Subgroups — C₇₃×#25611 #32935015

Order 18688.

1222 conjugacy classes of subgroups.

The subgroup lattice has 526 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#540×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#496×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#488×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₇₃×#2620	C₂	1	1	yes	maximal, characteristic, complemented
5	C₇₃×#2000	C₂	1	2	yes	maximal, complemented
6	C₇₃×#1999	C₂	1	2	yes	maximal, complemented
7	C₇₃×#1992	C₂	1	1	yes	maximal, characteristic, complemented
8	C₇₃×#1957	C₂	1	1	yes	maximal, characteristic, complemented
9	C₇₃×#1879	C₂	1	2	yes	maximal, complemented
10	C₇₃×#1877	C₂	1	2	yes	maximal, complemented
11	C₇₃×#1750	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×SD₁₆×C₇₃	C₂²	1	2	yes	—
13	C₂²×D₈×C₇₃	C₂²	1	2	yes	—
14	#540×C₇₃	—	2	4	no	—
15	#540×C₇₃	—	2	4	no	—
16	C₂×#127×C₇₃	C₂²	1	1	yes	characteristic
17	C₂×#125×C₇₃	C₂²	1	1	yes	characteristic
18	C₂×#124×C₇₃	C₂²	1	1	yes	characteristic
19	C₂×#123×C₇₃	—	2	2	no	—
20	C₂×C₂²⋊Q₈×C₇₃	C₂²	1	1	yes	characteristic
21	C₂×#121×C₇₃	—	2	2	no	—
22	C₂×#121×C₇₃	C₂²	1	2	yes	—
23	C₂×#121×C₇₃	C₂²	1	1	yes	characteristic
24	C₂×C₄×D₄×C₇₃	C₂²	1	2	yes	—
25	C₂×#117×C₇₃	C₂²	1	1	yes	characteristic
26	#496×C₇₃	—	2	4	no	—
27	#488×C₇₃	—	2	4	no	—
28	C₂×#103×C₇₃	C₂²	1	2	yes	—
29	C₂×#102×C₇₃	C₂²	1	2	yes	—
30	C₂×#102×C₇₃	C₂²	1	2	yes	—
31	C₂×#102×C₇₃	C₂²	1	2	yes	—
32	C₂×C₂²⋊C₈×C₇₃	C₂²	1	2	yes	—
33	C₂×#97×C₇₃	C₂²	1	1	yes	characteristic
34	C₂×C₄×C₈×C₇₃	C₂²	1	1	yes	characteristic
35	#396×C₇₃	—	2	2	no	—
36	#394×C₇₃	—	2	2	no	—
37	#391×C₇₃	C₂²	1	1	yes	characteristic
38	#390×C₇₃	C₂²	1	1	yes	characteristic
39	#384×C₇₃	C₂²	1	1	yes	characteristic
40	#340×C₇₃	C₂²	1	2	yes	—
41	#340×C₇₃	C₂²	1	2	yes	—
42	#336×C₇₃	C₂²	1	2	yes	—
43	C₂²×Q₈×C₇₃	C₂³	1	1	yes	characteristic
44	C₂²×D₄×C₇₃	—	2	2	no	—
45	C₂²×D₄×C₇₃	—	2	1	no	—
46	C₂²×D₄×C₇₃	—	2	2	no	—
47	C₂²×D₄×C₇₃	C₂³	1	1	yes	characteristic
48	C₂²×D₄×C₇₃	C₂³	1	2	yes	—
49	C₂³×C₄×C₇₃	—	2	2	no	—
