Subgroups — C₆₇×#60272 #30739523

Order 17152.

1832 conjugacy classes of subgroups.

The subgroup lattice has 1176 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₇×#3475	C₂	1	1	yes	maximal, characteristic
2	C₆₇×#2995	C₂	1	2	yes	maximal, complemented
3	C₆₇×#2995	C₂	1	2	yes	maximal, complemented
4	C₆₇×#2994	C₂	1	2	yes	maximal, complemented
5	C₆₇×#2993	C₂	1	2	yes	maximal, complemented
6	C₆₇×#2992	C₂	1	2	yes	maximal, complemented
7	C₆₇×#2992	C₂	1	2	yes	maximal, complemented
8	C₆₇×#2990	C₂	1	2	yes	maximal, complemented
9	C₆₇×#2989	C₂	1	2	yes	maximal, complemented
10	C₆₇×#2962	C₂	1	1	yes	maximal, characteristic, complemented
11	C₆₇×#2961	C₂	1	1	yes	maximal, characteristic, complemented
12	D₄×M₁₆×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
13	C₆₇×#2933	C₂	1	1	yes	maximal, characteristic, complemented
14	C₆₇×#2933	C₂	1	1	yes	maximal, characteristic, complemented
15	C₆₇×#2930	C₂	1	1	yes	maximal, characteristic, complemented
16	C₆₇×#2929	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂×#435×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
18	C₆₇×#2924	C₂	1	1	yes	maximal, characteristic, complemented
19	C₆₇×#2924	C₂	1	1	yes	maximal, characteristic, complemented
20	C₆₇×#2923	C₂	1	1	yes	maximal, characteristic, complemented
21	C₆₇×#2906	C₂	1	1	yes	maximal, characteristic, complemented
22	C₆₇×#2905	C₂	1	1	yes	maximal, characteristic, complemented
23	C₂×#424×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#131×C₆₇	C₂²	1	1	yes	characteristic
25	C₂×#131×C₆₇	C₂²	1	1	yes	characteristic
26	C₂²×M₁₆×C₆₇	C₂²	1	1	yes	characteristic
27	C₂²×M₁₆×C₆₇	C₂²	1	1	yes	characteristic
28	C₂²×M₁₆×C₆₇	C₂²	1	1	yes	characteristic
29	C₂³×C₈×C₆₇	C₂²	1	1	yes	characteristic
30	#556×C₆₇	C₄	1	1	yes	characteristic
31	#555×C₆₇	C₄	1	1	yes	characteristic
32	#554×C₆₇	C₄	1	1	yes	characteristic
33	#553×C₆₇	C₄	1	1	yes	characteristic
34	#553×C₆₇	C₄	1	1	yes	characteristic
35	#552×C₆₇	C₄	1	1	yes	characteristic
36	#552×C₆₇	C₄	1	1	yes	characteristic
37	#552×C₆₇	C₄	1	2	yes	—
38	#551×C₆₇	C₄	1	2	yes	—
39	#551×C₆₇	C₄	1	2	yes	—
40	#547×C₆₇	C₄	1	1	yes	characteristic
41	#546×C₆₇	C₄	1	2	yes	—
42	#533×C₆₇	C₂²	1	1	yes	characteristic
43	#529×C₆₇	C₂²	1	2	yes	—
44	#529×C₆₇	C₂²	1	2	yes	—
45	#529×C₆₇	C₂²	1	2	yes	—
46	#525×C₆₇	C₂²	1	1	yes	characteristic
47	#525×C₆₇	C₂²	1	1	yes	characteristic
48	C₄×#41×C₆₇	C₂²	1	2	yes	—
49	C₄×#41×C₆₇	C₂²	1	1	yes	characteristic
50	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
51	C₂×#117×C₆₇	C₂²	1	1	yes	characteristic
52	C₂×#117×C₆₇	C₂²	1	1	yes	characteristic
53	#446×C₆₇	C₂²	1	2	yes	complemented
54	#446×C₆₇	C₂²	1	2	yes	complemented
55	#446×C₆₇	C₂²	1	2	yes	complemented
56	#446×C₆₇	C₂²	1	2	yes	complemented
57	#446×C₆₇	C₂²	1	2	yes	complemented
58	#446×C₆₇	C₂²	1	2	yes	complemented
59	#446×C₆₇	C₂²	1	2	yes	complemented
60	C₈×Q₈×C₆₇	C₂²	1	2	yes	complemented
61	#436×C₆₇	C₂²	1	2	yes	—
62	#436×C₆₇	C₂²	1	2	yes	complemented
63	#436×C₆₇	C₂²	1	2	yes	complemented
64	#436×C₆₇	C₂²	1	2	yes	complemented
65	#436×C₆₇	C₂²	1	2	yes	complemented
66	#435×C₆₇	C₂²	1	1	yes	characteristic
67	#435×C₆₇	C₂²	1	1	yes	characteristic
68	#435×C₆₇	C₂²	1	1	yes	characteristic
69	#435×C₆₇	C₂²	1	1	yes	characteristic
70	#435×C₆₇	C₂²	1	1	yes	characteristic
71	#435×C₆₇	C₂²	1	1	yes	characteristic
72	#435×C₆₇	C₂²	1	1	yes	characteristic
73	#435×C₆₇	C₂²	1	1	yes	characteristic
74	#435×C₆₇	C₂²	1	2	yes	—
75	#435×C₆₇	C₂²	1	2	yes	—
76	#435×C₆₇	C₂²	1	2	yes	complemented
77	#435×C₆₇	C₂²	1	2	yes	complemented
78	#435×C₆₇	C₂²	1	2	yes	complemented
79	#435×C₆₇	C₂²	1	2	yes	complemented
80	#435×C₆₇	C₂²	1	2	yes	complemented
81	#435×C₆₇	C₂²	1	2	yes	complemented
82	#435×C₆₇	C₂²	1	2	yes	complemented
83	#435×C₆₇	C₂²	1	2	yes	complemented
84	C₈×D₄×C₆₇	C₂²	1	2	yes	—
85	C₈×D₄×C₆₇	C₂²	1	2	yes	complemented
86	C₈×D₄×C₆₇	C₂²	1	2	yes	complemented
87	C₈×D₄×C₆₇	C₂²	1	2	yes	complemented
88	C₈×D₄×C₆₇	C₂²	1	2	yes	complemented
89	#433×C₆₇	C₂²	1	2	yes	complemented
90	#433×C₆₇	C₂²	1	2	yes	complemented
91	#433×C₆₇	C₂²	1	2	yes	complemented
92	#433×C₆₇	C₂²	1	2	yes	complemented
93	#433×C₆₇	C₂²	1	2	yes	complemented
94	#433×C₆₇	C₂²	1	2	yes	complemented
95	#432×C₆₇	C₂²	1	2	yes	complemented
96	#432×C₆₇	C₂²	1	2	yes	complemented
97	#432×C₆₇	C₂²	1	2	yes	complemented
98	#432×C₆₇	C₂²	1	2	yes	complemented
99	#431×C₆₇	C₂²	1	2	yes	complemented
100	#431×C₆₇	C₂²	1	2	yes	complemented
101	#424×C₆₇	C₂²	1	1	yes	characteristic
102	#424×C₆₇	C₂²	1	1	yes	characteristic
103	#424×C₆₇	C₂²	1	1	yes	characteristic
104	#424×C₆₇	C₂²	1	1	yes	characteristic
105	#424×C₆₇	C₂²	1	1	yes	characteristic
106	#424×C₆₇	C₂²	1	1	yes	characteristic
107	#424×C₆₇	C₂²	1	1	yes	characteristic
108	#424×C₆₇	C₂²	1	1	yes	characteristic
109	#424×C₆₇	C₂²	1	2	yes	complemented
110	#424×C₆₇	C₂²	1	2	yes	complemented
111	#424×C₆₇	C₂²	1	2	yes	complemented
112	#424×C₆₇	C₂²	1	2	yes	complemented
113	#424×C₆₇	C₂²	1	2	yes	complemented
114	#424×C₆₇	C₂²	1	2	yes	complemented
115	#423×C₆₇	C₂²	1	1	yes	characteristic
116	#423×C₆₇	C₂²	1	2	yes	complemented
117	#423×C₆₇	C₂²	1	2	yes	complemented
118	#423×C₆₇	C₂²	1	2	yes	complemented
119	C₂×C₄⋊C₈×C₆₇	C₂²	1	1	yes	characteristic
120	C₂×C₄⋊C₈×C₆₇	C₂²	1	2	yes	complemented
121	C₂×C₄⋊C₈×C₆₇	C₂²	1	2	yes	complemented
122	C₂×C₄⋊C₈×C₆₇	C₂²	1	2	yes	complemented
123	#408×C₆₇	C₂²	1	1	yes	characteristic
124	#408×C₆₇	C₂²	1	1	yes	characteristic
125	#407×C₆₇	C₂²	1	1	yes	characteristic
126	#407×C₆₇	C₂²	1	1	yes	characteristic
127	C₂×C₂²⋊C₈×C₆₇	C₂²	1	1	yes	characteristic
128	C₂×C₂²⋊C₈×C₆₇	C₂²	1	1	yes	characteristic
129	#405×C₆₇	C₂²	1	1	yes	characteristic
130	#405×C₆₇	C₂²	1	1	yes	characteristic
131	#405×C₆₇	C₂²	1	1	yes	characteristic
132	#405×C₆₇	C₂²	1	1	yes	characteristic
133	C₄×M₁₆×C₆₇	C₂²	1	1	yes	characteristic
134	C₂×#97×C₆₇	C₂²	1	1	yes	characteristic
135	C₂×#41×C₆₇	C₂×C₄	1	2	yes	—
136	C₂×#41×C₆₇	C₂³	1	1	yes	characteristic
137	C₂²×D₄×C₆₇	C₂×C₄	1	1	yes	characteristic
138	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
139	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
140	#131×C₆₇	—	4	2	no	—
141	#131×C₆₇	—	4	2	no	—
142	C₂×M₁₆×C₆₇	—	4	2	no	—
143	C₂×M₁₆×C₆₇	—	4	2	no	—
144	C₂×M₁₆×C₆₇	—	4	2	no	—
145	C₂×M₁₆×C₆₇	C₂³	1	1	yes	characteristic
146	C₂×M₁₆×C₆₇	C₂³	1	1	yes	characteristic
147	C₂×M₁₆×C₆₇	C₂³	1	1	yes	characteristic
148	C₂×M₁₆×C₆₇	C₂³	1	1	yes	characteristic
149	C₂×M₁₆×C₆₇	C₂³	1	1	yes	characteristic
150	C₂×M₁₆×C₆₇	C₂³	1	1	yes	characteristic
151	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
152	C₂×M₁₆×C₆₇	C₂³	1	1	yes	characteristic
153	C₂×M₁₆×C₆₇	C₂³	1	1	yes	characteristic
154	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
