Subgroups — C₇₃×#24651 #32934055

Order 18688.

980 conjugacy classes of subgroups.

The subgroup lattice has 588 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#461×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#431×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇₃×#2857	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄×#121×C₇₃	C₂	1	1	yes	maximal, characteristic
5	C₇₃×#2035	C₂	1	2	yes	maximal, complemented
6	C₇₃×#2000	C₂	1	2	yes	maximal
7	C₇₃×#1981	C₂	1	1	yes	maximal, characteristic, complemented
8	C₇₃×#1968	C₂	1	2	yes	maximal, complemented
9	C₇₃×#1948	C₂	1	1	yes	maximal, characteristic, complemented
10	C₇₃×#1933	C₂	1	2	yes	maximal, complemented
11	C₇₃×#1802	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×SD₁₆×C₇₃	C₂²	1	2	yes	—
13	C₂×C₄⋊Q₈×C₇₃	C₂²	1	1	yes	characteristic
14	C₂×C₂²⋊Q₈×C₇₃	C₂²	1	2	yes	—
15	C₂×#121×C₇₃	C₂²	1	1	yes	characteristic
16	C₂×C₄×D₄×C₇₃	—	2	1	no	—
17	C₂×C₄×D₄×C₇₃	C₂²	1	1	yes	characteristic
18	C₂²×C₄²×C₇₃	C₂²	1	1	yes	characteristic
19	#461×C₇₃	—	2	4	no	—
20	#431×C₇₃	—	2	4	no	—
21	C₂×#106×C₇₃	C₂²	1	2	yes	—
22	C₂×C₄⋊C₈×C₇₃	C₂²	1	1	yes	characteristic
23	C₂×C₄⋊C₈×C₇₃	C₂²	1	1	yes	characteristic
24	C₂×#103×C₇₃	C₂²	1	2	yes	—
25	C₂×#103×C₇₃	C₂²	1	2	yes	—
26	C₂×#103×C₇₃	C₂²	1	2	yes	—
27	C₂×#102×C₇₃	C₂²	1	2	yes	—
28	C₂×C₂²⋊C₈×C₇₃	C₂²	1	2	yes	—
29	C₂×C₄×C₈×C₇₃	C₂²	1	2	yes	—
30	#391×C₇₃	C₂²	1	2	yes	—
31	#390×C₇₃	C₂²	1	1	yes	characteristic
32	#389×C₇₃	—	2	1	no	—
33	#389×C₇₃	—	2	1	no	—
34	#389×C₇₃	C₂²	1	1	yes	characteristic
35	#388×C₇₃	—	2	1	no	—
36	#386×C₇₃	—	2	1	no	—
37	#384×C₇₃	C₂²	1	1	yes	characteristic
38	#380×C₇₃	—	2	1	no	—
39	#380×C₇₃	—	2	1	no	—
40	#380×C₇₃	C₂²	1	1	yes	characteristic
41	C₄×C₄⋊C₄×C₇₃	C₂²	1	1	yes	characteristic
42	C₄×C₂²⋊C₄×C₇₃	—	2	1	no	—
43	#340×C₇₃	C₂²	1	2	yes	—
44	#340×C₇₃	C₂²	1	2	yes	—
45	C₂²×Q₈×C₇₃	C₂³	1	2	yes	—
46	C₂²×D₄×C₇₃	—	2	1	no	—
47	C₂²×D₄×C₇₃	C₂³	1	1	yes	characteristic
48	C₂³×C₄×C₇₃	—	2	1	no	—
49	C₂³×C₄×C₇₃	D₄	1	1	yes	characteristic
50	C₂³×C₄×C₇₃	D₄	1	1	yes	characteristic
51	C₂³×C₄×C₇₃	C₂³	1	1	yes	characteristic
52	C₂×SD₁₆×C₇₃	—	2	4	no	—
53	C₂×SD₁₆×C₇₃	—	2	4	no	—
54	C₂×SD₁₆×C₇₃	—	4	2	no	—
55	C₂²×C₈×C₇₃	C₂³	1	2	yes	—
56	C₂²×C₈×C₇₃	C₂³	1	2	yes	—
57	C₄⋊Q₈×C₇₃	—	2	2	no	—