50	C₂³×C₄×C₇₃	C₂³	1	1	yes	characteristic
51	C₂×SD₁₆×C₇₃	—	2	4	no	—
52	C₂×SD₁₆×C₇₃	—	2	4	no	—
53	C₂×SD₁₆×C₇₃	—	4	2	no	—
54	C₂×D₈×C₇₃	—	2	4	no	—
55	C₂×D₈×C₇₃	—	2	4	no	—
56	C₂×D₈×C₇₃	—	4	2	no	—
57	C₂²×C₈×C₇₃	C₂³	1	2	yes	—
58	C₂²×C₈×C₇₃	C₂³	1	2	yes	—
59	#127×C₇₃	—	2	2	no	—
60	#127×C₇₃	D₄	1	4	yes	complemented
61	#125×C₇₃	—	2	2	no	—
62	#125×C₇₃	D₄	1	4	yes	complemented
63	#124×C₇₃	—	2	2	no	—
64	#124×C₇₃	—	2	2	no	—
65	#123×C₇₃	—	2	16	no	—
66	C₂²⋊Q₈×C₇₃	—	4	2	no	—
67	#121×C₇₃	—	2	16	no	—
68	#121×C₇₃	—	2	4	no	—
69	#121×C₇₃	—	2	4	no	—
70	#121×C₇₃	—	4	2	no	—
71	C₄×D₄×C₇₃	—	2	4	no	—
72	C₄×D₄×C₇₃	—	2	4	no	—
73	#117×C₇₃	—	2	2	no	—
74	#117×C₇₃	—	2	2	no	—
75	C₂×C₄⋊C₄×C₇₃	—	2	2	no	—
76	C₂×C₄⋊C₄×C₇₃	—	2	1	no	—
77	C₂×C₄⋊C₄×C₇₃	—	2	2	no	—
78	C₂×C₄⋊C₄×C₇₃	D₄	1	2	yes	—
79	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
80	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
81	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
82	C₂×C₂²⋊C₄×C₇₃	—	2	2	no	—
83	C₂×C₂²⋊C₄×C₇₃	—	2	2	no	—
84	C₂×C₂²⋊C₄×C₇₃	—	2	1	no	—
85	C₂×C₂²⋊C₄×C₇₃	—	2	2	no	—
86	C₂×C₂²⋊C₄×C₇₃	—	2	1	no	—
87	C₂×C₂²⋊C₄×C₇₃	—	2	2	no	—
88	C₂×C₂²⋊C₄×C₇₃	D₄	1	2	yes	—
89	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
90	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
91	#103×C₇₃	—	2	4	no	—
92	#102×C₇₃	—	2	4	no	—
93	#102×C₇₃	—	4	2	no	—
94	#102×C₇₃	—	4	2	no	—
95	C₂²⋊C₈×C₇₃	—	2	4	no	—
96	#97×C₇₃	—	2	2	no	—
97	C₄×C₈×C₇₃	—	2	2	no	—
98	#95×C₇₃	—	2	2	no	—
99	C₂⁴×C₇₃	—	2	2	no	—
100	C₂⁴×C₇₃	—	2	1	no	—
101	C₂⁴×C₇₃	C₂×D₄	1	1	yes	characteristic
102	C₂×Q₈×C₇₃	—	2	1	no	—
103	C₂×Q₈×C₇₃	—	2	1	no	—
104	C₂×Q₈×C₇₃	—	2	2	no	—
105	C₂×Q₈×C₇₃	—	2	2	no	—
106	C₂×D₄×C₇₃	—	2	8	no	—
107	C₂×D₄×C₇₃	—	2	8	no	—
108	C₂×D₄×C₇₃	—	2	2	no	—
109	C₂×D₄×C₇₃	—	2	1	no	—
110	C₂×D₄×C₇₃	—	2	1	no	—
111	C₂×D₄×C₇₃	—	2	2	no	—
112	C₂×D₄×C₇₃	—	2	2	no	—
113	C₂×D₄×C₇₃	—	2	2	no	—
114	C₂×D₄×C₇₃	—	2	2	no	—
115	C₂×D₄×C₇₃	—	2	2	no	—
116	C₂×D₄×C₇₃	—	2	2	no	—
117	C₂×D₄×C₇₃	—	4	2	no	—
118	C₂×D₄×C₇₃	—	8	2	no	—
119	C₂×D₄×C₇₃	—	8	2	no	—
120	C₂×D₄×C₇₃	—	8	2	no	—