155	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
156	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
157	C₂²×C₈×C₆₇	—	4	2	no	—
158	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
159	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
160	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
161	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
162	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
163	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
164	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
165	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
166	C₂²×C₈×C₆₇	C₂³	1	2	yes	—
167	C₂²×C₈×C₆₇	C₂³	1	2	yes	—
168	C₂²×C₈×C₆₇	C₂³	1	2	yes	—
169	C₂²×C₈×C₆₇	C₂³	1	2	yes	—
170	C₄⋊Q₈×C₆₇	C₂×C₄	1	1	yes	characteristic
171	C₄⋊Q₈×C₆₇	C₂×C₄	1	1	yes	characteristic
172	#126×C₆₇	C₂×C₄	1	2	yes	—
173	#126×C₆₇	C₂×C₄	1	2	yes	—
174	#126×C₆₇	C₂×C₄	1	2	yes	—
175	#126×C₆₇	C₂×C₄	1	2	yes	—
176	#126×C₆₇	C₂×C₄	1	2	yes	—
177	#126×C₆₇	C₂×C₄	1	2	yes	—
178	#125×C₆₇	C₂×C₄	1	2	yes	—
179	#125×C₆₇	C₂×C₄	1	2	yes	—
180	#125×C₆₇	C₂×C₄	1	2	yes	—
181	#125×C₆₇	C₂×C₄	1	1	yes	characteristic
182	#125×C₆₇	C₂×C₄	1	1	yes	characteristic
183	#124×C₆₇	C₂×C₄	1	2	yes	—
184	#124×C₆₇	C₂×C₄	1	2	yes	—
185	#124×C₆₇	C₂×C₄	1	2	yes	—
186	#123×C₆₇	C₂×C₄	1	2	yes	—
187	#123×C₆₇	C₂×C₄	1	2	yes	—
188	#123×C₆₇	C₂×C₄	1	2	yes	—
189	#123×C₆₇	C₂×C₄	1	2	yes	—
190	#123×C₆₇	C₂×C₄	1	2	yes	—
191	#123×C₆₇	C₂×C₄	1	2	yes	—
192	#123×C₆₇	C₂×C₄	1	2	yes	—
193	#123×C₆₇	C₂×C₄	1	2	yes	—
194	C₂²⋊Q₈×C₆₇	C₂×C₄	1	1	yes	characteristic
195	C₂²⋊Q₈×C₆₇	C₂×C₄	1	1	yes	characteristic
196	C₂²⋊Q₈×C₆₇	C₂×C₄	1	1	yes	characteristic
197	C₂²⋊Q₈×C₆₇	C₂×C₄	1	1	yes	characteristic
198	C₂²⋊Q₈×C₆₇	C₂×C₄	1	2	yes	—
199	C₂²⋊Q₈×C₆₇	C₂×C₄	1	2	yes	—
200	C₂²⋊Q₈×C₆₇	C₂×C₄	1	2	yes	—
201	C₂²⋊Q₈×C₆₇	C₂×C₄	1	2	yes	—
202	C₂²⋊Q₈×C₆₇	C₂×C₄	1	2	yes	—
203	#121×C₆₇	C₂×C₄	1	1	yes	characteristic
204	#121×C₆₇	C₂×C₄	1	1	yes	characteristic
205	#121×C₆₇	C₂×C₄	1	1	yes	characteristic
206	#121×C₆₇	C₂×C₄	1	1	yes	characteristic
207	#121×C₆₇	C₂×C₄	1	2	yes	—
208	#121×C₆₇	C₂×C₄	1	2	yes	—
209	#121×C₆₇	C₂×C₄	1	2	yes	—
210	#120×C₆₇	C₂×C₄	1	2	yes	—
211	#120×C₆₇	C₂×C₄	1	2	yes	—
212	C₄×Q₈×C₆₇	C₂×C₄	1	1	yes	characteristic
213	C₄×Q₈×C₆₇	C₂×C₄	1	2	yes	—
214	C₄×Q₈×C₆₇	C₂×C₄	1	1	yes	characteristic
215	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
216	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
217	C₄×D₄×C₆₇	C₂×C₄	1	1	yes	characteristic
218	C₄×D₄×C₆₇	C₂×C₄	1	1	yes	characteristic
219	C₄×D₄×C₆₇	C₂×C₄	1	1	yes	characteristic
220	C₄×D₄×C₆₇	C₂×C₄	1	1	yes	characteristic
221	C₄×D₄×C₆₇	C₂×C₄	1	2	yes	—
222	C₄×D₄×C₆₇	C₂×C₄	1	2	yes	—
223	C₄×D₄×C₆₇	C₂×C₄	1	1	yes	characteristic
224	C₄×D₄×C₆₇	C₂×C₄	1	2	yes	—
225	C₄×D₄×C₆₇	C₂×C₄	1	2	yes	—
226	C₄×D₄×C₆₇	C₂×C₄	1	2	yes	—
227	C₄×D₄×C₆₇	C₂×C₄	1	1	yes	characteristic
228	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
229	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
230	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
231	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
232	C₄×D₄×C₆₇	C₂³	1	2	yes	—
233	C₄×D₄×C₆₇	C₂³	1	2	yes	—
234	C₄×D₄×C₆₇	C₂³	1	2	yes	—
235	C₄×D₄×C₆₇	C₂³	1	2	yes	—
236	#117×C₆₇	C₂×C₄	1	2	yes	—
237	#117×C₆₇	C₂×C₄	1	2	yes	—
238	#117×C₆₇	C₂×C₄	1	1	yes	characteristic
239	#117×C₆₇	C₂×C₄	1	1	yes	characteristic
240	#117×C₆₇	C₂×C₄	1	1	yes	characteristic
241	#117×C₆₇	C₂×C₄	1	1	yes	characteristic
242	#117×C₆₇	C₂×C₄	1	2	yes	—
243	#117×C₆₇	C₂×C₄	1	2	yes	—
244	#117×C₆₇	C₂×C₄	1	2	yes	—
245	#117×C₆₇	C₂³	1	1	yes	characteristic
246	#117×C₆₇	C₂³	1	1	yes	characteristic
247	#117×C₆₇	C₂³	1	1	yes	characteristic
248	#117×C₆₇	C₂³	1	2	yes	—
249	#117×C₆₇	C₂³	1	2	yes	—
250	#117×C₆₇	C₂³	1	2	yes	—
251	C₂×C₄⋊C₄×C₆₇	C₂×C₄	1	1	yes	characteristic
252	C₂×C₄⋊C₄×C₆₇	C₂×C₄	1	1	yes	characteristic
253	C₂×C₄⋊C₄×C₆₇	C₂×C₄	1	1	yes	characteristic
254	C₂×C₄⋊C₄×C₆₇	C₂×C₄	1	1	yes	characteristic
255	C₂×C₄⋊C₄×C₆₇	C₂×C₄	1	1	yes	characteristic
256	C₂×C₂²⋊C₄×C₆₇	C₂×C₄	1	2	yes	—
257	C₂×C₂²⋊C₄×C₆₇	C₂×C₄	1	2	yes	—
258	C₂×C₂²⋊C₄×C₆₇	C₂×C₄	1	1	yes	characteristic
259	C₂×C₂²⋊C₄×C₆₇	C₂×C₄	1	1	yes	characteristic
260	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
261	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
262	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
263	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
264	C₄⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
265	C₄⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
266	C₄⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
267	C₄⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
268	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
269	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
270	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
271	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
272	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
273	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
274	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
275	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
276	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
277	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
278	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
279	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
280	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
281	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
282	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
283	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
284	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
285	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
286	C₂²⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
287	C₂²⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
288	C₂²⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
289	C₂²⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
290	C₂²⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
291	C₂²⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
292	C₂²⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
293	C₂²⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
294	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
295	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
296	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
297	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
298	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
299	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
300	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
