Subgroups — C₇₃×#32775 #32942179

Order 18688.

774 conjugacy classes of subgroups.

The subgroup lattice has 520 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇₃×#2857	C₂	1	1	yes	maximal, characteristic, complemented
2	C₇₃×#2850	C₂	1	1	yes	maximal, characteristic
3	C₇₃×#2096	C₂	1	1	yes	maximal, characteristic, complemented
4	C₇₃×#2093	C₂	1	1	yes	maximal, characteristic, complemented
5	C₇₃×#2085	C₂	1	2	yes	maximal, complemented
6	C₇₃×#2042	C₂	1	2	yes	maximal, complemented
7	C₇₃×#2036	C₂	1	2	yes	maximal, complemented
8	C₇₃×#2034	C₂	1	2	yes	maximal
9	C₇₃×#2024	C₂	1	1	yes	maximal, characteristic, complemented
10	C₇₃×#2023	C₂	1	1	yes	maximal, characteristic, complemented
11	C₇₃×#1817	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₄⋊Q₈×C₇₃	C₂²	1	1	yes	characteristic
13	C₂×#124×C₇₃	C₂²	1	1	yes	characteristic
14	C₂×C₂²⋊Q₈×C₇₃	—	2	1	no	—
15	C₂×C₂²⋊Q₈×C₇₃	C₂²	1	1	yes	characteristic
16	C₂×#121×C₇₃	C₂²	1	1	yes	characteristic
17	C₂²×C₄²×C₇₃	C₂²	1	1	yes	characteristic
18	C₂×#107×C₇₃	C₂²	1	2	yes	—
19	C₂×#106×C₇₃	C₂²	1	2	yes	—
20	C₂×#103×C₇₃	C₂²	1	2	yes	—
21	C₂×#103×C₇₃	C₂²	1	2	yes	—
22	C₂×#102×C₇₃	C₂²	1	2	yes	—
23	C₂×#102×C₇₃	C₂²	1	2	yes	—
24	C₂×C₂²⋊C₈×C₇₃	C₂²	1	2	yes	—
25	#391×C₇₃	—	2	1	no	—
26	#391×C₇₃	C₂²	1	1	yes	characteristic
27	#390×C₇₃	C₂²	1	1	yes	characteristic
28	#389×C₇₃	—	2	1	no	—
29	#389×C₇₃	C₂²	1	2	yes	—
30	#388×C₇₃	—	2	1	no	—
31	#388×C₇₃	—	2	1	no	—
32	#386×C₇₃	—	2	1	no	—
33	#386×C₇₃	—	2	1	no	—
34	#384×C₇₃	C₂²	1	1	yes	characteristic
35	#382×C₇₃	C₂²	1	1	yes	characteristic
36	#380×C₇₃	—	2	1	no	—
37	#380×C₇₃	C₂²	1	2	yes	—
38	#340×C₇₃	C₂²	1	2	yes	—
39	#340×C₇₃	C₂²	1	2	yes	—
40	#336×C₇₃	C₂²	1	1	yes	characteristic
41	#336×C₇₃	C₂²	1	1	yes	characteristic
42	#336×C₇₃	C₂²	1	2	yes	—
43	C₂²×Q₈×C₇₃	—	2	1	no	—
44	C₂²×Q₈×C₇₃	C₂³	1	1	yes	characteristic
45	C₂²×D₄×C₇₃	—	2	1	no	—
46	C₂²×D₄×C₇₃	C₂³	1	1	yes	characteristic
47	C₂³×C₄×C₇₃	D₄	1	1	yes	characteristic
48	C₂³×C₄×C₇₃	D₄	1	1	yes	characteristic
49	C₂³×C₄×C₇₃	C₂³	1	1	yes	characteristic
50	C₂²×C₈×C₇₃	C₂³	1	2	yes	—