121	C₂×D₄×C₇₃	—	8	2	no	—
122	C₂×D₄×C₇₃	—	8	2	no	—
123	C₂×D₄×C₇₃	C₂×D₄	1	4	yes	—
124	C₂²×C₄×C₇₃	—	2	2	no	—
125	C₂²×C₄×C₇₃	—	2	8	no	—
126	C₂²×C₄×C₇₃	—	2	1	no	—
127	C₂²×C₄×C₇₃	—	2	1	no	—
128	C₂²×C₄×C₇₃	—	2	2	no	—
129	C₂²×C₄×C₇₃	—	2	2	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	—	8	2	no	—
134	C₂²×C₄×C₇₃	—	8	2	no	—
135	C₂²×C₄×C₇₃	C₂×D₄	1	2	yes	—
136	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
137	C₂²×C₄×C₇₃	C₂×D₄	1	2	yes	—
138	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
139	SD₁₆×C₇₃	—	4	8	no	—
140	D₈×C₇₃	—	4	8	no	—
141	C₂×C₈×C₇₃	—	2	2	no	—
142	C₂×C₈×C₇₃	—	2	2	no	—
143	C₂×C₈×C₇₃	—	2	2	no	—
144	C₂×C₈×C₇₃	—	2	2	no	—
145	C₂×C₈×C₇₃	—	2	2	no	—
146	C₂×C₈×C₇₃	#41	1	4	yes	—
147	C₄⋊C₄×C₇₃	—	2	8	no	—
148	C₄⋊C₄×C₇₃	—	2	4	no	—
149	C₄⋊C₄×C₇₃	—	2	2	no	—
150	C₄⋊C₄×C₇₃	—	2	2	no	—
151	C₄⋊C₄×C₇₃	—	2	2	no	—
152	C₄⋊C₄×C₇₃	—	4	2	no	—
153	C₄⋊C₄×C₇₃	—	8	2	no	—
154	C₄⋊C₄×C₇₃	C₂×D₄	1	4	yes	—
155	C₂²⋊C₄×C₇₃	—	2	8	no	—
156	C₂²⋊C₄×C₇₃	—	2	8	no	—
157	C₂²⋊C₄×C₇₃	—	2	4	no	—
158	C₂²⋊C₄×C₇₃	—	4	2	no	—
159	C₂²⋊C₄×C₇₃	—	4	2	no	—
160	C₂²⋊C₄×C₇₃	—	4	4	no	—
161	C₂²⋊C₄×C₇₃	—	8	2	no	—
162	C₄²×C₇₃	—	2	1	no	—
163	C₄²×C₇₃	—	2	1	no	—
164	C₄²×C₇₃	C₂×D₄	1	2	yes	—
165	C₄²×C₇₃	C₂×D₄	1	2	yes	—
166	C₂³×C₇₃	—	2	1	no	—
167	C₂³×C₇₃	—	2	4	no	—
168	C₂³×C₇₃	—	2	1	no	—
169	C₂³×C₇₃	—	2	1	no	—
170	C₂³×C₇₃	—	2	2	no	—
171	C₂³×C₇₃	—	2	2	no	—
172	C₂³×C₇₃	—	4	2	no	—
173	C₂³×C₇₃	—	4	2	no	—
174	C₂³×C₇₃	—	4	2	no	—
175	C₂³×C₇₃	—	4	2	no	—
176	C₂³×C₇₃	—	4	2	no	—
177	C₂³×C₇₃	—	4	2	no	—
178	C₂³×C₇₃	—	4	1	no	—
179	C₂³×C₇₃	—	4	1	no	—
180	C₂³×C₇₃	—	4	1	no	—
181	C₂³×C₇₃	—	4	2	no	—
182	C₂³×C₇₃	—	4	2	no	—
183	C₂³×C₇₃	C₂²×D₄	1	1	yes	characteristic
184	Q₈×C₇₃	—	4	2	no	—
185	Q₈×C₇₃	—	4	2	no	—
186	D₄×C₇₃	—	2	4	no	—
187	D₄×C₇₃	—	2	4	no	—
188	D₄×C₇₃	—	4	2	no	—
189	D₄×C₇₃	—	4	2	no	—
190	D₄×C₇₃	—	4	2	no	—
191	D₄×C₇₃	—	4	2	no	—
192	D₄×C₇₃	—	8	8	no	—
193	D₄×C₇₃	—	8	8	no	—
194	D₄×C₇₃	—	8	4	no	—
195	C₂×C₄×C₇₃	—	2	2	no	—
196	C₂×C₄×C₇₃	—	2	2	no	—
197	C₂×C₄×C₇₃	—	2	2	no	—
198	C₂×C₄×C₇₃	—	2	1	no	—
199	C₂×C₄×C₇₃	—	2	4	no	—
