Subgroups — C₇₃×#22271 #32931675

Order 18688.

950 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#495×C₇₃	C₂	1	1	yes	maximal, characteristic
2	C₄×#124×C₇₃	C₂	1	2	yes	maximal, complemented
3	C₇₃×#1958	C₂	1	2	yes	maximal, complemented
4	C₇₃×#1880	C₂	1	2	yes	maximal, complemented
5	C₇₃×#1879	C₂	1	2	yes	maximal
6	C₇₃×#1878	C₂	1	2	yes	maximal, complemented
7	C₇₃×#1877	C₂	1	2	yes	maximal, complemented
8	C₇₃×#1835	C₂	1	1	yes	maximal, characteristic, complemented
9	C₇₃×#1744	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂²×Q₁₆×C₇₃	C₂²	1	1	yes	characteristic
11	C₂²×SD₁₆×C₇₃	C₂²	1	2	yes	—
12	C₂²×D₈×C₇₃	C₂²	1	1	yes	characteristic
13	C₂×#124×C₇₃	C₂²	1	2	yes	—
14	C₂×C₄×Q₈×C₇₃	C₂²	1	2	yes	—
15	C₂×C₄×D₄×C₇₃	C₂²	1	2	yes	—
16	#495×C₇₃	C₄	1	8	yes	complemented
17	C₂×#103×C₇₃	C₂²	1	2	yes	—
18	C₂×#103×C₇₃	C₂²	1	2	yes	—
19	C₂×#102×C₇₃	C₂²	1	2	yes	—
20	C₂×#102×C₇₃	C₂²	1	2	yes	—
21	C₂×C₄×C₈×C₇₃	C₂²	1	1	yes	characteristic
22	C₂×C₄×C₈×C₇₃	C₂²	1	1	yes	characteristic
23	#391×C₇₃	C₂²	1	2	yes	—
24	#390×C₇₃	C₂²	1	2	yes	—
25	#388×C₇₃	—	2	2	no	—
26	#388×C₇₃	—	2	2	no	—
27	#382×C₇₃	C₂²	1	2	yes	—
28	C₄×C₂²⋊C₄×C₇₃	—	2	2	no	—
29	C₄×C₂²⋊C₄×C₇₃	—	2	2	no	—
30	C₄³×C₇₃	C₂²	1	1	yes	characteristic
31	#340×C₇₃	C₂²	1	1	yes	characteristic
32	#340×C₇₃	C₂²	1	2	yes	—
33	#340×C₇₃	C₂²	1	1	yes	characteristic
34	#336×C₇₃	C₂²	1	2	yes	—
35	#336×C₇₃	C₂²	1	2	yes	—
36	C₂²×Q₈×C₇₃	C₂³	1	2	yes	—
37	C₂²×D₄×C₇₃	C₂³	1	2	yes	—
38	C₂³×C₄×C₇₃	—	2	2	no	—
39	C₂×Q₁₆×C₇₃	—	4	2	no	—
40	C₂×Q₁₆×C₇₃	C₂×C₄	1	4	yes	complemented
41	C₂×SD₁₆×C₇₃	—	4	2	no	—
42	C₂×SD₁₆×C₇₃	—	4	2	no	—
43	C₂×SD₁₆×C₇₃	C₂×C₄	1	8	yes	complemented
44	C₂×D₈×C₇₃	—	4	2	no	—
45	C₂×D₈×C₇₃	C₂×C₄	1	4	yes	—
46	C₂²×C₈×C₇₃	C₂³	1	2	yes	—
47	C₂²×C₈×C₇₃	C₂³	1	1	yes	characteristic
48	C₂²×C₈×C₇₃	C₂³	1	1	yes	characteristic
49	#124×C₇₃	—	2	4	no	—
50	#124×C₇₃	C₂×C₄	1	8	yes	complemented
51	C₄×Q₈×C₇₃	—	4	2	no	—
52	C₄×Q₈×C₇₃	—	4	2	no	—
