Subgroups — C₂₃×#60342 #19207968

Order 5888.

1702 conjugacy classes of subgroups.

The subgroup lattice has 1098 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃×#3482	C₂	1	1	yes	maximal, characteristic
2	C₂₃×#2995	C₂	1	2	yes	maximal, complemented
3	C₂₃×#2994	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂₃×#2993	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂₃×#2992	C₂	1	2	yes	maximal, complemented
6	C₂₃×#2990	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂₃×#2989	C₂	1	2	yes	maximal, complemented
8	C₂₃×#2989	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂₃×#2987	C₂	1	2	yes	maximal, complemented
10	C₂₃×#2985	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂₃×#2984	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂₃×#2983	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂₃×#2970	C₂	1	2	yes	maximal, complemented
14	C₂₃×#2970	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂₃×#2969	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂₃×#2968	C₂	1	2	yes	maximal, complemented
17	C₂₃×#2967	C₂	1	2	yes	maximal, complemented
18	C₂₃×#2966	C₂	1	1	yes	maximal, characteristic, complemented
19	C₂₃×#2965	C₂	1	1	yes	maximal, characteristic, complemented
20	Q₈×M₁₆×C₂₃	C₂	1	1	yes	maximal, characteristic, complemented
21	C₂₃×#2962	C₂	1	1	yes	maximal, characteristic, complemented
22	C₂₃×#2961	C₂	1	2	yes	maximal, complemented
23	C₂×C₂₃×#446	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂₃×#557	C₄	1	1	yes	characteristic
25	C₂₃×#556	C₄	1	2	yes	—
26	C₂₃×#556	C₄	1	1	yes	characteristic
27	C₂₃×#552	C₄	1	1	yes	characteristic
28	C₂₃×#552	C₄	1	2	yes	—
29	C₂₃×#552	C₄	1	1	yes	characteristic
30	C₂₃×#552	C₄	1	2	yes	—
31	D₄×Q₈×C₂₃	C₄	1	1	yes	characteristic
32	C₂₃×#548	C₄	1	1	yes	characteristic
33	C₂₃×#548	C₄	1	1	yes	characteristic
34	C₂₃×#547	C₄	1	1	yes	characteristic
35	C₂₃×#547	C₄	1	2	yes	—
36	C₂₃×#533	C₂²	1	2	yes	—
37	C₂₃×#533	C₂²	1	1	yes	characteristic
38	C₂₃×#529	C₂²	1	1	yes	characteristic
39	C₂₃×#529	C₂²	1	2	yes	—
40	C₂₃×#529	C₂²	1	2	yes	—
41	C₂₃×#529	C₂²	1	1	yes	characteristic
42	C₄×#41×C₂₃	C₂²	1	1	yes	characteristic
43	C₄×#41×C₂₃	C₂²	1	2	yes	—
44	C₄×#41×C₂₃	C₂²	1	1	yes	characteristic
45	C₂×C₄×Q₈×C₂₃	C₂²	1	1	yes	characteristic
46	C₂×C₄×Q₈×C₂₃	C₂²	1	1	yes	characteristic
47	C₂₃×#446	C₂²	1	2	yes	—
48	C₂₃×#446	C₂²	1	1	yes	characteristic
49	C₂₃×#446	C₂²	1	1	yes	characteristic
50	C₂₃×#446	C₂²	1	1	yes	characteristic
51	C₂₃×#446	C₂²	1	1	yes	characteristic
52	C₂₃×#446	C₂²	1	2	yes	—
53	C₂₃×#446	C₂²	1	1	yes	characteristic
54	C₂₃×#446	C₂²	1	2	yes	—
55	C₂₃×#446	C₂²	1	2	yes	—
56	C₂₃×#446	C₂²	1	2	yes	—
57	C₂₃×#446	C₂²	1	2	yes	—
58	C₂₃×#446	C₂²	1	2	yes	—
59	C₂₃×#446	C₂²	1	2	yes	—
60	C₂₃×#446	C₂²	1	1	yes	characteristic
61	C₂₃×#446	C₂²	1	2	yes	—
62	C₂₃×#446	C₂²	1	1	yes	characteristic
63	C₂₃×#446	C₂²	1	2	yes	—
64	C₂₃×#446	C₂²	1	1	yes	characteristic
65	C₂₃×#446	C₂²	1	1	yes	characteristic
66	C₂₃×#446	C₂²	1	2	yes	—
67	C₂₃×#446	C₂²	1	2	yes	—
68	C₂₃×#446	C₂²	1	1	yes	characteristic
69	C₂₃×#446	C₂²	1	2	yes	—
70	C₈×Q₈×C₂₃	C₂²	1	1	yes	characteristic
71	C₈×Q₈×C₂₃	C₂²	1	1	yes	characteristic
72	C₈×Q₈×C₂₃	C₂²	1	1	yes	characteristic
73	C₈×Q₈×C₂₃	C₂²	1	1	yes	characteristic
74	C₂₃×#436	C₂²	1	1	yes	characteristic
75	C₂₃×#436	C₂²	1	1	yes	characteristic
76	C₂₃×#436	C₂²	1	1	yes	characteristic
77	C₂₃×#436	C₂²	1	2	yes	—
78	C₂₃×#436	C₂²	1	1	yes	characteristic
79	C₂₃×#436	C₂²	1	2	yes	—
80	C₂₃×#435	C₂²	1	1	yes	characteristic
81	C₂₃×#435	C₂²	1	1	yes	characteristic
82	C₂₃×#435	C₂²	1	1	yes	characteristic
83	C₂₃×#435	C₂²	1	1	yes	characteristic
84	C₂₃×#435	C₂²	1	2	yes	—
85	C₂₃×#435	C₂²	1	2	yes	—
86	C₂₃×#435	C₂²	1	2	yes	—
87	C₂₃×#435	C₂²	1	2	yes	—
88	C₂₃×#435	C₂²	1	2	yes	—
89	C₂₃×#435	C₂²	1	2	yes	—
90	C₂₃×#435	C₂²	1	2	yes	—
91	C₂₃×#435	C₂²	1	2	yes	—
92	C₂₃×#435	C₂²	1	2	yes	—
93	C₂₃×#435	C₂²	1	2	yes	—
94	C₈×D₄×C₂₃	C₂²	1	2	yes	—
95	C₈×D₄×C₂₃	C₂²	1	1	yes	characteristic
96	C₈×D₄×C₂₃	C₂²	1	2	yes	—
97	C₈×D₄×C₂₃	C₂²	1	2	yes	—
98	C₈×D₄×C₂₃	C₂²	1	1	yes	characteristic
99	C₂₃×#433	C₂²	1	2	yes	—
100	C₂₃×#433	C₂²	1	2	yes	—
101	C₂₃×#433	C₂²	1	2	yes	—
102	C₂₃×#433	C₂²	1	2	yes	—
103	C₂₃×#433	C₂²	1	2	yes	—
104	C₂₃×#433	C₂²	1	2	yes	—
105	C₂₃×#432	C₂²	1	1	yes	characteristic
106	C₂₃×#432	C₂²	1	2	yes	—
107	C₂₃×#432	C₂²	1	2	yes	—
108	C₂₃×#432	C₂²	1	2	yes	—
109	C₂₃×#432	C₂²	1	1	yes	characteristic
110	C₂₃×#432	C₂²	1	2	yes	—
111	C₂₃×#432	C₂²	1	2	yes	—
112	C₂₃×#431	C₂²	1	1	yes	characteristic
113	C₂₃×#431	C₂²	1	1	yes	characteristic
114	C₂₃×#431	C₂²	1	1	yes	characteristic
115	C₂₃×#431	C₂²	1	2	yes	—
116	C₂₃×#431	C₂²	1	1	yes	characteristic
117	C₂₃×#424	C₂²	1	2	yes	—
118	C₂₃×#424	C₂²	1	2	yes	—
119	C₂₃×#424	C₂²	1	2	yes	—
120	C₂₃×#423	C₂²	1	2	yes	—
121	C₂₃×#423	C₂²	1	2	yes	—
122	C₂₃×#423	C₂²	1	1	yes	characteristic
123	C₂×C₂₃×C₄⋊C₈	C₂²	1	2	yes	—
124	C₂×C₂₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
125	C₂×C₂₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
126	C₂₃×#405	C₂²	1	2	yes	—
127	C₂₃×#405	C₂²	1	2	yes	—
128	C₂₃×#405	C₂²	1	2	yes	—
129	C₄×M₁₆×C₂₃	C₂²	1	1	yes	characteristic
130	C₄×M₁₆×C₂₃	C₂²	1	1	yes	characteristic
131	C₄×M₁₆×C₂₃	C₂²	1	2	yes	—
132	C₂×C₂₃×#97	C₂²	1	2	yes	—
133	C₂×C₂₃×#97	C₂²	1	2	yes	—
134	C₂×C₄×C₈×C₂₃	C₂²	1	1	yes	characteristic
135	C₂×#41×C₂₃	C₂×C₄	1	1	yes	characteristic
136	C₂×#41×C₂₃	C₂×C₄	1	2	yes	—
137	C₂×#41×C₂₃	C₂×C₄	1	1	yes	characteristic
138	C₂²×Q₈×C₂₃	C₂×C₄	1	1	yes	characteristic
139	C₂²×Q₈×C₂₃	C₂×C₄	1	1	yes	characteristic
140	C₂×M₁₆×C₂₃	C₂³	1	1	yes	characteristic
141	C₂×M₁₆×C₂₃	C₂³	1	1	yes	characteristic
142	C₂×M₁₆×C₂₃	C₂³	1	2	yes	—
143	C₂×M₁₆×C₂₃	C₂³	1	1	yes	characteristic
144	C₂×M₁₆×C₂₃	C₂³	1	1	yes	characteristic
145	C₂×M₁₆×C₂₃	C₂³	1	2	yes	—
146	C₂×M₁₆×C₂₃	C₂³	1	2	yes	—
147	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
148	C₂²×C₈×C₂₃	C₂³	1	2	yes	—
