Subgroups — C₇₃×#25628 #32935032

Order 18688.

1218 conjugacy classes of subgroups.

The subgroup lattice has 460 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#556×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#492×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#459×C₇₃	C₂	1	1	yes	maximal, characteristic
4	C₇₃×#2548	C₂	1	1	yes	maximal, characteristic, complemented
5	C₇₃×#2012	C₂	1	4	yes	maximal, complemented
6	C₇₃×#1984	C₂	1	1	yes	maximal, characteristic, complemented
7	C₇₃×#1981	C₂	1	1	yes	maximal, characteristic, complemented
8	C₇₃×#1880	C₂	1	4	yes	maximal, complemented
9	C₄×#102×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂²×SD₁₆×C₇₃	C₂²	1	4	yes	—
11	C₂²×D₈×C₇₃	C₂²	1	2	yes	—
12	#556×C₇₃	—	2	4	no	—
13	#556×C₇₃	—	2	4	no	—
14	C₂×C₄⋊Q₈×C₇₃	C₂²	1	1	yes	characteristic
15	C₂×#127×C₇₃	C₂²	1	1	yes	characteristic
16	C₂×#126×C₇₃	—	2	2	no	—
17	C₂×#124×C₇₃	—	2	1	no	—
18	C₂×#124×C₇₃	C₂²	1	2	yes	—
19	C₂×C₂²⋊Q₈×C₇₃	—	2	1	no	—
20	C₂×C₄×Q₈×C₇₃	C₂²	1	2	yes	—
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	#492×C₇₃	—	2	4	no	—
25	#459×C₇₃	—	2	4	no	—
26	C₂×C₄⋊C₈×C₇₃	C₂²	1	1	yes	characteristic
27	C₂×#103×C₇₃	C₂²	1	4	yes	—
28	C₂×#102×C₇₃	C₂²	1	2	yes	—
29	C₂×#102×C₇₃	C₂²	1	2	yes	—
30	C₂×C₄×C₈×C₇₃	C₂²	1	1	yes	characteristic
31	#394×C₇₃	—	2	2	no	—
32	#390×C₇₃	—	2	1	no	—
33	#390×C₇₃	C₂²	1	4	yes	—
34	C₄×C₄⋊C₄×C₇₃	C₂²	1	1	yes	characteristic
35	#340×C₇₃	C₂²	1	2	yes	—
36	#336×C₇₃	C₂²	1	4	yes	—
37	C₂²×Q₈×C₇₃	D₄	1	1	yes	characteristic
38	C₂²×Q₈×C₇₃	C₂³	1	2	yes	—
39	C₂²×D₄×C₇₃	—	2	1	no	—
40	C₂²×D₄×C₇₃	—	2	1	no	—
41	C₂²×D₄×C₇₃	C₂³	1	2	yes	—
42	C₂²×D₄×C₇₃	C₂³	1	1	yes	characteristic
43	C₂³×C₄×C₇₃	—	2	1	no	—
44	C₂×SD₁₆×C₇₃	—	2	8	no	—
45	C₂×SD₁₆×C₇₃	—	2	8	no	—
46	C₂×SD₁₆×C₇₃	—	4	4	no	—
47	C₂×D₈×C₇₃	—	2	4	no	—
48	C₂×D₈×C₇₃	—	4	4	no	—
49	C₂²×C₈×C₇₃	C₂³	1	2	yes	—
50	C₂²×C₈×C₇₃	C₂³	1	2	yes	—
51	C₄⋊Q₈×C₇₃	—	2	2	no	—
52	C₄⋊Q₈×C₇₃	D₄	1	4	yes	—
53	#127×C₇₃	—	2	2	no	—
54	#127×C₇₃	—	2	2	no	—
55	#126×C₇₃	—	2	16	no	—
56	#124×C₇₃	—	2	4	no	—