301	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
302	#97×C₆₇	C₂³	1	1	yes	characteristic
303	#97×C₆₇	C₂³	1	1	yes	characteristic
304	#97×C₆₇	C₂³	1	1	yes	characteristic
305	#97×C₆₇	C₂³	1	1	yes	characteristic
306	#97×C₆₇	C₂³	1	2	yes	—
307	#97×C₆₇	C₂³	1	2	yes	—
308	#97×C₆₇	C₂³	1	2	yes	—
309	#97×C₆₇	C₂³	1	2	yes	—
310	#97×C₆₇	C₂³	1	2	yes	—
311	C₄×C₈×C₆₇	C₂³	1	2	yes	—
312	C₄×C₈×C₆₇	C₂³	1	2	yes	—
313	C₄×C₈×C₆₇	C₂³	1	2	yes	—
314	C₄×C₈×C₆₇	C₂³	1	2	yes	—
315	C₄×C₈×C₆₇	C₂³	1	2	yes	—
316	C₂⁴×C₆₇	C₂²×C₄	1	1	yes	characteristic
317	C₂⁴×C₆₇	C₂²×C₄	1	1	yes	characteristic
318	#41×C₆₇	—	2	2	no	—
319	#41×C₆₇	—	2	2	no	—
320	#41×C₆₇	—	4	4	no	—
321	C₂×Q₈×C₆₇	C₂²×C₄	1	1	yes	characteristic
322	C₂×Q₈×C₆₇	C₂²×C₄	1	2	yes	—
323	C₂×Q₈×C₆₇	C₂²×C₄	1	2	yes	—
324	C₂×D₄×C₆₇	—	4	2	no	—
325	C₂×D₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
326	C₂×D₄×C₆₇	C₂²×C₄	1	2	yes	—
327	C₂×D₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
328	C₂×D₄×C₆₇	C₂²×C₄	1	2	yes	—
329	C₂×D₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
330	C₂×D₄×C₆₇	C₂²×C₄	1	2	yes	—
331	C₂×D₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
332	C₂×D₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
333	C₂×D₄×C₆₇	C₂²×C₄	1	2	yes	—
334	C₂×D₄×C₆₇	C₂²×C₄	1	2	yes	—
335	C₂²×C₄×C₆₇	—	2	2	no	—
336	C₂²×C₄×C₆₇	—	2	2	no	—
337	C₂²×C₄×C₆₇	—	2	2	no	—
338	C₂²×C₄×C₆₇	—	2	2	no	—
339	C₂²×C₄×C₆₇	C₂²×C₄	1	2	yes	—
340	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
341	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
342	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
343	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
344	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
345	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
346	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
347	C₂²×C₄×C₆₇	C₂²×C₄	1	2	yes	—
348	C₂²×C₄×C₆₇	C₂²×C₄	1	2	yes	—
349	C₂²×C₄×C₆₇	C₂²×C₄	1	2	yes	—
350	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
351	C₂²×C₄×C₆₇	C₂²×C₄	1	2	yes	—
352	C₂²×C₄×C₆₇	C₂²×C₄	1	2	yes	—
353	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
354	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
355	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
356	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
357	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
358	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
359	M₁₆×C₆₇	—	2	2	no	—
360	M₁₆×C₆₇	—	2	2	no	—
361	M₁₆×C₆₇	—	2	2	no	—
362	M₁₆×C₆₇	—	2	2	no	—
363	M₁₆×C₆₇	—	4	1	no	—
364	M₁₆×C₆₇	—	4	1	no	—
365	M₁₆×C₆₇	—	4	1	no	—
366	M₁₆×C₆₇	—	4	1	no	—
367	M₁₆×C₆₇	—	4	2	no	—
368	M₁₆×C₆₇	—	4	2	no	—
369	M₁₆×C₆₇	—	4	2	no	—
370	M₁₆×C₆₇	—	4	2	no	—
371	C₂×C₈×C₆₇	—	2	2	no	—
372	C₂×C₈×C₆₇	—	2	2	no	—
373	C₂×C₈×C₆₇	—	2	2	no	—
374	C₂×C₈×C₆₇	—	2	2	no	—
375	C₂×C₈×C₆₇	—	4	1	no	—
376	C₂×C₈×C₆₇	—	4	1	no	—
377	C₂×C₈×C₆₇	—	4	1	no	—
378	C₂×C₈×C₆₇	—	4	1	no	—
379	C₂×C₈×C₆₇	—	4	2	no	—
380	C₂×C₈×C₆₇	—	4	2	no	—
381	C₂×C₈×C₆₇	—	4	2	no	—
382	C₂×C₈×C₆₇	—	4	2	no	—
383	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
384	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
385	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
386	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
387	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
388	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
389	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
390	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
391	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
392	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
393	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
394	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
395	C₄⋊C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
396	C₄⋊C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
397	C₄⋊C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
398	C₄⋊C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
399	C₄⋊C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
400	C₄⋊C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
401	C₄⋊C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
402	C₄⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
403	C₄⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
404	C₄⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
405	C₄⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
406	C₄⋊C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
407	C₄⋊C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
408	C₄⋊C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
409	C₄⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
410	C₄⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
411	C₄⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
412	C₄⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
413	C₄⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
414	C₄⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
415	C₄⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
416	C₄⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
417	C₄⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
418	C₄⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
419	C₄⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
420	C₄⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
421	C₂²⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
422	C₂²⋊C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
423	C₂²⋊C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
424	C₂²⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
425	C₂²⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
426	C₂²⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
427	C₂²⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
428	C₂²⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
429	C₂²⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
430	C₂²⋊C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
431	C₂²⋊C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
432	C₂²⋊C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
433	C₂²⋊C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
434	C₂²⋊C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
435	C₂²⋊C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
436	C₂²⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
437	C₂²⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
438	C₂²⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
439	C₂²⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
