Subgroups — C₆₇×#34261 #30713512

Order 17152.

2718 conjugacy classes of subgroups.

The subgroup lattice has 1068 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#518×C₆₇	C₂	1	1	yes	maximal, characteristic
2	C₆₇×#2357	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₇×#2354	C₂	1	1	yes	maximal, characteristic, complemented
4	C₆₇×#2353	C₂	1	2	yes	maximal, complemented
5	C₆₇×#2352	C₂	1	2	yes	maximal, complemented
6	C₆₇×#2349	C₂	1	1	yes	maximal, characteristic, complemented
7	D₄×C₄⋊C₄×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
8	C₆₇×#2347	C₂	1	1	yes	maximal, characteristic, complemented
9	C₆₇×#2346	C₂	1	1	yes	maximal, characteristic, complemented
10	C₆₇×#2342	C₂	1	2	yes	maximal, complemented
11	C₆₇×#2342	C₂	1	2	yes	maximal, complemented
12	D₄×C₂²⋊C₄×C₆₇	C₂	1	1	yes	maximal, characteristic
13	D₄×C₂²⋊C₄×C₆₇	C₂	1	1	yes	maximal, characteristic
14	C₆₇×#2319	C₂	1	1	yes	maximal, characteristic, complemented
15	C₆₇×#2318	C₂	1	2	yes	maximal, complemented
16	C₆₇×#2314	C₂	1	1	yes	maximal, characteristic, complemented
17	C₆₇×#2312	C₂	1	2	yes	maximal, complemented
18	C₆₇×#2298	C₂	1	1	yes	maximal, characteristic, complemented
19	C₆₇×#2293	C₂	1	1	yes	maximal, characteristic, complemented
20	C₆₇×#2290	C₂	1	2	yes	maximal, complemented
21	C₂×#388×C₆₇	C₂	1	2	yes	maximal, complemented
22	C₆₇×#2275	C₂	1	1	yes	maximal, characteristic, complemented
23	C₄²×D₄×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂³×D₄×C₆₇	C₂²	1	1	yes	characteristic
25	#518×C₆₇	C₄	1	16	yes	complemented
26	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
27	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
28	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
29	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
30	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
31	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
32	C₂×C₄×D₄×C₆₇	C₂²	1	2	yes	—
33	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
34	C₂×C₄×D₄×C₆₇	C₂²	1	2	yes	—
35	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
36	C₂×#117×C₆₇	C₂²	1	1	yes	characteristic
37	C₂×#117×C₆₇	C₂²	1	1	yes	characteristic
38	C₂×#117×C₆₇	C₂²	1	2	yes	complemented
39	C₂×#117×C₆₇	C₂²	1	2	yes	complemented
40	C₂²×C₄⋊C₄×C₆₇	C₂²	1	2	yes	complemented
41	C₂²×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	—
42	C₂²×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	—
43	C₂²×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	—
44	C₂²×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	—
45	C₂²×C₄²×C₆₇	C₂²	1	2	yes	complemented
46	#390×C₆₇	C₂²	1	1	yes	characteristic
47	#390×C₆₇	C₂²	1	1	yes	characteristic
48	#390×C₆₇	C₂²	1	1	yes	characteristic
49	#390×C₆₇	C₂²	1	1	yes	characteristic
50	#389×C₆₇	C₂²	1	1	yes	characteristic, complemented
51	#389×C₆₇	C₂²	1	1	yes	characteristic, complemented
52	#389×C₆₇	C₂²	1	1	yes	characteristic, complemented
53	#389×C₆₇	C₂²	1	1	yes	characteristic, complemented
54	#388×C₆₇	C₂²	1	1	yes	characteristic
55	#388×C₆₇	C₂²	1	2	yes	—
56	#388×C₆₇	C₂²	1	2	yes	—
57	#388×C₆₇	C₂²	1	2	yes	—
58	#388×C₆₇	C₂²	1	1	yes	characteristic
59	#388×C₆₇	C₂²	1	1	yes	characteristic
60	#388×C₆₇	C₂²	1	1	yes	characteristic
61	#388×C₆₇	C₂²	1	2	yes	—
62	#388×C₆₇	C₂²	1	2	yes	—
63	#388×C₆₇	C₂²	1	2	yes	—
64	#388×C₆₇	C₂²	1	2	yes	complemented
65	#388×C₆₇	C₂²	1	2	yes	complemented
66	#388×C₆₇	C₂²	1	2	yes	complemented
67	#388×C₆₇	C₂²	1	2	yes	complemented
68	#388×C₆₇	C₂²	1	2	yes	complemented
69	#388×C₆₇	C₂²	1	2	yes	complemented
70	#388×C₆₇	C₂²	1	2	yes	complemented
71	#388×C₆₇	C₂²	1	2	yes	complemented
72	#387×C₆₇	C₂²	1	1	yes	characteristic, complemented
73	#387×C₆₇	C₂²	1	2	yes	complemented
74	#387×C₆₇	C₂²	1	1	yes	characteristic, complemented
75	#387×C₆₇	C₂²	1	1	yes	characteristic, complemented
76	#387×C₆₇	C₂²	1	1	yes	characteristic, complemented
77	#387×C₆₇	C₂²	1	2	yes	complemented
78	#386×C₆₇	C₂²	1	2	yes	—
79	#386×C₆₇	C₂²	1	2	yes	—
80	#386×C₆₇	C₂²	1	2	yes	—
81	#386×C₆₇	C₂²	1	2	yes	—
82	#385×C₆₇	C₂²	1	2	yes	complemented
83	#385×C₆₇	C₂²	1	2	yes	complemented
84	#385×C₆₇	C₂²	1	2	yes	complemented
85	#385×C₆₇	C₂²	1	2	yes	complemented
86	#384×C₆₇	C₂²	1	1	yes	characteristic, complemented
87	#383×C₆₇	C₂²	1	2	yes	complemented
88	#382×C₆₇	C₂²	1	1	yes	characteristic, complemented
89	#382×C₆₇	C₂²	1	2	yes	complemented
90	#381×C₆₇	C₂²	1	2	yes	complemented
91	#381×C₆₇	C₂²	1	2	yes	complemented
92	#380×C₆₇	C₂²	1	1	yes	characteristic
93	#380×C₆₇	C₂²	1	1	yes	characteristic
94	#380×C₆₇	C₂²	1	2	yes	complemented
95	#380×C₆₇	C₂²	1	2	yes	complemented
96	#380×C₆₇	C₂²	1	2	yes	complemented
97	#380×C₆₇	C₂²	1	2	yes	complemented
98	#379×C₆₇	C₂²	1	2	yes	—
99	#379×C₆₇	C₂²	1	2	yes	—
100	C₄×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic, complemented
101	C₄×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic, complemented
102	C₄×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic, complemented
103	C₄×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic, complemented
104	C₄×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic, complemented
105	C₄×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic, complemented
106	C₄×C₄⋊C₄×C₆₇	C₂²	1	2	yes	complemented
107	C₄×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic, complemented
108	C₄×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic, complemented
109	C₄×C₂²⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
110	C₄×C₂²⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
111	C₄×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	complemented
112	C₄×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	complemented
113	C₄×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	complemented
114	C₄×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	complemented
115	C₄×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	complemented
