Subgroups — C₇₃×#25673 #32935077

Order 18688.

1374 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	C₂×#532×C₇₃	C₂	1	1	yes	maximal, characteristic
2	C₂×#500×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#486×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₇₃×#2857	C₂	1	1	yes	maximal, characteristic, complemented
5	C₇₃×#2033	C₂	1	4	yes	maximal, complemented
6	C₇₃×#1990	C₂	1	1	yes	maximal, characteristic, complemented
7	C₇₃×#1957	C₂	1	1	yes	maximal, characteristic, complemented
8	C₇₃×#1862	C₂	1	4	yes	maximal, complemented
9	C₄×C₂²⋊C₈×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂²×#41×C₇₃	—	2	1	no	—
11	#532×C₇₃	—	2	4	no	—
12	#532×C₇₃	—	2	4	no	—
13	C₂×C₄⋊Q₈×C₇₃	C₂²	1	1	yes	characteristic
14	C₂×C₄⋊Q₈×C₇₃	C₂²	1	1	yes	characteristic
15	C₂×#127×C₇₃	C₂²	1	1	yes	characteristic
16	C₂×#124×C₇₃	—	2	1	no	—
17	C₂×C₂²⋊Q₈×C₇₃	—	2	1	no	—
18	C₂×#121×C₇₃	—	2	1	no	—
19	C₂×#121×C₇₃	C₂²	1	2	yes	—
20	C₂×C₄×D₄×C₇₃	—	2	1	no	—
21	C₂×C₄×D₄×C₇₃	C₂²	1	2	yes	—
22	C₂²×C₄²×C₇₃	C₂²	1	1	yes	characteristic
23	#500×C₇₃	—	2	4	no	—
24	#486×C₇₃	—	2	4	no	—
25	C₂×#107×C₇₃	C₂²	1	4	yes	—
26	C₂×#102×C₇₃	C₂²	1	4	yes	—
27	C₂×#102×C₇₃	C₂²	1	4	yes	—
28	C₂×C₂²⋊C₈×C₇₃	C₂²	1	2	yes	—
29	C₂×C₄×C₈×C₇₃	C₂²	1	1	yes	characteristic
30	C₂×C₄×C₈×C₇₃	C₂²	1	1	yes	characteristic
31	#391×C₇₃	—	2	1	no	—
32	#389×C₇₃	—	2	1	no	—
33	#389×C₇₃	C₂²	1	2	yes	—
34	#384×C₇₃	C₂²	1	1	yes	characteristic
35	#380×C₇₃	—	2	1	no	—
36	#380×C₇₃	C₂²	1	2	yes	—
37	#340×C₇₃	C₂²	1	4	yes	—
38	#336×C₇₃	C₂²	1	2	yes	—
39	C₂×#41×C₇₃	—	2	8	no	—
40	C₂×#41×C₇₃	—	4	4	no	—
41	C₂×#41×C₇₃	—	4	4	no	—
42	C₂²×Q₈×C₇₃	—	2	1	no	—
43	C₂²×Q₈×C₇₃	—	2	1	no	—
44	C₂²×D₄×C₇₃	—	2	2	no	—
45	C₂²×D₄×C₇₃	—	2	1	no	—
46	C₂²×D₄×C₇₃	—	2	1	no	—
47	C₂²×D₄×C₇₃	C₂³	1	2	yes	—
48	C₂³×C₄×C₇₃	—	2	2	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	C₂²×C₈×C₇₃	C₂³	1	2	yes	—
53	C₂²×C₈×C₇₃	C₂³	1	2	yes	—
54	C₄⋊Q₈×C₇₃	—	2	2	no	—
55	C₄⋊Q₈×C₇₃	—	2	2	no	—
56	C₄⋊Q₈×C₇₃	—	2	2	no	—
57	C₄⋊Q₈×C₇₃	D₄	1	4	yes	—
58	#127×C₇₃	—	2	2	no	—
