Subgroups — C₇₃×#25715 #32935119

Order 18688.

1038 conjugacy classes of subgroups.

The subgroup lattice has 540 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#552×C₇₃	C₂	1	1	yes	maximal, characteristic
2	C₂×#501×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#475×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₇₃×#2563	C₂	1	1	yes	maximal, characteristic
5	C₇₃×#2036	C₂	1	2	yes	maximal, complemented
6	C₇₃×#2035	C₂	1	2	yes	maximal, complemented
7	C₇₃×#1989	C₂	1	1	yes	maximal, characteristic, complemented
8	C₇₃×#1955	C₂	1	1	yes	maximal, characteristic
9	C₇₃×#1854	C₂	1	2	yes	maximal, complemented
10	C₇₃×#1853	C₂	1	2	yes	maximal, complemented
11	C₇₃×#1763	C₂	1	1	yes	maximal, characteristic, complemented
12	#552×C₇₃	—	2	4	no	—
13	#552×C₇₃	—	2	4	no	—
14	C₂×C₄⋊Q₈×C₇₃	C₂²	1	1	yes	characteristic
15	C₂×#126×C₇₃	—	2	1	no	—
16	C₂×#125×C₇₃	—	2	1	no	—
17	C₂×#125×C₇₃	C₂²	1	1	yes	characteristic
18	C₂×#123×C₇₃	—	2	1	no	—
19	C₂×C₂²⋊Q₈×C₇₃	C₂²	1	1	yes	characteristic
20	C₂×C₂²⋊Q₈×C₇₃	C₂²	1	1	yes	characteristic
21	C₂×C₄×Q₈×C₇₃	C₂²	1	1	yes	characteristic
22	C₂×C₄×D₄×C₇₃	C₂²	1	1	yes	characteristic
23	C₂×#117×C₇₃	—	2	1	no	—
24	C₂×#117×C₇₃	C₂²	1	1	yes	characteristic
25	C₂²×C₄⋊C₄×C₇₃	C₂²	1	1	yes	characteristic
26	#501×C₇₃	—	2	4	no	—
27	#475×C₇₃	—	2	4	no	—
28	C₂×#107×C₇₃	C₂²	1	2	yes	—
29	C₂×#106×C₇₃	C₂²	1	2	yes	—
30	C₂×#106×C₇₃	C₂²	1	2	yes	—
31	C₂×C₄⋊C₈×C₇₃	C₂²	1	1	yes	characteristic
32	C₂×#103×C₇₃	C₂²	1	2	yes	—
33	C₂×#103×C₇₃	C₂²	1	2	yes	—
34	C₂×C₂²⋊C₈×C₇₃	C₂²	1	2	yes	—
35	C₂×C₂²⋊C₈×C₇₃	C₂²	1	2	yes	—
36	C₂×#97×C₇₃	C₂²	1	1	yes	characteristic
37	#393×C₇₃	—	2	1	no	—
38	#393×C₇₃	—	2	1	no	—
39	#390×C₇₃	—	2	1	no	—
40	#382×C₇₃	—	2	1	no	—
41	#380×C₇₃	C₂²	1	2	yes	—
42	#380×C₇₃	C₂²	1	2	yes	—
43	C₄×C₄⋊C₄×C₇₃	C₂²	1	1	yes	characteristic
44	#340×C₇₃	C₂²	1	2	yes	—
45	#340×C₇₃	C₂²	1	2	yes	—
46	#340×C₇₃	C₂²	1	2	yes	—
47	C₂²×Q₈×C₇₃	—	2	1	no	—
48	C₂²×Q₈×C₇₃	C₂³	1	1	yes	characteristic
49	C₂²×D₄×C₇₃	D₄	1	1	yes	characteristic
50	C₂³×C₄×C₇₃	—	2	1	no	—
51	C₂³×C₄×C₇₃	C₂³	1	1	yes	characteristic