149	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
150	C₂²×C₈×C₂₃	C₂³	1	2	yes	—
151	C₂²×C₈×C₂₃	C₂³	1	2	yes	—
152	C₂²×C₈×C₂₃	C₂³	1	2	yes	—
153	C₂₃×C₄⋊Q₈	C₂×C₄	1	2	yes	—
154	C₂₃×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
155	C₂₃×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
156	C₂₃×C₄⋊Q₈	C₂×C₄	1	2	yes	—
157	C₂₃×#126	C₂×C₄	1	2	yes	—
158	C₂₃×#126	C₂×C₄	1	2	yes	—
159	C₂₃×#126	C₂×C₄	1	2	yes	—
160	C₂₃×#126	C₂×C₄	1	2	yes	—
161	C₂₃×#126	C₂×C₄	1	2	yes	—
162	C₂₃×#126	C₂×C₄	1	2	yes	—
163	C₂₃×#125	C₂×C₄	1	2	yes	—
164	C₂₃×#125	C₂×C₄	1	2	yes	—
165	C₂₃×#125	C₂×C₄	1	2	yes	—
166	C₂₃×#125	C₂×C₄	1	1	yes	characteristic
167	C₂₃×#125	C₂×C₄	1	2	yes	—
168	C₂₃×#125	C₂×C₄	1	2	yes	—
169	C₂₃×#125	C₂×C₄	1	1	yes	characteristic
170	C₂₃×#124	C₂×C₄	1	1	yes	characteristic
171	C₂₃×#124	C₂×C₄	1	1	yes	characteristic
172	C₂₃×#124	C₂×C₄	1	2	yes	—
173	C₂₃×#124	C₂×C₄	1	2	yes	—
174	C₂₃×#123	C₂×C₄	1	2	yes	—
175	C₂₃×#123	C₂×C₄	1	2	yes	—
176	C₂₃×#123	C₂×C₄	1	2	yes	—
177	C₂₃×#123	C₂×C₄	1	2	yes	—
178	C₂₃×#123	C₂×C₄	1	2	yes	—
179	C₂₃×#123	C₂×C₄	1	2	yes	—
180	C₂₃×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
181	C₂₃×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
182	C₂₃×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
183	C₂₃×C₂²⋊Q₈	C₂×C₄	1	1	yes	characteristic
184	C₂₃×C₂²⋊Q₈	C₂×C₄	1	1	yes	characteristic
185	C₂₃×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
186	C₂₃×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
187	C₂₃×C₂²⋊Q₈	C₂×C₄	1	1	yes	characteristic
188	C₂₃×C₂²⋊Q₈	C₂×C₄	1	1	yes	characteristic
189	C₂₃×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
190	C₂₃×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
191	C₂₃×#121	C₂×C₄	1	1	yes	characteristic
192	C₂₃×#121	C₂×C₄	1	1	yes	characteristic
193	C₂₃×#121	C₂×C₄	1	2	yes	—
194	C₂₃×#121	C₂×C₄	1	2	yes	—
195	C₄×Q₈×C₂₃	C₂×C₄	1	1	yes	characteristic
196	C₄×Q₈×C₂₃	C₂×C₄	1	1	yes	characteristic
197	C₄×Q₈×C₂₃	C₂×C₄	1	1	yes	characteristic
198	C₄×Q₈×C₂₃	C₂×C₄	1	1	yes	characteristic
199	C₄×Q₈×C₂₃	C₂×C₄	1	1	yes	characteristic
200	C₄×Q₈×C₂₃	C₂×C₄	1	2	yes	—
201	C₄×Q₈×C₂₃	C₂×C₄	1	2	yes	—
202	C₄×Q₈×C₂₃	C₂×C₄	1	1	yes	characteristic
203	C₄×Q₈×C₂₃	C₂×C₄	1	2	yes	—
204	C₄×Q₈×C₂₃	C₂³	1	1	yes	characteristic
205	C₄×Q₈×C₂₃	C₂³	1	1	yes	characteristic
206	C₄×Q₈×C₂₃	C₂³	1	1	yes	characteristic
207	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
208	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
209	C₄×Q₈×C₂₃	C₂³	1	1	yes	characteristic
210	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
211	C₄×D₄×C₂₃	C₂×C₄	1	1	yes	characteristic
212	C₄×D₄×C₂₃	C₂×C₄	1	2	yes	—
213	C₄×D₄×C₂₃	C₂×C₄	1	1	yes	characteristic
214	C₄×D₄×C₂₃	C₂×C₄	1	2	yes	—
215	C₄×D₄×C₂₃	C₂×C₄	1	1	yes	characteristic
216	C₄×D₄×C₂₃	C₂×C₄	1	1	yes	characteristic
217	C₄×D₄×C₂₃	C₂×C₄	1	2	yes	—
218	C₄×D₄×C₂₃	C₂×C₄	1	2	yes	—
219	C₄×D₄×C₂₃	C₂³	1	2	yes	—
220	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
221	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
222	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
223	C₄×D₄×C₂₃	C₂³	1	2	yes	—
224	C₄×D₄×C₂₃	C₂³	1	2	yes	—
225	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
226	C₂₃×#117	C₂×C₄	1	1	yes	characteristic
227	C₂₃×#117	C₂×C₄	1	2	yes	—
228	C₂₃×#117	C₂×C₄	1	1	yes	characteristic
229	C₂₃×#117	C₂×C₄	1	2	yes	—
230	C₂₃×#117	C₂×C₄	1	1	yes	characteristic
231	C₂₃×#117	C₂×C₄	1	2	yes	—
232	C₂₃×#117	C₂×C₄	1	1	yes	characteristic
233	C₂₃×#117	C₂×C₄	1	2	yes	—
234	C₂₃×#117	C₂³	1	2	yes	—
235	C₂₃×#117	C₂³	1	2	yes	—
236	C₂₃×#117	C₂³	1	2	yes	—
237	C₂×C₄⋊C₄×C₂₃	C₂×C₄	1	1	yes	characteristic
238	C₂×C₄⋊C₄×C₂₃	C₂×C₄	1	2	yes	—
239	C₂×C₄⋊C₄×C₂₃	C₂×C₄	1	1	yes	characteristic
240	C₂×C₄⋊C₄×C₂₃	C₂×C₄	1	2	yes	—
241	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
242	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
243	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
244	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
245	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
246	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
247	C₂₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
248	C₂₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
249	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
250	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
251	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
252	C₂₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
253	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
254	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
255	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
256	C₂₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
257	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
258	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
259	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
260	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
261	C₂₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
262	C₂₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
263	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
264	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
265	C₂₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
266	C₂₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
267	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
268	C₂₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
269	C₂₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
270	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
271	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
272	C₂₃×C₂²⋊C₈	C₂³	1	1	yes	characteristic
273	C₂₃×C₂²⋊C₈	C₂³	1	1	yes	characteristic
274	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
275	C₂₃×C₂²⋊C₈	C₂³	1	1	yes	characteristic