53	C₄×D₄×C₇₃	—	4	2	no	—
54	C₄×D₄×C₇₃	—	4	2	no	—
55	C₂×C₄⋊C₄×C₇₃	—	2	2	no	—
56	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
57	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
58	C₂×C₂²⋊C₄×C₇₃	—	2	2	no	—
59	C₂×C₂²⋊C₄×C₇₃	—	2	2	no	—
60	C₂×C₂²⋊C₄×C₇₃	—	2	2	no	—
61	C₂×C₂²⋊C₄×C₇₃	—	2	2	no	—
62	C₂×C₂²⋊C₄×C₇₃	—	2	2	no	—
63	C₂×C₄²×C₇₃	—	2	2	no	—
64	C₂×C₄²×C₇₃	D₄	1	2	yes	—
65	C₂×C₄²×C₇₃	D₄	1	1	yes	characteristic
66	C₂×C₄²×C₇₃	D₄	1	1	yes	characteristic
67	C₂×C₄²×C₇₃	C₂³	1	2	yes	—
68	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
69	#103×C₇₃	—	4	2	no	—
70	#103×C₇₃	—	4	2	no	—
71	#102×C₇₃	—	4	2	no	—
72	#102×C₇₃	—	4	2	no	—
73	C₄×C₈×C₇₃	—	2	2	no	—
74	C₄×C₈×C₇₃	C₂×C₄	1	4	yes	complemented
75	#95×C₇₃	—	2	2	no	—
76	#95×C₇₃	—	2	2	no	—
77	#95×C₇₃	—	2	2	no	—
78	#95×C₇₃	—	2	2	no	—
79	C₂⁴×C₇₃	—	2	2	no	—
80	C₂×Q₈×C₇₃	—	2	2	no	—
81	C₂×Q₈×C₇₃	—	2	2	no	—
82	C₂×Q₈×C₇₃	—	2	2	no	—
83	C₂×Q₈×C₇₃	—	2	2	no	—
84	C₂×Q₈×C₇₃	—	2	2	no	—
85	C₂×Q₈×C₇₃	C₂²×C₄	1	4	yes	—
86	C₂×D₄×C₇₃	—	2	2	no	—
87	C₂×D₄×C₇₃	—	2	2	no	—
88	C₂×D₄×C₇₃	—	2	2	no	—
89	C₂×D₄×C₇₃	—	2	2	no	—
90	C₂×D₄×C₇₃	—	2	2	no	—
91	C₂×D₄×C₇₃	C₂²×C₄	1	4	yes	—
92	C₂²×C₄×C₇₃	—	2	2	no	—
93	C₂²×C₄×C₇₃	—	2	2	no	—
94	C₂²×C₄×C₇₃	—	2	2	no	—
95	C₂²×C₄×C₇₃	—	4	4	no	—
96	C₂²×C₄×C₇₃	—	4	4	no	—
97	C₂²×C₄×C₇₃	—	4	4	no	—
98	C₂²×C₄×C₇₃	C₂×D₄	1	2	yes	—
99	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
100	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
101	C₂²×C₄×C₇₃	C₂×D₄	1	2	yes	—
102	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
103	Q₁₆×C₇₃	—	4	4	no	—
104	SD₁₆×C₇₃	—	4	8	no	—
105	D₈×C₇₃	—	4	4	no	—
106	C₂×C₈×C₇₃	—	2	2	no	—
107	C₂×C₈×C₇₃	—	2	2	no	—
108	C₂×C₈×C₇₃	—	2	2	no	—
109	C₂×C₈×C₇₃	—	2	2	no	—
110	C₂×C₈×C₇₃	—	2	2	no	—
111	C₂×C₈×C₇₃	C₂²×C₄	1	2	yes	—
112	C₂×C₈×C₇₃	C₂²×C₄	1	2	yes	—
113	C₄⋊C₄×C₇₃	—	2	2	no	—
114	C₄⋊C₄×C₇₃	—	2	2	no	—
115	C₄⋊C₄×C₇₃	—	2	2	no	—