116	C₄×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	complemented
117	C₄×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	complemented
118	C₄×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	complemented
119	#376×C₆₇	C₂²	1	1	yes	characteristic, complemented
120	#376×C₆₇	C₂²	1	2	yes	complemented
121	C₂×#95×C₆₇	C₂²	1	2	yes	complemented
122	C₂×#95×C₆₇	C₂²	1	2	yes	complemented
123	C₄³×C₆₇	C₂²	1	1	yes	characteristic, complemented
124	C₂⁵×C₆₇	C₂³	1	2	yes	—
125	C₂²×D₄×C₆₇	—	2	4	no	—
126	C₂²×D₄×C₆₇	—	2	4	no	—
127	C₂²×D₄×C₆₇	C₂×C₄	1	8	yes	—
128	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
129	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
130	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
131	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
132	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
133	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
134	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
135	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
136	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
137	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
138	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
139	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
140	C₄×D₄×C₆₇	—	2	4	no	—
141	C₄×D₄×C₆₇	—	2	4	no	—
142	C₄×D₄×C₆₇	—	2	4	no	—
143	C₄×D₄×C₆₇	—	2	4	no	—
144	C₄×D₄×C₆₇	C₂×C₄	1	8	yes	—
145	C₄×D₄×C₆₇	C₂×C₄	1	8	yes	—
146	C₄×D₄×C₆₇	C₂×C₄	1	8	yes	complemented
147	C₄×D₄×C₆₇	C₂×C₄	1	8	yes	complemented
148	C₄×D₄×C₆₇	C₂×C₄	1	16	yes	complemented
149	C₄×D₄×C₆₇	C₂×C₄	1	16	yes	complemented
150	#117×C₆₇	—	4	4	no	—
151	#117×C₆₇	—	4	4	no	—
152	#117×C₆₇	C₂×C₄	1	8	yes	complemented
153	#117×C₆₇	C₂×C₄	1	8	yes	complemented
154	C₂×C₄⋊C₄×C₆₇	—	4	4	no	—
155	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
156	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
157	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
158	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
159	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
160	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
161	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
162	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
163	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
164	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
165	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
166	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
167	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
168	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
169	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
170	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
171	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
172	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
173	C₂×C₂²⋊C₄×C₆₇	—	4	4	no	—
174	C₂×C₂²⋊C₄×C₆₇	—	4	4	no	—
175	C₂×C₂²⋊C₄×C₆₇	C₂×C₄	1	16	yes	complemented
176	C₂×C₂²⋊C₄×C₆₇	C₂×C₄	1	16	yes	complemented
177	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
178	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
179	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
180	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
181	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
182	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
183	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
184	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
185	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
186	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
187	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
188	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
189	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
190	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
191	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
192	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
193	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
194	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
195	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
196	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
197	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
198	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
199	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
200	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
201	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
202	C₂×C₄²×C₆₇	—	4	4	no	—
203	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
204	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
205	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
206	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
207	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
208	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
209	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
210	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
211	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
212	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
213	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
214	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
215	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
216	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
217	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
218	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
219	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
220	#95×C₆₇	C₂³	1	1	yes	characteristic
221	#95×C₆₇	C₂³	1	1	yes	characteristic
222	#95×C₆₇	C₂³	1	2	yes	—
223	#95×C₆₇	C₂³	1	2	yes	—
224	#95×C₆₇	C₂³	1	2	yes	—
225	#95×C₆₇	C₂³	1	2	yes	—
226	#95×C₆₇	C₂³	1	2	yes	—
227	#95×C₆₇	C₂³	1	2	yes	—
228	#95×C₆₇	C₂³	1	1	yes	characteristic