200	C₂×C₄×C₇₃	—	2	1	no	—
201	C₂×C₄×C₇₃	—	2	1	no	—
202	C₂×C₄×C₇₃	—	2	2	no	—
203	C₂×C₄×C₇₃	—	2	2	no	—
204	C₂×C₄×C₇₃	—	4	2	no	—
205	C₂×C₄×C₇₃	—	4	2	no	—
206	C₂×C₄×C₇₃	—	4	2	no	—
207	C₂×C₄×C₇₃	—	4	2	no	—
208	C₂×C₄×C₇₃	—	4	1	no	—
209	C₂×C₄×C₇₃	—	4	1	no	—
210	C₂×C₄×C₇₃	—	4	1	no	—
211	C₂×C₄×C₇₃	—	4	1	no	—
212	C₂×C₄×C₇₃	—	4	1	no	—
213	C₂×C₄×C₇₃	—	4	2	no	—
214	C₂×C₄×C₇₃	—	4	2	no	—
215	C₂×C₄×C₇₃	—	8	8	no	—
216	C₂×C₄×C₇₃	#120	1	4	yes	—
217	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
218	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
219	C₂×C₄×C₇₃	C₂×#41	1	2	yes	—
220	C₂×C₄×C₇₃	H(5,𝔽₂)	1	2	yes	—
221	C₈×C₇₃	—	2	4	no	—
222	C₈×C₇₃	—	4	2	no	—
223	C₂²×C₇₃	—	4	2	no	—
224	C₂²×C₇₃	—	4	1	no	—
225	C₂²×C₇₃	—	4	4	no	—
226	C₂²×C₇₃	—	4	1	no	—
227	C₂²×C₇₃	—	4	1	no	—
228	C₂²×C₇₃	—	4	4	no	—
229	C₂²×C₇₃	—	4	2	no	—
230	C₂²×C₇₃	—	4	4	no	—
231	C₂²×C₇₃	—	8	2	no	—
232	C₂²×C₇₃	—	8	2	no	—
233	C₂²×C₇₃	—	8	2	no	—
234	C₂²×C₇₃	—	8	2	no	—
235	C₂²×C₇₃	—	8	2	no	—
236	C₂²×C₇₃	—	8	1	no	—
237	C₂²×C₇₃	—	8	1	no	—
238	C₂²×C₇₃	—	8	1	no	—
239	C₂²×C₇₃	—	8	2	no	—
240	C₂²×C₇₃	C₂×#120	1	1	yes	characteristic
241	C₂²×C₇₃	#532	1	1	yes	characteristic
242	C₂²×C₇₃	#535	1	1	yes	characteristic
243	C₂²×C₇₃	#576	1	2	yes	—
244	C₂²×C₇₃	#577	1	2	yes	—
245	C₄×C₇₃	—	2	4	no	—
246	C₄×C₇₃	—	4	1	no	—
247	C₄×C₇₃	—	4	2	no	—
248	C₄×C₇₃	—	4	4	no	—
249	C₄×C₇₃	—	8	1	no	—
250	C₄×C₇₃	—	8	1	no	—
251	C₄×C₇₃	—	8	1	no	—
252	C₄×C₇₃	#546	1	2	yes	—
253	C₄×C₇₃	#550	1	2	yes	—
254	#25611	C₇₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
255	C₂×C₇₃	—	8	1	no	—
256	C₂×C₇₃	—	8	4	no	—
257	C₂×C₇₃	—	16	1	no	—
258	C₂×C₇₃	#2431	1	1	yes	characteristic
259	C₂×C₇₃	#3012	1	2	yes	—
260	C₂×C₇₃	#3179	1	2	yes	—
261	C₂×C₇₃	#3220	1	1	yes	characteristic
262	C₂×C₇₃	#3221	1	1	yes	characteristic
263	C₂×#540	C₂×C₇₃	1	1	yes	characteristic, complemented
264	C₂×#496	C₂×C₇₃	1	1	yes	characteristic, complemented
265	C₂×#488	C₂×C₇₃	1	1	yes	characteristic, complemented
266	#2620	C₂×C₇₃	1	1	yes	characteristic, complemented
267	#2000	C₂×C₇₃	1	2	yes	complemented
