Subgroups — C₇₃×#23755 #32933159

Order 18688.

880 conjugacy classes of subgroups.

The subgroup lattice has 512 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×#121×C₇₃	C₂	1	1	yes	maximal, characteristic
2	C₇₃×#2285	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇₃×#2100	C₂	1	1	yes	maximal, characteristic, complemented
4	C₇₃×#2094	C₂	1	1	yes	maximal, characteristic, complemented
5	C₇₃×#2084	C₂	1	1	yes	maximal, characteristic, complemented
6	C₇₃×#2077	C₂	1	2	yes	maximal, complemented
7	C₇₃×#2071	C₂	1	1	yes	maximal, characteristic, complemented
8	C₇₃×#2034	C₂	1	2	yes	maximal
9	C₄×#106×C₇₃	C₂	1	2	yes	maximal, complemented
10	C₄×#102×C₇₃	C₂	1	2	yes	maximal, complemented
11	C₄×C₂²⋊C₈×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#121×C₇₃	C₂²	1	1	yes	characteristic
13	C₂×C₄×D₄×C₇₃	—	2	1	no	—
14	C₂×C₄×D₄×C₇₃	C₂²	1	1	yes	characteristic
15	C₂×#117×C₇₃	—	2	1	no	—
16	C₂²×C₄²×C₇₃	C₂²	1	1	yes	characteristic
17	C₂×#106×C₇₃	C₂²	1	2	yes	—
18	C₂×#106×C₇₃	C₂²	1	2	yes	—
19	C₂×#102×C₇₃	C₂²	1	2	yes	—
20	C₂×#102×C₇₃	C₂²	1	2	yes	—
21	C₂×C₂²⋊C₈×C₇₃	C₂²	1	2	yes	—
22	C₂×C₄×C₈×C₇₃	C₂²	1	2	yes	—
23	#390×C₇₃	C₂²	1	1	yes	characteristic
24	#389×C₇₃	C₂²	1	1	yes	characteristic
25	#388×C₇₃	—	2	1	no	—
26	#386×C₇₃	—	2	1	no	—
27	#384×C₇₃	C₂²	1	1	yes	characteristic
28	#384×C₇₃	C₂²	1	1	yes	characteristic
29	#382×C₇₃	—	2	1	no	—
30	#380×C₇₃	—	2	1	no	—
31	#380×C₇₃	C₂²	1	2	yes	—
32	#380×C₇₃	C₂²	1	1	yes	characteristic
33	C₄×C₄⋊C₄×C₇₃	—	2	1	no	—
34	C₄×C₄⋊C₄×C₇₃	C₂²	1	2	yes	—
35	C₄×C₄⋊C₄×C₇₃	C₂²	1	1	yes	characteristic
36	C₄×C₂²⋊C₄×C₇₃	—	2	1	no	—
37	#340×C₇₃	C₂²	1	2	yes	—
38	#340×C₇₃	C₂²	1	2	yes	—
39	#340×C₇₃	C₂²	1	2	yes	—
40	#340×C₇₃	C₂²	1	2	yes	—
41	#336×C₇₃	C₂²	1	1	yes	characteristic
42	#336×C₇₃	C₂²	1	1	yes	characteristic
43	C₂²×D₄×C₇₃	—	2	1	no	—
44	C₂²×D₄×C₇₃	C₂³	1	1	yes	characteristic
45	C₂³×C₄×C₇₃	—	2	1	no	—
46	C₂³×C₄×C₇₃	D₄	1	1	yes	characteristic
47	C₂³×C₄×C₇₃	D₄	1	1	yes	characteristic
48	C₂³×C₄×C₇₃	C₂³	1	1	yes	characteristic
49	C₂²×C₈×C₇₃	C₂³	1	2	yes	—
50	C₂²×C₈×C₇₃	C₂³	1	2	yes	—
51	#121×C₇₃	—	2	2	no	—
52	#121×C₇₃	—	2	2	no	—
53	C₄×D₄×C₇₃	—	2	4	no	—
54	C₄×D₄×C₇₃	—	4	4	no	—
55	#117×C₇₃	—	4	4	no	—
56	C₂×C₄⋊C₄×C₇₃	—	2	1	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	C₂³	1	2	yes	—
62	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
