×C₇₃	1	1	yes	characteristic
300	C₂×#126	—	2	1	no	—
301	C₂×#125	C₂²×C₇₃	1	1	yes	characteristic
302	C₂×#124	—	2	1	no	—
303	C₂×#123	—	2	1	no	—
304	C₂×#121	—	2	1	no	—
305	C₂×#121	C₂²×C₇₃	1	1	yes	characteristic
306	C₂×#121	C₂²×C₇₃	1	1	yes	characteristic
307	C₂×C₄×D₄	—	2	1	no	—
308	C₂×C₄×D₄	C₂²×C₇₃	1	1	yes	characteristic
309	C₂×C₄×D₄	C₂²×C₇₃	1	1	yes	characteristic
310	C₂×#117	C₂²×C₇₃	1	1	yes	characteristic
311	C₂²×C₄⋊C₄	C₂²×C₇₃	1	1	yes	characteristic
312	#501	—	2	4	no	—
313	#476	—	2	4	no	—
314	C₂×#107	C₂²×C₇₃	1	2	yes	—
315	C₂×#106	C₂²×C₇₃	1	2	yes	—
316	C₂×#106	C₂²×C₇₃	1	2	yes	—
317	C₂×C₄⋊C₈	C₂²×C₇₃	1	1	yes	characteristic
318	C₂×#102	C₂²×C₇₃	1	2	yes	—
319	C₂×#102	C₂²×C₇₃	1	2	yes	—
320	C₂×C₂²⋊C₈	C₂²×C₇₃	1	2	yes	—
321	C₂×C₂²⋊C₈	C₂²×C₇₃	1	2	yes	—
322	C₂×#97	C₂²×C₇₃	1	1	yes	characteristic
323	#397	—	2	1	no	—
324	#397	—	2	1	no	—
325	#391	—	2	1	no	—
326	#380	C₂²×C₇₃	1	2	yes	—
327	#380	C₂²×C₇₃	1	2	yes	—
328	C₄×C₄⋊C₄	C₂²×C₇₃	1	1	yes	characteristic
329	#340	C₂²×C₇₃	1	2	yes	—
330	#340	C₂²×C₇₃	1	2	yes	—
331	#340	C₂²×C₇₃	1	2	yes	—
332	C₂²×Q₈	—	2	1	no	—
333	C₂²×D₄	—	2	1	no	—
334	C₂²×D₄	—	2	1	no	—
335	C₂²×D₄	D₄×C₇₃	1	1	yes	characteristic
336	C₂²×D₄	C₂³×C₇₃	1	1	yes	characteristic
337	C₂³×C₄	—	2	1	no	—
338	C₂³×C₄	—	2	1	no	—
339	C₂³×C₄	C₂³×C₇₃	1	1	yes	characteristic
340	C₂³×C₄	C₂³×C₇₃	1	1	yes	characteristic
341	C₂²×C₈	C₂³×C₇₃	1	2	yes	—
342	C₂²×C₈	C₂³×C₇₃	1	2	yes	—
343	C₄⋊Q₈	—	2	2	no	—
344	C₄⋊Q₈	—	2	2	no	—
345	#126	—	2	8	no	—
346	#125	—	2	2	no	—
347	#125	D₄×C₇₃	1	4	yes	—
348	#124	—	4	4	no	—
349	#123	—	2	8	no	—
350	#121	—	2	8	no	—
351	#121	—	2	2	no	—
352	#121	—	2	2	no	—
353	#121	—	2	2	no	—
354	#121	—	2	2	no	—
355	C₄×D₄	—	2	8	no	—
356	C₄×D₄	—	2	2	no	—
357	C₄×D₄	—	2	2	no	—
358	C₄×D₄	—	2	2	no	—
359	C₄×D₄	D₄×C₇₃	1	4	yes	—
360	#117	—	2	2	no	—
361	#117	—	2	2	no	—
362	C₂×C₄⋊C₄	—	2	1	no	—
363	C₂×C₄⋊C₄	—	2	1	no	—
364	C₂×C₄⋊C₄	—	2	1	no	—
365	C₂×C₄⋊C₄	—	2	2	no	—
366	C₂×C₄⋊C₄	—	2	2	no	—
367	C₂×C₄⋊C₄	—	2	1	no	—
368	C₂×C₄⋊C₄	D₄×C₇₃	1	1	yes	characteristic
369	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