268	#1999	C₂×C₇₃	1	2	yes	complemented
269	#1992	C₂×C₇₃	1	1	yes	characteristic, complemented
270	#1957	C₂×C₇₃	1	1	yes	characteristic, complemented
271	#1879	C₂×C₇₃	1	2	yes	complemented
272	#1877	C₂×C₇₃	1	2	yes	complemented
273	#1750	C₂×C₇₃	1	1	yes	characteristic, complemented
274	C₇₃	#25611	1	1	yes	characteristic, direct product factor, Sylow
275	C₂²×SD₁₆	C₂²×C₇₃	1	2	yes	—
276	C₂²×D₈	C₂²×C₇₃	1	2	yes	—
277	#540	—	2	4	no	—
278	#540	—	2	4	no	—
279	C₂×#127	C₂²×C₇₃	1	1	yes	characteristic
280	C₂×#125	C₂²×C₇₃	1	1	yes	characteristic
281	C₂×#124	C₂²×C₇₃	1	1	yes	characteristic
282	C₂×#123	—	2	2	no	—
283	C₂×C₂²⋊Q₈	C₂²×C₇₃	1	1	yes	characteristic
284	C₂×#121	—	2	2	no	—
285	C₂×#121	C₂²×C₇₃	1	2	yes	—
286	C₂×#121	C₂²×C₇₃	1	1	yes	characteristic
287	C₂×C₄×D₄	C₂²×C₇₃	1	2	yes	—
288	C₂×#117	C₂²×C₇₃	1	1	yes	characteristic
289	#496	—	2	4	no	—
290	#488	—	2	4	no	—
291	C₂×#103	C₂²×C₇₃	1	2	yes	—
292	C₂×#102	C₂²×C₇₃	1	2	yes	—
293	C₂×#102	C₂²×C₇₃	1	2	yes	—
294	C₂×#102	C₂²×C₇₃	1	2	yes	—
295	C₂×C₂²⋊C₈	C₂²×C₇₃	1	2	yes	—
296	C₂×#97	C₂²×C₇₃	1	1	yes	characteristic
297	C₂×C₄×C₈	C₂²×C₇₃	1	1	yes	characteristic
298	#396	—	2	2	no	—
299	#394	—	2	2	no	—
300	#391	C₂²×C₇₃	1	1	yes	characteristic
301	#390	C₂²×C₇₃	1	1	yes	characteristic
302	#384	C₂²×C₇₃	1	1	yes	characteristic
303	#340	C₂²×C₇₃	1	2	yes	—
304	#340	C₂²×C₇₃	1	2	yes	—
305	#336	C₂²×C₇₃	1	2	yes	—
306	C₂²×Q₈	C₂³×C₇₃	1	1	yes	characteristic
307	C₂²×D₄	—	2	2	no	—
308	C₂²×D₄	—	2	1	no	—
309	C₂²×D₄	—	2	2	no	—
310	C₂²×D₄	C₂³×C₇₃	1	1	yes	characteristic
311	C₂²×D₄	C₂³×C₇₃	1	2	yes	—
312	C₂³×C₄	—	2	2	no	—
313	C₂³×C₄	C₂³×C₇₃	1	1	yes	characteristic
314	C₂×SD₁₆	—	2	4	no	—
315	C₂×SD₁₆	—	2	4	no	—
316	C₂×SD₁₆	—	4	2	no	—
317	C₂×D₈	—	2	4	no	—
318	C₂×D₈	—	2	4	no	—
319	C₂×D₈	—	4	2	no	—
320	C₂²×C₈	C₂³×C₇₃	1	2	yes	—
321	C₂²×C₈	C₂³×C₇₃	1	2	yes	—
322	#127	—	2	2	no	—
323	#127	D₄×C₇₃	1	4	yes	complemented
324	#125	—	2	2	no	—
325	#125	D₄×C₇₃	1	4	yes	complemented
326	#124	—	2	2	no	—
327	#124	—	2	2	no	—
328	#123	—	2	16	no	—
329	C₂²⋊Q₈	—	4	2	no	—