229	#95×C₆₇	C₂³	1	1	yes	characteristic
230	#95×C₆₇	C₂³	1	1	yes	characteristic
231	#95×C₆₇	C₂³	1	1	yes	characteristic
232	#95×C₆₇	C₂³	1	2	yes	—
233	#95×C₆₇	C₂³	1	2	yes	—
234	#95×C₆₇	C₂³	1	1	yes	characteristic
235	#95×C₆₇	C₂³	1	1	yes	characteristic
236	#95×C₆₇	C₂³	1	1	yes	characteristic
237	#95×C₆₇	C₂³	1	2	yes	—
238	#95×C₆₇	C₂³	1	2	yes	—
239	#95×C₆₇	C₂³	1	2	yes	—
240	#95×C₆₇	C₂³	1	1	yes	characteristic
241	#95×C₆₇	C₂³	1	2	yes	—
242	#95×C₆₇	C₂³	1	2	yes	—
243	#95×C₆₇	C₂³	1	2	yes	—
244	#95×C₆₇	C₂³	1	1	yes	characteristic
245	#95×C₆₇	C₂³	1	1	yes	characteristic
246	C₂⁴×C₆₇	—	2	4	no	—
247	C₂⁴×C₆₇	—	2	4	no	—
248	C₂⁴×C₆₇	—	4	2	no	—
249	C₂⁴×C₆₇	—	4	2	no	—
250	C₂⁴×C₆₇	—	4	2	no	—
251	C₂⁴×C₆₇	—	4	2	no	—
252	C₂⁴×C₆₇	C₂²×C₄	1	8	yes	—
253	C₂⁴×C₆₇	C₂⁴	1	1	yes	characteristic
254	C₂⁴×C₆₇	C₂⁴	1	2	yes	—
255	C₂⁴×C₆₇	C₂⁴	1	2	yes	—
256	C₂×D₄×C₆₇	—	2	4	no	—
257	C₂×D₄×C₆₇	—	2	4	no	—
258	C₂×D₄×C₆₇	—	2	32	no	—
259	C₂×D₄×C₆₇	—	2	2	no	—
260	C₂×D₄×C₆₇	—	2	2	no	—
261	C₂×D₄×C₆₇	C₂²×C₄	1	8	yes	—
262	C₂×D₄×C₆₇	C₂²×C₄	1	4	yes	—
263	C₂×D₄×C₆₇	C₂²×C₄	1	4	yes	—
264	C₂×D₄×C₆₇	#41	1	4	yes	—
265	C₂×D₄×C₆₇	#41	1	4	yes	—
266	C₂²×C₄×C₆₇	—	2	2	no	—
267	C₂²×C₄×C₆₇	—	2	2	no	—
268	C₂²×C₄×C₆₇	—	2	4	no	—
269	C₂²×C₄×C₆₇	—	2	4	no	—
270	C₂²×C₄×C₆₇	—	2	4	no	—
271	C₂²×C₄×C₆₇	—	2	4	no	—
272	C₂²×C₄×C₆₇	—	2	4	no	—
273	C₂²×C₄×C₆₇	—	2	4	no	—
274	C₂²×C₄×C₆₇	—	4	2	no	—
275	C₂²×C₄×C₆₇	—	4	2	no	—
276	C₂²×C₄×C₆₇	—	4	2	no	—
277	C₂²×C₄×C₆₇	—	4	2	no	—
278	C₂²×C₄×C₆₇	—	4	2	no	—
279	C₂²×C₄×C₆₇	—	4	2	no	—
280	C₂²×C₄×C₆₇	—	4	2	no	—
281	C₂²×C₄×C₆₇	—	4	2	no	—
282	C₂²×C₄×C₆₇	—	4	2	no	—
283	C₂²×C₄×C₆₇	—	4	2	no	—
284	C₂²×C₄×C₆₇	—	4	2	no	—
285	C₂²×C₄×C₆₇	—	4	2	no	—
286	C₂²×C₄×C₆₇	—	4	2	no	—
287	C₂²×C₄×C₆₇	—	4	2	no	—
288	C₂²×C₄×C₆₇	C₂²×C₄	1	4	yes	—
289	C₂²×C₄×C₆₇	C₂²×C₄	1	8	yes	—
290	C₂²×C₄×C₆₇	C₂²×C₄	1	8	yes	—
291	C₂²×C₄×C₆₇	C₂²×C₄	1	8	yes	—
292	C₂²×C₄×C₆₇	C₂²×C₄	1	8	yes	—
293	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
294	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
295	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
296	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
297	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
298	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
299	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
300	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
301	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
302	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
303	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
304	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
305	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
306	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
307	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
308	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
309	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
310	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
311	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
312	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
313	C₄⋊C₄×C₆₇	—	2	2	no	—
314	C₄⋊C₄×C₆₇	—	2	2	no	—
315	C₄⋊C₄×C₆₇	—	2	2	no	—
316	C₄⋊C₄×C₆₇	—	2	2	no	—
317	C₄⋊C₄×C₆₇	—	2	2	no	—
318	C₄⋊C₄×C₆₇	—	2	4	no	—
319	C₄⋊C₄×C₆₇	—	2	2	no	—
320	C₄⋊C₄×C₆₇	—	4	2	no	—
321	C₄⋊C₄×C₆₇	—	4	2	no	—
322	C₄⋊C₄×C₆₇	—	4	1	no	—
323	C₄⋊C₄×C₆₇	—	4	1	no	—
324	C₄⋊C₄×C₆₇	—	4	2	no	—
325	C₄⋊C₄×C₆₇	—	4	2	no	—
326	C₄⋊C₄×C₆₇	—	4	2	no	—
327	C₄⋊C₄×C₆₇	C₂²×C₄	1	4	yes	—
328	C₄⋊C₄×C₆₇	C₂²×C₄	1	4	yes	—
329	C₄⋊C₄×C₆₇	C₂²×C₄	1	4	yes	—
330	C₄⋊C₄×C₆₇	C₂²×C₄	1	4	yes	—
331	C₂²⋊C₄×C₆₇	—	2	4	no	—
332	C₂²⋊C₄×C₆₇	—	2	4	no	—
333	C₂²⋊C₄×C₆₇	—	2	4	no	—
334	C₂²⋊C₄×C₆₇	—	2	4	no	—
335	C₂²⋊C₄×C₆₇	—	2	2	no	—
336	C₂²⋊C₄×C₆₇	—	2	2	no	—
337	C₂²⋊C₄×C₆₇	—	2	4	no	—
338	C₂²⋊C₄×C₆₇	—	2	4	no	—
339	C₂²⋊C₄×C₆₇	—	4	2	no	—
340	C₂²⋊C₄×C₆₇	—	4	2	no	—
341	C₂²⋊C₄×C₆₇	—	4	2	no	—
342	C₂²⋊C₄×C₆₇	—	4	2	no	—
343	C₂²⋊C₄×C₆₇	—	4	1	no	—
344	C₂²⋊C₄×C₆₇	—	4	2	no	—
345	C₂²⋊C₄×C₆₇	—	4	1	no	—
346	C₂²⋊C₄×C₆₇	—	4	2	no	—
347	C₂²⋊C₄×C₆₇	—	4	2	no	—
348	C₂²⋊C₄×C₆₇	—	4	2	no	—
349	C₂²⋊C₄×C₆₇	C₂²×C₄	1	4	yes	—
350	C₂²⋊C₄×C₆₇	C₂²×C₄	1	4	yes	—
351	C₂²⋊C₄×C₆₇	C₂²×C₄	1	8	yes	—
352	C₂²⋊C₄×C₆₇	C₂²×C₄	1	8	yes	—
353	C₂²⋊C₄×C₆₇	C₂²×C₄	1	8	yes	—
354	C₂²⋊C₄×C₆₇	C₂²×C₄	1	8	yes	—
355	C₂²⋊C₄×C₆₇	C₂²×C₄	1	8	yes	—
356	C₄²×C₆₇	—	2	2	no	—
357	C₄²×C₆₇	—	2	2	no	—
358	C₄²×C₆₇	—	2	2	no	—
359	C₄²×C₆₇	—	2	2	no	—
360	C₄²×C₆₇	—	2	2	no	—
361	C₄²×C₆₇	—	2	4	no	—
362	C₄²×C₆₇	—	2	2	no	—
363	C₄²×C₆₇	—	4	2	no	—
364	C₄²×C₆₇	—	4	2	no	—
365	C₄²×C₆₇	—	4	1	no	—
366	C₄²×C₆₇	—	4	2	no	—
367	C₄²×C₆₇	—	4	1	no	—
368	C₄²×C₆₇	—	4	2	no	—
369	C₄²×C₆₇	—	4	2	no	—
370	C₄²×C₆₇	C₂²×C₄	1	4	yes	—
371	C₄²×C₆₇	C₂²×C₄	1	4	yes	—
372	C₄²×C₆₇	C₂²×C₄	1	8	yes	—
373	C₂³×C₆₇	—	2	2	no	—
374	C₂³×C₆₇	—	2	2	no	—
375	C₂³×C₆₇	—	2	2	no	—
376	C₂³×C₆₇	—	2	2	no	—
377	C₂³×C₆₇	—	2	1	no	—
378	C₂³×C₆₇	—	2	1	no	—
379	C₂³×C₆₇	—	2	2	no	—
380	C₂³×C₆₇	—	2	2	no	—
381	C₂³×C₆₇	—	2	2	no	—
382	C₂³×C₆₇	—	2	2	no	—
383	C₂³×C₆₇	—	2	1	no	—
384	C₂³×C₆₇	—	2	1	no	—
385	C₂³×C₆₇	—	2	2	no	—
386	C₂³×C₆₇	—	2	2	no	—
387	C₂³×C₆₇	—	2	1	no	—
388	C₂³×C₆₇	—	2	1	no	—
389	C₂³×C₆₇	—	2	16	no	—
390	C₂³×C₆₇	—	4	8	no	—
391	C₂³×C₆₇	—	4	8	no	—
392	C₂³×C₆₇	—	8	4	no	—
393	C₂³×C₆₇	—	8	4	no	—
394	C₂³×C₆₇	—	8	4	no	—
395	C₂³×C₆₇	—	8	4	no	—
396	C₂³×C₆₇	C₂³×C₄	1	2	yes	—
397	C₂³×C₆₇	C₂³×C₄	1	4	yes	—
398	C₂³×C₆₇	C₂³×C₄	1	4	yes	—
399	C₂³×C₆₇	C₂×#41	1	4	yes	—
400	C₂³×C₆₇	C₂×#41	1	4	yes	—
401	C₂³×C₆₇	C₂⁵	1	1	yes	characteristic
402	D₄×C₆₇	—	2	16	no	—
403	D₄×C₆₇	—	2	8	no	—
404	D₄×C₆₇	#117	1	16	yes	complemented
405	C₂×C₄×C₆₇	—	2	1	no	—
406	C₂×C₄×C₆₇	—	2	1	no	—
407	C₂×C₄×C₆₇	—	2	1	no	—
408	C₂×C₄×C₆₇	—	2	1	no	—
409	C₂×C₄×C₆₇	—	2	1	no	—
410	C₂×C₄×C₆₇	—	2	2	no	—
411	C₂×C₄×C₆₇	—	2	1	no	—
412	C₂×C₄×C₆₇	—	2	1	no	—
413	C₂×C₄×C₆₇	—	2	1	no	—
414	C₂×C₄×C₆₇	—	2	1	no	—
415	C₂×C₄×C₆₇	—	2	2	no	—
416	C₂×C₄×C₆₇	—	2	1	no	—
417	C₂×C₄×C₆₇	—	2	2	no	—