63	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
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	1	no	—
67	C₂×C₂²⋊C₄×C₇₃	—	2	2	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×C₄²×C₇₃	—	2	4	no	—
73	C₂×C₄²×C₇₃	—	2	1	no	—
74	C₂×C₄²×C₇₃	—	2	2	no	—
75	C₂×C₄²×C₇₃	D₄	1	1	yes	characteristic
76	C₂×C₄²×C₇₃	D₄	1	1	yes	characteristic
77	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
78	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
79	#106×C₇₃	—	2	4	no	—
80	#106×C₇₃	—	2	4	no	—
81	#102×C₇₃	—	2	4	no	—
82	#102×C₇₃	—	2	4	no	—
83	C₂²⋊C₈×C₇₃	—	2	4	no	—
84	C₄×C₈×C₇₃	—	2	4	no	—
85	#95×C₇₃	—	2	1	no	—
86	#95×C₇₃	—	2	1	no	—
87	#95×C₇₃	—	2	2	no	—
88	#95×C₇₃	—	2	2	no	—
89	#95×C₇₃	—	2	1	no	—
90	C₂⁴×C₇₃	—	2	1	no	—
91	C₂⁴×C₇₃	C₂×D₄	1	1	yes	characteristic
92	C₂×D₄×C₇₃	—	2	4	no	—
93	C₂×D₄×C₇₃	—	2	2	no	—
94	C₂×D₄×C₇₃	—	2	2	no	—
95	C₂×D₄×C₇₃	—	2	1	no	—
96	C₂×D₄×C₇₃	—	4	2	no	—
97	C₂×D₄×C₇₃	—	4	2	no	—
98	C₂×D₄×C₇₃	#41	1	2	yes	—
99	C₂²×C₄×C₇₃	—	2	2	no	—
100	C₂²×C₄×C₇₃	—	2	2	no	—
101	C₂²×C₄×C₇₃	—	2	1	no	—
102	C₂²×C₄×C₇₃	—	2	2	no	—
103	C₂²×C₄×C₇₃	—	2	2	no	—
104	C₂²×C₄×C₇₃	—	2	2	no	—
105	C₂²×C₄×C₇₃	—	2	2	no	—
106	C₂²×C₄×C₇₃	—	2	1	no	—
107	C₂²×C₄×C₇₃	—	2	1	no	—
108	C₂²×C₄×C₇₃	—	2	1	no	—
109	C₂²×C₄×C₇₃	—	2	2	no	—
110	C₂²×C₄×C₇₃	—	2	2	no	—
111	C₂²×C₄×C₇₃	—	2	1	no	—
112	C₂²×C₄×C₇₃	—	4	1	no	—
113	C₂²×C₄×C₇₃	—	4	2	no	—
114	C₂²×C₄×C₇₃	—	4	2	no	—
115	C₂²×C₄×C₇₃	—	4	2	no	—
116	C₂²×C₄×C₇₃	SD₁₆	1	4	yes	—
117	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
118	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
119	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
120	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
121	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
122	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
123	C₂×C₈×C₇₃	—	2	2	no	—
124	C₂×C₈×C₇₃	—	2	2	no	—
125	C₂×C₈×C₇₃	—	2	2	no	—
126	C₂×C₈×C₇₃	—	2	2	no	—
127	C₂×C₈×C₇₃	—	2	2	no	—
128	C₂×C₈×C₇₃	#41	1	4	yes	—
129	C₄⋊C₄×C₇₃	—	2	1	no	—
130	C₄⋊C₄×C₇₃	—	2	2	no	—
131	C₄⋊C₄×C₇₃	—	2	2	no	—
132	C₄⋊C₄×C₇₃	—	2	2	no	—
133	C₄⋊C₄×C₇₃	—	2	2	no	—
134	C₄⋊C₄×C₇₃	—	2	2	no	—
135	C₄⋊C₄×C₇₃	—	2	2	no	—
136	C₄⋊C₄×C₇₃	—	4	2	no	—
137	C₄⋊C₄×C₇₃	—	4	2	no	—
138	C₄⋊C₄×C₇₃	—	4	2	no	—
139	C₄⋊C₄×C₇₃	—	4	2	no	—
140	C₄⋊C₄×C₇₃	—	4	2	no	—