440	C₂²⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
441	C₂²⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
442	C₂²⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
443	C₂²⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
444	C₂²⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
445	C₂²⋊C₄×C₆₇	C₂²×C₄	1	2	yes	—
446	C₄²×C₆₇	C₂²×C₄	1	2	yes	—
447	C₄²×C₆₇	C₂²×C₄	1	2	yes	—
448	C₄²×C₆₇	C₂²×C₄	1	2	yes	—
449	C₄²×C₆₇	C₂²×C₄	1	2	yes	—
450	C₄²×C₆₇	C₂²×C₄	1	2	yes	—
451	C₄²×C₆₇	C₂²×C₄	1	1	yes	characteristic
452	C₄²×C₆₇	C₂²×C₄	1	1	yes	characteristic
453	C₄²×C₆₇	C₂²×C₄	1	2	yes	—
454	C₄²×C₆₇	C₂⁴	1	2	yes	—
455	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
456	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
457	C₄²×C₆₇	C₂⁴	1	2	yes	—
458	C₄²×C₆₇	C₂⁴	1	2	yes	—
459	C₂³×C₆₇	—	2	2	no	—
460	C₂³×C₆₇	—	2	2	no	—
461	C₂³×C₆₇	—	2	2	no	—
462	C₂³×C₆₇	—	4	1	no	—
463	C₂³×C₆₇	—	4	1	no	—
464	C₂³×C₆₇	—	4	1	no	—
465	C₂³×C₆₇	C₂³×C₄	1	1	yes	characteristic
466	C₂³×C₆₇	C₂³×C₄	1	1	yes	characteristic
467	C₂³×C₆₇	C₂³×C₄	1	2	yes	—
468	C₂³×C₆₇	C₂³×C₄	1	1	yes	characteristic
469	C₂³×C₆₇	C₂³×C₄	1	1	yes	characteristic
470	C₂³×C₆₇	C₂³×C₄	1	1	yes	characteristic
471	Q₈×C₆₇	—	2	2	no	—
472	Q₈×C₆₇	—	4	2	no	—
473	Q₈×C₆₇	—	4	2	no	—
474	D₄×C₆₇	—	2	4	no	—
475	D₄×C₆₇	—	2	2	no	—
476	D₄×C₆₇	—	2	2	no	—
477	D₄×C₆₇	—	2	4	no	—
478	D₄×C₆₇	—	2	2	no	—
479	D₄×C₆₇	—	4	1	no	—
480	D₄×C₆₇	—	4	1	no	—
481	D₄×C₆₇	—	4	2	no	—
482	D₄×C₆₇	—	4	2	no	—
483	D₄×C₆₇	—	4	2	no	—
484	C₂×C₄×C₆₇	—	2	2	no	—
485	C₂×C₄×C₆₇	—	2	2	no	—
486	C₂×C₄×C₆₇	—	2	4	no	—
487	C₂×C₄×C₆₇	—	2	2	no	—
488	C₂×C₄×C₆₇	—	2	2	no	—
489	C₂×C₄×C₆₇	—	2	2	no	—
490	C₂×C₄×C₆₇	—	2	2	no	—
491	C₂×C₄×C₆₇	—	2	1	no	—
492	C₂×C₄×C₆₇	—	2	1	no	—
493	C₂×C₄×C₆₇	—	2	1	no	—
494	C₂×C₄×C₆₇	—	2	2	no	—
495	C₂×C₄×C₆₇	—	2	1	no	—
496	C₂×C₄×C₆₇	—	2	1	no	—
497	C₂×C₄×C₆₇	—	2	1	no	—
498	C₂×C₄×C₆₇	—	2	1	no	—
499	C₂×C₄×C₆₇	—	2	1	no	—
500	C₂×C₄×C₆₇	—	2	2	no	—
501	C₂×C₄×C₆₇	—	4	2	no	—
502	C₂×C₄×C₆₇	—	4	2	no	—
503	C₂×C₄×C₆₇	—	4	2	no	—
504	C₂×C₄×C₆₇	—	4	1	no	—
505	C₂×C₄×C₆₇	—	4	1	no	—
506	C₂×C₄×C₆₇	—	4	2	no	—
507	C₂×C₄×C₆₇	—	4	2	no	—
508	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
509	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
510	C₂×C₄×C₆₇	C₂³×C₄	1	2	yes	—
511	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
512	C₂×C₄×C₆₇	C₂³×C₄	1	2	yes	—
513	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
514	C₂×C₄×C₆₇	C₂³×C₄	1	2	yes	—
515	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
516	C₂×C₄×C₆₇	C₂³×C₄	1	2	yes	—
517	C₂×C₄×C₆₇	C₂³×C₄	1	2	yes	—
518	C₂×C₄×C₆₇	C₂³×C₄	1	2	yes	—
519	C₂×C₄×C₆₇	C₂³×C₄	1	2	yes	—
520	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
521	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
522	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
523	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
524	C₂×C₄×C₆₇	H(5,𝔽₂)	1	2	yes	—
525	C₂×C₄×C₆₇	2₋¹⁺⁴	1	2	yes	—
526	C₂×C₄×C₆₇	C₂⁵	1	1	yes	characteristic
527	C₈×C₆₇	—	2	1	no	—
528	C₈×C₆₇	—	2	1	no	—
529	C₈×C₆₇	—	2	1	no	—
530	C₈×C₆₇	—	2	1	no	—
531	C₈×C₆₇	—	2	1	no	—
532	C₈×C₆₇	—	2	1	no	—
533	C₈×C₆₇	—	2	2	no	—
534	C₈×C₆₇	—	2	2	no	—
535	C₈×C₆₇	—	2	2	no	—
536	C₈×C₆₇	—	2	1	no	—
537	C₈×C₆₇	—	2	1	no	—
538	C₈×C₆₇	—	2	2	no	—
539	C₂²×C₆₇	—	2	1	no	—
540	C₂²×C₆₇	—	2	1	no	—
541	C₂²×C₆₇	—	2	1	no	—
542	C₂²×C₆₇	—	2	1	no	—
543	C₂²×C₆₇	—	2	1	no	—
544	C₂²×C₆₇	—	2	1	no	—
545	C₂²×C₆₇	—	2	1	no	—
546	C₂²×C₆₇	—	2	2	no	—
547	C₂²×C₆₇	—	2	1	no	—
548	C₂²×C₆₇	—	2	2	no	—
549	C₂²×C₆₇	—	2	1	no	—
550	C₂²×C₆₇	—	2	1	no	—
551	C₂²×C₆₇	—	2	1	no	—
552	C₂²×C₆₇	—	2	2	no	—
553	C₂²×C₆₇	—	2	1	no	—
554	C₂²×C₆₇	—	2	1	no	—
555	C₂²×C₆₇	—	4	4	no	—
556	C₂²×C₆₇	—	8	2	no	—
557	C₂²×C₆₇	#520	1	2	yes	—
558	C₂²×C₆₇	#568	1	2	yes	—
559	C₂²×C₆₇	C₂⁴×C₄	1	1	yes	characteristic
560	C₄×C₆₇	—	2	1	no	—
561	C₄×C₆₇	—	2	1	no	—
562	C₄×C₆₇	—	2	1	no	—
563	C₄×C₆₇	—	2	1	no	—
564	C₄×C₆₇	—	2	2	no	—
565	C₄×C₆₇	—	2	2	no	—
566	C₄×C₆₇	—	2	2	no	—
567	C₄×C₆₇	—	2	1	no	—
568	C₄×C₆₇	—	2	1	no	—
569	C₄×C₆₇	—	2	2	no	—
570	C₄×C₆₇	—	2	1	no	—
571	C₄×C₆₇	—	2	2	no	—
572	C₄×C₆₇	—	2	2	no	—
573	C₄×C₆₇	—	2	2	no	—
574	C₄×C₆₇	—	2	1	no	—
575	C₄×C₆₇	#520	1	2	yes	—
576	C₄×C₆₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
577	C₄×C₆₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
578	#60272	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
579	C₂×C₆₇	—	2	2	no	—
580	C₂×C₆₇	—	2	2	no	—
581	C₂×C₆₇	—	4	2	no	—
582	C₂×C₆₇	—	4	1	no	—
583	C₂×C₆₇	—	4	1	no	—
584	C₂×C₆₇	—	4	1	no	—
585	C₂×C₆₇	C₂×#520	1	1	yes	characteristic
586	C₂×C₆₇	C₂×#568	1	1	yes	characteristic
587	C₂×C₆₇	#3573	1	1	yes	characteristic
588	#3475	C₂×C₆₇	1	1	yes	characteristic
589	#2995	C₂×C₆₇	1	2	yes	complemented
590	#2995	C₂×C₆₇	1	2	yes	complemented
591	#2994	C₂×C₆₇	1	2	yes	complemented
592	#2993	C₂×C₆₇	1	2	yes	complemented
593	#2992	C₂×C₆₇	1	2	yes	complemented
594	#2992	C₂×C₆₇	1	2	yes	complemented
595	#2990	C₂×C₆₇	1	2	yes	complemented
596	#2989	C₂×C₆₇	1	2	yes	complemented
597	#2962	C₂×C₆₇	1	1	yes	characteristic, complemented
598	#2961	C₂×C₆₇	1	1	yes	characteristic, complemented
599	D₄×M₁₆	C₂×C₆₇	1	1	yes	characteristic, complemented
600	#2933	C₂×C₆₇	1	1	yes	characteristic, complemented
601	#2933	C₂×C₆₇	1	1	yes	characteristic, complemented
602	#2930	C₂×C₆₇	1	1	yes	characteristic, complemented
603	#2929	C₂×C₆₇	1	1	yes	characteristic, complemented
604	C₂×#435	C₂×C₆₇	1	1	yes	characteristic, complemented
605	#2924	C₂×C₆₇	1	1	yes	characteristic, complemented
606	#2924	C₂×C₆₇	1	1	yes	characteristic, complemented
607	#2923	C₂×C₆₇	1	1	yes	characteristic, complemented
608	#2906	C₂×C₆₇	1	1	yes	characteristic, complemented
609	#2905	C₂×C₆₇	1	1	yes	characteristic, complemented
610	C₂×#424	C₂×C₆₇	1	1	yes	characteristic, complemented
611	C₆₇	#60272	1	1	yes	characteristic, direct product factor, Sylow
612	C₂×#131	C₂²×C₆₇	1	1	yes	characteristic
613	C₂×#131	C₂²×C₆₇	1	1	yes	characteristic
614	C₂²×M₁₆	C₂²×C₆₇	1	1	yes	characteristic
615	C₂²×M₁₆	C₂²×C₆₇	1	1	yes	characteristic
616	C₂²×M₁₆	C₂²×C₆₇	1	1	yes	characteristic
617	C₂³×C₈	C₂²×C₆₇	1	1	yes	characteristic
618	#556	C₄×C₆₇	1	1	yes	characteristic
619	#555	C₄×C₆₇	1	1	yes	characteristic
620	#554	C₄×C₆₇	1	1	yes	characteristic
621	#553	C₄×C₆₇	1	1	yes	characteristic
622	#553	C₄×C₆₇	1	1	yes	characteristic
623	#552	C₄×C₆₇	1	1	yes	characteristic
624	#552	C₄×C₆₇	1	1	yes	characteristic
625	#552	C₄×C₆₇	1	2	yes	—
626	#551	C₄×C₆₇	1	2	yes	—
627	#551	C₄×C₆₇	1	2	yes	—
628	#547	C₄×C₆₇	1	1	yes	characteristic
629	#546	C₄×C₆₇	1	2	yes	—
630	#533	C₂²×C₆₇	1	1	yes	characteristic
631	#529	C₂²×C₆₇	1	2	yes	—
632	#529	C₂²×C₆₇	1	2	yes	—
633	#529	C₂²×C₆₇	1	2	yes	—
