Subgroups — C₇₃×#25778 #32935182

Order 18688.

1522 conjugacy classes of subgroups.

The subgroup lattice has 538 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#135×C₇₃	C₂	1	1	yes	maximal, characteristic
2	C₂×#495×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#494×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#467×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#452×C₇₃	C₂	1	2	yes	maximal, complemented
6	C₇₃×#2432	C₂	1	2	yes	maximal, complemented
7	C₇₃×#2015	C₂	1	2	yes	maximal, complemented
8	C₇₃×#2013	C₂	1	2	yes	maximal, complemented
9	C₇₃×#1970	C₂	1	1	yes	maximal, characteristic, complemented
10	C₇₃×#1969	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈×C₂²⋊C₄×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×#41×C₇₃	C₂²	1	2	yes	—
13	C₂×#135×C₇₃	—	2	4	no	—
14	C₂×#135×C₇₃	—	2	4	no	—
15	C₂×#135×C₇₃	—	2	4	no	—
16	C₂²×Q₁₆×C₇₃	C₂²	1	1	yes	characteristic
17	C₂²×Q₁₆×C₇₃	C₂²	1	2	yes	—
18	C₂²×Q₁₆×C₇₃	C₂²	1	1	yes	characteristic
19	C₂²×SD₁₆×C₇₃	C₂²	1	2	yes	—
20	C₂²×SD₁₆×C₇₃	C₂²	1	2	yes	—
21	C₂²×D₈×C₇₃	C₂²	1	1	yes	characteristic
22	C₂³×C₈×C₇₃	C₂²	1	1	yes	characteristic
23	C₂×C₄⋊Q₈×C₇₃	C₂²	1	2	yes	—
24	C₂×#124×C₇₃	C₂²	1	2	yes	—
25	C₂×C₂²⋊Q₈×C₇₃	C₂²	1	2	yes	—
26	#495×C₇₃	—	2	4	no	—
27	#494×C₇₃	—	2	4	no	—
28	#467×C₇₃	—	2	4	no	—
29	#452×C₇₃	—	2	8	no	—
30	C₂×#107×C₇₃	C₂²	1	1	yes	characteristic
31	C₂×#103×C₇₃	C₂²	1	2	yes	—
32	C₂×#103×C₇₃	C₂²	1	2	yes	—
33	C₂×#102×C₇₃	C₂²	1	2	yes	—
34	C₂×C₂²⋊C₈×C₇₃	C₂²	1	1	yes	characteristic
35	C₂×C₄×C₈×C₇₃	C₂²	1	1	yes	characteristic
36	C₂×C₄×C₈×C₇₃	C₂²	1	1	yes	characteristic
37	#394×C₇₃	—	2	4	no	—
38	#391×C₇₃	C₂²	1	2	yes	—
39	#390×C₇₃	C₂²	1	2	yes	—
40	#385×C₇₃	—	2	4	no	—
41	C₄×C₂²⋊C₄×C₇₃	C₂²	1	1	yes	characteristic
42	#336×C₇₃	C₂²	1	1	yes	characteristic
43	#336×C₇₃	C₂²	1	1	yes	characteristic
44	C₂×#41×C₇₃	—	2	4	no	—
45	C₂×#41×C₇₃	—	2	4	no	—
46	C₂×#41×C₇₃	—	2	4	no	—
47	C₂×#41×C₇₃	—	2	4	no	—
48	C₂×#41×C₇₃	—	4	2	no	—
49	C₂×#41×C₇₃	—	4	2	no	—
50	C₂²×Q₈×C₇₃	C₂³	1	2	yes	—
51	C₂²×Q₈×C₇₃	C₂³	1	2	yes	—
52	C₂²×D₄×C₇₃	—	2	2	no	—
53	C₂²×D₄×C₇₃	C₂³	1	2	yes	—