141	C₄⋊C₄×C₇₃	#41	1	2	yes	—
142	C₂²⋊C₄×C₇₃	—	2	4	no	—
143	C₂²⋊C₄×C₇₃	—	4	4	no	—
144	C₂²⋊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	C₄²×C₇₃	—	2	2	no	—
149	C₄²×C₇₃	—	2	2	no	—
150	C₄²×C₇₃	—	2	2	no	—
151	C₄²×C₇₃	—	4	2	no	—
152	C₄²×C₇₃	—	4	4	no	—
153	C₄²×C₇₃	#41	1	4	yes	—
154	C₂³×C₇₃	—	2	1	no	—
155	C₂³×C₇₃	—	2	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	2	no	—
161	C₂³×C₇₃	—	4	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	C₂×SD₁₆	1	2	yes	—
168	C₂³×C₇₃	C₂²×D₄	1	1	yes	characteristic
169	D₄×C₇₃	—	2	4	no	—
170	D₄×C₇₃	—	4	8	no	—
171	D₄×C₇₃	—	4	2	no	—
172	C₂×C₄×C₇₃	—	2	1	no	—
173	C₂×C₄×C₇₃	—	2	1	no	—
174	C₂×C₄×C₇₃	—	2	1	no	—
175	C₂×C₄×C₇₃	—	2	1	no	—
176	C₂×C₄×C₇₃	—	2	1	no	—
177	C₂×C₄×C₇₃	—	2	1	no	—
178	C₂×C₄×C₇₃	—	2	8	no	—
179	C₂×C₄×C₇₃	—	2	1	no	—
180	C₂×C₄×C₇₃	—	2	1	no	—
181	C₂×C₄×C₇₃	—	2	2	no	—
182	C₂×C₄×C₇₃	—	2	1	no	—
183	C₂×C₄×C₇₃	—	4	4	no	—
184	C₂×C₄×C₇₃	—	4	1	no	—
185	C₂×C₄×C₇₃	—	4	1	no	—
186	C₂×C₄×C₇₃	—	4	2	no	—
187	C₂×C₄×C₇₃	—	4	2	no	—
188	C₂×C₄×C₇₃	—	4	1	no	—
189	C₂×C₄×C₇₃	—	4	2	no	—
190	C₂×C₄×C₇₃	—	4	1	no	—
191	C₂×C₄×C₇₃	—	4	2	no	—
192	C₂×C₄×C₇₃	—	4	1	no	—
193	C₂×C₄×C₇₃	—	4	1	no	—
194	C₂×C₄×C₇₃	—	4	1	no	—
195	C₂×C₄×C₇₃	—	4	2	no	—
196	C₂×C₄×C₇₃	—	4	2	no	—
197	C₂×C₄×C₇₃	—	4	2	no	—
198	C₂×C₄×C₇₃	—	4	1	no	—
199	C₂×C₄×C₇₃	—	4	2	no	—
200	C₂×C₄×C₇₃	—	8	4	no	—
201	C₂×C₄×C₇₃	#123	1	2	yes	—
202	C₂×C₄×C₇₃	#123	1	2	yes	—
203	C₂×C₄×C₇₃	C₂×SD₁₆	1	2	yes	—
204	C₂×C₄×C₇₃	C₂×SD₁₆	1	2	yes	—
205	C₂×C₄×C₇₃	#135	1	2	yes	—
206	C₂×C₄×C₇₃	AGL(1,ℤ/8)	1	2	yes	—
207	C₂×C₄×C₇₃	C₂×#41	1	2	yes	—
208	C₂×C₄×C₇₃	C₂×#41	1	1	yes	characteristic
209	C₂×C₄×C₇₃	C₂×#41	1	1	yes	characteristic
210	C₂×C₄×C₇₃	C₂×#41	1	2	yes	—
211	C₈×C₇₃	—	2	4	no	—
212	C₈×C₇₃	—	4	2	no	—
213	C₂²×C₇₃	—	2	2	no	—
214	C₂²×C₇₃	—	2	2	no	—
215	C₂²×C₇₃	—	2	2	no	—
216	C₂²×C₇₃	—	4	1	no	—
217	C₂²×C₇₃	—	4	1	no	—
218	C₂²×C₇₃	—	4	1	no	—
219	C₂²×C₇₃	—	4	1	no	—
220	C₂²×C₇₃	—	4	2	no	—
221	C₂²×C₇₃	—	4	2	no	—
222	C₂²×C₇₃	—	4	2	no	—
223	C₂²×C₇₃	—	8	1	no	—
224	C₂²×C₇₃	—	8	1	no	—
225	C₂²×C₇₃	—	8	1	no	—
226	C₂²×C₇₃	—	8	1	no	—
227	C₂²×C₇₃	C₂×#123	1	1	yes	characteristic
228	C₂²×C₇₃	#525	1	1	yes	characteristic
229	C₂²×C₇₃	#532	1	1	yes	characteristic
230	C₂²×C₇₃	C₂²×SD₁₆	1	1	yes	characteristic
231	C₂²×C₇₃	C₂×#135	1	1	yes	characteristic
232	C₂²×C₇₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