59	#127×C₇₃	D₄	1	4	yes	—
60	#124×C₇₃	—	2	8	no	—
61	C₂²⋊Q₈×C₇₃	—	4	4	no	—
62	#121×C₇₃	—	2	8	no	—
63	#121×C₇₃	—	2	4	no	—
64	#121×C₇₃	—	2	4	no	—
65	C₄×D₄×C₇₃	—	2	8	no	—
66	C₄×D₄×C₇₃	—	2	4	no	—
67	C₄×D₄×C₇₃	—	2	4	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	1	no	—
72	C₂×C₄⋊C₄×C₇₃	—	2	2	no	—
73	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
74	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
75	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
76	C₂×C₂²⋊C₄×C₇₃	—	2	2	no	—
77	C₂×C₂²⋊C₄×C₇₃	—	2	2	no	—
78	C₂×C₂²⋊C₄×C₇₃	—	2	2	no	—
79	C₂×C₄²×C₇₃	—	2	2	no	—
80	C₂×C₄²×C₇₃	—	2	2	no	—
81	C₂×C₄²×C₇₃	D₄	1	1	yes	characteristic
82	C₂×C₄²×C₇₃	D₄	1	1	yes	characteristic
83	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
84	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
85	#107×C₇₃	—	2	8	no	—
86	#102×C₇₃	—	2	8	no	—
87	#102×C₇₃	—	2	8	no	—
88	C₂²⋊C₈×C₇₃	—	2	4	no	—
89	C₄×C₈×C₇₃	—	2	2	no	—
90	C₄×C₈×C₇₃	—	2	2	no	—
91	#95×C₇₃	—	2	2	no	—
92	#95×C₇₃	—	2	2	no	—
93	C₂⁴×C₇₃	—	2	2	no	—
94	C₂⁴×C₇₃	C₂×D₄	1	1	yes	characteristic
95	#41×C₇₃	—	4	32	no	—
96	C₂×Q₈×C₇₃	—	2	4	no	—
97	C₂×Q₈×C₇₃	—	4	2	no	—
98	C₂×Q₈×C₇₃	—	4	2	no	—
99	C₂×Q₈×C₇₃	—	4	2	no	—
100	C₂×Q₈×C₇₃	—	4	2	no	—
101	C₂×Q₈×C₇₃	—	4	2	no	—
102	C₂×D₄×C₇₃	—	2	8	no	—
103	C₂×D₄×C₇₃	—	2	4	no	—
104	C₂×D₄×C₇₃	—	2	4	no	—
105	C₂×D₄×C₇₃	—	2	2	no	—
106	C₂×D₄×C₇₃	—	2	4	no	—
107	C₂×D₄×C₇₃	—	2	4	no	—
108	C₂×D₄×C₇₃	—	4	4	no	—
109	C₂×D₄×C₇₃	—	4	4	no	—
110	C₂×D₄×C₇₃	—	4	2	no	—
111	C₂×D₄×C₇₃	—	4	2	no	—
112	C₂×D₄×C₇₃	—	4	2	no	—
113	C₂×D₄×C₇₃	—	4	2	no	—
114	C₂×D₄×C₇₃	C₂×D₄	1	4	yes	—
115	C₂²×C₄×C₇₃	—	2	2	no	—
116	C₂²×C₄×C₇₃	—	2	2	no	—
117	C₂²×C₄×C₇₃	—	2	8	no	—
118	C₂²×C₄×C₇₃	—	2	2	no	—
119	C₂²×C₄×C₇₃	—	2	2	no	—
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	1	no	—
124	C₂²×C₄×C₇₃	—	2	2	no	—
125	C₂²×C₄×C₇₃	—	2	2	no	—
126	C₂²×C₄×C₇₃	—	2	2	no	—
127	C₂²×C₄×C₇₃	—	2	2	no	—
128	C₂²×C₄×C₇₃	—	4	4	no	—
129	C₂²×C₄×C₇₃	—	4	4	no	—
130	C₂²×C₄×C₇₃	D₈	1	4	yes	—
131	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
