Subgroups — C₇₃×#20717 #32930121

Order 18688.

1426 conjugacy classes of subgroups.

The subgroup lattice has 430 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#117×C₇₃	C₂	1	1	yes	maximal, characteristic
2	C₂×#432×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#431×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₇₃×#1817	C₂	1	2	yes	maximal, complemented
5	C₇₃×#1798	C₂	1	4	yes	maximal, complemented
6	C₇₃×#1779	C₂	1	2	yes	maximal
7	C₇₃×#1750	C₂	1	4	yes	maximal, complemented
8	C₂⁴×C₄×C₇₃	C₂²	1	1	yes	characteristic
9	C₂×#117×C₇₃	—	2	4	no	—
10	C₂×#117×C₇₃	—	2	4	no	—
11	C₂×#117×C₇₃	C₄	1	2	yes	—
12	C₂×#117×C₇₃	C₄	1	2	yes	—
13	C₂×#117×C₇₃	C₂²	1	2	yes	—
14	C₂×#117×C₇₃	C₂²	1	2	yes	—
15	C₂²×C₄⋊C₄×C₇₃	C₄	1	1	yes	characteristic
16	C₂²×C₄⋊C₄×C₇₃	C₄	1	1	yes	characteristic
17	C₂²×C₂²⋊C₄×C₇₃	C₄	1	1	yes	characteristic
18	C₂²×C₂²⋊C₄×C₇₃	C₄	1	1	yes	characteristic
19	C₂²×C₄²×C₇₃	C₂²	1	1	yes	characteristic
20	C₂²×C₄²×C₇₃	C₂²	1	1	yes	characteristic
21	#432×C₇₃	—	2	4	no	—
22	#431×C₇₃	—	2	4	no	—
23	C₂×C₄⋊C₈×C₇₃	C₂²	1	2	yes	complemented
24	C₂×C₄⋊C₈×C₇₃	C₂²	1	2	yes	complemented
25	C₂×C₂²⋊C₈×C₇₃	C₂²	1	8	yes	—
26	C₂×C₂²⋊C₈×C₇₃	C₂²	1	2	yes	—
27	C₂×C₂²⋊C₈×C₇₃	C₂²	1	2	yes	—
28	C₂×#97×C₇₃	C₂²	1	2	yes	complemented
29	C₂×C₄×C₈×C₇₃	C₂²	1	2	yes	complemented
30	#336×C₇₃	C₂²	1	8	yes	complemented
31	C₂⁵×C₇₃	C₂×C₄	1	1	yes	characteristic
32	C₂³×C₄×C₇₃	—	2	2	no	—
33	C₂³×C₄×C₇₃	—	2	2	no	—
34	C₂³×C₄×C₇₃	—	2	8	no	—
35	C₂³×C₄×C₇₃	C₂×C₄	1	1	yes	characteristic
36	C₂³×C₄×C₇₃	C₂×C₄	1	1	yes	characteristic
37	C₂³×C₄×C₇₃	C₂×C₄	1	2	yes	—
38	C₂³×C₄×C₇₃	C₂×C₄	1	1	yes	characteristic
39	C₂³×C₄×C₇₃	C₂×C₄	1	1	yes	characteristic
40	C₂³×C₄×C₇₃	C₂×C₄	1	1	yes	characteristic
41	C₂³×C₄×C₇₃	C₂³	1	1	yes	characteristic
42	C₂³×C₄×C₇₃	C₂³	1	2	yes	—