54	C₂³×C₄×C₇₃	—	2	2	no	—
55	C₂³×C₄×C₇₃	C₂³	1	1	yes	characteristic
56	#135×C₇₃	—	2	32	no	—
57	C₂×Q₁₆×C₇₃	—	2	4	no	—
58	C₂×Q₁₆×C₇₃	—	2	2	no	—
59	C₂×Q₁₆×C₇₃	—	2	2	no	—
60	C₂×Q₁₆×C₇₃	—	2	4	no	—
61	C₂×Q₁₆×C₇₃	—	2	2	no	—
62	C₂×Q₁₆×C₇₃	—	2	2	no	—
63	C₂×Q₁₆×C₇₃	—	2	2	no	—
64	C₂×Q₁₆×C₇₃	—	4	2	no	—
65	C₂×Q₁₆×C₇₃	D₄	1	4	yes	—
66	C₂×SD₁₆×C₇₃	—	2	4	no	—
67	C₂×SD₁₆×C₇₃	—	2	4	no	—
68	C₂×SD₁₆×C₇₃	—	2	4	no	—
69	C₂×SD₁₆×C₇₃	—	2	4	no	—
70	C₂×SD₁₆×C₇₃	—	2	4	no	—
71	C₂×SD₁₆×C₇₃	—	4	2	no	—
72	C₂×D₈×C₇₃	—	2	2	no	—
73	C₂×D₈×C₇₃	—	2	2	no	—
74	C₂×D₈×C₇₃	D₄	1	4	yes	—
75	C₂²×C₈×C₇₃	—	2	2	no	—
76	C₂²×C₈×C₇₃	—	2	2	no	—
77	C₂²×C₈×C₇₃	D₄	1	4	yes	—
78	C₂²×C₈×C₇₃	C₂³	1	1	yes	characteristic
79	C₂²×C₈×C₇₃	C₂³	1	1	yes	characteristic
80	C₂²×C₈×C₇₃	C₂³	1	1	yes	characteristic
81	C₂²×C₈×C₇₃	C₂³	1	1	yes	characteristic
82	C₄⋊Q₈×C₇₃	—	2	4	no	—
83	C₄⋊Q₈×C₇₃	—	4	2	no	—
84	#124×C₇₃	—	2	4	no	—
85	#124×C₇₃	—	4	2	no	—
86	C₂²⋊Q₈×C₇₃	—	2	4	no	—
87	C₂²⋊Q₈×C₇₃	—	2	4	no	—
88	C₂×C₄⋊C₄×C₇₃	—	2	2	no	—
89	C₂×C₄⋊C₄×C₇₃	—	2	4	no	—
90	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
91	C₂×C₂²⋊C₄×C₇₃	—	2	2	no	—
92	C₂×C₂²⋊C₄×C₇₃	—	2	4	no	—
93	C₂×C₂²⋊C₄×C₇₃	—	2	4	no	—
94	C₂×C₂²⋊C₄×C₇₃	D₄	1	2	yes	—
95	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
96	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
97	#107×C₇₃	—	2	2	no	—
98	#103×C₇₃	—	2	4	no	—
99	#103×C₇₃	—	2	4	no	—
100	#102×C₇₃	—	2	4	no	—
101	C₂²⋊C₈×C₇₃	D₄	1	4	yes	—
102	C₄×C₈×C₇₃	—	2	2	no	—
103	C₄×C₈×C₇₃	—	2	2	no	—
104	#95×C₇₃	—	2	4	no	—
105	#95×C₇₃	D₄	1	2	yes	—
106	C₂⁴×C₇₃	—	2	2	no	—
107	C₂⁴×C₇₃	C₂×D₄	1	1	yes	characteristic
108	#41×C₇₃	—	2	16	no	—
109	#41×C₇₃	—	4	8	no	—
110	#41×C₇₃	—	4	8	no	—
111	#41×C₇₃	—	4	8	no	—
112	C₂×Q₈×C₇₃	—	2	2	no	—
113	C₂×Q₈×C₇₃	—	2	2	no	—
114	C₂×Q₈×C₇₃	—	2	2	no	—
115	C₂×Q₈×C₇₃	—	2	2	no	—
116	C₂×Q₈×C₇₃	—	2	2	no	—
117	C₂×Q₈×C₇₃	—	2	2	no	—
118	C₂×Q₈×C₇₃	—	2	2	no	—
119	C₂×Q₈×C₇₃	—	2	2	no	—
120	C₂×Q₈×C₇₃	—	2	2	no	—
121	C₂×Q₈×C₇₃	—	2	2	no	—
122	C₂×Q₈×C₇₃	—	2	2	no	—
123	C₂×Q₈×C₇₃	C₂×D₄	1	4	yes	—
124	C₂×D₄×C₇₃	—	2	2	no	—
125	C₂×D₄×C₇₃	—	2	2	no	—
126	C₂×D₄×C₇₃	—	2	2	no	—
127	C₂×D₄×C₇₃	—	2	2	no	—