52	C₂³×C₄×C₇₃	C₂³	1	1	yes	characteristic
53	C₂²×C₈×C₇₃	C₂³	1	2	yes	—
54	C₂²×C₈×C₇₃	C₂³	1	2	yes	—
55	C₄⋊Q₈×C₇₃	—	2	2	no	—
56	C₄⋊Q₈×C₇₃	—	2	2	no	—
57	#126×C₇₃	—	2	8	no	—
58	#125×C₇₃	—	2	8	no	—
59	#125×C₇₃	—	2	2	no	—
60	#125×C₇₃	D₄	1	4	yes	—
61	#123×C₇₃	—	2	8	no	—
62	C₂²⋊Q₈×C₇₃	—	2	2	no	—
63	C₂²⋊Q₈×C₇₃	—	2	2	no	—
64	C₂²⋊Q₈×C₇₃	—	2	2	no	—
65	C₂²⋊Q₈×C₇₃	—	2	2	no	—
66	C₄×Q₈×C₇₃	—	2	2	no	—
67	C₄×Q₈×C₇₃	D₄	1	4	yes	—
68	C₄×D₄×C₇₃	—	2	2	no	—
69	C₄×D₄×C₇₃	—	2	2	no	—
70	#117×C₇₃	—	2	8	no	—
71	#117×C₇₃	—	2	2	no	—
72	#117×C₇₃	—	2	2	no	—
73	C₂×C₄⋊C₄×C₇₃	—	2	1	no	—
74	C₂×C₄⋊C₄×C₇₃	—	2	1	no	—
75	C₂×C₄⋊C₄×C₇₃	—	2	1	no	—
76	C₂×C₄⋊C₄×C₇₃	—	2	1	no	—
77	C₂×C₄⋊C₄×C₇₃	—	2	1	no	—
78	C₂×C₄⋊C₄×C₇₃	—	2	1	no	—
79	C₂×C₄⋊C₄×C₇₃	—	2	2	no	—
80	C₂×C₄⋊C₄×C₇₃	—	2	2	no	—
81	C₂×C₄⋊C₄×C₇₃	—	2	1	no	—
82	C₂×C₄⋊C₄×C₇₃	D₄	1	1	yes	characteristic
83	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
84	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
85	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
86	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
87	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
88	C₂×C₂²⋊C₄×C₇₃	—	2	1	no	—
89	C₂×C₂²⋊C₄×C₇₃	—	2	1	no	—
90	C₂×C₂²⋊C₄×C₇₃	—	2	1	no	—
91	C₂×C₂²⋊C₄×C₇₃	—	2	2	no	—
92	C₂×C₂²⋊C₄×C₇₃	—	2	2	no	—
93	C₂×C₂²⋊C₄×C₇₃	D₄	1	1	yes	characteristic
94	C₂×C₂²⋊C₄×C₇₃	D₄	1	1	yes	characteristic
95	C₂×C₄²×C₇₃	—	2	1	no	—
96	C₂×C₄²×C₇₃	—	2	1	no	—
97	C₂×C₄²×C₇₃	—	2	1	no	—
98	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
99	#107×C₇₃	—	2	4	no	—
100	#106×C₇₃	—	2	4	no	—
101	#106×C₇₃	—	2	4	no	—
102	C₄⋊C₈×C₇₃	—	2	2	no	—
103	#103×C₇₃	—	2	4	no	—
104	#103×C₇₃	—	2	4	no	—
105	C₂²⋊C₈×C₇₃	—	2	4	no	—
106	C₂²⋊C₈×C₇₃	—	2	4	no	—
107	#97×C₇₃	—	2	2	no	—
108	#95×C₇₃	—	2	1	no	—
109	#95×C₇₃	—	2	2	no	—
110	#95×C₇₃	—	2	2	no	—
111	C₂⁴×C₇₃	C₂×D₄	1	1	yes	characteristic
112	C₂⁴×C₇₃	C₂×D₄	1	1	yes	characteristic
113	C₂×Q₈×C₇₃	—	2	1	no	—
114	C₂×Q₈×C₇₃	—	2	2	no	—
115	C₂×Q₈×C₇₃	—	2	2	no	—
116	C₂×Q₈×C₇₃	—	4	2	no	—
117	C₂×Q₈×C₇₃	—	8	2	no	—
118	C₂×Q₈×C₇₃	C₂×D₄	1	2	yes	—