116	C₄⋊C₄×C₇₃	—	2	2	no	—
117	C₄⋊C₄×C₇₃	—	4	4	no	—
118	C₂²⋊C₄×C₇₃	—	2	8	no	—
119	C₂²⋊C₄×C₇₃	—	2	8	no	—
120	C₂²⋊C₄×C₇₃	—	4	4	no	—
121	C₂²⋊C₄×C₇₃	—	4	4	no	—
122	C₂²⋊C₄×C₇₃	—	4	4	no	—
123	C₄²×C₇₃	—	2	4	no	—
124	C₄²×C₇₃	—	2	2	no	—
125	C₄²×C₇₃	—	2	2	no	—
126	C₄²×C₇₃	—	4	1	no	—
127	C₄²×C₇₃	—	4	1	no	—
128	C₄²×C₇₃	—	4	4	no	—
129	C₄²×C₇₃	C₂²×C₄	1	2	yes	—
130	C₄²×C₇₃	#41	1	2	yes	—
131	C₂³×C₇₃	—	2	4	no	—
132	C₂³×C₇₃	—	4	2	no	—
133	C₂³×C₇₃	—	4	2	no	—
134	C₂³×C₇₃	—	4	2	no	—
135	C₂³×C₇₃	—	4	2	no	—
136	C₂³×C₇₃	—	4	2	no	—
137	C₂³×C₇₃	—	4	2	no	—
138	C₂³×C₇₃	C₂²×D₄	1	1	yes	characteristic
139	Q₈×C₇₃	—	2	4	no	—
140	Q₈×C₇₃	—	2	4	no	—
141	Q₈×C₇₃	—	4	2	no	—
142	Q₈×C₇₃	—	4	2	no	—
143	D₄×C₇₃	—	2	4	no	—
144	D₄×C₇₃	—	2	4	no	—
145	D₄×C₇₃	—	4	2	no	—
146	D₄×C₇₃	—	4	2	no	—
147	C₂×C₄×C₇₃	—	2	2	no	—
148	C₂×C₄×C₇₃	—	2	2	no	—
149	C₂×C₄×C₇₃	—	2	2	no	—
150	C₂×C₄×C₇₃	—	2	1	no	—
151	C₂×C₄×C₇₃	—	2	1	no	—
152	C₂×C₄×C₇₃	—	2	4	no	—
153	C₂×C₄×C₇₃	—	2	2	no	—
154	C₂×C₄×C₇₃	—	2	2	no	—
155	C₂×C₄×C₇₃	—	2	2	no	—
156	C₂×C₄×C₇₃	—	4	2	no	—
157	C₂×C₄×C₇₃	—	4	2	no	—
158	C₂×C₄×C₇₃	—	4	2	no	—
159	C₂×C₄×C₇₃	—	4	2	no	—
160	C₂×C₄×C₇₃	—	4	2	no	—
161	C₂×C₄×C₇₃	—	4	2	no	—
162	C₂×C₄×C₇₃	—	4	2	no	—
163	C₂×C₄×C₇₃	—	4	2	no	—
164	C₂×C₄×C₇₃	—	8	8	no	—
165	C₂×C₄×C₇₃	C₄×D₄	1	2	yes	—
166	C₂×C₄×C₇₃	C₄×D₄	1	2	yes	—
167	C₂×C₄×C₇₃	#135	1	4	yes	—
168	C₂×C₄×C₇₃	C₂³×C₄	1	1	yes	characteristic
169	C₂×C₄×C₇₃	C₂×#41	1	1	yes	characteristic
170	C₂×C₄×C₇₃	H(5,𝔽₂)	1	2	yes	—
171	C₂×C₄×C₇₃	H(5,𝔽₂)	1	2	yes	—
172	C₈×C₇₃	—	2	2	no	—
173	C₈×C₇₃	—	2	2	no	—
174	C₈×C₇₃	—	4	2	no	—
175	C₂²×C₇₃	—	4	4	no	—
176	C₂²×C₇₃	—	4	4	no	—
177	C₂²×C₇₃	—	4	4	no	—
178	C₂²×C₇₃	—	8	2	no	—
179	C₂²×C₇₃	—	8	2	no	—
180	C₂²×C₇₃	—	8	2	no	—
181	C₂²×C₇₃	—	8	2	no	—
182	C₂²×C₇₃	C₂×C₄×D₄	1	1	yes	characteristic
183	C₂²×C₇₃	#535	1	2	yes	—
184	C₂²×C₇₃	C₂×#135	1	2	yes	—
185	C₂²×C₇₃	#575	1	1	yes	characteristic
186	C₂²×C₇₃	#575	1	1	yes	characteristic