128	C₂×D₄×C₇₃	—	2	2	no	—
129	C₂×D₄×C₇₃	—	4	4	no	—
130	C₂×D₄×C₇₃	—	4	4	no	—
131	C₂×D₄×C₇₃	—	4	4	no	—
132	C₂×D₄×C₇₃	C₂×D₄	1	4	yes	—
133	C₂²×C₄×C₇₃	—	2	1	no	—
134	C₂²×C₄×C₇₃	—	2	1	no	—
135	C₂²×C₄×C₇₃	—	2	1	no	—
136	C₂²×C₄×C₇₃	—	2	1	no	—
137	C₂²×C₄×C₇₃	—	2	2	no	—
138	C₂²×C₄×C₇₃	—	2	2	no	—
139	C₂²×C₄×C₇₃	—	2	2	no	—
140	C₂²×C₄×C₇₃	—	4	4	no	—
141	C₂²×C₄×C₇₃	—	4	4	no	—
142	C₂²×C₄×C₇₃	—	4	4	no	—
143	C₂²×C₄×C₇₃	C₂×D₄	1	2	yes	—
144	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
145	C₂²×C₄×C₇₃	C₂×D₄	1	2	yes	—
146	C₂²×C₄×C₇₃	C₂×D₄	1	2	yes	—
147	C₂²×C₄×C₇₃	C₂×D₄	1	2	yes	—
148	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
149	Q₁₆×C₇₃	—	2	8	no	—
150	Q₁₆×C₇₃	—	4	8	no	—
151	Q₁₆×C₇₃	—	4	4	no	—
152	SD₁₆×C₇₃	—	2	16	no	—
153	SD₁₆×C₇₃	—	4	8	no	—
154	D₈×C₇₃	—	2	8	no	—
155	C₂×C₈×C₇₃	—	2	1	no	—
156	C₂×C₈×C₇₃	—	2	1	no	—
157	C₂×C₈×C₇₃	—	2	1	no	—
158	C₂×C₈×C₇₃	—	2	1	no	—
159	C₂×C₈×C₇₃	—	2	1	no	—
160	C₂×C₈×C₇₃	—	2	1	no	—
161	C₂×C₈×C₇₃	—	2	8	no	—
162	C₂×C₈×C₇₃	C₂×D₄	1	2	yes	—
163	C₂×C₈×C₇₃	C₂×D₄	1	2	yes	—
164	C₂×C₈×C₇₃	C₂×D₄	1	2	yes	—
165	C₂×C₈×C₇₃	C₂×D₄	1	2	yes	—
166	C₂×C₈×C₇₃	C₂×D₄	1	2	yes	—
167	C₂×C₈×C₇₃	C₂×D₄	1	2	yes	—
168	C₄⋊C₄×C₇₃	—	2	2	no	—
169	C₄⋊C₄×C₇₃	—	2	2	no	—
170	C₄⋊C₄×C₇₃	—	4	8	no	—
171	C₄⋊C₄×C₇₃	—	4	4	no	—
172	C₂²⋊C₄×C₇₃	—	2	4	no	—
173	C₂²⋊C₄×C₇₃	—	4	8	no	—
174	C₂²⋊C₄×C₇₃	—	4	4	no	—
175	C₂²⋊C₄×C₇₃	—	4	8	no	—
176	C₄²×C₇₃	—	2	1	no	—
177	C₄²×C₇₃	—	2	1	no	—
178	C₄²×C₇₃	—	2	1	no	—
179	C₄²×C₇₃	—	2	1	no	—
180	C₂³×C₇₃	—	2	1	no	—
181	C₂³×C₇₃	—	2	1	no	—
182	C₂³×C₇₃	—	2	2	no	—
183	C₂³×C₇₃	—	2	2	no	—
184	C₂³×C₇₃	—	2	4	no	—
185	C₂³×C₇₃	—	4	2	no	—
186	C₂³×C₇₃	—	4	2	no	—
187	C₂³×C₇₃	—	4	4	no	—
188	C₂³×C₇₃	—	4	4	no	—
189	C₂³×C₇₃	#127	1	2	yes	—
190	C₂³×C₇₃	C₂²×D₄	1	1	yes	characteristic
191	Q₈×C₇₃	—	2	4	no	—
192	Q₈×C₇₃	—	2	4	no	—
193	Q₈×C₇₃	—	4	2	no	—
194	Q₈×C₇₃	—	4	2	no	—
195	Q₈×C₇₃	—	4	2	no	—
196	Q₈×C₇₃	—	4	2	no	—
197	Q₈×C₇₃	—	4	2	no	—
198	Q₈×C₇₃	—	4	2	no	—
199	D₄×C₇₃	—	2	4	no	—
200	D₄×C₇₃	—	2	4	no	—
201	D₄×C₇₃	—	4	16	no	—
202	D₄×C₇₃	—	4	2	no	—
203	D₄×C₇₃	—	4	2	no	—
204	C₂×C₄×C₇₃	—	2	2	no	—
205	C₂×C₄×C₇₃	—	2	1	no	—