276	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
277	C₂₃×C₂²⋊C₈	C₂³	1	1	yes	characteristic
278	C₂₃×C₂²⋊C₈	C₂³	1	1	yes	characteristic
279	C₂₃×C₂²⋊C₈	C₂³	1	1	yes	characteristic
280	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
281	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
282	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
283	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
284	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
285	C₂₃×#97	C₂³	1	2	yes	—
286	C₂₃×#97	C₂³	1	1	yes	characteristic
287	C₂₃×#97	C₂³	1	2	yes	—
288	C₂₃×#97	C₂³	1	2	yes	—
289	C₂₃×#97	C₂³	1	2	yes	—
290	C₂₃×#97	C₂³	1	2	yes	—
291	C₂₃×#97	C₂³	1	2	yes	—
292	C₂₃×#97	C₂³	1	1	yes	characteristic
293	C₂₃×#97	C₂³	1	1	yes	characteristic
294	C₂₃×#97	C₂³	1	2	yes	—
295	C₂₃×#97	C₂³	1	1	yes	characteristic
296	C₂₃×#97	C₂³	1	2	yes	—
297	C₂₃×#97	C₂³	1	2	yes	—
298	C₂₃×#97	C₂³	1	2	yes	—
299	C₄×C₈×C₂₃	C₂³	1	1	yes	characteristic
300	C₄×C₈×C₂₃	C₂³	1	1	yes	characteristic
301	C₄×C₈×C₂₃	C₂³	1	1	yes	characteristic
302	C₄×C₈×C₂₃	C₂³	1	1	yes	characteristic
303	C₄×C₈×C₂₃	C₂³	1	2	yes	—
304	C₄×C₈×C₂₃	C₂³	1	1	yes	characteristic
305	C₄×C₈×C₂₃	C₂³	1	1	yes	characteristic
306	C₄×C₈×C₂₃	C₂³	1	2	yes	—
307	C₄×C₈×C₂₃	C₂³	1	2	yes	—
308	C₄×C₈×C₂₃	C₂³	1	2	yes	—
309	C₄×C₈×C₂₃	C₂³	1	2	yes	—
310	#41×C₂₃	—	4	2	no	—
311	#41×C₂₃	—	4	4	no	—
312	#41×C₂₃	—	4	2	no	—
313	C₂×Q₈×C₂₃	—	4	2	no	—
314	C₂×Q₈×C₂₃	—	4	2	no	—
315	C₂×Q₈×C₂₃	C₂²×C₄	1	1	yes	characteristic
316	C₂×Q₈×C₂₃	C₂²×C₄	1	1	yes	characteristic
317	C₂×Q₈×C₂₃	C₂²×C₄	1	1	yes	characteristic
318	C₂×Q₈×C₂₃	C₂²×C₄	1	2	yes	—
319	C₂×Q₈×C₂₃	C₂²×C₄	1	2	yes	—
320	C₂×Q₈×C₂₃	C₂²×C₄	1	1	yes	characteristic
321	C₂×Q₈×C₂₃	C₂²×C₄	1	2	yes	—
322	C₂×D₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
323	C₂×D₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
324	C₂×D₄×C₂₃	C₂²×C₄	1	2	yes	—
325	C₂×D₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
326	C₂×D₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
327	C₂×D₄×C₂₃	C₂²×C₄	1	2	yes	—
328	C₂×D₄×C₂₃	C₂²×C₄	1	2	yes	—
329	C₂²×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
330	C₂²×C₄×C₂₃	C₂²×C₄	1	2	yes	—
331	C₂²×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
332	C₂²×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
333	C₂²×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
334	C₂²×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
335	C₂²×C₄×C₂₃	C₂²×C₄	1	2	yes	—
336	C₂²×C₄×C₂₃	C₂²×C₄	1	2	yes	—
337	C₂²×C₄×C₂₃	C₂²×C₄	1	2	yes	—
338	C₂²×C₄×C₂₃	C₂²×C₄	1	2	yes	—
339	C₂²×C₄×C₂₃	C₂²×C₄	1	2	yes	—
340	C₂²×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
341	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
342	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
343	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
344	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
345	M₁₆×C₂₃	—	2	2	no	—
346	M₁₆×C₂₃	—	2	2	no	—
347	M₁₆×C₂₃	—	4	1	no	—
348	M₁₆×C₂₃	—	4	2	no	—
349	M₁₆×C₂₃	—	4	2	no	—
350	M₁₆×C₂₃	—	4	2	no	—
351	M₁₆×C₂₃	—	4	1	no	—
352	C₂×C₈×C₂₃	—	2	2	no	—
353	C₂×C₈×C₂₃	—	2	4	no	—
354	C₂×C₈×C₂₃	—	4	2	no	—
355	C₂×C₈×C₂₃	—	4	2	no	—
356	C₂×C₈×C₂₃	—	4	2	no	—
357	C₂×C₈×C₂₃	—	4	1	no	—
358	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
359	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
360	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
361	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
362	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
363	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
364	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
365	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
366	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
367	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
368	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
369	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
370	C₄⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
371	C₄⋊C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
372	C₄⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
373	C₄⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
374	C₄⋊C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
375	C₄⋊C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
376	C₄⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
377	C₄⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
378	C₄⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
379	C₄⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
380	C₄⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
381	C₄⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
382	C₄⋊C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
383	C₄⋊C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
384	C₄⋊C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
385	C₄⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
386	C₄⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
387	C₄⋊C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
388	C₄⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
389	C₄⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
390	C₄⋊C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
391	C₄⋊C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
392	C₄⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
393	C₄⋊C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
394	C₄⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
395	C₄⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
396	C₄⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
397	C₄⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
398	C₄⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
399	C₄⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