132	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
133	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
134	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
135	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
136	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
137	C₂×C₈×C₇₃	—	2	2	no	—
138	C₂×C₈×C₇₃	—	2	2	no	—
139	C₂×C₈×C₇₃	—	2	2	no	—
140	C₂×C₈×C₇₃	—	2	2	no	—
141	C₂×C₈×C₇₃	—	2	2	no	—
142	C₂×C₈×C₇₃	#41	1	4	yes	complemented
143	C₄⋊C₄×C₇₃	—	2	4	no	—
144	C₄⋊C₄×C₇₃	—	2	2	no	—
145	C₄⋊C₄×C₇₃	—	2	2	no	—
146	C₄⋊C₄×C₇₃	—	2	2	no	—
147	C₄⋊C₄×C₇₃	—	2	4	no	—
148	C₄⋊C₄×C₇₃	—	4	2	no	—
149	C₄⋊C₄×C₇₃	—	4	2	no	—
150	C₄⋊C₄×C₇₃	—	4	4	no	—
151	C₄⋊C₄×C₇₃	—	4	2	no	—
152	C₄⋊C₄×C₇₃	C₂×D₄	1	4	yes	—
153	C₂²⋊C₄×C₇₃	—	2	8	no	—
154	C₂²⋊C₄×C₇₃	—	2	8	no	—
155	C₂²⋊C₄×C₇₃	—	4	4	no	—
156	C₄²×C₇₃	—	2	2	no	—
157	C₄²×C₇₃	—	2	2	no	—
158	C₄²×C₇₃	—	2	1	no	—
159	C₄²×C₇₃	—	2	1	no	—
160	C₄²×C₇₃	C₂×D₄	1	2	yes	—
161	C₄²×C₇₃	C₂×D₄	1	2	yes	—
162	C₂³×C₇₃	—	2	1	no	—
163	C₂³×C₇₃	—	2	1	no	—
164	C₂³×C₇₃	—	2	1	no	—
165	C₂³×C₇₃	—	2	1	no	—
166	C₂³×C₇₃	—	2	1	no	—
167	C₂³×C₇₃	—	2	1	no	—
168	C₂³×C₇₃	—	2	4	no	—
169	C₂³×C₇₃	—	4	2	no	—
170	C₂³×C₇₃	—	4	2	no	—
171	C₂³×C₇₃	—	4	2	no	—
172	C₂³×C₇₃	—	4	2	no	—
173	C₂³×C₇₃	—	4	2	no	—
174	C₂³×C₇₃	—	4	2	no	—
175	C₂³×C₇₃	C₂×D₈	1	2	yes	—
176	C₂³×C₇₃	C₂²×D₄	1	1	yes	characteristic
177	Q₈×C₇₃	—	4	8	no	—
178	Q₈×C₇₃	—	8	4	no	—
179	D₄×C₇₃	—	2	8	no	—
180	D₄×C₇₃	—	4	16	no	—
181	D₄×C₇₃	—	4	4	no	—
182	D₄×C₇₃	—	4	8	no	—
183	D₄×C₇₃	—	4	8	no	—
184	C₂×C₄×C₇₃	—	2	1	no	—
185	C₂×C₄×C₇₃	—	2	1	no	—
186	C₂×C₄×C₇₃	—	2	8	no	—
187	C₂×C₄×C₇₃	—	2	1	no	—
188	C₂×C₄×C₇₃	—	2	1	no	—
189	C₂×C₄×C₇₃	—	2	4	no	—
190	C₂×C₄×C₇₃	—	2	1	no	—
191	C₂×C₄×C₇₃	—	2	1	no	—
192	C₂×C₄×C₇₃	—	2	1	no	—
193	C₂×C₄×C₇₃	—	2	1	no	—
194	C₂×C₄×C₇₃	—	4	16	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	2	no	—
199	C₂×C₄×C₇₃	—	4	4	no	—
200	C₂×C₄×C₇₃	—	4	2	no	—
201	C₂×C₄×C₇₃	—	4	2	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	2	no	—
206	C₂×C₄×C₇₃	#120	1	2	yes	—