119	C₂×D₄×C₇₃	—	2	2	no	—
120	C₂×D₄×C₇₃	—	2	2	no	—
121	C₂×D₄×C₇₃	—	4	1	no	—
122	C₂²×C₄×C₇₃	—	2	4	no	—
123	C₂²×C₄×C₇₃	—	2	1	no	—
124	C₂²×C₄×C₇₃	—	2	1	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	2	no	—
132	C₂²×C₄×C₇₃	—	2	2	no	—
133	C₂²×C₄×C₇₃	—	2	2	no	—
134	C₂²×C₄×C₇₃	—	2	2	no	—
135	C₂²×C₄×C₇₃	—	2	2	no	—
136	C₂²×C₄×C₇₃	—	2	2	no	—
137	C₂²×C₄×C₇₃	—	4	2	no	—
138	C₂²×C₄×C₇₃	—	4	2	no	—
139	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
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	C₂⁴	1	1	yes	characteristic
144	C₂×C₈×C₇₃	—	2	2	no	—
145	C₂×C₈×C₇₃	—	2	2	no	—
146	C₂×C₈×C₇₃	—	2	2	no	—
147	C₂×C₈×C₇₃	—	2	2	no	—
148	C₂×C₈×C₇₃	—	2	2	no	—
149	C₂×C₈×C₇₃	#41	1	4	yes	—
150	C₄⋊C₄×C₇₃	—	2	4	no	—
151	C₄⋊C₄×C₇₃	—	2	4	no	—
152	C₄⋊C₄×C₇₃	—	2	4	no	—
153	C₄⋊C₄×C₇₃	—	2	4	no	—
154	C₄⋊C₄×C₇₃	—	2	4	no	—
155	C₄⋊C₄×C₇₃	—	2	4	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	1	no	—
160	C₄⋊C₄×C₇₃	—	2	2	no	—
161	C₄⋊C₄×C₇₃	—	2	2	no	—
162	C₄⋊C₄×C₇₃	—	2	2	no	—
163	C₄⋊C₄×C₇₃	—	2	2	no	—
164	C₄⋊C₄×C₇₃	—	4	2	no	—
165	C₄⋊C₄×C₇₃	C₂×D₄	1	2	yes	—
166	C₄⋊C₄×C₇₃	C₂×D₄	1	2	yes	—
167	C₄⋊C₄×C₇₃	C₂×D₄	1	2	yes	—
168	C₂²⋊C₄×C₇₃	—	2	4	no	—
169	C₂²⋊C₄×C₇₃	—	2	4	no	—
170	C₂²⋊C₄×C₇₃	—	2	4	no	—
171	C₂²⋊C₄×C₇₃	—	2	2	no	—
172	C₂²⋊C₄×C₇₃	—	2	2	no	—
173	C₂²⋊C₄×C₇₃	—	8	2	no	—
174	C₂²⋊C₄×C₇₃	—	8	2	no	—
175	C₄²×C₇₃	—	2	4	no	—
176	C₄²×C₇₃	—	2	4	no	—
177	C₄²×C₇₃	—	4	2	no	—
178	C₄²×C₇₃	C₂×D₄	1	2	yes	—
179	C₄²×C₇₃	C₂×D₄	1	2	yes	—
180	C₂³×C₇₃	—	2	1	no	—
181	C₂³×C₇₃	—	2	2	no	—
182	C₂³×C₇₃	—	2	1	no	—
183	C₂³×C₇₃	—	2	2	no	—
184	C₂³×C₇₃	—	2	1	no	—
185	C₂³×C₇₃	—	2	2	no	—
186	C₂³×C₇₃	—	2	1	no	—
187	C₂³×C₇₃	—	2	1	no	—
188	C₂³×C₇₃	—	2	2	no	—
189	C₂³×C₇₃	#137	1	2	yes	—
190	C₂³×C₇₃	C₂²×D₄	1	1	yes	characteristic
191	Q₈×C₇₃	—	2	2	no	—
192	Q₈×C₇₃	—	2	2	no	—
193	Q₈×C₇₃	—	4	2	no	—
194	Q₈×C₇₃	—	8	4	no	—
195	D₄×C₇₃	—	4	4	no	—
196	C₂×C₄×C₇₃	—	2	1	no	—
197	C₂×C₄×C₇₃	—	2	1	no	—
198	C₂×C₄×C₇₃	—	2	2	no	—
199	C₂×C₄×C₇₃	—	2	1	no	—
200	C₂×C₄×C₇₃	—	2	2	no	—
201	C₂×C₄×C₇₃	—	2	2	no	—
202	C₂×C₄×C₇₃	—	2	2	no	—