418	C₂×C₄×C₆₇	—	2	1	no	—
419	C₂×C₄×C₆₇	—	2	1	no	—
420	C₂×C₄×C₆₇	—	2	1	no	—
421	C₂×C₄×C₆₇	—	2	2	no	—
422	C₂×C₄×C₆₇	—	2	1	no	—
423	C₂×C₄×C₆₇	—	2	8	no	—
424	C₂×C₄×C₆₇	—	2	1	no	—
425	C₂×C₄×C₆₇	—	2	1	no	—
426	C₂×C₄×C₆₇	—	2	1	no	—
427	C₂×C₄×C₆₇	—	2	1	no	—
428	C₂×C₄×C₆₇	—	2	1	no	—
429	C₂×C₄×C₆₇	—	2	1	no	—
430	C₂×C₄×C₆₇	—	2	2	no	—
431	C₂×C₄×C₆₇	—	2	2	no	—
432	C₂×C₄×C₆₇	—	2	2	no	—
433	C₂×C₄×C₆₇	—	2	2	no	—
434	C₂×C₄×C₆₇	—	2	2	no	—
435	C₂×C₄×C₆₇	—	2	1	no	—
436	C₂×C₄×C₆₇	—	2	1	no	—
437	C₂×C₄×C₆₇	—	2	2	no	—
438	C₂×C₄×C₆₇	—	2	2	no	—
439	C₂×C₄×C₆₇	—	2	2	no	—
440	C₂×C₄×C₆₇	—	2	2	no	—
441	C₂×C₄×C₆₇	—	2	1	no	—
442	C₂×C₄×C₆₇	—	2	1	no	—
443	C₂×C₄×C₆₇	—	2	2	no	—
444	C₂×C₄×C₆₇	—	2	1	no	—
445	C₂×C₄×C₆₇	—	2	1	no	—
446	C₂×C₄×C₆₇	—	2	1	no	—
447	C₂×C₄×C₆₇	—	2	1	no	—
448	C₂×C₄×C₆₇	—	2	1	no	—
449	C₂×C₄×C₆₇	—	2	2	no	—
450	C₂×C₄×C₆₇	—	2	1	no	—
451	C₂×C₄×C₆₇	—	2	1	no	—
452	C₂×C₄×C₆₇	—	2	2	no	—
453	C₂×C₄×C₆₇	—	2	1	no	—
454	C₂×C₄×C₆₇	—	4	8	no	—
455	C₂×C₄×C₆₇	—	4	8	no	—
456	C₂×C₄×C₆₇	—	4	8	no	—
457	C₂×C₄×C₆₇	—	4	8	no	—
458	C₂×C₄×C₆₇	—	4	8	no	—
459	C₂×C₄×C₆₇	—	4	8	no	—
460	C₂×C₄×C₆₇	—	8	4	no	—
461	C₂×C₄×C₆₇	—	8	4	no	—
462	C₂×C₄×C₆₇	C₂³×C₄	1	2	yes	—
463	C₂×C₄×C₆₇	C₂³×C₄	1	2	yes	—
464	C₂×C₄×C₆₇	C₂³×C₄	1	2	yes	—
465	C₂×C₄×C₆₇	C₂³×C₄	1	2	yes	—
466	C₂×C₄×C₆₇	C₂³×C₄	1	2	yes	—
467	C₂×C₄×C₆₇	C₂³×C₄	1	4	yes	—
468	C₂×C₄×C₆₇	C₂³×C₄	1	4	yes	—
469	C₂×C₄×C₆₇	C₂³×C₄	1	2	yes	—
470	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
471	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
472	C₂×C₄×C₆₇	H(5,𝔽₂)	1	2	yes	—
473	C₂×C₄×C₆₇	H(5,𝔽₂)	1	2	yes	—
474	C₂²×C₆₇	—	2	4	no	—
475	C₂²×C₆₇	—	2	4	no	—
476	C₂²×C₆₇	—	2	4	no	—
477	C₂²×C₆₇	—	2	4	no	—
478	C₂²×C₆₇	—	2	4	no	—
479	C₂²×C₆₇	—	2	4	no	—
480	C₂²×C₆₇	—	2	2	no	—
481	C₂²×C₆₇	—	2	4	no	—
482	C₂²×C₆₇	—	2	4	no	—
483	C₂²×C₆₇	—	2	4	no	—
484	C₂²×C₆₇	—	2	2	no	—
485	C₂²×C₆₇	—	2	2	no	—
486	C₂²×C₆₇	—	4	2	no	—
487	C₂²×C₆₇	—	4	1	no	—
488	C₂²×C₆₇	—	4	2	no	—
489	C₂²×C₆₇	—	4	1	no	—
490	C₂²×C₆₇	—	4	2	no	—
491	C₂²×C₆₇	—	4	1	no	—
492	C₂²×C₆₇	—	4	2	no	—
493	C₂²×C₆₇	—	4	1	no	—
494	C₂²×C₆₇	—	8	16	no	—
495	C₂²×C₆₇	C₂×#117	1	8	yes	—
496	C₂²×C₆₇	C₂⁴×C₄	1	1	yes	characteristic
497	C₂²×C₆₇	C₂²×#41	1	1	yes	characteristic
498	C₂²×C₆₇	C₂²×#41	1	1	yes	characteristic
499	C₂²×C₆₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
500	C₂²×C₆₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
501	C₂²×C₆₇	#585	1	1	yes	characteristic
502	C₂²×C₆₇	#585	1	1	yes	characteristic
503	C₄×C₆₇	—	2	2	no	—
504	C₄×C₆₇	—	2	2	no	—
505	C₄×C₆₇	—	2	4	no	—
506	C₄×C₆₇	—	2	2	no	—
507	C₄×C₆₇	—	2	2	no	—
508	C₄×C₆₇	—	2	2	no	—
509	C₄×C₆₇	—	2	4	no	—
510	C₄×C₆₇	—	2	2	no	—
511	C₄×C₆₇	—	2	2	no	—
512	C₄×C₆₇	—	4	1	no	—
513	C₄×C₆₇	—	4	2	no	—
514	C₄×C₆₇	—	4	1	no	—
515	C₄×C₆₇	—	4	2	no	—
516	C₄×C₆₇	—	4	1	no	—
517	C₄×C₆₇	—	4	2	no	—
518	C₄×C₆₇	—	4	2	no	—
519	C₄×C₆₇	—	4	1	no	—
520	C₄×C₆₇	—	4	1	no	—
521	C₄×C₆₇	—	4	1	no	—
522	C₄×C₆₇	C₂×#117	1	4	yes	—
523	#34261	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
524	C₂×C₆₇	—	2	8	no	—
525	C₂×C₆₇	—	4	4	no	—
526	C₂×C₆₇	—	4	2	no	—
527	C₂×C₆₇	C₂²×#117	1	1	yes	characteristic
528	C₂×C₆₇	C₄×H(5,𝔽₂)	1	1	yes	characteristic
529	C₂×C₆₇	C₄×H(5,𝔽₂)	1	1	yes	characteristic
530	C₂×C₆₇	#3513	1	1	yes	characteristic
531	C₂×C₆₇	#3514	1	1	yes	characteristic
532	C₂×C₆₇	#3519	1	1	yes	characteristic
533	C₂×C₆₇	#3521	1	1	yes	characteristic
534	C₂×#518	C₂×C₆₇	1	1	yes	characteristic
535	#2357	C₂×C₆₇	1	1	yes	characteristic, complemented
536	#2354	C₂×C₆₇	1	1	yes	characteristic, complemented
537	#2353	C₂×C₆₇	1	2	yes	complemented
538	#2352	C₂×C₆₇	1	2	yes	complemented
539	#2349	C₂×C₆₇	1	1	yes	characteristic, complemented
540	D₄×C₄⋊C₄	C₂×C₆₇	1	1	yes	characteristic, complemented
541	#2347	C₂×C₆₇	1	1	yes	characteristic, complemented
542	#2346	C₂×C₆₇	1	1	yes	characteristic, complemented
543	#2342	C₂×C₆₇	1	2	yes	complemented
544	#2342	C₂×C₆₇	1	2	yes	complemented
545	D₄×C₂²⋊C₄	C₂×C₆₇	1	1	yes	characteristic
546	D₄×C₂²⋊C₄	C₂×C₆₇	1	1	yes	characteristic
547	#2319	C₂×C₆₇	1	1	yes	characteristic, complemented
548	#2318	C₂×C₆₇	1	2	yes	complemented
549	#2314	C₂×C₆₇	1	1	yes	characteristic, complemented
550	#2312	C₂×C₆₇	1	2	yes	complemented
551	#2298	C₂×C₆₇	1	1	yes	characteristic, complemented
552	#2293	C₂×C₆₇	1	1	yes	characteristic, complemented
553	#2290	C₂×C₆₇	1	2	yes	complemented
554	C₂×#388	C₂×C₆₇	1	2	yes	complemented
555	#2275	C₂×C₆₇	1	1	yes	characteristic, complemented
556	C₄²×D₄	C₂×C₆₇	1	1	yes	characteristic, complemented
557	C₆₇	#34261	1	1	yes	characteristic, direct product factor, Sylow
558	C₂³×D₄	C₂²×C₆₇	1	1	yes	characteristic
559	#518	C₄×C₆₇	1	16	yes	complemented
560	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
561	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
562	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
563	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
564	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
565	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
566	C₂×C₄×D₄	C₂²×C₆₇	1	2	yes	—
567	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
568	C₂×C₄×D₄	C₂²×C₆₇	1	2	yes	—
569	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
570	C₂×#117	C₂²×C₆₇	1	1	yes	characteristic
571	C₂×#117	C₂²×C₆₇	1	1	yes	characteristic
572	C₂×#117	C₂²×C₆₇	1	2	yes	complemented
573	C₂×#117	C₂²×C₆₇	1	2	yes	complemented
574	C₂²×C₄⋊C₄	C₂²×C₆₇	1	2	yes	complemented
575	C₂²×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
576	C₂²×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
577	C₂²×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
578	C₂²×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
579	C₂²×C₄²	C₂²×C₆₇	1	2	yes	complemented
580	#390	C₂²×C₆₇	1	1	yes	characteristic
581	#390	C₂²×C₆₇	1	1	yes	characteristic
582	#390	C₂²×C₆₇	1	1	yes	characteristic
583	#390	C₂²×C₆₇	1	1	yes	characteristic