43	C₂²×C₈×C₇₃	C₂³	1	4	yes	—
44	C₂²×C₈×C₇₃	C₂³	1	4	yes	—
45	#117×C₇₃	—	2	8	no	—
46	#117×C₇₃	—	2	8	no	—
47	#117×C₇₃	—	2	4	no	—
48	#117×C₇₃	—	2	4	no	—
49	#117×C₇₃	—	2	4	no	—
50	#117×C₇₃	—	2	4	no	—
51	C₂×C₄⋊C₄×C₇₃	—	2	4	no	—
52	C₂×C₄⋊C₄×C₇₃	—	2	4	no	—
53	C₂×C₄⋊C₄×C₇₃	C₂×C₄	1	2	yes	—
54	C₂×C₄⋊C₄×C₇₃	C₂×C₄	1	2	yes	—
55	C₂×C₄⋊C₄×C₇₃	C₂×C₄	1	2	yes	—
56	C₂×C₄⋊C₄×C₇₃	C₂×C₄	1	2	yes	—
57	C₂×C₂²⋊C₄×C₇₃	—	2	4	no	—
58	C₂×C₂²⋊C₄×C₇₃	—	2	4	no	—
59	C₂×C₂²⋊C₄×C₇₃	C₂×C₄	1	2	yes	—
60	C₂×C₂²⋊C₄×C₇₃	C₂×C₄	1	2	yes	—
61	C₂×C₂²⋊C₄×C₇₃	C₂×C₄	1	2	yes	—
62	C₂×C₂²⋊C₄×C₇₃	C₂×C₄	1	2	yes	—
63	C₂×C₄²×C₇₃	—	2	2	no	—
64	C₂×C₄²×C₇₃	—	2	2	no	—
65	C₂×C₄²×C₇₃	C₂×C₄	1	2	yes	—
66	C₂×C₄²×C₇₃	C₂×C₄	1	1	yes	characteristic
67	C₂×C₄²×C₇₃	C₂×C₄	1	1	yes	characteristic
68	C₂×C₄²×C₇₃	D₄	1	4	yes	—
69	C₂×C₄²×C₇₃	D₄	1	4	yes	—
70	C₂×C₄²×C₇₃	C₂³	1	2	yes	—
71	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
72	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
73	C₄⋊C₈×C₇₃	—	2	4	no	—
74	C₄⋊C₈×C₇₃	—	2	4	no	—
75	C₂²⋊C₈×C₇₃	—	2	4	no	—
76	C₂²⋊C₈×C₇₃	—	2	4	no	—
77	C₂²⋊C₈×C₇₃	—	2	16	no	—
78	#97×C₇₃	—	2	4	no	—
79	C₄×C₈×C₇₃	—	2	4	no	—
80	C₂⁴×C₇₃	—	2	2	no	—
81	C₂⁴×C₇₃	—	2	4	no	—
82	C₂⁴×C₇₃	—	2	4	no	—
83	C₂⁴×C₇₃	—	4	2	no	—
84	C₂⁴×C₇₃	C₂²×C₄	1	2	yes	—
85	C₂⁴×C₇₃	C₂²×C₄	1	1	yes	characteristic
86	C₂²×C₄×C₇₃	—	2	16	no	—
87	C₂²×C₄×C₇₃	—	2	16	no	—
88	C₂²×C₄×C₇₃	—	2	2	no	—
89	C₂²×C₄×C₇₃	—	2	4	no	—
90	C₂²×C₄×C₇₃	—	2	4	no	—
91	C₂²×C₄×C₇₃	—	2	4	no	—
92	C₂²×C₄×C₇₃	—	2	4	no	—
93	C₂²×C₄×C₇₃	—	2	4	no	—
94	C₂²×C₄×C₇₃	—	2	2	no	—
95	C₂²×C₄×C₇₃	—	2	2	no	—
96	C₂²×C₄×C₇₃	—	2	4	no	—
97	C₂²×C₄×C₇₃	—	2	4	no	—
98	C₂²×C₄×C₇₃	—	2	2	no	—
99	C₂²×C₄×C₇₃	—	2	2	no	—
100	C₂²×C₄×C₇₃	—	2	4	no	—
101	C₂²×C₄×C₇₃	—	4	2	no	—
102	C₂²×C₄×C₇₃	—	4	2	no	—
103	C₂²×C₄×C₇₃	C₂²⋊C₄	1	4	yes	—
104	C₂²×C₄×C₇₃	C₂²⋊C₄	1	4	yes	—