400	C₄⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
401	C₂²⋊C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
402	C₂²⋊C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
403	C₂²⋊C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
404	C₂²⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
405	C₂²⋊C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
406	C₂²⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
407	C₂²⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
408	C₂²⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
409	C₂²⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
410	C₂²⋊C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
411	C₂²⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
412	C₂²⋊C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
413	C₂²⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
414	C₂²⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
415	C₂²⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
416	C₂²⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
417	C₂²⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
418	C₂²⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
419	C₂²⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
420	C₄²×C₂₃	C₂²×C₄	1	2	yes	—
421	C₄²×C₂₃	C₂²×C₄	1	1	yes	characteristic
422	C₄²×C₂₃	C₂²×C₄	1	1	yes	characteristic
423	C₄²×C₂₃	C₂²×C₄	1	2	yes	—
424	C₄²×C₂₃	C₂²×C₄	1	1	yes	characteristic
425	C₄²×C₂₃	C₂²×C₄	1	2	yes	—
426	C₄²×C₂₃	C₂²×C₄	1	2	yes	—
427	C₄²×C₂₃	C₂²×C₄	1	1	yes	characteristic
428	C₄²×C₂₃	C₂²×C₄	1	2	yes	—
429	C₄²×C₂₃	C₂²×C₄	1	2	yes	—
430	C₄²×C₂₃	C₂²×C₄	1	1	yes	characteristic
431	C₄²×C₂₃	C₂²×C₄	1	1	yes	characteristic
432	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
433	C₄²×C₂₃	C₂⁴	1	2	yes	—
434	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
435	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
436	C₄²×C₂₃	C₂⁴	1	2	yes	—
437	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
438	C₄²×C₂₃	C₂⁴	1	2	yes	—
439	#60342	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
440	C₂³×C₂₃	C₂³×C₄	1	1	yes	characteristic
441	C₂³×C₂₃	C₂³×C₄	1	2	yes	—
442	C₂³×C₂₃	C₂³×C₄	1	1	yes	characteristic
443	C₂³×C₂₃	C₂³×C₄	1	1	yes	characteristic
444	Q₈×C₂₃	—	2	2	no	—
445	Q₈×C₂₃	—	2	2	no	—
446	Q₈×C₂₃	—	2	2	no	—
447	Q₈×C₂₃	—	4	2	no	—
448	Q₈×C₂₃	—	4	2	no	—
449	Q₈×C₂₃	—	4	1	no	—
450	Q₈×C₂₃	—	4	2	no	—
451	D₄×C₂₃	—	2	2	no	—
452	D₄×C₂₃	—	2	4	no	—
453	D₄×C₂₃	—	2	2	no	—
454	D₄×C₂₃	—	2	2	no	—
455	D₄×C₂₃	—	4	1	no	—
456	D₄×C₂₃	—	4	2	no	—
457	D₄×C₂₃	—	4	2	no	—
458	C₂×C₄×C₂₃	—	2	2	no	—
459	C₂×C₄×C₂₃	—	2	4	no	—
460	C₂×C₄×C₂₃	—	2	2	no	—
461	C₂×C₄×C₂₃	—	2	2	no	—
462	C₂×C₄×C₂₃	—	2	2	no	—
463	C₂×C₄×C₂₃	—	2	1	no	—
464	C₂×C₄×C₂₃	—	2	2	no	—
465	C₂×C₄×C₂₃	—	2	1	no	—
466	C₂×C₄×C₂₃	—	2	1	no	—
467	C₂×C₄×C₂₃	—	2	1	no	—
468	C₂×C₄×C₂₃	—	2	1	no	—
469	C₂×C₄×C₂₃	—	2	2	no	—
470	C₂×C₄×C₂₃	—	2	1	no	—
471	C₂×C₄×C₂₃	—	4	2	no	—
472	C₂×C₄×C₂₃	—	4	2	no	—
473	C₂×C₄×C₂₃	—	4	2	no	—
474	C₂×C₄×C₂₃	—	4	1	no	—
475	C₂×C₄×C₂₃	—	4	2	no	—
476	C₂×C₄×C₂₃	—	4	1	no	—
477	C₂×C₄×C₂₃	—	4	2	no	—
478	C₂×C₄×C₂₃	C₂³×C₄	1	1	yes	characteristic
479	C₂×C₄×C₂₃	C₂³×C₄	1	1	yes	characteristic
480	C₂×C₄×C₂₃	C₂³×C₄	1	1	yes	characteristic
481	C₂×C₄×C₂₃	C₂³×C₄	1	1	yes	characteristic
482	C₂×C₄×C₂₃	C₂³×C₄	1	2	yes	—
483	C₂×C₄×C₂₃	C₂³×C₄	1	1	yes	characteristic
484	C₂×C₄×C₂₃	C₂³×C₄	1	2	yes	—
485	C₂×C₄×C₂₃	C₂³×C₄	1	2	yes	—
486	C₂×C₄×C₂₃	C₂³×C₄	1	1	yes	characteristic
487	C₂×C₄×C₂₃	C₂³×C₄	1	1	yes	characteristic
488	C₂×C₄×C₂₃	C₂³×C₄	1	1	yes	characteristic
489	C₂×C₄×C₂₃	C₂³×C₄	1	2	yes	—
490	C₂×C₄×C₂₃	C₂³×C₄	1	2	yes	—
491	C₂×C₄×C₂₃	C₂³×C₄	1	2	yes	—
492	C₂×C₄×C₂₃	C₂³×C₄	1	1	yes	characteristic
493	C₂×C₄×C₂₃	C₂³×C₄	1	2	yes	—
494	C₂×C₄×C₂₃	C₂³×C₄	1	1	yes	characteristic
495	C₂×C₄×C₂₃	C₂³×C₄	1	1	yes	characteristic
496	C₂×C₄×C₂₃	C₂⁵	1	1	yes	characteristic
497	C₈×C₂₃	—	2	1	no	—
498	C₈×C₂₃	—	2	2	no	—
499	C₈×C₂₃	—	2	1	no	—
500	C₈×C₂₃	—	2	1	no	—
501	C₈×C₂₃	—	2	2	no	—
502	C₈×C₂₃	—	2	2	no	—
503	C₈×C₂₃	—	2	1	no	—
504	C₈×C₂₃	—	2	2	no	—
505	C₈×C₂₃	—	2	1	no	—
506	C₈×C₂₃	—	2	1	no	—
507	C₈×C₂₃	—	2	1	no	—
508	C₈×C₂₃	2₋¹⁺⁴	1	2	yes	—
509	#3482	C₂×C₂₃	1	1	yes	characteristic
510	#2995	C₂×C₂₃	1	2	yes	complemented
511	#2994	C₂×C₂₃	1	1	yes	characteristic, complemented
512	#2993	C₂×C₂₃	1	1	yes	characteristic, complemented
513	#2992	C₂×C₂₃	1	2	yes	complemented
514	#2990	C₂×C₂₃	1	1	yes	characteristic, complemented
515	#2989	C₂×C₂₃	1	2	yes	complemented
516	#2989	C₂×C₂₃	1	1	yes	characteristic, complemented
517	#2987	C₂×C₂₃	1	2	yes	complemented
518	#2985	C₂×C₂₃	1	1	yes	characteristic, complemented
519	#2984	C₂×C₂₃	1	1	yes	characteristic, complemented
520	#2983	C₂×C₂₃	1	1	yes	characteristic, complemented
521	#2970	C₂×C₂₃	1	2	yes	complemented
522	#2970	C₂×C₂₃	1	1	yes	characteristic, complemented
523	#2969	C₂×C₂₃	1	1	yes	characteristic, complemented
524	#2968	C₂×C₂₃	1	2	yes	complemented
525	#2967	C₂×C₂₃	1	2	yes	complemented
526	#2966	C₂×C₂₃	1	1	yes	characteristic, complemented
527	#2965	C₂×C₂₃	1	1	yes	characteristic, complemented
528	Q₈×M₁₆	C₂×C₂₃	1	1	yes	characteristic, complemented
529	#2962	C₂×C₂₃	1	1	yes	characteristic, complemented
530	#2961	C₂×C₂₃	1	2	yes	complemented
531	C₂×#446	C₂×C₂₃	1	1	yes	characteristic, complemented
532	C₂²×C₂₃	—	2	1	no	—
533	C₂²×C₂₃	—	2	1	no	—
534	C₂²×C₂₃	—	2	2	no	—
535	C₂²×C₂₃	—	2	1	no	—
536	C₂²×C₂₃	—	2	1	no	—
537	C₂²×C₂₃	—	2	1	no	—
538	C₂²×C₂₃	—	2	1	no	—
539	C₂²×C₂₃	—	2	1	no	—
540	C₂²×C₂₃	—	2	1	no	—
541	C₂²×C₂₃	—	2	2	no	—
542	C₂²×C₂₃	—	2	2	no	—
543	C₂²×C₂₃	#568	1	2	yes	—
544	C₂²×C₂₃	C₂⁴×C₄	1	1	yes	characteristic
545	C₄×C₂₃	—	2	1	no	—
546	C₄×C₂₃	—	2	2	no	—
547	C₄×C₂₃	—	2	1	no	—
548	C₄×C₂₃	—	2	1	no	—
549	C₄×C₂₃	—	2	1	no	—
550	C₄×C₂₃	—	2	2	no	—
551	C₄×C₂₃	—	2	1	no	—
552	C₄×C₂₃	—	2	1	no	—
553	C₄×C₂₃	—	2	2	no	—
554	C₄×C₂₃	—	2	1	no	—
555	C₄×C₂₃	—	2	1	no	—