51	C₂²×C₈×C₇₃	C₂³	1	2	yes	—
52	C₄⋊Q₈×C₇₃	—	4	2	no	—
53	#124×C₇₃	—	4	2	no	—
54	C₂²⋊Q₈×C₇₃	—	4	2	no	—
55	C₂²⋊Q₈×C₇₃	—	4	4	no	—
56	#121×C₇₃	—	4	2	no	—
57	C₂×C₄⋊C₄×C₇₃	—	2	1	no	—
58	C₂×C₄⋊C₄×C₇₃	—	2	1	no	—
59	C₂×C₄⋊C₄×C₇₃	—	2	1	no	—
60	C₂×C₄⋊C₄×C₇₃	—	2	1	no	—
61	C₂×C₄⋊C₄×C₇₃	—	2	2	no	—
62	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
63	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
64	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
65	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
66	C₂×C₂²⋊C₄×C₇₃	—	2	2	no	—
67	C₂×C₂²⋊C₄×C₇₃	—	2	1	no	—
68	C₂×C₂²⋊C₄×C₇₃	—	2	1	no	—
69	C₂×C₂²⋊C₄×C₇₃	—	2	1	no	—
70	C₂×C₂²⋊C₄×C₇₃	—	2	1	no	—
71	C₂×C₂²⋊C₄×C₇₃	—	2	1	no	—
72	C₂×C₂²⋊C₄×C₇₃	—	2	1	no	—
73	C₂×C₄²×C₇₃	—	4	2	no	—
74	C₂×C₄²×C₇₃	D₄	1	1	yes	characteristic
75	C₂×C₄²×C₇₃	D₄	1	1	yes	characteristic
76	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
77	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
78	#107×C₇₃	—	4	2	no	—
79	#106×C₇₃	—	4	2	no	—
80	#103×C₇₃	—	4	2	no	—
81	#103×C₇₃	—	4	2	no	—
82	#102×C₇₃	—	4	2	no	—
83	#102×C₇₃	—	4	2	no	—
84	C₂²⋊C₈×C₇₃	—	4	2	no	—
85	#95×C₇₃	—	2	2	no	—
86	#95×C₇₃	—	2	2	no	—
87	#95×C₇₃	—	2	1	no	—
88	#95×C₇₃	—	2	1	no	—
89	#95×C₇₃	—	2	1	no	—
90	#95×C₇₃	—	2	1	no	—
91	C₂⁴×C₇₃	—	2	1	no	—
92	C₂⁴×C₇₃	C₂×D₄	1	1	yes	characteristic
93	C₂×Q₈×C₇₃	—	2	2	no	—
94	C₂×Q₈×C₇₃	—	2	2	no	—
95	C₂×Q₈×C₇₃	—	2	1	no	—
96	C₂×Q₈×C₇₃	—	2	1	no	—
97	C₂×Q₈×C₇₃	—	4	2	no	—
98	C₂×Q₈×C₇₃	—	4	2	no	—
99	C₂×Q₈×C₇₃	—	4	2	no	—
100	C₂×D₄×C₇₃	—	2	2	no	—
101	C₂×D₄×C₇₃	—	2	2	no	—
102	C₂×D₄×C₇₃	—	2	1	no	—
103	C₂×D₄×C₇₃	—	2	1	no	—
104	C₂×D₄×C₇₃	—	4	2	no	—
105	C₂×D₄×C₇₃	—	4	2	no	—
106	C₂×D₄×C₇₃	—	4	2	no	—
107	C₂²×C₄×C₇₃	—	2	2	no	—
108	C₂²×C₄×C₇₃	—	2	2	no	—
109	C₂²×C₄×C₇₃	—	2	2	no	—
110	C₂²×C₄×C₇₃	—	2	2	no	—
111	C₂²×C₄×C₇₃	—	2	2	no	—
112	C₂²×C₄×C₇₃	—	2	1	no	—
113	C₂²×C₄×C₇₃	—	2	1	no	—
114	C₂²×C₄×C₇₃	—	2	1	no	—
115	C₂²×C₄×C₇₃	—	2	1	no	—
116	C₂²×C₄×C₇₃	—	2	1	no	—
117	C₂²×C₄×C₇₃	—	2	2	no	—
118	C₂²×C₄×C₇₃	—	2	2	no	—
119	C₂²×C₄×C₇₃	—	4	1	no	—
120	C₂²×C₄×C₇₃	—	4	1	no	—