206	C₂×C₄×C₇₃	—	2	1	no	—
207	C₂×C₄×C₇₃	—	2	2	no	—
208	C₂×C₄×C₇₃	—	2	2	no	—
209	C₂×C₄×C₇₃	—	2	2	no	—
210	C₂×C₄×C₇₃	—	2	2	no	—
211	C₂×C₄×C₇₃	—	2	2	no	—
212	C₂×C₄×C₇₃	—	2	2	no	—
213	C₂×C₄×C₇₃	—	2	4	no	—
214	C₂×C₄×C₇₃	—	2	2	no	—
215	C₂×C₄×C₇₃	—	2	2	no	—
216	C₂×C₄×C₇₃	—	4	16	no	—
217	C₂×C₄×C₇₃	—	4	2	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	4	no	—
224	C₂×C₄×C₇₃	#127	1	2	yes	—
225	C₂×C₄×C₇₃	#135	1	4	yes	complemented
226	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
227	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
228	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
229	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
230	C₂×C₄×C₇₃	H(5,𝔽₂)	1	1	yes	characteristic
231	C₂×C₄×C₇₃	H(5,𝔽₂)	1	1	yes	characteristic
232	C₈×C₇₃	—	2	2	no	—
233	C₈×C₇₃	—	2	2	no	—
234	C₈×C₇₃	—	2	2	no	—
235	C₈×C₇₃	#120	1	4	yes	—
236	C₂²×C₇₃	—	2	2	no	—
237	C₂²×C₇₃	—	2	2	no	—
238	C₂²×C₇₃	—	2	2	no	—
239	C₂²×C₇₃	—	4	2	no	—
240	C₂²×C₇₃	—	4	2	no	—
241	C₂²×C₇₃	—	4	4	no	—
242	C₂²×C₇₃	—	4	8	no	—
243	C₂²×C₇₃	—	8	2	no	—
244	C₂²×C₇₃	—	8	2	no	—
245	C₂²×C₇₃	—	8	4	no	—
246	C₂²×C₇₃	C₂×#127	1	1	yes	characteristic
247	C₂²×C₇₃	D₄²	1	1	yes	characteristic
248	C₂²×C₇₃	D₄²	1	1	yes	characteristic
249	C₂²×C₇₃	C₂×#135	1	2	yes	—
250	C₂²×C₇₃	#578	1	2	yes	—
251	C₄×C₇₃	—	2	2	no	—
252	C₄×C₇₃	—	2	4	no	—
253	C₄×C₇₃	—	4	4	no	—
254	C₄×C₇₃	—	4	2	no	—
255	C₄×C₇₃	—	8	2	no	—
256	C₄×C₇₃	—	8	2	no	—
257	C₄×C₇₃	C₂×#120	1	1	yes	characteristic
258	C₄×C₇₃	#535	1	1	yes	characteristic
259	C₄×C₇₃	D₄²	1	1	yes	characteristic
260	C₄×C₇₃	D₄²	1	1	yes	characteristic
261	#25778	C₇₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
262	C₂×C₇₃	—	4	2	no	—
263	C₂×C₇₃	—	8	4	no	—
264	C₂×C₇₃	#2433	1	1	yes	characteristic
265	C₂×C₇₃	#3147	1	1	yes	characteristic
266	C₂×C₇₃	#3156	1	1	yes	characteristic
267	C₂×C₇₃	#3283	1	2	yes	—
268	C₂×C₇₃	#3285	1	2	yes	—
269	C₂²×#135	C₂×C₇₃	1	1	yes	characteristic
270	C₂×#495	C₂×C₇₃	1	1	yes	characteristic, complemented
271	C₂×#494	C₂×C₇₃	1	1	yes	characteristic, complemented
272	C₂×#467	C₂×C₇₃	1	1	yes	characteristic, complemented
273	C₂×#452	C₂×C₇₃	1	2	yes	complemented