207	C₂×C₄×C₇₃	#120	1	2	yes	—
208	C₂×C₄×C₇₃	C₂×D₈	1	2	yes	—
209	C₂×C₄×C₇₃	C₂×D₈	1	2	yes	—
210	C₂×C₄×C₇₃	#135	1	2	yes	—
211	C₂×C₄×C₇₃	AGL(1,ℤ/8)	1	2	yes	—
212	C₂×C₄×C₇₃	#137	1	2	yes	—
213	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
214	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
215	C₂×C₄×C₇₃	C₂×#41	1	2	yes	—
216	C₂×C₄×C₇₃	2₋¹⁺⁴	1	2	yes	—
217	C₈×C₇₃	—	2	4	no	—
218	C₈×C₇₃	—	4	2	no	—
219	C₂²×C₇₃	—	2	2	no	—
220	C₂²×C₇₃	—	2	2	no	—
221	C₂²×C₇₃	—	2	2	no	—
222	C₂²×C₇₃	—	4	1	no	—
223	C₂²×C₇₃	—	4	1	no	—
224	C₂²×C₇₃	—	4	1	no	—
225	C₂²×C₇₃	—	4	1	no	—
226	C₂²×C₇₃	—	4	4	no	—
227	C₂²×C₇₃	—	4	4	no	—
228	C₂²×C₇₃	—	4	4	no	—
229	C₂²×C₇₃	—	8	2	no	—
230	C₂²×C₇₃	—	8	2	no	—
231	C₂²×C₇₃	—	8	2	no	—
232	C₂²×C₇₃	—	8	2	no	—
233	C₂²×C₇₃	C₂×#120	1	1	yes	characteristic
234	C₂²×C₇₃	#532	1	1	yes	characteristic
235	C₂²×C₇₃	#536	1	1	yes	characteristic
236	C₂²×C₇₃	C₂²×D₈	1	1	yes	characteristic
237	C₂²×C₇₃	C₂×#135	1	1	yes	characteristic
238	C₂²×C₇₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
239	C₂²×C₇₃	C₂×#137	1	1	yes	characteristic
240	C₄×C₇₃	—	2	2	no	—
241	C₄×C₇₃	—	4	1	no	—
242	C₄×C₇₃	—	4	4	no	—
243	C₄×C₇₃	—	4	1	no	—
244	C₄×C₇₃	—	8	2	no	—
245	C₄×C₇₃	—	8	2	no	—
246	C₄×C₇₃	#447	1	4	yes	—
247	C₄×C₇₃	#452	1	4	yes	—
248	C₄×C₇₃	#547	1	2	yes	—
249	C₄×C₇₃	#548	1	2	yes	—
250	#25673	C₇₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
251	C₂×C₇₃	—	4	2	no	—
252	C₂×C₇₃	—	8	4	no	—
253	C₂×C₇₃	#2432	1	1	yes	characteristic
254	C₂×C₇₃	C₂×#447	1	1	yes	characteristic
255	C₂×C₇₃	C₂×#452	1	1	yes	characteristic
256	C₂×C₇₃	#3169	1	1	yes	characteristic
257	C₂×C₇₃	#3182	1	1	yes	characteristic
258	C₂×C₇₃	#3226	1	1	yes	characteristic
259	C₂×C₇₃	#3228	1	1	yes	characteristic
260	C₂×#532	C₂×C₇₃	1	1	yes	characteristic
261	C₂×#500	C₂×C₇₃	1	1	yes	characteristic, complemented
262	C₂×#486	C₂×C₇₃	1	1	yes	characteristic, complemented
263	#2857	C₂×C₇₃	1	1	yes	characteristic, complemented
264	#2033	C₂×C₇₃	1	4	yes	complemented