121	C₂²×C₄×C₇₃	—	4	1	no	—
122	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
123	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
124	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
125	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
126	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
127	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
128	C₂×C₈×C₇₃	—	2	2	no	—
129	C₂×C₈×C₇₃	—	2	2	no	—
130	C₂×C₈×C₇₃	—	2	2	no	—
131	C₂×C₈×C₇₃	—	2	2	no	—
132	C₂×C₈×C₇₃	—	2	2	no	—
133	C₂×C₈×C₇₃	—	2	2	no	—
134	C₄⋊C₄×C₇₃	—	2	2	no	—
135	C₄⋊C₄×C₇₃	—	2	2	no	—
136	C₄⋊C₄×C₇₃	—	2	2	no	—
137	C₄⋊C₄×C₇₃	—	2	2	no	—
138	C₄⋊C₄×C₇₃	—	2	2	no	—
139	C₄⋊C₄×C₇₃	—	2	2	no	—
140	C₄⋊C₄×C₇₃	—	4	2	no	—
141	C₄⋊C₄×C₇₃	—	4	4	no	—
142	C₄⋊C₄×C₇₃	—	4	2	no	—
143	C₄⋊C₄×C₇₃	—	4	2	no	—
144	C₄⋊C₄×C₇₃	—	4	2	no	—
145	C₂²⋊C₄×C₇₃	—	4	2	no	—
146	C₂²⋊C₄×C₇₃	—	4	2	no	—
147	C₂²⋊C₄×C₇₃	—	4	2	no	—
148	C₂²⋊C₄×C₇₃	—	4	2	no	—
149	C₂²⋊C₄×C₇₃	—	4	4	no	—
150	C₂²⋊C₄×C₇₃	—	4	2	no	—
151	C₂²⋊C₄×C₇₃	—	4	2	no	—
152	C₄²×C₇₃	—	2	2	no	—
153	C₄²×C₇₃	—	2	2	no	—
154	C₄²×C₇₃	—	4	1	no	—
155	C₄²×C₇₃	—	4	1	no	—
156	C₂³×C₇₃	—	2	1	no	—
157	C₂³×C₇₃	—	2	1	no	—
158	C₂³×C₇₃	—	2	1	no	—
159	C₂³×C₇₃	—	2	1	no	—
160	C₂³×C₇₃	—	2	1	no	—
161	C₂³×C₇₃	—	2	1	no	—
162	C₂³×C₇₃	—	4	1	no	—
163	C₂³×C₇₃	—	4	1	no	—
164	C₂³×C₇₃	—	4	1	no	—
165	C₂³×C₇₃	—	4	1	no	—
166	C₂³×C₇₃	—	4	1	no	—
167	C₂³×C₇₃	—	4	1	no	—
168	C₂³×C₇₃	—	4	1	no	—
169	C₂³×C₇₃	#137	1	2	yes	—
170	C₂³×C₇₃	C₂²×D₄	1	1	yes	characteristic
171	Q₈×C₇₃	—	4	2	no	—
172	Q₈×C₇₃	—	4	2	no	—
173	Q₈×C₇₃	—	8	4	no	—
174	D₄×C₇₃	—	4	2	no	—
175	D₄×C₇₃	—	4	2	no	—
176	D₄×C₇₃	—	8	4	no	—
177	C₂×C₄×C₇₃	—	2	1	no	—
178	C₂×C₄×C₇₃	—	2	1	no	—
179	C₂×C₄×C₇₃	—	2	1	no	—
180	C₂×C₄×C₇₃	—	2	1	no	—
181	C₂×C₄×C₇₃	—	2	1	no	—
182	C₂×C₄×C₇₃	—	2	1	no	—
183	C₂×C₄×C₇₃	—	2	1	no	—
184	C₂×C₄×C₇₃	—	2	1	no	—
185	C₂×C₄×C₇₃	—	2	1	no	—
186	C₂×C₄×C₇₃	—	2	1	no	—
187	C₂×C₄×C₇₃	—	2	1	no	—
188	C₂×C₄×C₇₃	—	2	1	no	—
189	C₂×C₄×C₇₃	—	2	1	no	—
190	C₂×C₄×C₇₃	—	4	4	no	—
191	C₂×C₄×C₇₃	—	4	4	no	—
192	C₂×C₄×C₇₃	—	4	2	no	—
193	C₂×C₄×C₇₃	—	4	2	no	—