105	C₂²×C₄×C₇₃	C₂²×C₄	1	2	yes	—
106	C₂²×C₄×C₇₃	C₂²×C₄	1	2	yes	—
107	C₂²×C₄×C₇₃	C₂²×C₄	1	1	yes	characteristic
108	C₂²×C₄×C₇₃	C₂²×C₄	1	1	yes	characteristic
109	C₂²×C₄×C₇₃	C₂²×C₄	1	1	yes	characteristic
110	C₂²×C₄×C₇₃	C₂²×C₄	1	1	yes	characteristic
111	C₂²×C₄×C₇₃	C₂²×C₄	1	1	yes	characteristic
112	C₂²×C₄×C₇₃	C₂²×C₄	1	2	yes	—
113	C₂²×C₄×C₇₃	C₂×D₄	1	2	yes	—
114	C₂²×C₄×C₇₃	C₂×D₄	1	2	yes	—
115	C₂²×C₄×C₇₃	#41	1	8	yes	—
116	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
117	C₂×C₈×C₇₃	—	2	4	no	—
118	C₂×C₈×C₇₃	—	2	4	no	—
119	C₂×C₈×C₇₃	—	2	8	no	—
120	C₂×C₈×C₇₃	—	2	8	no	—
121	C₄⋊C₄×C₇₃	—	2	4	no	—
122	C₄⋊C₄×C₇₃	—	2	4	no	—
123	C₄⋊C₄×C₇₃	—	2	4	no	—
124	C₄⋊C₄×C₇₃	—	2	4	no	—
125	C₂²⋊C₄×C₇₃	—	2	4	no	—
126	C₂²⋊C₄×C₇₃	—	2	4	no	—
127	C₂²⋊C₄×C₇₃	—	2	4	no	—
128	C₂²⋊C₄×C₇₃	—	2	4	no	—
129	C₄²×C₇₃	—	2	4	no	—
130	C₄²×C₇₃	—	2	2	no	—
131	C₄²×C₇₃	—	2	2	no	—
132	C₄²×C₇₃	C₂²⋊C₄	1	4	yes	—
133	C₄²×C₇₃	C₂²⋊C₄	1	4	yes	—
134	C₄²×C₇₃	C₂×D₄	1	2	yes	—
135	C₄²×C₇₃	C₂×D₄	1	2	yes	—
136	C₄²×C₇₃	C₂×D₄	1	2	yes	—
137	C₄²×C₇₃	C₂×D₄	1	2	yes	—
138	C₂³×C₇₃	—	2	2	no	—
139	C₂³×C₇₃	—	2	2	no	—
140	C₂³×C₇₃	—	2	8	no	—
141	C₂³×C₇₃	—	2	2	no	—
142	C₂³×C₇₃	—	2	2	no	—
143	C₂³×C₇₃	—	2	4	no	—
144	C₂³×C₇₃	—	2	4	no	—
145	C₂³×C₇₃	—	4	16	no	—
146	C₂³×C₇₃	—	4	4	no	—
147	C₂³×C₇₃	—	4	4	no	—
148	C₂³×C₇₃	C₂×C₂²⋊C₄	1	2	yes	—
149	C₂³×C₇₃	#117	1	4	yes	—
150	C₂³×C₇₃	#131	1	4	yes	—
151	C₂³×C₇₃	C₂³×C₄	1	1	yes	characteristic
152	C₂×C₄×C₇₃	—	2	16	no	—
153	C₂×C₄×C₇₃	—	2	8	no	—
154	C₂×C₄×C₇₃	—	2	2	no	—
155	C₂×C₄×C₇₃	—	2	2	no	—
156	C₂×C₄×C₇₃	—	2	2	no	—
157	C₂×C₄×C₇₃	—	2	2	no	—
158	C₂×C₄×C₇₃	—	2	2	no	—
159	C₂×C₄×C₇₃	—	2	2	no	—
160	C₂×C₄×C₇₃	—	2	2	no	—
161	C₂×C₄×C₇₃	—	2	8	no	—
162	C₂×C₄×C₇₃	—	2	4	no	—
163	C₂×C₄×C₇₃	—	2	4	no	—
164	C₂×C₄×C₇₃	—	2	8	no	—
165	C₂×C₄×C₇₃	—	2	8	no	—