203	C₂×C₄×C₇₃	—	2	1	no	—
204	C₂×C₄×C₇₃	—	2	2	no	—
205	C₂×C₄×C₇₃	—	2	2	no	—
206	C₂×C₄×C₇₃	—	2	2	no	—
207	C₂×C₄×C₇₃	—	4	8	no	—
208	C₂×C₄×C₇₃	—	4	2	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	1	no	—
215	C₂×C₄×C₇₃	—	4	1	no	—
216	C₂×C₄×C₇₃	—	4	1	no	—
217	C₂×C₄×C₇₃	—	4	1	no	—
218	C₂×C₄×C₇₃	—	4	2	no	—
219	C₂×C₄×C₇₃	—	4	2	no	—
220	C₂×C₄×C₇₃	—	4	2	no	—
221	C₂×C₄×C₇₃	—	4	2	no	—
222	C₂×C₄×C₇₃	—	4	2	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	#120	1	2	yes	—
227	C₂×C₄×C₇₃	#120	1	2	yes	—
228	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
229	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
230	C₂×C₄×C₇₃	C₂×#41	1	2	yes	—
231	C₂×C₄×C₇₃	2₋¹⁺⁴	1	2	yes	—
232	C₈×C₇₃	—	2	4	no	—
233	C₈×C₇₃	—	4	2	no	—
234	C₂²×C₇₃	—	2	4	no	—
235	C₂²×C₇₃	—	2	2	no	—
236	C₂²×C₇₃	—	4	2	no	—
237	C₂²×C₇₃	—	4	1	no	—
238	C₂²×C₇₃	—	4	1	no	—
239	C₂²×C₇₃	—	4	2	no	—
240	C₂²×C₇₃	—	4	2	no	—
241	C₂²×C₇₃	—	4	1	no	—
242	C₂²×C₇₃	—	4	1	no	—
243	C₂²×C₇₃	—	4	1	no	—
244	C₂²×C₇₃	C₂×#120	1	1	yes	characteristic
245	C₂²×C₇₃	#547	1	2	yes	—
246	C₂²×C₇₃	C₂×#137	1	1	yes	characteristic
247	C₂²×C₇₃	#575	1	1	yes	characteristic
248	C₂²×C₇₃	#577	1	2	yes	—
249	C₄×C₇₃	—	2	2	no	—
250	C₄×C₇₃	—	2	2	no	—
251	C₄×C₇₃	—	4	1	no	—
252	C₄×C₇₃	—	4	1	no	—
253	C₄×C₇₃	—	4	2	no	—
254	C₄×C₇₃	—	4	2	no	—
255	C₄×C₇₃	—	4	2	no	—
256	C₄×C₇₃	—	4	2	no	—
257	C₄×C₇₃	—	8	2	no	—
258	C₄×C₇₃	—	8	2	no	—
259	C₄×C₇₃	#532	1	1	yes	characteristic
260	C₄×C₇₃	#536	1	1	yes	characteristic
261	C₄×C₇₃	#548	1	2	yes	—
262	#25715	C₇₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
263	C₂×C₇₃	—	4	2	no	—
264	C₂×C₇₃	—	8	1	no	—
265	C₂×C₇₃	#2432	1	1	yes	characteristic
266	C₂×C₇₃	#3007	1	1	yes	characteristic
267	C₂×C₇₃	#3010	1	1	yes	characteristic
268	C₂×C₇₃	#3344	1	2	yes	—
269	C₂×C₇₃	#3348	1	2	yes	—
270	C₂×#552	C₂×C₇₃	1	1	yes	characteristic
271	C₂×#501	C₂×C₇₃	1	1	yes	characteristic, complemented
272	C₂×#475	C₂×C₇₃	1	1	yes	characteristic, complemented
273	#2563	C₂×C₇₃	1	1	yes	characteristic
274	#2036	C₂×C₇₃	1	2	yes	complemented