265	#1990	C₂×C₇₃	1	1	yes	characteristic, complemented
266	#1957	C₂×C₇₃	1	1	yes	characteristic, complemented
267	#1862	C₂×C₇₃	1	4	yes	complemented
268	C₄×C₂²⋊C₈	C₂×C₇₃	1	1	yes	characteristic, complemented
269	C₇₃	#25673	1	1	yes	characteristic, direct product factor, Sylow
270	C₂²×#41	—	2	1	no	—
271	#532	—	2	4	no	—
272	#532	—	2	4	no	—
273	C₂×C₄⋊Q₈	C₂²×C₇₃	1	1	yes	characteristic
274	C₂×C₄⋊Q₈	C₂²×C₇₃	1	1	yes	characteristic
275	C₂×#127	C₂²×C₇₃	1	1	yes	characteristic
276	C₂×#124	—	2	1	no	—
277	C₂×C₂²⋊Q₈	—	2	1	no	—
278	C₂×#121	—	2	1	no	—
279	C₂×#121	C₂²×C₇₃	1	2	yes	—
280	C₂×C₄×D₄	—	2	1	no	—
281	C₂×C₄×D₄	C₂²×C₇₃	1	2	yes	—
282	C₂²×C₄²	C₂²×C₇₃	1	1	yes	characteristic
283	#500	—	2	4	no	—
284	#486	—	2	4	no	—
285	C₂×#107	C₂²×C₇₃	1	4	yes	—
286	C₂×#102	C₂²×C₇₃	1	4	yes	—
287	C₂×#102	C₂²×C₇₃	1	4	yes	—
288	C₂×C₂²⋊C₈	C₂²×C₇₃	1	2	yes	—
289	C₂×C₄×C₈	C₂²×C₇₃	1	1	yes	characteristic
290	C₂×C₄×C₈	C₂²×C₇₃	1	1	yes	characteristic
291	#391	—	2	1	no	—
292	#389	—	2	1	no	—
293	#389	C₂²×C₇₃	1	2	yes	—
294	#384	C₂²×C₇₃	1	1	yes	characteristic
295	#380	—	2	1	no	—
296	#380	C₂²×C₇₃	1	2	yes	—
297	#340	C₂²×C₇₃	1	4	yes	—
298	#336	C₂²×C₇₃	1	2	yes	—
299	C₂×#41	—	2	8	no	—
300	C₂×#41	—	4	4	no	—
301	C₂×#41	—	4	4	no	—
302	C₂²×Q₈	—	2	1	no	—
303	C₂²×Q₈	—	2	1	no	—
304	C₂²×D₄	—	2	2	no	—
305	C₂²×D₄	—	2	1	no	—
306	C₂²×D₄	—	2	1	no	—
307	C₂²×D₄	C₂³×C₇₃	1	2	yes	—
308	C₂³×C₄	—	2	2	no	—
309	C₂³×C₄	D₄×C₇₃	1	1	yes	characteristic
310	C₂³×C₄	D₄×C₇₃	1	1	yes	characteristic
311	C₂³×C₄	C₂³×C₇₃	1	1	yes	characteristic
312	C₂²×C₈	C₂³×C₇₃	1	2	yes	—
313	C₂²×C₈	C₂³×C₇₃	1	2	yes	—
314	C₄⋊Q₈	—	2	2	no	—
315	C₄⋊Q₈	—	2	2	no	—
316	C₄⋊Q₈	—	2	2	no	—
317	C₄⋊Q₈	D₄×C₇₃	1	4	yes	—
318	#127	—	2	2	no	—
319	#127	D₄×C₇₃	1	4	yes	—
320	#124	—	2	8	no	—
321	C₂²⋊Q₈	—	4	4	no	—
322	#121	—	2	8	no	—
323	#121	—	2	4	no	—
324	#121	—	2	4	no	—
325	C₄×D₄	—	2	8	no	—
326	C₄×D₄	—	2	4	no	—
327	C₄×D₄	—	2	4	no	—
328	C₂×C₄⋊C₄	—	2	1	no	—
329	C₂×C₄⋊C₄	—	2	1	no	—
330	C₂×C₄⋊C₄	—	2	2	no	—
331	C₂×C₄⋊C₄	—	2	1	no	—
332	C₂×C₄⋊C₄	—	2	1	no	—