194	C₂×C₄×C₇₃	—	4	1	no	—
195	C₂×C₄×C₇₃	—	4	2	no	—
196	C₂×C₄×C₇₃	—	4	1	no	—
197	C₂×C₄×C₇₃	—	4	1	no	—
198	C₂×C₄×C₇₃	—	4	1	no	—
199	C₂×C₄×C₇₃	—	4	2	no	—
200	C₂×C₄×C₇₃	—	4	1	no	—
201	C₂×C₄×C₇₃	—	4	1	no	—
202	C₂×C₄×C₇₃	—	4	2	no	—
203	C₂×C₄×C₇₃	—	4	2	no	—
204	C₂×C₄×C₇₃	—	4	2	no	—
205	C₂×C₄×C₇₃	—	4	1	no	—
206	C₂×C₄×C₇₃	—	4	1	no	—
207	C₂×C₄×C₇₃	—	4	1	no	—
208	C₂×C₄×C₇₃	—	4	2	no	—
209	C₂×C₄×C₇₃	#135	1	2	yes	—
210	C₂×C₄×C₇₃	AGL(1,ℤ/8)	1	2	yes	—
211	C₂×C₄×C₇₃	H(5,𝔽₂)	1	2	yes	—
212	C₂×C₄×C₇₃	H(5,𝔽₂)	1	2	yes	—
213	C₂×C₄×C₇₃	2₋¹⁺⁴	1	1	yes	characteristic
214	C₂×C₄×C₇₃	2₋¹⁺⁴	1	1	yes	characteristic
215	C₈×C₇₃	—	4	2	no	—
216	C₈×C₇₃	—	4	2	no	—
217	C₂²×C₇₃	—	2	2	no	—
218	C₂²×C₇₃	—	2	2	no	—
219	C₂²×C₇₃	—	2	2	no	—
220	C₂²×C₇₃	—	4	1	no	—
221	C₂²×C₇₃	—	4	1	no	—
222	C₂²×C₇₃	—	4	1	no	—
223	C₂²×C₇₃	—	4	1	no	—
224	C₂²×C₇₃	—	8	1	no	—
225	C₂²×C₇₃	—	8	1	no	—
226	C₂²×C₇₃	—	8	1	no	—
227	C₂²×C₇₃	—	8	1	no	—
228	C₂²×C₇₃	—	8	1	no	—
229	C₂²×C₇₃	—	8	1	no	—
230	C₂²×C₇₃	—	8	1	no	—
231	C₂²×C₇₃	#534	1	1	yes	characteristic
232	C₂²×C₇₃	#535	1	1	yes	characteristic
233	C₂²×C₇₃	#536	1	1	yes	characteristic
234	C₂²×C₇₃	C₂×#135	1	1	yes	characteristic
235	C₂²×C₇₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
236	C₂²×C₇₃	C₂×#137	1	1	yes	characteristic
237	C₂²×C₇₃	#575	1	1	yes	characteristic
238	C₄×C₇₃	—	2	2	no	—
239	C₄×C₇₃	—	2	2	no	—
240	C₄×C₇₃	—	4	1	no	—
241	C₄×C₇₃	—	4	1	no	—
242	C₄×C₇₃	—	4	1	no	—
243	C₄×C₇₃	—	8	1	no	—
244	C₄×C₇₃	—	8	2	no	—
245	C₄×C₇₃	—	8	1	no	—
246	C₄×C₇₃	—	8	2	no	—
247	C₄×C₇₃	—	8	1	no	—
248	C₄×C₇₃	#562	1	2	yes	—
249	C₄×C₇₃	#562	1	2	yes	—
250	#32775	C₇₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
251	C₂×C₇₃	—	4	2	no	—
252	C₂×C₇₃	—	16	1	no	—
253	C₂×C₇₃	#2816	1	1	yes	characteristic
254	C₂×C₇₃	#3190	1	1	yes	characteristic
255	C₂×C₇₃	#3194	1	1	yes	characteristic
256	C₂×C₇₃	#3207	1	1	yes	characteristic
257	C₂×C₇₃	#3215	1	1	yes	characteristic
258	C₂×C₇₃	#3233	1	1	yes	characteristic
259	C₂×C₇₃	#3239	1	1	yes	characteristic
260	#2857	C₂×C₇₃	1	1	yes	characteristic, complemented