233	C₂²×C₇₃	#575	1	1	yes	characteristic
234	C₄×C₇₃	—	2	2	no	—
235	C₄×C₇₃	—	2	2	no	—
236	C₄×C₇₃	—	2	2	no	—
237	C₄×C₇₃	—	4	2	no	—
238	C₄×C₇₃	—	4	1	no	—
239	C₄×C₇₃	—	8	1	no	—
240	C₄×C₇₃	—	8	2	no	—
241	C₄×C₇₃	—	8	1	no	—
242	C₄×C₇₃	—	8	2	no	—
243	C₄×C₇₃	#481	1	4	yes	—
244	C₄×C₇₃	#529	1	2	yes	—
245	C₄×C₇₃	#529	1	2	yes	—
246	#23755	C₇₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
247	C₂×C₇₃	—	4	2	no	—
248	C₂×C₇₃	—	8	2	no	—
249	C₂×C₇₃	#2395	1	1	yes	characteristic
250	C₂×C₇₃	C₂×#481	1	1	yes	characteristic
251	C₂×C₇₃	#3091	1	1	yes	characteristic
252	C₂×C₇₃	#3101	1	1	yes	characteristic
253	C₂×C₇₃	#3106	1	1	yes	characteristic
254	C₂×C₇₃	#3167	1	1	yes	characteristic
255	C₂×C₇₃	#3171	1	1	yes	characteristic
256	C₄×#121	C₂×C₇₃	1	1	yes	characteristic
257	#2285	C₂×C₇₃	1	1	yes	characteristic, complemented
258	#2100	C₂×C₇₃	1	1	yes	characteristic, complemented
259	#2094	C₂×C₇₃	1	1	yes	characteristic, complemented
260	#2084	C₂×C₇₃	1	1	yes	characteristic, complemented
261	#2077	C₂×C₇₃	1	2	yes	complemented
262	#2071	C₂×C₇₃	1	1	yes	characteristic, complemented
263	#2034	C₂×C₇₃	1	2	yes	—
264	C₄×#106	C₂×C₇₃	1	2	yes	complemented
265	C₄×#102	C₂×C₇₃	1	2	yes	complemented
266	C₄×C₂²⋊C₈	C₂×C₇₃	1	1	yes	characteristic, complemented
267	C₇₃	#23755	1	1	yes	characteristic, direct product factor, Sylow
268	C₂×#121	C₂²×C₇₃	1	1	yes	characteristic
269	C₂×C₄×D₄	—	2	1	no	—
270	C₂×C₄×D₄	C₂²×C₇₃	1	1	yes	characteristic
271	C₂×#117	—	2	1	no	—
272	C₂²×C₄²	C₂²×C₇₃	1	1	yes	characteristic
273	C₂×#106	C₂²×C₇₃	1	2	yes	—
274	C₂×#106	C₂²×C₇₃	1	2	yes	—
275	C₂×#102	C₂²×C₇₃	1	2	yes	—
276	C₂×#102	C₂²×C₇₃	1	2	yes	—
277	C₂×C₂²⋊C₈	C₂²×C₇₃	1	2	yes	—
278	C₂×C₄×C₈	C₂²×C₇₃	1	2	yes	—
279	#390	C₂²×C₇₃	1	1	yes	characteristic
280	#389	C₂²×C₇₃	1	1	yes	characteristic
281	#388	—	2	1	no	—
282	#386	—	2	1	no	—
283	#384	C₂²×C₇₃	1	1	yes	characteristic
284	#384	C₂²×C₇₃	1	1	yes	characteristic
285	#382	—	2	1	no	—
286	#380	—	2	1	no	—
287	#380	C₂²×C₇₃	1	1	yes	characteristic
288	#380	C₂²×C₇₃	1	2	yes	—
289	C₄×C₄⋊C₄	—	2	1	no	—
290	C₄×C₄⋊C₄	C₂²×C₇₃	1	2	yes	—
291	C₄×C₄⋊C₄	C₂²×C₇₃	1	1	yes	characteristic
292	C₄×C₂²⋊C₄	—	2	1	no	—
293	#340	C₂²×C₇₃	1	2	yes	—
294	#340	C₂²×C₇₃	1	2	yes	—
295	#340	C₂²×C₇₃	1	2	yes	—
296	#340	C₂²×C₇₃	1	2	yes	—
297	#336	C₂²×C₇₃	1	1	yes	characteristic