634	#525	C₂²×C₆₇	1	1	yes	characteristic
635	#525	C₂²×C₆₇	1	1	yes	characteristic
636	C₄×#41	C₂²×C₆₇	1	2	yes	—
637	C₄×#41	C₂²×C₆₇	1	1	yes	characteristic
638	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
639	C₂×#117	C₂²×C₆₇	1	1	yes	characteristic
640	C₂×#117	C₂²×C₆₇	1	1	yes	characteristic
641	#446	C₂²×C₆₇	1	2	yes	complemented
642	#446	C₂²×C₆₇	1	2	yes	complemented
643	#446	C₂²×C₆₇	1	2	yes	complemented
644	#446	C₂²×C₆₇	1	2	yes	complemented
645	#446	C₂²×C₆₇	1	2	yes	complemented
646	#446	C₂²×C₆₇	1	2	yes	complemented
647	#446	C₂²×C₆₇	1	2	yes	complemented
648	C₈×Q₈	C₂²×C₆₇	1	2	yes	complemented
649	#436	C₂²×C₆₇	1	2	yes	—
650	#436	C₂²×C₆₇	1	2	yes	complemented
651	#436	C₂²×C₆₇	1	2	yes	complemented
652	#436	C₂²×C₆₇	1	2	yes	complemented
653	#436	C₂²×C₆₇	1	2	yes	complemented
654	#435	C₂²×C₆₇	1	1	yes	characteristic
655	#435	C₂²×C₆₇	1	1	yes	characteristic
656	#435	C₂²×C₆₇	1	1	yes	characteristic
657	#435	C₂²×C₆₇	1	1	yes	characteristic
658	#435	C₂²×C₆₇	1	1	yes	characteristic
659	#435	C₂²×C₆₇	1	1	yes	characteristic
660	#435	C₂²×C₆₇	1	1	yes	characteristic
661	#435	C₂²×C₆₇	1	1	yes	characteristic
662	#435	C₂²×C₆₇	1	2	yes	—
663	#435	C₂²×C₆₇	1	2	yes	—
664	#435	C₂²×C₆₇	1	2	yes	complemented
665	#435	C₂²×C₆₇	1	2	yes	complemented
666	#435	C₂²×C₆₇	1	2	yes	complemented
667	#435	C₂²×C₆₇	1	2	yes	complemented
668	#435	C₂²×C₆₇	1	2	yes	complemented
669	#435	C₂²×C₆₇	1	2	yes	complemented
670	#435	C₂²×C₆₇	1	2	yes	complemented
671	#435	C₂²×C₆₇	1	2	yes	complemented
672	C₈×D₄	C₂²×C₆₇	1	2	yes	—
673	C₈×D₄	C₂²×C₆₇	1	2	yes	complemented
674	C₈×D₄	C₂²×C₆₇	1	2	yes	complemented
675	C₈×D₄	C₂²×C₆₇	1	2	yes	complemented
676	C₈×D₄	C₂²×C₆₇	1	2	yes	complemented
677	#433	C₂²×C₆₇	1	2	yes	complemented
678	#433	C₂²×C₆₇	1	2	yes	complemented
679	#433	C₂²×C₆₇	1	2	yes	complemented
680	#433	C₂²×C₆₇	1	2	yes	complemented
681	#433	C₂²×C₆₇	1	2	yes	complemented
682	#433	C₂²×C₆₇	1	2	yes	complemented
683	#432	C₂²×C₆₇	1	2	yes	complemented
684	#432	C₂²×C₆₇	1	2	yes	complemented
685	#432	C₂²×C₆₇	1	2	yes	complemented
686	#432	C₂²×C₆₇	1	2	yes	complemented
687	#431	C₂²×C₆₇	1	2	yes	complemented
688	#431	C₂²×C₆₇	1	2	yes	complemented
689	#424	C₂²×C₆₇	1	1	yes	characteristic
690	#424	C₂²×C₆₇	1	1	yes	characteristic
691	#424	C₂²×C₆₇	1	1	yes	characteristic
692	#424	C₂²×C₆₇	1	1	yes	characteristic
693	#424	C₂²×C₆₇	1	1	yes	characteristic
694	#424	C₂²×C₆₇	1	1	yes	characteristic
695	#424	C₂²×C₆₇	1	1	yes	characteristic
696	#424	C₂²×C₆₇	1	1	yes	characteristic
697	#424	C₂²×C₆₇	1	2	yes	complemented
698	#424	C₂²×C₆₇	1	2	yes	complemented
699	#424	C₂²×C₆₇	1	2	yes	complemented
700	#424	C₂²×C₆₇	1	2	yes	complemented
701	#424	C₂²×C₆₇	1	2	yes	complemented
702	#424	C₂²×C₆₇	1	2	yes	complemented
703	#423	C₂²×C₆₇	1	1	yes	characteristic
704	#423	C₂²×C₆₇	1	2	yes	complemented
705	#423	C₂²×C₆₇	1	2	yes	complemented
706	#423	C₂²×C₆₇	1	2	yes	complemented
707	C₂×C₄⋊C₈	C₂²×C₆₇	1	1	yes	characteristic
708	C₂×C₄⋊C₈	C₂²×C₆₇	1	2	yes	complemented
709	C₂×C₄⋊C₈	C₂²×C₆₇	1	2	yes	complemented
710	C₂×C₄⋊C₈	C₂²×C₆₇	1	2	yes	complemented
711	#408	C₂²×C₆₇	1	1	yes	characteristic
712	#408	C₂²×C₆₇	1	1	yes	characteristic
713	#407	C₂²×C₆₇	1	1	yes	characteristic
714	#407	C₂²×C₆₇	1	1	yes	characteristic
715	C₂×C₂²⋊C₈	C₂²×C₆₇	1	1	yes	characteristic
716	C₂×C₂²⋊C₈	C₂²×C₆₇	1	1	yes	characteristic
717	#405	C₂²×C₆₇	1	1	yes	characteristic
718	#405	C₂²×C₆₇	1	1	yes	characteristic
719	#405	C₂²×C₆₇	1	1	yes	characteristic
720	#405	C₂²×C₆₇	1	1	yes	characteristic
721	C₄×M₁₆	C₂²×C₆₇	1	1	yes	characteristic
722	C₂×#97	C₂²×C₆₇	1	1	yes	characteristic
723	C₂×#41	C₂×C₄×C₆₇	1	2	yes	—
724	C₂×#41	C₂³×C₆₇	1	1	yes	characteristic
725	C₂²×D₄	C₂×C₄×C₆₇	1	1	yes	characteristic
726	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
727	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
728	#131	—	4	2	no	—
729	#131	—	4	2	no	—
730	C₂×M₁₆	—	4	2	no	—
731	C₂×M₁₆	—	4	2	no	—
732	C₂×M₁₆	—	4	2	no	—
733	C₂×M₁₆	C₂³×C₆₇	1	1	yes	characteristic
734	C₂×M₁₆	C₂³×C₆₇	1	1	yes	characteristic
735	C₂×M₁₆	C₂³×C₆₇	1	1	yes	characteristic
736	C₂×M₁₆	C₂³×C₆₇	1	1	yes	characteristic
737	C₂×M₁₆	C₂³×C₆₇	1	1	yes	characteristic
738	C₂×M₁₆	C₂³×C₆₇	1	1	yes	characteristic
739	C₂×M₁₆	C₂³×C₆₇	1	2	yes	—
740	C₂×M₁₆	C₂³×C₆₇	1	1	yes	characteristic
741	C₂×M₁₆	C₂³×C₆₇	1	1	yes	characteristic
742	C₂×M₁₆	C₂³×C₆₇	1	2	yes	—
743	C₂×M₁₆	C₂³×C₆₇	1	2	yes	—
744	C₂×M₁₆	C₂³×C₆₇	1	2	yes	—
745	C₂²×C₈	—	4	2	no	—
746	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
747	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
748	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
749	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
750	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
751	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
752	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
753	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
754	C₂²×C₈	C₂³×C₆₇	1	2	yes	—
755	C₂²×C₈	C₂³×C₆₇	1	2	yes	—
756	C₂²×C₈	C₂³×C₆₇	1	2	yes	—
757	C₂²×C₈	C₂³×C₆₇	1	2	yes	—
758	C₄⋊Q₈	C₂×C₄×C₆₇	1	1	yes	characteristic
759	C₄⋊Q₈	C₂×C₄×C₆₇	1	1	yes	characteristic
760	#126	C₂×C₄×C₆₇	1	2	yes	—
761	#126	C₂×C₄×C₆₇	1	2	yes	—
762	#126	C₂×C₄×C₆₇	1	2	yes	—
763	#126	C₂×C₄×C₆₇	1	2	yes	—
764	#126	C₂×C₄×C₆₇	1	2	yes	—
765	#126	C₂×C₄×C₆₇	1	2	yes	—
766	#125	C₂×C₄×C₆₇	1	2	yes	—
767	#125	C₂×C₄×C₆₇	1	2	yes	—
768	#125	C₂×C₄×C₆₇	1	2	yes	—
769	#125	C₂×C₄×C₆₇	1	1	yes	characteristic
770	#125	C₂×C₄×C₆₇	1	1	yes	characteristic
771	#124	C₂×C₄×C₆₇	1	2	yes	—
772	#124	C₂×C₄×C₆₇	1	2	yes	—
773	#124	C₂×C₄×C₆₇	1	2	yes	—
774	#123	C₂×C₄×C₆₇	1	2	yes	—
775	#123	C₂×C₄×C₆₇	1	2	yes	—
776	#123	C₂×C₄×C₆₇	1	2	yes	—
777	#123	C₂×C₄×C₆₇	1	2	yes	—
778	#123	C₂×C₄×C₆₇	1	2	yes	—
779	#123	C₂×C₄×C₆₇	1	2	yes	—
780	#123	C₂×C₄×C₆₇	1	2	yes	—
781	#123	C₂×C₄×C₆₇	1	2	yes	—
782	C₂²⋊Q₈	C₂×C₄×C₆₇	1	1	yes	characteristic
783	C₂²⋊Q₈	C₂×C₄×C₆₇	1	1	yes	characteristic
784	C₂²⋊Q₈	C₂×C₄×C₆₇	1	1	yes	characteristic
785	C₂²⋊Q₈	C₂×C₄×C₆₇	1	1	yes	characteristic
786	C₂²⋊Q₈	C₂×C₄×C₆₇	1	2	yes	—
787	C₂²⋊Q₈	C₂×C₄×C₆₇	1	2	yes	—
788	C₂²⋊Q₈	C₂×C₄×C₆₇	1	2	yes	—
789	C₂²⋊Q₈	C₂×C₄×C₆₇	1	2	yes	—
790	C₂²⋊Q₈	C₂×C₄×C₆₇	1	2	yes	—
791	#121	C₂×C₄×C₆₇	1	1	yes	characteristic
792	#121	C₂×C₄×C₆₇	1	1	yes	characteristic
793	#121	C₂×C₄×C₆₇	1	1	yes	characteristic
794	#121	C₂×C₄×C₆₇	1	1	yes	characteristic
795	#121	C₂×C₄×C₆₇	1	2	yes	—
796	#121	C₂×C₄×C₆₇	1	2	yes	—
797	#121	C₂×C₄×C₆₇	1	2	yes	—
798	#120	C₂×C₄×C₆₇	1	2	yes	—
799	#120	C₂×C₄×C₆₇	1	2	yes	—
800	C₄×Q₈	C₂×C₄×C₆₇	1	1	yes	characteristic
801	C₄×Q₈	C₂×C₄×C₆₇	1	2	yes	—
802	C₄×Q₈	C₂×C₄×C₆₇	1	1	yes	characteristic
803	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