58	C₄⋊Q₈×C₇₃	—	2	2	no	—
59	C₂²⋊Q₈×C₇₃	—	4	2	no	—
60	C₂²⋊Q₈×C₇₃	—	4	2	no	—
61	#121×C₇₃	—	2	2	no	—
62	#121×C₇₃	—	2	2	no	—
63	C₄×D₄×C₇₃	—	2	2	no	—
64	C₄×D₄×C₇₃	—	2	2	no	—
65	C₄×D₄×C₇₃	—	4	4	no	—
66	C₂×C₄⋊C₄×C₇₃	—	2	1	no	—
67	C₂×C₄⋊C₄×C₇₃	—	2	1	no	—
68	C₂×C₄⋊C₄×C₇₃	—	2	1	no	—
69	C₂×C₄⋊C₄×C₇₃	—	2	1	no	—
70	C₂×C₄⋊C₄×C₇₃	—	2	1	no	—
71	C₂×C₄⋊C₄×C₇₃	—	2	2	no	—
72	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
73	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
74	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
75	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
76	C₂×C₂²⋊C₄×C₇₃	—	2	1	no	—
77	C₂×C₂²⋊C₄×C₇₃	—	2	2	no	—
78	C₂×C₂²⋊C₄×C₇₃	—	2	1	no	—
79	C₂×C₂²⋊C₄×C₇₃	—	2	1	no	—
80	C₂×C₂²⋊C₄×C₇₃	—	2	1	no	—
81	C₂×C₂²⋊C₄×C₇₃	—	2	1	no	—
82	C₂×C₄²×C₇₃	—	2	2	no	—
83	C₂×C₄²×C₇₃	—	2	2	no	—
84	C₂×C₄²×C₇₃	—	2	1	no	—
85	C₂×C₄²×C₇₃	D₄	1	1	yes	characteristic
86	C₂×C₄²×C₇₃	D₄	1	1	yes	characteristic
87	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
88	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
89	#106×C₇₃	—	4	2	no	—
90	C₄⋊C₈×C₇₃	—	2	2	no	—
91	C₄⋊C₈×C₇₃	D₄	1	4	yes	complemented
92	#103×C₇₃	—	2	4	no	—
93	#103×C₇₃	—	2	4	no	—
94	#103×C₇₃	—	4	2	no	—
95	#102×C₇₃	—	4	2	no	—
96	C₂²⋊C₈×C₇₃	—	2	4	no	—
97	C₄×C₈×C₇₃	—	2	4	no	—
98	#95×C₇₃	—	2	1	no	—
99	#95×C₇₃	—	2	1	no	—
100	#95×C₇₃	—	2	1	no	—
101	#95×C₇₃	—	2	2	no	—
102	#95×C₇₃	—	2	2	no	—
103	C₂⁴×C₇₃	—	2	1	no	—
104	C₂⁴×C₇₃	C₂×D₄	1	1	yes	characteristic
105	C₂×Q₈×C₇₃	—	2	2	no	—
106	C₂×Q₈×C₇₃	—	2	2	no	—
107	C₂×Q₈×C₇₃	—	2	2	no	—
108	C₂×Q₈×C₇₃	—	2	2	no	—
109	C₂×Q₈×C₇₃	—	2	2	no	—
110	C₂×Q₈×C₇₃	—	2	2	no	—
111	C₂×D₄×C₇₃	—	2	4	no	—
112	C₂×D₄×C₇₃	—	2	1	no	—
113	C₂×D₄×C₇₃	—	2	1	no	—
114	C₂×D₄×C₇₃	—	2	1	no	—
115	C₂×D₄×C₇₃	—	2	1	no	—
116	C₂×D₄×C₇₃	—	2	1	no	—
117	C₂×D₄×C₇₃	—	4	2	no	—
118	C₂×D₄×C₇₃	—	4	2	no	—
119	C₂×D₄×C₇₃	#41	1	2	yes	—
120	C₂²×C₄×C₇₃	—	2	2	no	—
121	C₂²×C₄×C₇₃	—	2	2	no	—
122	C₂²×C₄×C₇₃	—	2	1	no	—
123	C₂²×C₄×C₇₃	—	2	2	no	—
124	C₂²×C₄×C₇₃	—	2	2	no	—
125	C₂²×C₄×C₇₃	—	2	1	no	—
126	C₂²×C₄×C₇₃	—	2	1	no	—
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	1	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	—	4	1	no	—
136	C₂²×C₄×C₇₃	—	4	2	no	—
137	C₂²×C₄×C₇₃	—	4	2	no	—
138	C₂²×C₄×C₇₃	—	4	2	no	—