275	#2035	C₂×C₇₃	1	2	yes	complemented
276	#1989	C₂×C₇₃	1	1	yes	characteristic, complemented
277	#1955	C₂×C₇₃	1	1	yes	characteristic
278	#1854	C₂×C₇₃	1	2	yes	complemented
279	#1853	C₂×C₇₃	1	2	yes	complemented
280	#1763	C₂×C₇₃	1	1	yes	characteristic, complemented
281	C₇₃	#25715	1	1	yes	characteristic, direct product factor, Sylow
282	#552	—	2	4	no	—
283	#552	—	2	4	no	—
284	C₂×C₄⋊Q₈	C₂²×C₇₃	1	1	yes	characteristic
285	C₂×#126	—	2	1	no	—
286	C₂×#125	—	2	1	no	—
287	C₂×#125	C₂²×C₇₃	1	1	yes	characteristic
288	C₂×#123	—	2	1	no	—
289	C₂×C₂²⋊Q₈	C₂²×C₇₃	1	1	yes	characteristic
290	C₂×C₂²⋊Q₈	C₂²×C₇₃	1	1	yes	characteristic
291	C₂×C₄×Q₈	C₂²×C₇₃	1	1	yes	characteristic
292	C₂×C₄×D₄	C₂²×C₇₃	1	1	yes	characteristic
293	C₂×#117	—	2	1	no	—
294	C₂×#117	C₂²×C₇₃	1	1	yes	characteristic
295	C₂²×C₄⋊C₄	C₂²×C₇₃	1	1	yes	characteristic
296	#501	—	2	4	no	—
297	#475	—	2	4	no	—
298	C₂×#107	C₂²×C₇₃	1	2	yes	—
299	C₂×#106	C₂²×C₇₃	1	2	yes	—
300	C₂×#106	C₂²×C₇₃	1	2	yes	—
301	C₂×C₄⋊C₈	C₂²×C₇₃	1	1	yes	characteristic
302	C₂×#103	C₂²×C₇₃	1	2	yes	—
303	C₂×#103	C₂²×C₇₃	1	2	yes	—
304	C₂×C₂²⋊C₈	C₂²×C₇₃	1	2	yes	—
305	C₂×C₂²⋊C₈	C₂²×C₇₃	1	2	yes	—
306	C₂×#97	C₂²×C₇₃	1	1	yes	characteristic
307	#393	—	2	1	no	—
308	#393	—	2	1	no	—
309	#390	—	2	1	no	—
310	#382	—	2	1	no	—
311	#380	C₂²×C₇₃	1	2	yes	—
312	#380	C₂²×C₇₃	1	2	yes	—
313	C₄×C₄⋊C₄	C₂²×C₇₃	1	1	yes	characteristic
314	#340	C₂²×C₇₃	1	2	yes	—
315	#340	C₂²×C₇₃	1	2	yes	—
316	#340	C₂²×C₇₃	1	2	yes	—
317	C₂²×Q₈	—	2	1	no	—
318	C₂²×Q₈	C₂³×C₇₃	1	1	yes	characteristic
319	C₂²×D₄	D₄×C₇₃	1	1	yes	characteristic
320	C₂³×C₄	—	2	1	no	—
321	C₂³×C₄	C₂³×C₇₃	1	1	yes	characteristic
322	C₂³×C₄	C₂³×C₇₃	1	1	yes	characteristic
323	C₂²×C₈	C₂³×C₇₃	1	2	yes	—
324	C₂²×C₈	C₂³×C₇₃	1	2	yes	—
325	C₄⋊Q₈	—	2	2	no	—
326	C₄⋊Q₈	—	2	2	no	—
327	#126	—	2	8	no	—
328	#125	—	2	8	no	—
329	#125	—	2	2	no	—
330	#125	D₄×C₇₃	1	4	yes	—
331	#123	—	2	8	no	—
332	C₂²⋊Q₈	—	2	2	no	—
333	C₂²⋊Q₈	—	2	2	no	—
334	C₂²⋊Q₈	—	2	2	no	—
335	C₂²⋊Q₈	—	2	2	no	—
336	C₄×Q₈	—	2	2	no	—
337	C₄×Q₈	D₄×C₇₃	1	4	yes	—
338	C₄×D₄	—	2	2	no	—
339	C₄×D₄	—	2	2	no	—