556	C₄×C₂₃	—	2	1	no	—
557	C₄×C₂₃	—	2	2	no	—
558	C₄×C₂₃	—	2	1	no	—
559	C₄×C₂₃	—	2	2	no	—
560	C₄×C₂₃	—	2	2	no	—
561	C₄×C₂₃	—	2	2	no	—
562	C₄×C₂₃	#568	1	2	yes	—
563	C₄×C₂₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
564	C₄×C₂₃	#585	1	1	yes	characteristic
565	#557	C₄×C₂₃	1	1	yes	characteristic
566	#556	C₄×C₂₃	1	2	yes	—
567	#556	C₄×C₂₃	1	1	yes	characteristic
568	#552	C₄×C₂₃	1	1	yes	characteristic
569	#552	C₄×C₂₃	1	2	yes	—
570	#552	C₄×C₂₃	1	1	yes	characteristic
571	#552	C₄×C₂₃	1	2	yes	—
572	D₄×Q₈	C₄×C₂₃	1	1	yes	characteristic
573	#548	C₄×C₂₃	1	1	yes	characteristic
574	#548	C₄×C₂₃	1	1	yes	characteristic
575	#547	C₄×C₂₃	1	1	yes	characteristic
576	#547	C₄×C₂₃	1	2	yes	—
577	#533	C₂²×C₂₃	1	2	yes	—
578	#533	C₂²×C₂₃	1	1	yes	characteristic
579	#529	C₂²×C₂₃	1	1	yes	characteristic
580	#529	C₂²×C₂₃	1	2	yes	—
581	#529	C₂²×C₂₃	1	2	yes	—
582	#529	C₂²×C₂₃	1	1	yes	characteristic
583	C₄×#41	C₂²×C₂₃	1	1	yes	characteristic
584	C₄×#41	C₂²×C₂₃	1	2	yes	—
585	C₄×#41	C₂²×C₂₃	1	1	yes	characteristic
586	C₂×C₄×Q₈	C₂²×C₂₃	1	1	yes	characteristic
587	C₂×C₄×Q₈	C₂²×C₂₃	1	1	yes	characteristic
588	#446	C₂²×C₂₃	1	2	yes	—
589	#446	C₂²×C₂₃	1	1	yes	characteristic
590	#446	C₂²×C₂₃	1	1	yes	characteristic
591	#446	C₂²×C₂₃	1	1	yes	characteristic
592	#446	C₂²×C₂₃	1	1	yes	characteristic
593	#446	C₂²×C₂₃	1	2	yes	—
594	#446	C₂²×C₂₃	1	1	yes	characteristic
595	#446	C₂²×C₂₃	1	2	yes	—
596	#446	C₂²×C₂₃	1	2	yes	—
597	#446	C₂²×C₂₃	1	2	yes	—
598	#446	C₂²×C₂₃	1	2	yes	—
599	#446	C₂²×C₂₃	1	2	yes	—
600	#446	C₂²×C₂₃	1	2	yes	—
601	#446	C₂²×C₂₃	1	1	yes	characteristic
602	#446	C₂²×C₂₃	1	2	yes	—
603	#446	C₂²×C₂₃	1	1	yes	characteristic
604	#446	C₂²×C₂₃	1	2	yes	—
605	#446	C₂²×C₂₃	1	1	yes	characteristic
606	#446	C₂²×C₂₃	1	1	yes	characteristic
607	#446	C₂²×C₂₃	1	2	yes	—
608	#446	C₂²×C₂₃	1	2	yes	—
609	#446	C₂²×C₂₃	1	1	yes	characteristic
610	#446	C₂²×C₂₃	1	2	yes	—
611	C₈×Q₈	C₂²×C₂₃	1	1	yes	characteristic
612	C₈×Q₈	C₂²×C₂₃	1	1	yes	characteristic
613	C₈×Q₈	C₂²×C₂₃	1	1	yes	characteristic
614	C₈×Q₈	C₂²×C₂₃	1	1	yes	characteristic
615	#436	C₂²×C₂₃	1	1	yes	characteristic
616	#436	C₂²×C₂₃	1	1	yes	characteristic
617	#436	C₂²×C₂₃	1	1	yes	characteristic
618	#436	C₂²×C₂₃	1	2	yes	—
619	#436	C₂²×C₂₃	1	1	yes	characteristic
620	#436	C₂²×C₂₃	1	2	yes	—
621	#435	C₂²×C₂₃	1	1	yes	characteristic
622	#435	C₂²×C₂₃	1	1	yes	characteristic
623	#435	C₂²×C₂₃	1	1	yes	characteristic
624	#435	C₂²×C₂₃	1	1	yes	characteristic
625	#435	C₂²×C₂₃	1	2	yes	—
626	#435	C₂²×C₂₃	1	2	yes	—
627	#435	C₂²×C₂₃	1	2	yes	—
628	#435	C₂²×C₂₃	1	2	yes	—
629	#435	C₂²×C₂₃	1	2	yes	—
630	#435	C₂²×C₂₃	1	2	yes	—
631	#435	C₂²×C₂₃	1	2	yes	—
632	#435	C₂²×C₂₃	1	2	yes	—
633	#435	C₂²×C₂₃	1	2	yes	—
634	#435	C₂²×C₂₃	1	2	yes	—
635	C₈×D₄	C₂²×C₂₃	1	2	yes	—
636	C₈×D₄	C₂²×C₂₃	1	1	yes	characteristic
637	C₈×D₄	C₂²×C₂₃	1	2	yes	—
638	C₈×D₄	C₂²×C₂₃	1	2	yes	—
639	C₈×D₄	C₂²×C₂₃	1	1	yes	characteristic
640	#433	C₂²×C₂₃	1	2	yes	—
641	#433	C₂²×C₂₃	1	2	yes	—
642	#433	C₂²×C₂₃	1	2	yes	—
643	#433	C₂²×C₂₃	1	2	yes	—
644	#433	C₂²×C₂₃	1	2	yes	—
645	#433	C₂²×C₂₃	1	2	yes	—
646	#432	C₂²×C₂₃	1	1	yes	characteristic
647	#432	C₂²×C₂₃	1	2	yes	—
648	#432	C₂²×C₂₃	1	2	yes	—
649	#432	C₂²×C₂₃	1	2	yes	—
650	#432	C₂²×C₂₃	1	1	yes	characteristic
651	#432	C₂²×C₂₃	1	2	yes	—
652	#432	C₂²×C₂₃	1	2	yes	—
653	#431	C₂²×C₂₃	1	1	yes	characteristic
654	#431	C₂²×C₂₃	1	1	yes	characteristic
655	#431	C₂²×C₂₃	1	1	yes	characteristic
656	#431	C₂²×C₂₃	1	2	yes	—
657	#431	C₂²×C₂₃	1	1	yes	characteristic
658	#424	C₂²×C₂₃	1	2	yes	—
659	#424	C₂²×C₂₃	1	2	yes	—
660	#424	C₂²×C₂₃	1	2	yes	—
661	#423	C₂²×C₂₃	1	2	yes	—
662	#423	C₂²×C₂₃	1	2	yes	—
663	#423	C₂²×C₂₃	1	1	yes	characteristic
664	C₂×C₄⋊C₈	C₂²×C₂₃	1	2	yes	—
665	C₂×C₄⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
666	C₂×C₄⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
667	#405	C₂²×C₂₃	1	2	yes	—
668	#405	C₂²×C₂₃	1	2	yes	—
669	#405	C₂²×C₂₃	1	2	yes	—
670	C₄×M₁₆	C₂²×C₂₃	1	1	yes	characteristic
671	C₄×M₁₆	C₂²×C₂₃	1	1	yes	characteristic
672	C₄×M₁₆	C₂²×C₂₃	1	2	yes	—
673	C₂×#97	C₂²×C₂₃	1	2	yes	—
674	C₂×#97	C₂²×C₂₃	1	2	yes	—
675	C₂×C₄×C₈	C₂²×C₂₃	1	1	yes	characteristic
676	C₂×C₂₃	—	2	2	no	—
677	C₂×C₂₃	—	4	1	no	—
678	C₂×C₂₃	—	4	1	no	—
679	C₂×C₂₃	—	4	2	no	—
680	C₂×C₂₃	C₄×2₋¹⁺⁴	1	1	yes	characteristic
681	C₂×C₂₃	C₂×#568	1	1	yes	characteristic
682	C₂×C₂₃	C₂×#568	1	1	yes	characteristic
683	C₂×#41	C₂×C₄×C₂₃	1	1	yes	characteristic
684	C₂×#41	C₂×C₄×C₂₃	1	2	yes	—
685	C₂×#41	C₂×C₄×C₂₃	1	1	yes	characteristic
686	C₂²×Q₈	C₂×C₄×C₂₃	1	1	yes	characteristic
687	C₂²×Q₈	C₂×C₄×C₂₃	1	1	yes	characteristic
688	C₂×M₁₆	C₂³×C₂₃	1	1	yes	characteristic
689	C₂×M₁₆	C₂³×C₂₃	1	1	yes	characteristic
690	C₂×M₁₆	C₂³×C₂₃	1	2	yes	—
691	C₂×M₁₆	C₂³×C₂₃	1	1	yes	characteristic
692	C₂×M₁₆	C₂³×C₂₃	1	1	yes	characteristic
693	C₂×M₁₆	C₂³×C₂₃	1	2	yes	—
694	C₂×M₁₆	C₂³×C₂₃	1	2	yes	—
695	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
696	C₂²×C₈	C₂³×C₂₃	1	2	yes	—
697	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
698	C₂²×C₈	C₂³×C₂₃	1	2	yes	—
699	C₂²×C₈	C₂³×C₂₃	1	2	yes	—
700	C₂²×C₈	C₂³×C₂₃	1	2	yes	—
701	C₄⋊Q₈	C₂×C₄×C₂₃	1	2	yes	—
702	C₄⋊Q₈	C₂×C₄×C₂₃	1	1	yes	characteristic
703	C₄⋊Q₈	C₂×C₄×C₂₃	1	1	yes	characteristic
704	C₄⋊Q₈	C₂×C₄×C₂₃	1	2	yes	—
705	#126	C₂×C₄×C₂₃	1	2	yes	—
706	#126	C₂×C₄×C₂₃	1	2	yes	—
707	#126	C₂×C₄×C₂₃	1	2	yes	—
708	#126	C₂×C₄×C₂₃	1	2	yes	—
709	#126	C₂×C₄×C₂₃	1	2	yes	—
710	#126	C₂×C₄×C₂₃	1	2	yes	—
711	#125	C₂×C₄×C₂₃	1	1	yes	characteristic
712	#125	C₂×C₄×C₂₃	1	2	yes	—
713	#125	C₂×C₄×C₂₃	1	2	yes	—
714	#125	C₂×C₄×C₂₃	1	1	yes	characteristic
715	#125	C₂×C₄×C₂₃	1	2	yes	—
716	#125	C₂×C₄×C₂₃	1	2	yes	—
717	#125	C₂×C₄×C₂₃	1	2	yes	—
718	#124	C₂×C₄×C₂₃	1	1	yes	characteristic
719	#124	C₂×C₄×C₂₃	1	1	yes	characteristic
720	#124	C₂×C₄×C₂₃	1	2	yes	—
721	#124	C₂×C₄×C₂₃	1	2	yes	—
722	#123	C₂×C₄×C₂₃	1	2	yes	—
723	#123	C₂×C₄×C₂₃	1	2	yes	—