333	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
334	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
335	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
336	C₂×C₂²⋊C₄	—	2	2	no	—
337	C₂×C₂²⋊C₄	—	2	2	no	—
338	C₂×C₂²⋊C₄	—	2	2	no	—
339	C₂×C₄²	—	2	2	no	—
340	C₂×C₄²	—	2	2	no	—
341	C₂×C₄²	D₄×C₇₃	1	1	yes	characteristic
342	C₂×C₄²	D₄×C₇₃	1	1	yes	characteristic
343	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
344	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
345	#107	—	2	8	no	—
346	#102	—	2	8	no	—
347	#102	—	2	8	no	—
348	C₂²⋊C₈	—	2	4	no	—
349	C₄×C₈	—	2	2	no	—
350	C₄×C₈	—	2	2	no	—
351	#95	—	2	2	no	—
352	#95	—	2	2	no	—
353	C₂⁴	—	2	2	no	—
354	C₂⁴	C₂×D₄×C₇₃	1	1	yes	characteristic
355	#41	—	4	32	no	—
356	C₂×Q₈	—	2	4	no	—
357	C₂×Q₈	—	4	2	no	—
358	C₂×Q₈	—	4	2	no	—
359	C₂×Q₈	—	4	2	no	—
360	C₂×Q₈	—	4	2	no	—
361	C₂×Q₈	—	4	2	no	—
362	C₂×D₄	—	2	8	no	—
363	C₂×D₄	—	2	4	no	—
364	C₂×D₄	—	2	4	no	—
365	C₂×D₄	—	2	2	no	—
366	C₂×D₄	—	2	4	no	—
367	C₂×D₄	—	2	4	no	—
368	C₂×D₄	—	4	4	no	—
369	C₂×D₄	—	4	4	no	—
370	C₂×D₄	—	4	2	no	—
371	C₂×D₄	—	4	2	no	—
372	C₂×D₄	—	4	2	no	—
373	C₂×D₄	—	4	2	no	—
374	C₂×D₄	C₂×D₄×C₇₃	1	4	yes	—
375	C₂²×C₄	—	2	2	no	—
376	C₂²×C₄	—	2	2	no	—
377	C₂²×C₄	—	2	8	no	—
378	C₂²×C₄	—	2	2	no	—
379	C₂²×C₄	—	2	2	no	—
380	C₂²×C₄	—	2	2	no	—
381	C₂²×C₄	—	2	2	no	—
382	C₂²×C₄	—	2	1	no	—
383	C₂²×C₄	—	2	1	no	—
384	C₂²×C₄	—	2	2	no	—
385	C₂²×C₄	—	2	2	no	—
386	C₂²×C₄	—	2	2	no	—
387	C₂²×C₄	—	2	2	no	—
388	C₂²×C₄	—	4	4	no	—
389	C₂²×C₄	—	4	4	no	—
390	C₂²×C₄	D₈×C₇₃	1	4	yes	—
391	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
392	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
393	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
394	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
395	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
396	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
397	C₂×C₈	—	2	2	no	—
398	C₂×C₈	—	2	2	no	—
399	C₂×C₈	—	2	2	no	—
400	C₂×C₈	—	2	2	no	—
401	C₂×C₈	—	2	2	no	—
402	C₂×C₈	#41×C₇₃	1	4	yes	complemented