139	C₂²×C₄×C₇₃	SD₁₆	1	4	yes	complemented
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	C₂×D₄	1	1	yes	characteristic
144	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
145	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
146	SD₁₆×C₇₃	—	4	8	no	—
147	C₂×C₈×C₇₃	—	2	2	no	—
148	C₂×C₈×C₇₃	—	2	2	no	—
149	C₂×C₈×C₇₃	—	2	2	no	—
150	C₂×C₈×C₇₃	—	2	2	no	—
151	C₂×C₈×C₇₃	—	2	2	no	—
152	C₂×C₈×C₇₃	C₂×D₄	1	4	yes	—
153	C₄⋊C₄×C₇₃	—	2	1	no	—
154	C₄⋊C₄×C₇₃	—	2	1	no	—
155	C₄⋊C₄×C₇₃	—	2	1	no	—
156	C₄⋊C₄×C₇₃	—	2	2	no	—
157	C₄⋊C₄×C₇₃	—	2	1	no	—
158	C₄⋊C₄×C₇₃	—	2	1	no	—
159	C₄⋊C₄×C₇₃	—	2	2	no	—
160	C₄⋊C₄×C₇₃	—	4	2	no	—
161	C₄⋊C₄×C₇₃	—	4	4	no	—
162	C₄⋊C₄×C₇₃	—	4	2	no	—
163	C₄⋊C₄×C₇₃	—	4	2	no	—
164	C₄⋊C₄×C₇₃	—	4	2	no	—
165	C₄⋊C₄×C₇₃	—	4	2	no	—
166	C₄⋊C₄×C₇₃	#41	1	2	yes	—
167	C₂²⋊C₄×C₇₃	—	2	4	no	—
168	C₂²⋊C₄×C₇₃	—	4	4	no	—
169	C₂²⋊C₄×C₇₃	—	4	2	no	—
170	C₂²⋊C₄×C₇₃	—	4	2	no	—
171	C₂²⋊C₄×C₇₃	—	4	2	no	—
172	C₂²⋊C₄×C₇₃	—	4	2	no	—
173	C₄²×C₇₃	—	2	2	no	—
174	C₄²×C₇₃	—	2	2	no	—
175	C₄²×C₇₃	—	2	1	no	—
176	C₄²×C₇₃	—	2	1	no	—
177	C₄²×C₇₃	—	4	2	no	—
178	C₄²×C₇₃	C₂×D₄	1	2	yes	—
179	C₄²×C₇₃	#41	1	2	yes	—
180	C₂³×C₇₃	—	2	1	no	—
181	C₂³×C₇₃	—	2	1	no	—
182	C₂³×C₇₃	—	2	1	no	—
183	C₂³×C₇₃	—	2	1	no	—
184	C₂³×C₇₃	—	2	1	no	—
185	C₂³×C₇₃	—	2	1	no	—
186	C₂³×C₇₃	—	2	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	1	no	—
192	C₂³×C₇₃	—	4	1	no	—
193	C₂³×C₇₃	C₂×SD₁₆	1	2	yes	—
194	C₂³×C₇₃	C₂²×D₄	1	1	yes	characteristic
195	Q₈×C₇₃	—	4	2	no	—
196	Q₈×C₇₃	—	4	2	no	—
197	Q₈×C₇₃	—	4	2	no	—
198	Q₈×C₇₃	—	4	2	no	—
199	D₄×C₇₃	—	2	2	no	—
200	D₄×C₇₃	—	2	2	no	—
201	D₄×C₇₃	—	4	8	no	—
202	D₄×C₇₃	—	4	1	no	—
203	D₄×C₇₃	—	4	1	no	—
204	C₂×C₄×C₇₃	—	2	1	no	—
205	C₂×C₄×C₇₃	—	2	1	no	—
206	C₂×C₄×C₇₃	—	2	1	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	8	no	—
211	C₂×C₄×C₇₃	—	2	1	no	—
212	C₂×C₄×C₇₃	—	2	1	no	—
213	C₂×C₄×C₇₃	—	2	2	no	—
214	C₂×C₄×C₇₃	—	2	1	no	—
215	C₂×C₄×C₇₃	—	4	4	no	—
216	C₂×C₄×C₇₃	—	4	1	no	—
217	C₂×C₄×C₇₃	—	4	1	no	—
218	C₂×C₄×C₇₃	—	4	1	no	—
219	C₂×C₄×C₇₃	—	4	1	no	—
220	C₂×C₄×C₇₃	—	4	1	no	—
221	C₂×C₄×C₇₃	—	4	1	no	—
222	C₂×C₄×C₇₃	—	4	1	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	1	no	—
228	C₂×C₄×C₇₃	—	4	1	no	—
229	C₂×C₄×C₇₃	—	4	1	no	—
230	C₂×C₄×C₇₃	—	4	2	no	—