584	#389	C₂²×C₆₇	1	1	yes	characteristic, complemented
585	#389	C₂²×C₆₇	1	1	yes	characteristic, complemented
586	#389	C₂²×C₆₇	1	1	yes	characteristic, complemented
587	#389	C₂²×C₆₇	1	1	yes	characteristic, complemented
588	#388	C₂²×C₆₇	1	1	yes	characteristic
589	#388	C₂²×C₆₇	1	2	yes	—
590	#388	C₂²×C₆₇	1	2	yes	—
591	#388	C₂²×C₆₇	1	2	yes	—
592	#388	C₂²×C₆₇	1	2	yes	—
593	#388	C₂²×C₆₇	1	1	yes	characteristic
594	#388	C₂²×C₆₇	1	1	yes	characteristic
595	#388	C₂²×C₆₇	1	2	yes	—
596	#388	C₂²×C₆₇	1	2	yes	—
597	#388	C₂²×C₆₇	1	1	yes	characteristic
598	#388	C₂²×C₆₇	1	2	yes	complemented
599	#388	C₂²×C₆₇	1	2	yes	complemented
600	#388	C₂²×C₆₇	1	2	yes	complemented
601	#388	C₂²×C₆₇	1	2	yes	complemented
602	#388	C₂²×C₆₇	1	2	yes	complemented
603	#388	C₂²×C₆₇	1	2	yes	complemented
604	#388	C₂²×C₆₇	1	2	yes	complemented
605	#388	C₂²×C₆₇	1	2	yes	complemented
606	#387	C₂²×C₆₇	1	2	yes	complemented
607	#387	C₂²×C₆₇	1	2	yes	complemented
608	#387	C₂²×C₆₇	1	1	yes	characteristic, complemented
609	#387	C₂²×C₆₇	1	1	yes	characteristic, complemented
610	#387	C₂²×C₆₇	1	1	yes	characteristic, complemented
611	#387	C₂²×C₆₇	1	1	yes	characteristic, complemented
612	#386	C₂²×C₆₇	1	2	yes	—
613	#386	C₂²×C₆₇	1	2	yes	—
614	#386	C₂²×C₆₇	1	2	yes	—
615	#386	C₂²×C₆₇	1	2	yes	—
616	#385	C₂²×C₆₇	1	2	yes	complemented
617	#385	C₂²×C₆₇	1	2	yes	complemented
618	#385	C₂²×C₆₇	1	2	yes	complemented
619	#385	C₂²×C₆₇	1	2	yes	complemented
620	#384	C₂²×C₆₇	1	1	yes	characteristic, complemented
621	#383	C₂²×C₆₇	1	2	yes	complemented
622	#382	C₂²×C₆₇	1	1	yes	characteristic, complemented
623	#382	C₂²×C₆₇	1	2	yes	complemented
624	#381	C₂²×C₆₇	1	2	yes	complemented
625	#381	C₂²×C₆₇	1	2	yes	complemented
626	#380	C₂²×C₆₇	1	1	yes	characteristic
627	#380	C₂²×C₆₇	1	1	yes	characteristic
628	#380	C₂²×C₆₇	1	2	yes	complemented
629	#380	C₂²×C₆₇	1	2	yes	complemented
630	#380	C₂²×C₆₇	1	2	yes	complemented
631	#380	C₂²×C₆₇	1	2	yes	complemented
632	#379	C₂²×C₆₇	1	2	yes	—
633	#379	C₂²×C₆₇	1	2	yes	—
634	C₄×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic, complemented
635	C₄×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic, complemented
636	C₄×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic, complemented
637	C₄×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic, complemented
638	C₄×C₄⋊C₄	C₂²×C₆₇	1	2	yes	complemented
639	C₄×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic, complemented
640	C₄×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic, complemented
641	C₄×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic, complemented
642	C₄×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic, complemented
643	C₄×C₂²⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
644	C₄×C₂²⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
645	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	complemented
646	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	complemented
647	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	complemented
648	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	complemented
649	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	complemented
650	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	complemented
651	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	complemented
652	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	complemented
653	#376	C₂²×C₆₇	1	1	yes	characteristic, complemented
654	#376	C₂²×C₆₇	1	2	yes	complemented
655	C₂×#95	C₂²×C₆₇	1	2	yes	complemented
656	C₂×#95	C₂²×C₆₇	1	2	yes	complemented
657	C₄³	C₂²×C₆₇	1	1	yes	characteristic, complemented
658	C₂⁵	C₂³×C₆₇	1	2	yes	—
659	C₂²×D₄	—	2	4	no	—
660	C₂²×D₄	—	2	4	no	—
661	C₂²×D₄	C₂×C₄×C₆₇	1	8	yes	—
662	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
663	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
664	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
665	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
666	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
667	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
668	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
669	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
670	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
671	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
672	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
673	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
674	C₄×D₄	—	2	4	no	—
675	C₄×D₄	—	2	4	no	—
676	C₄×D₄	—	2	4	no	—
677	C₄×D₄	—	2	4	no	—
678	C₄×D₄	C₂×C₄×C₆₇	1	8	yes	—
679	C₄×D₄	C₂×C₄×C₆₇	1	8	yes	—
680	C₄×D₄	C₂×C₄×C₆₇	1	8	yes	complemented
681	C₄×D₄	C₂×C₄×C₆₇	1	8	yes	complemented
682	C₄×D₄	C₂×C₄×C₆₇	1	16	yes	complemented
683	C₄×D₄	C₂×C₄×C₆₇	1	16	yes	complemented
684	#117	—	4	4	no	—
685	#117	—	4	4	no	—
686	#117	C₂×C₄×C₆₇	1	8	yes	complemented
687	#117	C₂×C₄×C₆₇	1	8	yes	complemented
688	C₂×C₄⋊C₄	—	4	4	no	—
689	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
690	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
691	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
692	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
693	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
694	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
695	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
696	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
697	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
698	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
699	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
700	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
701	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
702	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
703	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
704	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