403	C₄⋊C₄	—	2	4	no	—
404	C₄⋊C₄	—	2	2	no	—
405	C₄⋊C₄	—	2	2	no	—
406	C₄⋊C₄	—	2	2	no	—
407	C₄⋊C₄	—	2	4	no	—
408	C₄⋊C₄	—	4	2	no	—
409	C₄⋊C₄	—	4	2	no	—
410	C₄⋊C₄	—	4	4	no	—
411	C₄⋊C₄	—	4	2	no	—
412	C₄⋊C₄	C₂×D₄×C₇₃	1	4	yes	—
413	C₂²⋊C₄	—	2	8	no	—
414	C₂²⋊C₄	—	2	8	no	—
415	C₂²⋊C₄	—	4	4	no	—
416	C₄²	—	2	2	no	—
417	C₄²	—	2	2	no	—
418	C₄²	—	2	1	no	—
419	C₄²	—	2	1	no	—
420	C₄²	C₂×D₄×C₇₃	1	2	yes	—
421	C₄²	C₂×D₄×C₇₃	1	2	yes	—
422	C₂³	—	2	1	no	—
423	C₂³	—	2	1	no	—
424	C₂³	—	2	1	no	—
425	C₂³	—	2	1	no	—
426	C₂³	—	2	1	no	—
427	C₂³	—	2	1	no	—
428	C₂³	—	2	4	no	—
429	C₂³	—	4	2	no	—
430	C₂³	—	4	2	no	—
431	C₂³	—	4	2	no	—
432	C₂³	—	4	2	no	—
433	C₂³	—	4	2	no	—
434	C₂³	—	4	2	no	—
435	C₂³	C₂×D₈×C₇₃	1	2	yes	—
436	C₂³	C₂²×D₄×C₇₃	1	1	yes	characteristic
437	Q₈	—	4	8	no	—
438	Q₈	—	8	4	no	—
439	D₄	—	2	8	no	—
440	D₄	—	4	16	no	—
441	D₄	—	4	8	no	—
442	D₄	—	4	8	no	—
443	D₄	—	4	4	no	—
444	C₂×C₄	—	2	1	no	—
445	C₂×C₄	—	2	1	no	—
446	C₂×C₄	—	2	8	no	—
447	C₂×C₄	—	2	1	no	—
448	C₂×C₄	—	2	1	no	—
449	C₂×C₄	—	2	4	no	—
450	C₂×C₄	—	2	1	no	—
451	C₂×C₄	—	2	1	no	—
452	C₂×C₄	—	2	1	no	—
453	C₂×C₄	—	2	1	no	—
454	C₂×C₄	—	4	16	no	—
455	C₂×C₄	—	4	2	no	—
456	C₂×C₄	—	4	2	no	—
457	C₂×C₄	—	4	4	no	—
458	C₂×C₄	—	4	2	no	—
459	C₂×C₄	—	4	2	no	—
460	C₂×C₄	—	4	2	no	—
461	C₂×C₄	—	4	2	no	—
462	C₂×C₄	—	4	2	no	—
463	C₂×C₄	—	4	2	no	—
464	C₂×C₄	—	4	2	no	—
465	C₂×C₄	—	4	2	no	—
466	C₂×C₄	#120×C₇₃	1	2	yes	—
467	C₂×C₄	#120×C₇₃	1	2	yes	—
468	C₂×C₄	C₂×D₈×C₇₃	1	2	yes	—
469	C₂×C₄	C₂×D₈×C₇₃	1	2	yes	—
470	C₂×C₄	#135×C₇₃	1	2	yes	—
471	C₂×C₄	AGL(1,ℤ/8)×C₇₃	1	2	yes	—
472	C₂×C₄	#137×C₇₃	1	2	yes	—
473	C₂×C₄	C₂²×D₄×C₇₃	1	1	yes	characteristic
474	C₂×C₄	C₂²×D₄×C₇₃	1	1	yes	characteristic
475	C₂×C₄	C₂×#41×C₇₃	1	2	yes	—
476	C₂×C₄	2₋¹⁺⁴×C₇₃	1	2	yes	—
477	C₈	—	2	4	no	—
478	C₈	—	4	2	no	—
479	C₂²	—	2	2	no	—
480	C₂²	—	2	2	no	—
481	C₂²	—	2	2	no	—
482	C₂²	—	4	1	no	—
483	C₂²	—	4	1	no	—
484	C₂²	—	4	1	no	—
485	C₂²	—	4	1	no	—
486	C₂²	—	4	4	no	—
487	C₂²	—	4	4	no	—
488	C₂²	—	4	4	no	—
489	C₂²	—	8	2	no	—
490	C₂²	—	8	2	no	—