330	#121	—	2	16	no	—
331	#121	—	2	4	no	—
332	#121	—	2	4	no	—
333	#121	—	4	2	no	—
334	C₄×D₄	—	2	4	no	—
335	C₄×D₄	—	2	4	no	—
336	#117	—	2	2	no	—
337	#117	—	2	2	no	—
338	C₂×C₄⋊C₄	—	2	2	no	—
339	C₂×C₄⋊C₄	—	2	1	no	—
340	C₂×C₄⋊C₄	—	2	2	no	—
341	C₂×C₄⋊C₄	D₄×C₇₃	1	2	yes	—
342	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
343	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
344	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
345	C₂×C₂²⋊C₄	—	2	2	no	—
346	C₂×C₂²⋊C₄	—	2	2	no	—
347	C₂×C₂²⋊C₄	—	2	1	no	—
348	C₂×C₂²⋊C₄	—	2	1	no	—
349	C₂×C₂²⋊C₄	—	2	2	no	—
350	C₂×C₂²⋊C₄	—	2	2	no	—
351	C₂×C₂²⋊C₄	D₄×C₇₃	1	2	yes	—
352	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
353	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
354	#103	—	2	4	no	—
355	#102	—	2	4	no	—
356	#102	—	4	2	no	—
357	#102	—	4	2	no	—
358	C₂²⋊C₈	—	2	4	no	—
359	#97	—	2	2	no	—
360	C₄×C₈	—	2	2	no	—
361	#95	—	2	2	no	—
362	C₂⁴	—	2	2	no	—
363	C₂⁴	—	2	1	no	—
364	C₂⁴	C₂×D₄×C₇₃	1	1	yes	characteristic
365	C₂×Q₈	—	2	1	no	—
366	C₂×Q₈	—	2	1	no	—
367	C₂×Q₈	—	2	2	no	—
368	C₂×Q₈	—	2	2	no	—
369	C₂×D₄	—	2	8	no	—
370	C₂×D₄	—	2	8	no	—
371	C₂×D₄	—	2	2	no	—
372	C₂×D₄	—	2	1	no	—
373	C₂×D₄	—	2	1	no	—
374	C₂×D₄	—	2	2	no	—
375	C₂×D₄	—	2	2	no	—
376	C₂×D₄	—	2	2	no	—
377	C₂×D₄	—	2	2	no	—
378	C₂×D₄	—	2	2	no	—
379	C₂×D₄	—	2	2	no	—
380	C₂×D₄	—	4	2	no	—
381	C₂×D₄	—	8	2	no	—
382	C₂×D₄	—	8	2	no	—
383	C₂×D₄	—	8	2	no	—
384	C₂×D₄	—	8	2	no	—
385	C₂×D₄	—	8	2	no	—
386	C₂×D₄	C₂×D₄×C₇₃	1	4	yes	—
387	C₂²×C₄	—	2	2	no	—
388	C₂²×C₄	—	2	8	no	—
389	C₂²×C₄	—	2	1	no	—
390	C₂²×C₄	—	2	1	no	—
391	C₂²×C₄	—	2	2	no	—
392	C₂²×C₄	—	2	2	no	—
393	C₂²×C₄	—	2	1	no	—
394	C₂²×C₄	—	2	1	no	—
395	C₂²×C₄	—	2	1	no	—
396	C₂²×C₄	—	8	2	no	—
397	C₂²×C₄	—	8	2	no	—
398	C₂²×C₄	C₂×D₄×C₇₃	1	2	yes	—
399	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
400	C₂²×C₄	C₂×D₄×C₇₃	1	2	yes	—
401	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
402	SD₁₆	—	4	8	no	—
403	D₈	—	4	8	no	—
404	C₂×C₈	—	2	2	no	—
405	C₂×C₈	—	2	2	no	—
406	C₂×C₈	—	2	2	no	—
407	C₂×C₈	—	2	2	no	—