804	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
805	C₄×D₄	C₂×C₄×C₆₇	1	1	yes	characteristic
806	C₄×D₄	C₂×C₄×C₆₇	1	1	yes	characteristic
807	C₄×D₄	C₂×C₄×C₆₇	1	1	yes	characteristic
808	C₄×D₄	C₂×C₄×C₆₇	1	1	yes	characteristic
809	C₄×D₄	C₂×C₄×C₆₇	1	2	yes	—
810	C₄×D₄	C₂×C₄×C₆₇	1	2	yes	—
811	C₄×D₄	C₂×C₄×C₆₇	1	1	yes	characteristic
812	C₄×D₄	C₂×C₄×C₆₇	1	2	yes	—
813	C₄×D₄	C₂×C₄×C₆₇	1	2	yes	—
814	C₄×D₄	C₂×C₄×C₆₇	1	2	yes	—
815	C₄×D₄	C₂×C₄×C₆₇	1	1	yes	characteristic
816	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
817	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
818	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
819	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
820	C₄×D₄	C₂³×C₆₇	1	2	yes	—
821	C₄×D₄	C₂³×C₆₇	1	2	yes	—
822	C₄×D₄	C₂³×C₆₇	1	2	yes	—
823	C₄×D₄	C₂³×C₆₇	1	2	yes	—
824	#117	C₂×C₄×C₆₇	1	2	yes	—
825	#117	C₂×C₄×C₆₇	1	2	yes	—
826	#117	C₂×C₄×C₆₇	1	1	yes	characteristic
827	#117	C₂×C₄×C₆₇	1	1	yes	characteristic
828	#117	C₂×C₄×C₆₇	1	1	yes	characteristic
829	#117	C₂×C₄×C₆₇	1	1	yes	characteristic
830	#117	C₂×C₄×C₆₇	1	2	yes	—
831	#117	C₂×C₄×C₆₇	1	2	yes	—
832	#117	C₂×C₄×C₆₇	1	2	yes	—
833	#117	C₂³×C₆₇	1	1	yes	characteristic
834	#117	C₂³×C₆₇	1	1	yes	characteristic
835	#117	C₂³×C₆₇	1	1	yes	characteristic
836	#117	C₂³×C₆₇	1	2	yes	—
837	#117	C₂³×C₆₇	1	2	yes	—
838	#117	C₂³×C₆₇	1	2	yes	—
839	C₂×C₄⋊C₄	C₂×C₄×C₆₇	1	1	yes	characteristic
840	C₂×C₄⋊C₄	C₂×C₄×C₆₇	1	1	yes	characteristic
841	C₂×C₄⋊C₄	C₂×C₄×C₆₇	1	1	yes	characteristic
842	C₂×C₄⋊C₄	C₂×C₄×C₆₇	1	1	yes	characteristic
843	C₂×C₄⋊C₄	C₂×C₄×C₆₇	1	1	yes	characteristic
844	C₂×C₂²⋊C₄	C₂×C₄×C₆₇	1	2	yes	—
845	C₂×C₂²⋊C₄	C₂×C₄×C₆₇	1	2	yes	—
846	C₂×C₂²⋊C₄	C₂×C₄×C₆₇	1	1	yes	characteristic
847	C₂×C₂²⋊C₄	C₂×C₄×C₆₇	1	1	yes	characteristic
848	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
849	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
850	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
851	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
852	C₄⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
853	C₄⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
854	C₄⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
855	C₄⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
856	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
857	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
858	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
859	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
860	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
861	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
862	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
863	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
864	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
865	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
866	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
867	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
868	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
869	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
870	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
871	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
872	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
873	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
874	C₂²⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
875	C₂²⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
876	C₂²⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
877	C₂²⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
878	C₂²⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
879	C₂²⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
880	C₂²⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
881	C₂²⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
882	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
883	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
884	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
885	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
886	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
887	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
888	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
889	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
890	#97	C₂³×C₆₇	1	1	yes	characteristic
891	#97	C₂³×C₆₇	1	1	yes	characteristic
892	#97	C₂³×C₆₇	1	1	yes	characteristic
893	#97	C₂³×C₆₇	1	1	yes	characteristic
894	#97	C₂³×C₆₇	1	2	yes	—
895	#97	C₂³×C₆₇	1	2	yes	—
896	#97	C₂³×C₆₇	1	2	yes	—
897	#97	C₂³×C₆₇	1	2	yes	—
898	#97	C₂³×C₆₇	1	2	yes	—
899	C₄×C₈	C₂³×C₆₇	1	2	yes	—
900	C₄×C₈	C₂³×C₆₇	1	2	yes	—
901	C₄×C₈	C₂³×C₆₇	1	2	yes	—
902	C₄×C₈	C₂³×C₆₇	1	2	yes	—
903	C₄×C₈	C₂³×C₆₇	1	2	yes	—
904	C₂⁴	C₂²×C₄×C₆₇	1	1	yes	characteristic
905	C₂⁴	C₂²×C₄×C₆₇	1	1	yes	characteristic
906	#41	—	2	2	no	—
907	#41	—	2	2	no	—
908	#41	—	4	4	no	—
909	C₂×Q₈	C₂²×C₄×C₆₇	1	1	yes	characteristic
910	C₂×Q₈	C₂²×C₄×C₆₇	1	2	yes	—
911	C₂×Q₈	C₂²×C₄×C₆₇	1	2	yes	—
912	C₂×D₄	—	4	2	no	—
913	C₂×D₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
914	C₂×D₄	C₂²×C₄×C₆₇	1	2	yes	—
915	C₂×D₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
916	C₂×D₄	C₂²×C₄×C₆₇	1	2	yes	—
917	C₂×D₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
918	C₂×D₄	C₂²×C₄×C₆₇	1	2	yes	—
919	C₂×D₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
920	C₂×D₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
921	C₂×D₄	C₂²×C₄×C₆₇	1	2	yes	—
922	C₂×D₄	C₂²×C₄×C₆₇	1	2	yes	—
923	C₂²×C₄	—	2	2	no	—
924	C₂²×C₄	—	2	2	no	—
925	C₂²×C₄	—	2	2	no	—
926	C₂²×C₄	—	2	2	no	—
927	C₂²×C₄	C₂²×C₄×C₆₇	1	2	yes	—
928	C₂²×C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
929	C₂²×C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
930	C₂²×C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
931	C₂²×C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
932	C₂²×C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
933	C₂²×C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
934	C₂²×C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
935	C₂²×C₄	C₂²×C₄×C₆₇	1	2	yes	—
936	C₂²×C₄	C₂²×C₄×C₆₇	1	2	yes	—
937	C₂²×C₄	C₂²×C₄×C₆₇	1	2	yes	—
938	C₂²×C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
939	C₂²×C₄	C₂²×C₄×C₆₇	1	2	yes	—
940	C₂²×C₄	C₂²×C₄×C₆₇	1	2	yes	—
941	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
942	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
943	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
944	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
945	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