261	#2850	C₂×C₇₃	1	1	yes	characteristic
262	#2096	C₂×C₇₃	1	1	yes	characteristic, complemented
263	#2093	C₂×C₇₃	1	1	yes	characteristic, complemented
264	#2085	C₂×C₇₃	1	2	yes	complemented
265	#2042	C₂×C₇₃	1	2	yes	complemented
266	#2036	C₂×C₇₃	1	2	yes	complemented
267	#2034	C₂×C₇₃	1	2	yes	—
268	#2024	C₂×C₇₃	1	1	yes	characteristic, complemented
269	#2023	C₂×C₇₃	1	1	yes	characteristic, complemented
270	#1817	C₂×C₇₃	1	1	yes	characteristic, complemented
271	C₇₃	#32775	1	1	yes	characteristic, direct product factor, Sylow
272	C₂×C₄⋊Q₈	C₂²×C₇₃	1	1	yes	characteristic
273	C₂×#124	C₂²×C₇₃	1	1	yes	characteristic
274	C₂×C₂²⋊Q₈	—	2	1	no	—
275	C₂×C₂²⋊Q₈	C₂²×C₇₃	1	1	yes	characteristic
276	C₂×#121	C₂²×C₇₃	1	1	yes	characteristic
277	C₂²×C₄²	C₂²×C₇₃	1	1	yes	characteristic
278	C₂×#107	C₂²×C₇₃	1	2	yes	—
279	C₂×#106	C₂²×C₇₃	1	2	yes	—
280	C₂×#103	C₂²×C₇₃	1	2	yes	—
281	C₂×#103	C₂²×C₇₃	1	2	yes	—
282	C₂×#102	C₂²×C₇₃	1	2	yes	—
283	C₂×#102	C₂²×C₇₃	1	2	yes	—
284	C₂×C₂²⋊C₈	C₂²×C₇₃	1	2	yes	—
285	#391	—	2	1	no	—
286	#391	C₂²×C₇₃	1	1	yes	characteristic
287	#390	C₂²×C₇₃	1	1	yes	characteristic
288	#389	—	2	1	no	—
289	#389	C₂²×C₇₃	1	2	yes	—
290	#388	—	2	1	no	—
291	#388	—	2	1	no	—
292	#386	—	2	1	no	—
293	#386	—	2	1	no	—
294	#384	C₂²×C₇₃	1	1	yes	characteristic
295	#382	C₂²×C₇₃	1	1	yes	characteristic
296	#380	—	2	1	no	—
297	#380	C₂²×C₇₃	1	2	yes	—
298	#340	C₂²×C₇₃	1	2	yes	—
299	#340	C₂²×C₇₃	1	2	yes	—
300	#336	C₂²×C₇₃	1	2	yes	—
301	#336	C₂²×C₇₃	1	1	yes	characteristic
302	#336	C₂²×C₇₃	1	1	yes	characteristic
303	C₂²×Q₈	—	2	1	no	—
304	C₂²×Q₈	C₂³×C₇₃	1	1	yes	characteristic
305	C₂²×D₄	—	2	1	no	—
306	C₂²×D₄	C₂³×C₇₃	1	1	yes	characteristic
307	C₂³×C₄	D₄×C₇₃	1	1	yes	characteristic
308	C₂³×C₄	D₄×C₇₃	1	1	yes	characteristic
309	C₂³×C₄	C₂³×C₇₃	1	1	yes	characteristic
310	C₂²×C₈	C₂³×C₇₃	1	2	yes	—
311	C₂²×C₈	C₂³×C₇₃	1	2	yes	—
312	C₄⋊Q₈	—	4	2	no	—
313	#124	—	4	2	no	—
314	C₂²⋊Q₈	—	4	2	no	—
315	C₂²⋊Q₈	—	4	4	no	—
316	#121	—	4	2	no	—
317	C₂×C₄⋊C₄	—	2	1	no	—
318	C₂×C₄⋊C₄	—	2	2	no	—
319	C₂×C₄⋊C₄	—	2	1	no	—
320	C₂×C₄⋊C₄	—	2	1	no	—
321	C₂×C₄⋊C₄	—	2	1	no	—