274	#2432	C₂×C₇₃	1	2	yes	complemented
275	#2015	C₂×C₇₃	1	2	yes	complemented
276	#2013	C₂×C₇₃	1	2	yes	complemented
277	#1970	C₂×C₇₃	1	1	yes	characteristic, complemented
278	#1969	C₂×C₇₃	1	1	yes	characteristic, complemented
279	C₈×C₂²⋊C₄	C₂×C₇₃	1	1	yes	characteristic, complemented
280	C₇₃	#25778	1	1	yes	characteristic, direct product factor, Sylow
281	C₂²×#41	C₂²×C₇₃	1	2	yes	—
282	C₂×#135	—	2	4	no	—
283	C₂×#135	—	2	4	no	—
284	C₂×#135	—	2	4	no	—
285	C₂²×Q₁₆	C₂²×C₇₃	1	1	yes	characteristic
286	C₂²×Q₁₆	C₂²×C₇₃	1	2	yes	—
287	C₂²×Q₁₆	C₂²×C₇₃	1	1	yes	characteristic
288	C₂²×SD₁₆	C₂²×C₇₃	1	2	yes	—
289	C₂²×SD₁₆	C₂²×C₇₃	1	2	yes	—
290	C₂²×D₈	C₂²×C₇₃	1	1	yes	characteristic
291	C₂³×C₈	C₂²×C₇₃	1	1	yes	characteristic
292	C₂×C₄⋊Q₈	C₂²×C₇₃	1	2	yes	—
293	C₂×#124	C₂²×C₇₃	1	2	yes	—
294	C₂×C₂²⋊Q₈	C₂²×C₇₃	1	2	yes	—
295	#495	—	2	4	no	—
296	#494	—	2	4	no	—
297	#467	—	2	4	no	—
298	#452	—	2	8	no	—
299	C₂×#107	C₂²×C₇₃	1	1	yes	characteristic
300	C₂×#103	C₂²×C₇₃	1	2	yes	—
301	C₂×#103	C₂²×C₇₃	1	2	yes	—
302	C₂×#102	C₂²×C₇₃	1	2	yes	—
303	C₂×C₂²⋊C₈	C₂²×C₇₃	1	1	yes	characteristic
304	C₂×C₄×C₈	C₂²×C₇₃	1	1	yes	characteristic
305	C₂×C₄×C₈	C₂²×C₇₃	1	1	yes	characteristic
306	#394	—	2	4	no	—
307	#391	C₂²×C₇₃	1	2	yes	—
308	#390	C₂²×C₇₃	1	2	yes	—
309	#385	—	2	4	no	—
310	C₄×C₂²⋊C₄	C₂²×C₇₃	1	1	yes	characteristic
311	#336	C₂²×C₇₃	1	1	yes	characteristic
312	#336	C₂²×C₇₃	1	1	yes	characteristic
313	C₂×#41	—	2	4	no	—
314	C₂×#41	—	2	4	no	—
315	C₂×#41	—	2	4	no	—
316	C₂×#41	—	2	4	no	—
317	C₂×#41	—	4	2	no	—
318	C₂×#41	—	4	2	no	—
319	C₂²×Q₈	C₂³×C₇₃	1	2	yes	—
320	C₂²×Q₈	C₂³×C₇₃	1	2	yes	—
321	C₂²×D₄	—	2	2	no	—
322	C₂²×D₄	C₂³×C₇₃	1	2	yes	—
323	C₂³×C₄	—	2	2	no	—
324	C₂³×C₄	C₂³×C₇₃	1	1	yes	characteristic
325	#135	—	2	32	no	—
326	C₂×Q₁₆	—	2	4	no	—
327	C₂×Q₁₆	—	2	2	no	—
328	C₂×Q₁₆	—	2	2	no	—
329	C₂×Q₁₆	—	2	4	no	—
330	C₂×Q₁₆	—	2	2	no	—
331	C₂×Q₁₆	—	2	2	no	—
332	C₂×Q₁₆	—	2	2	no	—
333	C₂×Q₁₆	—	4	2	no	—
334	C₂×Q₁₆	D₄×C₇₃	1	4	yes	—
335	C₂×SD₁₆	—	2	4	no	—
336	C₂×SD₁₆	—	2	4	no	—
337	C₂×SD₁₆	—	2	4	no	—
338	C₂×SD₁₆	—	2	4	no	—
339	C₂×SD₁₆	—	2	4	no	—
340	C₂×SD₁₆	—	4	2	no	—