724	#123	C₂×C₄×C₂₃	1	2	yes	—
725	#123	C₂×C₄×C₂₃	1	2	yes	—
726	#123	C₂×C₄×C₂₃	1	2	yes	—
727	#123	C₂×C₄×C₂₃	1	2	yes	—
728	C₂²⋊Q₈	C₂×C₄×C₂₃	1	1	yes	characteristic
729	C₂²⋊Q₈	C₂×C₄×C₂₃	1	1	yes	characteristic
730	C₂²⋊Q₈	C₂×C₄×C₂₃	1	2	yes	—
731	C₂²⋊Q₈	C₂×C₄×C₂₃	1	2	yes	—
732	C₂²⋊Q₈	C₂×C₄×C₂₃	1	2	yes	—
733	C₂²⋊Q₈	C₂×C₄×C₂₃	1	2	yes	—
734	C₂²⋊Q₈	C₂×C₄×C₂₃	1	2	yes	—
735	C₂²⋊Q₈	C₂×C₄×C₂₃	1	1	yes	characteristic
736	C₂²⋊Q₈	C₂×C₄×C₂₃	1	1	yes	characteristic
737	C₂²⋊Q₈	C₂×C₄×C₂₃	1	2	yes	—
738	C₂²⋊Q₈	C₂×C₄×C₂₃	1	2	yes	—
739	#121	C₂×C₄×C₂₃	1	1	yes	characteristic
740	#121	C₂×C₄×C₂₃	1	1	yes	characteristic
741	#121	C₂×C₄×C₂₃	1	2	yes	—
742	#121	C₂×C₄×C₂₃	1	2	yes	—
743	C₄×Q₈	C₂×C₄×C₂₃	1	1	yes	characteristic
744	C₄×Q₈	C₂×C₄×C₂₃	1	1	yes	characteristic
745	C₄×Q₈	C₂×C₄×C₂₃	1	1	yes	characteristic
746	C₄×Q₈	C₂×C₄×C₂₃	1	1	yes	characteristic
747	C₄×Q₈	C₂×C₄×C₂₃	1	2	yes	—
748	C₄×Q₈	C₂×C₄×C₂₃	1	2	yes	—
749	C₄×Q₈	C₂×C₄×C₂₃	1	1	yes	characteristic
750	C₄×Q₈	C₂×C₄×C₂₃	1	1	yes	characteristic
751	C₄×Q₈	C₂×C₄×C₂₃	1	2	yes	—
752	C₄×Q₈	C₂³×C₂₃	1	1	yes	characteristic
753	C₄×Q₈	C₂³×C₂₃	1	1	yes	characteristic
754	C₄×Q₈	C₂³×C₂₃	1	1	yes	characteristic
755	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
756	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
757	C₄×Q₈	C₂³×C₂₃	1	1	yes	characteristic
758	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
759	C₄×D₄	C₂×C₄×C₂₃	1	1	yes	characteristic
760	C₄×D₄	C₂×C₄×C₂₃	1	2	yes	—
761	C₄×D₄	C₂×C₄×C₂₃	1	1	yes	characteristic
762	C₄×D₄	C₂×C₄×C₂₃	1	2	yes	—
763	C₄×D₄	C₂×C₄×C₂₃	1	1	yes	characteristic
764	C₄×D₄	C₂×C₄×C₂₃	1	1	yes	characteristic
765	C₄×D₄	C₂×C₄×C₂₃	1	2	yes	—
766	C₄×D₄	C₂×C₄×C₂₃	1	2	yes	—
767	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
768	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
769	C₄×D₄	C₂³×C₂₃	1	2	yes	—
770	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
771	C₄×D₄	C₂³×C₂₃	1	2	yes	—
772	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
773	C₄×D₄	C₂³×C₂₃	1	2	yes	—
774	#117	C₂×C₄×C₂₃	1	1	yes	characteristic
775	#117	C₂×C₄×C₂₃	1	2	yes	—
776	#117	C₂×C₄×C₂₃	1	1	yes	characteristic
777	#117	C₂×C₄×C₂₃	1	2	yes	—
778	#117	C₂×C₄×C₂₃	1	1	yes	characteristic
779	#117	C₂×C₄×C₂₃	1	2	yes	—
780	#117	C₂×C₄×C₂₃	1	1	yes	characteristic
781	#117	C₂×C₄×C₂₃	1	2	yes	—
782	#117	C₂³×C₂₃	1	2	yes	—
783	#117	C₂³×C₂₃	1	2	yes	—
784	#117	C₂³×C₂₃	1	2	yes	—
785	C₂×C₄⋊C₄	C₂×C₄×C₂₃	1	1	yes	characteristic
786	C₂×C₄⋊C₄	C₂×C₄×C₂₃	1	2	yes	—
787	C₂×C₄⋊C₄	C₂×C₄×C₂₃	1	1	yes	characteristic
788	C₂×C₄⋊C₄	C₂×C₄×C₂₃	1	2	yes	—
789	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
790	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
791	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
792	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
793	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
794	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
795	C₄⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
796	C₄⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
797	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
798	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
799	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
800	C₄⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
801	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
802	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
803	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
804	C₄⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
805	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
806	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
807	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
808	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
809	C₄⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
810	C₄⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
811	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
812	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
813	C₄⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
814	C₄⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
815	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
816	C₄⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
817	C₄⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
818	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
819	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
820	C₂²⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
821	C₂²⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
822	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
823	C₂²⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
824	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
825	C₂²⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
826	C₂²⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
827	C₂²⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
828	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
829	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
830	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
831	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
832	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
833	#97	C₂³×C₂₃	1	2	yes	—
834	#97	C₂³×C₂₃	1	1	yes	characteristic
835	#97	C₂³×C₂₃	1	2	yes	—
836	#97	C₂³×C₂₃	1	2	yes	—
837	#97	C₂³×C₂₃	1	2	yes	—
838	#97	C₂³×C₂₃	1	2	yes	—
839	#97	C₂³×C₂₃	1	2	yes	—
840	#97	C₂³×C₂₃	1	1	yes	characteristic
841	#97	C₂³×C₂₃	1	1	yes	characteristic
842	#97	C₂³×C₂₃	1	2	yes	—
843	#97	C₂³×C₂₃	1	1	yes	characteristic
844	#97	C₂³×C₂₃	1	2	yes	—
845	#97	C₂³×C₂₃	1	2	yes	—
846	#97	C₂³×C₂₃	1	2	yes	—
847	C₄×C₈	C₂³×C₂₃	1	1	yes	characteristic
848	C₄×C₈	C₂³×C₂₃	1	1	yes	characteristic
849	C₄×C₈	C₂³×C₂₃	1	1	yes	characteristic
850	C₄×C₈	C₂³×C₂₃	1	1	yes	characteristic