166	C₂×C₄×C₇₃	—	2	2	no	—
167	C₂×C₄×C₇₃	—	2	2	no	—
168	C₂×C₄×C₇₃	—	2	4	no	—
169	C₂×C₄×C₇₃	—	2	4	no	—
170	C₂×C₄×C₇₃	—	4	4	no	—
171	C₂×C₄×C₇₃	—	4	4	no	—
172	C₂×C₄×C₇₃	—	4	4	no	—
173	C₂×C₄×C₇₃	C₂×C₂²⋊C₄	1	2	yes	—
174	C₂×C₄×C₇₃	C₂×C₂²⋊C₄	1	2	yes	—
175	C₂×C₄×C₇₃	C₂×C₂²⋊C₄	1	2	yes	—
176	C₂×C₄×C₇₃	C₂×C₂²⋊C₄	1	2	yes	—
177	C₂×C₄×C₇₃	C₂×C₂²⋊C₄	1	2	yes	—
178	C₂×C₄×C₇₃	#117	1	4	yes	—
179	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
180	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
181	C₂×C₄×C₇₃	C₂×#41	1	4	yes	—
182	C₈×C₇₃	—	4	4	no	—
183	C₈×C₇₃	—	4	4	no	—
184	C₂²×C₇₃	—	2	2	no	—
185	C₂²×C₇₃	—	2	8	no	—
186	C₂²×C₇₃	—	2	2	no	—
187	C₂²×C₇₃	—	2	8	no	—
188	C₂²×C₇₃	—	2	4	no	—
189	C₂²×C₇₃	—	4	16	no	—
190	C₂²×C₇₃	—	4	2	no	—
191	C₂²×C₇₃	—	4	2	no	—
192	C₂²×C₇₃	—	4	4	no	—
193	C₂²×C₇₃	#408	1	4	yes	—
194	C₂²×C₇₃	C₂²×C₂²⋊C₄	1	1	yes	characteristic
195	C₂²×C₇₃	C₂×#117	1	2	yes	—
196	C₂²×C₇₃	C₂×#131	1	2	yes	—
197	C₂²×C₇₃	#568	1	2	yes	—
198	C₄×C₇₃	—	2	2	no	—
199	C₄×C₇₃	—	2	2	no	—
200	C₄×C₇₃	—	2	2	no	—
201	C₄×C₇₃	—	2	2	no	—
202	C₄×C₇₃	—	2	2	no	—
203	C₄×C₇₃	—	2	4	no	—
204	C₄×C₇₃	—	4	2	no	—
205	C₄×C₇₃	—	4	2	no	—
206	C₄×C₇₃	#525	1	2	yes	—
207	C₄×C₇₃	#525	1	2	yes	—
208	#20717	C₇₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
209	C₂×C₇₃	—	2	4	no	—
210	C₂×C₇₃	—	4	4	no	—
211	C₂×C₇₃	#2280	1	1	yes	characteristic
212	C₂×C₇₃	C₂×#408	1	1	yes	characteristic
213	C₂×C₇₃	#2879	1	1	yes	characteristic
214	C₂×C₇₃	#2924	1	4	yes	—
215	C₂²×#117	C₂×C₇₃	1	1	yes	characteristic
216	C₂×#432	C₂×C₇₃	1	1	yes	characteristic, complemented
217	C₂×#431	C₂×C₇₃	1	1	yes	characteristic, complemented
218	#1817	C₂×C₇₃	1	2	yes	complemented
219	#1798	C₂×C₇₃	1	4	yes	complemented
220	#1779	C₂×C₇₃	1	2	yes	—
221	#1750	C₂×C₇₃	1	4	yes	complemented