370	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
371	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
372	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
373	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
374	C₂×C₂²⋊C₄	—	2	1	no	—
375	C₂×C₂²⋊C₄	—	2	1	no	—
376	C₂×C₂²⋊C₄	—	2	1	no	—
377	C₂×C₂²⋊C₄	—	2	1	no	—
378	C₂×C₂²⋊C₄	—	2	2	no	—
379	C₂×C₂²⋊C₄	—	2	2	no	—
380	C₂×C₂²⋊C₄	D₄×C₇₃	1	1	yes	characteristic
381	C₂×C₂²⋊C₄	D₄×C₇₃	1	1	yes	characteristic
382	C₂×C₄²	—	2	1	no	—
383	C₂×C₄²	—	2	1	no	—
384	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
385	#107	—	2	4	no	—
386	#106	—	2	4	no	—
387	#106	—	2	4	no	—
388	C₄⋊C₈	—	2	2	no	—
389	#102	—	2	4	no	—
390	#102	—	2	4	no	—
391	C₂²⋊C₈	—	2	4	no	—
392	C₂²⋊C₈	—	2	4	no	—
393	#97	—	2	2	no	—
394	#95	—	2	1	no	—
395	#95	—	2	2	no	—
396	#95	—	2	2	no	—
397	C₂⁴	—	2	1	no	—
398	C₂⁴	C₂×D₄×C₇₃	1	1	yes	characteristic
399	C₂⁴	C₂×D₄×C₇₃	1	1	yes	characteristic
400	C₂×Q₈	—	4	2	no	—
401	C₂×Q₈	—	4	2	no	—
402	C₂×Q₈	—	4	2	no	—
403	C₂×D₄	—	2	4	no	—
404	C₂×D₄	—	2	2	no	—
405	C₂×D₄	—	2	4	no	—
406	C₂×D₄	—	2	2	no	—
407	C₂×D₄	—	2	1	no	—
408	C₂×D₄	—	2	2	no	—
409	C₂×D₄	—	2	2	no	—
410	C₂×D₄	—	4	1	no	—
411	C₂×D₄	—	4	2	no	—
412	C₂×D₄	—	4	2	no	—
413	C₂×D₄	—	8	2	no	—
414	C₂×D₄	C₂×D₄×C₇₃	1	2	yes	—
415	C₂²×C₄	—	2	1	no	—
416	C₂²×C₄	—	2	1	no	—
417	C₂²×C₄	—	2	1	no	—
418	C₂²×C₄	—	2	4	no	—
419	C₂²×C₄	—	2	1	no	—
420	C₂²×C₄	—	2	1	no	—
421	C₂²×C₄	—	2	1	no	—
422	C₂²×C₄	—	2	1	no	—
423	C₂²×C₄	—	2	2	no	—
424	C₂²×C₄	—	2	2	no	—
425	C₂²×C₄	—	2	2	no	—
426	C₂²×C₄	—	2	2	no	—
427	C₂²×C₄	—	2	4	no	—
428	C₂²×C₄	—	2	2	no	—
429	C₂²×C₄	—	2	2	no	—
430	C₂²×C₄	—	8	2	no	—
431	C₂²×C₄	—	8	2	no	—
432	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
433	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
434	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
435	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
436	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
437	C₂×C₈	—	2	2	no	—
438	C₂×C₈	—	2	2	no	—
439	C₂×C₈	—	2	2	no	—
440	C₂×C₈	—	2	2	no	—
441	C₂×C₈	—	2	2	no	—
442	C₂×C₈	#41×C₇₃	1	4	yes	—