298	#336	C₂²×C₇₃	1	1	yes	characteristic
299	C₂²×D₄	—	2	1	no	—
300	C₂²×D₄	C₂³×C₇₃	1	1	yes	characteristic
301	C₂³×C₄	—	2	1	no	—
302	C₂³×C₄	D₄×C₇₃	1	1	yes	characteristic
303	C₂³×C₄	D₄×C₇₃	1	1	yes	characteristic
304	C₂³×C₄	C₂³×C₇₃	1	1	yes	characteristic
305	C₂²×C₈	C₂³×C₇₃	1	2	yes	—
306	C₂²×C₈	C₂³×C₇₃	1	2	yes	—
307	#121	—	2	2	no	—
308	#121	—	2	2	no	—
309	C₄×D₄	—	2	4	no	—
310	C₄×D₄	—	4	4	no	—
311	#117	—	4	4	no	—
312	C₂×C₄⋊C₄	—	2	1	no	—
313	C₂×C₄⋊C₄	—	2	1	no	—
314	C₂×C₄⋊C₄	—	2	1	no	—
315	C₂×C₄⋊C₄	—	2	1	no	—
316	C₂×C₄⋊C₄	—	2	1	no	—
317	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
318	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
319	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
320	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
321	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
322	C₂×C₂²⋊C₄	—	2	1	no	—
323	C₂×C₂²⋊C₄	—	2	2	no	—
324	C₂×C₂²⋊C₄	—	2	1	no	—
325	C₂×C₂²⋊C₄	—	2	1	no	—
326	C₂×C₂²⋊C₄	—	2	1	no	—
327	C₂×C₂²⋊C₄	—	2	1	no	—
328	C₂×C₄²	—	2	4	no	—
329	C₂×C₄²	—	2	2	no	—
330	C₂×C₄²	—	2	1	no	—
331	C₂×C₄²	D₄×C₇₃	1	1	yes	characteristic
332	C₂×C₄²	D₄×C₇₃	1	1	yes	characteristic
333	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
334	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
335	#106	—	2	4	no	—
336	#106	—	2	4	no	—
337	#102	—	2	4	no	—
338	#102	—	2	4	no	—
339	C₂²⋊C₈	—	2	4	no	—
340	C₄×C₈	—	2	4	no	—
341	#95	—	2	1	no	—
342	#95	—	2	1	no	—
343	#95	—	2	2	no	—
344	#95	—	2	2	no	—
345	#95	—	2	1	no	—
346	C₂⁴	—	2	1	no	—
347	C₂⁴	C₂×D₄×C₇₃	1	1	yes	characteristic
348	C₂×D₄	—	2	4	no	—
349	C₂×D₄	—	2	2	no	—
350	C₂×D₄	—	2	2	no	—
351	C₂×D₄	—	2	1	no	—
352	C₂×D₄	—	4	2	no	—
353	C₂×D₄	—	4	2	no	—
354	C₂×D₄	#41×C₇₃	1	2	yes	—
355	C₂²×C₄	—	2	2	no	—
356	C₂²×C₄	—	2	2	no	—
357	C₂²×C₄	—	2	1	no	—
358	C₂²×C₄	—	2	2	no	—
359	C₂²×C₄	—	2	2	no	—
360	C₂²×C₄	—	2	2	no	—
361	C₂²×C₄	—	2	2	no	—
362	C₂²×C₄	—	2	1	no	—
363	C₂²×C₄	—	2	1	no	—
364	C₂²×C₄	—	2	1	no	—
365	C₂²×C₄	—	2	2	no	—
366	C₂²×C₄	—	2	2	no	—
367	C₂²×C₄	—	2	1	no	—
368	C₂²×C₄	—	4	1	no	—
369	C₂²×C₄	—	4	2	no	—
370	C₂²×C₄	—	4	2	no	—
371	C₂²×C₄	—	4	2	no	—
372	C₂²×C₄	SD₁₆×C₇₃	1	4	yes	—
373	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
374	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
375	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