946	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
947	M₁₆	—	2	2	no	—
948	M₁₆	—	2	2	no	—
949	M₁₆	—	2	2	no	—
950	M₁₆	—	2	2	no	—
951	M₁₆	—	4	1	no	—
952	M₁₆	—	4	1	no	—
953	M₁₆	—	4	1	no	—
954	M₁₆	—	4	1	no	—
955	M₁₆	—	4	2	no	—
956	M₁₆	—	4	2	no	—
957	M₁₆	—	4	2	no	—
958	M₁₆	—	4	2	no	—
959	C₂×C₈	—	2	2	no	—
960	C₂×C₈	—	2	2	no	—
961	C₂×C₈	—	2	2	no	—
962	C₂×C₈	—	2	2	no	—
963	C₂×C₈	—	4	1	no	—
964	C₂×C₈	—	4	1	no	—
965	C₂×C₈	—	4	1	no	—
966	C₂×C₈	—	4	1	no	—
967	C₂×C₈	—	4	2	no	—
968	C₂×C₈	—	4	2	no	—
969	C₂×C₈	—	4	2	no	—
970	C₂×C₈	—	4	2	no	—
971	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
972	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
973	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
974	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
975	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
976	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
977	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
978	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
979	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
980	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
981	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
982	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
983	C₄⋊C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
984	C₄⋊C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
985	C₄⋊C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
986	C₄⋊C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
987	C₄⋊C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
988	C₄⋊C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
989	C₄⋊C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
990	C₄⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
991	C₄⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
992	C₄⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
993	C₄⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
994	C₄⋊C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
995	C₄⋊C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
996	C₄⋊C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
997	C₄⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
998	C₄⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
999	C₄⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
1000	C₄⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
1001	C₄⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
1002	C₄⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
1003	C₄⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
1004	C₄⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
1005	C₄⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
1006	C₄⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
1007	C₄⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
1008	C₄⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
1009	C₂²⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
1010	C₂²⋊C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
1011	C₂²⋊C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
1012	C₂²⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
1013	C₂²⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
1014	C₂²⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
1015	C₂²⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
1016	C₂²⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
1017	C₂²⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
1018	C₂²⋊C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
1019	C₂²⋊C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
1020	C₂²⋊C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
1021	C₂²⋊C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
1022	C₂²⋊C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
1023	C₂²⋊C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
1024	C₂²⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
1025	C₂²⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
1026	C₂²⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
1027	C₂²⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
1028	C₂²⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
1029	C₂²⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
1030	C₂²⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
1031	C₂²⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
1032	C₂²⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
1033	C₂²⋊C₄	C₂²×C₄×C₆₇	1	2	yes	—
1034	C₄²	C₂²×C₄×C₆₇	1	2	yes	—
1035	C₄²	C₂²×C₄×C₆₇	1	2	yes	—
1036	C₄²	C₂²×C₄×C₆₇	1	2	yes	—
1037	C₄²	C₂²×C₄×C₆₇	1	2	yes	—
1038	C₄²	C₂²×C₄×C₆₇	1	2	yes	—
1039	C₄²	C₂²×C₄×C₆₇	1	1	yes	characteristic
1040	C₄²	C₂²×C₄×C₆₇	1	1	yes	characteristic
1041	C₄²	C₂²×C₄×C₆₇	1	2	yes	—
1042	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
1043	C₄²	C₂⁴×C₆₇	1	2	yes	—
1044	C₄²	C₂⁴×C₆₇	1	2	yes	—
1045	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
1046	C₄²	C₂⁴×C₆₇	1	2	yes	—
1047	C₂³	—	2	2	no	—
1048	C₂³	—	2	2	no	—
1049	C₂³	—	2	2	no	—
1050	C₂³	—	4	1	no	—
1051	C₂³	—	4	1	no	—
1052	C₂³	—	4	1	no	—
1053	C₂³	C₂³×C₄×C₆₇	1	1	yes	characteristic
1054	C₂³	C₂³×C₄×C₆₇	1	1	yes	characteristic
1055	C₂³	C₂³×C₄×C₆₇	1	2	yes	—
1056	C₂³	C₂³×C₄×C₆₇	1	1	yes	characteristic
1057	C₂³	C₂³×C₄×C₆₇	1	1	yes	characteristic
1058	C₂³	C₂³×C₄×C₆₇	1	1	yes	characteristic
1059	Q₈	—	2	2	no	—
1060	Q₈	—	4	2	no	—
1061	Q₈	—	4	2	no	—
1062	D₄	—	2	4	no	—
1063	D₄	—	2	2	no	—
1064	D₄	—	2	2	no	—
1065	D₄	—	2	4	no	—
1066	D₄	—	2	2	no	—
1067	D₄	—	4	1	no	—
1068	D₄	—	4	1	no	—
1069	D₄	—	4	2	no	—
1070	D₄	—	4	2	no	—
1071	D₄	—	4	2	no	—
1072	C₂×C₄	—	2	2	no	—
1073	C₂×C₄	—	2	2	no	—
1074	C₂×C₄	—	2	4	no	—
1075	C₂×C₄	—	2	2	no	—
1076	C₂×C₄	—	2	2	no	—
1077	C₂×C₄	—	2	2	no	—
1078	C₂×C₄	—	2	2	no	—
1079	C₂×C₄	—	2	1	no	—
1080	C₂×C₄	—	2	1	no	—
1081	C₂×C₄	—	2	1	no	—
1082	C₂×C₄	—	2	2	no	—
1083	C₂×C₄	—	2	1	no	—
1084	C₂×C₄	—	2	1	no	—
1085	C₂×C₄	—	2	1	no	—
1086	C₂×C₄	—	2	1	no	—
1087	C₂×C₄	—	2	1	no	—
1088	C₂×C₄	—	2	2	no	—
1089	C₂×C₄	—	4	1	no	—
1090	C₂×C₄	—	4	2	no	—
1091	C₂×C₄	—	4	2	no	—
1092	C₂×C₄	—	4	2	no	—
1093	C₂×C₄	—	4	2	no	—
1094	C₂×C₄	—	4	2	no	—
1095	C₂×C₄	—	4	1	no	—
1096	C₂×C₄	C₂³×C₄×C₆₇	1	1	yes	characteristic
1097	C₂×C₄	C₂³×C₄×C₆₇	1	1	yes	characteristic
1098	C₂×C₄	C₂³×C₄×C₆₇	1	2	yes	—
1099	C₂×C₄	C₂³×C₄×C₆₇	1	1	yes	characteristic
1100	C₂×C₄	C₂³×C₄×C₆₇	1	2	yes	—
1101	C₂×C₄	C₂³×C₄×C₆₇	1	1	yes	characteristic
1102	C₂×C₄	C₂³×C₄×C₆₇	1	2	yes	—
1103	C₂×C₄	C₂³×C₄×C₆₇	1	1	yes	characteristic
1104	C₂×C₄	C₂³×C₄×C₆₇	1	2	yes	—
1105	C₂×C₄	C₂³×C₄×C₆₇	1	2	yes	—
1106	C₂×C₄	C₂³×C₄×C₆₇	1	2	yes	—