340	#117	—	2	8	no	—
341	#117	—	2	2	no	—
342	#117	—	2	2	no	—
343	C₂×C₄⋊C₄	—	2	1	no	—
344	C₂×C₄⋊C₄	—	2	1	no	—
345	C₂×C₄⋊C₄	—	2	1	no	—
346	C₂×C₄⋊C₄	—	2	1	no	—
347	C₂×C₄⋊C₄	—	2	1	no	—
348	C₂×C₄⋊C₄	—	2	1	no	—
349	C₂×C₄⋊C₄	—	2	2	no	—
350	C₂×C₄⋊C₄	—	2	2	no	—
351	C₂×C₄⋊C₄	—	2	1	no	—
352	C₂×C₄⋊C₄	D₄×C₇₃	1	1	yes	characteristic
353	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
354	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
355	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
356	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
357	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
358	C₂×C₂²⋊C₄	—	2	1	no	—
359	C₂×C₂²⋊C₄	—	2	1	no	—
360	C₂×C₂²⋊C₄	—	2	1	no	—
361	C₂×C₂²⋊C₄	—	2	2	no	—
362	C₂×C₂²⋊C₄	—	2	2	no	—
363	C₂×C₂²⋊C₄	D₄×C₇₃	1	1	yes	characteristic
364	C₂×C₂²⋊C₄	D₄×C₇₃	1	1	yes	characteristic
365	C₂×C₄²	—	2	1	no	—
366	C₂×C₄²	—	2	1	no	—
367	C₂×C₄²	—	2	1	no	—
368	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
369	#107	—	2	4	no	—
370	#106	—	2	4	no	—
371	#106	—	2	4	no	—
372	C₄⋊C₈	—	2	2	no	—
373	#103	—	2	4	no	—
374	#103	—	2	4	no	—
375	C₂²⋊C₈	—	2	4	no	—
376	C₂²⋊C₈	—	2	4	no	—
377	#97	—	2	2	no	—
378	#95	—	2	1	no	—
379	#95	—	2	2	no	—
380	#95	—	2	2	no	—
381	C₂⁴	C₂×D₄×C₇₃	1	1	yes	characteristic
382	C₂⁴	C₂×D₄×C₇₃	1	1	yes	characteristic
383	C₂×Q₈	—	2	1	no	—
384	C₂×Q₈	—	2	2	no	—
385	C₂×Q₈	—	2	2	no	—
386	C₂×Q₈	—	4	2	no	—
387	C₂×Q₈	—	8	2	no	—
388	C₂×Q₈	C₂×D₄×C₇₃	1	2	yes	—
389	C₂×D₄	—	2	2	no	—
390	C₂×D₄	—	2	2	no	—
391	C₂×D₄	—	4	1	no	—
392	C₂²×C₄	—	2	4	no	—
393	C₂²×C₄	—	2	1	no	—
394	C₂²×C₄	—	2	1	no	—
395	C₂²×C₄	—	2	1	no	—
396	C₂²×C₄	—	2	1	no	—
397	C₂²×C₄	—	2	1	no	—
398	C₂²×C₄	—	2	1	no	—
399	C₂²×C₄	—	2	1	no	—
400	C₂²×C₄	—	2	1	no	—
401	C₂²×C₄	—	2	2	no	—
402	C₂²×C₄	—	2	2	no	—
403	C₂²×C₄	—	2	2	no	—
404	C₂²×C₄	—	2	2	no	—
405	C₂²×C₄	—	2	2	no	—
406	C₂²×C₄	—	2	2	no	—
407	C₂²×C₄	—	4	2	no	—
408	C₂²×C₄	—	4	2	no	—
409	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
410	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