376	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
377	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
378	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
379	C₂×C₈	—	2	2	no	—
380	C₂×C₈	—	2	2	no	—
381	C₂×C₈	—	2	2	no	—
382	C₂×C₈	—	2	2	no	—
383	C₂×C₈	—	2	2	no	—
384	C₂×C₈	#41×C₇₃	1	4	yes	—
385	C₄⋊C₄	—	2	1	no	—
386	C₄⋊C₄	—	2	2	no	—
387	C₄⋊C₄	—	2	2	no	—
388	C₄⋊C₄	—	2	2	no	—
389	C₄⋊C₄	—	2	2	no	—
390	C₄⋊C₄	—	2	2	no	—
391	C₄⋊C₄	—	2	2	no	—
392	C₄⋊C₄	—	4	2	no	—
393	C₄⋊C₄	—	4	2	no	—
394	C₄⋊C₄	—	4	2	no	—
395	C₄⋊C₄	—	4	2	no	—
396	C₄⋊C₄	—	4	2	no	—
397	C₄⋊C₄	#41×C₇₃	1	2	yes	—
398	C₂²⋊C₄	—	2	4	no	—
399	C₂²⋊C₄	—	4	4	no	—
400	C₂²⋊C₄	—	4	2	no	—
401	C₂²⋊C₄	—	4	2	no	—
402	C₂²⋊C₄	—	4	2	no	—
403	C₂²⋊C₄	—	4	2	no	—
404	C₄²	—	2	2	no	—
405	C₄²	—	2	2	no	—
406	C₄²	—	2	2	no	—
407	C₄²	—	4	2	no	—
408	C₄²	—	4	4	no	—
409	C₄²	#41×C₇₃	1	4	yes	—
410	C₂³	—	2	1	no	—
411	C₂³	—	2	1	no	—
412	C₂³	—	2	1	no	—
413	C₂³	—	2	1	no	—
414	C₂³	—	2	1	no	—
415	C₂³	—	2	1	no	—
416	C₂³	—	2	2	no	—
417	C₂³	—	4	1	no	—
418	C₂³	—	4	1	no	—
419	C₂³	—	4	1	no	—
420	C₂³	—	4	1	no	—
421	C₂³	—	4	1	no	—
422	C₂³	—	4	1	no	—
423	C₂³	C₂×SD₁₆×C₇₃	1	2	yes	—
424	C₂³	C₂²×D₄×C₇₃	1	1	yes	characteristic
425	D₄	—	2	4	no	—
426	D₄	—	4	8	no	—
427	D₄	—	4	2	no	—
428	C₂×C₄	—	2	1	no	—
429	C₂×C₄	—	2	1	no	—
430	C₂×C₄	—	2	1	no	—
431	C₂×C₄	—	2	1	no	—
432	C₂×C₄	—	2	1	no	—
433	C₂×C₄	—	2	1	no	—
434	C₂×C₄	—	2	8	no	—
435	C₂×C₄	—	2	1	no	—
436	C₂×C₄	—	2	1	no	—
437	C₂×C₄	—	2	2	no	—
438	C₂×C₄	—	2	1	no	—
439	C₂×C₄	—	4	4	no	—
440	C₂×C₄	—	4	1	no	—
441	C₂×C₄	—	4	1	no	—
442	C₂×C₄	—	4	2	no	—
443	C₂×C₄	—	4	2	no	—
444	C₂×C₄	—	4	1	no	—
445	C₂×C₄	—	4	2	no	—
446	C₂×C₄	—	4	1	no	—
447	C₂×C₄	—	4	2	no	—
448	C₂×C₄	—	4	1	no	—
449	C₂×C₄	—	4	1	no	—
450	C₂×C₄	—	4	1	no	—
451	C₂×C₄	—	4	2	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	—	8	4	no	—
457	C₂×C₄	#123×C₇₃	1	2	yes	—
458	C₂×C₄	#123×C₇₃	1	2	yes	—
459	C₂×C₄	C₂×SD₁₆×C₇₃	1	2	yes	—
460	C₂×C₄	C₂×SD₁₆×C₇₃	1	2	yes	—
461	C₂×C₄	#135×C₇₃	1	2	yes	—
462	C₂×C₄	AGL(1,ℤ/8)×C₇₃	1	2	yes	—
463	C₂×C₄	C₂×#41×C₇₃	1	2	yes	—
464	C₂×C₄	C₂×#41×C₇₃	1	1	yes	characteristic
465	C₂×C₄	C₂×#41×C₇₃	1	1	yes	characteristic
466	C₂×C₄	C₂×#41×C₇₃	1	2	yes	—
467	C₈	—	2	4	no	—
468	C₈	—	4	2	no	—
469	C₂²	—	2	2	no	—
470	C₂²	—	2	2	no	—
471	C₂²	—	2	2	no	—
472	C₂²	—	4	1	no	—