705	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
706	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
707	C₂×C₂²⋊C₄	—	4	4	no	—
708	C₂×C₂²⋊C₄	—	4	4	no	—
709	C₂×C₂²⋊C₄	C₂×C₄×C₆₇	1	16	yes	complemented
710	C₂×C₂²⋊C₄	C₂×C₄×C₆₇	1	16	yes	complemented
711	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
712	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
713	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
714	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
715	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
716	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
717	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
718	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
719	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
720	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
721	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
722	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
723	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
724	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
725	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
726	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
727	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
728	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
729	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
730	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
731	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
732	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
733	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
734	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
735	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
736	C₂×C₄²	—	4	4	no	—
737	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
738	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
739	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
740	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
741	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
742	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
743	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
744	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
745	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
746	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
747	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
748	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
749	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
750	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
751	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
752	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
753	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
754	#95	C₂³×C₆₇	1	1	yes	characteristic
755	#95	C₂³×C₆₇	1	1	yes	characteristic
756	#95	C₂³×C₆₇	1	2	yes	—
757	#95	C₂³×C₆₇	1	2	yes	—
758	#95	C₂³×C₆₇	1	2	yes	—
759	#95	C₂³×C₆₇	1	2	yes	—
760	#95	C₂³×C₆₇	1	2	yes	—
761	#95	C₂³×C₆₇	1	2	yes	—
762	#95	C₂³×C₆₇	1	1	yes	characteristic
763	#95	C₂³×C₆₇	1	1	yes	characteristic
764	#95	C₂³×C₆₇	1	1	yes	characteristic
765	#95	C₂³×C₆₇	1	1	yes	characteristic
766	#95	C₂³×C₆₇	1	2	yes	—
767	#95	C₂³×C₆₇	1	2	yes	—
768	#95	C₂³×C₆₇	1	1	yes	characteristic
769	#95	C₂³×C₆₇	1	1	yes	characteristic
770	#95	C₂³×C₆₇	1	1	yes	characteristic
771	#95	C₂³×C₆₇	1	2	yes	—
772	#95	C₂³×C₆₇	1	2	yes	—
773	#95	C₂³×C₆₇	1	2	yes	—
774	#95	C₂³×C₆₇	1	1	yes	characteristic
775	#95	C₂³×C₆₇	1	2	yes	—
776	#95	C₂³×C₆₇	1	2	yes	—
777	#95	C₂³×C₆₇	1	2	yes	—
778	#95	C₂³×C₆₇	1	1	yes	characteristic
779	#95	C₂³×C₆₇	1	1	yes	characteristic
780	C₂⁴	—	2	4	no	—
781	C₂⁴	—	2	4	no	—
782	C₂⁴	—	4	2	no	—
783	C₂⁴	—	4	2	no	—
784	C₂⁴	—	4	2	no	—
785	C₂⁴	—	4	2	no	—
786	C₂⁴	C₂²×C₄×C₆₇	1	8	yes	—
787	C₂⁴	C₂⁴×C₆₇	1	1	yes	characteristic
788	C₂⁴	C₂⁴×C₆₇	1	2	yes	—
789	C₂⁴	C₂⁴×C₆₇	1	2	yes	—
790	C₂×D₄	—	2	4	no	—
791	C₂×D₄	—	2	4	no	—
792	C₂×D₄	—	2	32	no	—
793	C₂×D₄	—	2	2	no	—
794	C₂×D₄	—	2	2	no	—
795	C₂×D₄	C₂²×C₄×C₆₇	1	8	yes	—
796	C₂×D₄	C₂²×C₄×C₆₇	1	4	yes	—
797	C₂×D₄	C₂²×C₄×C₆₇	1	4	yes	—
798	C₂×D₄	#41×C₆₇	1	4	yes	—
799	C₂×D₄	#41×C₆₇	1	4	yes	—
800	C₂²×C₄	—	2	2	no	—
801	C₂²×C₄	—	2	2	no	—
802	C₂²×C₄	—	2	4	no	—
803	C₂²×C₄	—	2	4	no	—
804	C₂²×C₄	—	2	4	no	—
805	C₂²×C₄	—	2	4	no	—
806	C₂²×C₄	—	2	4	no	—
807	C₂²×C₄	—	2	4	no	—
808	C₂²×C₄	—	4	2	no	—
809	C₂²×C₄	—	4	2	no	—
810	C₂²×C₄	—	4	2	no	—
811	C₂²×C₄	—	4	2	no	—
812	C₂²×C₄	—	4	2	no	—
813	C₂²×C₄	—	4	2	no	—
814	C₂²×C₄	—	4	2	no	—
815	C₂²×C₄	—	4	2	no	—
816	C₂²×C₄	—	4	2	no	—
817	C₂²×C₄	—	4	2	no	—
818	C₂²×C₄	—	4	2	no	—
819	C₂²×C₄	—	4	2	no	—
820	C₂²×C₄	—	4	2	no	—
821	C₂²×C₄	—	4	2	no	—
822	C₂²×C₄	C₂²×C₄×C₆₇	1	4	yes	—
823	C₂²×C₄	C₂²×C₄×C₆₇	1	8	yes	—
824	C₂²×C₄	C₂²×C₄×C₆₇	1	8	yes	—
825	C₂²×C₄	C₂²×C₄×C₆₇	1	8	yes	—
826	C₂²×C₄	C₂²×C₄×C₆₇	1	8	yes	—
827	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
828	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
829	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
830	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
831	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
832	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
833	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
834	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
835	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
836	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
837	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
838	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
839	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
840	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
841	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
842	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
843	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