57	#124×C₇₃	—	2	4	no	—
58	#124×C₇₃	—	4	4	no	—
59	C₂²⋊Q₈×C₇₃	—	2	8	no	—
60	C₄×Q₈×C₇₃	—	2	4	no	—
61	C₄×Q₈×C₇₃	—	2	4	no	—
62	C₄×Q₈×C₇₃	—	2	2	no	—
63	C₄×Q₈×C₇₃	—	2	2	no	—
64	C₄×D₄×C₇₃	—	2	2	no	—
65	C₄×D₄×C₇₃	D₄	1	4	yes	—
66	#117×C₇₃	—	2	8	no	—
67	C₂×C₄⋊C₄×C₇₃	—	2	1	no	—
68	C₂×C₄⋊C₄×C₇₃	—	2	2	no	—
69	C₂×C₄⋊C₄×C₇₃	—	2	1	no	—
70	C₂×C₄⋊C₄×C₇₃	D₄	1	1	yes	characteristic
71	C₂×C₄⋊C₄×C₇₃	D₄	1	2	yes	—
72	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
73	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
74	C₂×C₂²⋊C₄×C₇₃	—	2	2	no	—
75	C₂×C₂²⋊C₄×C₇₃	—	2	1	no	—
76	C₂×C₂²⋊C₄×C₇₃	—	2	2	no	—
77	C₂×C₂²⋊C₄×C₇₃	—	2	4	no	—
78	C₂×C₂²⋊C₄×C₇₃	—	2	4	no	—
79	C₂×C₄²×C₇₃	—	2	2	no	—
80	C₂×C₄²×C₇₃	—	2	1	no	—
81	C₂×C₄²×C₇₃	C₂³	1	2	yes	—
82	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
83	C₄⋊C₈×C₇₃	—	2	2	no	—
84	#103×C₇₃	—	4	4	no	—
85	#102×C₇₃	—	2	4	no	—
86	#102×C₇₃	—	2	4	no	—
87	C₄×C₈×C₇₃	—	2	2	no	—
88	#95×C₇₃	—	2	1	no	—
89	C₂⁴×C₇₃	—	2	1	no	—
90	C₂⁴×C₇₃	—	2	2	no	—
91	C₂×Q₈×C₇₃	—	2	2	no	—
92	C₂×Q₈×C₇₃	—	2	2	no	—
93	C₂×Q₈×C₇₃	—	2	2	no	—
94	C₂×Q₈×C₇₃	—	2	2	no	—
95	C₂×Q₈×C₇₃	—	2	4	no	—
96	C₂×Q₈×C₇₃	—	2	4	no	—
97	C₂×Q₈×C₇₃	C₂×D₄	1	4	yes	—
98	C₂×D₄×C₇₃	—	2	1	no	—
99	C₂×D₄×C₇₃	—	2	2	no	—
100	C₂×D₄×C₇₃	—	2	2	no	—
101	C₂×D₄×C₇₃	—	2	2	no	—
102	C₂×D₄×C₇₃	—	2	4	no	—
103	C₂×D₄×C₇₃	—	2	2	no	—
104	C₂×D₄×C₇₃	—	2	4	no	—
105	C₂×D₄×C₇₃	—	4	2	no	—
106	C₂×D₄×C₇₃	—	4	2	no	—
107	C₂×D₄×C₇₃	—	4	2	no	—
108	C₂×D₄×C₇₃	—	4	2	no	—
109	C₂×D₄×C₇₃	—	8	2	no	—
110	C₂×D₄×C₇₃	C₂×D₄	1	2	yes	—
111	C₂²×C₄×C₇₃	—	2	1	no	—
112	C₂²×C₄×C₇₃	—	2	2	no	—
113	C₂²×C₄×C₇₃	—	2	4	no	—
114	C₂²×C₄×C₇₃	—	2	2	no	—
115	C₂²×C₄×C₇₃	—	4	2	no	—
116	C₂²×C₄×C₇₃	—	4	2	no	—
117	C₂²×C₄×C₇₃	C₂×D₄	1	2	yes	—
118	C₂²×C₄×C₇₃	C₂×D₄	1	2	yes	—
119	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
120	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
121	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
122	SD₁₆×C₇₃	—	4	16	no	—
123	D₈×C₇₃	—	4	8	no	—
124	C₂×C₈×C₇₃	—	2	2	no	—
125	C₂×C₈×C₇₃	—	2	2	no	—
126	C₂×C₈×C₇₃	—	2	2	no	—