231	C₂×C₄×C₇₃	—	4	1	no	—
232	C₂×C₄×C₇₃	—	4	1	no	—
233	C₂×C₄×C₇₃	—	4	2	no	—
234	C₂×C₄×C₇₃	—	8	4	no	—
235	C₂×C₄×C₇₃	#121	1	2	yes	—
236	C₂×C₄×C₇₃	#121	1	2	yes	—
237	C₂×C₄×C₇₃	C₂×SD₁₆	1	2	yes	—
238	C₂×C₄×C₇₃	C₂×SD₁₆	1	2	yes	—
239	C₂×C₄×C₇₃	#135	1	2	yes	—
240	C₂×C₄×C₇₃	#137	1	2	yes	—
241	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
242	C₂×C₄×C₇₃	C₂×#41	1	1	yes	characteristic
243	C₂×C₄×C₇₃	C₂×#41	1	1	yes	characteristic
244	C₂×C₄×C₇₃	C₂×#41	1	1	yes	characteristic
245	C₂×C₄×C₇₃	H(5,𝔽₂)	1	1	yes	characteristic
246	C₂×C₄×C₇₃	H(5,𝔽₂)	1	1	yes	characteristic
247	C₈×C₇₃	—	2	4	no	—
248	C₈×C₇₃	—	4	2	no	—
249	C₂²×C₇₃	—	2	2	no	—
250	C₂²×C₇₃	—	2	2	no	—
251	C₂²×C₇₃	—	2	2	no	—
252	C₂²×C₇₃	—	4	1	no	—
253	C₂²×C₇₃	—	4	1	no	—
254	C₂²×C₇₃	—	4	1	no	—
255	C₂²×C₇₃	—	4	1	no	—
256	C₂²×C₇₃	—	4	2	no	—
257	C₂²×C₇₃	—	4	2	no	—
258	C₂²×C₇₃	—	4	2	no	—
259	C₂²×C₇₃	—	8	1	no	—
260	C₂²×C₇₃	—	8	1	no	—
261	C₂²×C₇₃	—	8	1	no	—
262	C₂²×C₇₃	—	8	1	no	—
263	C₂²×C₇₃	C₂×#121	1	1	yes	characteristic
264	C₂²×C₇₃	#525	1	1	yes	characteristic
265	C₂²×C₇₃	#535	1	1	yes	characteristic
266	C₂²×C₇₃	C₂²×SD₁₆	1	1	yes	characteristic
267	C₂²×C₇₃	C₂×#135	1	1	yes	characteristic
268	C₂²×C₇₃	C₂×#137	1	1	yes	characteristic
269	C₂²×C₇₃	#575	1	1	yes	characteristic
270	C₄×C₇₃	—	2	2	no	—
271	C₄×C₇₃	—	2	2	no	—
272	C₄×C₇₃	—	2	2	no	—
273	C₄×C₇₃	—	4	2	no	—
274	C₄×C₇₃	—	4	1	no	—
275	C₄×C₇₃	—	8	2	no	—
276	C₄×C₇₃	—	8	1	no	—
277	C₄×C₇₃	—	8	2	no	—
278	C₄×C₇₃	—	8	1	no	—
279	C₄×C₇₃	#465	1	4	yes	—
280	C₄×C₇₃	#546	1	1	yes	characteristic
281	C₄×C₇₃	#550	1	1	yes	characteristic
282	C₄×C₇₃	#553	1	1	yes	characteristic
283	C₄×C₇₃	#555	1	1	yes	characteristic
284	#24651	C₇₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
285	C₂×C₇₃	—	4	2	no	—
286	C₂×C₇₃	—	8	2	no	—
287	C₂×C₇₃	#2414	1	1	yes	characteristic
288	C₂×C₇₃	C₂×#465	1	1	yes	characteristic
289	C₂×C₇₃	#3056	1	1	yes	characteristic
290	C₂×C₇₃	#3101	1	1	yes	characteristic
291	C₂×C₇₃	#3107	1	1	yes	characteristic
292	C₂×C₇₃	#3206	1	1	yes	characteristic
293	C₂×C₇₃	#3212	1	1	yes	characteristic
294	C₂×#461	C₂×C₇₃	1	1	yes	characteristic, complemented
295	C₂×#431	C₂×C₇₃	1	1	yes	characteristic, complemented
296	#2857	C₂×C₇₃	1	1	yes	characteristic, complemented