408	C₂×C₈	—	2	2	no	—
409	C₂×C₈	#41×C₇₃	1	4	yes	—
410	C₄⋊C₄	—	2	8	no	—
411	C₄⋊C₄	—	2	4	no	—
412	C₄⋊C₄	—	2	2	no	—
413	C₄⋊C₄	—	2	2	no	—
414	C₄⋊C₄	—	2	2	no	—
415	C₄⋊C₄	—	4	2	no	—
416	C₄⋊C₄	—	8	2	no	—
417	C₄⋊C₄	C₂×D₄×C₇₃	1	4	yes	—
418	C₂²⋊C₄	—	2	8	no	—
419	C₂²⋊C₄	—	2	8	no	—
420	C₂²⋊C₄	—	2	4	no	—
421	C₂²⋊C₄	—	4	2	no	—
422	C₂²⋊C₄	—	4	2	no	—
423	C₂²⋊C₄	—	4	4	no	—
424	C₂²⋊C₄	—	8	2	no	—
425	C₄²	—	2	1	no	—
426	C₄²	—	2	1	no	—
427	C₄²	C₂×D₄×C₇₃	1	2	yes	—
428	C₄²	C₂×D₄×C₇₃	1	2	yes	—
429	C₂³	—	2	1	no	—
430	C₂³	—	2	4	no	—
431	C₂³	—	2	1	no	—
432	C₂³	—	2	1	no	—
433	C₂³	—	2	2	no	—
434	C₂³	—	2	2	no	—
435	C₂³	—	4	2	no	—
436	C₂³	—	4	2	no	—
437	C₂³	—	4	2	no	—
438	C₂³	—	4	2	no	—
439	C₂³	—	4	2	no	—
440	C₂³	—	4	2	no	—
441	C₂³	—	4	1	no	—
442	C₂³	—	4	1	no	—
443	C₂³	—	4	1	no	—
444	C₂³	—	4	2	no	—
445	C₂³	—	4	2	no	—
446	C₂³	C₂²×D₄×C₇₃	1	1	yes	characteristic
447	Q₈	—	4	2	no	—
448	Q₈	—	4	2	no	—
449	D₄	—	2	4	no	—
450	D₄	—	2	4	no	—
451	D₄	—	4	2	no	—
452	D₄	—	4	2	no	—
453	D₄	—	4	2	no	—
454	D₄	—	4	2	no	—
455	D₄	—	8	8	no	—
456	D₄	—	8	8	no	—
457	D₄	—	8	4	no	—
458	C₂×C₄	—	2	2	no	—
459	C₂×C₄	—	2	2	no	—
460	C₂×C₄	—	2	2	no	—
461	C₂×C₄	—	2	1	no	—
462	C₂×C₄	—	2	4	no	—
463	C₂×C₄	—	2	1	no	—
464	C₂×C₄	—	2	1	no	—
465	C₂×C₄	—	2	2	no	—
466	C₂×C₄	—	2	2	no	—
467	C₂×C₄	—	4	2	no	—
468	C₂×C₄	—	4	2	no	—
469	C₂×C₄	—	4	2	no	—
470	C₂×C₄	—	4	2	no	—
471	C₂×C₄	—	4	1	no	—
472	C₂×C₄	—	4	1	no	—
473	C₂×C₄	—	4	1	no	—
474	C₂×C₄	—	4	1	no	—
475	C₂×C₄	—	4	1	no	—
476	C₂×C₄	—	4	2	no	—
477	C₂×C₄	—	4	2	no	—
478	C₂×C₄	—	8	8	no	—
479	C₂×C₄	#120×C₇₃	1	4	yes	—
480	C₂×C₄	C₂²×D₄×C₇₃	1	1	yes	characteristic
481	C₂×C₄	C₂²×D₄×C₇₃	1	1	yes	characteristic
482	C₂×C₄	C₂×#41×C₇₃	1	2	yes	—
483	C₂×C₄	H(5,𝔽₂)×C₇₃	1	2	yes	—
484	C₈	—	2	4	no	—
485	C₈	—	4	2	no	—
486	C₂²	—	4	1	no	—
487	C₂²	—	4	1	no	—
488	C₂²	—	4	4	no	—
489	C₂²	—	4	2	no	—
490	C₂²	—	4	4	no	—
491	C₂²	—	4	2	no	—
492	C₂²	—	4	1	no	—
493	C₂²	—	4	4	no	—
494	C₂²	—	8	2	no	—
495	C₂²	—	8	2	no	—
496	C₂²	—	8	2	no	—
497	C₂²	—	8	2	no	—
498	C₂²	—	8	1	no	—
499	C₂²	—	8	1	no	—
500	C₂²	—	8	2	no	—