222	C₇₃	#20717	1	1	yes	characteristic, direct product factor, Sylow
223	C₂⁴×C₄	C₂²×C₇₃	1	1	yes	characteristic
224	C₂×#117	—	2	4	no	—
225	C₂×#117	—	2	4	no	—
226	C₂×#117	C₄×C₇₃	1	2	yes	—
227	C₂×#117	C₄×C₇₃	1	2	yes	—
228	C₂×#117	C₂²×C₇₃	1	2	yes	—
229	C₂×#117	C₂²×C₇₃	1	2	yes	—
230	C₂²×C₄⋊C₄	C₄×C₇₃	1	1	yes	characteristic
231	C₂²×C₄⋊C₄	C₄×C₇₃	1	1	yes	characteristic
232	C₂²×C₂²⋊C₄	C₄×C₇₃	1	1	yes	characteristic
233	C₂²×C₂²⋊C₄	C₄×C₇₃	1	1	yes	characteristic
234	C₂²×C₄²	C₂²×C₇₃	1	1	yes	characteristic
235	C₂²×C₄²	C₂²×C₇₃	1	1	yes	characteristic
236	#432	—	2	4	no	—
237	#431	—	2	4	no	—
238	C₂×C₄⋊C₈	C₂²×C₇₃	1	2	yes	complemented
239	C₂×C₄⋊C₈	C₂²×C₇₃	1	2	yes	complemented
240	C₂×C₂²⋊C₈	C₂²×C₇₃	1	8	yes	—
241	C₂×C₂²⋊C₈	C₂²×C₇₃	1	2	yes	—
242	C₂×C₂²⋊C₈	C₂²×C₇₃	1	2	yes	—
243	C₂×#97	C₂²×C₇₃	1	2	yes	complemented
244	C₂×C₄×C₈	C₂²×C₇₃	1	2	yes	complemented
245	#336	C₂²×C₇₃	1	8	yes	complemented
246	C₂⁵	C₂×C₄×C₇₃	1	1	yes	characteristic
247	C₂³×C₄	—	2	2	no	—
248	C₂³×C₄	—	2	2	no	—
249	C₂³×C₄	—	2	8	no	—
250	C₂³×C₄	C₂×C₄×C₇₃	1	1	yes	characteristic
251	C₂³×C₄	C₂×C₄×C₇₃	1	1	yes	characteristic
252	C₂³×C₄	C₂×C₄×C₇₃	1	2	yes	—
253	C₂³×C₄	C₂×C₄×C₇₃	1	1	yes	characteristic
254	C₂³×C₄	C₂×C₄×C₇₃	1	1	yes	characteristic
255	C₂³×C₄	C₂×C₄×C₇₃	1	1	yes	characteristic
256	C₂³×C₄	C₂³×C₇₃	1	1	yes	characteristic
257	C₂³×C₄	C₂³×C₇₃	1	2	yes	—
258	C₂²×C₈	C₂³×C₇₃	1	4	yes	—
259	C₂²×C₈	C₂³×C₇₃	1	4	yes	—
260	#117	—	2	8	no	—
261	#117	—	2	8	no	—
262	#117	—	2	4	no	—
263	#117	—	2	4	no	—
264	#117	—	2	4	no	—
265	#117	—	2	4	no	—
266	C₂×C₄⋊C₄	—	2	4	no	—
267	C₂×C₄⋊C₄	—	2	4	no	—
268	C₂×C₄⋊C₄	C₂×C₄×C₇₃	1	2	yes	—
269	C₂×C₄⋊C₄	C₂×C₄×C₇₃	1	2	yes	—
270	C₂×C₄⋊C₄	C₂×C₄×C₇₃	1	2	yes	—
271	C₂×C₄⋊C₄	C₂×C₄×C₇₃	1	2	yes	—
272	C₂×C₂²⋊C₄	—	2	4	no	—
273	C₂×C₂²⋊C₄	—	2	4	no	—
274	C₂×C₂²⋊C₄	C₂×C₄×C₇₃	1	2	yes	—