322	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
323	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
324	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
325	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
326	C₂×C₂²⋊C₄	—	2	2	no	—
327	C₂×C₂²⋊C₄	—	2	1	no	—
328	C₂×C₂²⋊C₄	—	2	1	no	—
329	C₂×C₂²⋊C₄	—	2	1	no	—
330	C₂×C₂²⋊C₄	—	2	1	no	—
331	C₂×C₂²⋊C₄	—	2	1	no	—
332	C₂×C₂²⋊C₄	—	2	1	no	—
333	C₂×C₄²	—	4	2	no	—
334	C₂×C₄²	D₄×C₇₃	1	1	yes	characteristic
335	C₂×C₄²	D₄×C₇₃	1	1	yes	characteristic
336	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
337	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
338	#107	—	4	2	no	—
339	#106	—	4	2	no	—
340	#103	—	4	2	no	—
341	#103	—	4	2	no	—
342	#102	—	4	2	no	—
343	#102	—	4	2	no	—
344	C₂²⋊C₈	—	4	2	no	—
345	#95	—	2	2	no	—
346	#95	—	2	2	no	—
347	#95	—	2	1	no	—
348	#95	—	2	1	no	—
349	#95	—	2	1	no	—
350	#95	—	2	1	no	—
351	C₂⁴	—	2	1	no	—
352	C₂⁴	C₂×D₄×C₇₃	1	1	yes	characteristic
353	C₂×Q₈	—	2	2	no	—
354	C₂×Q₈	—	2	2	no	—
355	C₂×Q₈	—	2	1	no	—
356	C₂×Q₈	—	2	1	no	—
357	C₂×Q₈	—	4	2	no	—
358	C₂×Q₈	—	4	2	no	—
359	C₂×Q₈	—	4	2	no	—
360	C₂×D₄	—	2	2	no	—
361	C₂×D₄	—	2	2	no	—
362	C₂×D₄	—	2	1	no	—
363	C₂×D₄	—	2	1	no	—
364	C₂×D₄	—	4	2	no	—
365	C₂×D₄	—	4	2	no	—
366	C₂×D₄	—	4	2	no	—
367	C₂²×C₄	—	2	2	no	—
368	C₂²×C₄	—	2	2	no	—
369	C₂²×C₄	—	2	2	no	—
370	C₂²×C₄	—	2	2	no	—
371	C₂²×C₄	—	2	2	no	—
372	C₂²×C₄	—	2	1	no	—
373	C₂²×C₄	—	2	1	no	—
374	C₂²×C₄	—	2	1	no	—
375	C₂²×C₄	—	2	1	no	—
376	C₂²×C₄	—	2	1	no	—
377	C₂²×C₄	—	2	2	no	—
378	C₂²×C₄	—	2	2	no	—
379	C₂²×C₄	—	4	1	no	—
380	C₂²×C₄	—	4	1	no	—
381	C₂²×C₄	—	4	1	no	—
382	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
383	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
384	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
385	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
386	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
387	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
388	C₂×C₈	—	2	2	no	—
389	C₂×C₈	—	2	2	no	—
390	C₂×C₈	—	2	2	no	—
391	C₂×C₈	—	2	2	no	—