443	C₄⋊C₄	—	2	4	no	—
444	C₄⋊C₄	—	2	4	no	—
445	C₄⋊C₄	—	2	4	no	—
446	C₄⋊C₄	—	2	2	no	—
447	C₄⋊C₄	—	2	1	no	—
448	C₄⋊C₄	—	2	1	no	—
449	C₄⋊C₄	—	2	1	no	—
450	C₄⋊C₄	—	2	2	no	—
451	C₄⋊C₄	—	2	2	no	—
452	C₄⋊C₄	—	2	2	no	—
453	C₄⋊C₄	—	2	2	no	—
454	C₄⋊C₄	—	4	2	no	—
455	C₄⋊C₄	C₂×D₄×C₇₃	1	2	yes	—
456	C₄⋊C₄	C₂×D₄×C₇₃	1	2	yes	—
457	C₄⋊C₄	C₂×D₄×C₇₃	1	2	yes	—
458	C₂²⋊C₄	—	2	4	no	—
459	C₂²⋊C₄	—	2	4	no	—
460	C₂²⋊C₄	—	2	4	no	—
461	C₂²⋊C₄	—	2	4	no	—
462	C₂²⋊C₄	—	2	2	no	—
463	C₂²⋊C₄	—	2	2	no	—
464	C₂²⋊C₄	—	4	4	no	—
465	C₂²⋊C₄	—	4	4	no	—
466	C₄²	—	2	4	no	—
467	C₄²	—	4	2	no	—
468	C₄²	C₂×D₄×C₇₃	1	2	yes	—
469	C₄²	C₂×D₄×C₇₃	1	2	yes	—
470	C₂³	—	2	1	no	—
471	C₂³	—	2	2	no	—
472	C₂³	—	2	1	no	—
473	C₂³	—	2	2	no	—
474	C₂³	—	2	1	no	—
475	C₂³	—	2	2	no	—
476	C₂³	—	2	2	no	—
477	C₂³	—	2	1	no	—
478	C₂³	—	2	1	no	—
479	C₂³	—	2	2	no	—
480	C₂³	—	4	2	no	—
481	C₂³	—	4	1	no	—
482	C₂³	—	4	1	no	—
483	C₂³	—	4	2	no	—
484	C₂³	AGL(1,ℤ/8)×C₇₃	1	2	yes	—
485	C₂³	C₂²×D₄×C₇₃	1	1	yes	characteristic
486	Q₈	—	8	4	no	—
487	D₄	—	2	2	no	—
488	D₄	—	2	2	no	—
489	D₄	—	4	4	no	—
490	D₄	—	4	8	no	—
491	D₄	—	4	2	no	—
492	D₄	—	8	4	no	—
493	C₂×C₄	—	2	1	no	—
494	C₂×C₄	—	2	1	no	—
495	C₂×C₄	—	2	2	no	—
496	C₂×C₄	—	2	1	no	—
497	C₂×C₄	—	2	2	no	—
498	C₂×C₄	—	2	2	no	—
499	C₂×C₄	—	2	1	no	—
500	C₂×C₄	—	2	2	no	—
501	C₂×C₄	—	2	2	no	—
502	C₂×C₄	—	2	2	no	—
503	C₂×C₄	—	4	1	no	—
504	C₂×C₄	—	4	1	no	—
505	C₂×C₄	—	4	2	no	—
506	C₂×C₄	—	4	2	no	—
507	C₂×C₄	—	4	1	no	—
508	C₂×C₄	—	4	1	no	—
509	C₂×C₄	—	4	1	no	—
510	C₂×C₄	—	4	1	no	—
511	C₂×C₄	—	4	2	no	—
512	C₂×C₄	—	4	2	no	—
513	C₂×C₄	—	4	2	no	—
514	C₂×C₄	—	4	2	no	—
515	C₂×C₄	—	4	2	no	—
516	C₂×C₄	—	4	2	no	—
517	C₂×C₄	—	4	2	no	—
518	C₂×C₄	—	4	2	no	—
519	C₂×C₄	—	8	4	no	—
520	C₂×C₄	—	8	4	no	—
521	C₂×C₄	#120×C₇₃	1	2	yes	—
522	C₂×C₄	#120×C₇₃	1	2	yes	—
523	C₂×C₄	C₂²×D₄×C₇₃	1	1	yes	characteristic
524	C₂×C₄	C₂²×D₄×C₇₃	1	1	yes	characteristic
525	C₂×C₄	C₂×#41×C₇₃	1	2	yes	—
526	C₂×C₄	2₋¹⁺⁴×C₇₃	1	2	yes	—
527	C₈	—	2	4	no	—
528	C₈	—	4	2	no	—
529	C₂²	—	2	2	no	—
530	C₂²	—	2	4	no	—
531	C₂²	—	4	1	no	—
532	C₂²	—	4	2	no	—
533	C₂²	—	4	1	no	—
534	C₂²	—	4	1	no	—