473	C₂²	—	4	1	no	—
474	C₂²	—	4	1	no	—
475	C₂²	—	4	1	no	—
476	C₂²	—	4	2	no	—
477	C₂²	—	4	2	no	—
478	C₂²	—	4	2	no	—
479	C₂²	—	8	1	no	—
480	C₂²	—	8	1	no	—
481	C₂²	—	8	1	no	—
482	C₂²	—	8	1	no	—
483	C₂²	C₂×#123×C₇₃	1	1	yes	characteristic
484	C₂²	#525×C₇₃	1	1	yes	characteristic
485	C₂²	#532×C₇₃	1	1	yes	characteristic
486	C₂²	C₂²×SD₁₆×C₇₃	1	1	yes	characteristic
487	C₂²	C₂×#135×C₇₃	1	1	yes	characteristic
488	C₂²	C₂×AGL(1,ℤ/8)×C₇₃	1	1	yes	characteristic
489	C₂²	#575×C₇₃	1	1	yes	characteristic
490	C₄	—	2	2	no	—
491	C₄	—	2	2	no	—
492	C₄	—	2	2	no	—
493	C₄	—	4	2	no	—
494	C₄	—	4	1	no	—
495	C₄	—	8	1	no	—
496	C₄	—	8	2	no	—
497	C₄	—	8	1	no	—
498	C₄	—	8	2	no	—
499	C₄	#481×C₇₃	1	4	yes	—
500	C₄	#529×C₇₃	1	2	yes	—
501	C₄	#529×C₇₃	1	2	yes	—
502	C₂	—	4	2	no	—
503	C₂	—	8	2	no	—
504	C₂	C₇₃×#2395	1	1	yes	characteristic
505	C₂	C₂×#481×C₇₃	1	1	yes	characteristic
506	C₂	C₇₃×#3091	1	1	yes	characteristic
507	C₂	C₇₃×#3101	1	1	yes	characteristic
508	C₂	C₇₃×#3106	1	1	yes	characteristic
509	C₂	C₇₃×#3167	1	1	yes	characteristic
510	C₂	C₇₃×#3171	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄×C₇₃	C₂×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₇₃
socle	C₂³×C₇₃	C₂²×D₄
prime radical	C₂×#121×C₇₃	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₇₃ ◁ C₂²×C₄²×C₇₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₇₃×#2285	C₂	semidirect
3. C₇₃×#2100	C₂	semidirect
4. C₇₃×#2094	C₂	semidirect
5. C₇₃×#2084	C₂	semidirect
6. C₇₃×#2077	C₂	semidirect
7. C₇₃×#2071	C₂	semidirect
9. C₄×#106×C₇₃	C₂	semidirect
10. C₄×#102×C₇₃	C₂	semidirect
11. C₄×C₂²⋊C₈×C₇₃	C₂	semidirect
246. #23755	C₇₃	direct (N × H)
257. #2285	C₂×C₇₃	semidirect
258. #2100	C₂×C₇₃	semidirect
259. #2094	C₂×C₇₃	semidirect
260. #2084	C₂×C₇₃	semidirect
261. #2077	C₂×C₇₃	semidirect
262. #2071	C₂×C₇₃	semidirect
264. C₄×#106	C₂×C₇₃	semidirect
265. C₄×#102	C₂×C₇₃	semidirect
266. C₄×C₂²⋊C₈	C₂×C₇₃	semidirect
267. C₇₃	#23755	direct (N × H)

Maximal subgroups

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

subgroup	index
C₄×#121×C₇₃	2
C₇₃×#2285	2
C₇₃×#2100	2
C₇₃×#2094	2
C₇₃×#2084	2
C₇₃×#2077	2
C₇₃×#2071	2
C₇₃×#2034	2
C₄×#106×C₇₃	2
C₄×#102×C₇₃	2
C₄×C₂²⋊C₈×C₇₃	2
#23755	73

Subgroups — C73×#23755 #32933159

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₃×#23755 #32933159