392	C₂×C₈	—	2	2	no	—
393	C₂×C₈	—	2	2	no	—
394	C₄⋊C₄	—	2	2	no	—
395	C₄⋊C₄	—	2	2	no	—
396	C₄⋊C₄	—	2	2	no	—
397	C₄⋊C₄	—	2	2	no	—
398	C₄⋊C₄	—	2	2	no	—
399	C₄⋊C₄	—	2	2	no	—
400	C₄⋊C₄	—	4	2	no	—
401	C₄⋊C₄	—	4	4	no	—
402	C₄⋊C₄	—	4	2	no	—
403	C₄⋊C₄	—	4	2	no	—
404	C₄⋊C₄	—	4	2	no	—
405	C₂²⋊C₄	—	4	2	no	—
406	C₂²⋊C₄	—	4	2	no	—
407	C₂²⋊C₄	—	4	2	no	—
408	C₂²⋊C₄	—	4	2	no	—
409	C₂²⋊C₄	—	4	4	no	—
410	C₂²⋊C₄	—	4	2	no	—
411	C₂²⋊C₄	—	4	2	no	—
412	C₄²	—	2	2	no	—
413	C₄²	—	2	2	no	—
414	C₄²	—	4	1	no	—
415	C₄²	—	4	1	no	—
416	C₂³	—	2	1	no	—
417	C₂³	—	2	1	no	—
418	C₂³	—	2	1	no	—
419	C₂³	—	2	1	no	—
420	C₂³	—	2	1	no	—
421	C₂³	—	2	1	no	—
422	C₂³	—	4	1	no	—
423	C₂³	—	4	1	no	—
424	C₂³	—	4	1	no	—
425	C₂³	—	4	1	no	—
426	C₂³	—	4	1	no	—
427	C₂³	—	4	1	no	—
428	C₂³	—	4	1	no	—
429	C₂³	#137×C₇₃	1	2	yes	—
430	C₂³	C₂²×D₄×C₇₃	1	1	yes	characteristic
431	Q₈	—	4	2	no	—
432	Q₈	—	4	2	no	—
433	Q₈	—	8	4	no	—
434	D₄	—	4	2	no	—
435	D₄	—	4	2	no	—
436	D₄	—	8	4	no	—
437	C₂×C₄	—	2	1	no	—
438	C₂×C₄	—	2	1	no	—
439	C₂×C₄	—	2	1	no	—
440	C₂×C₄	—	2	1	no	—
441	C₂×C₄	—	2	1	no	—
442	C₂×C₄	—	2	1	no	—
443	C₂×C₄	—	2	1	no	—
444	C₂×C₄	—	2	1	no	—
445	C₂×C₄	—	2	1	no	—
446	C₂×C₄	—	2	1	no	—
447	C₂×C₄	—	2	1	no	—
448	C₂×C₄	—	2	1	no	—
449	C₂×C₄	—	2	1	no	—
450	C₂×C₄	—	4	4	no	—
451	C₂×C₄	—	4	4	no	—
452	C₂×C₄	—	4	2	no	—
453	C₂×C₄	—	4	2	no	—
454	C₂×C₄	—	4	1	no	—
455	C₂×C₄	—	4	2	no	—
456	C₂×C₄	—	4	1	no	—
457	C₂×C₄	—	4	1	no	—
458	C₂×C₄	—	4	1	no	—
459	C₂×C₄	—	4	2	no	—
460	C₂×C₄	—	4	1	no	—
461	C₂×C₄	—	4	1	no	—
462	C₂×C₄	—	4	2	no	—
463	C₂×C₄	—	4	2	no	—
464	C₂×C₄	—	4	2	no	—
465	C₂×C₄	—	4	1	no	—
466	C₂×C₄	—	4	1	no	—
467	C₂×C₄	—	4	1	no	—
468	C₂×C₄	—	4	2	no	—
469	C₂×C₄	#135×C₇₃	1	2	yes	—
470	C₂×C₄	AGL(1,ℤ/8)×C₇₃	1	2	yes	—
471	C₂×C₄	H(5,𝔽₂)×C₇₃	1	2	yes	—
472	C₂×C₄	H(5,𝔽₂)×C₇₃	1	2	yes	—
473	C₂×C₄	2₋¹⁺⁴×C₇₃	1	1	yes	characteristic
474	C₂×C₄	2₋¹⁺⁴×C₇₃	1	1	yes	characteristic
475	C₈	—	4	2	no	—
476	C₈	—	4	2	no	—
477	C₂²	—	2	2	no	—
478	C₂²	—	2	2	no	—
479	C₂²	—	2	2	no	—
480	C₂²	—	4	1	no	—
481	C₂²	—	4	1	no	—
482	C₂²	—	4	1	no	—
483	C₂²	—	4	1	no	—