187	C₄×C₇₃	—	2	2	no	—
188	C₄×C₇₃	—	2	2	no	—
189	C₄×C₇₃	—	2	4	no	—
190	C₄×C₇₃	—	4	4	no	—
191	C₄×C₇₃	—	4	2	no	—
192	C₄×C₇₃	—	8	2	no	—
193	C₄×C₇₃	—	8	2	no	—
194	C₄×C₇₃	#518	1	1	yes	characteristic
195	C₄×C₇₃	#518	1	1	yes	characteristic
196	C₄×C₇₃	#540	1	2	yes	—
197	#22271	C₇₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
198	C₂×C₇₃	—	8	4	no	—
199	C₂×C₇₃	#2328	1	1	yes	characteristic
200	C₂×C₇₃	C₄×#135	1	1	yes	characteristic
201	C₂×C₇₃	#2943	1	1	yes	characteristic
202	C₂×C₇₃	#3211	1	2	yes	—
203	C₂×C₇₃	#3212	1	2	yes	—
204	C₂×#495	C₂×C₇₃	1	1	yes	characteristic
205	C₄×#124	C₂×C₇₃	1	2	yes	complemented
206	#1958	C₂×C₇₃	1	2	yes	complemented
207	#1880	C₂×C₇₃	1	2	yes	complemented
208	#1879	C₂×C₇₃	1	2	yes	—
209	#1878	C₂×C₇₃	1	2	yes	complemented
210	#1877	C₂×C₇₃	1	2	yes	complemented
211	#1835	C₂×C₇₃	1	1	yes	characteristic, complemented
212	#1744	C₂×C₇₃	1	1	yes	characteristic, complemented
213	C₇₃	#22271	1	1	yes	characteristic, direct product factor, Sylow
214	C₂²×Q₁₆	C₂²×C₇₃	1	1	yes	characteristic
215	C₂²×SD₁₆	C₂²×C₇₃	1	2	yes	—
216	C₂²×D₈	C₂²×C₇₃	1	1	yes	characteristic
217	C₂×#124	C₂²×C₇₃	1	2	yes	—
218	C₂×C₄×Q₈	C₂²×C₇₃	1	2	yes	—
219	C₂×C₄×D₄	C₂²×C₇₃	1	2	yes	—
220	#495	C₄×C₇₃	1	8	yes	complemented
221	C₂×#103	C₂²×C₇₃	1	2	yes	—
222	C₂×#103	C₂²×C₇₃	1	2	yes	—
223	C₂×#102	C₂²×C₇₃	1	2	yes	—
224	C₂×#102	C₂²×C₇₃	1	2	yes	—
225	C₂×C₄×C₈	C₂²×C₇₃	1	1	yes	characteristic
226	C₂×C₄×C₈	C₂²×C₇₃	1	1	yes	characteristic
227	#391	C₂²×C₇₃	1	2	yes	—
228	#390	C₂²×C₇₃	1	2	yes	—
229	#388	—	2	2	no	—
230	#388	—	2	2	no	—
231	#382	C₂²×C₇₃	1	2	yes	—
232	C₄×C₂²⋊C₄	—	2	2	no	—
233	C₄×C₂²⋊C₄	—	2	2	no	—
234	C₄³	C₂²×C₇₃	1	1	yes	characteristic
235	#340	C₂²×C₇₃	1	1	yes	characteristic
236	#340	C₂²×C₇₃	1	2	yes	—
237	#340	C₂²×C₇₃	1	1	yes	characteristic
238	#336	C₂²×C₇₃	1	2	yes	—
239	#336	C₂²×C₇₃	1	2	yes	—
240	C₂²×Q₈	C₂³×C₇₃	1	2	yes	—
241	C₂²×D₄	C₂³×C₇₃	1	2	yes	—