275	C₂×C₂²⋊C₄	C₂×C₄×C₇₃	1	2	yes	—
276	C₂×C₂²⋊C₄	C₂×C₄×C₇₃	1	2	yes	—
277	C₂×C₂²⋊C₄	C₂×C₄×C₇₃	1	2	yes	—
278	C₂×C₄²	—	2	2	no	—
279	C₂×C₄²	—	2	2	no	—
280	C₂×C₄²	C₂×C₄×C₇₃	1	2	yes	—
281	C₂×C₄²	C₂×C₄×C₇₃	1	1	yes	characteristic
282	C₂×C₄²	C₂×C₄×C₇₃	1	1	yes	characteristic
283	C₂×C₄²	D₄×C₇₃	1	4	yes	—
284	C₂×C₄²	D₄×C₇₃	1	4	yes	—
285	C₂×C₄²	C₂³×C₇₃	1	2	yes	—
286	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
287	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
288	C₄⋊C₈	—	2	4	no	—
289	C₄⋊C₈	—	2	4	no	—
290	C₂²⋊C₈	—	2	4	no	—
291	C₂²⋊C₈	—	2	4	no	—
292	C₂²⋊C₈	—	2	16	no	—
293	#97	—	2	4	no	—
294	C₄×C₈	—	2	4	no	—
295	C₂⁴	—	2	2	no	—
296	C₂⁴	—	2	4	no	—
297	C₂⁴	—	2	4	no	—
298	C₂⁴	—	4	2	no	—
299	C₂⁴	C₂²×C₄×C₇₃	1	2	yes	—
300	C₂⁴	C₂²×C₄×C₇₃	1	1	yes	characteristic
301	C₂²×C₄	—	2	16	no	—
302	C₂²×C₄	—	2	16	no	—
303	C₂²×C₄	—	2	2	no	—
304	C₂²×C₄	—	2	4	no	—
305	C₂²×C₄	—	2	4	no	—
306	C₂²×C₄	—	2	4	no	—
307	C₂²×C₄	—	2	4	no	—
308	C₂²×C₄	—	2	4	no	—
309	C₂²×C₄	—	2	2	no	—
310	C₂²×C₄	—	2	2	no	—
311	C₂²×C₄	—	2	4	no	—
312	C₂²×C₄	—	2	4	no	—
313	C₂²×C₄	—	2	2	no	—
314	C₂²×C₄	—	2	2	no	—
315	C₂²×C₄	—	2	4	no	—
316	C₂²×C₄	—	4	2	no	—
317	C₂²×C₄	—	4	2	no	—
318	C₂²×C₄	C₂²⋊C₄×C₇₃	1	4	yes	—
319	C₂²×C₄	C₂²⋊C₄×C₇₃	1	4	yes	—
320	C₂²×C₄	C₂²×C₄×C₇₃	1	2	yes	—
321	C₂²×C₄	C₂²×C₄×C₇₃	1	2	yes	—
322	C₂²×C₄	C₂²×C₄×C₇₃	1	1	yes	characteristic
323	C₂²×C₄	C₂²×C₄×C₇₃	1	1	yes	characteristic
324	C₂²×C₄	C₂²×C₄×C₇₃	1	1	yes	characteristic
325	C₂²×C₄	C₂²×C₄×C₇₃	1	1	yes	characteristic
326	C₂²×C₄	C₂²×C₄×C₇₃	1	1	yes	characteristic
327	C₂²×C₄	C₂²×C₄×C₇₃	1	2	yes	—
328	C₂²×C₄	C₂×D₄×C₇₃	1	2	yes	—
329	C₂²×C₄	C₂×D₄×C₇₃	1	2	yes	—
330	C₂²×C₄	#41×C₇₃	1	8	yes	—
331	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
332	C₂×C₈	—	2	4	no	—
333	C₂×C₈	—	2	4	no	—
334	C₂×C₈	—	2	8	no	—