127	C₂×C₈×C₇₃	—	2	4	no	—
128	C₂×C₈×C₇₃	#41	1	4	yes	—
129	C₄⋊C₄×C₇₃	—	2	8	no	—
130	C₄⋊C₄×C₇₃	—	2	4	no	—
131	C₄⋊C₄×C₇₃	—	2	4	no	—
132	C₄⋊C₄×C₇₃	—	2	2	no	—
133	C₄⋊C₄×C₇₃	—	2	4	no	—
134	C₄⋊C₄×C₇₃	—	2	1	no	—
135	C₄⋊C₄×C₇₃	—	2	2	no	—
136	C₄⋊C₄×C₇₃	—	2	2	no	—
137	C₄⋊C₄×C₇₃	C₂×D₄	1	2	yes	—
138	C₂²⋊C₄×C₇₃	—	2	8	no	—
139	C₂²⋊C₄×C₇₃	—	2	8	no	—
140	C₂²⋊C₄×C₇₃	—	2	4	no	—
141	C₂²⋊C₄×C₇₃	—	4	8	no	—
142	C₂²⋊C₄×C₇₃	—	8	4	no	—
143	C₄²×C₇₃	—	2	8	no	—
144	C₄²×C₇₃	—	2	2	no	—
145	C₄²×C₇₃	—	2	2	no	—
146	C₄²×C₇₃	—	4	2	no	—
147	C₄²×C₇₃	C₂×D₄	1	2	yes	—
148	C₄²×C₇₃	C₂×D₄	1	2	yes	—
149	C₂³×C₇₃	—	2	2	no	—
150	C₂³×C₇₃	—	4	2	no	—
151	C₂³×C₇₃	—	4	1	no	—
152	C₂³×C₇₃	—	4	1	no	—
153	C₂³×C₇₃	—	4	2	no	—
154	C₂³×C₇₃	—	4	2	no	—
155	C₂³×C₇₃	—	4	4	no	—
156	C₂³×C₇₃	—	4	2	no	—
157	C₂³×C₇₃	—	4	2	no	—
158	C₂³×C₇₃	—	4	4	no	—
159	C₂³×C₇₃	C₂²×D₄	1	1	yes	characteristic
160	Q₈×C₇₃	—	2	8	no	—
161	Q₈×C₇₃	—	4	2	no	—
162	Q₈×C₇₃	—	4	2	no	—
163	Q₈×C₇₃	—	4	4	no	—
164	D₄×C₇₃	—	2	2	no	—
165	D₄×C₇₃	—	2	2	no	—
166	D₄×C₇₃	—	4	2	no	—
167	D₄×C₇₃	—	4	2	no	—
168	D₄×C₇₃	—	4	2	no	—
169	D₄×C₇₃	—	4	4	no	—
170	D₄×C₇₃	—	8	4	no	—
171	D₄×C₇₃	—	8	4	no	—
172	C₂×C₄×C₇₃	—	2	2	no	—
173	C₂×C₄×C₇₃	—	2	2	no	—
174	C₂×C₄×C₇₃	—	2	2	no	—
175	C₂×C₄×C₇₃	—	2	4	no	—
176	C₂×C₄×C₇₃	—	2	2	no	—
177	C₂×C₄×C₇₃	—	2	2	no	—
178	C₂×C₄×C₇₃	—	2	2	no	—
179	C₂×C₄×C₇₃	—	2	4	no	—
180	C₂×C₄×C₇₃	—	4	4	no	—
181	C₂×C₄×C₇₃	—	4	1	no	—
182	C₂×C₄×C₇₃	—	4	1	no	—
183	C₂×C₄×C₇₃	—	4	8	no	—
184	C₂×C₄×C₇₃	—	4	2	no	—
185	C₂×C₄×C₇₃	—	4	2	no	—
186	C₂×C₄×C₇₃	—	4	2	no	—
187	C₂×C₄×C₇₃	#120	1	2	yes	—
188	C₂×C₄×C₇₃	#120	1	2	yes	—
189	C₂×C₄×C₇₃	#135	1	2	yes	—
190	C₂×C₄×C₇₃	AGL(1,ℤ/8)	1	2	yes	—
191	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
192	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
193	C₂×C₄×C₇₃	C₂×#41	1	2	yes	—
194	C₂×C₄×C₇₃	H(5,𝔽₂)	1	2	yes	—
195	C₈×C₇₃	—	2	4	no	—
196	C₈×C₇₃	—	4	2	no	—
197	C₂²×C₇₃	—	4	2	no	—
198	C₂²×C₇₃	—	4	2	no	—
199	C₂²×C₇₃	—	4	2	no	—
200	C₂²×C₇₃	—	8	2	no	—
201	C₂²×C₇₃	—	8	2	no	—
202	C₂²×C₇₃	—	8	4	no	—
203	C₂²×C₇₃	—	8	4	no	—