341	C₂×D₈	—	2	2	no	—
342	C₂×D₈	—	2	2	no	—
343	C₂×D₈	D₄×C₇₃	1	4	yes	—
344	C₂²×C₈	—	2	2	no	—
345	C₂²×C₈	—	2	2	no	—
346	C₂²×C₈	D₄×C₇₃	1	4	yes	—
347	C₂²×C₈	C₂³×C₇₃	1	1	yes	characteristic
348	C₂²×C₈	C₂³×C₇₃	1	1	yes	characteristic
349	C₂²×C₈	C₂³×C₇₃	1	1	yes	characteristic
350	C₂²×C₈	C₂³×C₇₃	1	1	yes	characteristic
351	C₄⋊Q₈	—	2	4	no	—
352	C₄⋊Q₈	—	4	2	no	—
353	#124	—	2	4	no	—
354	#124	—	4	2	no	—
355	C₂²⋊Q₈	—	2	4	no	—
356	C₂²⋊Q₈	—	2	4	no	—
357	C₂×C₄⋊C₄	—	2	2	no	—
358	C₂×C₄⋊C₄	—	2	4	no	—
359	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
360	C₂×C₂²⋊C₄	—	2	2	no	—
361	C₂×C₂²⋊C₄	—	2	4	no	—
362	C₂×C₂²⋊C₄	—	2	4	no	—
363	C₂×C₂²⋊C₄	D₄×C₇₃	1	2	yes	—
364	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
365	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
366	#107	—	2	2	no	—
367	#103	—	2	4	no	—
368	#103	—	2	4	no	—
369	#102	—	2	4	no	—
370	C₂²⋊C₈	D₄×C₇₃	1	4	yes	—
371	C₄×C₈	—	2	2	no	—
372	C₄×C₈	—	2	2	no	—
373	#95	—	2	4	no	—
374	#95	D₄×C₇₃	1	2	yes	—
375	C₂⁴	—	2	2	no	—
376	C₂⁴	C₂×D₄×C₇₃	1	1	yes	characteristic
377	#41	—	2	16	no	—
378	#41	—	4	8	no	—
379	#41	—	4	8	no	—
380	#41	—	4	8	no	—
381	C₂×Q₈	—	2	2	no	—
382	C₂×Q₈	—	2	2	no	—
383	C₂×Q₈	—	2	2	no	—
384	C₂×Q₈	—	2	2	no	—
385	C₂×Q₈	—	2	2	no	—
386	C₂×Q₈	—	2	2	no	—
387	C₂×Q₈	—	2	2	no	—
388	C₂×Q₈	—	2	2	no	—
389	C₂×Q₈	—	2	2	no	—
390	C₂×Q₈	—	2	2	no	—
391	C₂×Q₈	—	2	2	no	—
392	C₂×Q₈	C₂×D₄×C₇₃	1	4	yes	—
393	C₂×D₄	—	2	2	no	—
394	C₂×D₄	—	2	2	no	—
395	C₂×D₄	—	2	2	no	—
396	C₂×D₄	—	2	2	no	—
397	C₂×D₄	—	2	2	no	—
398	C₂×D₄	—	4	4	no	—
399	C₂×D₄	—	4	4	no	—
400	C₂×D₄	—	4	4	no	—
401	C₂×D₄	C₂×D₄×C₇₃	1	4	yes	—
402	C₂²×C₄	—	2	1	no	—
403	C₂²×C₄	—	2	1	no	—
404	C₂²×C₄	—	2	1	no	—
405	C₂²×C₄	—	2	1	no	—
406	C₂²×C₄	—	2	2	no	—
407	C₂²×C₄	—	2	2	no	—
408	C₂²×C₄	—	2	2	no	—
409	C₂²×C₄	—	4	4	no	—
410	C₂²×C₄	—	4	4	no	—
411	C₂²×C₄	—	4	4	no	—
412	C₂²×C₄	C₂×D₄×C₇₃	1	2	yes	—
413	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
414	C₂²×C₄	C₂×D₄×C₇₃	1	2	yes	—
415	C₂²×C₄	C₂×D₄×C₇₃	1	2	yes	—
416	C₂²×C₄	C₂×D₄×C₇₃	1	2	yes	—
417	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
418	Q₁₆	—	2	8	no	—