335	C₂×C₈	—	2	8	no	—
336	C₄⋊C₄	—	2	4	no	—
337	C₄⋊C₄	—	2	4	no	—
338	C₄⋊C₄	—	2	4	no	—
339	C₄⋊C₄	—	2	4	no	—
340	C₂²⋊C₄	—	2	4	no	—
341	C₂²⋊C₄	—	2	4	no	—
342	C₂²⋊C₄	—	2	4	no	—
343	C₂²⋊C₄	—	2	4	no	—
344	C₄²	—	2	4	no	—
345	C₄²	—	2	2	no	—
346	C₄²	—	2	2	no	—
347	C₄²	C₂²⋊C₄×C₇₃	1	4	yes	—
348	C₄²	C₂²⋊C₄×C₇₃	1	4	yes	—
349	C₄²	C₂×D₄×C₇₃	1	2	yes	—
350	C₄²	C₂×D₄×C₇₃	1	2	yes	—
351	C₄²	C₂×D₄×C₇₃	1	2	yes	—
352	C₄²	C₂×D₄×C₇₃	1	2	yes	—
353	C₂³	—	2	2	no	—
354	C₂³	—	2	2	no	—
355	C₂³	—	2	8	no	—
356	C₂³	—	2	2	no	—
357	C₂³	—	2	2	no	—
358	C₂³	—	2	4	no	—
359	C₂³	—	2	4	no	—
360	C₂³	—	4	16	no	—
361	C₂³	—	4	4	no	—
362	C₂³	—	4	4	no	—
363	C₂³	C₂×C₂²⋊C₄×C₇₃	1	2	yes	—
364	C₂³	#117×C₇₃	1	4	yes	—
365	C₂³	#131×C₇₃	1	4	yes	—
366	C₂³	C₂³×C₄×C₇₃	1	1	yes	characteristic
367	C₂×C₄	—	2	16	no	—
368	C₂×C₄	—	2	8	no	—
369	C₂×C₄	—	2	8	no	—
370	C₂×C₄	—	2	2	no	—
371	C₂×C₄	—	2	2	no	—
372	C₂×C₄	—	2	2	no	—
373	C₂×C₄	—	2	2	no	—
374	C₂×C₄	—	2	2	no	—
375	C₂×C₄	—	2	2	no	—
376	C₂×C₄	—	2	2	no	—
377	C₂×C₄	—	2	4	no	—
378	C₂×C₄	—	2	4	no	—
379	C₂×C₄	—	2	8	no	—
380	C₂×C₄	—	2	8	no	—
381	C₂×C₄	—	2	2	no	—
382	C₂×C₄	—	2	2	no	—
383	C₂×C₄	—	2	4	no	—
384	C₂×C₄	—	2	4	no	—
385	C₂×C₄	—	4	4	no	—
386	C₂×C₄	—	4	4	no	—
387	C₂×C₄	—	4	4	no	—
388	C₂×C₄	C₂×C₂²⋊C₄×C₇₃	1	2	yes	—
389	C₂×C₄	C₂×C₂²⋊C₄×C₇₃	1	2	yes	—
390	C₂×C₄	C₂×C₂²⋊C₄×C₇₃	1	2	yes	—
391	C₂×C₄	C₂×C₂²⋊C₄×C₇₃	1	2	yes	—
392	C₂×C₄	C₂×C₂²⋊C₄×C₇₃	1	2	yes	—
393	C₂×C₄	#117×C₇₃	1	4	yes	—
394	C₂×C₄	C₂²×D₄×C₇₃	1	1	yes	characteristic
395	C₂×C₄	C₂²×D₄×C₇₃	1	1	yes	characteristic
396	C₂×C₄	C₂×#41×C₇₃	1	4	yes	—
397	C₈	—	4	4	no	—
398	C₈	—	4	4	no	—
399	C₂²	—	2	2	no	—
400	C₂²	—	2	2	no	—
401	C₂²	—	2	8	no	—
402	C₂²	—	2	4	no	—
403	C₂²	—	2	8	no	—
404	C₂²	—	4	16	no	—
405	C₂²	—	4	2	no	—
406	C₂²	—	4	2	no	—
407	C₂²	—	4	4	no	—
408	C₂²	#408×C₇₃	1	4	yes	—