844	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
845	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
846	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
847	C₄⋊C₄	—	2	2	no	—
848	C₄⋊C₄	—	2	2	no	—
849	C₄⋊C₄	—	2	2	no	—
850	C₄⋊C₄	—	2	2	no	—
851	C₄⋊C₄	—	2	2	no	—
852	C₄⋊C₄	—	2	4	no	—
853	C₄⋊C₄	—	2	2	no	—
854	C₄⋊C₄	—	4	2	no	—
855	C₄⋊C₄	—	4	2	no	—
856	C₄⋊C₄	—	4	2	no	—
857	C₄⋊C₄	—	4	2	no	—
858	C₄⋊C₄	—	4	1	no	—
859	C₄⋊C₄	—	4	1	no	—
860	C₄⋊C₄	—	4	2	no	—
861	C₄⋊C₄	C₂²×C₄×C₆₇	1	4	yes	—
862	C₄⋊C₄	C₂²×C₄×C₆₇	1	4	yes	—
863	C₄⋊C₄	C₂²×C₄×C₆₇	1	4	yes	—
864	C₄⋊C₄	C₂²×C₄×C₆₇	1	4	yes	—
865	C₂²⋊C₄	—	2	4	no	—
866	C₂²⋊C₄	—	2	4	no	—
867	C₂²⋊C₄	—	2	4	no	—
868	C₂²⋊C₄	—	2	4	no	—
869	C₂²⋊C₄	—	2	2	no	—
870	C₂²⋊C₄	—	2	2	no	—
871	C₂²⋊C₄	—	2	4	no	—
872	C₂²⋊C₄	—	2	4	no	—
873	C₂²⋊C₄	—	4	2	no	—
874	C₂²⋊C₄	—	4	2	no	—
875	C₂²⋊C₄	—	4	2	no	—
876	C₂²⋊C₄	—	4	2	no	—
877	C₂²⋊C₄	—	4	2	no	—
878	C₂²⋊C₄	—	4	2	no	—
879	C₂²⋊C₄	—	4	1	no	—
880	C₂²⋊C₄	—	4	2	no	—
881	C₂²⋊C₄	—	4	1	no	—
882	C₂²⋊C₄	—	4	2	no	—
883	C₂²⋊C₄	C₂²×C₄×C₆₇	1	4	yes	—
884	C₂²⋊C₄	C₂²×C₄×C₆₇	1	4	yes	—
885	C₂²⋊C₄	C₂²×C₄×C₆₇	1	8	yes	—
886	C₂²⋊C₄	C₂²×C₄×C₆₇	1	8	yes	—
887	C₂²⋊C₄	C₂²×C₄×C₆₇	1	8	yes	—
888	C₂²⋊C₄	C₂²×C₄×C₆₇	1	8	yes	—
889	C₂²⋊C₄	C₂²×C₄×C₆₇	1	8	yes	—
890	C₄²	—	2	2	no	—
891	C₄²	—	2	2	no	—
892	C₄²	—	2	2	no	—
893	C₄²	—	2	2	no	—
894	C₄²	—	2	2	no	—
895	C₄²	—	2	4	no	—
896	C₄²	—	2	2	no	—
897	C₄²	—	4	2	no	—
898	C₄²	—	4	2	no	—
899	C₄²	—	4	2	no	—
900	C₄²	—	4	2	no	—
901	C₄²	—	4	1	no	—
902	C₄²	—	4	2	no	—
903	C₄²	—	4	1	no	—
904	C₄²	C₂²×C₄×C₆₇	1	4	yes	—
905	C₄²	C₂²×C₄×C₆₇	1	4	yes	—
906	C₄²	C₂²×C₄×C₆₇	1	8	yes	—
907	C₂³	—	2	2	no	—
908	C₂³	—	2	2	no	—
909	C₂³	—	2	2	no	—
910	C₂³	—	2	2	no	—
911	C₂³	—	2	1	no	—
912	C₂³	—	2	1	no	—
913	C₂³	—	2	2	no	—
914	C₂³	—	2	2	no	—
915	C₂³	—	2	2	no	—
916	C₂³	—	2	2	no	—
917	C₂³	—	2	1	no	—
918	C₂³	—	2	1	no	—
919	C₂³	—	2	2	no	—
920	C₂³	—	2	2	no	—
921	C₂³	—	2	1	no	—
922	C₂³	—	2	1	no	—
923	C₂³	—	2	16	no	—
924	C₂³	—	4	8	no	—
925	C₂³	—	4	8	no	—
926	C₂³	—	8	4	no	—
927	C₂³	—	8	4	no	—
928	C₂³	—	8	4	no	—
929	C₂³	—	8	4	no	—
930	C₂³	C₂³×C₄×C₆₇	1	2	yes	—
931	C₂³	C₂³×C₄×C₆₇	1	4	yes	—
932	C₂³	C₂³×C₄×C₆₇	1	4	yes	—
933	C₂³	C₂×#41×C₆₇	1	4	yes	—
934	C₂³	C₂×#41×C₆₇	1	4	yes	—
935	C₂³	C₂⁵×C₆₇	1	1	yes	characteristic
936	D₄	—	2	16	no	—
937	D₄	—	2	8	no	—
938	D₄	#117×C₆₇	1	16	yes	complemented
939	C₂×C₄	—	2	1	no	—
940	C₂×C₄	—	2	1	no	—
941	C₂×C₄	—	2	1	no	—
942	C₂×C₄	—	2	1	no	—
943	C₂×C₄	—	2	1	no	—
944	C₂×C₄	—	2	2	no	—
945	C₂×C₄	—	2	1	no	—
946	C₂×C₄	—	2	1	no	—
947	C₂×C₄	—	2	1	no	—
948	C₂×C₄	—	2	1	no	—
949	C₂×C₄	—	2	2	no	—
950	C₂×C₄	—	2	1	no	—
951	C₂×C₄	—	2	2	no	—
952	C₂×C₄	—	2	1	no	—
953	C₂×C₄	—	2	1	no	—
954	C₂×C₄	—	2	1	no	—
955	C₂×C₄	—	2	2	no	—
956	C₂×C₄	—	2	1	no	—
957	C₂×C₄	—	2	8	no	—
958	C₂×C₄	—	2	1	no	—
959	C₂×C₄	—	2	1	no	—
960	C₂×C₄	—	2	1	no	—
961	C₂×C₄	—	2	1	no	—
962	C₂×C₄	—	2	1	no	—
963	C₂×C₄	—	2	1	no	—
964	C₂×C₄	—	2	2	no	—
965	C₂×C₄	—	2	2	no	—
966	C₂×C₄	—	2	2	no	—
967	C₂×C₄	—	2	2	no	—
968	C₂×C₄	—	2	2	no	—
969	C₂×C₄	—	2	1	no	—
970	C₂×C₄	—	2	1	no	—
971	C₂×C₄	—	2	2	no	—
972	C₂×C₄	—	2	2	no	—
973	C₂×C₄	—	2	2	no	—
974	C₂×C₄	—	2	2	no	—
975	C₂×C₄	—	2	1	no	—
976	C₂×C₄	—	2	1	no	—
977	C₂×C₄	—	2	2	no	—
978	C₂×C₄	—	2	1	no	—
979	C₂×C₄	—	2	1	no	—
980	C₂×C₄	—	2	1	no	—
981	C₂×C₄	—	2	1	no	—
982	C₂×C₄	—	2	1	no	—
983	C₂×C₄	—	2	2	no	—
984	C₂×C₄	—	2	1	no	—
985	C₂×C₄	—	2	1	no	—
986	C₂×C₄	—	2	2	no	—
987	C₂×C₄	—	2	1	no	—
988	C₂×C₄	—	4	8	no	—
989	C₂×C₄	—	4	8	no	—
990	C₂×C₄	—	4	8	no	—
991	C₂×C₄	—	4	8	no	—
992	C₂×C₄	—	4	8	no	—
993	C₂×C₄	—	4	8	no	—
994	C₂×C₄	—	8	4	no	—
995	C₂×C₄	—	8	4	no	—
996	C₂×C₄	C₂³×C₄×C₆₇	1	2	yes	—
997	C₂×C₄	C₂³×C₄×C₆₇	1	2	yes	—
998	C₂×C₄	C₂³×C₄×C₆₇	1	2	yes	—
999	C₂×C₄	C₂³×C₄×C₆₇	1	2	yes	—
1000	C₂×C₄	C₂³×C₄×C₆₇	1	2	yes	—
1001	C₂×C₄	C₂³×C₄×C₆₇	1	4	yes	—
1002	C₂×C₄	C₂³×C₄×C₆₇	1	4	yes	—
1003	C₂×C₄	C₂³×C₄×C₆₇	1	2	yes	—
1004	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
1005	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
1006	C₂×C₄	H(5,𝔽₂)×C₆₇	1	2	yes	—
1007	C₂×C₄	H(5,𝔽₂)×C₆₇	1	2	yes	—
1008	C₂²	—	2	4	no	—
1009	C₂²	—	2	4	no	—
1010	C₂²	—	2	4	no	—
1011	C₂²	—	2	4	no	—
1012	C₂²	—	2	4	no	—
1013	C₂²	—	2	4	no	—
1014	C₂²	—	2	2	no	—
1015	C₂²	—	2	4	no	—
1016	C₂²	—	2	4	no	—
1017	C₂²	—	2	4	no	—
1018	C₂²	—	2	2	no	—
1019	C₂²	—	2	2	no	—
1020	C₂²	—	4	1	no	—
1021	C₂²	—	4	2	no	—
1022	C₂²	—	4	1	no	—
1023	C₂²	—	4	2	no	—
1024	C₂²	—	4	1	no	—
1025	C₂²	—	4	2	no	—
1026	C₂²	—	4	1	no	—
1027	C₂²	—	4	2	no	—
1028	C₂²	—	8	16	no	—
1029	C₂²	C₂×#117×C₆₇	1	8	yes	—
1030	C₂²	C₂⁴×C₄×C₆₇	1	1	yes	characteristic
1031	C₂²	C₂²×#41×C₆₇	1	1	yes	characteristic
1032	C₂²	C₂²×#41×C₆₇	1	1	yes	characteristic
1033	C₂²	C₂×H(5,𝔽₂)×C₆₇	1	1	yes	characteristic
1034	C₂²	C₂×H(5,𝔽₂)×C₆₇	1	1	yes	characteristic
1035	C₂²	#585×C₆₇	1	1	yes	characteristic
1036	C₂²	#585×C₆₇	1	1	yes	characteristic
1037	C₄	—	2	2	no	—
1038	C₄	—	2	2	no	—
1039	C₄	—	2	4	no	—
1040	C₄	—	2	2	no	—
1041	C₄	—	2	2	no	—
1042	C₄	—	2	2	no	—
1043	C₄	—	2	4	no	—
1044	C₄	—	2	2	no	—
1045	C₄	—	2	2	no	—
1046	C₄	—	4	1	no	—
1047	C₄	—	4	1	no	—
1048	C₄	—	4	2	no	—
1049	C₄	—	4	1	no	—
1050	C₄	—	4	1	no	—
1051	C₄	—	4	2	no	—
1052	C₄	—	4	1	no	—
1053	C₄	—	4	2	no	—
1054	C₄	—	4	1	no	—
1055	C₄	—	4	2	no	—
1056	C₄	C₂×#117×C₆₇	1	4	yes	—
1057	C₂	—	2	8	no	—
1058	C₂	—	4	2	no	—
1059	C₂	—	4	4	no	—
1060	C₂	C₂²×#117×C₆₇	1	1	yes	characteristic
1061	C₂	C₄×H(5,𝔽₂)×C₆₇	1	1	yes	characteristic
1062	C₂	C₄×H(5,𝔽₂)×C₆₇	1	1	yes	characteristic
1063	C₂	C₆₇×#3513	1	1	yes	characteristic
1064	C₂	C₆₇×#3514	1	1	yes	characteristic
1065	C₂	C₆₇×#3519	1	1	yes	characteristic
1066	C₂	C₆₇×#3521	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₆₇	C₂⁵
commutator	C₂²	C₂⁴×C₄×C₆₇
Frattini, cosocle	C₂³	C₂⁵×C₆₇
prime radical	C₂³×D₄×C₆₇	C₂²
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₆₇ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₆₇×#2357	C₂	semidirect
3. C₆₇×#2354	C₂	semidirect
4. C₆₇×#2353	C₂	semidirect