242	C₂³×C₄	—	2	2	no	—
243	C₂×Q₁₆	—	4	2	no	—
244	C₂×Q₁₆	C₂×C₄×C₇₃	1	4	yes	complemented
245	C₂×SD₁₆	—	4	2	no	—
246	C₂×SD₁₆	—	4	2	no	—
247	C₂×SD₁₆	C₂×C₄×C₇₃	1	8	yes	complemented
248	C₂×D₈	—	4	2	no	—
249	C₂×D₈	C₂×C₄×C₇₃	1	4	yes	—
250	C₂²×C₈	C₂³×C₇₃	1	2	yes	—
251	C₂²×C₈	C₂³×C₇₃	1	1	yes	characteristic
252	C₂²×C₈	C₂³×C₇₃	1	1	yes	characteristic
253	#124	—	2	4	no	—
254	#124	C₂×C₄×C₇₃	1	8	yes	complemented
255	C₄×Q₈	—	4	2	no	—
256	C₄×Q₈	—	4	2	no	—
257	C₄×D₄	—	4	2	no	—
258	C₄×D₄	—	4	2	no	—
259	C₂×C₄⋊C₄	—	2	2	no	—
260	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
261	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
262	C₂×C₂²⋊C₄	—	2	2	no	—
263	C₂×C₂²⋊C₄	—	2	2	no	—
264	C₂×C₂²⋊C₄	—	2	2	no	—
265	C₂×C₂²⋊C₄	—	2	2	no	—
266	C₂×C₂²⋊C₄	—	2	2	no	—
267	C₂×C₄²	—	2	2	no	—
268	C₂×C₄²	D₄×C₇₃	1	2	yes	—
269	C₂×C₄²	D₄×C₇₃	1	1	yes	characteristic
270	C₂×C₄²	D₄×C₇₃	1	1	yes	characteristic
271	C₂×C₄²	C₂³×C₇₃	1	2	yes	—
272	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
273	#103	—	4	2	no	—
274	#103	—	4	2	no	—
275	#102	—	4	2	no	—
276	#102	—	4	2	no	—
277	C₄×C₈	—	2	2	no	—
278	C₄×C₈	C₂×C₄×C₇₃	1	4	yes	complemented
279	#95	—	2	2	no	—
280	#95	—	2	2	no	—
281	#95	—	2	2	no	—
282	#95	—	2	2	no	—
283	C₂⁴	—	2	2	no	—
284	C₂×Q₈	—	2	2	no	—
285	C₂×Q₈	—	2	2	no	—
286	C₂×Q₈	—	2	2	no	—
287	C₂×Q₈	—	2	2	no	—
288	C₂×Q₈	—	2	2	no	—
289	C₂×Q₈	C₂²×C₄×C₇₃	1	4	yes	—
290	C₂×D₄	—	2	2	no	—
291	C₂×D₄	—	2	2	no	—
292	C₂×D₄	—	2	2	no	—
293	C₂×D₄	—	2	2	no	—
294	C₂×D₄	—	2	2	no	—
295	C₂×D₄	C₂²×C₄×C₇₃	1	4	yes	—
296	C₂²×C₄	—	2	2	no	—
297	C₂²×C₄	—	2	2	no	—
298	C₂²×C₄	—	2	2	no	—
299	C₂²×C₄	—	4	4	no	—
300	C₂²×C₄	—	4	4	no	—
301	C₂²×C₄	—	4	4	no	—
302	C₂²×C₄	C₂×D₄×C₇₃	1	2	yes	—
303	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
304	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
305	C₂²×C₄	C₂×D₄×C₇₃	1	2	yes	—
306	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