204	C₂²×C₇₃	—	8	2	no	—
205	C₂²×C₇₃	—	8	2	no	—
206	C₂²×C₇₃	—	8	2	no	—
207	C₂²×C₇₃	C₂×#120	1	1	yes	characteristic
208	C₂²×C₇₃	#550	1	2	yes	—
209	C₂²×C₇₃	C₂×#135	1	1	yes	characteristic
210	C₂²×C₇₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
211	C₂²×C₇₃	#577	1	2	yes	—
212	C₄×C₇₃	—	2	2	no	—
213	C₄×C₇₃	—	4	4	no	—
214	C₄×C₇₃	—	4	2	no	—
215	C₄×C₇₃	—	4	2	no	—
216	C₄×C₇₃	—	4	2	no	—
217	C₄×C₇₃	—	8	2	no	—
218	C₄×C₇₃	#449	1	4	yes	—
219	C₄×C₇₃	#532	1	1	yes	characteristic
220	C₄×C₇₃	#535	1	1	yes	characteristic
221	C₄×C₇₃	#546	1	2	yes	—
222	#25628	C₇₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
223	C₂×C₇₃	—	8	2	no	—
224	C₂×C₇₃	—	16	2	no	—
225	C₂×C₇₃	#2431	1	1	yes	characteristic
226	C₂×C₇₃	C₂×#449	1	1	yes	characteristic
227	C₂×C₇₃	#3010	1	1	yes	characteristic
228	C₂×C₇₃	#3394	1	2	yes	—
229	C₂×C₇₃	#3397	1	2	yes	—
230	C₂×#556	C₂×C₇₃	1	1	yes	characteristic, complemented
231	C₂×#492	C₂×C₇₃	1	1	yes	characteristic, complemented
232	C₂×#459	C₂×C₇₃	1	1	yes	characteristic
233	#2548	C₂×C₇₃	1	1	yes	characteristic, complemented
234	#2012	C₂×C₇₃	1	4	yes	complemented
235	#1984	C₂×C₇₃	1	1	yes	characteristic, complemented
236	#1981	C₂×C₇₃	1	1	yes	characteristic, complemented
237	#1880	C₂×C₇₃	1	4	yes	complemented
238	C₄×#102	C₂×C₇₃	1	1	yes	characteristic, complemented
239	C₇₃	#25628	1	1	yes	characteristic, direct product factor, Sylow
240	C₂²×SD₁₆	C₂²×C₇₃	1	4	yes	—
241	C₂²×D₈	C₂²×C₇₃	1	2	yes	—
242	#556	—	2	4	no	—
243	#556	—	2	4	no	—
244	C₂×C₄⋊Q₈	C₂²×C₇₃	1	1	yes	characteristic
245	C₂×#127	C₂²×C₇₃	1	1	yes	characteristic
246	C₂×#126	—	2	2	no	—
247	C₂×#124	—	2	1	no	—
248	C₂×#124	C₂²×C₇₃	1	2	yes	—
249	C₂×C₂²⋊Q₈	—	2	1	no	—
250	C₂×C₄×Q₈	C₂²×C₇₃	1	2	yes	—
251	C₂×C₄×Q₈	C₂²×C₇₃	1	1	yes	characteristic
252	C₂×C₄×D₄	C₂²×C₇₃	1	1	yes	characteristic
253	C₂×#117	—	2	1	no	—
254	#492	—	2	4	no	—
255	#459	—	2	4	no	—
256	C₂×C₄⋊C₈	C₂²×C₇₃	1	1	yes	characteristic
257	C₂×#103	C₂²×C₇₃	1	4	yes	—
258	C₂×#102	C₂²×C₇₃	1	2	yes	—
259	C₂×#102	C₂²×C₇₃	1	2	yes	—
260	C₂×C₄×C₈	C₂²×C₇₃	1	1	yes	characteristic