851	C₄×C₈	C₂³×C₂₃	1	2	yes	—
852	C₄×C₈	C₂³×C₂₃	1	1	yes	characteristic
853	C₄×C₈	C₂³×C₂₃	1	1	yes	characteristic
854	C₄×C₈	C₂³×C₂₃	1	2	yes	—
855	C₄×C₈	C₂³×C₂₃	1	2	yes	—
856	C₄×C₈	C₂³×C₂₃	1	2	yes	—
857	C₄×C₈	C₂³×C₂₃	1	2	yes	—
858	C₂₃	#60342	1	1	yes	characteristic, direct product factor, Sylow
859	#41	—	4	2	no	—
860	#41	—	4	4	no	—
861	#41	—	4	2	no	—
862	C₂×Q₈	—	4	2	no	—
863	C₂×Q₈	—	4	2	no	—
864	C₂×Q₈	C₂²×C₄×C₂₃	1	1	yes	characteristic
865	C₂×Q₈	C₂²×C₄×C₂₃	1	1	yes	characteristic
866	C₂×Q₈	C₂²×C₄×C₂₃	1	1	yes	characteristic
867	C₂×Q₈	C₂²×C₄×C₂₃	1	2	yes	—
868	C₂×Q₈	C₂²×C₄×C₂₃	1	2	yes	—
869	C₂×Q₈	C₂²×C₄×C₂₃	1	1	yes	characteristic
870	C₂×Q₈	C₂²×C₄×C₂₃	1	2	yes	—
871	C₂×D₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
872	C₂×D₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
873	C₂×D₄	C₂²×C₄×C₂₃	1	2	yes	—
874	C₂×D₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
875	C₂×D₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
876	C₂×D₄	C₂²×C₄×C₂₃	1	2	yes	—
877	C₂×D₄	C₂²×C₄×C₂₃	1	2	yes	—
878	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
879	C₂²×C₄	C₂²×C₄×C₂₃	1	2	yes	—
880	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
881	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
882	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
883	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
884	C₂²×C₄	C₂²×C₄×C₂₃	1	2	yes	—
885	C₂²×C₄	C₂²×C₄×C₂₃	1	2	yes	—
886	C₂²×C₄	C₂²×C₄×C₂₃	1	2	yes	—
887	C₂²×C₄	C₂²×C₄×C₂₃	1	2	yes	—
888	C₂²×C₄	C₂²×C₄×C₂₃	1	2	yes	—
889	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
890	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
891	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
892	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
893	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
894	M₁₆	—	2	2	no	—
895	M₁₆	—	2	2	no	—
896	M₁₆	—	4	1	no	—
897	M₁₆	—	4	2	no	—
898	M₁₆	—	4	2	no	—
899	M₁₆	—	4	2	no	—
900	M₁₆	—	4	1	no	—
901	C₂×C₈	—	2	2	no	—
902	C₂×C₈	—	2	4	no	—
903	C₂×C₈	—	4	2	no	—
904	C₂×C₈	—	4	2	no	—
905	C₂×C₈	—	4	2	no	—
906	C₂×C₈	—	4	1	no	—
907	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
908	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
909	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
910	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
911	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
912	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
913	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
914	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
915	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
916	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
917	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
918	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
919	C₄⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
920	C₄⋊C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
921	C₄⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
922	C₄⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
923	C₄⋊C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
924	C₄⋊C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
925	C₄⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
926	C₄⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
927	C₄⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
928	C₄⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
929	C₄⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
930	C₄⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
931	C₄⋊C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
932	C₄⋊C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
933	C₄⋊C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
934	C₄⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
935	C₄⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
936	C₄⋊C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
937	C₄⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
938	C₄⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
939	C₄⋊C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
940	C₄⋊C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
941	C₄⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
942	C₄⋊C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
943	C₄⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
944	C₄⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
945	C₄⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
946	C₄⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
947	C₄⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
948	C₄⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
949	C₄⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
950	C₂²⋊C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
951	C₂²⋊C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
952	C₂²⋊C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
953	C₂²⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
954	C₂²⋊C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
955	C₂²⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
956	C₂²⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
957	C₂²⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
958	C₂²⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
959	C₂²⋊C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
960	C₂²⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
961	C₂²⋊C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
962	C₂²⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
963	C₂²⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
964	C₂²⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
965	C₂²⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