307	Q₁₆	—	4	4	no	—
308	SD₁₆	—	4	8	no	—
309	D₈	—	4	4	no	—
310	C₂×C₈	—	2	2	no	—
311	C₂×C₈	—	2	2	no	—
312	C₂×C₈	—	2	2	no	—
313	C₂×C₈	—	2	2	no	—
314	C₂×C₈	—	2	2	no	—
315	C₂×C₈	C₂²×C₄×C₇₃	1	2	yes	—
316	C₂×C₈	C₂²×C₄×C₇₃	1	2	yes	—
317	C₄⋊C₄	—	2	2	no	—
318	C₄⋊C₄	—	2	2	no	—
319	C₄⋊C₄	—	2	2	no	—
320	C₄⋊C₄	—	2	2	no	—
321	C₄⋊C₄	—	4	4	no	—
322	C₂²⋊C₄	—	2	8	no	—
323	C₂²⋊C₄	—	2	8	no	—
324	C₂²⋊C₄	—	4	4	no	—
325	C₂²⋊C₄	—	4	4	no	—
326	C₂²⋊C₄	—	4	4	no	—
327	C₄²	—	2	4	no	—
328	C₄²	—	2	2	no	—
329	C₄²	—	2	2	no	—
330	C₄²	—	4	1	no	—
331	C₄²	—	4	1	no	—
332	C₄²	—	4	4	no	—
333	C₄²	C₂²×C₄×C₇₃	1	2	yes	—
334	C₄²	#41×C₇₃	1	2	yes	—
335	C₂³	—	2	4	no	—
336	C₂³	—	4	2	no	—
337	C₂³	—	4	2	no	—
338	C₂³	—	4	2	no	—
339	C₂³	—	4	2	no	—
340	C₂³	—	4	2	no	—
341	C₂³	—	4	2	no	—
342	C₂³	C₂²×D₄×C₇₃	1	1	yes	characteristic
343	Q₈	—	2	4	no	—
344	Q₈	—	2	4	no	—
345	Q₈	—	4	2	no	—
346	Q₈	—	4	2	no	—
347	D₄	—	2	4	no	—
348	D₄	—	2	4	no	—
349	D₄	—	4	2	no	—
350	D₄	—	4	2	no	—
351	C₂×C₄	—	2	2	no	—
352	C₂×C₄	—	2	2	no	—
353	C₂×C₄	—	2	2	no	—
354	C₂×C₄	—	2	1	no	—
355	C₂×C₄	—	2	1	no	—
356	C₂×C₄	—	2	4	no	—
357	C₂×C₄	—	2	2	no	—
358	C₂×C₄	—	2	2	no	—
359	C₂×C₄	—	2	2	no	—
360	C₂×C₄	—	4	2	no	—
361	C₂×C₄	—	4	2	no	—
362	C₂×C₄	—	4	2	no	—
363	C₂×C₄	—	4	2	no	—
364	C₂×C₄	—	4	2	no	—
365	C₂×C₄	—	4	2	no	—
366	C₂×C₄	—	4	2	no	—
367	C₂×C₄	—	4	2	no	—
368	C₂×C₄	—	8	8	no	—
369	C₂×C₄	C₄×D₄×C₇₃	1	2	yes	—
370	C₂×C₄	C₄×D₄×C₇₃	1	2	yes	—
371	C₂×C₄	#135×C₇₃	1	4	yes	—
372	C₂×C₄	C₂³×C₄×C₇₃	1	1	yes	characteristic
373	C₂×C₄	C₂×#41×C₇₃	1	1	yes	characteristic
374	C₂×C₄	H(5,𝔽₂)×C₇₃	1	2	yes	—
375	C₂×C₄	H(5,𝔽₂)×C₇₃	1	2	yes	—
376	C₈	—	2	2	no	—
377	C₈	—	2	2	no	—
378	C₈	—	4	2	no	—
379	C₂²	—	4	4	no	—
380	C₂²	—	4	4	no	—
381	C₂²	—	4	4	no	—
382	C₂²	—	8	2	no	—
383	C₂²	—	8	2	no	—
384	C₂²	—	8	2	no	—
385	C₂²	—	8	2	no	—
386	C₂²	C₂×C₄×D₄×C₇₃	1	1	yes	characteristic
387	C₂²	#535×C₇₃	1	2	yes	—
388	C₂²	C₂×#135×C₇₃	1	2	yes	—