261	#394	—	2	2	no	—
262	#390	—	2	1	no	—
263	#390	C₂²×C₇₃	1	4	yes	—
264	C₄×C₄⋊C₄	C₂²×C₇₃	1	1	yes	characteristic
265	#340	C₂²×C₇₃	1	2	yes	—
266	#336	C₂²×C₇₃	1	4	yes	—
267	C₂²×Q₈	D₄×C₇₃	1	1	yes	characteristic
268	C₂²×Q₈	C₂³×C₇₃	1	2	yes	—
269	C₂²×D₄	—	2	1	no	—
270	C₂²×D₄	—	2	1	no	—
271	C₂²×D₄	C₂³×C₇₃	1	2	yes	—
272	C₂²×D₄	C₂³×C₇₃	1	1	yes	characteristic
273	C₂³×C₄	—	2	1	no	—
274	C₂×SD₁₆	—	2	8	no	—
275	C₂×SD₁₆	—	2	8	no	—
276	C₂×SD₁₆	—	4	4	no	—
277	C₂×D₈	—	2	4	no	—
278	C₂×D₈	—	4	4	no	—
279	C₂²×C₈	C₂³×C₇₃	1	2	yes	—
280	C₂²×C₈	C₂³×C₇₃	1	2	yes	—
281	C₄⋊Q₈	—	2	2	no	—
282	C₄⋊Q₈	D₄×C₇₃	1	4	yes	—
283	#127	—	2	2	no	—
284	#127	—	2	2	no	—
285	#126	—	2	16	no	—
286	#124	—	2	4	no	—
287	#124	—	2	4	no	—
288	#124	—	4	4	no	—
289	C₂²⋊Q₈	—	2	8	no	—
290	C₄×Q₈	—	2	4	no	—
291	C₄×Q₈	—	2	4	no	—
292	C₄×Q₈	—	2	2	no	—
293	C₄×Q₈	—	2	2	no	—
294	C₄×D₄	—	2	2	no	—
295	C₄×D₄	D₄×C₇₃	1	4	yes	—
296	#117	—	2	8	no	—
297	C₂×C₄⋊C₄	—	2	1	no	—
298	C₂×C₄⋊C₄	—	2	2	no	—
299	C₂×C₄⋊C₄	—	2	1	no	—
300	C₂×C₄⋊C₄	D₄×C₇₃	1	1	yes	characteristic
301	C₂×C₄⋊C₄	D₄×C₇₃	1	2	yes	—
302	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
303	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
304	C₂×C₂²⋊C₄	—	2	2	no	—
305	C₂×C₂²⋊C₄	—	2	1	no	—
306	C₂×C₂²⋊C₄	—	2	2	no	—
307	C₂×C₂²⋊C₄	—	2	4	no	—
308	C₂×C₂²⋊C₄	—	2	4	no	—
309	C₂×C₄²	—	2	2	no	—
310	C₂×C₄²	—	2	1	no	—
311	C₂×C₄²	C₂³×C₇₃	1	2	yes	—
312	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
313	C₄⋊C₈	—	2	2	no	—
314	#103	—	4	4	no	—
315	#102	—	2	4	no	—
316	#102	—	2	4	no	—
317	C₄×C₈	—	2	2	no	—
318	#95	—	2	1	no	—
319	C₂⁴	—	2	1	no	—
320	C₂⁴	—	2	2	no	—
321	C₂×Q₈	—	2	2	no	—
322	C₂×Q₈	—	2	2	no	—
323	C₂×Q₈	—	2	2	no	—
324	C₂×Q₈	—	2	2	no	—
325	C₂×Q₈	—	2	4	no	—
326	C₂×Q₈	—	2	4	no	—
327	C₂×Q₈	C₂×D₄×C₇₃	1	4	yes	—
328	C₂×D₄	—	2	1	no	—
329	C₂×D₄	—	2	2	no	—
330	C₂×D₄	—	2	2	no	—
331	C₂×D₄	—	2	2	no	—
332	C₂×D₄	—	2	4	no	—
333	C₂×D₄	—	2	2	no	—
334	C₂×D₄	—	2	4	no	—
335	C₂×D₄	—	4	2	no	—
336	C₂×D₄	—	4	2	no	—
337	C₂×D₄	—	4	2	no	—
338	C₂×D₄	—	4	2	no	—