535	C₂²	—	4	2	no	—
536	C₂²	—	4	2	no	—
537	C₂²	—	4	1	no	—
538	C₂²	—	4	2	no	—
539	C₂²	—	4	2	no	—
540	C₂²	—	4	1	no	—
541	C₂²	—	4	2	no	—
542	C₂²	—	8	2	no	—
543	C₂²	—	8	2	no	—
544	C₂²	C₂×#120×C₇₃	1	1	yes	characteristic
545	C₂²	#547×C₇₃	1	2	yes	—
546	C₂²	C₂×AGL(1,ℤ/8)×C₇₃	1	1	yes	characteristic
547	C₂²	#575×C₇₃	1	1	yes	characteristic
548	C₂²	#577×C₇₃	1	2	yes	—
549	C₄	—	2	2	no	—
550	C₄	—	2	2	no	—
551	C₄	—	4	2	no	—
552	C₄	—	4	2	no	—
553	C₄	—	4	2	no	—
554	C₄	—	4	1	no	—
555	C₄	—	4	1	no	—
556	C₄	—	8	2	no	—
557	C₄	—	8	2	no	—
558	C₄	#532×C₇₃	1	1	yes	characteristic
559	C₄	#536×C₇₃	1	1	yes	characteristic
560	C₄	#548×C₇₃	1	2	yes	—
561	C₂	—	4	2	no	—
562	C₂	—	8	1	no	—
563	C₂	—	8	2	no	—
564	C₂	C₇₃×#2432	1	1	yes	characteristic
565	C₂	C₇₃×#3006	1	1	yes	characteristic
566	C₂	C₇₃×#3009	1	1	yes	characteristic
567	C₂	C₇₃×#3345	1	2	yes	—
568	C₂	C₇₃×#3350	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₇₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₇₃
prime radical	C₂×#553×C₇₃	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₇₃ ◁ C₂×C₄×D₄×C₇₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×#501×C₇₃	C₂	semidirect
3. C₂×#476×C₇₃	C₂	semidirect
4. C₇₃×#2547	C₂	semidirect
5. C₇₃×#2034	C₂	semidirect
6. C₇₃×#2033	C₂	semidirect
7. C₇₃×#1989	C₂	semidirect
8. C₇₃×#1955	C₂	semidirect
9. C₇₃×#1854	C₂	semidirect
10. C₇₃×#1853	C₂	semidirect
11. C₇₃×#1762	C₂	semidirect
276. #25714	C₇₃	direct (N × H)
286. C₂×#501	C₂×C₇₃	semidirect
287. C₂×#476	C₂×C₇₃	semidirect
288. #2547	C₂×C₇₃	semidirect
289. #2034	C₂×C₇₃	semidirect
290. #2033	C₂×C₇₃	semidirect
291. #1989	C₂×C₇₃	semidirect
292. #1955	C₂×C₇₃	semidirect
293. #1854	C₂×C₇₃	semidirect
294. #1853	C₂×C₇₃	semidirect
295. #1762	C₂×C₇₃	semidirect
296. C₇₃	#25714	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×#553×C₇₃	2
C₂×#501×C₇₃	2
C₂×#476×C₇₃	2
C₇₃×#2547	2
C₇₃×#2034	2
C₇₃×#2033	2
C₇₃×#1989	2
C₇₃×#1955	2
C₇₃×#1854	2
C₇₃×#1853	2
C₇₃×#1762	2
#25714	73

Subgroups — C73×#25714 #32935118

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₃×#25714 #32935118