297	C₄×#121	C₂×C₇₃	1	1	yes	characteristic
298	#2035	C₂×C₇₃	1	2	yes	complemented
299	#2000	C₂×C₇₃	1	2	yes	—
300	#1981	C₂×C₇₃	1	1	yes	characteristic, complemented
301	#1968	C₂×C₇₃	1	2	yes	complemented
302	#1948	C₂×C₇₃	1	1	yes	characteristic, complemented
303	#1933	C₂×C₇₃	1	2	yes	complemented
304	#1802	C₂×C₇₃	1	1	yes	characteristic, complemented
305	C₇₃	#24651	1	1	yes	characteristic, direct product factor, Sylow
306	C₂²×SD₁₆	C₂²×C₇₃	1	2	yes	—
307	C₂×C₄⋊Q₈	C₂²×C₇₃	1	1	yes	characteristic
308	C₂×C₂²⋊Q₈	C₂²×C₇₃	1	2	yes	—
309	C₂×#121	C₂²×C₇₃	1	1	yes	characteristic
310	C₂×C₄×D₄	—	2	1	no	—
311	C₂×C₄×D₄	C₂²×C₇₃	1	1	yes	characteristic
312	C₂²×C₄²	C₂²×C₇₃	1	1	yes	characteristic
313	#461	—	2	4	no	—
314	#431	—	2	4	no	—
315	C₂×#106	C₂²×C₇₃	1	2	yes	—
316	C₂×C₄⋊C₈	C₂²×C₇₃	1	1	yes	characteristic
317	C₂×C₄⋊C₈	C₂²×C₇₃	1	1	yes	characteristic
318	C₂×#103	C₂²×C₇₃	1	2	yes	—
319	C₂×#103	C₂²×C₇₃	1	2	yes	—
320	C₂×#103	C₂²×C₇₃	1	2	yes	—
321	C₂×#102	C₂²×C₇₃	1	2	yes	—
322	C₂×C₂²⋊C₈	C₂²×C₇₃	1	2	yes	—
323	C₂×C₄×C₈	C₂²×C₇₃	1	2	yes	—
324	#391	C₂²×C₇₃	1	2	yes	—
325	#390	C₂²×C₇₃	1	1	yes	characteristic
326	#389	—	2	1	no	—
327	#389	—	2	1	no	—
328	#389	C₂²×C₇₃	1	1	yes	characteristic
329	#388	—	2	1	no	—
330	#386	—	2	1	no	—
331	#384	C₂²×C₇₃	1	1	yes	characteristic
332	#380	—	2	1	no	—
333	#380	—	2	1	no	—
334	#380	C₂²×C₇₃	1	1	yes	characteristic
335	C₄×C₄⋊C₄	C₂²×C₇₃	1	1	yes	characteristic
336	C₄×C₂²⋊C₄	—	2	1	no	—
337	#340	C₂²×C₇₃	1	2	yes	—
338	#340	C₂²×C₇₃	1	2	yes	—
339	C₂²×Q₈	C₂³×C₇₃	1	2	yes	—
340	C₂²×D₄	—	2	1	no	—
341	C₂²×D₄	C₂³×C₇₃	1	1	yes	characteristic
342	C₂³×C₄	—	2	1	no	—
343	C₂³×C₄	D₄×C₇₃	1	1	yes	characteristic
344	C₂³×C₄	D₄×C₇₃	1	1	yes	characteristic
345	C₂³×C₄	C₂³×C₇₃	1	1	yes	characteristic
346	C₂×SD₁₆	—	2	4	no	—
347	C₂×SD₁₆	—	2	4	no	—
348	C₂×SD₁₆	—	4	2	no	—
349	C₂²×C₈	C₂³×C₇₃	1	2	yes	—
350	C₂²×C₈	C₂³×C₇₃	1	2	yes	—
351	C₄⋊Q₈	—	2	2	no	—
352	C₄⋊Q₈	—	2	2	no	—
353	C₂²⋊Q₈	—	4	2	no	—
354	C₂²⋊Q₈	—	4	2	no	—
355	#121	—	2	2	no	—
356	#121	—	2	2	no	—
357	C₄×D₄	—	2	2	no	—
358	C₄×D₄	—	2	2	no	—
359	C₄×D₄	—	4	4	no	—
360	C₂×C₄⋊C₄	—	2	1	no	—
361	C₂×C₄⋊C₄	—	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	1	no	—
366	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