339	C₂×D₄	—	8	2	no	—
340	C₂×D₄	C₂×D₄×C₇₃	1	2	yes	—
341	C₂²×C₄	—	2	1	no	—
342	C₂²×C₄	—	2	2	no	—
343	C₂²×C₄	—	2	4	no	—
344	C₂²×C₄	—	2	2	no	—
345	C₂²×C₄	—	4	2	no	—
346	C₂²×C₄	—	4	2	no	—
347	C₂²×C₄	C₂×D₄×C₇₃	1	2	yes	—
348	C₂²×C₄	C₂×D₄×C₇₃	1	2	yes	—
349	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
350	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
351	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
352	SD₁₆	—	4	16	no	—
353	D₈	—	4	8	no	—
354	C₂×C₈	—	2	2	no	—
355	C₂×C₈	—	2	2	no	—
356	C₂×C₈	—	2	2	no	—
357	C₂×C₈	—	2	4	no	—
358	C₂×C₈	#41×C₇₃	1	4	yes	—
359	C₄⋊C₄	—	2	8	no	—
360	C₄⋊C₄	—	2	4	no	—
361	C₄⋊C₄	—	2	4	no	—
362	C₄⋊C₄	—	2	2	no	—
363	C₄⋊C₄	—	2	4	no	—
364	C₄⋊C₄	—	2	1	no	—
365	C₄⋊C₄	—	2	2	no	—
366	C₄⋊C₄	—	2	2	no	—
367	C₄⋊C₄	C₂×D₄×C₇₃	1	2	yes	—
368	C₂²⋊C₄	—	2	8	no	—
369	C₂²⋊C₄	—	2	8	no	—
370	C₂²⋊C₄	—	2	4	no	—
371	C₂²⋊C₄	—	4	8	no	—
372	C₂²⋊C₄	—	8	4	no	—
373	C₄²	—	2	8	no	—
374	C₄²	—	2	2	no	—
375	C₄²	—	2	2	no	—
376	C₄²	—	4	2	no	—
377	C₄²	C₂×D₄×C₇₃	1	2	yes	—
378	C₄²	C₂×D₄×C₇₃	1	2	yes	—
379	C₂³	—	2	2	no	—
380	C₂³	—	4	2	no	—
381	C₂³	—	4	1	no	—
382	C₂³	—	4	1	no	—
383	C₂³	—	4	2	no	—
384	C₂³	—	4	2	no	—
385	C₂³	—	4	4	no	—
386	C₂³	—	4	2	no	—
387	C₂³	—	4	2	no	—
388	C₂³	—	4	4	no	—
389	C₂³	C₂²×D₄×C₇₃	1	1	yes	characteristic
390	Q₈	—	2	8	no	—
391	Q₈	—	4	4	no	—
392	Q₈	—	4	2	no	—
393	Q₈	—	4	2	no	—
394	D₄	—	2	2	no	—
395	D₄	—	2	2	no	—
396	D₄	—	4	2	no	—
397	D₄	—	4	2	no	—
398	D₄	—	4	2	no	—
399	D₄	—	4	4	no	—
400	D₄	—	8	4	no	—
401	D₄	—	8	4	no	—
402	C₂×C₄	—	2	2	no	—
403	C₂×C₄	—	2	2	no	—
404	C₂×C₄	—	2	2	no	—
405	C₂×C₄	—	2	4	no	—
406	C₂×C₄	—	2	2	no	—
407	C₂×C₄	—	2	2	no	—
408	C₂×C₄	—	2	2	no	—
409	C₂×C₄	—	2	4	no	—
410	C₂×C₄	—	4	4	no	—
411	C₂×C₄	—	4	1	no	—
412	C₂×C₄	—	4	1	no	—
413	C₂×C₄	—	4	8	no	—
414	C₂×C₄	—	4	2	no	—
415	C₂×C₄	—	4	2	no	—
416	C₂×C₄	—	4	2	no	—
417	C₂×C₄	#120×C₇₃	1	2	yes	—
418	C₂×C₄	#120×C₇₃	1	2	yes	—
419	C₂×C₄	#135×C₇₃	1	2	yes	—
420	C₂×C₄	AGL(1,ℤ/8)×C₇₃	1	2	yes	—
421	C₂×C₄	C₂²×D₄×C₇₃	1	1	yes	characteristic
422	C₂×C₄	C₂²×D₄×C₇₃	1	1	yes	characteristic