409	C₂²	C₂²×C₂²⋊C₄×C₇₃	1	1	yes	characteristic
410	C₂²	C₂×#117×C₇₃	1	2	yes	—
411	C₂²	C₂×#131×C₇₃	1	2	yes	—
412	C₂²	#568×C₇₃	1	2	yes	—
413	C₄	—	2	2	no	—
414	C₄	—	2	4	no	—
415	C₄	—	2	2	no	—
416	C₄	—	2	2	no	—
417	C₄	—	2	2	no	—
418	C₄	—	2	2	no	—
419	C₄	—	4	2	no	—
420	C₄	—	4	2	no	—
421	C₄	#525×C₇₃	1	2	yes	—
422	C₄	#525×C₇₃	1	2	yes	—
423	C₂	—	2	4	no	—
424	C₂	—	4	4	no	—
425	C₂	C₇₃×#2280	1	1	yes	characteristic
426	C₂	C₂×#408×C₇₃	1	1	yes	characteristic
427	C₂	C₇₃×#2879	1	1	yes	characteristic
428	C₂	C₇₃×#2924	1	4	yes	—

	subgroup	G/H
center	C₂²×C₄×C₇₃	C₂⁴
commutator	C₂³	C₂³×C₄×C₇₃
Frattini, cosocle	C₂²×C₄	C₂⁴×C₇₃
socle	C₂³×C₇₃	C₂³×C₄
prime radical	C₂⁵×C₇₃	C₂×C₄
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₇₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×#432×C₇₃	C₂	semidirect
3. C₂×#431×C₇₃	C₂	semidirect
4. C₇₃×#1817	C₂	semidirect
5. C₇₃×#1798	C₂	semidirect
7. C₇₃×#1750	C₂	semidirect
23. C₂×C₄⋊C₈×C₇₃	C₂²	semidirect
24. C₂×C₄⋊C₈×C₇₃	C₂²	semidirect
28. C₂×#97×C₇₃	C₂²	semidirect
29. C₂×C₄×C₈×C₇₃	C₂²	semidirect
30. #336×C₇₃	C₂²	semidirect
208. #20717	C₇₃	direct (N × H)
216. C₂×#432	C₂×C₇₃	semidirect
217. C₂×#431	C₂×C₇₃	semidirect
218. #1817	C₂×C₇₃	semidirect
219. #1798	C₂×C₇₃	semidirect
221. #1750	C₂×C₇₃	semidirect
222. C₇₃	#20717	direct (N × H)
238. C₂×C₄⋊C₈	C₂²×C₇₃	semidirect
239. C₂×C₄⋊C₈	C₂²×C₇₃	semidirect
243. C₂×#97	C₂²×C₇₃	semidirect
244. C₂×C₄×C₈	C₂²×C₇₃	semidirect
245. #336	C₂²×C₇₃	semidirect

Maximal subgroups

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

subgroup	index
C₂²×#117×C₇₃	2
C₂×#432×C₇₃	2
C₂×#431×C₇₃	2
C₇₃×#1817	2
C₇₃×#1798	2
C₇₃×#1779	2
C₇₃×#1750	2
#20717	73

Subgroups — C73×#20717 #32930121

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₃×#20717 #32930121