411	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
412	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
413	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
414	C₂×C₈	—	2	2	no	—
415	C₂×C₈	—	2	2	no	—
416	C₂×C₈	—	2	2	no	—
417	C₂×C₈	—	2	2	no	—
418	C₂×C₈	—	2	2	no	—
419	C₂×C₈	#41×C₇₃	1	4	yes	—
420	C₄⋊C₄	—	2	4	no	—
421	C₄⋊C₄	—	2	4	no	—
422	C₄⋊C₄	—	2	4	no	—
423	C₄⋊C₄	—	2	4	no	—
424	C₄⋊C₄	—	2	4	no	—
425	C₄⋊C₄	—	2	4	no	—
426	C₄⋊C₄	—	2	2	no	—
427	C₄⋊C₄	—	2	1	no	—
428	C₄⋊C₄	—	2	1	no	—
429	C₄⋊C₄	—	2	1	no	—
430	C₄⋊C₄	—	2	2	no	—
431	C₄⋊C₄	—	2	2	no	—
432	C₄⋊C₄	—	2	2	no	—
433	C₄⋊C₄	—	2	2	no	—
434	C₄⋊C₄	—	4	2	no	—
435	C₄⋊C₄	C₂×D₄×C₇₃	1	2	yes	—
436	C₄⋊C₄	C₂×D₄×C₇₃	1	2	yes	—
437	C₄⋊C₄	C₂×D₄×C₇₃	1	2	yes	—
438	C₂²⋊C₄	—	2	4	no	—
439	C₂²⋊C₄	—	2	4	no	—
440	C₂²⋊C₄	—	2	4	no	—
441	C₂²⋊C₄	—	2	2	no	—
442	C₂²⋊C₄	—	2	2	no	—
443	C₂²⋊C₄	—	8	2	no	—
444	C₂²⋊C₄	—	8	2	no	—
445	C₄²	—	2	4	no	—
446	C₄²	—	2	4	no	—
447	C₄²	—	4	2	no	—
448	C₄²	C₂×D₄×C₇₃	1	2	yes	—
449	C₄²	C₂×D₄×C₇₃	1	2	yes	—
450	C₂³	—	2	1	no	—
451	C₂³	—	2	2	no	—
452	C₂³	—	2	1	no	—
453	C₂³	—	2	2	no	—
454	C₂³	—	2	1	no	—
455	C₂³	—	2	2	no	—
456	C₂³	—	2	1	no	—
457	C₂³	—	2	1	no	—
458	C₂³	—	2	2	no	—
459	C₂³	#137×C₇₃	1	2	yes	—
460	C₂³	C₂²×D₄×C₇₃	1	1	yes	characteristic
461	Q₈	—	2	2	no	—
462	Q₈	—	2	2	no	—
463	Q₈	—	4	2	no	—
464	Q₈	—	8	4	no	—
465	D₄	—	4	4	no	—
466	C₂×C₄	—	2	1	no	—
467	C₂×C₄	—	2	1	no	—
468	C₂×C₄	—	2	2	no	—
469	C₂×C₄	—	2	1	no	—
470	C₂×C₄	—	2	2	no	—
471	C₂×C₄	—	2	2	no	—
472	C₂×C₄	—	2	2	no	—
473	C₂×C₄	—	2	1	no	—
474	C₂×C₄	—	2	2	no	—
475	C₂×C₄	—	2	2	no	—
476	C₂×C₄	—	2	2	no	—
477	C₂×C₄	—	4	8	no	—
478	C₂×C₄	—	4	2	no	—
479	C₂×C₄	—	4	1	no	—
480	C₂×C₄	—	4	1	no	—
481	C₂×C₄	—	4	1	no	—
482	C₂×C₄	—	4	1	no	—
483	C₂×C₄	—	4	2	no	—
484	C₂×C₄	—	4	1	no	—
485	C₂×C₄	—	4	1	no	—
486	C₂×C₄	—	4	1	no	—
487	C₂×C₄	—	4	1	no	—
488	C₂×C₄	—	4	2	no	—
489	C₂×C₄	—	4	2	no	—
490	C₂×C₄	—	4	2	no	—
491	C₂×C₄	—	4	2	no	—
492	C₂×C₄	—	4	2	no	—
493	C₂×C₄	—	4	2	no	—
494	C₂×C₄	—	4	2	no	—
495	C₂×C₄	—	4	2	no	—
496	C₂×C₄	#120×C₇₃	1	2	yes	—
497	C₂×C₄	#120×C₇₃	1	2	yes	—