419	Q₁₆	—	4	8	no	—
420	Q₁₆	—	4	4	no	—
421	SD₁₆	—	2	16	no	—
422	SD₁₆	—	4	8	no	—
423	D₈	—	2	8	no	—
424	C₂×C₈	—	2	1	no	—
425	C₂×C₈	—	2	1	no	—
426	C₂×C₈	—	2	1	no	—
427	C₂×C₈	—	2	1	no	—
428	C₂×C₈	—	2	1	no	—
429	C₂×C₈	—	2	1	no	—
430	C₂×C₈	—	2	8	no	—
431	C₂×C₈	C₂×D₄×C₇₃	1	2	yes	—
432	C₂×C₈	C₂×D₄×C₇₃	1	2	yes	—
433	C₂×C₈	C₂×D₄×C₇₃	1	2	yes	—
434	C₂×C₈	C₂×D₄×C₇₃	1	2	yes	—
435	C₂×C₈	C₂×D₄×C₇₃	1	2	yes	—
436	C₂×C₈	C₂×D₄×C₇₃	1	2	yes	—
437	C₄⋊C₄	—	2	2	no	—
438	C₄⋊C₄	—	2	2	no	—
439	C₄⋊C₄	—	4	8	no	—
440	C₄⋊C₄	—	4	4	no	—
441	C₂²⋊C₄	—	2	4	no	—
442	C₂²⋊C₄	—	4	8	no	—
443	C₂²⋊C₄	—	4	4	no	—
444	C₂²⋊C₄	—	4	8	no	—
445	C₄²	—	2	1	no	—
446	C₄²	—	2	1	no	—
447	C₄²	—	2	1	no	—
448	C₄²	—	2	1	no	—
449	C₂³	—	2	1	no	—
450	C₂³	—	2	1	no	—
451	C₂³	—	2	2	no	—
452	C₂³	—	2	2	no	—
453	C₂³	—	2	4	no	—
454	C₂³	—	4	2	no	—
455	C₂³	—	4	2	no	—
456	C₂³	—	4	4	no	—
457	C₂³	—	4	4	no	—
458	C₂³	#127×C₇₃	1	2	yes	—
459	C₂³	C₂²×D₄×C₇₃	1	1	yes	characteristic
460	Q₈	—	2	4	no	—
461	Q₈	—	2	4	no	—
462	Q₈	—	4	2	no	—
463	Q₈	—	4	2	no	—
464	Q₈	—	4	2	no	—
465	Q₈	—	4	2	no	—
466	Q₈	—	4	2	no	—
467	Q₈	—	4	2	no	—
468	D₄	—	2	4	no	—
469	D₄	—	2	4	no	—
470	D₄	—	4	16	no	—
471	D₄	—	4	2	no	—
472	D₄	—	4	2	no	—
473	C₂×C₄	—	2	2	no	—
474	C₂×C₄	—	2	1	no	—
475	C₂×C₄	—	2	1	no	—
476	C₂×C₄	—	2	2	no	—
477	C₂×C₄	—	2	2	no	—
478	C₂×C₄	—	2	2	no	—
479	C₂×C₄	—	2	2	no	—
480	C₂×C₄	—	2	2	no	—
481	C₂×C₄	—	2	2	no	—
482	C₂×C₄	—	2	4	no	—
483	C₂×C₄	—	2	2	no	—
484	C₂×C₄	—	2	2	no	—
485	C₂×C₄	—	4	16	no	—
486	C₂×C₄	—	4	2	no	—
487	C₂×C₄	—	4	2	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	4	no	—
493	C₂×C₄	#127×C₇₃	1	2	yes	—
494	C₂×C₄	#135×C₇₃	1	4	yes	complemented
495	C₂×C₄	C₂²×D₄×C₇₃	1	1	yes	characteristic
496	C₂×C₄	C₂²×D₄×C₇₃	1	1	yes	characteristic
497	C₂×C₄	C₂²×D₄×C₇₃	1	1	yes	characteristic
498	C₂×C₄	C₂²×D₄×C₇₃	1	1	yes	characteristic
499	C₂×C₄	H(5,𝔽₂)×C₇₃	1	1	yes	characteristic
500	C₂×C₄	H(5,𝔽₂)×C₇₃	1	1	yes	characteristic
501	C₈	—	2	2	no	—
502	C₈	—	2	2	no	—
503	C₈	—	2	2	no	—
504	C₈	#120×C₇₃	1	4	yes	—
505	C₂²	—	2	2	no	—
506	C₂²	—	2	2	no	—
507	C₂²	—	2	2	no	—
508	C₂²	—	4	2	no	—
509	C₂²	—	4	2	no	—
510	C₂²	—	4	8	no	—