389	C₂²	#575×C₇₃	1	1	yes	characteristic
390	C₂²	#575×C₇₃	1	1	yes	characteristic
391	C₄	—	2	4	no	—
392	C₄	—	2	2	no	—
393	C₄	—	2	2	no	—
394	C₄	—	4	2	no	—
395	C₄	—	4	4	no	—
396	C₄	—	8	2	no	—
397	C₄	—	8	2	no	—
398	C₄	#518×C₇₃	1	1	yes	characteristic
399	C₄	#518×C₇₃	1	1	yes	characteristic
400	C₄	#540×C₇₃	1	2	yes	—
401	C₂	—	8	4	no	—
402	C₂	C₇₃×#2328	1	1	yes	characteristic
403	C₂	C₄×#135×C₇₃	1	1	yes	characteristic
404	C₂	C₇₃×#2943	1	1	yes	characteristic
405	C₂	C₇₃×#3211	1	2	yes	—
406	C₂	C₇₃×#3212	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₇₃	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₇₃
Frattini, cosocle	C₂²×C₄	C₂⁴×C₇₃
prime radical	C₂²×D₈×C₇₃	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₇₃ ◁ C₄³×C₇₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₄×#124×C₇₃	C₂	semidirect
3. C₇₃×#1958	C₂	semidirect
4. C₇₃×#1880	C₂	semidirect
6. C₇₃×#1878	C₂	semidirect
7. C₇₃×#1877	C₂	semidirect
8. C₇₃×#1835	C₂	semidirect
9. C₇₃×#1744	C₂	semidirect
16. #495×C₇₃	C₄	semidirect
40. C₂×Q₁₆×C₇₃	C₂×C₄	semidirect
43. C₂×SD₁₆×C₇₃	C₂×C₄	semidirect
50. #124×C₇₃	C₂×C₄	semidirect
74. C₄×C₈×C₇₃	C₂×C₄	semidirect
197. #22271	C₇₃	direct (N × H)
205. C₄×#124	C₂×C₇₃	semidirect
206. #1958	C₂×C₇₃	semidirect
207. #1880	C₂×C₇₃	semidirect
209. #1878	C₂×C₇₃	semidirect
210. #1877	C₂×C₇₃	semidirect
211. #1835	C₂×C₇₃	semidirect
212. #1744	C₂×C₇₃	semidirect
213. C₇₃	#22271	direct (N × H)
220. #495	C₄×C₇₃	semidirect
244. C₂×Q₁₆	C₂×C₄×C₇₃	semidirect
247. C₂×SD₁₆	C₂×C₄×C₇₃	semidirect
254. #124	C₂×C₄×C₇₃	semidirect
278. C₄×C₈	C₂×C₄×C₇₃	semidirect

Maximal subgroups

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

subgroup	index
C₂×#495×C₇₃	2
C₄×#124×C₇₃	2
C₇₃×#1958	2
C₇₃×#1880	2
C₇₃×#1879	2
C₇₃×#1878	2
C₇₃×#1877	2
C₇₃×#1835	2
C₇₃×#1744	2
#22271	73

Subgroups — C73×#22271 #32931675

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₃×#22271 #32931675