1107	C₂×C₄	C₂³×C₄×C₆₇	1	2	yes	—
1108	C₂×C₄	C₂³×C₄×C₆₇	1	1	yes	characteristic
1109	C₂×C₄	C₂³×C₄×C₆₇	1	1	yes	characteristic
1110	C₂×C₄	C₂³×C₄×C₆₇	1	1	yes	characteristic
1111	C₂×C₄	C₂³×C₄×C₆₇	1	1	yes	characteristic
1112	C₂×C₄	H(5,𝔽₂)×C₆₇	1	2	yes	—
1113	C₂×C₄	2₋¹⁺⁴×C₆₇	1	2	yes	—
1114	C₂×C₄	C₂⁵×C₆₇	1	1	yes	characteristic
1115	C₈	—	2	1	no	—
1116	C₈	—	2	1	no	—
1117	C₈	—	2	1	no	—
1118	C₈	—	2	1	no	—
1119	C₈	—	2	1	no	—
1120	C₈	—	2	1	no	—
1121	C₈	—	2	2	no	—
1122	C₈	—	2	2	no	—
1123	C₈	—	2	2	no	—
1124	C₈	—	2	1	no	—
1125	C₈	—	2	1	no	—
1126	C₈	—	2	2	no	—
1127	C₂²	—	2	1	no	—
1128	C₂²	—	2	1	no	—
1129	C₂²	—	2	1	no	—
1130	C₂²	—	2	1	no	—
1131	C₂²	—	2	1	no	—
1132	C₂²	—	2	2	no	—
1133	C₂²	—	2	1	no	—
1134	C₂²	—	2	1	no	—
1135	C₂²	—	2	1	no	—
1136	C₂²	—	2	2	no	—
1137	C₂²	—	2	1	no	—
1138	C₂²	—	2	1	no	—
1139	C₂²	—	2	1	no	—
1140	C₂²	—	2	1	no	—
1141	C₂²	—	2	1	no	—
1142	C₂²	—	2	2	no	—
1143	C₂²	—	4	4	no	—
1144	C₂²	—	8	2	no	—
1145	C₂²	#520×C₆₇	1	2	yes	—
1146	C₂²	#568×C₆₇	1	2	yes	—
1147	C₂²	C₂⁴×C₄×C₆₇	1	1	yes	characteristic
1148	C₄	—	2	2	no	—
1149	C₄	—	2	2	no	—
1150	C₄	—	2	1	no	—
1151	C₄	—	2	1	no	—
1152	C₄	—	2	2	no	—
1153	C₄	—	2	1	no	—
1154	C₄	—	2	2	no	—
1155	C₄	—	2	2	no	—
1156	C₄	—	2	2	no	—
1157	C₄	—	2	1	no	—
1158	C₄	—	2	1	no	—
1159	C₄	—	2	1	no	—
1160	C₄	—	2	1	no	—
1161	C₄	—	2	1	no	—
1162	C₄	—	2	2	no	—
1163	C₄	#520×C₆₇	1	2	yes	—
1164	C₄	C₂×H(5,𝔽₂)×C₆₇	1	1	yes	characteristic
1165	C₄	C₂×2₋¹⁺⁴×C₆₇	1	1	yes	characteristic
1166	C₂	—	2	2	no	—
1167	C₂	—	2	2	no	—
1168	C₂	—	4	1	no	—
1169	C₂	—	4	1	no	—
1170	C₂	—	4	1	no	—
1171	C₂	—	4	2	no	—
1172	C₂	C₂×#520×C₆₇	1	1	yes	characteristic
1173	C₂	C₂×#568×C₆₇	1	1	yes	characteristic
1174	C₂	C₆₇×#3573	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₆₇	C₂⁵
commutator	C₂²	C₂⁴×C₄×C₆₇
Frattini, cosocle	C₂×C₄	C₂⁵×C₆₇
socle	C₂²×C₆₇	C₂⁴×C₄
prime radical	C₆₇×#3475	C₂
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₆₇ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₆₇×#2995	C₂	semidirect
3. C₆₇×#2995	C₂	semidirect
4. C₆₇×#2994	C₂	semidirect
5. C₆₇×#2993	C₂	semidirect
6. C₆₇×#2992	C₂	semidirect
7. C₆₇×#2992	C₂	semidirect
8. C₆₇×#2990	C₂	semidirect
9. C₆₇×#2989	C₂	semidirect
10. C₆₇×#2962	C₂	semidirect
11. C₆₇×#2961	C₂	semidirect
12. D₄×M₁₆×C₆₇	C₂	semidirect
13. C₆₇×#2933	C₂	semidirect
14. C₆₇×#2933	C₂	semidirect
15. C₆₇×#2930	C₂	semidirect
16. C₆₇×#2929	C₂	semidirect
17. C₂×#435×C₆₇	C₂	semidirect
18. C₆₇×#2924	C₂	semidirect
19. C₆₇×#2924	C₂	semidirect
20. C₆₇×#2923	C₂	semidirect
21. C₆₇×#2906	C₂	semidirect
22. C₆₇×#2905	C₂	semidirect
23. C₂×#424×C₆₇	C₂	semidirect
53. #446×C₆₇	C₂²	semidirect
54. #446×C₆₇	C₂²	semidirect
55. #446×C₆₇	C₂²	semidirect
56. #446×C₆₇	C₂²	semidirect
57. #446×C₆₇	C₂²	semidirect
58. #446×C₆₇	C₂²	semidirect
59. #446×C₆₇	C₂²	semidirect
60. C₈×Q₈×C₆₇	C₂²	semidirect
62. #436×C₆₇	C₂²	semidirect
63. #436×C₆₇	C₂²	semidirect
64. #436×C₆₇	C₂²	semidirect
65. #436×C₆₇	C₂²	semidirect
76. #435×C₆₇	C₂²	semidirect
77. #435×C₆₇	C₂²	semidirect
78. #435×C₆₇	C₂²	semidirect
79. #435×C₆₇	C₂²	semidirect
80. #435×C₆₇	C₂²	semidirect
81. #435×C₆₇	C₂²	semidirect
82. #435×C₆₇	C₂²	semidirect
83. #435×C₆₇	C₂²	semidirect
85. C₈×D₄×C₆₇	C₂²	semidirect
86. C₈×D₄×C₆₇	C₂²	semidirect
87. C₈×D₄×C₆₇	C₂²	semidirect
88. C₈×D₄×C₆₇	C₂²	semidirect
89. #433×C₆₇	C₂²	semidirect
90. #433×C₆₇	C₂²	semidirect
91. #433×C₆₇	C₂²	semidirect
92. #433×C₆₇	C₂²	semidirect
93. #433×C₆₇	C₂²	semidirect
94. #433×C₆₇	C₂²	semidirect
95. #432×C₆₇	C₂²	semidirect
96. #432×C₆₇	C₂²	semidirect
97. #432×C₆₇	C₂²	semidirect
98. #432×C₆₇	C₂²	semidirect
99. #431×C₆₇	C₂²	semidirect
100. #431×C₆₇	C₂²	semidirect
109. #424×C₆₇	C₂²	semidirect
110. #424×C₆₇	C₂²	semidirect
111. #424×C₆₇	C₂²	semidirect
112. #424×C₆₇	C₂²	semidirect
113. #424×C₆₇	C₂²	semidirect
114. #424×C₆₇	C₂²	semidirect
116. #423×C₆₇	C₂²	semidirect
117. #423×C₆₇	C₂²	semidirect
118. #423×C₆₇	C₂²	semidirect
120. C₂×C₄⋊C₈×C₆₇	C₂²	semidirect
121. C₂×C₄⋊C₈×C₆₇	C₂²	semidirect
122. C₂×C₄⋊C₈×C₆₇	C₂²	semidirect
578. #60272	C₆₇	direct (N × H)
589. #2995	C₂×C₆₇	semidirect
590. #2995	C₂×C₆₇	semidirect
591. #2994	C₂×C₆₇	semidirect
592. #2993	C₂×C₆₇	semidirect
593. #2992	C₂×C₆₇	semidirect
594. #2992	C₂×C₆₇	semidirect
595. #2990	C₂×C₆₇	semidirect
596. #2989	C₂×C₆₇	semidirect
597. #2962	C₂×C₆₇	semidirect
598. #2961	C₂×C₆₇	semidirect
599. D₄×M₁₆	C₂×C₆₇	semidirect
600. #2933	C₂×C₆₇	semidirect
601. #2933	C₂×C₆₇	semidirect
602. #2930	C₂×C₆₇	semidirect
603. #2929	C₂×C₆₇	semidirect
604. C₂×#435	C₂×C₆₇	semidirect
605. #2924	C₂×C₆₇	semidirect
606. #2924	C₂×C₆₇	semidirect
607. #2923	C₂×C₆₇	semidirect
608. #2906	C₂×C₆₇	semidirect
609. #2905	C₂×C₆₇	semidirect
610. C₂×#424	C₂×C₆₇	semidirect
611. C₆₇	#60272	direct (N × H)
641. #446	C₂²×C₆₇	semidirect
642. #446	C₂²×C₆₇	semidirect
643. #446	C₂²×C₆₇	semidirect
644. #446	C₂²×C₆₇	semidirect
645. #446	C₂²×C₆₇	semidirect
646. #446	C₂²×C₆₇	semidirect
647. #446	C₂²×C₆₇	semidirect
648. C₈×Q₈	C₂²×C₆₇	semidirect
650. #436	C₂²×C₆₇	semidirect
651. #436	C₂²×C₆₇	semidirect
652. #436	C₂²×C₆₇	semidirect
653. #436	C₂²×C₆₇	semidirect
664. #435	C₂²×C₆₇	semidirect
665. #435	C₂²×C₆₇	semidirect
666. #435	C₂²×C₆₇	semidirect
667. #435	C₂²×C₆₇	semidirect
668. #435	C₂²×C₆₇	semidirect
669. #435	C₂²×C₆₇	semidirect
670. #435	C₂²×C₆₇	semidirect
671. #435	C₂²×C₆₇	semidirect
673. C₈×D₄	C₂²×C₆₇	semidirect
674. C₈×D₄	C₂²×C₆₇	semidirect
675. C₈×D₄	C₂²×C₆₇	semidirect
676. C₈×D₄	C₂²×C₆₇	semidirect
677. #433	C₂²×C₆₇	semidirect
678. #433	C₂²×C₆₇	semidirect
679. #433	C₂²×C₆₇	semidirect
680. #433	C₂²×C₆₇	semidirect
681. #433	C₂²×C₆₇	semidirect
682. #433	C₂²×C₆₇	semidirect
683. #432	C₂²×C₆₇	semidirect
684. #432	C₂²×C₆₇	semidirect
685. #432	C₂²×C₆₇	semidirect
686. #432	C₂²×C₆₇	semidirect
687. #431	C₂²×C₆₇	semidirect
688. #431	C₂²×C₆₇	semidirect
697. #424	C₂²×C₆₇	semidirect
698. #424	C₂²×C₆₇	semidirect
699. #424	C₂²×C₆₇	semidirect
700. #424	C₂²×C₆₇	semidirect
701. #424	C₂²×C₆₇	semidirect
702. #424	C₂²×C₆₇	semidirect
704. #423	C₂²×C₆₇	semidirect
705. #423	C₂²×C₆₇	semidirect
706. #423	C₂²×C₆₇	semidirect
708. C₂×C₄⋊C₈	C₂²×C₆₇	semidirect
709. C₂×C₄⋊C₈	C₂²×C₆₇	semidirect
710. C₂×C₄⋊C₈	C₂²×C₆₇	semidirect

Maximal subgroups

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

subgroup	index
C₆₇×#3475	2
C₆₇×#2995	2
C₆₇×#2994	2
C₆₇×#2993	2
C₆₇×#2992	2
C₆₇×#2990	2
C₆₇×#2989	2
C₆₇×#2962	2
C₆₇×#2961	2
D₄×M₁₆×C₆₇	2
C₆₇×#2933	2
C₆₇×#2930	2
C₆₇×#2929	2
C₂×#435×C₆₇	2
C₆₇×#2924	2
C₆₇×#2923	2
C₆₇×#2906	2
C₆₇×#2905	2
C₂×#424×C₆₇	2
#60272	67

Subgroups — C67×#60272 #30739523

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#60272 #30739523