423	C₂×C₄	C₂×#41×C₇₃	1	2	yes	—
424	C₂×C₄	H(5,𝔽₂)×C₇₃	1	2	yes	—
425	C₈	—	2	4	no	—
426	C₈	—	4	2	no	—
427	C₂²	—	4	2	no	—
428	C₂²	—	4	2	no	—
429	C₂²	—	4	2	no	—
430	C₂²	—	8	2	no	—
431	C₂²	—	8	2	no	—
432	C₂²	—	8	2	no	—
433	C₂²	—	8	2	no	—
434	C₂²	—	8	4	no	—
435	C₂²	—	8	4	no	—
436	C₂²	—	8	2	no	—
437	C₂²	C₂×#120×C₇₃	1	1	yes	characteristic
438	C₂²	#550×C₇₃	1	2	yes	—
439	C₂²	C₂×#135×C₇₃	1	1	yes	characteristic
440	C₂²	C₂×AGL(1,ℤ/8)×C₇₃	1	1	yes	characteristic
441	C₂²	#577×C₇₃	1	2	yes	—
442	C₄	—	2	2	no	—
443	C₄	—	4	2	no	—
444	C₄	—	4	2	no	—
445	C₄	—	4	2	no	—
446	C₄	—	4	4	no	—
447	C₄	—	8	2	no	—
448	C₄	#449×C₇₃	1	4	yes	—
449	C₄	#532×C₇₃	1	1	yes	characteristic
450	C₄	#535×C₇₃	1	1	yes	characteristic
451	C₄	#546×C₇₃	1	2	yes	—
452	C₂	—	8	2	no	—
453	C₂	—	16	2	no	—
454	C₂	C₇₃×#2431	1	1	yes	characteristic
455	C₂	C₂×#449×C₇₃	1	1	yes	characteristic
456	C₂	C₇₃×#3010	1	1	yes	characteristic
457	C₂	C₇₃×#3394	1	2	yes	—
458	C₂	C₇₃×#3397	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₇₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₇₃
prime radical	C₂×#459×C₇₃	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₇₃ ◁ C₂×C₄×Q₈×C₇₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×#556×C₇₃	C₂	semidirect
2. C₂×#492×C₇₃	C₂	semidirect
4. C₇₃×#2548	C₂	semidirect
5. C₇₃×#2012	C₂	semidirect
6. C₇₃×#1984	C₂	semidirect
7. C₇₃×#1981	C₂	semidirect
8. C₇₃×#1880	C₂	semidirect
9. C₄×#102×C₇₃	C₂	semidirect
222. #25628	C₇₃	direct (N × H)
230. C₂×#556	C₂×C₇₃	semidirect
231. C₂×#492	C₂×C₇₃	semidirect
233. #2548	C₂×C₇₃	semidirect
234. #2012	C₂×C₇₃	semidirect
235. #1984	C₂×C₇₃	semidirect
236. #1981	C₂×C₇₃	semidirect
237. #1880	C₂×C₇₃	semidirect
238. C₄×#102	C₂×C₇₃	semidirect
239. C₇₃	#25628	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×#556×C₇₃	2
C₂×#492×C₇₃	2
C₂×#459×C₇₃	2
C₇₃×#2548	2
C₇₃×#2012	2
C₇₃×#1984	2
C₇₃×#1981	2
C₇₃×#1880	2
C₄×#102×C₇₃	2
#25628	73

Subgroups — C73×#25628 #32935032

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₃×#25628 #32935032