501	C₂²	—	8	2	no	—
502	C₂²	—	8	1	no	—
503	C₂²	C₂×#120×C₇₃	1	1	yes	characteristic
504	C₂²	#532×C₇₃	1	1	yes	characteristic
505	C₂²	#535×C₇₃	1	1	yes	characteristic
506	C₂²	#576×C₇₃	1	2	yes	—
507	C₂²	#577×C₇₃	1	2	yes	—
508	C₄	—	2	4	no	—
509	C₄	—	4	2	no	—
510	C₄	—	4	4	no	—
511	C₄	—	4	1	no	—
512	C₄	—	8	1	no	—
513	C₄	—	8	1	no	—
514	C₄	—	8	1	no	—
515	C₄	#546×C₇₃	1	2	yes	—
516	C₄	#550×C₇₃	1	2	yes	—
517	C₂	—	8	1	no	—
518	C₂	—	8	4	no	—
519	C₂	—	16	1	no	—
520	C₂	C₇₃×#2431	1	1	yes	characteristic
521	C₂	C₇₃×#3012	1	2	yes	—
522	C₂	C₇₃×#3179	1	2	yes	—
523	C₂	C₇₃×#3220	1	1	yes	characteristic
524	C₂	C₇₃×#3221	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₇₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₇₃
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₇₃ ◁ C₂×#117×C₇₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×#540×C₇₃	C₂	semidirect
2. C₂×#496×C₇₃	C₂	semidirect
3. C₂×#488×C₇₃	C₂	semidirect
4. C₇₃×#2620	C₂	semidirect
5. C₇₃×#2000	C₂	semidirect
6. C₇₃×#1999	C₂	semidirect
7. C₇₃×#1992	C₂	semidirect
8. C₇₃×#1957	C₂	semidirect
9. C₇₃×#1879	C₂	semidirect
10. C₇₃×#1877	C₂	semidirect
11. C₇₃×#1750	C₂	semidirect
60. #127×C₇₃	D₄	semidirect
62. #125×C₇₃	D₄	semidirect
254. #25611	C₇₃	direct (N × H)
263. C₂×#540	C₂×C₇₃	semidirect
264. C₂×#496	C₂×C₇₃	semidirect
265. C₂×#488	C₂×C₇₃	semidirect
266. #2620	C₂×C₇₃	semidirect
267. #2000	C₂×C₇₃	semidirect
268. #1999	C₂×C₇₃	semidirect
269. #1992	C₂×C₇₃	semidirect
270. #1957	C₂×C₇₃	semidirect
271. #1879	C₂×C₇₃	semidirect
272. #1877	C₂×C₇₃	semidirect
273. #1750	C₂×C₇₃	semidirect
274. C₇₃	#25611	direct (N × H)
323. #127	D₄×C₇₃	semidirect
325. #125	D₄×C₇₃	semidirect

Maximal subgroups

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

subgroup	index
C₂×#540×C₇₃	2
C₂×#496×C₇₃	2
C₂×#488×C₇₃	2
C₇₃×#2620	2
C₇₃×#2000	2
C₇₃×#1999	2
C₇₃×#1992	2
C₇₃×#1957	2
C₇₃×#1879	2
C₇₃×#1877	2
C₇₃×#1750	2
#25611	73

Subgroups — C73×#25611 #32935015

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₃×#25611 #32935015