491	C₂²	—	8	2	no	—
492	C₂²	—	8	2	no	—
493	C₂²	C₂×#120×C₇₃	1	1	yes	characteristic
494	C₂²	#532×C₇₃	1	1	yes	characteristic
495	C₂²	#536×C₇₃	1	1	yes	characteristic
496	C₂²	C₂²×D₈×C₇₃	1	1	yes	characteristic
497	C₂²	C₂×#135×C₇₃	1	1	yes	characteristic
498	C₂²	C₂×AGL(1,ℤ/8)×C₇₃	1	1	yes	characteristic
499	C₂²	C₂×#137×C₇₃	1	1	yes	characteristic
500	C₄	—	2	2	no	—
501	C₄	—	4	4	no	—
502	C₄	—	4	1	no	—
503	C₄	—	4	1	no	—
504	C₄	—	8	2	no	—
505	C₄	—	8	2	no	—
506	C₄	#447×C₇₃	1	4	yes	—
507	C₄	#452×C₇₃	1	4	yes	—
508	C₄	#547×C₇₃	1	2	yes	—
509	C₄	#548×C₇₃	1	2	yes	—
510	C₂	—	4	2	no	—
511	C₂	—	8	4	no	—
512	C₂	C₇₃×#2432	1	1	yes	characteristic
513	C₂	C₂×#447×C₇₃	1	1	yes	characteristic
514	C₂	C₂×#452×C₇₃	1	1	yes	characteristic
515	C₂	C₇₃×#3169	1	1	yes	characteristic
516	C₂	C₇₃×#3182	1	1	yes	characteristic
517	C₂	C₇₃×#3226	1	1	yes	characteristic
518	C₂	C₇₃×#3228	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₇₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₇₃
prime radical	C₂×#532×C₇₃	C₂
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
2. C₂×#500×C₇₃	C₂	semidirect
3. C₂×#486×C₇₃	C₂	semidirect
4. C₇₃×#2857	C₂	semidirect
5. C₇₃×#2033	C₂	semidirect
6. C₇₃×#1990	C₂	semidirect
7. C₇₃×#1957	C₂	semidirect
8. C₇₃×#1862	C₂	semidirect
9. C₄×C₂²⋊C₈×C₇₃	C₂	semidirect
142. C₂×C₈×C₇₃	#41	semidirect
250. #25673	C₇₃	direct (N × H)
261. C₂×#500	C₂×C₇₃	semidirect
262. C₂×#486	C₂×C₇₃	semidirect
263. #2857	C₂×C₇₃	semidirect
264. #2033	C₂×C₇₃	semidirect
265. #1990	C₂×C₇₃	semidirect
266. #1957	C₂×C₇₃	semidirect
267. #1862	C₂×C₇₃	semidirect
268. C₄×C₂²⋊C₈	C₂×C₇₃	semidirect
269. C₇₃	#25673	direct (N × H)
402. C₂×C₈	#41×C₇₃	semidirect

Maximal subgroups

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

subgroup	index
C₂×#532×C₇₃	2
C₂×#500×C₇₃	2
C₂×#486×C₇₃	2
C₇₃×#2857	2
C₇₃×#2033	2
C₇₃×#1990	2
C₇₃×#1957	2
C₇₃×#1862	2
C₄×C₂²⋊C₈×C₇₃	2
#25673	73

Subgroups — C73×#25673 #32935077

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₃×#25673 #32935077