5. C₆₇×#2352	C₂	semidirect
6. C₆₇×#2349	C₂	semidirect
7. D₄×C₄⋊C₄×C₆₇	C₂	semidirect
8. C₆₇×#2347	C₂	semidirect
9. C₆₇×#2346	C₂	semidirect
10. C₆₇×#2342	C₂	semidirect
11. C₆₇×#2342	C₂	semidirect
14. C₆₇×#2319	C₂	semidirect
15. C₆₇×#2318	C₂	semidirect
16. C₆₇×#2314	C₂	semidirect
17. C₆₇×#2312	C₂	semidirect
18. C₆₇×#2298	C₂	semidirect
19. C₆₇×#2293	C₂	semidirect
20. C₆₇×#2290	C₂	semidirect
21. C₂×#388×C₆₇	C₂	semidirect
22. C₆₇×#2275	C₂	semidirect
23. C₄²×D₄×C₆₇	C₂	semidirect
25. #518×C₆₇	C₄	semidirect
38. C₂×#117×C₆₇	C₂²	semidirect
39. C₂×#117×C₆₇	C₂²	semidirect
40. C₂²×C₄⋊C₄×C₆₇	C₂²	semidirect
45. C₂²×C₄²×C₆₇	C₂²	semidirect
50. #389×C₆₇	C₂²	semidirect
51. #389×C₆₇	C₂²	semidirect
52. #389×C₆₇	C₂²	semidirect
53. #389×C₆₇	C₂²	semidirect
64. #388×C₆₇	C₂²	semidirect
65. #388×C₆₇	C₂²	semidirect
66. #388×C₆₇	C₂²	semidirect
67. #388×C₆₇	C₂²	semidirect
68. #388×C₆₇	C₂²	semidirect
69. #388×C₆₇	C₂²	semidirect
70. #388×C₆₇	C₂²	semidirect
71. #388×C₆₇	C₂²	semidirect
72. #387×C₆₇	C₂²	semidirect
73. #387×C₆₇	C₂²	semidirect
74. #387×C₆₇	C₂²	semidirect
75. #387×C₆₇	C₂²	semidirect
76. #387×C₆₇	C₂²	semidirect
77. #387×C₆₇	C₂²	semidirect
82. #385×C₆₇	C₂²	semidirect
83. #385×C₆₇	C₂²	semidirect
84. #385×C₆₇	C₂²	semidirect
85. #385×C₆₇	C₂²	semidirect
86. #384×C₆₇	C₂²	semidirect
87. #383×C₆₇	C₂²	semidirect
88. #382×C₆₇	C₂²	semidirect
89. #382×C₆₇	C₂²	semidirect
90. #381×C₆₇	C₂²	semidirect
91. #381×C₆₇	C₂²	semidirect
94. #380×C₆₇	C₂²	semidirect
95. #380×C₆₇	C₂²	semidirect
96. #380×C₆₇	C₂²	semidirect
97. #380×C₆₇	C₂²	semidirect
100. C₄×C₄⋊C₄×C₆₇	C₂²	semidirect
101. C₄×C₄⋊C₄×C₆₇	C₂²	semidirect
102. C₄×C₄⋊C₄×C₆₇	C₂²	semidirect
103. C₄×C₄⋊C₄×C₆₇	C₂²	semidirect
104. C₄×C₄⋊C₄×C₆₇	C₂²	semidirect
105. C₄×C₄⋊C₄×C₆₇	C₂²	semidirect
106. C₄×C₄⋊C₄×C₆₇	C₂²	semidirect
107. C₄×C₄⋊C₄×C₆₇	C₂²	semidirect
108. C₄×C₄⋊C₄×C₆₇	C₂²	semidirect
111. C₄×C₂²⋊C₄×C₆₇	C₂²	semidirect
112. C₄×C₂²⋊C₄×C₆₇	C₂²	semidirect
113. C₄×C₂²⋊C₄×C₆₇	C₂²	semidirect
114. C₄×C₂²⋊C₄×C₆₇	C₂²	semidirect
115. C₄×C₂²⋊C₄×C₆₇	C₂²	semidirect
116. C₄×C₂²⋊C₄×C₆₇	C₂²	semidirect
117. C₄×C₂²⋊C₄×C₆₇	C₂²	semidirect
118. C₄×C₂²⋊C₄×C₆₇	C₂²	semidirect
119. #376×C₆₇	C₂²	semidirect
120. #376×C₆₇	C₂²	semidirect
121. C₂×#95×C₆₇	C₂²	semidirect
122. C₂×#95×C₆₇	C₂²	semidirect
123. C₄³×C₆₇	C₂²	semidirect
146. C₄×D₄×C₆₇	C₂×C₄	semidirect
147. C₄×D₄×C₆₇	C₂×C₄	semidirect
148. C₄×D₄×C₆₇	C₂×C₄	semidirect
149. C₄×D₄×C₆₇	C₂×C₄	semidirect
152. #117×C₆₇	C₂×C₄	semidirect
153. #117×C₆₇	C₂×C₄	semidirect
175. C₂×C₂²⋊C₄×C₆₇	C₂×C₄	semidirect
176. C₂×C₂²⋊C₄×C₆₇	C₂×C₄	semidirect
404. D₄×C₆₇	#117	semidirect
523. #34261	C₆₇	direct (N × H)
535. #2357	C₂×C₆₇	semidirect
536. #2354	C₂×C₆₇	semidirect
537. #2353	C₂×C₆₇	semidirect
538. #2352	C₂×C₆₇	semidirect
539. #2349	C₂×C₆₇	semidirect
540. D₄×C₄⋊C₄	C₂×C₆₇	semidirect
541. #2347	C₂×C₆₇	semidirect
542. #2346	C₂×C₆₇	semidirect
543. #2342	C₂×C₆₇	semidirect
544. #2342	C₂×C₆₇	semidirect
547. #2319	C₂×C₆₇	semidirect
548. #2318	C₂×C₆₇	semidirect
549. #2314	C₂×C₆₇	semidirect
550. #2312	C₂×C₆₇	semidirect
551. #2298	C₂×C₆₇	semidirect
552. #2293	C₂×C₆₇	semidirect
553. #2290	C₂×C₆₇	semidirect
554. C₂×#388	C₂×C₆₇	semidirect
555. #2275	C₂×C₆₇	semidirect
556. C₄²×D₄	C₂×C₆₇	semidirect
557. C₆₇	#34261	direct (N × H)
559. #518	C₄×C₆₇	semidirect
572. C₂×#117	C₂²×C₆₇	semidirect
573. C₂×#117	C₂²×C₆₇	semidirect
574. C₂²×C₄⋊C₄	C₂²×C₆₇	semidirect
579. C₂²×C₄²	C₂²×C₆₇	semidirect
584. #389	C₂²×C₆₇	semidirect
585. #389	C₂²×C₆₇	semidirect
586. #389	C₂²×C₆₇	semidirect
587. #389	C₂²×C₆₇	semidirect
598. #388	C₂²×C₆₇	semidirect
599. #388	C₂²×C₆₇	semidirect
600. #388	C₂²×C₆₇	semidirect
601. #388	C₂²×C₆₇	semidirect
602. #388	C₂²×C₆₇	semidirect
603. #388	C₂²×C₆₇	semidirect
604. #388	C₂²×C₆₇	semidirect
605. #388	C₂²×C₆₇	semidirect
606. #387	C₂²×C₆₇	semidirect
607. #387	C₂²×C₆₇	semidirect
608. #387	C₂²×C₆₇	semidirect
609. #387	C₂²×C₆₇	semidirect
610. #387	C₂²×C₆₇	semidirect
611. #387	C₂²×C₆₇	semidirect
616. #385	C₂²×C₆₇	semidirect
617. #385	C₂²×C₆₇	semidirect
618. #385	C₂²×C₆₇	semidirect
619. #385	C₂²×C₆₇	semidirect
620. #384	C₂²×C₆₇	semidirect
621. #383	C₂²×C₆₇	semidirect
622. #382	C₂²×C₆₇	semidirect
623. #382	C₂²×C₆₇	semidirect
624. #381	C₂²×C₆₇	semidirect
625. #381	C₂²×C₆₇	semidirect
628. #380	C₂²×C₆₇	semidirect
629. #380	C₂²×C₆₇	semidirect
630. #380	C₂²×C₆₇	semidirect
631. #380	C₂²×C₆₇	semidirect
634. C₄×C₄⋊C₄	C₂²×C₆₇	semidirect
635. C₄×C₄⋊C₄	C₂²×C₆₇	semidirect
636. C₄×C₄⋊C₄	C₂²×C₆₇	semidirect
637. C₄×C₄⋊C₄	C₂²×C₆₇	semidirect
638. C₄×C₄⋊C₄	C₂²×C₆₇	semidirect
639. C₄×C₄⋊C₄	C₂²×C₆₇	semidirect
640. C₄×C₄⋊C₄	C₂²×C₆₇	semidirect
641. C₄×C₄⋊C₄	C₂²×C₆₇	semidirect
642. C₄×C₄⋊C₄	C₂²×C₆₇	semidirect
645. C₄×C₂²⋊C₄	C₂²×C₆₇	semidirect
646. C₄×C₂²⋊C₄	C₂²×C₆₇	semidirect
647. C₄×C₂²⋊C₄	C₂²×C₆₇	semidirect
648. C₄×C₂²⋊C₄	C₂²×C₆₇	semidirect
649. C₄×C₂²⋊C₄	C₂²×C₆₇	semidirect
650. C₄×C₂²⋊C₄	C₂²×C₆₇	semidirect
651. C₄×C₂²⋊C₄	C₂²×C₆₇	semidirect
652. C₄×C₂²⋊C₄	C₂²×C₆₇	semidirect
653. #376	C₂²×C₆₇	semidirect
654. #376	C₂²×C₆₇	semidirect
655. C₂×#95	C₂²×C₆₇	semidirect
656. C₂×#95	C₂²×C₆₇	semidirect
657. C₄³	C₂²×C₆₇	semidirect
680. C₄×D₄	C₂×C₄×C₆₇	semidirect
681. C₄×D₄	C₂×C₄×C₆₇	semidirect
682. C₄×D₄	C₂×C₄×C₆₇	semidirect
683. C₄×D₄	C₂×C₄×C₆₇	semidirect
686. #117	C₂×C₄×C₆₇	semidirect
687. #117	C₂×C₄×C₆₇	semidirect
709. C₂×C₂²⋊C₄	C₂×C₄×C₆₇	semidirect
710. C₂×C₂²⋊C₄	C₂×C₄×C₆₇	semidirect
938. D₄	#117×C₆₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×#518×C₆₇	2
C₆₇×#2357	2
C₆₇×#2354	2
C₆₇×#2353	2
C₆₇×#2352	2
C₆₇×#2349	2
D₄×C₄⋊C₄×C₆₇	2
C₆₇×#2347	2
C₆₇×#2346	2
C₆₇×#2342	2
D₄×C₂²⋊C₄×C₆₇	2
C₆₇×#2319	2
C₆₇×#2318	2
C₆₇×#2314	2
C₆₇×#2312	2
C₆₇×#2298	2
C₆₇×#2293	2
C₆₇×#2290	2
C₂×#388×C₆₇	2
C₆₇×#2275	2
C₄²×D₄×C₆₇	2
#34261	67

Subgroups — C67×#34261 #30713512

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#34261 #30713512