367	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
368	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
369	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
370	C₂×C₂²⋊C₄	—	2	1	no	—
371	C₂×C₂²⋊C₄	—	2	1	no	—
372	C₂×C₂²⋊C₄	—	2	2	no	—
373	C₂×C₂²⋊C₄	—	2	1	no	—
374	C₂×C₂²⋊C₄	—	2	1	no	—
375	C₂×C₂²⋊C₄	—	2	1	no	—
376	C₂×C₄²	—	2	2	no	—
377	C₂×C₄²	—	2	2	no	—
378	C₂×C₄²	—	2	1	no	—
379	C₂×C₄²	D₄×C₇₃	1	1	yes	characteristic
380	C₂×C₄²	D₄×C₇₃	1	1	yes	characteristic
381	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
382	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
383	#106	—	4	2	no	—
384	C₄⋊C₈	—	2	2	no	—
385	C₄⋊C₈	D₄×C₇₃	1	4	yes	complemented
386	#103	—	2	4	no	—
387	#103	—	2	4	no	—
388	#103	—	4	2	no	—
389	#102	—	4	2	no	—
390	C₂²⋊C₈	—	2	4	no	—
391	C₄×C₈	—	2	4	no	—
392	#95	—	2	1	no	—
393	#95	—	2	1	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	C₂×Q₈	—	2	2	no	—
400	C₂×Q₈	—	2	2	no	—
401	C₂×Q₈	—	2	2	no	—
402	C₂×Q₈	—	2	2	no	—
403	C₂×Q₈	—	2	2	no	—
404	C₂×Q₈	—	2	2	no	—
405	C₂×D₄	—	2	4	no	—
406	C₂×D₄	—	2	1	no	—
407	C₂×D₄	—	2	1	no	—
408	C₂×D₄	—	2	1	no	—
409	C₂×D₄	—	2	1	no	—
410	C₂×D₄	—	2	1	no	—
411	C₂×D₄	—	4	2	no	—
412	C₂×D₄	—	4	2	no	—
413	C₂×D₄	#41×C₇₃	1	2	yes	—
414	C₂²×C₄	—	2	2	no	—
415	C₂²×C₄	—	2	2	no	—
416	C₂²×C₄	—	2	1	no	—
417	C₂²×C₄	—	2	2	no	—
418	C₂²×C₄	—	2	2	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	1	no	—
424	C₂²×C₄	—	2	1	no	—
425	C₂²×C₄	—	2	1	no	—
426	C₂²×C₄	—	2	1	no	—
427	C₂²×C₄	—	2	2	no	—
428	C₂²×C₄	—	2	2	no	—
429	C₂²×C₄	—	4	1	no	—
430	C₂²×C₄	—	4	2	no	—
431	C₂²×C₄	—	4	2	no	—
432	C₂²×C₄	—	4	2	no	—
433	C₂²×C₄	SD₁₆×C₇₃	1	4	yes	complemented
434	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
435	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
436	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
437	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
438	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
439	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
440	SD₁₆	—	4	8	no	—
441	C₂×C₈	—	2	2	no	—
442	C₂×C₈	—	2	2	no	—
443	C₂×C₈	—	2	2	no	—
444	C₂×C₈	—	2	2	no	—
445	C₂×C₈	—	2	2	no	—
446	C₂×C₈	C₂×D₄×C₇₃	1	4	yes	—
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	1	no	—
452	C₄⋊C₄	—	2	1	no	—
453	C₄⋊C₄	—	2	2	no	—