511	C₂²	—	4	4	no	—
512	C₂²	—	8	4	no	—
513	C₂²	—	8	2	no	—
514	C₂²	—	8	2	no	—
515	C₂²	C₂×#127×C₇₃	1	1	yes	characteristic
516	C₂²	D₄²×C₇₃	1	1	yes	characteristic
517	C₂²	D₄²×C₇₃	1	1	yes	characteristic
518	C₂²	C₂×#135×C₇₃	1	2	yes	—
519	C₂²	#578×C₇₃	1	2	yes	—
520	C₄	—	2	4	no	—
521	C₄	—	2	2	no	—
522	C₄	—	4	2	no	—
523	C₄	—	4	4	no	—
524	C₄	—	8	2	no	—
525	C₄	—	8	2	no	—
526	C₄	C₂×#120×C₇₃	1	1	yes	characteristic
527	C₄	#535×C₇₃	1	1	yes	characteristic
528	C₄	D₄²×C₇₃	1	1	yes	characteristic
529	C₄	D₄²×C₇₃	1	1	yes	characteristic
530	C₂	—	4	2	no	—
531	C₂	—	8	4	no	—
532	C₂	C₇₃×#2433	1	1	yes	characteristic
533	C₂	C₇₃×#3147	1	1	yes	characteristic
534	C₂	C₇₃×#3156	1	1	yes	characteristic
535	C₂	C₇₃×#3283	1	2	yes	—
536	C₂	C₇₃×#3285	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₇₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₇₃
prime radical	C₂²×#135×C₇₃	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₇₃ ◁ C₄×C₂²⋊C₄×C₇₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×#495×C₇₃	C₂	semidirect
3. C₂×#494×C₇₃	C₂	semidirect
4. C₂×#467×C₇₃	C₂	semidirect
5. C₂×#452×C₇₃	C₂	semidirect
6. C₇₃×#2432	C₂	semidirect
7. C₇₃×#2015	C₂	semidirect
8. C₇₃×#2013	C₂	semidirect
9. C₇₃×#1970	C₂	semidirect
10. C₇₃×#1969	C₂	semidirect
11. C₈×C₂²⋊C₄×C₇₃	C₂	semidirect
225. C₂×C₄×C₇₃	#135	semidirect
261. #25778	C₇₃	direct (N × H)
270. C₂×#495	C₂×C₇₃	semidirect
271. C₂×#494	C₂×C₇₃	semidirect
272. C₂×#467	C₂×C₇₃	semidirect
273. C₂×#452	C₂×C₇₃	semidirect
274. #2432	C₂×C₇₃	semidirect
275. #2015	C₂×C₇₃	semidirect
276. #2013	C₂×C₇₃	semidirect
277. #1970	C₂×C₇₃	semidirect
278. #1969	C₂×C₇₃	semidirect
279. C₈×C₂²⋊C₄	C₂×C₇₃	semidirect
280. C₇₃	#25778	direct (N × H)
494. C₂×C₄	#135×C₇₃	semidirect

Maximal subgroups

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

subgroup	index
C₂²×#135×C₇₃	2
C₂×#495×C₇₃	2
C₂×#494×C₇₃	2
C₂×#467×C₇₃	2
C₂×#452×C₇₃	2
C₇₃×#2432	2
C₇₃×#2015	2
C₇₃×#2013	2
C₇₃×#1970	2
C₇₃×#1969	2
C₈×C₂²⋊C₄×C₇₃	2
#25778	73

Subgroups — C73×#25778 #32935182

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₃×#25778 #32935182