484	C₂²	—	8	1	no	—
485	C₂²	—	8	1	no	—
486	C₂²	—	8	1	no	—
487	C₂²	—	8	1	no	—
488	C₂²	—	8	1	no	—
489	C₂²	—	8	1	no	—
490	C₂²	—	8	1	no	—
491	C₂²	#534×C₇₃	1	1	yes	characteristic
492	C₂²	#535×C₇₃	1	1	yes	characteristic
493	C₂²	#536×C₇₃	1	1	yes	characteristic
494	C₂²	C₂×#135×C₇₃	1	1	yes	characteristic
495	C₂²	C₂×AGL(1,ℤ/8)×C₇₃	1	1	yes	characteristic
496	C₂²	C₂×#137×C₇₃	1	1	yes	characteristic
497	C₂²	#575×C₇₃	1	1	yes	characteristic
498	C₄	—	2	2	no	—
499	C₄	—	2	2	no	—
500	C₄	—	4	1	no	—
501	C₄	—	4	1	no	—
502	C₄	—	4	1	no	—
503	C₄	—	8	1	no	—
504	C₄	—	8	2	no	—
505	C₄	—	8	1	no	—
506	C₄	—	8	1	no	—
507	C₄	—	8	2	no	—
508	C₄	#562×C₇₃	1	2	yes	—
509	C₄	#562×C₇₃	1	2	yes	—
510	C₂	—	4	2	no	—
511	C₂	—	16	1	no	—
512	C₂	C₇₃×#2816	1	1	yes	characteristic
513	C₂	C₇₃×#3190	1	1	yes	characteristic
514	C₂	C₇₃×#3194	1	1	yes	characteristic
515	C₂	C₇₃×#3207	1	1	yes	characteristic
516	C₂	C₇₃×#3215	1	1	yes	characteristic
517	C₂	C₇₃×#3233	1	1	yes	characteristic
518	C₂	C₇₃×#3239	1	1	yes	characteristic

	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 ◁ C₂²×C₄²×C₇₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₇₃×#2857	C₂	semidirect
3. C₇₃×#2096	C₂	semidirect
4. C₇₃×#2093	C₂	semidirect
5. C₇₃×#2085	C₂	semidirect
6. C₇₃×#2042	C₂	semidirect
7. C₇₃×#2036	C₂	semidirect
9. C₇₃×#2024	C₂	semidirect
10. C₇₃×#2023	C₂	semidirect
11. C₇₃×#1817	C₂	semidirect
250. #32775	C₇₃	direct (N × H)
260. #2857	C₂×C₇₃	semidirect
262. #2096	C₂×C₇₃	semidirect
263. #2093	C₂×C₇₃	semidirect
264. #2085	C₂×C₇₃	semidirect
265. #2042	C₂×C₇₃	semidirect
266. #2036	C₂×C₇₃	semidirect
268. #2024	C₂×C₇₃	semidirect
269. #2023	C₂×C₇₃	semidirect
270. #1817	C₂×C₇₃	semidirect
271. C₇₃	#32775	direct (N × H)

Maximal subgroups

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

subgroup	index
C₇₃×#2857	2
C₇₃×#2850	2
C₇₃×#2096	2
C₇₃×#2093	2
C₇₃×#2085	2
C₇₃×#2042	2
C₇₃×#2036	2
C₇₃×#2034	2
C₇₃×#2024	2
C₇₃×#2023	2
C₇₃×#1817	2
#32775	73

Subgroups — C73×#32775 #32942179

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₃×#32775 #32942179