966	C₂²⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
967	C₂²⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
968	C₂²⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
969	C₄²	C₂²×C₄×C₂₃	1	2	yes	—
970	C₄²	C₂²×C₄×C₂₃	1	1	yes	characteristic
971	C₄²	C₂²×C₄×C₂₃	1	1	yes	characteristic
972	C₄²	C₂²×C₄×C₂₃	1	2	yes	—
973	C₄²	C₂²×C₄×C₂₃	1	1	yes	characteristic
974	C₄²	C₂²×C₄×C₂₃	1	2	yes	—
975	C₄²	C₂²×C₄×C₂₃	1	2	yes	—
976	C₄²	C₂²×C₄×C₂₃	1	1	yes	characteristic
977	C₄²	C₂²×C₄×C₂₃	1	2	yes	—
978	C₄²	C₂²×C₄×C₂₃	1	2	yes	—
979	C₄²	C₂²×C₄×C₂₃	1	1	yes	characteristic
980	C₄²	C₂²×C₄×C₂₃	1	1	yes	characteristic
981	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
982	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
983	C₄²	C₂⁴×C₂₃	1	2	yes	—
984	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
985	C₄²	C₂⁴×C₂₃	1	2	yes	—
986	C₄²	C₂⁴×C₂₃	1	2	yes	—
987	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
988	C₂³	C₂³×C₄×C₂₃	1	1	yes	characteristic
989	C₂³	C₂³×C₄×C₂₃	1	2	yes	—
990	C₂³	C₂³×C₄×C₂₃	1	1	yes	characteristic
991	C₂³	C₂³×C₄×C₂₃	1	1	yes	characteristic
992	Q₈	—	2	2	no	—
993	Q₈	—	2	2	no	—
994	Q₈	—	2	2	no	—
995	Q₈	—	4	2	no	—
996	Q₈	—	4	2	no	—
997	Q₈	—	4	1	no	—
998	Q₈	—	4	2	no	—
999	D₄	—	2	2	no	—
1000	D₄	—	2	2	no	—
1001	D₄	—	2	4	no	—
1002	D₄	—	2	2	no	—
1003	D₄	—	4	1	no	—
1004	D₄	—	4	2	no	—
1005	D₄	—	4	2	no	—
1006	C₂×C₄	—	2	2	no	—
1007	C₂×C₄	—	2	4	no	—
1008	C₂×C₄	—	2	2	no	—
1009	C₂×C₄	—	2	2	no	—
1010	C₂×C₄	—	2	2	no	—
1011	C₂×C₄	—	2	1	no	—
1012	C₂×C₄	—	2	2	no	—
1013	C₂×C₄	—	2	1	no	—
1014	C₂×C₄	—	2	1	no	—
1015	C₂×C₄	—	2	1	no	—
1016	C₂×C₄	—	2	1	no	—
1017	C₂×C₄	—	2	2	no	—
1018	C₂×C₄	—	2	1	no	—
1019	C₂×C₄	—	4	2	no	—
1020	C₂×C₄	—	4	2	no	—
1021	C₂×C₄	—	4	2	no	—
1022	C₂×C₄	—	4	1	no	—
1023	C₂×C₄	—	4	2	no	—
1024	C₂×C₄	—	4	1	no	—
1025	C₂×C₄	—	4	2	no	—
1026	C₂×C₄	C₂³×C₄×C₂₃	1	1	yes	characteristic
1027	C₂×C₄	C₂³×C₄×C₂₃	1	1	yes	characteristic
1028	C₂×C₄	C₂³×C₄×C₂₃	1	1	yes	characteristic
1029	C₂×C₄	C₂³×C₄×C₂₃	1	1	yes	characteristic
1030	C₂×C₄	C₂³×C₄×C₂₃	1	2	yes	—
1031	C₂×C₄	C₂³×C₄×C₂₃	1	1	yes	characteristic
1032	C₂×C₄	C₂³×C₄×C₂₃	1	2	yes	—
1033	C₂×C₄	C₂³×C₄×C₂₃	1	2	yes	—
1034	C₂×C₄	C₂³×C₄×C₂₃	1	1	yes	characteristic
1035	C₂×C₄	C₂³×C₄×C₂₃	1	1	yes	characteristic
1036	C₂×C₄	C₂³×C₄×C₂₃	1	1	yes	characteristic
1037	C₂×C₄	C₂³×C₄×C₂₃	1	2	yes	—
1038	C₂×C₄	C₂³×C₄×C₂₃	1	2	yes	—
1039	C₂×C₄	C₂³×C₄×C₂₃	1	2	yes	—
1040	C₂×C₄	C₂³×C₄×C₂₃	1	1	yes	characteristic
1041	C₂×C₄	C₂³×C₄×C₂₃	1	2	yes	—
1042	C₂×C₄	C₂³×C₄×C₂₃	1	1	yes	characteristic
1043	C₂×C₄	C₂³×C₄×C₂₃	1	1	yes	characteristic
1044	C₂×C₄	C₂⁵×C₂₃	1	1	yes	characteristic
1045	C₈	—	2	1	no	—
1046	C₈	—	2	2	no	—
1047	C₈	—	2	1	no	—
1048	C₈	—	2	1	no	—
1049	C₈	—	2	2	no	—
1050	C₈	—	2	2	no	—
1051	C₈	—	2	1	no	—
1052	C₈	—	2	2	no	—
1053	C₈	—	2	1	no	—
1054	C₈	—	2	1	no	—
1055	C₈	—	2	1	no	—
1056	C₈	C₂₃×2₋¹⁺⁴	1	2	yes	—
1057	C₂²	—	2	1	no	—
1058	C₂²	—	2	1	no	—
1059	C₂²	—	2	2	no	—
1060	C₂²	—	2	1	no	—
1061	C₂²	—	2	1	no	—
1062	C₂²	—	2	1	no	—
1063	C₂²	—	2	1	no	—
1064	C₂²	—	2	1	no	—
1065	C₂²	—	2	1	no	—
1066	C₂²	—	2	2	no	—
1067	C₂²	—	2	2	no	—
1068	C₂²	C₂₃×#568	1	2	yes	—
1069	C₂²	C₂⁴×C₄×C₂₃	1	1	yes	characteristic
1070	C₄	—	2	1	no	—
1071	C₄	—	2	2	no	—
1072	C₄	—	2	1	no	—
1073	C₄	—	2	1	no	—
1074	C₄	—	2	1	no	—
1075	C₄	—	2	2	no	—
1076	C₄	—	2	1	no	—
1077	C₄	—	2	1	no	—
1078	C₄	—	2	2	no	—
1079	C₄	—	2	1	no	—
1080	C₄	—	2	1	no	—
1081	C₄	—	2	1	no	—
1082	C₄	—	2	2	no	—
1083	C₄	—	2	1	no	—
1084	C₄	—	2	2	no	—
1085	C₄	—	2	2	no	—
1086	C₄	—	2	2	no	—
1087	C₄	C₂₃×#568	1	2	yes	—
1088	C₄	C₂×C₂₃×2₋¹⁺⁴	1	1	yes	characteristic
1089	C₄	C₂₃×#585	1	1	yes	characteristic
1090	C₂	—	2	2	no	—
1091	C₂	—	4	1	no	—
1092	C₂	—	4	1	no	—
1093	C₂	—	4	2	no	—
1094	C₂	C₄×C₂₃×2₋¹⁺⁴	1	1	yes	characteristic
1095	C₂	C₂×C₂₃×#568	1	1	yes	characteristic
1096	C₂	C₂×C₂₃×#568	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₂₃	C₂⁵
commutator	C₂²	C₂⁴×C₄×C₂₃
Frattini, cosocle	C₂×C₄	C₂⁵×C₂₃
socle	C₂²×C₂₃	C₂⁴×C₄
prime radical	C₂₃×#3482	C₂
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₂₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂₃×#2995	C₂	semidirect
3. C₂₃×#2994	C₂	semidirect
4. C₂₃×#2993	C₂	semidirect
5. C₂₃×#2992	C₂	semidirect
6. C₂₃×#2990	C₂	semidirect
7. C₂₃×#2989	C₂	semidirect
8. C₂₃×#2989	C₂	semidirect
9. C₂₃×#2987	C₂	semidirect
10. C₂₃×#2985	C₂	semidirect
11. C₂₃×#2984	C₂	semidirect
12. C₂₃×#2983	C₂	semidirect
13. C₂₃×#2970	C₂	semidirect
14. C₂₃×#2970	C₂	semidirect
15. C₂₃×#2969	C₂	semidirect
16. C₂₃×#2968	C₂	semidirect
17. C₂₃×#2967	C₂	semidirect
18. C₂₃×#2966	C₂	semidirect
19. C₂₃×#2965	C₂	semidirect
20. Q₈×M₁₆×C₂₃	C₂	semidirect
21. C₂₃×#2962	C₂	semidirect
22. C₂₃×#2961	C₂	semidirect
23. C₂×C₂₃×#446	C₂	semidirect
439. #60342	C₂₃	direct (N × H)
510. #2995	C₂×C₂₃	semidirect
511. #2994	C₂×C₂₃	semidirect
512. #2993	C₂×C₂₃	semidirect
513. #2992	C₂×C₂₃	semidirect
514. #2990	C₂×C₂₃	semidirect
515. #2989	C₂×C₂₃	semidirect
516. #2989	C₂×C₂₃	semidirect
517. #2987	C₂×C₂₃	semidirect
518. #2985	C₂×C₂₃	semidirect
519. #2984	C₂×C₂₃	semidirect
520. #2983	C₂×C₂₃	semidirect
521. #2970	C₂×C₂₃	semidirect
522. #2970	C₂×C₂₃	semidirect
523. #2969	C₂×C₂₃	semidirect
524. #2968	C₂×C₂₃	semidirect
525. #2967	C₂×C₂₃	semidirect
526. #2966	C₂×C₂₃	semidirect
527. #2965	C₂×C₂₃	semidirect
528. Q₈×M₁₆	C₂×C₂₃	semidirect
529. #2962	C₂×C₂₃	semidirect
530. #2961	C₂×C₂₃	semidirect
531. C₂×#446	C₂×C₂₃	semidirect
858. C₂₃	#60342	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂₃×#3482	2
C₂₃×#2995	2
C₂₃×#2994	2
C₂₃×#2993	2
C₂₃×#2992	2
C₂₃×#2990	2
C₂₃×#2989	2
C₂₃×#2987	2
C₂₃×#2985	2
C₂₃×#2984	2
C₂₃×#2983	2
C₂₃×#2970	2
C₂₃×#2969	2
C₂₃×#2968	2
C₂₃×#2967	2
C₂₃×#2966	2
C₂₃×#2965	2
Q₈×M₁₆×C₂₃	2
C₂₃×#2962	2
C₂₃×#2961	2
C₂×C₂₃×#446	2
#60342	23

Subgroups — C23×#60342 #19207968

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#60342 #19207968