454	C₄⋊C₄	—	4	2	no	—
455	C₄⋊C₄	—	4	4	no	—
456	C₄⋊C₄	—	4	2	no	—
457	C₄⋊C₄	—	4	2	no	—
458	C₄⋊C₄	—	4	2	no	—
459	C₄⋊C₄	—	4	2	no	—
460	C₄⋊C₄	#41×C₇₃	1	2	yes	—
461	C₂²⋊C₄	—	2	4	no	—
462	C₂²⋊C₄	—	4	4	no	—
463	C₂²⋊C₄	—	4	2	no	—
464	C₂²⋊C₄	—	4	2	no	—
465	C₂²⋊C₄	—	4	2	no	—
466	C₂²⋊C₄	—	4	2	no	—
467	C₄²	—	2	2	no	—
468	C₄²	—	2	2	no	—
469	C₄²	—	2	1	no	—
470	C₄²	—	2	1	no	—
471	C₄²	—	4	2	no	—
472	C₄²	C₂×D₄×C₇₃	1	2	yes	—
473	C₄²	#41×C₇₃	1	2	yes	—
474	C₂³	—	2	1	no	—
475	C₂³	—	2	1	no	—
476	C₂³	—	2	1	no	—
477	C₂³	—	2	1	no	—
478	C₂³	—	2	1	no	—
479	C₂³	—	2	1	no	—
480	C₂³	—	2	2	no	—
481	C₂³	—	4	1	no	—
482	C₂³	—	4	1	no	—
483	C₂³	—	4	1	no	—
484	C₂³	—	4	1	no	—
485	C₂³	—	4	1	no	—
486	C₂³	—	4	1	no	—
487	C₂³	C₂×SD₁₆×C₇₃	1	2	yes	—
488	C₂³	C₂²×D₄×C₇₃	1	1	yes	characteristic
489	Q₈	—	4	2	no	—
490	Q₈	—	4	2	no	—
491	Q₈	—	4	2	no	—
492	Q₈	—	4	2	no	—
493	D₄	—	2	2	no	—
494	D₄	—	2	2	no	—
495	D₄	—	4	8	no	—
496	D₄	—	4	1	no	—
497	D₄	—	4	1	no	—
498	C₂×C₄	—	2	1	no	—
499	C₂×C₄	—	2	1	no	—
500	C₂×C₄	—	2	1	no	—
501	C₂×C₄	—	2	1	no	—
502	C₂×C₄	—	2	1	no	—
503	C₂×C₄	—	2	1	no	—
504	C₂×C₄	—	2	8	no	—
505	C₂×C₄	—	2	1	no	—
506	C₂×C₄	—	2	1	no	—
507	C₂×C₄	—	2	2	no	—
508	C₂×C₄	—	2	1	no	—
509	C₂×C₄	—	4	4	no	—
510	C₂×C₄	—	4	1	no	—
511	C₂×C₄	—	4	1	no	—
512	C₂×C₄	—	4	1	no	—
513	C₂×C₄	—	4	1	no	—
514	C₂×C₄	—	4	1	no	—
515	C₂×C₄	—	4	1	no	—
516	C₂×C₄	—	4	1	no	—
517	C₂×C₄	—	4	2	no	—
518	C₂×C₄	—	4	2	no	—
519	C₂×C₄	—	4	2	no	—
520	C₂×C₄	—	4	2	no	—
521	C₂×C₄	—	4	1	no	—
522	C₂×C₄	—	4	1	no	—
523	C₂×C₄	—	4	1	no	—
524	C₂×C₄	—	4	2	no	—
525	C₂×C₄	—	4	1	no	—
526	C₂×C₄	—	4	1	no	—
527	C₂×C₄	—	4	2	no	—
528	C₂×C₄	—	8	4	no	—
529	C₂×C₄	#121×C₇₃	1	2	yes	—
530	C₂×C₄	#121×C₇₃	1	2	yes	—
531	C₂×C₄	C₂×SD₁₆×C₇₃	1	2	yes	—
532	C₂×C₄	C₂×SD₁₆×C₇₃	1	2	yes	—
533	C₂×C₄	#135×C₇₃	1	2	yes	—
534	C₂×C₄	#137×C₇₃	1	2	yes	—
535	C₂×C₄	C₂²×D₄×C₇₃	1	1	yes	characteristic
536	C₂×C₄	C₂×#41×C₇₃	1	1	yes	characteristic
537	C₂×C₄	C₂×#41×C₇₃	1	1	yes	characteristic
538	C₂×C₄	C₂×#41×C₇₃	1	1	yes	characteristic
539	C₂×C₄	H(5,𝔽₂)×C₇₃	1	1	yes	characteristic
540	C₂×C₄	H(5,𝔽₂)×C₇₃	1	1	yes	characteristic
541	C₈	—	2	4	no	—
542	C₈	—	4	2	no	—
543	C₂²	—	2	2	no	—
544	C₂²	—	2	2	no	—
545	C₂²	—	2	2	no	—
546	C₂²	—	4	1	no	—
547	C₂²	—	4	1	no	—
548	C₂²	—	4	1	no	—