498	C₂×C₄	C₂²×D₄×C₇₃	1	1	yes	characteristic
499	C₂×C₄	C₂²×D₄×C₇₃	1	1	yes	characteristic
500	C₂×C₄	C₂×#41×C₇₃	1	2	yes	—
501	C₂×C₄	2₋¹⁺⁴×C₇₃	1	2	yes	—
502	C₈	—	2	4	no	—
503	C₈	—	4	2	no	—
504	C₂²	—	2	2	no	—
505	C₂²	—	2	4	no	—
506	C₂²	—	4	1	no	—
507	C₂²	—	4	2	no	—
508	C₂²	—	4	1	no	—
509	C₂²	—	4	1	no	—
510	C₂²	—	4	1	no	—
511	C₂²	—	4	2	no	—
512	C₂²	—	4	2	no	—
513	C₂²	—	4	1	no	—
514	C₂²	C₂×#120×C₇₃	1	1	yes	characteristic
515	C₂²	#547×C₇₃	1	2	yes	—
516	C₂²	C₂×#137×C₇₃	1	1	yes	characteristic
517	C₂²	#575×C₇₃	1	1	yes	characteristic
518	C₂²	#577×C₇₃	1	2	yes	—
519	C₄	—	2	2	no	—
520	C₄	—	2	2	no	—
521	C₄	—	4	2	no	—
522	C₄	—	4	2	no	—
523	C₄	—	4	2	no	—
524	C₄	—	4	1	no	—
525	C₄	—	4	1	no	—
526	C₄	—	4	2	no	—
527	C₄	—	8	2	no	—
528	C₄	—	8	2	no	—
529	C₄	#532×C₇₃	1	1	yes	characteristic
530	C₄	#536×C₇₃	1	1	yes	characteristic
531	C₄	#548×C₇₃	1	2	yes	—
532	C₂	—	4	2	no	—
533	C₂	—	8	1	no	—
534	C₂	C₇₃×#2432	1	1	yes	characteristic
535	C₂	C₇₃×#3007	1	1	yes	characteristic
536	C₂	C₇₃×#3010	1	1	yes	characteristic
537	C₂	C₇₃×#3344	1	2	yes	—
538	C₂	C₇₃×#3348	1	2	yes	—

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

Complements

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

N	H ≅ G/N	type
2. C₂×#501×C₇₃	C₂	semidirect
3. C₂×#475×C₇₃	C₂	semidirect
5. C₇₃×#2036	C₂	semidirect
6. C₇₃×#2035	C₂	semidirect
7. C₇₃×#1989	C₂	semidirect
9. C₇₃×#1854	C₂	semidirect
10. C₇₃×#1853	C₂	semidirect
11. C₇₃×#1763	C₂	semidirect
262. #25715	C₇₃	direct (N × H)
271. C₂×#501	C₂×C₇₃	semidirect
272. C₂×#475	C₂×C₇₃	semidirect
274. #2036	C₂×C₇₃	semidirect
275. #2035	C₂×C₇₃	semidirect
276. #1989	C₂×C₇₃	semidirect
278. #1854	C₂×C₇₃	semidirect
279. #1853	C₂×C₇₃	semidirect
280. #1763	C₂×C₇₃	semidirect
281. C₇₃	#25715	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×#552×C₇₃	2
C₂×#501×C₇₃	2
C₂×#475×C₇₃	2
C₇₃×#2563	2
C₇₃×#2036	2
C₇₃×#2035	2
C₇₃×#1989	2
C₇₃×#1955	2
C₇₃×#1854	2
C₇₃×#1853	2
C₇₃×#1763	2
#25715	73

Subgroups — C73×#25715 #32935119

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₃×#25715 #32935119