549	C₂²	—	4	1	no	—
550	C₂²	—	4	2	no	—
551	C₂²	—	4	2	no	—
552	C₂²	—	4	2	no	—
553	C₂²	—	8	1	no	—
554	C₂²	—	8	1	no	—
555	C₂²	—	8	1	no	—
556	C₂²	—	8	1	no	—
557	C₂²	C₂×#121×C₇₃	1	1	yes	characteristic
558	C₂²	#525×C₇₃	1	1	yes	characteristic
559	C₂²	#535×C₇₃	1	1	yes	characteristic
560	C₂²	C₂²×SD₁₆×C₇₃	1	1	yes	characteristic
561	C₂²	C₂×#135×C₇₃	1	1	yes	characteristic
562	C₂²	C₂×#137×C₇₃	1	1	yes	characteristic
563	C₂²	#575×C₇₃	1	1	yes	characteristic
564	C₄	—	2	2	no	—
565	C₄	—	2	2	no	—
566	C₄	—	2	2	no	—
567	C₄	—	4	2	no	—
568	C₄	—	4	1	no	—
569	C₄	—	8	2	no	—
570	C₄	—	8	1	no	—
571	C₄	—	8	2	no	—
572	C₄	—	8	1	no	—
573	C₄	#465×C₇₃	1	4	yes	—
574	C₄	#546×C₇₃	1	1	yes	characteristic
575	C₄	#550×C₇₃	1	1	yes	characteristic
576	C₄	#553×C₇₃	1	1	yes	characteristic
577	C₄	#555×C₇₃	1	1	yes	characteristic
578	C₂	—	4	2	no	—
579	C₂	—	8	2	no	—
580	C₂	C₇₃×#2414	1	1	yes	characteristic
581	C₂	C₂×#465×C₇₃	1	1	yes	characteristic
582	C₂	C₇₃×#3056	1	1	yes	characteristic
583	C₂	C₇₃×#3101	1	1	yes	characteristic
584	C₂	C₇₃×#3107	1	1	yes	characteristic
585	C₂	C₇₃×#3206	1	1	yes	characteristic
586	C₂	C₇₃×#3212	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. C₂×#461×C₇₃	C₂	semidirect
2. C₂×#431×C₇₃	C₂	semidirect
3. C₇₃×#2857	C₂	semidirect
5. C₇₃×#2035	C₂	semidirect
7. C₇₃×#1981	C₂	semidirect
8. C₇₃×#1968	C₂	semidirect
9. C₇₃×#1948	C₂	semidirect
10. C₇₃×#1933	C₂	semidirect
11. C₇₃×#1802	C₂	semidirect
91. C₄⋊C₈×C₇₃	D₄	semidirect
139. C₂²×C₄×C₇₃	SD₁₆	semidirect
284. #24651	C₇₃	direct (N × H)
294. C₂×#461	C₂×C₇₃	semidirect
295. C₂×#431	C₂×C₇₃	semidirect
296. #2857	C₂×C₇₃	semidirect
298. #2035	C₂×C₇₃	semidirect
300. #1981	C₂×C₇₃	semidirect
301. #1968	C₂×C₇₃	semidirect
302. #1948	C₂×C₇₃	semidirect
303. #1933	C₂×C₇₃	semidirect
304. #1802	C₂×C₇₃	semidirect
305. C₇₃	#24651	direct (N × H)
385. C₄⋊C₈	D₄×C₇₃	semidirect
433. C₂²×C₄	SD₁₆×C₇₃	semidirect

Maximal subgroups

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

subgroup	index
C₂×#461×C₇₃	2
C₂×#431×C₇₃	2
C₇₃×#2857	2
C₄×#121×C₇₃	2
C₇₃×#2035	2
C₇₃×#2000	2
C₇₃×#1981	2
C₇₃×#1968	2
C₇₃×#1948	2
C₇₃×#1933	2
C₇₃×#1802	2
#24651	73

Subgroups — C73×#24651 #32934055

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₃×#24651 #32934055